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</div><h2>SL Paper 2</h2><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">A lobster trap is made in the shape of half a cylinder. It is constructed from a steel frame with netting pulled tightly around it. The steel frame consists of a rectangular base, two semicircular ends and two further support rods, as shown in the following diagram.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; min-height: 25px; text-align: center; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;"><br><img src="images/Schermafbeelding_2014-09-20_om_14.54.16.png" alt><br></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The semicircular ends each have radius \(r\) and the support rods each have length \(l\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(T\) be the total length of steel used in the frame of the lobster trap.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down an expression for \(T\) in terms of \(r\), \(l\) and \(\pi \).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The volume of the lobster trap is \(0.75{\text{ }}{{\text{m}}^{\text{3}}}\).</span></p>
<p><span>Write down an equation for the volume of the lobster trap in terms of \(r\), \(l\) and \(\pi \).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The volume of the lobster trap is \(0.75{\text{ }}{{\text{m}}^{\text{3}}}\).</span></p>
<p><span>Show that \(T = (2\pi + 4)r + \frac{6}{{\pi {r^2}}}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The volume of the lobster trap is \(0.75{\text{ }}{{\text{m}}^{\text{3}}}\).</span></p>
<p><span>Find \(\frac{{{\text{d}}T}}{{{\text{d}}r}}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The lobster trap is designed so that the length of steel used in its frame is a minimum.</span></p>
<p><span>Show that the value of \(r\) for which \(T\) is a minimum is \(0.719 {\text{ m}}\), correct to three significant figures.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The lobster trap is designed so that the length of steel used in its frame is a minimum.</span></p>
<p><span>Calculate the value of \(l\) for which \(T\) is a minimum.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The lobster trap is designed so that the length of steel used in its frame is a minimum.</span></p>
<p><span>Calculate the minimum value of \(T\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(2\pi r + 4r + 4l\) <strong><em>(A1)(A1)(A1)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes:</strong> Award <strong><em>(A1) </em></strong>for \(2\pi r\) (“\(\pi \)” must be seen), <strong><em>(A1) </em></strong>for \(4r\), <strong><em>(A1) </em></strong>for \(4l\). Accept equivalent forms. Accept \(T = 2\pi r + 4r + 4l\). Award a maximum of <strong><em>(A1)(A1)(A0) </em></strong>if extra terms are seen.</span></p>
<p> </p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(0.75 = \frac{{\pi {r^2}l}}{2}\) <strong><em>(A1)(A1)(A1)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes:</strong> Award <strong><em>(A1) </em></strong>for their formula equated to \(0.75\), <strong><em>(A1) </em></strong>for \(l\) substituted into volume of cylinder formula, <strong><em>(A1) </em></strong>for volume of cylinder formula divided by \(2\).</span></p>
<p><span>If “\(\pi \)” not seen in part (a) accept use of \(3.14\) or greater accuracy. Award a maximum of <strong><em>(A1)(A1)(A0) </em></strong>if extra terms are seen.</span></p>
<p> </p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(T = 2\pi r + 4r + 4\left( {\frac{{1.5}}{{\pi {r^2}}}} \right)\) <strong><em>(A1)</em>(ft)<em>(A1)</em></strong></span></p>
<p><span>\( = (2\pi + 4)r + \frac{6}{{\pi {r^2}}}\) <strong><em>(AG)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(A1)</em>(ft) </strong>for correct rearrangement of their volume formula in part (b) seen, award <strong><em>(A1) </em></strong>for the correct substituted formula for \(T\)<em>. </em>The final line must be seen, with no incorrect working, for this second <strong><em>(A1) </em></strong>to be awarded.</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{{\text{d}}T}}{{{\text{d}}r}} = 2\pi + 4 - \frac{{12}}{{\pi {r^3}}}\) <strong><em>(A1)(A1)(A1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for \(2\pi + 4\), <strong><em>(A1)</em></strong> for \(\frac{{ - 12}}{\pi }\), <strong><em>(A1)</em></strong> for \({r^{ - 3}}\).</span></p>
<p><span> Accept 10.3 (10.2832…) for \(2\pi + 4\), accept \(–3.82\) \(–3.81971…\) for \(\frac{{ - 12}}{\pi }\). Award a maximum of <strong><em>(A1)(A1)(A0) </em></strong>if extra terms are seen.</span></p>
<p> </p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(2\pi + 4 - \frac{{12}}{{\pi {r^3}}} = 0\) <strong>OR</strong> \(\frac{{{\text{d}}T}}{{{\text{d}}r}} = 0\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for setting their derivative equal to zero.</span></p>
<p> </p>
<p><span>\(r = 0.718843 \ldots \) <strong>OR</strong> \(\sqrt[3]{{0.371452 \ldots }}\) <strong>OR</strong> \(\sqrt[3]{{\frac{{12}}{{\pi (2\pi + 4)}}}}\) <strong>OR</strong> \(\sqrt[3]{{\frac{{3.81971}}{{10.2832 \ldots }}}}\) <strong><em>(A1)</em></strong></span></p>
<p><span>\(r = 0.719{\text{ (m)}}\) <strong><em>(AG)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>The rounded and unrounded or formulaic answers must be seen for the final <strong><em>(A1) </em></strong>to be awarded. The use of \(3.14\) gives an unrounded answer of \(r = 0.719039 \ldots \).</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(0.75 = \frac{{\pi \times {{(0.719)}^2}l}}{2}\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substituting \(0.719\) into their volume formula. Follow through from part (b).</span></p>
<p> </p>
<p><span>\(l = 0.924{\text{ (m)}}\) \((0.923599 \ldots )\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(T = (2\pi + 4) \times 0.719 + \frac{6}{{\pi {{(0.719)}^2}}}\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for substituting \(0.719\) in their expression for \(T\). Accept alternative methods, for example substitution of their \(l\) and \(0.719\) into their part (a) (for which the answer is \(11.08961024\)). Follow through from their answer to part (a).</span></p>
<p> </p>
<p><span>\( = 11.1{\text{ (m)}}\) \((11.0880 \ldots )\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></span></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>Abdallah owns a plot of land, near the river Nile, in the form of a quadrilateral ABCD.</p>
<p>The lengths of the sides are \({\text{AB}} = {\text{40 m, BC}} = {\text{115 m, CD}} = {\text{60 m, AD}} = {\text{84 m}}\) and angle \({\rm{B\hat AD}} = 90^\circ \).</p>
<p>This information is shown on the diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-13_om_14.24.18.png" alt="N17/5/MATSD/SP2/ENG/TZ0/03"></p>
</div>
<div class="specification">
<p>The formula that the ancient Egyptians used to estimate the area of a quadrilateral ABCD is</p>
<p style="text-align: center;">\({\text{area}} = \frac{{({\text{AB}} + {\text{CD}})({\text{AD}} + {\text{BC}})}}{4}\).</p>
<p>Abdallah uses this formula to estimate the area of his plot of land.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that \({\text{BD}} = 93{\text{ m}}\) correct to the nearest metre.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate angle \({\rm{B\hat CD}}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of ABCD.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate Abdallah’s estimate for the area.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the percentage error in Abdallah’s estimate.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\({\text{B}}{{\text{D}}^2} = {40^2} + {84^2}\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into Pythagoras.</p>
<p>Accept correct substitution into cosine rule.</p>
<p>\({\text{BD}} = 93.0376 \ldots \) <strong><em>(A1)</em></strong></p>
<p>\( = 93\) <strong><em>(AG)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Both the rounded and unrounded value must be seen for the <strong><em>(A1) </em></strong>to be awarded.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\cos C = \frac{{{{115}^2} + {{60}^2} - {{93}^2}}}{{2 \times 115 \times 60}}{\text{ }}({93^2} = {115^2} + {60^2} - 2 \times 115 \times 60 \times \cos C)\) <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substitution into cosine formula, <strong><em>(A1) </em></strong>for correct substitutions.</p>
<p> </p>
<p>\( = 53.7^\circ {\text{ }}(53.6679 \ldots ^\circ )\) <strong><em>(A1)(G2)</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{1}{2}(40)(84) + \frac{1}{2}(115)(60)\sin (53.6679 \ldots )\) <strong><em>(M1)(M1)(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into right-angle triangle area. Award <strong><em>(M1) </em></strong>for substitution into area of triangle formula and <strong><em>(A1)</em>(ft) </strong>for correct substitution.</p>
<p> </p>
<p>\( = 4460{\text{ }}{{\text{m}}^2}{\text{ }}(4459.30 \ldots {\text{ }}{{\text{m}}^2})\) <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Follow through from part (b).</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{(40 + 60)(84 + 115)}}{4}\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution in the area formula used by ‘Ancient Egyptians’.</p>
<p> </p>
<p>\( = 4980{\text{ }}{{\text{m}}^2}{\text{ }}(4975{\text{ }}{{\text{m}}^2})\) <strong><em>(A1)(G2)</em></strong></p>
<p> </p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\left| {\frac{{4975 - 4459.30 \ldots }}{{4459.30 \ldots }}} \right| \times 100\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into percentage error formula.</p>
<p> </p>
<p>\( = 11.6{\text{ }}(\% ){\text{ }}(11.5645 \ldots )\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Follow through from parts (c) and (d)(i).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following diagram shows two triangles, OBC and OBA, on a set of axes. Point C lies on the \(y\)-axis, and O is the origin.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-04_om_16.03.31.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The equation of the line BC is \(y = 4\).</p>
<p class="p1">Write down the coordinates of point C.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The \(x\)-coordinate of point B is \(a\).</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>Write down the coordinates of point B;</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Write down the gradient of the line OB.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Point A lies on the \(x\)-axis and the line AB is perpendicular to line OB.</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>Write down the gradient of line AB.</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Show that the equation of the line AB is \(4y + ax - {a^2} - 16 = 0\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The area of triangle AOB is <strong>three times</strong> the area of triangle OBC.</p>
<p class="p1">Find an expression, <strong>in terms of <em>a</em></strong>, for</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>the area of triangle OBC;</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>the <em>x</em>-coordinate of point A.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the value of \(a\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\((0,{\text{ }}4)\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1"><strong>Notes: </strong>Accept \(x = 0,{\text{ }}y = 4\).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>\((a,{\text{ }}4)\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)</strong></p>
<p class="p1"><strong>Notes: </strong>Follow through from part (a).</p>
<p class="p2"> </p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\(\frac{4}{a}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)</strong></p>
<p class="p1"><strong>Note: </strong>Follow through from part (b)(i).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) \( - \frac{a}{4}\) <strong><em>(A1)</em>(ft)</strong></p>
<p><strong>Note: </strong>Follow through from part (b)(ii).</p>
<p> </p>
<p>(ii) \(y = - \frac{a}{4}x + c\) <strong><em>(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substitution of their gradient from part (c)(i) in the equation.</p>
<p> </p>
<p>\(4 = - \frac{a}{4} \times a + c\)</p>
<p>\(c = \frac{1}{4} \times {a^2} + 4\)</p>
<p>\(y = - \frac{a}{4}x + \frac{1}{4}{a^2} + 4\) <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>OR</strong></p>
<p>\(y - 4 = - \frac{a}{4}(x - a)\) <strong><em>(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substitution of their gradient from part (c)(i) in the equation.</p>
<p> </p>
<p>\(y = - \frac{{ax}}{4} + \frac{{{a^2}}}{4} + 4\) <strong><em>(A1)</em></strong></p>
<p>\(4y = - ax + {a^2} + 16\)</p>
<p>\(4y + ax - {a^2} - 16 = 0\) <strong><em>(AG)</em></strong></p>
<p><strong>Note: </strong>Both the simplified and the not simplified equations must be seen for the final <strong><em>(A1) </em></strong>to be awarded.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) \(2a\) <strong><em>(A1)</em></strong></p>
<p> </p>
<p>(ii) \(\frac{{4x}}{2} = 3 \times 2a\) <strong><em>(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct equation.</p>
<p> </p>
<p>\(x = 3a\) <strong><em>(A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from part (d)(i).</p>
<p> </p>
<p><strong>OR</strong></p>
<p>\(0 - 4 = - \frac{a}{4}(x - a)\) <strong><em>(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution of their gradient and the coordinates of their point into the equation of a line.</p>
<p> </p>
<p>\(\frac{{16}}{a} = x - a\)</p>
<p>\(x = a + \frac{{16}}{a}\) <strong><em>(A1)</em>(ft)</strong></p>
<p><strong>Note: </strong>Follow through from parts (b)(i) and (c)(i).</p>
<p> </p>
<p><strong>OR</strong></p>
<p>\(4 \times 0 + ax - {a^2} - 16 = 0\) <strong><em>(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution of the coordinates of \({\text{A}}(x,{\text{ }}0)\) into the equation of line AB.</p>
<p> </p>
<p>\(ax - {a^2} - 16 = 0\)</p>
<p>\(x = a + \frac{{16}}{a}\;\;\;\)<strong>OR</strong>\(\;\;\;x = \frac{{({a^2} + 16)}}{a}\) <strong><em>(A1)(G1)</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(4(0) + a(3a) - {a^2} - 16 = 0\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution of their \(3a\) from part (d)(ii) into the equation of line AB.</p>
<p class="p2"> </p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">\(\frac{1}{2}\left( {a + \frac{{16}}{a}} \right) \times 4 = 3\left( {\frac{{4a}}{2}} \right)\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for area of triangle AOB (with their substituted \(a + \frac{{16}}{a}\) and 4) equated to three times their area of triangle AOB.</p>
<p class="p1"> </p>
<p class="p1">\(a = 2.83\;\;\;\left( {2.82842...,{\text{ }}2\sqrt 2 ,{\text{ }}\sqrt 8 } \right)\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(G1)</em></strong></p>
<p class="p1"><strong>Note:<span class="Apple-converted-space"> </span></strong>Follow through from parts (d)(i) and (d)(ii).</p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The base of an electric iron can be modelled as a pentagon ABCDE, where:</p>
<p>\[\begin{array}{*{20}{l}} {{\text{BCDE is a rectangle with sides of length }}(x + 3){\text{ cm and }}(x + 5){\text{ cm;}}} \\ {{\text{ABE is an isosceles triangle, with AB}} = {\text{AE and a height of }}x{\text{ cm;}}} \\ {{\text{the area of ABCDE is 222 c}}{{\text{m}}^{\text{2}}}{\text{.}}} \end{array}\]</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_11.05.55.png" alt="M17/5/MATSD/SP2/ENG/TZ1/02"></p>
</div>
<div class="specification">
<p>Insulation tape is wrapped around the perimeter of the base of the iron, ABCDE.</p>
</div>
<div class="specification">
<p>F is the point on AB such that \({\text{BF}} = {\text{8 cm}}\). A heating element in the iron runs in a straight line, from C to F.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an <strong>equation </strong>for the area of ABCDE using the above information.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the equation in part (a)(i) simplifies to \(3{x^2} + 19x - 414 = 0\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the length of CD.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that angle \({\rm{B\hat AE}} = 67.4^\circ \), correct to one decimal place.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the length of the perimeter of ABCDE.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the length of CF.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(222 = \frac{1}{2}x(x + 3) + (x + 3)(x + 5)\) <strong><em>(M1)(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct area of triangle, <strong><em>(M1) </em></strong>for correct area of rectangle, <strong><em>(A1) </em></strong>for equating the sum to 222.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>\(222 = (x + 3)(2x + 5) - 2\left( {\frac{1}{4}} \right)x(x + 3)\) <strong><em>(M1)(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for area of bounding rectangle, <strong><em>(M1) </em></strong>for area of triangle, <strong><em>(A1) </em></strong>for equating the difference to 222.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(222 = \frac{1}{2}{x^2} + \frac{3}{2}x + {x^2} + 3x + 5x + 15\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for complete expansion of the brackets, leading to the final answer, with no incorrect working seen. The final answer must be seen to award <strong><em>(M1)</em></strong>.</p>
<p> </p>
<p>\(3{x^2} + 19x - 414 = 0\) <strong><em>(AG)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(x = 9{\text{ }}\left( {{\text{and }}x = - \frac{{46}}{3}} \right)\) <strong><em>(A1)</em></strong></p>
<p>\({\text{CD}} = 12{\text{ (cm)}}\) <strong><em>(A1)(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{1}{2}({\text{their }}x + 3) = 6\) <strong><em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (b).</p>
<p> </p>
<p>\(\tan \left( {\frac{{{\rm{B\hat AE}}}}{2}} \right) = \frac{6}{9}\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for their correct substitutions in tangent ratio.</p>
<p> </p>
<p>\({\rm{B\hat AE}} = 67.3801 \ldots ^\circ \) <strong><em>(A1)</em></strong></p>
<p>\( = 67.4^\circ \) <strong><em>(AG)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Do not award the final <strong><em>(A1) </em></strong>unless both the correct unrounded and rounded answers are seen.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>\(\frac{1}{2}({\text{their }}x + 3) = 6\) <strong><em>(A1)</em>(ft)</strong></p>
<p>\(\tan ({\rm{A\hat BE}}) = \frac{9}{6}\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for their correct substitutions in tangent ratio.</p>
<p> </p>
<p>\({\rm{B\hat AE}} = 180^\circ - 2({\rm{A\hat BE}})\)</p>
<p>\({\rm{B\hat AE}} = 67.3801 \ldots ^\circ \) <strong><em>(A1)</em></strong></p>
<p>\( = 67.4^\circ \) <strong><em>(AG)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Do not award the final <strong><em>(A1) </em></strong>unless both the correct unrounded and rounded answers are seen.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(2\sqrt {{9^2} + {6^2}} + 12 + 2(14)\) <strong><em>(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution into Pythagoras. Award <strong><em>(M1) </em></strong>for the addition of 5 sides of the pentagon, consistent with their \(x\).</p>
<p> </p>
<p>\(61.6{\text{ (cm) }}\left( {61.6333 \ldots {\text{ (cm)}}} \right)\) <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (b).</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\({\rm{F\hat BC}} = 90 + \left( {\frac{{180 - 67.4}}{2}} \right){\text{ }}( = 146.3^\circ )\) <strong><em>(M1)</em></strong></p>
<p><strong>OR</strong></p>
<p>\(180 - \frac{{67.4}}{2}\) <strong><em>(M1)</em></strong></p>
<p>\({\rm{C}}{{\text{F}}^2} = {8^2} + {14^2} - 2(8)(14)\cos (146.3^\circ )\) <strong><em>(M1)(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for substituted cosine rule formula and <strong><em>(A1) </em></strong>for correct substitutions. Follow through from part (b).</p>
<p> </p>
<p>\({\text{CF}} = 21.1{\text{ (cm) }}(21.1271 \ldots )\) <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p><strong>OR</strong></p>
<p>\({\rm{G\hat BF}} = \frac{{67.4}}{2} = 33.7^\circ \) <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for angle \({\rm{G\hat BF}} = 33.7^\circ \), where G is the point such that CG is a projection/extension of CB and triangles BGF and CGF are right-angled triangles. The candidate may use another variable.</p>
<p><img src="images/Schermafbeelding_2017-08-16_om_13.44.50.png" alt="M17/5/MATSD/SP2/ENG/TZ1/02.e/M"></p>
<p> </p>
<p>\({\text{GF}} = 8\sin 33.7^\circ = 4.4387 \ldots \)\(\,\,\,\)<strong>AND</strong>\(\,\,\,\)\({\text{BG}} = 8\cos 33.7^\circ = 6.6556 \ldots \) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution into trig formulas to find both GF and BG.</p>
<p> </p>
<p>\({\text{C}}{{\text{F}}^2} = {(14 + 6.6556 \ldots )^2} + {(4.4387 \ldots )^2}\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution into Pythagoras formula to find CF.</p>
<p> </p>
<p>\({\text{CF}} = 21.1{\text{ (cm) }}(21.1271 \ldots )\) <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The diagram below shows the graph of a line \(L\) passing through (1, 1) and (2 , 3) and the graph \(P\) of the function \(f (x) = x^2 − 3x − 4\)</span></p>
<p><img src="data:image/png;base64,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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the gradient of the line <em>L</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Differentiate \(f (x)\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the coordinates of the point where the tangent to <em>P</em> is parallel to the line <em>L</em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the coordinates of the point where the tangent to <em>P</em> is perpendicular to the line<em> L</em>.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find</span></p>
<p><span>(i) the gradient of the tangent to <em>P</em> at the point with coordinates (2, − 6).</span></p>
<p><span>(ii) the equation of the tangent to <em>P</em> at this point.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State the equation of the axis of symmetry of <em>P</em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the coordinates of the vertex of <em>P</em> and state the gradient of the curve at this point.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><em>for attempt at substituted</em> \(\frac{{ydistance}}{{xdistance}}\) <em><strong>(M1)</strong></em></span></p>
<p><span>gradient = 2 <em><strong>(A1)(G2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(2x - 3\) <em><strong>(A1)(A1)</strong></em></span></p>
<p><span><em><strong>(A1)</strong> for</em> \(2x\) , <em><strong>(A1)</strong> for</em> \(-3\)</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>for their</em> \(2x - 3 =\) <em>their gradient and attempt to solve <strong>(M1)</strong></em></span></p>
<p><span>\(x = 2.5\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>\(y = -5.25\) <em>(</em><strong>(ft)</strong><em> from their x value) <strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><em><strong>[3 marks]<br></strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><span>for seeing </span></em><span>\(\frac{{ - 1}}{{their(a)}}\) <em><strong>(M1)</strong></em></span></p>
<p><span><em>solving</em> \(2x – 3 = - \frac{1}{2}\) <em>(or their value) <strong>(M1)</strong></em></span></p>
<p><span><em>x</em> = 1.25 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G1)</strong></em><br></span></p>
<p><span><em>y</em> = – 6.1875 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G1)</strong><strong><br></strong></em></span></p>
<p><span><em><strong>[4 marks]<br></strong></em></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(2 \times 2 - 3 = 1\) <em>(</em><strong>(ft)</strong> <em>from (b)) <strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G1)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span>(ii) \(y = mx + c\) <em>or equivalent method to find</em> \(c \Rightarrow -6 = 2 + c\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(y = x - 8\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span><em><strong>[3 marks]<br></strong></em></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(x = 1.5\) <em><strong>(A1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>for substituting their answer to part (f) into the equation of the parabola</em> (1.5, −6.25) <em>accept</em> <em>x</em> = 1.5, <em>y</em> = −6.25 <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span>gradient is zero <em>(accept</em> \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\)<em>) <strong>(A1)</strong></em></span></p>
<p><span><em><strong>[3 marks]<br></strong></em></span></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Parts (a) and (b) were very well done. After that, only the stronger candidates were able to cope. The equation of the tangent at the point with coordinates (2, 6) was badly done but some candidates managed to find the equation of the tangent line from their GDC. The equation of the axis of symmetry was reasonably well done although many just wrote down 1.5 instead of <em>x</em> = 1.5.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Some forgot to write down that the gradient at the vertex was 0.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Parts (a) and (b) were very well done. After that, only the stronger candidates were able to cope. The equation of the tangent at the point with coordinates (2, 6) was badly done but some candidates managed to find the equation of the tangent line from their GDC. The equation of the axis of symmetry was reasonably well done although many just wrote down 1.5 instead of <em>x</em> = 1.5.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Some forgot to write down that the gradient at the vertex was 0.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Parts (a) and (b) were very well done. After that, only the stronger candidates were able to cope. The equation of the tangent at the point with coordinates (2, 6) was badly done but some candidates managed to find the equation of the tangent line from their GDC. The equation of the axis of symmetry was reasonably well done although many just wrote down 1.5 instead of <em>x</em> = 1.5.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Some forgot to write down that the gradient at the vertex was 0.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Parts (a) and (b) were very well done. After that, only the stronger candidates were able to cope. The equation of the tangent at the point with coordinates (2, 6) was badly done but some candidates managed to find the equation of the tangent line from their GDC. The equation of the axis of symmetry was reasonably well done although many just wrote down 1.5 instead of <em>x</em> = 1.5.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Some forgot to write down that the gradient at the vertex was 0.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Parts (a) and (b) were very well done. After that, only the stronger candidates were able to cope. The equation of the tangent at the point with coordinates (2, 6) was badly done but some candidates managed to find the equation of the tangent line from their GDC. The equation of the axis of symmetry was reasonably well done although many just wrote down 1.5 instead of <em>x</em> = 1.5.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Some forgot to write down that the gradient at the vertex was 0.</span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Parts (a) and (b) were very well done. After that, only the stronger candidates were able to cope. The equation of the tangent at the point with coordinates (2, 6) was badly done but some candidates managed to find the equation of the tangent line from their GDC. The equation of the axis of symmetry was reasonably well done although many just wrote down 1.5 instead of <em>x</em> = 1.5.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Some forgot to write down that the gradient at the vertex was 0.</span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Parts (a) and (b) were very well done. After that, only the stronger candidates were able to cope. The equation of the tangent at the point with coordinates (2, 6) was badly done but some candidates managed to find the equation of the tangent line from their GDC. The equation of the axis of symmetry was reasonably well done although many just wrote down 1.5 instead of <em>x</em> = 1.5.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Some forgot to write down that the gradient at the vertex was 0.</span></p>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">A manufacturer has a contract to make \(2600\) solid blocks of wood. Each block is in the shape of a right triangular prism, \({\text{ABCDEF}}\), as shown in the diagram.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{AB}} = 30{\text{ cm}},{\text{ BC}} = 24{\text{ cm}},{\text{ CD}} = 25{\text{ cm}}\) and angle \({\rm{A\hat BC}} = 35^\circ {\text{ }}\).</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><br><span style="font-family: 'times new roman', times; font-size: medium;"><img src="images/Schermafbeelding_2014-09-03_om_12.17.46.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the length of \({\text{AC}}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the area of triangle \({\text{ABC}}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Assuming that no wood is wasted, show that the volume of wood required to make all \(2600\) blocks is \({\text{13}}\,{\text{400}}\,{\text{000 c}}{{\text{m}}^3}\), correct to three significant figures.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write \({\text{13}}\,{\text{400}}\,{\text{000}}\) in the form \(a \times {10^k}\) where \(1 \leqslant a < 10\) and \(k \in \mathbb{Z}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that the total surface area of one block is \({\text{2190 c}}{{\text{m}}^2}\), correct to three significant figures.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The blocks are to be painted. One litre of paint will cover \(22{\text{ }}{{\text{m}}^2}\).</span></p>
<p><span>Calculate the number of litres required to paint all \(2600\) blocks.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{A}}{{\text{C}}^2} = {30^2} + {24^2} - 2 \times 30 \times 24 \times \cos 35^\circ \) <strong><em>(M1)(A1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substituted cosine rule formula,</span></p>
<p><span> <strong><em>(A1) </em></strong>for correct substitutions.</span></p>
<p> </p>
<p><span>\({\text{AC}} = 17.2{\text{ cm}}\) \((17.2168…)\) <strong><em>(A1)(G2)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Use of radians gives \(52.7002…\) Award <strong><em>(M1)(A1)(A0)</em></strong>.</span></p>
<p><span> No marks awarded in this part of the question where candidates assume that angle \({\text{ACB}} = 90^\circ \).</span></p>
<p> </p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><strong><em>Units are required in part (b).</em></strong></span></p>
<p><span>Area of triangle \({\text{ABC = }}\frac{1}{2} \times 24 \times 30 \times \sin 35^\circ \) <strong><em>(M1)(A1)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for substitution into area formula, <strong><em>(A1) </em></strong>for correct substitutions.</span></p>
<p><span> <strong>Special Case: </strong>Where a candidate has assumed that angle \({\text{ACB}} = 90^\circ \) in part (a), award <strong><em>(M1)(A1) </em></strong>for a correct alternative substituted formula for the area of the triangle \(\left( {ie{\text{ }}\frac{1}{2} \times {\text{base}} \times {\text{height}}} \right)\).</span></p>
<p> </p>
<p><span>\( = 206{\text{ c}}{{\text{m}}^2}\) \((206.487 \ldots {\text{c}}{{\text{m}}^2})\) <strong><em>(A1)(G2)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Use of radians gives negative answer, \(–154.145…\) Award (<strong><em>M1)(A1)(A0)</em></strong>.</span></p>
<p><span> <strong>Special Case: </strong>Award <strong><em>(A1)</em>(ft) </strong>where the candidate has arrived at an area which is correct to the standard rounding rules from their lengths (units required).</span></p>
<p> </p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(206.487… \times 25 \times 2600\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for multiplication of their answer to part (b) by \(25\) and \(2600\).</span></p>
<p> </p>
<p><span>\({\text{13}}\,{\text{421}}\,{\text{688.61}}\) <strong><em>(A1)</em></strong></span></p>
<p> </p>
<address><span><strong>Note: </strong>Accept unrounded answer of \({\text{13}}\,{\text{390}}\,{\text{000}}\) for use of \(206\).</span></address>
<p> </p>
<p><span>\({\text{13}}\,{\text{400}}\,{\text{000}}\) <strong><em>(AG)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>The final <strong><em>(A1) </em></strong>cannot be awarded unless both the unrounded and rounded answers are seen.</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(1.34 \times {10^7}\) <strong><em>(A2)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes:</strong></span><strong> </strong><span>Award <em><strong>(A2)</strong></em> for the correct answer<span>.</span></span></p>
<p><span> Award <strong><em>(A1)(A0) </em></strong>for \(1.34\) and an incorrect index value.</span></p>
<p><span> Award <strong><em>(A0)(A0) </em></strong>for any other combination (including answers such as \(13.4 \times {10^6}\)).</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(2 \times 206.487 \ldots + 24 \times 25 + 30 \times 25 + 17.2168 \ldots \times 25\) <strong><em>(M1)(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for multiplication of their answer to part (b) by \(2\) for area of two triangular ends, <strong><em>(M1) </em></strong>for three correct rectangle areas using \(24\), \(30\) and their \(17.2\).</span></p>
<p> </p>
<p><span>\(2193.26…\) <strong><em>(A1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Accept \(2192\) for use of 3 sf answers.</span></p>
<p> </p>
<p><span>\(2190\) <strong><em>(AG)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>The final <strong><em>(A1) </em></strong>cannot be awarded unless both the unrounded and rounded answers are seen.</span></p>
<p> </p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{2190 \times 2600}}{{22 \times 10\,000}}\) <strong><em>(M1)(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for multiplication by \(2600\) and division by \(22\), <strong><em>(M1) </em></strong>for division by \({10\,000}\).</span></p>
<p><span> The use of \(22\) may be implied <em>ie </em>division by \(2200\) would be acceptable.</span></p>
<p> </p>
<p><span>\(25.9\) litres \((25.8818…)\) <strong><em>(A1)(G2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Accept \(26\).</span></p>
<p> </p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Some candidates assumed that triangle ACB was a right angled triangle with angle \({\text{ACB}} = 90^\circ \). Such candidates earned no marks for part (a) but were able to recover most of the marks in the remainder of the question. For those candidates who correctly used the cosine rule for part (a), most achieved all 3 marks for this part and used a correct formula for the area of the triangle in part (b) to obtain at least 2 marks for this part. The final mark was not awarded, however, if no units or the incorrect units were given. Parts (c) and (e) were generally well done with many candidates showing the unrounded answer before the required answer. Part (f) proved to be quite problematic for many candidates. Whilst many were able to earn a method mark for \(\frac{{2190 \times 2600}}{{22}}\), a significant number of these candidates were unable to convert the units correctly and very few correct answers were seen. Indeed, the most popular answer seemed to be 2590 litres.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Some candidates assumed that triangle ACB was a right angled triangle with angle \({\text{ACB}} = 90^\circ \). Such candidates earned no marks for part (a) but were able to recover most of the marks in the remainder of the question. For those candidates who correctly used the cosine rule for part (a), most achieved all 3 marks for this part and used a correct formula for the area of the triangle in part (b) to obtain at least 2 marks for this part. The final mark was not awarded, however, if no units or the incorrect units were given. Parts (c) and (e) were generally well done with many candidates showing the unrounded answer before the required answer. Part (f) proved to be quite problematic for many candidates. Whilst many were able to earn a method mark for \(\frac{{2190 \times 2600}}{{22}}\), a significant number of these candidates were unable to convert the units correctly and very few correct answers were seen. Indeed, the most popular answer seemed to be 2590 litres.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Some candidates assumed that triangle ACB was a right angled triangle with angle \({\text{ACB}} = 90^\circ \). Such candidates earned no marks for part (a) but were able to recover most of the marks in the remainder of the question. For those candidates who correctly used the cosine rule for part (a), most achieved all 3 marks for this part and used a correct formula for the area of the triangle in part (b) to obtain at least 2 marks for this part. The final mark was not awarded, however, if no units or the incorrect units were given. Parts (c) and (e) were generally well done with many candidates showing the unrounded answer before the required answer. Part (f) proved to be quite problematic for many candidates. Whilst many were able to earn a method mark for \(\frac{{2190 \times 2600}}{{22}}\), a significant number of these candidates were unable to convert the units correctly and very few correct answers were seen. Indeed, the most popular answer seemed to be 2590 litres.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Some candidates assumed that triangle ACB was a right angled triangle with angle \({\text{ACB}} = 90^\circ \). Such candidates earned no marks for part (a) but were able to recover most of the marks in the remainder of the question. For those candidates who correctly used the cosine rule for part (a), most achieved all 3 marks for this part and used a correct formula for the area of the triangle in part (b) to obtain at least 2 marks for this part. The final mark was not awarded, however, if no units or the incorrect units were given. Parts (c) and (e) were generally well done with many candidates showing the unrounded answer before the required answer. Part (f) proved to be quite problematic for many candidates. Whilst many were able to earn a method mark for \(\frac{{2190 \times 2600}}{{22}}\), a significant number of these candidates were unable to convert the units correctly and very few correct answers were seen. Indeed, the most popular answer seemed to be 2590 litres.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Some candidates assumed that triangle ACB was a right angled triangle with angle \({\text{ACB}} = 90^\circ \). Such candidates earned no marks for part (a) but were able to recover most of the marks in the remainder of the question. For those candidates who correctly used the cosine rule for part (a), most achieved all 3 marks for this part and used a correct formula for the area of the triangle in part (b) to obtain at least 2 marks for this part. The final mark was not awarded, however, if no units or the incorrect units were given. Parts (c) and (e) were generally well done with many candidates showing the unrounded answer before the required answer. Part (f) proved to be quite problematic for many candidates. Whilst many were able to earn a method mark for \(\frac{{2190 \times 2600}}{{22}}\), a significant number of these candidates were unable to convert the units correctly and very few correct answers were seen. Indeed, the most popular answer seemed to be 2590 litres.</span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Some candidates assumed that triangle ACB was a right angled triangle with angle \({\text{ACB}} = 90^\circ \). Such candidates earned no marks for part (a) but were able to recover most of the marks in the remainder of the question. For those candidates who correctly used the cosine rule for part (a), most achieved all 3 marks for this part and used a correct formula for the area of the triangle in part (b) to obtain at least 2 marks for this part. The final mark was not awarded, however, if no units or the incorrect units were given. Parts (c) and (e) were generally well done with many candidates showing the unrounded answer before the required answer. Part (f) proved to be quite problematic for many candidates. Whilst many were able to earn a method mark for \(\frac{{2190 \times 2600}}{{22}}\), a significant number of these candidates were unable to convert the units correctly and very few correct answers were seen. Indeed, the most popular answer seemed to be 2590 litres.</span></p>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the curve \(y = {x^3} + \frac{3}{2}{x^2} - 6x - 2\)</span> .</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Write down the value of \(y\) when \(x\) is \(2\).</span></p>
<p><span>(ii) Write down the coordinates of the point where the curve intercepts the \(y\)-axis.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Sketch the curve for \( - 4 \leqslant x \leqslant 3\) and \( - 10 \leqslant y \leqslant 10\). Indicate clearly the information found in (a).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Let \({L_1}\) be the tangent to the curve at \(x = 2\).</span></p>
<p><span>Let \({L_2}\) be a tangent to the curve, parallel to \({L_1}\).</span></p>
<p><span>(i) Show that the gradient of \({L_1}\) is \(12\).</span></p>
<p><span>(ii) Find the \(x\)-coordinate of the point at which \({L_2}\) and the curve meet.</span></p>
<p><span>(iii) Sketch and label \({L_1}\) and \({L_2}\) on the diagram drawn in (b).</span></p>
<div class="marks">[8]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>It is known that \(\frac{{{\text{d}}y}}{{{\text{d}}x}} > 0\) for \(x < - 2\) and \(x > b\) where \(b\) is positive.</span></p>
<p><span>(i) Using your graphic display calculator, or otherwise, find the value of \(b\).</span></p>
<p><span>(ii) Describe the behaviour of the curve in the interval \( - 2 < x < b\) .</span></p>
<p><span>(iii) Write down the equation of the tangent to the curve at \(x = - 2\).</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(y = 0\) <em><strong>(A1)</strong></em></span></p>
<p><span>(ii) \((0{\text{, }}{- 2})\) <em><strong>(A1)(A1)</strong></em></span></p>
<p><br><span><strong>Note: </strong>Award <em><strong>(A1)(A0)</strong></em> if brackets missing.</span></p>
<p><br><span><strong>OR</strong></span></p>
<p><span>\(x = 0{\text{, }}y = - 2\) <em><strong>(A1)(A1)</strong></em></span></p>
<p><br><span><strong>Note: </strong>If coordinates reversed award <strong><em>(A0)(A1)</em>(ft)</strong>. Two coordinates must be given.</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt></span><span> <em><strong>(A4)</strong></em></span></p>
<p><span><strong>Notes: <em>(A1)</em></strong> for appropriate window. Some indication of scale on the \(x\)-axis must be present (for example ticks). Labels not required. <em><strong>(A1)</strong></em> for smooth curve and shape, <em><strong>(A1)</strong></em> for maximum and minimum in approximately correct position, <em><strong>(A1)</strong></em> for \(x\) and \(y\) intercepts found in (a) in approximately correct position.</span></p>
<p><span><em><strong>[4 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 3{x^2} + 3x - 6\) <em><strong>(A1)(A1)(A1)</strong></em></span></p>
<p><span><strong> Note: <em>(A1)</em></strong> for each correct term. Award <em><strong>(A1)(A1)(A0)</strong></em> at most if any other term is present.</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(3 \times 4 + 3 \times 2 - 6 = 12\) <em><strong>(M1)(A1)(AG)</strong></em></span></p>
<p><br><span><strong>Note: <em>(M1)</em></strong> for using the derivative and substituting \(x = 2\) . <em><strong>(A1)</strong></em> for correct (and clear) substitution. The \(12\) must be seen.</span></p>
<p><br><span>(ii) Gradient of \({L_2}\) is \(12\) (can be implied) <em><strong>(A1)</strong></em></span></p>
<p><span>\(3{x^2} + 3x - 6 = 12\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(x = - 3\) <em><strong>(A1)(G2)</strong></em></span><br><br></p>
<p><span><strong>Note: <em>(M1)</em></strong> for equating the derivative to \(12\) or showing a sketch of the derivative together with a line at \(y = 12\) or a table of values showing the \(12\) in the derivative column.</span></p>
<p><br><span>(iii) <em><strong>(A1)</strong></em> for \({L_1}\) correctly drawn at approx the correct point <em><strong>(A1)</strong></em></span></p>
<p><span><em><strong>(A1)</strong></em> for \({L_2}\) correctly drawn at approx the correct point</span><span> <em><strong>(A1)</strong></em></span></p>
<p><span><em><strong>(A1)</strong></em> for 2 parallel lines</span><span> <em><strong>(A1)</strong></em></span></p>
<p><br><span><strong>Note: </strong>If lines are not labelled award at most <em><strong>(A1)(A1)(A0)</strong></em>. Do not accept 2 horizontal or 2 vertical parallel lines.</span></p>
<p><span><em><strong>[8 marks]</strong></em><br></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(b = 1\) <em><strong>(G2)</strong></em></span></p>
<p><span>(ii) The curve is decreasing. <em><strong>(A1)</strong></em></span></p>
<p><br><span><strong>Note: </strong>Accept any valid description.</span></p>
<p><br><span>(iii) \(y = 8\) <em><strong>(A1)(A1)(G2)</strong></em></span></p>
<p><br><span><strong>Note: <em>(A1)</em></strong> for “\(y =\) a constant”, <em><strong>(A1)</strong></em> for \(8\).</span></p>
<p><span><em><strong>[5 marks]</strong></em><br></span></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates managed to gain good marks in this question as they were able to answer the first three parts of the question. Good sketches were drawn with the required information shown on them. Very few candidates did not recognise the notation \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) but they showed that they knew how to differentiate as in (d)(i) they found the derivative to show that the gradient of \({L_1}\) was \(12\). Candidates found it difficult to find the other \(x\) for which the derivative was \(12\). However, some could draw both tangents without having found this value of \(x\) . In general, tangents were not well drawn. The last part question did act as a discriminating question. However, those candidates that had the function drawn either in their GDC or on paper recognised that at \(x = - 2\) there was a maximum and so wrote down the correct equation of the tangent at that point.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates managed to gain good marks in this question as they were able to answer the first three parts of the question. Good sketches were drawn with the required information shown on them. Very few candidates did not recognise the notation \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) but they showed that they knew how to differentiate as in (d)(i) they found the derivative to show that the gradient of \({L_1}\) was \(12\). Candidates found it difficult to find the other \(x\) for which the derivative was \(12\). However, some could draw both tangents without having found this value of \(x\) . In general, tangents were not well drawn. The last part question did act as a discriminating question. However, those candidates that had the function drawn either in their GDC or on paper recognised that at \(x = - 2\) there was a maximum and so wrote down the correct equation of the tangent at that point.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates managed to gain good marks in this question as they were able to answer the first three parts of the question. Good sketches were drawn with the required information shown on them. Very few candidates did not recognise the notation \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) but they showed that they knew how to differentiate as in (d)(i) they found the derivative to show that the gradient of \({L_1}\) was \(12\). Candidates found it difficult to find the other \(x\) for which the derivative was \(12\). However, some could draw both tangents without having found this value of \(x\) . In general, tangents were not well drawn. The last part question did act as a discriminating question. However, those candidates that had the function drawn either in their GDC or on paper recognised that at \(x = - 2\) there was a maximum and so wrote down the correct equation of the tangent at that point.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates managed to gain good marks in this question as they were able to answer the first three parts of the question. Good sketches were drawn with the required information shown on them. Very few candidates did not recognise the notation \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) but they showed that they knew how to differentiate as in (d)(i) they found the derivative to show that the gradient of \({L_1}\) was \(12\). Candidates found it difficult to find the other \(x\) for which the derivative was \(12\). However, some could draw both tangents without having found this value of \(x\) . In general, tangents were not well drawn. The last part question did act as a discriminating question. However, those candidates that had the function drawn either in their GDC or on paper recognised that at \(x = - 2\) there was a maximum and so wrote down the correct equation of the tangent at that point.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates managed to gain good marks in this question as they were able to answer the first three parts of the question. Good sketches were drawn with the required information shown on them. Very few candidates did not recognise the notation \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) but they showed that they knew how to differentiate as in (d)(i) they found the derivative to show that the gradient of \({L_1}\) was \(12\). Candidates found it difficult to find the other \(x\) for which the derivative was \(12\). However, some could draw both tangents without having found this value of \(x\) . In general, tangents were not well drawn. The last part question did act as a discriminating question. However, those candidates that had the function drawn either in their GDC or on paper recognised that at \(x = - 2\) there was a maximum and so wrote down the correct equation of the tangent at that point.</span></p>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagram shows a sketch of the function <em>f</em> (<em>x</em>) = 4<em>x</em><sup>3</sup> − 9<em>x</em><sup>2</sup> − 12<em>x</em> + 3.</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;"><img 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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the values of <em>x</em> where the graph of <em>f</em> (<em>x</em>) intersects the <em>x</em>-axis.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down <em>f </em>′(<em>x</em>).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of the local maximum of <em>y</em> = <em>f</em> (<em>x</em>).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Let P be the point where the graph of <em>f</em> (<em>x</em>) intersects the <em>y</em> axis.<br></span></p>
<p><span>Write down the coordinates of P.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>Let P be the point where the graph of <em>f</em> (<em>x</em>) intersects the <em>y</em> axis.</span></span></p>
<p><span>Find the gradient of the curve at P.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The line, <em>L</em>, is the tangent to the graph of <em>f</em> (<em>x</em>) at P.</span></p>
<p><span>Find the equation of <em>L</em> in the form <em>y</em> = <em>mx</em> +<em> c</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>There is a second point, Q, on the curve at which the tangent to <em>f</em> (<em>x</em>) is parallel to <em>L</em>.</span></p>
<p><span>Write down the gradient of the tangent at Q.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>There is a second point, Q, on the curve at which the tangent to <em>f</em> (<em>x</em>) is parallel to <em>L</em>.</span></p>
<p><span>Calculate the <em>x</em>-coordinate of Q.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>–1.10, 0.218, 3.13 <em><strong>(A1)(A1)(A1)</strong></em></span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>f </em><span>′</span>(<em>x</em>) = 12<em>x</em><sup>2</sup> – 18<em>x</em> – 12 <em><strong>(A1)(A1)(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong> </em>for each correct term and award maximum of<em><strong> (A1)(A1)</strong></em> if other terms seen.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span><em>f </em>′(<em>x</em>)</span> = 0<em><strong> (M1)</strong></em></span><br><span><em>x</em> = –0.5, 2</span><br><span><em>x</em> = –0.5 <em><strong> (A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> If <em>x</em> = –0.5 not stated, can be inferred from working below.</span></p>
<p><br><span><em>y</em> = 4(–0.5)<sup>3</sup> – 9(–0.5)<sup>2 </sup>– 12(–0.5) + 3 <em><strong>(M1)</strong></em></span><br><span><em>y</em> = 6.25 <em><strong> (A1)(G3)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their value of <em>x</em> substituted into <em>f</em> (<em>x</em>).</span></p>
<p><span>Award <em><strong>(M1)(G2)</strong></em> if sketch shown as method. If coordinate pair given then award <em><strong>(M1)(A1)(M1)(A0)</strong></em>. If coordinate pair given with no working award <em><strong>(G2)</strong></em>.</span></p>
<p><span> </span></p>
<p><em><strong><span>[4 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(0, 3) <em><strong>(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Accept <em>x</em> = 0,<em> y</em> = 3.</span></p>
<p><span> </span></p>
<p><em><strong><span>[1 mark]</span></strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>f </em>′(0) = –12 <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong> </em>for substituting <em>x</em> = 0 into their derivative.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Tangent: <em>y</em> = –12<em>x</em> + 3 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)(G2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for their gradient, <em><strong>(A1)</strong></em> for intercept = 3.</span></p>
<p><span>Award<em><strong> (A1)(A0)</strong></em> if <em>y</em> = not seen.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>–12 <strong> <em>(A1)</em>(ft)</strong></span></p>
<p><br><span><strong>Note:</strong> Follow through from their part (e).</span></p>
<p><span> </span></p>
<p><em><strong><span>[1 mark]</span></strong></em></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>12<em>x</em><sup>2</sup> – 18<em>x </em></span><span><span>– 12 = </span></span><span><span><span>–12</span></span> <em><strong>(M1)</strong></em></span></p>
<p><span>12<em>x</em><sup>2</sup> </span><span><span>– </span>18<em>x</em> = 0 <em><strong>(M1)</strong></em></span></p>
<p><span><em>x</em> = 1.5, 0</span></p>
<p><span>At Q <em>x</em> = 1.5 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><em><strong><span> </span></strong></em></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)(G2)</strong></em> for 12<em>x</em><sup>2</sup> </span><span><span>– 18</span><em>x </em></span><span><span>– 12 = </span></span><span><span><span>–12</span></span> followed by </span><span><em>x</em> = 1.5.</span></p>
<p><span>Follow through from their part (g).</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was either very well done – by the majority – or very poor and incomplete attempts were seen. This would perhaps indicate a lack of preparation in this area of the syllabus from some centres, though it is recognised that the differential calculus is one of the more problematic topics for the candidature.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">It was however disappointing to note the number of candidates who do not use the GDC to good effect; in part (a) for example, the zeros were not found accurately due to “trace” being used; this is not a suitable approach – there is a built-in zero finder which should be used. Much of the question was accessible via a GDC approach, a sketch was given that could have been verified on the GDC; this was lost on many.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was either very well done – by the majority – or very poor and incomplete attempts were seen. This would perhaps indicate a lack of preparation in this area of the syllabus from some centres, though it is recognised that the differential calculus is one of the more problematic topics for the candidature.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">It was however disappointing to note the number of candidates who do not use the GDC to good effect; in part (a) for example, the zeros were not found accurately due to “trace” being used; this is not a suitable approach – there is a built-in zero finder which should be used. Much of the question was accessible via a GDC approach, a sketch was given that could have been verified on the GDC; this was lost on many.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was either very well done – by the majority – or very poor and incomplete attempts were seen. This would perhaps indicate a lack of preparation in this area of the syllabus from some centres, though it is recognised that the differential calculus is one of the more problematic topics for the candidature.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">It was however disappointing to note the number of candidates who do not use the GDC to good effect; in part (a) for example, the zeros were not found accurately due to “trace” being used; this is not a suitable approach – there is a built-in zero finder which should be used. Much of the question was accessible via a GDC approach, a sketch was given that could have been verified on the GDC; this was lost on many.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was either very well done – by the majority – or very poor and incomplete attempts were seen. This would perhaps indicate a lack of preparation in this area of the syllabus from some centres, though it is recognised that the differential calculus is one of the more problematic topics for the candidature.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">It was however disappointing to note the number of candidates who do not use the GDC to good effect; in part (a) for example, the zeros were not found accurately due to “trace” being used; this is not a suitable approach – there is a built-in zero finder which should be used. Much of the question was accessible via a GDC approach, a sketch was given that could have been verified on the GDC; this was lost on many.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was either very well done – by the majority – or very poor and incomplete attempts were seen. This would perhaps indicate a lack of preparation in this area of the syllabus from some centres, though it is recognised that the differential calculus is one of the more problematic topics for the candidature.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">It was however disappointing to note the number of candidates who do not use the GDC to good effect; in part (a) for example, the zeros were not found accurately due to “trace” being used; this is not a suitable approach – there is a built-in zero finder which should be used. Much of the question was accessible via a GDC approach, a sketch was given that could have been verified on the GDC; this was lost on many.</span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was either very well done – by the majority – or very poor and incomplete attempts were seen. This would perhaps indicate a lack of preparation in this area of the syllabus from some centres, though it is recognised that the differential calculus is one of the more problematic topics for the candidature.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">It was however disappointing to note the number of candidates who do not use the GDC to good effect; in part (a) for example, the zeros were not found accurately due to “trace” being used; this is not a suitable approach – there is a built-in zero finder which should be used. Much of the question was accessible via a GDC approach, a sketch was given that could have been verified on the GDC; this was lost on many.</span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was either very well done – by the majority – or very poor and incomplete attempts were seen. This would perhaps indicate a lack of preparation in this area of the syllabus from some centres, though it is recognised that the differential calculus is one of the more problematic topics for the candidature.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">It was however disappointing to note the number of candidates who do not use the GDC to good effect; in part (a) for example, the zeros were not found accurately due to “trace” being used; this is not a suitable approach – there is a built-in zero finder which should be used. Much of the question was accessible via a GDC approach, a sketch was given that could have been verified on the GDC; this was lost on many.</span></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was either very well done – by the majority – or very poor and incomplete attempts were seen. This would perhaps indicate a lack of preparation in this area of the syllabus from some centres, though it is recognised that the differential calculus is one of the more problematic topics for the candidature.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">It was however disappointing to note the number of candidates who do not use the GDC to good effect; in part (a) for example, the zeros were not found accurately due to “trace” being used; this is not a suitable approach – there is a built-in zero finder which should be used. Much of the question was accessible via a GDC approach, a sketch was given that could have been verified on the GDC; this was lost on many.</span></p>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A farmer owns a plot of land in the shape of a quadrilateral <span class="s1">ABCD</span>.</p>
<p class="p1">\({\text{AB}} = 105{\text{ m, BC}} = 95{\text{ m, CD}} = 40{\text{ m, DA}} = 70{\text{ m}}\) and angle \({\text{DCB}} = 90^\circ \).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2017-03-07_om_08.23.38.png" alt="N16/5/MATSD/SP2/ENG/TZ0/05"></p>
<p class="p1">The farmer wants to divide the land into two equal areas. He builds a fence in a straight line from point <span class="s1">B </span>to point <span class="s1">P </span>on <span class="s1">AD</span>, so that the area of <span class="s1">PAB </span>is equal to the area of <span class="s1">PBCD</span>.</p>
<p class="p1">Calculate</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">the length of <span class="s1">BD</span><span class="s2">;</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">the size of angle <span class="s1">DAB</span><span class="s2">;</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">the area of triangle <span class="s1">ABD</span><span class="s2">;</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">the area of quadrilateral <span class="s1">ABCD</span><span class="s2">;</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">the length of <span class="s1">AP</span><span class="s2">;</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">the length of the fence, <span class="s1">BP</span><span class="s2">.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(({\text{BD}} = ){\text{ }}\sqrt {{{95}^2} + {{40}^2}} \) </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for correct substitution into Pythagoras’ theorem.</p>
<p class="p4"> </p>
<p class="p3"><span class="Apple-converted-space">\( = 103{\text{ }}({\text{m}}){\text{ }}\left( {103.077 \ldots ,{\text{ }}25\sqrt {17} } \right)\) </span><strong><em>(A1)(G2)</em></strong></p>
<p class="p3"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="s1">\(\cos {\rm{B\hat AD}} = \frac{{{{105}^2} + {{70}^2} - {{(103.077 \ldots )}^2}}}{{2 \times 105 \times 70}}\) <span class="Apple-converted-space"> </span></span><strong><em>(M1)(A1)</em>(ft)</strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for substitution into cosine rule, <strong><em>(A1)</em>(ft) </strong>for their correct substitutions. Follow through from part (a).</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\(({\rm{B\hat AD}}) = 68.9^\circ {\text{ }}(68.8663 \ldots )\) </span><strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>If their <span class="s2">103 </span>used, the answer is \(68.7995 \ldots \)</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(({\text{Area of ABD}} = )\frac{1}{2} \times 105 \times 70 \times \sin (68.8663 \ldots )\) </span><strong><em>(M1)(A1)</em>(ft)</strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for substitution into the trig form of the area of a triangle formula.</p>
<p class="p1">Award <strong><em>(A1)</em>(ft) </strong>for their correct substitutions.</p>
<p class="p1">Follow through from part (b).</p>
<p class="p1">If <span class="s1">68.8° </span>is used the area \( = 3426.28 \ldots {\text{ }}{{\text{m}}^2}\).</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\( = 3430{\text{ }}{{\text{m}}^2}{\text{ }}(3427.82 \ldots )\) </span><strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\({\text{area of ABCD}} = \frac{1}{2} \times 40 \times 95 + 3427.82 \ldots \) </span><strong><em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for correctly substituted area of triangle formula <strong>added </strong>to their answer to part (c).</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\( = 5330{\text{ }}{{\text{m}}^2}{\text{ }}(5327.83 \ldots )\) </span><strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(\frac{1}{2} \times 105 \times {\text{AP}} \times \sin (68.8663 \ldots ) = 0.5 \times 5327.82 \ldots \) </span><strong><em>(M1)(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for the correct substitution into triangle formula.</p>
<p class="p1">Award <strong><em>(M1) </em></strong>for equating their triangle area to half their part (d).</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\(({\text{AP}} = ){\text{ }}54.4{\text{ }}({\text{m}}){\text{ }}(54.4000 \ldots )\) </span><strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: <span class="Apple-converted-space"> </span></strong>Follow through from parts (b) and (d).</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\({\text{B}}{{\text{P}}^2} = {105^2} + {(54.4000 \ldots )^2} - 2 \times 105 \times (54.4000 \ldots ) \times \cos (68.8663 \ldots )\) </span><strong><em>(M1)(A1)</em>(ft)</strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for substituted cosine rule formula.</p>
<p class="p1">Award <strong><em>(A1)</em>(ft) </strong>for their correct substitutions. Accept the exact fraction \(\frac{{53}}{{147}}\) in place of \(\cos (68.8663 \ldots )\).</p>
<p class="p1">Follow through from parts (b) and (e).</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\(({\text{BP}} = ){\text{ }}99.3{\text{ }}({\text{m}}){\text{ }}(99.3252 \ldots )\) </span><strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: <span class="Apple-converted-space"> </span></strong>If 54.4 and \(\cos (68.9)\) are used the answer is \(99.3567 \ldots \)</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A farmer has a triangular field, ABC, as shown in the diagram.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">AB = 35 m, BC = 80 m and BÂC = 105°, and D is the midpoint of BC.</span></p>
<p> </p>
<p> </p>
<p style="text-align: center;"><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the size of BĈA.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the length of AD.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The farmer wants to build a fence around ABD.</span></p>
<p><span>Calculate the total length of the fence.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The farmer wants to build a fence around ABD.</span></p>
<p><span>The farmer pays 802.50 USD for the fence. Find the cost per metre.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>Calculate the area of the triangle ABD.</span></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A layer of earth 3 cm thick is removed from ABD. Find the volume removed in cubic metres.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{\sin {\text{BCA}}}}{{35}} = \frac{{\sin 105^\circ }}{{80}}\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substituted formula, <em><strong>(A1)</strong></em> for correct substitutions.</span></p>
<p><br><span>\({\text{B}}{\operatorname{\hat C}}{\text{A}} = 25.0^{\circ}\) <em><strong>(A1)(G2)</strong></em></span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong><span>Note: Unit penalty (UP) applies in parts (b)(c) and (e)</span></strong></em></p>
<p><span> </span></p>
<p><span>Length BD = 40 m <em><strong>(A1)</strong></em></span></p>
<p><span>Angle ABC = 180° − 105° </span><span><span>−</span> 25° = 50° <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Note: (ft)</strong> from their answer to (a).</span></p>
<p><br><span>AD<sup>2</sup> = 35</span><span><span><sup>2</sup></span> + 40</span><span><span><sup>2</sup></span> </span><span><span><span>−</span></span> (2 × 35</span><span><span> × </span>40</span><span><span> × </span>cos 50°) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substituted formula, <em><strong>(A1)</strong></em><strong>(ft)</strong> for correct</span> <span>substitutions.</span></p>
<p><br><span><em><strong>(UP)</strong></em> AD = 32.0 m <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G3)</strong></em> <br></span></p>
<p><br><span><strong>Notes:</strong> If 80 is used for BD award at most <em><strong>(A0)(A1)</strong></em><strong>(ft)</strong><em><strong>(M1)(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong></span> <span>for an answer of 63.4 m.</span></p>
<p><span>If the angle ABC is incorrectly calculated <strong>in this part</strong> award at most </span><em><strong><span>(A1)(A0)(M1)(A1)</span></strong></em><strong><span>(ft)</span></strong><em><strong><span>(A1)</span></strong></em><strong><span>(ft)</span></strong><span>.</span></p>
<p><span>If angle BCA is used award at most <em><strong>(A1)(A0)(M1)(A0)(A0)</strong></em>.</span></p>
<p><span> </span></p>
<p><em><strong><span>[5 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong><span>Note: Unit penalty (UP) applies in parts (b)(c) and (e)</span></strong></em></p>
<p><span> </span></p>
<p><span>length of fence = 35 + 40 + 32 <em><strong>(M1)</strong></em></span></p>
<p><span><em><strong>(UP)</strong></em> = 107 m <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em> </span></p>
<p><br><span><strong>Note: <em>(M1)</em></strong> for adding 35 + 40 + their (b).</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>cost per metre \( = \frac{802.50}{107}\)</span> <em><strong><span>(M1)</span></strong></em></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for dividing 802.50 by their (c).</span></p>
<p><br><span>cost per metre = 7.50 USD (7.5 USD) (USD not required) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong><span>Note: Unit penalty (UP) applies in parts (b)(c) and (e)</span></strong></em></p>
<p><span> </span></p>
<p><span>Area of ABD \( = \frac{1}{2} \times 35 \times 40 \times \sin 50^\circ \) <em><strong>(M1)</strong></em></span></p>
<p><span>= 536.2311102 <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><em><strong>(UP)</strong></em> = 536 m<sup>2</sup> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em> </span></p>
<p><br><span><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for correct substituted formula, <em><strong>(A1)</strong></em><strong>(ft)</strong> for correct</span> <span>substitution, <strong>(ft)</strong> from their value of BD and their angle ABC in (b).</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Volume = 0.03 × 536 <em><strong>(A1)(M1)</strong></em></span></p>
<p><span>= 16.08</span></p>
<p><span>= 16.1 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em> </span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for 0.03, <em><strong>(M1)</strong></em> for correct formula. <strong>(ft)</strong> from their (e).</span></p>
<p><span>If 3 is used award at most <em><strong>(A0)(M1)(A0)</strong></em>.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This was a simple application of non-right angled trigonometry and most </span><span style="font-size: medium; font-family: times new roman,times;">candidates answered it well. Some candidates lost marks in both parts due to the incorrect </span><span style="font-size: medium; font-family: times new roman,times;">setting of the calculators. Those that did not score well overall primarily used Pythagoras.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This was a simple application of non-right angled trigonometry and most </span><span style="font-size: medium; font-family: times new roman,times;">candidates answered it well. Some candidates lost marks in both parts due to the incorrect </span><span style="font-size: medium; font-family: times new roman,times;">setting of the calculators. Those that did not score well overall primarily used Pythagoras.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;"><span style="font-size: medium; font-family: times new roman,times;">Most candidates scored full marks, many by follow through from an incorrect part</span> <span style="font-size: medium; font-family: times new roman,times;">(b). The main error was using the value for BC and not BD.</span></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;"><span style="font-size: medium; font-family: times new roman,times;"><span style="font-size: medium; font-family: times new roman,times;">Most candidates scored full marks, many by follow through from an incorrect part</span> <span style="font-size: medium; font-family: times new roman,times;">(b). The main error was using the value for BC and not BD.</span></span></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;"><span style="font-size: medium; font-family: times new roman,times;">Done well; again some candidates used the right-angled formula.</span></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;"><span style="font-size: medium; font-family: times new roman,times;"><span style="font-size: medium; font-family: times new roman,times;">This part was poorly done; many candidates unable to convert 3 cm to 0.03 m. A</span> <span style="font-size: medium; font-family: times new roman,times;">significant number used the wrong formula, multiplying their answer by 1/3.</span></span></span></p>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>The quadrilateral ABCD represents a park, where \({\text{AB}} = 120{\text{ m}}\), \({\text{AD}} = 95{\text{ m}}\) and \({\text{DC}} = 100{\text{ m}}\). Angle DAB is 70° and angle DCB is 110°. This information is shown in the following diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_17.35.40.png" alt="M17/5/MATSD/SP2/ENG/TZ2/04"></p>
<p>A straight path through the park joins the points B and D.</p>
</div>
<div class="specification">
<p>A new path, CE, is to be built such that E is the point on BD closest to C.</p>
</div>
<div class="specification">
<p>The section of the park represented by triangle DCE will be used for a charity race. A track will be marked along the sides of this section.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the length of the path BD.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that angle DBC is 48.7°, correct to three significant figures.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of the park.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the length of the path CE.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the total length of the track.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(({\text{B}}{{\text{D}}^2} = ){\text{ }}{95^2} + {120^2} - 2 \times 95 \times 120 \times \cos 70^\circ \) <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for substituted cosine rule, <strong><em>(A1) </em></strong>for correct substitution.</p>
<p> </p>
<p>\(({\text{BD}} = ){\text{ }}125{\text{ (m) }}\left( {125.007 \ldots {\text{ (m)}}} \right)\) <strong><em>(A1)(G2)</em></strong></p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{\sin {\text{DBC}}}}{{100}} = \frac{{\sin 110^\circ }}{{125.007 \ldots }}\) <strong><em>(M1)(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for substituted sine rule, <strong><em>(A1)</em>(ft) </strong>for correct substitution.</p>
<p>Follow through from their answer to part (a).</p>
<p> </p>
<p>\(({\text{DBC}} = ){\text{ }}48.7384 \ldots ^\circ \) <strong><em>(A1)</em>(ft)</strong></p>
<p>\(({\text{DBC}} = ){\text{ }}48.7^\circ \) <strong><em>(AG)</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Award the final <strong><em>(A1)(ft) </em></strong>only if both their unrounded answer and 48.7° is seen. Follow through from their answer to part (a), only if their unrounded answer rounds to 48.7°.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{1}{2} \times 125.007 \ldots \times 100 \times \sin 21.3^\circ + \frac{1}{2} \times 95 \times 120 \times \sin 70^\circ \) <strong><em>(A1)(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for 21.3° (21.2615…) seen, <strong><em>(M1) </em></strong>for substitution into (at least) one area of triangle formula in the form \(\frac{1}{2}ab\sin c\), <strong><em>(M1) </em></strong>for <strong>their </strong>correct substitutions and adding the two areas.</p>
<p> </p>
<p>\(7630{\text{ }}{{\text{m}}^2}{\text{ }}(7626.70 \ldots {{\text{m}}^2})\) <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Follow through from their answers to part (a). Accept \(7620{\text{ }}{{\text{m}}^2}{\text{ }}(7622.79 \ldots {{\text{m}}^2})\) from use of 48.7384…</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(({\text{CE}} = ){\text{ }}100 \times \sin 21.3^\circ \) <strong><em>(M1)</em></strong></p>
<p>\(({\text{CE}} = ){\text{ }}36.3{\text{ (m) }}\left( {36.3251 \ldots {\text{ (m)}}} \right)\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from their angle 21.3° in part (c). Award <strong><em>(M0)(A0) </em></strong>for halving 110° and/or assuming E is the midpoint of BD in any method seen.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>\({\text{area of BCD}} = \frac{1}{2}{\text{BD}} \times {\text{CE}}\) <strong><em>(M1)</em></strong></p>
<p>\(({\text{CE}} = ){\text{ }}36.3{\text{ (m) }}\left( {36.3251 \ldots {\text{ (m)}}} \right)\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from parts (a) and (c). Award <strong><em>(M0)(A0) </em></strong>for halving 110° and/or assuming E is the midpoint of BD in any method seen.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\sqrt {{{100}^2} - 36.3251{ \ldots ^2}} + 100 + 36.3251 \ldots \) <strong><em>(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct use of Pythagoras to find DE (or correct trigonometric equation, \(100 \times \cos 21.3\), to find DE), <strong><em>(M1) </em></strong>for the sum of 100, their DE and their CE.</p>
<p> </p>
<p>\(229{\text{ (m) }}\left( {229.494 \ldots {\text{ (m)}}} \right)\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (d). Use of 3 sf values gives an answer of \(230{\text{ (m) }}\left( {229.5{\text{ (m)}}} \right)\).</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A boat race takes place around a triangular course, \({\text{ABC}}\), with \({\text{AB}} = 700{\text{ m}}\), \({\text{BC}} = 900{\text{ m}}\)<span class="s1"> </span>and angle \({\text{ABC}} = 110^\circ \). The race starts and finishes at point \({\text{A}}\).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-21_om_07.47.08.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the total length of the course.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">It is estimated that the fastest boat in the race can travel at an average speed of \(1.5\;{\text{m}}\,{{\text{s}}^{ - 1}}\)<span class="s1">.</span></p>
<p class="p2">Calculate an estimate of the winning time of the race. Give your answer to the nearest minute.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">It is estimated that the fastest boat in the race can travel at an average speed of \(1.5\;{\text{m}}\,{{\text{s}}^{ - 1}}\)<span class="s1">.</span></p>
<p class="p1">Find the size of angle \({\text{ACB}}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">To comply with safety regulations, the area inside the triangular course must be kept clear of other boats, and the shortest distance from \({\text{B}}\)<span class="s1"> </span>to \({\text{AC}}\)<span class="s1"> </span>must be greater than \(375\)<span class="s1"> </span>metres.</p>
<p class="p1">Calculate the area that must be kept clear of boats.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">To comply with safety regulations, the area inside the triangular course must be kept clear of other boats, and the shortest distance from \({\text{B}}\)<span class="s1"> </span>to \({\text{AC}}\)<span class="s1"> </span>must be greater than \(375\)<span class="s1"> </span>metres.</p>
<p class="p1">Determine, giving a reason, whether the course complies with the safety regulations.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The race is filmed from a helicopter, \({\text{H}}\), which is flying vertically above point \({\text{A}}\).</p>
<p class="p1">The angle of elevation of \({\text{H}}\)<span class="s1"> </span>from \({\text{B}}\)<span class="s1"> </span>is \(15^\circ\).</p>
<p class="p1">Calculate the vertical height, \({\text{AH}}\), of the helicopter above \({\text{A}}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The race is filmed from a helicopter, \({\text{H}}\), which is flying vertically above point \({\text{A}}\).</p>
<p class="p1">The angle of elevation of \({\text{H}}\)<span class="s1"> </span>from \({\text{B}}\)<span class="s1"> </span>is \(15^\circ\).</p>
<p class="p1">Calculate the maximum possible distance from the helicopter to a boat on the course.</p>
<div class="marks">[3]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\({\text{A}}{{\text{C}}^2} = {700^2} + {900^2} - 2 \times 700 \times 900 \times \cos 110^\circ \) <span class="Apple-converted-space"> </span><strong><em>(M1)(A1)</em></strong></p>
<p class="p1">\({\text{AC}} = 1315.65 \ldots \) <span class="Apple-converted-space"> </span><strong><em>(A1)(G2)</em></strong></p>
<p class="p1">length of course \( = 2920{\text{ (m)}}\;\;\;(2915.65 \ldots {\text{ m)}}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for substitution into cosine rule formula, <strong><em>(A1) </em></strong>for correct substitution, <strong><em>(A1) </em></strong>for correct answer.</p>
<p class="p1">Award <strong><em>(G3) </em></strong>for \(2920\;\;\;(2915.65 \ldots )\)<span class="s1"> </span>seen without working.</p>
<p class="p1">The final <strong><em>(A1) </em></strong>is awarded for adding \(900\)<span class="s1"> </span>and \(700\)<span class="s1"> </span>to their \({\text{AC}}\)<span class="s1"> </span>irrespective of working seen.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\frac{{2915.65}}{{1.5}}\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for their length of course divided by \(1.5\)<span class="s1">.</span></p>
<p class="p3">Follow through from part (a).</p>
<p class="p4"> </p>
<p class="p1">\( = 1943.76 \ldots {\text{ (seconds)}}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)</strong></p>
<p class="p1">\( = 32{\text{ (minutes)}}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p class="p1"><strong>Notes:<span class="Apple-converted-space"> </span></strong>Award the final <strong><em>(A1) </em></strong>for correct conversion of <strong>their </strong>answer in seconds to minutes, correct to the nearest minute.</p>
<p class="p1">Follow through from part (a).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\frac{{700}}{{\sin {\text{ACB}}}} = \frac{{1315.65 \ldots }}{{\sin 110^\circ }}\) <span class="Apple-converted-space"> </span><strong><em>(M1)(A1)</em>(ft)</strong></p>
<p class="p1"> </p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">\(\cos {\text{ACB}} = \frac{{{{900}^2} + 1315.65{ \ldots ^2} - {{700}^2}}}{{2 \times 900 \times 1315.65 \ldots }}\) <span class="Apple-converted-space"> </span><strong><em>(M1)(A1)</em>(ft)</strong></p>
<p class="p1">\({\text{ACB}} = 30.0^\circ \;\;\;(29.9979 \ldots ^\circ )\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p class="p1"><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for substitution into sine rule or cosine rule formula, <strong><em>(A1) </em></strong>for their correct substitution, <strong><em>(A1) </em></strong>for correct answer.</p>
<p class="p1">Accept \(29.9^\circ\) for sine rule and \(29.8^\circ\) for cosine rule from use of correct three significant figure values. Follow through from their answer to (a).</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\frac{1}{2} \times 700 \times 900 \times \sin 110^\circ \) <span class="Apple-converted-space"> </span><strong><em>(M1)(A1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Accept \(\frac{1}{2} \times {\text{their AC}} \times {\text{900}} \times {\text{sin(their ACB)}}\). Follow through from <span class="s1">parts (a) and (c).</span></p>
<p class="p3"> </p>
<p class="p1">\( = 296000{\text{ }}{{\text{m}}^2}\;\;\;(296003{\text{ }}{{\text{m}}^2})\) <span class="Apple-converted-space"> </span><strong><em>(A1)(G2)</em></strong></p>
<p class="p1"><strong>Notes:<span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for substitution into area of triangle formula, <strong><em>(A1) </em></strong>for correct substitution, <strong><em>(A1) </em></strong>for correct answer.</p>
<p class="p1">Award <strong><em>(G1) </em></strong>if \(296000\)<span class="s2"> </span>is seen without units or working.</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\sin 29.9979 \ldots = \frac{{{\text{distance}}}}{{900}}\) <strong><em>(M1)</em></strong></p>
<p>\({\text{(distance}} = ){\text{ }}450{\text{ (m)}}\;\;\;{\text{(449.971}} \ldots {\text{)}}\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><strong>Note: </strong>Follow through from part (c).</p>
<p> </p>
<p><strong>OR</strong></p>
<p>\(\frac{1}{2} \times {\text{distance}} \times 1315.65 \ldots = 296003\) <strong><em>(M1)</em></strong></p>
<p>\(({\text{distance}} = ){\text{ }}450{\text{ (m)}}\;\;\;{\text{(449.971}} \ldots {\text{)}}\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><strong>Note: </strong>Follow through from part (a) and part (d).</p>
<p> </p>
<p>\(450\) is greater than \(375\), thus the course complies with the safety regulations <strong><em>(R1)</em></strong></p>
<p><strong>Notes: </strong>A comparison of their area from (d) and the area resulting from the use of \(375\) as the perpendicular distance is a valid approach and should be given full credit. Similarly a comparison of angle \({\text{ACB}}\) and \({\sin ^{ - 1}}\left( {\frac{{375}}{{900}}} \right)\) should be given full credit.</p>
<p>Award <strong><em>(R0) </em></strong>for correct answer without any working seen. Award <strong><em>(R1)</em>(ft) </strong>for a justified reason consistent with their working.</p>
<p>Do not award <strong><em>(M0)(A0)(R1)</em></strong>.</p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\tan 15^\circ = \frac{{{\text{AH}}}}{{700}}\) <strong><em>(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into trig formula.</p>
<p> </p>
<p>\({\text{AH}} = 188{\text{ (m)}}\;\;\;(187.564 \ldots )\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\({\text{H}}{{\text{C}}^2} = 187.564{ \ldots ^2} + 1315.65{ \ldots ^2}\) <span class="Apple-converted-space"> </span><strong><em>(M1)(A1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substitution into Pythagoras, <strong><em>(A1) </em></strong>for their \(1315.65{ \ldots}\) and their \(187.564{ \ldots}\)<span class="s1"> </span>correctly substituted in formula.</p>
<p class="p1"> </p>
