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</div><h2>SL Paper 1</h2><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The equation of the straight line \({L_1}\) is \(y = 2x - 3.\)</p>
<p>Write down the \(y\)-intercept of \({L_1}\) .</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>Write down the gradient of \({L_1}\) .</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>The line \({L_2}\) is parallel to \({L_1}\) and passes through the point \((0,\,\,3)\) .</p>
<p>Write down the equation of \({L_2}\) .</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>The line \({L_3}\) is perpendicular to \({L_1}\) and passes through the point \(( - 2,\,\,6).\)</p>
<p>Write down the gradient of \({L_3}.\)</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>Find the equation of \({L_3}\) . Give your answer in the form \(ax + by + d = 0\) , where \(a\) , \(b\) and \(d\) are integers.</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>\((0,\,\, - 3)\) <em><strong>(A1) (C1)</strong></em></p>
<p>Note: Accept \( - 3\) or \(y = - 3.\)</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(2\) <em><strong>(A1) (C1)</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(y = 2x + 3\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C1)</strong></em></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for correct equation. Follow through from part (b)<br>Award <em><strong>(A0)</strong></em> for \({L_2} = 2x + 3\).</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\( - \frac{1}{2}\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C1)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (b).</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(6 = - \frac{1}{2}( - 2) + c\) <em><strong>(M1)</strong></em></p>
<p>\(c = 5\) (may be implied)</p>
<p><strong>OR</strong></p>
<p>\(y - 6 = - \frac{1}{2}(x + 2)\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of their gradient in part (d) and the point \(( - 2,\,\,6)\). Follow through from part (d).</p>
<p>\(x + 2y - 10 = 0\) (or any integer multiple) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note:</strong> Follow through from (d). The answer must be in the form \(ax + by + d = 0\) for the <strong><em>(A1)</em>(ft)</strong> to be awarded. Accept any integer multiple.</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>Question 12: Linear function.</p>
<p>Many candidates demonstrated a good understanding of linear functions so successfully found the \(y\)-intercepts, gradient and equation in the form \(y = mx + c\). However only the very best were able to rewrite this in the form \(ax + by + d = 0\) where \(a\), \(b\) and \(d\) are integers.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 12: Linear function.</p>
<p>Many candidates demonstrated a good understanding of linear functions so successfully found the \(y\)-intercepts, gradient and equation in the form \(y = mx + c\). However only the very best were able to rewrite this in the form \(ax + by + d = 0\) where \(a\), \(b\) and \(d\) are integers.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin-top: 0cm;"><span style="font-size: 11.0pt; font-family: 'Arial','sans-serif'; color: #3f3f3f;">Question 12: Linear function.</span></p>
<p style="margin-top: 0cm; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; text-align: start; widows: 2; -webkit-text-stroke-width: 0px; word-spacing: 0px;"><span style="font-size: 11.0pt; font-family: 'Arial','sans-serif'; color: #3f3f3f;">Many candidates demonstrated a good understanding of linear functions so successfully found the \(y\)-intercepts, gradient and equation in the form \(y = mx + c\). However only the very best were able to rewrite this in the form \(ax + by + d = 0\) where \(a\), \(b\) and \(d\) are integers.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin-top: 0cm;"><span style="font-size: 11.0pt; font-family: 'Arial','sans-serif'; color: #3f3f3f;">Question 12: Linear function.</span></p>
<p style="margin-top: 0cm;">Many candidates demonstrated a good understanding of linear functions so successfully found the \(y\)-intercepts, gradient and equation in the form \(y = mx + c\). However only the very best were able to rewrite this in the form \(ax + by + d = 0\) where \(a\), \(b\) and \(d\) are integers.</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin-top: 0cm;"><span style="font-size: 11.0pt; font-family: 'Arial','sans-serif'; color: #3f3f3f;">Question 12: Linear function.</span></p>
<p style="margin-top: 0cm; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; text-align: start; widows: 2; -webkit-text-stroke-width: 0px; word-spacing: 0px;"><span style="font-size: 11.0pt; font-family: 'Arial','sans-serif'; color: #3f3f3f;">Many candidates demonstrated a good understanding of linear functions so successfully found the \(y\)-intercepts, gradient and equation in the form \(y = mx + c\). However only the very best were able to rewrite this in the form \(ax + by + d = 0\) where \(a\), \(b\) and \(d\) are integers.</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;">The equation of a line <em>L</em><sub>1</sub> is \(2x + 5y = −4\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the gradient of the line <em>L</em><sub>1</sub>.</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>A second line <em>L</em><sub>2</sub> is perpendicular to <em>L</em><sub>1</sub>.</span></p>
<p><span>Write down the gradient of <em>L</em><sub>2</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>The point (5, 3) is on <em>L</em><sub>2</sub>.</span></p>
<p><span>Determine the equation of <em>L</em><sub>2</sub>.</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>Lines <em>L</em><sub>1</sub> and <em>L</em><sub>2</sub> intersect at point P.</span></p>
<p><span>Using your graphic display calculator or otherwise, find the coordinates of P.</span></p>
<div class="marks">[2]</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>\(\frac{-2}{{5}}\) <strong><em>(A1)</em></strong> <em><strong>(C1)</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{5}{{2}}\) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from their answer to part (a).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(3 = \frac{5}{2} \times 5 + c\) <em><strong>(M1)</strong></em></span><br><br></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of their gradient into equation of line. Follow through from their answer to part (b).</span></p>
<p><br><span>\(y = \frac{5}{2}x - \frac{19}{2}\) <em><strong>(A1)(ft)</strong></em><br></span></p>
<p><strong><span>OR</span></strong></p>
<p><span>\(y - 3 = \frac{5}{2}(x - 5)\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of their gradient into equation of line.</span> <span>Follow through from their answer to part (b).</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(3, −2) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong> <strong><em>(C2)</em></strong></span></p>
<p><br><span><strong>Notes:</strong> If parentheses not seen award at most <em><strong>(A0)(A1)</strong></em><strong>(ft)</strong>. Accept <em>x</em> = 3, <em>y</em> = −2. Follow through from their answer to part (c), even if no working is seen. Award <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong> for a sensible attempt to solve \(2x + 5y = −4\) and their \(y = \frac{5}{2}x - \frac{19}{2}\) or equivalent, simultaneously.</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><span style="font-family: times new roman,times; font-size: medium;">Triangle \({\text{ABC}}\)</span><span style="font-family: times new roman,times; font-size: medium;"> is such that \({\text{AC}}\)</span><span style="font-family: times new roman,times; font-size: medium;"> is \(7{\text{ cm}}\), angle \({\text{ABC}}\)</span><span style="font-family: times new roman,times; font-size: medium;"> is \({65^ \circ }\) and angle \({\text{ACB}}\)</span><span style="font-family: times new roman,times; font-size: medium;"> is \({30^ \circ }\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Sketch the triangle writing in the side length and angles.</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 \({\text{AB}}\).</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 area of triangle \({\text{ABC}}\).</span></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><span><img src="data:image/png;base64,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" alt><span> <em><strong>(A1) (C1)</strong></em></span></span></p>
<p><span><em><strong><br></strong></em><strong>Note:</strong> <em><strong>(A1)</strong></em> for fully labelled sketch.</span></p>
<p><span><em><strong>[1 mark]</strong></em><br></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> may apply in this question.</em><br></span></p>
<p><span>\(\frac{{{\text{AB}}}}{{\sin 30}} = \frac{7}{{\sin 65}}\) <em><strong>(M1)</strong></em></span></p>
<p><span><em><strong>(UP)</strong></em><strong> </strong>\({\text{AB}} = 3.86{\text{ cm}}\) <em><strong>(A1)</strong></em><strong>(ft) <em>(C2)</em></strong></span></p>
<p><span><strong>Note: <em>(M1)</em></strong> for use of sine rule with correct values substituted.</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>Unit penalty <strong>(UP)</strong> may apply in this question.</em></span></p>
<p><span>\({\text{Angle BAC}} = {85^ \circ }\) <em><strong>(A1)</strong></em></span></p>
<p><span>\({\text{Area}} = \frac{1}{2} \times 7 \times 3.86 \times \sin {85^ \circ }\) <em><strong>(M1)</strong></em></span></p>
<p><span><em><strong>(UP)</strong></em> \( = 13.5{\text{ }}{{\text{cm}}^2}\) <em><strong>(A1)</strong></em><strong>(ft) <em>(C3)</em></strong></span></p>
<p><span><strong><em>[3 marks]<br></em></strong></span></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;">The triangle was drawn correctly by most and a majority correctly found the length of AB - a few did not write down the units (cm) and so lost a Unit penalty mark. There was still a significant number who tried to use right-angled trigonometry to find the length.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Finding the area of the triangle was mixed with many again assuming the existence of a right angle. Some candidates had their calculators in radian mode rather than degree mode.</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;">The triangle was drawn correctly by most and a majority correctly found the length of AB - a few did not write down the units (cm) and so lost a Unit penalty mark. There was still a significant number who tried to use right-angled trigonometry to find the length.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Finding the area of the triangle was mixed with many again assuming the existence of a right angle. Some candidates had their calculators in radian mode rather than degree mode.</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;">The triangle was drawn correctly by most and a majority correctly found the length of AB - a few did not write down the units (cm) and so lost a Unit penalty mark. There was still a significant number who tried to use right-angled trigonometry to find the length.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Finding the area of the triangle was mixed with many again assuming the existence of a right angle. Some candidates had their calculators in radian mode rather than degree mode.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The equation of the line \({R_1}\) is \(2x + y - 8 = 0\) . The line \({R_2}\) is perpendicular to \({R_1}\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the gradient of \({R_2}\) .</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>The point of intersection of \({R_1}\) and \({R_2}\) is \((4{\text{, }}k)\) .</span><br><span>Find</span><br><span>(i) the value of \(k\) ;</span><br><span>(ii) the equation of \({R_2}\) .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(y = - 2x + 8\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for rearrangement of equation or for \( - 2\) seen.</span></p>
<p> </p>
<p><span><span>\(m({\text{perp}}) = \frac{1}{2}\) </span><span> <em><strong>(A1)</strong></em> <strong><em>(C2)</em></strong></span></span></p>
<p><span><span><strong><em>[2 marks]<br></em></strong></span></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(2(4) + k - 8 = 0\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for evidence of substituting \(x = 4\) into \({R_1}\) .</span></p>
<p> </p>
<p><span>\(k = 0\) <em><strong>(A1) (C2)</strong></em></span></p>
<p><span> </span></p>
<p><span>(ii) \(y = \frac{1}{2}x + c\) <em>(can be implied)</em> <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution of \(\frac{1}{2}\) into equation of the line.</span></p>
<p> </p>
<p><span>\(0 = \frac{1}{2}(4) + c\)</span></p>
<p><span>\(y = \frac{1}{2}x - 2\) <em><strong>(A1)</strong></em><strong>(ft) </strong><em><strong> (C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Follow through from parts (a) and (b)(i). Accept equivalent forms for the equation of a line.</span></p>
<p><span><strong>OR</strong></span></p>
<p><span>\(y - {y_1} = \frac{1}{2}(x - {x_1})\) <strong><em>(M1)</em></strong></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution of \(\frac{1}{2}\) into equation of the line.</span></p>
<p> </p>
<p><span>\(y = \frac{1}{2}(x - 4)\) <em><strong>(A1)</strong></em><strong>(ft) </strong><em><strong>(C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Follow through from parts (a) and (b)(i). Accept equivalent forms for the equation of a line.</span></p>
<p><span> </span></p>
<p><span><em><strong>[4 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</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;">Parts a and bi of Question 13 appeared to be accessible to most candidates, but part bii was not well attempted. Many candidates did not show their working and lost method marks due to their incorrect answers.</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;">Parts a and bi of Question 13 appeared to be accessible to most candidates, but part bii was not well attempted. Many candidates did not show their working and lost method marks due to their incorrect answers.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A type of candy is packaged in a right circular cone that has volume \({\text{100 c}}{{\text{m}}^{\text{3}}}\) and vertical height 8 cm.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_11.14.55.png" alt="M17/5/MATSD/SP1/ENG/TZ1/09"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the radius, \(r\), of the circular base of the cone.</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>Find the slant height, \(l\), of the cone.</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 curved surface area of the cone.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(100 = \frac{1}{3}\pi {r^2}(8)\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution into volume of cone formula.</p>
<p> </p>
<p>\(r = 3.45{\text{ (cm) }}\left( {3.45494 \ldots {\text{ (cm)}}} \right)\) <strong><em>(A1)</em></strong> <strong><em>(C2)</em></strong></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>\({l^2} = {8^2} + {(3.45494 \ldots )^2}\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution into Pythagoras’ theorem.</p>
<p> </p>
<p>\(l = 8.71{\text{ (cm) }}\left( {8.71416 \ldots {\text{ (cm)}}} \right)\) <strong><em>(A1)</em>(ft)</strong><em> </em><strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (a).</p>
<p> </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>\(\pi \times 3.45494 \ldots \times 8.71416 \ldots \) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for their correct substitutions into curved surface area of a cone formula.</p>
<p> </p>
<p>\( = 94.6{\text{ c}}{{\text{m}}^2}{\text{ }}(94.5836 \ldots {\text{ c}}{{\text{m}}^2})\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from parts (a) and (b). Accept \(94.4{\text{ c}}{{\text{m}}^2}\) from use of 3 sf values.</p>
<p> </p>
<p><strong><em>[2 marks]</em></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><span style="font-family: times new roman,times; font-size: medium;">The straight line, <em>L</em><sub>1</sub>, has equation <em>y</em> = −2<em>x</em> + 5.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the gradient of <em>L</em><sub>1</sub> .</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>Line <em>L</em><sub>2</sub>, is perpendicular to line <em>L</em><sub>1</sub>, and passes through the point (4, 5) .</span></p>
<p><span>(i) Write down the gradient of <em>L</em><sub>2</sub> .</span></p>
<p><span>(ii) Find the equation of <em>L</em><sub>2</sub> .</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><span>Line <em>L</em><sub>2</sub>, is perpendicular to line <em>L</em><sub>1</sub>, and passes through the point (4, 5) .</span></span></p>
<p><span>Write down the coordinates of the point of intersection of <em>L</em><sub>1</sub> and <em>L</em><sub>2</sub> .</span></p>
<div class="marks">[2]</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>–2 <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span> </p>
<p><span><strong>Note:</strong> Do not accept \(\frac{{ - 2}}{1}\)</span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(\frac{1}{2}(0.5)\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Note:</strong> Follow through from their part (a).</span></p>
<p> </p>
<p><span>(ii) \(5 = \frac{1}{2}(4) + c\) <em><strong>(M1)</strong></em></span> </p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their gradient substituted correctly.</span></p>
<p> </p>
<p><span>\(y = \frac{1}{2}x + 3\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Note:</strong> Follow through from their part (b)(i).</span></p>
<p> </p>
<p><strong><span>OR</span></strong></p>
<p><span>\(y - 5 = \frac{1}{2}(x - 4)\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong> <em><strong>(C3)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for their gradient substituted correctly, <em><strong>(A1)</strong></em><strong>(ft)</strong> for 5 and 4 seen in the correct places. Follow through from their part (b)(i).</span></p>
<p><span> </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>(0.8, 3.4) or \(\left( {\frac{4}{5},\frac{{17}}{5}} \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Accept </span><span><span><em>x</em> = </span>0.8 and </span><span><span><em>y</em> = </span>3.4. Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for an attempt to solve the equations analytically, (attempt to eliminate either <em>x</em> or <em>y</em>), or graphically with a sketch (two reasonably accurate straight line graphs (from their answer to part (b)) and an indication of scale). Follow through from their <em>L</em><sub>2</sub> if it intersects <em>L</em><sub>1</sub>, <strong>OR</strong> follow through from their equation, or expression in <em>x</em>, from their part (b)(ii). Award at most <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A0)</strong></em><strong>(ft)</strong> if brackets missing. Award <strong><em>(A0)</em>(ft)<em>(A1)</em>(ft)</strong> for an answer of (0, 5) following an equation (or expression in <em>x</em>) of the form <em>y</em> = <em>mx</em> + 5 (<em>m</em> ≠ –2) found in part (b).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></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-size: medium; font-family: times new roman,times;">The majority of candidates were able to write down the gradient of the straight line in part (a) but a correct answer for the gradient of the perpendicular proved to be more elusive in part (b)(i). Many however recovered in the remainder of the question as they were able to find the equation of a line using their gradient and the coordinates of a point on the line but, in some case, did not always show clear working. A significant minority of candidates, who attempted to substitute (4, 5) into the equation <em>y</em> = <em>mx</em> + <em>c</em> , incorrectly identified the value of<em> c</em> as 5.</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 majority of candidates were able to write down the gradient of the straight line in part (a) but a correct answer for the gradient of the perpendicular proved to be more elusive in part (b)(i). Many however recovered in the remainder of the question as they were able to find the equation of a line using their gradient and the coordinates of a point on the line but, in some case, did not always show clear working. A significant minority of candidates, who attempted to substitute (4, 5) into the equation <em>y</em> = <em>mx</em> + <em>c</em> , incorrectly identified the value of<em> c</em> as 5.</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 majority of candidates were able to write down the gradient of the straight line in part (a) but a correct answer for the gradient of the perpendicular proved to be more elusive in part (b)(i). Many however recovered in the remainder of the question as they were able to find the equation of a line using their gradient and the coordinates of a point on the line but, in some case, did not always show clear working. A significant minority of candidates, who attempted to substitute (4, 5) into the equation <em>y</em> = <em>mx</em> + <em>c</em> , incorrectly identified the value of<em> c</em> as 5.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A cylindrical container with a radius of 8 cm is placed on a flat surface. The container is filled with water to a height of 12 cm, as shown in the following diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_06.17.11.png" alt="M17/5/MATSD/SP1/ENG/TZ2/12"></p>
</div>
<div class="specification">
<p>A heavy ball with a radius of 2.9 cm is dropped into the container. As a result, the height of the water increases to \(h\) cm, as shown in the following diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_06.18.54.png" alt="M17/5/MATSD/SP1/ENG/TZ2/12.b"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the volume of water in the container.</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>Find the value of \(h\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(\pi \times {8^2} \times 12\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution into the volume of a cylinder formula.</p>
<p> </p>
<p>\(2410{\text{ c}}{{\text{m}}^3}{\text{ }}(2412.74 \ldots {\text{ c}}{{\text{m}}^3},{\text{ }}768\pi {\text{ c}}{{\text{m}}^3})\) <strong><em>(A1)</em></strong> <strong><em>(C2)</em></strong></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>\(\frac{4}{3}\pi \times {2.9^3} + 768\pi = \pi \times {8^2}h\) <strong><em>(M1)(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution into the volume of a sphere formula (this may be implied by seeing 102.160…), <strong><em>(M1) </em></strong>for adding their volume of the ball to their part (a), <strong><em>(M1) </em></strong>for equating <strong>a </strong>volume to the volume of a cylinder with a height of \(h\).</p>
<p> </p>
<p><strong>OR</strong></p>
<p>\(\frac{4}{3}\pi \times {2.9^3} = \pi \times {8^2}(h - 12)\) <strong><em>(M1)(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution into the volume of a sphere formula (this may be implied by seeing 102.160…), <strong><em>(M1) </em></strong>for equating to the volume of a cylinder, <strong><em>(M1) </em></strong>for the height of the water level increase, \(h - 12\). Accept \(h\) for \(h - 12\) if adding 12 is implied by their answer.</p>
<p> </p>
<p>\((h = ){\text{ }}12.5{\text{ (cm) }}\left( {12.5081 \ldots {\text{ (cm)}}} \right)\) <strong><em>(A1)</em>(ft)</strong> <strong><em>(C4)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> If 3 sf answer used, answer is 12.5 (12.4944…). Follow through from part (a) if first method is used.</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</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>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;"><em>P</em> (4, 1) and <em>Q</em> (0, –5) are points on the coordinate plane.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Determine the</span></p>
<p><span>(i) coordinates of <em>M</em>, the midpoint of <em>P</em> and <em>Q</em>.</span></p>
<p><span>(ii) gradient of the line drawn through <em>P</em> and <em>Q</em>.</span></p>