<p class="p1">\({\text{HC}} = 1330 \ldots {\text{ (m)}}\;\;\;(1328.95 \ldots )\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p class="p1"><strong>Note: </strong>Follow through from their answer to parts (a) and (f).</p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Most candidates were able to recognize and use the cosine rule correctly in part (a) and then to complete part (b) – though perhaps not giving the answer to the correct level of accuracy. It is expected that candidates can use “distance = speed x time” without the formula being given. The work involving sine rule was less successful, though correct responses were given by the great majority and the area of the course was again successfully completed by most candidates. A common error throughout these parts was the use of the total length of the course. A more fundamental error was the halving of the angle and/or the base in calculations – this error has been seen in a number of sessions and perhaps needs more emphasis.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most candidates were able to recognize and use the cosine rule correctly in part (a) and then to complete part (b) – though perhaps not giving the answer to the correct level of accuracy. It is expected that candidates can use “distance = speed x time” without the formula being given. The work involving sine rule was less successful, though correct responses were given by the great majority and the area of the course was again successfully completed by most candidates. A common error throughout these parts was the use of the total length of the course. A more fundamental error was the halving of the angle and/or the base in calculations – this error has been seen in a number of sessions and perhaps needs more emphasis.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most candidates were able to recognize and use the cosine rule correctly in part (a) and then to complete part (b) – though perhaps not giving the answer to the correct level of accuracy. It is expected that candidates can use “distance = speed x time” without the formula being given. The work involving sine rule was less successful, though correct responses were given by the great majority and the area of the course was again successfully completed by most candidates. A common error throughout these parts was the use of the total length of the course. A more fundamental error was the halving of the angle and/or the base in calculations – this error has been seen in a number of sessions and perhaps needs more emphasis.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most candidates were able to recognize and use the cosine rule correctly in part (a) and then to complete part (b) – though perhaps not giving the answer to the correct level of accuracy. It is expected that candidates can use “distance = speed x time” without the formula being given. The work involving sine rule was less successful, though correct responses were given by the great majority and the area of the course was again successfully completed by most candidates. A common error throughout these parts was the use of the total length of the course. A more fundamental error was the halving of the angle and/or the base in calculations – this error has been seen in a number of sessions and perhaps needs more emphasis.</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>In part (e), unless evidence was presented, reasoning marks did not accrue; the interpretative nature of this part was a significant discriminator in determining the quality of a response.</p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>There were many instances of parts (f) and (g) being left blank and angle of elevation is still not well understood. Again, the interpretative nature of part (g) – even when part (f) was correct – caused difficulties</p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>There were many instances of parts (f) and (g) being left blank and angle of elevation is still not well understood. Again, the interpretative nature of part (g) – even when part (f) was correct – caused difficulties</p>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A greenhouse ABCDPQ is constructed on a rectangular concrete base ABCD and is made of glass. Its shape is a right prism, with cross section, ABQ, an isosceles triangle. The length of BC is 50 m, the length of AB is 10 m and the size of angle QBA is 35°.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img 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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the size of angle AQB.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the length of AQ.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the length of AC.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that the length of CQ is 50.37 m, correct to 4 significant figures.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the size of the angle AQC.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the total area of the glass needed to construct</span></p>
<p><span>(i) the two rectangular faces of the greenhouse;</span></p>
<p><span>(ii) the two triangular faces of the greenhouse.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The cost of one square metre of glass used to construct the greenhouse is 4.80 USD.</span></p>
<p><span>Calculate the cost of glass to make the greenhouse. Give your answer correct to the nearest 100 USD.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>110° <em><strong>(A1)</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{AQ}}{{\sin 35^\circ }} = \frac{{10}}{{\sin 110^\circ }}\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituted sine rule formula, <em><strong>(A1)</strong></em> for their correct substitutions.</span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span>\(AQ = \frac{5}{{\cos 35^\circ }}\) <em><strong>(A1)(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for 5 seen, <em><strong>(M1)</strong></em> for correctly substituted trigonometric ratio.</span></p>
<p><br><span>\(AQ = 6.10\) (6.10387...) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><br><strong>Notes:</strong> Follow through from their answer to part (a).<em><strong><br></strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(AC^2 = 10^2 + 50^2\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted Pythagoras formula.</span></p>
<p><br><span>\(AC = 51.0 (\sqrt{2600}, 50.9901...)\) <em><strong>(A1)(G2)</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(QC^2 = (6.10387...)^2 + (50)^2\) <em><strong>(M1)</strong></em></span><br><br></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted Pythagoras formula.</span></p>
<p><br><span>\(QC = 50.3711...\) <em><strong>(A1)</strong></em></span></p>
<p><span>\(= 50.37\) <em><strong>(AG)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Both the unrounded and rounded answers must be seen to award <em><strong>(A1)</strong></em>. </span></p>
<p><span> If 6.10 is used then 50.3707... is the unrounded answer.</span></p>
<p><span> For an incorrect follow through from part (b) award a maximum of <em><strong>(M1)(A0)</strong></em> – the given answer must be reached to award the final<em><strong> (A1)(AG)</strong></em>.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\cos AQC = \frac{{{{(6.10387...)}^2} + {{(50.3711...)}^2} - {{(50.9901...)}^2}}}{{2(6.10387...)(50.3711...)}}\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong><br><br></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituted cosine rule formula, <em><strong>(A1)</strong></em><strong>(ft)</strong> for their correct substitutions.</span></p>
<p><span><br>= 92.4</span><span>°</span><span> (\({92.3753...^\circ }\))</span><span> </span><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p><span><em><strong><br></strong></em><strong>Notes:</strong> Follow through from their answers to parts (b), (c) and (d). Accept 92.2 if the 3 sf answers to parts (b), (c) and (d) are used. </span></p>
<p><span> Accept 92.5°</span><span> (<span>\({92.4858...^\circ }\)</span><span>)</span> if the 3 sf answers to parts (b), (c) and 4 sf answers to part (d) used.</span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(2(50 \times 6.10387...)\) <em><strong>(M1)</strong></em><br><br></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their correctly substituted rectangular area formula, the area of one rectangle is not sufficient.</span></p>
<p><br><span>= 610 m<sup>2</sup> (610.387...) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)<br><br></strong></em></span></p>
<p><span><strong>Notes:</strong> Follow through from their answer to part (b). </span></p>
<p><span> The answer is 610 m<sup>2</sup>. The units are required.</span></p>
<p><br><span>(ii) Area of triangular fa</span><span>ce \( = \frac{1}{2} \times 10 \times 6.10387... \times \sin 35^\circ \) </span> <span> <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><strong><span>OR</span></strong></p>
<p><span>Area of triangular face \( = \frac{1}{2} \times 6.10387... \times 6.10387... \times \sin 110^\circ \) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>\(= 17.5051...\)<br><br></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituted triangle area formula, <em><strong>(A1)</strong></em><strong>(ft)</strong> for</span> <span>correct substitutions. <br></span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span>(Height of triangle) \( = {(6.10387...)^2} - {5^2}\)</span><span><br></span></p>
<p><span>\(= 3.50103...\)</span></p>
<p><span>Area of triangular face \( = \frac{1}{2} \times 10 \times their{\text{ }} height\)<br></span></p>
<p><span>\(= 17.5051...\)<br></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituted triangle area formula, <em><strong>(A1)</strong></em><strong>(ft)</strong> for correctly substituted area formula. If 6.1 is used, the height is 3.49428... and the area of both triangular faces 34.9 m<sup>2<br></sup></span></p>
<p><span> </span></p>
<p><span>Area of both triangular faces = 35.0 m<sup>2</sup></span><span> (35.0103...) <em><strong>(A1)(ft)(G2)</strong></em><br></span></p>
<p><span><strong> </strong></span></p>
<p><span><strong>Notes:</strong> The answer is 35.0 m<sup>2</sup>. The units are required. Do not penalize if already penalized in part (f)(i). Follow through from their part (b).</span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(610.387... + 35.0103...) × 4.80 <em><strong>(M1)</strong></em></span></p>
<p><span>= 3097.90... <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Notes:</strong> Follow through from their answers to parts (f)(i) and (f)(ii). </span></p>
<p><span> Accept 3096 if the 3 sf answers to part (f) are used.</span></p>
<p><span> </span></p>
<p><span>= 3100 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em> </span><br><br></p>
<p><span><strong>Notes:</strong> Follow through from their unrounded answer, irrespective of whether it is correct. Award <em><strong>(M1)(A2)</strong></em> if working is shown and 3100 seen without the unrounded answer being given.<br></span></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates used the appropriate area formula – however, some did not read the question with the attention it required and found the area of three rectangles – one of which being the stated “concrete base”.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates used the appropriate area formula – however, some did not read the question with the attention it required and found the area of three rectangles – one of which being the stated “concrete base”.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates were able to recognize sine rule, substitute correctly and reach the required result.<br></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates were able to recognize sine rule, substitute correctly and reach the required result. The use of Pythagoras’ theorem was also successful, the major source of error being the lack of unrounded and rounded answers in part (d).<br></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Again, most candidates used the appropriate area formula – however, some did not read the question with the attention it required and found the area of three rectangles – one of which being the stated “concrete base”.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates were able to recognize sine rule, substitute correctly and reach the required result. Part (e) was less well answered, due in part to the triangle being in three dimensions. However, all three sides had either been asked for in previous parts or given and all that was required was a sketch of a triangle with the vertices labelled; such a diagram was never on any script and this technique should be encouraged.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Again, most candidates used the appropriate area formula – however, some did not read the question with the attention it required and found the area of three rectangles – one of which being the stated “concrete base”.</span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates used the appropriate area formula – however, some did not read the question with the attention it required and found the area of three rectangles – one of which being the stated “concrete base”.</span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates used the appropriate area formula – however, some did not read the question with the attention it required and found the area of three rectangles – one of which being the stated “concrete base”.</span></p>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A tent is in the shape of a triangular right prism as shown in the diagram below.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The tent has a rectangular base PQRS .</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">PTS and QVR are isosceles triangles such that PT = TS and QV = VR .</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">PS is 3.2 m , SR is 4.7 m and the angle TSP is 35 °.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that the length of side ST is 1.95 m, correct to 3 significant figures.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the area of the triangle PTS.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the area of the rectangle STVR.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the <strong>total</strong> surface area of the tent, including the base.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the volume of the tent.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A pole is placed from V to M, the midpoint of PS.</span></p>
<p><span>Find in metres,</span></p>
<p><span>(i) the height of the tent, TM;</span></p>
<p><span>(ii) the length of the pole, VM.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the angle between VM and the base of the tent.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{ST}} = \frac{{1.6}}{{\cos 35^\circ }}\) <em><strong>(M1)(A1)</strong></em><br></span></p>
<p><span><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted trig equation, <em><strong>(A1)</strong></em> for 1.6 seen.<br></span></p>
<p><span><br><strong>OR</strong><br></span></p>
<p><span>\(\frac{{{\text{ST}}}}{{\sin 35^\circ }} = \frac{{3.2}}{{\sin 110^\circ }}\) <em><strong>(M1)(A1)</strong></em><br></span></p>
<p><span><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituted sine rule equation, <em><strong>(A1)</strong></em> for correct substitutions.<br></span></p>
<p><span><br>ST = 1.95323... <em><strong>(A1)</strong></em><br></span></p>
<p><span>= 1.95 (m) <em><strong>(AG)</strong></em><br></span></p>
<p><span><br><strong>Notes:</strong> Both unrounded and rounded answer must be seen for final <em><strong>(A1)</strong></em> to be awarded.<br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{1}{2} \times 3.2 \times 1.95323... \times \sin 35^\circ \) <strong>or</strong> \(\frac{1}{2} \times 1.95323... \times 1.95323... \times \sin 110^\circ \) <em><strong>(M1)(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituted area formula, <em><strong>(A1)</strong></em> for correct substitutions. Do not award</span> <span>follow through marks.</span></p>
<p><br><span>= 1.79 m<sup>2</sup> (1.79253...m<sup>2</sup>) <em><strong>(A1)(G2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> The answer is 1.79 m<sup>2</sup>, <strong>units are required</strong>. Accept 1.78955... from using 1.95.</span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span>\(\frac{1}{2} \times 3.2 \times 1.12033...\) <em><strong>(A1)</strong> <strong>(M1)</strong></em></span><br><br></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for the correct value for TM (1.12033...) <strong>OR</strong> correct expression for TM (i.e. 1.6tan35°, \(\sqrt {{{(1.95323...)}^2} - {{1.6}^2}} \)), <em><strong>(M1)</strong></em> for correctly substituted formula for triangle area.</span></p>
<p><br><span>= 1.79 m<sup>2</sup> (1.79253...m<sup>2</sup>) <em><strong>(A1)(G2)</strong></em> </span></p>
<p><br><span><strong>Notes:</strong> The answer is 1.79 m<sup>2</sup>, <strong>units are required</strong>. Accept 1.78 m<sup>2</sup> from using 1.95.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>9.18 </span><span><span>m<sup>2</sup></span> (9.18022 m<sup>2</sup>) <em><strong>(A1)(G1)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> The answer is 9.18 </span><span><span>m<sup>2</sup></span>, <strong>units are required</strong>. Do not penalize if lack of units was</span> <span>already penalized in (b). Do not award follow through marks here. </span><span>Accept 9.17 </span><span><span>m<sup>2</sup></span> (9.165 </span><span><span>m<sup>2</sup></span>) from using 1.95.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(2 \times 1.79253... + 2 \times 9.18022... + 4.7 \times 3.2\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for addition of three products, <em><strong>(A1)</strong></em><strong>(ft)</strong> for three correct products.</span></p>
<p><br><span> = 37.0 m<sup>2</sup> (36.9855...</span><span><span>m<sup>2</sup></span>) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> The answer is 37.0 </span><span><span><span>m<sup>2</sup></span></span>, <strong>units are required</strong>. Accept 36.98 </span><span><span><span>m<sup>2</sup></span></span> from using 3sf</span> <span>answers.</span> <span>Follow through from their answers to (b) and (c).</span> <span>Do not penalize if lack of units was penalized earlier in the question.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(1.79253... \times 4.7\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for their correctly substituted volume formula.</span></p>
<p><br><span>= 8.42 m<sup>3</sup> (8.42489...</span><span><span>m<sup>3</sup></span>) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> The answer is 8.42 </span><span><span>m<sup>3</sup></span>, <strong>units are required</strong>. Accept 8.41 </span><span><span>m<sup>3</sup></span> from use of 1.79.</span> <span>An answer of 8.35, from use of TM = 1.11, will receive follow-through marks if </span><span>working is shown. Follow through from their answer to part (b). Do not penalize if</span> <span>lack of units was penalized earlier in the question.</span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) </span><span><span>\({\text{TM}} = 1.6\tan {35^\circ }\)</span> <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for their correct substitution in trig ratio.</span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span>\({\text{TM}} = \sqrt {{{(1.95323...)}^2} - {{1.6}^2}} \) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in Pythagoras’ theorem.</span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span>\(\frac{{3.2 \times {\text{TM}}}}{2} = 1.79253...\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their correct substitution in area of triangle formula.</span></p>
<p><br><span>= 1.12 (m) (1.12033...) <em><strong>(A1)(ft)(G2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Follow through from their answer to (b) if area of triangle is used. Accept 1.11 (1.11467) from use of ST = 1.95.</span></p>
<p><br><span>(ii) \({\text{VM}} = \sqrt {{{1.12033...}^2} + {{4.7}^2}} \) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their correct substitution in Pythagoras’ theorem.</span></p>
<p><br><span>= 4.83 (m) (4.83168 ) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Follow through from (f)(i).</span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\sin ^{ - 1}}\left( {\frac{{1.12033...}}{{4.83168...}}} \right)\) <em><strong>(M1)</strong></em></span></p>
<p><strong><span>OR</span></strong></p>
<p><span>\({\cos^{ - 1}}\left( {\frac{{4.7}}{{4.83168...}}} \right)\) <em><strong>(M1)</strong></em></span></p>
<p><strong><span>OR</span></strong></p>
<p><span>\({\tan^{ - 1}}\left( {\frac{{1.12033...}}{{4.7}}} \right)\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted trig equation.</span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span>\({\cos ^{ - 1}}\left( {\frac{{{{4.7}^2} + {{(4.83168...)}^2} - {{(1.12033...)}^2}}}{{2 \times 4.7 \times 4.83168...}}} \right)\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted cosine formula.</span></p>
<p><br><span>= 13.4° (13.4073...) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em> </span><br><br></p>
<p><span><strong>Notes:</strong> Accept 13.3°. Follow through from part (f).</span></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A playground, when viewed from above, is shaped like a quadrilateral, \({\text{ABCD}}\), where \({\text{AB}} = 21.8\,{\text{m}}\) and \({\text{CD}} = 11\,{\text{m}}\) . Three of the internal angles have been measured and angle \({\text{ABC}} = 47^\circ \) , angle \({\text{ACB}} = 63^\circ \) and angle \({\text{CAD}} = 30^\circ \) . This information is represented in the following diagram.</p>
<p><img src="data:image/png;base64,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" alt></p>
<p>Calculate the distance \({\text{AC}}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate angle \({\text{ADC}}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>There is a tree at \({\text{C}}\), perpendicular to the ground. The angle of elevation to the top of the tree from \({\text{D}}\) is \(35^\circ \).</p>
<p>Calculate the height of the tree.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Chavi estimates that the height of the tree is \(6\,{\text{m}}\).</p>
<p>Calculate the percentage error in Chavi’s estimate.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Chavi is celebrating her birthday with her friends on the playground. Her mother brings a \(2\,\,{\text{litre}}\) bottle of orange juice to share among them. She also brings <strong>cone-shaped</strong> paper cups.</p>
<p>Each cup has a vertical height of \(10\,{\text{cm}}\) and the top of the cup has a diameter of \(6\,{\text{cm}}\).</p>
<p>Calculate the volume of one paper cup.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the maximum number of cups that can be completely filled with the \(2\,\,{\text{litre}}\) bottle of orange juice.</p>
<p> </p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{21.8}}{{\sin 63^\circ }} = \frac{{{\text{AC}}}}{{\sin 47^\circ }}\) <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution into the sine rule formula, <em><strong>(A1)</strong></em> for correct substitution.</p>
<p>\(({\text{AC}} = )\,\,17.9\,({\text{m}})\,\,\,(17.8938...\,({\text{m}}))\) <em><strong>(A1)(G2)</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{11}}{{\sin 30}} = \frac{{17.8938...}}{{\sin {\text{ADC}}}}\) <strong><em>(M1)(A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution into the sine rule formula, <em><strong>(A1)</strong></em> for correct substitution.</p>
<p>\(\left( {{\text{Angle ADC}} = } \right)\,\,\,54.4^\circ \,\,\,(54.4250...^\circ )\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><strong>Note:</strong> Accept \(54.5\,\,(54.4527...)\) or \(126\,\,(125.547...)\) from using their \(3\) sf answer.<br>Follow through from part (a). Accept \(125.575...\)</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(11 \times \tan 35^\circ \) (or equivalent) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into trigonometric ratio.</p>
<p>\(7.70\,({\text{m}})\,\,\,(7.70228...\,({\text{m}}))\) <em><strong>(A1)(G2)</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\left| {\frac{{6 - 7.70228...}}{{7.70228...}}} \right| \times 100\,\% \) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into the percentage error formula.</p>
<p><strong>OR</strong></p>
<p>\(100 - \left| {\frac{{6 \times 100}}{{7.70228...}}} \right|\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for the alternative method.</p>
<p>\(22.1\,(\% )\,\,\,(22.1009...\,(\% ))\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p><strong>Note:</strong> Award at most <em><strong>(M1)(A0)</strong></em> for a final answer that is negative. Follow through from part (c).</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{1}{3}\pi \times {3^2} \times 10\) <em><strong>(A1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(3\) seen, <em><strong>(M1)</strong></em> for their correct substitution into volume of a cone formula.</p>
<p>\(94.2\,{\text{c}}{{\text{m}}^3}\,\,\,(30\pi \,{\text{c}}{{\text{m}}^3},\,\,94.2477...\,{\text{c}}{{\text{m}}^3})\) <em><strong>(A1)(G3)</strong></em></p>
<p><strong>Note:</strong> The answer is \(94.2\,{\text{c}}{{\text{m}}^3}\), units are required. Award at most <em><strong>(A0)(M1)(A0</strong></em>) if an incorrect value for \(r\) is used.</p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{2000}}{{94.2477...}}\) <strong>OR</strong> \(\frac{2}{{0.0942477...}}\) <em><strong>(M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct conversion (litres to \({\text{c}}{{\text{m}}^3}\) or \({\text{c}}{{\text{m}}^3}\) to litres), <em><strong>(M1)</strong></em> for dividing by their part (e) (or their converted part (e)).</p>
<p>\(21\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p><strong>Note:</strong> The final <em><strong>(A1)</strong></em> is not awarded if the final answer is not an integer. Follow through from part (e), but only if the answer is rounded <strong>down</strong>.</p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Question 4: Trigonometry and volumes of 3D solids<br>This question was done well by most candidates. Trigonometry was a real strength with competent use of the sine rule. A small minority treated CB as parallel to AB and hence used alternate angles. The lack of a diagram in part (c) held some candidates back as they struggled to form the correct trigonometric ratio. Percentage error in part (d) was generally good. Most candidates scored the two marks as their answer to part (c) was followed through in part (d). Some candidates are still giving negative answers to percentage error problems. The common mistake in this part was the use of the new value in the denominator rather than the original value. Part (f) was less successful, in general, with a number of candidates not able to do the conversion.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 4: Trigonometry and volumes of 3D solids<br>This question was done well by most candidates. Trigonometry was a real strength with competent use of the sine rule. A small minority treated CB as parallel to AB and hence used alternate angles. The lack of a diagram in part (c) held some candidates back as they struggled to form the correct trigonometric ratio. Percentage error in part (d) was generally good. Most candidates scored the two marks as their answer to part (c) was followed through in part (d). Some candidates are still giving negative answers to percentage error problems. The common mistake in this part was the use of the new value in the denominator rather than the original value. Part (f) was less successful, in general, with a number of candidates not able to do the conversion.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 4: Trigonometry and volumes of 3D solids<br>This question was done well by most candidates. Trigonometry was a real strength with competent use of the sine rule. A small minority treated CB as parallel to AB and hence used alternate angles. The lack of a diagram in part (c) held some candidates back as they struggled to form the correct trigonometric ratio. Percentage error in part (d) was generally good. Most candidates scored the two marks as their answer to part (c) was followed through in part (d). Some candidates are still giving negative answers to percentage error problems. The common mistake in this part was the use of the new value in the denominator rather than the original value. Part (f) was less successful, in general, with a number of candidates not able to do the conversion.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 4: Trigonometry and volumes of 3D solids<br>This question was done well by most candidates. Trigonometry was a real strength with competent use of the sine rule. A small minority treated CB as parallel to AB and hence used alternate angles. The lack of a diagram in part (c) held some candidates back as they struggled to form the correct trigonometric ratio. Percentage error in part (d) was generally good. Most candidates scored the two marks as their answer to part (c) was followed through in part (d). Some candidates are still giving negative answers to percentage error problems. The common mistake in this part was the use of the new value in the denominator rather than the original value. Part (f) was less successful, in general, with a number of candidates not able to do the conversion.</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 4: Trigonometry and volumes of 3D solids<br>This question was done well by most candidates. Trigonometry was a real strength with competent use of the sine rule. A small minority treated CB as parallel to AB and hence used alternate angles. The lack of a diagram in part (c) held some candidates back as they struggled to form the correct trigonometric ratio. Percentage error in part (d) was generally good. Most candidates scored the two marks as their answer to part (c) was followed through in part (d). Some candidates are still giving negative answers to percentage error problems. The common mistake in this part was the use of the new value in the denominator rather than the original value. Part (f) was less successful, in general, with a number of candidates not able to do the conversion.</p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 4: Trigonometry and volumes of 3D solids<br>This question was done well by most candidates. Trigonometry was a real strength with competent use of the sine rule. A small minority treated CB as parallel to AB and hence used alternate angles. The lack of a diagram in part (c) held some candidates back as they struggled to form the correct trigonometric ratio. Percentage error in part (d) was generally good. Most candidates scored the two marks as their answer to part (c) was followed through in part (d). Some candidates are still giving negative answers to percentage error problems. The common mistake in this part was the use of the new value in the denominator rather than the original value. Part (f) was less successful, in general, with a number of candidates not able to do the conversion.</p>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagram shows an office tower of total height 126 metres. It consists of a square based pyramid VABCD on top of a cuboid ABCDPQRS.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">V is directly above the centre of the base of the office tower.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The length of the sloping edge VC is 22.5 metres and the angle that VC makes with the base ABCD (angle VCA) is 53.1°.</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the length of VA in metres.<br></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Sketch the triangle VCA showing clearly the length of VC and the size of angle VCA.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that the height of the pyramid is 18.0 metres correct to 3 significant figures.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the length of AC in metres.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that the length of BC is 19.1 metres correct to 3 significant figures.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the volume of the tower.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>To calculate the cost of air conditioning, engineers must estimate the weight of air in the tower. They estimate that 90 % of the volume of the tower is occupied by air and they know that 1 m<sup>3</sup> of air weighs 1.2 kg.</span></p>
<p><span>Calculate the weight of air in the tower.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>22.5 (m) <em><strong> (A1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span><img alt="onbekend.png"></span><span><span> </span><strong><em>(A1)</em></strong></span></span></p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>h</em> = 22.5 sin 53.1° <em><strong>(M1)</strong></em></span><br><span>= 17.99<em><strong> (</strong><strong>A1)</strong></em></span><br><span>= 18.0 <em><strong>(AG)</strong></em> </span></p>
<p><span> </span></p>
<p><span><strong>Note:</strong> Unrounded answer must be seen for <em><strong>(A1)</strong></em> to be awarded.</span></p>
<p><span>Accept 18 as <em><strong>(AG)</strong></em>.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{AC}} = 2\sqrt {{{22.5}^2} - {{17.99...}^2}} \) <em><strong>(M1)(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong> </em>for multiplying by 2, <em><strong>(M1)</strong></em> for correct</span><span> substitution into formula.</span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span>AC = 2(22.5)cos53.1° <em><strong>(M1)(M1)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award<em><strong> (M1)</strong></em> for correct use of cosine trig ratio,<em><strong> (M1)</strong></em> for</span> <span>multiplying by 2.</span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span>AC<sup>2</sup> = 22.5</span><span><span><sup>2</sup></span> + 22.5</span><span><span><sup>2</sup></span> – 2(22.5)(22.5) cos73.8° <em><strong>(M1)(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award<em><strong> (M1)</strong> </em>for substituted cosine formula, <strong><em>(A1)</em></strong> for</span> <span>correct substitutions.</span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span>\(\frac{{{\text{AC}}}}{{\sin (73.8^\circ )}} = \frac{{22.5}}{{\sin (53.1^\circ )}}\) </span><em><strong><span>(M1)(A1)</span></strong></em></p>
<p><span> </span></p>
<p><span><strong>Note:</strong> Award<em><strong> (M1)</strong> </em>for substituted sine formula, <em><strong>(A1)</strong></em> for correct</span> <span>substitutions.</span></p>
<p><br><span>AC = 27.0 <em><strong>(A1)(G2)</strong></em></span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{BC}} = \sqrt {{{13.5}^2} + {{13.5}^2}} \) <em><strong>(M1)</strong></em></span></p>
<p><span>= 19.09 <em><strong>(A1)</strong></em></span></p>
<p><span>= 19.1 <em><strong> (AG)</strong></em></span></p>
<p><strong><span>OR</span></strong></p>
<p><span><em>x</em><sup>2</sup> + <em>x</em><sup>2</sup> = 27<sup>2</sup> <em><strong> (M1)</strong></em></span></p>
<p><span>2<em>x</em><sup>2</sup> = 27<sup>2</sup> <em><strong> (A1)</strong></em></span></p>
<p><span>BC = 19.09… <em><strong>(A1)</strong></em></span></p>
<p><span>= 19.1 <em><strong> (AG)</strong></em></span></p>
<p><span><strong> </strong></span></p>
<p><span><strong>Notes:</strong> Unrounded answer must be seen for<em><strong> (A1)</strong></em> to be awarded.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Volume = Pyramid + Cuboid</span></p>
<p><span>\( = \frac{1}{3}(18)({19.1^2}) + (108)({19.1^2})\) <em><strong> (A1)(M1)(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award<em><strong> (A1)</strong></em> for 108, the height of the cuboid seen. Award <em><strong>(M1)</strong></em> for correctly substituted volume of cuboid and <em><strong>(M1)</strong></em> for correctly substituted volume of pyramid.</span></p>
<p><br><span>= \(41\,588\) <em>(41\(\,\)553 if</em> 2(13.5<sup>2</sup>) <em>is used)</em></span></p>
<p><span>= \(41\,600\) m<sup>3</sup> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G3)</strong></em></span></p>
<p><span><em><strong>[4 marks]</strong></em></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Weight of air = \(41\,600 \times 1.2 \times 0.9\) <em><strong> (M1)(M1)</strong></em></span></p>
<p><span>= \(44\,900{\text{ kg}}\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span> </span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their part (e) × 1.2,<em><strong> (M1)</strong></em> for × 0.9.</span></p>
<p><span>Award at most <em><strong>(M1)(M1)(A0)</strong> </em>if the volume of the cuboid</span> <span>is used.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question also caused many problems for the candidature. There seems to be a lack of ability in visualising a problem in three dimensions – clearly, further exposure to such problems is needed by the students. Further, as in question 2, the final two parts of the question were independent of those preceding them; many candidates did not reach these parts, though for some, these were the only parts of the question attempted. There is also a lack of awareness of the appropriate volume formula on the formula sheet to use.</span></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">This question also caused many problems for the candidature. There seems to be a lack of ability in visualising a problem in three dimensions – clearly, further exposure to such problems is needed by the students. Further, as in question 2, the final two parts of the question were independent of those preceding them; many candidates did not reach these parts, though for some, these were the only parts of the question attempted. There is also a lack of awareness of the appropriate volume formula on the formula sheet to use.</span></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question also caused many problems for the candidature. There seems to be a lack of ability in visualising a problem in three dimensions – clearly, further exposure to such problems is needed by the students. Further, as in question 2, the final two parts of the question were independent of those preceding them; many candidates did not reach these parts, though for some, these were the only parts of the question attempted. There is also a lack of awareness of the appropriate volume formula on the formula sheet to use.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question also caused many problems for the candidature. There seems to be a lack of ability in visualising a problem in three dimensions – clearly, further exposure to such problems is needed by the students. Further, as in question 2, the final two parts of the question were independent of those preceding them; many candidates did not reach these parts, though for some, these were the only parts of the question attempted. There is also a lack of awareness of the appropriate volume formula on the formula sheet to use.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question also caused many problems for the candidature. There seems to be a lack of ability in visualising a problem in three dimensions – clearly, further exposure to such problems is needed by the students. Further, as in question 2, the final two parts of the question were independent of those preceding them; many candidates did not reach these parts, though for some, these were the only parts of the question attempted. There is also a lack of awareness of the appropriate volume formula on the formula sheet to use.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question also caused many problems for the candidature. There seems to be a lack of ability in visualising a problem in three dimensions – clearly, further exposure to such problems is needed by the students. Further, as in question 2, the final two parts of the question were independent of those preceding them; many candidates did not reach these parts, though for some, these were the only parts of the question attempted. There is also a lack of awareness of the appropriate volume formula on the formula sheet to use.</span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question also caused many problems for the candidature. There seems to be a lack of ability in visualising a problem in three dimensions – clearly, further exposure to such problems is needed by the students. Further, as in question 2, the final two parts of the question were independent of those preceding them; many candidates did not reach these parts, though for some, these were the only parts of the question attempted. There is also a lack of awareness of the appropriate volume formula on the formula sheet to use.</span></p>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagram represents a small, triangular field, ABC , with \({\text{BC}} = 25{\text{ m}}\) , \({\text{angle BAC}} = {55^ \circ }\) and \({\text{angle ACB}} = {75^ \circ }\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img 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Pjjjw8ePFhyswqqwlqq2s48mUzGYjG2BYNj9fX2NrndBAesaLrmGL0Y3nLHpl8c+Pf7ZOmWtbtP639Rx4wba/6gre3O73zHfptVOFNhQ2jfyhn3KTFwtYBRuGEsLG2a5sieCW5Y0xUdzp7dvXauS/7eKyeu1b86ZrkFFgfY7UQbJGaiGCiD4IDVlWyO7LUTr6zy7FSvZUV2cO/Dy2RpRcfApRqevbYtsCo8VkFz2Mmbb77Jv6RAGQQHbKBkc1w6/Ixno3ImK4QQ2csD226TXIs29SdLHekouVmFPhtr0hwAHEK7homjfbC6Es2RPf/OIzcuaV6zrnXd+tZ161vXrFgiueS5G//j7NWit3xw7YOrVq406jA4zWEnXIgDTIcbxsI2pjbHldO7Nqx6+di1iT+5enb3xnnSgpWT/lAIIZLJpIE/CTSHnWiX7Bi9CsB0CA7YyZTmSB/puqut6JBG9vw7j9zokpdtO3y5+PyK9vNQzcbVo6mzx45MUC9ksjM9emXoyLvKr4+en/SWNIetsJ05MBXBAZspao5rQ+88/o2HlKHitLgQ9t8hS0vHL/KYpLorm64d3/HXfzbnuuu1//707/cMZss/Oprc//wTP4/Ewt0/+km0cHcymsNO2M4cKKIdSKbFYScFzZE9H339yb+7VZa/vbHr9YO/H8m3wJe/D7+yaflCWXLJiz3tr4QLHsoJhUKV7VGTvXyka/UjL/1ij+at357+cqZHLx8PbH7t9BVx9cPtvnfOF7x1JBKhOWyDggQKccNY2FLd7itb0V682TN71j+2Z/BaVY9mLx7+t0fXt3q37jr2RWHscDTeZtglFtAQHLCret7LXrsv2vSPZy8fee6b110/54Zv3f/ka++dHs5W8WgJ2r7ms141AJgIwQEbq2dzzPSj8uWpN/xr/+6vltxw/Zzrrp9zQ/Pm/ecylT5agt/nY1rdTqq5EhmwJ+1f0bK/vAEWVs/mEBVOz2Y+j+35l3vn3TDnhtUvxIare7SALLk4Gm8nTW4331A4HDeMhb3VuTlEpdOzo6nYSytvuP6rP95fKivKPzrxUWa7VpgJB67gcAQHbK/+zSEqnJ7NJn716K1zWt44W/LCjfKPChGJRDj8aDM0B5yM4IATNKQ5REXTs5ePB1Z9ZcPb52t5VGzr6GDbSpvp6+3lkg44U6A70OLxEBywvUY1h5gx27OJXz3a3Pb2NAcyyj/KuX8AdsENY+EcDWwOMXl6Nps69vN/7tjx3qeprBDiytD+px98on9ofDvz8o8WicViLR5PQ1cOADogOOAojW2OwunZ7PnwE3f+jznXXf+VJd9tXnrnhsChwqQo/2iRQHegr7e3oSuH/pLJJBuuwFEIDjhNY5tDFE3PZi6cKnFft3HlHx2XTqc5sWJLbH8ORyE44EANbw5Ry71ny4lEIm1eb12eCqai5anRqwD0EI/HZcnFDWPhNHo0h6hr0bd5vfyg2pUsuYxeAtBw3KEejqVTc4gq7j1bjqqqXD1qY/wrDNsjOOBk+jWHqMemN36fj8sMAVgUwQGH07U5xMz3ni1HO8jBtjkArCidTrd4PNwwFk6md3PM5jbNLR4Pvx/YW6A7wLcYtsQd6gGhf3OICu89O0VQURhXsb2gonDuDPZDcAAaA5pDVD89q2UKg+y2R3PAfggOIM+Y5hBVTs/6fT42HnWCWCzGtmCwmW0dHdwwFtAY1hyi4ulZzqo4CjvMwk64Qz1QyMjmEBX8QMZiMc6qALAiggMoYnBziLLTs8yyOxDfbtgDwQFMZXxzTHeBlTbLzhWFTsP257CBoKJwK0pgKuObQ5SanuVKb8dq8Xg4lQZL44axwHRM0Rxi8vQsweFkfp9PVVWjVwHUiOAAyjBLc4jxn9VPP/2U4HCyQHeAf69hUQQHUJ6JmkMIEQqFbpo7d/sLLxi9EACojqqqsuSqfKtDwIHM1RxCiGeefoaLvQFYC0N2QCVM1xxidveehdUlk8lQKGT0KoAqEBxAhczYHFxD6mSqqrL9OSyE4AAqZ8bmELXeexY2QHPAQtLpdJPbzTZCQIVM2hyi+nvPwh7S6TTbgsESOCILVMu8zSEYPHMqrueA+REcQA1M3Ryi4nvPAoBuCA6gNmZvDsGtkgCYTJvXy1VHQA0s0ByC6VmH2dbRwQk1mBa/BQE1s0ZzcCTTUfp6exkEgDkRHMBsWKM5BNOzThJUFJoDJkRwALNkmeYQTM86Bs0BE+rr7eV6dmCWrNQcgulZZ0in08lk0uhVABP4lweoC4s1h2B6FoC+CA6gXqzXHIKzqg7Av+8wCYIDqCNLNodgetbu2P4cZhCJRGTJRXAA9WLV5mB61t5kycVxLBiLG8YCdWfV5hBMz9qa3+dTVdXoVcC5CA6gESzcHILpWftiK1IYiOAAGsTazSG4wgtAXWnBwc2NgUawfHMIpmcB1AkXigENZYfmEEzP2k48HueUGXRGcACNZpPmEEzP2kssFuNe4dATwQHowD7NwT8ZdqKqKs0B3Wj/evBLC9Bo9mkOwfSsjcTj8RaPx+hVwCk4OQvow1bNIZietRFuLQt9EByAbuzWHILpWQAVIzgAPdmwOQTTswAqQHAAOrNncwj+NbE+tiJFQ2m/mfB3DNCTbZtDMD1rcX6fj+ty0CCcgQUMYefmYHrW0oKKwmWkaASCAzCKnZtDMD1rZTQHGoHgAAxk8+YQTM9aVjqdTiaTRq8CthKPx2XJxS8hgFHs3xyC32wAcId6wAQc0RyC6VlrIhNRLwQHYAZOaQ7B9KwFyZLL6CXADggOwCQc1ByC6VmroTkwe+l0usnt7uvtNXohABzWHEzPWkuT281lpJgNfuQBU3FWcwimZy2FrUgxGwQHYDaOaw7B9CzgAAQHYEJObA7B9Cxgd36fr83rNXoVACZxaHMIpmetIB6PczgKNWBIDTAn5zaH4B8m0wsqCsfGUS1+rgHTcnRzCKZnzU1VVb/PZ/QqYCUEB2BmTm8OLjQzM5oDVQkqCvPVgJk5vTkE07MmlkwmQ6GQ0auANXBhOGB+NIcQTM8CFkdwAJZAc+TwbxZgUfzwAlZBc0xgetaEAt0BXktQRiwWkyWXqqpGLwTAzGiOSbjo3Wz8Ph8vJ5gON4wFrIXmKMb0rKkEugNcRoqSCA7AcmiOYkzPmkpQUYKKYvQqYDoEB2BFNEcJTM+aRzKZ5HoOFNF+QolRwHJojtKYngXMiSORgHXRHNNiAM8k2FYSeQQHYGk0RzlMzxouHo+3eDxGrwKmQHAAVkdzzIDpWcPJksvoJcAU2rxeZsoAS6M5Zsb0rLFoDgjqH7AFmmNmHNE1VpvXy1U1DkdwAPZAc1SE6VnAKAQHYBs0R6WYngX0F+gOtHg8BAdgDzRHFZieNUQ8Hudr7kz8xAE2Q3NUh+lZ/bH9uTMRHID90BxV4+yyziKRCHNDTkNwALZEc9SC6Vk9qarq9/mMXgX0E4lEZMlFcAD2Q3PUgulZPSWTSc6tOAc3jAVsjOaoEdOzQN0RHIC90Ry1Y3oWqCOCA7A9mmNWuNJNH4HuAHeXtTeCA3ACmmO2mJ7Vgd/nU1XV6FWgUdLpdIvHwwVSgO3RHHXA9Gyj0Rw2xhXZgHPQHPXB9GxD9fX2MrpiSzUFRzZz6bPDoX3vn0iMZBu1MACNQHPUB7+rNVQ8Hud6Dvup7acme/H9bc0LZcklS7c90HVgKEN3AJZBc9QN07NAVbZ1dFR/UvLK6V3rv/HQv4eP/GZ3+6p50sK7t+4jOwCroDnqienZxuE4h83UehVUKtr52E51RAghMvGDXQ8ulRY2b9p9IjXagDUCqDOao86Ynm0Etj+3mRqCI5s6ubfrxxseerh19WPBRGb8T784vrNtqSQvfej/Dpw6ui98igu5ATOjOepPyw7GWOoomUzKksvoVaA+ajrCMXz0xZZ5kkuWXHLR+ZRcdrjmNT8dHrrSgPUCqBuaoyGYnq07msMetP1sqjsQOJrJZI6+1OzfO3QlO/KH/q2r50kL797667MjY7k3yES73I/8x2l+3ACzozkaZVtHB9OzddTkdhu9BMxWTWceL6s9j2x85aXN/xQe1v4g899He7TzKb3HU6Mim0mffO/t419wHSlgfjRHozA9O+7KBTUW1Xx0LlX6lWE0de547m2in1xgDMGOarzU6WrspbtukiXXood/OVh8PkVeev8TP3lm+y85wgFYBM3RQOl0mulZIa5cOBV5u+P+myWXPHftzlOXS7xJ+kjXnTfJ0k1Nm3oP0hx2VOu11dkr0R3/1PfWrk3fKx6LzX5x/JV1N89d/dTB/+KvC2AVNEdjMT2bk1BaJZcs3XRX55Epv5OOXgxv+YbkkqUVXdHUdE8Qj8eZBrIoVVVlyVX2p2D0y0t/zEz/sMjEw8WXcVwZ/OWzT78XL/deAEyG5mi4WCzG9KxIKK033ua+7Sb5xkeCQ9cmPXTtxE6P2/3theWbI6gobH9uRRXcMDabGfr1P/71s4cvlz1gMekyjpGLnxz/+GyS4ACshebQA9OzIqG0Lt7c8/LaedKClS8fK4iObDr6/Hc39Lz57IryzfHqjh3PPfssd3qzlsqCY9+TzQvluffvPDUyw9ONj8XK0u0bdn40zbVBAMyL5tCJ06dnE0rr4s7o5/2Pz3fJX98Svji+a2T2THDDPVsP/SHaWa45+np75dzeDC5HfxktpZrgWP1khWdJsoN7H/4ewQFYFM2hH0dPz2rNkRmOdq6SpVvW7j6dFUKI7LVTO++7d6d6LVWmObSrAQr/YxrI/LQLqPt6e8u+VfbywLbbKg8OIUT6w5+99iHBAVgUzaEfR0/P5ppDZIeUjTe65Dufj6azIvt5uH31RuVMVpRrjqCiFDUH+6CbXBV/1dNHulY/e/jy6MiFE+FdXe3/+6HWdQ/9sD2w9zjXagA2RHPoyrnTs+PNIbKfh9vvkqVlj7wzODakbPzL56PprCjbHKFQiOawkCrbOvXRi2vX+x/3LJYnfZerOvgBwCJoDr05dHo23xwie+3Uzpa5rnmef+35F899uz4ZE6J8cySTySa3u/AFyYnRZhE1HMwbU3tWSS557vc29YQ+Oj2YSCSGTsf6X9ywdOqIEwCLozkM4MTp2Ynm0K4bXSpLhReTlmsOIUQ8Hm/zemXJ9a1l32Ri1szavN6qj0JlP/3Zo08GTw1Pukgjmzzccd8G5SxXbgB2QnMYw3HTs4XNIbLp6PN3Tdof7OKhLXfK0v/sGBgu8xx+n49ZWTOrYDhrNHXq3e72H7au27jpmZ8dTmi3gc1mMqNT3zQT7XTn/8oAsAWawzCOmZ798veH3urb0nKzdNcPX/z5u0fPZ4UQ107svG9TcOiaENmR0+8H+55+4FZZluSl657b/cv3fz9S+pfbbR0dnFUxrUqC4+LAc3fPnThHNq+54+D56aIie/nQ056ek2PTPAzAimgOIzl6erZ68Xg8mUwavQqUUFFAp4903blg6boX+4+eHjp3cuDnm++eW3IvfCFENnMx+vID3tJ35wFgWTSHkRw9PQu76OvtreREYfbc7gfmPrTrdH6z0ZGzymNLl20r2vI8e35gh/9+99yFd3e8f5GrOQB7oTkM5tzp2Zo44FSUxVRxw9iL/Zu+PvkCjauxl+667+UThd/TsdSR7XfPXerpeG+I2wsDtkNzGM+h07PVU1WVnTlMpbo71Gc/D29+au+kCzj+GO1cs6n/c+1/RtV3f3603EXEAKyO5jAFJ07PVk9V1Tav1+hVIKe64BBCCJH97zN/SBWOqIxe7H9io3JOe/DKQMfSDcoQRzcA+6I5zMJx07M1kSWX0UuAEELEYjFZcs1+dDkT7Vrx4tFRIbKpj3760O3y3I3/cfZqXVYIwIRoDhNxzPRs7WgOM6jghrGVyp7bvaEzmsmc629fwX7ngO3RHObC9Gx5BJnh6hgcQgiRUH7wT6/v3bp6HsEBOADNYS5Mz8LM6hwcQoiE0iq5ZOn2DbtOjMz81gCsjeYwHaZny1BVlX8vLf0AAAz7SURBVEMdRtGCIxQK1fNJE0qrdPuGnR+luHQUcACaw4yYnp1OX28v93gzRKOOwKU+/MUvjhEcgEPQHCbF9GxJQUWhOfTHKT8AdUFzmBfTs1OFQiFe+XRGcACoF5rD1JieLRKPxznOoSctOJilAlAXNIfZMT0LA1G9AOqI5jA7jmzDKAQHgPqiOSyA6dlC5Jc+CA4AdUdzWAPTs3my5OKFsNEIDgCNQHNYBtOzGr/PN/tbi6GMGm4YCwCVoDmshOlZQXM0GMEBoHFoDovhoHcsFksmk0avwp4IDgANRXNYD9OzaASCA0Cj0RzWw/Sskw/zNEg8HpclF7NRABqK5rAkJ0/PqqrKYZ76qv8d6gGgFJrDqhw7Pauqqt/nM3oV9kFwANANzWFhzpye1V4jjV6FTRAcAPREc1ibM6dnZcll9BLsIJ1Ot3g8Tr4wCIDOaA7Lc+D0LLOys8eVyAD0R3PYAdOzqArBAcAQNIcdOO0lRFVVRx3XqS+n/W0BYB40h004anp2W0eHQz7TRvD7fG1er9GrAOBENId9OGd6NqgoQUUxehWW5MCrfwCYB81hKw6ZnqU5akNwADAWzWE3TpiejcVifb29Rq/CYggOAIajOWyIVxcUCSpKk9vNjDEAY9Ec9sT0LPK4YSwAk6A57Mn285A2/tTqi+AAYB40h23Ze3qW7c8rQXAAMBWaw85sPD3b4vHwUlqeqqqy5LLldx+ARdEcNmfX6Vm/z6eqqtGrMC9uGAvAhGgO+7Pl9GwsFrPZZ1RHBAcAc6I5HIHpWecgOACYFs3hFEzPOkEymWxyu9mkFYA50RxOYbPp2UgkYpvPpV5s9i0GYD80h4PYaXpWVVW/z2f0KkyE4ABgfjSHs9hmepbmKERwALAEmsNx7DE9m06n2RYsr83rpcAAmB/N4UT2mJ7ljmUahpIAWAXN4VC8UNkD30cAFkJzOJfVp2fZFozgAGAtNIdzWf3CQ4dvfx7oDrR4PAQHAAuhORzN0tOzge5AKBQyehXG4IaxAKyI5nA6607PBhXFmRtuEhwALIrmgFWnZyORiAOPcxAcAKyL5oAQ469kTJ+aXCQSkSUXwQHAomgO5DAEYXLcMBaA1dEcmLCto8Na21n29fYavQSdEBwAbIDmwATLTc86ZPtzggOAPdAcmESbnrXKtZlOaA4tOKzyHQGAMmgOFLPQb9VtXq+9twWz3JEnACiD5kAJVpmejUQiNr7oleAAYDM0B0pjetZYBAcA+6E5MC2mZ41CcACwJZoD5Zh8ejYUCtny4sptHR3UHgD7oTlQjsl/4Y7FYmZOotpweAmAXdEcmIGZp2dVVbVZcxAcAGyM5sDMTDs9q6pqm9dr9CrqhuAAYG80Bypi2ulZEy6pNqFQyJxfYQCoF5oDlWJ6tnG4Qz0AJ6A5UAUTHvy3wes0wQHAIWgOVMds07N+n8/S258THACcg+ZAdcw2Pev3+WKxmNGrqFE8Hpcll3XXDwBVoTlQNVNNzwYVJagoRq+iFqadBgKABqE5UAvzvF5adCtS83wBAUA3NAdqZNrpWfMjOAA4E82B2jE9WwPtzFRfb6/RCwEAvdEcmBXDp2fT6bSFzq2Y7QpcANATzYHZMnZ6Np1Oy5LLqI9eFYIDgMPRHJgtw19KLdEchn+VAMBwNAfqwNjpWUtcU+L3+ex0OzoAqAHNgfowcBYjFAqZajv2qQy/6gUAzIDmQN0wPVsSwQEAGpoD9cT0bBGCAwDyaA7Umf6vsqbdirSvt7fJ7SY4AEBDc6D+dJ6eDSqKCbfY4oaxAFCE5kD96TwXqqqqgRuElERwAMBUNAcaQs/pWbM1B8EBACXRHGgUPadnzfMCH4vFZMmlqqrRCwEA06E50EBOm57lhrEAUAbNgcbSYXo2mUwePHhQVVVVVUOhUFBRYrGY9r96zowQHABQHs2Bhqvv9Gw6nVZVNagofp+vxeORJVeT233nd77zg7Y2v88X6A5oD2n/yZJLllx+n6+vtzcSiTQufQgOAJgRzQE9zH56NplMhkKhNq9XllxtXq/WEPmzNn6fb7pLKAobpcntbvF4+np7Y7HYbBYzdW1NbndQUer4nABgPzQH9FDz9Gw6ndZSo8ntDnQHYrFYyeMl2zo6KjzGoKpqX29v4RNWu6SpK+SGsQBQCZoDOql2ejaZTAa6A01ut9/nm7EnatiKNJlMBhWlxeNp8XiCilLbaReCAwAqR3NAPxVe9KDVhiy5At0BHW7doqpq/sNVNeNKcABAVWgO6Kr89Gw6nQ4qinbWQ+cbxWmHPbTDKpWUhxYc2zo6dFgbANgDzQG9TTc9q6pqi8fj9/lq2M9Du+xj9mvLR4/f5ysfPdwwFgCqRXPAAEUv2Ol0WrsFa83dEI/HWzyeei1PKw9ZcvX19pasCoIDAGpAc8AY+enZZDLZ5vXOeFxhRrLkqtPScpLJpLYFSNGpFoIDAGpDc8AY2vUQW7dsbXK763In+ro3h0a7ACW/wkB3oMXjITgAoAY0BwyTTqdv/fPF27dvr/Yds6mzR48U+fDZ7p7xx0dTZ48VPKReyGSFuDJ05F3l10fPZ7LVfjjtSEyb18sNYwFgNmgOGKmmLcO/PB64Z85110/+7+uP77+Qe/za8R1//Wf5h/707/cMZkeT+59/4ueRWLj7Rz+JXq5pqdu3b7/j9tsJDgCoGc0Bg1V979nLH/zrX97zeOD1PeNef6rlT7/q2z88JoQQInv5SNfqR176Re7Bt357+kshLh8PbH7t9BVx9cPtvnfOV79IjnAAwOzRHDBeNfeezV4e+OlLv0sWnCBJxV74q6/+eP8vQ6FIJCKyZ/asf2zP4LXid7t4+N8eXd/q3brr2BfVnlwhOACgLmgOmELtwyBXP3zhW998fP+FoKIElTcvH3num9ddP+eGb93/5GvvnR6u+tqNKbhhLADUC80Bs6jp3rPZq7Ht3/qqb//wWCQS2dbx5Kk3/Gv/7q+W3HD9nOuun3ND8+b95zKzWBLBAQB1RHPALGq6fUnuxMqwEKqqTiRL5vPYnn+5d94Nc25Y/UJsuLb1EBwAUF80B0yk2nvP5k+saO87efOu0VTspZU3XK8VSbUIDgCoO5oD5lLNi/3EiZVpHk/86tFb57S8cbbKyzrS6XSLx8MNYwGgvmgOmE7F07MTJ1Y0UyZfLh8PrPrKhrerGo7lDvUA0CA0B8yoounZghMrmuJ3ySZ+9Whz29tVHOYgOACgcWgOmNRM07MlTqz4H2t94Uebdrz3aSorhLgytP/pB5/oH6p4s3OCAwAaiuaAeZWdni0+sSKE8D265uFlX51z3fVfWfLd5qV3bggcqjw4tA/HDWMBoHFoDphX2QMPX57+7d7fnv6y8I/6entDv/rFqYn7ulWBO9QDQKPRHDC1qqdna0JwAIAOaA6YXaO3yiA4AEAfNAcsoMLp2XQ6HYvFqnrmoKJUfHs5AMCs0BywhkqmZydtf17xc3LDWADQB80By5jxJEgymWxyuyt8NoIDAHRGc8BKZrz3rCy5KnkeggMA9EdzwEpm3Larkh29VFWVJVe1V34AAGaJ5oDFzHJ6lhvGAoBRaA5YT83dQHAAgIFoDljSdNOzoVBoupMmBAcAGIvmgFWVnJ4NKkpQUaa+sXZGpuRDAAB90BywsKnTsyWbgxvGAoAZ0BywtqLp2VgsVjRMS3AAgEnQHLC2oqRIp9Oqqk73KADAQDQHLK/M9Gyb11vVbugAgMahOWAHhTMp+atKuWEsAJgKzQGbyE/PatufExwAYDY0B+xDm579X6tXb92yleAAALOhOWArge7Asr/4i28t+ybBAQBmQ3PAbn73u99xw1gAMCGaAwAA6IHmAAAAeqA5AACAHmgO2Eo2deZw/1vK67t+puz9zYnzGTF6Mfr+R6kxo9cFAKA5YBuZoYGXH2m68a4Nz+369aEPDoff3vWc9+5mz998+/svn2CGBQCMR3PAFjLx8NbV825c98qxL7ITfzqaOvbqAzeu6IqmjFsZACCH5oANjJzd/fDN0p+39Jy4VvzQZbVn07aBYSNWBQCYhOaA9aWPdN15kyw9uOv0lakPZod+88ah8/ovCgBQhOaA5Y2eePm7kkte3BnNGL0UAMD0aA5Y3ej5d340T3LJf/nyiVGj1wIAmB7NAavLJJSHZcklr+xRGYkFABOjOWB12SsDHbdILvlrHYevZGd+cwCAQWgOWN8fD279uixLa3aqI0YvBQAwLZoDNnBZ7Vk7T7rpro7/98fiIx2jqWN9//wzdcoMLQBAbzQHbGHkxK6Hbpel2ze88sH5TL47RlPHX9+8bf9QhnMuAGA8mgM2kU192v8Tb9Nc17xv/+0P/E93Pbf1/3haNr74W4IDAEyC5oC9ZC6o0UP9v+w/dOT4uRSzswBgIjQHAADQA80BAAD0QHMAAAA90BwAAEAP/x9+NjQDz9HFpwAAAABJRU5ErkJggg==" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the size of angle ABC.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the length of AC.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the area of the field ABC.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>N is the point on AB such that CN is perpendicular to AB. M is the midpoint of CN. </span></p>
<p><span>Calculate the length of NM.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A goat is attached to one end of a rope of length 7 m. The other end of the rope is attached to the point M.</span></p>
<p><span>Decide whether the goat can reach point P, the midpoint of CB. Justify your answer.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><span>\({\text{Angle ABC}} = {50^ \circ }\) </span><span> <em><strong>(A1)</strong></em></span></span></p>
<p><span><span><em><strong>[1 mark]</strong></em></span></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{{\text{AC}}}}{{\sin {{50}^ \circ }}} = \frac{{25}}{{\sin {{55}^ \circ }}}\) <strong><em>(M1)(A1)</em>(ft)</strong></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for substitution into the correct formula, <strong><em>(A1)</em>(ft)</strong> for correct substitution. Follow through from their angle ABC.</span></p>
<p> </p>
<p><span><span>\({\text{AC}} = 23.4{\text{ m}}\) </span><span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></span></p>
<p><span><span><em><strong>[3 marks]</strong></em></span></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{Area of }}\Delta {\text{ ABC}} = \frac{1}{2} \times 23.379 \ldots \times 25 \times \sin {75^ \circ }\) <strong><em>(M1)(A1)</em>(ft)</strong></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for substitution into the correct formula, <em><strong>(A1)</strong></em><strong>(ft)</strong> for correct substitution. Follow through from their AC.</span></p>
<p> </p>
<p><span><strong>OR</strong></span></p>
<p><span>\({\text{Area of triangle ABC}} = \frac{{29.479 \ldots \times 19.151 \ldots }}{2}\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> <strong><em>(A1)</em>(ft)</strong> for correct values of AB (29.479…) and CN (19.151…). Follow through from their (a) and /or (b). Award <em><strong>(M1)</strong></em> for substitution of their values of AB and CN into the correct formula.</span></p>
<p><br><span>\({\text{Area of }}\Delta {\text{ ABC}} = 282{\text{ }}{{\text{m}}^2}\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><strong>Note:</strong> Accept \(283{\text{ }}{{\text{m}}^2}\) if \(23.4\) is used.</span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{NM}} = \frac{{25 \times \sin {{50}^ \circ }}}{2}\) <em><strong>(M1)(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for \({25 \times \sin {{50}^ \circ }}\) or equivalent for the length of CN. <em><strong>(M1)</strong></em> for dividing their CN by \(2\).</span></p>
<p> </p>
<p><span>\({\text{NM}} = 9.58{\text{ m}}\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their angle ABC.</span></p>
<p><span><strong>Notes:</strong> Premature rounding of CN leads to the answers \(9.60\) or \(9.6\). Award at most <em><strong>(M1)(M1)(A0)</strong></em> if working seen. Do not penalize with <em><strong>(AP)</strong></em>. CN may be found in (c).</span></p>
<p><span><strong>Note:</strong> The working for this part of the question may be in part (b).</span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{Angle NCB}} = {40^ \circ }\) seen <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span><strong>Note:</strong> Follow through from their (a).</span></p>
<p> </p>
<p><span>From triangle MCP:</span></p>
<p><span>\({\text{M}}{{\text{P}}^2} = {(9.5756 \ldots )^2} + {12.5^2} - 2 \times 9.5756 \ldots \times 12.5 \times \cos ({40^ \circ })\) <strong><em>(M1)(A1)</em>(ft)</strong></span></p>
<p><span>\({\text{MP}} = 8.034 \ldots {\text{ m}}\) <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for substitution into the correct formula, <strong><em>(A1)</em>(ft)</strong> for their correct substitution. Follow through from their d). Award <em><strong>(G3)</strong></em> for correct value of MP seen without working.</span></p>
<p> </p>
<p><span><strong>OR</strong></span></p>
<p><span>From right triangle MCP</span></p>
<p><span>\({\text{CP}} = 12.5{\text{ m}}\) seen <em><strong>(A1)</strong></em></span></p>
<p><span>\({\text{M}}{{\text{P}}^2} = {(12.5)^2} - {(9.575 \ldots )^2}\) <strong><em>(M1)(A1)</em>(ft)</strong></span></p>
<p><span>\({\text{MP}} = 8.034 \ldots {\text{ m}}\) <strong><em>(A1)(G3)</em>(ft)</strong></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for substitution into the correct formula, <strong><em>(A1)</em>(ft)</strong> for their correct substitution. Follow through from their (d). Award <em><strong>(G3)</strong></em> for correct value of MP seen without working.</span></p>
<p> </p>
<p><span><strong>OR</strong></span></p>
<p><span>From right triangle MCP</span></p>
<p><span>\({\text{Angle MCP}} = {40^ \circ }\) seen <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span>\(\frac{{{\text{MP}}}}{{12.5}} = \sin ({40^ \circ })\) or equivalent <strong><em>(M1)(A1)</em>(ft)</strong></span></p>
<p><span>\({\text{MP}} = 8.034 \ldots {\text{ m}}\) <strong><em>(A1)(G3)</em>(ft)</strong></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for substitution into the correct formula, <strong><em>(A1)</em>(ft)</strong> for their correct substitution. Follow through from their (a). Award <em><strong>(G3)</strong></em> for correct value of MP seen without working. </span></p>
<p> </p>
<p><span>The goat cannot reach point P as \({\text{MP}} > 7{\text{ m}}\) . <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> only if their value of MP is compared to \(7{\text{ m}}\), and conclusion is stated.</span></p>
<p><em><strong><span>[5 marks]</span></strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates assumed incorrectly that the triangle ABC is isosceles or/and that CN is an angle bisector, and those assumptions led them to use incorrect methods. Wherever those assumptions were made first, all or most of the marks were lost in that specific part of</span> <span style="font-family: times new roman,times; font-size: medium;">Question 4. There were provisions in the mark scheme to follow through in subsequent parts. Most candidates at least attempted parts a), b) and c). Some candidates incorrectly used an area formula for a right triangle in c) and lost all marks. Many candidates lost a mark for premature rounding in d). Part e) proved to be especially difficult for the candidates. Here many candidates offered guesses instead of sound mathematical reasoning.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates assumed incorrectly that the triangle ABC is isosceles or/and that CN is an angle bisector, and those assumptions led them to use incorrect methods. Wherever those assumptions were made first, all or most of the marks were lost in that specific part of</span> <span style="font-family: times new roman,times; font-size: medium;">Question 4. There were provisions in the mark scheme to follow through in subsequent parts. Most candidates at least attempted parts a), b) and c). Some candidates incorrectly used an area formula for a right triangle in c) and lost all marks. Many candidates lost a mark for premature rounding in d). Part e) proved to be especially difficult for the candidates. Here many candidates offered guesses instead of sound mathematical reasoning.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates assumed incorrectly that the triangle ABC is isosceles or/and that CN is an angle bisector, and those assumptions led them to use incorrect methods. Wherever those assumptions were made first, all or most of the marks were lost in that specific part of</span> <span style="font-family: times new roman,times; font-size: medium;">Question 4. There were provisions in the mark scheme to follow through in subsequent parts. Most candidates at least attempted parts a), b) and c). Some candidates incorrectly used an area formula for a right triangle in c) and lost all marks. Many candidates lost a mark for premature rounding in d). Part e) proved to be especially difficult for the candidates. Here many candidates offered guesses instead of sound mathematical reasoning.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates assumed incorrectly that the triangle ABC is isosceles or/and that CN is an angle bisector, and those assumptions led them to use incorrect methods. Wherever those assumptions were made first, all or most of the marks were lost in that specific part of</span> <span style="font-family: times new roman,times; font-size: medium;">Question 4. There were provisions in the mark scheme to follow through in subsequent parts. Most candidates at least attempted parts a), b) and c). Some candidates incorrectly used an area formula for a right triangle in c) and lost all marks. Many candidates lost a mark for premature rounding in d). Part e) proved to be especially difficult for the candidates. Here many candidates offered guesses instead of sound mathematical reasoning.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates assumed incorrectly that the triangle ABC is isosceles or/and that CN is an angle bisector, and those assumptions led them to use incorrect methods. Wherever those assumptions were made first, all or most of the marks were lost in that specific part of</span> <span style="font-family: times new roman,times; font-size: medium;">Question 4. There were provisions in the mark scheme to follow through in subsequent parts. Most candidates at least attempted parts a), b) and c). Some candidates incorrectly used an area formula for a right triangle in c) and lost all marks. Many candidates lost a mark for premature rounding in d). Part e) proved to be especially difficult for the candidates. Here many candidates offered guesses instead of sound mathematical reasoning.</span></p>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The points A (</span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">−</span>4, 1), B (0, 9) and C (4, 2) are plotted on the diagram below. The diagram also shows the lines AB,<em> L</em><sub>1</sub> and <em>L</em><sub>2</sub>.</span></p>
<p> </p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the gradient of AB.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><em>L</em><sub>1</sub> passes through C and is parallel to AB.</span></p>
<p><span>Write down the <em>y</em>-intercept of <em>L</em><sub>1</sub>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><em>L</em><sub>2</sub> passes through A and is perpendicular to AB.</span></p>
<p><span>Write down the equation of <em>L</em><sub>2</sub>. Give your answer in the form <strong><em>ax</em> + <em>by</em> + <em>d</em> = 0</strong> where <em>a</em>, <em>b</em> and <em>d</em> \( \in \mathbb{Z}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the coordinates of the point D, the intersection of <em>L</em><sub>1</sub> and <em>L</em><sub>2</sub>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>There is a point R on <em>L</em><sub>1</sub> such that ABRD is a rectangle.</span></p>
<p><span>Write down the coordinates of R.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The distance between A and D is \(\sqrt {45} \).</span></p>
<p><span>(i) Find the distance between D and R .</span></p>
<p><span>(ii) Find the area of the triangle BDR .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{9 - 1}}{{0 - ( - 4)}}\) <em><strong>(M1)</strong></em></span></p>
<p><span>= 2 <em><strong>(A1)(G2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into the gradient formula.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>–6 <em><strong>(A1)</strong></em> </span></p>
<p><br><span><strong>Note:</strong> Accept (0, –6) .</span></p>
<p><span><em><strong>[1 mark]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(y = - \frac{1}{2}x - 1\) (or equivalent) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <strong><em>(A1)</em>(ft)</strong> for gradient, <em><strong>(A1)</strong></em> for correct <em>y</em>-intercept. Follow through from their gradient in (a).</span></p>
<p><span> </span></p>
<p><span><em>x</em> + 2<em>y</em> + 2 = 0 <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span><br><strong>Notes:</strong> Award <strong><em>(A1)</em>(ft)</strong> from their gradient and their y-intercept. Accept any multiple of this equation with integer coefficients.</span></p>
<p><span><br><strong>OR</strong><br></span></p>
<p><span>\(y - 1 = - \frac{1}{2}(x + 4)\) (or equivalent) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em></span></p>
<p><span><br><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for gradient, <em><strong>(A1)</strong></em> for any point on the line correctly substituted in equation.</span></p>
<p><span><br><em>x</em> + 2<em>y</em> + 2 = 0 <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span><br><strong>Notes:</strong> Award <strong><em>(A1)</em>(ft)</strong> from their equation. Accept any multiple of this equation with integer coefficients.<br></span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>D(2, –2) or <em>x</em> = 2, <em>y</em> = –2 <em><strong>(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A0)</strong></em> if brackets not present.</span></p>
<p><span><em><strong>[1 mark]</strong></em><br></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>R(6, 6) <strong>or</strong> <em>x</em> = 6, <em>y</em> = 6 <em><strong>(A1)(A1)</strong></em> </span></p>
<p><br><span><strong>Note:</strong> Award at most <em><strong>(A0)(A1)</strong></em><strong>(ft)</strong> if brackets not present and absence of </span><span>brackets has not already been penalised in part (d).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) </span><span><span>\({\text{DR}} = \sqrt {{8^2} + {4^2}} \) </span> <em><strong>(M1)</strong></em></span></p>
<p><span>\({\text{DR}} = \sqrt {80} \) (8.94) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into the distance</span> <span>formula. Follow through from their D and R.</span></p>
<p><span> </span></p>
<p><span>(ii) \({\text{Area}} = \frac{{\sqrt {80} \times \sqrt {45} }}{2}\)</span><span> </span><em><strong><span>(M1)</span></strong></em></p>
<p><span><em><strong>=</strong></em> 30 (30.0) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in the area of triangle</span> <span>formula. Follow through from their answer to part (f) (i).</span></p>
<p><span><em><strong>[4 marks]</strong></em><br></span></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was in general well answered. In part (a) the gradient of the line AB was correctly found although some candidates did not substitute well in the gradient formula and found answers as \(\frac{1}{2}\) or –2. Also some students read B as (0, 8) instead of (0, 9). In part (b) many students again did not make good use of time as they found the equation of the line instead of just extending it to find the <em>y</em> - intercept. The equation of <em>L</em><sub>2</sub> in (c) was correctly found in the form <em>y</em> = <em>mx</em> + <em>c</em> but very few students were able to rearrange the equation in the form <em>ax</em> + <em>by</em> + <em>d</em> = 0 where <em>a</em>, <em>b</em>, <em>d</em> \( \in \mathbb{Z}\). In (d) many candidates found the coordinates of point D by solving simultaneous equations which led again to a waste of time. The last two parts of this question were well done by those students that attempted them.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was in general well answered. In part (a) the gradient of the line AB was correctly found although some candidates did not substitute well in the gradient formula and found answers as \(\frac{1}{2}\) or –2. Also some students read B as (0, 8) instead of (0, 9). In part (b) many students again did not make good use of time as they found the equation of the line instead of just extending it to find the <em>y</em> - intercept. The equation of <em>L</em><sub>2</sub> in (c) was correctly found in the form <em>y</em> = <em>mx</em> + <em>c</em> but very few students were able to rearrange the equation in the form <em>ax</em> + <em>by</em> + <em>d</em> = 0 where <em>a</em>, <em>b</em>, <em>d</em> \( \in \mathbb{Z}\). In (d) many candidates found the coordinates of point D by solving simultaneous equations which led again to a waste of time. The last two parts of this question were well done by those students that attempted them.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was in general well answered. In part (a) the gradient of the line AB was correctly found although some candidates did not substitute well in the gradient formula and found answers as \(\frac{1}{2}\) or –2. Also some students read B as (0, 8) instead of (0, 9). In part (b) many students again did not make good use of time as they found the equation of the line instead of just extending it to find the <em>y</em> - intercept. The equation of <em>L</em><sub>2</sub> in (c) was correctly found in the form <em>y</em> = <em>mx</em> + <em>c</em> but very few students were able to rearrange the equation in the form <em>ax</em> + <em>by</em> + <em>d</em> = 0 where <em>a</em>, <em>b</em>, <em>d</em> \( \in \mathbb{Z}\). In (d) many candidates found the coordinates of point D by solving simultaneous equations which led again to a waste of time. The last two parts of this question were well done by those students that attempted them.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was in general well answered. In part (a) the gradient of the line AB was correctly found although some candidates did not substitute well in the gradient formula and found answers as \(\frac{1}{2}\) or –2. Also some students read B as (0, 8) instead of (0, 9). In part (b) many students again did not make good use of time as they found the equation of the line instead of just extending it to find the <em>y</em> - intercept. The equation of <em>L</em><sub>2</sub> in (c) was correctly found in the form <em>y</em> = <em>mx</em> + <em>c</em> but very few students were able to rearrange the equation in the form <em>ax</em> + <em>by</em> + <em>d</em> = 0 where <em>a</em>, <em>b</em>, <em>d</em> \( \in \mathbb{Z}\). In (d) many candidates found the coordinates of point D by solving simultaneous equations which led again to a waste of time. The last two parts of this question were well done by those students that attempted them.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was in general well answered. In part (a) the gradient of the line AB was correctly found although some candidates did not substitute well in the gradient formula and found answers as \(\frac{1}{2}\) or –2. Also some students read B as (0, 8) instead of (0, 9). In part (b) many students again did not make good use of time as they found the equation of the line instead of just extending it to find the <em>y</em> - intercept. The equation of <em>L</em><sub>2</sub> in (c) was correctly found in the form <em>y</em> = <em>mx</em> + <em>c</em> but very few students were able to rearrange the equation in the form <em>ax</em> + <em>by</em> + <em>d</em> = 0 where <em>a</em>, <em>b</em>, <em>d</em> \( \in \mathbb{Z}\). In (d) many candidates found the coordinates of point D by solving simultaneous equations which led again to a waste of time. The last two parts of this question were well done by those students that attempted them.</span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was in general well answered. In part (a) the gradient of the line AB was correctly found although some candidates did not substitute well in the gradient formula and found answers as \(\frac{1}{2}\) or –2. Also some students read B as (0, 8) instead of (0, 9). In part (b) many students again did not make good use of time as they found the equation of the line instead of just extending it to find the <em>y</em> - intercept. The equation of <em>L</em><sub>2</sub> in (c) was correctly found in the form <em>y</em> = <em>mx</em> + <em>c</em> but very few students were able to rearrange the equation in the form <em>ax</em> + <em>by</em> + <em>d</em> = 0 where <em>a</em>, <em>b</em>, <em>d</em> \( \in \mathbb{Z}\). In (d) many candidates found the coordinates of point D by solving simultaneous equations which led again to a waste of time. The last two parts of this question were well done by those students that attempted them.</span></p>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the functions \(f(x) = \frac{{2x + 3}}{{x + 4}}\) and \(g(x) = x + 0.5\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Sketch the graph of the function \(f(x)\), for \( - 10 \leqslant x \leqslant 10\) . Indicating clearly the axis intercepts and any asymptotes.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the equation of the vertical asymptote.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>On the same diagram as part (a) sketch the graph of \(g(x) = x + 0.5\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using your graphical display calculator write down the coordinates of <strong>one</strong> of the points of intersection on the graphs of \(f\) and \(g\), <strong>giving your answer correct to five decimal places</strong>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the gradient of the line \(g(x) = x + 0.5\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The line \(L\) passes through the point with coordinates \(( - 2{\text{, }} - 3)\) and is perpendicular to the line \(g(x)\) . Find the equation of \(L\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span> <em><strong>(A6)</strong></em></span></span></p>
<p><span><strong>Notes:</strong> <em><strong>(A1)</strong></em> for labels and some idea of scale.</span><br><span><em><strong>(A1)</strong></em> for \(x\)-intercept seen, <em><strong>(A1)</strong></em> for \(y\)-intercept seen in roughly the correct places (coordinates not required).</span><br><span><em><strong>(A1)</strong></em> for vertical asymptote seen, <em><strong>(A1)</strong></em> for horizontal asymptote seen in roughly the correct places (equations of the lines not required).</span><br><span><em><strong>(A1)</strong></em> for correct general shape.</span></p>
<p><span><em><strong>[6 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(x = - 4\) <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Note: <em>(A1)</em></strong> for \(x =\), <strong><em>(A1)</em>(ft)</strong> for \( - 4\).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOoAAAD6CAIAAAAgIEyCAAAUTUlEQVR4nO2db2gcZ37H933yNpD3R503TYIp08YhBIemloRJt2D9waFsi7ukts/lnMIIavwP44VLZVz3JkZHHeGu8Vlq42ntnk7VOhiTMpwhCDbCJ9yBA9W7F5WiLHZYa4gjaZ++GHs8nn/7PPP8Zmdm9/thXjjab777SPvxeDTz29kCAyC3FNJeAADxgb4gx0DfLLG9+p9/t+/3Svra9m/nPvxbfW0z7QVlHeibMTaXpv5gamnzd7/6+89/u5X2YjIP9M0Ym0tTO49d+3z6F//9OO2l5ADomzUaeulPjv7yAY4beIC+2aLz3d3L1a/bnbTXkROgb3b43S8PDhfP1r7ZhLy8QF+QY6Bv0my1G/eWlhv28UCn3Vh+9mcgD/RNlCdri5WDk2cmx3btPnnn/765dezoxVv6mf0n76zDYAqgbxSGYbRaLYmCx+aS2Was05ib+NHk1NmRibnVzvb9mT37plc2yFY5wEjpu7D4RULhjJSrqmqapnz51srP95747J9Kw2fvPmKsoZd2T95etx8yDEN/BuHKY4R7kCcH+kZBo+/m6r8f+9mvv1vVn+u7d2qp7TyFpmnQNx7QN4pCoWBZllR55+HX//zZ4jffs83//a/Kn03MrXa27k2/U55r/GA/bv8NiVlOGu5BnhzoG0WhUJAq7zz6zcxfK7v3lUp/Pvbex9e/rp0++unC9anJmeX2szD0lQH6RiGrr5/OxsNHT9xfgL4yQN8o6PX1AX1lgL5RQF/aPDnQNwroS5snB/pGAX1p8+RA3yigL22eHOgbBfSlzZMDfaOAvrR5cqBvFNCXNk8O9I0C+tLmyYG+UUBf2jw50DeK3uhbq9VM0+SUOAs/lth5crj0XVj8YjC3QqGQ9FOMjo0PDY+Mjo2Pjo2n/v0mvaWjbxhCCxJdferlpmmWy+WEyh1w8CAD9A3FNE1VVRMqd4C+MkDfUKAveZ4c6BsK9CXPkwN9Q4G+5HlyoG8o0Jc8Tw70DQX6kufJgb6hQF/yPDnQNxToS54nB/qGUq/XoS9tnhzoG4pz5xvoS5UnB/qGAn3J8+RA31CgL3meHOgbCvQlz5ODgcnQ7fiJU8dPnEr6WQouUv+Wk97S0TcMoQWJrj71cux9yfPkQN9QoC95nhzoGwr0Jc+TA31Dgb7keXKgbyjQlzxPDvQNRVXVer2eULn7WaBvbKBvKI5Y0JcqTw70DQX6kufJgb6hQF/yPDnQNxToS54nB/qGAn3J8+RA31CgL3meHOgbSrlchr60eXKgbyj27SUTKneAvjJgYDJ0680EIwYmE9c3DKEFia4+9XLsfcnz5EDfUKAveZ4c6BsK9CXPkwN9Q4G+5HlyoG8wzWazWCwmVO4G+soAfYNx7hCVRLkb6CsD9A0G+iaRJwf6BgN9k8iTA32Dgb5J5MmBvsFA3yTy5EDfYGq1mqZpCZW7gb4yQN9gnLcZJ1HuBvrKAH2Dgb5J5MmBvsFA3yTy5GBgMnjrze0lFzAw2QN9wxBakOjq0y2vVqvY+5LnyYG+wbitgr5UeXKgbzDQN4k8OdA3GOibRJ4c6BsM9E0iTw70DaZQKLRarYTK3UBfGaBvMM5bLZIodwN9ZYC+wUDfJPLkQN9goG8SeXKgbwCmaTpvdCMv9wB9ZYC+AbiHfcnLPQyIvs1m0/0jpQL6BkCt7/ffrrU2GWOMddqN5eVGu/P8sUHQt9lsKopiGIZQOQ/QNwBKfZ+szB549+WSvsbY9tqtY0cv3tLP7D95Z/2ZwX2vb3LuMugbiK7r1WqVrHxNL5X0NdZemhqZmFvtbN+f2bNvemXDfrC/9U3UXQZ9A3EP+xKUP9W3oZeGz959xFhDL+2evL1uP6iqaq1WM02TU+Ls/My75pN2l2HeN3AjHva9duqP3z91dfHa8feV0j/cWFi8dvz9P/or7T/sR0fHxoeGR0bHxkfHxlP/xgm3K1dnd+x47dz5C+4vpqNvGEILEl19iuXOBxLSlD/d+26sTE9MzK12tu5Nv1Oea/zgPFf/HTz0YL9rA30D8CglVd5pP6hV3tt1cv5Bu7N+5/TRTxeuT03OLLdDnkusnDRMle+Zuwz6BuJ8qgV9eWfj4aMn7i/0mb69dJdB30DcV4zJyz30k749dpdB30Cgb4x8791l0NdPq9VSFCWhcj/9oW8q7jLo68dzyY223E8f6JuWuwz6+oG+QvkU3WXQ14/nijFtuZ9c63vl6myK7jLo68dzxZi23E9+9W02mzt2vJaiuwz6+vFccqMtD3y6POprHzOcO39BqJ8c6OvF7xP09eAc74r2kwN9vRQKBcuyEir3kzt93b+rQd/MlXuuWdCW+8mXvp7zDPnQdyHt6buebZdmLg8Nj/TyGXN0g9TAGUihLR19wxBakOjqUyk3DKNSqSRUHkhe9r6GYRQKBc95hiSMFAL6voD/rBlheSC50DfQ3Rj95EDfF6hUKvIvUp/pG+ZujH5yoO8LeCZ9acsDybi+Ee7G6CcH+r6A/7QDYXkgWdY32t0Y/eRA3+d47g1FWx5GZvXt6m6MfnKg73MCTztQlYeRTX153I3RTw70fY7704TIy8PIoL6c7sboJwf6Pifw9zaq8jCypi+/uzH6yYG+T7Esyz/tQFUeQab0PXf+Ar+7MfrJgb5PMU2zXC4nVB5BdvQV2u/G6E8C6PuUarXqeZMFYXkEGdHXdld0fhf6ZqU87MCXpDyCLOjr7HcT/U6TAPoyxlir1Qq8YEFSHk3q+rqPGfpT34W0R/WS3s5WfvoXf3kgladOd2Dy3PkLkjOQQls6+oYhtCDR1feyPHBSh6o8mhT3voZhKIrSbDbjlcfIkwN9nx45BJ4yky/vSlr6+t0VLY+RJwf6slqtpmlaQuVdSUXfQHdFy2PkyYG+rFgset4ZT1jeld7rG+auaHmMPDmDrq9hGIFTZiTlPPRY3wh3Rctj5MkZdH1VVSWfq8qsvtHuipbHyJMz0Pry7Hpjl3PSM327uitaHiNPzuDqa1lWsVhMYiwwg/ryuCtaHiNPzuDqq+s656fs5l1fTndFy2PkyRlQfS/NXFYUpdVqJVGeKX353RUtj5EnZxD1tSzrrV1v12q1JMpF84nqe+78BX53Rctj5MkZOH0tyyqXy4cOH0loJaL55PQ1DGPHjtf43RUqj5cnZ7D0td0tl8vZWXlC+trHDFeuzvI385fHzpMzQPo67lqWlZ2VJ6Gvc7ybtI750HchjUlC2u3K1dmh4ZFDh4/cuDmf+mLcG/nApD0DeeXqbOrfmn9LR98whBYkunrC8lqtpiiK+03w2Vk57d7Xc54h0ZXHyJPT5/rab8AsFosy9/vPi769n9+FvkmVt1otTdM8O12qcsI8lb6pzO9CX/ryer1eqVQURalWq2EXJrKzchJ905rfhb5k5c1ms1qtFovFYrFYq9Ui3j0Ro5w/LJqX1zfF+V3oK5W3LKter1er1bd2va0oiqZpSVwdzbK+6c7vQl/hfKvVspUtl8uFQkFVVV3XEz0/n1l9U5/fhb5d8pZlmaZZq9Wq1aqqqoqiKIpiK2uapnOEkOJZOcl8bH2zML8LfZ9jmqZtqq7rlUpldGzcPpmvqqqmabavJL+KieYzqG9G5ncHSN8rV2fdgtqOqqpqHwMUCoViseiYahjGpZnLnAONoisRzWdN3+zM7+ZVX/vf9Eszlz1G2qjPcNQsFApv7Xrb/mKlUrFjhmHY/3vgU2THsEzpKzQDCX0ZY6xarRZ8qKo6OjbuMdKmXq+bz3BK8mtYdvQVnYGEvowx1mw25e/bnF/DMqJvjBlI6BtFdiTIbzmnvvFmIKFvFNn5Uea3nEdf9+9q2Vl5jDw5gzLvm9mt67xvlud3Rbd09A1DaEGiqx+Q8ui9r+QMZKIrj5EnB/qmXB6hr/wMZEIrt0+bus+cmqZpGIYegn3FNOyjQ2SAvimXh+lLMgMZFm61WoHaHT9xStM09UWKxWLgaVP3mVP/yVMPpmkKveeZE+ibcnmgvrFnIG0j6/W6o6Ojl6Iojnz23Ihfu+MnTtmquSEcCSIH+qZc7te36wykW1DPDtK+8G6PNNk6OpeQeK7A49iXJjw45R59Pe7a06G6rtv/ptt70HK5bB9KOhc4Me8bh+xIkN9yt76GYezcuXNxcdH+Xcf5V75ardZqNXsPmp2Vx8iTA31TLrfvj20Yxscff/zSSy+9+eabzjRz4D/32Vl5jDw50De18larZd+AolAofPTRRzt27Pjqq69oF5NhfR+biz/7yd4fX5z55NBPpu8+3IrXAn1TKDcMwz6Q1TStWCzOzs4mNAOZYX0ZY+2lqT17Zu5vS1RA396VW5al67p9OGsYhj3E9+GHH77++usJzUBmWt/t/9EP/P6PppY241fI6RvxOcCS4VarJfTp5kLlonn5cre47vMMuq6/+uqrX375ZUKLSfTHIpp33S9m6+Hdz44dPPGLL6ulnX/646u/eSL0rO4FxP0fGUvyR2ma5ujYeELlonnJctM07dOxnvO79k2ADh48KPRui/zq+0J487uHj7cY23r88Ls+3Pv2jb7ValVRFP+d3G13m82m6JuF+kRfIrga7XOQAMigKEo6+oaRnV8jslZu3wpb0zT/m6yc/a79nyl+onzv8+RAX/ryGzfnbXf9D3ncZdBXjgzq+/23a61NxhYWv+i0G8vLjXaHeCWiedHyoeERTndZ/+v79NW04X9BOcmYvk9WZg+8+3JJX2Ns/tpPjx29eEs/s//knfVu33B29NU0bWh4JPDrgdcm+llf16vJGNteu8X/gnKSMX0ZY2t6qaSvsfY/lv9wYm61s31/Zs++6ZUNwpWI5vnD9XpdUZQbN+c9Xw9zl/W3vsx5NRlj7aWpEf4XlJPM6ts4/r5y9u4jxhp6affk7XXClYjmOcOWZSmKUq/XPfkId9kA6dvQS8P8LygnqerbNm+731By22yzQH33Ti21CVdCsPIgNE2rVCqefLS7bED17f6CcpLZve/Gz/9m98Tcamfr3vQ75bnGD4QrEc3zhFutlvMhyU6+q7tsgPTdWJme4H9BOcmYvp32g1rlvV0n5x+0f/Wv504f/XTh+tTkzHLXv6qp62vfGNOd53GX9be+rlezw1hn/Q7/C8pJxvT15DsbDx9xjXOkq6+963XfK5vTXdbf+vrhfkE5yba+OSmvVqvuE72HDh/hn98dLH2pgb4EYbes9nlf/htrQ18ZoK9s2DCMcrls/1nTtHK57D/vGwH0lQH6yoYrlYo9D2m7K/px9dBXBtxhUmq7cXO+UCj8y+f/dujwkaHhkRgfV+98Ak2B6BPls7ylo28YQgsSXX0uyuv1uj1cZu93Y5Rj7ysD9JUK2+K63RUth74yQF+p8BtvvLF//37PTDr07RnQN374k08+eeWVV/zvp4C+PQP6xgxrmvbBBx+cPn1ashz6ygB944TtQ95Lly657l0Qsxz6ygB9hcPOeYZyuRxoHvTtGdBXLOw+R1YIuXEB9O0Z0Fcg7HbXNE3nWrFMOfSVAfryhj3XJmq1WuDbiUXLoa8M0Jcr7HGXMWbfm1++HPrKAH27c+jwEY+7jDFVVev1unw59JUB+nbBnt/1X5uI/vAf/pVAXxmgbxQR87thpx1EFwN9ZcDAZOgWMQN5aeby0PAIybO478GY+rec9JaOvmEILUh09emWu39X84fr9bqqqiSLwd5XBugbQNf5Xfu2KiSLgb4yQF8v/nNk/nDEWTPRxUBfGaDvC/jdDQxHOwd9ewb0fU6gu4HhsGGdGIuBvjJA36eEuRsYjjhrJroY6CsD9GUs0t3AcugbL08O9O3irr88YtYsxmKgrwyDrm9Xd/3lpmlGnPQVXQz0lWGg9eVx119uGIZ9G2qSxUBfGQZXX053/eXR1yxEFwN9ZRhQfQNnIDnLoW/sPDmDqG/YDCRneaVSMQyDajHQV4aB0zfGPUw95V2Fg749Y7D0jXcPU+hLlSdngOZ9Y9/D1LO9tevtK1dnqVaFG6Qmrm8YQgsSXT1tucw9TD3h6EtuouXY+8owEPryzEDyl0Pf2Hly+l9fzhlIznLLsqBv7Dw5fa4v/wwkZ3nXK8ai5dBXhn7WV2gGkrMc+srkyelbfUVnIDnLoa9Mnpz+1Fd0BpK/POLWZvHKoa8MfahvjBlI/vKuAw+i5dBXhr7S175ldIwZSP4w9JXJk9M/+vK7G6Pc+TP0lcmT0yf63rg5z++uaLnnyMT+CFiqcugrQz/oa1nW0PAIv7uii3GHeWyDvj0j9/raxwxC87uii4G+VHly8q2vc7wrNL8ruhjoS5UnJ8cDkzduzg8Nj5DMQPJvo2Pjl2YuExbiBqmJ6xuG0IJEVx+d95xnoC2PCBeLxbCbqscrx95Xhlzq6z9H1jN9u46biZZDXxnyp2/g+V3oKx/uQZ6cnOkbdm0C+sqHe5AnJ0/6RlxXg77y4R7kycmNvtHXhKGvfLgHeXLyoW/XeYbe6Nv13pIxyqGvDDnQ13ZXVVWq+V3RvFvfrrPqouXQV4as62u7SzshLpqHvlR5cjKtL6e78cpjhKGvZJ6c7Oprz0DyuBujHPqmkicno/raM5Cc7oqWi+bl9P3+27XWJmOMsU67sbzcaHdeCENfGbKor33McOjwkYRWIpp3wrquV6tVgfInK7MH3n25pK8xtr1269jRi7f0M/tP3ll3GQx9ZciovrquZ+d1cuvb9Z1C3vI1vVTS11h7aWpkYm61s31/Zs++6ZUN53HoK0MW9c1suYS+Db00fPbuI8Yaemn35O1153H3wGRyK89InhwpfQcN0zSj9pRt87bu4rbZZoH67p1aavdu0X0N9E2Yp/purExPTMytdrbuTb9Tnmv8kPay+gTomySd9oNa5b1dJ+cftDvrd04f/XTh+tTkzDL2vVRA3x7S2Xj46Enai+groC/IMdAX5BjoC3LM/wMo7wEqnHm6mQAAAABJRU5ErkJggg==" alt><span> <em><strong>(A1)(A1)</strong></em></span></span></p>
<p><span><span><strong>Note:</strong> <em><strong>(A1)</strong></em> for correct axis intercepts, <em><strong>(A1)</strong></em> for straight line</span><br></span></p>
<p><span><span><em><strong>[2 marks]</strong></em><br></span></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(( - 2.85078{\text{, }} - 2.35078)\) OR \((0.35078{\text{, }}0.85078)\) <em><strong>(G1)(G1)(A1)</strong></em><strong>(ft)</strong><br></span></p>
<p><br><span><strong>Notes: <em>(A1)</em></strong> for \(x\)-coordinate, <em><strong>(A1)</strong></em> for \(y\)-coordinate, <strong><em>(A1)</em>(ft)</strong> for correct accuracy. Brackets required. If brackets not used award <strong><em>(G1)(G0)(A1)</em>(ft)</strong>.<br>Accept \(x = - 2.85078\), \(y = - 2.35078\) or \(x = 0.35078\), \(y = 0.85078\).</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{gradient}} = 1\) <em><strong>(A1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{gradient of perpendicular}} = - 1\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><em>(can be implied in the next step)</em></span></p>
<p><span>\(y = mx + c\)</span></p>
<p><span>\( - 3 = - 1 \times - 2 + c\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(c = - 5\)</span></p>
<p><span>\(y = - x - 5\) <em><strong>(A1)</strong></em><strong>(ft)<em>(G2)</em></strong></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>\(y + 3 = - (x + 2)\) <em><strong>(M1)</strong></em><em><strong>(A1)</strong></em><strong>(ft)<em>(G2)</em></strong></span></p>
<p><br><span><strong>Note: </strong>Award <em><strong>(G2)</strong></em> for correct answer with no working at all but <em><strong>(A1)(G1)</strong></em> if the gradient is mentioned as \( - 1\) then correct answer with no further working.</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This was not very well done. The graph was often correct but was so small that it was difficult to check if axes intercepts were correct or not. Often the vertical asymptote looked as if it were joined to the rest of the graph. Very few of the candidates put a scale and/or labels on their axes.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Reasonably well done. Some put \(y = - 4\) while others omitted the minus sign.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Fairly well done – but once again too small to check the axes intercepts properly. Also, many candidates did not appear to have a ruler to draw the straight line.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Well done.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most could find the gradient of the line.</span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many forgot to find the gradient of the perpendicular line. Others had problems with the equation of a line in general.</span></p>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The Great Pyramid of Giza in Egypt is a right pyramid with a square base. The pyramid is made of solid stone. The sides of the base are \(230\,{\text{m}}\) long. The diagram below represents this pyramid, labelled \({\text{VABCD}}\).</p>
<p>\({\text{V}}\) is the vertex of the pyramid. \({\text{O}}\) is the centre of the base, \({\text{ABCD}}\) . \({\text{M}}\) is the midpoint of \({\text{AB}}\). Angle \({\text{ABV}} = 58.3^\circ \) .</p>
<p><img 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" alt></p>
<p>Show that the length of \({\text{VM}}\) is \(186\) metres, correct to three significant figures.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the height of the pyramid, \({\text{VO}}\) .</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the volume of the pyramid.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down your answer to part (c) in the form \(a \times {10^k}\) where \(1 \leqslant a < 10\) and \(k \in \mathbb{Z}\) .</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Ahmad is a tour guide at the Great Pyramid of Giza. He claims that the amount of stone used to build the pyramid could build a wall \(5\) metres high and \(1\) metre wide stretching from Paris to Amsterdam, which are \(430\,{\text{km}}\) apart.</p>
<p>Determine whether Ahmad’s claim is correct. Give a reason.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Ahmad and his friends like to sit in the pyramid’s shadow, \({\text{ABW}}\), to cool down.<br>At mid-afternoon, \({\text{BW}} = 160\,{\text{m}}\) and angle \({\text{ABW}} = 15^\circ .\)</p>
<p><img 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" alt></p>
<p>i) Calculate the length of \({\text{AW}}\) at mid-afternoon.</p>
<p>ii) Calculate the area of the shadow, \({\text{ABW}}\), at mid-afternoon.</p>
<div class="marks">[6]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(\tan \,(58.3) = \frac{{{\text{VM}}}}{{115}}\) <strong>OR</strong> \(115 \times \tan \,(58.3^\circ )\) <em><strong>(A1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(115\,\,\left( {ie\,\frac{{230}}{2}} \right)\) seen, <em><strong>(M1)</strong></em> for correct substitution into trig formula.</p>
<p>\(\left( {{\text{VM}} = } \right)\,\,186.200\,({\text{m}})\) <em><strong>(A1)</strong></em></p>
<p>\(\left( {{\text{VM}} = } \right)\,\,186\,({\text{m}})\) <em><strong>(AG)</strong></em></p>
<p><strong>Note:</strong> Both the rounded and unrounded answer must be seen for the final <em><strong>(A1)</strong></em> to be awarded.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\({\text{V}}{{\text{O}}^2} + {115^2} = {186^2}\) <strong>OR</strong> \(\sqrt {{{186}^2} - {{115}^2}} \) <strong>(M1)</strong></p>
<p>Note: Award <em><strong>(M1)</strong></em> for correct substitution into Pythagoras formula. Accept alternative methods.</p>
<p>\({\text{(VO}} = )\,\,146\,({\text{m}})\,\,(146.188...)\) <em><strong>(A1)(G2)</strong></em></p>
<p><strong>Note:</strong> Use of full calculator display for \({\text{VM}}\) gives \(146.443...\,{\text{(m)}}\).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>Units are required in part (c)</strong></p>
<p>\(\frac{1}{3}({230^2} \times 146.188...)\) <em><strong> (M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in volume formula. Follow through from part (b).</p>
<p>\( = 2\,580\,000\,{{\text{m}}^3}\,\,(2\,577\,785...\,{{\text{m}}^3})\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p><strong>Note:</strong> The answer is \(2\,580\,000\,{{\text{m}}^3}\) , the units are required. Use of \({\text{OV}} = 146.442\) gives \(2582271...\,{{\text{m}}^3}\)</p>
<p>Use of \({\text{OV}} = 146\) gives \(2574466...\,{{\text{m}}^3}.\)</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(2.58 \times {10^6}\,({{\text{m}}^3})\) <em><strong>(A1)</strong></em><strong>(ft)<em>(A1)</em><strong>(ft)</strong></strong></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for \(2.58\) and <strong><em>(A1)</em>(ft)</strong> for \( \times {10^6}.\,\)</p>
<p>Award <em><strong>(A0)(A0)</strong></em> for answers of the type: \(2.58 \times {10^5}\,({{\text{m}}^3}).\)</p>
<p>Follow through from part (c).</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the volume of a wall would be \(430\,000 \times 5 \times 1\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into volume formula.</p>
<p>\(2150000\,({{\text{m}}^3})\) <em><strong>(A1)(G2)</strong></em></p>
<p>which is less than the volume of the pyramid <em><strong>(R1)(ft)</strong></em></p>
<p>Ahmad is correct. <em><strong>(A1)(ft)</strong></em></p>
<p><strong>OR</strong></p>
<p>the length of the wall would be \(\frac{{{\text{their part (c)}}}}{{5 \times 1 \times 1000}}\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for dividing their part (c) by \(5000.\)</p>
<p>\(516\,({\text{km}})\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p>which is more than the distance from Paris to Amsterdam <em><strong>(R1)(ft)</strong></em></p>
<p>Ahmad is correct. <em><strong>(A1)(ft)</strong></em></p>
<p><strong>Note:</strong> Do not award final <em><strong>(A1)</strong></em> without an explicit comparison. Follow through from part (c) or part (d). Award <em><strong>(R1)</strong></em> for reasoning that is consistent with their working in part (e); comparing two volumes, or comparing two lengths.</p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>Units are required in part (f)(ii).</strong></p>
<p> </p>
<p>i) \({\text{A}}{{\text{W}}^2} = {160^2} + {230^2} - 2 \times 160 \times 230 \times \cos \,(15^\circ )\) <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution into cosine rule formula, <em><strong>(A1)</strong></em> for correct substitution.</p>
<p>\({\text{AW}} = 86.1\,({\text{m}})\,\,\,(86.0689...)\) <em><strong>(A1)(G2)</strong></em></p>
<p>Note: Award <em><strong>(M0)(A0)(A0)</strong></em> if \({\text{BAW}}\) or \({\text{AWB}}\) is considered to be a right angled triangle.</p>
<p> </p>
<p>ii) \({\text{area}} = \frac{1}{2} \times 230 \times 160 \times \sin \,(15^\circ )\) <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution into area formula, <em><strong>(A1)</strong></em> for correct substitutions.</p>
<p>\( = 4760\,{{\text{m}}^2}\,\,\,(4762.27...\,{{\text{m}}^2})\) <em><strong>(A1)(G2)</strong></em></p>
<p><strong>Note:</strong> The answer is \(4760\,{{\text{m}}^2}\) , the units are required.</p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Question 4: Trigonometry, volume and area.<br>Many were able to write a correct trig ratio for part (a). The most common error was not to write the unrounded or the rounded answer. Some incorrectly used the given value of 186 in their proof. Part (b) was mostly answered correctly, with only a few candidates using Pythagoras’ Theorem incorrectly. Most candidates used the correct formula to calculate the volume of the pyramid, but some did not find the correct area for the base of the pyramid. Some lost a mark for missing or for incorrect units. Even with an incorrect answer for part (c), candidates did very well on part (d). In part (e) some excellent justifications were given. However, many struggled to convert kilometres to metres, others were confused and compared surface area instead of volume. Some thought the volumes needed to be the same. For part (f) candidates often assumed a right angle at BAW or BWA. When they used the sine and cosine rule, this was mostly done correctly.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 4: Trigonometry, volume and area.<br>Many were able to write a correct trig ratio for part (a). The most common error was not to write the unrounded or the rounded answer. Some incorrectly used the given value of 186 in their proof. Part (b) was mostly answered correctly, with only a few candidates using Pythagoras’ Theorem incorrectly. Most candidates used the correct formula to calculate the volume of the pyramid, but some did not find the correct area for the base of the pyramid. Some lost a mark for missing or for incorrect units. Even with an incorrect answer for part (c), candidates did very well on part (d). In part (e) some excellent justifications were given. However, many struggled to convert kilometres to metres, others were confused and compared surface area instead of volume. Some thought the volumes needed to be the same. For part (f) candidates often assumed a right angle at BAW or BWA. When they used the sine and cosine rule, this was mostly done correctly.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 4: Trigonometry, volume and area.<br>Many were able to write a correct trig ratio for part (a). The most common error was not to write the unrounded or the rounded answer. Some incorrectly used the given value of 186 in their proof. Part (b) was mostly answered correctly, with only a few candidates using Pythagoras’ Theorem incorrectly. Most candidates used the correct formula to calculate the volume of the pyramid, but some did not find the correct area for the base of the pyramid. Some lost a mark for missing or for incorrect units. Even with an incorrect answer for part (c), candidates did very well on part (d). In part (e) some excellent justifications were given. However, many struggled to convert kilometres to metres, others were confused and compared surface area instead of volume. Some thought the volumes needed to be the same. For part (f) candidates often assumed a right angle at BAW or BWA. When they used the sine and cosine rule, this was mostly done correctly.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 4: Trigonometry, volume and area.<br>Many were able to write a correct trig ratio for part (a). The most common error was not to write the unrounded or the rounded answer. Some incorrectly used the given value of 186 in their proof. Part (b) was mostly answered correctly, with only a few candidates using Pythagoras’ Theorem incorrectly. Most candidates used the correct formula to calculate the volume of the pyramid, but some did not find the correct area for the base of the pyramid. Some lost a mark for missing or for incorrect units. Even with an incorrect answer for part (c), candidates did very well on part (d). In part (e) some excellent justifications were given. However, many struggled to convert kilometres to metres, others were confused and compared surface area instead of volume. Some thought the volumes needed to be the same. For part (f) candidates often assumed a right angle at BAW or BWA. When they used the sine and cosine rule, this was mostly done correctly.</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 4: Trigonometry, volume and area.<br>Many were able to write a correct trig ratio for part (a). The most common error was not to write the unrounded or the rounded answer. Some incorrectly used the given value of 186 in their proof. Part (b) was mostly answered correctly, with only a few candidates using Pythagoras’ Theorem incorrectly. Most candidates used the correct formula to calculate the volume of the pyramid, but some did not find the correct area for the base of the pyramid. Some lost a mark for missing or for incorrect units. Even with an incorrect answer for part (c), candidates did very well on part (d). In part (e) some excellent justifications were given. However, many struggled to convert kilometres to metres, others were confused and compared surface area instead of volume. Some thought the volumes needed to be the same. For part (f) candidates often assumed a right angle at BAW or BWA. When they used the sine and cosine rule, this was mostly done correctly.</p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 4: Trigonometry, volume and area.<br>Many were able to write a correct trig ratio for part (a). The most common error was not to write the unrounded or the rounded answer. Some incorrectly used the given value of 186 in their proof. Part (b) was mostly answered correctly, with only a few candidates using Pythagoras’ Theorem incorrectly. Most candidates used the correct formula to calculate the volume of the pyramid, but some did not find the correct area for the base of the pyramid. Some lost a mark for missing or for incorrect units. Even with an incorrect answer for part (c), candidates did very well on part (d). In part (e) some excellent justifications were given. However, many struggled to convert kilometres to metres, others were confused and compared surface area instead of volume. Some thought the volumes needed to be the same. For part (f) candidates often assumed a right angle at BAW or BWA. When they used the sine and cosine rule, this was mostly done correctly.</p>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The diagram shows triangle ABC in which \({\text{AB}} = 28{\text{ cm}}\), \({\text{BC}} = 13{\text{ cm}}\), \({\text{BD}} = 12{\text{ cm}}\) and \({\text{AD}} = 20{\text{ cm}}\).</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img 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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the size of angle ADB.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the area of triangle ADB.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the size of angle BCD.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that the triangle ABC is not right angled.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\cos {\text{ADB}} = \frac{{{{12}^2} + {{20}^2} - {{28}^2}}}{{2(12)(20)}}\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for substituted cosine rule formula, <em><strong>(A1)</strong></em> for correct substitutions.</span></p>
<p><br><span><span>\(\angle {\text{ADB}} = </span></span><span><span><span>120\</span>) </span><span> <em><strong>(A1)(G2)</strong></em></span></span></p>
<p><span><span><em><strong>[3 marks]<br></strong></em></span></span></p>
<p><span><span><em><strong> </strong></em></span></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{Area}} = \frac{{(12)(20)\sin {{120}^ \circ }}}{2}\) <strong><em>(M1)(A1)</em>(ft)</strong></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for substituted area formula, <strong><em>(A1)</em>(ft)</strong> for their correct substitutions.</span></p>
<p><br><span>\( = 104{\text{ c}}{{\text{m}}^2}\) (\(103.923 \ldots {\text{ c}}{{\text{m}}^2}\)) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><strong>Note:</strong> The final answer is \(104{\text{ c}}{{\text{m}}^2}\) , <strong>the units are required</strong>. Accept \(100{\text{ c}}{{\text{m}}^2}\) .</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{\sin {\text{BCD}}}}{{12}} = \frac{{\sin {{60}^ \circ }}}{{13}}\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(M1)(A1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for their 60 seen, <em><strong>(M1)</strong></em> for substituted sine rule formula, <em><strong>(A1)</strong></em> for correct substitutions.</span></p>
<p> </p>
<p><span>\({\text{BCD}} = {53.1^ \circ }\) (\(53.0736 \ldots \)) <em><strong>(A1)(G3)</strong></em></span></p>
<p><span><strong>Note:</strong> Accept \(53\), do not accept \(50\) or \(53.0\).</span></p>
<p><span><em><strong>[4 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Using triangle ABC</span></p>
<p><span>\(\frac{{\sin {\text{BAC}}}}{{13}} = \frac{{\sin {{53.1}^ \circ }}}{{28}}\) <strong><em>(M1)(A1)</em>(ft)</strong></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>Using triangle ABD</span></p>
<p><span>\(\frac{{\sin {\text{BAD}}}}{{12}} = \frac{{\sin {{120}^ \circ }}}{{28}}\) <strong><em>(M1)(A1)</em>(ft)</strong></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituted sine rule formula (one of the above), <strong><em>(A1)</em>(ft)</strong> for their correct substitutions. Follow through from (a) or (c) as appropriate.</span></p>
<p> </p>
<p><span>\({\text{BAC}} = {\text{BAD}} = {21.8^ \circ }\) (\(21.7867 \ldots \)) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></span></p>
<p><span><strong>Notes:</strong> Accept \(22\), do not accept \(20\) or \(21.7\). Accept equivalent methods, for example cosine rule.</span></p>
<p><span> </span></p>
<p><span>\({180^ \circ } - ({53.1^ \circ } + {21.8^ \circ }) \ne {90^ \circ }\), hence triangle ABC is not right angled <em><strong>(R1)(AG)</strong></em></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>\(\frac{{{\text{CD}}}}{{\sin {{66.9}^ \circ }}} = \frac{{13}}{{\sin {{60}^ \circ }}}\) <strong><em>(M1)(A1)</em>(ft)</strong></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituted sine rule formula, <strong><em>(A1)</em>(ft)</strong> for their correct substitutions. Follow through from (a) and (c).</span></p>
<p> </p>
<p><span>\({\text{CD}} = 13.8{\text{ }}(13.8075 \ldots )\) <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span>\({13^3} + {28^2} \ne {33.8^2}\), hence triangle ABC is not right angled. <em><strong>(R1)</strong></em><strong>(ft)</strong><em><strong>(AG)</strong></em></span> </p>
<p><span><strong>Note:</strong> The complete statement is required for the final <em><strong>(R1)</strong></em> to be awarded.</span></p>
<p><span><em><strong>[4 marks]</strong></em><br></span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The vast majority of candidates scored very well on this question. Those who did not attempted it using the trigonometry associated with right angled triangles. There were few problems with the use of radians and part (d), which was expected to prove challenging, was successfully overcome by more than half of the candidature. Problems arose mainly because of a lack of clarity in identifying the correct triangle.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The vast majority of candidates scored very well on this question. Those who did not attempted it using the trigonometry associated with right angled triangles. There were few problems with the use of radians and part (d), which was expected to prove challenging, was successfully overcome by more than half of the candidature. Problems arose mainly because of a lack of clarity in identifying the correct triangle.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The vast majority of candidates scored very well on this question. Those who did not attempted it using the trigonometry associated with right angled triangles. There were few problems with the use of radians and part (d), which was expected to prove challenging, was successfully overcome by more than half of the candidature. Problems arose mainly because of a lack of clarity in identifying the correct triangle.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The vast majority of candidates scored very well on this question. Those who did not attempted it using the trigonometry associated with right angled triangles. There were few problems with the use of radians and part (d), which was expected to prove challenging, was successfully overcome by more than half of the candidature. Problems arose mainly because of a lack of clarity in identifying the correct triangle.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">An office block, ABCPQR, is built in the shape of a triangular prism with its “footprint”, ABC, on horizontal ground. \({\text{AB}} = 70{\text{ m}}\), \({\text{BC}} = 50{\text{ m}}\) and \({\text{AC}} = 30{\text{ m}}\). The vertical height of the office block is \(120{\text{ m}}\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img 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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the size of angle ACB.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the area of the building’s footprint, ABC.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the volume of the office block.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>To stabilize the structure, a steel beam must be made that runs from point C to point Q.</span></p>
<p><span>Calculate the length of CQ.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the angle CQ makes with BC.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\cos {\text{ACB}} = \frac{{{{30}^2} + {{50}^2} - {{70}^2}}}{{2 \times 30 \times 50}}\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituted cosine rule formula, <em><strong>(A1)</strong></em> for correct substitution.</span></p>
<p><br><span><span>\({\text{ACB}} = {120^ \circ }\) </span> <span><em><strong>(A1)(G2)</strong></em></span></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{Area of triangle ABC}} = \frac{{30(50)\sin {{120}^ \circ }}}{2}\) <strong><em>(M1)(A1)</em>(ft)</strong></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituted area formula, <strong><em>(A1)</em>(ft)</strong> for correct substitution.</span></p>
<p><br><span>\( = 650{\text{ }}{{\text{m}}^2}\) \((649.519 \ldots {\text{ }}{{\text{m}}^2})\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> The answer is \(650{\text{ }}{{\text{m}}^2}\) ; the units are required. Follow through from their answer in part (a).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{Volume}} = 649.519 \ldots \times 120\) <em><strong>(M1)</strong></em></span><br><span>\( = 77900{\text{ }}{{\text{m}}^3}\) (\(77942.2 \ldots {\text{ }}{{\text{m}}^3}\)) <em><strong>(A1)(G2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> The answer is \(77900{\text{ }}{{\text{m}}^3}\) ; the units are required. Do not penalise lack of units if already penalized in part (b). Accept \(78000{\text{ }}{{\text{m}}^3}\) from use of 3sf answer \(650{\text{ }}{{\text{m}}^2}\) from part (b).</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{C}}{{\text{Q}}^2} = {50^2} + {120^2}\) <em><strong>(M1)</strong></em></span><br><span>\({\text{CQ}} = 130{\text{ (m)}}\) <em><strong>(A1)(G2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> The units are <strong>not</strong> required.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\tan {\text{QCB}} = \frac{{120}}{{50}}\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substituted trig formula.</span></p>
<p><br><span>\({\text{QCB}} = {67.4^ \circ }\) (\(67.3801 \ldots \)) <em><strong>(A1)(G2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Accept equivalent methods.</span></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">In the diagram below A, B and C represent three villages and the line segments AB, BC and CA represent the roads joining them. The lengths of AC and CB are 10 km and 8 km respectively and the size of the angle between them is 150°.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the length of the road AB.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the size of the angle CAB.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Village D is halfway between A and B. A new road perpendicular to AB and passing through D is built. Let T be the point where this road cuts AC. This information is shown in the diagram below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Write down the distance from A to D.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that the distance from D to T is 2.06 km correct to three significant figures.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A bus starts and ends its journey at A taking the route AD to DT to TA.</span></p>
<p><span>Find the total distance for this journey.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The average speed of the bus while it is moving on the road is 70 km h<sup>–1</sup>. The bus stops for <strong>5 minutes</strong> at each of D and T .</span></p>
<p><span>Estimate the time taken by the bus to complete its journey. Give your answer correct to the nearest minute.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>AB<sup>2</sup> = 10<sup>2</sup> + 8<sup>2</sup> – 2 × 10 </span><span><span>×</span> 8 </span><span><span>×</span> cos150° <em><strong>(M1)(A1)</strong></em></span></p>
<p><span>AB = 17.4 km <em><strong>(A1)(G2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution into correct formula, <em><strong>(A1)</strong></em> for correct substitution, <em><strong>(A1)</strong></em> for correct answer.</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{8}{{\sin {\text{C}}\hat {\rm A}{\text{B}}}} = \frac{{17.4}}{{\sin 150^\circ }}\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span>\({\text{C}}\hat {\rm A}{\text{B}} = 13.3^\circ \) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <strong><em>(M1)</em></strong> for substitution into correct formula, <em><strong>(A1)</strong></em> for correct substitution, <em><strong>(A1)</strong></em> for correct answer. Follow through from their answer to part (a).</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>AD = 8.70 km (8.7 km) <em><strong>(A1)</strong></em><strong>(ft)</strong> </span></p>
<p><br><span><strong>Note:</strong> Follow through from their answer to part (a).</span></p>
<p><span><em><strong>[1 mark]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>DT = tan (13.29...°) × 8.697... = 2.0550... <em><strong>(M1)(A1)</strong></em></span></p>
<p><span>= 2.06 <em><strong>(AG)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in the correct formula,</span> <span>award <em><strong>(A1)</strong></em> for the unrounded answer seen. </span><span>If 2.06 not seen award at most <em><strong>(M1)(AO)</strong>.</em></span></p>
<p><span><em><strong>[2 marks]</strong><br></em></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\sqrt {{{8.70}^2} + {{2.06}^2}} + 8.70 + 2.06\) <em><strong>(A1)(M1)</strong></em></span></p>
<p><span>= 19.7 km <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em> </span></p>
<p><br><span><strong>Note:</strong> Award <strong><em>(A1)</em></strong> for AT, <em><strong>(M1)</strong></em> for adding the three sides of </span><span>the triangle ADT, <em><strong>(A1)</strong></em><strong>(ft)</strong> for answer.</span> <span>Follow through from their answer to part (c).</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{19.7}}{{70}} \times 60 + 10\) <em><strong>(M1)(M1)</strong></em></span></p>
<p><span>= 26.9 <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for time on road in minutes, <em><strong>(M1)</strong></em> for adding 10, <em><strong>(A1)</strong></em><strong>(ft)</strong> for unrounded answer. Follow through from their answer to (e).</span></p>
<p><br><span>= 27 (nearest minute) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G3)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for their unrounded answer given to the nearest minute.</span></p>
<p><span><em><strong>[4 marks]</strong></em><br></span></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The weak students answered parts (a) and (b) using right-angled trigonometry. Different types of mistakes were seen in (a) when applying the cosine rule: some forgot to square root their answer and others calculated each part separately and then missed the 2 minuses. Part (b) was better done than (a). Follow through was applied from (a) to (c). Part (d) was not well done. Most of the students lost one mark in this part question as they did not show the unrounded answer (2.0550...). Part (e) was fairly well done by those who attempted it. In (f) there were very few correct answers. Students found it difficult to find the time when the average speed and distance were given.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The weak students answered parts (a) and (b) using right-angled trigonometry. Different types of mistakes were seen in (a) when applying the cosine rule: some forgot to square root their answer and others calculated each part separately and then missed the 2 minuses. Part (b) was better done than (a). Follow through was applied from (a) to (c). Part (d) was not well done. Most of the students lost one mark in this part question as they did not show the unrounded answer (2.0550...). Part (e) was fairly well done by those who attempted it. In (f) there were very few correct answers. Students found it difficult to find the time when the average speed and distance were given.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The weak students answered parts (a) and (b) using right-angled trigonometry. Different types of mistakes were seen in (a) when applying the cosine rule: some forgot to square root their answer and others calculated each part separately and then missed the 2 minuses. Part (b) was better done than (a). Follow through was applied from (a) to (c). Part (d) was not well done. Most of the students lost one mark in this part question as they did not show the unrounded answer (2.0550...). Part (e) was fairly well done by those who attempted it. In (f) there were very few correct answers. Students found it difficult to find the time when the average speed and distance were given.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The weak students answered parts (a) and (b) using right-angled trigonometry. Different types of mistakes were seen in (a) when applying the cosine rule: some forgot to square root their answer and others calculated each part separately and then missed the 2 minuses. Part (b) was better done than (a). Follow through was applied from (a) to (c). Part (d) was not well done. Most of the students lost one mark in this part question as they did not show the unrounded answer (2.0550...). Part (e) was fairly well done by those who attempted it. In (f) there were very few correct answers. Students found it difficult to find the time when the average speed and distance were given.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The weak students answered parts (a) and (b) using right-angled trigonometry. Different types of mistakes were seen in (a) when applying the cosine rule: some forgot to square root their answer and others calculated each part separately and then missed the 2 minuses. Part (b) was better done than (a). Follow through was applied from (a) to (c). Part (d) was not well done. Most of the students lost one mark in this part question as they did not show the unrounded answer (2.0550...). Part (e) was fairly well done by those who attempted it. In (f) there were very few correct answers. Students found it difficult to find the time when the average speed and distance were given.</span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The weak students answered parts (a) and (b) using right-angled trigonometry. Different types of mistakes were seen in (a) when applying the cosine rule: some forgot to square root their answer and others calculated each part separately and then missed the 2 minuses. Part (b) was better done than (a). Follow through was applied from (a) to (c). Part (d) was not well done. Most of the students lost one mark in this part question as they did not show the unrounded answer (2.0550...). Part (e) was fairly well done by those who attempted it. In (f) there were very few correct answers. Students found it difficult to find the time when the average speed and distance were given.</span></p>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>Farmer Brown has built a new barn, on horizontal ground, on his farm. The barn has a cuboid base and a triangular prism roof, as shown in the diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The cuboid has a width of 10 m, a length of 16 m and a height of 5 m.<br>The roof has two sloping faces and two vertical and identical sides, ADE and GLF.<br>The face DEFL slopes at an angle of 15° to the horizontal and ED = 7 m .</p>
</div>
<div class="specification">
<p>The roof was built using metal supports. Each support is made from <strong>five</strong> lengths of metal AE, ED, AD, EM and MN, and the design is shown in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">ED = 7 m , AD = 10 m and angle ADE = 15° .<br>M is the midpoint of AD.<br>N is the point on ED such that MN is at right angles to ED.</p>
</div>
<div class="specification">
<p>Farmer Brown believes that N is the midpoint of ED.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the area of triangle EAD.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the <strong>total</strong> volume of the barn.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the length of MN.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the length of AE.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that Farmer Brown is incorrect.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the <strong>total</strong> length of metal required for one support.</p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>(Area of EAD =) \(\frac{1}{2} \times 10 \times 7 \times {\text{sin}}15\) <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution into area of a triangle formula, <strong>(A1)</strong> for correct substitution. Award <em><strong>(M0)(A0)(A0)</strong></em> if EAD or AED is considered to be a right-angled triangle.</p>
<p>= 9.06 m<sup>2</sup> (9.05866… m<sup>2</sup>) <em><strong>(A1) (G3)</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(10 × 5 × 16) + (9.05866… × 16) <em><strong>(M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into volume of a cuboid, <em><strong>(M1)</strong></em> for adding the correctly substituted volume of their triangular prism.</p>
<p>= 945 m<sup>3</sup> (944.938… m<sup>3</sup>) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (G3)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (a).</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{{\text{MN}}}}{5} = \,\,\,{\text{sin}}15\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into trigonometric equation.</p>
<p>(MN =) 1.29(m) (1.29409… (m)) <em><strong>(A1) (G2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(AE<sup>2</sup> =) 10<sup>2</sup> + 7<sup>2</sup> − 2 × 10 × 7 × cos 15 <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution into cosine rule formula, and <em><strong>(A1)</strong></em> for correct substitution.</p>
<p>(AE =) 3.71(m) (3.71084… (m)) <em><strong>(A1) (G2)</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>ND<sup>2</sup> = 5<sup>2</sup> − (1.29409…)<sup>2</sup> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into Pythagoras theorem.</p>
<p>(ND =) 4.83 (4.82962…) <strong><em>(A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from part (c).</p>
<p><strong>OR</strong></p>
<p>\(\frac{{1.29409 \ldots }}{{{\text{ND}}}} = {\text{tan}}\,15^\circ \) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into tangent.</p>
<p>(ND =) 4.83 (4.82962…) <strong><em>(A1)</em>(ft)</strong></p>
<p><strong>Note: </strong>Follow through from part (c).<strong><br></strong></p>
<p><strong>OR</strong></p>
<p>\(\frac{{{\text{ND}}}}{5} = {\text{cos }}15^\circ \) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into cosine.</p>
<p>(ND =) 4.83 (4.82962…) <strong><em>(A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from part (c).</p>
<p><strong>OR</strong></p>
<p>ND<sup>2</sup> = 1.29409…<sup>2</sup> + 5<sup>2</sup> − 2 × 1.29409… × 5 × cos 75° <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into cosine rule.</p>
<p>(ND =) 4.83 (4.82962…) <strong><em>(A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from part (c).</p>
<p>4.82962… ≠ 3.5 (ND ≠ 3.5) <strong><em>(R1)</em>(ft)</strong></p>
<p><strong>OR</strong></p>
<p>4.82962… ≠ 2.17038… (ND ≠ NE) <strong><em>(R1)</em>(ft)</strong></p>
<p>(hence Farmer Brown is incorrect)</p>
<p><strong>Note:</strong> Do not award <strong><em>(M0)(A0)(R1)</em>(ft)</strong>. Award <em><strong>(M0)(A0)(R0)</strong></em> for a correct conclusion without any working seen.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(EM<sup>2</sup> =) 1.29409…<sup>2</sup> + (7 − 4.82962…)<sup>2</sup> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their correct substitution into Pythagoras theorem.</p>
<p><strong>OR</strong></p>
<p>(EM<sup>2</sup> =) 5<sup>2</sup> + 7<sup>2</sup> − 2 × 5 × 7 × cos 15 <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into cosine rule formula.</p>
<p>(EM =) 2.53(m) (2.52689...(m)) <strong><em>(A1)(</em>ft) <em>(G2)</em>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from parts (c), (d) and (e).</p>
<p>(Total length =) 2.52689… + 3.71084… + 1.29409… +10 + 7 <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for adding their EM, their parts (c) and (d), and 10 and 7.</p>
<p>= 24.5 (m) (24.5318… (m)) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (G4)</strong></em></p>
<p><strong>Note:</strong> Follow through from parts (c) and (d).</p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">A parcel is in the shape of a rectangular prism, as shown in the diagram. It has a length \(l\) cm, width \(w\) cm and height of \(20\) cm.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The total volume of the parcel is \(3000{\text{ c}}{{\text{m}}^3}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Express the volume of the parcel in terms of \(l\) and \(w\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that \(l = \frac{{150}}{w}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The parcel is tied up using a length of string that fits <strong>exactly </strong>around the parcel, as shown in the following diagram.</span></p>
<p><span><br><img src="images/Schermafbeelding_2014-09-02_om_11.55.29_2.png" alt><br></span></p>
<p><span>Show that the length of string, \(S\) cm, required to tie up the parcel can be written as</span></p>
<p><span>\[S = 40 + 4w + \frac{{300}}{w},{\text{ }}0 < w \leqslant 20.\]</span></p>
<p><span> </span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The parcel is tied up using a length of string that fits <strong>exactly </strong>around the parcel, as shown in the following diagram.</span></p>
<p><span><br><img src="images/Schermafbeelding_2014-09-02_om_11.55.29_4.png" alt><br></span></p>
<p><span>Draw the graph of \(S\) for \(0 < w \leqslant 20\) and \(0 < S \leqslant 500\), clearly showing the local minimum point. Use a scale of \(2\) cm to represent \(5\) units on the horizontal axis \(w\)<em> </em>(cm), and a scale of \(2\) cm to represent \(100\) units on the vertical axis \(S\) (cm).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The parcel is tied up using a length of string that fits <strong>exactly </strong>around the parcel, as shown in the following diagram.</span></p>
<p><span><br><img src="images/Schermafbeelding_2014-09-02_om_11.55.29_5.png" alt><br></span></p>
<p><span>Find \(\frac{{{\text{d}}S}}{{{\text{d}}w}}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The parcel is tied up using a length of string that fits <strong>exactly </strong>around the parcel, as shown in the following diagram.</span></p>
<p><span><br><img src="images/Schermafbeelding_2014-09-02_om_11.55.29_3.png" alt><br></span></p>
<p><span>Find the value of \(w\) for which \(S\) is a minimum.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The parcel is tied up using a length of string that fits <strong>exactly </strong>around the parcel, as shown in the following diagram.</span></p>
<p><span><br><img src="images/Schermafbeelding_2014-09-02_om_11.55.29.png" alt><br></span></p>
<p><span>Write down the value, \(l\), of the parcel for which the length of string is a minimum.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The parcel is tied up using a length of string that fits <strong>exactly </strong>around the parcel, as shown in the following diagram.</span></p>
<p><span><br><img src="images/Schermafbeelding_2014-09-02_om_11.55.29_1.png" alt><br></span></p>
<p><span>Find the minimum length of string required to tie up the parcel.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(20lw\) <strong>OR</strong> \(V = 20lw\) <strong><em>(A1)</em></strong></span></p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(3000 = 20lw\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for equating their answer to part (a) to \(3000\).</span></p>
<p> </p>
<p><span>\(l = \frac{{3000}}{{20w}}\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for rearranging equation to make \(l\) subject of the formula. The above equation must be seen to award <strong><em>(M1)</em></strong>.</span></p>
<p> </p>
<p><span><strong>OR</strong></span></p>
<p><span>\(150 = lw\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for division by \(20\) on both sides. The above equation must be seen to award <strong><em>(M1)</em></strong>.</span></p>
<p> </p>
<p><span>\(l = \frac{{150}}{w}\) <strong><em>(AG)</em></strong></span></p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(S = 2l + 4w + 2(20)\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for setting up a correct expression for \(S\).</span></p>
<p> </p>
<p><span>\(2\left( {\frac{{150}}{w}} \right) + 4w + 2(20)\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into the expression for \(S\). The above expression must be seen to award <strong><em>(M1)</em></strong>.</span></p>
<p> </p>
<p><span>\( = 40 + 4w + \frac{{300}}{w}\) <strong><em>(AG)</em></strong></span></p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span><span><strong><br><img src="images/curvy.jpg" alt> </strong> <strong><em>(A1)(A1)(A1)(A1)</em></strong></span></span></span></p>
<p><span><strong><em> </em></strong></span></p>
<p><span><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for correct scales, window and labels on axes, <strong><em>(A1) </em></strong>for approximately correct shape, <strong><em>(A1) </em></strong>for minimum point in approximately correct position, <strong><em>(A1) </em></strong>for asymptotic behaviour at \(w = 0\).</span></p>
<p><span> Axes must be drawn with a ruler and labeled \(w\) and \(S\)<em>.</em></span></p>
<p><span> For a smooth curve (with approximately correct shape) there should be <strong>one </strong>continuous thin line, no part of which is straight and no (one-to-many) mappings of \(w\).</span></p>
<p><span> The \(S\)-axis must be an asymptote. The curve must not touch the \(S\)-axis nor must the curve approach the asymptote then deviate away later.</span></p>
<p> </p>
<p><span><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(4 - \frac{{300}}{{{w^2}}}\) <strong><em>(A1)(A1)(A1)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for \(4\), <strong><em>(A1) </em></strong>for \(-300\), <strong><em>(A1) </em></strong>for \(\frac{1}{{{w^2}}}\) or \({w^{ - 2}}\). If extra terms present, award at most <strong><em>(A1)(A1)(A0)</em></strong><em>.</em></span></p>
<p><span><em> </em></span></p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(4 - \frac{{300}}{{{w^2}}} = 0\) <strong>OR</strong> \(\frac{{300}}{{{w^2}}} = 4\) <strong>OR</strong> \(\frac{{{\text{d}}S}}{{{\text{d}}w}} = 0\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for equating their derivative to zero.</span></p>
<p> </p>
<p><span>\(w = 8.66{\text{ }}\left( {\sqrt {75} ,{\text{ 8.66025}} \ldots } \right)\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Follow through from their answer to part (e).</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(17.3 \left( {\frac{{150}}{{\sqrt {75} }},{\text{ 17.3205}} \ldots } \right)\) <strong><em>(A1)</em>(ft)</strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Follow through from their answer to part (f).</span></p>
<p> </p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(40 + 4\sqrt {75} + \frac{{300}}{{\sqrt {75} }}\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substitution of their answer to part (f) into the expression for \(S\).</span></p>
<p> </p>
<p><span>\( = 110{\text{ (cm) }}\left( {40 + 40\sqrt 3 ,{\text{ 109.282}} \ldots } \right)\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Do not accept \(109\).</span></p>
<p><span> Follow through from their answers to parts (f) and (g).</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">ABC is a triangular field on horizontal ground. The lengths of AB and AC are 70 m and 50 m respectively. The size of angle BCA is 78°.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; min-height: 25px; text-align: center; margin: 0px;"><br><img src="images/Schermafbeelding_2014-09-20_om_14.52.16.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the size of angle \(ABC\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the area of the triangular field.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>\({\text{M}}\) is the midpoint of \({\text{AC}}\).</span></p>
<p><span>Find the length of \({\text{BM}}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A vertical mobile phone mast, \({\text{TB}}\), is built next to the field with its base at \({\text{B}}\). The angle of elevation of \({\text{T}}\) from \({\text{M}}\) is \(63.4^\circ \). \({\text{N}}\) is the midpoint of the mast.</span></p>
<p><br><span><img src="images/Schermafbeelding_2014-09-21_om_08.02.34.png" alt></span></p>
<p> </p>
<p><span>Calculate the angle of elevation of \({\text{N}}\) from \({\text{M}}\).</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{70}}{{\sin 78}} = \frac{{50}}{{\sin {\rm{A\hat BC}}}}\) <strong><em>(M1)(A1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substituted sine rule, <strong><em>(A1) </em></strong>for correct substitution.</span></p>
<p> </p>
<p><span>\({\rm{A\hat BC}} = 44.3^\circ \) (\(44.3209...\)) <strong><em>(A1)(G3)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>If radians are used the answer is \(0.375918...\), award at most <strong><em>(M1)(A1)(A0)</em></strong>.</span></p>
<p> </p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{area }}\Delta {\text{ABC}} = \frac{1}{2} \times 70 \times 50 \times \sin (57.6790 \ldots )\) <em><strong>(A1)(M1)(A1)</strong></em><strong>(ft)</strong><br></span> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(A1)</em>(ft) </strong>for their \(57.6790…\) seen, <strong><em>(M1) </em></strong>for substituted area formula, <strong><em>(A1)</em>(ft) </strong>for correct substitution.</span></p>
<p><span> Follow through from part (a).</span></p>
<p> </p>
<p><span>\( = 1480{\text{ }}{{\text{m}}^2}\) \((1478.86 \ldots )\) <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>The answer is \(1480{\text{ }}{{\text{m}}^2}\), units are required. \(1479.20…\) if 3 sf used.</span></p>
<p><span> If radians are used the answer is \(1554.11 \ldots {{\text{m}}^2}\), award <strong><em>(A1)</em>(ft)<em>(M1)(A1)</em>(ft)<em>(A1)</em>(ft)<em>(G3)</em></strong>.</span></p>
<p> </p>
<p><span><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{B}}{{\text{M}}^2} = {70^2} + {25^2} - 2 \times 70 \times 25 \times \cos (57.6790 \ldots )\) <strong><em>(M1)(A1)(ft)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes:</strong> Award <strong><em>(M1) </em></strong>for substituted cosine rule, <strong><em>(A1)</em>(ft) </strong>for correct substitution. Follow through from their angle in part (b).</span></p>
<p> </p>
<p><span>\({\text{BM}} = 60.4{\text{ (m)}}\) \((60.4457 \ldots )\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>If the 3 sf answer is used the answer is \(60.5{\text{ }}({\text{m}})\).</span></p>
<p><span> If radians are used the answer is \(62.5757… {\text{ }} ({\text{m}})\), award <strong><em>(M1)(A1)</em>(ft)<em>(A1)</em>(ft)<em>(G2)</em></strong>.</span></p>
<p> </p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\tan 63.4^\circ = \frac{{{\text{TB}}}}{{60.4457 \ldots }}\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for their correctly substituted trig equation.</span></p>
<p> </p>
<p><span>\({\text{TB}} = 120.707 \ldots \) <strong><em>(A1)</em>(ft)</strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Follow through from part (c). If 3 sf answers are used throughout, \({\text{TB}} = 120.815 \ldots \)</span></p>
<p><span>If \({\text{TB}} = 120.707 \ldots \) is seen without working, award <strong><em>(A2)</em></strong>.</span></p>
<p> </p>
<p><span>\(\tan {\rm{N\hat MB = }}\frac{{\left( {\frac{{120.707 \ldots }}{2}} \right)}}{{60.4457 \ldots }}\) <strong><em>(A1)</em>(ft)<em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(A1)</em>(ft) </strong>for their \({\text{TB}}\) divided by \(2\) seen, <strong><em>(M1) </em></strong>for their correctly substituted trig equation.</span></p>
<p><span> Follow through from part (c) and <strong>within part (d)</strong>.</span></p>
<p> </p>
<p><span>\({\rm{N\hat MB = 45.0^\circ }}\) \({\text{(44.9563}} \ldots {\text{)}}\) <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes:</strong> If 3 sf are used throughout, answer is \(45^\circ \).</span></p>
<p><span> If radians are used the answer is \(0.308958…\), and if full working is shown, award at most <strong><em>(M1)(A1)</em>(ft)<em>(A1)</em>(ft)<em>(M1)(A0)</em></strong>.</span></p>
<p><span> If no working is shown for radians answer, award <strong><em>(G2)</em></strong>.</span></p>
<p> </p>
<p><span><strong>OR</strong></span></p>
<p> </p>
<p><span>\(\tan {\rm{N\hat MB}} = \frac{{{\text{NB}}}}{{{\text{BM}}}}\) <strong><em>(M1)</em></strong></span></p>
<p><span>\(\tan 63.4^\circ = \frac{{2 \times {\text{NB}}}}{{{\text{BM}}}}\) <strong><em>(A1)(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for \(2 \times {\text{NB}}\) seen.</span></p>
<p> </p>
<p><span>\(\tan {\rm{N\hat MB}} = \frac{1}{2}\tan 63.4^\circ \) <strong><em>(M1)</em></strong></span></p>
<p><span>\({\rm{N\hat MB}} = 45.0^\circ \) \((44.9563 \ldots )\) <strong><em>(A1)(G3)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes:</strong> If radians are used the answer is \(0.308958…\), and if full working is shown, award at most <strong><em>(M1)(A1)(M1)(M1)(A0)</em></strong>. If no working is shown for radians answer, award <strong><em>(G2)</em></strong>.</span></p>
<p> </p>
<p><span><strong><em>[5 marks]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A water container is made in the shape of a cylinder with internal height \(h\) cm and internal base radius \(r\) cm.</p>
<p class="p2" style="text-align: center;"><img src="images/Schermafbeelding_2017-03-07_om_08.31.01.png" alt="N16/5/MATSD/SP2/ENG/TZ0/06"></p>
<p class="p1">The water container has no top. The inner surfaces of the container are to be coated with a water-resistant material.</p>
</div>
<div class="specification">
<p class="p1">The volume of the water container is \(0.5{\text{ }}{{\text{m}}^3}\).</p>
</div>
<div class="specification">
<p class="p1">The water container is designed so that the area to be coated is minimized.</p>
</div>
<div class="specification">
<p class="p1">One can of water-resistant material coats a surface area of \(2000{\text{ c}}{{\text{m}}^2}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down a formula for \(A\), <span class="s1">the surface area to be coated.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Express this volume in \({\text{c}}{{\text{m}}^3}\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">Write down, in terms of \(r\) </span>and \(h\), an equation for the volume of this water container.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that \(A = \pi {r^2}\frac{{1\,000\,000}}{r}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that \(A = \pi {r^2} + \frac{{1\,000\,000}}{r}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find \(\frac{{{\text{d}}A}}{{{\text{d}}r}}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Using your answer to part (e), find the value of \(r\) <span class="s1">which minimizes \(A\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of this minimum area.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the least number of cans of water-resistant material that will coat the area in <span class="s1">part (g).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\((A = ){\text{ }}\pi {r^2} + 2\pi rh\) </span><strong><em>(A1)(A1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1) </em></strong>for either \(\pi {r^2}\) <strong>OR</strong> \(2\pi rh\) seen. Award <strong><em>(A1) </em></strong>for two correct terms added together.</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(500\,000\) </span><strong><em>(A1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: <span class="Apple-converted-space"> </span></strong>Units <strong>not </strong>required.</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(500\,000 = \pi {r^2}h\) </span><strong><em>(A1)</em>(ft)</strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1)</em>(ft) </strong>for \(\pi {r^2}h\) equating to their part (b).</p>
<p class="p1"><span class="s1">Do not accept </span>unless \(V = \pi {r^2}h\) is explicitly defined as their part (b).</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(A = \pi {r^2} + 2\pi r\left( {\frac{{500\,000}}{{\pi {r^2}}}} \right)\) </span><strong><em>(A1)</em>(ft)<em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1)</em>(ft) </strong>for their \({\frac{{500\,000}}{{\pi {r^2}}}}\) seen.</p>
<p class="p1">Award <strong><em>(M1) </em></strong>for correctly substituting <strong>only</strong> \({\frac{{500\,000}}{{\pi {r^2}}}}\) into a <strong>correct </strong>part (a).</p>
<p class="p1">Award <strong><em>(A1)</em>(ft)<em>(M1) </em></strong>for rearranging part (c) to \(\pi rh = \frac{{500\,000}}{r}\) and substituting for \(\pi rh\) <span class="s1">in expression for \(A\).</span></p>
<p class="p3"> </p>
<p class="p4"><span class="Apple-converted-space">\(A = \pi {r^2} + \frac{{1\,000\,000}}{r}\) </span><span class="s2"><strong><em>(AG)</em></strong></span></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: <span class="Apple-converted-space"> </span></strong>The conclusion, \(A = \pi {r^2} + \frac{{1\,000\,000}}{r}\), must be consistent with their working seen for the <strong><em>(A1) </em></strong>to be awarded.</p>
<p class="p4">Accept \({10^6}\) as equivalent to \({1\,000\,000}\).</p>
<p class="p3"> </p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(A = \pi {r^2} + 2\pi r\left( {\frac{{500\,000}}{{\pi {r^2}}}} \right)\) </span><strong><em>(A1)</em>(ft)<em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1)</em>(ft) </strong>for their \({\frac{{500\,000}}{{\pi {r^2}}}}\) seen.</p>
<p class="p1">Award <strong><em>(M1) </em></strong>for correctly substituting <strong>only</strong> \({\frac{{500\,000}}{{\pi {r^2}}}}\) into a <strong>correct </strong>part (a).</p>
<p class="p1">Award <strong><em>(A1)</em>(ft)<em>(M1) </em></strong>for rearranging part (c) to \(\pi rh = \frac{{500\,000}}{r}\) and substituting for \(\pi rh\) <span class="s1">in expression for \(A\).</span></p>
<p class="p3"> </p>
<p class="p4"><span class="Apple-converted-space">\(A = \pi {r^2} + \frac{{1\,000\,000}}{r}\) </span><span class="s2"><strong><em>(AG)</em></strong></span></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: <span class="Apple-converted-space"> </span></strong>The conclusion, \(A = \pi {r^2} + \frac{{1\,000\,000}}{r}\), must be consistent with their working seen for the <strong><em>(A1) </em></strong>to be awarded.</p>
<p class="p4">Accept \({10^6}\) as equivalent to \({1\,000\,000}\).</p>
<p class="p3"> </p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(2\pi r - \frac{{{\text{1}}\,{\text{000}}\,{\text{000}}}}{{{r^2}}}\) </span><strong><em>(A1)(A1)(A1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1) </em></strong>for \(2\pi r\), <strong><em>(A1) </em></strong>for \(\frac{1}{{{r^2}}}\) or \({r^{ - 2}}\), <strong><em>(A1) </em></strong>for \( - {\text{1}}\,{\text{000}}\,{\text{000}}\).</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(2\pi r - \frac{{1\,000\,000}}{{{r^2}}} = 0\) </span><strong><em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for equating their part (e) to zero.</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\({r^3} = \frac{{1\,000\,000}}{{2\pi }}\) <strong>OR</strong> \(r = \sqrt[3]{{\frac{{1\,000\,000}}{{2\pi }}}}\) </span><strong><em>(M1)</em></strong></p>
<p class="p3"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for isolating \(r\).</p>
<p class="p2"> </p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">sketch of derivative function <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">with its zero indicated <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\((r = ){\text{ }}54.2{\text{ }}({\text{cm}}){\text{ }}(54.1926 \ldots )\) </span><strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(\pi {(54.1926 \ldots )^2} + \frac{{1\,000\,000}}{{(54.1926 \ldots )}}\) </span><strong><em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for correct substitution of their part (f) into the given equation.</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\( = 27\,700{\text{ }}({\text{c}}{{\text{m}}^2}){\text{ }}(27\,679.0 \ldots )\) </span><strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(\frac{{27\,679.0 \ldots }}{{2000}}\) </span><strong><em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for dividing their part (g) by <span class="s1">2000</span>.</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\( = 13.8395 \ldots \) </span><strong><em>(A1)</em>(ft)</strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: <span class="Apple-converted-space"> </span></strong>Follow through from part (g).</p>
<p class="p2"> </p>
<p class="p1"><span class="s1">14 </span>(cans) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: <span class="Apple-converted-space"> </span></strong>Final <strong><em>(A1) </em></strong>awarded for rounding up their \(13.8395 \ldots \) to the next integer.</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The line \({L_1}\) has equation \(2y - x - 7 = 0\) and is shown on the diagram.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2017-03-07_om_07.59.34.png" alt="N16/5/MATSD/SP2/ENG/TZ0/03"></p>
<p class="p1" style="text-align: left;">The point <span class="s1">A </span>has coordinates \((1,{\text{ }}4)\).</p>
</div>
<div class="specification">
<p class="p1">The point <span class="s1">C </span>has coordinates \((5,{\text{ }}12)\). <span class="s1">M </span>is the midpoint of <span class="s1">AC</span>.</p>
</div>
<div class="specification">
<p class="p1">The straight line, \({L_2}\), is perpendicular to <span class="s1">AC </span>and passes through <span class="s1">M</span>.</p>
</div>
<div class="specification">
<p class="p1">The point <span class="s1">D </span>is the intersection of \({L_1}\) and \({L_2}\).</p>
</div>
<div class="specification">
<p class="p1">The length of <span class="s1">MD </span>is \(\frac{{\sqrt {45} }}{2}\).</p>
</div>
<div class="specification">
<p class="p1">The point <span class="s1">B </span>is such that <span class="s1">ABCD </span>is a rhombus.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">Show that </span><span class="s2">A </span>lies on \({L_1}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the coordinates of <span class="s1">M</span><span class="s2">.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the length of <span class="s1">AC</span><span class="s2">.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that the equation of \({L_2}\) <span class="s1">is \(2y + x - 19 = 0\).</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the coordinates of <span class="s1">D</span><span class="s2">.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">Write down the length of </span><span class="s2">MD </span>correct to five significant figures.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the area of <span class="s1">ABCD</span><span class="s2">.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(2 \times 4 - 1 - 7 = 0\) (or equivalent) <span class="Apple-converted-space"> </span><strong><em>(R1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>For <strong><em>(R1) </em></strong>accept substitution of \(x = 1\) or \(y = 4\) into the equation followed by a confirmation that \(y = 4\) or \(x = 1\).</p>
<p class="p2"> </p>
<p class="p1">(since the point satisfies the equation of the line,) <span class="s1">A </span>lies on \({L_1}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Do not award <strong><em>(A1)(R0)</em></strong>.</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\frac{{1 + 5}}{2}\) <strong>OR</strong> \(\frac{{4 + 12}}{2}\) seen <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for at least one correct substitution into the midpoint formula.</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\((3,{\text{ }}8)\) </span><strong><em>(A1)(G2)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: <span class="Apple-converted-space"> </span></strong>Accept \(x = 3,{\text{ }}y = 8\).</p>
<p class="p1">Award <strong><em>(M1)(A0) </em></strong>for \(\left( {\frac{{1 + 5}}{2},{\text{ }}\frac{{4 + 12}}{2}} \right)\).</p>
<p class="p1">Award <strong><em>(G1) </em></strong>for each correct coordinate seen without working.</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(\sqrt {{{(5 - 1)}^2} + {{(12 - 4)}^2}} \) </span><strong><em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for a correct substitution into distance between two points formula.</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\( = 8.94{\text{ }}\left( {4\sqrt 5 ,{\text{ }}\sqrt {80} ,{\text{ }}8.94427 \ldots } \right)\) </span><strong><em>(A1)(G2)</em></strong></p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">gradient of \({\text{AC}} = \frac{{12 - 4}}{{5 - 1}}\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for correct substitution into gradient formula.</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\( = 2\) </span><strong><em>(A1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1)(A1) </em></strong>for gradient of \({\text{AC}} = 2\) with or without working</p>
<p class="p2"> </p>
<p class="p1">gradient of the normal \( = - \frac{1}{2}\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for the negative reciprocal of their gradient of <span class="s1">AC</span>.</p>
<p class="p2"> </p>
<p class="p1">\(y - 8 = - \frac{1}{2}(x - 3)\) <strong>OR</strong> \(8 = - \frac{1}{2}(3) + c\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for substitution of their point and gradient into straight line formula. This <strong><em>(M1) </em></strong>can <strong>only </strong>be awarded where \( - \frac{1}{2}\) (gradient) is correctly determined as the gradient of the normal to <span class="s1">AC</span>.</p>
<p class="p2"> </p>
<p class="p1">\(2y - 16 = - (x - 3)\) <strong>OR</strong> \( - 2y + 16 = x - 3\) <strong>OR</strong> \(2y = - x + 19\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1) </em></strong>for correctly removing fractions, <strong>but only </strong>if their equation is equivalent to the given equation.</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\(2y + x - 19 = 0\) </span><strong><em>(AG)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>The conclusion \(2y + x - 19 = 0\) must be seen for the <strong><em>(A1) </em></strong>to be awarded.</p>
<p class="p1">Where the candidate has <strong>shown </strong>the gradient of the normal to \({\text{AC}} = - 0.5\), award <strong><em>(M1) </em></strong>for \(2(8) + 3 - 19 = 0\) and <strong><em>(A1) </em></strong>for (therefore) \(2y + x - 19 = 0\).</p>
<p class="p1">Simply substituting \((3,{\text{ }}8)\) into the equation of \({L_2}\) with no other prior working, earns no marks.</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\((6,{\text{ }}6.5)\) </span><strong><em>(A1)(A1)(G2)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1) </em></strong>for <span class="s1">6</span>, <strong><em>(A1) </em></strong>for <span class="s1">6.5</span>. Award a maximum of <strong><em>(A1)(A0) </em></strong>if answers are not given as a coordinate pair. Accept \(x = 6,{\text{ }}y = 6.5\).</p>
<p class="p1">Award <strong><em>(M1)(A0) </em></strong>for an attempt to solve the two simultaneous equations \(2y - x - 7 = 0\) and \(2y + x - 19 = 0\) algebraically, leading to at least one incorrect or missing coordinate.</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">3.3541 <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Answer <span>must</span> be to <span class="s2">5 </span>significant figures.</p>
<p class="p2"> </p>
<p class="p3"><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="s1">\(2 \times \frac{1}{2} \times \sqrt {80} \times \frac{{\sqrt {45} }}{2}\) <span class="Apple-converted-space"> </span></span><strong><em>(M1)(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for correct substitution into area of triangle formula.</p>
<p class="p1">If their triangle is a quarter of the rhombus then award <strong><em>(M1) </em></strong>for multiplying their triangle by <span class="s2">4</span>.</p>
<p class="p1">If their triangle is a half of the rhombus then award <strong><em>(M1) </em></strong>for multiplying their triangle by <span class="s2">2</span>.</p>
<p class="p2"> </p>
<p class="p1"><strong>OR</strong></p>
<p class="p1"><span class="Apple-converted-space">\(\frac{1}{2} \times \sqrt {80} \times \sqrt {45} \) </span><strong><em>(M1)(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for doubling <span class="s2">MD </span>to get the diagonal <span class="s2">BD</span>, <strong><em>(M1) </em></strong>for correct substitution into the area of a rhombus formula.</p>
<p class="p1">Award <strong><em>(M1)(M1) </em></strong>for \(\sqrt {80} \times \) their (f).</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\( = 30\) </span><strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: <span class="Apple-converted-space"> </span></strong>Follow through from parts (c) and (f).</p>
<p class="p1">\(8.94 \times 3.3541 = 29.9856 \ldots \)</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Jenny has a circular cylinder with a lid. The cylinder has height 39 <strong>cm</strong> and diameter 65 <strong>mm</strong>.</span></p>
</div>
<div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">An old tower (BT) leans at 10° away from the vertical (represented by line TG).</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The base of the tower is at B so that \({\text{M}}\hat {\rm B}{\text{T}} = 100^\circ \).</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Leonardo stands at L on flat ground 120 m away from B in the direction of the lean.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">He measures the angle between the ground and the top of the tower T to be \({\text{B}}\hat {\rm L}{\text{T}} = 26.5^\circ \).</span></p>
<p> </p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the volume of the cylinder<strong> in cm<sup>3</sup></strong>. Give your answer correct to <strong>two</strong> decimal places.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The cylinder is used for storing tennis balls. Each ball has a <strong>radius</strong> of 3.25 cm.</span></p>
<p><span>Calculate how many balls Jenny can fit in the cylinder if it is filled to the top.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Jenny fills the cylinder with the number of balls found in part (b) and puts the lid on. Calculate the volume of air inside the cylinder in the spaces between the tennis balls.</span></p>
<p><span>(ii) Convert your answer to (c) (i) into cubic metres.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">i.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Find the value of angle \({\text{B}}\hat {\rm T}{\text{L}}\).</span></p>
<p><span>(ii) Use triangle BTL to calculate the sloping distance BT from the base,</span> <span>B to the top, T of the tower.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the vertical height TG of the top of the tower.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Leonardo now walks to point M, a distance 200 m from B on the opposite side of the tower. Calculate the distance from M to the top of the tower at T.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">ii.c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\pi \times 3.25^2 \times 39\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span>(= 1294.1398)</span></p>
<p><span>Answer 1294.14 (cm<sup>3</sup>)(2dp) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><em><strong>(UP)</strong> not applicable in this part due to wording of question.</em></span><em> <span><strong>(M1)</strong> is for substituting appropriate numbers from the problem</span> <span>into the correct formula, even if the units are mixed up. <strong>(A1)</strong></span> <span>is for correct substitutions or correct answer with more than</span> <span>2dp in cubic centimetres seen.</span> <span>Award <strong>(G1)</strong> for answer to > 2dp with no working and no</span> <span>attempt to correct to 2dp.</span> <span>Award <strong>(M1)(A0)(A1)(ft)</strong> for </span></em><span>\(\pi \times {32.5^2} \times 39{\text{ c}}{{\text{m}}^3}\)</span><span> (= 129413.9824) = 129413.98</span></p>
<p><span><em>Use of \(\pi = \frac{22}{7}\) </em><strong>or</strong> 3.142<em> etc is premature rounding and is</em></span><em> <span>awarded at most <strong>(M1)(A1)(A0)</strong> or <strong>(M1)(A0)(A1)(ft)</strong></span> <span>depending on whether the intermediate value is seen or not. </span><span>For all other incorrect substitutions, award <strong>(M1)(A0)</strong> and only</span> <span>follow through the 2 dp correction if the intermediate answer</span> <span>to more decimal places is seen.</span> <span>Answer given as a multiple of </span></em><span>\(\pi\)</span><em><span> is awarded at most</span> <strong><span>(M1)(A1)(A0).</span></strong> <span>As usual, an <strong>unsubstituted</strong> formula followed by correct answer</span> <span>only receives the G marks.</span></em></p>
<p><em><span><strong>[3 marks]</strong><br></span></em></p>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>39/6.5 = 6 <em><strong>(A1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>Unit penalty <strong>(UP)</strong> is applicable where indicated in the left hand column.</em><br></span></p>
<p><span><em> </em></span></p>
<p><span><em><strong>(UP)</strong> </em>(i) Volume of one ball is \(\frac{4}{3} \pi \times 3.25^3 {\text{ cm}}^3\) <em><strong>(M1)</strong></em></span></p>
<p><span>\({\text{Volume of air}} = \pi \times {3.25^2} \times 39 - 6 \times \frac{4}{3}\pi \times {3.25^3} = 431{\text{ c}}{{\text{m}}^3}\)</span><span> <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><em><span>Award first <strong>(M1)</strong> for substituted volume of sphere formula</span> <span>or for numerical value of sphere volume seen (143.79… or</span> <span>45.77… </span></em><span>\( \times \pi\)</span><em><span>).</span> <span>Award second <strong>(M1)</strong> for subtracting candidate’s sphere</span> <span>volume multiplied by their answer to (b).</span> <span>Follow through from parts (a) and (b) only, but negative </span><span>or zero answer is always awarded <strong>(A0)</strong></span></em><span><strong>(ft)</strong></span></p>
<p><br><span><em><strong>(UP)</strong></em> (ii) 0.000431m<sup>3</sup> or 4.31×10<sup>−4</sup></span><span> m</span><span><sup>3</sup> <em><strong>(A1)</strong></em><strong>(ft)</strong><br></span></p>
<p><span><strong> </strong></span></p>
<p><span><strong><em>[4 marks]</em><br></strong></span></p>
<div class="question_part_label">i.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>Unit penalty <strong>(UP)</strong> is applicable where indicated in the left hand column.</em></span></p>
<p><span>(i) \({\text{Angle B}}\widehat {\text{T}}{\text{L}} = 180 - 80 - 26.5\)</span><span> or \(180 - 90 - 26.5 - 10\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(= 73.5^\circ\) <em><strong>(A1)(G2)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span>(ii) \(\frac{{BT}}{{\sin (26.5^\circ )}} = \frac{{120}}{{\sin (73.5^\circ )}}\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><em><strong>(UP)</strong></em> BT = 55.8 m (3sf) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong> </strong></span></p>
<p><span><strong><em>[5 marks]</em><br></strong></span></p>
<p><span><strong><em><br></em></strong><em>If radian mode has been used throughout the question, award <strong>(A0)</strong> to the first incorrect answer then follow through, but</em><br><em>negative lengths are always awarded <strong>(A0)(ft)</strong>.</em></span></p>
<p><em><span>The answers are (all 3sf)</span></em></p>
<p><em><span>(ii)(a) – 124 m <strong>(A0)</strong></span></em><strong><span>(ft)</span></strong><span></span></p>
<p><em><span>(ii)(b) 123 m </span><span><strong>(A0)</strong></span></em><span></span><span></span><span></span></p>
<p><em><span>(ii)(c) 313 m </span><span><strong>(A0)</strong></span></em><span></span><span></span></p>
<p><span><em>If radian mode has been used throughout the question, award <strong>(A0)</strong> to the first incorrect answer then follow through, but negative lengths are always awarded <strong>(A0)</strong></em><strong>(ft)</strong></span></p>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>Unit penalty <strong>(UP)</strong> is applicable where indicated in the left hand column.</em></span></p>
<p><span>TG = 55.8sin(80°) or 55.8cos(10°) <em><strong>(M1)</strong></em></span></p>
<p><span><em><strong>(UP) =</strong></em> 55.0 m (3sf) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><em>Apply <strong>(AP)</strong> if 0 missing</em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span><span><strong><br></strong></span></p>
<p><span><strong><em><br></em></strong><em>If radian mode has been used throughout the question, award <strong>(A0)</strong> to the first incorrect answer then follow through, but</em><br><em>negative lengths are always awarded <strong>(A0)(ft)</strong>.</em></span></p>
<p><em><span>The answers are (all 3sf)</span></em></p>
<p><em><span>(ii)(a) – 124 m <strong>(A0)</strong></span></em><strong><span>(ft)</span></strong><span></span></p>
<p><em><span>(ii)(b) 123 m </span><span><strong>(A0)</strong></span></em><span></span><span></span><span></span></p>
<p><em><span>(ii)(c) 313 m </span><span><strong>(A0)</strong></span></em><span></span><span></span></p>
<p><span><em>If radian mode has been used throughout the question, award <strong>(A0)</strong> to the first incorrect answer then follow through, but negative lengths are always awarded <strong>(A0)</strong></em><strong>(ft)</strong></span></p>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>Unit penalty <strong>(UP)</strong> is applicable where indicated in the left hand column.</em></span></p>
<p><span>\({\text{MT}}^2 = 200^2 + 55.8^2 - 2 \times 200 \times 55.8 \times \cos(100^\circ)\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><em><strong>(UP)</strong></em> MT = 217 m (3sf) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><em><span>Follow through only from part (ii)(a)(ii).</span> <span>Award marks at discretion for any valid alternative method.</span></em></p>
<p><em><span><strong>[3 marks]</strong></span></em><em><span><strong><span><strong><span><strong><br></strong></span></strong></span></strong></span></em></p>
<p><span><strong><em><br></em></strong><em>If radian mode has been used throughout the question, award <strong>(A0)</strong> to the first incorrect answer then follow through, but</em><br><em>negative lengths are always awarded <strong>(A0)(ft)</strong>.</em></span></p>
<p><em><span>The answers are (all 3sf)</span></em></p>
<p><em><span>(ii)(a) – 124 m <strong>(A0)</strong></span></em><strong><span>(ft)</span></strong><span></span></p>
<p><em><span>(ii)(b) 123 m </span><span><strong>(A0)</strong></span></em><span></span><span></span><span></span></p>
<p><em><span>(ii)(c) 313 m </span><span><strong>(A0)</strong></span></em><span></span><span></span></p>
<p><span><em>If radian mode has been used throughout the question, award <strong>(A0)</strong> to the first incorrect answer then follow through, but negative lengths are always awarded <strong>(A0)</strong></em><strong>(ft)</strong></span></p>
<p></p>
<div class="question_part_label">ii.c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">(i) Many candidates incurred the new one-off unit penalty here. Too many ignored the call for two decimal places and some extrapolated that instruction to later parts (which was clearly not intended). There was the predictable confusion of using radius instead of diameter. Another common error was to divide the cylinder volume by that of the ball, to decide how many would fit. Some follow-through was allowed later from this error, however, this led to zero or negligible air volume, which was clearly ridiculous.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Choice and use of the formulae for volumes was often competent but the conversion to cubic metres was very badly done. Almost no correct answers were seen at all.</span></p>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">(i) Many candidates incurred the new one-off unit penalty here. Too many ignored the call for two decimal places and some extrapolated that instruction to later parts (which was clearly not intended). There was the predictable confusion of using radius instead of diameter. Another common error was to divide the cylinder volume by that of the ball, to decide how many would fit. Some follow-through was allowed later from this error, however, this led to zero or negligible air volume, which was clearly ridiculous.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Choice and use of the formulae for volumes was often competent but the conversion to cubic metres was very badly done. Almost no correct answers were seen at all.</span></p>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">(i) Many candidates incurred the new one-off unit penalty here. Too many ignored the call for two decimal places and some extrapolated that instruction to later parts (which was clearly not intended). There was the predictable confusion of using radius instead of diameter. Another common error was to divide the cylinder volume by that of the ball, to decide how many would fit. Some follow-through was allowed later from this error, however, this led to zero or negligible air volume, which was clearly ridiculous.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Choice and use of the formulae for volumes was often competent but the conversion to cubic metres was very badly done. Almost no correct answers were seen at all.</span></p>
<div class="question_part_label">i.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">(ii) Candidates were often sloppy in reading the information. In particular, despite the statement BL = 120 clearly written, many took GL as 120. Triangle TBL was often taken as right-angled. Angle BTL presented few problems, though sometimes the method was very long-winded. Candidates often managed part (a) then went awry in later parts. Many unit penalties were applied, if not already used in questions 1 or 2.</span></p>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">(ii) Candidates were often sloppy in reading the information. In particular, despite the statement BL = 120 clearly written, many took GL as 120. Triangle TBL was often taken as right-angled. Angle BTL presented few problems, though sometimes the method was very long-winded. Candidates often managed part (a) then went awry in later parts. Many unit penalties were applied, if not already used in questions 1 or 2.</span></p>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">(ii) Candidates were often sloppy in reading the information. In particular, despite the statement BL = 120 clearly written, many took GL as 120. Triangle TBL was often taken as right-angled. Angle BTL presented few problems, though sometimes the method was very long-winded. Candidates often managed part (a) then went awry in later parts. Many unit penalties were applied, if not already used in questions 1 or 2.</span></p>
<div class="question_part_label">ii.c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The graph of the function \(f(x) = \frac{{14}}{x} + x - 6\), for 1 ≤ <em>x</em> ≤ 7 is given below.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate \(f (1)\). </span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \(f ′(x)\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><strong>Use your answer to part (b)</strong> to show that the <em>x</em>-coordinate of the local minimum point of the graph of \(f\) is 3.7 correct to 2 significant figures.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the range of \(f\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Points A and B lie on the graph of \(f\). The <em>x</em>-coordinates of A and B are 1 and 7 respectively.</span></p>
<p><span>Write down the <em>y</em>-coordinate of B.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Points A and B lie on the graph of f . The <em>x</em>-coordinates of A and B are 1 and 7 respectively.<br></span></p>
<p><span>Find the gradient of the straight line passing through A and B.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>M is the midpoint of the line segment AB.</span></p>
<p><span>Write down the coordinates of M.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><em>L</em> is the tangent to the graph of the function \(y = f (x)\), at the point on the graph with the same <em>x</em>-coordinate as M.</span></p>
<p><span>Find the gradient of <em>L</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">h.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the equation of <em>L</em>. Give your answer in the form \(y = mx + c\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">i.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{14}}{{(1)}} + (1) - 6\) <em><strong>(M1)</strong></em></span><br><br></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting \(x = 1\) into \(f\).</span><br><br></p>
<p><span>\(= 9\) <em><strong>(A1)(G2)</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\( - \frac{{14}}{{{x^2}}} + 1\) <em><strong>(A3)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(-14\), <em><strong>(A1)</strong></em> for \(\frac{{14}}{{{x^2}}}\) or for \(x^{-2}\), <em><strong>(A1)</strong></em> for \(1\). </span></p>
<p><span> Award at most <em><strong>(A2)</strong></em> if any extra terms are present.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\( - \frac{{14}}{{{x^2}}} + 1 = 0\) or \(f ' (x) = 0 \) <em><strong>(M1)</strong></em><br><br></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for equating <strong>their</strong> derivative in part (b) to 0.<br><br></span></p>
<p><span>\(\frac{{14}}{{{x^2}}} = 1\)</span><span><span> or \({x^2} = 14\)</span> or equivalent <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct rearrangement of their equation.</span></p>
<p><span><br>\(x = 3.74165...(\sqrt {14})\) <em><strong>(A1)</strong></em><br></span></p>
<p><span>\(x = 3.7\) <em><strong>(AG)</strong></em></span></p>
<p><span><strong>Notes:</strong> Both the unrounded and rounded answers must be seen to award the <em><strong>(A1)</strong></em>. This is a “show that” question; appeals to their GDC are not accepted –award a maximum of <em><strong>(M1)(M0)(A0)</strong></em>. </span></p>
<p><span>Specifically, </span><span><span>\( - \frac{{14}}{{{x^2}}} + 1 = 0\)</span> followed by \(x = 3.74165..., x = 3.7\) is awarded <em><strong>(M1)(M0)(A0)</strong></em>.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(1.48 \leqslant y \leqslant 9\) <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em></span></p>
<p><span><em><strong><br><br></strong></em><strong>Note:</strong> Accept alternative notations, for example [1.48,9]. (\(x = \sqrt{14}\) leads to answer 1.48331...)</span></p>
<p><span><br><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for 1.48331…seen, accept 1.48378… from using the given answer \(x = 3.7\), <em><strong>(A1)</strong></em><strong>(ft)</strong> for their 9 from part (a) seen, <em><strong>(A1)</strong></em> for the correct notation for their interval (accept \( \leqslant y \leqslant \)</span><span> or \( \leqslant f \leqslant \)</span><span> ).<br></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>3 <em><strong>(A1)</strong></em> </span></p>
<p><br><span><strong>Note:</strong> Do not accept a coordinate pair.</span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{3 - 9}}{{7 - 1}}\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their correct substitution into the gradient formula.</span></p>
<p><br><span>\(= -1\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em> </span></p>
<p><br><span><strong>Note:</strong> Follow through from their answers to parts (a) and (e).</span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(4, 6) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Accept \(x = 4\), \(y = 6\). Award at most <em><strong>(A1)(A0)</strong></em> if parentheses not seen. </span></p>
<p><span>If coordinates reversed award <em><strong>(A0)(A1)</strong></em><strong>(ft)</strong>. </span></p>
<p><span>Follow through from their answers to parts (a) and (e).</span></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\( - \frac{{14}}{{{4^2}}} + 1\) <em><strong>(M1)</strong></em></span></p>
<p><span><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution into their gradient function. </span></p>
<p><span>Follow through from their answers to parts (b) and (g).<br></span></p>
<p><span><br>\( = \frac{1}{8}(0.125)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em><br></span></p>
<div class="question_part_label">h.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(y - 1.5 = \frac{1}{8}(x - 4)\) <em><strong>(M1)</strong></em><strong>(ft)</strong><em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting their (4, 1.5) in any straight line formula, </span></p>
<p><span><em><strong>(</strong></em></span><em><strong>M1)</strong></em><span> for substituting their gradient in any straight line formula.</span></p>
<p><br><span>\(y = \frac{x}{8} + 4\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> The form of the line has been specified in the question.</span></p>
<div class="question_part_label">i.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates were able to evaluate the function and find the derivative for \(x + 6\) but the term with the negative index was problematic. The few candidates who equated their derivative to zero at the local minimum point progressed well and showed a thorough understanding of the differential calculus. Many did not attain full marks for the range of the function, either confusing this with the statistical concept of range or using the <em>y</em>-coordinate at B. Most were able to find the gradient and midpoint of the straight line passing through A and B. The final parts were also challenging for the majority: many had difficulty finding the gradient of the tangent L, instead using the slope formula for a straight line; the most common error in part (i) was to substitute in the coordinates of midpoint M rather than the point on the curve. Greater insight into the problem would have come from using the given sketch of the curve and annotating it; it seems that many candidates do not link the algebraic nature of the differential calculus with the curve in question.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates were able to evaluate the function and find the derivative for \(x + 6\) but the term with the negative index was problematic. The few candidates who equated their derivative to zero at the local minimum point progressed well and showed a thorough understanding of the differential calculus. Many did not attain full marks for the range of the function, either confusing this with the statistical concept of range or using the <em>y</em>-coordinate at B. Most were able to find the gradient and midpoint of the straight line passing through A and B. The final parts were also challenging for the majority: many had difficulty finding the gradient of the tangent L, instead using the slope formula for a straight line; the most common error in part (i) was to substitute in the coordinates of midpoint M rather than the point on the curve. Greater insight into the problem would have come from using the given sketch of the curve and annotating it; it seems that many candidates do not link the algebraic nature of the differential calculus with the curve in question.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates were able to evaluate the function and find the derivative for \(x + 6\) but the term with the negative index was problematic. The few candidates who equated their derivative to zero at the local minimum point progressed well and showed a thorough understanding of the differential calculus. Many did not attain full marks for the range of the function, either confusing this with the statistical concept of range or using the <em>y</em>-coordinate at B. Most were able to find the gradient and midpoint of the straight line passing through A and B. The final parts were also challenging for the majority: many had difficulty finding the gradient of the tangent L, instead using the slope formula for a straight line; the most common error in part (i) was to substitute in the coordinates of midpoint M rather than the point on the curve. Greater insight into the problem would have come from using the given sketch of the curve and annotating it; it seems that many candidates do not link the algebraic nature of the differential calculus with the curve in question.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates were able to evaluate the function and find the derivative for \(x + 6\) but the term with the negative index was problematic. The few candidates who equated their derivative to zero at the local minimum point progressed well and showed a thorough understanding of the differential calculus. Many did not attain full marks for the range of the function, either confusing this with the statistical concept of range or using the <em>y</em>-coordinate at B. Most were able to find the gradient and midpoint of the straight line passing through A and B. The final parts were also challenging for the majority: many had difficulty finding the gradient of the tangent L, instead using the slope formula for a straight line; the most common error in part (i) was to substitute in the coordinates of midpoint M rather than the point on the curve. Greater insight into the problem would have come from using the given sketch of the curve and annotating it; it seems that many candidates do not link the algebraic nature of the differential calculus with the curve in question.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates were able to evaluate the function and find the derivative for \(x + 6\) but the term with the negative index was problematic. The few candidates who equated their derivative to zero at the local minimum point progressed well and showed a thorough understanding of the differential calculus. Many did not attain full marks for the range of the function, either confusing this with the statistical concept of range or using the <em>y</em>-coordinate at B. Most were able to find the gradient and midpoint of the straight line passing through A and B. The final parts were also challenging for the majority: many had difficulty finding the gradient of the tangent L, instead using the slope formula for a straight line; the most common error in part (i) was to substitute in the coordinates of midpoint M rather than the point on the curve. Greater insight into the problem would have come from using the given sketch of the curve and annotating it; it seems that many candidates do not link the algebraic nature of the differential calculus with the curve in question.</span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates were able to evaluate the function and find the derivative for \(x + 6\) but the term with the negative index was problematic. The few candidates who equated their derivative to zero at the local minimum point progressed well and showed a thorough understanding of the differential calculus. Many did not attain full marks for the range of the function, either confusing this with the statistical concept of range or using the <em>y</em>-coordinate at B. Most were able to find the gradient and midpoint of the straight line passing through A and B. The final parts were also challenging for the majority: many had difficulty finding the gradient of the tangent L, instead using the slope formula for a straight line; the most common error in part (i) was to substitute in the coordinates of midpoint M rather than the point on the curve. Greater insight into the problem would have come from using the given sketch of the curve and annotating it; it seems that many candidates do not link the algebraic nature of the differential calculus with the curve in question.</span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates were able to evaluate the function and find the derivative for \(x + 6\) but the term with the negative index was problematic. The few candidates who equated their derivative to zero at the local minimum point progressed well and showed a thorough understanding of the differential calculus. Many did not attain full marks for the range of the function, either confusing this with the statistical concept of range or using the <em>y</em>-coordinate at B. Most were able to find the gradient and midpoint of the straight line passing through A and B. The final parts were also challenging for the majority: many had difficulty finding the gradient of the tangent L, instead using the slope formula for a straight line; the most common error in part (i) was to substitute in the coordinates of midpoint M rather than the point on the curve. Greater insight into the problem would have come from using the given sketch of the curve and annotating it; it seems that many candidates do not link the algebraic nature of the differential calculus with the curve in question.</span></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates were able to evaluate the function and find the derivative for \(x + 6\) but the term with the negative index was problematic. The few candidates who equated their derivative to zero at the local minimum point progressed well and showed a thorough understanding of the differential calculus. Many did not attain full marks for the range of the function, either confusing this with the statistical concept of range or using the <em>y</em>-coordinate at B. Most were able to find the gradient and midpoint of the straight line passing through A and B. The final parts were also challenging for the majority: many had difficulty finding the gradient of the tangent L, instead using the slope formula for a straight line; the most common error in part (i) was to substitute in the coordinates of midpoint M rather than the point on the curve. Greater insight into the problem would have come from using the given sketch of the curve and annotating it; it seems that many candidates do not link the algebraic nature of the differential calculus with the curve in question.</span></p>
<div class="question_part_label">h.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates were able to evaluate the function and find the derivative for \(x + 6\) but the term with the negative index was problematic. The few candidates who equated their derivative to zero at the local minimum point progressed well and showed a thorough understanding of the differential calculus. Many did not attain full marks for the range of the function, either confusing this with the statistical concept of range or using the <em>y</em>-coordinate at B. Most were able to find the gradient and midpoint of the straight line passing through A and B. The final parts were also challenging for the majority: many had difficulty finding the gradient of the tangent L, instead using the slope formula for a straight line; the most common error in part (i) was to substitute in the coordinates of midpoint M rather than the point on the curve. Greater insight into the problem would have come from using the given sketch of the curve and annotating it; it seems that many candidates do not link the algebraic nature of the differential calculus with the curve in question.</span></p>
<div class="question_part_label">i.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">On the coordinate axes below, \({\text{D}}\) is a point on the \(y\)-axis and \({\text{E}}\) is a point on the \(x\)-axis. \({\text{O}}\) is the origin. The equation of the line \({\text{DE}}\) is \(y + \frac{1}{2}x = 4\).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the coordinates of point \({\text{E}}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>\({\text{C}}\) is a point on the line </span><span><span>\({\text{DE}}\)</span>. </span><span><span>\({\text{B}}\)</span> is a point on the \(x\)-axis such that </span><span><span>\({\text{BC}}\)</span> is parallel to the \(y\)-axis. The \(x\)-coordinate of </span><span><span>\({\text{C}}\)</span> is \(t\).</span></p>
<p><span>Show that the \(y\)-coordinate of </span><span><span>\({\text{C}}\)</span> is \(4 - \frac{1}{2}t\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>\({\text{OBCD}}\) </span>is a trapezium. The \(y\)-coordinate of point </span><span><span>\({\text{D}}\)</span> is \(4\).<br></span></p>
<p><span>Show that the area of </span><span><span><span>\({\text{OBCD}}\) </span></span>is \(4t - \frac{1}{4}{t^2}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The area of </span><span><span><span>\({\text{OBCD}}\) </span></span>is \(9.75\) square units. Write down a quadratic equation that expresses this information.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Using your graphic display calculator, or otherwise, find the two solutions to the quadratic equation written in part (d).</span></p>