<p><span>(iii) gradient of the line drawn through <em>M</em>, perpendicular to <em>PQ</em>.</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>The perpendicular line drawn through <em>M</em> meets the <em>y</em>-axis at <em>R</em> (0, <em>k</em>).</span></p>
<p><span>Find <em>k</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>(i) (2, – 2) <em>parentheses not required. <strong>(A1)</strong></em></span></p>
<p> </p>
<p><span>(ii) gradient of PQ \( = \left( {\frac{{ - 5 - 1}}{{0 - 4}}} \right) = \frac{6}{4} = \frac{3}{2}(1.5)\) <em><strong>(M1)(A1)<br><br></strong></em></span><span><em><strong>(M1)</strong> for gradient formula with correct substitution</em></span></p>
<p><span><em>Award <strong>(A1)</strong> for </em>\(y = \frac{3}{2}x - 5\) <em>with no other working<br><br></em></span></p>
<p><span>(iii) gradient of perpendicular is \( - \frac{2}{3}\) <em><strong>(A1)</strong></em><strong>(ft) <em>(C4)</em></strong></span></p>
<p> </p>
<p><span><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\left( {\frac{{k + 2}}{{0 - 2}}} \right) = - \frac{2}{3}\), \(k = - \frac{2}{3}\) <strong>or</strong> \(y = - \frac{2}{3}x + c\), \(c = - \frac{2}{3}\therefore k = - \frac{2}{3}\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><em>Allow</em> <em>(</em>\(0, - \frac{2}{3}\)<em>)</em></span></p>
<p><span><em><strong>(M1)</strong> is for equating gradients or substituting gradient into</em> \(y = mx + c\) <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">b.</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;">There were some good answers, but many candidates showed a shaky understanding of coordinate geometry and some difficulty in dealing with negative numbers. Evidently a favourite question for some centres that consistently scored high marks here.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">a) This was done quite well by most candidates with the main errors being reversal of the <em>x</em>, <em>y</em> values in the formula and using the negative, rather than the negative reciprocal for the perpendicular.</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;">There were some good answers, but many candidates showed a shaky understanding of coordinate geometry and some difficulty in dealing with negative numbers. Evidently a favourite question for some centres that consistently scored high marks here.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">b) Poorly answered though many candidates did gain a mark by substituting the correct value for gradient into \(y = mx + c\).</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: 'times new roman', times; font-size: medium;">The area of a circle is equal to 8 cm<sup>2</sup>.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the radius of the circle.</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>This circle is the base of a <strong>solid</strong> cylinder of height 25 cm.</span></p>
<p><span>Write down the volume of the <strong>solid</strong> cylinder.</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><span>This circle is the base of a <strong>solid</strong> cylinder of height 25 cm.</span></span></p>
<p><span>Find the <strong>total</strong> surface area of the <strong>solid</strong> cylinder.</span></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><span>π<em>r</em><sup>2 </sup>= 8 <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct area formula.<br></span></p>
<p><span> </span></p>
<p><span><em>r</em> = 1.60 (cm) (1.59576...) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></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>200 cm<sup>3</sup> <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Units are required. Follow through from their part (a). Accept 201 cm<sup>3</sup> (201.061…) for use of <em>r</em> = 1.60 .</span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Surface area = 16 + 2</span><span><span>π</span>(1.59576...)25 <em><strong>(M1)(M1)</strong></em></span></p>
<p><span><strong>Note: </strong> Award <em><strong>(M1)</strong></em> for correct substitution of their <em>r</em> into curved surface area formula, <em><strong>(M1)</strong></em> for adding 16 or 2 × </span><span><span><span>π × </span></span>(their answer to part (a))<sup>2</sup><br></span></p>
<p><span> </span></p>
<p><span>267 cm<sup>2 </sup>(266.662...cm<sup>2</sup>) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C3)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their part (a).</span></p>
<p><span><em><strong>[3 marks]</strong></em></span></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;">There were two common errors identified on a number of scripts in this question. In part (a), the majority of candidates correctly wrote down π<em>r</em><sup>2</sup> = 8 for method but a significant number of candidates then went on to write down <em>r</em> = 2.55 (forgetting to square root). Such candidates were able to recover in subsequent parts of the question with the allowable follow through marks, but a method mark and final accuracy mark was lost on many scripts in part (c) with incomplete methods shown for the total surface area of the cylinder. Leaving off the addition of either one or both end surfaces of the cylinder resulted in the final two marks being lost.</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;">There were two common errors identified on a number of scripts in this question. In part (a), the majority of candidates correctly wrote down π<em>r</em><sup>2</sup> = 8 for method but a significant number of candidates then went on to write down <em>r</em> = 2.55 (forgetting to square root). Such candidates were able to recover in subsequent parts of the question with the allowable follow through marks, but a method mark and final accuracy mark was lost on many scripts in part (c) with incomplete methods shown for the total surface area of the cylinder. Leaving off the addition of either one or both end surfaces of the cylinder resulted in the final two marks being lost.</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;">There were two common errors identified on a number of scripts in this question. In part (a), the majority of candidates correctly wrote down π<em>r</em><sup>2</sup> = 8 for method but a significant number of candidates then went on to write down <em>r</em> = 2.55 (forgetting to square root). Such candidates were able to recover in subsequent parts of the question with the allowable follow through marks, but a method mark and final accuracy mark was lost on many scripts in part (c) with incomplete methods shown for the total surface area of the cylinder. Leaving off the addition of either one or both end surfaces of the cylinder resulted in the final two marks being lost.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Triangle \({\text{ABC}}\) is drawn such that angle </span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\({\text{ABC}}\) </span>is \({90^ \circ }\), angle </span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\({\text{ACB}}\) </span>is \({60^ \circ }\) and </span><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>is \(7.3{\text{ cm}}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Sketch a diagram to illustrate this information. Label the points \({\text{A, B, C}}\). Show the angles \({90^ \circ }\), \({60^ \circ }\) and the length \(7.3{\text{ cm}}\) on your diagram.</span></p>
<p><span>(ii) Find the length of \({\text{BC}}\).</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>Point </span><span><span><span>\({\text{D}}\)</span></span> is on the straight line </span><span><span><span>\({\text{AC}}\)</span></span> extended and is such that angle </span><span><span><span>\({\text{CDB}}\)</span></span> is \({20^ \circ }\).</span></p>
<p><span>(i) Show the point </span><span><span><span>\({\text{D}}\)</span></span> and the angle \({20^ \circ }\) on your diagram.</span></p>
<p><span>(ii) Find the size of angle </span><span><span><span>\({\text{CBD}}\)</span></span>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</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 where indicated in the left hand column.</em></span></p>
<p><span>(i)</span></p>
<p><span><img src="data:image/png;base64,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" alt> <em><strong>(A1)</strong></em></span></p>
<p><span>For </span><span><span>\({\text{A}}\)</span>, </span><span><span><span><span>\({\text{B}}\)</span></span></span>, </span><span><span><span><span>\({\text{C}}\)</span></span></span>, \(7.3\), \({60^ \circ }\), \({90^ \circ }\), shown in correct places <em><strong>(A1)</strong></em></span></p>
<p><span><br><strong>Note: </strong>The \({90^ \circ }\) should look like \({90^ \circ }\) (allow \( \pm {10^ \circ }\))</span></p>
<p><span><br>(ii) Using \(\tan 60\) or \(\tan 30\) <em><strong>(M1)</strong></em></span></p>
<p><span><em><strong>(UP)</strong></em> \(4.21{\text{ cm}}\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Note: (ft)</strong> on their diagram</span></p>
<p><br><span><strong>Or</strong></span></p>
<p><span>Using sine rule with their correct values <em><strong>(M1)</strong></em></span></p>
<p><span><em><strong>(UP)</strong></em> \( = 4.21{\text{ cm}}\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Or</strong></span></p>
<p><span>Using special triangle \(\frac{{7.3}}{{\sqrt 3 }}\) <em><strong>(M1)</strong></em></span></p>
<p><span><em><strong>(UP)</strong></em> \(4.21{\text{ cm}}\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Or</strong></span></p>
<p><span>Any other valid solution<br></span></p>
<p><span><strong>Note:</strong> If A and B are swapped then \({\text{BC}} = 8.43{\text{ cm}}\) <em><strong>(C3)</strong></em></span></p>
<p><span><em><strong>[3 marks]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) For </span><span><span><span>\({\text{ACD}}\) </span></span>in a straight line and all joined up to </span><span><span>\({\text{B}}\)</span>, for \({20^ \circ }\) shown in correct place and </span><span><span><span>\({\text{D}}\)</span></span> labelled. </span><span><span><span>\({\text{D}}\)</span></span> must be on </span><span><span><span>\({\text{AC}}\) </span></span>extended. <em><strong>(A1)</strong></em></span></p>
<p><span>(ii) \({\text{B}}\hat {\text{C}}{\text{D}} = {120^ \circ }\) <em><strong>(A1)</strong></em></span></p>
<p><span>\({\text{C}}\hat {\text{B}}{\text{D}} = {40^ \circ }\) <em><strong>(A1) (C3)</strong></em></span></p>
<p><span><em><strong>[3 marks]<br></strong></em></span></p>
<div class="question_part_label">b.</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;">The initial diagram was well drawn by most candidates but few could extend </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;">\({\text{AC}}\)</span></span></span> to find </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;">\({\text{D}}\)</span></span></span>. The point </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;">\({\text{D}}\)</span></span></span> was either drawn between </span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\({\text{A}}\)</span></span><span style="font-family: times new roman,times; font-size: medium;"> and </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;">\({\text{C}}\)</span></span></span> or on </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;">\({\text{CA}}\)</span></span></span> extended. When on </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;">\({\text{CA}}\)</span></span></span> extended the candidates could be awarded A1 follow through for the angle. A surprising number of candidates could not find the correct answer for the length of </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>.</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;">The initial diagram was well drawn by most candidates but few could extend </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;">\({\text{AC}}\)</span></span></span> to find </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;">\({\text{D}}\)</span></span></span>. The point </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;">\({\text{D}}\)</span></span></span> was either drawn between </span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\({\text{A}}\)</span></span><span style="font-family: times new roman,times; font-size: medium;"> and </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;">\({\text{C}}\)</span></span></span> or on </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;">\({\text{CA}}\)</span></span></span> extended. When on </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;">\({\text{CA}}\)</span></span></span> extended the candidates could be awarded A1 follow through for the angle. A surprising number of candidates could not find the correct answer for the length of </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>.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A and B are points on a straight line as shown on the graph below.</span></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>Write down the <em>y</em>-intercept of the line AB.</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 gradient of the line AB.</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 acute angle between the line AB and the <em>x</em>-axis is <em>θ</em>.</span></p>
<p><span>Show <em>θ</em> on the 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><span>The acute angle between the line AB and the <em>x</em>-axis is <em>θ</em></span></span><span><span>.</span></span></p>
<p><span>Calculate the size of <em>θ</em>.</span></p>
<div class="marks">[2]</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>6</span></p>
<p><strong><span>OR</span></strong></p>
<p><span>(0, 6) <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{(2 - 5)}}{{(8 - 2)}}\) <strong><em>(M1)</em></strong></span></p>
<p><span><span><br> </span><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for substitution in gradient formula.</span></p>
<p><span><span><br> </span>\( = - \frac{1}{2}\) <strong><em>(A1)</em></strong> <strong><em>(C2)</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>Angle clearly identified. <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\tan \theta = \frac{1}{2}\) (or equivalent fraction) <em><strong>(M1)</strong></em></span></p>
<p><span>\(\theta = 26.6^\circ\) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note: (ft)</strong> from (b).</span></p>
<p><span>Accept alternative correct trigonometrical methods.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></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;">This was generally well answered.</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;"><span style="font-family: times new roman,times; font-size: medium;">This was generally well answered, the errors coming from incorrect substitution into the gradient formula rather than using the two intercepts.</span></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;"><span style="font-family: times new roman,times; font-size: medium;">There was often a lack of accuracy in the answers. Also, the use of the sine rule overly complicated matters for many.</span></span></p>
<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="question">
<p><span>The following diagrams show six lines with equations of the form <em>y</em> =<em>mx</em> +<em>c</em>.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>In the table below there are four possible conditions for the pair of values <em>m</em> and <em>c</em>. Match each of the given conditions with one of the lines drawn above.</span></p>
<p><span><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbcAAADMCAIAAAB/Z3oKAAAgAElEQVR4nO3c708bV6I+8PMH+I1f+gWypVGkGAWxEUIKVYSI1EZOVjIoVRRlqSyTBOHoCpHelXwTYciLkGhvfQUX1F2qrixTt1Gge6ewcaqSH65FWoV8YawSJbS2s2FFEtsNyIWRgwyYmfN9MYP5ZWxIAj3Gz0fzIrhjz0z09GHOmeMQCgAAmyO/9wkAADANLQkAkA1aEgAgG7UlOb0BGzZs2LCltwwt+TtUNMBayCEwAi0JjEIOgRFoSWAUcgiMQEsCo5BDYARaEhiFHAIj0JLAKOQQGIGWBEYhh8AItCQwCjkERqAlgVHIITACLQmMQg6BEWhJYBRyCIxASwKjkENgBFoSGIUcAiMKqiWlRHhowN18XP13Pg7Vt3/tD4tUDPh/Sryzg8T665f/HZGy9kBKeTEx0mEqLjn7ZTAhZX5Xzh0Kz97N4RtKBdrL1v1bNWf7Yxl2nAm0n+CMtp6guOvnuDcVTkuKQbetRG/gTM1fBmJKFUmxkS+bzZz+WEfg3bUkpVQK9piLV7fkcr5XH0hKBL7sWf4x0w6Fbo/m8C1N+5srOb2B09f2hJOZd0kFOv6w9pc0vJ0Cacl0Rbb5Ywtr/9NMoL3xXXfTi4GzB3PcSyZGOkzmlePiXnKDvZjDt5cItB/j9AZO3zgQ26wDcS/5jhVES0qR/vNGA6cvrnEHM5TQux1xU5qhJddJPOk5ewh3jtntvRy+C1tpSXjHCqElk2F3bY5BSloi7Gs/V6I3cPri481uf1j9bbwyJfSHtoGH1x2mYk5ffLy5P5y+9ZNiAY8y42l29H/Xs6olV00nNQ7EFhLhfoepeNXsUuM/+v+yaodU1jNJ/09iKPuk//+tHDG49+p2z+XwncjVksvDbU5/sL7/xdYCI4bvddUblaRdD6wfbEFBtKR6Z5f71680OWA7xOlPdARm1D+vDFvSVWu+7I9Iot9hTAdx5b+WNPtFuhAb6a43rp4YSsX6G1efwIZZyPU7ZDuT5UlPztTmjyVFf2vJHr2z2HM5fCe2cC+pPj9cDmeOwCiTUYfO909KUrDHXFxi649g1mcttGSapAboD0q3rS4+ulJkf1DvD9dMkKulWenwT68+4pu2ZPYzWfPhe/ixz57L4Tux/ZbMHhg1usqnKR++B7P0lgqhJbfwWJDSlfypqyvW1mLWlpTC7po1VfWWLZn9TNCShSxLS07/6P85RbfXkhlWF628EVSF0JLLt2bKsGLT3d68JTdUFVryHdhzOXwnNm9JKey9GZbom7XkFqbsC1ghtGR6ms/AmboC65faLMT8vH/1ONfsDks0Hce3GXGvf+92R9yZzwQtWcg2bUkpfP2yUovbacnlYVD2G4hCVxgtSdOLbwwlZ7t8y0+upVhgoP3CefeTxOp9lOckiZEOU3GGpzfGVr8oLddi+m5xJtB+gtMbSmz9EWkhNvRp/fvFqwYv6RJUf2MvR7PS4Y9Ehh48k9bvkO1MlifjS5r94sptMlqyQKSnj9K/khUzgfZz6itqSy6ve8semPQNhBqwhVjAj8fc6xRMS1JKqRj29/c0m5fnX5a/objayvqbNX26Zvrm7F861MdBq35jp99oPNc18vAbW2MH3+8NxKR171VHzWtWuWfaYbMzWVnYwekP1rf/Jf1tyL33mHvv5vANZZpDXL0d6wgkVq0EUl6J5Q7MJpmHtIJqScgnyCEwAi0JjEIOgRFoSWAUcgiMQEsCo5BDYARaEhiFHAIj0JLAKOQQGIGWBEYhh8AItCQwCjkERqAlgVHIITACLQmMQg6BEWhJYBRyCIxASwKjkENgBFoSGIUcAiMytyQ2bNiwYUtvGVpyN3saICPkEBiBlgRGIYfACLQkMAo5BEagJYFRyCEwAi0JjEIOgRFoSWAUcgiMQEsCo5BDYARaEhiFHAIj0JLAKOQQGIGWBEYhh8AItCQwCjkERqAlgVHIITACLQmMQg6BEWjJNDkV/bHb9pHtSqvtVFP3g0hqh48nxQJed/Nxszss7fCR1lhKPLv9v7ZzF65carC29o3Pyrt58O0o1BwCc9CSy5KPus2l1a7xRUrlCF+nO9X9JLGDh5OCPeZiTm/gdrcl5am7F8tL6/hJmcqLIVf1/gZPaCcv8y0UaA6BPXu1JZcSYSEQndvyjdJihD+vJbWeiXlKKZVfem0HtHV8ZEdvtJSi3NWWnBWcJqK75BMlSimVn3qqi3b8Mt/Unsgh7AV7tSVT08IXdvMxq/P/Hjz7LffYWZ7oPc0Rzimou74e6zQRzZneyYUdPMfdb0nRZ9cRUu2ZUGsxITirCDnpCiV36wy2YU/kEPaCPGrJuahwu8/V0dJ4pu37qVT0gcteU2buEhKSnHjc1/KnKvNVX3RxzTtS8ZDPZf/j4T/aXb5QPFtXvr7fUrS6PlJRvoGQipb78Z27nnfUkgnBecbu8grR3IW+NNZ5kBBt0+DyVSmXub/BG3mbM9ghrOYQCk4etSSl88NtBkK0TTefCl//reUjHSGkgZ8M3XZ90liuJaTKKWSaYpPnogLvtB4zX+jqF14mM44uo7yFEGLho+rPSn1wFv755mezEAtcd5iKOb2B05sd/UH12Imwn2+vP+EOi8GBZjOnN5Sc/TKYkDa861C963rHllpSTs2EfB7XjcEffhj8e1vXj1PrLiER8v3DadEdsDj5rF25FB/8s5asumNWL1N7uPvxUvZT+D2wm0MoMPnUknKUt2qItv6vN+88ikd4q4aQ9y7fuDv6YnaopYisTLdlfvNcVLj1mf3DI1YnPzqZSK1tmu23pBR21xgvDEQWKBWDbluJvrYnnKR02t9cyekNnKmxw/MwJlEq+h3G4hp3UKKU0oWYv+24qc0fW6B0ITb0af37OVtyKfHkK1vFh87RuCy/+O7jSo2m0TuVqdOkqMArXdnrC4mZPkq5qI0tufoVhjCbQyg0edSSqVfeJi3R7Dv9+Zi4qNwWaY5dG4otzAvOUkK0Nu+r3E8hFmdC/2w5YuCqPxtb/WhHGXGvtOT8hKc2+4hbCrtrjK1+UVL/rLYkVYsy3X1SsMdcXNLsFymliZEO0/sO//TyR+QecctTdy+Wa3UXBuMypXRmzHPtat/jRJbLVLtSV2V3behK3EsCvIk8aslpn72MkP11/KRM4/dbKggxVLvGF2ky5DpJCHe6dyJHSa4eeo+9WnP3pDy9Odg5prbF7HDb4a08vZFiAS/fXm80cLlbUhL9rSUru22lJWcFp+mNpkef8xZu472wMi9paBueV1+YG++uxrwkQHb505LK89kD14bnZDo/6izVEG2T91VKWc5CyElXKD4zu0mp5X6Msxjhz2s1Nj6aonRrS2Sk2GjnubKz7d/cDESCW7mX3H5LKne4pK73+eIme2w8q6gw8Lm9qizzuFv5O1y5ZVZ+2eAZN0A2+dKS8tzwtQOE6Ow+kdKl8e7DhGisfFSmdMrboCHEcPHGne8eTq0vQDn5Urj1md18zOrkRyfFbLNvyUfd5nJr779SynJrbfZV5cmwuzZdcFsccUthd42+cmXELfodxqyrypXZ0vQqTkppSpx5vcngeGVeMssznFnBaSJFl++/limlVPrFdVSH9ZIA2eVLS4qC8wNCSpsGf12eNNQddf0iUUoTI53mg2WnrvaH1nzZTk6+FHin9ciJC139wpaWl2/rG4rT/uZKztQVSEhUigU8zcf1lY57gaGhCSnLvKQ0OWA7xBnPdY3EJCoG+9vPm7J+/Wbhp873tIRoy+19YxP/Dgl3+P7RaGrDpWypH5cvcuruxfLK//K9kqk8J/xPhdbiCuK7NwDZ5EtLbtdidLCj1eULzWx5rLpNUuzeZWVBT/udcOSew1h8vLk/LP6sfu9Qb+CMrf4X9xxGg/qjUoWJsK/9XInewBltPT8/7DGfcLi/DcQ2q7alROiWs6mmTLOvynKxy/v4t40Vqa6X9IUSW1x1uZR49u0n1roLVy41WFu+En5l8Om2Yk/kEPaCvdqSkPeQQ2AEWhIYhRwCI9CSwCjkEBiBlgRGIYfACLQkMAo5BEagJYFRyCEwAi0JjEIOgRFoSWAUcgiMQEsCo5BDYARaEhiFHAIj0JLAKOQQGIGWBEYhh8CIzC2JDRs2bNjSW4aW3M2eBsgIOQRGoCWBUcghMAItCYxCDoERaElgFHIIjEBLAqOQQ2AEWhIYhRwCI9CSwCjkEBiBlgRGIYfACLQkMAo5BEagJYFRyCEwAi0JjEIOgRFoSWAUcgiMQEsCo5BDYARaMk1ORX/stn1ku9JqO9XU/SCS2uHjSbGA19183OwOSzt8pDWWEs9u/6/t3IUrlxqsrX3js/JuHnw7CjWHwBy05LLko25zabVrfJFSOcLX6U51P0ns4OGkYI+5mNMbuN1tSXnq7sXy0jp+UqbyYshVvb/BE9rJy3wLBZpDYE9BtqQ8F330aCKxtOqlxQh/XktqPRPzlFIqv/TaDmjr+MiO3mgpRbmrLTkrOE1Ed8knSpRSKj/1VBft+GW+qb2fQ8gTBdaS8lxU4J1W0we27gdTq4bU8kTvaY5wTkF97fVYp4lozvROLuzgyex+S4o+u46Qas+EWosJwVlFyElXKLlbZ7ANezmHkFfyqCXnosLtPldHS+OZtu+nUtEHLntNmblLSEhy4nFfy5+qzFd90cVN352Kh3xfXLEcM9tdvlB8/Zzj6/stRavrIxXlGwipaLkf37nreUctmRCcZ+wurxDNXehLY50HCdE2DS5flXKZ+xu8kbc5gx3Cag6h4ORRS1I6P9xmIETbdPOp8PXfWj7SEUIa+MnQbdcnjeVaQqqcQoYpNjn5atznspuPWT+5MbSxHxVR3kIIsfBR9WelPjgL/3zzs1mIBa47TMWc3sDpzY7+oHrsRNjPt9efcIfF4ECzmdMbSs5+GUxIG951qN51vWNLLSmnZkI+j+vG4A8/DP69revHqXUD5ETI9w+nRXfA4uSzduVSfPDPWrLqjlm9TO3h7sdLm7/t98JuDqHA5FNLylHeqiHa+r/evPMoHuGtGkLeu3zj7uiL2aGWIrIy3ZbeP/lS4J3Wiiqrkxeic9km37bfklLYXWO8MBBZoFQMum0l+tqecJLSaX9zJac3cKbGDs/DmESp6HcYi2vcQYlSShdi/rbjpjZ/bIHShdjQp/Xv52zJpcSTr2wVHzpH47L84ruPKzWaRu9Upk6TogKvdGWvLyRm+ijloja25OpXGMJsDqHQ5FFLpl55m7REs+/052PionJbpDl2bSi2MC84SwnR2ryvVhWhNDnwH+X7jrT8MzSz+TA8TRlxr7Tk/ISnNvuIWwq7a4ytflFS/6y2JFWLMt19UrDHXFzS7BcppYmRDtP7Dv/08kfkHnHLU3cvlmt1FwbjMqV0Zsxz7Wrf40SWvle7Uldld23oStxLAryJPGrJaZ+9jJD9dfykTOP3WyoIMVS7xhdpMuQ6SQh3undiTXuk4iGfy24+ZrnyRYaJyHWUpzcHO8fUtpgdbju8lac3Uizg5dvrjQYud0tKor+1ZGW3rbTkrOA0vdH06HPewm28F1bmJQ1tw/PqC3Pj3dWYlwTILn9aUnk+e+Da8JxM50edpRqibfK+SinLWQg56QrFZ2Y3lFr2hzYrFiP8ea3GxkdTlG5tiYwUG+08V3a2/ZubgUhwK/eS229J5Q6X1PU+38LtsPqZUWHgc3tVWeZxt/J3uHLLrPyywTNugGzypSXlueFrBwjR2X0ipUvj3YcJ0Vj5qEzplLdBQ4jh4o073z2c2qQG1QVAVRVWJy+8TGbsvuSjbnO5tfdfKWW5tTb7qvJk2F2bLrgtjrilsLtGX7ky4hb9DmPWVeXKbGl6FSelNCXOvN5kcLwyL5nlGc6s4DSRosv3X8uUUir94jqqw3pJgOzypSVFwfkBIaVNg78uTxrqjrp+kSiliZFO88GyU1f7Q7m+bCcnp8fvuewfHrH+942h0Exq3e7b+obitL+5kjN1BRISlWIBT/NxfaXjXmBoaELKMi8pTQ7YDnHGc10jMYmKwf7286asX79Z+KnzPS0h2nJ739jEv0PCHb5/NLr+tLfYj8sXOXX3Ynnlf/leyVSeE/6nQmtxBfHdG4Bs8qUl36HFmdD3X7Rd63u7YaYUu3dZWdDTficcuecwFh9v7g+LP6vfO9QbOGOr/8U9h9Gg/qhUYSLsaz9XojdwRlvPzw97zCcc7m8Dsc2qbSkRuuVsqinT7KuyXOzyPv5tY0Wq6yV9ocQWV10uJZ59+4m17sKVSw3Wlq+EXxl8uq3Y6zmEvFGALQn5ATkERqAlgVHIITACLQmMQg6BEWhJYBRyCIxASwKjkENgBFoSGIUcAiPQksAo5BAYgZYERiGHwAi0JDAKOQRGoCWBUcghMAItCYxCDoERaElgFHIIjMjcktiwYcOGLb1laMnd7GmAjJBDYARaEhiFHAIj0JLAKOQQGIGWBEYhh8AItCQwCjkERqAlgVHIITACLQmMQg6BEWhJYBRyCIxASwKjkENgBFoSGIUcAiPQksAo5BAYgZYERiGHwAi0JDAKOQRGoCXT5FT0x27bR7YrrbZTTd0PIqkdPp4UC3jdzcfN7rC0w0daTRafDXbarB9fcZy3Xvx6PLG0i8fenkLNITAHLbks+ajbXFrtGl+kVI7wdbpT3U8SO3g4KdhjLub0Bm5XWzI15Wst157nI4uUzoVctfutX4WS8q4dflsKNIfAnoJsSXku+ujRxJrbqMUIf15Laj0T85RSKr/02g5o6/jIjhaIUpS72ZJzI84Krc7uEymllMoTnmqyv46fZLMm934OIU8UWEvKc1GBd1pNH9i6H0ytGlLLE72nOcI5BfW112OdJqI50zu5sIMns9stKYm+SzpSVO15qtZiSnByhBx1hXZzyL9lezmHkFfyqCXnosLtPldHS+OZtu+nUtEHLntNmblLSEhy4nFfy5+qzFd90cVN352Kh3xfXLEcM9tdvlB8/Zzj6/stRYRUeyaW+yPKNxBS0XI/vnPXs5MtuRAVeKflP/no6gt9PdZpIqS0afDX5Vee8xaOaBq9UyzOTrKaQyg4edSSlM4PtxkI0TbdfCp8/beWj3SEkAZ+MnTb9UljuZaQKqeQYSZRTr4a97ns5mPWT24MbexHRZS3EEIsfFT9WWlJzsI/3/xsFmKB6w5TMac3cHqzoz+oHjsR9vPt9SfcYTE40Gzm9IaSs18GE9KGdx2qd13v2FJLyqmZkM/jujH4ww+Df2/r+nEq2whZDPl6nZYDOouTF6JrP/jXwabStX9Lz3kLR0h19/hc9jP4XbCbQygw+dSScpS3aoi2/q837zyKR3irhpD3Lt+4O/pidqiliBDdJZ+4phbk5EuBd1orqqxOXojOZeuW7bekFHbXGC8MRBYoFYNuW4m+tiecpHTa31zJ6Q2cqbHD8zAmUSr6HcbiGndQopTShZi/7bipzR9boHQhNvRp/fs5W3Ip8eQrW8WHztG4LL/47uNKzaa3fmLI57JXcVV2ly8kZtpB6cSNLZn5t8vvjtkcQqHJo5ZMvfI2aYlm3+nPx8TF+OCftYRojl0bii3MC85SQrQ276tVRShNDvxH+b4jLf8MzWw+DE9TRtwrLTk/4anNPuKWwu4aY6tflNQ/qy1J1aJMd58U7DEXlzT7RUppYqTD9L7DP738EblH3PLU3YvlWt2FwbhMKZ0Z81y72vc4sb7vlX4sszh7N+lHBe4lAd5EHrXktM9eRtRnsvH7LRWEGKpd44s0GXKdJIQ73Tuxpj1S8ZDPZTcfs1z5IsNE5DrK05uDnWPqXdrscNvhrTy9kWIBL99ebzRwuVtSEv2tJSu7baUlZwWnKcf0qPIEhpTZfdOb7qNS5iUPtw3Pqi8sPe4+rMW8JEB2+dOSos+uI+TAteE5mc6POks1RNvkfZWi8lNPdREhJ12h+MzshlLL/tBmxWKEP6/V2NTHHfJTT3VRjpVAUmy081zZ2fZvbgYiwa3cS26/JZU7XFLX+zzr7bAUFQY+zzrWVvcTfZd0q6cRlM/HM26ArPKlJeW54WsHCFHW+i2Ndx8mRGPlozKlU94GDSGGizfufPdwapMaVBcAVVVYnbzwMvMy6uSjbnO5tfdfKSovhlzV2uyrypNhd2264LY44pbC7hp95cqIW/Q7jFlXlSuzpelVnJTSlDjzerP7PmXcrcv03GbZ3IizQlvUcv+1cmoh11GslwTIJV9aUhScHyyvYlEmDXVHXb9IlNLESKf5YNmpq/2h2Rz/t8vJ6fF7LvuHR6z/fWMoNJNat/u2vqE47W+u5ExdgYREpVjA03xcX+m4FxgampCyzEtKkwO2Q5zxXNdITKJisL/9vCnr128Wfup8T0uIttzeNzbx75Bwh+8fja4/7fV/UZs/46bqd2/2O3zxJWU4rz3lDuK7NwBZ5UtLvkOLM6Hvv2i71hdK5t53c1Ls3mVlQU/7nXDknsNYfLy5Pyz+rH7vUG/gjK3+F/ccRoP6o1KFibCv/VyJ3sAZbT0/P+wxn3C4vw3ENpv9XEqEbjmbaso0+6osF7u8j3/LUZFpGddLUkoplcVnt5xWi/I97uvC1HymtzNhr+cQ8kYBtiTkB+QQGIGWBEYhh8AItCQwCjkERqAlgVHIITACLQmMQg6BEWhJYBRyCIxASwKjkENgBFoSGIUcAiPQksAo5BAYgZYERiGHwAi0JDAKOQRGoCWBUcghMCJzS2LDhg0btvSWoSV3s6cBMkIOgRFoSWAUcgiMQEsCo5BDYARaEhiFHAIj0JLAKOQQGIGWBEYhh8AItCQwCjkERqAlgVHIITACLQmMQg6BEWhJYBRyCIxASwKjkENgBFoSGIUcAiPQksAo5BAYgZZMk1PRH7ttH9mutNpONXU/iKR2+HhSLOB1Nx83u8PSDh9pNVl8Nthps358xXHeevHr8cTSLh57ewo1h8ActOSy5KNuc2m1a3yRUjnC1+lOdT9J7ODhpGCPuZjTG7hdbcnUlK+1XHuejyxSOhdy1e63fhVKyrt2+G0p0BwCe/ZqSy4lwkIgOrflAliM8Oe1pNYzMU8ppfJLr+2Ato6P7GiBKEW5my05N+Ks0OrsPpFSSqk84akm++v4STZrck/kEPaCvdqSqWnhC7v5mNX5fw+e/ZZ77CxP9J7mCOcU1F1fj3WaiOZM7+TCDp7jbrekJPou6UhRteepWospwckRctQV2s0h/5btiRzCXpBHLTkXFW73uTpaGs+0fT+Vij5w2WvKzF1CQpITj/ta/lRlvuqLLq55Ryoe8rnsfzz8R7vLF4pn68rX91uKCKn2TCz3R5RvIKSi5X58565nJ1tyISrwTst/8tHVF/16rNNESGnT4K/LrzznLRzRNHqnWJydZDWHUHDyqCUpnR9uMxCibbr5VPj6by0f6QghDfxk6Lbrk8ZyLSFVTiHTTKI8FxV4p/WY+UJXv/Ay8yxclLcQQix8VP1ZaUnOwj/f/GwWYoHrDlMxpzdwerOjP6geOxH28+31J9xhMTjQbOb0hpKzXwYT0oZ3Hap3Xe/YUkvKqZmQz+O6MfjDD4N/b+v6cSrbCFkM+XqdlgM6i5MXoms/+NfBptK1f0vPeQtHSHX3+Fz2M/hdsJtDKDD51JJylLdqiLb+rzfvPIpHeKuGkPcu37g7+mJ2qKWIEN0ln7h538hzUeHWZ/YPj1id/OhkIrW2abbfklLYXWO8MBBZoFQMum0l+tqecJLSaX9zJac3cKbGDs/DmESp6HcYi2vcQYlSShdi/rbjpjZ/bIHShdjQp/Xv52zJpcSTr2wVHzpH47L84ruPKzWb3vqJIZ/LXsVV2V2+kJhpB6UTN7bkJr9dfm/M5hAKTR61ZOqVt0lLNPtOfz4mLsYH/6wlRHPs2lBsYV5wlhKitXlf5X4MsTgT+mfLEQNX/dnY6kc7yoh7pSXnJzy12UfcUthdY2z1i5L6Z7UlqVqU6e6Tgj3m4pJmv0gpTYx0mN53+KeXPyL3iFueunuxXKu7MBiXKaUzY55rV/seJ9ZfptKPZRZn7yb9qMC9JMCbyKOWnPbZy4j6TDZ+v6WCEEO1a3yRJkOuk4Rwp3sncpTk6qH32Ks105TK05uDnWPqXdrscNvhrTy9kWIBL99ebzRwuVtSEv2tJSu7baUlZwWnKcf0qPIEhpTZfdOb7qNS5iUPtw3Pqi8sPe4+rMW8JEB2+dOSos+uI+TAteE5mc6POks1RNvkfZWi8lNPdREhJ12h+MzsJqWW+zHOYoQ/r9XY1Mcd8lNPdVGOlUBSbLTzXNnZ9m9uBiLBrdxLbr8llTtcUtf7fHGTPZTPiQoDn2cda6v7ib5LutXTCMrn4xk3QFb50pLy3PC1A4Qoa/2WxrsPE6Kx8lGZ0ilvg4YQw8Ubd757OLW+AOXkS+HWZ3bzMauTH50Usz3mTj7qNpdbe/+VovJiyFWtzb6qPBl216YLbosjbinsrtFXroy4Rb/DmHVVuTJbml7FSSlNiTOvN7vvU8bdukzPbZbNjTgrtEUt918rpxZyHcV6SYBc8qUlRcH5wfIqFmXSUHfU9YtEKU2MdJoPlp262h+aXf1/u5x8KfBO65ETF7r6hS0tL9/WNxSn/c2VnKkrkJCoFAt4mo/rKx33AkNDE1KWeUlpcsB2iDOe6xqJSVQM9refN2X9+s3CT53vaQnRltv7xib+HRLu8P2j0VT2S8nyjJuq373Z7/DFl5ThvPaUO4jv3gBklS8tuV2L0cGOVpcvNJN1rPoWpNi9y8qCnvY74cg9h7H4eHN/WPxZ/d6h3sAZW/0v7jmMBvVHpQoTYV/7uRK9gTPaen5+2GM+4XB/G4htNvu5lAjdcjbVlGn2VVkudnkf/5ajItMyrpeklFIqi89uOa0W5Xvc14Wp+UxvZ8KeyCHsBXu1JSHvIYfACLQkMAo5BEagJYFRyCEwAi0JjEIOgRFoScc7NNoAAABfSURBVGAUcgiMQEsCo5BDYARaEhiFHAIj0JLAKOQQGIGWBEYhh8AItCQwCjkERqAlgVHIITACLQmMQg6BEZlbEhs2bNiwpbf1LQkAABmhJQEAskFLAgBkg5YEAMjm/wMcFmIdHTeBZAAAAABJRU5ErkJggg==" alt></span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span><img src="data:image/png;base64,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" alt><span> <em><strong> (A6) (C6)</strong></em></span></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(A6)</strong></em> for all correct, <em><strong>(A5)</strong></em> for 3 correct, <em><strong>(A3)</strong></em> for 2 correct,</span> <span><em><strong>(A1)</strong></em> for 1 correct.</span></p>