<p><span>(ii) Hence find the correct value for \(t\). Give a reason for your answer.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{E}}(8{\text{, }}0)\) <em><strong>(A1)(A1)</strong></em></span></p>
<p><span><strong>Notes: </strong>Brackets required but do not penalize again if mark lost in <strong>Q4</strong> (i)(d). If missing award <em><strong>(A1)(A0)</strong></em>.</span><br><span>Accept \(x = 8\), \(y = 0\)</span><br><span>Award <em><strong>(A1)</strong></em> for \(x = 8\)</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(y + \frac{1}{2}t = 4\) <em><strong>(M1)(M1)<br><br></strong></em></span></p>
<p><span><strong>Note: <em>(M1)</em></strong> for the equation of the line seen. <em><strong>(M1)</strong></em> for substituting \(t\).</span></p>
<p><br><span>\(y = 4 - \frac{1}{2}t\) <em><strong>(AG)</strong></em></span></p>
<p><span><strong>Note: </strong>Final line must be seen or previous <em><strong>(M1)</strong></em> mark is lost.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{Area}} = \frac{1}{2} \times (4 + 4 - \frac{1}{2}t) \times t\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span><strong><br>Note: <em>(M1)</em></strong> for substituting in correct formula, <em><strong>(A1)</strong></em> for correct substitution.</span></p>
<p><br><span>\( = \frac{1}{2} \times (8 - \frac{1}{2}t) \times t = \frac{1}{2}(8t - \frac{1}{2}{t^2})\) <em><strong>(A1)</strong></em></span><br><span>\( = 4t - \frac{1}{4}{t^2}\) <em><strong>(AG)</strong></em></span></p>
<p><span><strong>Note: </strong>Final line must be seen or previous <em><strong>(A1)</strong></em> mark is lost.</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span>\(4t - \frac{1}{4}{t^2} = 9.75\) or any equivalent form. </span> <span><em><strong>(A1)</strong></em></span></span></p>
<p><span><span><em><strong>[1 mark]<br></strong></em></span></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(t = 3\) or \(t =13\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)<br></strong></em><br></span></p>
<p><span><strong>Note: </strong>Follow through from candidate’s equation to part (d). Award <strong><em>(A0)(A1)</em>(ft)</strong> for \((3{\text{, }}0)\) and \((13{\text{, }}0)\).</span></p>
<p><br><span>(ii) \(t\) must be a value between \(0\) and \(8\) then \(t = 3\)</span></p>
<p><span><strong>Note: </strong>Accept \({\text{B}}\) is between \({\text{O}}\) and \({\text{E}}\). Do not award <em><strong>(R0)(A1)</strong></em>.</span></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">A number of candidates did not attempt this question worth 12 marks but the majority answered this question partially and were able to gain some marks. Parts (a) and (b) were mostly well done. Very few candidates managed to answer part (c) well; this part of the question required good algebra along with a clear understanding of the situation given in the diagram. Many recovered then in (d) when they were asked to write down the quadratic equation. Solving the equation was not always found to be easy. Use of the GDC was expected but many used the formula. The correct solution, \(t = 3\), was chosen in the last part of the question. However, their justification was often false causing them to lose both the reasoning and the answer mark.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">A number of candidates did not attempt this question worth 12 marks but the majority answered this question partially and were able to gain some marks. Parts (a) and (b) were mostly well done. Very few candidates managed to answer part (c) well; this part of the question required good algebra along with a clear understanding of the situation given in the diagram. Many recovered then in (d) when they were asked to write down the quadratic equation. Solving the equation was not always found to be easy. Use of the GDC was expected but many used the formula. The correct solution, \(t = 3\), was chosen in the last part of the question. However, their justification was often false causing them to lose both the reasoning and the answer mark.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">A number of candidates did not attempt this question worth 12 marks but the majority answered this question partially and were able to gain some marks. Parts (a) and (b) were mostly well done. Very few candidates managed to answer part (c) well; this part of the question required good algebra along with a clear understanding of the situation given in the diagram. Many recovered then in (d) when they were asked to write down the quadratic equation. Solving the equation was not always found to be easy. Use of the GDC was expected but many used the formula. The correct solution, \(t = 3\), was chosen in the last part of the question. However, their justification was often false causing them to lose both the reasoning and the answer mark.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">A number of candidates did not attempt this question worth 12 marks but the majority answered this question partially and were able to gain some marks. Parts (a) and (b) were mostly well done. Very few candidates managed to answer part (c) well; this part of the question required good algebra along with a clear understanding of the situation given in the diagram. Many recovered then in (d) when they were asked to write down the quadratic equation. Solving the equation was not always found to be easy. Use of the GDC was expected but many used the formula. The correct solution, \(t = 3\), was chosen in the last part of the question. However, their justification was often false causing them to lose both the reasoning and the answer mark.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">A number of candidates did not attempt this question worth 12 marks but the majority answered this question partially and were able to gain some marks. Parts (a) and (b) were mostly well done. Very few candidates managed to answer part (c) well; this part of the question required good algebra along with a clear understanding of the situation given in the diagram. Many recovered then in (d) when they were asked to write down the quadratic equation. Solving the equation was not always found to be easy. Use of the GDC was expected but many used the formula. The correct solution, \(t = 3\), was chosen in the last part of the question. However, their justification was often false causing them to lose both the reasoning and the answer mark.</span></p>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A dog food manufacturer has to cut production costs. She wishes to use as little aluminium as possible in the construction of cylindrical cans. In the following diagram, <em>h</em> represents the height of the can in cm and <em>x</em>, the radius of the base of the can in cm.</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The volume of the dog food cans is 600 cm<sup>3</sup>.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that \(h = \frac{{600}}{{\pi {x^2}}}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find an expression for the curved surface area of the can, in terms of <em>x</em>. Simplify your answer.<br></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Hence write down an expression for <em>A</em>, the total surface area of the can, in terms of <em>x</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Differentiate <em>A</em> in terms of <em>x</em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of <em>x</em> that makes <em>A</em> a minimum.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the minimum total surface area of the dog food can.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(600 = \pi x^2 h\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span>\(\frac{600}{\pi x^2} = h\) <em><strong>(AG)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substituted formula, <em><strong>(A1)</strong></em> for correct substitution. If answer given not shown award at most <em><strong>(M1)(A0)</strong></em>.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(C = 2 \pi x \frac{600}{\pi x^2}\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(C = \frac{1200}{x}\) (or 1200<em>x</em><sup>–1</sup>) <em><strong>(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in formula, <em><strong>(A1)</strong></em> for correct simplification.<br></span></p>
<p><span> </span></p>
<p><em><strong><span>[??? marks]</span></strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(A = 2 \pi x^2 + 1200x^{-1}\) <strong><em>(A1)(A1)</em>(ft)</strong></span></p>
<p><span> </span></p>
<p><span><strong>Note:</strong> Award <strong><em>(A1)</em></strong> for multiplying the area of the base by two, <strong><em>(A1)</em></strong> for adding on their answer to part (b) (i).</span></p>
<p><span>For both marks to be awarded answer must be in terms of<em> x</em>.</span></p>
<p> </p>
<p><span><em><strong>[??? marks]</strong></em></span></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{{\text{d}}A}}{{{\text{d}}x}} = 4\pi x - \frac{{1200}}{{{x^2}}}\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span> </span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for \(4 \pi x\), <em><strong>(A1)</strong></em> for \(-1200\), <em><strong>(A1)</strong></em> for \(x^{-2}\). Award at most <em><strong>(A2)</strong></em> if any extra term is written. Follow through from their part (b) (ii).</span></p>
<p><span> </span></p>
<p><em><strong><span>[??? marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(4 \pi x - \frac{1200}{x^2} = 0\) <em><strong>(M1)(M1)</strong></em></span></p>
<p><span>\(x^3 = \frac{1200}{4 \pi}\) (or equivalent)</span></p>
<p><span>\(x = 4.57\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for using their derivative, <em><strong>(M1)</strong></em> for setting the derivative to zero, <strong><em>(A1)</em>(ft)</strong> for answer.</span></p>
<p><span>Follow through from their derivative.</span></p>
<p><span>Last mark is lost if value of <em>x</em> is zero or negative.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(A = 2 \pi (4.57)^2 + 1200(4.57)^{-1}\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(A = 394\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em> </span></p>
<p><br><span><strong>Note:</strong> Follow through from their answers to parts (b) (ii) and (d).</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This was the most difficult question for the candidates. It was clear that the vast majority of them had not had exposure to this style of question. Part (a) was well answered by most of the students. In part (b) the correct expression “in terms of <em>x</em> ” for the curve surface area was not frequently seen. In many cases the impression was that they did not know what “in terms of <em>x</em> ” meant as correct equivalent expressions were seen but where the <em>h</em> was also involved. Those candidates that made progress in the question, even with the wrong expression for the total area of the can, <em>A</em> were able to earn follow through marks.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This was the most difficult question for the candidates. It was clear that the vast majority of them had not had exposure to this style of question. Part (a) was well answered by most of the students. In part (b) the correct expression “in terms of <em>x</em> ” for the curve surface area was not frequently seen. In many cases the impression was that they did not know what “in terms of <em>x</em> ” meant as correct equivalent expressions were seen but where the <em>h</em> was also involved. Those candidates that made progress in the question, even with the wrong expression for the total area of the can, <em>A</em> were able to earn follow through marks.</span></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">This was the most difficult question for the candidates. It was clear that the vast majority of them had not had exposure to this style of question. Part (a) was well answered by most of the students. In part (b) the correct expression “in terms of <em>x</em> ” for the curve surface area was not frequently seen. In many cases the impression was that they did not know what “in terms of <em>x</em> ” meant as correct equivalent expressions were seen but where the <em>h</em> was also involved. Those candidates that made progress in the question, even with the wrong expression for the total area of the can, <em>A</em> were able to earn follow through marks.</span></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This was the most difficult question for the candidates. It was clear that the vast majority of them had not had exposure to this style of question. Part (a) was well answered by most of the students. In part (b) the correct expression “in terms of <em>x</em> ” for the curve surface area was not frequently seen. In many cases the impression was that they did not know what “in terms of <em>x</em> ” meant as correct equivalent expressions were seen but where the <em>h</em> was also involved. Those candidates that made progress in the question, even with the wrong expression for the total area of the can, A were able to earn follow through marks.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This was the most difficult question for the candidates. It was clear that the vast majority of them had not had exposure to this style of question. Part (a) was well answered by most of the students. In part (b) the correct expression “in terms of <em>x</em> ” for the curve surface area was not frequently seen. In many cases the impression was that they did not know what “in terms of <em>x</em> ” meant as correct equivalent expressions were seen but where the <em>h</em> was also involved. Those candidates that made progress in the question, even with the wrong expression for the total area of the can, A were able to earn follow through marks.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This was the most difficult question for the candidates. It was clear that the vast majority of them had not had exposure to this style of question. Part (a) was well answered by most of the students. In part (b) the correct expression “in terms of <em>x</em> ” for the curve surface area was not frequently seen. In many cases the impression was that they did not know what “in terms of <em>x</em> ” meant as correct equivalent expressions were seen but where the <em>h</em> was also involved. Those candidates that made progress in the question, even with the wrong expression for the total area of the can, A were able to earn follow through marks.</span></p>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A solid metal <strong>cylinder</strong> has a base radius of 4 cm and a height of 8 cm.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the area of the base of the cylinder.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that the volume of the metal used in the cylinder is 402 cm<sup>3</sup>, given correct to three significant figures.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the total surface area of the cylinder.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The cylinder was melted and recast into a solid cone, shown in the following diagram. The base radius OB is 6 cm.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Find the height, OC, of the cone.</span></p>
<p> </p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The cylinder was melted and recast into a solid cone, shown in the following diagram. The base radius OB is 6 cm.</span></p>
<p><span><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAATUAAAD+CAIAAADUJQWQAAAVq0lEQVR4nO2dz2scR5vH6y9414d42Tk54EMuvjljsC+SL4LkJcwpJnnfRYYwh+TNyYcesJ2FQOiDo6BLhxgSJng2L/iF0MgQCBmbIZdGi4N4R8EsopU9hB1nLqYJQtBBLEPtoaRya6Zn1NNdv/v7IYd4pChtPfOZqm919VOEAgBMhei+AADAXOCnFRyNd77rdtYIY7XTfbQz/r/40aN4ovvKgFTgp/Ec7oWdNdJY3wh3xkzHyXgn3FhvNNa6e/DTbeCn4fy+s/Fn0vgwfH50+vXJ4c7mWmdwoOeqgCLgp9FM4u4aaaxuPD3M+eKLH8P/gp9uAz9N5o+4+zYhlzuDF7qvBOgBfprMi0HnMvysM/DTZOBn3YGfJjM5GNxuEKzT1hf4aTaTX8P3LuWt31I6Ge/8GOetGwF3gJ+mMxk/vr3aOHX/k04O48GD7nd7hxhWHQd+2sBkvPPoy85q49T+IbhZA+AnAOYCPwEwF/hpE2maEkKePXum+0KAIuCnTXieRwhptVppmuq+FqAC+GkNYRi2221CiO/7nufpvhygAvhpB3EcN5vN0WhECEnTtN1uh2Go+6KAdOCnBaRp2mw2oyiilBJCKKWj0ajZbMZxrPvSgFzgpwV4nhcEAft35ielNIqiZrOJIOo28NN0WOzkHnI/KaVBECCIug38NBoeO/krWT8RRJ0HfppLmqatVqvf72dfzPpJEURdB36ai+/7vu9PvTjlJ0UQdRr4aSj9fj93H8KsnxRB1F3gp4mw+5zZ2MnJ9RNB1FXgp3Hkxk5Orp8UQdRR4Kdx5MZOzjw/6UkQTZJEznUBDcBPs5gXOzkL/KSUBkHQbrclXBfQA/w0iAWxk7PYT0ppu93u9XpCrwtoA36awuLYyTnTzyRJms3mcDgUd2lAG/DTFBbHTs6ZflJKh8MhgqgbwE8jODN2cor4SSnt9XoIog4AP/Wz1K2Rgn5SBFEngJ+aWXZrQXE/EUQdAH5qZtmtecX9pAii9gM/dVJia/tSflIEUcuBn9ootyNvWT8pgqjNwE89lN7RXsJPFkRZ+yJgF/BTD6WfCCvhJz0Joot3JgEDgZ8aqPJEdTk/6UwfI2AF8FM1FR8EK+0nPd0HEFgB/FRK9Qepq/iZ7aMLrAB+KqXX61VsRFLFT5rXEBCYDPxUh5DdAhX9pAiiVgE/FSFqt111PymCqD3AT0WI2iQgxE8EUVuAnyoQuMlOiJ8UQdQS4Kd0xG5SF+UnRRC1AfgpF+EPeQn0kyKIGg/8lIvwveli/WRB9MymR0AX8FMiMp7tEusnLdY0EOgCfspC0rPRwv2ky3Q/AoqBn1KQ11tEhp+0cPdAoBj4KQXP8yQ9Ei3Jz4Ldd4Fi4Kd4pN63kOQnRRA1EvgpGNn3/eX5SRFEzQN+ikTBvjmpflIEUcOAnyJRcLtftp8IokYBP4WhZrucbD8ppaPR6N/O/yuCqAnATzEo226uwM/9/f1//+tfEURNAH4KQOXjWgr83N3dvXvnju/7FVs9gOrATwGo3GWuwM/7X9x/8uRJ9VZJoDrwsyqKn9JSsD508cKrbFtixVaDoDrwsxLqn3KW7ef9L+7f/+I+/2OVVr2gOvCzPFpuRUj1c39///rKytSe/tKt7kF14Gd5tNzKl+fn8+fPr6+s7O7uTr2OIKoR+FkSXVvhJPnJ5Nze3s79KoKoLuBnGTRuJZfh5+7u7gI5GQiiWoCfS6N3B5zw/iZ//+ab3GntLAii6oGfS6N3B7lAP/f399+5cePunTsFmzwgiKoHfi6H9iewhPi5v79/986dM+e0syCIKgZ+LoEJTzBX9HN7e/tvH3xwfWXl0dZWuU8ZFkSF91UCucDPohjy4FU5P3d3d+9/cf/6ysrfPvhg2TFzliAIhPclBLnAz6IY8uBycT+TJNne3v703r3rKyvv3Ljx92++ef78uajLEN7XF+QCPwuhPXZy5vmZpun+/v729vajrS2WLa+vrHx6796TJ09kzEXlNSgEWeDn2Ri1KHLuT//yaGvr/hf37965w/5558aNixdevXjh1bt37nx6796jra3d3V0F+VBSg1+QBX6egWk3FZifT5482T9B4Kx1WWQ0yAdZ4OcZmHZTXsHzn0uBICoVs4ptGgZuajPNTwRRqZhVbKMwKnZyTPOTIojKxLhiG4JpsZNjoJ8UQVQaJhbbBEyLnRwz/aQIonIwtNh6MTB2coz1kwVRNU0M64OhxdaImbGTY6yf9CSIorG1QMwtthaMjZ0ck/2kyrsZOo/RxVZPr9czM3ZyDPeTqu0G7DymF1slVtwnMN9Pld30ncf0YivDlvvs5vtJdbQFdhULiq0GW24PWOEnRRAVhB3Flo1Ft9dt8ZMiiIrAmmLLw4rYybHITwTR6lhTbEnYEjs5FvlJEUQrY1OxZWBL7OTY5SdFEK2GZcUWi0Wxk2OdnxRBtAL2FVsUdsVOjo1+siCqvfWhjdhXbCFYFzs5NvpJzWgdbCNWFrs6nufZFTs5lvpJTeqBaBG2FrsKVq9Y2OsnNaaHsEVYXOxy2L7ib7WfhvTgtwiLi10CB+6YW+0nRRBdEruLvSwOLPTb7idFEF0G64tdHKtjJ8cBPymCaGFcKHYRbI+dHDf8RBAtiAvFPhMHYifHDT8pgmgxHCn2YhyInRxn/KQIogVwp9jzcCN2clzyk1Lq+77hDZ/04lSxZ3EmdnIc89P8hol6carYUzi5COGYn9T4hsN6ca3YWZxcxHfPT2p2w369OFhshqtrD076SQ0+8EYvbhbb4bV7V/1EEM3FwWI7GTs5rvpJEUTzcLDYTsZOjsN+UgTRGVwrtquxk+O2nxRB9DROFdvh2Mlx3k8E0SzuFNvt2Mlx3k+KIJrBnWK7HTs5dfCTngRR67orCseRYjsfOzk18ZNSGgSBdd2JheNCsWs1HaqPn9TC7v7Csb7YdVtOqJWf9rYpFoX1xa7bcnyt/KTWtvkXhd3FruHt7Lr5Se08JkcUFhe7VrGTU0M/aY2DqK3Frlvs5NTTz9oGUVuLXbfYyamnn7SuQdTKYtcwdnJq6yetZRC1r9j1jJ2cOvtJ6xdELSt2bWMnp+Z+siDqRivjIlhW7F6vV8/Yyam5n/QkiLr9lBLHpmLXc4VgCvhJnetpvABril3bFfYp4CfDpTMBFmBNseu2MDAP+Mlw6UydBdhR7BourM8DfnLcOxxgFguKjdiZBX5mcT6Iml5sxM4p4OcUbgdR04uN2DkF/JzC7SBqdLERO2eBn7M4HETNLTZiZy7wMxdXg6ihxUbsnAf8nIeTQdTQYnueh9iZC/ycBwuijjVANrHYrs5VhAA/F+DeAQLGFdvhrC8E+LkYxzohm1Vst9fKhQA/z8SlkwTMKraTEV8s8PNMXDqJx6BiI3YWAX4WwZkgakqxETsLAj8L4kYQNaLYiJ3FgZ/FcSCIGlFsxM7iwM/iOBBE9RcbsXMp4OdS2B5ENRcbsXNZ4OeyWB1EdRbbgemHeuBnCXzft7Tto85iOxDf1QM/S2Bv22RtxbZ61qER+FkOS48d0FNs21O7RuBnaWw8tkdDsRE7qwA/q2DdsXcaio3YWQX4WQXrgqjqYiN2VgR+VsSuIKq02Iid1YGf1bEoiKorNmKnEOCnEGwJouqKjdgpBPgpBFuCqKJiI3aKAn6KwoogqqLY7BeB2CkE+CkQFkRN7rEsvdi2TCRsAX6KJQgCk88okF5sW4K4LcBP4Zh8xo/cYlu0kG0L8FM4Jh9WILHYVuRv64CfMjD2sB9ZxUbslAT8lISZh+XJKjZipyTgpzwMDKJSio3YKQ/4KQ8Dg6j4YiN2SgV+SsW0ICq42IidsoGfsjEqiAoudq/XQ+yUCvxUgDlBVGSx2dwAsVMq8FMBLIiacKCBsGIbmK2dBH6qgQ022jeNCyu2OVMCt4GfyjDhZAMxxTYqUrsN/FSJ9pOBBBTbtCVpt4GfKtF+sl7VYiN2KgZ+KkbvEUFVi43YmaZpvJBypSUnzHv9TET85QClWoNopSrWKnZGUeSd0G63syZ4CxH7+SVVvCRJCCHNZnPq+sMM/HOnVjfSdAXR8sWuW+yMomg4HPJ3p67LUDAwJkmSHf+zcrL9Jwz22dRqtTzP833f7XeCriBasthWxE4+82TvLXbIHBv6dF9aeUy7+NFoFMdxFEVu+0k1BdGSxRY+basIU7Hf74dhmJ1/Zmdo/X5f79AnBNP8rAJ7zolNHcMwZNMTk6fN6oNomWKzqxR+KSVgQyJX0fd9XmbdlyYLl/ykJ3Pp3A9WVk32qWrO4Kw4iC5dbKNOpGfFM/kTVziO+ZkLmw1FUcRTSbPZJIS02+0gCPr9vsa3Hwuiyo5BWK7Y2m/Xgjr4OQ820rLJsMbLUHmM0HLFFj64s0/KMAz17qKyiDr7aQ7KzkNYotiiwnGSJFEU+b7farWyk5aKP7YmwE9DUHOeUNFiV4ydaZpGURQEQavVajabvu+z6Fjup9UZ+FkONk0TmF3VnMdXqNjlYmeapsPhkO0xYityYRgasrBkL/CzHMxP3/ebzSYfISq+GxUE0ULFLh47p5xku3MN38ZgF/CzOqPRaHY2V04z2UH07GIvGzvZOIm5qyTgp1jYaghztdVqBUGw7HAiNYieUWyj7nYCCj9lMhqN2NSPDapRFBUZlqQG0UXFZv9j3O00CvipgCRJ+v2+7/uEkCIzQXlBdFGxcSK9gcBPlRSPdZKC6Nxi40R6M4GfxsK2Ior9mfnFVrmDCSwF/DQWGYcn5BQ7m3f7/T7ujhgF/DQZ4YcP5RSbxc7RaNRut9vtNkZRo4CfhiP28L7pYrPY+fDhQ0IIjjlSzkE8+MfG+qXjvkaN9Y1vf4wPJ9nvgJ/mc9bht5ODwe1GTke3S+sb/xjEB9lvPVVsFjvfffddDJsaOHzWXb/UWN8Id8bMyMn46YPOGlm9HWZqBj9NhrUHKBZEXww6l8laNz7++D0a7/xnZ7VByJ83dn7n3/Sy2GmaXrlyBcOmHia/hu9dIqubO6dHy5PXPx6Mj9gL8NNkhsMha5j27Nmzs4LolJ+UUjqJu2uENDoD/nn8sthvvfXW66+/jmFTB2zC01jr7k3O+hL8NJw0TXu9HiGE7cWfH0SX8XNzc/PcuXO//PKLxAsHc/kj7r5NyOXO4EXOFw8GnQbhhYSfVsCWV69evXrr1q053zLt53GcmZ3fbm1tEUJ++ukn2RcN5vBi0Ll8hp+N24ODCYWf9pCm6ebm5muvvfbw4cO8r7OiTzH9HiBpmp4/f/6zzz5Tc9EgD4yfzvLJJ5+cP3/+559/nvnK1Pg5OYx//HZjvUEaq7cfj08GVXLr1q0rV66ou16Qw4L8yTIJ8qfF3Lp16/z587/99tvpl3Py5+xMipw7d24wGKi6VDAHtk7b+DB8fpTzemZdd85hSMB0rl27drrkxfx88803pb3pwDIcPuuuXyKrnQfH9z8nh/GgO3P/E9hImqYXLlz46KOPMq/N+HkYD7qdVUIa6w/2+Mfx+++/r/hawVwm451HX3ZWT/aW5O0fApby/fffv/LKKz/88MP8/UM5Fcf4CaRyNN75rttZI6dv69UTQsiyB6MQ4U+sAXDM4V7YWcMsgHP16tWvv/56qf+ECNxrD9TDGibqvoo8Jr+G711qrH/+dHx09je7BTtzcfb1a9eudbvdpX4U8TwPvdstpd/vN5tNow56POGPuPt2znJ0PWDHkE+dWZymKXtxqR9F2I5e0VcIJJIkSRiG7HQMQog5Z++95GDQaTRWO19+u7HeIISQtU64d5j/rUfjnfDkkbq1zoOn4wnlN+svdh4/j3/YWL9Eju/aH42ffr7eIIRcWt+MxgZPmVlvMSYkm+CwhmPL/hxCKRX7xDeQCtt7bQ5518jWJ7lsB3F4e5Vcei/8dUaoo/Hg49Xjp3Mmh3sP1huXO4MXx1umCDl52m5yuLO5+vLxSPbH/O1Wun8f+bTb7TfeeKNEK0xCKWVHoy77XwJdjEajIAjYkZjExPGTTW6PNwxTSufci6d0stddu5a/q3Gy111rvFzyPRh0Gi83UU3i7tq87ZBmEAQBNzOKoq+++qrckdbHn38KTnoBYknTlL0JzCvc5GBwu3HKz1ljKaXMujmaWe5ns9lstVpsWjocDpvNZrmP0WM/WV8jtKK2jjiOTTw6dVq8P+Lu2zn3Pyd73bWLqxtPc6KpzX6yI4jYbZEkSZrNZuk19pf5IYoiQggUBSI4eh5+2DgOlkfjp5+vX8xdyz0aDz5ePbV69Mf/7Pz3AbXbTw5rdFJlgf1Uvmetx6AoEMFB/Hhz/XiZZ/Px3C3EvO8OIYQ0/vIf3/7zd9ZG4Ji17t7eyz82Oo//N7M5zuQ9SewR7Yqzm+n1NzbR5aMzAKAELHNWvzWd35/a8zy08AOgHL1er0rmzDL3Yd8wDEX9PwCoCWxO63meqJteix7GZ3HUvOV7AEyE+SL9/JUso9GI9fPEBiMA5hHHsed5/IanQAo1s2FzXYGjNgBuwM2UdNejaLOpNE3DMCSEBEEASwFgZgqf0E6xXDO4JEnYnrIgCLC6C+pJFEXcTNm3Ics0a0yShK0gs72/uFMK6oCWt32lZqpRFLXbbXYfFpNe4CrD4ZA9zxkEgeKFUgHNjvnjThhOgUuMRqNer9dqtdjTXVre2MKakadpGkUR+5jxfR+beIGlJEnS7/fZxFD9gDmF+MMCpv562IEErIANMJ7nkUxTEu1IPMyD5elWqwVRgbEkSTI17zMqoKk4bIfN49mIauCvANQQPsszU0uO0sOwZn8pWPUFKskOFUEQGKslR89hddnFJPaAOVwFkojjOAxDdtp8q9WyK2rpP0yS/frYhgz26+v3+9icBEozGo2iKAqCgM3U+ABg45tKv59ZRqMRa+PLVpU8zwvDMI5jwychQC9JkgyHw+ynvO/77J2j+9KqYpafWdjCWq/XY0ve2V86dK05aZryWSvro+95Xq/XGw6HjqUkc/2cgk1aoGs9YUL2+303Zq3FscbPKaZ0ZZPhXq/X7/dhrO1wG1l9Wad81guP1Vf3BarDVj+nSJKETXiCIMg11u1PWauJ43jWRs/zgiBg86M6184RP2eZMpaf9sXaN7Has/JjvJUNOw+TLeGw0DivInEcOxYgK+Ksn/Pgn9ZhGLIPbDbe8iGXjbphGLKBF/YWgf2ioijKGsiCIlssYL9Y9tUoimo+Khandn4ugA25bNTlA+88e7MCO+wwi4LZD7Xs59rUGMhW7LiBtQqKkoCfRZmyNyswdzirMR8uOPxdy1F5/VnTpnyb/evwwwtZFGTwUMBzAcZA2cBPwbCslY1bHDbr4/Dp3xR8NpjLzZs3b968ueAbpuzKMvVtWd+y1iEEmgP8NA5ueC79fj87r84FdjkD/ATAXOAnAOby/2qnbwzyaazaAAAAAElFTkSuQmCC" alt></span></p>
<p><span>Find the size of angle BCO.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The cylinder was melted and recast into a solid cone, shown in the following diagram. The base radius OB is 6 cm.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Find the slant height, CB.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The cylinder was melted and recast into a solid cone, shown in the following diagram. The base radius OB is 6 cm.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Find the total surface area of the cone.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\( \pi \times 4^2\) <em><strong>(M1)</strong></em></span></p>
<p><span>= 50.3 (16\(\pi\)) cm<sup>2 </sup>(50.2654...) <em><strong>(A1)(G2)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in area formula. The answer is 50.3 cm<sup>2</sup>, the units are required.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>50.265...× 8 <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in the volume formula.</span></p>
<p><br><span>= 402.123... <em><strong>(A1)</strong></em></span><br><span><em><strong>=</strong></em> 402 (cm<sup>3</sup>) <em><strong>(AG)</strong></em></span></p>
<p><span><strong>Note:</strong> Both the unrounded and the rounded answer must be seen for the <em><strong>(A1)</strong></em> to be awarded. The units are <strong>not</strong> required</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(2 \times \pi \times 4 \times 8 + 2 \times \pi \times 4^2\) <em><strong>(M1)(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in the curved surface area formula, <em><strong>(M1)</strong></em> for adding the area of their two bases.</span><br><br></p>
<p><span>= 302 cm<sup>2</sup> (96π cm<sup>2</sup>) (301.592...) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><strong>Notes:</strong> The answer is 302 cm<sup>2</sup>, the units are required. Do not penalise for missing or incorrect units if penalised in part (a). Follow through from their answer to part (a).</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{1}{3} \pi \times 6^2 \times \text{OC} = 402\) <em><strong>(M1)(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted volume formula, <em><strong>(M1)</strong></em> for equating to 402 (402.123…).</span></p>
<p><br><span>\({\text{OC}} = 10.7{\text{ (cm)}}\left( {{\text{10}}\frac{2}{3},{\text{ }}10.6666...} \right)\) <em><strong>(A1)(G2)</strong></em></span></p>
<p><span><em><strong>[3 marks]<br></strong></em></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\tan \text{BCO} = \frac{6}{10.66...}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for use of correct tangent ratio.</span></p>
<p><br><span>\({\text{B}}{\operatorname{\hat C}}{\text{O}} = 29.4^\circ \) (29.3577...) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Accept 29.3° (29.2814...) if 10.7 is used. An acceptable alternative method is to calculate CB first and then angle BCO.</span> <span>Allow follow through from parts (d) and (f). Answers range from 29.2° to 29.5°.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\text{CB} = \sqrt{{6^2} + {(10.66...)^2}}\) <em><strong>(M1)</strong></em></span></p>
<p><em><strong><span>OR</span></strong></em></p>
<p><span>\(\sin 29.35...^\circ = \frac{6}{\text{CB}}\) <em><strong>(M1)</strong></em></span></p>
<p><em><strong><span>OR</span></strong></em></p>
<p><span>\(\cos 29.35...^\circ = \frac{10.66...}{\text{CB}}\) <em><strong>(M1)</strong></em></span></p>
<p><span>CB = 12.2 (cm) (12.2383...) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><strong>Note:</strong> Accept 12.3 (12.2674...) if 10.7 (and/or 29.3) used. Follow through from part (d) or part (e) as appropriate.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\pi \times 6 \times 12.2383... + \pi \times 6^2\) <em><strong>(M1)(M1)(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in curved surface area formula, <em><strong>(M1)</strong></em> for correct substitution in area of circle formula, <em><strong>(M1)</strong></em> for addition of the two areas.</span></p>
<p><br><span>= 344 cm<sup>2</sup> (343.785...) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G3)</strong></em></span></p>
<p><span><strong>Note:</strong> The answer is 344 cm<sup>2</sup>, the units are required. Do not penalise for missing or incorrect units if already penalised in either part (a) or (c). Accept 345 cm<sup>2</sup> if 12.3 is used and 343 cm<sup>2</sup> if 12.2 is used. Follow through from their part (f).</span></p>
<p><span><em><strong>[4 marks]</strong></em><br></span></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was either very well done – by the majority – or very poorly (but not both). Many incomplete attempts were seen. This would perhaps indicate a lack of preparation in this area of the syllabus from some centres, since it was that the formulas for cones were not well understood. Further, the idea of “total surface area” was a mystery to many – a slavish reliance of formulas, irrespective of context, led to many errors and a consequent loss of marks.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The invariance of volume for solids and liquids that provided the link in this question was not understood by many, but was felt to be an appropriate subject for an examination.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was either very well done – by the majority – or very poorly (but not both). Many incomplete attempts were seen. This would perhaps indicate a lack of preparation in this area of the syllabus from some centres, since it was that the formulas for cones were not well understood. Further, the idea of “total surface area” was a mystery to many – a slavish reliance of formulas, irrespective of context, led to many errors and a consequent loss of marks.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The invariance of volume for solids and liquids that provided the link in this question was not understood by many, but was felt to be an appropriate subject for an examination.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was either very well done – by the majority – or very poorly (but not both). Many incomplete attempts were seen. This would perhaps indicate a lack of preparation in this area of the syllabus from some centres, since it was that the formulas for cones were not well understood. Further, the idea of “total surface area” was a mystery to many – a slavish reliance of formulas, irrespective of context, led to many errors and a consequent loss of marks.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The invariance of volume for solids and liquids that provided the link in this question was not understood by many, but was felt to be an appropriate subject for an examination.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was either very well done – by the majority – or very poorly (but not both). Many incomplete attempts were seen. This would perhaps indicate a lack of preparation in this area of the syllabus from some centres, since it was that the formulas for cones were not well understood. Further, the idea of “total surface area” was a mystery to many – a slavish reliance of formulas, irrespective of context, led to many errors and a consequent loss of marks.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The invariance of volume for solids and liquids that provided the link in this question was not understood by many, but was felt to be an appropriate subject for an examination.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was either very well done – by the majority – or very poorly (but not both). Many incomplete attempts were seen. This would perhaps indicate a lack of preparation in this area of the syllabus from some centres, since it was that the formulas for cones were not well understood. Further, the idea of “total surface area” was a mystery to many – a slavish reliance of formulas, irrespective of context, led to many errors and a consequent loss of marks.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The invariance of volume for solids and liquids that provided the link in this question was not understood by many, but was felt to be an appropriate subject for an examination.</span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was either very well done – by the majority – or very poorly (but not both). Many incomplete attempts were seen. This would perhaps indicate a lack of preparation in this area of the syllabus from some centres, since it was that the formulas for cones were not well understood. Further, the idea of “total surface area” was a mystery to many – a slavish reliance of formulas, irrespective of context, led to many errors and a consequent loss of marks.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The invariance of volume for solids and liquids that provided the link in this question was not understood by many, but was felt to be an appropriate subject for an examination.</span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was either very well done – by the majority – or very poorly (but not both). Many incomplete attempts were seen. This would perhaps indicate a lack of preparation in this area of the syllabus from some centres, since it was that the formulas for cones were not well understood. Further, the idea of “total surface area” was a mystery to many – a slavish reliance of formulas, irrespective of context, led to many errors and a consequent loss of marks.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The invariance of volume for solids and liquids that provided the link in this question was not understood by many, but was felt to be an appropriate subject for an examination.</span></p>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>A restaurant serves desserts in glasses in the shape of a cone and in the shape of a hemisphere. The diameter of a cone shaped glass is 7.2 cm and the height of the cone is 11.8 cm as shown.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-13_om_14.40.46.png" alt="N17/5/MATSD/SP2/ENG/TZ0/06"></p>
</div>
<div class="specification">
<p>The volume of a hemisphere shaped glass is \(225{\text{ c}}{{\text{m}}^3}\).</p>
</div>
<div class="specification">
<p>The restaurant offers two types of dessert.</p>
<p>The <strong>regular dessert </strong>is a hemisphere shaped glass completely filled with chocolate mousse. The cost, to the restaurant, of the chocolate mousse for one regular dessert is $1.89.</p>
</div>
<div class="specification">
<p>The <strong>special dessert </strong>is a cone shaped glass filled with two ingredients. It is first filled with orange paste to half of its height and then with chocolate mousse for the remaining volume.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-13_om_14.44.32.png" alt="N17/5/MATSD/SP2/ENG/TZ0/06.d.e.f"></p>
</div>
<div class="specification">
<p>The cost, to the restaurant, of \(100{\text{ c}}{{\text{m}}^3}\) of orange paste is $7.42.</p>
</div>
<div class="specification">
<p>A chef at the restaurant prepares 50 desserts; \(x\) regular desserts and \(y\) special desserts. The cost of the ingredients for the 50 desserts is $111.44.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the volume of a cone shaped glass is \(160{\text{ c}}{{\text{m}}^3}\), correct to 3 significant figures.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the radius, \(r\), of a hemisphere shaped glass.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the cost of \(100{\text{ c}}{{\text{m}}^3}\) of chocolate mousse.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that there is \(20{\text{ c}}{{\text{m}}^3}\) of orange paste in each special dessert.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total cost of the ingredients of one special dessert.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(x\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\((V = ){\text{ }}\frac{1}{3}\pi {(3.6)^2} \times 11.8\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into volume of a cone formula.</p>
<p> </p>
<p>\( = 160.145 \ldots {\text{ }}({\text{c}}{{\text{m}}^3})\) <strong><em>(A1)</em></strong></p>
<p>\( = 160{\text{ }}({\text{c}}{{\text{m}}^3})\) <strong><em>(AG)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Both rounded and unrounded answers must be seen for the final <strong><em>(A1) </em></strong>to be awarded.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{1}{2} \times \frac{4}{3}\pi {r^3} = 225\) <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for multiplying volume of sphere formula by \(\frac{1}{2}\) (or equivalent).</p>
<p>Award <strong><em>(A1) </em></strong>for equating the volume of hemisphere formula to 225.</p>
<p> </p>
<p><strong><em>OR</em></strong></p>
<p>\(\frac{4}{3}\pi {r^3} = 450\) <strong><em>(A1)(M1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for 450 seen, <strong><em>(M1) </em></strong>for equating the volume of sphere formula to 450.</p>
<p> </p>
<p>\((r = ){\text{ }}4.75{\text{ }}({\text{cm}}){\text{ }}(4.75380 \ldots )\) <strong><em>(A1)(G2)</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{1.89 \times 100}}{{225}}\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for dividing 1.89 by 2.25, or equivalent.</p>
<p> </p>
<p>\( = 0.84\) <strong><em>(A1)(G2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Accept 84 cents if the units are explicit.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\({r_2} = 1.8\) <strong><em>(A1)</em></strong></p>
<p>\({V_2} = \frac{1}{3}\pi {(1.8)^2} \times 5.9\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into volume of a cone formula, but only if the result rounds to 20.</p>
<p> </p>
<p>\( = 20{\text{ c}}{{\text{m}}^3}\) <strong><em>(AG)</em></strong></p>
<p><strong>OR</strong></p>
<p>\({r_2} = \frac{1}{2}r\) <strong><em>(A1)</em></strong></p>
<p>\({V_2} = {\left( {\frac{1}{2}} \right)^3}160\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for multiplying 160 by \({\left( {\frac{1}{2}} \right)^3}\). Award <strong><em>(A0)(M1) </em></strong>for \(\frac{1}{8} \times 160\) if \(\frac{1}{2}\) is not seen.</p>
<p> </p>
<p>\( = 20{\text{ }}({\text{c}}{{\text{m}}^3})\) <strong><em>(AG)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Do not award any marks if the response substitutes in the known value \((V = 20)\) to find the radius of the cone.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{20}}{{100}} \times 7.42 + \frac{{140}}{{100}} \times 0.84\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for the sum of two correct products.</p>
<p> </p>
<p>$ 2.66 <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from part (c).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(x + y = 50\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct equation.</p>
<p> </p>
<p>\(1.89x + 2.66y = 111.44\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for setting up correct equation, including their 2.66 from part (e).</p>
<p> </p>
<p>\((x = ){\text{ }}28\) <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from part (e), but only if their answer for \(x\) is rounded to the nearest positive integer, where \(0 < x < 50\).</p>
<p>Award at most <strong><em>(M1)(M1)(A0) </em></strong>for a final answer of “28, 22”, where the \(x\)-value is not clearly defined.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Tepees were traditionally used by nomadic tribes who lived on the Great Plains of North America. They are cone-shaped dwellings and can be modelled as a cone, with vertex O, shown below. The cone has radius, \(r\), height, \(h\), and slant height, \(l\).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-04_om_10.28.13.png" alt></p>
<p class="p1">A model tepee is displayed at a Great Plains exhibition. The curved surface area of this tepee is covered by a piece of canvas that is \(39.27{\text{ }}{{\text{m}}^2}\), and has the shape of a semicircle, as shown in the following diagram.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-04_om_10.29.53.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that the slant height, \(l\), is \(5\) m, correct to the nearest metre.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Find the circumference of the base of the cone.</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Find the radius, \(r\), of the base.</p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>Find the height, \(h\).</p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">A company designs cone-shaped tents to resemble the traditional tepees.</p>
<p class="p1">These cone-shaped tents come in a range of sizes such that the sum of the diameter and the height is equal to <strong>9.33 m</strong>.</p>
<p class="p1">Write down an expression for the height, \(h\), in terms of the radius, \(r\), of these cone-shaped tents.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">A company designs cone-shaped tents to resemble the traditional tepees.</p>
<p class="p1">These cone-shaped tents come in a range of sizes such that the sum of the diameter and the height is equal to <strong>9.33 m</strong>.</p>
<p class="p1">Show that the volume of the tent, \(V\), can be written as</p>
<p class="p1">\[V = 3.11\pi {r^2} - \frac{2}{3}\pi {r^3}.\]</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">A company designs cone-shaped tents to resemble the traditional tepees.</p>
<p class="p1">These cone-shaped tents come in a range of sizes such that the sum of the diameter and the height is equal to <strong>9.33 m</strong>.</p>
<p class="p1">Find \(\frac{{{\text{d}}V}}{{{\text{d}}r}}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">A company designs cone-shaped tents to resemble the traditional tepees.</p>
<p class="p1">These cone-shaped tents come in a range of sizes such that the sum of the diameter and the height is equal to <strong>9.33 m</strong>.</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>Determine the exact value of \(r\) for which the volume is a maximum.</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Find the maximum volume.</p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\frac{{\pi {l^2}}}{2} = 39.27\) <span class="Apple-converted-space"> </span><strong><em>(M1)(A1)</em></strong></p>
<p class="p1"><strong>Note:<span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for equating the formula for area of a semicircle to \(39.27\), award <strong><em>(A1) </em></strong>for correct substitution of \(l\) into the formula for area of a semicircle.</p>
<p class="p2"> </p>
<p class="p1">\(l = 5{\text{ (m)}}\) <span class="Apple-converted-space"> </span><strong><em>(AG)</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>\(5 \times \pi \) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">\( = 15.7\;\;\;(15.7079...,{\text{ }}5\pi )\;{\text{(m)}}\) <span class="Apple-converted-space"> </span><strong><em>(A1)(G2)</em></strong></p>
<p class="p1"> </p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\(2\pi r = 15.7079…\;\;\;\)<strong>OR</strong>\(\;\;\;5\pi r = 39.27\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">\((r = ){\text{ 2.5 (m)}}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p class="p1"><strong>Note:<span class="Apple-converted-space"> </span></strong>Follow through from part (b)(i).</p>
<p class="p2"> </p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>\(({h^2} = ){\text{ }}{5^2} - {2.5^2}\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into Pythagoras’ theorem. Follow through from part (b)(ii).</p>
<p class="p2"> </p>
<p class="p1">\((h = ){\text{ 4.33 }}(4.33012 \ldots ){\text{ (m)}}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(9.33 - 2 \times r\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(V = \frac{{\pi {r^2}}}{3} \times (9.33 - 2r)\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution in the volume formula.</p>
<p class="p1"> </p>
<p class="p1">\(V = 3.11\pi {r^2} - \frac{2}{3}{\pi ^3}\) <span class="Apple-converted-space"> </span><strong><em>(AG)</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(6.22\pi r - 2\pi {r^2}\) <span class="Apple-converted-space"> </span><strong><em>(A1)(A1)</em></strong></p>
<p class="p1"><strong>Notes:<span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1) </em></strong>for \(6.22\pi r\), <strong><em>(A1) </em></strong>for \( - 2\pi {r^2}\).</p>
<p class="p1">If extra terms present, award at most <strong><em>(A1)(A0)</em></strong><em>.</em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>\(6.22\pi r - 2\pi {r^2} = 0\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Note:<span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for setting their derivative from part (e) to 0.</p>
<p class="p2"> </p>
<p class="p1">\(r = 3.11{\text{ (m)}}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p class="p1"><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for identifying 3.11 as the answer.</p>
<p class="p1">Follow through from their answer to part (e).</p>
<p class="p2"> </p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\(\frac{1}{3}\pi {(3.11)^3}\;\;\;\)<strong>OR</strong>\(\;\;\;3.11\pi {(3.11)^2} - \frac{2}{3}\pi {(3.11)^3}\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Note:<span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for correct substitution into the correct volume formula.</p>
<p class="p2"> </p>
<p class="p1">\(31.5{\text{ (}}{{\text{m}}^3}{\text{)}}{\text{(31.4999}} \ldots {\text{)}}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p class="p1"><strong>Note: </strong>Follow through from their answer to part (f)(i).</p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following diagram shows a perfume bottle made up of a cylinder and a cone.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-22_om_07.37.58.png" alt></p>
<p class="p1">The radius of both the cylinder and the base of the cone is <span class="s1">3 cm</span>.</p>
<p class="p1">The height of the cylinder is <span class="s1">4.5 cm</span>.</p>
<p class="p1">The slant height of the cone is <span class="s1">4 cm</span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) Show that the vertical height of the cone is \(2.65\)<span class="s1"> cm </span>correct to three significant figures.</p>
<p class="p1">(ii) Calculate the volume of the perfume bottle.</p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">The bottle contains \({\text{125 c}}{{\text{m}}^{\text{3}}}\) </span>of perfume. The bottle is <strong>not </strong>full and all of the perfume is in the cylinder part.</p>
<p class="p1">Find the height of the perfume in the bottle.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Temi makes some crafts with perfume bottles, like the one above, once they are empty. Temi wants to know the surface area of one perfume bottle.</p>
<p class="p1">Find the <strong>total </strong>surface area of the perfume bottle.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Temi covers the perfume bottles with a paint that costs 3 South African rand (ZAR) per millilitre. One millilitre of this paint covers an area of \({\text{7 c}}{{\text{m}}^{\text{2}}}\).</p>
<p class="p2"><span class="s1">Calculate the cost, in ZAR</span>, of painting the perfume bottle. <strong>Give your answer correct to two decimal places</strong>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Temi sells her perfume bottles in a craft fair for <span class="s1">325 ZAR </span>each. Dominique from France buys one and wants to know how much she has spent, in euros <span class="s1">(EUR)</span>. The exchange rate is 1 EUR = 13.03 ZAR<span class="s2">.</span></p>
<p class="p1">Find the price, in <span class="s1">EUR</span>, that Dominique paid for the perfume bottle. <strong>Give your answer </strong><strong>correct to two decimal places</strong>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>(i) \({x^2} + {3^2} = {4^2}\) <strong><em>(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into Pythagoras’ formula.</p>
<p>Accept correct alternative method using trigonometric ratios.</p>
<p> </p>
<p>\(x = 2.64575 \ldots \) <strong><em>(A1)</em></strong></p>
<p>\(x = 2.65{\text{ }}({\text{cm}})\) <strong><em>(AG)</em></strong></p>
<p><strong>Note: </strong>The unrounded and rounded answer must be seen for the <strong><em>(A1) </em></strong>to be awarded.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>\(\sqrt {{4^2} - {3^2}} \) <strong><em>(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into Pythagoras’ formula.</p>
<p> </p>
<p>\( = \sqrt 7 \) <strong><em>(A1)</em></strong></p>
<p>\( = 2.65{\text{ (cm)}}\) <strong><em>(AG)</em></strong></p>
<p><strong>Note: </strong>The exact answer must be seen for the final <strong><em>(A1) </em></strong>to be awarded.</p>
<p> </p>
<p>(ii) \(\pi \times {3^2} \times 4.5 + \frac{1}{3}\pi \times {3^2} \times 2.65\) <strong><em>(M1)(M1)(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into the volume of a cylinder formula, <strong><em>(M1) </em></strong>for correct substitution into the volume of a cone formula, <strong><em>(M1) </em></strong>for adding both of their volumes.</p>
<p> </p>
<p>\( = 152{\text{ c}}{{\text{m}}^3}\;\;\;(152.210 \ldots {\text{ c}}{{\text{m}}^3},{\text{ }}48.45\pi {\text{ c}}{{\text{m}}^3})\) <strong><em>(A1)(G3)</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\pi {3^2}h = 125\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Note:<span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for correct substitution into the volume of a cylinder formula.</p>
<p class="p1">Accept alternative methods. Accept \(4.43\)<span class="s1"> </span>(\(4.42913 \ldots \)) from using rounded answers in \(h = \frac{{125 \times 4.5}}{{127}}\).</p>
<p class="p2"> </p>
<p class="p1">\(h = 4.42{\text{ (cm)}}\;\;\;\left( {4.42097 \ldots {\text{ (cm)}}} \right)\) <span class="Apple-converted-space"> </span><strong><em>(A1)(G2)</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(2\pi \times 3 \times 4.5 + \pi \times 3 \times 4 + \pi \times {3^2}\) <strong><em>(M1)(M1)(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into curved surface area of a cylinder formula, <strong><em>(M1) </em></strong>for correct substitution into the curved surface area of a cone formula, <strong><em>(M1) </em></strong>for adding the area of the base of the cylinder to the other two areas.</p>
<p> </p>
<p>\( = 151{\text{ c}}{{\text{m}}^2}\;\;\;(150.796 \ldots {\text{ c}}{{\text{m}}^2},{\text{ }}48\pi {\text{ c}}{{\text{m}}^2})\) <strong><em>(A1)(G3)</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\frac{{150.796 \ldots }}{7} \times 3\) <span class="Apple-converted-space"> </span><strong><em>(M1)(M1)</em></strong></p>
<p class="p1"><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for dividing their answer to (c) by \(7\), <strong><em>(M1) </em></strong>for multiplying by \(3\). Accept equivalent methods.</p>
<p class="p2"> </p>
<p class="p1">\( = 64.63{\text{ (ZAR)}}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p class="p1"><strong>Notes: </strong>The <strong><em>(A1) </em></strong>is awarded for their correct answer, correctly rounded to <span class="s1">2 </span>decimal places. Follow through from their answer to part (c). If rounded answer to part (c) is used the answer is \(64.71\)<span class="s1"> (ZAR)</span>.</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\frac{{325}}{{13.03}}\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for dividing \(325\)<span class="s1"> </span>by \(13.03\).</p>
<p class="p2"> </p>
<p class="p1">\( = 24.94{\text{ (EUR)}}\) <span class="Apple-converted-space"> </span><strong><em>(A1)(G2)</em></strong></p>
<p class="p1"><strong>Note: </strong>The <strong><em>(A1) </em></strong>is awarded for the correct answer rounded to <span class="s1">2 </span>decimal places, unless already penalized in part (d).</p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A closed rectangular box has a height \(y{\text{ cm}}\) and width \(x{\text{ cm}}\). Its length is twice its width. It has a fixed outer surface area of \(300{\text{ c}}{{\text{m}}^2}\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Factorise \(3{x^2} + 13x - 10\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Solve the equation \(3{x^2} + 13x - 10 = 0\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Consider a function \(f(x) = 3{x^2} + 13x - 10\) .</span></p>
<p><span>Find the equation of the axis of symmetry on the graph of this function.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Consider a function \(f(x) = 3{x^2} + 13x - 10\) .</span></p>
<p><span>Calculate the minimum value of this function.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that \(4{x^2} + 6xy = 300\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find an expression for \(y\) in terms of \(x\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Hence show that the volume \(V\) of the box is given by \(V = 100x - \frac{4}{3}{x^3}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \(\frac{{{\text{d}}V}}{{{\text{d}}x}}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Hence find the value of \(x\) and of \(y\) required to make the volume of the box a maximum.</span></p>
<p><span>(ii) Calculate the maximum volume.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">ii.e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\((3x - 2)(x + 5)\) <em><strong>(A1)(A1)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\((3x - 2)(x + 5) = 0\)</span></p>
<p><span>\(x = \frac{2}{3}\) or \(x = - 5\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(x = \frac{{ - 13}}{6}{\text{ }}( - 2.17)\) <em><strong>(A1)(A1)</strong></em><strong>(ft)<em>(G2)</em></strong></span></p>
<p><br><span><strong>Note: <em>(A1)</em></strong> is for \(x = \), <em><strong>(A1)</strong></em> for value. <strong>(ft)</strong> if value is half way between roots in (b).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">i.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Minimum \(y = 3{\left( {\frac{{ - 13}}{6}} \right)^2} + 13\left( {\frac{{ - 13}}{6}} \right) - 10\) <em><strong>(M1)</strong></em></span><br><br><span><strong>Note: <em>(M1)</em></strong> for substituting their value of \(x\) from (c) into \(f(x)\) .</span></p>
<p><br><span>\( = - 24.1\) <em><strong>(A1)</strong></em><strong>(ft)<em>(G2)</em></strong></span></p>
<p><span><strong><em>[2 marks]<br></em></strong></span></p>
<div class="question_part_label">i.d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{Area}} = 2(2x)x + 2xy + 2(2x)y\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><br><span><strong>Note: <em>(M1)</em></strong> for using the correct surface area formula (which can</span> <span>be implied if numbers in the correct place). <em><strong>(A1)</strong></em> for using correct numbers.</span><br><br></p>
<p><span>\(300 = 4{x^2} + 6xy\) <em><strong>(AG)</strong></em></span></p>
<p><span><span><strong><br>Note: </strong>Final line must be seen or previous</span> <span><em><strong>(A1)</strong></em> mark is lost.</span></span></p>
<p><span><span><em><strong>[2 marks]</strong></em><br></span></span></p>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(6xy = 300 - 4{x^2}\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(y = \frac{{300 - 4{x^2}}}{{6x}}\) <em>or</em> \(\frac{{150 - 2{x^2}}}{{3x}}\) <em><strong>(A1)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{Volume}} = x(2x)y\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(V = 2{x^2}\left( {\frac{{300 - 4{x^2}}}{{6x}}} \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>\( = 100x - \frac{4}{3}{x^3}\) <strong>(AG)</strong></span></p>
<p><br><span><strong>Note: </strong>Final line must be seen or previous <em><strong>(A1)</strong></em> mark is lost.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">ii.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{{\text{d}}V}}{{{\text{d}}x}} = 100 - \frac{{12{x^2}}}{3}\) or \(100 - 4{x^2}\) <em><strong>(A1)(A1)</strong></em></span></p>
<p><span><em><strong> </strong></em><strong>Note: <em>(A1)</em></strong> for each term.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">ii.d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>Unit penalty <strong>(UP)</strong> is applicable where indicated in the left hand column</em></span></p>
<p><span>(i) For maximum \(\frac{{{\text{d}}V}}{{{\text{d}}x}} = 0\) or \(100 - 4{x^2} = 0\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(x = 5\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>\(y = \frac{{300 - 4{{(5)}^2}}}{{6(5)}}\) or \(\left( {\frac{{150 - 2{{(5)}^2}}}{{3(5)}}} \right)\) <em><strong>(M1)</strong></em></span></p>
<p><span>\( = \frac{{20}}{3}\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><em><strong>(UP)</strong></em> (ii) \(333\frac{1}{3}{\text{ c}}{{\text{m}}^3}{\text{ }}(333{\text{ c}}{{\text{m}}^3})\)</span></p>
<p><span><strong><br>Note: (ft)</strong> from their (e)(i) if working for volume is seen.</span></p>
<p><span><em><strong>[5 marks]</strong></em><br></span></p>
<div class="question_part_label">ii.e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates made a good attempt to factorise the expression.</span></p>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many gained both marks here from a correct answer or ft from the previous part.</span></p>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many used the formula correctly. Some forgot to put \(x = \)</span> .</p>
<div class="question_part_label">i.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates found this value from their GDC.</span></p>
<div class="question_part_label">i.d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">A good attempt was made to show the correct surface area.</span></p>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many could rearrange the equation correctly.</span></p>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Although this was not a difficult question it probably looked complicated for the candidates and it was often left out.</span></p>
<div class="question_part_label">ii.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Those who reached this length could usually manage the differentiation.</span></p>
<div class="question_part_label">ii.d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(i) Many found the correct value of \(x\) but not of \(y\).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) This was well done and again the units were included in most scripts.</span></p>
<div class="question_part_label">ii.e.</div>
</div>
<br><hr><br><div class="specification">
<p>A pan, in which to cook a pizza, is in the shape of a cylinder. The pan has a diameter of 35 cm and a height of 0.5 cm.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_11.14.51.png" alt="M17/5/MATSD/SP2/ENG/TZ1/04"></p>
</div>
<div class="specification">
<p>A chef had enough pizza dough to exactly fill the pan. The dough was in the shape of a sphere.</p>
</div>
<div class="specification">
<p>The pizza was cooked in a hot oven. Once taken out of the oven, the pizza was placed in a dining room.</p>
<p>The temperature, \(P\), of the pizza, in degrees Celsius, °C, can be modelled by</p>
<p>\[P(t) = a{(2.06)^{ - t}} + 19,{\text{ }}t \geqslant 0\]</p>
<p>where \(a\) is a constant and \(t\) is the time, in minutes, since the pizza was taken out of the oven.</p>
<p>When the pizza was taken out of the oven its temperature was 230 °C.</p>
</div>
<div class="specification">
<p>The pizza can be eaten once its temperature drops to 45 °C.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the volume of this pan.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the radius of the sphere in cm, correct to one decimal place.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(a\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the temperature that the pizza will be 5 minutes after it is taken out of the oven.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, to the nearest second, the time since the pizza was taken out of the oven until it can be eaten.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In the context of this model, state what the value of 19 represents.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\((V = ){\text{ }}\pi \times {{\text{(17.5)}}^2} \times 0.5\) <strong><em>(A1)(M1)</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Award <strong><em>(A1) </em></strong>for 17.5 (or equivalent) seen.</p>
<p>Award <strong><em>(M1) </em></strong>for correct substitutions into volume of a cylinder formula.</p>
<p> </p>
<p>\( = 481{\text{ c}}{{\text{m}}^3}{\text{ }}(481.056 \ldots {\text{ c}}{{\text{m}}^3},{\text{ }}153.125\pi {\text{ c}}{{\text{m}}^3})\) <strong><em>(A1)(G2)</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{4}{3} \times \pi \times {r^3} = 481.056 \ldots \) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for equating <strong>their </strong>answer to part (a) to the volume of sphere.</p>
<p> </p>
<p>\({r^3} = \frac{{3 \times 481.056 \ldots }}{{4\pi }}{\text{ }}( = 114.843 \ldots )\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correctly rearranging so \({r^3}\) is the subject.</p>
<p> </p>
<p>\(r = 4.86074 \ldots {\text{ (cm)}}\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for correct unrounded answer seen. Follow through from part (a).</p>
<p> </p>
<p>\( = 4.9{\text{ (cm)}}\) <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> The final <strong><em>(A1)</em>(ft) </strong>is awarded for rounding their unrounded answer to one decimal place.</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(230 = a{(2.06)^0} + 19\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution.</p>
<p> </p>
<p>\(a = 211\) <strong><em>(A1)(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\((P = ){\text{ }}211 \times {(2.06)^{ - 5}} + 19\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution into the function, \(P(t)\). Follow through from part (c). The negative sign in the exponent is required for correct substitution.</p>
<p> </p>
<p>\( = 24.7\) (°C) \((24.6878 \ldots \) (°C)) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(45 = 211 \times {(2.06)^{ - t}} + 19\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for equating 45 to the exponential equation and for correct substitution (follow through for their \(a\) in part (c)).</p>
<p> </p>
<p>\((t = ){\text{ }}2.89711 \ldots \) <strong><em>(A1)</em>(ft)<em>(G1)</em></strong></p>
<p>\(174{\text{ (seconds) }}\left( {173.826 \ldots {\text{ (seconds)}}} \right)\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award final <strong><em>(A1)</em>(ft) </strong>for converting their \({\text{2.89711}} \ldots \) minutes into seconds.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the temperature of the (dining) room <strong><em>(A1)</em></strong></p>
<p><strong>OR</strong></p>
<p>the lowest final temperature to which the pizza will cool <strong><em>(A1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Amir needs to construct an isosceles triangle \({\text{ABC}}\)</span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;"> whose area is \(100{\text{ cm}}^2\). The equal sides, </span></span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\({\text{AB}}\) </span></span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">and </span></span></span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\({\text{BC}}\)</span></span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">, are \(20{\text{ cm}}\) long.</span></span></span></span></p>
</div>
<div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Sylvia is making a square-based pyramid. Each triangle has a base of length \(12{\text{ cm}}\) and a height of \(10{\text{ cm}}\).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Angle </span><span><span>\({\text{ABC}}\) </span>is acute. Show that the angle </span><span><span>\({\text{ABC}}\) </span>is \({30^ \circ }\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the length of </span><span><span>\({\text{AC}}\)</span>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that the <strong>height</strong> of the pyramid is \(8{\text{ cm}}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>\({\text{M}}\) is the midpoint of the base of one of the triangles and </span><span><span>\({\text{O}}\)</span> is the apex of the pyramid. </span></p>
<p><span>Find the angle that the line </span><span><span>\({\text{MO}}\)</span> makes with the base of the pyramid.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the volume of the pyramid.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Daniel wants to make a rectangular prism with the same volume as that of Sylvia’s pyramid. The base of his prism is to be a square of side \(10{\text{ cm}}\). Calculate the height of the prism.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{1}{2}{20^2}\sin B = 100\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span>\(B = {30^ \circ }\) <em><strong>(AG)</strong></em></span></p>
<p><span><span><strong>Note: <em>(M1)</em></strong> for correct substituted formula and</span><span> <em><strong>(A1)</strong></em> for correct substitution. \(B = {30^ \circ }\) must be seen or previous <em><strong>(A1)</strong></em> mark is lost.</span></span></p>
<p><span><span><em><strong>[2 marks]</strong></em><br></span></span></p>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>Unit penalty <strong>(UP)</strong> is applicable where indicated in the left hand column.</em></span></p>
<p><span>\({\overline {{\text{AC}}} ^2} = 2 \times {20^2} - 2 \times {20^2} \times \cos {30^ \circ }\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span><span><em><strong>(UP)</strong></em> </span>\(\overline {{\text{AC}}} = 10.4{\text{ cm}}\)</span><span> <em><strong>(A1)(G2)</strong></em></span></p>
<p><span><strong>Note: <em>(M1)</em></strong> for using cosine rule, <em><strong>(A1)</strong></em> for correct substitution. Last <em><strong>(A1)</strong></em> is for the correct answer. Accept use of sine rule or any correct method e.g. \({\text{AC}} = 2 \times 20\sin {15^ \circ }\) .</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({x^2} + {6^2} = {10^2}\) </span><span><em><strong>(A1)(M1)</strong></em></span></p>
<p><span>\(x = 8{\text{ cm}}\) </span><span><em><strong>(AG)</strong></em></span></p>
<p><span><strong>Note: </strong></span><span><em><strong>(A1)</strong></em> for \(6\) (or \(36\)) seen and <em><strong>(M1)</strong></em> for using Pythagoras with correct substitution. \(x = 8\) must be seen or previous <em><strong>(M1)</strong></em> mark is lost.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\cos \beta = \frac{6}{{10}}\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span>\(\beta = {53.1^ \circ }\) <em><strong>(A1)(G2)</strong></em></span></p>
<p><span><strong>OR</strong> equivalent</span></p>
<p><span><strong>Note: <em>(M1)</em></strong> for use of trigonometric ratio with numbers from question. <em><strong>(A1)</strong></em> for use of correct numbers, and <em><strong>(A1)</strong></em> for correct answer.</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>Unit penalty <strong>(UP)</strong> is applicable where indicated in the left hand column.</em></span></p>
<p><span>\(vol = \frac{{{{12}^2} \times 8}}{3}\) <em><strong>(M1)</strong></em></span></p>
<p><span><span><em><strong>(UP)</strong></em> </span>\( = 384{\text{ c}}{{\text{m}}^3}\) <em><strong>(A1)(G2)</strong></em><br></span></p>
<p><span><strong>Note: <em>(M1)</em></strong> for correct formula and correct substitution, <em><strong>(A1)</strong></em> for correct answer.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">ii.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>Unit penalty <strong>(UP)</strong> is applicable where indicated in the left hand column.</em></span></p>
<p><span><em>Let h be the height</em></span></p>
<p><span>\({10^2}h = 384\) <em><strong>(M1)</strong></em></span></p>
<p><span><span><em><strong>(UP)</strong></em> </span>\( = 3.84{\text{ cm}}\) <em><strong>(A1)</strong></em><strong>(ft)<em>(G2)</em></strong></span></p>
<p><span><strong>Note: <em>(M1)</em></strong> for correct formula and correct substitution, <em><strong>(A1)</strong></em> for correct answer. <strong>(ft)</strong> from answer to part (c).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">ii.d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many students did not write the units in their answers and were penalized with the UP in this question.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Part (a) was not very well answered. It looked as if the candidates did not understand the question. Many candidates did not draw a sketch of the triangle; this would have helped them to solve the question. Many candidates simply calculated the remaining angles of the triangle and showed that the sum was \({180^ \circ }\) . This was a clear example of the misunderstanding of the term "show that". Part (b) was well done though some candidates lost a mark for not giving the answer to the correct accuracy.</span></p>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many students did not write the units in their answers and were penalized with the UP in this question.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Part (a) was not very well answered. It looked as if the candidates did not understand the question. Many candidates did not draw a sketch of the triangle; this would have helped them to solve the question. Many candidates simply calculated the remaining angles of the triangle and showed that the sum was \({180^ \circ }\) . This was a clear example of the misunderstanding of the term "show that". Part (b) was well done though some candidates lost a mark for not giving the answer to the correct accuracy.</span></p>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many students did not write the units in their answers and were penalized with the UP in this question.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The weaker candidates spent a lot of time in (a) using the wrong triangle to find half of the diagonal of the base. Finally they used Pythagoras theorem with the wrong numbers. Part (b) was well answered by most of the students. For the volume of the pyramid in (c) they used the correct formula though not always with the correct substitutions. To find the height of the prism in (d) the most common error was multiplying the volume of the prism by \(\frac{1}{3}\). It seemed that many did not know the term 'prism'.</span></p>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many students did not write the units in their answers and were penalized with the UP in this question.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The weaker candidates spent a lot of time in (a) using the wrong triangle to find half of the diagonal of the base. Finally they used Pythagoras theorem with the wrong numbers. Part (b) was well answered by most of the students. For the volume of the pyramid in (c) they used the correct formula though not always with the correct substitutions. To find the height of the prism in (d) the most common error was multiplying the volume of the prism by \(\frac{1}{3}\). It seemed that many did not know the term 'prism'.</span></p>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many students did not write the units in their answers and were penalized with the UP in this question.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The weaker candidates spent a lot of time in (a) using the wrong triangle to find half of the diagonal of the base. Finally they used Pythagoras theorem with the wrong numbers. Part (b) was well answered by most of the students. For the volume of the pyramid in (c) they used the correct formula though not always with the correct substitutions. To find the height of the prism in (d) the most common error was multiplying the volume of the prism by \(\frac{1}{3}\). It seemed that many did not know the term 'prism'.</span></p>
<div class="question_part_label">ii.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many students did not write the units in their answers and were penalized with the UP in this question.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The weaker candidates spent a lot of time in (a) using the wrong triangle to find half of the diagonal of the base. Finally they used Pythagoras theorem with the wrong numbers. Part (b) was well answered by most of the students. For the volume of the pyramid in (c) they used the correct formula though not always with the correct substitutions. To find the height of the prism in (d) the most common error was multiplying the volume of the prism by \(\frac{1}{3}\). It seemed that many did not know the term 'prism'.</span></p>
<div class="question_part_label">ii.d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The quadrilateral ABCD shown below represents a sandbox. AB and BC have the same length. AD is \(9{\text{ m}}\) long and CD is \(4.2{\text{ m}}\) long. Angles ADC and ABC are \({95^ \circ }\) and \({130^ \circ }\) respectively.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the length of AC.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Write down the size of angle BCA.</span></p>
<p><span>(ii) Calculate the length of AB.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that the area of the sandbox is \(31.1{\text{ }}{{\text{m}}^2}\) correct to 3 s.f.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The sandbox is a prism. Its edges are \(40{\text{ cm}}\) high. The sand occupies one third of the volume of the sandbox. Calculate the volume of sand in the sandbox.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{A}}{{\text{C}}^2} = {9^2} + {4.2^2} - 2 \times 9 \times 4.2 \times \cos {95^ \circ }\) <em><strong>(M1)(A1)</strong></em></span><br><span>\({\text{AC}} = 10.3{\text{ m}}\) <em><strong>(A1)(G2)</strong></em></span></p>
<p><span><strong>Note: <em>(M1)</em></strong> for correct substituted formula and <em><strong>(A1)</strong></em> for correct substitution. If radians used answer is \(6.59\). Award at most <em><strong>(M1)(A1)(A0)</strong></em>.</span></p>
<p><span><strong>Note: </strong>The final <em><strong>A1</strong></em> is only awarded if the correct units are present; only penalize once for the lack of units or incorrect units.<br></span></p>
<p><span> </span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \({\text{B}}\hat{\text{C}}{\text{A}} = {25^ \circ }\) <em><strong>(</strong><strong>A1)</strong></em></span></p>
<p><span> </span></p>
<p><span>(ii) \(\frac{{{\text{AB}}}}{{\sin {{25}^ \circ }}} = \frac{{10.258 \ldots }}{{\sin {{130}^ \circ }}}\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span>\({\text{AB}} = 5.66{\text{ m}}\) <em><strong>(A1)</strong></em><strong>(ft)<em>(G2)</em></strong></span></p>
<p><span><strong>Note: <em>(M1)</em></strong> for correct substituted formula and <em><strong>(A1)</strong></em> for correct substitution. <em><strong>(A1)</strong></em> for correct answer.</span></p>
<p><span> </span></p>
<p><span>Follow through with angle </span><span>\({\text{B}}\)\(\hat{\text{C}}\)\({\text{A}}\)</span><span> and their AC. Allow \({\text{AB}} = 5.68\) if \({\text{AC}} = 10.3\) used.</span> <span>If radians used answer is \(0.938\) (unreasonable answer). Award at most <strong><em>(M1)(A1)(A0)</em>(ft)</strong>.</span></p>
<p><span><strong>OR</strong></span></p>
<p><span>Using that ABC is isosceles</span></p>
<p><span>\({\text{cos2}}{{\text{5}}^ \circ } = \frac{{\frac{1}{2} \times 10.258 \ldots }}{{{\text{AB}}}}\) (<em>or equivalent</em>) <em><strong>(A1)(M1)</strong></em><strong>(ft)</strong></span></p>
<p><span>\({\text{AB}} = 5.66{\text{ m}}\) <em><strong>(A1)</strong></em><strong>(ft)<em>(G2)</em></strong></span></p>
<p><span><strong>Note: <em>(A1)</em></strong> for \(\frac{1}{2}\) of their AB seen, <em><strong>(M1)</strong></em> for correct trigonometric ratio and correct substitution, <em><strong>(A1)</strong></em> for correct answer. If \(\frac{1}{2}{\text{AB}}\) seen and correct answer is given award <em><strong>(A1)(G1)</strong></em>. Allow \({\text{AB}} = 5.68\) if \({\text{AC}} = 10.3\) used. If radians used answer is \(3.32\). Award <em><strong>(A1)(M1)(A1)</strong></em><strong>(ft)</strong>. If \(\sin 65\) and radians used answer is \(3.99\). Award <strong><em>(A1)(M1)(A1)</em>(ft)</strong>.</span></p>
<p><span><strong>Note: </strong>The final <em><strong>A1</strong></em> is only awarded in (ii) if the correct units are present; only penalize once for the lack of units or incorrect units.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Area \( = \frac{1}{2} \times 9 \times 4.2 \times \sin {95^ \circ } + \frac{1}{2} \times {(5.6592 \ldots )^2} \times \sin {130^ \circ }\) <em><strong>(M1)(M1)</strong></em><strong>(ft)<em>(M1)</em></strong></span></p>
<p><span>\( = 31.095 \ldots = 31.1{\text{ }}{{\text{m}}^2}\) (<em>correct to 3 s.f.</em>) <em><strong>(A1)(AG)</strong></em></span></p>
<p><span><strong>Note: <em>(M1)(M1)</em></strong> each for correct substitution in the formula of the area of each triangle, <em><strong>(M1)</strong></em> for adding both areas. <em><strong>(A1)</strong></em> for unrounded answer. Follow through with their length of AB but last mark is lost if they do not reach the correct answer.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Volume of sand \( = \frac{1}{3}(31.09 \ldots \times 0.4)\) <em><strong>(M1)(M1)</strong></em></span></p>
<p><span>\( = 4.15{\text{ }}{{\text{m}}^3}\) <em><strong>(A1)(G2)</strong></em></span></p>
<p><span><strong>Note: <em>(M1)</em></strong> for correct formula of volume of prism and for correct substitution, <em><strong>(M1)</strong></em> for multiplying by \(\frac{1}{3}\) and last <em><strong>(A1)</strong></em> for correct answer only.</span></p>
<p><span><strong>Note: </strong>The final <em><strong>A1</strong></em> is only awarded if the correct units are present; only penalize once for the lack of units or incorrect units.</span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">It could have been written that the diagram was representing the plan of the sandbox. However, examiner’s comments did not find this lack of information an obstacle for the candidates.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Overall the lengths of AC and AB were well done. Sine rule and cosine rule were in general well used. To find the length of AB many students used correctly right- angled trigonometry. The area of the sandbox was in general well done though some students did not gain the final mark due to premature rounding or for not showing the unrounded answer. The volume of the prism was poorly answered by the majority of the students. Most of the students did not use the correct formula. Very few candidates noticed that the value \(40\) was given in cm. It was good to see very few students losing marks for having their GDC setting in radians.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">It could have been written that the diagram was representing the plan of the sandbox. However, examiner’s comments did not find this lack of information an obstacle for the candidates.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Overall the lengths of AC and AB were well done. Sine rule and cosine rule were in general well used. To find the length of AB many students used correctly right- angled trigonometry. The area of the sandbox was in general well done though some students did not gain the final mark due to premature rounding or for not showing the unrounded answer. The volume of the prism was poorly answered by the majority of the students. Most of the students did not use the correct formula. Very few candidates noticed that the value \(40\) was given in cm. It was good to see very few students losing marks for having their GDC setting in radians.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">It could have been written that the diagram was representing the plan of the sandbox. However, examiner’s comments did not find this lack of information an obstacle for the candidates.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Overall the lengths of AC and AB were well done. Sine rule and cosine rule were in general well used. To find the length of AB many students used correctly right- angled trigonometry. The area of the sandbox was in general well done though some students did not gain the final mark due to premature rounding or for not showing the unrounded answer. The volume of the prism was poorly answered by the majority of the students. Most of the students did not use the correct formula. Very few candidates noticed that the value \(40\) was given in cm. It was good to see very few students losing marks for having their GDC setting in radians.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">It could have been written that the diagram was representing the plan of the sandbox. However, examiner’s comments did not find this lack of information an obstacle for the candidates.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Overall the lengths of AC and AB were well done. Sine rule and cosine rule were in general well used. To find the length of AB many students used correctly right- angled trigonometry. The area of the sandbox was in general well done though some students did not gain the final mark due to premature rounding or for not showing the unrounded answer. The volume of the prism was poorly answered by the majority of the students. Most of the students did not use the correct formula. Very few candidates noticed that the value \(40\) was given in cm. It was good to see very few students losing marks for having their GDC setting in radians.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the function \(f(x) = \frac{3}{4}{x^4} - {x^3} - 9{x^2} + 20\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \(f( - 2)\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \(f'(x)\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The graph of the function \(f(x)\) has a local minimum at the point where \(x = - 2\).</span></p>
<p><span>Using your answer to part (b), show that there is a second local minimum at \(x = 3\).</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The graph of the function \(f(x)\) has a local minimum at the point where \(x = - 2\).</span></p>
<p><span>Sketch the graph of the function \(f(x)\) for \( - 5 \leqslant x \leqslant 5\) and \( - 40 \leqslant y \leqslant 50\). Indicate on your</span></p>
<p><span>sketch the coordinates of the \(y\)-intercept.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The graph of the function \(f(x)\) has a local minimum at the point where \(x = - 2\).</span></p>
<p><span>Write down the coordinates of the local maximum.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Let \(T\) be the tangent to the graph of the function \(f(x)\) at the point \((2, –12)\).</span></p>
<p><span>Find the gradient of \(T\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The line \(L\) passes through the point \((2, −12)\) and is perpendicular to \(T\).</span></p>
<p><span>\(L\) has equation \(x + by + c = 0\), where \(b\) and \(c \in \mathbb{Z}\).</span></p>
<p><span>Find</span></p>
<p><span>(i) the gradient of \(L\);</span></p>
<p><span>(ii) the value of \(b\) and the value of \(c\).</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{3}{4}{( - 2)^4} - {( - 2)^3} - 9{( - 2)^2} + 20\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substituting \(x = - 2\) in the function.</span></p>
<p> </p>
<p><span>\(= 4\) <strong><em>(A1)(G2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>If the coordinates \(( - 2,{\text{ }}4)\) are given as the answer award, at most, <strong><em>(M1)(A0)</em></strong><em>. </em>If no working shown award <strong><em>(G1)</em></strong><em>.</em></span></p>
<p><span><em> </em>If \(x = - 2,{\text{ }}y = 4\) seen then award full marks.</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(3{x^3} - 3{x^2} - 18x\) <strong><em>(A1)(A1)(A1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for each correct term, award at most <strong><em>(A1)(A1)(A0) </em></strong>if extra terms seen.</span></p>
<p> </p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(f'(3) = 3 \times {(3)^3} - 3 \times {(3)^2} - 18 \times 3\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substitution in their \(f'(x)\) of \(x = 3\).</span></p>
<p> </p>
<p><span>\( = 0\) <em><strong>(A1)</strong></em></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>\(3{x^3} - 3{x^2} - 18x = 0\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for equating their \(f'(x)\) to zero.</span></p>
<p> </p>
<p><span>\(x = 3\) <strong><em>(A1)</em></strong></span></p>
<p><span>\(f'({x_1}) = 3 \times {({x_1})^3} - 3 \times {({x_1})^2} - 18 \times {x_1} < 0\) where \(0 < {x_1} < 3\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substituting a value of \({x_1}\) in the range \(0 < {x_1} < 3\) into their \(f'\) and showing it is negative (decreasing).</span></p>
<p> </p>
<p><span>\(f'({x_2}) = 3 \times {({x_2})^3} - 3 \times {({x_2})^2} - 18 \times {x_2} > 0\) where \({x_2} > 3\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substituting a value of \({x_2}\) in the range \({x_2} > 3\) into their \(f'\) and showing it is positive (increasing).</span></p>
<p><span><strong>OR</strong></span></p>
<p><span><em>With or without a sketch:</em></span></p>
<p><span>Showing \(f({x_1}) > f(3)\) where \({x_1} < 3\) and \({x_1}\) is close to 3. <strong><em>(M1)</em></strong></span></p>
<p><span>Showing \(f({x_2}) > f(3)\) where \({x_2} > 3\) and \({x_2}\) is close to 3. <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>If a sketch of \(f(x)\) is drawn <strong>in this part of the question and</strong> \(x = 3\) is identified as a stationary point on the curve, then</span></p>
<p><span> (i) award, at most, <strong><em>(M1)(A1)(M1)(M0) </em></strong>if the stationary point has been found;</span></p>
<p><span> (ii) award, at most, <strong><em>(M0)(A0)(M1)(M0) </em></strong>if the stationary point has not been previously found.</span></p>
<p> </p>
<p><span>Since the gradients go from negative (decreasing) through zero to positive (increasing) it is a local minimum <strong><em>(R1)(AG)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Only award <strong><em>(R1) </em></strong>if the first two marks have been awarded <em>ie</em> \(f'(3)\) has been shown to be equal to \(0\).</span></p>
<p> </p>
<p><span><strong><em>[5 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><img src="images/Schermafbeelding_2014-09-03_om_16.12.18.png" alt><span> <strong><em>(A1)(A1)(A1)(A1)</em></strong></span></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for labelled axes and indication of scale on both axes.</span></p>
<p><span> Award <strong><em>(A1) </em></strong>for smooth curve with correct shape.</span></p>
<p><span> Award <strong><em>(A1) </em></strong>for local minima in \({2^{{\text{nd}}}}\) and \({4^{{\text{th}}}}\) quadrants.</span></p>
<p><span> Award <strong><em>(A1) </em></strong>for <em>y </em>intercept \((0, 20)\) seen and labelled. Accept \(20\) on \(y\)<em>-</em>axis.</span></p>
<p><span> Do <strong>not </strong>award the third <strong><em>(A1) </em></strong>mark if there is a turning point on the \(x\)-axis.</span></p>
<p><span> If the derivative function is sketched then award, at most, <strong><em>(A1)(A0)(A0)(A0)</em></strong>.</span></p>
<p><span> For a smooth curve (with correct shape) there should be <strong>ONE </strong>continuous thin line, no part of which is straight and no (one to many) mappings of \(x\).</span></p>
<p> </p>
<p><span><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\((0, 20)\) <strong><em>(G1)(G1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>If parentheses are omitted award <strong><em>(G0)(G1)</em></strong>.</span></p>
<p><span><strong>OR</strong></span></p>
<p><span>\(x = 0,{\text{ }}y = 20\) <strong><em>(G1)(G1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>If the derivative function is sketched in part (d), award <strong><em>(G1)</em>(ft)<em>(G1)</em>(ft) </strong>for \((–1.12, 12.2)\).</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(f'(2) = 3{(2)^3} - 3{(2)^2} - 18(2)\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for substituting \(x = 2\) into their \(f'(x)\).</span></p>
<p> </p>
<p><span>\( = - 24\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></span></p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) Gradient of perpendicular \( = \frac{1}{{24}}\) \((0.0417, 0.041666…)\) <strong><em>(A1)</em>(ft)<em>(G1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Follow through from part (f).</span></p>
<p> </p>
<p><span>(ii) \(y + 12 = \frac{1}{{24}}(x - 2)\) <strong><em>(M1)(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution of \((2, –12)\), <strong><em>(M1) </em></strong>for correct substitution of their perpendicular gradient into equation of line.</span></p>
<p><span><strong>OR</strong></span></p>
<p><span>\( - 12 = \frac{1}{{24}} \times 2 + d\) <strong><em>(M1)</em></strong></span></p>
<p><span>\(d = - \frac{{145}}{{12}}\)</span></p>
<p><span>\(y = \frac{1}{{24}}x - \frac{{145}}{{12}}\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution of \((2, –12)\) and gradient into equation of a straight line, <strong><em>(M1) </em></strong>for correct substitution of the perpendicular gradient and correct substitution of \(d\)into equation of line.</span></p>
<p> </p>
<p><span>\(b = - 24,{\text{ }}c = - 290\) <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)<em>(G3)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Follow through from parts (f) and g(i).</span></p>
<p><span> To award <strong>(ft) </strong>marks, \(b\) and \(c\) must be integers.</span></p>
<p><span> Where candidate has used \(0.042\) from g(i), award <strong><em>(A1)</em>(ft) </strong>for \(–288\).</span></p>
<p> </p>