<p><span>Deduct <em><strong>(A1)</strong></em> for any repetition.</span></p>
<p><span> </span></p>
<p><em><strong><span>[6 marks]</span></strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-size: medium; font-family: times new roman,times;">Many candidates received full marks and a number received 3 marks for giving two correct answers. Very few candidates were awarded zero marks. As most candidates did not show working for this question it is difficult to comment on the errors that might have been made.</span></p>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A ladder is standing on horizontal ground and leaning against a vertical wall. The length of the ladder is \(4.5\) metres. The distance between the bottom of the ladder and the base of the wall is \(2.2\) metres.</p>
<p>Use the above information to sketch a labelled diagram showing the ground, the ladder and the wall.</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>Calculate the distance between the top of the ladder and the base of the wall.</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>Calculate the <strong>obtuse</strong> angle made by the ladder with the ground.</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><img 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" alt></p>
<p><em><strong>(A1) (C1)</strong></em></p>
<p><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for drawing an approximately right angled triangle, with correct labelling of the distances \(4.5\,({\text{m}})\) and \(2.2\,({\text{m}})\).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\sqrt {\,{{4.5}^2} - {{2.2}^2}} \,\,\,({\text{accept eqivalent }}eg\,\,{d^2} + {2.2^2} = {4.5^2})\) <em><strong>(M1)</strong></em></p>
<p>\( = 3.93\,({\text{m}})\,\,\,\left( {\sqrt {\,15.41} \,({\text{m}}),\,\,3.92555...\,({\text{m}})} \right)\) <em><strong>(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> Award<em><strong> (M1)</strong></em> for a correct substitution in the Pythagoras formula.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(180^\circ - {\cos ^{ - 1}}\left( {\frac{{2.2}}{{4.5}}} \right)\)<em> <strong>(M1)(M1)</strong></em></p>
<p><strong>OR</strong></p>
<p>\(180^\circ - {\tan ^{ - 1}}\left( {\frac{{3.92555...}}{{2.2}}} \right)\)<em> <strong>(M1)(M1)</strong></em></p>
<p><strong>OR</strong></p>
<p>\(180^\circ - {\sin ^{ - 1}}\left( {\frac{{3.92555...}}{{4.5}}} \right)\)<em> <strong>(M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for a correct substitution in the correct trigonometric ratio.<br>Award <em><strong>(M1)</strong></em> for subtraction from \(180^\circ \) (this may be implied if the sum of their inverse of the trigonometric ratio and their final answer equals \(180\)).</p>
<p>\( = 119^\circ \,\,\,(119.267...^\circ )\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></p>
<p><strong>Note:</strong> Follow through from their part (b) if cosine is not used. Accept \(119.239...\) or \(119.151...\) from use of \(3\) sf values.</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>Question 3: Right angle trigonometry.<br>Candidates sketched the ladder leaning against the wall and recognized that Pythagoras’ theorem was needed to find the distance between the top of the ladder and the base of the wall (but not always correctly). Although it was a right triangle a number of the candidates used the law of sines (instead of Pythagoras’ theorem) and law of cosines (instead of a trigonometry ratio). Many candidates failed to find the obtuse angle made by the ladder with the ground even though the word obtuse was in bold type in the question.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 3: Right angle trigonometry.<br>Candidates sketched the ladder leaning against the wall and recognized that Pythagoras’ theorem was needed to find the distance between the top of the ladder and the base of the wall (but not always correctly). Although it was a right triangle a number of the candidates used the law of sines (instead of Pythagoras’ theorem) and law of cosines (instead of a trigonometry ratio). Many candidates failed to find the obtuse angle made by the ladder with the ground even though the word obtuse was in bold type in the question.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 3: Right angle trigonometry.<br>Candidates sketched the ladder leaning against the wall and recognized that Pythagoras’ theorem was needed to find the distance between the top of the ladder and the base of the wall (but not always correctly). Although it was a right triangle a number of the candidates used the law of sines (instead of Pythagoras’ theorem) and law of cosines (instead of a trigonometry ratio). Many candidates failed to find the obtuse angle made by the ladder with the ground even though the word obtuse was in bold type in the question.</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;">The quadrilateral ABCD has AB = 10 cm, AD = 12 cm and CD = 7 cm.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The size of angle ABC is 100° and the size of angle ACB is 50°.</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 AC in centimetres.</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 angle ADC.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{{\text{AC}}}}{{\sin 100^\circ }} = \frac{{10}}{{\sin 50^\circ }}\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution in the sine rule formula, <em><strong>(A1)</strong></em> for correct substitutions.</span></p>
<p><br><span>\(=12.9 (12.8557...)\) <em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Radian answer is 19.3, award <em><strong>(M1)(A1)(A0)</strong></em>.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{{{12}^2} + {7^2} - {{12.8557...}^2}}}{{2 \times 12 \times 7}}\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution in the cosine rule formula, <em><strong>(A1)</strong></em><strong>(ft)</strong> for correct substitutions.</span></p>
<p><br><span>= 80.5° (80.4994...°) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C3)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Follow through from their answer to part (a). Accept 80.9</span><span><span>°</span> for using 12.9. Using the radian answer from part (a) leads to an impossible triangle, award <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong><em><strong>(A0)</strong></em>.</span></p>
<div class="question_part_label">b.</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>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The straight line, <em>L</em><sub>1</sub>, has equation \(2y − 3x =11\). The point A has coordinates (6, 0).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Give a reason why <em>L</em><sub>1</sub> <strong>does not</strong> pass through A.</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 gradient of <em>L</em><sub>1</sub>.</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><em>L</em><sub>2</sub> is a line perpendicular to <em>L</em><sub>1</sub>. The equation of <em>L</em><sub>2</sub> is \(y = mx + c\).</span></p>
<p><span>Write down the value of <em>m</em>.</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><em>L</em><sub>2</sub> <strong>does</strong> pass through A.</span></p>
<p><span>Find the value of <em>c</em>.</span></p>
<div class="marks">[2]</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>\(2 \times 0 - 3 \times 6 \ne 11\) <em><strong>(R1)</strong></em></span><br><br></p>
<p><span><strong>Note:</strong> Stating </span><span><span>\(2 \times 0 - 3 \times 6 = - 18\)</span> without a conclusion is not sufficient.</span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span>Clear sketch of <em>L</em><sub>1</sub> and A.</span></p>
<p><span><img src="data:image/png;base64,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" alt> <em><strong>(R1)</strong></em></span></p>
<p><strong><span>OR</span></strong></p>
<p><span>Point <strong>A</strong> is (6, 0) and \(2y - 3x = 11\) has <em>x</em>-intercept at \(- \frac{11}{3}\) or the line has only</span> <span>one <em>x</em>-intercept which occurs when <em>x</em> is negative. <em><strong>(R1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(2y = 3x + 11\) <strong>or</strong> \(y - \frac{3}{2}x = \frac{{11}}{2}\) </span><span> <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for a correct first step in making <em>y</em> the subject of the equation.</span></p>
<p><br><span>\(({\text{gradient equals}}) = \frac{3}{2}(1.5)\) </span><span> <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Do not accept 1.5<em>x</em>.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\((m = ) - \frac{2}{3}\) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C1)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Follow through from their part (b).</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(0 = - \frac{2}{3}(6) + c\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of their gradient and (6, 0) into any form of the equation.</span></p>
<p><br><span>(<em>c</em> =) 4 <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from part (c).</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;">There were multiple acceptable reasons why the line did not pass through a given point (including numerically substituting values in the equation; drawing a graph or algebraically finding the <em>x</em>-intercept of the line). This was one of two reasoning marks in the paper.</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;">There were multiple acceptable reasons why the line did not pass through a given point (including numerically substituting values in the equation; drawing a graph or algebraically finding the <em>x</em>-intercept of the line). This was one of two reasoning marks in the paper.</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;">There were multiple acceptable reasons why the line did not pass through a given point (including numerically substituting values in the equation; drawing a graph or algebraically finding the <em>x</em>-intercept of the line). This was one of two reasoning marks in the paper.</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;">There were multiple acceptable reasons why the line did not pass through a given point (including numerically substituting values in the equation; drawing a graph or algebraically finding the <em>x</em>-intercept of the line). This was one of two reasoning marks in the paper.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The diagram shows a triangle \({\rm{ABC}}\). The size of angle \({\rm{C\hat AB}}\) is \(55^\circ\) and the length of \({\rm{AM}}\) is \(10\) m, where \({\rm{M}}\) is the midpoint of \({\rm{AB}}\). Triangle \({\rm{CMB}}\) is isosceles with \({\text{CM}} = {\text{MB}}\)<span class="s1">.</span></p>
<p class="p1" style="text-align: center;"><span class="s1"><img src="images/Schermafbeelding_2015-12-20_om_14.30.17.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down the length of \({\rm{MB}}\).</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">Find the size of angle \({\rm{C\hat MB}}\).</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 \({\rm{CB}}\).</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 class="p1">\(10\) m <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(A1)(C1)</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\({\rm{A\hat MC}} = 70^\circ \;\;\;\)<strong>OR</strong>\(\;\;\;{\rm{A\hat CM}} = 55^\circ \) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1">\({\rm{C\hat MB}} = 110^\circ \) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C2)</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\({\text{C}}{{\text{B}}^2} = {10^2} + {10^2} - 2 \times 10 \times 10 \times \cos 110^\circ \) <strong><em>(M1)(A1)</em>(ft)</strong></p>
<p><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for substitution into the cosine rule formula, <strong><em>(A1)</em>(ft) </strong>for correct substitution. Follow through from their answer to part (b).</p>
<p> </p>
<p><strong>OR</strong></p>
<p>\(\frac{{{\text{CB}}}}{{\sin 110^\circ }} = \frac{{10}}{{\sin 35^\circ }}\) <strong><em>(M1)(A1)</em>(ft)</strong></p>
<p><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for substitution into the sine rule formula, <strong><em>(A1)</em>(ft) </strong>for correct substitution. Follow through from their answer to part (b).</p>
<p> </p>
<p><strong>OR</strong></p>
<p>\({\rm{A\hat CB}} = 90^\circ \) <strong><em>(A1)</em></strong></p>
<p>\(\sin 55^\circ = \frac{{{\text{CB}}}}{{55}}\;\;\;\)<strong>OR</strong>\(\;\;\;\cos 35^\circ = \frac{{{\text{CB}}}}{{20}}\) <strong><em>(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for some indication that \({\rm{A\hat CB}} = 90^\circ \), <strong><em>(M1) </em></strong>for correct trigonometric equation.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>Perpendicular \({\rm{MN}}\) is drawn from \({\rm{M}}\) to \({\rm{CB}}\). <strong><em>(A1)</em></strong></p>
<p>\(\frac{{\frac{1}{2}{\text{CB}}}}{{10}} = \cos 35^\circ \) <strong><em>(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for some indication of the perpendicular bisector of \({\rm{BC}}\), <strong><em>(M1) </em></strong>for correct trigonometric equation.</p>
<p> </p>
<p>\({\text{CB}} = 16.4{\text{ (m)}}\;\;\;\left( {16.3830 \ldots {\text{ (m)}}} \right)\) <strong><em>(A1)</em>(ft)<em>(C3)</em></strong></p>
<p><strong>Notes: </strong>Where a candidate uses \({\rm{C\hat MB}} = 90^\circ \) and finds \({\text{CB}} = 14.1{\text{ (m)}}\) award, at most, <strong><em>(M1)(A1)(A0)</em></strong><em>.</em></p>
<p>Where a candidate uses \({\rm{C\hat MB}} = 60^\circ \) and finds \({\text{CB}} = 10{\text{ (m)}}\) award, at most, <strong><em>(M1)(A1)(A0)</em></strong><em>.</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.</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><span style="font-size: medium; font-family: times new roman,times;">The coordinates of point A are (−4, <em>p</em>) and the coordinates of point B are (2, −3) .</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The mid-point of the line segment AB, has coordinates (<em>q</em>, 1) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of</span></p>
<p><span>(i) <em>q</em> ;</span></p>
<p><span>(ii) <em>p</em> .</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>Calculate the distance AB.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(\frac{{ - 4 + 2}}{2} = q\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in the correct formula.</span></p>
<p><span><em> </em></span></p>
<p><span><em>q</em> = –1 <em><strong>(A1)</strong></em></span></p>
<p><span> </span></p>
<p><span>(ii) \(\frac{{p + ( - 3)}}{2} = 1\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into the correct formula or consistent with their equation in (i).</span></p>
<p><span><em> </em></span></p>
<p><span><em>p</em> = 5 <em><strong>(A1) </strong></em><em><strong>(C4)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award A marks for integer values. Penalise if answers left as a fraction the first time a fraction is seen.</span></p>
<p><span> </span></p>
<p><span><em><strong>[4 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{AB}} = \sqrt {{{(2 + 4)}^2} + {{( - 3 - 5)}^2}} \) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for the correct substitution of their coordinates for A and B in the correct formula.</span></p>
<p> </p>
<p><span>AB = 10 <em><strong>(A1)</strong></em><strong>(ft) </strong><em><strong>(C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their answer to part (a)(ii).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</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;">(a) Despite some good answers in this part of the question, sign errors in setting up one or both of the equations meant that marks were lost by some candidates. This error was particularly prevalent in finding the value of <em>p</em> and the equation \(\frac{{(p + 3)}}{2} = 1\) was seen quite often. In part (b), there was a requirement for a correct substitution of their coordinates for A and B into the correct formula for Pythagoras and, while (2 + 4)<sup>2</sup> was often seen, sign errors in the second component of (–3 – 5)<sup>2</sup> proved to be the downfall of a significant number of candidates. As a consequence, the final two marks were lost. Given these errors, there were still a significant number of full mark responses to this question.</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;">(a) Despite some good answers in this part of the question, sign errors in setting up one or both of the equations meant that marks were lost by some candidates. This error was particularly prevalent in finding the value of <em>p</em> and the equation \(\frac{{(p + 3)}}{2} = 1\) was seen quite often. In part (b), there was a requirement for a correct substitution of their coordinates for A and B into the correct formula for Pythagoras and, while (2 + 4)<sup>2</sup> was often seen, sign errors in the second component of (–3 – 5)<sup>2</sup> proved to be the downfall of a significant number of candidates. As a consequence, the final two marks were lost. Given these errors, there were still a significant number of full mark responses to this question.</span></p>
<div class="question_part_label">b.</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 diagram shows a wheelchair ramp, \({\text{A}}\), designed to descend from a height of \(80{\text{ cm}}\).</span></p>
<div style="text-align: center;"><br><img src="images/Schermafbeelding_2014-09-02_om_14.39.20.png" alt></div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use the diagram above to calculate the gradient of the ramp.</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>The gradient for a <strong>safe </strong>descending wheelchair ramp is \( - \frac{1}{{12}}\).</span></p>
<p><span>Using your answer to part (a), comment on why wheelchair ramp \({\text{A}}\) is <strong>not safe</strong>.</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 equation of a second wheelchair ramp, B, is \(2x + 24y - 1920 = 0\).</span></p>
<p><span><br><img src="images/Schermafbeelding_2014-09-02_om_14.42.07.png" alt><br></span></p>
<p><span>(i) Determine whether wheelchair ramp \({\text{B}}\) is safe or not. Justify your answer.</span></p>
<p><span>(ii) Find the horizontal distance of wheelchair ramp \({\text{B}}\).</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>\( - \frac{{80}}{{940}}{\text{ }}\left( {-0.0851, -0.085106 \ldots , -\frac{4}{{47}}} \right)\) <strong><em>(A1) (C1)</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>\(-0.0851{\text{ }} (-0.085106 \ldots ) < - \frac{1}{{12}}(-0.083333 \ldots )\) <strong><em>(A1)</em>(ft) <em>(C1)</em></strong></span></p>
<p><span> </span></p>
<p><span><strong>Notes: </strong>Accept “less than” in place of inequality.</span></p>
<p><span> Award <strong><em>(A0) </em></strong>if incorrect inequality seen.</span></p>
<p><span> Follow through from part (a).</span></p>
<p> </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>(i) ramp \({\text{B}}\) is safe <strong><em>(A1)</em></strong></span></p>
<p><span>the gradient of ramp \({\text{B}}\) is \( - \frac{1}{{12}}\) <strong><em>(R1)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(R1) </em></strong>for “the gradient of ramp \({\text{B}}\) is \( - \frac{1}{{12}}\)” seen.</span></p>
<p><span> Do not award <strong><em>(A1)(R0)</em></strong>.</span></p>
<p> </p>
<p><span>(ii) \(2x = 1920\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Accept alternative methods.</span></p>
<p> </p>
<p><span>\(960 {\text{ (cm)}}\) <strong><em>(A1) (C4)</em></strong></span></p>
<p><span><strong><em>[4 marks]</em></strong></span></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><span style="font-family: times new roman,times; font-size: medium;">In the diagram, \({\text{B}}\hat {\text{A}}{\text{C}} = {90^ \circ }\) . The length of the three sides are \(x{\text{ cm}}\), \((x + 7){\text{ cm}}\) and \((x + 8){\text{ cm}}\).</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>Write down and <strong>simplify</strong> a quadratic equation in \(x\) which links the three sides of the triangle.</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>Solve the quadratic equation found in part (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>Write down the value of the perimeter of the triangle.</span></p>
<div class="marks">[1]</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>\({(x + 8)^2} = {(x + 7)^2} + {x^2}\) <em><strong>(A1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for a correct equation.</span></p>
<p><span> </span></p>
<p><span>\({x^2} + 16x + 64 = {x^2} + 14x + 49 + {x^2}\) <em><strong>(A1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correctly removed parentheses.</span></p>
<p><span> </span></p>
<p><span>\({x^2} - 2x - 15 = 0\) <em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em> <br></span></p>
<p><span><strong>Note:</strong> Accept any equivalent form.</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>\(x = 5\), \(x = - 3\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span> </p>
<p><span><strong>Notes:</strong> Accept <strong><em>(A1)</em>(ft)</strong> only from the candidate’s <strong>quadratic</strong> equation.</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>\(30{\text{ cm}}\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C1)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from a positive answer found in part (b).</span></p>