<p><span><strong><em>[5 marks]</em></strong></span></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Surprisingly, a correct method for substituting the value of –2 into the given function led many candidates to a variety of incorrect answers. This suggests a poor handling of negative signs and/or poor use of the graphic display calculator. Many correct answers were seen in part (b) as candidates seemed to be well-drilled in the process of differentiation. Part (c), however, proved to be quite a discriminator. There were 5 marks for this part of the question and simply showing that \(x - 3\) is a turning point was not sufficient for all of these marks. Many simply scored only two marks by substituting \(x - 3\) into their answer to part (b). Once they had shown that there was a turning point at \(x - 3\), candidates were not expected to use the second derivative but to show that the function decreases for \(x < 3\) and increases for \(x > 3\). Part (d) required a sketch which could have either been done on lined paper or on graph paper. The majority of candidates obtained at least two marks here with the most common errors seen being incomplete labelled axes and curves which were far from being smooth. In part (e), many candidates identified the correct coordinates for the two marks available. But for many candidates, this is where responses stopped as, in part (f), connecting the gradient function found in part (b) to the given coordinates proved problematic and only a significant minority of candidates were able to arrive at the required answer of –24. Indeed, there were many NR (no responses) to this part and the final part of the question. As many candidates found part (f) difficult, even more candidates found getting beyond the gradient of <em>L</em> very difficult indeed. A minority of candidates wrote down the gradient of their perpendicular but then did not seem to know where to proceed from there. Substituting their gradient for <em>b</em> and the coordinates (2, –12) into the equation \(x + by + c = 0\) was a popular, but erroneous, method. It was a rare event indeed to see a script with a correct answer for this part of the question.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Surprisingly, a correct method for substituting the value of –2 into the given function led many candidates to a variety of incorrect answers. This suggests a poor handling of negative signs and/or poor use of the graphic display calculator. Many correct answers were seen in part (b) as candidates seemed to be well-drilled in the process of differentiation. Part (c), however, proved to be quite a discriminator. There were 5 marks for this part of the question and simply showing that \(x - 3\) is a turning point was not sufficient for all of these marks. Many simply scored only two marks by substituting \(x - 3\) into their answer to part (b). Once they had shown that there was a turning point at \(x - 3\), candidates were not expected to use the second derivative but to show that the function decreases for \(x < 3\) and increases for \(x > 3\). Part (d) required a sketch which could have either been done on lined paper or on graph paper. The majority of candidates obtained at least two marks here with the most common errors seen being incomplete labelled axes and curves which were far from being smooth. In part (e), many candidates identified the correct coordinates for the two marks available. But for many candidates, this is where responses stopped as, in part (f), connecting the gradient function found in part (b) to the given coordinates proved problematic and only a significant minority of candidates were able to arrive at the required answer of –24. Indeed, there were many NR (no responses) to this part and the final part of the question. As many candidates found part (f) difficult, even more candidates found getting beyond the gradient of <em>L</em> very difficult indeed. A minority of candidates wrote down the gradient of their perpendicular but then did not seem to know where to proceed from there. Substituting their gradient for <em>b</em> and the coordinates (2, –12) into the equation \(x + by + c = 0\) was a popular, but erroneous, method. It was a rare event indeed to see a script with a correct answer for this part of the question.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Surprisingly, a correct method for substituting the value of –2 into the given function led many candidates to a variety of incorrect answers. This suggests a poor handling of negative signs and/or poor use of the graphic display calculator. Many correct answers were seen in part (b) as candidates seemed to be well-drilled in the process of differentiation. Part (c), however, proved to be quite a discriminator. There were 5 marks for this part of the question and simply showing that \(x - 3\) is a turning point was not sufficient for all of these marks. Many simply scored only two marks by substituting \(x - 3\) into their answer to part (b). Once they had shown that there was a turning point at \(x - 3\), candidates were not expected to use the second derivative but to show that the function decreases for \(x < 3\) and increases for \(x > 3\). Part (d) required a sketch which could have either been done on lined paper or on graph paper. The majority of candidates obtained at least two marks here with the most common errors seen being incomplete labelled axes and curves which were far from being smooth. In part (e), many candidates identified the correct coordinates for the two marks available. But for many candidates, this is where responses stopped as, in part (f), connecting the gradient function found in part (b) to the given coordinates proved problematic and only a significant minority of candidates were able to arrive at the required answer of –24. Indeed, there were many NR (no responses) to this part and the final part of the question. As many candidates found part (f) difficult, even more candidates found getting beyond the gradient of <em>L</em> very difficult indeed. A minority of candidates wrote down the gradient of their perpendicular but then did not seem to know where to proceed from there. Substituting their gradient for <em>b</em> and the coordinates (2, –12) into the equation \(x + by + c = 0\) was a popular, but erroneous, method. It was a rare event indeed to see a script with a correct answer for this part of the question.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Surprisingly, a correct method for substituting the value of –2 into the given function led many candidates to a variety of incorrect answers. This suggests a poor handling of negative signs and/or poor use of the graphic display calculator. Many correct answers were seen in part (b) as candidates seemed to be well-drilled in the process of differentiation. Part (c), however, proved to be quite a discriminator. There were 5 marks for this part of the question and simply showing that \(x - 3\) is a turning point was not sufficient for all of these marks. Many simply scored only two marks by substituting \(x - 3\) into their answer to part (b). Once they had shown that there was a turning point at \(x - 3\), candidates were not expected to use the second derivative but to show that the function decreases for \(x < 3\) and increases for \(x > 3\). Part (d) required a sketch which could have either been done on lined paper or on graph paper. The majority of candidates obtained at least two marks here with the most common errors seen being incomplete labelled axes and curves which were far from being smooth. In part (e), many candidates identified the correct coordinates for the two marks available. But for many candidates, this is where responses stopped as, in part (f), connecting the gradient function found in part (b) to the given coordinates proved problematic and only a significant minority of candidates were able to arrive at the required answer of –24. Indeed, there were many NR (no responses) to this part and the final part of the question. As many candidates found part (f) difficult, even more candidates found getting beyond the gradient of <em>L</em> very difficult indeed. A minority of candidates wrote down the gradient of their perpendicular but then did not seem to know where to proceed from there. Substituting their gradient for <em>b</em> and the coordinates (2, –12) into the equation \(x + by + c = 0\) was a popular, but erroneous, method. It was a rare event indeed to see a script with a correct answer for this part of the question.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Surprisingly, a correct method for substituting the value of –2 into the given function led many candidates to a variety of incorrect answers. This suggests a poor handling of negative signs and/or poor use of the graphic display calculator. Many correct answers were seen in part (b) as candidates seemed to be well-drilled in the process of differentiation. Part (c), however, proved to be quite a discriminator. There were 5 marks for this part of the question and simply showing that \(x - 3\) is a turning point was not sufficient for all of these marks. Many simply scored only two marks by substituting \(x - 3\) into their answer to part (b). Once they had shown that there was a turning point at \(x - 3\), candidates were not expected to use the second derivative but to show that the function decreases for \(x < 3\) and increases for \(x > 3\). Part (d) required a sketch which could have either been done on lined paper or on graph paper. The majority of candidates obtained at least two marks here with the most common errors seen being incomplete labelled axes and curves which were far from being smooth. In part (e), many candidates identified the correct coordinates for the two marks available. But for many candidates, this is where responses stopped as, in part (f), connecting the gradient function found in part (b) to the given coordinates proved problematic and only a significant minority of candidates were able to arrive at the required answer of –24. Indeed, there were many NR (no responses) to this part and the final part of the question. As many candidates found part (f) difficult, even more candidates found getting beyond the gradient of <em>L</em> very difficult indeed. A minority of candidates wrote down the gradient of their perpendicular but then did not seem to know where to proceed from there. Substituting their gradient for <em>b</em> and the coordinates (2, –12) into the equation \(x + by + c = 0\) was a popular, but erroneous, method. It was a rare event indeed to see a script with a correct answer for this part of the question.</span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Surprisingly, a correct method for substituting the value of –2 into the given function led many candidates to a variety of incorrect answers. This suggests a poor handling of negative signs and/or poor use of the graphic display calculator. Many correct answers were seen in part (b) as candidates seemed to be well-drilled in the process of differentiation. Part (c), however, proved to be quite a discriminator. There were 5 marks for this part of the question and simply showing that \(x - 3\) is a turning point was not sufficient for all of these marks. Many simply scored only two marks by substituting \(x - 3\) into their answer to part (b). Once they had shown that there was a turning point at \(x - 3\), candidates were not expected to use the second derivative but to show that the function decreases for \(x < 3\) and increases for \(x > 3\). Part (d) required a sketch which could have either been done on lined paper or on graph paper. The majority of candidates obtained at least two marks here with the most common errors seen being incomplete labelled axes and curves which were far from being smooth. In part (e), many candidates identified the correct coordinates for the two marks available. But for many candidates, this is where responses stopped as, in part (f), connecting the gradient function found in part (b) to the given coordinates proved problematic and only a significant minority of candidates were able to arrive at the required answer of –24. Indeed, there were many NR (no responses) to this part and the final part of the question. As many candidates found part (f) difficult, even more candidates found getting beyond the gradient of <em>L</em> very difficult indeed. A minority of candidates wrote down the gradient of their perpendicular but then did not seem to know where to proceed from there. Substituting their gradient for <em>b</em> and the coordinates (2, –12) into the equation \(x + by + c = 0\) was a popular, but erroneous, method. It was a rare event indeed to see a script with a correct answer for this part of the question.</span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Surprisingly, a correct method for substituting the value of –2 into the given function led many candidates to a variety of incorrect answers. This suggests a poor handling of negative signs and/or poor use of the graphic display calculator. Many correct answers were seen in part (b) as candidates seemed to be well-drilled in the process of differentiation. Part (c), however, proved to be quite a discriminator. There were 5 marks for this part of the question and simply showing that \(x - 3\) is a turning point was not sufficient for all of these marks. Many simply scored only two marks by substituting \(x - 3\) into their answer to part (b). Once they had shown that there was a turning point at \(x - 3\), candidates were not expected to use the second derivative but to show that the function decreases for \(x < 3\) and increases for \(x > 3\). Part (d) required a sketch which could have either been done on lined paper or on graph paper. The majority of candidates obtained at least two marks here with the most common errors seen being incomplete labelled axes and curves which were far from being smooth. In part (e), many candidates identified the correct coordinates for the two marks available. But for many candidates, this is where responses stopped as, in part (f), connecting the gradient function found in part (b) to the given coordinates proved problematic and only a significant minority of candidates were able to arrive at the required answer of –24. Indeed, there were many NR (no responses) to this part and the final part of the question. As many candidates found part (f) difficult, even more candidates found getting beyond the gradient of <em>L</em> very difficult indeed. A minority of candidates wrote down the gradient of their perpendicular but then did not seem to know where to proceed from there. Substituting their gradient for <em>b</em> and the coordinates (2, –12) into the equation \(x + by + c = 0\) was a popular, but erroneous, method. It was a rare event indeed to see a script with a correct answer for this part of the question.</span></p>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">ABCDV is a solid glass pyramid. The base of the pyramid is a square of side 3.2 cm. The vertical height is 2.8 cm. The vertex V is directly above the centre O of the base.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the volume of the pyramid.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The glass weighs 9.3 grams per cm<sup>3</sup>. Calculate the weight of the pyramid.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that the length of the sloping edge VC of the pyramid is 3.6 cm.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the angle at the vertex, \({\text{B}}{\operatorname {\hat V}}{\text{C}}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the total surface area of the pyramid.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><em>Unit penalty <strong>(UP)</strong> is applicable in question parts (a), (b) and (e) <strong>only</strong>.</em><br></span></p>
<p><span>\({\text{V}} = \frac{1}{3} \times {3.2^2} \times 2.8\) <em><strong>(M1)</strong></em></span></p>
<p><span><em><strong>(M1) </strong>for substituting in correct formula</em></span></p>
<p><span><em><strong>(UP)</strong></em> = 9.56 cm<sup>3</sup><em><strong> (A1)(G2)<br></strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>Unit penalty <strong>(UP)</strong> is applicable in question parts (a), (b) and (e) <strong>only</strong>.</em></span></p>
<p><span>\(9.56 \times 9.3\) <em><strong>(M1)</strong></em></span></p>
<p><span><em><strong>(UP)</strong></em> = 88.9 grams <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{1}{2} {\text{base}} = 1.6 {\text{ seen}}\) <em><strong>(M1)</strong></em></span></p>
<p><span><em>award <strong>(M1)</strong> for halving base</em></span></p>
<p><span>\({\text{OC}}^2 = 1.6^2 + 1.6^2 = 5.12\) <em><strong>(A1)</strong></em></span></p>
<p><span><em>award <strong>(A1)</strong> for one correct use of Pythagoras</em></span></p>
<p><span>\(5.12 + 2.8^2 = 12.96 = {\text{VC}}^2\) <em><strong>(M1)</strong></em></span></p>
<p><span><em>award <strong>(M1)</strong> for using Pythagoras again to find VC<sup>2</sup></em></span></p>
<p><span>VC = 3.6 <strong>AG</strong></span></p>
<p><em><span>award <strong>(A1)</strong> for</span></em><span> 3</span><span>.6</span><em><span> obtained from</span></em><span> 1</span><span>2.96</span><em><span> only (not</span></em><span> 1</span><span>2.95…<em>)</em></span><em><span> <strong>(A1)</strong></span></em></p>
<p><span><strong>OR</strong><br></span></p>
<p><span>\({\text{AC}}^2 = 3.2^2 + 3.2^2 = 20.48\) <em><strong>(A1)</strong></em></span></p>
<p><em><span>award <strong>(A1)</strong> for one correct use of Pythagoras</span></em></p>
<p><span>({\text{OC}} = \frac{1}{2} \sqrt{20.48}\) ( = 2.26...) <em><strong>(M1)</strong></em></span></p>
<p><span><em>award <strong>(M1)</strong> for halving AC</em></span></p>
<p><span>\(2.8^2 + (2.26...)^2 = {\text{VC}}^2 = 12.96\) <em><strong>(M1)</strong></em></span></p>
<p><span><em>award <strong>(M1)</strong> for using Pythagoras again to find VC<sup>2</sup></em></span></p>
<p><span>VC = 3.6 <strong>AG <em>(A1)</em></strong></span></p>
<p><span><em>award <strong>(A1)</strong> for</em> 3.6<em> obtained from</em> 12.96<em> only (not</em> 12.95…<em>)</em></span><span><strong><br></strong></span></p>
<p><span><strong><em>[4 marks]</em><br></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(3.2^2 = 3.6^2 + 3.6^2 - 2 \times (3.6) (3.6) \cos\) </span><span>\({\text{B}}{\operatorname {\hat V}}{\text{C}}\)</span><span> <em><strong>(M1)(A1)</strong></em></span></p>
<p><span>\({\text{B}}{\operatorname {\hat V}}{\text{C}}\)</span><span><span> \( = {52.8^\circ }\) </span><em>(no</em> <strong>(ft)</strong> <em>here)</em> <em><strong>(A1)(G2)</strong></em></span></p>
<p><em><span>award <strong>(M1)</strong> for substituting in correct formula, <strong>(A1)</strong> for correct</span> <span>substitution</span></em></p>
<p><strong><span>OR</span></strong></p>
<p><span>\(\sin\) </span><span>\({\text{B}}{\operatorname {\hat V}}{\text{M}}\)</span><span><span> \( = \frac{{1.6}}{{3.6}}\)</span> </span><span>where <em>M</em> is the midpoint of BC <em><strong>(M1)(A1)</strong></em></span></p>
<p><span>\({\text{B}}{\operatorname {\hat V}}{\text{C}}\)</span><span><span><span> \( = {52.8^\circ}\)</span></span> <em>(no</em> <strong>(ft)</strong> <em>here)</em> <strong><em>(A1)</em></strong></span></p>
<p><span><strong><em>[3 marks]<br></em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>Unit penalty <strong>(UP)</strong> is applicable in question parts (a), (b) and (e) <strong>only</strong>.</em></span></p>
<p><span>\(4 \times \frac{1}{2}{(3.6)^2} \times \sin (52.8^\circ ) + {(3.2)^2}\) <em><strong>(M1)(M1)(M1)</strong></em></span></p>
<p><span><em>award <strong>(M1)</strong> for</em> \( \times 4\)<em>, <strong>(M1)</strong> for substitution in relevant triangle area,</em> (\(\frac{1}{2}(3.2)(2.8)\) <em>gets</em> <strong><em>(M0)</em></strong><em>)</em></span></p>
<p><span><em><strong>(M1)</strong> for</em> \(+ {(3.2)^2}\)</span></p>
<p><span><em><strong>(UP)</strong></em> = 30.9 cm<sup>2</sup> <em>(</em><strong>(ft)</strong> <em>from their</em> <em>(d))</em> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><em><strong>[4 marks]<br></strong></em></span></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The volume of the pyramid and the weight were well done. Many candidates lost their unit penalty here. They had trouble showing that the sloping edge was 3.6 cm. The angle BVC was done well but not the total surface area. They knew that they needed four sides and the base, but finding the area of the triangle proved difficult for the less able candidates.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The volume of the pyramid and the weight were well done. Many candidates lost their unit penalty here. They had trouble showing that the sloping edge was 3.6 cm. The angle BVC was done well but not the total surface area. They knew that they needed four sides and the base, but finding the area of the triangle proved difficult for the less able candidates.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The volume of the pyramid and the weight were well done. Many candidates lost their unit penalty here. They had trouble showing that the sloping edge was 3.6 cm. The angle BVC was done well but not the total surface area. They knew that they needed four sides and the base, but finding the area of the triangle proved difficult for the less able candidates.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The volume of the pyramid and the weight were well done. Many candidates lost their unit penalty here. They had trouble showing that the sloping edge was 3.6 cm. The angle BVC was done well but not the total surface area. They knew that they needed four sides and the base, but finding the area of the triangle proved difficult for the less able candidates.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The volume of the pyramid and the weight were well done. Many candidates lost their unit penalty here. They had trouble showing that the sloping edge was 3.6 cm. The angle BVC was done well but not the total surface area. They knew that they needed four sides and the base, but finding the area of the triangle proved difficult for the less able candidates.</span></p>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A surveyor has to calculate the area of a triangular piece of land, DCE.</p>
<p class="p1">The lengths of CE and DE cannot be directly measured because they go through a swamp.</p>
<p class="p1">AB, DE, BD and AE are straight paths. Paths AE and DB intersect at point C.</p>
<p class="p1">The length of AB is 15 km, BC is 10 km, AC is 12 km, and DC is 9 km.</p>
<p class="p1">The following diagram shows the surveyor’s information.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-04_om_11.57.28.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Find the size of angle \({\rm{ACB}}\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Show that the size of angle \({\rm{DCE}}\) is \(85.5^\circ\), correct to one decimal place.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The surveyor measures the size of angle \({\text{CDE}}\) to be twice that of angle \({\text{DEC}}\).</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>Using angle \({\text{DCE}} = 85.5^\circ \), <span class="s1">find </span>the size of angle \({\text{DEC}}\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Find the length of \({\text{DE}}\).</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the area of triangle \({\text{DEC}}\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>(i) \(\cos {\rm{A\hat CB}} = \frac{{{{10}^2} + {{12}^2} - {{15}^2}}}{{2 \times 10 \times 12}}\) <strong><em>(M1)(A1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substituted cosine rule,</p>
<p><strong><em>(A1) </em></strong>for correct substitution.</p>
<p> </p>
<p>\({\rm{A\hat CB}} = 85.5^\circ \;\;\;({\text{85.4593}} \ldots {\text{)}}\) <strong><em>(A1)(G2)</em></strong></p>
<p> </p>
<p>(ii) \({\rm{D\hat CE}} = {\rm{A\hat CB}}\;\;\;{\text{and}}\;\;\;{\rm{A\hat CB}} = 85.5^\circ \;\;\;({\text{85.4593}} \ldots ^\circ {\text{)}}\) <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>OR</strong></p>
<p>\({\rm{B\hat CE}} = 180^\circ - 85.5^\circ = 94.5^\circ \;\;\;{\text{and}}\;\;\;{\rm{D\hat CE}} = 180^\circ - 94.5^\circ = 85.5^\circ \) <strong><em>(A1)</em></strong></p>
<p><strong>Notes: </strong>Both reasons must be seen for the <strong><em>(A1) </em></strong>to be awarded.</p>
<p> </p>
<p>\({\rm{D\hat CE}} = 85.5^\circ \) <strong><em>(AG)</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) \({\rm{D\hat EC}} = \frac{{180^\circ - 85.5^\circ }}{3}\) <strong><em>(M1)</em></strong></p>
<p>\({\rm{D\hat EC}} = 31.5^\circ \) <strong><em>(A1)(G2)</em></strong></p>
<p> </p>
<p>(ii) \(\frac{{\sin (31.5^\circ )}}{9} = \frac{{\sin (85.5^\circ )}}{{{\text{DE}}}}\) <strong><em>(M1)(A1)</em>(ft)</strong></p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substituted sine rule, <strong><em>(A1) </em></strong>for correct substitution.</p>
<p> </p>
<p>\({\text{DE}} = 17.2{\text{ (km)}}(17.1718 \ldots )\). <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(0.5 \times 17.1718 \ldots \times 9 \times \sin (63^\circ )\) <strong><em>(A1)</em>(ft)<em>(M1)(A1)</em>(ft)</strong></p>
<p><strong>Note: </strong>Award <strong><em>(A1)</em>(ft) </strong>for \(63\) seen, <strong><em>(M1) </em></strong>for substituted triangle area formula, <strong><em>(A1)</em>(ft) </strong>for \(0.5 \times 17.1718 \ldots \times 9 \times \sin ({\text{their angle CDE}})\).</p>
<p> </p>
<p><strong>OR</strong></p>
<p>\({\text{(triangle height}} = ){\text{ }}9 \times \sin (63^\circ )\) <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong></p>
<p>\({\text{0.5}} \times {\text{17.1718}} \ldots \times {\text{9}} \times {\text{sin(their angle CDE)}}\) <strong><em>(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(A1)</em>(ft) </strong>for \(63\) seen, <strong><em>(A1)</em>(ft) </strong>for correct triangle height with their angle \({\text{CDE}}\), <strong><em>(M1) </em></strong>for \({\text{0.5}} \times {\text{17.1718}} \ldots \times {\text{9}} \times {\text{sin(their angle CDE)}}\).</p>
<p> </p>
<p>\( = 68.9{\text{ k}}{{\text{m}}^2}\;\;\;(68.8509 \ldots )\) <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p><strong>Notes: </strong>Units are required for the last <strong><em>(A1)</em>(ft) </strong>mark to be awarded.</p>
<p>Follow through from parts (b)(i) and (b)(ii).</p>
<p>Follow through from their angle \({\text{CDE}}\) <strong>within this part of the question</strong>.</p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">A cross-country running course consists of a beach section and a forest section. Competitors run from \({\text{A}}\) to \({\text{B}}\), then from \({\text{B}}\) to \({\text{C}}\) and from \({\text{C}}\) back to \({\text{A}}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The running course from \({\text{A}}\) to \({\text{B}}\) is along the beach, while the course from \({\text{B}}\), through \({\text{C}}\) and back to \({\text{A}}\), is through the forest.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The course is shown on the following diagram.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><br><img src="images/Schermafbeelding_2014-09-02_om_11.39.47.png" alt><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Angle \({\text{ABC}}\) is \(110^\circ\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">It takes Sarah \(5\) minutes and \(20\) seconds to run from \({\text{A}}\) to \({\text{B}}\) at a speed of \(3.8{\text{ m}}{{\text{s}}^{ - 1}}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using ‘<em>distance </em>= <em>speed </em>\( \times \) <em>time</em>’, show that the distance from \({\text{A}}\) to \({\text{B}}\) is \(1220\) metres correct to 3 significant figures.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The distance from \({\text{B}}\) to \({\text{C}}\) is \(850\) metres. Running this part of the course takes Sarah \(5\) minutes and \(3\) seconds.</span></p>
<p><span>Calculate the speed, in \({\text{m}}{{\text{s}}^{ - 1}}\), that Sarah runs from \({\text{B}}\) to \({\text{C}}\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The distance from \({\text{B}}\) to \({\text{C}}\) is \(850\) metres. Running this part of the course takes Sarah \(5\) minutes and \(3\) seconds.</span></p>
<p><span><span><span>Calculate the distance, in metres, from </span></span><span><span>\({\mathbf{C}}\)</span></span><span><span> </span></span><strong><span><span>to </span></span></strong><span><span>\({\mathbf{A}}\).</span></span></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The distance from \({\text{B}}\) to \({\text{C}}\) is \(850\) metres. Running this part of the course takes Sarah \(5\) minutes and \(3\) seconds.</span></p>
<p><span>Calculate the total distance, in metres, of the cross-country running course.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The distance from \({\text{B}}\) to \({\text{C}}\)</span><span> is \(850\) metres. Running this part of the course takes Sarah \(5\) minutes and \(3\) seconds.</span></p>
<p><span>Find the size of angle \({\text{BCA}}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The distance from \({\text{B}}\) to \({\text{C}}\)</span><span> is \(850\) metres. Running this part of the course takes Sarah \(5\) minutes and \(3\) seconds.</span></p>
<p><span>Calculate the area of the cross-country course bounded by the lines \({\text{AB}}\), \({\text{BC}}\) and \({\text{CA}}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(3.8 \times 320\) <strong><em>(A1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for \(320\) or equivalent seen.</span></p>
<p> </p>
<p><span>\( = 1216\) <strong><em>(A1)</em></strong></span></p>
<p><span>\( = 1220{\text{ (m)}}\) <strong><em>(AG)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Both unrounded and rounded answer must be seen for the final <strong><em>(A1) </em></strong>to be awarded.</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{850}}{{303}}{\text{ (m}}{{\text{s}}^{ - 1}}){\text{ (2.81, 2.80528}} \ldots {\text{)}}\) <strong><em>(A1)(G1)</em></strong></span></p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{A}}{{\text{C}}^2} = {1220^2} + {850^2} - 2(1220)(850)\cos 110^\circ \) <strong><em>(M1)(A1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substitution into cosine rule formula, <strong><em>(A1) </em></strong>for correct substitutions.</span></p>
<p> </p>
<p><span>\({\text{AC}} = 1710{\text{ (m) (1708.87}} \ldots {\text{)}}\) <strong><em>(A1)(G2)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Accept \(1705{\text{ }} (1705.33…)\).</span></p>
<p> </p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(1220 + 850 + {\text{1708.87}} \ldots \) <strong><em>(M1)</em></strong></span></p>
<p><span>\( = {\text{3780 (m) (3778.87}} \ldots {\text{)}}\) <strong><em>(A1)</em>(ft)<em>(G1)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for adding the three sides. Follow through from their answer to part (c). Accept \(3771{\text{ }} (3771.33…)\).</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{\sin C}}{{1220}} = \frac{{\sin 110^\circ }}{{{\text{1708.87}} \ldots }}\) <strong><em>(M1)(A1)</em>(ft)</strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for substitution into sine rule formula, <strong><em>(A1)</em>(ft) </strong>for correct substitutions. Follow through from their part (c).</span></p>
<p> </p>
<p><span>\(C = 42.1^\circ {\text{ (42.1339}} \ldots {\text{)}}\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Accept \(41.9^{\circ}, 42.0^{\circ}, 42.2^{\circ}, 42.3^{\circ}\).</span></p>
<p> </p>
<p><span><strong>OR</strong></span></p>
<p> </p>
<p><span>\(\cos C = \frac{{{\text{1708.87}}{ \ldots ^2} + {{850}^2} - {{1220}^2}}}{{2 \times {\text{1708.87}} \ldots \times 850}}\) <strong><em>(M1)(A1)</em>(ft)</strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for substitution into cosine rule formula, <strong><em>(A1)</em>(ft) </strong>for correct substitutions. Follow through from their part (c).</span></p>
<p> </p>
<p><span>\(C = 42.1^\circ {\text{ (42.1339}} \ldots {\text{)}}\) <em><strong>(A1)</strong></em><strong>(ft)<em>(G2)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Accept \(41.2^{\circ}, 41.8^{\circ}, 42.4^{\circ}\).</span></p>
<p> </p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{1}{2} \times 1220 \times 850 \times \sin 110^\circ \) <strong><em>(M1)(A1)</em>(ft)</strong></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>\(\frac{1}{2} \times {\text{1708.87}} \ldots \times 850 \times \sin {\text{42.1339}} \ldots ^\circ \) <strong><em>(M1)(A1)</em>(ft)</strong></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>\(\frac{1}{2} \times 1220 \times {\text{1708.87}} \ldots \times \sin {\text{27.8661}} \ldots ^\circ \) <strong><em>(M1)(A1)</em>(ft)</strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substitution into area formula, <strong><em>(A1)</em>(ft) </strong>for correct substitution.</span></p>
<p> </p>
<p><span>\( = 487\,000{\text{ }}{{\text{m}}^2}{\text{ (487}}\,{\text{230}} \ldots {\text{ }}{{\text{m}}^2})\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>The answer is \(487\,000{\text{ }}{{\text{m}}^2}\), <strong>units are required</strong>.</span></p>
<p><span> Accept \(486\,000{\text{ }}{{\text{m}}^2}{\text{ (485}}\,{\text{633}} \ldots {\text{ }}{{\text{m}}^2})\).</span></p>
<p><span> If workings are not shown and units omitted, award <strong><em>(G1) </em></strong>for \(487\,000{\text{ or }}486\,000\).</span></p>
<p><span> Follow through from parts (c) and (e).</span></p>
<p> </p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">A lobster trap is made in the shape of half a cylinder. It is constructed from a steel frame with netting pulled tightly around it. The steel frame consists of a rectangular base, two semicircular ends and two further support rods, as shown in the following diagram.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; min-height: 25px; text-align: center; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;"><br><img src="images/Schermafbeelding_2014-09-20_om_14.54.16.png" alt><br></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The semicircular ends each have radius \(r\) and the support rods each have length \(l\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(T\) be the total length of steel used in the frame of the lobster trap.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down an expression for \(T\) in terms of \(r\), \(l\) and \(\pi \).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The volume of the lobster trap is \({\text{0.75 }}{{\text{m}}^3}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Write down an equation for the volume of the lobster trap in terms of <em>r</em>, <em>l </em>and π.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The volume of the lobster trap is \({\text{0.75 }}{{\text{m}}^3}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Show that \(T = (2\pi + 4)r + \frac{6}{{\pi {r^2}}}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The volume of the lobster trap is \({\text{0.75 }}{{\text{m}}^3}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find \(\frac{{{\text{d}}T}}{{{\text{d}}r}}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The lobster trap is designed so that the length of steel used in its frame is a minimum.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Show that the value of <em>r </em>for which <em>T </em>is a minimum is 0.719 m, correct to three significant figures.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The lobster trap is designed so that the length of steel used in its frame is a minimum.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Calculate the value of <em>l </em>for which <em>T </em>is a minimum.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The lobster trap is designed so that the length of steel used in its frame is a minimum.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Calculate the minimum value of <em>T</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(2\pi r + 4r + 4l\) <strong><em>(A1)(A1)(A1)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for \(2\pi r\) (“\(\pi \)” must be seen), <strong><em>(A1) </em></strong>for \(4r\), <strong><em>(A1) </em></strong>for \(4l\). Accept equivalent forms. Accept \(T = 2\pi r + 4r + 4l\). Award a maximum of <strong><em>(A1)(A1)(A0) </em></strong>if extra terms are seen.</span></p>
<p> </p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(0.75 = \frac{{\pi {r^2}l}}{2}\) <strong><em>(A1)(A1)(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for their formula equated to 0.75, <strong><em>(A1) </em></strong>for <em>l </em>substituted into volume of cylinder formula, <strong><em>(A1) </em></strong>for volume of cylinder formula divided by 2.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">If “\(\pi \)” not seen in part (a) accept use of 3.14 or greater accuracy. Award a maximum of <strong><em>(A1)(A1)(A0) </em></strong>if extra terms are seen.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(T = 2\pi r + 4r + r\left( {\frac{{1.5}}{{\pi {r^2}}}} \right)\) <strong><em>(A1)</em>(ft)<em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( = (2\pi + 4)r + \frac{6}{{\pi {r^2}}}\) <strong><em>(AG)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Notes: </strong>Award <strong><em>(A1)</em>(ft) </strong>for correct rearrangement of their volume formula in part (b) seen, award <strong><em>(A1) </em></strong>for the correct substituted formula for <em>T. </em>The final line must be seen, with no incorrect working, for this second <strong><em>(A1) </em></strong>to be awarded.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}T}}{{{\text{d}}r}} = 2\pi + 4 - \frac{{12}}{{\pi {r^3}}}\) <strong><em>(A1)(A1)(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for \(2\pi + 4\). <strong><em>(A1) </em></strong>for \(\frac{{ - 12}}{\pi }\), <strong><em>(A1) </em></strong>for \({r^{ - 3}}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Accept 10.3 (10.2832…) for \(2\pi + 4\), accept –3.82 –3.81971… for \(\frac{{ - 12}}{\pi }\). Award a maximum of <strong><em>(A1)(A1)(A0) </em></strong>if extra terms are seen.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(2\pi + 4 - \frac{{12}}{{\pi {r^3}}} = 0\) <strong>OR</strong> \(\frac{{{\text{d}}T}}{{{\text{d}}r}} = 0\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for setting their derivative equal to zero.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(r = {\text{0.718843}} \ldots \) <strong>OR</strong> \(\sqrt[3]{{{\text{0.371452}} \ldots }}\) <strong>OR</strong> \(\sqrt[3]{{\frac{{12}}{{\pi (2\pi + 4)}}}}\) <strong>OR</strong> \(\sqrt[3]{{\frac{{3.81971}}{{{\text{10.2832}} \ldots }}}}\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(r = 0.719{\text{(m)}}\) <strong><em>(AG)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>The rounded and unrounded or formulaic answers must be seen for the final <strong><em>(A1) </em></strong>to be awarded. The use of 3.14 gives an unrounded answer of \(r = {\text{0.719039}} \ldots \).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-size: medium; font-family: 'times new roman', times;">\(0.75 = \frac{{\pi \times {{(0.719)}^2}l}}{2}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-size: medium; font-family: 'times new roman', times;"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substituting 0.719 into their volume formula. Follow through from part (b).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-size: medium; font-family: 'times new roman', times;">\(l = {\text{0.924(m) (0.923599}} \ldots {\text{)}}\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-size: medium; font-family: 'times new roman', times;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(T = (2\pi + 4) \times 0.719 + \frac{6}{{\pi {{(0.719)}^2}}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for substituting 0.719 in their expression for <em>T</em>. Accept alternative methods, for example substitution of their <em>l </em>and 0.719 into their part (a) (for which the answer is 11.08961024). Follow through from their answer to part (a).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {\text{11.1(m) (11.0880}} \ldots {\text{)}}\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The front view of the edge of a water tank is drawn on a set of axes shown below.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The edge is modelled by \(y = a{x^2} + c\).</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><br><img src="images/Schermafbeelding_2014-09-02_om_11.23.28.png" alt><br></span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: left; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">Point \({\text{P}}\) has coordinates \((-3, 1.8)\), point \({\text{O}}\) has coordinates \((0, 0)\) and point \({\text{Q}}\) has coordinates \((3, 1.8)\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of \(c\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of \(a\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Hence write down the equation of the quadratic function which models the edge of the water tank.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The water tank is shown below. It is partially filled with water.</span></p>
<p><br><span><img src="images/Schermafbeelding_2014-09-02_om_10.48.45_1.png" alt></span></p>
<p><span>Calculate the value of <em>y </em>when \(x = 2.4{\text{ m}}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The water tank is shown below. It is partially filled with water.</span></p>
<p><br><span><img src="images/Schermafbeelding_2014-09-02_om_10.48.45_3.png" alt></span></p>
<p><span>State what the value of \(x\) and the value of \(y\) represent for this water tank.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The water tank is shown below. It is partially filled with water.</span></p>
<p><br><span><img src="images/Schermafbeelding_2014-09-02_om_10.48.45_2.png" alt></span></p>
<p><span>Find the value of \(x\) when the height of water in the tank is \(0.9\) m.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The water tank is shown below. It is partially filled with water.</span></p>
<p><br><span><img src="images/Schermafbeelding_2014-09-02_om_10.48.45.png" alt></span></p>
<p> </p>
<p><span>The water tank has a length of 5 m.</span></p>
<p> </p>
<p><span>When the water tank is filled to a height of \(0.9\) m, the front cross-sectional area of the water is \({\text{2.55 }}{{\text{m}}^2}\).</span></p>
<p><span>(i) Calculate the volume of water in the tank.</span></p>
<p><span>The total volume of the tank is \({\text{36 }}{{\text{m}}^3}\).</span></p>
<p><span>(ii) Calculate the percentage of water in the tank.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(0\) <strong><em>(A1)(G1)</em></strong></span></p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(1.8 = a{(3)^2} + 0\) <strong><em>(M1)</em></strong></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>\(1.8 = a{( - 3)^2} + 0\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substitution of \(y = 1.8\) or \(x = 3\) and their value of \(c\) into equation. \(0\) may be implied.</span></p>
<p> </p>
<p><span>\(a = 0.2\) \(\left( {\frac{1}{5}} \right)\) <strong><em>(A1)</em>(ft)<em>(G1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Follow through from their answer to part (a).</span></p>
<p><span> Award <strong><em>(G1) </em></strong>for a correct answer only.</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(y = 0.2{x^2}\) <strong><em>(A1)</em>(ft)</strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Follow through from their answers to parts (a) and (b).</span></p>
<p><span> Answer must be an equation.</span></p>
<p> </p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(0.2 \times {(2.4)^2}\) <strong><em>(M1)</em></strong></span></p>
<p><span>\( = 1.15{\text{ (m)}}\) \((1.152)\) <strong><em>(A1)</em>(ft)<em>(G1)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for correctly substituted formula, <strong><em>(A1) </em></strong>for correct answer. Follow through from their answer </span><span>to part (c).</span></p>
<p><span> Award <strong><em>(G1) </em></strong>for a correct answer only.</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(y\) is the height <strong><em>(A1)</em></strong></span></p>
<p><span>positive value of \(x\) is half the width (<em>or equivalent</em>) <strong><em>(A1)</em></strong></span></p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(0.9 = 0.2{x^2}\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for setting their equation equal to \(0.9\).</span></p>
<p> </p>
<p><span>\(x = \pm 2.12{\text{ (m)}}\) \(\left( { \pm \frac{3}{2}\sqrt 2 ,{\text{ }} \pm \sqrt {4.5} ,{\text{ }} \pm {\text{2.12132}} \ldots } \right)\) <strong><em>(A1)</em>(ft)<em>(G1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Accept \(2.12\). Award <strong><em>(G1) </em></strong>for a correct answer only.</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(2.55 \times 5\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution in formula.</span></p>
<p> </p>
<p><span>\( = 12.8{\text{ (}}{{\text{m}}^3}{\text{)}}\) \(\left( {{\text{12.75 (}}{{\text{m}}^3}{\text{)}}} \right)\) <strong><em>(A1)(G2)</em></strong></span></p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<p><span><strong><em> </em></strong></span></p>
<p><span>(ii) \(\frac{{12.75}}{{36}} \times 100\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct quotient multiplied by \(100\).</span></p>
<p> </p>
<p><span>\( = 35.4 (\%)\) \((35.4166 \ldots )\) <strong><em>(A1)</em>(ft)(<em>G2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(G2) </em></strong>for \(35.6 (\%) (35.5555… (\%))\).</span></p>
<p><span> Follow through from their answer to part (g)(i).</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider the function \(f(x) = \frac{{96}}{{{x^2}}} + kx\), where \(k\) is a constant and \(x \ne 0\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down \(f'(x)\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The graph of \(y = f(x)\) has a local minimum point at \(x = 4\).</p>
<p class="p1">Show that \(k = 3\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The graph of \(y = f(x)\) has a local minimum point at \(x = 4\).</p>
<p class="p1">Find \(f(2)\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The graph of \(y = f(x)\) has a local minimum point at \(x = 4\).</p>
<p class="p1">Find \(f'(2)\)</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The graph of \(y = f(x)\) has a local minimum point at \(x = 4\).</p>
<p class="p1">Find the equation of the normal to the graph of \(y = f(x)\) at the point where \(x = 2\).</p>
<p class="p1">Give your answer in the form \(ax + by + d = 0\) where \(a,{\text{ }}b,{\text{ }}d \in \mathbb{Z}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The graph of \(y = f(x)\) has a local minimum point at \(x = 4\).</p>
<p class="p1"><span class="s1">Sketch the graph of \(y = f(x)\)</span>, for \( - 5 \leqslant x \leqslant 10\) and \( - 10 \leqslant y \leqslant 100\)<span class="s1">.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The graph of \(y = f(x)\) has a local minimum point at \(x = 4\).</p>
<p class="p1">Write down the coordinates of the point where the graph of \(y = f(x)\) intersects the \(x\)-axis.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The graph of \(y = f(x)\) has a local minimum point at \(x = 4\).</p>
<p class="p1">State the values of \(x\) for which \(f(x)\) is decreasing.</p>
<div class="marks">[2]</div>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\frac{{ - 192}}{{{x^3}}} + k\) <span class="Apple-converted-space"> </span><strong><em>(A1)(A1)(A1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for \(-192\), <strong><em>(A1) </em></strong>for \({x^{ - 3}}\), <strong><em>(A1) </em></strong>for \(k\) (only).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">at local minimum \(f'(x) = 0\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for seeing \(f'(x) = 0\) (may be implicit in their working).</p>
<p class="p2"> </p>
<p class="p1">\(\frac{{ - 192}}{{{4^3}}} + k = 0\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1">\(k = 3\) <span class="Apple-converted-space"> </span><strong><em>(AG)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for substituting \(x = 4\) in their \(f'(x) = 0\), provided it leads to \(k = 3\)<em>. </em>The conclusion \(k = 3\) must be seen for the <strong><em>(A1) </em></strong>to be awarded.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\frac{{96}}{{{2^2}}} + 3(2)\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Note:<span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for substituting \(x = 2\) and \(k = 3\) in \(f(x)\).</p>
<p class="p2"> </p>
<p class="p1">\( = 30\) <span class="Apple-converted-space"> </span><strong><em>(A1)(G2)</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{ - 192}}{{{2^3}}} + 3\) <strong><em>(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substituting \(x = 2\) and \(k = 3\) in their \(f'(x)\).</p>
<p> </p>
<p>\( = - 21\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><strong>Note: </strong>Follow through from part (a).</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(y - 30 = \frac{1}{{21}}(x - 2)\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(M1)</em></strong></p>
<p class="p1"><strong>Notes:<span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1)</em>(ft) </strong>for their \(\frac{1}{{21}}\) seen, <strong><em>(M1) </em></strong>for the correct substitution of their point and their normal gradient in equation of a line.</p>
<p class="p1">Follow through from part (c) and part (d).</p>
<p class="p2"> </p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">gradient of normal \( = \frac{1}{{21}}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)</strong></p>
<p class="p1">\(30 = \frac{1}{{21}} \times 2 + c\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">\(c = 29\frac{{19}}{{21}}\)</p>
<p class="p1">\(y = \frac{1}{{21}}x + 29\frac{{19}}{{21}}\;\;\;(y = 0.0476x + 29.904)\)</p>
<p class="p1">\(x - 21y + 628 = 0\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p class="p1"><strong>Notes: <span class="Apple-converted-space"> </span></strong>Accept equivalent answers.</p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="s1"><img src="images/Schermafbeelding_2015-12-21_om_09.26.22.png" alt> <span class="Apple-converted-space"> </span></span><strong><em>(A1)(A1)(A1)(A1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for correct window (at least one value, other than zero, labelled on each axis), the axes must also be labelled; <strong><em>(A1) </em></strong>for a smooth curve with the correct shape (graph should not touch \(y\)-axis and should not curve away from the \(y\)-axis), on the given domain; <strong><em>(A1) </em></strong>for axis intercept in approximately the correct position (nearer \(-5\)<span class="s2"> </span>than zero); <strong><em>(A1) </em></strong>for local minimum in approximately the correct position (first quadrant, nearer the \(y\)-axis than \(x = 10\)).</p>
<p class="p1">If there is no scale, award a maximum of <strong><em>(A0)(A1)(A0)(A1) </em></strong>– the final <strong><em>(A1) </em></strong>being awarded for the zero and local minimum in approximately correct positions relative to each other.</p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(( - 3.17,{\text{ }}0)\;\;\;\left( {( - 3.17480 \ldots ,{\text{ 0)}}} \right)\) <strong><em>(G1)(G1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>If parentheses are omitted award <strong><em>(G0)(G1)</em>(ft)</strong>.</p>
<p>Accept \(x = - 3.17,{\text{ }}y = 0\). Award <strong><em>(G1) </em></strong>for \(-3.17\) seen.</p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(0 < x \leqslant 4{\text{ or }}0 < x < 4\) <span class="Apple-converted-space"> </span><strong><em>(A1)(A1)</em></strong></p>
<p class="p1"><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for correct end points of interval, <strong><em>(A1) </em></strong>for correct notation (note: lower inequality must be strict).</p>
<p class="p1">Award a maximum of <strong><em>(A1)(A0) </em></strong>if \(y\) or \(f(x)\) used in place of \(x\).</p>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Differentiation of terms including negative indices remains a testing process; it will continue to be tested. There was, however, a noticeable improvement in responses compared to previous years. The parameter k was problematic for a number of candidates.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>In part (b), the manipulation of the derivative to find the local minimum point caused difficulties for all but the most able; note that a GDC approach is not accepted in such questions and that candidates are expected to be able to apply the theory of the calculus as appropriate. Further, once a parameter is given, candidates are expected to use this value in subsequent parts.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Parts (c) and (d) were accessible and all but the weakest candidates scored well.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Parts (c) and (d) were accessible and all but the weakest candidates scored well.</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Part (e) discriminated at the highest level; the gradient of the normal often was not used, the form of the answer not given correctly.</p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Curve sketching is a skill that most candidates find very difficult; axes must be labelled and some indication of the window must be present; care must be taken with the domain and the range; any asymptotic behaviour must be indicated. It was very rare to see sketches that attained full marks, yet this should be a skill that all can attain. There were many no attempts seen, yet some of these had correct answers to part (g).</p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Curve sketching is a skill that most candidates find very difficult; axes must be labelled and some indication of the window must be present; care must be taken with the domain and the range; any asymptotic behaviour must be indicated. It was very rare to see sketches that attained full marks, yet this should be a skill that all can attain. There were many no attempts seen, yet some of these had correct answers to part (g).</p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Part (h) was not well attempted in the main; decreasing (and increasing) functions is a testing concept for the majority.</p>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The diagram below shows a square based right pyramid. ABCD is a square of side 10 cm. VX is the perpendicular height of 8 cm. M is the midpoint of BC.</span></p>
<p style="text-align: center;"><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
<p> </p>
</div>
<div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">In a mountain region there appears to be a relationship between the number of trees growing in the region and the depth of snow in winter. A set of 10 areas was chosen, and in each area the number of trees was counted and the depth of snow measured. The results are given in the table below.</span></p>
<p style="text-align: center;"><span style="font-size: medium; font-family: times new roman,times;"><img 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" alt></span></p>
</div>
<div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A path goes around a forest so that it forms the three sides of a triangle. The lengths of two sides are 550 m and 290 m. These two sides meet at an angle of 115°. A diagram is shown below.</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the length of XM.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">A, a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to find the standard deviation of the number of trees.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">A, a, ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the length of VM.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A, b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the angle between VM and ABCD.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A, c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the length of the third side of the triangle. Give your answer correct to the nearest 10 m.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">B, a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the area enclosed by the path that goes around the forest.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">B, b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Inside the forest a second path forms the three sides of another triangle named ABC. Angle BAC is 53°, AC is 180 m and BC is 230 m.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Calculate the size of angle ACB.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">B, c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><em><strong>UP applies in this question</strong></em></span></p>
<p><span> </span></p>
<p><span><em><strong>(UP)</strong></em> XM = 5 cm <em><strong>(A1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">A, a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>16.8 <strong><em>(G1)</em></strong></span></p>
<div><span><strong><em>[1 mark]</em></strong></span></div>
<div class="question_part_label">A, a, ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong><span>UP applies in this question</span></strong></em></p>
<p><span> </span></p>
<p><span>VM<sup>2</sup> = 5</span><span><span><sup>2</sup></span> + 8</span><span><span><sup>2</sup></span> <strong><em>(M1)</em></strong></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct use of Pythagoras Theorem.<br><br></span></p>
<p><span><em><strong>(UP)</strong></em> VM = \(\sqrt{89}\) = 9.43 cm <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">A, b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\tan {\text{VMX}} = \frac{8}{5}\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Other trigonometric ratios may be used.</span></p>
<p><br><span>\({\rm{V\hat MX}} = 58.0^\circ \) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">A, c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><span><em>UP applies in this question</em></span></strong></p>
<p><span> </span></p>
<p><span><em>l</em></span><span><span><sup>2</sup></span> = 290<sup>2</sup> + 550</span><span><span><sup>2</sup></span> − 2 × 290</span><span><span> ×</span> 550</span><span><span> ×</span> cos115° <em><strong>(M1)(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituted cosine rule formula, <em><strong>(A1)</strong></em> for correct substitution.</span></p>
<p><br><span><em>l</em> = 722 <em><strong>(A1)(G2)</strong></em></span></p>
<p><span><em><strong>(UP) </strong></em> = 720 m <em><strong>(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> If 720 m seen without working award <em><strong>(G3)</strong></em>.</span></p>
<p><span>The final <em><strong>(A1)</strong></em> is awarded for the correct rounding of their answer.</span></p>
<p><span> </span></p>
<p><em><strong><span>[4 marks]</span></strong></em></p>
<div class="question_part_label">B, a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong><span>UP applies in this question</span></strong></em></p>
<p><span> </span></p>
<p><span>\({\text{Area}} = \frac{1}{2} \times 290 \times 550 \times \sin 115\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituted correct formula <em><strong>(A1)</strong></em> for correct substitution.</span></p>
<p><span><br><em><strong>(UP) </strong></em> = \(72\,300{\text{ }}{{\text{m}}^2}\) <em><strong>(A1)(G2)</strong></em></span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">B, b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{180}}{{\sin {\text{B}}}} = \frac{{230}}{{\sin 53}}\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituted sine rule formula, <em><strong>(A1)</strong></em> for correct substitution.</span></p>
<p><br><span>B = 38.7° <em><strong>(A1)(G2)</strong></em></span></p>
<p><span>\({\operatorname{A\hat CB}} = 180 - (53^\circ + 38.7^\circ )\)</span></p>
<p><span>\( = 88.3^\circ \)</span><span> <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong> <em>[4 marks]</em></strong></span></p>
<div class="question_part_label">B, c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This part proved accessible to the great majority of candidates. The common errors</span> <span style="font-size: medium; font-family: times new roman,times;">were (1) the inversion of the tangent ratio (2) the omission of the units and (3) the incorrect </span><span style="font-size: medium; font-family: times new roman,times;">rounding of the answer; with 58° being all too commonly seen.</span></p>
<div class="question_part_label">A, a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">A straightforward question that saw many fine attempts. Given its nature – where much of the work was done on the GDC – it must be emphasised to candidates that incorrect entry of data into the calculator will result in considerable penalties; they must check their data entry most carefully.</span></p>
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">The use of the inappropriate standard deviation was seen, but infrequently.</span></p>
<div class="question_part_label">A, a, ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This part proved accessible to the great majority of candidates. The common errors</span> <span style="font-size: medium; font-family: times new roman,times;">were (1) the inversion of the tangent ratio (2) the omission of the units and (3) the incorrect </span><span style="font-size: medium; font-family: times new roman,times;">rounding of the answer; with 58° being all too commonly seen.</span></p>
<div class="question_part_label">A, b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This part proved accessible to the great majority of candidates. The common errors</span> <span style="font-size: medium; font-family: times new roman,times;">were (1) the inversion of the tangent ratio (2) the omission of the units and (3) the incorrect </span><span style="font-size: medium; font-family: times new roman,times;">rounding of the answer; with 58° being all too commonly seen.</span></p>
<div class="question_part_label">A, c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Again, this part proved accessible to the majority with a large number of candidates attaining full marks. However, there were also a number of candidates who seemed not to have been prepared in the use of trigonometry in non right-angled triangles. Also, failing to round the answer in (a) to the nearest 10m was a common omission.</span></p>
<div class="question_part_label">B, a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Again, this part proved accessible to the majority with a large number of candidates attaining full marks. However, there were also a number of candidates who seemed not to have been prepared in the use of trigonometry in non right-angled triangles. Also, failing to round the answer in (a) to the nearest 10 m was a common omission.</span></p>
<div class="question_part_label">B, b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Again, this part proved accessible to the majority with a large number of candidates attaining full marks. However, there were also a number of candidates who seemed not to have been prepared in the use of trigonometry in non right-angled triangles. Also, failing to round the answer in (a) to the nearest 10 m was a common omission.</span></p>
<div class="question_part_label">B, c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the function \(f(x) = {x^3} + \frac{{48}}{x}{\text{, }}x \ne 0\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate \(f(2)\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Sketch the graph of the function \(y = f(x)\) for \( - 5 \leqslant x \leqslant 5\) and \( - 200 \leqslant y \leqslant 200\) .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \(f'(x)\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \(f'(2)\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the coordinates of the local maximum point on the graph of \(f\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<address><span>Find the range of \(f\) .</span></address>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the gradient of the tangent to the graph of \(f\) at \(x = 1\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>There is a second point on the graph of \(f\) at which the tangent is parallel to the tangent at \(x = 1\). </span></p>
<p><span>Find the \(x\)-coordinate of this point.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(f(2) = {2^3} + \frac{{48}}{2}\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(= 32\) <em><strong>(A1)(G2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span><em><strong>(A1)</strong></em> for labels and some indication of scale in an appropriate window</span><br><span><em><strong>(A1)</strong></em> for correct shape of the two unconnected and smooth branches</span><br><span><em><strong>(A1)</strong></em> for maximum and minimum in approximately correct positions</span><br><span><em><strong>(A1)</strong></em> for asymptotic behaviour at \(y\)-axis <em><strong>(A4)</strong></em></span></p>
<p><span><strong>Notes:</strong> Please be rigorous.</span><br><span>The axes need not be drawn with a ruler.</span><br><span>The branches must be smooth: a single continuous line that does not deviate from its proper direction.</span><br><span>The position of the maximum and minimum points must be symmetrical about the origin.</span><br><span>The \(y\)-axis must be an asymptote for both branches. Neither branch should touch the axis nor must the curve approach the</span><br><span>asymptote then deviate away later.</span></p>
<p><span><em><strong>[4 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(f'(x) = 3{x^2} - \frac{{48}}{{{x^2}}}\) <em><strong>(A1)(A1)(A1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for \(3{x^2}\) , <em><strong>(A1)</strong></em> for \( - 48\) , <em><strong>(A1)</strong></em> for \({x^{ - 2}}\) . Award a maximum of <em><strong>(A1)(A1)(A0)</strong></em> if extra terms seen.</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(f'(2) = 3{(2)^2} - \frac{{48}}{{{{(2)}^2}}}\) <em><strong>(M1)</strong></em></span> </p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution of \(x = 2\) into their derivative.</span></p>
<p> </p>
<p><span><span>\(= 0\)</span><span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G1)</strong></em></span></span></p>
<p><span><span><em><strong>[2 marks]<br></strong></em></span></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(( - 2{\text{, }} - 32)\) or \(x = - 2\), \(y = - 32\) <em><strong>(G1)(G1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(G0)(G0)</strong></em> for \(x = - 32\), \(y = - 2\) . Award at most <em><strong>(G0)(G1)</strong></em> if parentheses are omitted.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\{ y \geqslant 32\} \cup \{ y \leqslant - 32\} \) <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Notes:</strong> Award <strong><em>(A1)</em>(ft)</strong> \(y \geqslant 32\) or \(y > 32\) seen, <strong><em>(A1)</em>(ft)</strong> for \(y \leqslant - 32\) or \(y < - 32\) , <em><strong>(A1)</strong></em> for weak (non-strict) inequalities used in both of the above.</span><br><span>Accept use of \(f\) in place of \(y\). Accept alternative interval notation.</span><br><span>Follow through from their (a) and (e).</span><br><span>If domain is given award <em><strong>(A0)(A0)(A0)</strong></em>.</span><br><span>Award <strong><em>(A0)(A1)</em>(ft)<em>(A1)</em>(ft)</strong> for \([ - 200{\text{, }} - 32]\) , \([32{\text{, }}200]\).</span><br><span>Award <em><strong>(A0)(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong> for \(] - 200{\text{, }} - 32]\) , \([32{\text{, }}200[\).</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(f'(1) = - 45\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for \(f'(1)\) seen or substitution of \(x = 1\) into their derivative. Follow through from their derivative if working is seen.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(x = - 1\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for equating their derivative to their \( - 45\) or for seeing parallel lines on their graph in the approximately correct position.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">As usual and by intention, this question caused the most difficulty in terms of its content; however, for those with a sound grasp of the topic, there were many very successful attempts. Much of the question could have been answered successfully by using the GDC, however, it was also clear that a number of candidates did not connect the question they were attempting with the curve that they had either sketched or were viewing on their GDC. Where there was no alternative to using the calculus, many candidates struggled.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The majority of sketches were drawn sloppily and with little attention to detail. Teachers must impress on their students that a mathematical sketch is designed to illustrate the main points of a curve – the smooth nature by which it changes, any symmetries (reflectional or rotational), positions of turning points, intercepts with axes and the behaviour of a curve as it approaches an asymptote. There must also be some indication of the dimensions used for the “window”.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Differentiation of terms with negative indices remains a testing process for the majority; it will continue to be tested.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">It was also evident that some centres do not teach the differential calculus.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">As usual and by intention, this question caused the most difficulty in terms of its content; however, for those with a sound grasp of the topic, there were many very successful attempts. Much of the question could have been answered successfully by using the GDC, however, it was also clear that a number of candidates did not connect the question they were attempting with the curve that they had either sketched or were viewing on their GDC. Where there was no alternative to using the calculus, many candidates struggled.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The majority of sketches were drawn sloppily and with little attention to detail. Teachers must impress on their students that a mathematical sketch is designed to illustrate the main points of a curve – the smooth nature by which it changes, any symmetries (reflectional or rotational), positions of turning points, intercepts with axes and the behaviour of a curve as it approaches an asymptote. There must also be some indication of the dimensions used for the “window”.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Differentiation of terms with negative indices remains a testing process for the majority; it will continue to be tested.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">It was also evident that some centres do not teach the differential calculus.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">As usual and by intention, this question caused the most difficulty in terms of its content; however, for those with a sound grasp of the topic, there were many very successful attempts. Much of the question could have been answered successfully by using the GDC, however, it was also clear that a number of candidates did not connect the question they were attempting with the curve that they had either sketched or were viewing on their GDC. Where there was no alternative to using the calculus, many candidates struggled.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The majority of sketches were drawn sloppily and with little attention to detail. Teachers must impress on their students that a mathematical sketch is designed to illustrate the main points of a curve – the smooth nature by which it changes, any symmetries (reflectional or rotational), positions of turning points, intercepts with axes and the behaviour of a curve as it approaches an asymptote. There must also be some indication of the dimensions used for the “window”.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Differentiation of terms with negative indices remains a testing process for the majority; it will continue to be tested.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">It was also evident that some centres do not teach the differential calculus.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">As usual and by intention, this question caused the most difficulty in terms of its content; however, for those with a sound grasp of the topic, there were many very successful attempts. Much of the question could have been answered successfully by using the GDC, however, it was also clear that a number of candidates did not connect the question they were attempting with the curve that they had either sketched or were viewing on their GDC. Where there was no alternative to using the calculus, many candidates struggled.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The majority of sketches were drawn sloppily and with little attention to detail. Teachers must impress on their students that a mathematical sketch is designed to illustrate the main points of a curve – the smooth nature by which it changes, any symmetries (reflectional or rotational), positions of turning points, intercepts with axes and the behaviour of a curve as it approaches an asymptote. There must also be some indication of the dimensions used for the “window”.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Differentiation of terms with negative indices remains a testing process for the majority; it will continue to be tested.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">It was also evident that some centres do not teach the differential calculus.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">As usual and by intention, this question caused the most difficulty in terms of its content; however, for those with a sound grasp of the topic, there were many very successful attempts. Much of the question could have been answered successfully by using the GDC, however, it was also clear that a number of candidates did not connect the question they were attempting with the curve that they had either sketched or were viewing on their GDC. Where there was no alternative to using the calculus, many candidates struggled.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The majority of sketches were drawn sloppily and with little attention to detail. Teachers must impress on their students that a mathematical sketch is designed to illustrate the main points of a curve – the smooth nature by which it changes, any symmetries (reflectional or rotational), positions of turning points, intercepts with axes and the behaviour of a curve as it approaches an asymptote. There must also be some indication of the dimensions used for the “window”.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Differentiation of terms with negative indices remains a testing process for the majority; it will continue to be tested.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">It was also evident that some centres do not teach the differential calculus.</span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">As usual and by intention, this question caused the most difficulty in terms of its content; however, for those with a sound grasp of the topic, there were many very successful attempts. Much of the question could have been answered successfully by using the GDC, however, it was also clear that a number of candidates did not connect the question they were attempting with the curve that they had either sketched or were viewing on their GDC. Where there was no alternative to using the calculus, many candidates struggled.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The majority of sketches were drawn sloppily and with little attention to detail. Teachers must impress on their students that a mathematical sketch is designed to illustrate the main points of a curve – the smooth nature by which it changes, any symmetries (reflectional or rotational), positions of turning points, intercepts with axes and the behaviour of a curve as it approaches an asymptote. There must also be some indication of the dimensions used for the “window”.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Differentiation of terms with negative indices remains a testing process for the majority; it will continue to be tested.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">It was also evident that some centres do not teach the differential calculus.</span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">As usual and by intention, this question caused the most difficulty in terms of its content; however, for those with a sound grasp of the topic, there were many very successful attempts. Much of the question could have been answered successfully by using the GDC, however, it was also clear that a number of candidates did not connect the question they were attempting with the curve that they had either sketched or were viewing on their GDC. Where there was no alternative to using the calculus, many candidates struggled.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The majority of sketches were drawn sloppily and with little attention to detail. Teachers must impress on their students that a mathematical sketch is designed to illustrate the main points of a curve – the smooth nature by which it changes, any symmetries (reflectional or rotational), positions of turning points, intercepts with axes and the behaviour of a curve as it approaches an asymptote. There must also be some indication of the dimensions used for the “window”.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Differentiation of terms with negative indices remains a testing process for the majority; it will continue to be tested.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">It was also evident that some centres do not teach the differential calculus.</span></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">As usual and by intention, this question caused the most difficulty in terms of its content; however, for those with a sound grasp of the topic, there were many very successful attempts. Much of the question could have been answered successfully by using the GDC, however, it was also clear that a number of candidates did not connect the question they were attempting with the curve that they had either sketched or were viewing on their GDC. Where there was no alternative to using the calculus, many candidates struggled.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The majority of sketches were drawn sloppily and with little attention to detail. Teachers must impress on their students that a mathematical sketch is designed to illustrate the main points of a curve – the smooth nature by which it changes, any symmetries (reflectional or rotational), positions of turning points, intercepts with axes and the behaviour of a curve as it approaches an asymptote. There must also be some indication of the dimensions used for the “window”.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Differentiation of terms with negative indices remains a testing process for the majority; it will continue to be tested.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">It was also evident that some centres do not teach the differential calculus.</span></p>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A shipping container is to be made with six rectangular faces, as shown in the diagram.</span></p>
<p> </p>
<p> </p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAiUAAAC8CAIAAAAo+UkeAAATS0lEQVR4nO3d8W8TZ57H8f4nYzFH1eSIDkqBtCsRdY/SNFqlWVohJHYLNOQK1XHAdq9UcRq0DSuVIjkUriCoWltw2aMsMC5d2pQkOJReDthaBEqq7NwSHY2DVVAA15VDmtjP/TAzjp+QBBLyzNjJ+yX/ksZ2xtMvz8fPfBx4TAAAoN5jXh8AAGBWIG8AFJCEGTl5IrC+pNqICyHEYJ+xpURb0Ri94/WBzWbppHk2fDxQM78+kkhPcD/yBkChGIobm3TNp2vFVcHutBBC9IarF+iab2EgOuT1wc1aaTNYpfl0zadXBs2J4iYnb1paWpb98p+3vfmmv7aWGzfVt/379qdSKeV/FDDDpK+HN5Tq2uqQOSCEmGX7m0R3cNdh+4XfJ3k1VH9k4uVenaFoYOHIm4BxjeRN2DCe/Kf5ixc+de7cORNQ7L2dO1/fuDEWi6n+k4AZJW7UaD59/uzbziS7w/7KcTYQ6aRp1JUveOByr8yAGVytay80RpMT30/Km4aGP+7aFdA137lz5xQfHyDChvFsWVlHR4fXB4I8NxiPNtWVF+ta5Vv+tSWar8QfSQgh0vHoyeMhf2XuxbR0/OJhf6WulW78aP9bRTlXeNLxqBGoKfLpmk8vrw+biZGnT5oRu3u40x3cUFLklBDpePSQv0LzlWz4j4+3Lc3ZVCXMiBHyr62L3LJjwP5WwjTqK7TiisDFsddd+4DX1kVuOU8+6s6D8eipkL9S13y6VllndCeFECLRHdxQYl2w0ny6XVxlD/5qqLrU/pa2oMboHf95Rh9N0jTqyot1zVdSHThxPBi+lL3XYDxqNFpPW7R+z8V4Onv8Y5+QWxH/Ur1ILm/S8ejJj5znP9ydTIv786a1rf3QoabSRYvf3717zDMGTKPOzs5ny8r+8/Bhrw8EeWswHtlRoRVX1LfGh7pDlcW6trQucste4zSf86UQQqTjrdvLi/XyPdHkD9Z37ShK90XqK52FbygRqbeW7xJ/JOE0QCX+1r7ongrNZy+j9kNWNEb77fvbm6psh7Qp3HctvMFa619ojPb3GVtKxowEWzIaeEG3nr/7mnU88p2tXCndaFxP26/OWdDTuS98NLs+GVnux38e6WHdocpiK4/T8dbt5VvC8aGch1fWGd1J6yRYRzjuCREiEakrct4ECJHdb1X4DTN5PVy9QNc2WU8+Rt60trUb4c9eWvFy9avVXGGHarFY7PWNG/21tQwb7pfuMzYWZRdTKxuyq2dvuHrByDprVzvWomwt7vYC7RTa1gPtwBhZH+NGjVZc9dHRjyuLdc1XssHoS1u1kH2foWhgYe79h6KN83165buhwI7Qd+dDlcV6kT/cur8ueLkvUl8yfo1hH0bl/rbj774T6b0r3dn5iRuMvrTz0pz9yn2Jksu6lpU9vImeR2K9iqINoe6EEOnEpUvX0tmH27uutBmssnNrghOSTsivOif10/b/PmeXOXbetLa1f/7Fl1u3vvGLp5/hCjtUS6VS7+3cuWrlSoYNMuvtuXPRKRGpy71EZn1p7w/SSWt3Ur4nmswmk/222l6v7ffj9sZIXi5X7Qr4Nwav2leUkhcby4t1+2MIVj7lLNlxo0bzlZRvaIz0pa0+qeiFmkAknpZC7j52MOjLVm0/md15OJ2H9VqyUSp9aR1h7gbi/lPk/NCJnmeUQWdDVrk90mfnmHX/+4NtohMyaguVPZ4f7Ot15Tsi8UHracbNG+u2d+8+6hy4o6WlhToHkrGWXaetGfW2+lbuBbRRb6vtrU/5nmhyyI6lkY+0DZjB1XrRsir/SWfRTUvXi0Z/Ii539XfuaYWcdYVq7F3IyBHaOw9pZXeexz7gUV/aoTv2tmmsUzTO84zxYLsZkg/jvmCb8IRYByBfW7MvFZb7Qyej8Zwf/YC8aW1rP/LJMeocuMM0TeocZFnXbezV0H6LvbQu0t0ZHa/hsN5034kGVuiab2Gg4/rZDusyUTx6pNG/vsKqbaoD4ewyaIfElnDfoPNjnY1ItRHPbpvmB/56/fzZawPy23lpb2HtosbZhUy8ZbEv8Tltk/VanEScaI8yKlEmfB7pceZnJ60Mss6Vtc2SHy6EEIPxS1fj6YlOyKhXbf8vc3aWQqST5vnoQ+5vstfWqHPgjv7+fuocWEby5k5ftDVYN9+na6Xr/Ec7k+mR/UFf99loPD3SqP+QNE9bn60qWfvOiUt37CW13B8yjHDEHPVJrbFCIqcRSZptgfUlmk8vWl13/PLoa3r2D7XWVutRxVXB891nL8Xv20845Y0VDNaVtwU1xlXz7KV4Ojd+cur63AfOD0TvmGejo57YPtSFgYt3zfPR+MAEzyNJROrmWx88G+wztjgfyXOyxC51EmbkdDQ+OOEJsb61oMboTcejn0XMhF2VWSGXTppnP8s55ofKG+tGnQN3pFKp/fv2U+fAuXRTWXfoYjxxsbG8eOSjzHberG9stSLEKbr9wYh5LeJfOu7nibXiCr9hJq01cGS5lH6sdTmu3B+KdFsfAXAeIu1L5AjJHkD2yXONavWtL0trAqftO6fjf31/fYl9eMFIzse1nU9MZF9pLqfGr97TZj1k/OeRXuC1jrPdV63kGHmsEM5Hun26VloTMLL7kvFPiFMCjRxe9hnkfaQQYlJ5Q50DN1HnYDoMxqNGo//dcPRixDhi/07JQ/wmPFSYXN5Q58BN1Dl4VIlIXVFuutiXjPj71jwx6bzJ1jmvrl3HFXaoRp2DR2JVLCN/oYD126Oz5O9byztTyZuROqf0aa6wQzXqHDyKdDwatiruB7UaUG3qeUOdAzdR5wCF7pHyxqpzllDnwBXUOUBBe9S8oc6Bm6hzgMI1DXlDnQM3UecABWra8iZb5zQ3N3v4ejBLtLS06JqPOgcoINOZN7l1Dpc7oJpV5+zft9/rAwHwUKY5b3LrnP7+fg9fGGYDq855feNG3t8A+W/68ya3zjFN08PXhtnAqnOeLSujzgHynKq8oc6Bm6hzgPynMG+sOuf55c9T58AFsViMOgfIZ2rzxqpz1ryyljoHLkilUtQ5QN5SnjfWzV9bR50Dd1DnAPnJpbyx6pynFy+hzoELOjo6qHOAfONe3lDnwE3UOUC+cTVvqHPgJuocIK+4nTfUOXAZdQ6QJ7zJm9a29r1795UuWkydAxdQ5wD5wLO8aW1rP/LJseXLllPnwAXUOYDnvMyb1rb2z7/48re/eYU6By6gzgG85XHeWDd/bd0z1DlwBXUO4JW8yJtW6hy4yKpzWlpavD4QYHbJl7xppc6Bi7J1DsMGuCaP8qY1p87hcgdUy9Y5dIeAO/Irb6ybVed0dnZ6eF4wS1h1Dt0h4IJ8zJtWp845fvy4h6cGs0RHR8ezZWXUOYBqeZo3rU6ds6OhgSvsUC0Wi61auZI6B1Aqf/OmlToHLkqlUv7aWuocQJ28zhvr1tDwx5Lif/TX1nLjpvqma75ny8q8+/MIzGQFkDetbe265jMBV+iaz8M/kMAMVjB54+E5wqzCsAGKkDeAhGEDFCFvAAnDBihC3gAShg1QhLwBJAwboAh5A0gYNkAR8gaQMGyAIuQNIGHYAEXIG0DCsAGKkDeAhGEDFCFvAAnDBihC3gAShg1QhLwBJAwboAh5A0gYNkAR8gaQMGyAIuQNIGHYAEXIG0DCsAGKkDeAhGEDFCFvAAnDBihC3gAShg1QhLwBJAwboAh5A0gYNkAR8gaQMGyAIuQNIGHYAEXIG0DCsAGKkDeAhGEDFCFvAAnDBihC3gAShg1QhLwBJAwboAh5A0gYNkAR8gaQMGyAIuQNIGHYAEXIG0DCsAGKkDeAhGEDFCFvAAnDBihC3gAShg1QhLwBJAwboAh5A0gYNkAR8gaQMGyAIuQNIGHYAEXIG0DCsAGKkDeAhGEDFCFvAAnDBihC3gAShg1QhLwBJAwboAh5A0gYNkAR8gaQMGyAIuQNIGHYAEXIG0DCsAGKkDeAhGEDFCFvAAnDBihC3gAShg1QhLwBJAwboAh5A0gYNkAR8gaQMGyAIuQNIGHYAEUKN29+/O5oQ035Ql2raowmhBBC3Iz4f6k/tePrH9OunT7MPOQNoEjh5o0QQmRuntr8D3OfP9g1LIQQ926c27Pmqd9/fnPYnXOHGYm8ARQp7LwRw10Hn5u74N3z94QQQmRun9m+9dMbGTdOHGYq8gZQpMDzRvSGqxfo1UZcCCESlz/Y/mFX0o3ThpmLvAEUKfS8uRXxL9VfOdqbGU5eDtaHugbcOW2YucgbQJFCz5tkNPCCPj8QvX1x3/YTPT9zKQ2PirwBFCn0vBkwg6v1eev+vb7x9I177pwyzGzkDaBIoefNUNzYpM9Zve/yHbY2mBbkDaBIoefNQE/Ttm2nrg+5c7YwC5A3gCIFnTfDya5ju//r2yRbG0wf8gZQpBDzJjNgfrrjncORtoNvv9d2Y4i0wXQibwBFCjFv7vU0VT8+Z/m/HeyIEzaYbuQNoEgh5g2gEMMGKELeABKGDVCEvAEkDBugCHkDSBg2QBHyBpAwbIAi5A0gYdgARcgbQMKwAYqQN4CEYQMUIW8ACcMGKELeABKGDVCEvAEkDBugCHkDSBg2QJGRvOns7CxdtPjQoSbP04W8gYcYNkCRx3K/OHfu3DOlT+/aFfA8YMgbeIVhAxR5bNTXsVisqvLFrVvf+PyLLz2PGfIG7mPYAEVG540QIpVK/f6NN15a8fKRT455njTkDVzGsAGKjJE3lmAwWLpo8cEPP/I8bMgbuIlhAxQZN2+EU+fkw4fWWALgGoYNUGSivBFOnbPhtY3e1jksAXANwwYo8oC8EUKkUql3/vAHb+sclgC4hmEDFHlw3liO/vnPHtY5LAFwDcMGKPKweSOEiEajXtU5LAFwDcMGKDKJvBFCxGKxtWvWul/nsATANQwboMjk8kZ4VOewBMA1DBugyKTzxuJyncMSANcwbIAiU8wb4W6dwxIA1zBsgCJTzxvhYp3DEgDXMGyAIo+UN0KIVCq1o6FBdZ3DEgDXMGyAIo+aN5bjx48rrXNYAuAahg1QZHryRgjR2dmprs5hCYBrGDZAkWnLGyFELBZ7de06FXUOSwBcw7ABikxn3ghldQ5LAFzDsAGKTHPeWKa9zmEJgGsYNkCRSedNJn529+9Wlc3Rl7z55c3McLLrT5vLivUnt0duD+fezapz/LV15A0KC8MGKDK1/c3A90c3PTHntaaOE9u3Bb/65uuWdjOZGX0nq8757W9eefQ6hyUArmHYAEWmeD0t09O0Spu7sGLX1/K2ZhSrzlm+bPkj1jksAXANwwYoMtX+Zrjr4HNzS/yRxEPc16pz9u7dR94g/zFsgCJT3d/cPvP2U7r+3MHvJtrejDBN81HqHJYAuIZhAxSZUt5k+i/s3vnxgc1PaOuaeu6JoR/v/vTg2Onv759yncMSANcwbIAik8qb4WRP9ELP7dvnD+z4tOeeGazSSjf/pavr0AfHrqUe5vGpVOr93bunUOewBMA1DBugyKTy5lbEv1TX5v2qof1mRojh7tCL8/Q5v244ExuazLM0NzdPts5hCYBrGDZAkcldT8ske69c6XU++pwZuvX3b3vv/yD0g022zmEJgGsYNkARJX+/wMOYVJ3DEgDXMGyAIp7ljXDqnOeXP//AOoclAK5h2ABFvMwbS3Nz89OLl0xc57AEwDUMG6CI93kjhDBN8xcT1jksAXANwwYokhd5I5w6Z80ra8esc1gC4BqGDVAkX/JGTFjnsATANQwboEge5Y1lzDqHJQCuYdgARfIub8RYdQ5LAFzDsAGK5GPeCKfOeWnFy1adwxIA1zBsgCJ5mjfCqXOWLFp85JNjLAFwDcMGKJK/eWNpbm7WNZ+u+UzAFeQNoEi+540QwjTNqher/LW13Li5cHtv506vRx6YmQogbwAAMwB5AwBwA3kDAHADeQMAcAN5AwBwA3lTwDLJ6xdOnwx/evq//3ZrUv+kNwC4j7wpUMPJrsOvPalbv5yka4tW7jxzY2gK/7Q3ALiEvClMqW8aK6vfMy58n0zdvHz07Yp5urZog3GdwAGQt8ibQpS5Fz1QdyrmpEvm5+8+rNR8j//rqZueHhYATIC8mRESkboiX4k/kvD6QABgPOTNTJDpPbpGK918qi8jRCZ+dvfvVpXN0Ze8+eXNzHCy60+by4r1J7dHbg97fZgAZjXyZgb4+YaxuWRlyPw5W98MfH900xNzXmvqOLF9W/Crb75uaTeTdDsAPEXeFLzM7a8alr0W+ltS+o89Tau0uQsrdn3NtgZAfiBvClwmHql/veFMbPTv3wx3HXxuLo0OgPxB3hSyzN2u0Ftbj/7vz/d/5/aZt5/S9ecOfsf2BkB+IG8KVuZuV+itLaEr2WImk+y58n8/CSFEpv/C7p0fH9j8hLauqeeeGPrx7k/EDgCPkTeFKXO3K/T6kgp/0DDChhE2DKNpz5sr/uXAmf+50HP79vkDOz7tuWcGq7TSzX/p6jr0wbFrKa+PGMBsR94UoqTZtGmR/TfZjNweX/PR0dqlujbvVw3tNzNCDHeHXpynz/n1GO0OALiOvJlRMsneK1d6nStsmaFbf/+2lw9CA8gL/w9Ru3XJfg9qvwAAAABJRU5ErkJggg==" alt></span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The dimensions of the container are</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">length 2<em>x</em></span><br><span style="font-size: medium; font-family: times new roman,times;">width <em>x</em></span><br><span style="font-size: medium; font-family: times new roman,times;">height <em>y</em>.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">All of the measurements are in metres. The total length of all twelve edges is 48 metres.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that <em>y</em> =12 − 3<em>x </em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that the volume <em>V</em> m<sup>3</sup> of the container is given by</span></p>
<p><span><em>V</em> = 24<em>x</em><sup>2</sup> − 6<em>x</em><sup>3</sup></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \( \frac{{\text{d}V}}{{\text{d}x}}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of <em>x</em> for which <em>V</em> is a maximum.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the maximum volume of the container.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the length and height of the container for which the volume is a maximum.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The shipping container is to be painted. One litre of paint covers an area of 15 m<sup>2</sup> .</span> <span>Paint comes in tins containing four litres.</span></p>
<p><span>Calculate the number of tins required to paint the shipping container.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(4(2x) + 4y + 4x = 48\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for setting up the equation.</span></p>
<p><br><span>\(12x + 4y = 48\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for simplifying (can be implied).</span></p>
<p><br><span>\(y = \frac{{48 - 12x}}{{4}}\)</span> <span> </span><span> <strong>OR</strong> \(3x + y =12\) <em><strong>(A1)</strong></em></span></p>
<p><span>\(y =12 - 3x\) <em><strong>(AG)</strong></em></span></p>
<p><span><strong>Note:</strong> The last line must be seen for the <em><strong>(A1)</strong></em> to be awarded.</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(V = 2x \times x \times (12 - 3x)\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution into volume equation, <em><strong>(A1)</strong></em> for correct substitution.</span></p>
<p><br><span>\(= 24x^2 - 6x^3\) <em><strong>(AG)</strong></em></span></p>
<p><span><strong>Note:</strong> The last line must be seen for the <em><strong>(A1)</strong></em> to be awarded.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{\text{d}V}}{{\text{d}x}} = 48x - 18x^2\) <em><strong>(A1)(A1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for each correct term.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(48x -18x^2 = 0\) <em><strong>(M1)(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for using their derivative, <em><strong>(M1)</strong></em> for equating their answer to part (c) to 0.</span></p>
<p><br><span><strong>OR</strong></span></p>
<p><span><em><strong>(M1)</strong></em> for sketch of \(V = 24x^2 - 6x^3\), <em><strong>(M1)</strong></em> for the maximum point indicated <em><strong>(M1)(M1)</strong></em></span></p>
<p><span><strong>OR</strong></span></p>
<p><span><em><strong>(M1)</strong></em> for sketch of \(\frac{{\text{d}V}}{{\text{d}x}} = 48x - 18x^2\), <em><strong>(M1)</strong></em> for the positive root indicated <em><strong>(M1)(M1)</strong></em></span></p>
<p><span>\(2.67\left( {\frac{{24}}{9},{\text{ }}\frac{8}{3},{\text{ }}2.66666...} \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their part (c).</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(V = 24 \times {\left( {\frac{8}{3}} \right)^2} - 6 \times {\left( {\frac{8}{3}} \right)^3}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution of their value from part (d) into volume equation.</span></p>
<p><br><span>\(56.9({{\text{m}}^3})\left( {\frac{{512}}{9},{\text{ }}56.8888...} \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their answer to part (d).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\text{length} = \frac{{16}}{{3}}\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G1)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their answer to part (d). Accept 5.34 from use of 2.67</span></p>