<p><span><em><strong>[1 mark]</strong></em><br></span></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-size: medium;"><span style="font-family: times new roman,times;">This question proved to be difficult for the majority of candidates. Many simply were unable to see that, to relate the three given lengths, a Pythagorean equation needed to be produced. Indeed, many did not seem to appreciate the concept of a quadratic equation and, as a consequence, either wrote down a linear equation linking one length to the sum of the other two lengths or multiplied all three lengths together. For the minority who stated a correct Pythagorean equation, many could not remove brackets successfully and arrived at \({x^2} = 15\) . Consequently, very few candidates earned more than one mark for part (a). Where the</span> <span style="font-family: times new roman,times;">correct quadratic equation was seen in part (a), many were able to solve this quadratic correctly in part (b) and arrive at the required value of \(x = 5\) for the answer for part (c).</span></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium;"><span style="font-family: times new roman,times;">This question proved to be difficult for the majority of candidates. Many simply were unable to see that, to relate the three given lengths, a Pythagorean equation needed to be produced. Indeed, many did not seem to appreciate the concept of a quadratic equation and, as a consequence, either wrote down a linear equation linking one length to the sum of the other two lengths or multiplied all three lengths together. For the minority who stated a correct Pythagorean equation, many could not remove brackets successfully and arrived at \({x^2} = 15\) . Consequently, very few candidates earned more than one mark for part (a). Where the</span> <span style="font-family: times new roman,times;">correct quadratic equation was seen in part (a), many were able to solve this quadratic correctly in part (b) and arrive at the required value of \(x = 5\) for the answer for part (c).</span></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium;"><span style="font-family: times new roman,times;">This question proved to be difficult for the majority of candidates. Many simply were unable to see that, to relate the three given lengths, a Pythagorean equation needed to be produced. Indeed, many did not seem to appreciate the concept of a quadratic equation and, as a consequence, either wrote down a linear equation linking one length to the sum of the other two lengths or multiplied all three lengths together. For the minority who stated a correct Pythagorean equation, many could not remove brackets successfully and arrived at \({x^2} = 15\) . Consequently, very few candidates earned more than one mark for part (a). Where the</span> <span style="font-family: times new roman,times;">correct quadratic equation was seen in part (a), many were able to solve this quadratic correctly in part (b) and arrive at the required value of \(x = 5\) for the answer for part (c).</span></span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1"><span class="s1">The diagram shows the straight line \({L_1}\), which intersects the \(x\)-axis</span> at \({\text{A}}(6,{\text{ }}0)\) <span class="s1">and the \(y\)-ax</span>is at \({\text{B}}(0,{\text{ }}2)\) <span class="s1">.</span></p>
<p class="p1" style="text-align: center;"><span class="s1"><img src="images/Schermafbeelding_2015-12-18_om_17.19.23.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down the coordinates of <span class="s1">M</span>, the midpoint of line segment <span class="s1">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 class="p1">Calculate the gradient of \({L_1}\).</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"><span class="s1">The line \({L_2}\) is parallel to \({L_1}\) </span>and passes through the point \((3,{\text{ }}2)\)<span class="s1">.</span></p>
<p class="p2">Find the equation of \({L_2}\). Give your answer in the form \(y = mx + c\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\((3,{\text{ }}1)\) <span class="Apple-converted-space"> </span><strong><em>(A1)(A1) <span class="Apple-converted-space"> </span>(C2)</em></strong></p>
<p class="p1"><strong>Note: </strong>Accept \(x = 3\), \(y = 1\). Award <strong><em>(A0)(A1) </em></strong>if parentheses are missing.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{2 - 0}}{{0 - 6}}\) <strong><em>(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into gradient formula.</p>
<p> </p>
<p>\( = - \frac{1}{3}( - 0.333333 \ldots )\) <strong><em>(A1) (C2)</em></strong></p>
<p><strong>Note: </strong>Accept \( - \frac{2}{6}\).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\((y - 2) = - \frac{1}{3}(x - 3)\) <strong><em>(M1)</em></strong></p>
<p><strong>OR</strong></p>
<p>\(2 = - \frac{1}{3}(3) + c\) <strong><em>(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substitution of their gradient from part (b).</p>
<p> </p>
<p>\(y = - \frac{1}{3}x + 3\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></p>
<p><strong>Note: </strong>Follow through from part (b).</p>
<p>The answer must be an equation in the form \(y = mx + c\) for the <strong><em>(A1)</em>(ft) </strong>to be awarded.</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>Parts (a), finding the midpoint, and (b) finding the gradient, of this question were done well by the majority of candidates.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Parts (a), finding the midpoint, and (b) finding the gradient, of this question were done well by the majority of candidates. Some candidates substituted incorrectly into the gradient formula or reversed the numerator and denominator.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>There was a significant number of candidates who calculated the equation of the normal to the given line and not the equation of a parallel line. It seemed those candidates answered the question they expected and not the question asked.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A straight line, \({L_1}\) , has equation \(x + 4y + 34 = 0\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the gradient of \({L_1}\) .</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>The equation of line \({L_2}\) is \(y = mx\) . \({L_2}\) is perpendicular to \({L_1}\) . </span></p>
<p><span>Find the value of \(m\).</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 equation of line \({L_2}\) is \(y = mx\) . \({L_2}\) is perpendicular to \({L_1}\) . </span></p>
<p><span>Find the coordinates of the point of intersection of the lines \({L_1}\) and \({L_2}\) .</span></p>
<div class="marks">[2]</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>\(4y = - x - 34\) or similar rearrangement <em><strong>(M1)</strong></em></span></p>
<p><span>\({\text{Gradient}} = - \frac{1}{4}\) <em><strong>(A1) (C2)</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(m = 4\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span></p>
<p><span><strong>Note:</strong> <em><strong>(A1)</strong></em> Change of sign<br><em><strong>(A1)</strong></em> Use of reciprocal</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>Reasonable attempt to solve equations simultaneously</em> <em><strong>(M1)</strong></em></span></p>
<p><span>\(( - 2{\text{, }} - 8)\) <em><strong>(A1)</strong></em><strong>(ft) <em>(C2)</em></strong></span></p>
<p><span><strong>Note:</strong> Accept \(x = - 2\) \(y = - 8\). Award <em><strong>(A0)</strong></em> if brackets not included.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></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;">The omission of the negative sign was a common fault.</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 managed to answer this correctly from their (a).</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 part proved challenging for the majority. Once again, the use of the GDC was expected.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The equation of line \({L_1}\) is \(y = 2.5x + k\). Point \({\text{A}}\) \(\,(3,\, - 2)\) lies on \({L_1}\).</p>
<p>Find the value of \(k\).</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>The line \({L_2}\) is perpendicular to \({L_1}\) and intersects \({L_1}\) at point \({\text{A}}\).</p>
<p>Write down the gradient of \({L_2}\).</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>Find the equation of \({L_2}\). Give your answer in the form \(y = mx + c\) .</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 your answer to part (c) in the form \(ax + by + d = 0\) where \(a\), \(b\) and \(d \in \mathbb{Z}\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\( - 2 = 2.5\, \times 3 + k\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for correct substitution of \((3,\, - 2)\) into equation of \({L_1}\).</p>
<p>\((k = ) - 9.5\) <em><strong>(A1) (C2)</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\( - 0.4\,\left( { - \frac{2}{5}} \right)\) <em><strong>(A1) (C1)</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(y - ( - 2) = - 0.4\,(x - 3)\) <em><strong>(M1)</strong></em></p>
<p><strong>OR</strong></p>
<p>\( - 2 = - 0.4\,(3) + c\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their gradient and given point substituted into equation of a straight line. Follow through from part (b).</p>
<p>\(y = - 0.4x - 0.8\) \(\left( {y = - \frac{2}{5}x - \frac{4}{5}} \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(2x + 5y + 4 = 0\) (or any integer multiple) <strong><em>(A1)</em>(ft) <em>(C1)</em></strong></p>
<p><strong>Note:</strong> Follow through from part (c).</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>Question 7: Perpendicular Line<br>The response to this question was mixed.<br>Part (a) was well attempted by the majority.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>In part (b), the gradient was not fully calculated (being left as a reciprocal) by a large number of candidates.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>In part (c), the common error was the use of c from part (a) in the line.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>In part (d), the notation for integer was not understood by a large number of candidates.</p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The straight line, <em>L</em><sub>1</sub>, has equation \(y = - \frac{1}{2}x - 2\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<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">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the gradient 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>The line <em>L</em><sub>2</sub> is perpendicular to <em>L</em><sub>1</sub> and passes through the point (3, 7).</span></p>
<p><span>Write down the gradient of the line <em>L</em><sub>2</sub>.</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 line <em>L</em><sub>2</sub> is perpendicular to <em>L</em><sub>1</sub> and passes through the point (3, 7).</span></p>
<p><span>Find the equation of <em>L</em><sub>2</sub>. Give your answer in the form <em>ax</em> + <em>by</em> + <em>d</em> = 0 where \(a,{\text{ }}b,{\text{ }}d \in \mathbb{Z}\).</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>–2 <em><strong> (A1) (C1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Accept (0, –2).</span></p>
<p><span> </span></p>
<p><em><strong><span>[1 mark]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\( - \frac{1}{2}\) <em><strong> (A1) (C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>2 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C1)</strong></em></span></p>
<p><span> </span></p>
<p><span><strong>Note:</strong> Follow through from their answer to part (b).</span></p>
<p><span> </span></p>
<p><em><strong><span>[1 mark]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>y</em> = 2<em>x</em> + <em>c</em> (<em>can be implied</em>)</span><br><span>7 = 2 × 3 + <em>c</em> <em><strong> (M1)</strong></em></span><br><span><em>c</em> = 1 <strong><em>(A1)</em>(ft)</strong></span><br><span><em>y</em> = 2<em>x</em> + 1</span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(M1)</strong> </em>for substitution of (3, 7), <strong><em>(A1)</em>(ft)</strong> for <em>c</em>.</span></p>
<p><span>Follow through from their answer to part (c).</span></p>
<p><span> </span></p>
<p><strong><span>OR</span></strong></p>
<p><span><em>y</em> – 7 = 2(<em>x </em></span><span><span>– </span>3) <em><strong>(M1)(M1)</strong></em></span></p>
<p><span> </span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong> </em>for substitution of their answer to part (c), <em><strong>(M1)</strong></em> for</span> <span>substitution of (3, 7).</span></p>
<p><span> </span></p>
<p><span>2<em>x</em> </span><span><span>– </span><em>y</em> + 1 = 0 <strong>or</strong> –2<em>x</em> + <em>y </em></span><span><span>– </span>1 = 0 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></span></p>
<p><span> </span></p>
<p><span><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> 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">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;">Although the first three parts of this question were well answered, with most candidates knowing how to find the <em>y</em> intercept, gradient of a given line and gradient of the perpendicular line, very few candidates could find the equation of the perpendicular line and correctly state it in the required form.</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;">Although the first three parts of this question were well answered, with most candidates knowing how to find the <em>y</em> intercept, gradient of a given line and gradient of the perpendicular line, very few candidates could find the equation of the perpendicular line and correctly state it in the required form.</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;">Although the first three parts of this question were well answered, with most candidates knowing how to find the <em>y</em> intercept, gradient of a given line and gradient of the perpendicular line, very few candidates could find the equation of the perpendicular line and correctly state it in the required form.</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;">Although the first three parts of this question were well answered, with most candidates knowing how to find the <em>y</em> intercept, gradient of a given line and gradient of the perpendicular line, very few candidates could find the equation of the perpendicular line and correctly state it in the required form.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A hotel has a rectangular swimming pool. Its length is \(x\) metres, its width is \(y\) metres and its perimeter is \(44\) metres.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down an equation for \(x\) and \(y\).</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 area of the swimming pool is \({\text{112}}{{\text{m}}^2}\).</p>
<p class="p1">Write down a second equation for \(x\) and \(y\).</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">Use your graphic display calculator to find the value of \(x\) and the value of \(y\).</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">An Olympic sized swimming pool is \(50\) m long and \(25\) m wide.</p>
<p class="p1">Determine the area of the hotel swimming pool as a percentage of the area of an Olympic sized swimming pool.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(2x + 2y = 44\) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Accept equivalent forms.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(xy = 112\) <span class="Apple-converted-space"> </span><strong><em>(A1) (C1)</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(8\), \(14\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C2)</em></strong></p>
<p class="p1"> </p>
<p class="p1"><strong>Notes: </strong>Accept \(x = 8\), \(y = 14\) <span class="Apple-converted-space"> </span><strong>OR</strong> <span class="Apple-converted-space"> </span>\(x = 14\), \(y = 8\)</p>
<p class="p1">Follow through from their answers to parts (a) and (b) only if both values are positive.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\frac{{112}}{{1250}} \times 100\) <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 \(112\) divided by \(1250\).</p>
<p class="p2"> </p>
<p class="p1">\( = 8.96\) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C2)</em></strong></p>
<p class="p2"><strong>Note: </strong>Do not penalize if percentage sign seen.</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><span style="font-size: medium; font-family: times new roman,times;">A cuboid has the following dimensions: length = 8.7 cm, width = 5.6 cm and height = 3.4 cm.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the <strong>exact</strong> value of the volume of the cuboid, in cm<sup>3</sup>.</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>Write your answer to part (a) correct to</span></p>
<p><span>(i) one decimal place;</span></p>
<p><span>(ii) 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>Write your answer to <strong>part (b)(ii)</strong> in the form \(a \times 10^k\), where \(1 \leqslant a < 10 , k \in \mathbb{Z}\).</span></p>
<div class="marks">[2]</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>\({\text{V}} = 8.7 \times 5.6 \times 3.4\) <em><strong>(M1)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for multiplication of the 3 given values.</span></p>
<p><span><br>\(=165.648\) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) 165.6 <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><br><br></p>
<p><span>(ii) 166 <em><strong>(A1)</strong></em><strong>(ft) <em>(C2)</em><br></strong></span></p>
<p><br><span><strong>Note:</strong> Follow through from their answer to part (a).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(1.66 \times 10^2\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for 1.66, <em><strong>(A1)</strong></em><strong>(ft)</strong> for \(10^2\). Follow through from their answer to part (b)(ii) only. The follow through for the index should be dependent on the value of the mantissa in part (c) and their answer to part (b)(ii).</span></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><span style="font-size: medium; font-family: times new roman,times;">The coordinates of the vertices of a triangle ABC are A (4, 3), B (7, –3) and C (0.5, <em>p</em>).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the gradient of the line 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>Given that the line AC is perpendicular to the line AB</span></p>
<p><span>write down the gradient of the line AC.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b, i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Given that the line AC is perpendicular to the line AB</span></p>
<p><span>find the value of <em>p</em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b, ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(m({\rm{AB}}) = \frac{{ - 3 - 3}}{{7 - 4}} = - 2\) <em><strong>(M1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for attempt to substitute into correct 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>\(m({\rm{AC}}) = \frac{1}{2}\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><em><span><strong>[1 mark]<br></strong></span></em></p>
<div class="question_part_label">b, i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{p - 3}}{{0.5 - 4}} = \frac{1}{2}\)<em> (or equivalent method)</em> <strong><em>(M1)(A1)</em>(ft)</strong></p>
<p><span><br> </span><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for equating gradient to \(\frac{1}{2}\). <strong><em>(A1)</em></strong> for correct substitution.</p>
<p><span><br> </span>\(p = 1.25\) <strong><em>(A1)</em>(ft)</strong> <strong><em>(C4)</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b, ii.</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;">While parts (a) and (b)(i) were attempted with some success, few candidates made progress</span> <span style="font-size: medium; font-family: times new roman,times;">in (b)(ii). Some candidates used the coordinates of point <em>B</em> rather than <em>C</em> and others could </span><span style="font-size: medium; font-family: times new roman,times;">not find the unknown value p as they did not realise they had to equate their substituted </span><span style="font-size: medium; font-family: times new roman,times;">formula for the gradient to the answer to part (b)(i). A large number of candidates did not</span> <span style="font-size: medium; font-family: times new roman,times;">attempt this part of the question.</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;">While parts (a) and (b)(i) were attempted with some success, few candidates made progress</span> <span style="font-size: medium; font-family: times new roman,times;">in (b)(ii). Some candidates used the coordinates of point <em>B</em> rather than <em>C</em> and others could </span><span style="font-size: medium; font-family: times new roman,times;">not find the unknown value p as they did not realise they had to equate their substituted </span><span style="font-size: medium; font-family: times new roman,times;">formula for the gradient to the answer to part (b)(i). A large number of candidates did not</span> <span style="font-size: medium; font-family: times new roman,times;">attempt this part of the question.</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;">While parts (a) and (b)(i) were attempted with some success, few candidates made progressin (b)(ii). Some candidates used the coordinates of point <em>B</em> rather than <em>C</em> and others could not find the unknown value p as they did not realise they had to equate their substituted formula for the gradient to the answer to part (b)(i). A large number of candidates did notattempt this part of the question.</span></p>
<div class="question_part_label">b, ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The coordinates of point A are \((6,{\text{ }} - 7)\) and the coordinates of point B are \(( - 6,{\text{ }}2)\). Point M is the midpoint of AB.</p>
</div>
<div class="specification">
<p>\({L_1}\) is the line through A and B.</p>
</div>
<div class="specification">
<p>The line \({L_2}\) is perpendicular to \({L_1}\) and passes through M.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of M.</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>Find the gradient of \({L_1}\).</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>Write down the gradient of \({L_2}\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, in the form \(y = mx + c\), the equation of \({L_2}\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\((0,{\text{ }}2.5)\)\(\,\,\,\)<strong>OR</strong>\(\,\,\,\)\(\left( {0,{\text{ }} - \frac{5}{2}} \right)\) <strong><em>(A1)(A1) (C2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for 0 and <strong><em>(A1) </em></strong>for –2.5 written as a coordinate pair. Award at most <strong><em>(A1)(A0) </em></strong>if brackets are missing. Accept “\(x = 0\) and \(y = - 2.5\)”.</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>\(\frac{{2 - ( - 7)}}{{ - 6 - 6}}\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into gradient formula.</p>
<p> </p>
<p>\( = - \frac{3}{4}{\text{ }}( - 0.75)\) <strong><em>(A1) (C2)</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>\(\frac{4}{3}{\text{ }}(1.33333 \ldots )\) <strong><em>(A1)</em>(ft) <em>(C1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A0) </em></strong>for \(\frac{1}{{0.75}}\). Follow through from part (b).</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(y = \frac{4}{3}x - \frac{5}{2}{\text{ }}(y = 1.33 \ldots x - 2.5)\) <strong><em>(A1)</em>(ft) <em>(C1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from parts (c)(i) and (a). Award <strong><em>(A0) </em></strong>if final answer is not written in the form \(y = mx + c\).</p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A satellite travels around the Earth in a circular orbit \(500\) kilometres above the Earth’s surface. The radius of the Earth is taken as \(6400\) kilometres.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the radius of the satellite’s orbit.</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 distance travelled by the satellite in one orbit of the Earth. Give your answer correct to the nearest km.</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 your answer to (b) in the form \(a \times {10^k}\) , where \(1 \leqslant a < 10{\text{, }}k \in \mathbb{Z}\) .</span></p>
<div class="marks">[2]</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><span>\(6900\) km </span><span> <em><strong>(A1) (C1)</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>\(2\pi (6900)\) <strong><em>(M1)(A1)</em>(ft)</strong></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for substitution into circumference formula, <strong><em>(A1)</em>(ft) </strong>for correct substitution. Follow through from part (a).</span></p>
<p> </p>
<p><span>\( = 43354\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></span></p>
<p><span><strong>Notes:</strong> Follow through from part (a). The final <em><strong>(A1)</strong></em> is awarded for rounding their answer correct to the nearest km. Award <em><strong>(A2)</strong></em> for \(43 400\) shown with no working.</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>\(4.3354 \times {10^4}\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <strong><em>(A1)</em>(ft)</strong> for \(4.3354\), <strong><em>(A1)</em>(ft)</strong> for \( \times {10^4}\) . Follow through from part (b). Accept \(4.34 \times {10^4}\) .</span></p>
<p><em><strong><span>[2 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;">Candidates appeared to be confused by the context in this question. They had difficulty identifying the radius and many used the formula for the area of a circle, rather than the circumference. </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;">Candidates appeared to be confused by the context in this question. They had difficulty identifying the radius and many used the formula for the area of a circle, rather than the circumference. A large number of candidates misread the final sentence in part b and did not write their answer to the nearest kilometre.</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;">Candidates appeared to be confused by the context in this question. They had difficulty identifying the radius and many used the formula for the area of a circle, rather than the circumference.</span></p>
<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;">Chocolates in the shape of spheres are sold in boxes of 20.</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;">Each chocolate has a radius of 1 cm.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the volume of 1 chocolate.</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>Write down the volume of 20 chocolates.</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 diagram shows the chocolate box from above. The 20 chocolates fit perfectly in the box with each chocolate touching the ones around it or the sides of the box.</span></p>
<p><span><br><img src="images/Schermafbeelding_2014-09-02_om_14.27.38.png" alt><br></span></p>
<p><span>Calculate the volume of the box.</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 diagram shows the chocolate box from above. The 20 chocolates fit perfectly in the box with each chocolate touching the ones around it or the sides of the box.</span></p>
<p><span><br><img src="images/Schermafbeelding_2014-09-02_om_14.27.38_1.png" alt><br></span></p>
<p><span>Calculate the volume of empty space in the box.</span></p>
<div class="marks">[1]</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><strong><em>The first time a correct answer has incorrect or missing units, the final (A1) is not awarded.</em></strong></span></p>
<p><span>\(\frac{4}{3}\pi {(1)^3}\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into correct formula.</span></p>
<p> </p>
<p><span>\( = 4.19{\text{ }}\left( {{\text{4.18879}} \ldots ,{\text{ }}\frac{4}{3}\pi } \right){\text{ c}}{{\text{m}}^3}\) <strong><em>(A1) (C2)</em></strong></span></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><strong><em>The first time a correct answer has incorrect or missing units, the final (A1) is not awarded.</em></strong></span></p>
<p><span>\(83.8{\text{ }}\left( {{\text{83.7758}} \ldots ,{\text{ }}\frac{{80}}{3}\pi } \right){\text{ c}}{{\text{m}}^3}\) <strong><em>(A1)</em>(ft) <em>(C1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Follow through from their answer to part (a).</span></p>
<p> </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><strong><em>The first time a correct answer has incorrect or missing units, the final (A1) is not awarded.</em></strong></span></p>
<p><span>\(10 \times 8 \times 2\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into correct formula.</span></p>
<p> </p>
<p><span>\( = 160{\text{ c}}{{\text{m}}^3}\) <strong><em>(A1) (C2)</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><strong><em>The first time a correct answer has incorrect or missing units, the final (A1) is not awarded.</em></strong></span></p>
<p><span>\(76.2{\text{ }}\left( {{\text{76.2241}} \ldots ,{\text{ }}\left( {160 - \frac{{80}}{3}\pi } \right)} \right){\text{ c}}{{\text{m}}^3}\) <strong><em>(A1)</em>(ft) <em>(C1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Follow through from their part (b) and their part (c).</span></p>
<p> </p>
<p><span><strong><em>[1 mark] </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><span style="font-size: medium; font-family: times new roman,times;">In the diagram, triangle ABC is isosceles. AB = AC and angle ACB is 32°. The length of side AC is <em>x</em> cm.</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>Write down the size of angle CBA.</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>Write down the size of angle CAB.</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 area of triangle ABC is 360 cm<sup>2</sup>. Calculate the length of side AC. Express your answer in <strong>millimetres</strong>.</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>32° <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>116° <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(360 = \frac{1}{2} \times {x^2} \times \sin 116^\circ \) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for substitution into correct formula with 360 seen, </span><span><em><strong>(A1)</strong></em><strong>(ft)</strong> for correct substitution, follow through from their answer to </span><span>part (b).</span></p>
<p><br><span><em>x</em> = 28.3 (cm) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><em>x</em> = 283 (mm) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C4)</strong></em></span></p>
<p><span><strong>Notes:</strong> The final <em><strong>(A1)</strong></em><strong>(ft)</strong> is for their cm answer converted to mm. If their </span><span>incorrect cm answer is seen the final <em><strong>(A1)</strong></em><strong>(ft)</strong> can be awarded for </span><span>correct conversion to mm.</span></p>
<p><span><em><strong>[4 marks]</strong></em></span></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-size: medium; font-family: times new roman,times;">Candidates had difficulties finding the length of the side of the isosceles triangle and chose an incorrect angle in their substitution into the area formula. Many candidates thought this question related to right angle triangle trigonometry.</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;">Candidates had difficulties finding the length of the side of the isosceles triangle and chose an incorrect angle in their substitution into the area formula. Many candidates thought this question related to right angle triangle trigonometry.</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;">Candidates had difficulties finding the length of the side of the isosceles triangle and chose an incorrect angle in their substitution into the area formula. Many candidates thought this question related to right angle triangle trigonometry.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A triangular postage stamp, ABC, is shown in the diagram below, such that \({\text{AB}} = 5{\text{ cm}},{\rm{ B\hat AC}} = 34^\circ ,{\rm{ A\hat BC}} = 26^\circ \) and \({\rm{A\hat CB}} = 120^\circ \).</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_11.34.31.png" alt="M17/5/MATSD/SP1/ENG/TZ1/13"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the length of BC.</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 area of the postage stamp.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{{\text{BC}}}}{{\sin 34^\circ }} = \frac{5}{{\sin 120^\circ }}\) <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for substituted sine rule formula, <strong><em>(A1) </em></strong>for correct substitutions.</p>
<p> </p>
<p>\({\text{BC}} = 3.23{\text{ (cm) }}\left( {3.22850 \ldots {\text{ (cm)}}} \right)\) <strong><em>(A1)</em></strong> <strong><em>(C3)</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>\(\frac{1}{2}(5)(3.22850)\sin 26^\circ \) <strong><em>(M1)(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for substituted area of a triangle formula, <strong><em>(A1) </em></strong>for correct substitutions.</p>
<p> </p>
<p>\( = 3.54{\text{ }}({\text{c}}{{\text{m}}^2}){\text{ }}\left( {3.53820 \ldots {\text{ }}({\text{c}}{{\text{m}}^2})} \right)\) <strong><em>(A1)</em>(ft)</strong> <strong><em>(C3)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from part (a).</p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</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>
<br><hr><br><div class="specification">
<p class="p1">The equation of the line \({L_1}\) is \(2x + y = 10\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>the gradient of \({L_1}\);</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>the \(y\)-intercept of \({L_1}\).</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"><span class="s1">The line \({L_2}\) is parallel to \({L_1}\) </span>and passes through the point \({\text{P}}(0,{\text{ }}3)\)<span class="s1">.</span></p>
<p class="p2">Write down the equation of \({L_2}\).</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"><span class="s1">The line \({L_2}\) is parallel to \({L_1}\) </span>and passes through the point \({\text{P}}(0,{\text{ }}3)\)<span class="s1">.</span></p>
<p class="p1">Find the \(x\)-coordinate of the point where \({L_2}\) crosses the \(x\)-axis.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>\( - 2\) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C1)</em></strong></p>
<p class="p1">(ii) <span class="Apple-converted-space"> \(10\)</span> <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C1)</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(2x + y - 3 = 0\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(A1) <span class="Apple-converted-space"> </span>(C2)</em></strong></p>
<p class="p1"><strong>Notes: </strong>Award <strong><em>(A1)</em>(ft) </strong>for gradient, <strong><em>(A1) </em></strong>for correct \(y\)-intercept.</p>
<p class="p1">The answer must be an equation.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\( - 2x + 3 = 0\;\;\;\)or equivalent <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">\((x = ){\text{ }}1.5\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C2)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: </strong>Follow through from their equation in part (b). If answer given as coordinates \((1.5,{\text{ }}0)\) award at most <strong><em>(M1)(A0) </em></strong>if working seen or <strong><em>(A1)(A0) </em></strong>if no working seen.</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 class="p1">A right pyramid has apex \({\text{V}}\) and rectangular base \({\text{ABCD}}\), with \({\text{AB}} = 8{\text{ cm}}\), \({\text{BC}} = 6{\text{ cm}}\) and \({\text{VA}} = 13{\text{ cm}}\). The vertical height of the pyramid is \({\text{VM}}\)<span class="s1">.</span></p>
<p class="p1" style="text-align: center;"><span class="s1"><img src="images/Schermafbeelding_2015-12-20_om_06.32.41.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate \({\text{VM}}\).</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">Calculate the volume of the pyramid.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\({\text{A}}{{\text{C}}^2} = {8^2} + {6^2}\) <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 into Pythagoras, or recognition of Pythagorean triple.</p>
<p class="p2"> </p>
<p class="p1">\({\text{AC}} = 10\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(A2)</em></strong> for \({\text{AC}} = 10\;\;\;\)<strong>OR</strong>\(\;\;\;{\text{AM}} = 5\) with no working seen.</p>
<p class="p2"> </p>
<p class="p1">\({\text{V}}{{\text{M}}^2} = {13^2} - {5^2}\) <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 second use of Pythagoras, using the result from the first use of Pythagoras.</p>
<p class="p2"> </p>
<p class="p1">\({\text{VM}} = 12{\text{ (cm)}}\) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C4)</em></strong></p>
<p class="p1"><strong>Notes: </strong>Accept alternative methods and apply the markscheme as follows: Award <strong><em>(M1)(A1) </em></strong>for first correct use of Pythagoras with lengths from the question, <strong><em>(M1) </em></strong>for a correct second use of Pythagoras, consistent with the method chosen, <strong><em>(A1) </em></strong>for correct height.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{1}{3} \times 8 \times 6{\kern 1pt} \times 12\) <strong><em>(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for their correct substitutions into volume formula.</p>
<p> </p>
<p>\( = 192{\text{ c}}{{\text{m}}^3}\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></p>
<p><strong>Notes: </strong>Follow through from part (a), only if working seen.</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>In part (a) many candidates struggled to identify right angled triangles correctly. A regular mistake was to calculate the slant height and not the vertical height. Often values were used which did not correspond to a right angled triangle in the diagram, such as 13 and 8. Another common mistake was incorrect use of Pythagoras, where the hypotenuse was not correctly identified or was incorrectly substituted into the formula.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Despite the problems to obtain a correct answer for part (a), in part (b) many candidates wrote down a correctly substituted formula for the volume of a pyramid (with their height substituted) and received follow through marks. Very few, having calculated their volume correctly, failed to give the correct units. Some candidates used the perimeter (28) of the base and not the area.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The straight line, <em>L</em>, has equation \(2y - 27x - 9 = 0\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the gradient of <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>Sarah wishes to draw the tangent to \(f (x) = x^4\) parallel to <em>L</em>.</span></p>
<p><span>Write down \(f ′(x)\).</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>Find the <em>x</em> coordinate of the point at which the tangent must be drawn.<br></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>Write down the value of \(f (x)\) at this point.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c, ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><em>y</em> = 13.5<em>x</em> + 4.5 <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for 13.5<em>x</em> seen.</span></p>
<p><br><span>gradient = 13.5 <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></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>4<em>x</em><sup>3</sup> <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>4<em>x</em><sup>3</sup> = 13.5 <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for equating their answers to (a) and (b).</span></p>
<p><br><span><em>x</em> = 1.5 <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><em><span><strong>[2 marks]</strong></span></em></p>
<div class="question_part_label">c, i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{81}}{{16}}\) (5.0625, 5.06) <strong><em>(A1)</em>(ft)</strong> <strong><em>(C3)</em></strong></span></p>
<p><span><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for substitution of their (c)(i) into <em>x</em><span>4</span> with working seen.</span></p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">c, ii.</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 structure of this question was not well understood by the majority; the links between parts not being made. Again, this question was included to discriminate at the grade 6/7 level.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Most were successful in this part.</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 structure of this question was not well understood by the majority; the links between parts not being made. Again, this question was included to discriminate at the grade 6/7 level.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">This part was usually well attempted.</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 structure of this question was not well understood by the majority; the links between parts not being made. Again, this question was included to discriminate at the grade 6/7 level.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Only the best candidates succeeded in this part.</span></p>
<div class="question_part_label">c, i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">The structure of this question was not well understood by the majority; the links between parts not being made. Again, this question was included to discriminate at the grade 6/7 level.</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">Only the best candidates succeeded in this part.</span></p>
<div class="question_part_label">c, ii.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The length of one side of a rectangle is 2 cm longer than its width.</span></p>
<p><span>If the smaller side is <em>x</em> cm, find the perimeter of the rectangle in terms of <em>x</em>.</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>The length of one side of a rectangle is 2 cm longer than its width.</span></p>
<p><span>The perimeter of a square is equal to the perimeter of the rectangle in part (a).</span></p>
<p><span>Determine the length of each side of the square in terms of <em>x</em>.</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 length of one side of a rectangle is 2 cm longer than its width.</span></p>
<p><span>The perimeter of a square is equal to the perimeter of the rectangle in part (a).</span></p>
<p><span>The sum of the areas of the rectangle and the square is \(2x^2 + 4x +1\) (cm<sup>2</sup>).</span></p>
<p><span>(i) Given that this sum is 49 cm<sup>2</sup>, find <em>x</em>.</span></p>
<p><span>(ii) Find the area of the square.</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><span><em><strong>Unit penalty (UP) is applicable where indicated in the left hand column.</strong></em><br></span></span></p>
<p><span><span><em><strong>(UP)</strong></em> \({\text{P (rectangle)}} = 2x + 2(x + 2) = 4x + 4{\text{ cm}}\)</span> <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><em><span><strong>(UP)</strong> Simplification not required</span></em></p>
<p><em><span><strong>[1 mark]</strong><br></span></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em><strong>Unit penalty (UP) is applicable where indicated in the left hand column.</strong></em><br></span></p>
<p><span><em><strong>(UP)</strong></em> Side of square = (4<em>x</em> + 4)/4 = <em>x</em> + 1 cm <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(2x^2 + 4x + 1 = 49\) or equivalent <em><strong>(M1)</strong></em></span></p>
<p><span>\((x + 6)(x – 4) = 0\)</span></p>
<p><span>\(x = - 6\) and \(4\) <em><strong>(A1)</strong></em></span></p>
<p><span><em>Note: award <strong>(A1)</strong> for the values or for correct factors </em><br></span></p>
<p><span>Choose \(x = 4\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><em>Award </em><strong><em>(A1)</em>(ft)</strong><em> for choosing positive value. </em> <em><strong>(C3)</strong></em></span></p>
<address><em><span> </span></em></address>
<p><span>(ii) \({\text{Area of square}} = 5 \times 5 = 25{\text{ c}}{{\text{m}}^2}\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><em><span>Note: Follow through from both (b) and (c)(i). <strong>(C1)</strong></span></em></p>
<p><em><span><strong> </strong></span></em></p>
<p><em><span><strong>[4 marks]<br></strong></span></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-size: medium; font-family: times new roman,times;">a) and b) Two thirds of the candidates found the perimeter of the rectangle and the side of the square correctly, though most of them did not include units (thereby incurring a unit penalty).</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;">a) and b) Two thirds of the candidates found the perimeter of the rectangle and the side of the square correctly, though most of them did not include units (thereby incurring a unit penalty).</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;">c) Although a majority of candidates produced the quadratic equation many were unable to solve it correctly. This could easily be done using the GDC so it was disappointing.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"> </span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Two fixed points, A and B, are 40 m apart on horizontal ground. Two straight ropes, AP and BP, are attached to the same point, P, on the base of a hot air balloon which is vertically above the line AB. The length of BP is 30 m and angle BAP is 48°.</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>Angle APB is acute.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the diagram, draw and label with an <em>x</em> the angle of depression of B from P.</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 size of angle APB.</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 size of the angle of depression of B from P.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><img 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"><em><strong>(A1) (C1)</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>\(\frac{{40}}{{{\text{sin APB}}}} = \frac{{30}}{{{\text{sin 48}}^\circ }}\) <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution into sine rule, <em><strong>(A1)</strong></em> for correct substitution.</p>
<p>(angle APB =) 82.2° (82.2473…°) <em><strong>(A1) (C3)</strong></em></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>180 − 48 − 82.2473… <em><strong> (M1)</strong></em></p>
<p>49.8° (49.7526…°) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note:</strong> Follow through from parts (a) and (b).</p>
<p><em><strong>[2 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.</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><span style="font-family: times new roman,times; font-size: medium;">The base of a prism is a <strong>regular hexagon</strong>. The centre of the hexagon is O and the length of OA is 15 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>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the size of angle AOB.</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 area of the triangle AOB.</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 height of the prism is 20 cm.</span></p>
<p><span>Find the volume of the prism.</span></p>
<div class="marks">[2]</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>60° <em><strong> (A1) (C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{15 \times \sqrt {{{15}^2} - {{7.5}^2}} }}{2} = 97.4{\text{ c}}{{\text{m}}^2}\) (97.5 cm<sup>2</sup>) <em><strong>(A1)(M1)(A1)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for correct height, <em><strong>(M1)</strong></em> for substitution in the area formula, <em><strong>(A1)</strong></em> for correct answer.</span></p>
<p><span>Accept 97.5 cm<sup>2</sup> from taking the height to be 13 cm.</span></p>
<p><br><span><strong>OR</strong></span></p>
<p><span>\(\frac{1}{2} \times {15^2} \times \sin 60^\circ = 97.4{\text{ c}}{{\text{m}}^2}\) <em><strong>(M1)(A1)(A1)</strong></em><strong>(ft)</strong><em> <strong>(C3)</strong></em></span></p>
<p><span> </span></p>