<p><br><span>\(\text{height} = 12 - 3 \times \left( {\frac{{8}}{{3}}} \right) = 4\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for substitution of their answer to part (d), <em><strong>(A1)</strong></em><strong>(ft)</strong> for answer. Accept 3.99 from use of 2.67.</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\text{SA} = 2 \times \frac{{16}}{{3}} \times 4 + 2 \times \frac{{8}}{{3}} \times 4 + 2 \times \frac{{16}}{{3}} \times \frac{{8}}{{3}}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>\(\text{SA} = 4 \left( {\frac{{8}}{{3}}}\right)^2 + 6 \times \frac{{8}}{{3}} \times 4\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution of their values from parts (d) and (f) into formula for surface area.</span></p>
<p><br><span>92.4 (m<sup>2</sup>) (92.4444...(m<sup>2</sup>)) <em><strong>(A1)</strong></em></span></p>
<p><span><strong>Note:</strong> Accept 92.5 (92.4622...) from use of 3 sf answers.</span></p>
<p><span><br>\(\text{Number of tins} = \frac{{92.4444...}}{{15 \times 4}}( = 1.54)\) <em><strong>(M1)</strong></em></span></p>
<p><span><em><strong>[4 marks]<br></strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for division of their surface area by 60.</span></p>
<p><br><span>2 tins required <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Note:</strong> Follow through from their answers to parts (d) and (f).</span></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Many candidates did not answer this question at all and others did not get past part (c). It was</span> <span style="font-size: medium; font-family: times new roman,times;">unclear if this was because they could not do the question or they ran out of time.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">(a) This was very poorly done. Most candidates had no idea what they were supposed to </span><span style="font-size: medium; font-family: times new roman,times;">do here. Many tried to find values for <em>x</em>.</span></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Many candidates did not answer this question at all and others did not get past part (c). It was</span> <span style="font-size: medium; font-family: times new roman,times;">unclear if this was because they could not do the question or they ran out of time.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">(a) This was very poorly done. Most candidates had no idea what they were supposed to </span><span style="font-size: medium; font-family: times new roman,times;">do here. Many tried to find values for <em>x</em>.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">(b) Similar comment as for part (a) although more candidates made an attempt at finding </span><span style="font-size: medium; font-family: times new roman,times;">the Volume.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"> </span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Many candidates did not answer this question at all and others did not get past part (c). It was</span> <span style="font-size: medium; font-family: times new roman,times;">unclear if this was because they could not do the question or they ran out of time.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">(c) This part was very well done.</span></p>
<p> </p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Many candidates did not answer this question at all and others did not get past part (c). It was</span> <span style="font-size: medium; font-family: times new roman,times;">unclear if this was because they could not do the question or they ran out of time.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">(d) Not many correct answers seen. Many candidates graphed the wrong equation and </span><span style="font-size: medium; font-family: times new roman,times;">found 1.333 as their answer.</span></p>
<p> </p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Many candidates did not answer this question at all and others did not get past part (c). It was</span> <span style="font-size: medium; font-family: times new roman,times;">unclear if this was because they could not do the question or they ran out of time.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">(e) Some managed to gain follow through marks for this part.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"> </span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Many candidates did not answer this question at all and others did not get past part (c). It was</span> <span style="font-size: medium; font-family: times new roman,times;">unclear if this was because they could not do the question or they ran out of time.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">(f) Again here follow through marks were gained by those who attempted it.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"> </span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Many candidates did not answer this question at all and others did not get past part (c). It was</span> <span style="font-size: medium; font-family: times new roman,times;">unclear if this was because they could not do the question or they ran out of time.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">(g) Very few correct answers for the surface area were seen. Most candidates thought </span><span style="font-size: medium; font-family: times new roman,times;">that there were 4 equal faces 2 <em>xy</em> and 2 faces <em>xy</em>. Some managed to get follow</span> <span style="font-size: medium; font-family: times new roman,times;">through marks for the last part if they divided by 60.</span></p>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagram shows triangle ABC. Point C has coordinates (4, 7) and the equation of the line AB is <em>x</em> + 2<em>y</em> = 8.</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;"><img 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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the coordinates of </span><span>A</span><span>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the coordinates of B.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that the distance between A and B is 8.94 correct to 3 significant figures.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>N lies on the line AB. The line CN is perpendicular to the line AB.</span></p>
<p><span>Find </span><span>the gradient of CN</span><span>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>N lies on the line AB. The line CN is perpendicular to the line AB.</span></p>
<p><span>Find the equation of CN.</span></p>
<p> </p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>N lies on the line AB. The line CN is perpendicular to the line AB.</span></p>
<p><span>Calculate the coordinates of N.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>It is known that AC = 5 and BC = 8.06.</span></p>
<p><span>Calculate the size of angle ACB.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>It is known that AC = 5 and BC = 8.06.</span></p>
<p><span>Calculate the area of triangle ACB.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>A(0, 4) <em>Accept x</em> = 0, <em>y</em> = 4 <em><strong>(A1)</strong></em></span></p>
<p><span><strong><em>[1 mark]<br></em></strong></span></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>B(8, 0) <em>Accept x</em> = 8, <em>y</em> = 0 <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span><span><br> </span><strong>Note:</strong> Award <strong><em>(A0)</em></strong> if coordinates are reversed in (i) and <strong><em>(A1)</em>(ft)</strong> in (ii).</span></p>
<p> </p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{AB}} = \sqrt {{8^2} + {4^2}} {\text{ }} = \sqrt {80} \) <em><strong> (M1)</strong></em></span></p>
<p><span>AB = 8.944 <em><strong>(A1)</strong></em></span></p>
<p><span>= 8.94 <em><strong>(AG)</strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>y</em> = –0.5<em>x</em> + 4 <em><strong> (M1)</strong></em></span><br><span>Gradient AB = –0.5 <em><strong>(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A2)</strong> </em>if –0.5 seen.</span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span>Gradient \({\text{AB}} = \frac{{(0 - 4)}}{{(8 - 0)}}\) <em><strong>(M1)</strong></em></span><br><span>\( = -\frac{1}{2}\) <em><strong> (A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong> </em>for correct substitution in the gradient formula.</span> <span>Follow through from their answers to part (a).</span></p>
<p><span> </span></p>
<p><span>Gradient CN = 2 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Special case: Follow through for gradient CN from their</span> <span>gradient AB.</span></p>
<p><br><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>CN: <em>y</em> = 2<em>x</em> + <em>c</em></span></p>
<p><span>7 = 2(4) + <em>c</em> <strong><em>(M1)</em></strong></span></p>
<p><span><span><br> </span><strong>Note:</strong> Award <strong><em>(M1)</em></strong>for correct substitution in equation of a line.</span></p>
<p><span><span><br> </span><em>y</em> = 2<em>x</em> – 1 <strong><em>(A1)</em>(ft)<em>(G2)</em></strong><span><br> <br> </span><strong>Note:</strong> Accept alternative forms for the equation of a line including <em>y</em> – 7 = 2(<em>x</em> – 4) . Follow through from their gradient in (i).</span></p>
<p><span> </span></p>
<p><span><strong>Note:</strong> If <em>c</em> = –1 seen but final answer is not given, award <strong><em>(A1)(d)</em></strong>.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>x</em> + 2(2<em>x</em> – 1) = 8 <em> or equivalent <strong>(M1)</strong></em></span></p>
<p><span>N(2, 3) (<em>x</em> = 2, <em>y</em> = 3) <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong><em><strong>(G3)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for attempt to solve simultaneous equations or a sketch of the two lines with an indication of the point of intersection.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Cosine rule: </span><span>\(\cos ({\rm{A\hat CB)}} = \frac{{{5^2} + {{8.06}^2} - {{8.944}^2}}}{{2 \times 5 \times 8.06}}\) <em><strong>(M1)(A1)</strong></em></span><span><br></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong> </em>for use of cosine rule with numbers from the problem substituted, <em><strong>(A1)</strong> </em>for correct substitution.</span></p>
<p><span> </span></p>
<p><span>\({\rm{A\hat CB = 82.9^\circ }}\) <em><strong>(A1)(G2)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> If alternative right-angled trigonometry method used award</span> <span><em><strong>(M1)</strong></em> for use of trig ratio in both triangles,<em><strong> (A1)</strong> </em>for correct</span> <span>substitution of their values in each ratio,<em><strong> (A1)</strong> </em>for answer.</span></p>
<p> </p>
<p><span><strong>Note:</strong> Accept 82.8° with use of 8.94.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Area \({\text{ACB}} = \frac{{5 \times 8.06\sin (82.9)}}{2}\) <strong><em>(M1)(A1)</em>(ft)</strong></span></p>
<p><br><span><strong>Note:</strong> Award<em><strong> (M1)</strong></em> for substituted area formula, <em><strong>(A1)</strong> </em>for correct substitution. Follow through from their angle in part (e).</span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span>Area \({\text{ACB}} = \frac{{{\text{AB}} \times {\text{CN}}}}{2} = \frac{{8.94 \times \sqrt {{{(4 - 2)}^2} + {{(7 - 3)}^2}} }}{2}\) <strong><em>(M1)(M1)</em>(ft)</strong></span></p>
<p><br><span><strong>Note:</strong> Award<em><strong> (M1)</strong></em> substituted area formula with their values,<em><strong> (M1)</strong></em></span> <span>for substituted distance formula. Follow through from</span><br><span>coordinates of N.</span></p>
<p><br><span>Area ACB = 20.0 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Accept 20</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question had many correct solutions, but a large number of candidates were unable to follow the logical flow of the question to the end and many gave up. It should be pointed out to future candidates that parts (e) and (f) could be attempted independently from the rest and that care must be taken not to abandon hope too early in the longer questions of paper 2.</span></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">This question had many correct solutions, but a large number of candidates were unable to follow the logical flow of the question to the end and many gave up. It should be pointed out to future candidates that parts (e) and (f) could be attempted independently from the rest and that care must be taken not to abandon hope too early in the longer questions of paper 2.</span></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question had many correct solutions, but a large number of candidates were unable to follow the logical flow of the question to the end and many gave up. It should be pointed out to future candidates that parts (e) and (f) could be attempted independently from the rest and that care must be taken not to abandon hope too early in the longer questions of paper 2.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question had many correct solutions, but a large number of candidates were unable to follow the logical flow of the question to the end and many gave up. It should be pointed out to future candidates that parts (e) and (f) could be attempted independently from the rest and that care must be taken not to abandon hope too early in the longer questions of paper 2.</span></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">This question had many correct solutions, but a large number of candidates were unable to follow the logical flow of the question to the end and many gave up. It should be pointed out to future candidates that parts (e) and (f) could be attempted independently from the rest and that care must be taken not to abandon hope too early in the longer questions of paper 2.</span></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question had many correct solutions, but a large number of candidates were unable to follow the logical flow of the question to the end and many gave up. It should be pointed out to future candidates that parts (e) and (f) could be attempted independently from the rest and that care must be taken not to abandon hope too early in the longer questions of paper 2.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question had many correct solutions, but a large number of candidates were unable to follow the logical flow of the question to the end and many gave up. It should be pointed out to future candidates that parts (e) and (f) could be attempted independently from the rest and that care must be taken not to abandon hope too early in the longer questions of paper 2.</span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question had many correct solutions, but a large number of candidates were unable to follow the logical flow of the question to the end and many gave up. It should be pointed out to future candidates that parts (e) and (f) could be attempted independently from the rest and that care must be taken not to abandon hope too early in the longer questions of paper 2.</span></p>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>A manufacturer makes trash cans in the form of a cylinder with a hemispherical top. The trash can has a height of 70 cm. The base radius of both the cylinder and the hemispherical top is 20 cm.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>A designer is asked to produce a new trash can.</p>
<p>The new trash can will also be in the form of a cylinder with a hemispherical top.</p>
<p>This trash can will have a height of <em>H</em> cm and a base radius of <em>r</em> cm.</p>
<p style="text-align: center;"><img 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"></p>
<p>There is a design constraint such that <em>H</em> + 2<em>r</em> = 110 cm.</p>
<p>The designer has to maximize the volume of the trash can.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the height of the cylinder.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total volume of the trash can.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the height of the <strong>cylinder</strong>, <em>h</em> , of the new trash can, in terms of <em>r</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the volume, <em>V</em> cm<sup>3</sup> , of the new trash can is given by</p>
<p>\(V = 110\pi {r^3}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using your graphic display calculator, find the value of <em>r</em> which maximizes the value of <em>V</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The designer claims that the new trash can has a capacity that is at least 40% greater than the capacity of the original trash can.</p>
<p>State whether the designer’s claim is correct. Justify your answer.</p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>50 (cm) <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\pi \times 50 \times {20^2} + \frac{1}{2} \times \frac{4}{3} \times \pi \times {20^3}\) <em><strong>(M1)(M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their correctly substituted volume of cylinder, <em><strong>(M1)</strong></em> for correctly substituted volume of sphere formula, <em><strong>(M1)</strong></em> for halving the substituted volume of sphere formula. Award at most <em><strong>(M1)</strong></em><em><strong>(M1)</strong></em><em><strong>(M0)</strong></em> if there is no addition of the volumes.</p>
<p>\( = 79600\,\,\left( {{\text{c}}{{\text{m}}^3}} \right)\,\,\left( {79587.0 \ldots \left( {{\text{c}}{{\text{m}}^3}} \right)\,,\,\,\frac{{76000}}{3}\pi } \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (G3)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (a).</p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>h = H − r</em> (or equivalent) <em><strong>OR</strong></em> <em>H</em> = 110 − 2<em>r</em> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for writing h in terms of <em>H</em> and <em>r</em> or for writing <em>H</em> in terms of <em>r</em>.</p>
<p>(<em>h</em> =) 110 <em>− </em>3<em>r <strong>(A1) (G2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\left( {V = } \right)\,\,\,\,\frac{2}{3}\pi {r^3} + \pi {r^2} \times \left( {110 - 3r} \right)\) <em><strong>(M1)</strong></em><em><strong>(M1)</strong></em><em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for volume of hemisphere, <em><strong>(M1)</strong></em> for correct substitution of their h into the volume of a cylinder, <em><strong>(M1)</strong></em> for addition of two correctly substituted volumes leading to the given answer. Award at most <em><strong>(M1)</strong></em><em><strong>(M1)</strong></em><em><strong>(M0)</strong></em> for subsequent working that does not lead to the given answer. Award at most <em><strong>(M1)</strong></em><em><strong>(M1)</strong></em><em><strong>(M0)</strong></em> for substituting <em>H</em> = 110 − 2<em>r</em> as their <em>h</em>.</p>
<p>\(V = 110\pi {r^2} - \frac{7}{3}\pi {r^3}\) <em><strong>(AG)</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(r =) 31.4 (cm) (31.4285… (cm)) <em><strong>(G2)</strong></em></p>
<p><strong>OR</strong></p>
<p>\(\left( \pi \right)\left( {220r - 7{r^2}} \right) = 0\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for setting the correct derivative equal to zero.</p>
<p>(r =) 31.4 (cm) (31.4285… (cm)) <em><strong>(A1)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\left( {V = } \right)\,\,\,\,110\pi {\left( {31.4285 \ldots } \right)^3} - \frac{7}{3}\pi {\left( {31.4285 \ldots } \right)^3}\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of their 31.4285… into the given equation.</p>
<p>= 114000 (113781…) <em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note: </strong>Follow through from part (e).</p>
<p>(increase in capacity =) \(\frac{{113.781 \ldots - 79587.0 \ldots }}{{79587.0 \ldots }} \times 100 = 43.0\,\,\left( {\text{% }} \right)\) <em><strong>(R1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Award <em><strong>(R1)</strong></em><strong>(ft)</strong> for finding the correct percentage increase from their two volumes.</p>
<p><strong>OR</strong></p>
<p>1.4 × 79587.0… = 111421.81… <em><strong>(R1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Award <em><strong>(R1)</strong></em><strong>(ft)</strong> for finding the capacity of a trash can 40% larger than the original.</p>
<p>Claim is correct <em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from parts (b), (e) and within part (f). The final <strong><em>(R1)(A1)</em>(ft)</strong> can be awarded for their correct reason and conclusion. Do not award <strong><em>(R0)(A1)</em>(ft)</strong>.</p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The vertices of quadrilateral ABCD as shown in the diagram are A (3, 1), B (0, 2), C (–2, 1) and D (–1, –1).</span></p>
<p style="text-align: center;"><img src="data:image/png;base64,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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the gradient of line CD.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that line AD is perpendicular to line CD.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the equation of line CD. Give your answer in the form \(ax + by = c\) where \(a,{\text{ }}b,{\text{ }}c \in \mathbb{Z}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Lines AB and CD intersect at point E. The equation of line AB is \(x + 3y = 6\).</span></p>
<p><span>Find the coordinates of E.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>Lines AB and CD intersect at point E. The equation of line AB is \(x + 3y = 6\).</span></span></p>
<p><span>Find the distance between A and D.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The distance between D and E is \(\sqrt{20}\).</span></p>
<p><span>Find the area of triangle ADE.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{Gradient of CD}} = \frac{{1 - ( - 1)}}{{ - 2 - ( - 1)}}\) <em><strong>(M1)</strong></em></span></p>
<p><span>\( = - 2\) <em><strong>(A1)(G2)</strong></em> </span></p>
<p><strong><em> </em></strong></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in gradient formula.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{Gradient of AD}} = \frac{1}{2}\) <em><strong>(A1)</strong></em></span></p>
<p><span>\( - 2 \times \frac{1}{2} = - 1\) or \(\frac{1}{2}\) is negative reciprocal of –2 <em><strong>(M1)</strong></em></span></p>
<p><span>Hence AD is perpendicular for CD. <em><strong>(AG)</strong></em></span></p>
<p><strong><em> </em></strong></p>
<p><span><strong>Note:</strong> Last line must be seen for the <em><strong>(M1)</strong></em> to be awarded.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(y = -2x - 3\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for their (a), <strong><em>(A1)</em>(ft)</strong> for –3.</span></p>
<p><span>If part (a) incorrect award <em><strong>(A1)</strong></em><strong>(ft)</strong> for their <em>y</em>-intercept only if</span> <span>working is seen.</span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span>\(y - 1 = -2(x + 2)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em></span></p>
<p><strong><span>OR</span></strong></p>
<p><span><span>\(y + 1 = -2(x + 1)\) </span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for their (a), <em><strong>(A1)</strong></em> for correct substitution of point.</span></p>
<p><br><span>\(2x + y = -3\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong><em> </em></strong></span></p>
<p><span><strong>Note:</strong> The final <em><strong>(A1)</strong></em><strong>(ft)</strong> is for their equation in the stated form.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>E (−3, 3) (Accept <em>x</em> = −3, <em>y</em> = 3) <em><strong>(G2)</strong></em></span></p>
<p><strong><span>OR</span></strong></p>
<p><span>Award <em><strong>(M1)</strong></em> for solving the pair of simultaneous equations by hand. <em><strong>(A1)</strong></em><strong>(ft)</strong> for correct answer, <strong>(ft)</strong> from their (c). <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><strong><span>OR</span></strong></p>
<p><span>Award <em><strong>(M1)</strong></em> for having extended the lines in their own graph seen drawn on answer paper. <em><strong>(A1)</strong></em> for correct answer. <em><strong>(M1)(A1)</strong></em></span></p>
<p><strong><em> </em></strong></p>
<p><span><strong>Note:</strong> Missing coordinate brackets receive <em><strong>(G1)(G0)</strong></em> or <em><strong>(M1)(A0)</strong></em>.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Distance between A and D = \(\sqrt {4^2 + 2^2}\) <em><strong>(M1)</strong></em></span></p>
<p><span>\( = \sqrt{20}\) <strong>OR</strong> \(2 \sqrt {5}\) <strong>OR</strong> 4.47 (3 <em>s.f</em>.) <em><strong>(A1)(G2)</strong></em></span></p>
<p><strong><em> </em></strong></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into the distance formula, <em><strong>(A1)</strong></em> for correct answer.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Area of ADE = \(\frac{1}{2}\sqrt {20} \times \sqrt {20} \) <em><strong>(M1)</strong></em></span></p>
<p><span>= 10 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em> </span></p>
<p><span>Follow through from (e).</span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This was well done overall. Almost all students could calculate the gradient of the straight line. Gradient of perpendicular line was found, but some candidates failed to communicate the requirement, in terms of gradients for two lines to be perpendicular (Example: They are perpendicular because their gradients are opposite and reciprocal or they are perpendicular because the product of their gradients is −1) </span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Distance between points and area of triangle was answered well by most candidates. Both formulae for the area of the triangle were correctly used.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This was well done overall. Almost all students could calculate the gradient of the straight line. Gradient of perpendicular line was found, but some candidates failed to communicate the requirement, in terms of gradients for two lines to be perpendicular (Example: They are perpendicular because their gradients are opposite and reciprocal or they are perpendicular because the product of their gradients is −1) </span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Distance between points and area of triangle was answered well by most candidates. Both formulae for the area of the triangle were correctly used.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This was well done overall. Almost all students could calculate the gradient of the straight line. Gradient of perpendicular line was found, but some candidates failed to communicate the requirement, in terms of gradients for two lines to be perpendicular (Example: They are perpendicular because their gradients are opposite and reciprocal or they are perpendicular because the product of their gradients is −1) </span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Distance between points and area of triangle was answered well by most candidates. Both formulae for the area of the triangle were correctly used.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This was well done overall. Almost all students could calculate the gradient of the straight line. Gradient of perpendicular line was found, but some candidates failed to communicate the requirement, in terms of gradients for two lines to be perpendicular (Example: They are perpendicular because their gradients are opposite and reciprocal or they are perpendicular because the product of their gradients is −1) </span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Distance between points and area of triangle was answered well by most candidates. Both formulae for the area of the triangle were correctly used.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This was well done overall. Almost all students could calculate the gradient of the straight line. Gradient of perpendicular line was found, but some candidates failed to communicate the requirement, in terms of gradients for two lines to be perpendicular (Example: They are perpendicular because their gradients are opposite and reciprocal or they are perpendicular because the product of their gradients is −1) </span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Distance between points and area of triangle was answered well by most candidates. Both formulae for the area of the triangle were correctly used.</span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This was well done overall. Almost all students could calculate the gradient of the straight line. Gradient of perpendicular line was found, but some candidates failed to communicate the requirement, in terms of gradients for two lines to be perpendicular (Example: They are perpendicular because their gradients are opposite and reciprocal or they are perpendicular because the product of their gradients is −1) </span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Distance between points and area of triangle was answered well by most candidates. Both formulae for the area of the triangle were correctly used.</span></p>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A chocolate bar has the shape of a triangular right prism ABCDEF as shown in the diagram. The ends are equilateral triangles of side 6 cm and the length of the chocolate bar is 23 cm.</span></p>
<p style="text-align: center;"><img 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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the size of angle BAF.<br></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a, i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Hence or otherwise find the area of the triangular end of the chocolate bar.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a, ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the total surface area of the chocolate bar.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>It is known that 1 cm<sup>3</sup> of this chocolate weighs 1.5 g. Calculate the weight of the chocolate bar.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A different chocolate bar made with the same mixture also has the shape of a triangular prism. The ends are triangles with sides of length 4 cm, 6 cm and 7 cm.</span></p>
<p><span>Show that the size of the angle between the sides of 6 cm and 4 cm is 86.4° correct to 3 significant figures.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The weight of this chocolate bar is 500 g. Find its length.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>60° <em><strong>(A1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">a, i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><strong><em>Unit penalty (UP) applies in this part</em></strong></span></p>
<p><span><strong><em> </em></strong></span></p>
<p><span>\({\text{Area}} = \frac{{6 \times 6 \times \sin 60^\circ }}{2}\) <strong><em>(M1)(A1)</em></strong></span></p>
<p><span><strong><em>(UP)</em></strong> = 15.6 cm<sup><span>2</span></sup> \((9 \sqrt{3})\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></span></p>
<p><span><strong><em> </em></strong></span></p>
<p><span><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for substitution into correct formula, <strong><em>(A1)</em></strong> for correct values. Accept alternative correct methods.</span></p>
<p><span> </span></p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">a, ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><strong><em>Unit penalty (UP) applies in this part</em></strong></span></p>
<p><span><strong><em> </em></strong></span></p>
<p><span>\({\text{Surface Area}} =15.58 \times 2 + 23 \times 6 \times 3\) <em><strong>(M1)(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for two terms with 2 and 3 respectively, <em><strong>(M1)</strong></em> for \(23 \times 6\) (138).</span></p>
<p><br><span><em><strong>(UP)</strong></em> Surface Area = 445 cm<sup>2</sup> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><strong><em>Unit penalty (UP) applies in this part</em></strong></span></p>
<p><span><strong><em> </em></strong></span></p>
<p><span>\({\text{weight}} = 1.5 \times 15.59 \times 23\) <em><strong>(M1)(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for finding the volume, <em><strong>(M1)</strong></em> for multiplying their volume by 1.5.</span></p>
<p><br><span><em><strong>(UP)</strong></em> weight = 538 g <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G3)</strong></em></span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\cos \alpha = \frac{{{4^2} + {6^2} - {7^2}}}{{2 \times 4 \times 6}}\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for using cosine rule with values from the problem,</span> <span><em><strong>(A1)</strong></em> for correct substitution.</span></p>
<p><br><span>\(\alpha = 86.41…\) <em><strong>(A1)</strong></em></span></p>
<p><span><span>\(\alpha = 86.4^{\circ}\) </span> <em><strong>(AG)</strong></em> </span></p>
<p><strong><em> </em></strong></p>
<p><span><strong>Note:</strong> 86.41… must be seen for final <em><strong>(A1)</strong></em> to be awarded.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><strong><em>Unit penalty (UP) applies in this part</em></strong></span></p>
<p><span><strong><em> </em></strong></span></p>
<p><span>\(l \times \frac{{4 \times 6 \times \sin 86.4^\circ }}{2} \times 1.5 = 500\) <em><strong>(M1)(A1)(M1)</strong></em></span></p>
<p><br><span><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for finding an expression for the volume, <em><strong>(A1)</strong></em> for correct substitution, <em><strong>(M1)</strong></em> for multiplying the volume by 1.5 and equating to 500, or for equating the volume to \(\frac{500}{1.5}\).</span></span></p>
<p><span><span>If formula for volume is not correct but consistent with that in</span> <span>(c) award at most <em><strong>(M1)(A0)</strong></em><strong>(ft)</strong><em><strong>(M1)(A0)</strong></em>.</span></span></p>
<p><br><span><em><strong>(UP) </strong></em> <em>l</em> = 27.8 cm <em><strong>(A1)(G3)</strong></em></span></p>
<p><span><em><strong>[4 marks]</strong></em></span></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">It was pleasing to show candidate working throughout this question. Follow through marks </span><span style="font-size: medium; font-family: times new roman,times;">could be awarded when incorrect answers were given. Many candidates incorrectly calculated </span><span style="font-size: medium; font-family: times new roman,times;">the weight of the chocolate bar by multiplying the surface area by 1.5<em>g</em>. Also a large number </span><span style="font-size: medium; font-family: times new roman,times;">of students incorrectly used the formula for the volume of a pyramid rather than for a prism.</span> <span style="font-size: medium; font-family: times new roman,times;">Most candidates were successful in their use of the cosine rule but did not give the answer </span><span style="font-size: medium; font-family: times new roman,times;">before it was rounded to 86.4, resulting in the loss of the final <em>A</em> mark. The last part acted as </span><span style="font-size: medium; font-family: times new roman,times;">a clear discriminator, very few students were able to find the correct length of the new </span><span style="font-size: medium; font-family: times new roman,times;">chocolate bar. Most students used units correctly.</span></p>
<div class="question_part_label">a, i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">It was pleasing to show candidate working throughout this question. Follow through marks could be awarded when incorrect answers were given. Many candidates incorrectly calculated the weight of the chocolate bar by multiplying the surface area by 1.5<em>g</em>. Also a large number of students incorrectly used the formula for the volume of a pyramid rather than for a prism.Most candidates were successful in their use of the cosine rule but did not give the answer before it was rounded to 86.4, resulting in the loss of the final <em>A</em> mark. The last part acted as a clear discriminator, very few students were able to find the correct length of the new chocolate bar. Most students used units correctly.</span></p>
<div class="question_part_label">a, ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">It was pleasing to show candidate working throughout this question. Follow through marks </span><span style="font-size: medium; font-family: times new roman,times;">could be awarded when incorrect answers were given. Many candidates incorrectly calculated </span><span style="font-size: medium; font-family: times new roman,times;">the weight of the chocolate bar by multiplying the surface area by 1.5<em>g</em>. Also a large number </span><span style="font-size: medium; font-family: times new roman,times;">of students incorrectly used the formula for the volume of a pyramid rather than for a prism.</span> <span style="font-size: medium; font-family: times new roman,times;">Most candidates were successful in their use of the cosine rule but did not give the answer </span><span style="font-size: medium; font-family: times new roman,times;">before it was rounded to 86.4, resulting in the loss of the final <em>A</em> mark. The last part acted as </span><span style="font-size: medium; font-family: times new roman,times;">a clear discriminator, very few students were able to find the correct length of the new </span><span style="font-size: medium; font-family: times new roman,times;">chocolate bar. Most students used units correctly.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">It was pleasing to show candidate working throughout this question. Follow through marks </span><span style="font-size: medium; font-family: times new roman,times;">could be awarded when incorrect answers were given. Many candidates incorrectly calculated </span><span style="font-size: medium; font-family: times new roman,times;">the weight of the chocolate bar by multiplying the surface area by 1.5<em>g</em>. Also a large number </span><span style="font-size: medium; font-family: times new roman,times;">of students incorrectly used the formula for the volume of a pyramid rather than for a prism.</span> <span style="font-size: medium; font-family: times new roman,times;">Most candidates were successful in their use of the cosine rule but did not give the answer </span><span style="font-size: medium; font-family: times new roman,times;">before it was rounded to 86.4, resulting in the loss of the final <em>A</em> mark. The last part acted as </span><span style="font-size: medium; font-family: times new roman,times;">a clear discriminator, very few students were able to find the correct length of the new </span><span style="font-size: medium; font-family: times new roman,times;">chocolate bar. Most students used units correctly.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">It was pleasing to show candidate working throughout this question. Follow through marks </span><span style="font-size: medium; font-family: times new roman,times;">could be awarded when incorrect answers were given. Many candidates incorrectly calculated </span><span style="font-size: medium; font-family: times new roman,times;">the weight of the chocolate bar by multiplying the surface area by 1.5<em>g</em>. Also a large number </span><span style="font-size: medium; font-family: times new roman,times;">of students incorrectly used the formula for the volume of a pyramid rather than for a prism.</span> <span style="font-size: medium; font-family: times new roman,times;">Most candidates were successful in their use of the cosine rule but did not give the answer </span><span style="font-size: medium; font-family: times new roman,times;">before it was rounded to 86.4, resulting in the loss of the final <em>A</em> mark. The last part acted as </span><span style="font-size: medium; font-family: times new roman,times;">a clear discriminator, very few students were able to find the correct length of the new </span><span style="font-size: medium; font-family: times new roman,times;">chocolate bar. Most students used units correctly.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">It was pleasing to show candidate working throughout this question. Follow through marks </span><span style="font-size: medium; font-family: times new roman,times;">could be awarded when incorrect answers were given. Many candidates incorrectly calculated </span><span style="font-size: medium; font-family: times new roman,times;">the weight of the chocolate bar by multiplying the surface area by 1.5<em>g</em>. Also a large number </span><span style="font-size: medium; font-family: times new roman,times;">of students incorrectly used the formula for the volume of a pyramid rather than for a prism.</span> <span style="font-size: medium; font-family: times new roman,times;">Most candidates were successful in their use of the cosine rule but did not give the answer </span><span style="font-size: medium; font-family: times new roman,times;">before it was rounded to 86.4, resulting in the loss of the final <em>A</em> mark. The last part acted as </span><span style="font-size: medium; font-family: times new roman,times;">a clear discriminator, very few students were able to find the correct length of the new </span><span style="font-size: medium; font-family: times new roman,times;">chocolate bar. Most students used units correctly.</span></p>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Nadia designs a wastepaper bin made in the shape of an <strong>open</strong> cylinder with a volume of \(8000{\text{ c}}{{\text{m}}^3}\).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Nadia decides to make the radius, \(r\) , of the bin \(5{\text{ cm}}\).</span></p>
</div>
<div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Merryn also designs a cylindrical wastepaper bin with a volume of \(8000{\text{ c}}{{\text{m}}^3}\). She decides to fix the radius of its base so that the <strong>total external surface area</strong> of the bin is minimized.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Let the radius of the base of Merryn’s wastepaper bin be \(r\) , and let its height be \(h\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate</span><br><span>(i) the area of the base of the wastepaper bin;</span><br><span>(ii) the height, \(h\) , of Nadia’s wastepaper bin;</span><br><span>(iii) the total <strong>external</strong> surface area of the wastepaper bin.</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State whether Nadia’s design is practical. Give a reason.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down an equation in \(h\) and \(r\) , using the given volume of the bin.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that the total external surface area, \(A\) , of the bin is \(A = \pi {r^2} + \frac{{16000}}{r}\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down \(\frac{{{\text{d}}A}}{{{\text{d}}r}}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Find the value of \(r\) that minimizes the total external surface area of the wastepaper bin.</span><br><span>(ii) Calculate the value of \(h\) corresponding to this value of \(r\) .</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Determine whether Merryn’s design is an improvement upon Nadia’s. Give a reason.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \({\text{Area}} = \pi {(5)^2}\) <em><strong>(M1)</strong></em></span><br><span>\( = 78.5{\text{ (c}}{{\text{m}}^2}{\text{)}}\) (\(78.5398 \ldots \)) <em><strong>(A1)(G2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Accept \(25\pi \) .</span></p>
<p><br><span>(ii) \(8000 = 78.5398 \ldots \times h\) <em><strong>(M1)</strong></em></span><br><span>\(h = 102{\text{ (cm)}}\) (\(101.859 \ldots \)) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from their answer to part (a)(i).</span></p>
<p><br><span>(iii) \({\text{Area}} = \pi {(5)^2} + 2\pi (5)(101.859 \ldots )\) <em><strong>(M1)(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their substitution in curved surface area formula, <em><strong>(M1)</strong></em> for addition of their two areas.</span></p>
<p><br><span>\( = 3280{\text{ (c}}{{\text{m}}^2}{\text{)}}\) (\(3278.53 \ldots \)) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from their answers to parts (a)(i) and (ii).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>No, it is too tall/narrow. <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(R1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from their value for \(h\).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span>\(8000 = \pi {r^2}h\) </span> <span><em><strong>(A1)</strong></em></span></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(A = \pi {r^2} + 2\pi r\left( {\frac{{8000}}{{\pi {r^2}}}} \right)\) <em><strong>(A1)(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct rearrangement of <strong>their</strong> part (c), <em><strong>(M1)</strong></em> for substitution of <strong>their</strong> rearrangement into area formula.</span></p>
<p><br><span>\( = \pi {r^2} + \frac{{16000}}{r}\) <em><strong>(AG)</strong></em></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{{\text{d}}A}}{{{\text{d}}r}} = 2\pi r - 16000{r^{ - 2}}\) <em><strong>(A1)(A1)(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(2\pi r\) , <em><strong>(A1)</strong></em> for \( - 16000\) <em><strong>(A1)</strong></em> for \({r^{ - 2}}\) . If an extra term is present award at most <em><strong>(A1)(A1)(A0)</strong></em>.</span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(\frac{{{\text{d}}A}}{{{\text{d}}r}} = 0\) <em><strong>(M1)</strong></em></span><br><span>\(2\pi {r^3} - 16000 = 0\) <em><strong>(M1)</strong></em></span><br><span>\(r = 13.7{\text{ cm}}\) (\(13.6556 \ldots \)) <strong><em>(A1)</em>(ft)</strong></span></p>
<p><br><span><strong>Note:</strong> Follow through from their part (e).</span></p>
<p><br><span>(ii) \(h = \frac{{8000}}{{\pi {{(13.65 \ldots )}^2}}}\) <em><strong>(M1)</strong></em></span><br><span>\( = 13.7{\text{ cm}}\) (\(13.6556 \ldots \)) <strong><em>(A1)</em>(ft)</strong></span></p>
<p><br><span><strong>Note:</strong> Accept \(13.6\) if \(13.7\) used.</span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Yes or No, accompanied by a consistent and sensible reason. <em><strong>(A1)(R1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A0)(R0)</strong></em> if no reason is given.</span></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Pauline owns a piece of land ABCD in the shape of a quadrilateral. The length of BC is \(190{\text{ m}}\) , the length of CD is </span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\(120{\text{ m}}\)</span> , the length of AD is </span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\(70{\text{ m}}\)</span> , the size of angle BCD is \({75^ \circ }\) and the size of angle BAD is \({115^ \circ }\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img 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" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Pauline decides to sell the triangular portion of land ABD . She first builds a straight fence from B to D .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the length of the fence.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The fence costs \(17\) USD per metre to build. </span></p>
<p><span>Calculate the cost of building the fence. Give your answer correct to the </span><span>nearest USD.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that the size of angle ABD is \({18.8^ \circ }\) , correct to three significant figures.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the area of triangle ABD .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>She sells the land for \(120\) USD per square metre. </span></p>
<p><span>Calculate the value of the land that Pauline sells. Give your answer correct </span><span>to the nearest USD.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Pauline invests \(300 000\) USD from the sale of the land in a bank that pays compound interest compounded annually. </span></p>
<p><span>Find the interest rate that the bank pays so that the investment will double in value in 15 years.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{B}}{{\text{D}}^2} = {190^2} + {120^2} - 2(190)(120)\cos {75^ \circ }\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituted cosine formula, <em><strong>(A1)</strong></em> for correct substitution.</span></p>
<p> </p>
<p><span>\(= 197\) m <em><strong>(A1)(G2)</strong></em></span></p>
<p><span><strong>Note:</strong> If radians are used award a maximum of <em><strong>(M1)(A1)(A0)</strong></em>.</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{cost}} = 196.717 \ldots \times 17\) <em><strong>(M1)</strong></em></span></p>
<p><span>\( = 3344{\text{ USD}}\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><strong>Note:</strong> Accept \(3349\) from \(197\).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{\sin ({\text{ABD}})}}{{70}} = \frac{{\sin ({{115}^ \circ })}}{{196.7}}\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituted sine formula, <em><strong>(A1)</strong></em> for correct substitution.</span></p>
<p> </p>
<p><span>\( = {18.81^ \circ } \ldots \) <strong><em>(A1)</em>(ft)</strong></span><br><span>\( = {18.8^ \circ } \) <em><strong>(AG)</strong></em></span></p>
<p><span><strong>Notes:</strong> Both the unrounded and rounded answers must be seen for the final <em><strong>(A1)</strong></em> to be awarded. Follow through from their (a). If 197 is used the unrounded answer is </span><span>\( = {18.78^ \circ } \ldots \)</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{angle BDA}} = {46.2^ \circ }\) <em><strong>(A1)</strong></em></span><br><span>\({\text{Area}} = \frac{{70 \times (196.717 \ldots ) \times \sin ({{46.2}^ \circ })}}{2}\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituted area formula, <em><strong>(A1)</strong></em> for correct substitution.</span></p>
<p> </p>
<p><span>\({\text{Area ABD}} = 4970{\text{ }}{{\text{m}}^2}\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><strong>Notes:</strong> If \(197\) used answer is \(4980\).</span></p>
<p><span><strong>Notes:</strong> Follow through from (a) only. Award <em><strong>(G2)</strong></em> if there is no working shown and \({46.2^ \circ }\) not seen. If \({46.2^ \circ }\) seen without subsequent working, award <em><strong>(A1)(G2)</strong></em>.</span></p>
<p><span><em><strong>[4 marks]</strong></em><br></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(4969.38 \ldots \times 120\) <em><strong>(M1)</strong></em></span><br><span>\( = 596 327{\text{ USD}}\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Follow through from their (d).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(300000{\left( {1 + \frac{r}{{100}}} \right)^{15}} = 600000\) or equivalent <em><strong>(A1)(M1)(A1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for \(600 000\) seen or implied by alternative formula, <em><strong>(M1)</strong></em> for substituted CI formula, <em><strong>(A1)</strong></em> for correct substitutions.</span></p>
<p> </p>
<p><span>\(r = 4.73\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G3)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(G3)</strong></em> for \(4.73\) with no working. Award <em><strong>(G2)</strong></em> for \(4.7\) with no working.</span></p>
<p><span><em><strong>[4 marks]</strong></em><br></span></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates were able to recognise cosine rule, and substitute correctly. Where the final answer was not attained, this was mainly due to further unnecessary manipulation; the GDC should be used efficiently in such a case. Some students used the answer given and sine rule – this gained no credit.</span></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates were able to recognise cosine rule, and substitute correctly. Where the final answer was not attained, this was mainly due to further unnecessary manipulation; the GDC should be used efficiently in such a case. Some students used the answer given and sine rule – this gained no credit.</span></p>
<p> </p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates were able to recognise cosine rule, and substitute correctly. Where the final answer was not attained, this was mainly due to further unnecessary manipulation; the GDC should be used efficiently in such a case. Some students used the answer given and sine rule – this gained no credit.</span></p>
<p> </p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Again, most candidates used the appropriate area formula – however, some did not appreciate the purpose of the given answer and were unable to complete the question accurately.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Again, most candidates used the appropriate area formula – however, some did not appreciate the purpose of the given answer and were unable to complete the question accurately.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The final part, in which compound interest was again asked for, tested most candidates but there were many successful attempts using either the GDC's finance package or correct use of the formula. Care must be taken with the former to show some indication of the values to be used in the context of the question. With the latter approach marks were again lost due to a lack of appreciation of the difference between interest and value.</span></p>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagram shows part of the graph of \(f(x) = {x^2} - 2x + \frac{9}{x}\) , where \(x \ne 0\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down</span></p>
<p><span>(i) the equation of the vertical asymptote to the graph of \(y = f (x)\) ;</span></p>
<p><span>(ii) the solution to the equation \(f (x) = 0\) ;</span></p>
<p><span>(iii) the coordinates of the local minimum point.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \(f'(x)\) . </span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that \(f'(x)\) can be written as \(f'(x) = \frac{{2{x^3} - 2{x^2} - 9}}{{{x^2}}}\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the gradient of the tangent to \(y = f (x)\) at the point \({\text{A}}(1{\text{, }}8)\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The line, \(L\), passes through the point A and is perpendicular to the tangent at A. </span></p>
<p><span>Write down the gradient of \(L\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The line, \(L\) , passes through the point A and is perpendicular to the tangent at A. </span></p>
<p><span>Find the equation of \(L\) . Give your answer in the form \(y = mx + c\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>The line, \(L\) , passes through the point A and is perpendicular to the tangent at A. </span></span></p>
<p><span>\(L\) also intersects the graph of \(y = f (x)\) at points B and C . Write down the <strong><em>x</em>-coordinate</strong> of B and of C .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(x = 0\) <em><strong>(A1)(A1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(x = \) a constant, <em><strong>(A1)</strong></em> for the constant in their equation being \(0\).</span></p>
<p> </p>
<p><span>(ii) \( - 1.58\) (\( - 1.58454 \ldots \)) <em><strong>(G1)</strong></em></span></p>
<p><span><strong>Note:</strong> Accept \( - 1.6\), do not accept \( - 2\) or \( - 1.59\).</span></p>
<p> </p>
<p><span>(iii) \((2.06{\text{, }}4.49)\) \((2.06020 \ldots {\text{, }}4.49253 \ldots )\) <em><strong>(G1)(G1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award at most <em><strong>(G1)(G0)</strong></em> if brackets not used. Award <strong><em>(G0)(G1)</em>(ft)</strong> if coordinates are reversed.</span></p>
<p><span><strong>Note:</strong> Accept \(x = 2.06\), \(y = 4.49\) .</span></p>
<p><span><strong>Note:</strong> Accept \(2.1\), do not accept \(2.0\) or \(2\). Accept \(4.5\), do not accept \(5\) or \(4.50\).</span></p>
<p> </p>
<p><em><strong><span>[5 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(f'(x) = 2x - 2 - \frac{9}{{{x^2}}}\) <em><strong>(A1)(A1)(A1)(A1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for \(2x\), <em><strong>(A1)</strong></em> for \( - 2\), <em><strong>(A1)</strong></em> for \( - 9\), <em><strong>(A1)</strong></em> for \({x^{ - 2}}\) . Award a maximum of <em><strong>(A1)(A1)(A1)(A0)</strong></em> if there are extra terms present.</span></p>
<p><em><strong><span>[4 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><strong></strong>\(f'(x) = \frac{{{x^2}(2x - 2)}}{{{x^2}}} - \frac{9}{{{x^2}}}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for taking the correct common denominator.</span></p>
<p> </p>
<p><span>\( = \frac{{(2{x^3} - 2{x^2})}}{{{x^2}}} - \frac{9}{{{x^2}}}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for multiplying brackets or equivalent.</span></p>
<p><span> </span></p>
<p><span>\( = \frac{{2{x^3} - 2{x^2} - 9}}{{{x^2}}}\) <em><strong>(AG)</strong></em></span></p>
<p><span><strong>Note:</strong> The final <em><strong>(M1)</strong></em> is not awarded if the given answer is not seen.</span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(f'(1) = \frac{{2{{(1)}^3} - 2(1) - 9}}{{{{(1)}^2}}}\) <em><strong>(M1)</strong></em></span></p>
<p><span>\( = - 9\) <em><strong>(A1)(G2)</strong></em></span></p>
<p><span><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution into <strong>given</strong> (or their correct) </span><span><span>\(f'(x)\)</span> . There is no follow through for use of their incorrect derivative.</span></span></p>
<p><em><strong><span><span>[2 marks]</span></span></strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{1}{9}\) <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span><strong>Note:</strong> Follow through from part (d).</span></p>
<p><em><strong><span>[1 mark]</span></strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(y - 8 = \frac{1}{9}(x - 1)\) <em><strong>(M1)(M1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for substitution of their gradient from (e), <em><strong>(M1)</strong></em> for substitution of given point. Accept all forms of straight line.</span></p>
<p> </p>
<p><span>\(y = \frac{1}{9}x + \frac{{71}}{9}\) (\(y = 0.111111 \ldots x + 7.88888 \ldots \)) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G3)</strong></em></span></p>
<p><span><strong>Note:</strong> Award the final <strong><em>(A1)</em>(ft)</strong> for a correctly rearranged formula of <strong>their</strong> straight line in (f). Accept \(0.11x\), do not accept \(0.1x\). Accept \(7.9\), do not accept \(7.88\), do not accept \(7.8\).</span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\( - 2.50\), \(3.61\) (\( - 2.49545 \ldots \), \(3.60656 \ldots \)) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Notes:</strong> Follow through from their line \(L\) from part (f) even if no working shown. Award at most <em><strong>(A0)(A1)</strong></em><strong>(ft)</strong> if their correct coordinate pairs given.</span></p>
<p><span><strong>Note:</strong> Accept \( - 2.5\), do not accept \( - 2.49\). Accept \(3.6\), do not accept \(3.60\).</span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">As usual, the content in this question caused difficulty for many candidates. However, for those with a sound grasp of the topic, there were many very successful attempts. The curve was given so that a comparison could be made to a GDC version and the correct form of the derivative was also given to permit weaker candidates to progress to the latter stages. Unfortunately, some decided to proceed with their own incorrect versions, in which case <strong>very limited follow through accrued</strong>. It should be emphasized to candidates that when an answer is given in this way it should be used in subsequent parts of the question.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">As in previous years, much of the question could have been answered successfully by using the GDC. However, it was also clear that a large number of candidates did not attempt either to verify their work with their GDC or to use it in place of an algebraic approach.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Differentiation of terms with negative indices remains a testing process for the majority; it will continue to be tested. Some centres still do not teach the differential calculus.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">As usual, the content in this question caused difficulty for many candidates. However, for those with a sound grasp of the topic, there were many very successful attempts. The curve was given so that a comparison could be made to a GDC version and the correct form of the derivative was also given to permit weaker candidates to progress to the latter stages. Unfortunately, some decided to proceed with their own incorrect versions, in which case <strong>very limited follow through accrued</strong>. It should be emphasized to candidates that when an answer is given in this way it should be used in subsequent parts of the question.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">As in previous years, much of the question could have been answered successfully by using the GDC. However, it was also clear that a large number of candidates did not attempt either to verify their work with their GDC or to use it in place of an algebraic approach.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Differentiation of terms with negative indices remains a testing process for the majority; it will continue to be tested. Some centres still do not teach the differential calculus.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">As usual, the content in this question caused difficulty for many candidates. However, for those with a sound grasp of the topic, there were many very successful attempts. The curve was given so that a comparison could be made to a GDC version and the correct form of the derivative was also given to permit weaker candidates to progress to the latter stages. Unfortunately, some decided to proceed with their own incorrect versions, in which case <strong>very limited follow through accrued</strong>. It should be emphasized to candidates that when an answer is given in this way it should be used in subsequent parts of the question.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">As in previous years, much of the question could have been answered successfully by using the GDC. However, it was also clear that a large number of candidates did not attempt either to verify their work with their GDC or to use it in place of an algebraic approach.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Differentiation of terms with negative indices remains a testing process for the majority; it will continue to be tested. Some centres still do not teach the differential calculus.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">As usual, the content in this question caused difficulty for many candidates. However, for those with a sound grasp of the topic, there were many very successful attempts. The curve was given so that a comparison could be made to a GDC version and the correct form of the derivative was also given to permit weaker candidates to progress to the latter stages. Unfortunately, some decided to proceed with their own incorrect versions, in which case<strong> very limited follow through accrued</strong>. It should be emphasized to candidates that when an answer is given in this way it should be used in subsequent parts of the question.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">As in previous years, much of the question could have been answered successfully by using the GDC. However, it was also clear that a large number of candidates did not attempt either to verify their work with their GDC or to use it in place of an algebraic approach.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Differentiation of terms with negative indices remains a testing process for the majority; it will continue to be tested. Some centres still do not teach the differential calculus.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">As usual, the content in this question caused difficulty for many candidates. However, for those with a sound grasp of the topic, there were many very successful attempts. The curve was given so that a comparison could be made to a GDC version and the correct form of the derivative was also given to permit weaker candidates to progress to the latter stages. Unfortunately, some decided to proceed with their own incorrect versions, in which case <strong>very limited follow through accrued</strong>. It should be emphasized to candidates that when an answer is given in this way it should be used in subsequent parts of the question.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">As in previous years, much of the question could have been answered successfully by using the GDC. However, it was also clear that a large number of candidates did not attempt either to verify their work with their GDC or to use it in place of an algebraic approach.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Differentiation of terms with negative indices remains a testing process for the majority; it will continue to be tested. Some centres still do not teach the differential calculus.</span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">As usual, the content in this question caused difficulty for many candidates. However, for those with a sound grasp of the topic, there were many very successful attempts. The curve was given so that a comparison could be made to a GDC version and the correct form of the derivative was also given to permit weaker candidates to progress to the latter stages. Unfortunately, some decided to proceed with their own incorrect versions, in which case <strong>very limited follow through accrued</strong>. It should be emphasized to candidates that when an answer is given in this way it should be used in subsequent parts of the question.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">As in previous years, much of the question could have been answered successfully by using the GDC. However, it was also clear that a large number of candidates did not attempt either to verify their work with their GDC or to use it in place of an algebraic approach.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Differentiation of terms with negative indices remains a testing process for the majority; it will continue to be tested. Some centres still do not teach the differential calculus.</span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">As usual, the content in this question caused difficulty for many candidates. However, for those with a sound grasp of the topic, there were many very successful attempts. The curve was given so that a comparison could be made to a GDC version and the correct form of the derivative was also given to permit weaker candidates to progress to the latter stages. Unfortunately, some decided to proceed with their own incorrect versions, in which case <strong>very limited follow through accrued</strong>. It should be emphasized to candidates that when an answer is given in this way it should be used in subsequent parts of the question.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">As in previous years, much of the question could have been answered successfully by using the GDC. However, it was also clear that a large number of candidates did not attempt either to verify their work with their GDC or to use it in place of an algebraic approach.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Differentiation of terms with negative indices remains a testing process for the majority; it will continue to be tested. Some centres still do not teach the differential calculus.</span></p>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The diagram shows an <strong>aerial</strong> view of a bicycle track. The track can be modelled by the quadratic function</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">\(y = \frac{{ - {x^2}}}{{10}} + \frac{{27}}{2}x\), where \(x \geqslant 0,{\text{ }}y \geqslant 0\)</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">(<em>x</em> , <em>y</em>) are the coordinates of a point <em>x</em> metres east and <em>y</em> metres north of O , where O is the origin (0, 0) . B is a point on the bicycle track with coordinates (100, 350) .<br></span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The coordinates of point A are (75, 450). Determine whether point A is on the bicycle track. Give a reason for your answer.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the derivative of \(y = \frac{{ - {x^2}}}{{10}} + \frac{{27}}{2}x\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use the answer in part (b) to determine if A (75, 450) is the point furthest north on the track between O and B. Give a reason for your answer.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Write down the midpoint of the line segment OB.</span></p>
<p><span>(ii) Find the gradient of the line segment OB.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Scott starts from a point C(0,150) . He hikes along a straight road towards the bicycle track, parallel to the line segment OB.</span></p>
<p><span>Find the equation of Scott’s road. Express your answer in the form \(ax + by = c\), where \(a, b {\text{ and }} c \in \mathbb{R}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to find the coordinates of the point where Scott first crosses the bicycle track.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(y = - \frac{{{{75}^2}}}{{10}} + \frac{{27}}{2} \times 75\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong> </strong></span></p>
<p><span><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for substitution of 75 in the formula of the function.</span></p>
<p><br><span>= 450 <em><strong>(A1)</strong></em></span></p>
<p><span>Yes, point A is on the bike track. <em><strong>(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Do not award the final <em><strong>(A1)</strong></em> if correct working is not seen.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = - \frac{{2x}}{{10}} + \frac{{27}}{2}\left( {\frac{{{\text{d}}y}}{{{\text{d}}x}} = - 0.2x + 13.5} \right)\) <em><strong>(A1)(A1)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for each correct term. If extra terms are seen award at most <em><strong>(A1)(A0)</strong></em>. Accept equivalent forms.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\( - \frac{{2x}}{{10}} + \frac{{27}}{2} = 0\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for equating their derivative from part (b) to zero.</span></p>
<p><br><span>\(x = 67.5\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Note:</strong> Follow through from their derivative from part (b).</span></p>
<p><br><span>\( {\text{(Their) }} 67.5 \ne 75\) <em><strong>(R1)</strong></em></span></p>
<p><span><strong> </strong></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(R1)</strong></em> for a comparison of their 67.5 with 75. Comparison may be implied</span> <span>(<em>eg</em> 67.5 is the <em>x</em>-coordinate of the furthest north point).</span></p>
<p><span><br><strong>OR</strong><br></span></p>
<p><span>\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = - \frac{{2 \times (75)}}{{10}} + \frac{{27}}{2}\) <em><strong>(M1)</strong></em></span></p>
<p><span><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution of 75 into their derivative from part (b).</span></p>
<p><span><br>\(= -1.5\) <em><strong>(A1)</strong></em><strong>(ft)</strong><br></span></p>
<p><span><strong><br>Note: </strong>Follow through from their derivative from part (b).<strong><br></strong></span></p>
<p><span><strong> </strong></span></p>
<p><span>\({\text{(Their)}} -1.5 \ne 0\) <em><strong>(R1)</strong></em><br></span></p>
<p><span><strong><br>Note:</strong> Award <em><strong>(R1)</strong></em> for a comparison of their –1.5 with 0. Comparison may be implied (<em>eg</em> The gradient of the parabola at the furthest north point (vertex) is 0).<strong><br></strong></span></p>
<p><span><strong> </strong></span></p>
<p><span>Hence A is not the furthest north point. <em><strong>(A1)</strong></em><strong>(ft)</strong> <br></span></p>
<p><span><br><strong>Note:</strong> Do not award <em><strong>(R0)(A1)</strong></em><strong>(ft)</strong>. Follow through from their derivative from part (b).<br></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) M(50,175) <em><strong>(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> If parentheses are omitted award <em><strong>(A0)</strong></em>. </span><span>Accept <em>x</em> = 50, <em>y</em> = 175.</span></p>
<p><br><span>(ii) \(\frac{{350 - 0}}{{100 - 0}}\)</span><span> </span><em><strong><span>(M1)</span></strong></em></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in gradient formula.</span></p>
<p><br><span>\( = 3.5\left( {\frac{{350}}{{100}},\frac{7}{2}} \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from (d)(i) if midpoint is used to calculate gradient. Award <em><strong>(G1)(G0)</strong></em> for answer 3.5<em>x</em> without working.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(y = 3.5x + 150\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for using their gradient from part (d), <em><strong>(A1)</strong></em><strong>(ft)</strong> for correct equation of line.</span><br><br></p>
<p><span>\(3.5x - y = -150\) <strong>or</strong> \(7x - 2y = -300\) (or equivalent) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for expressing their equation in the form \(ax + by = c\).</span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(18.4, 214) (18.3772..., 214.320...) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Notes:</strong> Follow through from their equation in (e). Coordinates must be positive for follow through marks to be awarded. If parentheses are omitted and not already penalized in (d)(i) award at most <em><strong>(A0)(A1)</strong></em><strong>(ft)</strong>. If coordinates of the two intersection points are given award <em><strong>(A0)(A1)</strong></em><strong>(ft)</strong>. Accept <em>x</em> = 18.4, <em>y</em> = 214.</span></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">A gardener has to pave a rectangular area 15.4 metres long and 5.5 metres wide using rectangular bricks. The bricks are 22 cm long and 11 cm wide.</span></p>
</div>
<div class="specification">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">The gardener decides to have a triangular lawn ABC, instead of paving, in the middle of the rectangular area, as shown in the diagram below.</span></p>
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><img src="onbekend.html" alt="onbekend.png"></span></p>
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">The distance AB is 4 metres, AC is 6 metres and angle BAC is 40°.</span></p>
</div>
<div class="specification">
<div style="color: #3f3f3f; font: normal normal normal 14px/1.5em 'Lucida Grande', Helvetica, Arial, sans-serif; padding-top: 40px; padding-right: 10px !important; padding-bottom: 10px !important; padding-left: 10px !important; background-image: url('body-bg.html'); background-attachment: initial; background-origin: initial; background-clip: initial; background-color: #f7f7f7; height: 94% !important; font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 14px; line-height: 20px; display: inline; float: none; background-position: 50% 0%; background-repeat: no-repeat repeat; margin: 0px;">
<p style="margin-top: 0px; margin-right: 0px; margin-bottom: 10px; margin-left: 0px; font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif;"><span style="font-family: times new roman,times; font-size: medium;">In another garden, twelve of the same rectangular bricks are to be used to make an edge around a small garden bed as shown in the diagrams below. FH is the length of a brick and C is the centre of the garden bed. M and N are the midpoints of the long edges of the bricks on opposite sides of the garden bed.</span></p>
<p style="margin-top: 0px; margin-right: 0px; margin-bottom: 10px; margin-left: 0px; font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif;"><span style="font-family: times new roman,times; font-size: medium;"><img style="border-style: initial; border-color: initial; max-width: 100%; vertical-align: middle; border-width: 0px;" 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Dm/d0ye7fqp3ocDu2Hf5GHRYkM0u78z4deTcEDYGvPsOHnsYBzC1mIH8JnTsxGdMDqy2/TdmMbt7e8LlatNEMzIwp5NS919K6cL6c310RRfnC9su97i+I334cBB2DcZNOs6PRHidofWtX7vPQwHuuV3QRTF9kYFNraFbBaaHvvh57Q8Fm+xCVvbxWma5u1qo6UsTB3Lpzfz3OpN3//+wKoYv2pPcWaBzHMXRtObGq9IC1Plf09v4mJrdjzz/Pdvb3iWvTJVFka2ree5GM9t3i2cbjg/ZuTiwZFtm3cXP6mczg+sun13cbr+JRO7N67mV+18/rnvNQ5X6BW5KDy3e/O+4sxcRRZ2b1xduzGTmzS3ZaT8aafvo3bAd6WLM8aLb3y6XGm4pS9MlQ89t3vjap6L8Rv3FOQZXV+onM4PrDJ6x9WKLYyDPz26Y43RWc6Y8u/wOu1I4Ijx3PqB4RdffkaQ6i+8MFV+dTRd+6sfl6YWjD8nb8T65HO5/7MqthhHZoq7V8XWpIsN/8yVqfJrY+nNPBfjV+0YO734Nx6HAzdhnwwAtIwYm2zCRsYVsLpX1/WhTKb+Q/vTR0cOje/tv4aL8cs2PfyTidePX6w2tSJYEX/wyYnXj097vXGL+fhN+3iSy12v8FgZGI7KYyO4fNEuu0NuxsQrpXrehak3Htu4mt/4RHFqRh69l+fITWhhpriH3BQX70kLF4p7yL1Zrf1tLTdcmSo+scm4S80Ud5N77ao9xZkrtfnyVXuKF46ObFxdnzgnX7J60/CxSu3zjZOKPA7F+G3ChQtCkrzU2uHylXOFHSR8XD8gdBj8nysP31ibmD9+gRxPy82+cmJs23p+1SOFC1dqB1m7+86Sb/zGjk/mC6fHNq9uOueXfJ3mr5NH72r8ZmvBgmSR1ZvSglyZnSo+sal+hPU34uly5ZNi+vaG4yHvhRGq6m/ExieKU19MCTtbahE8Dgfuw357j7DxfL5l+/YotDu0hZ1NbI23r+WWn8vmjDfRq64JmJAOBsvjWEYZHc/F1q/7s1/96lc9P9bgsVWso+s6raHWBXLHJTeeueY7DfnfxQf9C8Ija+pZgdyJa7mhdvusfyE5c2rDD3rtnNn8TOG5e3kuRu6pC+SuTz5nrjyytvHzyYuvvmv4wEh64lT5ubu42Jr0wTd//MTY6Q+L6duXnHqvHca9z7/x4mN735j6tPm2XftO1yeFc4sHSW7MtS9suPs2vqo8elfjt2PyOs1qP6Jt+dOVBV1XpfK5hVoNR6w2nrFwemzz6jU7hAsLLW8EqTAwjme6+bv+tDy8pTZ8Uvuqph+Il+GA3Bjcn3MtPcIaHzobq3DxVEGQH5ffR9GkZc2IMfxjvLOeXJtQyh4MlsNBLptr3NEj4isYbTGGUa2MClBoulwfHqiNvbfchMj/1m97lWMjG1fXh/RJbqg/wTc9W9df07ibzhR3r1p919C/7N5BbpN6/fZWr3MkZ9riIr3ai2/a9vTiYMbGHSPFCwttMaLpmyF3ce72u/a8dmGBHIYRdOpHVcsKzf9Lnv47v2ztM+vDJ6av0/ql9aGOjU8Up640/EjbU8hCpfz0psU3gvyW1X/yTYMTtc9cky5+VpuD2PxY8ULjP+5ZOCCLCzwsCWx8vhRFsT+RcLnCHnrJ6DYhiiIZT6Kx6xUWwQeA5XDQst0Xz8UwNGid3QIsT5suk3tV/Q5KbkLGO958T2qaR2h9YCWDCltGyp/WM8TiAocFefQu7vpNm/cULtQbSDfNI7Suj2i+g9aOkLwauf03T70bjFDySOHClbbbcPN32vS/pjd4sy9s/982ZALCOOYlU8h04zxCbXSh6Sff8i/GarUdo6+Vp1rbcnsWDiitPjdW45AnCTwmtnNQzdczsix/5a/+6s//7Ob2ahKvoGyNddbCgaIo7eEgmo0R3bA1Z9deCT6UyTi5xpIH8dodlDzNx9ak3zj/+99/2PrkXZuV57cJU8Zj7trh/zl39K0PZ3VSSTecHiAFeqseGBHK9SI78oX1QXhd1xcf8XcWpubqYeLOkWOn3nrr7GJG6fBMT16q8+B/56DTMrVRP29rB9A0XrLEDb6WY4wYZPI6TRbkw6+SLyHfIPk9avudWpg6IU1dqQ+9kJGY2htx43Dp3FulDxeav+v2GZDKqVeLZ70fOaDdt64/kXDZTTmsSF2e30exJLJb0tM//rEn800dmfTiBL/ZK48l1QaNH6+88orf30Ig2eq7bJRwiaLIczEnz3iL4eDCVPnwWHoDz8XWbN338u8/bXjy/lB+6/dTtVtUbE26OFOR3xx+YA0X41fdu/sXxyu1rLB59+gvCsJbcsttktzMmp+VG2bxP5XfeHpgVYzn1v9t+qBUWWh5UO5U2XDvWPn4W0b2aPmH6nfxWnHitl/I8tHyVPNAAnmaN5YYLM6JXJDf+n3L69YOde1w+VP5rfLUgsnrNH/dTHHPjdty/zN1hYyy1L6FWhJaPzB6oqIvVOS3XiXfyOIt/5OKfJgs+qi9EYs/wNmp8uGi/GHTUMpU+dVDrT8Lb8IB1Y73WNRuQlEUlvcakCSppWqEhvZdPCCIJElqTAb79u5zs54FbM3DFovFa5avID95+yN8tSH9TemJ8tQn5eEtDasQyV1w/cDwYXK/r1fSpceKpy8U96zhSL39QttSwKalfbWba0vT39qsxObdo0X5whu7VzV+SeN0AEkk9Wd646ua1knqTf9QPYXUn+kbjmSq9LSx0nK0uBhi6gWGxnfa9LK1wskHRt6QK+av02T2w7dKp0+T23zjKy/UVmZysTXbhguLt3XjjRit3/7r32a9cGHNtqffJAsv66/QPEKzyINwQHvREdrhBVFLxSjV4gBUJoaGqqoFQSgIgvFu2lrQDy2s910m9Qo+loIuTJULw3seE46Wi4deJiMKS87fQy94EA6o7pmGRvrm2LwjktmElovRYDJJrzigY4clCJyOCaBxQT9GEB3o2EKmRTqVavzo+YVlupi+vSkKNE6xgx/chgOqF2VswWdOURQGa/XJpbz9It6DESbUrwXdYDK51AoFdDdxaakeJGwgI/+LQ/0LU288tvH6aOzFwChX4YD2cC7VUoYQKAgCaz8f85OBanEAeuoFnaZpPBczfwdtLeiHduzuW7swVRaGF2sONqbHijKSgY9chYPGtneew7W+K1VVmZqIJbMJJp/QgzSJVS3BpWmalVGBliZpPTiwkDF6kGANMJhwHg5Mdj3wBNVSBvAcWT3V9WJdEASq81A8F8MzZRR41YQ7suz2XYaocR4OqDafIS0RKb14OEiSxM6cgq0HOKrLT1DBGlzpVMruSICtBf3QztaW6xApDsMBVqb5LpfNMTIqaLeSgOqEEWnjjYehwHFTXYvG6m4YfZcZuZ4AI5yEA3Lzpnf9bd+GEdoVBIGF8XOyXEXTPpuWpXJnkjx9ueWrqBYHeLUBGPSSJElubk7WF/S7cHnxJH//fKXzpufzlfMn62f+mek5r3dGpwORGto5CQdUR25plzKAt0gDRF2/PC0fe/PAQzdzMX75ll1PDo8MD48M78+k7osv67BpOu3iAGy4EE3GfoN05q0uT39QejVz3zVcjF+2deyDLzp8ivbeyB0reG5F367828EJB5iMg3a2wwG5rNO7eeOyboUsy74PG+SyudZHjQ5b7FyefG3vI23hQKcfMamepeAti+sULKK7oJ+c5NyKDcPvtQ1QzF8q7r2Zi7XsNsk4tJOBjmyHg3QqRW9AmJQyYEC4q6FMxt+W0uP5fIe1CR3335uV3zxyvr0FKu2RTExOBYgkSZ6vYaHVd3lKGFh+S/yWFfzyhwuTV5v+6uqpsUQ8ftu1wQoHaCcDHdkLByglY4Tvj8VkR6XWP20NB3PTp89MLz2wSjULoqw1QChV1zb2XfbsRaeEgbV7Rg9sXcmt3nzgREM6qGrlp766ffTlJ+8MUDhAOxlYir1wgEVojPAxGYzn80v+6y3hoHqu8FDWvDU61VkkqmtqwEOqqtK7P3m8oH9KGFg7XP7k8KOrYvxNe4uX5mt/Xj1X2L5l35E/loeDFA7QTgaWYiMcUL150y5lAE903FFpEQkHy26/++8eGNi29e7buu+b0oNWWihhAd3DBf0kHMzNlIfv4rnrtx48W9V1Xa9e/WDsnm+NyVcrAQoHSM9gwmo4IEUr9AZpqZYyhIyPO9x3WSfWNHIwX/n41yP3/aTrpmpUiwMwaso+URR7E+CMBf3j+bzzU6IWDvTqpLBjeYy/46myVtWrnxR3f2OHcK6qByYcYN4NzFkNB9gyhxFkiKX3/66l6aTWmoNZ+VVRnjf/GuoXKaqnLriXTqV6WV3rtu9yPRzo1U+Kuzfw3PqHX7uwMCns+MpTZa2qByccjOfzmMYFE5bCQQ822/W39j5AVFXt/c+q645KNR1XK1hAtVs27UEvcMnVc7xTsiz3JxJOBuGMcKBXr34w1r8stjLxL6P/nLhn4syCrgclHGAaF7qyFA6oFq1Q3YkH3CONZSxdvp2GA53+OYaHJGjnpO/yYjggRYjreK6xMjEY4QDtZKCr7uGA6lMd5r3s6vEIub1nCxfhAKNT0SRJkr+//rb7LjeGA72qlZ/a0NQQ6dKRvXfw3F9njs5QO2S3MI0LVnQJB5gPZoqbzWkcyGVzlksF//TRkUPje/uv4WL8sq/v+teXfnn8ot3OsahriSBGNlRUFIUsdzRNkMZJvuGhZ+pn+NVTY/fsKkxe1fXq7Nl3CuM/vP8Gnuf4ddv2H3zlnY9mWWyfjKAMVnQJB6gkZ4ooij3LUqVSyWzVIgVYERM15B33+ygWGX2XSS9hsrohnUqlU6nQNAPAFBtYZBYOsAY94nqf29BLA3xn9F3+/qOP8lzM+AhBssQ0LlhnFg7QvY4pmqb15saWy+Z8fE5CF87oYHbUUFXVH/3wR43JgHwwe8AWYRoXrFsyHJARNvS9Z4ckST24sXXeUamHJEnC/h0RwfJAjizL7eEg0JcsMo3L7A8cWNM5HGDHPAZR2pymhaIovj8e9WDIyvfvEWjsxOghsut3mEYOsHwRbOkcDqiOvpLfOgRYu2RZpvpDM9tRqbdoFwfgKskCVVUZH8LJZXMt4cCXfk2ewDQu2NUhHJBLM6nXpQGXZgZ12VGp52jHU4yvghWiKKZTqaFMplQqkW5gffF44NYBYjYNHOgQDoYyGXp1uVRLGUKsVCpRvSRZ7QDTK6Qqhd7lzE4LB/CeqqoBrYxz3nfZP6jDBQdawwHV3gMkwAYud7OAPLvQeGVm3w6qA6EoifWXKIqBDmek73Ium2N//In2SDCEVWs4IFuaUnqORIB1zIN96DuxuqOST+jNQJGLO6a3/FIQBGZTqUWapuWyOXIWMTXq1oLqSDCEWOeaAwudRG0j3dAQYNlB9q5l+bpGozhAluXBZDJYw8LALKPvMpsz+uhCC4516XNgdBJ1DwHWMRrrFNgfDiU8LA4gYagvHg9NK9yA0jQtZA8JZArMw6ulV6hudgrhZtYhkbQW74vH3S/gQYB1w/PH3ACV43lSHGCcyblsDieh78bz+fA9JzB4jomiyPKkITCu+5bNnjxv9ScSCLDOkHoiD1+w9zsqueTyGuf5GBi4NJhMsjkI7x47o1MouQWXuocDws0CHgRYl3BXcxYuKVXPgEuhP59JXYu/u1GjCy24ZDUcEKTGeyiTsT5jjQDLDn93VHLD7rSUpmnj+Ty9dTcAXZVKpb54nNI6I3PoQgvu2QsHevMCHiufj33AXPKqZ5TvOyq5ZL2g1ceLMnQ1lMmEdU6hnV8hFV1owT3b4YCwuIAH+4C5pCiKV42AVFUNbjLQrS2FlWWZnJYYqWJWBC8IPe67jC604AmH4YDo+oiGAOuSLMvuJwLG8/lwzPKaNNGyO6AFvghu12T3jMJY2skVRTbgCVfhQK8v4Ok4boZ9wFjA2o5KbizVfttYQha1R1IIHNrnKrrQglfchgOifdyM9sY5UUCCl8sXEZgmuvIAABoLSURBVEUxHMmAaBkyDeIuOFEWsrPRGXqjXGTqDb8L4AlvwgHRuKAcAda9Uqnk5mcY1qFFMldlLCgP67cZPpqmeduxI9CM+hgPn6BQ/Q0e8jIcEGTcDAtp3HOz8jBMswktSFconou5b9wJvVQqlbDyvoWHfZfRhRa89SVd12VZLgiChx+5bC587VEDhP0dlVwqCIIoirKnkGV7IMTnpGNG2ZbLsIvqb/DWl/R6DYuH4QCnqXuOLxNRuMkVBIE8b3n10Z9I4IwFH7nsu4zqb/BcLRx4e2X0/AUjSBRFB9OHuWwuCqUeOGMDx8OOHSHmrMAWXWiBBoQDRqVTKbuldoHbUckxnLGBQ2Yb/T6KYLDbpR7V30ADwgGjSqVSFG7zzuCMDRxJksLRias3rPddJvW5UZhMhB5DOAiDXDYXqR84zliIAqNLvckgYjqVQvU30IBwwCJRFK2vfg76jkoO4IwNFkmSArodKAtM+i43LF+8PC1L5c4kefqyL0cOgYZwwCJbWwcFfUclB3DGBktw9wpnh9F3mSx97E8keC62ft2fvfLKK7qu6/rlafnYmwceupmL8cu37HpyeGR4eGR4fyZ1X3zZ9QPCeZ+PHgII4YBFg8mklU8LzY5KduGMDZbBZDKaJ6q3yLZVN11/PWkCRj6aGh9NCQNcjF87XJ4zvujy5Gt7H0E4APsQDoIqxD0Qu8IZC5H1F+v/vDEc8FxscVSmQzjQ9Vn5zSPnF/w4VAg0hAPmKIpi5ZYf5T1scMYGSASnvahqSQZkRUPt71rDwdz06TPTVd8OFQIN4YA5ffG4+cIkbDWEMzZA0qkUdmf10PYHH2wJB4sXhJZwUD1XeCjbNIoAYBnCAVtIizSTT4jybIIBZ2xQkJ0YI366emvr/fevXfNlIxk07WVFwsGy2+/+uwcGtm29+7bVrVMMAJYhHLBF0zST0q3Q76hkEc7YoNA0DW19vVUqlVRVJWds6yBi08jBfOXjX4/c9xOEA3AG4SAwUO9twBkLUUNWMHb5pNaag1n5VVGep35sEEoIBwzRNG2pOQUym9Dj42EWztigSKdS6OzrnqZpg8lk980pOq5WAHAE4YAhpVKp4wYqsiyjzqARzthAUBSlLx73+yjCQFVVSz2SEQ7AOwgHDJEkCSsRrMAZGwiyLOOn6pJ5EVIrhAPwDsIB03LZHDa6bYczFqKAzCZY21fpTx8dOTS+t/8aLsYv+/quf33pl8cvosEBuIFwwApVVVuWgxcEAbMJHeGMZZ+maRgGc0mSJDwbgF8QDlghimLLhUDTNCSDjnDGsk+SJJTQOobfffAdwgEr0qmU8aSVy+bQVM4Ezlj25bI5/EidIbMJ2McS/IVwQF21cu7dw4eEFyZ+Jrz+m1MX5/T5S+V33q+07oRiPCugB2JXOGPZh2dfx1BpBCxAOKBpbvLogYf7lm/Yvn/iv44ce7f46sT+5Nc2Je6+7dsHTi153ZQkCVdVczhjIcTw6w8sQDigZk4p7vvGyuXbnj3xWUPZ8HzlxPP3L79zpFwh/69pmiiK//jd7w5lMgVBwHXBCpyxjBNFsannP1hAZhPQCBUYgXBAyezHB3dew13XP3rqautffSGP7ho6OkP+ZzCZNPZQufOrGxEOrMAZy7ihTAZLFeyy1AMRoFcQDujQ3hu5YwXP/e3E2cvtf1md/M2LRy7qui7Lcsvuqz0/0EDCGcu4giCga7Jd2KEKmIJwQMX8qQNftdCqDOHAGZyxEBqapuWyOQwZAmsQDmiYv/jad1dyMf4rB06ZbommaVpfPG4kg44bK0A7nLEsK5VKeAi2yOqOSgA9h3BAw9yUsJPnYvzmUbl1xWIrRVGGMpl0KoWnB+twxrKsP5FAOLCIDBv4fRQAHSAc0FC9fDRzPRfjv5x59zIanHsPZyyzyGCY30cRAJqmodEZsAzhgI7P3953E89z947Js34fSgjhjIVAI7MJaC8NLEM4oOQLeXTrSm7FhsxvP28dO5ivnBj/p5/JbUscwSqcsczCMn0ryMYTmEYEliEcUDN7auLBW3nu1u3PHrs4ZwSE+crJF/YMvTk5h+kG53DGMovnYljEaAJdpSEoEA4oqlb+cPgnyb5lsZW3ffPv0z8c2b/vHxP9O575byQDl3DGskmWZQyVm8DaBAgQhAP65qbl8pHDrxw+8t7J8xXTpY1gDc5YNqmqinUKJsbzecwmQFAgHEDw4IyFIMKcAgQIwgEED85YBqmqii5eS8llc1i4CMGCcADBgzOWQaVSCTsxdpTL5jCbAIGDcADBgzOWQQVBwE6MHUmShGQAgYNwAMGDMxYCoSAIiAUQUAgHEDw4Y1mDdQrtMJsAgYZwAMGDM5Y14/n8eD7v91EwBBsxQ9AhHEDw4IxlzWAyiWp8AwZRIAQQDiB4cMayBi2TDWQ2we+jAHAL4QCCB2cssIk0kMZsAoQAwgEED85YpuSyOSxi1HUdmQDCBOEAggdnLFP64nFMK+SyOeyoBGGCcADBgzOWHZqmYZ2CKIqYTYCQQTiA4MEZC0zBjkoQPggHEDw4Y9khimKU5xSwoxKEFcIBBA/OWEZomsZzscg+NI/n85hNgLBCOIDgwRnLCEmSorxNM3ZUghCrhYN0KkWuj558kFfz+1uD0CoIQi6bk72Ty+ZwxoJ12FEJQu9Luq7LsuxhMiAfmIcDekqlUjqV8vYDK/UdiGa1AXZUgij4kuevqKpqOpXqi8fxywM0aJo2lMmgfb3vFEXpTyT8PgofYEcliAIvwwFZ8cxzMcwsAD0FQRhMJvvi8XQqFc0nV0aQyR2/j6KnEEkhOjwLB6VSqfF6raoqz8Vw7QZvkfNKUZTGJIrHOF/Isqwoit9H0Tu5bK4vHvf7KAB6xINwQPYa6U8kWmI1GT9w//oAhqFMprEfnzGHhYoBoEpRlL54PFJhCCLOVTjQNI2k6Y4zCJqm9cXjqEwEr8iy3LGWRZKk/kQinUrh2t0zpIrZ76PoEQxNQQQ5DwcFQeiLx81rc0qlUjRLloCG/kTCZITAygkJXonO4s9cNocRUIggJ+FAluX+RGIwmbRSnoPKRPAEqUM0/xxVVYcymb54XBTF3hxVZA1lMlEYpxFFEbMJEE32woFx8bU+xUvm6lCZCG6QKSqLteKkCMZieAUwoWkarl0QTVbDgaZpBUHgudh4Pm932DaXzQ1lMvaPDaAml83ZXTVHnvmGMhlc3D2nqmrof6qlUgnjTxBllsIBKR1wXPBl67EPoMVSdYhdNRbMohDBQ6FvKEkWZmM2AaKsSzhQFCWdSvUnEi4XHYii2HXCGKCjwWTSTdmKV+cwGEK/E6OiKEgGEHFLhgPSZMbDp67+RALDdGCXVwtejNGv0I+H90CIRwElSUIsANCXCgc05msdDw5DZHk7IeWmbgaiALMJAIbWcLBUu0NPtLS3AzA3ns97vsQcTRVdGkwmwzr6Mp7PIxkAEK3hgIwZUPrHVFVFMAeLqG7PIcsyz8WQD+wiv8J+H4X3cFECaNFhWoFqcQA2XACLqLbPQu9OZ1RVDV9PMzKbENbhEABnOoQDqsUBmqaZN8EF0OvbJdA7CbHrBxDkioSRA4AWnQsSqRYHUL3uQwjQTpAYvnIsfMMGANBR53BApnvppWlsuAAmqN68qZYyhJskSWHqVoKpJQATS/Y5wAUafEG7ahXB1LGCIIRmtRGZPMVsAsBSzJogUW0qR2OVGoTAUCZjdxsF6yRJQrMNIPBwAmDCrH1yD4rCQtxqDRyg3SkLxbCOhSZRlUolDB0BdNVlbwUsJ4NeGkwmsYyWTaIohmBvVfRABLCo+8ZLVIsDXO6pA2FCdXcuNOByaSiTCcGgC3ZUArCo+5bN4/k8vScGbLgABO1pJqqlDFFQKpUCPUmPHZUAbOkeDmhftXPZHK7akMvmkEGBEswmANjVPRzolIsDUJkIiqJQ7V9LtZQhCkRRDHRDyYIgIBkA2GIpHOiUiwMKghCm5ipgF9W6V1EUUffq0mAyGdD4jkwA4IzVcIA1ZkAJxqXYF9B0hR2VAByzGg50ysUBmBWOJtp7IFEtpwXGYUclAMdshAOyGIxqPXlomrOCRVR7D9AuZYgIRVGQ2gGixkY40Huy4QKSfnTQ3mID2yh4InABi8wm+H0UAMFmLxzolIsD0MMuUtKpFL2xIlLKgEdel2RZDlbBAenbhgImAJdshwOqxQG0d3sCduBECgRN0wI3mBe4AwZgkO1woOOBD7yAISjwFnZUAvCQk3CAqWJwqQfFK8GaJmeTqqpBmVOQJAmzCQAechIOdBSZgwu0l71QHdmKlFKpFJSFoIqiYBYJwEMOwwHtOV0sTw8xNMwICkmS2H8Wx0aLADQ4DAc65eIANLYLK7TaBA+RUUaMGQB4znk40NESH+yjugcSNunwkKqq7N90C4KALAhAg6twgM30wBaqgQ+jTd4qCALLe6mjJgmAKlfhQNf1XDZHrzgA88dhQvvmTbWUIYLSqRSzIwfksQRBEIAet+EAV3ywiGqRKXKk5zRNY/bnicoSANrchgNd10VRpDfRS3vZG/QGaWpLdQYKvTEAALziQTjQ6VeZodtd0FGtXSULZyi9eDTlsjkGy30URUH7VIDe8CYcYH0amJAkCateg6UvHmeteQAZRMR1AKA3vAkHuq4PZTI0igM0TSsIAs/FSPEBHhoCp1QqDSaT6VSK0pwC+mXRwOYcDWt5BSDEPAsHJNd7+9tLnjjTqZSiKLlsrj+R6IvHPRntrFbOv18mTp6vzDf+zdz0md+VDWem56ru/7loIrv9ko73uWyuLx73/JZDu5QBWKAoCvphA/SYZ+FA97Q4QFGUdCpldGg2pi1kWR5MJvsTCZfDyNXKx7/79YuZ+27huWu/9vhvLi4GgOrc9Jny2/lH49f27cq/jXDgiKqq6VSKDAIbcwot76knsEcXDeP5PDt5i6xaxGwCQI95GQ50L4oDNE0bz+d5LlYQBGMSoaXgURTFvnh8KJNxeQmrzhR/cG2M527dcfDM1aa/mXn3R3cNCOfdvHg0GdNA4/m88fY13sJLpVJfPO7JLAPVUobI0jSN52Ls/FSxoxKALzwOB5IkualMJHeOlrt+x7Z6HTOEbXPlkbUxnovxy7YMHZ1uGCKolIe3IBzYRVYNtN/4Wwb/jQDh5r0jW3/hgdJzZIDH76PQdeyoBOArj8OB7nSkd6n5AvNadLcj1XPlkbXbnxee3Lwsxt/wvcLHs/W/QDiwp+sb0V422Dj14OBfxALXcMNsAoC/vA8HqqraqhFTVdWkWs1KLXpj3aK9Y50rj6zdWZj6/OzBh9dxsZVff7r8OSlORDiwigzhkLfPZBhgqZBnvHe2ikhoVL8CwchPFTsqAfjL+3Cg6/p4Pm/xqa4gCH3x+FJrFK3Xonec6u6uFg7m9Or00cyWlRx/867XJueqCAcW2Sr+MNl1yfw0aDeUyaB8nQbyvO7vMaiqyk7FA0BkUQkHVvrSkHVu5o+MdmcoVFUdymRsjEYa4UDX9dlTEw/eynM33v/s8UoV4aALZ8tGTDppGgNIXZeqYhsFekRR9HcrE5JOUIEI4Dsq4UA37WhrcbLZcS06iR2DyWT3+1ZjONCrc5NvPL7pWp678weHTx1FOFiCkcAcNJzoel+3kjn6EwkGO/uGg6qq/vaaTKdSmE0AYAGtcKB3eu63PvhPatHdPEBYGqluCge6rs9XTjx///IYf8M9A9++A+Ggnd3x/3ZWttk0ma2gussXAAAQFMMBeUw0ru9LrXPryJNadE3TjFJHVVVJbWPTc0lrONB1/fLk4b19XIznrkc4aOS86rOZxW02O9Y5YhsFqmRZ9quSg8wmsNN5CQAohgO9/phod8EhWe/gVdW0LMvbH3zw2lWreS5GPhbHMy4fzXy5JRzoevXT4z+9dyXCQZ3LNYftrCe/ljPHyqgDOJbL5nxpN0kyH95ZAKbQDQfk177rOrcWnteiy7JsJAOei6VTKV3/00dHDk38aOs67pb7f/TvhSNnZxu/YO7c67u+jnDgSbeijmz1LyJjToPJJB4uqRrP5/1ax8jI+kkAMNANB7quS5Jk64JOoxa9JRz0f+tbXV+/Wpn84/RlD48hcDzsc9zO7rtMYgrqEENGURTsqAnAJurhwC5KPXEHk0kjHDw4MIDOuyZo7JDULp1KoVcBO2RZ7vGoDKk+wWwCAJvYCgcFQaBUi65pWqlUKggCGcD0qrwuZBpLOGn/W3Y7aQJVrbW69GmahqEgAGYxFA56XItORqr74nF7TRXDy6u9Lq3D/gjs6OVOjKqqos0RAOMYCge+1KK7aekTGjbaRnnKfTcL8ErPhtA0TRtMJjGjBMA4VsJBS1OE3v/rvtwdfed7NiIrETByEx2SJCEZALCPlXAwmEz6ssa6ERlXz2VzUZgIZ2dWxdke3+Ch/kSiByMHmqYhBQIEBRPhwGQjhh7rZUWej5iqx0R3PH+RVQO0/xUymxDlyTuAYPE/HDDYE1eW5R6s5fMFaXfI2krOXDaH9e5+UVW1BycDulsCBIv/4WA8n2ezZJ1qF6DeI7sV0Gh36B6DARG8xdopBwDm/A8HLD+j0+sf3GOMBx1VVfsTCQwe+ILqDBqZTWBh9goAbPE/HOhBuHV5u/NQLxlTJGw+l7M8nhEFkiRR3QJ7MJnEbAJAEDERDvQgPKMzVcRnBfvFlYyHwigoCALVhYVsRlIA6IqVcECw/4xOlv+RzW1Z/hjP51lelsn4eAa4RIIpmykfAKxgKxwQLD+jk9K5dCpFVuez+UECFptlnuyPZ0QHpcYDpM4AswkAgcZiOCCMZ3Smnj/G8/mhTIbcg/0+liUZIwesPZcb7ymb4xlRUyqVaBSBkilCz18WAHqJ3XCgM9Dct4XRrof9cFAQBHZaS+kRblDNsqFMxtvfLE3T2Fx2BAB2MR0OCFmWB5NJFu4rRqPfQIQDnY2m1KwlPDDIsuzhEA5mEwDCJADhgOj9hsItGrcICko4INtZ+TUvY6xA8X37BugBSZKQDABCIzDhQG+uZevxzaZlc+GghAPdv7a1LFeVgq7roih6tSYIOyoBhE+QwgGhKErvmyqSJQCN/xuUcND7zsS+vEFg12Ay6ckbRGYTWP51AAAHghcOCDLI35v+Oaqq8lys8R8KUDgg/0u1C54B7Q4DxKuVrthRCSCUghoO9B5OaadTqZYucsEKB7qu92AbRtLu0MeiEPAFUiBAKAU4HBC0myp2rOkLXDigWplIlpOg3WGAyLLs8mQgswl4xwHCKvDhgCDL6NOplOdXq47P3IELB7quD2UynnfRR7vDgCLtOty8AlYtAoRbSMIB4XlTxaVm64MYDkjlhIdrB9hsYQldkSTt/kU8ORgAYFOowoGu66qqkmdZ9y13VFVdqs4/iOFAb1tz4RjaHQad44yIHZUAIiJs4YDwZBbcpAw7oOGgpVuDA+xvmwn0kDqDwWQS4QAg9MIZDgg3TRXNK/gCGg705j6PtqDdYTiQvheOvxbDBgAREeZwoLtYeW/e1yW44UBv2CHCul52lQCqSqWSg6kl7KgEEDUhDweE3Z59XfczDHQ4MPaWtPJSaHcYMrIs250SMmYTKB0SADAoEuGAsNjt30q/4UCHA13Xx/P5oUzG/EXIoIsvO1kAUyRJQp0BQNREKBzo1ibOrdw4gx4OugYg3/fABBpUVXUwbEDpYACAZdEKB4SqqkOZTMeSe0VRWrZR6Cjo4UDXdVEUO06doN1hiBUEwVbnIuybABBZUQwHRMfF+haL9UIQDnRdH0wmG7tBeNgiAtiUTqWs146IoojZBIDIim44IBrb/JGiBCtXw3CEg8blmmh3CC00TcPJABBZUQ8HesMGAX3xuMXnqnCEA13Xc9kcWYxAY1sKYIr18pFcNofFKQARh3BQI8uy9X2JQhMOVFXtwW7OwIJcNmdlwmg8n8dsAgAgHDgRmnAA0dGfSFjZUkFRFCQDAEA4cILxuy/jhwe+6DpsMJ7PY+UqABAIB06Q7Q3JPZjBDwcNkiHictkcZhMAwIBw4IQsy74nAPMPVBdCo66jAgX0wQSABggHACGnaRrPxZa696McFQDaIRwAhBzZPavjX5HZhB4fDwCwD+EAIKJUVU2nUphNAIB2CAcAIdexAAULEwDABMIBQJgpitIXj7f8YS6b67r1KABEGcIBQJiJotiys2KpVMKqRQAwh3AAECTVyrl3Dx8SXpj4mfD6b05dnNPnL5Xfeb+ysNTnq6raPoOAZAAA5hAOAAJibvLogYf7lm/Yvn/iv44ce7f46sT+5Nc2Je6+7dsHTlm62eeyOXTHAgArEA4AgmBOKe77xsrl25498Vl18U/nKyeev3/5nSPlSvtXyLJ86NCh/U/uJ/+LHZUAwDqEAwD2zX58cOc13HX9o6eutv7VF/LorqGjM41/pGnaYDLJczHyQbYbxY5KAGAdwgEA87T3Ru5YwXN/O3H2cvtfVid/8+KRi41/ksvmjGRAPt5+++1eHSsAhAHCAQDr5k8d+CoX49cOl+csfX5fPN4SDg6+9BLlYwSAUEE4AGDdxde+u5KL8V85cGre0ue3hwPUIQKALQgHAKybEnbyXIzfPCovuWKxSfu0AnbpBABbEA4AWHf5aOZ6LsZ/OfPu5Wr3z9Z1TdPSqRSJBX3xOPZdBAC7EA4AmPf52/tu4nnu3jF51voXqaoqyzJWKACAAwgHAOz7Qh7dupJbsSHz289bxw7mKyfG/+lnctsSRwAA5xAOAIJg9tTEg7fy3K3bnz12cc4ICPOVky/sGXpzcs7SdAMAgEUIBwDBUK384fBPkn3LYitv++bfp384sn/fPyb6dzzz30gGAOA5hAOAQJmblstHDr9y+Mh7J89XrC1tBACwCeEAAAAAmiAcAAAAQJP/D4lXnE28X6wJAAAAAElFTkSuQmCC" alt></span></p>