<p> </p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for substituted formula of the area of a triangle, <em><strong>(A1)</strong></em> </span><span>for correct substitution, <em><strong>(A1)</strong></em><strong>(ft)</strong> for answer.</span></p>
<p> </p>
<p><span>Follow through from their answer to part (a).</span></p>
<p> </p>
<p><span>If radians used award at most <em><strong>(M1)(A1)(A0)</strong></em>.</span></p>
<p> </p>
<p><span><span> </span></span></p>
<p> </p>
<p><em><strong><span><span><span>[3 marks]</span></span></span></strong></em></p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>97.4 × 120 = 11700 cm<sup>3</sup> <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for multiplying their part (b) by 120.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 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;">This question proved to be difficult for a number of candidates. Most were able find the size of the angle in part a), but many had problems finding the area of the triangle in part b). A significant number of candidates were unable to use the Pythagoras Theorem correctly to find the height of the triangle AOB. Those who used the formula for the area of a triangle \({\text{A}} = \frac{1}{2}{\text{ab}}\sin {\text{C}}\) were more successful in this part of the question. It was surprising that a great number of candidates were unable to find the volume of the prism – many incorrectly used the formula for calculating volume of a pyramid rather than a hexagonal prism.</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 proved to be difficult for a number of candidates. Most were able find the size of the angle in part a), but many had problems finding the area of the triangle in part b). A significant number of candidates were unable to use the Pythagoras Theorem correctly to find the height of the triangle AOB. Those who used the formula for the area of a triangle \({\text{A}} = \frac{1}{2}{\text{ab}}\sin {\text{C}}\) were more successful in this part of the question. It was surprising that a great number of candidates were unable to find the volume of the prism – many incorrectly used the formula for calculating volume of a pyramid rather than a hexagonal prism.</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 proved to be difficult for a number of candidates. Most were able find the size of the angle in part a), but many had problems finding the area of the triangle in part b). A significant number of candidates were unable to use the Pythagoras Theorem correctly to find the height of the triangle AOB. Those who used the formula for the area of a triangle \({\text{A}} = \frac{1}{2}{\text{ab}}\sin {\text{C}}\) were more successful in this part of the question. It was surprising that a great number of candidates were unable to find the volume of the prism – many incorrectly used the formula for calculating volume of a pyramid rather than a hexagonal prism.</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 line joins the points A(2, 1) and B(4, 5).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the gradient of the line 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>Let M be the midpoint of the line segment AB.</span></p>
<p><span>Write down the coordinates of M.</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>Let M be the midpoint of the line segment AB.</span></p>
<p><span>Find the equation of the line perpendicular to AB and passing through M.</span></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><span>\({\text{Gradient}} = \frac{{(5 - 1)}}{{(4 - 2)}}\) </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 the gradient formula.</span></p>
<p><br><span>\(= 2\) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></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>Midpoint = (3, 3) (accept <em>x</em> = 3, <em>y</em> = 3 ) <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{Gradient of perpendicular}} = -\frac{{1}}{{2}}\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>\(y = - \frac{{1}}{{2}} x + c\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(3 = - \frac{{1}}{{2}} \times 3 + c\)</span></p>
<p><span>\(c = 4.5\)</span></p>
<p><span>\(y = -0.5x + 4.5\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><strong><span>OR</span></strong></p>
<p><span>\(y - 3 = -0.5(x - 3)\) <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for –0.5, <em><strong>(A1)</strong></em> for both threes.</span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span>\(2y + x = 9\) <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong> <em><strong>(C3)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for 2, <em><strong>(A1)</strong></em> for 9.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 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-size: medium; font-family: times new roman,times;">While parts (a) and (b) were answered or at least attempted with various success, few candidates made progress in part (c). Some candidates used the coordinates of point A or B rather than M and others could not find the gradient of the perpendicular line.</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;">While parts (a) and (b) were answered or at least attempted with various success, few candidates made progress in part (c). Some candidates used the coordinates of point A or B rather than M and others could not find the gradient of the perpendicular line.</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;">While parts (a) and (b) were answered or at least attempted with various success, few candidates made progress in part (c). Some candidates used the coordinates of point A or B rather than M and others could not find the gradient of the perpendicular line.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>In this question, give all answers to two decimal places.</strong></p>
<p>Karl invests 1000 US dollars (USD) in an account that pays a nominal annual interest of 3.5%, <strong>compounded quarterly</strong>. He leaves the money in the account for 5 years.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the amount of money he has in the account after 5 years.</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>Write down the amount of <strong>interest</strong> he earned after 5 years.</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>Karl decides to donate this <strong>interest</strong> to a charity in France. The charity receives 170 euros (EUR). The exchange rate is 1 USD = <em>t</em> EUR.</p>
<p>Calculate the value of <em>t</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(1000{\left( {1 + \frac{{3.5}}{{4 \times 100}}} \right)^{4 \times 5}}\) <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution in compound interest formula, <em><strong>(A1)</strong></em> for correct substitution.</p>
<p><strong>OR </strong></p>
<p><em>N</em> = 5</p>
<p><em>I</em> = 3.5</p>
<p><em>PV</em> = 1000</p>
<p><em>P</em>/<em>Y</em> = 1</p>
<p><em>C</em>/<em>Y</em> = 4</p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <em>C</em>/<em>Y</em> = 4 seen, <em><strong>(M1)</strong></em> for other correct entries.</p>
<p><strong>OR</strong></p>
<p><em>N</em> = 5 × 4</p>
<p><em>I</em> = 3.5</p>
<p><em>PV</em> = 1000</p>
<p><em>P</em>/<em>Y</em> = 1</p>
<p><em>C</em>/<em>Y</em> = 4</p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <em>C</em>/<em>Y</em> = 4 seen, <em><strong>(M1)</strong></em> for other correct entries.</p>
<p>= 1190.34 (USD) <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution in compound interest formula, <em><strong>(A1)</strong></em> for correct substitution.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>190.34 (USD) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C4)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for subtraction of 1000 from their part (a)(i). Follow through from (a)(i).</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{170}}{{190.34}}\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for division of 170 by their part (a)(ii).</p>
<p>= 0.89 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note:</strong> Follow through from their part (a)(ii).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</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>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A rectangle is 2680 cm long and 1970 cm wide.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the perimeter of the rectangle, giving your answer in the form \(a \times {10^k}\), where \(1 \leqslant a \leqslant 10\) and \(k \in \mathbb{Z}\).</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 rectangle, giving your answer correct to the nearest thousand square centimetres.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><strong><em>Note: Unit penalty (UP) applies in this part</em></strong></span></p>
<p><span> </span></p>
<p><span>(2680 + 1970) × 2 <em><strong>(M1)</strong></em></span></p>
<p><span><em><strong>(UP)</strong></em> = 9.30 </span><span><span>× </span>10<sup>3</sup> cm <em><strong>(A1)(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for correct formula.</span></p>
<p><span><em><strong>(A1)</strong></em> for 9.30 (Accept 9.3)</span>.</p>
<p><span><em><strong>(A1)</strong></em> for 10<sup>3</sup>.</span></p>
<p><span> </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><span>2680 × 1970 <em><strong>(M1)</strong></em></span></p>
<p><span>= 5279600 <em><strong>(A1)</strong></em></span></p>
<p><span>= 5,280,000 (5280 thousand) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C3)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted formula.</span></p>
<p><span>Accept 5.280 </span><span><span>× </span>10<sup>6</sup>.</span></p>
<p><br><span><strong>Note:</strong> The last <em><strong>(A1)</strong></em> is for specified accuracy, <strong>(ft)</strong> from their answer.</span></p>
<p><span>The <em><strong>(AP)</strong></em> for the paper is not applied here.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">b.</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 well answered by many candidates although the majority lost a mark as a unit penalty in part (a). Some candidates used the wrong formula for the perimeter. Most could give their answer in standard form.</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 well answered by many candidates although the majority lost a mark as a unit penalty in part (a). Some candidates used the wrong formula for the perimeter. Most could give their answer in standard form.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A store sells bread and milk. On Tuesday, 8 loaves of bread and 5 litres of milk were sold for $21.40. On Thursday, 6 loaves of bread and 9 litres of milk were sold for $23.40. </span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">If \(b =\) the price of a loaf of bread and \(m =\) the price of one litre of milk, Tuesday’s sales can be written</span> <span style="font-size: medium; font-family: times new roman,times;">as \(8b + 5m = 21.40\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using simplest terms, write an equation in <em>b</em> and <em>m</em> for Thursday’s sales.</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 <em>b</em> and <em>m</em>.</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>Draw a sketch, in the space provided, to show how the prices can be found graphically.</span></p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAcMAAAD3CAIAAADueKiGAAALlElEQVR4nO3dv2sbacLAcf8nEkwlgSAv17hy9RZZF8IcVxy42cMxZIuFFFscJ6HA8XYHMjGBhcAik7DwcrDIZIsXjixDmnB4Ee9bbCEG9iBshAqzBDGFEcswb+Ef5zgbe7JPohnZnw9TxEYiw8T+5nlmHs2s5ACEWSntb57F3UY9qh1vm3vJUWl7AhCmrJLOJ8N7rdppSduDJCtpRwCClVTS9GCn/dd4Jp/AdVBKSbNZ3GvVmuudr/bjJC1jDwA+oDJKmo332s3TM6TN9c4wSd85OI3OzgCcbj///PMidxbgSuVdccqmo6dfdW83o1pzvX/wrpHp2yVNkmSh+wlwlfJKeiybxL121OgVOWeaJImSAhVUdknz4+VQa9348MoXKilQTRUoaTbea39aZD2pkgLVVIGSzuL7vXhW4IVKClRTCSXNpqNvn46m2fGfX+x2+vF0XuSNSgpUUyklfXb/djOq1aPGnZ1vnl+yBOoCJQWqqQKz+8KUFKgmJQUIpaQAoZQUIJSSAoRSUoBQSgoQSkkBQikpQCglBQilpAChlBQglJIChFJSgFBKChBKSQFCKSlAKCUFCKWkAKGUFCCUkgKEUlKAUEoKEKrcks4nw3ut9iAp9sR7JQWqqcySZpPhZ416pKTAkiuvpOnBztYX3a1VJQWWXVklfT3qf7EzSuLOmpICy66Ukmbp6OF2/yDND4uUNKrVL2yL2k+AQsooaXqws/VwlGa5kgLXwuJL+nr04G/7k3me5wVLesbsHqimBZc0S0eP7g9fnpZTSYHrYMElPYw7a2/P1qNac2MwvjKnSgpUU7kr841JgetASQFCKSlAKHcwAQilpAChlBQglJIChFJSgFBKChBKSQFCKSlAKCUFCKWkAKGUFCCUkgKEUlKAUEoKEEpJAUIpKUAoJQUIpaQAoZQUIJSSAoRSUoBQSgoQqpSSzqcHX2436lGtud4ZJmmxZzQrKVBViy9plv7v0ycH0yzPs+mL3a3VVieeFXunkgLVtPCSZv96/vyn01FoNot7rUYvnhUaliopUE3lnic9SgafrvcP0mKvVlKgmsoraZrEg95279m06GlSJQUqqpSSZrO416rVo1o9ut3bT644TRodv/J0U1Kgakqc3c+no6+7t5tR497+ZH7J65QUqLiS15NmyWCjttaND4u82OweqKayV+Zn4732fyopsNTKLuks7t66YnZ/RkmBalp0SbPJ8LNGu/v4eGn+JO5tbg9+sAoKWGoLH5OmP+xtrR5fO2pt9fdHxRdBKSlQUWXP7t+HkgLVpKQAoZQUIJSSAoRSUoBQSgoQaiWfDreP1yR14lk63u+0o9rqZ8OXWT5Lnu1uN+pRe5AUX6n0MSkpUE0reZ7ns7jbWOsOn+11+vFPL3Zu1X/Xf/FT3O8OXsT9T6LCd2L+2JQUqKaV03vcfbJ9t7c3nuXT4XZt7c9ffXn/wUGaH8adNWNSgMut5PlRMtiMas2NwTg7u3Po7d1RmuWzuNs4/n4lKClQTSt5Nt5rN0+n8IdxZy2q/X5n9Pp0rLq5lxyVvZMnlBSoppU3Bp7HVT2Zzh8lg83qnCTNlRSoqpXjk6Q7ozQ/ue/yG1Vtdf7+3eC/R4UfSf9RKSlQTSvnBp5vTud/Ge3cKvScpYVRUqCarMwHCKWkAKGUFCCUkgKEUlKAUEoKEEpJAUIpKUAoJQUIpaQAoZQUIJSSAoQqo6Rp8l3/TqtWj2rN9c7Xo+m84PuUFKimhZc0e/ntg0ffJbM8z7Ppi92t1ZP78xegpEA1Lbqk2Y8vnk/+PQjNksFGba0bHxZ5r5IC1VT2edLjx5oqKbDMKlDSW/f2J4VOlSopUE3lljSbxX/d6B+kxV6tpEA1lVrS9GBn6+Hll5uiWv3CpqRA1ZRY0tejB/+1N77iIVFKClRfWSWdT54+enJVRi8wuweqqZSSzqfxo914cjqrn40ff/18dvWSUiUFqmnxJZ0lw976hTl7e5AUWJuvpEA1Lbik88nwXuviqc/mxmBc5ENOSgpUU9nrSd+HkgLVpKQAoZQUIJSSAoRSUoBQSgoQSkkBQikpQCglBQilpAChlBQglJIChFJSgFBKChBKSQFCKSlAKCUFCKWkAKGUFCCUkgKEUlKAUEoKEEpJAUKVVdIsTZ7vf9PfvtWLZ0WedZ/nSgpUVTklzZLBHz6986dGPWooKbD0SpzdHyWDTSUFrgElBQilpAChlBQg1BKUNKrVz29KClSNkgKEWoKSnjG7B6pJSQFCKSlAqJJKOou7jbNTn82NwbhITZUUqCZ3MAEIpaQAoZQUIJSSAoRSUoBQSgoQSkkBQikpQCglBQilpAChlBQglJIChFJSgFBKChBKSQFCKSlAKCUFCKWkAKGUFCCUkgKEUlKAUEoKEEpJAUIpKUAoJQUIVUZJs+nocWe9Vo8ad3YPplnh9ykpUE2LL+nrUf+P671n0yzPps/u3/7jzuh1wXcqKVBNiy5plgw2Gr14djwSzWZxr9UeJMXGpUoKVNOCS3qUDDaj8+mcxd3G5l5yVOTNSgpU02JLmo332s1WJ56dfWcWdxvNjcG4yKhUSYFqWmxJ3+7mVSWNanWbzWar4Ha+VEpqs9lsv2U7Xyqz++vm7X9jznN8CnKgLlF2SfOjZLB5vqRZMtioueL0IfkFuJzjU5ADdYnSS2oV1EfnF+Byjk9BDtQlyi9pyMr8V69edf7yl1evXn3U/Vt2fgEu5/gU5EBdogolzfNs+v2DO61aPbrdeTJ6j0+LUoRfAFi8ZbqDCUA1KSlAKCUFCKWkAKGUFCCUkgKEUlKAUEoKEEpJr5MsTZ7vf9PfvnX2eVzOZGnyj52t1ahWj2rt7uP3eYLYTXP22Zlauzscp2XvTiXNJ8N75z/pviQl/a0P0btRsmTwh0/v/KlRjxpKelE2+Z/dB/9I0izP59ODL7cbzfX+gUb8mtf/N/zm++n89ECtdePDsnepcrLJ8LNGPVq2kv72j+rfPEfJYFNJ33L04/N/Tv59SByld8p+fPF8Mj/96jDurL1xG0zyPE8Pdra+6G6tLllJQ24fdfNoRBHZLO61HKUrZeO9toHLBa9H/S92RkncWVuukgY9RO/mUdIislnc+93d4cRBeqcsTeK9zuf3YwfpvCwdPdzuH6T54bKVNOw2+zePkhZxGHfuGGq922HcWYtq9ajWXO8Mk9TP0qn0YGfr4SjN8uUr6fs/+ulmU9IrnQ0ruNTpZd6WwfuJ16MHf9s/OYmspNeckl4lPdjtfD02zirEj9OZLB09uj98eXoglq6kZvfvx4/+pbKX3z74u4wW9+b13pvs7IzHhe2kRZUvadhD9G4eJX23bBI/eBRPT5f4pD88GbywvudSLs29y9KNSa2Cej9K+g7peL/T/tXRBOfMJ8N7rdPHAmXTZ/fbn++N/XfztiUsqZX5Rc3ibkMmfk32cv/u6lvzMjObt2Xp+Mn2yU/R6nZ/ODobwvOGpSyph+gBlbYkJQWoMCUFCKWkAKGUFCCUkgKEUlKAUEoKEEpJAUIpKUAoJQUIpaQAoZQUIJSSAoRSUoBQSgoQSkkBQikpQCglBQilpAChlJSb4Jfp8POTB+FtDadl7w3Xj5JyY8zibsMjV/kolJQbIpvFvZYnM/NxKCk3xGHcWYtu9Ue/lL0jXEdKys3wy2jnVr3ViWdl7wjXkpJyI2TJYKO29ufB0yeddlSrR7V2dzhOy94rrg0l5SY4uXbf2vry++k8T3/Y21qNnDPlw1FSboLDuLMW3d4dpcfX7Y/D+snOyKiUD0NJuQEurn86SgabUe3z/anLT3wYSsr1d3yStBsfnn493ms3W3eHEytL+UCUlGvvKBlsRo1ePDsO53wyvNdq3N0bu4zPB6OkXHs/7W/9x8n6p2w6etxZr7Xvx8ajfEhKyrU3n46GO1urUa0e1ZrrnUGcGI3ygSkpQCglBQj1/0dmnfcCK+RdAAAAAElFTkSuQmCC" alt></p>
<div class="marks">[2]</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>Thursday's sales, \(6b + 9m = 23.40\) <em><strong>(A1)</strong></em></span></p>
<p><span>\(2b + 3m = 7.80\) <em><strong>(A1)</strong></em> <em><strong>(C2)</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>\(m = 1.40\) <em> (accept 1.4)</em></span><span><em> <strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>\(b = 1.80\) <em> (accept 1.8) <strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><em><span>Award <strong>(A1)</strong>(d) for a reasonable attempt to solve by hand and answer incorrect. <strong>(C2)</strong></span></em></p>
<p><em><span><strong>[2 marks]<br></strong></span></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><span><img src="data:image/png;base64,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" alt><strong><span> (A1)(A1)</span></strong></span></em><span><strong><span>(ft)</span></strong></span></p>
<p><em><span><strong>(A1)</strong> each for two reasonable straight lines. The intersection point must be approximately correct to earn both marks, otherwise penalise at least one line. </span></em></p>
<p><em><span>Note: The follow through mark is for candidate’s line from (a). <strong>(C2)</strong></span></em></p>
<p><em><span><strong>[2 marks]<br></strong></span></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-size: medium; font-family: times new roman,times;">a) Nearly all the candidates were able to write the equation but very few simplified it.</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;">b) A majority of candidates were able to find the values of <em>b</em> and <em>m</em>. Some used the right method but made arithmetical errors, many of which were due to them using the method of substitution which involved fractions. GDC use was expected.</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;">c) A majority of candidates did not attempt this part. For those who did, very few were able to sketch the graph correctly. Common errors were to plot the point (1.4, 1.8) or draw a straight line through that point and the origin.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The straight line \(L\) passes through the points \({\text{A}}( - 1{\text{, 4}})\) and \({\text{B}}(5{\text{, }}8)\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the gradient of \(L\) .</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 the equation of \(L\) .</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 line \(L\) also passes through the point \({\text{P}}(8{\text{, }}y)\) . Find the value of \(y\) .</span></p>
<div class="marks">[2]</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>\(\frac{{8 - 4}}{{5 - ( - 1)}}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into the gradient formula.</span></p>
<p> </p>
<p><span><span>\(\frac{2}{3}{\text{ }}\left( {\frac{4}{6}{\text{, }}0.667} \right)\)</span></span><span> <em><strong>(A1) (C2)</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>\(y = \frac{2}{3}x + c\) <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for their gradient substituted in their equation.</span></p>
<p><br><span>\(y = \frac{2}{3}x + \frac{{14}}{3}\) <strong><em>(A1)</em>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <strong><em>(A1)</em>(ft)</strong> for their correct equation. Accept any equivalent form. Accept decimal equivalents for coefficients to 3 sf.</span></p>
<p> </p>
<p><span><strong>OR</strong></span></p>
<p><span>\(y - {y_1} = \frac{2}{3}(x - {x_1})\) <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for their gradient substituted in the equation.</span></p>
<p> </p>
<p><span>\(y - 4 = \frac{2}{3}(x + 1)\) <strong>OR</strong> \(y - 8 = \frac{2}{3}(x - 5)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span></p>
<p><span><span><strong>Note:</strong> Award</span> <span><strong><em>(A1)</em>(ft)</strong> for correct equation.</span></span></p>
<p><span><span><em><strong>[2 marks]</strong></em><br></span></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(y = \frac{2}{3} \times 8 + \frac{{14}}{3}\) <strong>OR</strong> \(y - 4 = \frac{2}{3}(8 + 1)\) <strong>OR</strong> \(y - 8 = \frac{2}{3}(8 - 5)\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution of \(x = 8\) into their equation.</span></p>
<p> </p>
<p><span>\(y = 10\) (\(10.0\)) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their answer to part (b).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></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;">Generally, a well answered question with many candidates achieving full marks. Indeed, marks which tended to be lost were as a result of premature rounding rather than method. On a number of scripts, part (a) produced a rather curious wrong answer of \(8.2\) following a correct gradient expression. It would seem that this was as a result of typing into the calculator \(8 - 4 ÷ 5 + 1\).</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;">Generally, a well answered question with many candidates achieving full marks. Indeed, marks which tended to be lost were as a result of premature rounding rather than method.</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;">Generally, a well answered question with many candidates achieving full marks. Indeed, marks which tended to be lost were as a result of premature rounding rather than method. <br></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;">The length of a square garden is (<em>x</em> + 1) m. In one of the corners a square of 1 m length is used only for grass. The rest of the garden is only for planting roses and is shaded in the diagram below.</span></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>
<p><span style="font-size: medium; font-family: times new roman,times;">The area of the shaded region is <em>A</em> .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down an expression for <em>A</em> in terms of <em>x</em>.</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 <em>x</em> given that <em>A</em> = 109.25 m<sup>2</sup>.</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 owner of the garden puts a fence around the shaded region. Find the length of this fence.</span></p>
<div class="marks">[2]</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>(<em>x</em> + 1)<sup>2</sup> – 1 <strong><em>or</em></strong> <em>x</em><sup>2</sup> + 2<em>x</em> <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(<em>x</em> + 1)<sup>2</sup> – 1 = 109.25 <em><strong>(M1)</strong></em></span></p>
<p><span><em>x</em><sup>2</sup> + 2<em>x </em></span><span><span>– </span>109.25 = 0 <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for writing an equation consistent with their </span><span>expression in (a) (accept equivalent forms), <em><strong>(M1)</strong></em> for correctly </span><span>removing the brackets.</span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span>(<em>x</em> + 1)<sup>2 </sup></span><span><span>– </span>1 = 109.25 <em><strong>(M1)</strong></em></span></p>
<p><span><em>x</em> + 1 = \(\sqrt {110.25} \) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for writing an equation consistent with their</span> <span>expression in (a) (accept equivalent forms), <em><strong>(M1)</strong></em> for taking the </span><span>square root of both sides.</span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span>(<em>x</em> + 1)<sup>2</sup> – 10.5<sup>2</sup> = 0 <em><strong>(M1)</strong></em></span></p>
<p><span>(<em>x</em> </span><span><span>–</span> 9.5) (<em>x</em> + 11.5) = 0 <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for writing an equation consistent with their </span><span>expression in (a) (accept equivalent forms), <em><strong>(M1)</strong></em> for factorised left </span><span>side of the equation.</span></p>
<p><br><span><em>x</em> = 9.5 <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C3)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from their expression in part (a)</span>.</p>
<p><span>The last mark is lost if<em> x</em> is non positive.</span></p>