</div>
</div>
<div class="specification">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">The garden bed has an area of 5419 cm<sup>2</sup>. It is covered with soil to a depth of 2.5 cm.</span></p>
</div>
<div class="specification">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">It is estimated that 1 kilogram of soil occupies 514 cm<sup>3</sup>.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the total area to be paved. Give your answer in cm<sup>2</sup>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the area of each brick.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find how many bricks are required to pave the total area.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the length of BC.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Hence write down the perimeter of the triangular lawn.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the area of the lawn.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the percentage of the rectangular area which is to be lawn.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the angle FCH.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the distance MN from one side of the garden bed to the other, passing through C.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the volume of soil used.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number of kilograms of soil required for this garden bed.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>15.4 × 5.5 <em><strong>(M1)</strong></em></span></p>
<p><span>84.7 m<sup>2</sup> <em><strong>(A1)</strong></em></span></p>
<p><span>= 847000 cm</span><span><span><sup>2</sup> </span> <em><strong>(A1)(G3)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(G2)</strong></em> if 84.7 m</span><span><span><sup>2</sup></span> seen with no working.</span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span>1540 </span><span><span>× </span>550 <em><strong>(A1)(M1)</strong></em></span></p>
<p><span>= 847000 cm</span><span><span><sup>2</sup></span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G3)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for both dimensions converted correctly to cm,</span> <span><strong><em>(M1)</em></strong> for multiplication of both dimensions. <strong><em>(A1)</em>(ft)</strong> for</span> <span>correct product of their sides in cm.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>242 cm<sup>2</sup> (0.0242 m<sup>2</sup>) <strong><em>(A1)</em></strong></span></p>
<p><span><strong><em>[1 marks}</em></strong></span></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac {15.4}{0.22} = 70\) <strong><em>(M1)</em></strong></span></p>
<p><span>\(\frac{5.5}{0.11} = 50\)</span></p>
<p><span>\(70 \times 50 = 3500\) <strong><em>(A1)(G2)</em></strong></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>\(\frac {847000}{242} = 3500\) <strong><em>(M1)(A1)</em>(ft)<em>(G2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note:</strong> Follow through from parts (a) (i) and (ii).</span></p>
<p> </p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{B}}{{\text{C}}^2} = {4^2} + {6^2}-2 \times 4 \times 6 \times \cos 40^\circ \) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span>\({\text{BC}} = 3.90{\text{ m}}\) <em><strong>(A1)(G2)</strong></em></span></p>
<p><span> </span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substituted formula, <em><strong>(A1)</strong></em> for correct substitutions, <em><strong>(A1)</strong></em> for correct answer.</span></p>
<p><span> </span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>perimeter = 13.9 m <strong><em>(A1)</em>(ft)<em>(G1)</em></strong></span></p>
<p><span> </span></p>
<p><span><strong>Notes:</strong> Follow through from part (b) (i).</span></p>
<p><span> </span></p>
<p><em><strong><span>[1 mark]</span></strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p> </p>
<p><span>\({\text{Area}} = \frac{1}{2} \times 4 \times 6 \times \sin 40^\circ \) <strong><em>(M1)</em></strong></span></p>
<p><span>= 7.71 m<sup>2</sup> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></span></p>
<p><span> </span></p>
<p><span><strong>Notes:</strong> Award <strong><em>(M1)</em></strong> for correct formula and correct substitution, <strong><em>(A1)</em>(ft)</strong> for correct answer.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<p> </p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{7.713}}{{84.7}} \times 100{\text{ }}\% = 9.11{\text{ }}\% \) <strong><em>(A1)(M1)(A1)</em>(ft)<em>(G2)</em></strong></span></p>
<p><span> </span></p>
<p><span><strong>Notes:</strong> Accept 9.10 %.</span></p>
<p><span>Award <strong><em>(A1)</em></strong> for both measurements correctly written in the same unit, <strong><em>(M1)</em></strong> for correct method, <strong><em>(A1)</em>(ft)</strong> for correct answer.</span></p>
<p><span>Follow through from (b) (iii) and from consistent error in conversion of units throughout the question.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">b.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{360^\circ }}{{12}}\) <em><strong>(M1)</strong></em></span></p>
<p><span>\( = 30^\circ\) <em><strong>(A1)(G2)<br></strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\text{MN} = 2 \times \frac{11}{\tan 15} \) <strong><em>(A1)</em>(ft)<em>(M1)</em></strong></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>\(\text{MN} = 2 \times 11 \tan 75^\circ \)</span></p>
<p><span>\({\text{MN}} = 82.1{\text{ cm}}\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></span></p>
<p><span> </span></p>
<p><span><strong>Notes:</strong> Award <strong><em>(A1)</em></strong> for 11 and 2 seen (implied by 22 seen), <strong><em>(M1)</em></strong> for dividing by tan15 (or multiplying by tan 75).</span></p>
<p><span>Follow through from their angle in part (c) (i).</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>volume = 5419 × 2.5 <em><strong>(M1)</strong></em></span></p>
<p><span>= 13500 cm<sup>3</sup> <em><strong>(A1)(G2)</strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{13547.34 \ldots }}{{514}} = 26.4\)</span> <span><em><strong>(M1)(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em> </span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for dividing their part (d) by 514.</span></p>
<p><span>Accept 26.3.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Part (a) was well done except for the fact that very few students were able to convert correctly from m<sup>2</sup> to cm</span><span style="font-size: medium; font-family: times new roman,times;"><span style="font-size: medium; font-family: times new roman,times;"><sup>2</sup></span> and this was very disappointing.</span></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was well done except for the fact that very few students were able to convert correctly from m<sup>2</sup> to cm<sup>2</sup> and this was very disappointing.</span></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;">Part (a) was well done except for the fact that very few students were able to convert correctly from m<sup>2</sup> to m<sup>2</sup> and this was very disappointing.</p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;"><span style="font-size: medium; font-family: times new roman,times;">In part (b) the cosine rule and the area of a triangle were well done. In some cases units were </span><span style="font-size: medium; font-family: times new roman,times;">missing and therefore a unit penalty was applied.</span></span></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (b) the cosine rule and the area of a triangle were well done. In some cases units were missing and therefore a unit penalty was applied.</span></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (b) the cosine rule and the area of a triangle were well done. In some cases units were missing and therefore a unit penalty was applied.</span></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (b) the cosine rule and the area of a triangle were well done. In some cases units were missing and therefore a unit penalty was applied.</span></p>
<div class="question_part_label">b.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;"><span style="font-size: medium; font-family: times new roman,times;">Part (c) was clearly the most difficult one for the students. The general impression was that </span><span style="font-size: medium; font-family: times new roman,times;">they did not read the diagram in detail. A number of candidates could not distinguish the </span><span style="font-size: medium; font-family: times new roman,times;">circle from the triangle and hence used an incorrect method to find the radius.</span></span></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (c) was clearly the most difficult one for the students. The general impression was that they did not read the diagram in detail. A number of candidates could not distinguish the circle from the triangle and hence used an incorrect method to find the radius.</span></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">It was pleasing to see candidates recovering well to get full marks for the last two parts.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">It was pleasing to see candidates recovering well to get full marks for the last two parts.</span></p>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Mal is shopping for a school trip. He buys \(50\) tins of beans and \(20\) packets of cereal. The total cost is \(260\) Australian dollars (\({\text{AUD}}\)).</span></p>
</div>
<div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The triangular faces of a square based pyramid, \({\text{ABCDE}}\), are all inclined at \({70^ \circ }\) to the base. The edges of the base \({\text{ABCD}}\) are all \(10{\text{ cm}}\) and \({\text{M}}\) is the centre. \({\text{G}}\) is the mid-point of \({\text{CD}}\).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down an equation showing this information, taking \(b\) to be the cost of one tin of beans and \(c\) to be the cost of one packet of cereal in \({\text{AUD}}\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Stephen thinks that Mal has not bought enough so he buys \(12\) more tins of beans and \(6\) more packets of cereal. He pays \(66{\text{ AUD}}\).</span></p>
<p><span>Write down another equation to represent this information.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>Stephen thinks that Mal has not bought enough so he buys \(12\) more tins of beans and \(6\) more packets of cereal. He pays \(66{\text{ AUD}}\).</span></span></p>
<p><span>Find the cost of one tin of beans.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Sketch the graphs of the two equations from parts (a) and (b).</span></p>
<p><span>(ii) Write down the coordinates of the point of intersection of the two graphs.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">i.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using the letters on the diagram draw a triangle showing the position of a \({70^ \circ }\) angle.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that the height of the pyramid is \(13.7{\text{ cm}}\), to 3 significant figures.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate</span></p>
<p><span>(i) the length of \({\text{EG}}\);</span></p>
<p><span>(ii) the size of angle \({\text{DEC}}\).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">ii.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the total surface area of the pyramid.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the volume of the pyramid.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(50b + 20c = 260\) <em><strong>(A1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(12b + 6c = 66\) <em><strong>(A1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Solve to get \(b = 4\) <em><strong>(M1)(A1)</strong></em><strong>(ft)<em>(G2)</em></strong></span></p>
<p><span><strong>Note: <em>(M1)</em></strong> for attempting to solve the equations simultaneously.</span></p>
<p><span><strong><em>[2 marks]</em></strong><br></span></p>
<div class="question_part_label">i.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i)</span></p>
<p><span><img src="data:image/png;base64,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" alt> <em><strong>(A1)(A1)(A1)</strong></em></span></p>
<p><span><em><strong><br></strong></em><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for labels and some idea of scale, <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong> for each line.</span></span><span><strong><br></strong>The axis can be reversed.</span></p>
<p><span><br>(ii) \((4,3)\) or \((3,4)\) <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span><strong><br>Note: </strong>Accept \(b = 4\), \(c = 3\)<br></span></p>
<p><span><em><strong>[4 marks]</strong></em><br></span></p>
<div class="question_part_label">i.d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt></span><span><span> </span><span> <em><strong>(A1)</strong></em></span></span></p>
<p><span><span><em><strong>[1 mark]<br></strong></em></span></span></p>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\tan 70 = \frac{h}{5}\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(h = 5\tan 70 = 13.74\) <em><strong>(A1)</strong></em></span></p>
<p><span>\(h = 13.7{\text{ cm}}\) <em><strong>(AG)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>Unit penalty <strong>(UP)</strong> is applicable in this part of the question where indicated in the left hand column.</em></span></p>
<p><span>(i) \({\text{E}}{{\text{G}}^2} = {5^2} + {13.7^2}\) OR \({5^2} + {(5\tan 70)^2}\) <em><strong>(M1)</strong></em></span></p>
<p><span><em><strong>(UP)</strong></em> \({\text{EG}} = 14.6{\text{ cm}}\) <em><strong>(A1)(G2)</strong></em></span></p>
<p><span>(ii) \({\text{DEC}} = 2 \times {\tan ^{ - 1}}\left( {\frac{5}{{14.6}}} \right)\) <em><strong>(M1)</strong></em></span></p>
<p><span>\( = {37.8^ \circ }\) <em><strong>(A1)</strong></em><strong>(ft)<em>(G2)</em></strong></span></p>
<p><span><strong><em>[4 marks]<br></em></strong></span></p>
<div class="question_part_label">ii.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>Unit penalty <strong>(UP)</strong> is applicable in this part of the question where indicated in the left hand column.</em></span></p>
<p><span>\({\text{Area}} = 10 \times 10 + 4 \times 0.5 \times 10 \times 14.619\) <em><strong>(M1)</strong></em><br></span></p>
<p><span><em><strong>(UP)</strong></em> \( = 392{\text{ c}}{{\text{m}}^2}\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em><br></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">ii.d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>Unit penalty <strong>(UP)</strong> is applicable in this part of the question where indicated in the left hand column.</em></span></p>
<p><span>\({\text{Volume}} = \frac{1}{3} \times 10 \times 10 \times 13.7\) <em><strong>(M1)</strong></em></span></p>
<p><span><em><strong>(UP)</strong></em> \( = 457{\text{ c}}{{\text{m}}^3}\) (\(458{\text{ c}}{{\text{m}}^3}\)) <em><strong>(A1)(G2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">ii.e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates managed to write down the equation.</span></p>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates managed to write down the equation.</span></p>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many managed to find the correct answer and the others tried their best but made some mistake in the process.</span></p>
<div class="question_part_label">i.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(i) Few candidates sketched the graphs well. Few used a ruler.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Many candidates could not be awarded ft from their graph because the answer they gave was not possible.</span></p>
<div class="question_part_label">i.d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Very few correct drawings.</span></p>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Some managed to show this more by good fortune and ignoring their original triangle than by good reasoning.</span></p>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(i) Many found this as ft from the previous part. Some lost a UP here.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) This was not well done. The most common answer was \({40^ \circ }\).</span></p>
<div class="question_part_label">ii.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many managed this or were awarded ft points.</span></p>
<div class="question_part_label">ii.d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This was well done and most candidates also remembered their units on this part.</span></p>
<div class="question_part_label">ii.e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The Great Pyramid of Cheops in Egypt is a square based pyramid. The base of the pyramid is a square of side length 230.4 m and the vertical height is 146.5 m. The Great Pyramid is represented in the diagram below as ABCDV . The vertex V is directly above the centre O of the base. M is the midpoint of BC.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Write down the length of OM .</span></p>
<p><span>(ii) Find the length of VM .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the area of triangle VBC .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the volume of the pyramid.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that the angle between the line VM and the base of the pyramid is 52° correct to 2 significant figures.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Ahmed is at point P , a distance <em>x</em> metres from M on horizontal ground, as shown in the following diagram. The size of angle VPM is 27° . Q is a point on MP .</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Write down the size of angle VMP .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Ahmed is at point P , a distance <em>x</em> metres from M on horizontal ground, as shown in the following diagram. The size of angle VPM is 27° . Q is a point on MP .</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Using your value of VM from part (a)(ii), find the value of <em>x</em>.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Ahmed is at point P , a distance <em>x</em> metres from M on horizontal ground, as shown in the following diagram. The size of angle VPM is 27° . Q is a point on MP .</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Ahmed walks 50 m from P to Q.</span></p>
<p><span>Find the length of QV, the distance from Ahmed to the vertex of the pyramid.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>(i) 115.2 (m) <em><strong>(A1)</strong></em></span></p>
<p><span><strong>Note:</strong> Accept 115 (m)</span></p>
<p><br><span>(ii) \(\sqrt{(146.5^2 + 115.2^2)}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution.</span></p>
<p><br><span>186 (m) (186.368…) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em> </span></p>
<p><span><strong>Note:</strong> Follow through from part (a)(i).</span></p>
<p><span> </span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{1}{2} \times 230.4 \times 186.368...\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in area of the triangle formula.</span></p>
<p><br><span>21500 m<sup>2</sup> (21469.6…m</span><span><span><sup>2</sup></span>) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><strong>Notes:</strong> The final answer is 21500 m</span><span><span><sup>2</sup></span>; <strong>units are required</strong>.</span> <span>Accept 21400 m</span><span><span><sup>2</sup></span> for use of 186 m and/or 115 m.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{1}{3} \times 230.4^2 \times 146.5\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in volume formula.</span></p>
<p><br><span>2590000 m<sup>3</sup> (2592276.48 m</span><span><span><sup>3</sup></span>) <em><strong>(A1)(G2)</strong></em></span></p>
<p><span><strong>Note:</strong> The final answer is 2590000 m</span><span><span><sup>3</sup></span>; <strong>units are required</strong> but do not penalise missing or incorrect units if this has already been penalised in part (b).</span></p>
<p><span> <em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\tan^{-1}\left( {\frac{{146.5}}{{115.2}}} \right)\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for correct substituted trig ratio. Accept alternate correct trig ratios.</span></p>
<p><br><span>= 51.8203...= 52° <em><strong>(A1)(AG)</strong></em></span></p>
<p><span><strong>Notes:</strong> Both the unrounded answer and the final answer must be seen for the <em><strong>(A1)</strong></em> to be awarded. Accept 51.96° = 52°, 51.9° = 52° or 51.7° = 52°</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>128° <em><strong>(A1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{186.368}}{{\sin27}} = \frac{{x}}{{\sin25}}\) <em><strong>(A1)(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Notes:</strong> Award <strong><em>(A1)</em>(ft)</strong> for their angle MVP seen, follow through from their</span> <span>part (e). Award <em><strong>(M1)</strong></em> for substitution into sine formula, <em><strong>(A1)</strong></em> for </span><span>correct substitutions. Follow through from their VM and their</span> <span>angle VMP.</span></p>
<p><br><span><em>x</em> = 173 (m) (173.490...) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G3)</strong></em></span></p>
<p><span><strong>Note:</strong> Accept 174 from use of 186.4.</span></p>
<p><span><em><strong>[4 marks]</strong></em><br></span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>VQ<sup>2</sup> = (186.368...)</span><span><span><sup>2</sup></span> + (123.490...)</span><span><span><sup>2</sup></span> − 2 × (186.368...) </span><span><span>× </span>(123.490...) </span><span><span>× </span>cos128 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Notes:</strong> Award <strong><em>(A1)</em>(ft)</strong> for 123.490...(123) seen, follow through from their <em>x</em> (PM) in part (f), <em><strong>(M1)</strong></em> for substitution into cosine formula, <em><strong>(A1)</strong></em><strong>(ft)</strong> for correct substitutions. Follow through from their VM and their angle VMP.</span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span>173.490... </span><span><span>− </span>50 = 123.490... (123) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>115.2 + 123.490... = 238.690... <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>\(\text{VQ} = \sqrt{(146.5^2 + 238.690...^2)}\) <em><strong>(M1)</strong></em></span></p>
<p><span>VQ = 280 (m) (280.062...) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G3)</strong></em></span></p>
<p><span><strong>Note:</strong> Accept 279 (m) from use of 3 significant figure answers.</span></p>
<p><span><em><strong>[4 marks]</strong></em><br></span></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(a) This part was very well done on the whole.</span></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(b) Amazingly badly done. Many candidates used 146.4 for the height and others tried unsuccessfully to find slant heights and angles to that they could use the area of a triangle formula \(\frac{{1}}{{2}}ab \sin C\).</span></p>
<p> </p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(c) This was fairly well done.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(d) Quite a few candidates managed to show this although they did not always put down</span> <span style="font-family: times new roman,times; font-size: medium;">the unrounded answer and so lost the last mark. Some even tried to use 52° to verify </span><span style="font-family: times new roman,times; font-size: medium;">its value.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(e) Very well done on the whole – even if part (d) was wrong.</span></p>
<p> </p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(f) This was well done by those who attempted it. Not all candidates used VM to find <em>x</em></span> <span style="font-family: times new roman,times; font-size: medium;">and so lost one mark. There were quite a few different methods of finding the answer.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(g) Again this was well done by those who attempted it. Again there were many different</span> <span style="font-family: times new roman,times; font-size: medium;">ways to reach the correct answer.</span></p>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagram shows a Ferris wheel that moves with constant speed and completes a rotation every 40 seconds. The wheel has a radius of \(12\) m and its lowest point is \(2\) m above the ground.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img 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" alt></span></p>
<p> </p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Initially, a seat C is vertically below the centre of the wheel, O. It then rotates in an anticlockwise (counterclockwise) direction.</span></p>
<p><span>Write down</span></p>
<p><span>(i) the height of O above the ground;</span></p>
<p><span>(ii) the maximum height above the ground reached by C .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>In a revolution, C reaches points A and B , which are at the same height above the ground as the centre of the wheel. Write down the number of seconds taken for C to first reach A and then B .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The sketch below shows the graph of the function, \(h(t)\) , for the height above ground of C, where \(h\) is measured in metres and \(t\) is the time in seconds, \(0 \leqslant t \leqslant 40\) .</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span><strong>Copy</strong> the sketch and show the results of part (a) and part (b) on your diagram. Label the points clearly with their coordinates.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(14\) m <em><strong>(A1)</strong></em></span></p>
<p> </p>
<p><span>(ii) \(26\) m <em><strong>(A1)</strong></em></span></p>
<p> </p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>A:\(10\), B:\(30\) <em><strong>(A1)(A1)</strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAwMAAADZCAIAAADzDXugAAAgAElEQVR4nO3d7U9bZ5438OsP8Iv1vEMjpGhYtH4RCWUjtKJCoyAlKLuRcNURinAqRKqMCBsqQiKgGZmkaiHV5FQ7C52JyajWTKx6h3RiZaibO07H7Aw0MpnGcwcUrIzjhN48OQHqFGRsKDbnul9cxhw/YsD2efp+XrXmIedwHf/8PdfTIRQAAABArYjYBwAAAAAgGiQhAAAAUK/MSYgPzkx8M+r4o3V0ZrOIBwQAkA/R4MyTR6P3blm/RgkDgCwyJSF+bWpsqO90CSlvsk3z2X4DH/F7Jvzria8tP3s4uRjJ+nMAAIWz9q1r6L+bSgjRW6aylaIMFezvz4MoYADqkGV0LBpwXNSSerN3LfP3rPtH+tuv/tmfHHqiwUlLe7t1MhjNz2ECAOzWynBnibba9CRzGUIFA4BsSSgw2l1FDvSOrWe6M4osjlx9s90+LywifPDlS3YrFQ2OX29osU2jZwgARMCvu7kKUtU9GsjwDTtXMEPSVwFAiTInoc2n5toSbZsjUxXh/V+0HDxnm98QvLY2bbtosPi2Ksf3Yz11DRbvRrofBwAopDWvuZ5oLzoC6ft1+IV77RWJFYxfnjSfQwUDUJuMSYj325o0pXqLj4+8cn/2flP9O5ftzwUVYdnNHdeetS/E75ci867+0+VEb/KE4r9j3c1VlLfb/agkAFBc/LStqZzoLVP8+qLbermpofGyfWojXrAyVTDhfABWwTodi5FiHzwAFFGmJLS5MnyphOhN415n74XL5uudR0rIob7x+M3VynBnSak+fvMUGje31B8p05CyI/WNzb3DfsG3lTUMZp2wCACQd7FJQv/35ch/tVwe+LSzlpDjfeOrgq+iggEApZmT0IqbO0ZK267/lrsx/j0ffWKq1pKTgzNb9SA63neIHO4cXtr+iegTU7W2pHN4Rfhrok9M1VpNs32xMEcPAJAOmyRUefH6r9+/8fcgH/KY9IScHpyJ9U/vqoJlmSQAAAqQIQltPjXXlpCKmhard4NSfsqiJ8IlGNFF+7sacoRzB7d/wmuuJQfP2ucSb55mbI1lCZ1JAAAFt+Y11xOiq2r5w/MNnvI+i76UVJs8sUKUqYJVtDleJf6eGVtjmeAHAUCB0ich3m9r0hCN3uzd4LeW0x/j3PGbpYjf1kwS6kjEbzurIacsU4nbcrA6Usa5Mc4OAMXzytFWQTQGszdEKaUBR5tWU8E92ipPqGAAsC1tEuJXR6+UkkPnHS95SmPL6UsuDa/EN2pl2UhYR5aGOw+nu3PCHRUAFN3qaHcpKTnvCPB0q6AJx8IyVLBaszd5N2pUMADlS5uEQh6Tfjv6xEfK1/xTL2M3TFGPqZromu3zsZ9Yf8RVaCu4R+vBhZfCvcgwyg4ARRf1mKq3h7pCHpOeaC86AiuzUwuR7W8QVLCQq+cgKhiASqVLQrzPoi/VNNn8PKWU8jODJ0mp/ubY337d/+X8VtfxD4/73iiNzxyKekzV5HDnvbE7H3/+jzXBTCGsvACAYlufspwimrM2f4TS+HL63z3+m/mjL6djw1zpK9jDL39tf7GBCgagLumSUMDRpi2pNT9l/cRRj6maEFL+c/PksqAchLxmg2brgT6vh39RToim5kNnwuN7+NDY1YM643CGnc0AAArglaOtYnuoiy19JYeazBOCR4mlVjBNWd0vh1HBANQny9M24taXvBPepfXkl9cmTPrTsQmJdH3p2/nkBxbyC8Nd+tODz7CvIgCIh48sPfu7dyl50nNCBYsGXy6gggGoUy5JKBN+48XgmdOfPkn/kMJ1v+P9hstfpTzaEABAClDBAIDS/SUhSmk06Ln1Xpf50WJijxG/8sLOdfV/jSICABKGCgYA+01ClFLKB2e//S6p43k1vkYDAEDK+KT1YpRSuv6dP5BLBZudnS3IMQFAEeUhCe3Z7OwsISQQwAJVAJAfr9dLCLl//77YBwIA+yJmEuro6CCE9Pb2ingMAAB7wypYZWVlOBwW+1gAYO9ES0Jer7eyspLVEa/XK9ZhAADswYMHD/R6PbuXu3nzptiHAwB7J1oS0uv1Dx48IITYbLaOjg6xDgMAYA/iFSwQCFRWVmLCEIB8iZOE7t+/f+bMGUopISQcDqNbCABkJH7/RggR/i8AyJEISUgYfVgdefDgAQtGAAASl1rB6FYXkajHBQB7JEISEt4/oY4AgLx88sknn3zyCfvveAV7/Pgxpk4DyJQISUi4cj5eRx48eIDuZQCQvsrKytQKRint7e19/PixSAcFAHsnQhISbiAkrCPYWAgA5EVYwQBApkR+G6OOAIB8oYIBKACSEADAHqGCASgAkhAAwB6hggEoAJIQAMAeoYIBKACSEADAHqGCASgAkpAarPsnPP4ITykf8f+1/2xtGSGElFQ29Y/41+PfxAef2nsbjzVeutbTVl9vvOVZ5jP9tpHfnK0pJ4QQzRtNfX/1R9J+4/qS1+W4Ze67MerfXH72cHIx/bcByBgqGIACIAkpXWRu5ONLV52zEUr511/31v3sfN/N24O//bDxDQ0hmmP94yGeUkr5eUd7lbbp1nSEpzS6MvbLqvJmizeY8uuir11cXV17n+XzwU8/aKwsIaT0WN/fQwnfs744/seekz+tabv+5fhChFJKo8FJS3u7dTIYLcYpAxQLKhiAAiAJKRr/cuRKU7t9OkIppWte87mu4YVYzww/72ivIqSqezRAKR9yf1xFKtocr2I/GH1iqtZqT9vmk/pxNp+af3ZlOBALNPzCvXadhpReGV2Nf9+63/lhjeZQk3kimPCz0eD49YYW2zR6hkBBUMEAFABJSME2/Pb2g/E0w39765LFuxEPIvzq6JVSUtZom6E0MNpdRcgpy1R8sCww2l1FNO8MTv8g/I38zO1LZs/G9gvsB5tt/gillNLI4khvjab0GPdwJU3g+X6sp67B4t1I/QqAPKGCASgAkpByhb7hqg6dtc9l6oSJuLkycoxzr7AeIFJyaXhlc+uLa15zPRH2EqUXdHNHSAXnXue3/kUt0RnjnUaJ+HU3V1HebvcjC4FCoIIBKACSkFJtrgxfKkno5kmyPmU5Rao+dod4GnC0aQkp49yR+FcjflszISW15qebGX6eUkp5n0VfVsV9E6KU0mjAcVFLiObExWvdTUfKNJrDDUazK2E+9cpwZ0lZw+AURshAGVDBABQASUipVsf7jid28yTa8Jj1P22xz/CUUr+tkaRNQomvJeM3vGa9Lt7HszzWU01IeT1317O0zge/HTWdKSeJI2XRJ6ZqrabZvpifcwQQGSoYgAIgCSnVvL1ZlznIRBYc71Wft8+zDpuV4c6StElIW216knG5Fz/vaH/rfGw6NqV0xtZYRsjpwZmtwS9+2nZaR7QXHduDZTO2xjJyqG8ca8hAEVDBABQASUipZmyNZRmSEB+Zt19459Mn8TXtm0/NtSVJS8CmLKeyzhNan7d3vzMwLlggNm9v1glmT8d/yRHOHV+Nn+WoAOQHFQxAAZCElOqVo60ibebgg+7+ll86/cL5Q9+P9RxJ6M6JDXVlmmYUDY7faLnyVeKeiiGPSU+I3uSJ7y7EOpaO942vbr0yY2ssI9UmD/qEQBFQwQAUAElIqUIek55o3rUvJoQOPjhhbukafBEPK/zGi+G7nmBo7OpBcrhzeCn28uZTc21Jmv2EKKU0Gpy82XLu1ovtBfmhF3e/8vzA/zDe/wYRTohe85rrie790fhcJbZNUZsjkNdTBRALKhiAAiAJKRXLJcIeGkoj0/bzR2o6b9y2bRnsb2voc4d4ys/YWw4n7DGtOWmaDFJK6Ybvdku1trL99osQG1k7f/DfOz/9fOtX3B68fqGBLR9juzVW/XJsJUopm5RdfXrw2faieawdA2VBBQNQACQh5drwmPUH9Rbf1qbSL0eu/LuGJCk5ZnrCkgoffHqnp6mu6dK1nnfras6ZXPOxgbWVkW6dhq0j21j8y5Wa0uTfQd4yebbGvyJzI/3njh1p6Oh5/3zjme5bTwQTifjQ2NWDGXcbAiiuyNxI/7maMg0hRFN5pm9kLu3sNT447R4esphujqbbBwsVDEABkIQUjF+bvKF/0yzYV3qvIt/5bnUey7KOLKfDWRju0id0EQGIhV9y9TbUnf+V5fYfPv2wqVJDiObNvvGVhG8JPr3Tc6qy6myffTzT84NRwQAUAElI2UIvBi+cTljhtRd8cPxGe5/r9X6C0Lrf8X7D5a8yPLgeoKg2X3z29oV7Ww/hiyw4unSElHaPbvVt8hH/V5drDpQ3/T77Y4NRwQAUAElI6fhlz+AHXTceZrqpzcGq58s/PVrMtFd1Lsew8sLOdfV/jRgE0rAxc+ua2SuYQrc62l1KSKPNTymllF/8y5WaUs2xXz1a2SH9o4IBKACSkBpEg99OfydmCFmdnVrAFkIgXRE3V6ap4B6tU0rpsps7TsgbXcMLO75pUMEAFABJCHYWCAQCAax8B8Xipyx6cpxzL1NKY4/h09R1XvtF45FyoqmsN94c86fvE0UFA1AAJCHYgc1mYyvEbt68KfaxABRCyGs+pWv5ws9TSvn1sd4DhGjruXuexQgfnB41NZVrMo2UoYIBKACSEGQTCASEy+UfPHgg9hEB5Bm/cK+9utM+z3p92MboB04Ofrs1NLYxb2vRZnjyDCqYZIXDYV8G6OGGJEhCsM3n87lcrqGhodbWVp1Op9PpfvzjHwuT0I9+9COdTmc0GoeGhlwul8/nE/uQAfYnMm2/cH7gyfJW7oku2t/VkLJG20z8W/gpi37rCcUpm2ltV7AsX0r96t6+lOM/J/eD3POR/NM//dOPf/zj8vJyVr5+8pOfGLcQQn6yhX316NGjQ0NDPp8vlyOhoGhIQkDn5uYGBgYMBoPBYIinHPalcDgsLBBer5dSytISx3HsRwYGBnCbBbLEfz/e33HFOSuczh/1mKqJtlq4e5bf1kg0h/rGU4fHUMGkYGJiwmg0svs3q9UaL19CqS3l8/msVuvRo0d1Ot3AwAAqmJohCalXOBy2Wq3s3oilmbTf9vjx4zNnzpw5cybt0JjP5xsYGDAajTqdbmhoKBwOF/ioAfKEX540Xzwn3Opz4/ndu09/+OFx3xtaTcPg9FY30abXXEuqu0e/S/0dqGAimpub4ziOVbAdu6iztFQ4HB4aGtLpdOy+DkVMhZCE1CgcDg8MDLBxrnzdCcWrktVqRSkByVuft3ccrOn8dPshfP9zva2Zcy9vbbRY2zsW4CmNzac+Pfgi3V7tqGCi8Pl8HMex4a0cq00uLcV6x1kXEYb+VQVJSF1YBjp69CjHcYXoDQ4EAqx/CHkIJCyyONJbk/IQPnJswBOLO+v+kd+cPXasvuODnvOnG7v/6Mmw0zQqWJGxTuhdZSAm95YKBAJDQ0OsSCIPqQSSkFrE76IKlIGEWB46evSo0WhEKQEFQwUrJjatpzij8GzyACtiuKlTPCQhVWC3OE6ns5izAgOBgMvlOnr0KPqHQKlQwYpjbm6utbW1tbW1yPOaWSd6a2vrxMREMf9dKDIkIYULBAKsgszNzYlyAOFwmC3rSLugA0DWUMEKjY1VsQUZYh2Dy+UyGAwcx4l1AFBoSEJKFu+SEftAYkeCdRmgMKhgBeV0Otn8ZbFu5OLC4XBra+vRo0dFPxIoBCQhZWLrQo8ePSqdaTpzc3OscwhhCBQDFaxA8p488tJSLpeLLQfZ/68CSUESUiA2IlaEmdF7wMIQ7qtAGVDBCoHFoPx2IeerpQKBABspwx2dkiAJKc3ExIRERsQykVpnFcCeoYLl3dzcXCFWbOWxpQKBAFuHi2nUioEkpChOp1MW7082bUjEKZAAeYEKll9s+KkQqyvy3lLsnhMLQZQBSUg5OI6T0cATWxaLOdQga6hgecRu5ApUwQrRUnNzcxgpUwYkISWIb3ohrzdkfIG9BOczAeQCFSxf2EOgCzdoXqCWCofDHMcZjcZC/HIoGiQh2WPD6tKcH50LtpGrXLqyAIRQwfJCjjdycYWY3w1FhiQkbywGDQwMiH0g++J0Og0GA+oIyA4q2P7JOgYx8e5tsQ8E9ghJSMaUEYMY9lRF9AyBvKCC7YfC9hhjPUNiHwXsBZKQXCkpBjFsQZkyaiKoBCrYnrEKVrQFpEVoKTZMpphgpypIQrKkvBjEsFmT6BkCuUAF2xu2P6HT6Szav1i0ljIajcqrzIqHJCQ/So1BDFtJK9PZ36A2qGB7EA6Hi7/7a9FaivUM5X1nSCgoJCGZUXYMYqxWq4w2RgI1QwXbA47jiv9c92K2FFtar+wqrTBIQjKjkq5X9kQOhCGQOFSw3RJrpViRWyoQCEj8qUcghCQkG2z7RIPBIPaBFMnQ0BD2KwOJQwXbFREXzBe/pdiTsLHPkCwgCcmGAnbd2C2sSgWJQwXLnQorGNtnCHd00ockJA9sI2ZVFRG6NfcQPcwgWahgOVLz7qlFXiUHe4AkJANsox11Tpphw+144DNIEypYLubm5nQ6nTorGKXU5/MdPXp0YmJC7AOBjJCEpE7NMYiZmJhQ/HI5kClUsB2xnt2i7aCYibgtxYpY4Z4vC/uEJCRp7P2j5hjESKSYAiRBBcuO9elKYdaw6C3ldDrVNk1KRpCEpIsVEfSpMirvYAdpQgXLTjq7fkihpVQ4Z1wukIQkCpOFU2GgEKQGFSwLtuuHRD74JdJS0omGIIQkJFF4w6Q1NDSEmyqQDlSwTAYGBiR13yKRlmJPGsGEIalBEpIiPJU9C6PRiK4ykAhUsLTYrh/SiUFUSi2F2dMShCQkOWzJpaSKiKQEAgGdTof9OUAKUMFSoYLtCPe6UoMkJC3hcNhgMGD7nOzYY2hxUwWiQwVLwioYblR2hNnTkoIkJCFsljSmB+WCbVkr9lGA2qGCCaGC7Qomg0oHkpCEWK1WPKEmd62trRzH4aYKRIQKJiTlCibBlkJwlA4kIalgI8eBQEDsA5ENbDQAokMFi2PTgyRbwaTZUhhMlAgkIUlgE18wPWi32OxpzM0EsaCCMdJ/PqBkW4oVf8kmSJVAEpIE3BbsGXYYAhGhgjHS39tCyi1ltVpbW1vFPgpVQxIS39DQkGQH12VhYGAAf0AQBSoYlcmacIm3FCYMiQtJSGR4xur+sbF2PKANig8VzOVyyWKEWuIthf1TxIUkJCbpD67LxcTEhHSecATqofIKxp4dgQqWF9iRUkRIQmLiOA49ovnCdipDHYFiQgXjOE7so1AONutR7KNQIyQh0WCP0bwbGhrCKgwoJjVXMCxWKASDwYDb4+JDEhIHYlCBSHlvN1Ae1VYwPPGmQLCjiiiQhEQgi6UWMsUmLmD2NBSHOiuYHKcHyail5ubmdDod+raLCUmo2FgRwb1U4bDleKgjUATqrGByXPItr5ZC33aRIQkV28DAAOYYFhq2aJI2PvL98zG7ued823nj+9euXek8+24n97sv3XNrvOC7gl7Hp9315RoSU1LZeOnate53T9afbGq7fP3zEW8gItopxKiwgskxBlG5tZQce91kDUmoqDAuVhwyvW1Vh3W/60ZzZQkp/7l5cjmWfCKzzsv/riG6ust3vMGo4JujAUdHSSwJnR6c2aCU0sjSo756DSGEHGoyTwT5NP9G0aitgjmdToPBIPZR7IXsWkriz3FTGCSh4mG7B2FcrDhwUyVJkcWR3hoNIaSixT6XkGFC33BVWkI05U2feQVdQxE3VxZLQs02f6wPiJ+y6Nlrmp+ZJleLegaJVFXBZD2yL8eWQt920SAJFQkenF587KYKPXDSwS/ca9dpCCHk4NWxUFJnzvqU5RQhhJADdaaJta1X0yYhwaslteanm0U8hSTqqWBUtuNi8sU+NYaGhsQ+EOVDEioSPBtLFAMDA6jdkrHqMb3F8ou2zZHa6R/1mKpj8ebS8Eos3uyUhEgZ5xZxtpB6KpjT6cSmf8WH3QqKA0moGFwuF54FIQqMkUnI5lNzLZvzoznUNx5N/YZFe3NsevThzuEl9lr6JLQ62l3KXqxoc7wq2hmkkl8FC33DHb88HEjz588Cn8ciYrNLs+2ezy+O3/ltd30FIYRoDp94u/HtE4c1pLym+aNB9yvRVxXIApJQwWGHG3Fh4qFUrAx3xiY/lzXaZtJ8Q7oxr3RJiA+5P65ir1V+OPp6dx/q+SW3Cra5Mvq+juhO26Zzn2iOMRrR5bDUhl8f6z1ACGm0+SmllI8sjvWfLCeaE72uJVEXFcgDklDBYVxMdNi5QBL8tkaSYxLaHvNKSkL8WmDq0R+6akoJKTl88tqXL1bErfIyq2D8nP3sQUKIRm/2buT6l1PG20dmLZXCaDRmn2Yae6fEkhCllA+NXT1IiKbJ5kcU2ol8klDEPzHhF3T08ZHF8f/zcC5hsiS/7LV/1HCsyXjtg7b6U123nuy0wnZ9cfwvD2fXM3w1+nr0w8pYSY4Gn/19YjHTd2bEdvnDuJi49tgtt33JrS+6rV0ndIQQQnR1vU5/JH5hRYNee29DXaPxak+bob7rc09wpy6KyML4//nbbIZZvvzrv16uPMa5g5RSyi8/ezi5GFFKGQs42rQ5JiFttelJNOk1UtXYdupw7L8P1PW7xV0/z8jr85WfHmyovdB95iAhxzn3ci4/opguVXm1VKodlx6nJKGtew9xZ9LJhCySEB/x/+Xj9v9y+mNBhA8+H77eUqlJauLIgqNLp20enF6jlPIrrt6qyiaLZy3tr6TR4NTw9eZqDTkS+9RJ/Vdf//VypTb+b/DBid+1/8IS3wElB7JedKowu9x4WnjJ8WuTv21ouHp75G/uR3/5Q9dxDTnwpuUZSzL8wr123cGmwecRSikfGOs9nrQIPPG3rkwNX2+uLMlYm/jF0cs1ZPuajAYnLe3t1skd05UsbM8TyrDgazsqZZon5Hf1nohNJSpvs01neHMXkaw+X1c9JsOblqdLjo4SotF1j6zs9ANKGheTVUull32MLDUJbXrNtYQQvWVKAvcMEieDJMQv/uXKm5fs81v9MfxL912ny95TkxR2Q99wVVrBmpSQx6Qn2hbb/Eaa3/nSfdc5Yu85QTIlIX5x9ErDkZ8eEP4bfNDd39CRe/21Wq0K6FVWDKvVmuNTbxMuOX7uy6vm8XgWYZNdYuVm2c0dJ9qLjq35p1GPqTrjJIyNl+6vnK47PTWZklD09ehHPztSpU24JqPB8esNLbZpJfQMBcf7TrAYU9o9mroL0PYuQdo2+0LsD5Q8OrbykDsWmyytPfm7f2QKncUip8/X0DdcdattfoOGXD0HNZlqo5CSnvkgp5bKjOO4TIthk5NQZMbRdYSQwy32GQXUjkKTfBLiZ+wtx9J8tPhtjQlJiF8dvVJKSvUWH5/wSlnDYKZAHPHbmjMkoejKo/4zH3/152tHEj+0+NDY1UMNnz3PYYid5XcF9CorycDAwM4rgTNdcsz6WM+BrT4htoJJeMu1OtpdSjQNg5nno87YGsvSJiF+5eHHZ/pdf75alnxNfj/WU9dg8e7wqSUHvP+LFvb0jDf6x39I+htFFuysS6j0WN/fQ/FXk2dMR1ce/epYrF+o9Bj3UNyJQvL5fN1cGX3/0HlHgKdbkXS7azMthW3HJZ+WyibLGFnsnVJ2pL6xsbHxZ0fKNIQcbv7MI4VBZOmTeBLiQ+6PqwQ3iNuSk1DIY9ILO9XpVt9g2p1LKKVZkhC/8pAzfDT6etnNHUn+0Fp/xFVU7piyXS6XTqfDuJgEGY3GrL39mS85Sildn7df0p+/zca/2P43JZ3D26MMbABI0EuUIkMS4gOPuHNXRhcjbi4lCfHrbq6ivN3uV0AWWvc7P6zREELe6BpeSHgTbXjM+gOEaMqbfi8cDUy3diw4aToZy0L5WBrDB589mFjM8EtCzy2ntcK5F4lk8/nKz9nP1nWPfsf+LzZuUvWxO3l/y22tra1Op7NYxwe5yjRGJugT4iNL3ofOm911Oik8kUYWJJ6EloY7D6cf5kxOQq8cbRXJsYbNF6s1e9Pf+GRKQivjfa1XRhd5GkyThOjScOfhrDf9sb03sIeNNO20M0qmS46PLE06rrdUakoqm/pH/OuURgOOi9rk+YgztsYyQurN3kxDqGmTEB8a/43hyl9f8zRdEmJDcll6N+Vl3T/yq5PlGlL53p34yq/Iq2/6T2lJ6ZHzg4lTzlnPLnPKMrU1RL42aT5ZHntZ17E9dL5LfPD5/5q7TpRpMkzc4jeef9agTZyFmkguSYifHmyIP8p2W3U8GyXJqfcURJJ2jCx1nhAfcHbpNLnPjlczaSeh6HjfIU3CPXdcchJin0DpklDGmfNpkxC/Nvlbw4V7Czyl6ZNQyGPSE8279sWMk1gVM8dQqdhTJNN3+2e65PiA5/6dQfO1thM6QojmWP94aMNva065vtJdhwnSJaG1CZOh27EQoTRDEoo+MVVrNc32xd2frCTxke+9I4O/uXz+fOeHV7lrPd3nz2d4Fv0HjZVbD2AlmrITbdzvXf5Nup1RCCFEU37y6hfeHaf/ph6Ff+zO/TQzDuMizwdbThw5pJV/Elr1mE4eMz0RdCpuzNtatIRoz9oXUvK1wsbFlCfthrFp1o7FylGGjUxBQNpJaNHenLxAbEtyEloa7jycPglVmzzpr4J0SUjwmZQhCbGfOt43nv65j0NDQ7iXkr6MY2RZLjkmNg+xqnt0aWX4Ukn6JKQ3eUIZfj41CQUnTecuOObZ51H6JMR+CvWsEJIrSdzatO29lsE//6GxTPZJKPQN90aT5UVCzxkfcJwvIUTzdtLrlFKDwYBxMYljfdvCnUHSJKHYas3ypt1spKlO0k5CGYtU6pfWvOZ6Qqq6R7cnBbGlKLuZJxScNBne6L79jZsZtbQdJqVtlodut3cpkvGntrF7qWzbooM0zM3N6XS6NC2V5ZLbsuk115KyRtsMm2yRsAyK91n0pbuZJ8SvTd6oe5UbSc8AABpiSURBVKPbtnXNPbS0lZLDbZZRt/vZ0vZ6sYzzrGG/0rc4H5m2nXvH+nxj2ib7JLQxb2vRphnwDYx2VxGireK+EcZ2pY6LyaGldmdiYkLYt52chPjlf3zWqiNEU3PNJeo+7LIg7SQUcLRpc0xCbD/NAycHv42vHVsf6z2QsJosSWqmYTf06WyXQvZTaW76A4EA5hjKSPxhcLOzs9uvZrnk4vy2RnKMc6/EViOfHNyeP78+1nMg+wYeSZmGXU5pCR6zxX4qY+8m7EPaJMTP2FvbLc9Dsb+8jJPQ6pTzV43lGnL4bN+dccHc8tWp0f/pqS8nhBDN8U7zX6fW+HA4zGKQIsfFJN9SexHr2+YXx7/8fc/JCkIIIeVH6mMPHiNltc091jH/HmfRqYq0k1CW6RGp9Svk6jkonOGx5jXXZ90zI1vvDqU02zyhxJv+2dlZvV5PCPnXf/1XLJuXkf/8z//8t3/7N0JIR0dHrOF2npETDTg6SmMPK/h+rOeI8MHpm15z7Q4PddqhdyfLPKHMvZuwD2mSUGTB0W0wTaxRKv8ktAsKjkFUWS0Vt+PG05AjaSchtu9F2lvhNPVrw29vL0/YY7q8jpWzDd/tlmptZfvtF8KOnL0loeS1Y+FwmMUg5pNPPtnxrEEi/uM//iPecB0dHZTSNJfc5jPLmwc0lWf+2/5kaWNlesz63umPtrc793/RUi7cY7pWU3djco3PcMnRPSYhRa0dk5iUSsIv3Ltg+O1kbPK2WpKQ4mdJK6alkuTwcFbYmcSTEL/hNes1gtWzlFK6OjV652b3m1pCNDWdn96+Px6fw8Mve+/0NtS9Y7z2QVvdiWbTg9jzoVZGunWahGU+a1OjNnN3XRkhpTWdN27fHU+3J0m6JBRy9RysFm6FMjs7KxzS0Ov1e/lDQNEFAgFhw1VWVlJK011y6/4xa0/bO42N77Rd/s3gsGcpYbvnaND7p56Gt5qMV3va3qppvuFiISn1kqP82tTXtpvddVpCNMc7P/3j3fE0e9ik3U8oNHb1oM44nHHuEexDUhLiF4a7jp/su/coNnHrLneilJzgHG73xEyQpzR1FDP+m7J8KfWre/tSjv/cbr/EnqqRr+Pf/0FK58+VryMp6EEajcYCHSRVDYknIUppcNLU+KbZs99N5SLf+W51Htt6rONeRQPD3W+cHnyRuMc0G2Fhbt68ua9/AYqot7c33nCCzjxJXXLss1l/evCZAvZVlKKkJCTYyTFJ2o48ZXxaDAwMsE9TsQ+kgBR8duFwmBCCHez2Q/pJiNKNZ4NnWgee7OLRp6n44PiN9r79TaHnI/577zX0OhMnoM3Nzf3zP/9zT08Pi0GYJyQjXq+3t7f30KFD//Iv/+JwOLa/IJVLjlK67ne833D5K78SnjsmSTusFlT+6Fh8XEwB56JahBBs57sfckhClPLBJ4Pvdd949Gqvi4hXPV/+6dHifqbQR4Mvvuzt2hr7EMDeGwqQuvG0BC45SvmVF3auq/9rxKACUn0SilcwBZyLahFCWKLFrfjeyCMJUUopv/LttwHxPhD4tdn/9zLlA2loaEgxz2pWObbxdMJLIl9ylNLV2an0zz+DfMg843CbwpOQcPcguZ+LmrG2GxgY4DhO7GORJfkkIemZmJjAPopKstPDWQGSybqCKX69mJCsWypH4XDYYDCkPpIMdoQktEesiAg3Owe5y7jxNEAG8q1g7NlV6qlg8m2pXWFhCBOGdgtJaI/wmFVFyvZwVoAUMq1gbNm8qjoPZNpSe8AGK1DEdgVJaC/SzCkBpTAajar6hID9kGkFs1qtaptQItOW2huO49TWvvuEJLRrbE9PjKEoFbtdtlqtYh8IyIAcKxjrM0hdZCTHc8mdqs4OY2S7hSS0Oz6fT6fT4QpTtkAggAlDkAvZVbAs04Nkdy67orazU9V0+P1DEtod7B6kEqznD5tzQHayq2BZFlrL7lwgLm3bcRyHgf4cIQntAnYPUhU0N+xIXhUs++Z78joXEErbdqz/D7fuuUASyhWmB6kNG2tXzzJj2AMZVTC2kXqWkX0ZnQskydR22BkkR0hCOQkEAklPYwA1yDS3FICRSwVjMUjN3QNyaam8Q992LpCEcoIBV9WyWq2oI5CJXCpYa2urmmMQlU9L5R0Ww+YCSWhnbFwMk/DVCRvYQxayqGBOpzP+cDHVkkVLFQgb08AYWRZIQjtIfUo5qM2OEyxAtWRRwTBThMqhpQoKi2GzQxLKhs29x0cgZF90A6ol8Qq2qxAv8XPZJ5yd1WptbW3F4EZaSELZDAwMYI4IMFk2YgHVkngFMxqNuT8eUeLnsk84O0rpwMAAwlBaSEIZDQwM4GGcEMc6CPHYXRCScgUbGhra1ceelM8Fssu97XYVjtUDSSg9NhqCwXUQmpubw9N8QEiyFWwP+59J9lxgR7m3HZs9jSKWBEkoDbZcSOWLTiEt7DAEQtKsYHvb/0ya5wK52FXbYRJ9KiShNIxGI1ZNQyZs4qHYRwGSIM0Ktrf9Y6R5LvmCsxNyOp2Y+yGEJJSM7b2BSwSyaG1tRVYGKskKhqSelgRbSlwcx2G7xTgkoQTYPQhywbZtRRgCqVUwbPeQidRaSnRsCBXPVWSQhLaxIoKpZJALFoawCkPlUMHkQlItJRFs1iMmDFEkoTjsIwy75fP5dDodrhk1k04FY+s89nM1SudcCgFnlxYmDDFIQpTi/h72igVo3FSplkQqGM3H3DXpnEsh4Owywc55FEmIwZwP2LPd7l8HSiKRCsb2Dt7nL5HIucAe7LPtMHsaSQhPY4H9wrYLqiWFCmY0GvNSwaRwLrA3+2w7bLeo9iSEJ/TC/rEpGiq/qVIn0StYHnf9EP1cYM/233ZsoF+1+wmrOgnhkRqQL9h/QZ3ErWBOpzOPFQxJSL7y0nZq/kBUbxLCYjHIL9a/iP05VEXECpbfGKR4yHm52MPj6pRBpUkITxaDQsBgq9qIVcH29mQxNUMSypE6w5AakxA2CIbCGRgY4DgOE/BVQpQKNjc3h3lpu4UklDsVhiHVJSEWg7BYDAokHA7nay0PSJ8on68F2vxM2VkBZ7cragtDqktCiEFQBAMDA0ajUeyjgIIrfgXLy9ZBaSEryFchzk5VO6WpKwmpqmlBRKzr0Wg04mJTtiJXMBaDCnRRKTsrKFuB2k49O6WpKAm5XC6dTqee7j4QVzgcLujnFkhBMStYoS8nJCH5KlDbsTs6NUx8VEUSYlM3DAYDVjhDkRVuLAOkoGjpoQipGklIvgrXduzTk+O4Av1+iVB+EsIUaRCXSm6q1Kk46aE4nYtIQvJV0LaLr7ZWcBFTeBJCDALRhcNhjuNwESpSEdIDxljzAjlvP+JLYsU+kEJRchJCDALpYHMPcSkqTEEr2NzcHHZkyBckof1T8D58ik1CiEEgKfGbKszZV5LCVTD2OKBC7BukTkhC+6fgT1VlJiFWRLCGGaRmaGgID0lQkgJVMKfTaTAYEIPyCEkoX9gEaoXd0SkwCeHRqiBlbPNWhCFlKEQFE+tRvsrOCji7fAmHw+yOTkkfskpLQj6fD13KIHFsays8N0oB8l7B2GeMKDfcys4Kylb8tmMftYpZFauoJMTupZQUVEGpWM+lUqcfqkceK5joM8mQhORLxGeZK2PakEKSUDgcdjqdqnpiHMgde6K40WjERStf+apgExMTBoNB3NWFSELyJVbbsZ30FfDJq4QkZLVajx49ilU5IDvxEXeMlMlUXirY0NCQTqcTvTMbSUi+xG07Nhoj60kpaf986/4Jjz/CUxoNeu29DXWNxqs9bYb6rs89wWj6XxOZG+k/V1OmIYRoKs/0jcxFKKWU8sHnDycWIln++f21X3y/jUAgsJ/fAyCi+ONacRlLRYaClmqfFSwQCGBvheJAziuoQCDANtOXaRFLuTgicyMfX7rqnI1Qyi/ca9cdbBp8HqGU8oGx3uPlTZ951/jkH+GXXL0Nded/Zbn9h08/bKrUEKJ5s298hVJK+eXJ311qt0wEU34o9s/v4+pkM7awWx0oQDgcZl2boncMQLaClmI/FWxiYoJ1B6KCFQGSUKGxIiaF3s09SLw4+JcjV5ra7dMRSilddnPHifaiIxDrB4p6TNVEd9o2nZRqNr3mn3U5A7FXIwuOLh0hpd2jq7Hf+f14f3OLbSrtTdXerk42wQJPVAWF8fl8uLBFt/nis7cv3FvIVNAS7a2Cse2C0NDFhCRUHGwtCMdx8rq2hRfHht/efvC0bZ6VgNXR7lJC9JapePBZHe0uJZqGwcQotDFz65rZG9p+gf1go80ffyXk6jn0juV5iKbY7dUZn1ch6yFJgCzYoDu6CkSSQ0ET2FUFYws7DAZDa2urvD4nFABJqGjiC5g4jnM6nbKoY4KLI/QNV3XorH2O5Zyox1RNSEnn8Han8OZTc22JsJcovYibK9NUcI/Wt19acXO15S1f+FPGyHK/OlkGYmttsCsdKNvc3BzHcSzxy3TcXTnSFLRtOVawcDjscrlY+ZLs2IGyswLOrsjYRzarYy6XS+J1LP7n21wZvlRCTlmm2Ps9GnBc1BJSxrkFo1oztsYyQurN3rUsv5GfsujJcc69LHhtc2X4UonmncHpH5L/+Z3aLxwO+3y+eMCUbBEByDufz8dWqFqtVqfTKfFSolTpCto2Qkj2W16fzyf9DMRI8NM0j3B2YpmYmGB5yOl07tiLMTs7W5yjShL/862O9x0nJZeGVzYppZRG/LZmkj4JHeHcwcy/MOQ1n9KldP+wOUbN9vn4K4FAoLKykhBy5syZ1N8iDEBsRjo6k0GdfD7f0NAQi0RDQ0M+ny/tR29HRwchhBAiVilRqPQFjVJ6//59VsEqKysfPHiQ9NVAIMD6sGWRgRgpf5pCdtJvO5/Px5ZJsgfqpS6WvH//vl6vZ5HA6/UW+fDif755e7NOEHxYF1HaJKQ3edLM+GH4hXvt1Z32+ZSOZL+tkWgO9Y3Hx9XihZsQcvPmTUqpz+djN8EGg0Gn07HHvGEgDIAJBAIcxxmNRp1OZzAY2LuDBaP79+/H3016vV7sI1WOjAUtsYIRQlha1el0Op2OPf7ZarXKIgDFSf/TFDKRUdu5XC6r1crqGCtlVqt1aGhI+G7q6Ogo8lHF/3wztsYyYfDZ9Jprk1ZM8D6LvjTbPKHItP3C+YEny2mWzPttjYJcFQgEhKet0Wh0Oh3bUsVqtSL9AGTn8/lYNWltbdXpdD/60Y+Eb6ji31EpU5aCli4JDQ0NyWJyaCYy+jSFJPJtO9bnLZ0k9MrRVpHQBRRy9RzUkJODM/EysD7WcyBxNZkQ//14f8cV52z6Lcj8tkairTY9iWco1rHM9Pb25uVkANTp5s2b8XdTZWWlrD+PpSJ7QaO0t7c3/jdPO8QPkiLfrKASZ86cSRomKqb4xRHymPRE8659MZ5Vvh/rOSKYOcR6idLsJ0QppfzypPniucFnG/FXNp7fvfs0PkE66jFVk4o2x6v412dnZ+PzhFC4AfYjHA7H60jqnBXYtZ0KGqU0HA7bbDZCiM1mQwWTPiQhiWNvqDNnzohSweIXB//DeP8biXOAeP8XLeXCPaZrNXU3Jtd4uuG73VKtrWy//YJ98/q8veNgTeent21b/ud6W7NgtcXe144BABTXjgVtGyqYXKClIAvBxbHhMesP6i0+QZdPNOj9U0/DW03Gqz1tb9U033D51ymldGWkW6fZWlkWWRzprdGQZMcGPBvx3/T9WE+NbnsfasE/j6sTACQkl4K2DRVMLtBSqhIIBHa17Yjw4uDXJm/o3zR7073hk0W+893qPCaY95MFH3B2vXFu8EUe9pgGgCLQ6/X3798X+yhkQEkVTEnnkgpnpyqPHz9m841yHLlO+vOFXgxeOD0wnumBqXF8cPxGe5/rdQ5BKDLjeO/nlzNMPET7AUiQ1+vV6/V6vR7L0LJTUgVT0rmkwtmpTSAQ6OjoSLvdV6qUPx+/7Bn8oOvGw8VIljS06vnyT48W0+4+n/jLgs/svZf7XfOZ1l+g/QAk68GDB5WVlR0dHdjeOhMlVTAlnYvaoO0yefz4sV6v7+joyL7lbNo/XzT47fR3OQyR7WzNP/UyW2BC+wFIWXyFVO79zKqipAqmpHNRG7RdFrkUsWL/+VImIgKAPHzyySdFLhcSJHYjAMAeVVZWZureFjlIEiRZgDwpxLsJu+ZkhwomF2gpWch7M+XYq40kBKAQeX83xYfYMU8oE1QwuUBLyUJ+myn3mY5IQgAKkcd3E1t2odfrHz9+nK/fqUioYHKBlpKFfDXT7OzsDqtf+eDLl9ur5JGEABQij++mHYbDEouImqGCyQVaShby1Uxerzfb4nl+edJ8ziDYRxpJCEAhivVuWpu2XTQkbEavXkqqYEo6l1Q4O1koxolE5l39p8tJvdm7tv3vFvxfzUox7QcguiIWkYQHFIIyKLsa4+xkoeAnEho3t9QfKdOQsiP1jc29w352R6eQPx8AFFyGIgIAIBvRJ6ZqbUnn8IrgNSQhAMhZuiKiQnzwqZ1r1jddutbTVl9vvOVZlmUo5Je9D54sJRx6NOj9kjtd32S82tNmqO/63BPM5dmSUhKZG+k/V1OmIYRoKs/0jcwJnnCggLN75f7s0okyDSGElP2sd3hW9me34bU0VDbaZuIvFPrNtek115KKNscr4YuiJKFo0GvvbahrlFeDAUhR9PXoh5VlnDteEfllr/2jhmNNxmsftNWf6rr1JI9zmze95lpy8Kx9TpYf/PnCzzvaq7RNt6YjPKXRlbFfVpU3W7xBsQ9rN/iVqf81d57QEeGVQym/cK9dd7Bp8HmEUsoHxnqPlzd95l2TT2vzS67ehrrzv7Lc/sOnHzZVagjRvNk3Hsvtsj87Gpw0/byh9/ORR+5HI9aumlKiedvyIvYUB3meXei55bSWlG0noYK/uSJ+21kNOWWZSnj6hQhJSJ4NBiBF/Ou/Xq7UCj7PIguOLp22eXB6jVLKr7h6qyqbLJ61rL8kZ+mLiMrwIffHVcJ7yugTU7VWe9o2L5satuEfu+tw3empKUlMQstu7jjRXnQEYremUY+pmuhO26blcmabLz57+8K9hdjhRhYcXTpCSrtHVylVwNnxC/eu/tq9dWPDr45eKd3OEHI8Oz4y/XnLsZ8e2j6LIry5loY7D5Nas3cz4dXiJyE5NhiAJPGLo1cajvz0wPbnWegbrkqrbXNs7SMW8pj0RNtim9/Ix7+3NNx5mFSbPKruww2MdleRhDgYGO2uIpp3Bqd/EPO4dm3G1liWkIRWR7tLCdFbpviEVzQNgzKpzhszt66ZvYK5/OyMGm1+qoCzS8Kvj/UeiPcJyfHsIlO2c52DLkvjdhIq/Jsr5Oo5qK3gHq0HF14KBqOKnoTk2GAAUhRdedR/5uOv/nztyNbnGbtNLNVvL3GP3Tg2DE7l4e21/oirSFNE1CX6xFStJSWXhlfiN5VrXnM9SZl5IHnJSSjqMVUTkjAJbPOpubZEeOMqMxE3V6ap4B6tK+/sItP29lPnb/+DdffK8OzWpm1d71i8G37bdhIq/Jsr6jFVk8Od9x5++Wv7i43toljsJCTDBgOQIn7lIWf4aPT1spuLJ6GQx6Qn5HDn8FL82za95lpCBL1Ee7dVRMbufPz5P1Q7nB1wtGlJ4qBSxG9rJqSk1vx0M8sPSk5SEooGHBeTz4x9T+LOKzLCT1n05DjnXlbW2a0vjtv7mqs1pOIk9xd/hJfj2fH+L1rfsT7f4KkwCRX8zRV9PfyLcqIpq/vlsF/MeULyazAASVoZ72u9MrrI06AgCb1ytFUQcoRzCyYY+m2NhKSOi+8eKyJEU/Oh06/ieULs75mmWCeVNelLSkJpz4IV58QrSjZCXvMpXcsXfp4q6ez4pfG7tj+YubYTZRpCSo/1/T0ku7Pj5x0Xzpkmg5TShCRUjDdXNPhyIXURSZGTkNwaDECK+LXJ3xpiM0OFSSjdWylNcdmz9aVv59X+lI2V4c6StMVaW216Iqtu7aQktLkyfCn5zGJXlCw30uQX7rVXd9rnWWpX2tlRykf897oqtaT0yuhqVFZnF1lwdBtME7GeD2ESEu/NVeQkpLzLEaDo1iZMhm7HAnsPCZPQ0nDn4fRJSO3TnPOHjeaXXhldjUfC9SnLKQXME2IDqVsrrSillPI+i75UllMXItP2C+cHnmxvRaOos4thc2iabf6IjM6ODzi7Kt7u+/NDN+PgTpDSE9xdt/vJzMqkWG+uYs8TklGDAUhScNJkeKP79jexQjJqaTtMStssD91u78ykuZ6Qqu7R7UlB/JRFn6d5QkAppfT7sZ4jhJwenIkvx1se66km8ttcIGXtWMjVc1BDTg7ObH8MjfUcSFzgIgv89+P9HVecswndoIo5u20Rv62ZVHDudV5GZxdxc2UkrSOce0asN1fR147Jp8EAJIn1oabTeNs3dvUgOXBy8Nv42rH1sd4DCavJYJ/40NjVg8Jp6ZtPzbUlstpPiElJQizkCVbubHrNtbLb4oRfnjRfPDf4bHvfiI3nd+8+/UEZZyfEv3Scr9abPRuUyrjthKNj4r25ir+fkGwbDECKhKNjsTsNwdrMNa+5Pn/7CQGllFJ+xt5yOGEbXMFGxvKRmoQo7/+ipVy47W2t5lj/eEhGtXl93t5xsKbz09u2Lf9zva2Zcy9T+Z/d5gvLmxpN+cmrtvGFjeC3X5s7m3qd/sjWTosyPbuEJCTam0uMPaZTG6zuxqRqF+UC7EtiEqIbfnt7ecIe0+V18cmJkCd88Omdnqa6pkvXet6tqzlncs3LatUYvzb1te1md52WEM3xzk//eHd8cav+RoPeP/U0vNVkvNrT9lZN8w2XnNYJRhZHems0KX2lxwY8sZ1jZH12lEbmxz7jOpubGps7e02fj06tJH5qyvPskpKQSG8usZ47JsMGA5CipCREKb/svdPbUPeO8doHbXUnmk0P4neNAACQCs+iBwAAAPVCEgIAAAD1QhICAAAA9UISAgAAAPX6//PEJCnGFzXrAAAAAElFTkSuQmCC" alt width="771" height="217"><span> <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)<em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong></span></span></p>
<p><br><span><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for coordinates of each point clearly indicated either by scale or by coordinate pairs. Points need not be labelled A and B in the second diagram. Award a maximum of <strong><em>(A1)(A0)(A1)</em>(ft)<em>(A1)</em>(ft)</strong> if coordinates are reversed. Do not penalise reversed coordinates if this has already been penalised in Q4(a)(iii).</span></p>
<p><em><strong><span>[4 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates were able to start this question. Those of an average ability completed it to the end of part (c) and the best gained good success in the latter parts. Its purpose was to discriminate at the highest level and this it did.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Some concerns were raised on the G2 forms as to the appropriateness of this question. However, the MSSL course tries in part to link areas of the syllabus to “real-life” situations and address these. A look back to past years’ examination papers, and to the syllabus documentation, should yield similar examples.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates were able to start this question. Those of an average ability completed it to the end of part (c) and the best gained good success in the latter parts. Its purpose was to discriminate at the highest level and this it did.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Some concerns were raised on the G2 forms as to the appropriateness of this question. However, the MSSL course tries in part to link areas of the syllabus to “real-life” situations and address these. A look back to past years’ examination papers, and to the syllabus documentation, should yield similar examples.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates were able to start this question. Those of an average ability completed it to the end of part (c) and the best gained good success in the latter parts. Its purpose was to discriminate at the highest level and this it did.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Some concerns were raised on the G2 forms as to the appropriateness of this question. However, the MSSL course tries in part to link areas of the syllabus to “real-life” situations and address these. A look back to past years’ examination papers, and to the syllabus documentation, should yield similar examples.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A contractor is building a house. He first marks out three points A , B and C on the ground such that AB = 5 m , AC = 7 m and angle BAC = 112 °.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img 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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the length of BC.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>He next marks a fourth point, D, on the ground at a distance of 6 m from B , such that angle BDC is 40° .</span></p>
<p> </p>
<p><span><img 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" alt></span></p>
<p><span>Find the size of angle DBC .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>He next marks a fourth point, D, on the ground at a distance of 6 m from B , such that angle BDC is 40° .</span></p>
<p><img src="images/3c.png" alt> </p>
<p><span>Find the area of the quadrilateral ABDC.</span></p>
<p> </p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>He next marks a fourth point, D, on the ground at a distance of 6 m from B , such that angle BDC is 40° .</span></p>
<p> </p>
<p><span><img 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" alt></span></p>
<p><span> </span></p>
<p><span>The contractor digs up and removes the soil under the quadrilateral ABDC to a depth of 50 cm for the foundation of the house.</span></p>
<p><span>Find the volume of the soil removed. Give your answer in <strong>m<sup>3</sup></strong> .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>He next marks a fourth point, D, on the ground at a distance of 6 m from B , such that angle BDC is 40° .</span></p>
<p> </p>
<p><span><img 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" alt></span></p>
<p><span> </span></p>
<p><span>The contractor digs up and removes the soil under the quadrilateral ABDC to a depth of 50 cm for the foundation of the house.</span></p>
<p><span>To transport the soil removed, the contractor uses cylindrical drums with a diameter of 30 cm and a height of 40 cm.</span> </p>
<p><span>(i) Find the volume of a drum. Give your answer in <strong>m<sup>3</sup> </strong>.</span></p>
<p><span>(ii) Find the minimum number of drums required to transport the soil removed.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em><strong><span>Units are required in part (c) only.</span></strong></em></p>
<p><em><strong><span> </span></strong></em></p>
<p><span>BC<sup>2</sup> = 5<sup>2</sup> + 7<sup>2</sup> − 2(5)(7)cos112° <em><strong>(M1)(A1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution in cosine formula, <em><strong>(A1)</strong></em> for correct substitutions.</span></p>
<p> </p>
<p><span>BC = 10.0 (m) (10.0111...) <em><strong>(A1)(G2)</strong></em></span></p>
<p><span><strong>Note:</strong> If radians are used, award at most <em><strong>(M1)(A1)(A0)</strong></em>.</span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong><span>Units are required in part (c) only.</span></strong></em></p>
<p><em><strong><span><br></span></strong></em><span>\(\frac{{\sin 40^\circ }}{{10.0111...}} = \frac{{\sin {\text{D}}{\operatorname{\hat C}}{\text{B}}}}{6}\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for substitution in sine formula, <strong><em>(A1)</em>(ft)</strong> for their correct substitutions. Follow through from their part (a).</span></p>
<p> </p>
<p><span>\({\text{D}}{\operatorname {\hat C}}{\text{B}}\) = 22.7° (22.6589...) <em><strong>(A1)</strong></em><strong>(ft)</strong></span><span> </span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(A2)</strong></em> for 22.7° seen without working. Use of radians results in unrealistic answer. Award a maximum of <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong><em><strong>(A0)</strong></em><strong>(ft)</strong>. Follow through from their part (a).<br></span></p>
<p><span> </span></p>
<p><span><span>\({\text{D}}{\operatorname {\hat C}}{\text{B}}\) = </span>117° (117.341...) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G3)</strong></em></span><span> </span></p>
<p><span><strong>Notes:</strong> Do not penalize if use of radians was already penalized in part (a). Follow through from their answer to part (a).</span></p>
<p> </p>
<p><span><strong>OR</strong></span></p>
<p><span>From use of cosine formula </span></p>
<p><span>DC = 13.8(m) (13.8346…) (<em><strong>A</strong><strong>1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Note:</strong> Follow through from their answer to part (a).</span></p>
<p><span> </span></p>
<p><span>\(\frac{{\sin \alpha }}{{13.8346...}} = \frac{{\sin 40^\circ }}{{10.0111...}}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in the correct sine formula.</span></p>
<p> </p>
<p><span><span>α = </span>62.7° (62.6589) <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span><strong>Note:</strong> Accept 62.5</span><span><span>°</span> from use of 3sf.</span></p>
<p> </p>
<p><span><span><span>\({\text{D}}{\operatorname {\hat B}}{\text{C}}\) = </span></span>117(117.341...) <strong><em>(A1)</em>(ft)</strong> </span></p>
<p><span><strong>Note:</strong> Follow through from their part (a). Use of radians results in unrealistic answer, award a maximum of <em><strong>(A1)(M1)(A0)(A0)</strong></em>.</span></p>
<p><em><strong><span>[4 marks]</span></strong></em></p>
<p> </p>
<p> </p>
<p> </p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span><strong><em>Units are required in part (c) only.</em></strong></span></span></p>
<p> </p>
<p><span>\({\text{ABDC}} = \frac{1}{2}(5)(7)\sin 112^\circ + \frac{1}{2}(6)(10.0111...)\sin 117.341...^\circ \) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong><em><strong>(M1)</strong></em></span><span><strong>N</strong></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution in both <strong>triangle</strong> area formulae, <strong><em>(A1)</em>(ft)</strong> for their correct substitutions, <em><strong>(M1)</strong></em> for seen or implied addition of their two <strong>triangle</strong> areas. Follow through from their answer to part (a) and (b).</span></p>
<p> </p>
<p><span>= 42.9 m<sup>2</sup> (42.9039...) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G3)</strong></em></span></p>
<p><span><strong>Notes:</strong> Answer is 42.9 m<sup>2</sup> <em>i.e.</em> <strong>the units are required</strong> for the final <strong><em>(A1)</em>(ft)</strong> to be awarded. Accept 43.0 m<sup>2</sup> from using 3sf answers to parts (a) and (b). Do not penalize if use of radians was previously penalized.</span></p>
<p><em><strong><span>[4 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span><strong><em>Units are required in part (c) only.</em></strong></span></span></p>
<p> </p>
<p><span>42.9039... × 0.5 <em><strong>(M1)(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for 0.5 seen (or equivalent), <em><strong>(M1)</strong></em> for multiplication of their answer in part (c) with their value for depth.</span></p>
<p> </p>
<p><span>= 21.5 (m<sup>3</sup>) (21.4519...) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G3)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their part (c) only if working is seen. Do not penalize if use of radians was previously penalized. Award at most <em><strong>(A0)(M1)(A0)</strong></em><strong>(ft)</strong> for multiplying by 50.</span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span><strong><em>Units are required in part (c) only.</em></strong></span></span></p>
<p> </p>
<p><span>(i) π(0.15)<sup>2</sup>(0.4) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span><strong>OR</strong> </span></p>
<p><span><span>π </span></span><span><span><span>× </span></span>15<sup>2 </sup></span><span><span>×</span> 40 (28274.3...) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for substitution in the correct volume formula. <em><strong>(A1)</strong></em> for correct substitutions.</span></p>
<p><span> </span></p>
<p><span>= 0.0283 (m<sup>3</sup>) (0.0282743..., 0.09</span><span><span>π</span>)</span></p>
<p> </p>
<p><span>(ii) \(\frac{{21.4519...}}{{0.0282743...}}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct division of their volumes.</span></p>
<p><br><span>= 759 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Follow through from their parts (d) and (e)(i). Accept 760 from use of 3sf answers.</span> <span>Answer must be a positive integer for the final <em><strong>(A1)</strong></em><strong>(ft)</strong> mark to be awarded.</span></p>
<p> </p>
<p><em><strong><span>[5 marks]</span></strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The responses to this question showed appropriate use of sine and cosine formulae for the most part. A few students still used the Pythagorean formula incorrectly, although the given triangles were not right ones. There was an occasional use of GDC set to radians, and very few students lost marks for giving their answers in radians. In part (d), converting from cm<sup>3</sup> to m<sup>3</sup> was largely problematic for the great majority of students. Part (e) also was difficult for some students, as it requires some interpretation before the volume formula is used.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The responses to this question showed appropriate use of sine and cosine formulae for the most part. A few students still used the Pythagorean formula incorrectly, although the given triangles were not right ones. There was an occasional use of GDC set to radians, and very few students lost marks for giving their answers in radians. In part (d), converting from cm<sup>3</sup> to m<sup>3</sup> was largely problematic for the great majority of students. Part (e) also was difficult for some students, as it requires some interpretation before the volume formula is used.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The responses to this question showed appropriate use of sine and cosine formulae for the most part. A few students still used the Pythagorean formula incorrectly, although the given triangles were not right ones. There was an occasional use of GDC set to radians, and very few students lost marks for giving their answers in radians. In part (d), converting from cm<sup>3</sup> to m<sup>3</sup> was largely problematic for the great majority of students. Part (e) also was difficult for some students, as it requires some interpretation before the volume formula is used.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The responses to this question showed appropriate use of sine and cosine formulae for the most part. A few students still used the Pythagorean formula incorrectly, although the given triangles were not right ones. There was an occasional use of GDC set to radians, and very few students lost marks for giving their answers in radians. In part (d), converting from cm<sup>3</sup> to m<sup>3</sup> was largely problematic for the great majority of students. Part (e) also was difficult for some students, as it requires some interpretation before the volume formula is used.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The responses to this question showed appropriate use of sine and cosine formulae for the most part. A few students still used the Pythagorean formula incorrectly, although the given triangles were not right ones. There was an occasional use of GDC set to radians, and very few students lost marks for giving their answers in radians. In part (d), converting from cm<sup>3</sup> to m<sup>3</sup> was largely problematic for the great majority of students. Part (e) also was difficult for some students, as it requires some interpretation before the volume formula is used.</span></p>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Francesca is a chef in a restaurant. She cooks eight chickens and records their masses and cooking times. The mass <em>m</em> of each chicken, in kg, and its cooking time <em>t</em>, in minutes, are shown in the following table.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a scatter diagram to show the relationship between the mass of a chicken and its cooking time. Use 2 cm to represent 0.5 kg on the horizontal axis and 1 cm to represent 10 minutes on the vertical axis.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down for this set of data</span></p>
<p><span>(i) the mean mass, \(\bar m\) ;</span></p>
<p><span>(ii) the mean cooking time, </span><span><span>\(\bar t\)</span> .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Label the point \({\text{M}}(\bar m,\bar t)\) on the scatter diagram.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw the line of best fit on the scatter diagram.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using your line of best fit, estimate the cooking time, in minutes, for a 1.7 kg chicken.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the Pearson’s product–moment correlation coefficient, <em>r</em> .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using your value for <em>r</em> , comment on the correlation.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The cooking time of an additional 2.0 kg chicken is recorded. If the mass and cooking time of this chicken is included in the data, the correlation is weak.</span></p>
<p><span>(i) Explain how the cooking time of this additional chicken might differ from that of the other eight chickens.</span></p>
<p><span>(ii) Explain how a new line of best fit might differ from that drawn in part (d).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><em><span><strong>(A1)</strong> for correct scales and labels (mass or m on the horizontals axis, time or t on the vertical axis)</span></em></p>
<p><em><span><strong>(A3)</strong> for 7 or 8 correctly placed data points</span></em></p>
<p><em><span><strong>(A2)</strong> for 5 or 6 correctly placed data points</span></em></p>
<p><span><em><strong>(A1)</strong> for 3 or 4 correctly placed data points, <strong>(A0)</strong> otherwise. </em> <em><strong>(A4)</strong></em></span></p>
<p><br><span><strong>Note:</strong> If axes reversed award at most <em><strong>(A0)(A3)</strong></em><strong>(ft)</strong>. If graph paper not used, award at most <em><strong>(A1)(A0)</strong></em>.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) 1.91 (kg) (1.9125 kg) <em><strong>(G1)</strong></em></span></p>
<p><span>(ii) 83 (minutes) <em><strong>(G1)</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Their mean point labelled. <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Note:</strong> Follow through from part (b). Accept any clear indication of the mean point. For example: circle around point, (<em>m</em>, <em>t</em>), M , etc.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Line of best fit drawn on scatter diagram. <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span>Notes:Award </span><span><span><em><strong>(A1)</strong></em><strong>(ft)</strong></span> for straight line through their mean point, </span><span><span><em><strong>(A1)</strong></em><strong>(ft)</strong></span> for line of best fit with intercept 9(±2) . The second </span><span><span><em><strong>(A1)</strong></em><strong>(ft)</strong></span> can be awarded even if the line does not reach the <em>t</em>-axis but, if extended, the <em>t</em>-intercept is correct.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>75 <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Accept 74.77 from the regression line equation. Award <strong><em>(M1)</em></strong> for indication of the use of their graph to get an estimate <strong>OR</strong> for correct substitution of 1.7 in the correct regression line equation <em>t</em> = 38.5<em>m </em>+ 9.32.</span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>0.960 (0.959614...) <em><strong>(G2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(G0)(G1)</strong></em><strong>(ft</strong><strong>)</strong> for 0.95, 0.959</span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Strong and positive <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Note:</strong> Follow through from their correlation coefficient in part (f).</span></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) Cooking time is much larger (or smaller) than the other eight <em><strong>(A1)</strong></em></span></p>
<p><span>(ii) The gradient of the new line of best fit will be larger (or smaller) <em><strong>(A1)</strong></em> </span></p>
<p><br><span><strong>Note:</strong> Some acceptable explanations may include but are not limited to:</span></p>
<p><em><span>The line of best fit may be further away from the plotted points</span></em><br><em><span>It may be steeper than the previous line (as the mean would change)</span></em><br><em><span>The t-intercept of the new line is smaller (larger)</span></em></p>
<p><span>Do not accept vague explanations, like:</span></p>
<p><em><span>The new line would vary</span></em><br><em><span>It would not go through all points</span></em><br><em><span>It would not fit the patterns</span></em><br><em><span>The line may be slightly tilted</span></em></p>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>The Tower of Pisa is well known worldwide for how it leans.</p>
<p>Giovanni visits the Tower and wants to investigate how much it is leaning. He draws a diagram showing a non-right triangle, ABC.</p>
<p>On Giovanni’s diagram the length of AB is 56 m, the length of BC is 37 m, and angle ACB is 60°. AX is the perpendicular height from A to BC.</p>
<p style="text-align: center;"><img 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iyl7isPhZO7M2ReBu/GXuqiLD6syqYye4k9d/vwPh2F0/1qpU+jUpz25lEp3bgfCAQCgUAg0JwIBIHr5v9dJECS4nh7UfFK3S/lrzREIrysFEdxy0mlR5ha0lNYSc1zQ+LH5e0KJ0l+yhspe9++fZNdfrnMn4X0FDe/V8pdVAb5KS25S6WhcKXuh38gEAgEAoFAIFAKgTjMvhQyneivjr1Iyk/Z5+5y/gorqbBIkZjcXsrt49bb7suH3V8ibEhd3Je/4kqKBEHaMCJvXsouDBRHbj2f/OXOpfLM/eXW/aJ0yvkV3VOaIQOBQCAQCAQCgSIEQgNXhEon+KlzJ+ncjttfCuPD+SLl/opbKowIgpfY/UVc3c/tPt1K93zYvJy65/09MZMd+f7777cSOLn1nIqv8vrngKzpwl92kThJH0flUnq48zzkVtgiqTA+HR9OeeKHXeHzMN4d9kAgEAgEAoFAoAiBIHBFqNTRz3fSskuKsOAudVEUhc+LJX8vvZ3wIhMiD5Wkj5PnV+qe8lB4lUFuZO6HW5dwQOqCwL333ntt3NxTWkpPzyNi5gkb9uWWW64NifPhVG6l4ctbyq58dT93y18yT9u7vZ3wuJUe9jCBQCAQCAQCgUApBILAlUKmA/7qhElCdi+x6xJhQeLnZVF8XyyloXC4ZffhRAZEXnCL6GD3F/EUXrIoLR/O35ddZcnd8lfZkR4D7CJvEDhp4iQVXun6suuZPGlbfvnl25A43SMe4TFKw6epcsrPS3/P230Y2X3asvu88zJwr8iU8i8KG36BQCAQCAQCjY9AzIGrw3/sO/EiO375VURaCANRQYrIYcdIqrhyI3UpnO4pbE4cRCBEePx9EQX5+TRkRyqc98vteTmKyulx4Nl1Qd64Fi1aZDNnzjSI2FNPPdUmixVXXNHWWWcd69+/fyJjq6yyiq222mqJsImoicDJjeSi/Dy/ntM/j+y+/N5OIbzb230BlY7y8PnJXuk/8OnJrnTl9rLcPR8u7IFAIBAIBAK9G4EgcB34//KOW25kbsctUpaTFtzSMEkqDMXzafniKh/dV/pyE1bkAbvIQi4VBn8fx5OBauzE9XnnbpUXf8oqqecXeUP++9//tjfffNMmTpxo++67r6277rq21lpr2Yc//OEUj59XXnnF/v73v9uLL75oCxYssJdeesmee+65dH/nnXe2fv36JeIHiePZRN5E5ngm/PX8RPTP6Z+lkt3f9+kobZ9Xjr/cCos7T8O7082CH1/2/Ha5e3nYcAcCgUAgEAj0fASCwLXjP/KdtexIXSQpu6QIGW4RFkkNFYq8SXKf8ErPS2/3efzzn/+0V1991d54441EgD72sY/ZSiutlNIYMmRIIigQhJzE4CcCIUkk3/HLLpnfT5lkJK6o/CovUrh48gYekLfJkyfbQQcdZCNGjFDSVUmI3dlnn21bbrmlrbHGGgYGOXnzz1/qeclM5fd2+UmqULhJSxJ/pS18lW8udd9LH195SJb7D/w9hZfUPUn5hwwEAoFAIBDoXQgEgavh/1KH7SV2uSEjGBEv78buiZkIi8ibZD5k+JGPfMSGDh2ahgp9UT/0oQ+1aqOIc//999trr72WtFQbbLCBbbjhhklrhXbqnXfeSRqqGTNmJDI0YMAA+/jHP76MRo5O3V/kp46+lPRlIoywwN9jI3/5SYKLsBEm//jHP2zKlCntIm8qDyTu9ttvt2eeeSaRwc0339zABYIk8kR5RZjy51M6eo5qpI9DekpTeShv8lcZZJebMAqvNJROLslPfu2xl4vjnyXsgUAgEAgEAj0PgSBwVf4npQiIJyLYISOSIie4RU5EVkTYkLKjdbr11ltt2223ta233jqRMcjZtGnTklZNRSUtCMrf/va35IWGbfz48RU1VaT18MMP21133ZXKs95669maa65pzB3zxIFERR5kL5LeD7s3wkV+3i18kAyVQth4JrCBcDIMeuCBB1Z8HqVdSb7wwgt29913GwR2s802s/XXX98gxkVEyRMiyicjO2WlzLjlRxiGbxmqJd3c8FwQZs3P80O62LlE4CQphy8fafr/JHf7csteTub3lJ6X2DtiPD7eTprKX+nnbvmHDAQCgUAgEChGIAhcMS5tfH1nTWeMQeKPrOYSgZMUacMNIYAAQDDGjBlju+22W5v8O8MBAXzooYfssccea503xmKAIgKS5w+xgPQxPAkxESaEgyRieCbs7777rr311luJoOTpMG+NjnvQoEHpFnbIFQSW9OttKA8Y33nnnYk0oqWslji8/vrrScP50Y9+1CC+MhAu0hg4cKCxqKLIEPf5559P2kBIHP/xyiuv3Do/jzT85cl0KRKnchfJUn74+3u53bt5DrmLnqmcn8iaJGG9XXF9+qXsChsyEAgEAoFAoC0CQeDa4rGMi45HnY8nbfhJa4S/7JLeT3ZP2rDjP2/ePENDxNy1Aw44wJin1h0GogWpq8agJVu4cGEifs8++2ybKJAbNIIQEj0LpKzIQNI6g6gV5ZX7QeZENvN7RW4WT7CIoqOGFbXXXXedbb/99rb22muXJHEQGk/kcPuLcsjt7fhhiJv7K3wuRRJ9eNm9xF7OqJ0USfn5+CqryqN73l9+IQOBQCAQCATaIhAEri0ebVx0Ov6CcPkLsiYilttx6/IEDjvaGLQyjz/+uA0fPtyYn8XlV1i2KUg4GgqBRx99NM3xg/xutNFGNnLkyNYhVA2viryJXInklJIAVOoe/j4d2UtJn47S9bLozxBB8+3F24mjMD4t5SW/3C1/ZJhAIBAIBAKBDxAIAvcBFm1s6myQOWmDmOEHedMlAifS5qXiM6GezhuyNmzYMNt4442DtLVBvbkcaD3RxkHomfPI8CyaS4gVUsRLREvkJpegJj/CYvI4ciOLLuIrb6XlpfJIiS/94b5vJ3hT1/HTlbvz+CqXzws7/jK4MZLyDxkIBAKBQDMjEASu4N9X58MtkS9JCJvIGvO8cCPlh5vFBQrPylDszDVD27L//vt327BhwaOGVw9AYOrUqXbttdemRQ7MK2SeHGQOjayIDXMNZa9Wihx5iZ1LZK2cXfkofiWoqOdqO7QH7GoH8vdp+PSVB5ILo/tIGW9XGN0LGQgEAoFAMyEQBC77t31Ho84HKY2aJ23Y//WvfyUSN3/+/DQnbM6cOWm7Cu29RkfM4oBNNtmkLnOosuKGs4EQYC4k+/dxPfnkk61PxupkbVCMJ9vAQMCoV3wwrL766onsFJE8ESJJCBBxK10Kj/REKidQKqQnb769+DaEXcanSR6eUCpvH0Z2xZcsVR7db6/srHTbW56IFwgEAoFAjkAQOIcI5A0jzQFSmjVJETYk19tvv532YIPAsZUHk/i7a2K+e5SwNjACED329mMxCXMpX3755VQPGYqVgdRRD9kmhg8NTqVg5esKK6yQyJK2LoE45XbNw8tJlUhUTm700SOypo8dyGVO5tTGlJYnkjmR457Ceckz+jJ4u56/klQ58rQUL08zdytcyEAgEAgEuguBIHBLkdcLHamOCDudkL+YtyTNG9tjMIdp7NixttNOO8V8tu6qxZHvMgiwopi6ykIJSB7D+szBhNRtuummafsXCB0kiU2hRaSwe0KHv9eIYcd4QkM7UbuBvNF+aDO0E334YKcMDA+TBvG5RNryPH2+Przi5WXw5VkGjMyDsnqjuJLc83aFrdZP4UMGAoFAINCZCASBW4quOiF1RCJxdDxcdEjSukmy6S5Do3vvvXdn/keRdiBQNwRYRDN79uy0mIZNiTmdgiFZtnwRmfOETsQOEiUihcSI0KjtSPMm0iYN9QMPPGAPPvhgyov9Dlm8s8466yStoNIXgfOSfETkyItLZfD5qxzeLxUw+8mJm7+t9OWnNHOZ3y/lln/IQCAQCAQ6C4GmJ3B6qasTEnFTZyQCJ9KGVoOLczqDvHVWtYx0uwIB6jH7EJ533nnpI4QzY6WBg0jlZAryJALlCY/ajtqMtG+0mdtuuy1t1MzmxWj/2HvviSeeSO2HuX077LBDmssn0qh8lbcInPKVVP4iWOAlvyLs1M655+2K7+OWsisPScWV20vsYQKBQCAQ6EwEmprA6UWuDignb9K60dFB5JDMPeIEA7QXRx11VAybdmbtjLS7BAFWwU6cONFGjRqVNGOexEGgIFMQp5xMiejQfmg7OYFj6Pbmm2+2H/zgB4XthLl8559/fjqzd5tttqlqGLeIwKkcgJWTKrVx7uV2hfVSaeVSaXv/3E9uL7GHCQQCgUCgMxBoSgKXv8jVASE1/IMUaYO4oU1Aoj1gflGQt86ojpFmdyEAmbr00kvTUWojRoxICx5E3nJtGCTGEym1H5E4ffhw7i4rZcsdDUebYh4pYf/jP/4jzc3zWjgRR8pCviKRnkjJDnbeLiwpH5eMtxMe458HP7m5pzTxU1hJ3ctlCpgRSvmFDAQCgUCgHgg0NYHTi12aN9x0PhoC8gSOjobhJs7SPPbYY2NLkHrUvkijRyFAHb/33nvTnnRbbLFFmhunM1tzIiWCA3Hx7Yi2o4+fCRMm2CmnnFLVqmzm5l155ZVp1SxTE9gSBbLmL/LUlRMm/DHy98CKsOVS4ZH+eWSXVJreLTtSdsLJrrTxCxMIBAKBQGcg0FQELn+B4xZ589oDP++NTo1hU7RuDAedeOKJQd46oyZGmj0GAeap3XHHHYnMrbrqqjZw4EBDQk7YXBhSJ1KDVLuiDYnAsW8d4WpZ4ENbmzt3rt1www1J+81qWTR4InEiSJ40iTCJKOHG+HLhpowqp6TCKd1KUnlRHoXFDzdSF/f8pXyQYQKBQCAQqBcCTUHg9ML2EjsdDhKNgTofOiCGSyFxSMgbc3lYcXrQQQcZw0thAoFmQYANhdmKhCFW2glbgfAxs+6669qGG26YCBZY+Hb0z3/+05hX97WvfS2Rv/ZghUYOIkdegwcPNk6ogCCxvx1kUgTKEyXZyQ+72rvKh5t2zfY/3kBKWcBB+krXkzFv92RNxFJ+kj486WF82XzeYQ8EAoFAoL0INDSBy1/ggCTSxj3sIm6SIm6QNxG4a665xvbbbz9jonWYQCAQsLQNyY033pgIEQRr0KBBrVvt3H333XX72EEbyAWJXLBggbENiT+VQv8FxA5tHeSObVHU9pEQTzY7ZrNtJMTTm6effjrtjcf2JkUkToRMUkQNqdWz2P3l0/HkTYTO5x/2QCAQCATag0DDEjj/AsfuLxE3JC93Dfto6JShHBE5hnTQKBx++OHtwTfiBAINjQCauUmTJtlTTz1lm222Wdpjjo2tyy1c6AxA0NRB7KZPn24LFy5M+9rRtjmtgvaM5nzYsGFpDzo0bt5AEK+++upE8IYOHZq0cczBw0C4RNyQkDQt6vCLLWT39xVPBM5Ln3/YA4FAIBBoDwINR+A8cQMQ3BA1L3mx+wsCB2HT8KkIHMSNFXLVTsRuzx8QcQKBRkAAInfZZZclElfLvLfOePaZM2caWjU0crWcQaxNjtmf7rHHHitZNIaPt99++6TtQwOnCxKnLVhCG1cSvrgRCAQCdUKgoQictGzCxhM37Lq81g3S5gkc5E0Ejo5g+PDhXa5NUPlDBgKBQM9DgPl91157bSJxDLuKwEkWnTfrNXnSxPFk2MMEAoFAINAeBJZvT6SeHkdETgQOwobda93QuInIaehUw6Zo3vgCf+2119IZpz39eaN8gUAg0HUIjB49Omn22CYFbd1WW23V+nHIuweDNk52JBo5GYZWvQkS59EIeyAQCFSLQMNo4ETakNK0YRdpQ8smwpZr3SBuOvSbVadMdubonzigvtpqFOECgeZDAE39BRdcYG+//bbtuuuuibShfWOOnYZSJf2QqtfGgZoInGTzIRlPHAgEAu1BoCEIXBF58xo3DZFC4Ly2DTv3OBqLA7633XbbtEKNVXVrrbVWe/CMOIFAINBECEDiLrzwwnS0Hue6fvSjH20lcJA3CJ0WOEj6xQ3YRdyQsjcRhPGogdIlS1sAACAASURBVEAg0E4Eej2Bg7xhvOZNWjdp3DQ0KiLn3WxLwFy3b3/721XtGN9OnCNaIBAINDAC119/fTqlBa09H38ib0hdWuQAaUMj54mcyJsInGQDQxaPFggEAh1EoCEInDRwGjrVEKmk9nST9g03e0rNmTMn7TEVR2N1sBZF9EAgEEh741188cX2yU9+Mm0+jPZNF+RN2jjIG26ROMiaNHEicsAZJC4qVSAQCJRDoFcTuFz7Js2bNG1IkTeGOjjLFI0bB2ezunTUqFFxskK52hH3AoFAoCYE2I/uoosuSlq4zTffvJXAeY2chlJF5HJNHG6MCJykL4jefd6vyF4Utyhc+AUCgUDvQ6AhCJw0bxoyFYETeeM4IIZJeTHuuOOOxkHdq6yySu/7t6LEgUAg0OMR4GORPfFeffXVpI1jXpwInLRwGk5F8l6SNg47pEsXD1tEwqohcHm83N3jgYwCBgKBQFkEej2B0/Bprn3jJQqBY1XpH/7wBzvssMPS7uxl0YibgUAgEAjUCQFOqLjjjjvSavY111yzjTbOz4uTJk4kTuRNZK5UcSqROE/YvJ30cnepPMI/EAgEei4CDbEPnEic18RJG8fq0o022ijIW8+tg1GybkZg8fyr7SujrrAdp/zejhi6YjeXpnGy5zgxTm1gvzi0/qxu96vj9b5CC8c7DLdIHORNpohsefLm7Xkc4nIRpigdhUdWuu/Dhj0QCAS6H4FeS+D00kLmdty8DFm08MADDxiLFMIEAoFAEQLv2JMTr7CLFk61F6Y+a4cP3dQ+oA5F4cOvFgQ4g3Wdddax3/3ud/b3v//dmBen0QIROLnRyuUkTgQszzN/7/n7ImKKK0kYb8/j6D3q/YvsSp97xPHuovA91a/a56X8vfUZeyr2Ua76INBrh1DV+PxLUKtMkZymMGPGDPvIRz5i3X02Y33+qkglEOgEBN6aYT8//iazj19v33306zbnpiNsaDC4ugPNlI7LL7/c/va3vxn7xa244orLDKn6xQ3SxIlwiUDovYfUVVRYxdMwrNySxPF2uYvSyv2I1xOMyiFMfJnK3fPhiuL6+9iVlvcv8vP3wx4IdAUCvVYDVw4c/2JbbbXVygWNe4FAEyOw2BbN+ItN2fFg+8P679ovfnGuXThlH/vZLms2MSad8+icznD44Ycb8+KuueYa69evXxpeRSOnj1BJiJw0cRCFnCzo/ealL7XiiLxJ4u/txFFY2b30acpO+GpIj8J3l1QZJcuVo5owpeKDR5hAoLsQ6LUELn+R+EaIXVd3ARv5BgI9HoHFT9iffmH2rcs2tY/bbvalfj+1SyY+bD/YZReLNdqd8+8xL47rhRdesOuuu87uu+8+23LLLVuHVaWFQ0K2csKl9xoET3akjAgZUvGVhtx5GOLKz6cjuyRhikwp/6Kw9fBTfnpuuX3auic/7/b2ovvyQ/q0sXt3qXDeP+yBQGci0GsJHKD4hliqYbEKNUwgEAgsi8DiJ6fbXWM/YweuwpjpJ+3In4y3/zl5ks38wVjbJfktGyd86oPAwIED7Utf+pKdeeaZ6eitIUOGtG70KxLnh1GVK+88rlIEjnA5YSMd3o9Kr4jIiZzoPZpL5e+lwuDn7T5Mve0+H28vlY/6CEnCyS6puLkbf+WBLLoUhrgKq/RCBgKdjUCvJnClwFFD22CDDeyGG26IQ+lLARX+TYzA32zKhffYjkceZCsnFFa0IaP3sN0X/q9dOulrNnb/wbGYoZNrB3tRHnPMMXb22WenfeIGDRqUJPtYQuJEuDwxgChw5QSOLZPeeuutVGLCf+xjH0vzf0mjiMDJT2SPONgxen/6x/dlkL/383aloXD1lD4fb/d5iohJck+4yV4k8csNefirCC8fJy+Tvxf2QKDeCPTaRQwAoUbJy4yVXFrEwMuMRQxo3yZPnmxjxoyJExfqXXMivd6NwKLb7MRNd7X/WVjwGLtfGIsZCmDpLC9Ob2CV6sorr2xbb711IgyewJEvxECEROTtjTfesOeee84WLlxoLJLggxXzj3/8I2nzttlmm0TeRAQhH96OW4RE0pMVPW8RKVE4lU1hi9z+XkfsvhyyS5ZKV30E92WXlJ+XPh2lLWyEl5eE0X2Fl/RphT0Q6AwEGk4DR+NRo6JhsfcSm2mynD9MIBAIgMA79sSfJpj94RVrabNg4V82/+pv2agDbrapTx5iQ2NPuC6pLmuttZYdf/zxaZXq1KlT055xrJ6XlswTAsgHJzxA3F5++WX7j//4D/vMZz6Tju5SYSGEZ511lg0bNiyRCz+fjjSrJXFKD+nLILuXsudhfRodted5yC2pvMEII6LmpfwhwbIrfPJwP6TL5QmbsPM4EkXhkKSHDBMIdDYCDUPgaDD+Ajjc6623Xjr7lEnDzDsJEwg0PQJvPWx/vmsHO/LwfLXpCjZgt/3tS/2+aH+MPeG6tJpolSoE7tprr7XVV1/dOILLEwFGGRYsWJDI2q677pr2lCNebiCEkLbbb789vfPWXnvtdHSgJx0iJSIkendWo01SWPJV+Yr88nJ11O3zUt4+X5++SBt+snspLabue6l0SDvHSZpR0vKGcBj8VU5/P+yBQGcg0BBDqDQaXm7MHdEB9gyfMqzAUOqsWbNswIABNnr06M7AMNIMBHoPAovn220nH2FffP9Ee/xnBatNFz9uF+25ix15y+b2/ckX2U92GRBz4brh3+WDs8jU8hFKGo8//nha6YpWLjdssbTZZpulUQpPVopIkSclsvtwuT3Pqx7uPI/crTxErpD5JeImf+JIG4cdf9LFiMyK+CIhcPml+yJ7xPVlS4nFTyDQCQg0DIGjEXoCB3kTgZs7d66tscYaQeA6oQJFkr0IgVZytnTiWz7XLb9vZv1OmFxM9HrRY0dRixF48sknDY0fQ7JbbbVVWvQg4iES8+abb9prr72WzpUmFd6jK620UhvtoOJwX/Fye3EJin0hUTI+PfyUl5fyVxykCJpkTtzkz7zp119/PT2jj+/TFJFDk8mUHE7MgMQhV1hhhdZ5hl6bqTh5muEOBOqJQK8mcAChhqjjaCBxNEpp4JBz5swJAlfPWhNpBQKBQMMgAImbOHFiGrYVMYKAMM+O4Vjm0mlDdEjfSy+9ZGj02IwYIsNq2o9//OO2aNGitCUKw78dNS+++GIiiaysJV0ZSBRl5HgyDTHjxkjSJ2AgbYzAcPoFH/McZSYzf/781EeQxoYbbljVWdm33nqr7bjjjmmxiMgbBM5r5CBxlMMTOJVLeYcMBOqFQMMQOBqrhlEhcNLAQeAYRuClEkOo9ao2kU4gEAg0EgIQMt6Z3kDeiubYEYawGpZ99tlnW6OhzUKj11HDUDHHjXGtu+66rcmRF3nMnj07bZvC1itsmSKCSUBIHyQOAgr5Y6EHaUAyZXgunq8Ww5D0L3/5S/vCF76QVgyTBgQOMietnLRwInAib5K15BdhA4FKCDQcgROJywkcjfnoo4+uhEfcDwQCgUAgEOgFCEDOnnjiCXv66adbtWsQJTSC/fv3T6QNgleKhNb6iBMmTDA0gzvttFMibpBL0haBE4mDvHFB5jAib5K15hvhA4FSCDTsKlQaixrS+uuvb1OmTElfjfVqzKUADf9AIBAIBAKBzkcAosZed1xdYXbeeee06TLDrxBE+hhPymQXcaNM6odUPoWRO2Qg0BEElqx97kgK3RyXBqFGITtS5I3GxMUml/Pmzevm0kb2gUAgEAgEAr0RAYZcjz32WJsxY4ZB4tgwXpc2kddCOkaCtHACKaM523KHDAQ6gkBDaeAAQiROBE6SOXCovzlzMEwg0NsRuPnmm9NcI4ZtmAPEcA7zgJiTw0RvzKqrrpqGd3r7s0b5A4GeggAk7tBDD7WbbropLaSgf8Go38EOSfNuwkDifFiF6SnPFeXonQg0DIEDfjUaL2k0aODo5B5++OFYyNA762mUOkOAieK77LJLWrjDKjjmA7HKjouVgtR7v+oOcocfl4gdZA+3jIif3JBDwoYJBAKBDxBgXh1zqjn2jPbj+xuFwg9D3wNZUzuTv8Ihi/z8/bAHAqUQaEgCR2PxF42IpeLTp0+3OJGhVFUI/96EAPWbDxIM2yRg0MKxRxfaZs7VpM4j2UoBgsfwDot7OILJmwsuuMD+/Oc/26WXXpo0eHQokEIND0m7x2bYdF5svRAmEGhWBJhHzZQctqfadNNNE0HTMKmGTTVUKvLmiRztqxxpK3evWTGP5y5GoGEIHJWexoJRA6HR+IvNKh944IE4Uqu4LoRvL0GA+TZ0FOPGjWtTYogcWyiw8erbb7+d9utCykDkZCBhkD3aCpo4DPGKzgzWvops3UD7Ie4mm2wSZE5ghmw6BI466ijjw+eRRx6xLbfcMj2/+iD1Q3hipw/KDR9ghMeov5Jd8XU/jxvuQEAI9PptRPQgVHouOjYuOh0mkqJFQOtA54X83e9+Z6ecckpaaq64IQOB3oQARO3++++33XffvepiM5xK/Yfgsbs+Q7Bo5DBMzGY7hh122MFOPfXU1I7oPOh4fEejzNhb8R//+EdqU2zmynFMyDCBQDMhQHu67rrrEoljg98111wzzTnlg0gX0xBoR2i0pUzQ6BBYibxJys/L3I47TCAAAg1H4ETi6JwgcBA5GhqdDvLuu+9ODW3vvfeOGhAI9EoEIHD33XffMhq4Wh+GNoKGzm9wetFFF6XhoTwtPooIj6QDooPCzocRadBBDR8+PA3b0mmFCQSaBQHmnF5yySXptB8+ZiByDLPSRmgXtAekSJwInD6ORN6KpDDkHkZS/iGbG4GGGkLVX0klp3FA5vT1Q+Ohw2EYlbk+Y8aMCS2cAAvZqxDgo6QeL3LaBNo4mdNOO80ee+wx+9KXvpRIGcQMjR0kjd3v6ZAwtCM0cHwUUQ7mxWE48YQh1qFDh9onPvGJ5Bc/gUCjI8DOBieddJLde++9dssttxhzRdmbDgUC5M3LXAsnMqc+C6yKiB19GWEkCVePd0Cj/zeN/nwNo4Hjj6Jy66LR6JIWTsOp06ZNS0M+u+22W6P/v/F8DYgAc9EgT/UgSWjytBEqk7KZ28Z+iRxllBtpshmOJX+IHQsiIHkQOoZRObIIjcQ+++yTRw93INDwCNBGLrvssqSB40MGAqdLGrhSJE7ETaQOiZGEsOkSkDmJy90KF7IxEVjuVCa9NJihEkPkZETqcGNnyIjDmz/5yU8mtbbChQwEegMCCxcuTMXUGZFsaQCZYrUonUO1hukEf/zjH9OihGeeecZ+8YtfGGm/8cYbtu222yZSRtpo3Fi4QAdEHmwtssYaaySyttFGG6Vh0/XWWy/F41gjNHV0XmECgWZDgDbCXnHsE8cHDeRL/Q+StsSV230Ybwc/3EUmJ2tySxbFCb/GQqChCFxecUu56eRYcffSSy8Zx2zR6MIEAr0FAXaBZ44NHyI33nhj2pPq+eefNw76ZusQT+LYaoRhTbRmdCy6xzw6/DmQnLltjz76qO2xxx5pisH48ePt8MMPt9tuuy0tdnjqqacSmWNoyBvSIE8IHRckjm1LGHplm4UwgUAzIsARX5C0O+64I03T0XxRjQhxT3ZJ+eXkDjdGJM6TO/nlGOf+eT+Yhw9370WgoQgcf4Mqq2Spv4YhIlbycbGXT5yRWgqp8O9pCLB1weDBgxNxg4AxaZotQRjKZLgGN4bhUYYzP/KRjyTNGvPY+GDBPPjgg4m4TZ06NfkhWdW65557pnuQRMJCzIjP/onMdUMDh2G+j4jhrFmzkjYOLd2CBQvSB1GsSk0wxU+TIsCHFB80nJgCoeIjibaDFGmT1OIguZEiaiJ0cksCq+xIuQW3/HJ/3JX6RqURsucj8ME27D2/rDWXkIrKpTkFaB/QttHJ0Zg+/elPp2OHfv7zn9uECROMTowOL0wg0JMR4OVMHUb7BXGTgWgxFIph3ieLCtjUFw0ApI7hUeaqYdDI8dHCIgaIF4aOBMNRQczjkWaa9kPaDKdiSAOtHMOoEDxOOfnrX/+a7sVPIBAILEGAxQ3f+c530t6KfABdddVVafNt2hHaa0aAaH+aT4rkYh6dv7ShNpJ2TTvV5UkfZK/oKiJ6nuDF/9V7EWjIsUP/haEJoBo68n8V4ZjrwzwezklF64Dam8YzatSotL9VnJ3qEQt7T0BA9ZuXvx/WhHCJhEHQ+EhRvacdQOTQ2KG9g4Qx1HPDDTfYwQcf3OaxaBOEh6RpY18II3vHYZjnBvlT2pBIykKa5K821ybRcAQCTYgAbYxFQlychsJ+i7QfNNWQKD64IF1o69ZZZ500b46PJdoy7YsLkoakXUli1yUlhZd6RyD9RZ5yi8QpbBP+Pb3+kRuSwOlfUcVEqlNR5ZUfDYIzINFU0PlsscUWrZOxmeAtMrf99tunOURKO2Qg0F0IQMLQfJUzLERQnVc4SBjz0zB86ePG5NMHIH5ss3PFFVfYT37ykxRGL3scpC3tXLppljR0InDEDxMIBAJtEfBkzt+hPaOVg9hdf/31Rl/DAiWROEnas7fjpv9SX4abS32ct8uvSIrU+TKFvXcg0LAEjoqqToeKXGQIo0qP1NcNZI7GxsakdFbsjYWmgondYQKBnoAAZAmNWm5U1yFoOcniS98bNAIYFjdgRLwYphk9erRdeOGFaUoBWmjiijSSd076UgLxEwgEAjUjQPvjQks3bNiwNJ2HednMoxNhk0TJQD+lvkrS92N5v+bdsvtC4hckziPSe+wNS+D0F/jKSSXH7S9f8VFVy62GwUq/kSNHpi8j5jEU7Y+lvEIGAl2FACRLGjSfJ/UXw3yZ3BBntdVWa50Hx7QBjgCSYegGw2IH5rdx3uPkyZNN0whEGDWko3hItjFhLh3kjo+fMIFAIFA7AkxZYCiVIx/ZKYHpPfRBIm0icuqfJGn3CkP/Jrf6M0nCQNaQ3hAnTO9DoKEJXF4pcUsrh11uVXa0DGoQkvpLN998c5s0aVJo4QRIyG5BgLltWrig+W4qCMP9TAfAEK7oJQ3pg2Sx3QekS6coEEcaO5E/hlE5lWGvvfZKeXoNXZ42pE4Ejg4nTCAQCLQPAbRxxx9/vM2dOzeN/NC2aFP0T9zj44oPMfVb6quQsvt78qN9q4+jZCJ16gfxwx6m9yDQ0AROf0NeKam4UhkjcVOxaSiE5VLlJg3CsDHpn/70p7SdQmjhhGzIrkYALRqaMob2eTHnRkObkDARMoXxbsgfJzqI8BFGq1FpCxjqOeSNLUN22mmn1Ingz4KF0LIliOInEOgUBGjHaOO4GPnBMC2CleesLmf6A9v8SDsu8iZJ/0V7xy1Ju8YuJQZp0tfhT/gwvQ+BpiBwqqgibd6Nnyq0yJsk4UTskKGF630VvBFLTP0smuPGs/phTk/YuMc+ccxjYwsD1XntGcd9ETjua3iWzX2PPfbY1uO2ivDkw0d5Kd2icOEXCAQCtSPgFQYQNo6AhNQxIsSiB46/46OOoVfav0gcbZKLvgs/b3iHSHGB9O2We2F6BwJNQ+D4O6iYVFRfQeVX9HcRlspPZ4ZkYilaOL5+QgNRhFj4dTYCaN4gWhrm9PkxhMrQCgYtGYtxckNdZo4bX/isMj3//PNbg2iIlLquL3I0AMyTmz59etrkFw1gbiBw7AWH8W0rDxfuQCAQqA8CkDoW1dEXcdoK+5c+9NBDqX9Dqw6Zo63Sjvlo23jjjVvbJm1U5K1c/1efkkYqnYlAUxE4gCzVwfCFkn+piMDRQXHR+bEy6De/+Y0dcMABrerrzvyDIu1AwCOA5k1zzUSydJ+6Lc0ZQ6Sy674k5E8EUKSNe9LeeQKH/7hx4+ziiy+2M844I82tY/5cbvIv/Px+uAOBQKD+CKBIYMU4FwZCx7F6fOjJcOYx+82xPQkadxE43h/Yubxiw9uVRsieiUBTD3yr8kqqQiO56JSkhpbceuut09fMeeedlxpLz/xbo1SNigDEC9LFQoScoFFHSxniSUuGpo5hUowfntHiAzR0Pi029sXotAU+ZryBLIr8FZXLhw17IBAIdB4CEDq05iJ1yBNOOMG23HJLu/zyy9uc4CAFBZIrTO9DoKkJnP4uCJxMTuI8mROpo9Njjzi+dMIEAl2JAAQJspSvQKUMzHGTdq5IIyZSxgpV0mFKQClDXZeBKLKI4dxzz01eaOi8gdBpjzg2Cpbdhwl7IBAIdB8CEDkWPXB8F+23iLQFieu+/6e9OX/wlm5vCg0ST1o4Hkd2SZE4JH5I5hB5NXWDwBCP0cMRgHihKWMLEOpibkTgtKebvy8CxwucurvVVlv528to9HQTssgh99ddd51NnDixMJw0cIoTMhAIBHoWAsyN49QH2r8ncZ64eXvPKn2UpgiBIHAFqOTELXdD4NhkkeNOwgQCXYmAXrDMhcuHUH058sUGuCF3GF7eaI/zuWxoztDOFZEx7p122mlp5Rv13xvSy/38/bAHAoFA9yPw6KOPpjNXRd4ku79kUYL2ItD2TdzeVBoknohartnATQelCzf78fhNUBsEgniMHo4Amrci4gZB04IEhjFzQsXLWgSOOW6kwwHauSGdPH0RtM997nNpMQMHcXtDHL+fnL8X9kAgEOh+BFilyvw4tW19CHZ/yaIEHUEgCFwJ9ETikLIrKENKdIbaNFX+IQOBzkYAciYi5vPihaxhU8LoRe3DiODhx5YD2nIEguZNPr8OgsbqNTazZl84ti3wJieL/l7YA4FAoPsR4DxvdlDAFJG3Ir/uL3WUoBICQeDKICTy5iWdFR3k4MGDy8SMW4FA5yHAMGc+/ElumuOmLUJ8CSBhOoILf3Zz16pTT9iYG1e0AEIk7VOf+lRazMB2BbmJFag5IuEOBHoGApymwpSfIGo94/+oVymCwFVA0pM3by/q5CokFbcDgQ4hAEGS8aQLPwiaNHNsE5IbtGwQOLYPYQgVw7mKuWFunYigv6d5caxc3WGHHeyee+5pvc1wLBo6LbBovRGWQCAQ6HYEtHBB7TpIXLf/JXUrQBC4ElCKrHFbdi9LRAvvQKDTEIAgQboga/lL2M9xQ0OXD+/7IVURPIXxQ6hF2rv8hId9993Xrr32WlM6nfbAkXAgEAh0GAHaOX1XmMZDIAhclf+pyBtDSdEYqgQtgtUdAYibjsLKE5eWLN9ol3AQM5G4F1980Q4++ODW6BBCGcifhkvlR31XXDR/2n7kkUceUZBWmRPL1hthCQQCgW5BgMULaMkxap+S3VKgyLRuCASBy6DMyZmIG5KOLQhcBlg4uwwBiBb1sEhLBrHSIgVPyFQ44rAVCHPcIGmlDHFF1hRGQy9y80W/3377JS0c6eqEB+7n7UdxQgYCgUD3IpCTNrklu7d0kXt7EAgCV4CaJ22yi7xJ+vlIBUmEVyBQdwTQvDHXrGjoEq2bFiVwkL20cXkhmOP26quv2rBhw1pv+SHUfG4dgTjhId8jjnlwd911l82aNWsZwteacFgCgUCgxyBA24aslSNs8QHWY/6uqgoSBK4MTEXkjcULzENCJX399deXiR23AoH6IoC2C20YGrRKWjKfM+ROWjTSmD9/fuuWI4TzGjvqddFLnPy8do5hmeOOOy4tZtCCHp+Ozz/sgUAg0L0IcPTjyy+/3FoIEbmczOXu1ghh6ZEIBIGr8LeIxCGlfUO78elPf9qeeOKJIHEV8Ivb9UMAzRtEDI0ZddEbT668P3YInIY5IX/Tp09vc4qIJ2yVTnjwGrpRo0bZlVde2TokKw1hnn+4A4FAoHsR2HzzzdOHG6UoRdJK+XdvySP3cgi07QXKhWyie+rQJEXc0DTQgSIhcePGjbM5c+YEiWuiutGdjwr54sQDP+Sp8miOG9uEaENf3UNKS6ZTFNCgyUg7J7eXEEPNrctPeBg4cKDtv//+dv/99/soYQ8EAoEehgAEDg0c7wmMJ2vYvbuHFT2KUwaBIHAlwBF5Q3KJxCHpDEXmdtlll6TRmDRpUomUwjsQqA8Cesmi6SpHuvLcIHyqz5q76Qkcc9ww3BPRUxrkKUJYdMLDdtttZ6effno6G7iIWCqdkIFAINB9CLDwiJMYaOt6j1Aab+++0kXO7UUgCFwZ5ETevPTkTSSO3elvvvnmMinFrUCg4wiIhJGSH0LNiVPuRovG4gcMZyLuuuuuxkIHvsZ9WAicyJovrcgiw6u5oVOg/v/lL39J6Ulbl4cLdyAQCAQCgUB9EQgCVwJPdZYib9K8SYq80bmx0/Vmm21WIqXwDgTqgwD1jNWgGFaSQsIgVVw615RhEk/ulLNI2AYbbGBDhgxJc+CYG7dw4UIFSZJFDK+99lorwWPenU54gOAVpf2Vr3zFfv3rXxeujm2TeDgCgUCg2xFQ30ZB1L95v24vYBSgagSWrzpkEwdUJafzEoGjQ9RFp3j55ZenDky72zcxXPHonYgAq0E/+9nPpoUDL730krEpr188wHFZDItopSkfGmjgROCefvpp++QnP2ksQJBh3hwGLd2ee+6Z9oqDCOLPmaeDBg1K9yF3DKNC6igHdZ32sO2226b7nLe42267JXv8BAKBQM9CgLY/dOjQVtKWly5IXI5Iz3cHgSvzH/kKnZM4ETk6SIaNNtlkE2Nn+m222aZMinErEChGAJJ10003Jc0X29SgHaPOUc8wGgJ98MEHW/d440B71Te0cBAuCNyYMWNSXIgcBA/N3YABA1I6kD3ieaO08UPDxzV48ODWIJo3x1ApCynYDHjevHlJUwepW3311e2YY46x8847zw455JDWeGEJBAKBnoEAH2K8D3g/YNSf+T6uZ5Q0SlELAkHgqkTLV3g6VX9B4tBSTJ48ubVDrTLZCBYIJATQmFHH2CDXz0vjJvULIgax4h5aMOavoQljKxtt0Km94SCD3NeKM9LQ6tMLLrjAOJD+0ksvXQb5G2+8cRk/PKS9YyiViw+WjTbaKKUjv8985jN22GGHDMUzSQAAIABJREFU2YwZM9IWO4UJhWcgEAh0CwIQuHXXXbeVuFEIkTfJbilYZNohBILAVYDPV27sEDc6UdnpXPHr379/2k6B1agxjFQB1Li9DAJoydia5rnnnkvEy2++i8YLUoZBAybD3m4axtcHBffw42UNoeOrW/VVmjQIHNuRYJQudsiYJ30pgPshbzR4GO1JB5nEUBbmwjGVgE1D+dL3mr0UKH4CgUCgWxB4/PHHUxvlPUHf5fs1CpS7u6WQkWnNCASBqxmyJZVdHaaXzC267777Uuc5YsSIdqQcUZoVARYOjBw5sibSw5ApRI9hTBkIGEQNYoVmDqIljR7DnhjcaPRyo7lw8ocI6gNFaXCPOs+xXdyDpCHJj3l1X/3qV42tRfr165cWV6CtY8h2nXXWSQstgtgJ3ZCBQNcgwDuAXRI03UIETtKXIoicR6Pn24PA1fAfqcJLKqoqPRoMOjQ0JmECgVoQgDxphWm18WrVcN1yyy2277772h577JE0eZA9iJlOaeADRCctIFnlKsMcOxFFSCMXYdhXCql09tprL5s5c2YaTuV50CoSlnAsjEBCDPfZZx8lHTIQCAQ6EYG5c+faeuutZxtvvHFo2joR5+5IOghcB1AXcetAEhE1EEhkCs2Un8PGijHmrTHEyYcBcyz9woIcNq8907y0PAxDoOQzYcKEtN8bw6ukr5XTTAPwhnu+HJRv/fXXN05ggPyJ7BFHQ7uQs/Hjx9vee++dwvD1j0YQEsdiB/aZi3bjUQ57INC5CKBQWGONNTo3k0i9WxAIAtcB2OkAc4MmIjYzzVEJdzkEeMHqZASIEMMdDEtCxCBE+LHIgVXOLBbw5plnnkkLBwiPgRyhLWNrG4Y0RQq5d8UVV6QXOcObDIPKaB4bhE3hIV0TJ05MxEvlQAPHsVmPPvpo0uJBBmWIxxmrEDa2FWFBBKtWIXwMDWN4DuIWbRasdEIGAoFA/RHwH1v1Tz1S7C4EPniLd1cJemm+kDcROC+1104vfawodjcgwNCihkPvvPPONGcMN8SJIUiIEnPIIFAscpBB6wZpYhNfwnPxpQ1Be+GFF9J8TIWFkEHQ0OR58sZ9ETFp0fBjuxKMLwflIX3Seeyxx9J9fnBff/31ac848kYDd/fddydSSjluv/32RAxJC/KmIdvWBMISCAQCnY6A+qlOzygy6DIEgsDVALVImyRR0bjhRjLkxeo/aVNqSDqCNjECLGDQ8CXL/UWockikZZM/9Q1CBMnzRosMSFcGcgbJgmCVMhAsGchhqXKgbaO+yxCWPJnzhuTgbAwLehg2ZYWtDOXQClj5hQwEAoHOQ4ARITTjvt8it9wtv84rSaRcbwSCwLUDUVV8dWIicbNmzUqbqLYjyYjSxAhAgCA/yHLD78wjY/WnDMdgaf6a/CQZMvFDlc8//3y6VZR+0dYhLGDIiaHSRuOmo7vw40QIny5l2m+//dIQLOXw92g7YQKBQKDrEOD0Ba1AJ1f1X11XgsipsxAIAlcDsqr46oSQdKpIhrbQTMT2ITUAGkHbLGBgLlw+vCmI+EiAaPmVqoTXnDWFk4RkcaKDDHPPMCxAyA1hvamVSLIlSV4ONiS+66677KGHHkpaOKVP2gzFhgkEAoGuQYARoQ033DB9aOV9GCWQX9eUJnKpJwJB4KpEk0rujSo9ks714YcfNrZQCBMI1IKAX8AAESql9UKT5VeSMaeNupcPqypvPiwYzpdBA8dxb0Um18DVSiQZFs0JHJ3GcccdZ2xd4okk+QeBK/oXwi8Q6DwEWNDEZr7e5H2avxf23oFAELga/ydVeqTsJEGH5YeKakw2gjcpApA2zQljzlpOhAQLc1g8gSsiTQqLZMGDtHWEZUh066239kFa7ZA9b+pFJOk0OJlEq1whnaWez+cf9kAgEKgvAowMMb/Wz4uN7Xzqi3F3pBYErgrUPVEjuHdjZ+4bKwmDwFUBZgRpgwDaLmnKKs07E9EjAR291SaxpQ6GRKmLIkvkASnLD7FXXMihN7USSbY6KTIM16KVRguHgcCJVBaFD79AIBDoPAR23313QxMPcQvy1nk4d2XKQeDqgDYaji222KJwflEdko8kGhiBjixgEEHL4YHAsfpTho8LSBq7seeG4dN8W49aiCQLGEotpCBt5sKdcsoprV/+0XHk/0C4A4GuQYAFUE888USaZysS52XXlCJyqScCQeDqgCZDW77DrEOSkUQTIADxZz4YRKzWeWeEL0fg/LyzV199NW2g61eOCt6c7NVjAYNPm+O5OL7rsssuS1rq0MAJnZCBQNchwAfclVdeaWjhWCjFJfLmSxEfWB6Nnm8PAlfjf6RK7yX7Z+UTRGtMNoI3IQKQMG0LUq95Z8CYL2CAwPHlrbw81GjJPNmrlUiWm4untL/73e/a73//+zQPz29t4ssR9kAgEOg8BP7617+mds50DRE4kTgkRuRNsvNKEynXC4EgcFUi6Su1yJsaAh0gw1RMEg0TCFSLAKRN5KnWeWeltG/knS9goG5ilJcvH2TPL47oDCL5iU98ImXJ0VyxAtWjH/ZAoPMR4DSUO+64w3baaad0NB9zVlm9rv6LEvj+rfNLFDnUC4EgcFUgqcot4ualGgH77NBIwgQC1SKAtqsrFjBolWnRXDWGVvwJDLUSyVILGMCAtBkyRev2ve99L53xWqQFrBavCBcIBALVIYAyYebMmXbOOefYL3/5S9txxx3TxxPETeTN92Pq46pLPUL1FASCwLXzn/CVHxK35ZZbJgIXWrh2AtqE0bpqAQOk7OCDD14G4c5ewMDiCGkKx44da/fcc4/NmDFjmXKERyAQCNQXgauvvjqdk8zCpUMOOSQtYMo1b/Rbvh+Tvb4lidQ6E4EgcDWgqwouKe0bbrQbw4cPT1qGGpKMoE2KQFcuYCCvItPZCxj8wh7shx12mF1zzTVFRQm/QCAQqDMCG2ywga2zzjrpI4oPKQicLmnhROLqnHUk10UIBIGrEmhIGkbkzUs1ArYS4UQG5hyECQTKIdCVCxjQ9A0bNmyZ4miRgW6UW8DAMCzh/SrSahYwKG3kyJEj7YILLkgLKrx/2AOBQKD+CNAvibhB2Dx5E4GjH1P/Vf8SRIqdjUAQuCoQFnlT0Jy8qQHgT0d56623KmjIQKAQga5awEDmnNPLhtMQMF3417KAAW2dX+xQzVFePjxkb9CgQcaK1D/96U+FmIRnIBAI1A8B+iWImsibSJvvr3zf5u31K0Wk1JkIBIGrAd28gns3di4WM3AyAzvlhwkESiGQL2CgvnDhj8bs9ddfT9tusKI0P4EBMsZmu1zvvPNOKymDnPkTGPj65vis6dOn22abbZaKAmkjzvz589MiA7+AAVJG/pBLCBflYP4c+bz11lttCJyGZYkjUqjFEmSUL46AALKYgfk4P/jBD1o39i2FT/gHAoFA+xHg7GSRN0/ccvKmfsv3Ze3PNWJ2NQLFZ+B0dSl6eH7+6CwVVRVeDUD+kpyNGqY5EYDUQJ64ShktYOD+F77whRQMUgTRwUCkIFq8iP32H4MHD05DIfhzkc7ixYvTBelDyyXDlh2qh7vuumvFzabZ5BND+bkwnGPKRVn8SQ4829ChQxPRg8BB3sifMmGUb3IsTYe2stVWW7Vu7HvMMcfodshAIBCoIwLsS8qUniLtGyRORK6OWUZS3YBAELh2gg6p85eSWbBgQdKYFG3ZoDAhGxsBDnBHayUDkaI+MAcF4iMt2dy5c43TEUT0kNKISSoNSeag+Xlo8i8lRcT8goJSYeVPebVfW6ly4F/qHukoX6UJHgrPMOo3v/lNO/LII5NWTmFCBgKBQMcRYCcEtN28c6R9k/TETcoHKSM6nnOk0NUIBIHrIOKexGFn+AkZpjkRgLhAVqRVAwWvWWOYlGFRtFlorJ566qmkPYO8oelCmyUD4WMrDl6wvIAxIkGakIyfJ4GKK/noo4/aUUcdJWeXSRFAZajhXdza2Pemm26y/fffX0FCBgKBQB0QYCHdkCFDWsmbSJukiFsdsookuhmBIHA1/AEiZp60Ed27Gc5iuCpM8yIAGbv00ksTALn2De3ZCiuskLRwfm6b13pB5BiKZN4ZJA8DKWSYklMVNMwqhJlvJgOx0xc1pGny5Mm2cOHC1vIoXJG88cYbW7152XPxLCozixLkRtZiGOrdfPPNUxRt7MvxWkHgakExwgYClRFAs88G4bwHRNokRd70jqicWoToyQgEgevAv+OJG3Y6VzrfbbbZpgOpRtTejABEDII2bty4RHyKtG8QM0jX008/nbRvkC6GPfwiAIZZITo5kSJ97lHfMGjomJ9GXAibyB15YMgf4jRgwIDkLvdDOXKDRlFpMa+GMNRxJMQO7R+dBScslBvapbye9LGx7wEHHGB33XVX2iU+zzfcgUAgUDsCvFdYRMf8tyKyFsStdkx7coxl39g9ubTdWDZ1mEhdFEd25P33358maHdjMSPrbkYAAgXBEZmRpFga/ixXRF7AEDIWMWgeHSSKYddc+4aWTqQPoqdhVvwIjyHOwIED06pPESjNzyS84hAW4pkb7wdZxEDWyIOL9FnRSll4drR0/fv3TwsveF7lSXlkJw3m5J199tl28cUXB4HLQQ93INBOBDi0XguZROB8UvRTYRoHgSBw7fwvPXEjCToxOqgRI0a0M8WI1ggIoPGqhqiVelbIFZcnfkVhyQej4VYIlAifhl25f9ttt9mXv/zlkitQ/Zw70tAXOpI6joQc5kbkzxM8CB0k7plnnkmb9UJGIX39+vVLbQPtoTf77befHXvssWlvOFa0hgkEAoH2I8AG8nfeeaftttturYkEYWuFoiEtQeDq9Leito75PHUCsxcnwyKWrjiwXQRPsggy5r5hOKdX4UTu0PKhFfMErGgItShdOgVtXSKiJ0KHZIgXQxhIISuzIYoTJkxI24uwFQpaOjSD2tj3pJNOKsoq/AKBQKBKBK677rq0eIEPLq9gUHvN/dR2SR57mN6HQBC4dv5neYXX3KR2JhfRGgQBVplqCKO7H0kaOS0eoDx+LzfcECy0eBi0YLhF7vAT4UsBlv5Q90XYvD8kjYuOAk0cc/hWWmmlNKxKHDR0r776ahsNHavlvva1r6UNftdff32fXNgDgUCgSgRmzpyZpklsvPHGqZ3x8aRpDkjaqz66PMHL+7Eqs4tgPQSBIHAd+COo/LpoIGhf0CqEaV4EmLvmCVN3IvHss89WnJOpxQiUE61YKeOHakX4RO5E+NDmeY0eJA4SyQpUiB1TDDhcm1Mh0FIS76WXXkpz4H784x/bySefbBzAHSYQCARqQ4CPryuuuKKVpHnyJuKGH+QNt/qtIHC14dzTQgeBq/EfySu+3HR+jzzySKxArRHPRgvOgoNSc+C0IhUioyHNznx+hlBXXnllu+qqqxJZIi/mpKHpgkT5RQWlysHzcGEoM3F0xmk5bZ4In8gd8VnwAOmDtOGv+XEnnHBCIprf+973ShUj/AOBQKAMApx8MmbMGJszZ44NHz68jfYNrbrXwEHgcGtIVckGmRMSvUcGgavyv6JyU+Exquh8zYjAcQbqPffcY0wkDS1claA2WDB/PJYeDfLD6mQOlJeGCm0UL1Hmgo0cObIskSL+vHnz0jmp2Bmq52gthmnzRQHKE3nvvfcm4saHBS93kS6I05NPPmmPPfaY7bHHHiWJJAsRHnjggTRPDhKIYTsR0tphhx0KSarX5kH2wIM4kD62G2F4hzKL3EHkIJlo6jbaaCNjBR1hwgQCgUDtCEDgaHMsZOD9sv3226f3BGSNi/ZJn+W1cPRp6s9qzzFidDcCfVrESrq7JD04f0FEo9DFVw0dDyvttPUDHR4d47e+9a1lzoLswY8XRasTAnz9Mgdu9OjRKUU0bpw2wFwwSBAvURmGM7gPuYFIFWnDSI+5LcRnZSphqHMQQMgcQ7Xs95QbyJcIHKuid9pppzxIIlGUh7wx/gPl7rvvTquq0ZBpQQJhqPsQQPas22677UoOd7IT/OzZs1OHoY5D7QTSStz8eb/xjW+kPeEod5hAIBDoGAK8h9imBxKHxp33B22Zj0jaHpcndFJGdCzXiN3VCCy7P0BXl6AX5SdtG0X2Xy3y33TTTZNW5ZJLLkmkrhc9WhS1Dgjw0mRTWxlOQYAEoY3y5I37uNkLDUKGRiw30oBxWgPhWAzAyxeJNgt/Vj5D8nLzxBNPJMLIqk+28CgypMOCgtygEUOLjMbOkzfC8ZJHg8Y9SB5lzw3+lIkwDCVTVjDATlkYRr355pvzaGlIF7LKxr5hAoFAoGMIoKVni55p06bZ9OnT0+IkPhqlgEApIcUEOeXujuUesbsKgSBwVSDtyRrBRdikjsatLxjmH6BtoDMP01wIsIBBW4igIUNTBlEqZ/gyZvFLbphPSVq5pkrh8IcccZpDbigHL2pMTsIUlpc5X+C5YVhTJ0Dk9+QmbzSK2otO/riff/75RN6Kyk0bgYyCjbY4IS5ungWNwRlnnKHkQgYCgUAHEBCJY/oGGnHafBGJ80SuA9lF1G5AIAhcHUAXwROxowMM03wIQGC0gAF7EUHKUWEoXvPT/D1Wb/oVnf6e7BCi/OULGSJNSBym1HxMtGcim0oPCZksIl8+DHbmtuVz8PhogZBSrnKG9CG3MpQZLSUb+7KXFRrEMIFAINBxBCBxbOzL1AfeC6VIXMdzihS6A4Hyb9ruKFEPzDPvJKVulr9kDyx6FKmLEGDysCc0IjOVsuelykvWG8gfJKcSEYKEsajAG8gQWjcROH/P24nLlh65Ud65v3cTF3Lqn5f7kL9KpJNwtJdcM8nHjzb2veCCC3x2YQ8EAoE6IIBWPtfA4ef7s+jL6gB0FyYRBK5KsH0lJ0qRW/5VJhnBGggBP3zKYzFEWI0mCzKE9skb0qpGe4cWK9eiceoBcdmu4+CDD/bJtrEzzJ8TOMgf9Tqfr9cmolnqBPJ8CfPaa69V9cxoA6SpJB7z4oTBIYcckoZRSStMIBAI1AeBnLzhzslbfXKKVLoSgSBwVaCtrxKkr/iy66tGUuGrSDqCNAgCLAjwmjRIWDVECM1TrsmC0FRD/qhvftEEUFIO4jIXTdt/FEGM5i/PtxrtG2lBOosWRzDsW4l4QjpZ1OANfpp2sNVWW6U94S677DIfJOyBQCDQTgQeeuih1NZ5X+hS35WTOPqu6L/aCXQ3RAsCVwZ0X5l9RceuhkBHqEt+ZZKMWw2KAIRNZErz0CqRMIhQkSYLEsZcskoGLZo0VworLRhz1PKNdhVG9TSPy7BvJQJGGhAuT1bxE/mrZtiXhQze5PPpOB+VFXSc1RomEAgE2o8A7whWtPPBpX5KkveAJ3K+jwsS137MuzJmELgSaKsCi8Qhc+JGA6AxqEOUvUSS4d3ACPhNfDUPrdLjQuDyYUziQOAqESniMtfNk0T8GJ7E78EHH0wrO4vKQH0tWjjRXcO+bOzriewnPvEJGzVqVNpDr6j84RcIBALVIcBqdjbH5qNL/VSR9ORNKasPlDtkz0MgCFzBf6KKK/KWf6WoAdBhQtqQXPgTJzQHBaA2sBfaJybli0xpHlqlRy6ah0ZaDL22R5NFXA1FPv74421IkS8L+RYROJ2a4MPmdup40bBvtatXiS9NpdImPW94Bo7VOv3007132AOBQKBGBNgHjrZOu1NfhdSFv/o39XeSNWYVwbsBgSBwGeiqvJKq3L4BQNb4ovEXpG3u3Lk2adKk1GDy1YFZNuFsIAQYPhVx4rE0D63SI/ISzeehob2rpH0jXepgTsIgUZAhNuLF5MOcKg9x2Qg4N9Le5f7eTdx86JX7LJpo77AvQ7d5mnvuuWc6TSI29vXohz0QqA0BtNvsFUm71UW/hd0TOk/kvDaOfjBMz0UgCJz7b3xlFXFDUrl1qdL7xsDRQddcc03apJT5O4cffvgy2zu4bMLaYAiw6MBP6tc8tHKPqXqVExc20q2GCFEPOefUG4gk23hAxDCl0iGuH7JUGp6Eyi+X1PucOBKmvcO+Sl/aS7kpS2zsKzRCBgLtQ+CII45IowO33HJLOvGFd4Tvw7BzqX/z5K19OUasrkRg2a3YuzL3HpSXNG4USZVYnSyVWxXdV36+ZDjAng7tlFNOCdLWg/7PriwKhE1nkkJwIFBFJMeXiXpUFKbaoUjyyLV3lIN5ccxl22uvvXx2rXbqNGXMiSMBKq2aJQzDr7n2riPDvmgcSxm2FGExAxv7Dh06tFSw8A8EAoESCKCFP/roo9P5xSga0Gjz7mGe6QYbbJCmajBdQ9M20ODr8gqNfJpDiezCu4sRCA1ctqcbHVxO3Ly2jQ5M17x589Lmpfvuu2+Qty6uuD0pOwiMCJGfh1aujKXmoRE/10bl6VAfGWbNCZxOb4AU5Vt1KA1e3vkqUN2rlC/heKnn2ju+6qsd9s2HdSmr3xNOZUFSTjTasbGvRyXsgUDtCDClZ/To0XbiiSfaQQcdZJzTzPCqhlN5p/BuQFmhPhApxYYnc7XnHjE6C4GmJ3C+gmIvR96o7CJvDJvdfvvtdswxx5QcquqsPy3S7TkISIMkMqV5aJVKyAsz12SRFnWwkiaMl2xOolgFq3NPn332WRs2bFhhEai/pchdJRJG26ANiKwqg2rnv9FB5AsYSKPc1/1RRx0VG/sK6JCBQB0QGDJkiI0ZM8ZmzZrVOi9O5K3cUGqQuDqAX+ckmprA+QqJnUsEjgqti07Lkzc0DlOmTElz3XKNQp3/n0iuhyPgtW8UVfPQKhWbupWTsGq0b6QL+fNz7pSvVq6iGS41n418i0gUaVQ6Bou4Rdq7WoZ9c/LHh5DIbxFmDJ2i4Y6NfYvQCb9AoH0IQOAYUlXfxjvFa+GKNHHk5PvM9uUcseqJQNMSOFVEkTZJVVw6K1VqVXJJ/gBWnbK/TpjmRoAVlH4vt2oXMFC3cjLTkY10IVHSoDHPpRRJ4wMlJ45o76oxaO+KCFw1xJPnpXz5MC3trNyJEZQrNvat5t+JMIFA9QgwpLr++uun4+/U1yG51AfyrqBf9Ff1OUTIrkCgaQkc4PqKKc0blVdfIkgNmSKZOM7FUNdqq61mdLhhmhsBFgx4Aqd5aOVQ4SVZNIzZkY10IY6sOlWdLLWNDfU3n3PGCtJqDO0hX3hR7bAvcXPiSJ58CFXS/O24446xsW81f1CECQRqQGDTTTc1Vr3Tt9E+/RVkrgYguzFoU65ChbjJYIe8icCp4krbRuVmTtGTTz6Zvk7YpJVhU1TQAwcOVDIhmxQBtE8aAvTz0MrBQZ0q0mSxkW4p4qX0+MBgzpjylD/EEU0WaWOK0qFOFxFHkT6lVUrSNnISVo32jfQod1F7If5GG21UKstWf23su//++7f6hSUQCATajwBa+qeeeioNo2oVqlLjHeP7Sflrmobul5u/qjghOw+BpiRwwOm1bzmJ818iM2bMSGfJjR8/PnVeRZ1Q5/09kXJPRkD1REOhzH/TC65cuSFC+RAnaaEdyzVceTqEU366JxJF3px7iMaqyBC3iDiivavGED/X3kH+KmnQSBvyWDRftKiTKCoLG/secMABaRuEUs9XFC/8AoFAoBgBzkq++OKL01QgpjdA4iBkXHqPye2Jmr9XnHL4dhUCMYSaLV5AUyAt3PTp09NS65NOOslGjBhRqEHoqj8q8ul5CECcPKHx89DKlRZtb5Emq9TCA58WJConefk2HoMGDfJRWu2QqDxfbqK9q2RKae8Y9q20apa0i4gn/mCYaxOLyhIb+xahEn6BQPsRQEu/xx57pL1MGWWijdLOkVzqB+kTuTRSlSs/2l+CiNlRBILAlRhCpWPiCBK2MSi1o31HwY/4vRsBhtO9Rkvz0Co9VdE8NMhfNUSIIdJ8+xFWcmpxwOzZs9Pk5KIy8BLONX8M+ypuURz58UL3zyr/jpyfShqkWw2BIywb+1533XVpY1/lHzIQCATaj8Buu+2WVnmjVbvjjjsSgeMdwwWZE6GDzBWROHKuVove/lJGzFIINCWB0xeEKh9ufV0gqaxTp041hk2DvJWqOuHP5H9PptBkaSVoKXRKabIYiqyGSFFXcy2aFiGQNto47QeXl4GXcj78mmvv8jhyk3ZO/iBfkNFK5SZcni/p4l+LgUDGxr61IBZhA4HKCDC6dOCBB9omm2zSSuJo71y0US4ROJE49aFIjGTl3CJEPRFoSgInAFUJPXmjgjKsQ0dMxQ4TCJRCAPIjMkWdwbC7OUROu5zrJag0eBkWabLQ3lUif9RT0svJEGeisoCB+zfffHOyz58/37hIl0sLLHKyBfkjHoZyQ8j08pY/92gXelY9C89ciiwqDJJnzod98Sd+0bw4Hze3x8a+OSLhDgTqg8Dee+9tzItjj1ParN5dGkpF8k7Qpf4zyFt98G9PKk23iEGVzUvsqpR0VHRifmuI9gAbcRobAV5wbKEhMsUwIEfVQNyoP9zj4qUHMULKDB48WNZWSb3TalAWBUC0iMOwqid2ReRP57BC1DAclaPFNtrjTS/k1gyXWthKQORqwIABieipLag8iuPn++HH0C3pki9xKLMmOHvNddGwr9JUO5S7kvQb+3IKSphAIBCoHwJsms3RdQ899FDr+c5+AUNRTmrz3KsUtih++LUfgaYjcB4qOg9/qeOiMw0TCJRDAO2RyBvhIC9FxCxPg3hFc74YwpAhDMQIA0mCyHFBxsrlIbIm8kb8nHQpD0meQc/BAddFhrJQptxwXJcfQlZZ2duN8LQj4kLgcu0daaHBXGmllfJkK7oZRoUsH3nkkSVPnKiYSAQIBAKBZRDgwwstNySOkxq23HLL1gPvtSIVwiY7kj5UxM3bl0k8POqOQNMSOE/csIu8IcMEAhAQhhKYpA/JQCuGJgzyxcX5n7hFmkAMIpQPUeZIiizl/t7tw1QiYD4eK8lGjRrlvepi55lKlcP7e3s1GaOVRaX8AAAgAElEQVShrHQKQ1E6fmPf2BeuCKHwCwTaj4AncWjitt566zQSAHHjYlQAyQcaUn0pOYrItT/3iFkLAk1F4FTRkBi5PXmTvRYQI2zjIcDwIcvsGVLwJE07lzP3i7rCPoG8yHipQepkIHdsmquXnogf/lyQwlz7VCsBUl6SkM2xY8fK2eMlmrqijYWrKbg29mV/uGq2X6kmzQgTCAQCSxAQiTvrrLPS3pJDhgxJ7zIIGu86JJcUHiJuSPpVuQPPzkWgqQicoKSCqeLJLok/Qz5hmhuB559/Pr2oPHlDM1YNyWK4k8UBEBRIFYbhQs0Vo34xtEhd0xetFg541EUC8RMRxI5GzGvp0A5y/84770waLU4NKRqy9Gl7u0/L+3e2HS1nNacwFJVDG/vef//9JTcuLooXfoFAIFAdApC4L3/5y3b22Wen9wnTJSBmnsDx3sFP77Igb9VhW69QTUPgqFgysqM5oeJxyY5ctGhR6yRwxQnZXAhQB9DA3Xfffal+8NLyk/rRwKH5gWSJUEm7xjm5+DE8yFWK9LHgAbIHoWPhA0ZaPBY+4E99zI0nhv7evHnz0lYAs2bNap1D5+/zoqWMuRHJvPTSS1tviTzy3GgK9SwQQ2kTWwO306J22J7ofmPfOJmhPQhGnECgMgKsEt9nn33slltuMT6a9MGpD0reX7xXuGjPvk3jF6ZzEVj2bd65+XVr6r6CQdpwi8CJxNFh0nHWosHo1oeKzDsFAcjVfvvtVzJttEeQLsgUF24kL7S5c+emeKpf+HsDwcOITKEBg/DhRmJYHYpRfcROfhBH5UteED2Zq6++2s4///w22jndKyelgWMVqgz5ijzybBBL8uOZ0BZyjxWxDIGyPxztpRRRVZq5JF3IYHsNG/see+yx9uCDD9pWW23V3mQiXiAQCJRBYJtttrFHHnkknQfOKnDeU3zYicRhp//EiMxh510RJK4MsHW41VQETpWKiqVLBI4OSXY673zT0jpgHUn0EgQYNq1ELCA9Ij6VHkuaNggQmj3cIl58LLB60xvqIScqYHgBiugVDbMqHvUZw8uU4Vni8YLFSCZHlT+kw4UpOuuUMvI8kDA0k7ghlhC6fv36pdWpfL2Xw5Fylrtfqaja2Peyyy4LAlcJrLgfCHQAgc985jP2q1/9yjbccMP0fvHkjb5TRA1/vYvk14FsI2oFBJqCwImsSYqoUfH8RYfExYHgtW4wWgHnuN2LEIBg1VMD6xcraM+1HA7qHfliRPikacNPQ6t5PLmZs4dBi+brue4jeaHqpaowvHDl58NWshMPYsel5xOp41iw5557LrUlNIrsqcgHEW1KpBfyVg/DlgfsIH/cccfFtId6ABppBAIFCMyZMyeNMNCuIXF83PEO0Iee3iO8AzC4ZdrzflHckOURaAoC5yFQxyUSh/QkDm3C8OHD4wgtD1qT2SFLpYhWZ0GBlk3kRrIoL5E7T/goLy9WTJG2rCidWv1oNzKlXsie1Gl1KUQNLR1aRjSIxIVk8oz1wFgb+1577bUWG/vqHwoZCNQXAQgce1CykIE2LQLHe0h22jb9Ke8B3hel3hP1LVlzp9ZUBK4SeYPIsXnhYYcd1ty1osmfnq1CdLpBT4NC2i7KJQLE8TdPPfVUOieUbUQ8uYM8YaTN456Gb2t5tlIvY/8hpPT0VY4bDRyXyp0Tuquuuipp6AYNGmQcCaY5gEqrGqmNfZkTV3RSRTVpRJhAIBAojcCYMWPsvPPOS++OHXbYoXUenFd+iLjxTuAdIBNkTkjUXzY8gRNp81KdDp0ZFRBJxwJ5oxPxO9nXH/JIsacjwKKDjszN6o7ne/rpp9OWJTfddFOaZ0cZWEXLwgK0VJC83Eibxzw8DEMjGqqF5NEuKhle2lze0JYgjNK40fYYkqY8rB7lPoa8sCMhzcRBc4eGjnbIXLpqjDb2ZePl2Ni3GsQiTCBQGwLsA3fKKaekw+5vuOGGdEIDH7la0CAtnKT6W3Ip9fFXWwkidBECfVpAuoGNKhKkTV8LdBp0LnRcXAybTp06NXUuzKlh/5swzYkAdWPChAn2hS98oRAATg9gn7UFCxa0rryCwEA4eMm1l/iRbnviUt67777bzjzzTONoq1122aX165f6DhnlYr+1cqc08JLVq4BFHMwDRepjhxcz2i20foQjzWq1eZRDbY3yEp/5cBA15sZpZS3psRUKWkP2zYPQbbzxxlbqiC//B7EC9/TTT08dTGzs65EJeyBQXwRYiHXJJZek99W2226b+k3aMNpz+k6kiBzvRt4tQeLq+x8otYYmcOqQ1AmJwGk1nzoV9vpiiGfvvfcWLiGbFAFIy7Rp04xVV95APNiugqFKXlKQBGmeqF8QGkgY23+MHDnSRy20kx5aM+aW5EOakBrIYLlzT5Xo9ddfn7RYJ510UpoDNmLECN1qlZSPjYXXX3/9kiSOFyzt4vbbb09hIZOeCOkZaTMcrcPCAW+8Ng/ihZE2D4kfz4zhq530SIs8eeGz0IFhVL9yFSLNV762VEmRS/yAP2XmQyz2hSsBUngHAnVCgLbLeal8GPKu4p3IpYVNInDIIHB1Ar0gmaYYQuW5IXNcdBxcInN89bNDPodjhwkE0PwUrUC97bbb0tAkBIOXUm74AmWIEFJG/Sqn7ULDNGnSpJQEHw5oomSIC9mZPn16Inc777xzyXlhkD/CUibsReUmXYgmmjPIJwt0Smn6br755qRVg0yJnKpcSJ4REvbAAw8k6cmi5rj58OQzc+bMRAj1Zc59iK7KTdkhcZDYe++9N5E6bUVCXqWeyeeDHbLJjvFnnHFGELgcnHAHAnVGgPY8btw4+/Of/2wbbLBBa7+qflbKkzpnG8llCDQ8geN5faXyJA7yBpGj06UjCRMIoKnKSQPDiQwbQIKKiI1Qg9gxzFiOKEFKIEqcbFBEekgf4gNZgkyiUYLEFRnKBdl54YUX0u1ydZh00XyVG6qFSGlhRFF++KEtIwyHXKOFw11kKBsklGdkLluOG+2OEyCeeOIJ22OPPVpX4JLWs88+m+bE8eVeqTw+79jY16MR9kCgcxFA88ZUEtqyFCPqa5WzJ3IxjCpU6ifbzj6uX7rdnpIqkpe55o2KB4nD8EURJhCANOWbOEMyICI5CSlCCxLHMII/dsuHY/4cpKeIvPlw5AWRZHK/VpL6+9ghm6SFNgvT0TpcqUzKnzzJq1S5GIaGvEG+IJhFuIETW4lAZCdPnqykk2Sod7vttksfXqUIYpsISx2Q59NOO83Y2DdMIBAIdC4CvONoc76P9fbOzT1SB4GGJnA8oCqUvhAkIW+6oioEAkIA8pEPMULqaiES1LFS+7GxX1uevvLOJcQHolREBtGkQYK4Fi5caHvttVcefRk3HyvlnoO06mFYzQ0ZLJeX8iEc5QJ3bzRfzvtVY//c5z6XhlGllawmToQJBAKB2hFgHpyOBVQ/61PBL0znItBwBM5XJNlF2pDSuom8UQnLDT11LvyRek9CAFIE6fAECyJRifjkz0A9K0Ve0FqVupeng5t6WqQZU1kJgx1NVzmjul+0SbDIUi3lKvdyZtECQ8DVmiINHTi1p12yZQorydnYN0wgEAh0PgL+XeDtnZ9z5NBQBE6VB5mTNhE3OmNddFzMw6llnk1UmcZFACKUExyIhF+NWc3TU6+KDnYXGaxF00Vd9oRS+XNcFXPaMMwZYwuRcoY6z3BHkSk1FFoUVn7Mlyt6Ru4zpFsLGSw1N0btWXlWKw8//PB0yD2Lk8IEAoFA1yFQqi13XQmaK6eGIXB62SN1icRJ2ybihlRnypAWq+7CBAKQonwBA8OntbyUIDaltGHtIYOkl5NK/inKJQLH3mmVSCb1vVS5SKsWU+4ZGQqtRftGvhC+nAyyLUmpYehKZWUbkX333dfY2DdMIBAIdA4CtFv6Wr0fJTsnt0i1CIGGIHA5eRNx07BRkfYNEof2je0XOCYkTCDAXLNcG+s1XdUgRL0qR5RqecmVI0pol6Tluuuuu5ZZeJGXlbRycqowPGMtpp7PCLEsInwQuCLiWm05Dz300LSxL/vDhQkEAoH6I/DYY48VTnPQO06y/jlHikKgIQgcD1OkdaOj0UUHpksbiM6aNcv222+/tH+XAAnZvAhAGnKSw/5ktazuhJDkJFCI1pMMUi6/2pU96MoZ2ke+ulbh842E5V9KlntGrYwtFTf3Jy1WouaGr/v2auBIa88990xJ3n///XnS4Q4EAoE6IMC+jTp2shRZw7/UvToUoemT6NUETqRN0mveRNzoIETYIHCys1cXc5FiA9+mbwOtADDEmQ/loenSUGVrwDIW6l2pyfftIYNFaVFOkRvqM6YSgUMTVUqjVetcsXLPyAKGWggv2vGiM095xlKazDLwt95iSBktHBv7hgkEAoH6IsAqb945vBtF0CR9TvTNYToPgV5N4ICliLz5OW8QOC5p35B0pByLdOCBB3YespFyr0IAwpCv9mRRAyS/aJVkqYejrpUjSrWSwSKtGeXSy5INcysdHUV7IF8Nufqy6xm9XyV7uWcEx1oWaUBAi0gq7TT/PyqVK7/Pxr7XXXddauv5vXAHAoFAxxAoep90LMWIXSsCvZbAeWbvSZyf75YTN9yPPPKI3XnnncZKtaKOo1YAI3xjIACRyRcC4FfLS0pzLotWjYoo1UoGi9Jirp7XcnGGaDlDmyhFKiFc9XxGtHO1EDjabtEziqCWe65K92Jj30oIxf1AoOMIqP/1fXLHU40UqkGg1xI4Ho4KQ6cpmWvevNaNlXYTJ05M822+853vmD/HsRqgIkxjIwApylcjt2fOWrmtOupFlNi4VyRp9uzZ6ZD6cv8OWi5tuJmH47lr1QqWekZIatGChDxPuWm7tNEickm5ivwVt1oZG/tWi1SECwRqR0DkjZgicKVk7alHjEoI9EoCp0ojqblv0r55zRud1/PPP58O3d1nn33SsGml+UKVQIv7jYcApCgnObWSG+pdqXlbtaaFJqsUUWL1tMgg0wGKNFj+H6JcpRZW1LrogPZU6hnbQ3hLpUX59Yz+WWq1x8a+tSIW4QOB6hBAS64+WFIKlepSiFAdRaBXEjg9tCoN0mvf6PzotLjuu+8+mzFjhp144omhdRNwIZdBgEn+RStQayERaJPyNJRRPYmS3yj3hhtusA022EDZFEraR6lyQQBr1cAVzcsjY783XWFBMk/aZxFJxb+eJjb2rSeakVYgsGTRFIoR+lrfDwubIj/dC1k/BHolgaNyYFRJcg2cCNzMmTONrSFOOumkmO9WvzrTkCkV7TsGudFqz2oemvpYitzUiyj5jXIXLVqUiuXnwxWVs2ijXIVrzzOWI4O1EF7aaVFazMsr8leZa5WxsW+tiEX4QKA8AoxisX/q3LlzUz8szZuk+ujyqcTdjiLQ6wicKoYqisgbnYGIG1/wLHNmqxDORazUwXUUxP+fvTcB2qQq8z1P27fndo/Lnb52a7MUVQWFVLEUxVLIUgrSCCgKNKhdSuPS2GoopTG3L3MJNSbmGsE0QvTioE6P0h1qD4i4UQqCirZQFBayUxvFDgVUY181huFqR0+EPfFL+H/1fOc7mXlyeffnROR7MvPNPMtzMk/+8nnOedLPn2wJAEXxeCsgogm8IYEqVx19gRJaLg3wF8BVTcbhXigbl9Z3Hdu4XCkD3iZawZyrzx375kjJj3EJ5EsAgNuyZcu8z1ZKqRLHpKpnd34OfmSdBCYK4OKLgm0ADvOpYtZ5aKF9w02Iw1vdJeD/A0WxywoLSjkS4rorc9UBIDbRTJFfGQxaUyxjzpYvX15ZPO6FlKNcTuqzjoLBJrNs0Qymxu+hDRWkVlauwZ9y7Lthw4YGZ/mhLgGXQJkENJZcShQb61mtcx3eJIl+44kCOFVdF4O9YHiASgP31FNPFbP0fKapJOZxlQSAoliL1dQhLaAUa/GUJ0DSRKNEWmUwaMsF5K1atUrZJGPui5SjXA62aSVPjnZSrjLTJjNQm0CXgLcM4GKHylFRGm/Kse9nP/vZxuf6CS4Bl0BaAosXLy76EQEbz2St2zh9tu/tKoGJATh7MbBu4c2aT1lnlt4RRxzRVTZ+/oxIAE1UbMp75plnGmnNgJuymZ6AUhMNHHBTBkpouuRChEHEr3jFKypbqcxRLie1qWNq0gFpMcu2ibabOpYBb9fPaJUJRI59+XasB5eAS6C7BJhFTh/D/cxin8sxzHXPzVOIJTAxAKeCC+R0oejCsRCHJqBs3I/S8dglIAkARbEmiJcAgZKOq4oBuDKYagNKsU868iYPrnOVizLWaaq4X+K6qR591hEtpsql9KtiOv3YbYuOb+pPTufVxcDnRRddVHydoe5Y/98l4BKol8CyZcsKhQn9kp7FAjk9q5VKvK39HreXwEQAHA2voIsAgLMXDOuCOLQBHlwCORIAFgAjCzlsW1cdOelwXcbj6HReG1BKwQ2gaV9MrrrqqlLzKHlzj5Q5yu27jm0mMJRpLDE5l2kgJdO2sRz7PvDAA22T8PNcAi6BFyTAfYqFQc9iKVbi2D7DXXj9SWAiAI7qCtxsrIvEwhtmJS6o1atX9yclT2lqJQDAxVosQKmJORDhlLnq6BOUmLSgSQJosAgW6OJG4oWmzFFun3VU/ZvM2uWeLYO0JmPp4jrXbcux7/e+9726Q/1/l4BLoEYC3MP0oTyLBXHEejYT22e21muS9b8zJTAxAEd91Pi6OCy48bDCVQMfqT/nnHMaP4Az5eWHTZkEgKIYJBgT18QciJarDKT6BCXKJUiSlnnvvfcubRHgsWzMWp91tL7pSgsT/QGAlo2Bo2xWIxqd2nnTHft2FqEn4BIoJED/8/TTT89Zv2QFIxbI8dwWyLnY+pXA2AOcoM3GXAyifXvB8MWFU045JVQ91PoVn6c26RIAFmJTHuO5mswa5RrsE5TKtGa8oGgyBOWuC5QrhlOd02cdm7r9ACwBXtVFZVLM/4MEODn2vfbaa5Wlxy4Bl0BLCRx00EHh0UcfXQBxAjhi+/zWesvs/DQjgbEHOFPW4iKQ9k2xQG7Tpk0BVwFr1qyxp/i6S6BSAqnxVk3da3ANxhCoTNuAUhnA2XFmlHHt2rXKJhkDcPHsWh3YZx1/+tOflsKY8rMx8irzTWePG+Q6jn0//elPF/72BpmPp+0SmHYJnH322cUXGXippM/RM1mxntUxuLHtoZsEJgbg1PiKdVEQ33777cWFw1cXPLgEmkig7CsMTUyomANjP3IqQ1+ghCmWMmkMHOWug6AqTVabWaNldSStMm2a5GBjypWaZcsx1KtMa2jT6Lrujn27StDPdwk8LwEc+vJChHsexgJbiLPP6RjYBjnWdVbaZiIBTheFCP++++7zT2bNyhXbYz2BIsDDwgcDcumAmgAcHVOZya8vUKJc1qyL1mufffYplYbujVS5SIv6NakjMkmlRQEkx9LCRH9UuRDhUFvP6NTeNt2xb2+i9IRcAgF3Inxaiy8g0VfYhb5Iz2xiKWFioHMxNpfAWANc3NBs2wuBdS4OQtNZg81F5WdMmwQAmXggPfvKJiSk6s81WOaqo09Qih3lMlkn5WpEZeS+KDPrUi4LrTqnLNZ9FsuK49GmtQHeMi0b6Q3rzdwd+5a1uO93CTSXwGte85rACysLfUIK3EjVwa25bMvOGGuAU6EFcmp8gZwuEPbLrYLO8dglUCcBoCg25TErtYkGiI6qbMxan6AUa/Luv//+SlNjlZarTR3LJmmgfUOb1SSUAS9pYHKO3bo0SbvJsdTpsssuc8e+TYTmx7oESiSAEuXNb35zoG/i2ayFF0A9s/UsJ/bQXQITAXBUUxeAtAGKuUjwgO9+nbpfDLOWAlAUa7EYiNsE4NAYlcFNn6BkJzA8+eSTRVOVjUnjT8CyTAPXpo5lkIoMm2jMgLeytCj3oD6jVXZtn3zyyeHSSy8N7ti3TEK+3yWQL4Ejjzyy+DKD1cJZkBPMkaJgLj91PzKWwFgDnBpYMY2vRRcF8YoVK4rvOsaV822XQJUEAJn46wmAUhPzIqBUZg5Ew9cUBsvgBrMu6T311FNBAIdbETRgxCzAEYvujbJy9V1H+aarkrX+A3jL6sgxTU3YSrdtjGPfCy64wF8A2wrQz3MJRBLATc/jjz8+Nw6O/kjgpmc5sYfuEvh33ZMYTApqYNvgWhfEKcZc1GRA9mBK7KlOmgSAhdhchwYIGCJgGuSaQ8MkqOM6E5QBLgBcmasO0uF4oIpzNIO0TE4cVwZdp5122txpX/7yl8Of/MmfhBNOOCEwmYEy/OpXvypgjnXMkMSpMWskkqoj+1XvuI50wFV1lGzmClixQrmqNIcpty4VyfXy1xlnnFG4H2JMXJk2tZeMPBGXwAxIYOXKleG73/1uWLVq1ZzCRc9q+1yfAVEMvIpjC3C25ilwk5aBmIfYokWL7Cm+7hKolEDKfQgnvO1tb5s7j2MIQIU0XGi8eGEAttCIEcpmZ2La53igRcdyPO4/0ERZUAKCqkCpyOiFH87dY489CviMAdQeV7aeqiPHLl26tKhXqo5lMIg2j/ojEwBVMEfdWOKALMpgkGObmGPjtNtuW8e+uEPw4BJwCbSXAG5FeKEUtCnWc9xC3Cju9/Y1G78zxxLgbENrXReBBTc0Cd///veLKcyMZfHgEsiVAFAWm0/jcwVHiuP/67aPPvroBYeg9WMhYMJlXdozTItloGQT2rJlS0ilbY/JXbd1O/jgg3NPmzuOL5/wAgXQPvfccwXsco9KC8iBAlYAD/gsA16ORSZV/89l3PPKBz/4wfDxj388vPWtb208KaPnonhyLoGJl8CSJUuKYU24OqI/0PObWM90KimYc5Br1+RjCXC2KmpsXQAW4Hbs2FE8yE466SR7iq+7BGolAHSUDfKvPbnDAcCJAMXCU5MkGXA/Ltc8daiqB8CGRo8ANLOo/qk61wFe6pw+9uECgbBhw4bgL4N9SNTTmGUJLF++vHix47OWenbrWW5jB7duV8lYA5xtaK3rYsBk89BDD4U//uM/7iYBP3tqJYAJ9Oabb577XBLgwFR3xqNhymMGKtosNEOYOxXQgskUqH3jFK9fvz5ccskl41Sk0rIgRwGe4tKDR/gH4x3PP//88NnPftYBboTt4FlPhwQAuNtuuy3wnVT77Nb6dNRy9LUYe4BDRGp0wRtaOHzNrF692h34jv4aGtsSPP3008XYSK4TApogNDwExqRhupQJ85FHHimuM8ZtYf5TAPYwbQJ5LNKgMYGBbSDQwt6g4U8zUMcZhiS7pvGwPqNVVq43velN4V3velfxSSDGxXlwCbgE2kkAzRtKFhZemnl28xz30K8Exg7g1MiK1fCCN8X42DrqqKP6lYanNlUS2LVrV2BGlIIdX5YDQHQ+jMkC9BjfRcD0ythLrkN1UOwH9DAH6DjlKQDUMcSCQNbtVx+sFlDnx8dr/Ny0zpZEXqMK1rGvA9yoWsHznRYJ7LvvvkV/qG82SxFj42mp66jqMbresqLGgjfFKYiTdqUiGf9rxiXw7LPPhh/+8IeFFHg4A1hozYA3YrRoVoNmwYqTeHOMv9SQEqnGeAF0wB3mWbnkAPh0HetcjrdaPvZzzrZt23TIPK0eAInWmXD77beHI444IlxxxRVzx2oldkqs/WgV47EmVlMoaGJIgtyYoFW0wKu0BhmjHY3LOcj8Umkz/u2AAw4ovq2MjzgPLgGXQDcJCNhIJe4Lu6XsZ48lwNlmUePbGKAj8ID14BJISQBI4po555xzCrOpIAvAAqq4hoCoxx57rIAjIAfoAqQUACKAgv8ENMAOCzNY7SxW4K8KeCzcMZCfoPwoE5BWFmy6mHr333//sNdee807XJN75u2s2EAGcdi8eXMhC+CW9JhZSsCEzL2G/zZcBAB5FgDjdNpu0x45mtG26eecZx37OsDlSMyPcQmUS8A+t1knaJ/W6WPZN+qXt/JajO8/YwdwcSPH2jceLOzbc889C4/02No9uARiCWBqFPjYgfQcl3PNSEsGxLAAYPg8I8h0ynUIzNHxWC0Zx7BfXxxgnWChB9Mp5wFDFgRlIkUbRbmtNg/AQUvHFP04AJksuSH19YQyDR71p658BQIP69yj1Jd6USf8uqGpZB2QbRvIR7Jqm0Yf57lj3z6k6Gm4BBZq3PR8t7JxeLPSaLY+VgCnxiVmKYM3II4HBtqTnIdxM5H40dMgASYp5Jg/y+oKjLBUBeBK2jSr4QNuWDDh2pDSegFqXOcENF+CMIGjPZ91xn7y8sKAf2AJyNO5AKGW+Lwu24I9O16P9LgPKf/OnTuLGeHIg/zR1KFJo5xNNGqMH6xy8tulDk3Odce+TaTlx7oE6iWgZ3v9kX5EEwmMDcDZBhbACeJ4UEjzpnUenPEDpUnF/djplgAfU2YQ7SCDNFDkUQV7gjtrRtUYOZlRc8v5ox/9KJx33nkFGAF5um+4L+IAEBKAKt1T2idQjM9psi2tH/ehtI2UA5Pwo48+Wnwgnjrjb4+Fly2ATtAZ54X2UWPw4v+Gve2OfYctcc9vWiWgPkrxtNZzFPUaG4Cj8nrIEKOViBfBG/t561+7du0oZOZ5ToAEUh+qH1Wxq+BOZRLcsS3gE9zJjBpr9ABI7pU+YEzl6BpTFmtG5V4FNJl09MQTTxRwB+zxKbAY6Mapg3fHvl2vBD/fJeASGLQExgLgUuAmiBO08RBjYVvmMQZUe3AJpCSANqeJ+S6VxjD3MUlAk3LKgE+zVBmrxng0G9CsoQnDIe0wNNOAGaEOIFUuWyYBHUMgWOc+Xrx4caEptPBn6zfsdXfsO2yJe37TKgEsAATF01rPUdRrLABOFRfI8XCIwQ14Y7wNC+N/Vq1apdM8dgnMkwDXRxkE6UCuI7RCzOpkvBoTBAAjgANzHzMQ69JQWsOIceD7ta99rfjuLx0hGiyZQ8mf+wXTJZwyrasAACAASURBVFo67iN8JKKhK9PmpcoM9KIJJC1i0sfciVYtBkObt9LSCxbnq0xM0CANjkfmBMbUaVydNHSYXPn/m9/8ZiH/pUuXFuPhRtkG7ti3aC7/cQl0loDgTbESZDvep/88rpfAyAFO0GZjAZweCII3YkxjdPZnn312fe38iJmUQJ35lM9nsQAWaIaIcaLLNUgA7B5++OEC6DClNdUKAZB8KeSZZ54poEqNINNhUzjkeuezNADOkUcemSwPkAUsAVpA26233hpOPfXUSggV3DGzlKDvlCIPmWeBMfJFpgT86Qm+ih3mh3NYFARnMgUDmGjbmOSAvMkHmcuNCvc3ZWIbbeO9995b/M/x++23X3Fe07ZQWdrEcuz7hS98Ibhj3zYS9HNmXQIOZ4O9Anb3toPNpzZ1ARydvhYeHnTqdtm6dWs4/fTTiwdBbaJ+wExKgAkMPPRTAbDB/FgFIgAKsAVMfPvb364FIeXD8Zs2bSrOA6aAFbR5CjIdAofMkF2zZk0BMfo/FaMVo8wADzNQy77WoHPRdKFJBCK3b98+70sUOkYx2i3gUKbZlMwAQ+RBfQA8hi/ss88+Rd0EXkovjikLgBybT0mDMawynzJbFROqNXmTF/c9bcnxd911VwF2aOaOPvroOKuBbePYd926deGCCy4otLIDy8gTdglMoQSkYUvFU1jdoVdp5AAncFMMtFlw4+2fjp4H0gMPPFA8DNBCeHAJlEkAbREamzjcd999BbwBVSkToD1eICQoO+WUU+zfC9Y57vrrry9ApwyyACHBISbbG264oYBDNFFlAQhD68QxuNkAnnICn69hjJn9lFh8HvcUmj0LmfExdhuIA+jQUPI1CKsNo/4EgRfwpZm21FXBykAaOszDgKRmrDK5YdGiRYX2EMhkNvG1115bmI3Jf5hBjn0xX3/0ox8dZtael0tgKiQgeJuKyoxZJUYKcEAbQfAmzRuxBTne1n/84x8H3oarHkhjJlsvzogkAExYuKAYvAigaULLVAdvttgABJov0qwaj3XzzTcX8CZ3GjaNeJ380QDiGBioBIbKAtonwIlw1VVXhc9//vNlh87bD/AJqub9YTYw85J2FUCaw4tVtGmMGcTsumLFirm/JRvFc3+YFcCahXubNAh07sAe2jzgj/jBBx8s2op+QeZT6oJ59tBDDzUpDmdVjn0/8IEPFO02nFw9F5fAZEuAISTLli2bG+NWBXL856G5BEYGcII3ihwDnIU3OndMSO9///vdaW/z9p25MzA5AmsxwAkA2mhwAAfSLAukDZCUad7KzgN2gKgqgCNtTItopwjWHFmWLvu5h+pmadPB1h2TyoNxdrxUWYBLHcc+5IYWke+sokkHFrnf1ZkjNyZk8GJGPbnfATkCgIvzY4ZNENDoWTNrsXMIP3Lse+WVV4bzzz9/CDl6Fi6ByZeAXj51rwvS4u3Jr+noajAygKPKAjditG6KefjQkdP504HT4P7FhdFdJJOUc5n7ELRobeCNutdp7ICZJlosyZPysABpKc0VdeE+4Jhdu3YVp6XGqSk9GwN8ZZ/G0nFou3LNpzqHmHtVLk/s/nidet14443FfY1JF61jHEgLiPv+979fjIM79thj52SBTBjzhqn3zjvvDEwoaSPnOM8223LsixNlANaDS8AlUC4BhkXwvWb6Tp7figVv5Wf6P00k8Lyr9iZn9HxsDHGx9g1TzWtf+9qec/XkplUCgFrKmz+mO8ZftQkARgqwlFaXtLney9IG4KRxA7YIOeDEcYBf1WepgKLctFRPxbxY1YEfZWdMILCD1kz1UBqK6dgx4zKpg8klaNvjgEaOtou1qvFxg9yWY1/q5MEl4BKolwD9i+CNo2N4Y9tDNwmMBOCANgUBHG/iWniosc5DC/MJPq08uARyJABMpeAC81sb7Q3XIibUqnO7pl1WL2BUbjnQwDX58gj3VQpklRdyaquRBA6ZOVoVmBwBmOVCFyBHu/G1BjR3NrBdp020xw9iHRDFfPqlL31pEMl7mi6BqZMA/YQ0b4qpZAxyU1fxIVZoJABH/QRudl0AR8yDE7MJvqzajNMZogw9qzGSAGCSAhfGUwmGmhQXbVMqPZvGoNKmLiozGjPMkLmhTmuIew6lnZumjkMmdWDGTFVNvtB5dTGdPG/t8VcmcE7cpO51+bT9H8e+69evDxs3bmybhJ/nEpgJCTADnme8YM3GCEDaN8UzIZQBVHJkAKe60MgEAR3gpoWHzChmnalsHk+eBNDWxAPd2YcJDkBoGoAVzHtlYZBpA4bS/DEWNNeFCGXGZKlzU2XHtUcbE6ruzSqAAzbJv428U1CJCbUOolN17Hufdezbd9qenktgmiSAE25c8NAHsFiAE7TF8TTVf1h1af5E67FkgjareWOftnmA5Q7a7rFYntSESgCYSml9GI+lzqJp1YChKvPdINPGNKtxe/fcc09lOWy9gKw6jRUvR21MqKSdMlHb/AGutvJOTb6gXauA0eY96HVcGV1++eWFT8pB5+XpuwQmUQLcw/h1ZAyuAE4x/ULbvmESZTHoMo8U4FS5FMjxgMlxU6A0PHYJYHJMzRBkOnsbbRMSZRxHCgol7UGlLc2e8sHdSK4Wqk5rCHQCb20ALgVYKqNitIVV2j8dl4qRdwxr1Cfelzp3GPusY99h5Od5uAQmTQLMyl+yZEkBanXat0mr27iVd6QAJ3CzsbRvjHvJcYo6bgL18oxOApgF8SkWByYAtIEV0gEeYpOsTX9QaQOjelNlSj4hdyxoHWQBcF0Aq04Dx8tXm/Q19tXOyi3Tqto2GPb6O97xjvCxj32s8FM37Lw9P5fAuEuA8W/4xJS2rQzixr0ek1C+kQCcgA0BaZ1Y8EbMIOy6mW6TIGAv4/AkgGPalMmdT1C1AQocz9a9RAwq7dQYtVyA416q0tbZ2a1NWwcTalXapAd0tZE32rfYVxwAndKqNi13n8evWrUq8HUGHPt6cAm4BOZLAGsB9zEvzRbe7FF6OVVs//P1fAkMHeB4uChonThe2pq8lLbHsycBoD9lasMdTVugqAO4QaUNjKrMjCc57bTTshsU8LRarPhEzL6pyQLxcalttHtVaQNcgFgbjSfnxvLGHFsHjKlyDnofH7fHpQjXnAeXgEtgtwTQwHHPSgNHbEFO0KZ495m+1lQCQwc4FTCGN6t94y0fVwJVjkiVjscuASTAw5/B8zFcaEZkGymRZpW5cJBpo9kTBGHyjMGmrD45WsO2fuuQR93sVrRvbTVmlD2GNQC5agximRwGvf/www8vsnDHvoOWtKc/SRJguAfaNwtvAjXtm6T6jHtZhwpwsZbNQpvWgTceMJh5Fi1aNO7y8/KNiQQAh9RYNTuWrGlR0SSlTLJKZ1BpA0pWs8cb7YEHHqhsK2POrYM9O7u1MrHoT+7Nutmt3LfqsKPTazfpH+KXNiC5CqJrEx3QAUDqhRde6I59ByRfT3ZyJcCsfWnciLWoX3CQ669thwpwKrYFOYEbMQ8IYt7EFy9e3HrmoPLxeHYkAEylNDVtB9QjOWAo1uhZiQ4qbWDUDiFgVleuVqsOOgEimWZtXXLWkUdqkog9l3aQ6xO7P2c95XyYvqBteXPy7HLMCSec4I59uwjQz51aCTikDadphwZwMplSrRTACd4UD6f6nsu0SADNT2x+o26pyQA5deY6ZEmNqdP5g0obCJL5lLzw/B9rplSGOAbgqo7FzNxl/FuVRpKydDHPUq4Y1so0q3G9R7Htjn1HIXXPc5wlgOWAflMAl4rHufyTVrahARyCAdzQsAngpH3Tw1Ix+z24BJpIADBJgQtaMgtDuWlyLdaZ7gaVtp0lyoQDgtXIVdWBDrQOOmNIqkrP/sd9W5U2x7b9rBjyjgEcjd+4hzPPPNMd+457I3n5hiYB+i5p6QVvQ8t8BjMaCsAJ2JCvIE6wZmO0ByzYzPmotQeXQK4EMA3G5s5BOqwdZNposQRszPok1Gm+OIZ7CS1WFWTZ2a25suU4DW2IZWzTQFvW5yfLxln7pnrvvffegRmpX/va17TLY5fAzEqAbyDz/LbBQc5Ko9/1+ZLuN+0iNYBNQdo3YoEbwMabNosA7vHHHw+rV6/WaR67BColIMe0sWZJ+ytPLvmTa7FKAzfItK0Wizfa4447rqSU83dzT1UBFkfH5tn5KZRvIY+6yRHIhM66TeD+jz9Zhla17Xi6NmVoe4479m0rOT9v2iTAyycTnRzahtOyAwc4qiGtm2IAThAnaCOmE+cjuGjf+OagB5dAjgTQ1KTAxZoic9KxxwBDsUnP/j+otIEgTL56i2Vgf+5s7LovMOglKQZdW6+ydc6NnezGx/b9WTHaNYa6OM9x2HbHvuPQCl6GcZCAFDbEWqdcdn0cyjktZRgowKnR1JgCtzJ4u+uuuwot3J//+Z/PmZCmRdBej8FJAHBIwcUgHdYOKm2gxQLWtm3biu8K5kgPyKrSGpJ27mzWOD9esKqAluP7/qwYn9Orc1sSl3NU2+7Yd1SS93zHTQLxc1/b41bOaSjPQAEOAQneiAVw0rpJI4CrADp/nPf+2Z/9WfY3H6ehAbwO3SXAZAK+vReHLjMi6xzWDirtGAzJp2pMm60z91gVZCGntiZONJKpSSI2/74/K4YJtao+Nu9Rr7tj31G3gOc/DhIQrNnnfrw+DuWcljIMDODiRhO82bFvMpsS33PPPeHcc891zdu0XFlDrAcP+pQPOOCnzRgqrtE6zc+g0gayrAbuuuuuC0uXLs2SJjNQU86MdTJw2EYenJ/y0aZ0FVvnw9qXE3P/p8bXoTHMhdecfAZ5jDv2HaR0Pe1JkQCTqBjKET//tU09WPfQjwQGBnAqnhqOuMx0ipmID9cvW7ZMp3nsEsiWAA/6GFxiU2R2Yi848NVU+NR5g0wbMJSfNkyIuQFtNlrDqkDaFg6rjrX/AbQpH232GGYBa+as3Z+zTtlTs2zZPykARz3dsW9Oa/sx0yyB/fffvwA4nvV65mtdLED9WffQXQIDATg1lGKBGw8Cad3onDGdohV48MEHw1lnndW9Np7CzEkg5T4EITDbUiDUVCi8QaaAQukMMm2r2RPA4aqiLnA/pcYB2vPs7Fa7v26dtFOTROx5bWe3kgZ9QmyeBZJTWlWb57itu2PfcWsRL8+wJcB9zHAonvU89+0iHhC8aXvYZZym/HoHODUOQmLdNqAAzkIcs06Zcfqyl71smuTqdRmSBMrMp3wloY22SddtleZnUGkDo1aLBhQtX748S5LcW3UTGOzs1qxEXzgIgKtKm8Mw/bYFZtKP5c2+thMumtSt72PdsW/fEvX0JkkCjEXGDRjBQpxYQNBmOWGS6jduZe0d4KigbSQ1nLRwwJsAbseOHcUDa82aNeMmFy/PhEjgpz/9aRIuBumwdlBpA6N2kgGgiIuKnFCnNcQ9SRfASk0SseXq+7NitOukTGCwcpBj38svv9zu9nWXwExIAEXMUUcdFR599NE55Y0YQFyAIFj30F0CAwE4NZAaTPAGkUsLh3lo69at4W1ve1v3WngKMysBzIIpc2dbkx4vF6kB9VbAg0obaLFaQ/wh1oGTykW5Yy2W/iNmqELbMWrcx3XmTDRwfX6yjAkRdXna+o3TOo59L7300uKzYuNULi+LS2AYEjj22GPDww8/PAdwssKJBwRviodRpmnNYyAAp4ZSw1mAk/Zt06ZN4ZRTTkk+fKdV2F6v/iXAWKl4fBbmN64zC0O5OXNu1ViyQaYdz0DFLUc8OSNVD91fsRzssW0BizTqZrfK+XAbgCtzPgxw1pltbf3Gad0d+45Ta3hZhi0BtND0BbyASmljWUB8QLns+rDLOQ359QpwtjG0rocLD1TB29133108mNx0Og2X0OjqAEyxxJonoK7t+Cmu0SrT3aDTttB51VVXzX0YukrKlLkKOjm37QQGJhrZcXmpcgBwttypY8r2UfYUqLG/bZpleQ1zP459161bV7hfGWa+npdLYBwkcNpppwW+i5oCN7EBsYduEugV4FQUNZBtPIEcRL5ly5bw9re/XYd77BJoJQFgKqWhwsRpx5I1SRxwiGdE2vMHlbY0e9JioZki1METx3BundkXLVobH3A5cDiIz4oh51Tb2rYY53Uc+/I95+uvv36ci+llcwkMRAIHH3xwYKww/RjPfphAsYNbfyLvFeDUMAI4xVKjEjP2jTFLbcfj9Fd1T2nSJQA4pLRlXYAC0Ik1elZOXdMuM3PGmj1MiITU+D5bHtbRkqXkoOPi2a3anxMDhykNmT2XsradIEEHH8uEPCc9yLHvxRdfPOlV8fK7BFpJAIjDjAoHCN5ISFxA7KGbBHoDODWGGocGY7Hwxts8D5Ncz/LdquZnT7sE0NKk4AJfam1eELhWAZEqgOuadplZEDC0WkNAkpBTD+65QWoN6yCyrYNgQA0NYyyTMs3qpF3POPa9/fbbw8aNGyet6F5el0BnCeCcnz5NTKA4lTD/eWgugV4ATsJXAxEL4BQL5HCVQMN6cAl0lQAAl9I8tR3vBVDE2qC4jINKm7pYEyfOMNeuXRtnn9yu+8xVPDkimUjJzhyZWOfDJckkd5N26pNl9BFWFsmTJ2CnHPsyI9WDS2BWJWC5QKwwq7Lou969AByFso0EtAniBG6K8Q+zZMmSvuvh6c2gBNDUxMDFPsaRvehFzS9tgCKl0ZNoB5k2YGgDmuoU3NhjWKfMaA1jLZY9rq2PNmnQqzSSlLMqb1uOeJ0+IfXJMuT8u7/7u/HhE7mNY9/169eHBx54YCLL74V2CbSVAJMYNKbXpiFWsPt8vZ0Emj/lonzUGIpjjRudNKZTFt7UGfOS82mgKBvfdAnMkwAPefyExfAwSIe1g0wbUyL3ylNPPVUsvOgAkwASAMa9w8J4NxbAjcA5KS2kFZbA0+7LWc+ZwIC2rMv4t5R5Fo1hDrzm1GHUx7hj31G3gOc/KgnQX3EfwwYeBiOBf9c2WTVKDG56a7fgJoDDLMTMLA8uga4SAKZSrkKAHV4SGFgP3HHtEUsjpzFlvBnGb4dcy1XOY0lT5zctf13afE7Ohr/+678OH/jABwqv5phXqS+mUmCMe4ttjZM76KCD7Knz1jkOGTDGjs4U8EMWAl8rm3knhlDIsU4ThryVVnx+3TYySWn36iZl1KU7bv/j2Pewww4LF154Ya27l3Eru5fHJdBWAtzfjIGzY3tJK95um76fF0JrgEN4NJBi1gVvxII2G/MgOvDAA13uLoHOEgCmXvnKVy5Ih+uLBdCRloovHAAFOMYV0AAeXJsEQJDrFyCqcl1BesyiZgH+0JqRhoUgAR6dlAWburTjitx5551h2bJlRXmqysR51KksAEjnnHNOIQtkQuA+pDzIBA0fQEhA+0dg/Bll55gVK1YU+8p+BvFZMcqZAruyMoz7fuvY9/zzzx/34nr5XAK9SIDPanEvM8FKICd4U9xLRjOcSCuA42EXL9Z0aqGNhx4L+3bu3Bn22WefGRa3V70vCaDNrfrQux0bVwdAQAwBc2BVOOKIIwILAWgSOAGIXN/SkGkdACIARE2AROOl6spdJB5CVtoAmdJTrPMVA3oEC7915QYG65wIK30bI6My33X0F3X52rQmYR3HvjguP++885Ka40mog5fRJdBEAvhC/OIXv1j00wK4svMd6MokU72/EcABbQoCOIEbHbLMpoI2jdVh+8knnyxIHCr34BLoKgFgqW7sV24eAhrFOecBGIKMuvPaDvRvA0Y5Za87xsJv1bF6MbOaxqrj7X+cm6ofsqoyY9s0Jmn9uOOOm3Pse9ZZZ01S0b2sLoFWEti+fXt41ateVWjfGLYhiLNxq4T9pDkJNAI4zhLEEQveADfBGyAngCMG4tiHVuH000+fy9hXXAJlErjvvvsKba20Rtz8aLEYjyVY4NrLBY2yfIa1vw7w4nLwpZL3vve98e6x20ZTh8mYe5zAZAaNNawrLH1CGYCnxjbWpTcJ/zMGDse+DnCT0Fpexi4SYJjJTTfdVHxxKQVvXdL2c3dLIBvgpHHjVB6eArgyeKNTZ2EmCuN5DjnkkIBnZg8ugToJPP7448XYKzQxjHXjYY85km/oStXOy8EVV1xRJAU4YI5jXBr/A0yCPtKwGh2gTxBYV45R/c9YvbrJA6Mqm80XOTJTlvucfoC2UtCECdpEs1Q5XoDH8Snnw5ijy8BOaU9q/IY3vCGcffbZhWNfNHIeXALTKgFewnnm84LHPa/Fat/Ul0+rDIZRr2yAU2EEcgI3Ymnc6MhZZxYgC+aQDRs2hFNOOaUY/6E0PHYJlEmA64e3NwbwE1J+wuJzGYvGg5/AOhMUeMngGgT8WIAIOgzgyAZAif2ABoAB4An+OO4Vr3iFPbwwm8p0Ou+PHjfQwB199NE9pjiYpJDV6173ugWJ04Zo5wipCRO0EW2S0qDywmeBe0HiE7wDzeJll10WcOzrADfBDelFr5XAvffeW4x9E7gR088SEwRvxFqvTdQPWCCBLIATtEnrxsMRcEMzwkKHLY0bMZ3z/fffXyzvete75h7GC3L3HS6BSAJAPxoYrqlcTRlAleMcWkDHNcuEBbaBPa5l1gELC3hc59u2bStKKABk7B3H24D2T/8DggTBIOsWCNmOobA4wfww3OCkk04yeyZrlbrLbKw4twYA3zRPdMKlyLp164ohJYwP8uASmDYJ8AKOH8tjjz22eDGmTxTIpSBu2uo/zPrUAlwZvJUBHA9C6BtzCh1VylHnMCvoeU2WBJipDLxdffXVcwVHc4HLDiBJkwcYE8c+a26rM4+izpebj7ovLpA5kKeXFDRDBIAvDry0xAHQszCo/y0Uso8OjXopcF/huf81r3nNPJOk/o9jzk3N5qTTtG+2AimOZ7Gm5UFrFOMyV20j71xwr0pnXP9j4gYzUi+//PJwySWXjGsxvVwugVYS4Pn/jW98I+CbUtBGTF+khYRt39QqIz+pkMDuJ0dCIII3/tI6DyCrgeNhazVw99xzT6HJ+MhHPjL3sEwk7btcAkkJAEivfvWr55lO0coRgBv8jvGQx0SH2ZSZTgQ6BJnt2AbuAD+BjOCO/cCfBT+rLeNcmfYUFxlEP3RUaJqlzeNvII9t9gNwbYLGkaGFynn5QSYsVYH7VT7edBz3LPuBOcpLYEwhJmX2oSVkHBtykux07iBjNHCCzUHmM8q0maBywAEHuGPfUTaC5z0QCdB/8Qmt17/+9XMAR98smLMQN5ACzFiilQAnWVho42HBQ4pF4MbDjIXxbjww6aCk6VAaHrsEciQAhMUaIftATznvjdNFcwYIYhKVdowvERC4TtnHdUxnAqywreM4hn3SarFOEMSwzWIhUOUltmXlPEFlrjaP8hFy4I3juN9Y6gLgWhcYb8h9zf2OJpR1XtyAUeqMDNBcAncCu7o0m/xPe81CwHR6xhlnhCuvvDK4Y99ZaPHZqSMvg2j3BWw2Frwpnh2pDK6mpQAnjZtiOnW97Vt448HHw+lHP/pR8fB6+9vf7vA2uPaa6pSlza3SfOUIwJoHdXw8A5prmOuWIMiS5gxgYRyHDZokoX2cL80XcEOnxHaZ5s3OKlWnprRkIuZe4zugmE8BRILuOR07yJhyKd8Y+CgH7QMIA3dsc+8DdCx885N2E8y2KScAFwNwm3Qm4Rx37DsJreRlbCoB+ge9ZAvU4lhpar+2PW4ugSTA8SBREMARxxDHQ4xOHHjD5PO2t71Np3nsEmgsAUBqWA9waZQoZBUwCu7QjAF4XPMaDyeTaV1FuW84rywAi5gOCZiI0b4BcjbQ2ekeFDCieQO6CIMeNyZNnwU76sX9T6f9xBNPFPLhfzpwXIRQjyrZ2vqxDlALIOP/pm3bHftOW4t6fZAAfSR9Av2SAI3Yw2AkkAQ4sqoCN5lOaSi9lb/vfe8bTAk91ZmRAGMnUt75RymAHAAR3FFOAZ/gTsBXBSb2P2ZvYWKTCXeUda/Lm04aYLNQR3+ADNBYUnf6EUBur732KqCuSp6cZzWVdflP+v/u2HfSW9DLH0uALy7tueee8e552wK7eTt9o5UEFgCcwI3UeMPWgsmEDpmFTloQt3nz5qKD9k9ktZK/n2QkgNZp3333NXsmY9XObq0DFGok4BPcsU/AR9zFDDlqiaEJZJEvN/oN3spxx8Ls9Cqgo/0XLVo06ioMLX937Ds0UXtGQ5IAXFAX6AM89COBBQCnZAVyFuBiiHvsscfCI488Et75znfqNI9dAq0lgBnRzg5tndCYnlgFdyoyjnH/63/9r4XvxFibBwiVjbHT+YOO6RfoE2QiqcsP0ytAKigtAzrNuq17e6/Lb5L+d8e+k9RaXtYcCezYsaN4CaePEEMo5nzWbcy6m1gLkbT6mQdwEjSxbQDWY3j78Y9/XJhK3NdbK7n7SZEEeHNjEHsO5ESnTs3mgw8+WNRFWm6gB21WyrGt4C53dmtfQqKztbNe6RtYGE7Bf5QdkzBmVcrOfhtioKPdgVI+vcOxPAAYQ4cmDpgjjWkO7th3mlt3NuvGi4llCbs+mxIZXK3nAVycjQU3ARwdLuNbfv7znxffNs11dxCn7dsuASsBgGS84e2/hR/+l1PDH15y5wvF3iOc/Hc/DNf/6fLw/DQCU5tf7wp3fvsfwz9+4y/CBV/69+F/+cEN4ZMn/p45YPcqPu4wLTIRgHuKwCxPFiYrcL8BNnSKixcvLr4RC9hJVop3p7h7zZpqNeNWptq+tHlo4lgoqwJlxokx+QvscD3CIhcDHCunyCoT+ziX/UzmoIyMBWT8HDDHBBeOHbdxkqp3m9gd+7aRmp8zrhKAB+64447iU4DiB2IphVjXGDjXvHVvxd29rknLChuBs/BmLc0Ab9FoSybhe42mWr46xhIAYHLMp3zoHrgBdniYK6DxAWx44A9Ce/Prp24OV/yD4I1c14Q/XrNkAbz9etfG8KkLeNoQbgAAIABJREFUPxAuDe8K/8e7vh7+3y++KrxEhTQxoHLLLbcU4AaE4YMNcFm+fHlyJi4gxExPPlF36KGHFi9PJrnkqh2bh6sP8uRFjIkS5AUg2YA8aQMmEnAcQZBlj6tbR2vGonFw5Et/gXZNQAeU0U50+DKv0r8INKVhBOSAXOpOGmj3TjjhhOK8unJMyv9y7PvhD3+4cMcyKeX2croEYgmcffbZ4Utf+lIxq557VfxAf2I1cax76C6BBQAXC5kGQPiCOGaZbNy4sfhAvWvfujeAp/C8BBj/huuJssB1d9tttxXXIQ98gM1OnAESuHZ58KMhBo4OOeSQsHLlyrIka/fvhsWd4b6rPht++p7/M/zfB760yBvI2evfHg+//OWiOQAJz/0k/NU7PhI2n/634c6PHBf2WKCa253lD3/4wwJWMBeiwSIAS6tWrdp9kFmjM2Th6whMHCLEvu3M4QtWt2zZElgAK7R5yA6os4H/AGO+2gDIHXPMMQUsckwXbV4K6NROAB3/A7DStLEtzaI1H/ONWOrw0EMPTRXAybHvNddc44597QXp6xMngWXLloWTTz65uEfpX2AH8QMxyh/6O/pqmEJ9n2vj2jX1HMBZcCMpCdgSNA0AvL3//e/3N8V28vazSiQAwKF9SgXBB1BhXVbYY3noE4AcND9cq2h8gLBTTz210VgqNFR33XXXblj89c6w7Xu3hGsXLQorfvuosOLQFeF3/uVfwtatWwtzAeVeuXKfcN/ffiL81b4fDbfXwBvp4/uNDk4dGGVHy4SZsSpQT0yJmF35HJPqXXXOrbfeWkAZ5jrkUxaQLQtaTDRh1157bfFB6qVLlxbOufV1lRj8lJ7VoGlsnjXVSptHmVmsho4ZqLt27ZozmwJ0OAcmVpD2bsmSJdo1NbEc+zImbppMxFPTQF6RbAmsXr068DLCiwl9Bn0xCywRc0Z2on5gUgJzAGf/tYK2AMebOVoSOlYPLoE+JYBGJuXEF/MZAAc05MCKysSbHhpiwIAB8kcccYT+qoyBHbR9wOLzsPOv4cnvfCd8Gb+6P/tyuPSeL4ew6pzwiT9/e3jN3v+x6JgAsifv+GL4zAX/Gs79u/8evvyeQ8IFX9oS9njnX4Uvfuy88PpXvWxenhxvx4LpT8aNWY2T9scxcgC0ymRmj6fu3LcxLNpj4nWgEohDhmg90RLKzBkfa7etc2SOp+0AczpvAlo/ys1xyJZ66D/BHcDHOj4BgW80f5QdiGQ/ZtTUdWLLMYnrcuyLU/SzzjprEqvgZXYJFBIA2o4//vjCEkI/wIsdfYlAjv4FjRsxQKfgWjhJIj9eAHASqEjZAhxvyIy/8eAS6FMCPOhlMovTRdPEg78JvNk0ADFmd+YAnGAHQNitGfsfwt5v/N/CP77x/ws/23FHuO2mb4ZLv3xF+F//8j+Ev/3fzw4H/M5vht/7vZeFrT+6M3z/kD3COYeeFM7903PDf/7MlvD3H3p7OPn9Idzx7Y+EI16y254KiFjzr8p71VVXhc9//vPa7CXevn17MaZtd33yk6XzxTR9zz33FJq4nDM5/s477wy4GKLTBtjiIHM3MSDHm3rcr0ibR4xmEgjlQ9mYf9teC3E5xm1bjn3xD0c9PbgEJlUCK1asCOvXry+UPdzDvLQppi9igS2ANge39q28+6li0rDwxm5BnJ1pZg73VZdAJwlU+X9jckMKAnIz1Jtf3fHABGPLAL407PxWePkBx4Q3vu+i8LW/endYdc+N4ab7NYniV+Fff/7fwu8uPTAcs2d4fmLDSw4O7/7Y/xxO/tGl4aNXPxB+/UIByActUwwhaJoIuXUljTLoVV3R0FGXKrOpji2LAQnaJyeQ37e+9a1Ce4b2kwVNXrxgIkSrhjYfSMTU/e1vf7uAReUjbR7HHXbYYeHEE08s2ua1r32tDpm6GHC7/fbbC/P91FXOKzRTEmAsHP0BVgVp3uAI1sUT4gwbz5SQeqjsPIBDkDawjbAlYB6GHlwCfUugbAYqHQDXXBqo8krB9ZsT0AICTzFYLTz3t8LLDzszvPPtIXzv9kfCf+eAX/8/YddDPwu/8Vv/Pjyza9fcKS9admz445ND2Lzj6fDcC3upU0q7gnaJkDMxCAgEcOrKCnj1cc/mviHfdNNNRVsBaLn5InMgjbfzG264YU52qRVkB/BNa+C6uOyyy8Kll146rVX0es2QBBgLhyaee1uLhTlxheUOuz5Dompd1QLgJEilYre1TswMtaqZgjrfY5dAEwkw4D11XQEgXbW+dBxogOoCAJWvqfqd8Pt7Lwr77v3yUBi6XvQfwh7LXh5+/sgz4WcLePF/DIccsOecKxFgNQVEaNQImihQVV4ADk1hXWA2bh3k1aWBZjBHfhqv1vZbppzH+DaGaZQF6j3NAEe9mcSA6QmztQeXwCRLgHFwjF+mb+PetRDHurRxljEmub6jKPs8DRwFQJgKWpeAefDkmniUhscugToJlI2BY6xYDtBUpU/HkTOrD3DIh51fhX9+et/w9uP3fsEP3EvDq1avDr/72EPhsWd/Y3dxnns67Nh8+Dx/cWWgSP5r167dfW7FGh2fnZ1ZdigTOPLrlE4F+aXgOj4aWOzaNwBntHkqUI5ZCFyrzEi98sorZ6G6XscplgDjfIE4xiDTZwnapIUTwMmkiijEGlMsll6rtgDglHoMb2zTwaJB8OAS6EsCMoulQINrLbW/Sd64nsgBkFJz469/FnZsvC3s+NkLAPHrn4XtX/1quOeIk8OhL9bt86Lw4kPfHM47bGu4+P/aGO5/7tch/HpX+MnfXRHu+U//ObztVbsH8uMsN1UnIBYfbzmBOuWYWvsAOO77HG1fH3nRwZdpQblOpnH2aaq9ceyLGZXZ0B5cApMsAauFkwbOgpzgjX5Gw11YZ/FQLwE9gZJHxoLsMhYpmYHvnHkJAE5lgMBDOwU7TYRGp1CWvtLBdEenks7r38Ivt389fOAtJ4fXve5Pw1989b7wL8e8PbznsN+b/xWGF70yrHrHh8MXDr8tnPjS3wy/8ZvvDl//j+8PX/hPR82ZT8kPgEtBChqsHBcipIE2qm4CA3ViHFruWDTJIo4xf+SA0zDaKmV6jss7DdvWse801MfrMLsSkBYOJ9z0W1oEcYqtNk7c4RBXf90scCNSdgrCxKXDGWecUXaI73cJNJYA4MIg9jgAIFxzwwAQ8io1/73o98Jh770k/ON74xLO36Zj+u3/aUk49bw/D0//l3+Y/+cLW5ookfqTMU85rk7o6ACZurFgAFXX8YNo+nLGvw2jrbhO6qA1JddJ3eeOfSe15bzcsQTQwn3iE58I+++/f9Gf03+xoBDSOuewTogVRdofp+vbL3g8yBEEY1MOOuigpP+qnPP9GJdASgJMjOFD5XHoQ6OTCyA4je0KOwBc3Vg7tI1x56R6843THFMv+eSADGPthjV+cBiwSFumZu9KftMW49iXl2Uc+3pwCUyyBKSFYyycNHCK0cCVaeGos7Rxk1z/QZa90oRq6ZiHAW/BHlwCfUoArVRKm1Q22L9J3nQSORqkPsZvkVdKk2jLy5i+lPlUY51Szn3t+ayTTw7oNZuUEefy/HbuWLthwCL+pFLXSbrk07H3ne98Z7j44ovDr371q+mokNdiZiXA91H5Ao1mpArgiC3E2TFx1oRq12dWiImKlwKc1JaCOAZY01F7cAn0JQFp2VIPZgCkq/k0F0DQAqbHv+XXlE4opUm0KdTlkwNwuPXIcdWBtq9rnTDX1kEp9esLFqvGKuJqpup/K+dpWcexL4Hv8npwCUyyBFAA6SP39GEs9M9aBHHEgjhiq4FziFt4BRQAJ1jjbwGbjTH7lJl+Fibpe1wCeRJg7FSZObAPAOGGr9NW8QbIW2FX2CGNFIhaSTCBIWWq5c30tNNOs4eWrlOnOpBBrnSEXQGYTrasfWwBaauueQGLVW1FfWYtYDJGC+eOfWet5aezvjj2pa9jOJYgzoJcShsngHN4S18Tcxo4AZs9TODGf6zToTz77LP2EF93CbSWwDPPPJP0Z6YbuStUYXqqAxC0gH2MFQPMqgBO2sbUixDAlWPq5Y2UN9a6OpFe6aSMzNaiDUijrg0Ei3XH1WVbB4tAYs5s2Lp8Ju1/d+w7aS3m5S2TgLRwfJ8Zx98Mn6GfoU9Tn8+LmmakAm3SwilNBzlJ4vl4DuDsbsGcYoHckiVLig9L22N93SXQVgIAXMqfGbAzLABhXFof2qM6rRgAktK+ITs+N3PggQfWipHOLcekOaxJGRR4mLBYK6ApPICJMRdddJE79p3Ctp3FKq1ZsyaccMIJRb+Pa5Hvf//7CyAOgLMQJy3cLMqrrs4LAM5CmzRvPOBYMHHwvUMPLoE+JACopbRJQFUZ7OTmyxtd7lix1MSC3Hw4jrzqvoxQ5ZR4586dWdmhpcqpE2+2XTVi1CkF13FBhwGLXCcvfvGL46xnZvstb3mLO/admdae/ooeeeSR4aSTTgof+tCHCqvenXfeWaqFkwbOIS59XSwAOA6zECftG/HSpUuLLzFo1lw6Sd/rEqiXAJobQsrsyGSZPgAkx+RWN7Ggviah6HzqYKfqs2AbN24s7q26vICqqnFiOp+8usoPbV9OXsOYwUu9Z8mFiNpRMY59+TrDNddco10euwSmQgLnnntuMS4OpuA+p9+JzahuNi1v6jmAE7QRE7QtgJMW7pBDDinUnuVJ+j8ugXoJlGnfOBOo6qqBoxOogyryKvsyQn0Ndh9Bx5PSJO4+IgRAJ1UnjSnNGYdHneo0UZSlr0kZdXWifn0AMPWqmsHLDFT1S1ams7T+7ne/O6xbt66Q9yzV2+s63RJg5v373ve+sGnTpsAzwcIb2rdYA+cwN/96mAM47Ra4EVt44+HDcvDBB4dHHnnEv9MngXncSgJo2VKObwUgXc2aQEwdgFR9GSG3UozV4F5JaRKVBh0TL0DcT3EQwNXBJh0ZsqnTKpJXV20V+XCv12nx1FZ1x8V1jrfr2grIrqt3nOa0bbtj32lrUa+PJLD33nuH008/vXCXI4DTOLiU6dQhTpIr+RKDIM4CHA8gQRzTgT/3uc+FLVu27E7J11wCDSQAPL3iFa9YcAYAkqONWnCi2cHNz7VaBVUczsSCFFSZpGpXgZg6UKyawMDYOB7OdYGOLWemKulx/3YJ1KluUgbpDwsWmaXWdVJLF3mMy7nu2HdcWsLL0bcEsOzJ0a+dwBBr4PrOd9LTW6ASELwpTkHcsmXLiu82fuELX3BN3KRfASMqP5qnFCRgauRloUvIBZC+JkvUzQytGv+Gq5NFixbVVpc6pTSW8YloNrtqL+lA6yZlkG8fsEheqevA1gvYz5m8Yc+ZxnV37DuNrep1QgK8tGPd415302n+NTEP4OybO+uCN8XSwBEvXrw4HHPMMT4eLl/WfuQLEgBGGNeU0lz1ASCknwMgmOa6avuYGZrSJNrGBnTKzIzbtm0LuOepC2ihciYVUKeyvOry0P/kVWfS5Vg0i11hMaetMJl0rZPqNsmxO/ad5NbzstdJAIsJwylkNpWpNI7r0pml/+cBnCou7ZtiAE6TGGRKpUMF4rZu3arTPHYJZEkA01vZmKY+BsUDVTkA0sdkCTqXOg0S9S0DEICrztSLUHkrrcuH40ivD6hKwXXcuH20VQ4soqUsk19cpmnfdse+097Cs1s/TKhYGVJmU4e49HWxAODKtHACOGnh6FDvvvvu4vtm6aR9r0sgLQE0UmUw0geAMF6sDkAEVbyctA10NABIVV64S6HzKTMLX3fddVnaQt5My6BX5R/WpAzl10dboYGrkh95lWlrVY5Zit2x7yy19mzVFesLY13pL+NltiSRX9vk00uaN5LRutXCCeKwWePDCsF7cAnkSoDrJTVurC8AYVxVnVaramJBbj0AxbpxaQLFVJpoCgl1A/SBxJwJDMOalEGZ+2or+peqtgLwPMyXgDv2nS8P35oOCWA10QuvAG46aja4WiQBTtlZeNM4OAtyDCxesWJFuPrqq4uP0+o8j10CVRIANFIaOPZzzXUJPPBTcBin+dOf/rSzWQ4AqwO4qjF9evFhGn1VoE45ANfXpIycsXbDgkUAOMccXiW/afvPHftOW4t6fZAA/TYvqzYAcnFI7YuPmZXtLICzIGdNqZhRV65cWUx2+N73vjcrMvN6dpQAb1kpc+AwvPqr6OTVdQJDDizu2rWr1HwKBC1fvlxFKo3R9OVADGPSutYJKM2Z8dkXLObAtnfYCy8Nd+y7UCa+ZzokIO2b7nvF01G7fmtRCnBWE8K6NHAW4GRKPeqoo4pvpMok1G8RPbVpkgCmt7IxT30ACFBVNysUefbhrgSwSmkSbXs999xzpZo+3IusWrXKHp5cxyScoxVjTBr3ZJdAZ1lXJ9Lvo63oL+raCsit+/pEl/pO6rly7HvttddOahW83C6BbAk4xKVFVQpwOlzatxTEAXM8MJjejiuEzZs36zSPXQJJCfBALgMEoKArgOT4FcMspxeRZCEzdwKLKU2iTud/Jh+UzaB84oknagGGtJiFWQa9yktj7XjRahtyJmUo7WHBItral7zkJcrWYyMBHPt++tOfLq4Ps9tXXQITKwFATUtcCUGcVS7Fx8zadmVvbwVlAU7j4Hgw8cAlPuKII8JVV13lExpm7QpqWF9MbylzIACC+4thAAhQ0BUUcyYWUKeqCQpo56oAENECgaRRBoESP2DctU5oFHNMmsOERRw+O8CplefHcuy7YcOG+X/4lktgAiXASzVBoFYFcjpmAqvZa5ErAY6cADe7CN6kweChwYJWZc2aNeHv//7vfUJDr000XYkBGilIYL9u4LY1zpkVStrPPPNM57FigFXdBIa6cWK88NSNNyOfumOoE3nVQV6dXHPHv/UFi3Xyo7y4ECnT2NbVZ9r/l2Pfz372s9NeVa/fDEiAl1msMAQLaGXrMyCS2irWApxNQSAHxFmQA+B4+O67776FSejLX/6yQ5wVnK/PSQDtTcoc2Nes0NzZml1hBw1c3bg0ZpnW5VMHJwBcnZYO4VZ9rmtO+DUr5FVXJ5Loq61yAI4+x0O5BOTYF3dOHlwCkywBXlRhCQEbsV2f5LoNquxZACdws3EMcdLIMSuVh/Rf/MVfOMQNqtUmNF0mMODzKwU1fc1AzQEQmQC7iDFnrF3VmL4nn3yyyD5lTrblyp2Bivzo/LoE8sqZMNDXDN6ctgKCU8DfpZ7TdC4QfNFFF4X169dPU7W8LjMoAfqDp556akHNBXEL/vAdIQvgrJwEcQI4aeKkhSNmVioPap/UYCXn61XmsD4Ajhu9TqMlR5FdzbWYG6s0Y2izmMBQ9lkr/iPUuf3guDqAAUipD/dil5Cr7RsmLFKfFPB3qee0nSvHvg888MC0Vc3rM0MS0Fhfad5icIu3Z0g0pVXN7vEFbja2EMc68Gb35bxhl5bM/5g6CZRNYACqpMHtUmlgpwqqSLsP7Rvm06rJCcqnCs7wD7d27drK6qLl456q+lIBCfQxJo10cszPw4TFPtqqUsBT8qcc+7ovzilpUK+Gm04zr4FsgLPpxRDHNuCmmAdP2cPapuPrsyUBQCMF9TyoAZUuIWdWKOljkuuaF5qquvFbaKmqtHyYk+tmV5JPnUaROvUx/o106urEMcOawUte1L9O+8hxHkJwx75+FUyLBKwGTlq3OJ6WunatRyuAI9MqiMOOjRm1SgPRteB+/uRJoMyJ77BmhSIxytDVJJczLg1QLDOfUg4mAuyzzz6VjQjAvPKVr6w8hj/7mIFKOim4jjMfZltRf/oZD/UScMe+9TLyIyZTAoK3ySz9YEvdGOAEbhRL64q1D23InnvuOdiSe+oTJQG0bAyQT8ETUJDa36SCXHN1EwJID21V17zQMNfBDhMYqvK55557CgfYVXVknF0OwPVlaszR9vUBi7RVnfzUVnUm8Sr5zdp/7th31lp8OusrDRyOxVm0LZCL4+mUQl6tGgFc1duwIK7qmLwi+VHTKAHMp/itSgX+q4Kd1DnxPqAq5V/OHodGh3FyXfPK+TICXyogkGcq3H///bUQg6avzoTY16QMypgDS33AIm2VA4u0VZUWMyXXWd7njn1nufWnp+4W2qiVBTiHt/nt3G3g0QtpCdoUz8/Ct1wCz2u+9thjjwWiAEAAlarxYgtOSuxAW1UHO8BHGUQmkkzuAsg0Wyp5wAsTJfjGJ8cCe4AIgTpyLhpHAuNGAT32a1weMfuBHJa6CQx9ABUasZzQFyzWzeBVWagbviU95EmAa/v8888POPY9+eST807yo1wCYyIBtPu8sAFp0r6VwZyzxvON1hrgEKAVoraJeQB5cAlYCQAt+AiMA1BAkNNbwZyABm2ZrifBTZwGAFIHVZxDB9EVFIGyuskHgOTrX//6uJjFBADq+/DDDxf/IQ/KDqgANXRWyEEhRyOGSRhA5DzqRhpWZna9TJtVpiVUORT3BYt1M3iVH7LJ8Uun4z0O4U1velN417veFXDsy7g4Dy6BSZHAvffeW0yk0surII5trcMXsRbOcsik1LWvcrYGOBUgJTweFDxYPLgEJAEe/ikNGZByzjnnFBAjkMCkCpTwAGfSgW5eCzdAFLDHzQy45MygZFwa3x9FK4a2gvyAQ5lUrSaMdZY4cM7ee+8d787aRpvGcvPNN4f3vve94eCDD648D5nVhQMPPDCwICcFJkggG+pJGnSAlDuWn+qPfHMC5wusc45PHUOeOW3FuZRfbZNKy/ctlACyveyyywrHvg5wC+Xje8ZXAtu3bw9/+Id/OGd9oN/SCz3r9MdSENFn6cV+fGs0+JJ1Bri4iAiYT2I8/vjj8V++PaMSkJatyhxo4a5O8wQECG5Y52UBk2VdeO1rX1scQnlUJpwLswCMpAk00lmQJp0HQWZXOg3yy5ksUVUWIDLn+6ZWJlXp8Z+VmV1PnWflp/qnjov34buuK1Ah01z5UbYmMojLO6vbmE8POOCA4iUBH3EeXAKTIIHjjz++cP5/2GGHFR4s6If18k7MNnzBS7sW6pVSIk1CffsoYy8AFwsQh6CPPvpoH+XzNKZAAoBRnw9iIMJCSmpsXZXYpAnjGJtO2TmxdqtrXbZs2RKOPvrosuwGvt/KL6f+KhDgyVsvnadArkxTqXPimE44ZwZqfJ5v50sAaLvgggsCjn0d4PLl5keOVgK8ePCy/JOf/CScdNJJxQu0NHD0NxbmBHI2Hm3pR5N7LwBH0QVxxAhbGo7RVMtzHbYEgDQ0OzYIDjC95bjDsOeO07rqQZnsetsy8smjUQJc23KvWLGiUlPJ0AmAjo6WPkAmDruOWTQHgIHmnJmqbesy7eedccYZYc2aNYGP3eearKddJl6/8ZYAfmMBN4a63HXXXWH16tXFM4U+hWcLbEGfQv+iF0leJhXEINqehbgzwFmhaZ14r732Cnywu+14oVkQ/rTUcceOHYXqG80rNxQ3FzccY9kIuum2bt06ZzpkHwtBUMS2BtpjYuTBHwcdG++fpG0+PH7JJZdMUpGLsjLWrirEmkrenlnYj+aNa6LMF2Aq3a7j7VJpzso+69gX/3AeXAKTIgFePj71qU8Vw7CYhU6/QV8AyNGf6NkBZ/C8EXdMSv36LGdngCsrTO5Ms7Lzff/kSODBBx8sZryVmTIZD8m4J4BMY9d4oKON4ebElQY3JuuMeyJggmcfgfP4T+cUO80PN7f9jqd98KPtEQiy3/5XNW6Oc3I0RaYYWau8XRKqxgNmJTSGB1m4tuttigr8+wzUNpLbfc4HP/jB8PGPfzy89a1vnRvHuftfX3MJjKcE0MS95z3vCZ/85CeLDwII3IiBN5lSATdBHDWZRZBrDXBWWBKk4vG8LLxUg5AA3/wEwDZv3ly4xwBMYk0aD2JrUrdQ1aZMuNyQbzXOB4oEfmzLiS7rTEYA/uJAJ7Bt27a53Vy7Fu6YzMBSFwBHex7HkxadTSrIBxwzRVnKAppI5FgW+L/OxNhVzmV5D2M/10udu5ZhlGOS83jNa15TFH/Dhg3uF26SG3IGy84L/5FHHhn4LCdaOF7m6VNZeJEXzKGBkxaOmED/OyuhNcBVCWqWBDgrF0pZPRnYjraFmUNoTXjwcrMJsPhklG4wbjr+S7mYQWOr2Z4cp2tImhwLhQCh1c4AUSw5WjNAT5o96iSNIOuUGa2ggjSD2o5jINCmFf+f2t65c2d49atfXXRMqf9z95EvHVkcpG1kP21jA6CJnJAlC4DH267M1pg67QQPe+6w12kHyuqhvQS4n9yxb3v5+ZmjlQBjOL/4xS8W34ymv+O5wEI/Rt/HM0LLLMIbrdMJ4FLNK4Gm/vN90ycBnONiOgW0BFttaglIPfvss/OgBCCUZo0bWJo0QAstHDctIMJNTajSmgED0pRxjeoczouhheNYNPhb2i6rRSQvlYc0AA6AjvNIPwWpHEfHs3Tp0qHASWwCJm8LfdIAUm7CLbfcUkAsx1CPl73sZYWDZMYjog1D4xfLqjhxAD9cD/vtt98AUp6tJN2x72y19zTVlvHz+Mq86aabCv9wAjjBHH0/fRfxrIZWAMcDKiZeC272/1kV7KzUG8jq40ELbMTA0USGVpMWm1jRpAGHCtbEyj7OLQMu/k9pu7jGgZw4xFov/uc4AeOdd94ZlixZMs/MixZMQZ2UtvuM47SleVMe1iQLnHKPA6bUSbAKuAJ4ADHlZnbxIOBO/YvK5nE7Cbhj33Zy87PGQwJMaPjMZz4T+HY0MEdfSv8DuGmhr4hBjv55FsLCJ1BNrVNwxj67kAQd+2OPPeazUGvkOel/Y3brAl591b9tGYAzafkoS2xitWDHsTH8xeWvKwdpvPzlLy/VwAmQlK7uK7utdWK9faoD4/g+gkyxMeQpbcpJnpiEqZNgj/+BBgAPIKSuaO3q5KJ0Fcucq22P20vAHfu2l52fOXoJnHvYizh9AAAgAElEQVTuueETn/hEWLRo0ZwJlT6Hvk9aOPo9+qC++r/R1zqvBI0BjmT1dhw/XPiPfQiVgeV4A/cwvRJAc8XDWQ/7Sawpb3QWLuw69dlnn31KqxXDntUCxrCn8XTXXXddOPPMM0vTLAOm0hNe+EMavrrj7P+6j+2+3HWVM55tDtRRd2TBBBfenMkH4APqWIA6BinXgR3/e+guAXfs212GnsLoJIDfTFiCPgdLAM8bC3DwhljE9mmzAHOtAI6mtMKR8BAkDxLiSXfeOrrLdXJyxnxqzW6TU/J+SmonUpBiDH9xLpogwSe9rGNjOiOrBRTs6XyrBdS+PmJ7D5elR9k4DjCjc2SbDpR19ut+1/nc+3S0AjztJwbikAFuZeiUy8CONCb5pcDWeVzW3bHvuLSEl6OpBHhJZNwz8EZ/Qx+EGVUL++hLtOT0a03LMK7HtwI4BISwCKyz0OlKcKyjgbNje8ZVAF6u9hJgAkPudy3b5zI9Z2JuJKQ+b4RWKifEsBeP97Owx7F1Jt+6PDXOj06SYMGMDpQ86FgVc+8De2jPOJbxccyGZJ3+wJaHThmgE9jh+w+fgqRH/3L99dfPmWL5/BZpulaursXS/7tj37RcfO/4S2D//fcP3/nOd+a+k0pfw0KfRF+jhb5HXKJYTDL+tWxXwlYAp6wkHGIWBKqFz+488cQTxcBDHe/xdEmgrwkM0yWV8tqglebzMF1CbPKN06oy+cawZ02+pMNsUwXBlbZTse51C3U6Dihjoc4CMtLkbRqoQwMJlKHF1OxlWx6O5Vw0k5hiGU/L/+R12mmnOchJ0A1id+zbQFh+6NhIgBc/HPt++tOfLu7/VatWFRp69T+KATk4BHgTm4xNJQZUkM4ApzduYhYJkwfJ7bff7gA3oIYbh2THZQLDOMgipww48T3hhBNyDh3IMXSEVisem3wPPfTQ0nwtXPH2a02+MeyhBQS0UmAHzKG5Qxv5yCOPFJ2twI7xcUCdxscx68wGzr366qvtLl9vIAE59kWzedZZZzU40w91CYxWAvQJH/3oR8Pf/M3fFNY9+hZYI56VarVwswBxrQBOlKsmRWjsiwEO7/w33nhj8YFaHevxdEiABzrmLB+rtLA9d+3aVXyVAmADThS+9a1vFeZEzAHcKyxon+ygfh07bnEMe32bfPGxh6zKxsfRgfOGjc9BN6O2uzrk2PdLX/qSA1w7EfpZI5QAL59o32+44YaCKYA3XiZ5BsmMSiwemQUzaiuAow1Ft4r1QCJGsBAyb3zf/va3C79Xy5YtG2HTe9Z9S6DpBAa0dYyZw6ymwDWCSU0TISZ9jBNQe/PNNxfjujAN4gjXgg73Bk58uT8IdDZ8KgbzIGPBFi9eXHyloSsUI2vax/q+Q9bkr++/AmRd81E7VsXUNYY/e3ydyRcYph5o/JDV4Ycfbk/39YYScMe+DQXmh4+VBNDKM5OffgG3IvRhaPTpSwE2u4hNxqoCPRfmN/5NmNowYSsohKcBzcQ8pBlvQ8zDCU/KfNLFB7w3FPIYH37bbbcV45diM5ctMloVPqXFWEge5NxsQIQNvEFxzfA/GhhuOm5Mxjn0pWkBrCiLHeAP0AgcNQbLlqvpOnlgmgLcMAWmwute97pw2WWXJYcVIAPSwEx46qmnVkJPKm3O2759e7EgQ2QtUNTxVtYAERoZXqxYKHfLrkDJz8WqR9+Q+N3vfjccccQRc2Pm5jL0lUYSYCzRvffeGz7/+c83Os8PdgmMgwTuuOOOwPOHT22hAOA5QUyfp36P5wwmVvrCaQa51ho4NaQERIzAeAjINs06WgXG1jB2hRgv9ICcHYujtDyeHAnUTWB48sknw8aNGwtNLO3NNZETABEGr3/zm98My5cvLx7YOefFxwBsAA0vELxgcH3aa4582M+NjvYLbRkwyudb6ASaBjRvgBsgVBUEjfExyAcHuEDmpk2bwimnnBIfUroNMDFUgfuNiQjAaV2gHADzww8/HLZt21Z3eOX/kjXmT2RJ/iz2qxTIBrlST8COsW577rlnI1mTdpu2qSz8DP6JY99169aFCy64IDkjegZF4lWeIAkccsgh4aqrrio+dk8/w8svfTkLfSALQbEDXKJxJRSExLo0K3TQ7LPCROAEBi1DztDyhz70oUSqvmtSJFA1gQGgQOsKTDTVovGA5gHPeVwvBLQuTQLuKLjOADbArO6hz7UKzNx1113FcuyxxxZjrXLzpL6cX6VhBmgJVcfwPzLD1AwU5cgOEGVMCDM76+Axrg/3IYvM2jt27GjsfPu+++4rpvdTVsqg78eSlzWdKg/28w1WzKF8exVIX7lyZW0bcR5aQ5tmXB/fzpOAHPt+7WtfKwaG553lR7kExkMC9Ou8bNNP0ufF8AZ/CN7Go8SDK8V8e1aLfIA3u0h1KZOZ3saBOMavHH/88YWWYcuWLS1y81PGQQIACw/sMjD68Y9/XJgncwCkrD6kDQzgFwyYyQ2CN84FhsrKaNPjmqWsjFejQwA+SSc3oI2s0zACeASrBSxLn3smt84AFHVsCm82b/IjYJrIzZfj+a4r0Me4ujrNn/oBYrRxtA9aOOQMgAKiVaHu/6pz/b+FEsCx78c+9rFiRt/Cf32PS2C8JcCwD3xKCt5srJIL4hRr/zTFnQBOWjgEwkNQ8MbDTADHw0WdNw8vFkCOgYgeJlMCdRMY8NvF+KqugeuIaweTak4APtC8AWKc1yagkeL8W2+9NRtm0CjVgSKDbteuXZtVJEyFuePy0GSh+eojALFyNlyXHrIGrgGxurqXpUX7Uk/gDBisCrw01Gkvq873/+ZLQI59r7zyyvl/+JZLYAIkQD9toY11ad4UT0A1OhexE8CRu7Rvdt2CXAxzdPa4AuCh41q4zu03kgSqvsCAaRVI5xroI3Bj5sLY1q1bC3BsCxQqL+cDM4yhywmqc9WxHJMDWpgayyZBpNLnLTRXPqnz7T5euoDHnPD0008X7cz93TVgFmX8XF2Y5jfpuroP4n8c++JSJLfNB1EGT9Ml0EYCDAPA+iBYU0xas9RP9POUNSAnTZwgjoeCXXg4svClBtfCtbl0R38OGjHMX6mA9q2Ph7rS5mbMNcX2pfkjbzSIpJcT+Gwc13hVQEtX5TJD56KNQquVE3LAMScdHUPemEJzAhDfFzjyEsgM2aqA1reLmbgq7Vn9zzr2nVUZeL0nUwKMbWY4FhOwLLCVrU9mLetL3QvASQsnkyqxQE4aOB5wgjc6fswhroWrb6BxPAJzVtlgcuCurwc72jc0UmV5xbIBuOpAKj6nbJuZTTngiCy4rus0jrhTyTErU98yOI7L2jcsU+eyWbJx3kAr9e4jAG910MqMVjptD/1JgOvxwgsvLLRw/aXqKbkEhicBjSkG3ARviodXitHl1AvA2eIL5gRwsSZOEEd84IEHuhbOCm8C1tH6ADZlD+++H+zWEW6VeAApwLEOpKrSsP8BUjljrtAM5UDj/fffnwVmQGsuRPUJy9S9CSz3abrFZ2QOwOUAtW1DX6+XAJ92W79+feHyp/5oP8IlMD4SYLIZbp9mCdhi6fcKcII3xRbiWOdBZxdmr7kWLm6S8d6um8DQ94M9F+AoV5+mW7RROXljSiyDWbWkJmHkaJCYrZo7gaFPWKasOfXlOCCeQcR9BUy3dVpHXIjkgm1f5ZqFdABnnEt/4QtfmIXqeh2nTAL0vfDGrIZeAc4KURBHLC2cgE5mVWIfC2elNv7rORMY+qoFD3Z9+qkuzZyZoHVp2P/RCuWAFBAlNb49366TFqEO4NCAjWoCA+XLBThgmXu5r4AJtQ7OZrmT7kvOZemceeaZ4fLLLw8PPPBA2SG+3yUwdhLAQqIJOOINCjlLfUV/vbBpXitACVYQZzVw0LO0cPig8jD+EuDhXaYtGeWYLPKuA6lc6TYBKQCuzoSKrzM+wlwXRjmBgbLlwnKfExgwGVPvunGOaDHrjqmTr/+flgBmKL7KgGNfDy6BSZNAzBuTVv4u5R0IwFEggVscC+TQvmlBC8dH7z2MvwRmYQJDLkjlTmDAZ1qOZg1wLIPj+MroG5ZJv04LpjL0abrNmcCgfOtM1TrO4+YSeMc73uGOfZuLzc8YkQSwavBSxxAsWfZkFbBAN6LiDS3bgQGcamABzgpaZlS0F5hueMC5XzhJbTxjn8Awv13QRtZp3ziD77EyYacujGoCA+P9CLkarr7HOdZNYACU3YVI3dXT7f9Vq1YFvs7gjn27ydHPHo4Enn322WLiE0wRM4bdHk5pRpfLQAFOJGwFisCleRPE8Wa93377df6o9ujEOBs5AyxVWpq+H+xNxmRxLfUV+pzAQJlyv24wqgkMaBxzwygmMFC+HBcsuXXw49ISwIzqjn3TsvG94yUBxhNjCRBLWJCjpGIOrY9X6fsrzUABzgpPAiaOIY5GWLRoUfjJT34SNOC7vyp6Sn1JwCcwzJdkzgQGzti4cWNYunTp/JOjrSbj7gCaPmG5CcCNYgIDM1D1MhiJzTd7lACfOCRcf/31PabqSbkE+pcAn/Hji05YQOAHcQX9BOuzEoZSU3W+omIJ24Icbgl4yG3evHlWZD9x9fQJDPObLGcCA6p+Qt0ECyCqzpSo3DEp1qWnY3PiJi9No5jAAKzmzAjOqasfUy4Bd+xbLhv/Z7wkwKRHPqcleFMcs4a2x6v0/ZVmKACn4grgiAVvimkAzKg/+MEPdLjHYyYBn8Cwu0FyJzAI4OqcAjeZwABEcb/0Feo+Y2Xz6XsCQ46ZHNn06XfO1sfX50vAHfvOl4dvjZcEeNn8zGc+E5566qni04T0g4I3KYamHdpsiwwF4Cy4Cd4UqwGIUYky/uiWW26xZfT1MZCAT2CY3wi5ExiAreOOO27+yYmtUU5g0CSGRLEW7OrTdEtnnANwXHu532hdUGDf0UgC7ti3kbj84CFKgP4Cf4WYTf/oj/6omIHK+PmUGdUyxxCLOPSshgJwqVpByxKyyBmIW7lyZbjmmmuKKcKp83zfaCQwKxMYAKkcqADMctxa4GiS8Z11YZQTGHLqS/kBqT5Nt5iNc3zP8amcHFnXydj/z5OAO/bNk5MfNVwJbNiwoZi4cOyxxxb9geDNApyYgngWwtABTgJGuKxbkGObDp0H3uOPPz4L8p+YOgIsZWbAUT3YEV7fX2DIBancCQzbtm0LS5YsqWznphMYKCPffe0jAFG5ANe37zk0f1WzmlU/zNX+HVRJY/CxO/YdvIw9h2YSwMXYzTffXLhjAtwsvEkBJJYgnpUw1JqKigVxqW0J38e8jNclOMwJDABNzoMdCfUJj01AKmcCA+XD5FgHH6OewJCjBaMuOM7sCxzRdCLvHN9zyKdOhuN1t0x+adyx7+S34bTU4MYbbwxf+cpXAuMzly9fPk/7piFYgriYKaZFBmX1GCrAYQqJgxW4/mNf7gNc53g8WAkMawIDWhmWnAc7Nc4FqRzp5IJU7gQG8rzuuuuKsZ1V+QMyuV9gGMQEhtx7bRQTGGgTD8OXgDv2Hb7MPceFEkDzdsMNN4RTTjmlsM7xAsliNXBA3Cxq35DWUAFuYfOk9zQZVJ1Owff2KQG0XGhAuGlSoc8HOw/sXJNeE5BKlTvelwtSuRMY5J6jTps86gkMubA8igkMtLG7EImv1OFsu2Pf4cjZcymXAC+sjIunj7LgBrQx9k2aNwEcKaEAkmKoPOXp+GdkAIc2Ll4QKfuYIsw4DA/jIQGApWz8GyXs88HeBOByQSpXirkglTuBAZMjoe5azh13R1qjguU+TdXUg3bONd3OSmdcXCxj9OOOfceoMWawKLhgQvvGDHSNe7OaN6DNat8EbrPUX4wE4KwpVRDHw5PFw/hJYJgTGNBa5T7Yc0EqV6K5IAVE5czGBDAZs1EVmoy7A3pmbQIDk1RyNYRVcvb/mktAjn0vvvji5if7GS6BDhLg5fcv//Ivw8EHHxyWLVtW9LfSwAFxVgM3i+Am0Q4d4ARsxII2Ym3/4he/CCtWrFD5PB4DCQAiZWZNIIqbqa+AU9kmY7JyQCqnbE1ACoBDfV8XuJYZS1QVANZRfoEhF5ZHNYGBdvHvoFZdQYP9j4Hjt99+e/E5uMHm5Km7BJ6XAH3NZZddFtAAH3300QvgLXYbgiZOYZa0b9R5d80lgSHFMcgx7g2Q44HWJxAMqTpTnU3VOKQ+H+zTNoHhiSeeKJxNVl0caNV8AkO5hJ577jmfgVounoH/I8e+l1566cDz8gxcAoK3Y445pvhUVmw6lclUY94Eb9LCzZoEhwZwABtBmjbFVgvHOh+0P/LII2etHca2vox9qjJhjWpM1qgmMNDB5GjfaFDgY5999qls2yYax1HCcp/jHHlJK9PoxsLiQ/a5Gtn4XN/uRwI49l2/fn144IEH+knQU3EJJCTAjNNPfvKThdZt8eLFxaQFmU1lMiUWxAnaZk3rZkU3FICz8Ma64E2xIO6RRx4JRx11VGH3toX09dFJAPNp2QN0lGOyxn0CAy121VVXVX4CiuseGebOshwVLI9yAkOT77SO7i6Z7pzl2JfPGHlwCQxCAnw+E19vb3zjGwvH5wyNYQHgBHHWdIrmTVo4yjOrEDcUgLMNLoCL4Q3zGQOWffybldbo16smMKAF62sMGjWdpgkMarky+OV/4OSlL32pDq2MRwnLo/oCAwIB1HMBt1KA/mcnCeDYFzMqLxEeXAJ9SYA+/+qrrw6bNm0Kp556ajGcxMKbnXWa0r5RjlmFN+o+VIAD2ggW4gRyNCQauNxB1UVC/jNwCfgEhvkixpSYY0J98sknixOr3K9wzY9yAkOdexPVvE/TLVpHJiZUmeWVr8fjIwF37Ds+bTEtJcFNyKc+9anAC+KJJ55YWCukbYvBzWrcLLDZ9WmRS5N6DA3gLLRRQJlNNXlh8+bN4fjjjw8ve9nLmpTfjx2wBHwCw24BY0qkY9HA2d3/LFzD3QehSkM56gkMuRDVp+kWrWPu+Dfk/eIXv3ihcH3PSCSAY99169aFX/3qVyPJ3zOdLgn8wz/8Q6FdZ8y7nawQw1tqzBvgNuvwxtUwcICT1s1eehbmWEcTsX379gLg7HG+PloJ+ASG+fJvMu5u165dYe3atfMTiLZGOYGBzi/3+6KjmsCAuNyFSHTRjHATtw6rV68O119//QhL4VlPgwQeeuihYngEft40zk1xDHDSvvmYt4UtP3CAI0sLcYI37Wd769atxcQF174tbKBR7gFYysZwjXJMVhOQypEf2uCyetrzmzgOBn6rQpsJDHRwfQTaLlf7Rj2qtIhNy0PeucMkmIHaV52bltOPXygBd+y7UCa+p50EUNjgoJfhKBbY2E5NVpDVw7Vu8+U9FICbn+XzW4I6YiYuMIUYTZyH8ZGAT2CY3xaYEnNhhgk5Bx544PwEzFabCQx0dH2EJqbbUU5gQPOXC5p9yMXTqJeAO/atl5EfUS+Bbdu2FeN/BWyKZS5VLK2bTKaK63OYjSMGDnBVxCyI48G07777BgZLexgfCfgEhvltkTuBgbN27txZaf5rOoGhT1Mieb/yla+cX7mSrVFOYEAD99u//dslJfPdo5CAO/YdhdSnK08mL9CvcC0J3KR1szNNLbwhgSqWmC4J5ddm4ACXXxQ/ctwk4BMYdrcIpkReNKTK3/1Pem3jxo2VX1hoogUbxOfKcjVbo5rAgFS5/viQtYfxkgAuRdyx73i1ySSVhi/UHHDAAUnzqQU4adsUT1Idh1XWkQKcJeqnn37aZ6AOq9Uz8vEJDPOF1GTcnTTJVWM6m05g6Mt8yqxv7rtJmMCAhr6ves9vTd/qIgE0J8xIdce+XaQ4u+fybV18O8pMqpiXY6t1E7hZTphdqaVrPjKAU6OokXC7UPXASxff9w5KAj6BYb5km0xg0FjOsuu5zQSGvkBmlBMYkEvuBAakjwYuFzTnt5ZvDVoC733ve92x76CFPKXpM2mRTwxabVsK3Ka0+r1Wa+gAJ2CjFloXzPVaM0+skwSGPYEh16lsE5DKEQAvDjme/ptMYHj00UfDaaedVpr9rE5gaKJ1RHjApgNc6WU00j9e9apXhTPOOCNceeWVIy2HZz5ZEsDBuR37JoizWjjngvw2HRrAqVEoGutSlypmvzQX+cX3IwclgWFPYGgyJit3JmidbPgiQO6nrJpMYPjlL39ZmS7XOZ1YTkALNQ0TGDDdsuS2MzLsS+uYI2c/prkE3LFvc5nN+hm8gMt8WgVvkpMrdySJdDwUgLONoHViLUDc0qVLw4MPPpgupe8dugSGOYGB6yBX04ImjBlLfYRckGo6geGxxx4rPshcVsZJmcDwzDPP9AZR1Dn3CwzIDYDLhb0yOfv+wUrguOOOc8e+gxXx1KWOYoD72s46lRJHPEBMUDx1QuixQkMBuLi8tqHUePvtt19gcKOH0Utg2BMYch/UQCVaGa6ZPkIuSDWZwEC50NZVAWkTUyITIvrSRDWZwIBsMC/35Ui3KcAhR+/A+7jKB5vGhRdeGC6++OLBZuKpT4UE6Ms2bNgQ9thjj9rxb37v5zV5P0/CvLzmNG4COMEbMWOg+Ji9ZvBlJumHDUACOG8t+zLBIB7sf/AHf5BVC66NvrRvZJgLUk3H3V133XWFRjlVqUmZwAAs92WqRg5NJzDgCDkX7FNy9n3DkcAb3vCG4sUbtzkeXAJlEuD+v/rqq8NBBx1UTGSiH9diOcDBrUyC6f1DBTiKYOGNddt4y5cvD5s2bUqX1PcOTQKAUhlUjXJMVlOQqhJYE5DCbMsHvKk72jUWtFOMoWMhLQWcVBLK4AdozB3/JljuSwNHemXtqvIrRtaMUekr5MKy8kO+/iF7SWN8Y8ZnXnbZZcWM1PEtpZds1BJA84YFgK/TCNziiQujLuMk5j8UgBO0ia4VA28W4vbff/9w0003+WSGEV9JVS5EeLATgIE+Ag/2XE1Lk5mgdWUj39wJDMcee2w48cQTA9fn4sWLw1577VW8eABupMOH65966qliwUklges6BXx8XSAX4KQFAxL7CLwFj+ILDE0nMFBX6p7bPn3IxtNoLwF37NtedrNwJjNPea4fc8wxSXiTEoc+0y6zIJuudexnNHiDUqiBYnhjm8/m4KF58+bN4cgjj2yQqh/apwR4eFa51qCd0DShJSHwJsWbOFBHO0pjZNdpd+1XWZuMyeIcNF99fVopdwID+UoWilX+VPzVr341YFbim5GYAQE8FsYVAnxo5nK1YMAeWijkbIcWvOQlLynSxNGt1fTZ9dTYNcrRBJb7AiiuiyYTGJAr0OoauNQVNn77eCGRY99LLrlk/AroJRqpBHA1c/jhhxfjgumX0MDxLCDmGcEiLhhpQScw85EBnBpMDSh1KtoNPmzvADeaq6luAsPBBx8cWGxgxiALAehgATq0H3DABBkDHxCVCxRAJRAg8yV5tQVHzm1iTiwqlvlDmZAPsJcDfFXJou1jsYFyIwsC67/4xS8K2EGW7AeK2Z8CPu65qskVyofzaSsAkfrQ0RLidbZzAunlQqvS45rxMDkSwLEvL99MasjVME9O7bykbSVwyy23FH0O3zoH3gA3FvoOnv3EYgHFbfOaxfOGDnAImYZSzLoInJhvH/o4uMFfinfffXfxgOamQqulSQuou7WeWwqgQGCQAy0CO9LXeXV5AXqnnnrqvMNsOk3AEaAAEJrWc17mJRtcu3gZH1Sg87MyZkZXVaCuAj7OzQ2nnHJKcSjmdGAOjRjpEAOJgKMgSx0z2zHkAX/Ae5MvMJAx+dp65pbbjxuNBKxj3/PPP380hfBcx0oCWGmuueaacOaZZ85p3Ogf7CJoExNQAbs+VhUaw8IMFeBoGN7q1UhqPLvNwwBTE41f9imiMZTjRBWJB/HDDz8c6HR5IPOwfOCBB4ob67nnnise2I8//nhRJ4BaWlIgCjMdbYR5y5q4mjxsLfB1EZxNJyf/GPhyzmlTvj333LPNaQM5Jwa+nEzsOTky4noCFAkp4OM+HgQs59TFjxmeBDCjrlmzJpx33nm9Op8eXg08pz4l8PWvfz0cffTRhZWFPoWXORYBnJ4rUuBYHuizHNOc1tAATvBGTFBjpWLMqA5wg7vsMK9hjly5cmVlJtLeAHUExnSh6cKMicsXNDEEYrQsCmj0GBPHjUr7AgHcpCnwsxCm8wcV27xywKRNOS699NKAdnOWgjWD9yFXzPgOfJN3BVnHvmedddbkVcBL3JsE7rjjjmJyF2PfpKGPIS4GN7FBb4WYgYSGBnBlsrQAV3aM7+9XAswkzdESSROjh/KSJUtKC8IYLExtmNEARGI0Xmj4AD9paIjRsHLzAniAn0CQxBk4r7c0rg1Bl97e6AzihzsAQVlHHQSxlNlDNwnQ3h4mTwJy7OsAN3lt11eJGYbzrW99q5jIFUMbfT59v4W3vvKdxXRG0kvGpK1twdwsNsQw6wxgHXLIIb1miWlVsyCrZhxqPBaaPCCPBY0eQQPybcE4nv0KHC/gE7RJQ6hjiAWCXFN0GgTBIOsCQtZjc3Bx8As/9hy7P7W+c+fOYjemaQ/tJYAZFlD3MHkSYAb22WefHXDsi0bOw2xJgAmIX/nKVwrTKc8B9bP0wVosvPkzv9v1MRKA61ZkP7uLBNCAoRW79tprC3DhQclNBgyhyWLbTmogL2nguuSrc2VuU6z9NrbaPECPAOQBb2j5pOnSOam0qGMcYhjU/9IKsk2HYrU/sYZQ59hYsLht27ZiXOF3vvOdIh2Boz2Wdcor+LT/xS5SysCyCVTa9CdlHc0tYy89TJ4ErGNfB7jJa78uJWbYE19boN1///d/f+65IogjjrVv9LcExV3yn8VzRwJwmsgggWubmAWnqNLm6BiP+5EAEIMJklmGrMu0idaDGxBgweTJpAZMnSzSkFECwUoMfdyYdqZhF8joS5sXS6yNVicFh3G6gkXkdOihh84DwPhY5Il8c+boMUMAACAASURBVILVNnK8oC+GStqE/wBGYJt6sg8A7NIOOWUcxDHUj/J7mEwJ4Nh33bp14Z577gmrVq2azEp4qRtL4L777is+IcjLl6CNPol1YsGbYkGb4sYZ+glhJABn5S54s/vQskDwHvqXABotgYyFkxwtG0DB+AYCD1k0JUALEIhZEw0UNyM3bAoydFNzvvJD60R54nFt+r9KAiq/4tSxKW2eTLIpbV4qjbp9kufTTz89p8WsOifWtFUdm/ovrq8AEjjk5YcgMOc/2oY8cQCMnDFtEJOOoDCVz6j28WKx3377jSp7z7ejBOTYFweuDnAdhTlhpzPjHFizC8AmgBOsKZ6w6o1dcYcGcClQ0z5iraMJip2Xjp3UJrhAwEvVGLWqqgFgVRMZdK4d3yYTqMBCQKVtzpGmSfAHcACANkjzR0fAcYCHQEZAlDI5ooHScap37KeN/FVOld3CnYDPlie1zlg8vvU37CCAJF/JIi6DIBvtH6DJ/YaMaVPBM58EQ1bIbJRBfcEoy+B5d5OAHPt++MMfDnvvvXe3xPzsiZGAYE0AZ7Vt9NvapkJss3hoL4GhAZyKqM7ZxqyzyFyX+71GpelxvgSAEbxiDzIAUgp9QBPXBZBlA9q/ePICkMKxBGmWYk2g0hAQsm07FQuG/AfgyDRMGeiYABwAjyDwQ9OFyWhcx/1QL5YY8AR21IWB59SRThWQY6YymnC0oZJnUekB/9R9DWTA2XvyPUhAjn1x5OqOfXsQ6AQlof5UsbRvbAvaFE9QtcayqEMHOCsFgZti/uOh7Bo4K6V+1wENC1j9pp6fGmAkzZji1NnSiFktmTRiVkuWOpd9ZWnL7BifB/DFYGiPoRyaBav9dEbU5/777y9iQZ1gkg6M/wlWW6bzRxkL7CiDzNbUD7DDmfODDz5YwCrgx4sVn8QC6srk2lddhgmMfZXZ05kvATn2ZUycf15rvmymcYv+mL5Q2jfFAjn+89CvBIYKcIAawQKb1ol54OmYfqvpqUkCk6bdsLCZo81j/BRBcAdw2UkYkkMZSJXt13llscYGLl26tPUEHF37o+7o1PFabR1Ah2wxwSJTyorplU95oakT/JXJJ3c/mlWHt1xpjfdxaKNXr14dfvSjHwX3CzfebdVH6XiBZexqrGkjbfo0LX3k5Wk8L4GhAhxZ6iGldbZZBG9MQ/cwGAnwECZM2wOyqTZP4/CQhbR5QB5g0jYAjIQus6dHDW5VdZemTkCNlg458kk2ZiyzDmADc12ADoAbtHavqp7+X78SkGNf/MN5396vbMcttcceeywcc8wxBahZiGNdYZz7OJVxkuKhAxzCscCmdQCOhYHUuGLw0L8E0KD0pSnpv3SDT1HwYXOqmtCQq80jPa7btWvX2qSneh0tnXVRwr2LWfrRRx/tBHS8ZHgnPz2Xjhz73nXXXWM7PnR6pD36mshcSkwfIXiz2je7PvoST3YJRgJwEpm0b4p5CEDxGjSu4zzuRwLu4b5ejm21eRs2bCgmCOADqas2r76U/R7B/dc10FFjcpXZ1QIdphXAjJcHZjEzjq5My4ZGdJZfMrq2w7id7459x61FBlMehpAwzlEAJ0iz8WBynu1Uhw5wgjXFdPSsE9N5M0AaXzIe+pcAg/M1jqz/1GcrxVibB7S9+c1vnqc9tqZaafMEd2Vj80YhRTrZOHA/Yibl3uR/YsyoqWPjc9mOgU4mV3wF3nvvvUV63Ot77bVXWLRo0ZzrEkzRbcchpsrh+0YvAXfsO/o2GEYJeCkTwBHH8JbbdwyjrNOSx1AATrBGTNC2hTfWf/7zn4/Ej9a0NGZdPRiAfsABB9Qd5v+3kADjwE466aR5Z9ovSpRpnDhBcCfgs3An4JuX8BA21BHbrDCRUkZNYkBbKYfAgjxbdntubHIF6Jjxu3Xr1nD33XcXcMgsV/YP2s2NLZevD14C7th38DIedQ5YztCcy2yq/iOGuFGXc9ryHwrAWaEJ3hQDbgI5LoIzzzzTHu7rPUpgXFyI9FilsUlq/fr14ZJLLmlVniq4U4KCO7YFfIK7MmjSuX3FaMasdgyzKGVgZjPXFho6IIyZuGjXNGlGZbfl5Dw6e2kyOZZ6oYHDHIOfPma44gSW2MNkS8Ad+052+9WVHufgmMsBN+5rgVwMcK6Fq5Nks/+HDnAUT/BmYzp0vsWJOcXDYCTAAzIHFgaT+/SmKhcigxy7NY7avHhmqiAMTa8FOu5pgC71hQfBHVeHBVOGUwCG+KLjGEz/gKFrkCfzPsKxLxDnjn0ns/2qSs39uWXLlnDqqafOgZtMqIo5X/CmuCpN/y9PAkMFOAEbRdM6MRo43rwxnXRxw5BX5dk8Sv61eOh66FcCyJYwDs5KcwBd0IRGTE6HKT8TMLgPMW22CTlAhzYNEAN2OT4HTAHDhx56qHhIAHKDBOU29fZz8iTw7ne/O6xZsya4Y988eU3KUd/73vcKTTl9jzRvbkIdTusNFeBUJaCNYCFO/3k8GAm4f61ucsU9xo4dO8LPfvazeQkx65JPaL3xjW8sYn0wHjjJgal5iQ1pw0KTndQSu++RRsx+DQNNOUH+86qKHAMdWjnkh8sVQDHXTEo6K1asCLiiSGnxqsrg/42PBHDse8YZZ7hj3/Fpks4l4WXw9ttvD6effnoBb4yLtRAXm1A7Z+gJzJPAUAFOwEYJtK4xcDwYvHOe1za9buBCROONek14yhMDYm688cailozxQIPE26UC2iE6Mf7buXNnMcBfszcBFj4Ld/jhh0/ktS0AVaw62zilzeNeRrsXa/PiMXT8z9gZaybFCTAyi/N84oknChl6H2GlP3nr73znO8PFF18c3LHv5LVdqsR8ao97lfuSFy3grQri3HyakmL7fUMFOBVT8EZMIOZBSOftYTASwIVIE/cstAcPV6AEDQygzc2J+Qqtk3z1cfNy405jYAzWd7/73WKmZRn8UndktP/++xcaJSsHQA5N1Te/+c1w7LHHFqZD+3/bdTRYjLsjbUBJvusoI1otYjrUYcBOmTYvrludNk/DKPiyA37j6BMYN8eneYjRvsVQF+fh2+MvAcANgHPHvuPfVjklxC0QQyLog7S4+TRHcv0cMzSAE6yp2NpWjAuR5cuX62+Pe5YAA8sPOeSQ2lQBt+3btwduTDQmPKD1ZsVD9qmnnipgjv+5YTWGSuawgw46aCjgUFuRjgcghx/84AfFuLA6ECrTHgO8yAXgve2224oS0dm1DUAb6QCGaPxoG9qAQPsS0IjRgaL94zjyx9caJsi6ehQJDOhH8KU4lY3V5tEfsGzevHnuGtNLQ+pc3zcZEuC6RQt36aWX+pcZJqPJkqX853/+52JICfcn37mlH5LpVLG1VLjmLSnGzjuHAnCCNErLura1Toy2AxcEHgYjAc0KrEodaLnhhhuKhz9aD27EOMjTvvbjB4xA+mjs0KCgNeEj1n0EyvTII48Un2iKx58BJ0AMZeDBQJk1OL5r3kAs4JoDPdddd13lZ7RIhwkOP/nJT4rBvmw3DbfeemthamSiQdwGpCX3HsjEBtoF8yNaLQB+5cqV9u9O62jVAHpMoXTgwBnaP+pXBWplmVZp86644gr3D1cmuAnb7459J6zBouLyIvm5z32u6MsY+8u4X+5/7ntiwE1j37ROEg5xkSB72Bw4wAnWqsrKMbxt8wD2MBgJ8LCtm70HvGGSswPbc0uj8U3czPjzY8zd61//+tzTk8cxaQAnr3QKgFQ8/gw4IUj7xHgMYAJTPOPO2kCECkJaOSZnXN8QgI+qgHwAYmC0qSuM++67rwAlXnDsW21VfvrPtgvyxJSOObdLYEIHJjA0fOq0SQ/Y5l5GU6u2AThpP6495Enb5EBxqnxtz0ul5ftGJwFeZi666KJw5ZVXhlWrVo2uIJ5zKwnQbkx4wprAizP3Nwv9m9W+CeJaZeInZUlg4ABXVoocsCs71/c3k4BciFSdhR8f4KcrRHMDA4BoywCPthofNE6MLaOzl3YpLr/2K+Z/4AFIuf7668PBBx9cLPF5OdvIIgdkBXA5cgNA0FI2ATjaDjMF5sOm8GbrCWhRHzRmXduFN3BAvQ6oaAteCGR6B+wxATNJ4dWvfnUBf7aMvj47EnjLW95S3Acf/vCHC03O7NR8smt6yy23FBXAt6PATbGFt1jz5tq3wbT77ul0g0m/MlUgzkGuUkS9/JnjQoRPQXXRWNmCcvNi1mScHFqZpoFp6YAGUGThLCcd8saMCKzwmaY777wz57R5x2DOT5kp5x30wsY//dM/ZY/loaNrKg9clABLAFjXoHYBCLkmmga1C9q0OngjbfKj/ZAlbQKMo0VFY/qNb3xjznFvXTlyXkDq0vD/x0sC1rHveJXMS1MlAXy+HXnkkXOadwtvVgMHsHH/uxauSprd/xs4wOWQt0Nc94asSqHOhQgPSExeTWGpKk+AgwWNU5MAPDGODgCjA2gbyBvQwBTKrM0mQabAnHNwepv79RDSzQEfmy9lb3qOPT9eRy6YPdBuNglqFyCsS7twrrSqN998c1YRuD411jLrBD9oIiSAY99169YVw2cmosAzXkicafOSzwslsEZfYgGOe5vFoW14F0r7J+Twyug5dZQAZr6qB+CgNBwAodxH5FYB8x4D4btAgvKik2Hc1aZNm7QrK2aGVd2YNiWEljF3diTmxKp2UJo2xpRLR9lnQCPWFKzR0AJ+yLSPoK8+MJ4uJ/hLXo6UJusY69h3sko+m6VlYhffJqYPANzoo1kXuLEueLPx/9/emYDbUZR5/zWOCJhhEZTckEACIQkEMJgYtiiRJZEBERM/gguIgt/4ODAz+rAJyIyOooAyKjDDKIRtZPskEoGRsCPgEhKIAkJiCGHLBUGGJSigxu/5Nfnf1O30Oaf63tPn9Onz1vP0qerqPrX8a/v3W1VvdSdarcl1KQhcjJSuNXBUMxYISb31XExp0SDLYJA4QeCaZZBeIfnKQyQhvHkIZKPNIcoL6ahXDnpPNmluplRU4VLWpCWPQYoLgWumoZxjCBxp9T6imciXJywp9h3o8W3lyUn1U8ISCpa1iLTJFoEDARG36qNRjhwWTuDqfTl7p9yaSoDkp54UBz1meQhLbKoZePOsq2OaDpLQ7LSQd0hsrAGPeniF4VxxxRXJuq7Qr5abthAbLmEURVwa1Yes9KM0uNkkn/CQMDYyxJ2nHjUKz5+XBwEU+2LY1eymvAigo5GZGj6I6Z9F3mSLxInA+djemrIsnMCpQNPZUQHXep5+3+8HjgDSk3pSIp7HThnmSQWNOo80DcLCjsVmG4gCO1NjDSpt6JgaGTo1TOyGB9YZ1iuHdHxskMhD+NL/r3WP+o88kkDKBdNsYl0rfWl/CGcR9TMdj9+3HgE+2KTYt/Wxe4yxCND+kL7Rj4akjfGbfkHjuMZ1wg3dsfH4e/kQKJzA5UuOv91sBGLWt9Eoi2hsnNKQR3KC6pGiBupY6ZHISgyBk1SPdSGNDOHGpkFhgV8RpIm05CkXpnKbPX1KHiHrMThD4IqYShbObrcXART7zps3z+6+++72JsRjr4vADjvskOj3pE/SFRI3jSHyqxuYP2wKAi0jcFmFq4LWs6bkyAPphwAErtFgXcRCeUnS8kiQkAQWQViQlMVKnCArsRI10ht7/BvTp43KoV/BmSVnnRZBaME4j2SUfBZhIJIxmzookzzpLSKtHmZxCLArGcW+kDg35UWAjzik9yJvsjWOk3Ify1tbfi0jcGG2VOChzXMpRQ3fdffgEGDwrTf4FbVQHqkJHXMegyQwD+GLDZuOJjZcpF711m2GcbI2K1aTPCSSnZd5DGkpokPMKxktqlyoIzHEGqJXrw7nwdTfLScCKPblfFR2O7spJwKc5EIfJuImW32U7HKmvpqpaimBE2EDSrllI8ngzEY3zUWgkQoRBsciGh6Dc6wkSzmGTMZMqen9WJsdbrFrz0hDrNSL+opOpBiDRDIvCSmLZJRdykWUC5jESOBiCXVMOfg75URAin1RFOumfAgwjrBjnKPwQuKm8buIMaR8KJQvRS0lcMp+WOiqDAywMSoFFIbbcQg0UiFSloXy5AbS12yigMg/z9oz1uFRJ2MMkqmtttoq5tVkR+mwYcOi3uWlMklGIZJ5MIzNJB8PMUqKIeCxEtTYuP298iHgin3LVyZKEfo5OQJQ47XscCyXW/9xu3gE4kaqJqVDBZy2qQwoQ0XPjJvmItBo8CvLQvk8x1flQQgCl2ftWR6pF8dcxU6LlkmFSF7JKGpViiBwlE0Mgcs75Zunfvi75UFAin2vu+668iTKU2Is/0Ayut122yUf2HxkpwlcCBPju5vWINBSAqcsicCpEmCjMZ+BRTv79K7bg0OAwa/e9CHruGKnDPOkhDLNM2WINKaIqTLCjZ3mJH+oEIklKw8//HDUFCDhokIkD5Esi2SUTTDqsPOUf6N3wYPzUd04AiECqBQ555xzzBX7hqi0z814/L3vfS+ZOmUcUV8Qjt0az524tb6cWkLgVLAqaLIpd1gR6NCfeeaZ1qNQ0RiZhms09QTBU/k0E4a8UhM6iiKIZOw6K/IO2cNQJxuZJ598MnkF3UiNDOHmlXqBX0w6GsWdfs7XdB4iCYErQoUH5VJEeafz6/edhYAU+955552dlfAKppZ1b2effbZtvfXWNmXKlD6pm0icxnDZFYSg9FlqPFI1KQshSVCBi7xRIbhYIInkwU1zEIA4NBqs80wZxqaKwRnTiDyG4dFZFEVYYnY6khYIb6zUENwwMSQEyWJsuMKkKMkobS9PWtjFHLZdpW+wNnUzhvwytR6z0WGw6fH/lwMBKfb9j//4j3IkqItTwSYtPjwleRNx07iNrb4hbXcxbC3NessInHJFQXOFlQA3lYMOfdGiRXrV7UEiwO7BeoN1mRbK5zm+Kg8s1K1YIonUS+SzURyc2XrooYc2ei15PhAVIpSNOsWoSCJfgng2IvVhUGzUiJ1SDv/XyM2GFZZNxJgi4o+J199pDwKu2Lc9uKdjpa9g/JCARbbGbo3l6qdkp8Px++IQaDuBU6XAZiMDC5s1PVVctrsjZEhRPekFUpAiGt1ApgyRwFEHmm3yqhCJJXtIhmINpLAekc4KB4ITm5as/2f50bYwecLlIyDP+1nxZvmBSb26Gf6niDoahu/uciHgin3LUR7smn/iiSeS9bsibbJpk7ixvX22r7xaSuBU2KFNJWDg5isbe8yYMXbTTTe1D5EKxcz0V73pw6IWyjM414s3C+IiVIhAJPNIb1AhEksiITYcLRNjyFseFSKQwyLWnUHg8ipX5iucNtpsQ9nE7EClDse81+z0eXjtRcAV+7YXf2LniEDWviFQ0TiNrYt3nLy1t5ya3zPXyE9Y0CJwqgiqHAyeEyZMsOXLl9uyZctqhOTesQggfao3+JVloXxRKkRYe5ZnuhCyEkv4+DKNPR8UQptHilWkZDTvzk+kuEWRyXp1U3Wc3aox7+l9t6uBAIp9jzvuuER9RTVy1Jm5YF06hrFZ43U4fvNM9+EY35m57bxUt4zAhdCowFUhqBxcDJ5c6AO6+uqrE/0z4f/cnQ+BRjtBy7JQHsJShAoR1p4VpUKEg7djpWp5VYggCcxD+GJrBUQydt0ZYUqFSGz4se/lUSECqS6CQMam1d9rHwIf+tCH7JhjjklU+7QvFR4z43VI4Bi3RdZkO0rtQaClBE7ELbRD6ZsI3MiRI5M1Q76VfOCVImZHZVkWyneaChHpKowhQ5DTvCpEmDaMlQTmqSEQ2pidnwoTAlcUkYzFBPzoI9x0HwKu2Le9ZU4/x3Im+gyN0yJv4Rje3lR2d+xt6xnDCkClUAWRJG633XazO+64w6dSB1g/GfgaTfEVtVAe8pFn4M9zfFUeOMAgdi0eZLYRXoobIoSJIXBIFvNIAQm3qMPjaXN5ygUiSbtstqFc2LAUYyiX2HdjwvN3OguBz33uc67Ytw1FBnlDB9zuu++eHBcoCZxsETkljb7FTesRaH7v3CAPIXHDnUXeIAAMpnvssYddcsklxg5FN/kQYJF9vV1+RS6UjyE2YW6YJstDLML/1nNDnmLXTzHdHGs4s/eAAw6Ieh2yV68csgKBtNBRNtuAc71TOdLx0e6KkATy4RBLaouYWk/n0+/Li8B73/veJHE+G9O6MqLPuvDCC22XXXYxZsPoi0LiJvIWjuWtS53HFCLQcgIXRh4SOBE5BgxdrDHaZpttbOnSpeHf3B2BAIvP66muQAoC/s02hJt3oTzHVxVBWPKsPWM9YCyJZGoxNo+sO4t9V2VRxI5cdqDmJWN8hcdiorTH2JCyWFJbRB2NSaO/Uw4E+JA/+uijzRX7tq48OPeUJQ6MvRqLsUXinLi1riwaxdQ2AqdKQAJF3lRBsLmoNEhzUJrqJh8CTH/VW2RfloXyED4M5d1MQ7ix66yIFwIXm4YVK1bYqFGjopILGcszBYhkNHYqNyoBa16CwOWVjPIlTttstsmzsxQSmWcncbPT6uG1H4EDDzzQ5s2bZ2wcclMsAmh/WLBgQbKRUORN47HGaY3d+riSXWzKPPQsBJrfO2fFkvILC1yVgcqBW5WESoObQYfpQDf5EECFSD3pSVkWyjNdmIdoxaKAlKeeBDIdDnjRYcUYpJuxU7MDUSHCf5ptBiIZbbcKEWFQrx7rHberiwC6C1mPBYlzUywCl156qbH+PIu8MSZrjNYYLrvYVHnotRBoC4FTYij88IKwie3LpvE+9NBD+ovbkQg0UiFSloXypLOITgDp0aabbhqJ1hsSuFgCd/3119vo0aOjws4zjUuASEZjzleNijx4CVIYO23J38qgQiRIvju7HIHp06fbmWee6ctpCq4H9MfM3PDRJBKHLYGKBC1KRhF9t8J2uzECbSNwKvg0geM+lMJRcTC+kaFxYeoNpFqNpE9lWShPOoqQsEBYGmEgvDSNS71rZFQPY0hW3mlc4i5q5yeENnZHLukoSoUIU8qxEtei0tCojP15+RBwxb6tKxMIG32yrpC8icBp3G5dqjymLAQaj1hZ/yrATxVCFUQkDpvFlBo4C4i6ckFCHBqtoyrLQnkkTiLpzSwIMKi3BjCMCxLZCC+9r3oYo0+NdWexuy0VflGSUdpRHqJcFJEEk9g1gRC4PFJDYeh2NRFwxb7FlusDDzxgnLxAP0GfnEXcSIHG6mJT46HHINBWAkdFwKhCyE6TOL4IGFDcxCHAGaf1Br4yLZRHtQXl22zDGrhYwpJHhQjYjh8/Piq5kMh65ZAVSFGSUdb4lUGFCJjkIbWuRiSrlnSnnyv2Lbbc77nnnuQoS/pjXSGJ0/isVGj81r3brUegrQSO7IaVQu5Q+oabqR8ncPGVA0JST3UFg2hZFsqjQqQIApdn7VkeFSIQoYkTJ0YVBlLOeuWQFUhZJKNFqRAhz7Gklnrqg0RWLeleP1fsW0zZL1y40Pg43XrrrftNnUoSRzvUuKxxupiUeKh5EGg7gVNi1VHLlhSOezYy+BZyIdXYhuzWm6Yqy0J5BmgMZd1MQ7ix66yIl13OdFQx5vHHH6+LbRgGJLleOYTv4kYymifd6f/XumfaMq8qDqZym10upA8CHLuDF2KdR2pYK//uXx0EXLFv88sS1SFXXHGF7b333v3IGx/WaQlc82P3EAeDQHNHzsGkJJDGicRhM4hA4Jh24SvBTWMEGCTrTR8Wtb4p70J5pgtjNxo0zvXaN5h2yzNNl2caF2ITSyogkvXKYW2K33DxfhFThoSbBw9SAybNPkReUt9YAoc0sggSmcbd7zsHAVfs29yyYt3beeedZ/vtt18yztJfafqUtsfFOKyL2DU+NzclHtpAECgNgQsrhSpLaKO24Ve/+tVA8th1/2EKtZ7EBf1eeYhFLIA09jzhkk4N6rFxxLwHkYydpiM88IidxuVLtaenJyYZllfyxbRlzO7WqMiDl8A4Dx5FrcODkOVR7cL7zSaRASzu7FAEXLHv4AuOPvLaa6+1K6+80mbNmpVsFKTvof8WicuSvoXj9OBT4SEMFoHSEDhlRBVE5A1/3HTkRUgnFG9V7BipFjspY6cM8+CSd6F8nrVnedIBYYlde8ZOR0yMpIdODxMzzckavNg0JIGuUZUTkw69H2vnlYzmlRzGpgNCFrvblzBj6nJs3P5edRBwxb6DK0s+FM8//3x77LHHbPbs2ckac8ZXrpC8icBpLNbYPLjY/d/NRKD52/+amToX1+ZGk8G30SDJQNpsAoe0KVaKpUzlOb5K/4mxyV/s2jMIXCO8FCcdH2bEiBHyqmlDIvNK08oiGWVNYBFEkjqSRwIHCS5iir1mofmDjkEAxb7jxo2zo446ytAR56YxAnzIcc7pHXfcYZMnT7Ydd9wxIW0hcUuve6Mf4BJ5k904Nn+jFQiUTgKXzrRL3dKI1L+PUSESI0GqH8u6T/NOFxICEru8pG/dmNf1gTzFTuWyHjC2U8qzExoiHaMrLkx9WSSjeaaUw/Q3coNJHgIXWy6N4vXn1UNAin1/+MMfVi9zBeXozjvvtIcffthmzpxpO+ywQ5/ELZw2DQkc7S9sg6G7oCR6sDkRKC2Bg7iF5I2vca9AjUsXklFv6o5BNMS1cYhxbxBu3oXySOCKIHB5VIiwKSE2DaT30EMPjQIEKWDew+OLkIxSLrH5U8aoQ3mlh/pvIzuPRM1PYmiEZnc/R7HvySefbKgiclMfgSeffDKRvKFLj01EmjKlnYcSOE2bhpK3NJGrH5M/bSUCpSNwaXIhIvfMM88kOmpaCU4nxsXGgHrTh2VZKA+xwDR7qo5w80gYmS6Mldah5iOWpObdOFCUChHaT70NLVl1HFJbxMcSEtc8aWm0GScr7e7XPQhIse9ll13WPZkeQE6ZOv3BD35gu+yyS7JcBMIWErdw3ZuIm6ZNi+gHBpAF/0sNBEpD4ELiJtImP+zly5fblClTwRSBqAAAIABJREFUamTDvYUAC7/rERKm6ZpNmog770J50hm79kx5i7GpK7Eki/BQlxGLB2Rvq622ikmGQSRj1WUQIGRF9T0qgsiXKJc8eBAsmNSrQ5FR93sNQotpdrj9IvGbrkMAxb5z5sxJlmN0XeYjM8wJC/S19F20Py6k8rqQutWSvBGFk7hIoNvwWmkIXK28M6g98cQTybmWeaekaoVZZX+IQz0pR1kWykNYijAQljwqM8CDL9IYs3jx4ug1XKwJzEPgILRFTFvmlQSSjlg8YjDTO0wP51n/Jgmt/u+2I5BGAOXuZ599tj366KP2k5/8JP3Y79fsbL/mmmsS6ZsIm2wRNydvnVtVSkfgsqQQDLLvete7OhflFqWcabhGa4zKslC+KBUiEIV6awDDomCNFZ1XrGEBcAw5HIgKEU7HiJUExqaX9yBCHEUXa3i/iHRQLnkkrhDJGKxj8+XvVQeBpUuX2vHHH29Tp061GTNm2L/8y7/YJZdcUp0MNjEn9PdI3vg4FHELbSdvTQS7DUGVisBlkTcX38bXCgbfRoNkWRbKF6VCBIlTvTWAIZoQuFhpE4uAMTE7S0lDnnV4hFvEtCXh0qbySAKZJqaDb7ZBIpmHSBJ/Eelodr48vNYhwBrK0047LVEfQqzMzBx99NF2+OGH27x58/y4xYyiQCsB7V+kTVI3PtLSF2OtxlvZGUG6V4kQKBWBCytQiTDqmKQgxalHMMq0UL4oFSKQ2Nh1VnlUiECwMDHTnKQhlkSqcrGTLo80UP9rZOfZkUtYSLuLkMCBSb2p/ax8+CCShUp3+rF8Ya+99rIFCxbYfffdZ2eccUafPkYp9r3ooou6E5w6uabfos8ScQtt2nnWmOvtrg6gJXtUKgInbFSpsFXJ9Mzt2ghASOqtEyzTQvmiVIjk0UeXR4VIb2+vHXDAAbXBD54g5cyzcQByg2k2gSPcvJLAolSI0I4bTe8HEBrpyCM5DP/r7uogIKkbOyiRtl1++eU2ceLEdTKIYl9OF2B61U1/BGh7aeKGn65wvHXy1h+7st+VhsClK1FI3hho3TRGAIJWb91QWRbKM3WJoQNppkHalIewoJomVlpHmmPX1jFtWa8c0nmmXPKkO/3/WvekIw9pIpyiVIhQN/NI4ChLJ3C1SrY7/Fm28I//+I/GIvwlS5YkU6W1loi4Yt/sOsGHMv0sU6hpEpc15maH4r5lRaC5I2iTcinypgo3bNgwW7lyZZNCr24wEIF6g15ZFspDhmp1xIMpHdae5ZF8sWM1lkSuWLEi0V4ek7685ANyQ51vtiF/eXZ+En8Ra/EoF0wsWVY6YtcnJoH7T6UQYMqUEwMwHP0Uc1yWK/ZdtwqwbGb48OF95M2lbuti1Mk+bSdwGrhkU8FE4LAhcaNGjUrWPugsyk4GvMi0M2VWj8AVMTiTn7wL5ZkeK8KQ/3prANNx5lEhwoLpWNI5EBUiechNOh+17iFOeSRwfAAUQZqYUmadUh4DyS9CKpknDf5uexBAPQhTpmxO+P73vx/d7lyx77rl9eCDDyZ9IuOoyJtsjbnr/st9OgWBthM4gFJFkq0KJgkcg9C0adPsnHPOMSdx2VWLL61G03ZlWSjPNF0RhAWiUG8NYIgcBIH6FWsYVJAENzJI32KnWhUWktE8adH/GtkQ2pg0KxzeVxuUXzNsyiUvGaN8GtXnZqTNwygXArQz1IOg3401b3nNcccdl6gUYe1cN5tly5bZqaeemgg/Gk2fglMR7b6b8W9V3ktB4JRZKlEogWNQo/Ix2G+//fbGF9bpp59u1157rRM5gbbGZvAFq1qG55hmEwXCzTs4o6qi2ekgb0icYgd9CEIsidRHQww5JA158UAyWq/sapVpI38ko7F5JCxUDuR5v1H8ej4QFSKk3U13ITBY8gZa7373uxPQulmxL/0VevF23XVX23vvvZO+NiRxGmMZb3V1V02rTm5LQ+BUkUTi0lI4KuDWW29ts2fPNr4uIHI333xzdUpikDlppEKE6bE802mxyRnIQvmiCAtkst4UcpgnpnGpYzGGtWSYGAJHGgaiQqQIAoc0MM/GAdbixWISg5veAZM86eB/9ANuugeBZpA30GKZw4knntjVin2vv/56mzBhQt/aN5G3kLjJ3T01rJo5jRvBCs572FmLyFHBkNJICkcl5KKBvu9977Odd97ZbrjhBpfErSkbCEk9gsHgrMXkzSzOgSyUz7P2LE9a86w9Q0N5LGniqB6kvzFmoCpEmk2cBiIZZcdajJ67GBzCd8hb3o8HpAh5SV8Yp7s7BwF2m37+858f8LRpOqcst+lWxb5g+cgjj9jo0aP7xk/GUNqgLo23Gmt1n8bR78uPQCkInGAKKxRuKlxI4JjeYZE1F1KczTffXH/tehuCVm/6EAlcEdNjeRfK5117FluwedeeQRDy4DFy5MiopCCRrFcO6UCKlIzm2ZFLuqhDRXTmhDsQMpanfNK4+n1nIMBaNXabQroGsuYtK5fdrNgXJcfbbbddMnZK8iZBSEjkimjnWWXhfsUiUBoCF1YokTd9MaRJHB07krjJkyfn2nVYLJTtDR0iUG/6sCwL5SFwRex0hEjmkR7lUSHym9/8JlkMHFPCDEj1yiEdRpGS0TxEknQVsUsZqSjGyVi65P0eBDjHFDUXX/7yl5sKyMEHH9yVin3ZzMbGpVqkjbE1vJoKugfWcgRKQ+DIeVixapE4kTn0At15553GVJibNw4tr0ccilp3lnehPFO9lG2zDVOGRakQYcq3HrbKi6aoY97Vf5i2LILckJa8u2GLINYQuLwqRIqSSgpzt8uBwNy5c+3MM89MtAvEquiJTfmIESOMHak//OEPY/9SifdY7oHkXcKPtB2OsWS4iL64EkB2SCZKReCEWVjJwi8JRMIMdgw0KChlZyrr4Lrd8NXVaIoKFSKxa77y4Jl3oXye46vypKNIFSIsCmZNSSNDGvKSJggcdbzZhrTk3UxRRGc+kLV4/CcPCW42dh5e8QiwVmvWrFk2f/78vjNNmx3rxz72MTv55JONvq8bDLMK2l1PnxKSt3BM7QYsuiWPpSNwqmgUgNxUREneICEicmxkYMHmwoULu6W8MvPJgFdPesJzDDg20wxkcEaFSBESpzxrz9TJxWAhCW/M9CykKa8KEaZciyDWSODy4pz3/Rj8SMdmm20W82q/dyhPN9VFgClTJGScYVqU4cxUTme47LLLioqiVOGyrnfbbbdNxkqNmSGR03iKjZFdqkx4YnIh0NwRPVfU9V8OKxtufU2EBA7Sgp6bK664wvii61ZDw60nbSlqSopBNu9CeaZym00kKXckgbFSG0hkbBpE4GKmZ5kurFcOWfUTCVwRBC6vZJS0xWKSlY9afkgFGkmH0//lw8AHlzQq1bm/8cYbk/VpqPso2nSjYt9wvNQ4Cs5hmwrdRZeBh18cAqUlcMqyKiCDC18TuiSFY33NfvvtZ9/73ve6VqUIJKMekSrTQvkyqBAhDbGkCeW248ePV3Wsa0M88pw9WibJKBmLkTLWBSDjIe03rwoRSK3vMM8AswJeSJxPOeUUu/rqq3OvjRxI9rtRsS9jJZfGTtngF7oHgqf/p1wIlJbAqaJhqzKKxIm8aT0c65P22GOPRI8Q0qhuMxC0ejsOy7JQviwqRNhIETtdyIDDVEysyUNWkIw2e/E26RyIZJT/0daabZC45iVjSA9jCXaz0+vhFYuATkjYf//9i41oTei0r25T7BtOm4Zjp8bUlgDvkbQEgdISOOVelU5ETiSOSsog7CTOrJEKkbIslM+z9kzlH2OzzirP2jM2UlCPYszjjz8ePS0K2cszXQjxLsIwbVmP0NeKM5bU1vp/2p8p5YEQMcpzIP9Lx+/35UKA9vGNb3wjIVRFfLjUym03KfZlnKTtpEkc2PDMTbUQiBvF2pTnsMKFXxJUTiopl0gcNkdtIY278MILjUGsWwxTcfXWf9FxFjEg5l0on+f4qjxlR/7zrD1DKlRv00cYN2QvRoIEFpg8JKgoyWje3bDsYi7CQODqnQ5SK07Sk2cqulY47l8uBFotfVPuu0WxL/0rbU5CDo2ZjKMaS+XWvTByuzMRqH36eUnyo4rGtBDuUHLCoIk/gyY2Fwf43nPPPcki2aOOOqqQdT0lgSZJRowKEYhCT09P05Odd6E8a/WKIJIQlnprAMOMI62MJW/8jw0y3//+98MgMt2kIS/pKEoySrvIQ2i1Fu/9739/Zt5iPW+77bZ+rxJuHomk/qw2rXu3q4FAQ+nb6l5bdO1tdtvcr9txl7zVjr/lBjt97zWn7fDs0m/bsUecYbf3HG5nXfMN+6cpPbZWAvG69S74vp148NF2SW+PTTv+HPuvLx1sY4e+8QaKfY855phk5ys6RKtoGPfIG31sPRJXxbx3a55KT+AoGJE43CGBo6LyjEsEjnfe85739JE4tpGj1LGqhmm4eoREg3OIWzOwINw805bEmff4qth0UvaxU4akOxYLSXFj8gmByzstVJRklDzmkQRySgcmTcBi8ee9LPIHkRyIBC5s73nS4O+WFwEOq4dg1Fr7trr3bvvOiZ+1M+2T9t1PXm0vXzzWhvZl5wVbdNbn7NjnP2eX/eV02+KZm+yUj33OzvrmhXbspE2St1YvvdxOubrHTl76F7t46J+td8Ec+/b3F9qXPj8lCSdU7HvSSSf1hVwVxwMPPGBsuGItOOMiVziNqnGyKvn1fLyBwNoPmJIjogqIzQCsi0qqKVUGLS4IzaRJk5JBHQnKueeeW9kpVSRK9aQtZVooDyGKJU95qmNeFSJ0bjFGG2JiPgCYuhiIBC42LTHp1TukJY/ki6mXIgzlHaN+JR13UWsl0/H4fesQ4HD5s88+O/sjZ9UCO+tj/2SLJ55niy481j6yd0jezFYvnWsnnbW9fenEfaxniNmQnn3sxC9tb2edNNeWJisXXrVld/3cNp/xvjUSt/WsZ/I0G7fkIVv5xsqGJKNVVewLebvooots3333Tca+euTNP45aV+dbEVPHEDiBkSZyInAQNypuSOJQ9MsCVqQjfP1V0SA9qTd9WKaF8mVRIRJLIvMQG6ReeQgcJAUTm5bYuguZjZEYhuGxzq8IQ1ulPeY11Nk8BDRv+P5+axHgJASOzJo6dWpGxC/YovO+Ymdtc5Kd9k97JgSt/0uQsxvsxp3G2Ig106FmQ2yjyfvaYfffYHcte9XM1rcxU3e35+b/1JaugrG9br0Lb7cl47a34cEIVzXFvnwgocT+qquuSvShstaP9qYxkb4lHC+dvPWvWVW4C6p3+bOjCohN5dSlL46QvCGF07XddtvZb3/72/JncAApZMCuN31YloXyZVIhEqvvDOwOPfTQ6FLJo0IEPPJOucYkhGnLeoQ+KwyktEWYgagQKSIdHmZ7EYBksKwlSx1PIl077k922J6v2OWf2ikhHMM/+e9209I1Z1yvXmF3XXmX9UwcZcPWGa3usivvWmFQtiFjP2pfndVrXxv7ZnvTmybZiT8dbUd+ZnIwDfsGBij2ZS0cyxc6zUDYbr755mST3qmnnpocE4Zg4sADD7Rx48Yl453GQI2JIYlTfjWO6t7tzkUgbi6pRPmj8rHmCUPlZMDC5qtD/jzDX+viWMB/6623ligXzUsKmxjq7UAty0L5oqbFkK7mkTjxPpI1yD11BiMpkYgdzzBgG0uGGBDySI3ySPeSxET+IAmsN6WeFQyYNNswjcsgkteQfjfVQgACd/jhh2dkao10bdpE+9i79rXDPn2YHXvuAzbnHz5q0//ebOG1/2STVq+0Jfeb7TR7+DpkrH+A61nPlH+wi1f+g13c/0G/OxT7QibZETtz5sx+z8p+86Mf/Sjpu7bccsvkHHD6ffos+i/6rDR5o3+TkINx04lb2Us4f/ry97D542j6P1QRIWhpEkdkkDcGD57jZjBBvMxxWzHrmZqe4IIC1GBXj8AxbZmH4MQmlbhFfGL+A2GhrJptKNvhw4dHB3vAAQck7yJ1Ig9M1+FmhyxuvnK19g0dcGPGjEme6yOBekX9C/NOHcOEfo0SxLRlnvcbhafnkLE8Z49CUouQBOZdh6f0UxYDWTen/7tdPgQ4UP6uu+7KSNgqe3LJcuuZ8ln78KQ1O0qH7mhHnPx5u3LcKXbSVfvbTz6S8bdBeFHXUezLjthOI3CMZ5A3+jsRNtn0JfRNXFlTqIOAzP9aYgQ6ksCBZ5rEicxhU4FF4BhIqNwMCitWrKgUgWOwa6SjDALHVJYGabCAjIDPYAhV3gGatXrE2WwDCYuVkoVxS1pWD79vfetb9pnPfMZGjRqVnLWKNBMsIXsQJeoZHShuPhDyGEgihBHyF5JDdb55wgrfJbx6U+rhu7jBTwQ0/Www94QrjPOGQxt2Uw0Eli5dmmRk++23XzdDq5+zFYtXmqUOOhkyZg+bPd3slCUrbdXQ4TZuJ7NLcdt422jdUHL7sC561qxZxs7YPffcM/f/2/UH+gbOcaY/ot/RRb/KRd+u/oM+hTFSfTxujZntSr/H23wEmj+iNj+NNUNUhRR504vc62Jw4uI8y5tuuikRn2uqTO93qg0BoBHXMzNmzEgGaQiUpE0QDkmZ+D+NnEukjo4AUyvsgSyURwKncOuldyDP8hCWPOHfd999iQSult4opoW5ICtgksdMmTIl+R8dMqQQMo4NSQzJIXVX9VW2yikrPtJSTyKb/g/1QOGmnw3mnnQPtFzUrgcTv/+3HAiwQxJVTpkfOEM2t1ETh1vv4hX29GqzjfoJ6De0ncYNt6FDRtnU2VPNlvTPz+qnV9ji3qk2e+qoQBdc/3dq3ZEWdsSysaJTCNy1115rzAh84AMf6Js2pT+lj6Y/gLjJDsmb2pLsWpi4f2ci0NEEDsjDiombyktlFoHDZjBB7LzFFlvYnXfemWy37szi6p9qBv1GOx8lYaqlyJcwGPQhWJARpEtM70FIRPKQcPEOHQb4gmdeqRcL/B977LEkA0gDCSPsdOh8KL+8JI+1Z3kIS38Ea99JcjBy5MiaLxHvQOOWdErlk45E5BDSjRQVmzJC8qlyAUfqd0i+eZ4nTZQ3ZYtRGafTMpB7pqLzTOUqDvKYJ/36n9vlRODhhx82Playzdtt8ozp1nPpvfZA7yds7JZrPkZXse7t3Tb7bMgZO0w/YDudcrMtPHma7Z2wvNW26slldv/0D9jZY9bPDrqBrxT70s5rfaA1CKJljyHBCxYssA9/+MMJeYO00U/qktQNm76AKz0utiyxHlFLEeh4AheipUqLLRIHUaCiM7CxC+r222+3RYsWJV9eqBkZiKLRMM52upGqbbPNNoNKQiMiwaAOycNIWsS6KXb25jGoEJAaAf6v8CCKmpqEtCCFouxYt4ckStIhyjAkKvyfssUUMeCTFoymnpObFv6QJ65aBI+kCEdID6QbHPOSJtbUiMBB5sAfA+HOwl+DRSMoKCvKLK8h/iLKM286/P3mIPDoo4/WVN6bqAOZ9vd2zv4H2tEnXW47nHuYjd/wGVtwwQ9s8ReOtS+NfYOcDRk70077wqfs2G/cYtt/dT/b4plb7Bv/9pB94ZvH29h+Urv4NEux7/nnn29nnHFG/B9b/CYfa6gJQccb7UKkDZuP3lDqliZvjIMaE1ucbI+uRQi86a98wlfApCVuEDZdkAQupAJcvb29iTj6/vvvt8mTJycXi9U7zcyfPz9RWFxvkO+0PJFeSZ8gFumpX0gKRtO7EI2/+7u/a3o2586dm+xUizlGq+mRtyFAOnp1BSLt2CLXkEUIXYi/vvQZTA466CCjPmIom6eeeso+/vGP587Jvffem5D3HXbYIfd//Q/lQ4B6tWTJkvpSrlVL7abzvmafPO4S67XpdvxF/2b/fNiU/jrhVvfagu+caAd/4RLrnXa8XfTNf7bDtPFhgNlevHix7bLLLkkfkznFO8Bwm/E3iNsvfvELu+OOO2z33Xe3CRMmJO2KD1pJ4PiYgsCJuKk9irTJbkZ6PIxyIlAZCVxYWanIGoywqeRIa7i4R80CkjdE54imzzvvPDvhhBM6bvcbg6okaOWsXgNLlaRP/LvR1K+kRwOLqfa/kGg1mp6u/e/OfgIh00dBI/y1rpIc07a0i5cwBmIg750sFR9Inqv6HxT4RpmhY22/Yy+2lcfWUQAypMemfP5iW/n5Ou9ERbb2pVCx79FHH732QRtdaEpgrfby5cttp512skMOOSRpDxA32pTIWy3JG+NgOBa2MSsedQsQqAyBS2OlisxXCsRNXyu4w8pPI0Y6xzRhJ6kvEHEZ6ECZxqvT7osmrqw72W233ToNlpalV/iL6BExG2YGayBwA938MNi4/f/NRUBT/GVeY4ZiX5Z2HHnkkW1bLhGifsMNNyS3zCpA1iBujFe6tIQBu5bkLQzP3dVGYIArCMoJikgbdli5cYcVX40Bm3dZJF5vsXoZcwvhDAfPMqaxk9PE4ua8GzU6Ob9lSbsk52VJj6ej2giEin3LkFPq/7Bhw/rW+2qskgCC+3rkjfHMTfcgUCkCR7GFJE5ELk3e1Biw2RmJZm4tlu+Uomfqii80N8UgwOHb6Fty01oEWGfnxhFoFQJsUpJi31bF2SiecLzSWFWPuIm0yW4Uvj+vDgKVI3Bh0ahCp6Vxagw0DnZWZiqZDAMqoXsgOw5LmI1SJol1KBiXcLa+eNhRq+nZ1sfuMTYTARSnowOu7Gb//fc3zhRFsW8ZjAQPmjlKj18816X0aqzTvdvdgUCl18BRhKro6UagxsGO1E7cgYp+JXbZspPWTXMR0OLrvCo5mpuK1oc22EFgsP9Xjj/xiU/I6XYFEGhWvSgaCtbClWUKX+NWLRsswmdFY+PhlxOBShI4KrYaoio58IckDukb951qDj300E5Nekek+5hjjumIdHoiHQFHoNoIMIaFJhzTQn93dx8ClSRwFGO60kPW2IEqyZvWFnRfkXuOHQFHwBFwBMqMAAIICSFklzm9nrb2INC5IqgceOmLBfKGOyRxBLNs2bIcofmrjoAj4Ag4Ao5AMQiIvGFLd2lI4kJ3MSnwUDsFga4icCJvIYHjcGAU+aL3y40j4Ag4Ao6AI9AuBEaPHm0PPvhgQtwgb7pCUkfanMS1q4TKFW/lCVw4lRoSOJG4bbfd1iBxnDfnJK5cldNT4wg4Ao5ANyHAmafsfr/11lv7Sd9CApcmb+n7bsKr2/NambNQaxWkKr6+ZLA5xUAXpzBwgDZnbl5//fWJEsWtttoqUS3SibtTa+Hg/o6AI+AIOALlR4Dj6L797W8nYxCnWHC0YHgGKqfvIIDQRY5CQUX5c+gpbBYClZfACSgquC5J32SzoQHdUzNnzrTtttvO0EV1ySWXJOc66v9uVw2B1fbSrSfZ8KBeqH68Ye9kn/zmlXbr0pcqlPFaeT7E5ix91cwyns+YY0tXVwgCz4ojECCwuneRzfvhN+2TwzU+zLAT5lxni3pfsqXz5rel7kPWDjjgAHviiSeSqdJQCEHSXeIWFGCXOytP4PoPyv2P2IK4pS+I3IgRI5KDzFHu6KaqCAyxjfY+zVb+9Vm75fhJZtMvsCV/eWPn11//+pqtXHi8Dbv+87bPtM/bnIerQuLW5Pnlh+zq46e/UbA9X7RbXrzCPj12fRTtJJg8ueQCm27T7firH7KX53/axla+l6hqHfd81UbgdetdcK59atIRNnfFNvaPi15bQ5autX9+1+t224l72rj/eKr23wt+giDh0Ucf7UfgCo7Sg+9ABLqia4bEYUIbt0TQsiFzcnMeXVk0c3dgverwJK9nPZMOs6//11dteu8cO+XChVYVCpcUzNDxNvPrc+yWL043673I/u17C22VSmzVAjvr7+fapFvm2Ndnjreh8nfbEagQAqufus5OOfhr9vgXLrBzj51pk3p0LCFtf6Yde+4FdqatsCdXtUf8jBSOE4JY2iMJXIXg96w0CYGuIHBgVUsSFxK58J3ly5fbPvvs0ySYPRhHoGQIDNnS9j7pW3bB4ZvZ7cd9xc5b9ILZ6qfs1tO+aQ8dc659de8trWs6h5IVjSenaASes9u/e5rNsSPsS/93cvZHytDJ9n+/OKWtbYC12TKMTW4cgTQCXddHi6QJiPQ9/itXrrRNNtnEJk+erNfc7jIEVvcusEsvuNJu7Pm0ffVTk22jKuZ/6I52xGlftk/3XG/HHXuu/fCis+wHY06178zcuq0DVxWh9jyVB4HVS39sp5+xyGynMTZiaK0hcIhtNO1Am7ZRrefF5ofzmJ9++mnjOL80edM9tq+HK7Ycyh56ZU9iyAN82AjYnbpw4UI74YQT8gTh73Y6AjceaePefGQqF5Ps+Ft+YJ8eX0n6luR1yJYH23euPcuWT/6C/Z/1LrAlP9kxWyKRQsZvHYHORGC1rXpymXGCdM/EUTasPfysIXTz5s2z3XfffZ2Zo/QfRebS/n7fHQiUtPoWB364nkBu2agY4ZB49MK94x3vKC4RHnL5EFhnE8PVdubhr9kZ+7zfPjnngbVrxMqX8kGmaIhtOHxH231aj9mNc+3H970wyPD8746AIzAYBNBH+uKLL1pPT886BC6LsGX5DSZ+/2/nINB1BE5FI9KGHeqIe/755238+PF6ze2uRGDNQuYL/59dMP33dsmRX7GrEjUbFQRj9WN2zZdvtsn/eaWdOe1eO+7YC21RmxZuVxBdz1LpEBhiQ0eMsZ1Kl661CUIfKRsY2FAHORNBk82boXvtP93VbQh0BYELyVroDokbbhQo9vb2uvSt21pBrfwO2dxGTRxuZsttyZN9+zRrvd2B/i/YorP+3ZZ/5os2c/ye9tlvHmfTbj/Tjj3tFuttz+a7FmD4hvqIN/R+Dbf3nzDXlqYJ60u32gl9esGkHwx7uM2Y87BVFpoWoF+GKIaM2cNmT++x3ktvtoUvlas0kb49++yztsUWWyRQiaiFttxsixToAAAgAElEQVRlwNLT0F4EuoLAhRCLwEHYQunbX/7yF3vqqadsr732SrReh/9xd5cisPoVe+G518xsGxs3omoKNV633lvPt6vefpR9dtImiQ64oZOOtP+8YH9b8vUv2CnXPFZBorLaVt33E7vRZtqFK/9qf1n5/+ygp//Fpv3b7YGamNX20sKb7dLerDo/1WZPHeUbPLKg6SS/IWPtIyccYT1pFTr98vC69S76xbrkvt87zb9h5ym6SFFpJeOETUi4nUag8gQOkoYRWZMNgYO06eL+pZdeStYdpEHy++5DAA3tc8861Y6e83ub9sXP2P5jUHRbDZPk7ZufsffOf7ed/Olw08JGNv4jH7fDeh6wObMOtE/9+93VksStfswWvvhuO2xKT0LChvTsbkd+8oNm/SQxz9vCe99h/71Sil3XKHd+8RY7/oAP2NQK1YNq1OaB5AKF1SfarXysHHewffCEOf1PXFm11G69+HL7+dt2sLE1d6kOJN7G/+EUoOHDkfq7cQQaI1BpAheSt9At8iYbEvfnP//ZXn755eQs1Maw+Rudj4COjXqH7YNKgWQX6trpsjcPn2yzrh9mX73mWrvsq/tZTyVayqu2dM4hluTtuEvskTP2sfEn3LpW+sTU4fh97IxE+vSAXfKFqTb8zTpmq/NL3IaMtmnTRgYStNft6RWP2bgvHGxTpC5i9Wob8eEjbe8+xa7k+1Vb+sMLbPHMPWxMJepBBcpy0FnYyMZ/+j9t0cLv2WF2pe0zbuM1681m2AlXLbWNp3/UZrZh9znqQ1DiG45XuGvdDxoGD6CjEaj0YfZhpYekibChKoRD7LlY9/bHP/4xOdB+wYIF9sEPfjA5SqujS9UT7wg4AvURQMpy1UV28bL32zcaEfTVD9ucg86zTf7rDJu5pTT21w/enzoCA0GANXA/+tGPbN9997X111/fNthgg5qH2TPNyvSqT7EOBOlq/Kfy35OQOIibbJE4Sd2QvHFB6tw4Ao5A1RFYI3n923G2z5Fft0t+fpv9fFn9g9JWL/uZzZ1wkO3r5K3qlaPt+dtxxx1tvfXWS5TJh2MW4xYXJhRMhPdtT7wnoOUIVJbAUcnDiq4GoDVvIm4ib9h6v+Wl4BE6Ao5AixBg/dNptvKvr9nKhZfY8XaRzZp2ks196vUa8b9qy+5aYBNm7FzN0zhq5Nq924fArFmzbMmSJf2EDoxfjE+yNVbJbl9qPeZ2IlBZAidQqeC6QhInAofkDTeHBrOA1I0j4Ah0AwLo+jvMvv5fX7Xpvb+wXy6pIYVbvcLumvtOmzH57d0AiuexBAiMGTMm2cjAedwaszSGibDpvgTJ9SS0EYFKEjhVcnBVRdeXiyRwsu+77z5DcSInMEyZMsV1wLWxMnrUjkCrEXhDJ9hba0b7xvTpNJusTQ413/QHjkDzEGAN3K9//es+iVuayDUvJg+pkxGo7FmoIm6hDWmjIWAjdWPB6CuvvGLHHXecbbRRdc+77OQK6ml3BApFYNVKW/LILrbruKz2r+nTg3z6tNBC8MDTCIwYMSLRiPD444/buHHj+gQRGs94H7cMbt/MIDS6x66kBC5dfFRufcGIwP3hD38wdp0ecsghTt7SgPm9I1BBBFY/NdeOHD7DTrh4wRv67VY/Zbd+4zx7+qTP2vSsDQo+fVrBWtA5Wdp1113td7/7XT/yRupDEtc5ufGUFoFA5Qlc+itFRO5nP/uZHXzwwT5lWkSt8jAdgRIiMGTjsbbnfivtjCN2teFvfpMN/9Tl9sKs79iF/ZQZr0346mW/tLunHbhWR9zaR+5yBApHYOutt7bHHnusH2ELx7PCE+ARlB6BShM4VXZ9sWBD4JYtW2arVq2y97znPaUvIE9geRFAf+DcuXMN5ZtuOgCBoTvapy++v29AXHnxsTZz0hunMmSlfsjYT9oFx06xqh2ilpXXKvudc8459vzzz3dcFlnWQx+jcazjMuAJLhyBShO4EL2wEaDpGiM7fM/djkAMAosXL7aPfvSjxpZ/puPdOAKOQDkROOaYY2yzzTZLPrYgRJ1iUOiLYZ221rfJ7pQ8eDqLRaArCJzIm2zOmmMTA5I4N45AHgSQth1//PG2yy672Lx58/L81d91BByBNiLAx9Zee+1ld999dxtTER/1b37zm2SZD5I4iFv6ig/J36wqAl1B4PTVEtoTJkywu+66q6rl6vlqMgJ8uTMVM3LkSDvzzDObHLoH5wg4Aq1A4J577rGpU6cmH2FLly5tRZQDjuNtb3tbn/RN5I3AwnFswIH7HyuBQFcQuLDSq9RGjRpljzzyiL30Ug0FnnrR7a5HgHVufLkzFePGEXAEOh8BPsJQz1HW9XGouELd1bBhw2zIkCENpW8idZ1fMp6DPAhUmsCpUssOgcFvm222SVSJhP7udgSEAF/o7FRm6oUvdzeOgCNQLQT4KPvABz5QuvVx//M//2M777xzTfLG+JU1rlWrdDw3jRCorCLfrIyr0qviv/Od70xOYEDrtRtHII0AX8ErV65Me69zz5e8G0fAEehMBPg4i2nnrcod62xZo430TWNWjBSuVenzeMqDQOUJnMhaGnL8N998c7vtttvSj/zeEUgQmDlzpu2///52wQUX1J0+5eDpsWPHOmqOgCNQQgRqjQEklVN4jjrqqFK1X4533HbbbfvIm9IvO4Q4yy987u5qI1DpKdRqF53nrhUIbLDBBnb00UfbE088kXT2rYjT43AEHIFiEUAHKJvYzjjjjFKRN3KNRLCnpycBQAQtbReLjofeKQh0JYFDnYiuTikoT2d7EeBsQjp7vo4/9KEPtTcxHrsj4AgMGIGrr77a7rjjDttzzz0HHEZRf2RTHWMTU6ahkQos2eEzd3cvAv1rSQVxCIla6Carr776qh+lVcEyLzJLEydOtMsvv9wYBPwkjyKR9rAdgeYi8LWvfc1+//vfG0sjkKyX0UDgNtlkkz4BQzhmyS2b9ON2070IVHoNXFi5027ub775ZuPAYDeOQB4E6PwZBKZNm2aXXXZZnr/6u46AI9BiBJCYl3GqNAsGJP0vvvhicvQX06gc/chYJVvjGDaXplazwnK/6iPwpr+qRlQor6rcOrj+T3/6k3G9/vrr9tprryVHH9FIrrvuOjv55JP9SK0Klb1nxRFwBByBTkaA3e9XXXVVonAYTQkbbrihrb/++sk4xfGPb3nLW+zNb35zcqV3p3Zyvj3t+RGotAQOOMRPRepkc5j96NGjnbzlrzP+D0fAEXAEHIGCENhxxx3thRdeSI56RFMCggiU+uqCvEHcNLYVlAwPtgMQqPwauFpl8OyzzyZqRGo9d39HwBFwBBwBR6AdCKDEF0kcM0bohIO8aUYJ4qYpVWyMBBPtSKvH2T4EuoLAhZVbbhaLaqt2++D3mB0BR8ARcAQcgf4IcIA9x/ehvggCp0tSOJE4/iUS1z8Ev+sGBLqCwKkgqfQy0nSte7cdAUfAEXAEHIGyILD99tvb448/3kfeROKw0xI5CSbCMa4s+fB0FIdAVxG44mD0kB0BR8ARcAQcgeYh8NBDD9mmm27aj8CJuMl24tY8vDsxpK4icL7luhOrqKfZEXAEHIHuQwAJHCSODQ21pG9aCxdK3kJ396HWXTnuCgIHcRN5k5uKT8Nw4wg4Ao6AI+AIlA2BMWPG2BFHHGF33323oTUhTeJCKRxplzSubPnw9BSHQFcQuCz4Ro4cmRynkvXM/RwBR8ARcAQcgXYjgEqR2bNn2y233JKQOEibLhG20G53ej3+1iLQNQROkjfgxQ2Be/rpp43dqG4cAUfAEXAEHIEyIiASN3/+/OSUBmaP0ld62jR9X8Z8eZoGj0DlCVyauIX3W221VbLLZ/AwegiOgCPgCDgCjkAxCEDiOBJs4cKFfRK4cApVUrhiYvdQy4pA5QlcGngIHAYbLde+Di6NkN87Ao6AI+AIlA2BYcOGJevcJH0TaZNNeiV50zhXtjx4epqLQKUJXFiJs9yhX3Nh9dAcAUfAEXAEHIHmIwCBE2mTHcYiEhf6ubuaCFSawFGRG5G0V199tZol67lyBBwBR8ARqBwCIm1pohbeh+7KAeAZ6kOg8ofZ9+U05YDYvfzyy8bBwG4cAUfAEXAEHIFOQCAkcCJqsjsh/Z7G5iFQaQkcMNWr2Iii0XTtxhFwBBwBR8AR6AQE0gSu3hjXCfnxNA4cgcoTuCxokL5xLVu2zMaNG5f1ivs5Ao6AI+AIOAKlQQC1VxtvvHFp0uMJaT8CXUHgtA5OxA37mWeesaFDh9o73vGO9peCp8ARcAQcAUfAEaiDABoT1ltvvbqzSnX+7o8qiEClCZyIG+UWkjfcvb29NmnSpAoWqWfJEXAEHAFHoGoIPPzww7bZZptVLVuen0EgUGkCBy4hieN+yJAhyfXb3/7W3vWudw0COv+rI1B9BPykkuqXseewMxBYsWKFbbLJJpmJ1To42ZkvuWflEOiKXaiSvom8YW+44YaVK0zPkCPQLAQeeOABu/766+3ZZ5+10aNH21577WXbbbedvfWtb21WFB6OI+AI5ESA0xcw2sggd2gnL/hPVyDw5n/913/916rlNC11U2UP7eeff96ee+45GzVqlP3N33QFj61aMXt+CkDgtddes29961v24IMP2k477WQTJ05MpNhIrK+66qrk5JL//d//tddffz1pN07oCigED9IRyEDgqaeeSpb+jBgxwt7ylrck7Q8bVVhcElBIYJEeBzOCdK8OR+BNf62ozFVkTceO8OXy5z//OTlHjsGHBaE33XSTrVq1yg444IB+omkaiBtHoBsRePLJJ+3KK69M1ocyOIQDBAPCE088kbQjBhN2xf3xj3+0CRMm2MiRI23KlCm20UYbdSNsnmdHoHAEkIZfeOGFycfT7NmzE2n4BhtskLRREToROZG4whPlEbQVgcoTOIicSJwIHPaf/vSn5Hr88cft3nvv7SsEyN3KlSuTaSNUjHD+HIfe+8DUB5E7KowABO6aa66xd7/73cmONw0M+ron6/rmo13xYYQkmzbDIuttt93W9t13X/OPoApXEs9a2xC466677NFHH7Vdd93V1l9/fXMC17aiKEXElSdwoCwCx2CjCxIXEjq5Jan7/e9/n0gYWMQNyfOBqRT11RNRMAKsfbv77rv7JHCoLWCJQfhlTxL0YUR7EZGjDTHVunjxYttmm21sv/32cyJXcHl58N2FwOmnn2677bab9fT0JAQOEkcb1YeW2imo8NHlptoIVJbAUWyaRtVgw0CDWyQubWsgCgcluZcsWZIMTEjk2L2KdM51yFW7cXRj7vjC/93vfpdsWGBQYI1bPQKX/jjShxBr6O6///5k88N73/te3/zQjZXJ89xUBPi4mjdvnh144IGJ5A3yJgJHG6W9SlKuKVRfB9fUIihdYJUncCAuIicCp0FHtkhaeC/SJ5LHM9zLly83pHNMNWFjIHKso/NdeqWr356gnAiwUeFtb3ubjRkzJvmylwSOAYLBQQNC2KbUbkTeaCe4X3nllUSax38OOeQQ/+DJWRb+uiMQIsD6t8033zxZ0sOHVdYUKu2U9ha2VbXZMCx3VwOBShM4ioiBRrZIWTj4yE+DUPpe/rJF6GQzUEHkHnrooURycdhhhyWDXzWqh+ei2xBgimbvvfdOFIZqaoYve03NhINB2I5oH2oTInC0DS4kcb/4xS8SaRzTPy657rZa5fkdLAJsYPjud7+bCApE3iBwuLPaqQhc2F5D92DT4/8vBwKV159BpWWgweCmYmvg0TP5MQiJwOkdBiP54RaRw2Zwwo9p1Xe+853JWrmLL77YZsyYYVOnTi1HCXsqHIFIBBgkkJq9/e1v71tTwxe9pG/pQUFtRO2G5xA92gS2rl122SWRTv/mN7+x888/P2mDnILiu1YjC8Zf63oE+ABiXSljDh9UtLn0eIRfSNJojzKhv/zc7nwEKi+BUxEx2GCybA1EeqYBifu0m3tdNCCROPxwo57k5ptvTgYsdvKhXoGvJDeOQKsQQJfbnXfeabFrz3gf9SCsf4OsobSXQUKXiJg+gMJ8qO2oTcimbYQXbYOL3d8QxUceeSS5+Pghvh133DEM1t2OgCOwBgHa58knn5zs7mbXKRdjiiRxoQSO9kt7hbyFH1y0XZE42Q5w5yPQNQSOohJBy3LrmQYk3TMghX4aoPDTAIVfSOYYpJhSRbUCW75RFrz11lvbpptumtQYjkPx9XKd33jKmgOI2Pz5823o0KH28Y9/PHMnKLurf/3rXye7RtlwsOWWW9rw4cMTqRgDhCRvskXewoFA7SirfahNyNaHjmzaCG42B/385z9P4v3Qhz7kHztlrVSerrYhsHDhQrvhhhuSneEibSGB04eW1qvqgws7q92m23DbMuYRDxqBriJwQkvkjPvQHd5rUJKf7hmQ5Ia0ca+LAUkDVkjokDigvV5hoWoBJahMIe2www5O5hJk/KcZCPC1ftppp9nkyZMTEvazn/0sUYEThs006TPPPJOs1YS4obNNnb8GAzp/fc2nB4IwLNxqQ2HbUDvgmT50Qpu2ogtlwJDOP/zhD8kaH5fGpRH2+25GQBJ1SBzLERAG0DZF4iSBUxsO2y1tV5I42WDpJK4aNaorCVxYdBp8avmJrPFc7tBmUOJeJI57DV6hO/TDn8ELCR0a7ZFCHHroocmgG6bD3Y5AXgQgQvfdd1/yta6O/OWXX+7rxAmPjpyNBDzHrffo7NPEjee6anX61H+MbOq62ojc1PmwPagNyEYixzTuggULkqnbmTNn+magvIXv71caAQQB1113XXKcFkSOGR1IXEjg+ACjPetSmw7bMG5MrfZcaRArlrmuJ3BZ5amBiGehW/canGRrkMKud2kQky0JBNNZd9xxRyKJ82mkrBJxvxgEJH1jAw3qBup14nTsdOB05rhlh24951nY2eMOjdqIbJ7hpi1g1D6o9/JXG8BWO5C9YsWK5HQU1sfNmjXLT0EJwXZ31yOAPjjU/bDkAWm1TmOAyIVSuFCaHhI5tWu1Y9ldD2wHAlDJw+wHWw5U6PAiPN2HbvlpgMPWpYFQ99jyky0/Gh07jNBg/+KLLyZKggebB/9/9yHATjXO9h0/fnzf9AqduL7Q1aGL2NX6Wg/rJ3WUeo5RfU8jG/rXcyusejbPtEaUvPz3f/+3QUzRTefH2aWR9/tuRACNB3vssUfS1m+55ZakXTZqG/XaJc/cdCYCLoHLUW5pCQN/xU/+ki7IL32PJAKJg2wkDtwzfcQZrKwBuuKKK+zUU0/1wSpHufirluzsPPvssxMdbltssUXflzhkDMImUqaOXCSK+7Q7vNf7YBzb0as9pNuHJHFqF9yrLdSTyLEhiI+b0aNH23ve8x4/m9grvCOwBgEUynM6w6uvvpqcEITkXR9t4YcbfQD+6gdo47gxuN10JgJO4AZYbulBimDw08U9g1PorwGLd8IBCwKni8Hq3nvvTc6RZLBijYMbR6AeAqyNgbztueeeyQJnOm4uETdskTLZImZpm3j0Dm49rxd/rWdqI7J5T+0DW+1BdtbHDX760HnssceSXbOchiKz1VZbJcRu++239zVzAsXtrkOAnao//vGPk7aw8847962NY/yQ5F0Sd33UqZ0Ppo13HdAly7ATuCYUiAYo2QSpgSp0yw87PVhB4BiokMRxsgOLuRmYDzroIN/c0IQyqmoQIm9MqTANr6/vsLPWV7c66tAGF93LnWUPFj+1jdBWexCBC2194OCX5Vb7If/s8F62bJmxlpSPnunTp/uHz2ALzP/fcQiw1ABpHCefoIMUVVU6KzXsF0TgsGn7InIdl2FPsDmBa1Il0MCk4MJ7DVQ8Y0DiXrYGJxE4bEgcF6oe0JHFYlV25TVa56C43S4fAhCM8847zyZMmJB0rM04qSMkb+gaDHek0WHTQesSSZMNQrhDu547eXGQP+k2QXBhW5BbRI62gZ/IWprMhfe8gzoSpNdMK3H2qqsjGWSB+d87EgHq/2WXXZasG0VV1WabbZZI5CWNQyIv6bzIW9gvdGSmuzTRTuAKKvhagxXRibxpwGLw0Q48SeFE4rA5gujhhx+2Y445xs+RLKi8ig6Wg6jpLFmMj3Jn1Hh89KMfHbCkSORt9913T6ZN6Zz52pbkTQSOOHWRx6yOWkROz4vGQm0jtHGHl0gcfnKLsGXdh20IbNB/19PTYwceeKC3maIL1MMvJQKoFLrpppuSox3R9SgCpz4CEkfbD0lcKTPiiaqJgO9CrQnN4B5ooJRNaBoo1Wiy/PR+aKPvB+nbj370o0SqAAlw0zkI8EXM8WoTJ05MTkdAESf6/37605/a2LFjE1KXJzdZ5C0tfdMXNhI4EbiwTskddt74tcIobsUX3pMeDH5Kt2xJE7HD/IX+vMsJFOCK/rtrr722T4N9K/LmcTgCZUGA9aGQNU5cGTNmTNJmwrYUtju5y5J2T0ccAk7g4nAa9FthA8GNkZ9s+SkyvYcUQqQNCR0N003nIHD11VcbW//ZIabNBZyAgNTo+uuvTzpZdo5CShoZ1nlx0gLnnDJtqg0L2OGXtYgbdYhOW3UstIlLdaxRvEU9V/yhrfQSp9waeGrZyi/P5QZvMGZNkKQNakdF5cfDdQTKhAD9yk9+8pNkGc7GG2/ct6RCHz1hf6A2WKb0e1rqI9B4xKj/f3+aEwEaCYQsbCwMOrWMppBE4lhL1Yz1U7Xic//mIoD0jV2TTOVRzpAsbMqf9XAoq2V6/JprrkkOdUfDOtMdtQwKn9llhhRP5C2LuCmOsG6FdY7w0/e14izaP50OtQ8GGdzpizwxjSqb57rHD9KGzQWeEDh05CG5ZIMQx4yxPs7XyBVdsh5+mRBIt7Mypc3TMjAEnMANDLdB/SvdkHQvm8AZlGTkRvK2aNGiRLEpU2Zuyo8Ax1rttNNOCXGDaHFBTFTWSOIgcZMmTUrWxl166aUJ8dhnn32SacBw44pO7PjEJz6xzoYFJExcIi6Ej1vxyC4zYkojtuo86ZU/frrIm9yQN9zgCnnjHixwY7MzFck199gc2TV//ny76KKLkvVxSCkgzSgQpixk6hFpveO2I1BmBNiVOnLkyGQ9KO0o7BNIt9pWmfPgaauNgG9iqI1NS54w8GDCwYiBRoMNAw7bw7U79cYbb7Rdd93VVYu0pHQGFwmE6ytf+YpBuCBumj6FVIQdJ2UN6VC5QzDQeYZOQHaR6Xg11nMRJipDCCMMj3suddCyyUEY1+By1Pp/q30Qc5Zb7QYbDMNLeKbx1Tv4c/IJ1wsvvJDsYsUNjuxoZZ0ihmlXpquZkmU9KiSPDSMYCHZIshNP/3EE2oyAVIrQl+y///7G9Gm4zIL+iD5C/QR9RCf3E22Gu23RO4FrG/RrI9YghE84uDDAQODYiSoCxw7Ge+65x0444YS1ATTJxXQfAxlXaBiw+IpzqV+ISmM3yjXZQYx0TZ2nJHB0nBiVPeUeEg78IRFM/VH+qMU4/fTT7aijjkoW6UMyCAtb61mw1SEr/Kp0yuARGt2HNm61H9wibvJL38s//B9x4I+fLgZDNkQ899xzCd6PP/548gxsUfVDOckwtY1ED9U/tBvWPjrBEzpuF40AdZUlAxyxhfqQ973vfX264NIffPQR6i+q0k8UjW/ZwncCV5IS0WBBcsKBBgIHedPFYM5xWygrZS3PYAzSHC6m+SAbTCEhbXj729+eSP0IG9LGIAVx5CijcePGJdIIvuhQhYFROLg5iLwZhrRwyXTidBaEC4WaSG8gW7pCoiXyIDsse9WJO++8MzlKirDe//73J50uxC0kb3TEhEtHHF7Cr2o22MjInSZeWQQty0/YC2/CVVhyp+2sOPkPa+wge6+88oo9//zzSds5/PDD/ZQIFZbbhSGg3el8QLC+EzU69N/qd/TBp34jJG9O4AorlkIDdgJXKLz5AtcAogGFAYEBHRKnCwJHQ0WlCKc0hGt2smJ7+umnrbe3N5Ee/O53v0v+q/c23HDDRFLAlxrbzPlC0+CvdzRQYa9cuTI5rxWxPIMUgxVmgw02MNZyQTLpPDS9pDAGYkMaOd+PzgZN+wyGmspCGqj1SrxDHn/729/agw8+uE5Ue+21V1s081NG559/vs2aNatfJ5ruPLPKPCx/ZQidTkjy/vZv/zYhaiJs2OGl8uumDjmso+CVxlT3ImW17uUvm7D0n3S4vBM+13/UZmXT5m6//fZEFxebT1wal8DmP01GAMkb/Q3jwfjx4xPSRn8eSv7DvkcfkSRDfUaTk+TBtQABJ3AtADk2Cg0K2Bo4NBBA4ETmIEqsz+G4Lf2nVhxIyiTNojEzgKjBpr/A5J8e/DU4ySau0F0r7oH6K09hHLgha6tWrUqkGkzzco9BEojUkC9O/Uc2xIf8zJgxo6VSENar/eEPf0jWK6oTpQMNO9EQH9IblrnSH76j8gkJm8pQtspOdvj/qrvBDBPawlG2nnMvvEO/Wu50mOF7Clvhqc1i026pq3xcMJ3OR8jRRx/dJ70mHDeOwGAQYAZk7ty5Sd+47777Jn0M0raw34Gw0feEfYf6k27sKwaDd5n+6wSuTKWRGnw0IEDcwktkTn68p3c10ITZUgOl8WLChit3+ln4fw1Q+KXd8tP7ikv3ee10+hVf6C+/dNh6BzvEA9UrrAuhE0PaGBr82CXK2iVNCYfP87iRuv3qV79KdgpDND/ykY8kYaanLohTOMlWnkg3RukP4w/LCrfKDFvPeF9hhv/tJndYD8i3sJVbdvhe6M56Lj/Zep97lZXioV3ix0VbxcYPN0d9IS1mY8tg1sdR15C65FmygGQcCU0zliPwYcQHFOtmCRfVRs0IFzzdxCEAcUNJL6ctIHVDZQ5TpvpQVL9Df6OLvsL7izh8O+EtJ3AlLCUNBCRNA4FskbZwkOAZ/8HOMhrQNcinbf4jMhC+Gw5Scodp43/yz/zNBgYAAAnoSURBVIp3oH5hmHKH8cqvVvzCIcQFt6R2Cgs/BiEGQwZVNPgz5cl0cpZhwGQDyZIlS5Idoul3mErmAGnUvXCwPB1p2InqC7gegVPasvIWlk26DMNn6XR1432tOiL/tC285a97YZf21z126KZOhfUubK8icQ888ECyrAH9gEjkWFuaZXiftXRsmkgbJM5I0yGB9ZYsKG38n2UJbMSgzrOGdqBTuqT/xz/+cVLPmdLnY4Ud09tuu63tt99+TuTShTXIez5AWSaiJSwqS+oGH56sS4aYq6+hn6GPEZHDHRI3ETjCUb8xyCT639uEgBO4NgHfKFoNDKGtwSG0ea4BI+ysw/DVSEMbty7eDZ/pv/iFYSoteo4dPg/9Q3c6nPBZLXcYrtxpO/yvnuGHW5ewCTEL3SLC2EjpWMPHNERo+NJluprNBEjpIGmolGDgVMeoL1zZYScqP3Wk4CHCHMYTpl3u9POwnEI37+k+/Z9uvg/rBTik77P8wndCd/hu6C83tuqb3NyHdSx08yz9UZFVVkiNVbaN7PD/pCF9ESf1GVKA9IY1orvttlu09JmPmG9/+9uJtIflGSIDpEvrUCFytCGXyIWlkd+NdBPpGmuYIfmQfWFO38PSmLBvSfc5lI36HPVTlFO6DuVPmf+jLAg4gStLSaTSQceLCW0NDmlbnbSC0H/UUOWv+9DOcuv90FaY+IXurHv8FG4YRoy7Xtjhs9Adhou/nsmNDWbCjUFUfhpQeYaEgkPQ0bOGYfME65b40oW0sbMLKRt5U4coO+wow05Vbv6DW/8l/DRGSjfPQneSmOBH/0vbwSvurINAGtv0ffqv6efhfdrNvS7VubDeyS+sd3o/DIs0cK8y5l7utB0+C9Ou8BQ/97gVN5I4pIBLly7tO6Hiwx/+cDINF4YTupk6ZZkAbUR1X+nhPeIgvMWLFycSOSdyIXqN3ZBr8PvlL3+ZEDc0DSDNVz+CDe6hrWf4Q+LC57gpH9mkgPuwzBqnyt8oKwJO4MpaMsEgro4Yu9ZFNvRemKV0Q9W9bN6VW3b4/7RbcchOP2/2fRhP6E7HEz7DrXu5ZWsA1aCmwYx7NodA2OjseB88mJpgqkodIH64daXv5a8OVvfYvBte5IF7GaW51n36/ax7/dfteARU1mn8FUIt//RzvYcdXmGdk5vnchNO+L7CTduqK6pD4XM9C/0IExOGrThV77F13XDDDcm0KOQMSXNa7yPSN87h3XvvvZPnquNKj+JReBwRB5FDGTWSPt+BG5bOWndI2pgqZQkGG7JQPwTGImX0ISFZC/sWlYVsPVPZyCbWrLqyNjXu6iQEnMB1QGmFHTHJDe/lDv3TWcpqsKFf6Oa/6fswjjDsWv7hO3Knw5S/7Hph5X0Wvo87fTGIyY/BBrcGtvCZ0oZN+rlExMIOUn61nof+Ciu0w3hCN+mqZQjTTesQqFcW6We6x9YV1qu0m1zoPeWI+3QZ61623k3fy58wZHAr3rDOa5MFz/iA+elPf5q8x3QoZocddkjIGoSCqTyk1NOmTetHJBS/8kBYInGEz/o4iBxHmjUictqcoXSHNhs2kBoytUj4rOfj/dBwvjBqhvjwCvVIhu+k3e2c6kWiyek6rLtlPSPqmCBhrGejXxFhSxMz9T/qe9L3lAkX/hiVkew0Bn7fmQg4geugclOHLFtJT9/LP23HNt5a78XGk4632feN0hE+lxu71qWBTbbeC9MNJuGljjP0C91hxxn6Eyb3bqqHgOoaOZNbdUn31DE9Tz/TO7WQCetN6E6/z7MwLMXDe8Svei43NoQotPkPfuh6RAcja/U4ZgzpG2uxQkJBfIqT/4XhEAYkDnIIkbv77rsTErf99tsn9xBCGSR20ikpP9mEA8HB5pQLDBJCNh6FhvRC7Fj+QLyYEIvwXfwhhDoyjXVmHFM4duzYlkgLUTUEUUZBNxJPMNU6tpDAheRMbmEe9kNhnxO6yTPvu6keAk7gOqxM63VG9bLSqAE3ep4Ou1Y60u8VeR+TBr2TZeOni0FHbr2bTrs6zXo2/9FzubPsdNh+Xy0EVIdkk7t0/dK9ch6+Kz/Zjdpn1vMwvDCusK5DiHiGn4iX7vV/1WdsEQjZ8kvnT2FhS8pHXOhG5NQXSBNru5A4yWizhvKieHme5af/ZdlKez2bZ7pIJxJGLjZ4IMGDzKFiKD2VnI5PUjTyhmEKVCRX7yJhY9cvhilTTr9hrRvnlIbETQROBFk2eAuP0C0/wsXNM5kQM/m5XS0EnMBVoDzVScVkRY065t0yvxOT56x35IctN503Rn7yD/Mv3LBruXk/fBbep91h2O6uJgJhPcpyy092HhRUz2L+E4aPO7xE4PCjHXDJnQ5bxAFbl9IhW/+VTfgKN3TzXFc6HsJSeLVs/UfPdU+YoUnHoefyD22lExuCifoWpIZM+2666aZ9CtGZykVyhs0GJ9aqTZw4MTklhbiR/oXp4vQc1rax+QPDLl2IGueUYoekDcKmK403YYYXYaXv5ZdEFPRHune7Wgg4gatWeXpuMhBQp82jLLc6cf01fEd+YYcsd9qu966eud29CIT1KnS3AhHFF9q4w0vkTX6kC3dYz3FziVyEz3hX/8EdEqKse72b/GnNj8LjVm7ZtfzC/+MO0xE+S/tzH17Kv4gmz/74xz8mO3VJA8eisZEDFUJIC6VKiGe66qVR72CLAGOHhE33eh7+J3SH8dRzh/l3d/UQcAJXvTL1HDVAQB05r4XurPswKDrQtEn7pe/T7/u9IyAE0nVP/kXaijO0cesi7tAdpkV1G1sXz+Wvd/V/2SJG3OPG6Jn+k2UrXNm8E7qz/hP6EUdodC+bZ0oHttKJHbrDd8LwSIvSI3d4H76LO3wHNyQNO5wmlZ/s9H8UJv4yoVt+bncHAn/THdn0XDoCaxEYTIeX9d8sv7WxucsRyEaglfVGpCUdJ/d6JqKi1Mpf9+F/cetett5TOPq/nof+eiZb/8XW+/Xc4fuN3Ok4dB/auHWJvIX3xKH7MF2kVVfaP50u5Uvvyw6lbSFxw10vTIWXjsfvuwcBl8B1T1l7TiMRoKPOMt5hZqHifp2KgOq5bPJRy82zsP7XcodhKCzsLHf4Lm5MGO4ar5r+We8qnvC/uLP85RfaIXnjf7pXGLyreBvZ6TSk3w/JGs+yLsJI/y8drt93LwJO4Lq37D3njoAj4AisQ25EaGpBI0KRfo5/+r/hvdyy+X/oVnhZ4Wf56f0YOyueMH6e650st56l41K60nb6Pe71TujGL32Fz9Nu7t04AkLACZyQcNsRcAQcgS5GAJICmahFVkJoQjIS+qfdCkt2+rnu9Tw2XP0vfF9h6Fmsrf9l2Wm/MMwwbvwb3Wf9V/+RHYYT+oX/dbcjIAT+P+ekIKFaQUZjAAAAAElFTkSuQmCC"></p>
</div>
<div class="specification">
<p>Giovanni’s tourist guidebook says that the actual horizontal displacement of the Tower, BX, is 3.9 metres.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use Giovanni’s diagram to show that angle ABC, the angle at which the Tower is leaning relative to the<br>horizontal, is 85° to the nearest degree.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use Giovanni's diagram to calculate the length of AX.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use Giovanni's diagram to find the length of BX, the horizontal displacement of the Tower.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the percentage error on Giovanni’s diagram.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Giovanni adds a point D to his diagram, such that BD = 45 m, and another triangle is formed.</p>
<p><img 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"></p>
<p>Find the angle of elevation of A from D.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{{\text{sin BAC}}}}{{37}} = \frac{{{\text{sin 60}}}}{{56}}\) <em><strong>(M1)</strong></em><em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting the sine rule formula, <em><strong>(A1)</strong></em> for correct substitution.</p>
<p>angle \({\text{B}}\mathop {\text{A}}\limits^ \wedge {\text{C}}\) = 34.9034…° <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A0)</strong></em> if unrounded answer does not round to 35. Award <em><strong>(G2)</strong></em> if 34.9034… seen without working.</p>
<p>angle \({\text{A}}\mathop {\text{B}}\limits^ \wedge {\text{C}}\) = 180 − (34.9034… + 60) <em><strong>(M1)</strong></em></p>
<p>Note: Award <em><strong>(M1)</strong></em> for subtracting their angle BAC + 60 from 180.</p>
<p>85.0965…° <em><strong>(A1)</strong></em></p>
<p>85° <em><strong>(AG)</strong></em></p>
<p><strong>Note:</strong> Both the unrounded and rounded value must be seen for the final <em><strong>(A1)</strong></em> to be awarded. If the candidate rounds 34.9034...° to 35° while substituting to find angle \({\text{A}}\mathop {\text{B}}\limits^ \wedge {\text{C}}\), the final <em><strong>(A1)</strong></em> can be awarded but <strong>only</strong> if both 34.9034...° and 35° are seen.<br>If 85 is used as part of the workings, award at most <em><strong>(M1)(A0)(A0)(M0)(A0)(AG)</strong></em>. This is the reverse process and not accepted.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>sin 85… × 56 <em><strong>(M1)</strong></em></p>
<p>= 55.8 (55.7869…) (m) <em><strong>(A1)</strong></em><em><strong>(G2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in trigonometric ratio.</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\sqrt {{{56}^2} - 55.7869{ \ldots ^2}} \) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in the Pythagoras theorem formula. Follow through from part (a)(ii).</p>
<p><strong>OR</strong></p>
<p>cos(85) × 56 <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in trigonometric ratio.</p>
<p>= 4.88 (4.88072…) (m) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p><strong>Note:</strong> Accept 4.73 (4.72863…) (m) from using their 3 s.f answer. Accept equivalent methods.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\left| {\frac{{4.88 - 3.9}}{{3.9}}} \right| \times 100\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into the percentage error formula.</p>
<p>= 25.1 (25.1282) (%) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (a)(iii).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\({\text{ta}}{{\text{n}}^{ - 1}}\left( {\frac{{55.7869 \ldots }}{{40.11927 \ldots }}} \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for their 40.11927… seen. Award <em><strong>(M1)</strong></em> for correct substitution into trigonometric ratio.</p>
<p><strong>OR</strong></p>
<p>(37 − 4.88072…)<sup>2</sup> + 55.7869…<sup>2</sup></p>
<p>(AC =) 64.3725…</p>
<p>64.3726…<sup>2</sup> + 8<sup>2</sup> − 2 × 8 × 64.3726… × cos120</p>
<p>(AD =) 68.7226…</p>
<p>\(\frac{{{\text{sin 120}}}}{{68.7226 \ldots }} = \frac{{{\text{sin A}}\mathop {\text{D}}\limits^ \wedge {\text{C}}}}{{64.3725 \ldots }}\) <em><strong>(A1)</strong></em><strong>(ft)<em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for their correct values seen, <em><strong>(M1)</strong></em> for correct substitution into the sine formula.</p>
<p>= 54.3° (54.2781…°) <em><strong>(A1)</strong></em><strong>(ft)<em>(G2)</em></strong></p>
<p><strong>Note:</strong> Follow through from part (a). Accept equivalent methods.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br>