<p><span>If the follow through equation is not quadratic award at most</span> <em><strong><span>(M1)(M0)(A1)</span></strong></em><strong><span>(ft)</span></strong><span>.</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>4 × (9.5 + 1) = 42 m <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for correct method for finding the length of the fence. Accept equivalent methods.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 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;">Some candidates were able to answer this question correctly, but the majority experienced difficulty in finding the correct expression for the area of the shaded region. Those who showed working could then be awarded follow through marks for correctly equating their expressions to the given area and for their found value of <em>x</em>. Many candidates also could not find the perimeter of the shaded region in part c) even though they had found the value of <em>x</em> correctly.</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;">Some candidates were able to answer this question correctly, but the majority experienced difficulty in finding the correct expression for the area of the shaded region. Those who showed working could then be awarded follow through marks for correctly equating their expressions to the given area and for their found value of <em>x</em>. Many candidates also could not find the perimeter of the shaded region in part c) even though they had found the value of <em>x</em> correctly.</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;">Some candidates were able to answer this question correctly, but the majority experienced difficulty in finding the correct expression for the area of the shaded region. Those who showed working could then be awarded follow through marks for correctly equating their expressions to the given area and for their found value of <em>x</em>. Many candidates also could not find the perimeter of the shaded region in part c) even though they had found the value of <em>x</em> correctly.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A rectangular cuboid has the following dimensions.</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;">Length 0.80 metres (AD)</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;">Width 0.50 metres (DG)</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;">Height 1.80 metres (DC)</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>Calculate the length of AG.</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>Calculate the length of AF.</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 size of the angle between AF and AG.</span></p>
<div class="marks">[2]</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>\({\text{AG}} = \sqrt {{{0.8}^2} + {{0.5}^2}} \) <em><strong> (M1)</strong></em></span></p>
<p><span>AG = 0.943 m <em><strong> (A1) (C2)</strong></em></span></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>\({\text{AF}} = \sqrt {{\text{A}}{{\text{G}}^2} + {{1.80}^2}} \) <em><strong>(M1)</strong></em></span></p>
<p><span>= 2.03 m <em><strong> (A1)</strong></em><strong>(ft) </strong><em><strong> (C2)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Follow through from their answer to part (a).</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>\(\cos {\rm{G\hat AF}} = \frac{{0.943(39 \ldots )}}{{2.03(22 \ldots )}}\) <em><strong> (M1)</strong></em></span></p>
<p><span><span>\(\operatorname{G\hat AF} = 62.3^\circ \) </span><em><strong> (A1)</strong></em><strong>(ft) </strong><em><strong> (C2)</strong></em></span></p>
<p><span><strong> </strong></span></p>
<p><span><strong>Notes:</strong> Award<em><strong> (M1)</strong> </em>for substitution into correct trig ratio.</span></p>
<p><span>Accept alternative ratios which give 62.4° <strong>or</strong> 62.5°.</span></p>
<p><span>Follow through from their answers to parts (a) and (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>
<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 well answered. Surprisingly few candidates used the basic trigonometric ratios (for right angle triangles), opting instead to use the sine or cosine laws.</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 well answered. Surprisingly few candidates used the basic trigonometric ratios (for right angle triangles), opting instead to use the sine or cosine laws.</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 well answered. Surprisingly few candidates used the basic trigonometric ratios (for right angle triangles), opting instead to use the sine or cosine laws.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagram shows a triangle ABC in which AC = 17 cm. M is the midpoint of AC.</span><br><span style="font-family: times new roman,times; font-size: medium;">Triangle ABM is equilateral.</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 size of angle MCB.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.1.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down </span><span>the length of BM in cm.</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>Write down the size of angle BMC.</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>Calculate the length of BC in cm.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>30° <strong><em>(A1) (C3)</em></strong></span></p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">a.1.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>8.5 (cm) <strong><em>(A1)<br></em></strong></span></p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>120° <strong><em> (A1)</em></strong></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>\(\frac{{{\text{BC}}}}{{\sin 120}} = \frac{{8.5}}{{\sin 30}}\) <strong><em> (M1)(A1)</em>(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>for correct</span> <span>substitutions.</span></p>
<p><span> </span></p>
<p><span>\({\text{BC}} = {\text{14}}{\text{.7}}\left( {\frac{{17\sqrt 3 }}{2}} \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong><em>[3 marks]</em><br></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<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 generally well answered with many candidates gaining full marks. Some candidates went on to make incorrect assumptions about triangle BMC being right angled and used Pythagorus theorem incorrectly. Those who used either the Sine rule or the Cosine rule correctly were generally able to substitute correctly and gain at least two marks.</span></p>
<div class="question_part_label">a.1.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Part (a) was generally well answered with many candidates gaining full marks. Some candidates went on to make incorrect assumptions about triangle BMC being right angled and used Pythagorus theorem incorrectly. Those who used either the Sine rule or the Cosine rule correctly were generally able to substitute correctly and gain at least two marks.</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 generally well answered with many candidates gaining full marks. Some candidates went on to make incorrect assumptions about triangle BMC being right angled and used Pythagorus theorem incorrectly. Those who used either the Sine rule or the Cosine rule correctly were generally able to substitute correctly and gain at least two marks.</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;">Part (a) was generally well answered with many candidates gaining full marks. Some candidates went on to make incorrect assumptions about triangle BMC being right angled and used Pythagorus theorem incorrectly. Those who used either the Sine rule or the Cosine rule correctly were generally able to substitute correctly and gain at least two marks.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Tom stands at the top, T , of a vertical cliff \(150{\text{ m}}\) high and sees a fishing boat, F , and a ship, S . B represents a point at the bottom of the cliff directly below T . The angle of depression of the ship is \({40^ \circ }\) and the angle of depression of the fishing boat is \({55^ \circ }\) .</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, SB, the distance between the ship and the bottom of the cliff.</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>Calculate, SF, the distance between the ship and the fishing boat. Give your answer correct to the nearest metre.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(150\tan 50\) <em><strong>(M1)</strong></em></span></p>
<p> </p>
<p><span><strong>OR</strong></span></p>
<p> </p>
<p><span>\(\frac{{150}}{{\tan 40}}\) <em><strong>(M1)</strong></em></span></p>
<p><span>\( = 179{\text{ (m)}}\) (\(178.763 \ldots \)) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(150\tan 50 - 150\tan 35\) <em><strong>(M1)(M1)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for \(150\tan 35\), <em><strong>(M1)</strong></em> for subtraction from their part (a).</span></p>
<p> </p>
<p><span>\( = 73.7{\text{ (m)}}\) (\(73.7319 \ldots \)) <strong><em>(A1)</em>(ft)</strong></span><br><span>\( = 74{\text{ (m)}}\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C4)</strong></em></span></p>
<p><br><span><strong>Note:</strong> The final <em><strong>(A1)</strong></em> is awarded for the correct rounding of their answer to (b).</span><br><span><strong>Note:</strong> There will always be one answer with a specified degree of accuracy on each paper.</span></p>
<div class="question_part_label">b.</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>
<br><hr><br><div class="specification">
<p>Line \(L\) intersects the \(x\)-axis at point A and the \(y\)-axis at point B, as shown on the diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_17.18.01.png" alt="M17/5/MATSD/SP1/ENG/TZ2/04"></p>
<p>The length of line segment OB is three times the length of line segment OA, where O is the origin.</p>
</div>
<div class="specification">
<p>Point \({\text{(2, 6)}}\) lies on \(L\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the gradient of \(L\).</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>Find the equation of \(L\) in the form \(y = mx + c\).</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 \(x\)-coordinate of point A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\( - 3\) <strong><em>(A1)(A1)</em></strong> <strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Award <strong><em>(A1) </em></strong>for 3 and <strong><em>(A1) </em></strong>for a negative value.</p>
<p>Award <strong><em>(A1)(A0) </em></strong>for either \(3x\) or \( - 3x\).</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>\(6 = - 3(2) + c\)\(\,\,\,\)<strong>OR</strong>\(\,\,\,\)\((y - 6) = - 3(x - 2)\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for substitution of their gradient from part (a) into a correct equation with the coordinates \((2,{\text{ }}6)\) correctly substituted.</p>
<p>\(y = - 3x + 12\) <strong><em>(A1)(</em>ft)</strong> <strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Award <strong><em>(A1)(</em>ft) </strong>for their correct equation. Follow through from part (a).</p>
<p>If no method seen, award <strong><em>(A1)(A0) </em></strong>for \(y = - 3x\).</p>
<p>Award <strong><em>(A1)(A0) </em></strong>for \( - 3x + 12\).</p>
<p> </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>\(0 = - 3x + 12\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for substitution of \(y = 0\) in their equation from part (b).</p>
<p> </p>
<p>\((x = ){\text{ }}4\) <strong><em>(A1)</em>(ft)</strong> <strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Follow through from their equation from part (b). Do not follow through if no method seen. Do not award the final <strong><em>(A1) </em></strong>if the value of \(x\) is negative or zero.</p>
<p> </p>
<p><strong><em>[2 marks]</em></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><span style="font-size: medium; font-family: times new roman,times;">In triangle ABC, BC = 8 m, angle ACB = 110 °, angle CAB = 40°, and angle ABC = 30 °.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAogAAAC5CAIAAAAkklnMAAAbAklEQVR4nO3d4U+b94HAcf8BeZOXeVHZkq9SQUNrhHpKqy4s0lrRTCIounlUPbXpEVScXa7ZbU06TOmuTaUZKuhQFXeno7CYadF09LFCe4vqZC6p5HQpVlyV9MhTJR2Jidcxt/G5dUKI/dyL3+OHx8bAY7Dx48ffj3gDNo8f44Svf8/v9zzYFAAAYBq2au8AAKB8UnJIOjXU+YMu6YaiKIqyOC8dabLvH4p8XeUdq2uZlDwVmBjserAvlMyse2/CDACWcSPQudNpdzjtT43Jt/VfaR6MLFV53+pXRh5ttzucdoezbVRev8uEGQAsJDMvuRv0AairEXNydnTAr74jWSE1M9Z3ykgXK2EpMthsb2wfnTXy+IQZACxjKS4drtPxcWo24GlbZUiaSclSb+tOg12sgNvy6FNO+xNDkZSRexNmAKhxmXjkpGev3eFsPdLbuctp390bWlC/fnpizNOm6/RiPPK73tZGZ8Pht0d+3qQfw2XiEWmwq8HhtDucrX0BOaltPSVPvTN4sNkTSqZmxjp3NXlCSfU7Lvo9bU77LveI78W8YXpSDkljngO9oQW1l+qh9aQs9e21N+4dvFg0UJl4ZFIa6W17JZTM5DZeMNZfjEfeG/O0Oe0Op72tV5pNKYqiJGdHu5vEsWK7w9kpxfUbTc2Mde5Sb7Lv1Kbei22ncHdSstTb2ui0O5o6B9+ZGA1c0u61GI9IQ2KzDQeHL8aXf4YnPXvtjqbuN98+tls3obAQ8ux2NuRPMGfikdMjue37Z1PLNxFmAKhlmflQX5vT3vZyaH5JzGWqAVgIeXY77Y7lTiuL8dBxtYvJUG+DY3kMp25EFGIpGeoTnWvyhJJxqUvdiBwZ3K9NlGbiZ19ubXS2DkdSX4oHyuVfHbU77YcD81cD3SKKTwxFEvPSkaai7RSWIkMPqhOxs/NnX25tzE+pkgvwLrc0l1GfXa58mdmxtkbdM83/CeX9WNbcTt63zY61Neqe7JFAfEn37W290mxK/NzE01F/hvuHIgn1B/hg7g1RMtTb4NDe0Ggj+L0eSU7NBTp3Ou2HcxtXFMIMALVMTCHnfumLiC6PXG8EOndqQVKnn8WnooLaTerqJNEntay5kIhPn3pberPd7nCKnmXmAt3a0DwVGXwiL4pi422/Ghs8PvbZR2Ntjc4GT+Csr3f0k/lQX9OqU63ieG9j+8h77/QNhuLz+cnMPdNuaT6Te2q5bK9I78rNak9nre3kUX9E3WOzSUXJJC9duprRvl0d9Gfk0XY18HkvxFJksHn5ETPJ/Gete0+TWbEmQFEIMwDUMHXgK473FgZAvVUdnn4dGdzv1A4ji4TnRq5q2NQRnjrUznVlIeTZ7Wx7ZchzbGxWPYadigzvtTtEWnJt04354lKX3dHU2j0Ums+IB2p4omswFM+sSLieOuptfLztlcn5RXXn8wedy53O+1Q8cf2QVE88ndyDrrWdAou5IX7by6H5vB/pyncAqYtDrY25F0K8ldFiXzAo1/bnS/VQeevxUHxRvzHCDACbtDgvHWkydiZMWalByo23xG98bYVRfqfzjl2rwz7dBPNcoHuXs3U4klpSo6tN7mZmx9oam1o7eqW53PNb0B+7XjHm02cyt4ci4SK9xce12h6KAWhBawueadEnvspAvFjCV9lOkW9WZ6/VfV7tHUAm79i1ejghv/2F7zDEXL5n7HQkvuKhCTMAbI461Cs66qooMQBVE6gGtaEvdGMmcvV2wUAtd7D6cCC+lBvePTF08bOpqWsZRVGUxXjk1JDn4F4xtdw5GMj1Qnxj7sCv/vmKEaEYiDuaB8NzU+Gry5kUj5s3WlU3VXxcW7S12tg6f7W5ugO5tw5rjXoLNrvmdvK+T548LWItnqB4Q7Ny0fti/NJMPKMeLXd2SnHthXhw8OO5j6au3i541uIot+4AQyYlfxRhxAwA5ZNJRd509w+82GD0LNXyWQ7zrfilc6PHmu0OZ8NTvROfpBTdQdf52alIXLcu7Gv57HBXg8Np3/Ws5w/RVEZtT6tnTJICITl/fbJITv7B5+WVVl+m5PfF4uSmA6+8c0mXSRFC9Z4iQrkp5NGPZqcurRgmarfOZhRtIdjhgPzZVCSeP4DWrb0Su6Mdh/9aniocf6rJbB68eEv+KBK/vcZ28iRDvQ+K5daL89KRptyIOffuR0w8J+XQ+5H4Yt40dko+N3iwafmFEDft7JJuZOKRyZCcVN8hqbMPKXlqcsWYmTADwGYshDyHx+QbRc6HqTz1MHKrxx+ZT0aG99ob93okWZx4o4b54NBZOaVox1fbekdD8vzZ3gb9OVH5pxvpN5JXVk1uAZRnNCRfDXl26844yjvYqyZTHa1q35XbeN4zyV9WrR70zu28oiiZ+Me/Ptik7t5oaPlsLm1Rm+7OhbvqaOocPie+ZfXt5O3O1fDU7IxI7PL3KkrujC+H076ra1DSRrraCzEWmhUL3HJPMzdRvbx72hbyjkzoEWYAMCSdTofD4V6P54F/uD+dTosvZuTRf1qeTF1lWZOpLcYj0pDnV4HIxZB0Sj031/A1qlAJhBkA1iJ63O/1Ou2OA88881Bz85kzZ3I33pZHPXmLpIpPoJpYMtSbdxBePVpbj9cOMw3CDABF6Ht8yO0OBoMzMzN7WlrC4fDynZKh3v3agt7b8uhTzoYjgfnF4ls0J3HQePmwtrgISZ1cW9ukCDMALFvZ40QioShKLBYrrLK24jfvo/YOAmfikYBYr7TezCu2BmEGgFV7LBSrsqJkZsf2v5J/9eO5QPcug3/aD1gNYQZQ16LRqO+Er2iPheJVFmdJFQ6OxRh6609ohqUQZgD1SPR4T0vLaj0WVqmyuNzxD1auwVZPEFpxkUXAOMIMoI4Y7LGwapXVa0QUzijrvu5Y9YrQwHoIMwDrK6nHwmpVBiqNMAOwrA30WKDKqCLCDMBqNtxjgSqjuggzAIvYZI8FqoyqI8wAapvW4w6XKyBJG+uxQJVhBoQZQE3S93jc74/FYpvcIFWGSRBmALWk7D0WqDLMgzADqAEV6rFAlWEqhBmAeVW0xwJVhtkQZgCmE4vFxv3+ivZYeyCqDLMhzADMQvS4w+WqdI+1h6PKMCHCDKDKtrjH2oNSZZgTYQZQHVXpsfbQVBmmRZgBbKkq9ljbAaoMMyPMALZC1Xus7QZVhskRZgAVZJIeaztDlWF+hBlA+Wk93tPS4jvhq26PtV2iyqgJhBlA2RT0OBqNlm/b91JX/uet4d9fuHlnYztGlVErCDOAzdpEj7NLN6fffS+6kNV/8c7C5Q8mJ6TJD6+mcl/P3nz3xb4z84lLb/3rb6KL2SJbWnP3qDJqCGEGsEGxWOw3b73V3ta28fHx3Ssnn7zf5hyYXsp9JXtrZuS5h59+/fTU2d8f2/dY3/s3l7KKoixNv3Hg1BdZ5daF4z0TN5fW2OTKnaTKqC2EGUBp9OPjY0ePPdnRsdEtpWZHnt5us+nCfO+r868+ZNvvu/yNoijKtxcHHv7Okyev3FUUZenG2V8ePtJz+PmRT1Kl7CpVRs0hzAAMSSQSAUlaebx6T0vLhtZ2ZW/P/OeT//JS737Hcpgz8sl2h+3xkSsZ9THPv/SwbccLZxL3NrDDVBk1ijADWEsikQgGg4fc7tWOV4/7/b4TvlI3m01+NND+s4m5KxNPO7UwZ6+d3GezbX/+TEK9193rp5612ZqPnlsodftUGbWLMAMoYt0e6++5p6UlnU6XsPVs4uOBgz+dnFtSruvCnEme+8UO/YFtZenmxHM22/ZHfZ+WNGSmyqhphBnAMuM91vP09AQkyfCD3PsqPND+73/8MqsoeWEWGV4Z5rzFYeuiyqh1hBnABnuskWW5w+UyeOfsVx/07Xvt/FdiDFzmMFNlWABhBurXJnusd8jtNpbDv59/aff9P3qhf0Doebp5u237D5/3Drx57i//d/7l+4qE2fHjU18YOXOZKsMaCDNQd8rYY004HDY2aJ6ffO4BWxHbdv46ujR36sltth1HzyXVO3972bfPZntsYDq55jYVhSrDQggzUC+0Hjvtjn6vt6zXy1QURelwuUrvov5QtqJk5yaefcD2yHDu2l5/PfP8d20Pvz797ToDZqoMKyHMgMUV9DgcDpe2gtoww4NmvfwwK9lvo8OPbWsdmL6lKEo2cebIjmb35PW1s0yVYTGEGbCmLeuxXumD5oIwK4py5+bZVx/b85M3RoaPtv2w++QnqTWzTJVhPYQZsJSq9FizoUHzStmlBXl6+tKVhXX+kBRVhiURZsAKqttjPcPLszeLKsOqCDNQw9LpdDgcNkOPNbIsl3whsNJRZVgYYQZqj+hxv9drnh7rlXghsJJRZVgbYQZqhsl7rEkkEk67I5FIrH/X0lFlWB5hBsyuVnqsN+73e3p6yr5Zqox6QJgBk6rFHmvS6fSelpbyXsOEKqNOEGbAXGq6x3rRaLTD5SrXzlNl1A/CDJiCZXqs1+/1jvv9m98OVUZdIcxANel77OnpsUaPNYlEYk9LiyzLm9kIVUa9IcxAFeh7fMjtDgaDFVrDXHXBYHAzB7SpMuoQYQa2Tv30WK/f6+33ejfwjVQZ9YkwAxVXnz3WiBXapfaVKqNuEWagUuq8x3riOp2xWMzg/aky6hlhBsovGo3S4wIBSTrkdhuZbKbKqHOEGSibaDTqO+Hb09JCj4syMtlMlQHCDGwWPTYonU4fcrvXOLOZKgMKYQY2jB5vgDizuWh6qTIgEGagNPR4k4oGmCoDGsIMGEKPyygajTrtDm2RNlUG9AgzsBZ6XCHhcFicQEWVgQKEGShC63GHy0WPKyQcDj/6yCO7H32UKgN6hBlYpu/xuN9v/IIY2IBYLEaVgZUIM0CPq4Aj2MBqCDPqFz2uFqoMrIEwo+7Q4+qiysDaCDPqhSzL9LjqqDKwLsIMi4vFYuN+f4fLRY+rjioDRhBmWBM9NhuqDBhEmGEp9NicqDJgHGGGFdBjM6PKQEkIM2oYPTY/qgyUijCj9tDjWkGVgQ0gzKgZWo/3tLTQY/OjysDGEGaYnb7HvhO+aDRa7T3C+qgysGGEGSZFj2sXVQY2gzDDXOhxraPKwCYRZpgCPbYGqgxsHmFGNSUSCXpsGVQZKAvCjCpIJBLBYPCQ202PLYMqA+VCmLF16LFVUWWgjAgzKo4eWxtVBsqLMKNS6HE9oMpA2RFmlBk9rh9UGagEwozyoMf1hioDFUKYsSn0uD5RZaByCDM2Quux0+7o93rD4XA6na72TmGLUGWgoggzSkCPQZWBSiPMWB89hkCVgS1AmLEqegw9qgxsDcKMQul0mh6jAFUGtgxhhiqdTofD4X6vlx6jAFUGthJhrnf0GGujysAWI8x1ih7DCKoMbD3CXF/oMYyjykBVEOa6QI9RKqoMVAthtjJ6jI2hykAVEWYLosfYDKoMVBdhtg59jw+53cFgMJFIVHunUGOoMlB1hLnm0WOUC1UGzIAw1yp6jPKiyoBJEOYaQ49RCVQZMA/CXDPoMSqEKgOmQpjNLhqN+k749rS00GNUAlUGzIYwmxQ9xhagyoAJEWZzoceWJMtyOBwOSJLvhM/T07PyY9zvD0hSNBqNxWJbtldUGTAnwmwK9NhiEolEOBz2nfB1uFxiWUC/1xuQpGAwKBcTkKSAJHl6esT9Raqj0Wjl9pAqA6ZFmKuJHltMIpEIBoOH3G5xzTWR4VI3kk6nZVke9/u17ZQ9n1QZMDPCXAX02HrC4bCnp8dpd/hO+Mo40tVKv6elZdzvL8s/FaoMmBxh3jr02HrS6XRAksRrWtFrksdiMfGPp9/r3cAoXL8dqgyYHGGuOK3HHS7XuN+/lat7UDlakj09PZsp5cYetN/r3cAbO6oM1ATCXCn02MKCweAWJ1lP5Nlpd4z7/cbH6FQZqBWEuczosbXFYrFDbvcht7sqSdZLJBL9Xu+elhYjU9pUGaghhLk86HE9EOPUgCRVe0eWRaNRcWR7jaEzVQZqC2HeFHpcJ9LptKen55DbbcKXOJ1O93u9HS5X0X2jykDNIcwbEYvFxv3+DpeLHtcD0TbfCV/lFl1vXjAYdNodBQGmykAtIswloMd1SBwrrom2ybIsTncWn1JloEYR5vXR47oVDodrq21ibZrvhI8qA7WLMK8qFouNvv126+OP0+P6JKpcc697Op0+8Mwz/9jcTJWBGkWYC+nHx6Nvv/3oI49wia46JMuy0+6ouSorihKLxVq+9z2qDNQuwqxa7Xi174RPm7RDnajd48C1u+cANPUe5nXnj6PRaIfLVZV9Q1Wk0+kOlysYDFZ7R0pGlQFrqNMwaz0Wp8Gsfe2kWpxoxIb1e739Xm+196JkVBmwjPoKc0k91vhO+Gpx/IQNCAaDHS6Xmc9XLooqA1ZSF2HeWI814k/tVmjfYB6JRGJPS0vVL4JdKqoMWIyVw7zJHmsSiYTT7ijvvsGEPD09NbfQjyoD1mPBMJerx3odLlfNDaRQEnHZrNo6iE2VAUuyTpgTiUQwGDzkdpexxxqmmS2vw+UyULh7qWt/vnDtmxJvurNw+YPJCWnyw6upbO5r2VtX3v2v4fELN5eyxb5lfVQZsKqaD3NFe6wJBoO1uFIXBoXD4fVOirvzt6g00P240+Z8euK64ZsUJXtrZuS5h59+/fTU2d8f2/dY3/s3l7KKsnRz8rW+M18kPh351+FLi6XvMFUGLKxWw7w1PdbIsnzI7a7oQ6CK1h8uZ/9+5c+XP//jL+5bWd81blLufXX+1Yds+32Xv1EURfn24sDD33ny5JW7Smp64MVT1+8qdy4c75q4WeLeUmXA2moszFvcYz3Wf1mV8WvILE0PFB8Wr3ZTRj7Z7rA9PnIlIz5PnH/pYduOF84klpZuvv/L7p/2dB8dmblV0t5SZcDyaiPMBnucTV39cFKamHj3T5f/tlR4Y7F5PkXJpv733bdOjF+YX3H/QofcbtZ/WZKnp8dg50oNc/bayX022/bnz+Qutn73+qlnbbbmo+cWNrarVBmoB6YOcynj4+zda4Gffv8+m2rngZOXby/fWHSeT1GyNyZf9J6Z/+unb/UOR1Nr74zxX9+oIeLcZYOLsUsMcyZ57hc7bDbnwHTubd/SzYnnbLbtj/o+vVf6rlJloE6YMcwbOV599/LIT16bvJrMKvdSV6WjD223bf/ZmYT47bfaPJ+iLE0PHDh1PZu9c2Ggq9hvW72AJAUkabPPDSYz7vf7TvgM3rnEMIsMrwyz/itGUWWgfpgozFqPnXZHv9db2u+g23OXv9DOVLl14fijtm2HJ/92T1HWmOe7pyh3bp7t7z7yQvfzv51JZdZ+BBZmW1KHy2V8pUK1wkyVgbpS/TCv7PGmL/KQOP/Sow/1ffCVOFxdpnk+WZa5MKfFiOAZv3+JYc5+c/7l+4qE2fHjU18YP3mZKgP1pmphrkCPhXupK7/rfvJENCWOY5dtnq/UX+Iwv4AkGT+OrWxg8dfcqSe32XYcPZdUv/DtZd8+m+2xgenkyi0URZWBOrTVYa5YjxVFUbILH4+/euChbTab7YG2186qV3Io3zwfZ0xZjKenp6Qz7ko+XSo7N/HsA7ZHhqOLYoT81zPPf9f28OvT3xoaMFNloD5tUZgr2mO9bOovF/574MBDO2y2B56dmMuWO8y1dS1lrK3UF3RpesBpu2/fyc9XdnWVm7LfRocf29Y6MH1LUZRs4syRHc3uyetGskyVgbpV2TCn0+lwONzv9Va6x/myd6+M7Nsm5pXLM88neHp6OJXZMkq8mts3185Lv32pfbvNtr3tpd9OfHjtdtbATYqi3Ll59tXH9vzkjZHho20/7D75ScrAPzuqDNSzioS5Sj3WyX5+ct99YsHX5uf5NITZSgKStFV/5DG7tCBPT1+6snDHyL2pMlDnyhnm6vdYk/385L7mZyfmsspm5/n0CLOVlHxK3pagygDKEGYz9DibuvIn6b0PryWziqIo95Ifv9H+7NiMujB74/N8Bcb9fq4xYhkmvMYqVQagbCbMZuhxTnZx5q3Ht9lstvu//+ODz/1z+4+O/eFySn8y1Ebm+Vbi4l9WYrY19lQZgFBymM3UYz0xjTc9Pf3p9VTR85NLm+crijBbRjqdNlWYqTIAjdEwm7XHW4owW4apruNGlQHorRNmfY8Pud3BYLAOe6whzJZhnjBTZQAFiod5ZY8TiUTRe9YVwmwZJgkzVQawUmGYZVmmx6sRb1aqvRcoAzOEWfwpaKoMoEBhmJ12Bx988LFlH1X5bw/AzKr/Zx8BAICGMAMAYCKEGQAAEyHMAACYCGEGAMBECDMAACZCmAEAMJGCMC+EPLuLnG3ZcHBoYkpOZaqzj1hXSj43eLDJ7nDaHU2dw+fkZLV3CKtZjEf++E7uxXK2esZOR+JL8uRpmf9dAIRiI+ZkqLehsX10Vv1NkYlHTnr22h1Nnf5Z2mxCmblA967cq7MYDx3f29AXSvJKmU8m/vGvDzY1HBySIvGM+pWINNil/+8GoO4ZCLOiKMptefQpp313b2hhy/YMBmXk0Xb9S5OZHWv7Aa+U+SzOS0ea7PuHIl/nfz2Tigy3e0Ic5QAgEObalwz1NjTuHbyY0j59kBGz+SRDvQ2OpuIBXpiSPiLMAAQjYV6MR37X29rIoWyz+joyuN9p39U1OpPKzIf+o2/4YrzY65SUQ38Y6mzrDc3HL/q6GhxOe9vLoflMbqrC2dA9NksdKkS8teWQNYD1rRbmleu/GISZmJi8tDuc9qfG5NtF75EM9TXZHU77rq5BKRJfVHOuLevLzIf62pxto6xBqgyxrJJjTgDWZ2zxlzTY1cCIysySsvTm0OCxvXaHs/V4KL5Y9E75s9Ei1VrIb8ujT/H2q2IIMwCjDM4xi9/pDkZUppScHf35v0lzGUXJxM++3NrobB2OFJt0IMzVwyoNAEYZDbN6fJtf3OaTkUfb9UewUxeHWncWncskzFUk3tqusvgLAJYZHjHPS+4GRswmVNBXRVEWQp4fEGbzEUezV54upSiZeGRKTlVjnwCYkMFV2dJQ5y51Ee9W7h2MSF0cWl4zn0nN+rsePBKYLzLNTJirLDUz1rnLaW/rHQ3lrqOXSckh/+h7nO8AQGPskpz2xr2ekclI0ZNwUH2Z+EW/p8251iU5xRyn+mq2j16aXf50d2/oM93rzjxoJWXikdMjva2NTv0lOfl/BUCHP2IBAICJEGYAAEyEMAMAYCKEGQAAE/l/VE5rq/fkYfUAAAAASUVORK5CYII=" 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>Find the area of triangle ABC.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{{\text{AC}}}}{{\sin 30^\circ }} = \frac{8}{{\sin 40^\circ }}\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution in the sine rule formula, <em><strong>(A1)</strong></em> for correct substitutions.</span></p>
<p> </p>
<p><span>AC = 6.22 (m) (6.22289…) <em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><span><em><strong>[3 marks]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Area of triangle \({\text{ABC}} = \frac{1}{2} \times 8 \times 6.22289... \times \sin 110^\circ \) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution in the correct formula, <em><strong>(A1)</strong></em><strong>(ft)</strong> for their correct substitutions. Follow through from their part (a).</span></p>
<p> </p>
<p><span>Area triangle ABC = 23.4 m<sup>2</sup> (23.3904...m<sup>2</sup>) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C3)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from a positive answer to their part (a). The answer is 23.4 m<sup>2</sup>, units are required.</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</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;">Whilst using the sine rule to find an angle was tested in question 10, here the sine rule was required to be used to find a length. Many scripts showed the correct value of 6.22 m, but a significant number of candidates calculated AB instead of AC and the answer of 11.7 m proved to be a popular, but erroneous, answer. Some candidates turned the problem into two right angled triangles by dropping the perpendicular from C to the line AB. Much working was then required to find AC and again, some of these candidates simply determined the length of AB. Despite a significant number of candidates identifying the incorrect length in part (a), many of these recovered in part (b) to use their value correctly in the formula for the area of a triangle and many correct calculations were seen. Unfortunately, this good work was spoilt as some candidates either missed the units or gave the incorrect units in their final answer and, as a consequence, lost the last mark.</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;">Whilst using the sine rule to find an angle was tested in question 10, here the sine rule was required to be used to find a length. Many scripts showed the correct value of 6.22 m, but a significant number of candidates calculated AB instead of AC and the answer of 11.7 m proved to be a popular, but erroneous, answer. Some candidates turned the problem into two right angled triangles by dropping the perpendicular from C to the line AB. Much working was then required to find AC and again, some of these candidates simply determined the length of AB. Despite a significant number of candidates identifying the incorrect length in part (a), many of these recovered in part (b) to use their value correctly in the formula for the area of a triangle and many correct calculations were seen. Unfortunately, this good work was spoilt as some candidates either missed the units or gave the incorrect units in their final answer and, as a consequence, lost the last mark.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Assume the Earth is a perfect sphere with radius <span class="s1">6371 km</span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the volume of the Earth in \({\text{k}}{{\text{m}}^3}\)<span class="s1">. Give your answer in the form \(a \times {10^k}\)</span>, where \(1 \leqslant a < 10\) <span class="s1">and \(k \in \mathbb{Z}\).</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 class="p1">The volume of the Moon is \(2.1958 \times {10^{10}}\;{\text{k}}{{\text{m}}^3}\)<span class="s1">.</span></p>
<p class="p2">Calculate how many times greater in volume the Earth is compared to the Moon.</p>
<p class="p2">Give your answer correct to the nearest <strong>integer</strong>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{4}{3}\pi {(6371)^3}\) <strong><em>(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into volume formula.</p>
<p> </p>
<p>\( = 1.08 \times {10^{12}}\;\;\;(1.08320 \ldots \times {10^{12}})\) <strong><em>(A2) (C3)</em></strong></p>
<p><strong>Notes: </strong>Award <strong><em>(A1)(A0) </em></strong>for correct mantissa between 1 and 10, with incorrect index.</p>
<p>Award <strong><em>(A1)(A0) </em></strong>for \(1.08\rm{E}12\)</p>
<p>Award <strong><em>(A0)(A0) </em></strong>for answers of the type: \(108 \times {10^{10}}\).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{1.08320 \ldots \times {{10}^{12}}}}{{2.1958 \times {{10}^{10}}}}\) <strong><em>(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for dividing their answer to part (a) by \(2.1958 \times {10^{10}}\).</p>
<p> </p>
<p>\( = 49.3308 \ldots \) <strong><em>(A1)</em>(ft)</strong></p>
<p><strong>Note: </strong>Accept \(49.1848...\) from use of 3 sf answer to part (a).</p>
<p> </p>
<p>\( = 49\) <strong><em>(A1) (C3)</em></strong></p>
<p><strong>Notes: </strong>Follow through from part (a).</p>
<p>The final <strong><em>(A1) </em></strong>is awarded for their unrounded non-integer answer seen and given correct to the nearest integer.</p>
<p>Do not award the final <strong><em>(A1) </em></strong>for a rounded answer of 0 or if it is incorrect by a large order of magnitude.</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>In part (a) many candidates correctly substituted the volume formula and wrote correctly their answer using scientific notation. The calculator notation E12 was very rarely used. A minority converted to metres, resulting in an incorrect exponent. Some candidates used an incorrect equation or used their calculator incorrectly.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>In part (b) many candidates subtracted the values, where they should be divided, resulting in an answer of an unrealistic magnitude. Some reversed the numerator and denominator, leading to an answer of 0.02, which would have rounded to the unrealistic answer of 0. When a reasonable answer was found, the final mark for rounding was lost by some candidates when there was no rounding or when rounding was incorrect. There seemed to be little understanding of whether or not an answer was reasonable.</p>
<div class="question_part_label">b.</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;">In triangle \({\text{ABC}}\), \({\text{AC}} = 20 {\text{ cm}}\), \({\text{BC}} = 12 {\text { cm}}\) and \({\rm{A\hat BC}} = 90^\circ\)<span style="font: 16.0px 'Times New Roman';">.</span></span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><span style="font: normal normal normal 16px/normal 'Times New Roman'; font-family: 'times new roman', times; font-size: medium;"><br><img src="images/Schermafbeelding_2014-09-03_om_05.19.59.png" alt><span class="Apple-style-span" style="display: inline; float: none;"> <strong><em>diagram not to scale</em></strong></span></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the length of \({\text{AB}}\).</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>\({\text{D}}\) is the point on \({\text{AB}}\) such that \(\tan ({\rm{D\hat CB}}) = 0.6\).</span></p>
<p><span>Find the length of \({\text{DB}}\).</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>\({\text{D}}\)</span> is the point on \({\text{AB}}\) such that \(\tan ({\rm{D\hat CB}}) = 0.6\).</span></p>
<p><span>Find the area of triangle \({\text{ADC}}\).</span></p>
<div class="marks">[2]</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>\(({\text{A}}{{\text{B}}^2}) = {20^2} - {12^2}\) <strong><em>(M1)</em></strong></span></p>
<p><span> </span></p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correctly substituted Pythagoras formula.</span></p>
<p><span> </span></p>
<p><span>\({\text{AB}} = 16{\text{ cm}}\) <strong><em>(A1) (C2)</em></strong></span></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>\(\frac{{{\text{DB}}}}{{12}} = 0.6\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution in tangent ratio or equivalent <em>ie </em>seeing \(12 \times 0.6\).</span></p>
<p> </p>
<p><span>\({\text{DB}} = 7.2{\text{ cm}}\) <strong><em>(A1) (C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1)(A0) </em></strong>for using \(\tan 31\) to get an answer of \(7.21\).</span></p>
<p><span> Award <strong><em>(M1)(A0) </em></strong>for \(\frac{{12}}{{\sin 59}} = \frac{{{\text{DB}}}}{{\sin 31}}\) to get an answer of \(7.2103…\) or any other incorrect answer.</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>\(\frac{1}{2} \times 12 \times (16 - 7.2)\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for their correct substitution in triangle area formula.</span></p>
<p> </p>
<p><span><strong>OR</strong></span></p>
<p><span>\(\frac{1}{2} \times 12 \times 16 - \frac{1}{2} \times 12 \times 7.2\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for subtraction of their two correct area formulas.</span></p>
<p> </p>
<p><span>\( = 52.8{\text{ c}}{{\text{m}}^2}\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Follow through from parts (a) and (b).</span></p>
<p><span> Accept alternative methods.</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></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 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;">This question was not well answered. Many candidates could not use Pythagoras’ theorem correctly and many failed to appreciate the significance of \(\tan ( < {\text{DCB}}) = 0.6\) and calculated the size of the angle DCB, rounding it to 31°. Unfortunately, this method led to an inaccurate value for DB. Finding the area of triangle ADC was also difficult for many who did not realize that they needed to do a subtraction of triangle areas. Candidates who tried to find side lengths and angles for triangle ADC were generally unsuccessful in calculating its area.</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;">This question was not well answered. Many candidates could not use Pythagoras’ theorem correctly and many failed to appreciate the significance of \(\tan ( < {\text{DCB}}) = 0.6\) and calculated the size of the angle DCB, rounding it to 31°. Unfortunately, this method led to an inaccurate value for DB. Finding the area of triangle ADC was also difficult for many who did not realize that they needed to do a subtraction of triangle areas. Candidates who tried to find side lengths and angles for triangle ADC were generally unsuccessful in calculating its area.</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;">This question was not well answered. Many candidates could not use Pythagoras’ theorem correctly and many failed to appreciate the significance of \(\tan ( < {\text{DCB}}) = 0.6\) and calculated the size of the angle DCB, rounding it to 31°. Unfortunately, this method led to an inaccurate value for DB. Finding the area of triangle ADC was also difficult for many who did not realize that they needed to do a subtraction of triangle areas. Candidates who tried to find side lengths and angles for triangle ADC were generally unsuccessful in calculating its area.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1"><span class="s1">AC </span>is a vertical communications tower with its base at <span class="s1">C</span>.</p>
<p class="p1">The tower has an observation deck, <span class="s1">D</span>, three quarters of the way to the top of the tower, <span class="s1">A</span>.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2017-03-06_om_10.32.25.png" alt="N16/5/MATSD/SP1/ENG/TZ0/11"></p>
<p class="p1">From a point <span class="s1">B</span>, on horizontal ground <span class="s1">250 m </span>from <span class="s1">C</span>, the angle of elevation of <span class="s1">D </span>is <span class="s1">48°</span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">Calculate </span><span class="s2">CD</span>, the height of the observation deck above the ground.</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">Calculate the angle of depression from <span class="s1">A </span><span class="s2">to </span><span class="s1">B</span><span class="s2">.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(\tan 48^\circ = \frac{{{\text{CD}}}}{{250}}\) </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 the tangent ratio.</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\(({\text{CD}} = ){\text{ }}278{\text{ }}({\text{m}}){\text{ }}(277.653 \ldots )\) </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C2)</em></strong></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">\(\tan {\text{ABC (or equivalent)}} = \frac{{\frac{4}{3} \times 277.653 \ldots }}{{250}}\) <span class="Apple-converted-space"> </span><strong><em>(M1)(M1)(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 \(\frac{4}{3}\) multiplying their part (a), <strong><em>(M1) </em></strong>for substitution into the tangent ratio, <strong><em>(M1) </em></strong>for correct substitution.</p>
<p class="p2"> </p>
<p class="p1"><strong>OR</strong></p>
<p class="p1"><span class="Apple-converted-space">\(90 - {\tan ^{ - 1}}\left( {\frac{{250}}{{\frac{4}{3} \times 277.653 \ldots }}} \right)\) </span><strong><em>(M1)(M1)(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 \(\frac{4}{3}\) multiplying their part (a), <strong><em>(M1) </em></strong>for substitution into the tangent ratio, <strong><em>(M1) </em></strong>for subtracting from <span class="s1">90 </span>and for correct substitution.</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\({\text{(angle of depression}} = {\text{) }}56.0^\circ {\text{ }}(55.9687 \ldots )\) </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C4)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Follow through from part (a).</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</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>
<br><hr><br><div class="specification">
<p class="p1">Tuti has the following polygons to classify: rectangle (R), rhombus (H), isosceles triangle (I), regular pentagon (P), and scalene triangle (T).</p>
<p class="p1">In the Venn diagram below, set \(A\) consists of the polygons that have at least one pair of parallel sides, and set \(B\) consists of the polygons that have at least one pair of equal sides.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-03_om_08.19.15.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Complete the Venn diagram by placing the letter corresponding to each polygon in the appropriate region. For example, R has already been placed, and represents the rectangle.</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">State which polygons from Tuti’s list are elements of</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>\(A \cap B\);</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\((A \cup B)'\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2015-12-03_om_08.21.19.png" alt> <strong><em>(A3) (C3)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(A3) </em></strong>if all four letters placed correctly,</p>
<p class="p1"><strong><em>(A2) </em></strong>if three letters are placed correctly,</p>
<p class="p1"><strong><em>(A1) </em></strong>if two letters are placed correctly.</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>Rhombus and rectangle <strong>OR </strong>H and R <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)</strong></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Scalene triangle <strong>OR </strong>T <span class="Apple-converted-space"> </span><strong><em>(A2)</em>(ft) <span class="Apple-converted-space"> </span><em>(C3)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for a list R, H, I, P seen (identifying the union).</p>
<p class="p1">Follow through from their part (a).</p>
<div class="question_part_label">b.</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>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">On a map three schools A, B and C are situated as shown in the diagram.</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">Schools A and B are 625 metres apart.</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">Angle ABC = 102° and BC = 986 metres.</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>Find the distance between A and C.</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 angle BAC.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em><span>Unit penalty <strong>(UP)</strong> is applicable in question part (a) <strong>only</strong>.</span></em></p>
<p><span>\({\text{AC}}^2 = 625^2 + 986^2 - 2 \times 625 \times 986 \times \cos102^\circ\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span>( = 1619072.159)</span></p>
<p><span>AC = 1272.43</span></p>
<p><span><em><strong>(UP)</strong></em> =1270 m <em><strong>(A1)</strong></em> <em><strong>(C3)</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>\(\frac{{986}}{{\operatorname{sinA} }} = \frac{{1270}}{{\sin 102^\circ }}\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>\({\text{A}} = 49.4^\circ\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>\(\frac{{986}}{{\operatorname{sinA} }} = \frac{{1272.43}}{{\sin 102^\circ }}\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>\({\text{A}} = 49.3^\circ\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>\(\cos {\text{A}} = \left( {\frac{{{{625}^2} + {{1270}^2} - {{986}^2}}}{{2 \times 625 \times 1270}}} \right)\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>\({\text{A}} = 49.5^\circ\) <em><strong>(A1)</strong></em><strong>(ft) <em>(C3)</em></strong></span></p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<p> </p>
<p> </p>
<div class="question_part_label">b.</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 candidates who used the cosine and sine rules for this question were successful on the whole. Some had their calculators in radian mode (and hence the second answer for the angle was unrealistic) but this was less frequent than in previous sessions. Those candidates who used right-angled trigonometry scored no marks. Many candidates lost an accuracy penalty in this question.</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 candidates who used the cosine and sine rules for this question were successful on the whole. Some had their calculators in radian mode (and hence the second answer for the angle was unrealistic) but this was less frequent than in previous sessions. Those candidates who used right-angled trigonometry scored no marks. Many candidates lost an accuracy penalty in this question.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">An observatory is built in the shape of a cylinder with a hemispherical roof on the top as shown in the diagram. The height of the cylinder is 12 m and its radius is 15 m.</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 observatory.</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>The hemispherical roof is to be painted. </span></p>
<p><span>Calculate the area that is to be painted.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(V = \pi {(15)^2}(12) + 0.5 \times \frac{{4\pi {{(15)}^3}}}{3}\) <em><strong>(M1)(M1)(M1)</strong></em><strong> <br></strong></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted cylinder formula, <em><strong>(M1)</strong></em> for correctly substituted sphere formula, <em><strong>(M1)</strong></em> for dividing the sphere formula by 2.</span></p>
<p><span> </span></p>
<p><span>\( = 15550.8 \ldots \)</span></p>
<p><span>\( = 15600{\text{ }}{{\text{m}}^3}{\text{ }}(4950\pi {\text{ }}{{\text{m}}^3})\) <em><strong>(A1) (C4)</strong></em><strong> <br></strong></span></p>
<p><span><strong>Notes:</strong> The final answer is \(15600{\text{ }}{{\text{m}}^3}\); the units are required. The use of \(\pi = 3.14\) which gives a final answer of \(15 500\) (\(15 543\)) is premature rounding; the final <em><strong>(A1)</strong></em> is not awarded.</span></p>
<p><span><em><strong>[4 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(SA = 0.5 \times 4\pi {\left( {15} \right)^2}\) <em><strong>(M1)</strong></em></span></p>
<p><span>\( = 1413.71 \ldots \)</span></p>
<p><span>\( = 1410{\text{ }}{{\text{m}}^2}{\text{ }}(450\pi {\text{ }}{{\text{m}}^2})\) <em><strong>(A1) (C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> The final answer is \(1410{\text{ }}{{\text{m}}^2}\) ; do not penalize lack of units if this has </span><span>been penalized in part (a).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</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 only done well by the more able candidates. For the lower quartile of candidates, about a half of these scored no more than one mark in total for this question. In many cases, formulae were either misquoted or misused. Indeed, in part (a) many ignored the hemisphere, choosing to use the formula for the volume of a sphere instead. Some candidates who correctly used a hemisphere in part (a) then treated the surface area as a sphere in part (b). A minority of candidates thought the area to be painted in the last part of the question was a circle rather than a hemisphere.</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 only done well by the more able candidates. For the lower quartile of candidates, about a half of these scored no more than one mark in total for this question. In many cases, formulae were either misquoted or misused. Indeed, in part (a) many ignored the hemisphere, choosing to use the formula for the volume of a sphere instead. Some candidates who correctly used a hemisphere in part (a) then treated the surface area as a sphere in part (b). A minority of candidates thought the area to be painted in the last part of the question was a circle rather than a hemisphere.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the gradient of the line \(y = 3x + 4\).</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 gradient of the line which is perpendicular to the line \(y = 3x + 4\).</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>Find the equation of the line which is perpendicular to \(y = 3x + 4\) and which passes through the point \((6{\text{, }}7)\).</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 coordinates of the point of intersection of these two lines.</span></p>
<div class="marks">[2]</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>\(3\) <em><strong>(A1) (C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\( - 1/3\) <strong>(ft)</strong> <em>from (a)</em> <em><strong>(A1)</strong></em><strong>(ft)<em> (C1)</em></strong></span></p>
<p><span><strong><em>[1 mark]<br></em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Substituting \((6{\text{, }}7)\) in \(y ={\text{their }}mx + c\) or equivalent to find \(c\). <em><strong>(M1)</strong></em></span></p>
<p><span>\(y = \frac{{ - 1}}{3}x + 9\) or equivalent <em><strong>(A1)</strong></em><strong>(ft) <em>(C2)</em></strong></span></p>
<p><span><strong><em>[2 marks]<br></em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\((1.5{\text{, }}8.5)\) <em><strong>(A1)(A1)</strong></em><strong>(ft) <em>(C2)</em></strong></span></p>
<p><span><strong>Note: </strong>Award <em><strong>(A1)</strong></em> for \(1.5\), <em><strong>(A1)</strong></em> for \(8.5\). <strong>(ft)</strong> from (c), brackets not required.</span></p>
<p><span><em><strong>[2 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-family: times new roman,times; font-size: medium;">This question was well answered by some candidates and poorly answered by others. It seemed to be part of the syllabus that might have been fully taught by some schools and not by others. It was surprising to see how many candidates could not find the gradient of a perpendicular line when this has been tested for many years.</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 well answered by some candidates and poorly answered by others. It seemed to be part of the syllabus that might have been fully taught by some schools and not by others. It was surprising to see how many candidates could not find the gradient of a perpendicular line when this has been tested for many years.</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 well answered by some candidates and poorly answered by others. It seemed to be part of the syllabus that might have been fully taught by some schools and not by others. It was surprising to see how many candidates could not find the gradient of a perpendicular line when this has been tested for many years.</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 well answered by some candidates and poorly answered by others. It seemed to be part of the syllabus that might have been fully taught by some schools and not by others. It was surprising to see how many candidates could not find the gradient of a perpendicular line when this has been tested for many years.</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;">A room is in the shape of a cuboid. Its floor measures \(7.2\) m by \(9.6\) m and its height is \(3.5\) m.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img 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7y8LjtsQSIxRkdHG080opQJhF4CrbTrpe+psKKy/LWiVRxXzie2lyhlkmgxv5yVHn1n2/ZRYnuJUiYJegm00sP8csp974v9uy8kqpcoZVJptP9yUrx0WUzQ4dMoZVKhl0ArPfRSUZThtqYrI0u+Y5QyBbQ8PnbJUMoUQC+BVjrp5VKhlCmTpr1EKVMGvQRa6aiX8tif3zt0ZTTOcwZQyhRLu16ilCmGXgKttOjluNOSFfZU6Blst5RZnO7Y7wal1ETye/n0QcfFzw6WrmBYLuN3+z8+883dkcWdeIlSagK9BFqluJdPH3RcbDm8Yw3DckxeUVl5ZXnAIbJZB5zjMb1gAUqpobS4PglKqSH0EmiVZtcnQSk1p/NeopSaQy+BVmnTS5RSJ3TbS5RSJ9BLoFUa9BKl1BUd9pKUkmPYxhONKKXm0Eugla57iVLqkK56GVjK0dFRrYcDioJeAr102kuUUrd00kuUUrfQS6CVHntZajJxDMsxrLmuDm96e1tfULCrpkbzYaCUuoVeAq302EuOYUXQq101NZcvX9Z8DN3d3Vr/nkJkInoJlNJpL7UeAkRl1sF6rB7GANGgl0Ar9BLio4dW6WEMEA16CbRCLyE+emiVHsYA0aCXQCv0EuKjh1bpYQwQDXoJtEIvIT56aJUexgDRoJdAK/QSFEWZcovdQoieQSnSZUH00Co9jAGiQS+BVuglKIoy5RZvXm3a/TzDchn5L+8yN1j/s37f9qJVHLfqlTePfyNKs/6b6qFVehgDRINeAq3QS1CFX6LZM9x1vGoNw2YWNVwf8X1UD63SwxggGvQSaIVegiq8l4qiyGOCzZTJcGt2fz0sK4o+WqWHMUA06CXQCr0EVcReKoo82v5mFssxJcfvSoo+WqWHMUA06CXQCr0EVZReKvJP57at5JjsLc39Xn20Sg9jgGjQS6AVegmqaL1UJMFayDFsnlXw6KNVehgDRINeAq3QS1BF7eX4jcMb0UuIEXoJtEIvQRV1PfavLaYcjsmr4h/J+miVHsYA0aCXQCv0ElTRjvcZ5quXsdyyPY7hGUUfrdLDGCAa9BJohV6CKvL5JC7nHwo5ZqWpqWdSURR9tEoPY4Bo0EugFXoJqtBeyp6RO+csWzKZnM31V4Y9vhfH00Or9DAGiAa9BFqhl6AoytMHHRc/O1i6gmE5hs1cV1JRXlFRkp+ZkW/aZzt3azhwwrmrpqbxRKOD5zV8KzWZNB8D3qK9NZ5oRC+BSuglxKqzs7PUZDLX1Wn+jIxe6vPNXFfHMez6goLLly9r/dsKkHjoJSzMX0qdrILqZyRAkDXY9QUFDp6fmJjQejgASYFewnz0VkpCb+MxMpQSjAO9hMj0WUpCn6MymthLKUsPb7Rf5E+3fM63fd834lFmx4QfeiRvyoYKkBDoJYTScykJPY/NCOKYU3qGu5r2rF+2oeqDlm87bt5wXmr5oGZzkenlda819WEyCmkGvYQ5+i8lof8R0iq+1VfPY2f91sxl5Sfv/SLPfXRWuven7csKbYKU1KECJBx6CYqSPqUk0mWcNIl/P+Xko7O1K5iVpc19M6GfeiY27z/SNZ6EYQIkEXppdOlVSiK9RpvuFnlEz8Qt20vLOeaNloGp8E/Kw99/0TGSyFECJB96aVzpWEoiHcecjpZy7OtsX9M/Rr7cDUC6Qi+NiJSy1GTq7u7WeiyLgV4m25LPEpkdaf3XTIbl/qGpbzbxwwPQBHppLP5SdnZ2aj2WxUMvkydB51N6XHwtx7BccbOI00aAFuilUdBRSgK9TIaEvvKAPNXVsJphud803JiSF745QDpAL+lHUykJ9DKxkvIaPb9er/8txzFldnEyMXcIoDX0kmb0lZJALxMlma9m90xs3pHJLN/Q8L+/hs4wZ6V7n/3752LYeSYAuoZe0onWUhLo5dKl4nVfJ/tadr7IMS9Wnbw54vE3c1bqPX3gyNVhD9ZpIc2gl7Shu5QEerkUqXyFdFn6a/tHNesz2Mx1r/yz+T3bB/X/ZiqtPvZnxBLSEXpJDyOUkkAvF0eza4l43KLQ0X6hveNW76CE80sgXUXupSwN/NB6weG7mMD8ZqXBXmHOj+4l/+eIXsbLOKUk0Mt44apbAEsX3kt5ZuDiW5tyOIblGJZjXqxq6Zvv+LaZPrtppXpjdkUVP7zkhRb0MnZGKyWBXsZudHS08UQjSgmwdGG9nOn7dG9D28CvsjIrDVy0FCznlr3dPhZtCUWeEI6+uu+/eJ538LyD/7pj4OnSx4RexsKYpSTQy1iglACJFdbLyUd9P/mbN37j8EYu41/bRqL0Un7oqHnbMZzgw8LRy/kZuZQEejk/lBIgGeY/3mes4+DG9fV/Hou8xCpPCB9uYFguY0Ple599PxB2klXALT3u3sunv+6RPNJAp6P5j/YLgssjK8qsNNDpsNs/b+8JONwcvYwKpSTQy2hQSoDkmaeXs9Jfvtiz/eO7UY9neyaefafq9yUFGSzHsFzG1kPfPY5wcJA85GzYUZDBcsw2a3NDVdkblWWFeUzO5oYrvVcPm4peqyjJz2Ryio/d9v9xo5fhUMpA6GU4lBIg2aIcH+u+9fl7O9dnsByzxtTw3QInS3l+vssf2f4cx2WUHr8b8Rqw4zcOb+SYQssFUZIVRR5qq10b8O7Aue2rA6/7g14GQinDoZeBUEqA1Ig6v5Slhzd4a1VBNsesqeYfLnTQ66x0979MGWyu2RkpmJJgLeSYWofLE8O76KUPShkNekmglACpNP/+S3nmL/bSDHbFvvaxBe9J/lv7/he5bWcHI6QVvYwPSjk/9BKlBEi9hV7fR/5riyknpl4qE31Npsx/aR2J8Cn0MlYoZSyM3EuUEkArsfQyP4b1WDK/3Lq3NdL0Er2MAUoZO2P2EqUE0FZoL2VJ/P7CNz/4Tg6Z/fXWR69Wner1HSI78aD1yO7a4x0jHkVRZKn3fMP79u/vS7KiKFPD3/1n9aErUY4MQi/ng1LGy2i9JKXkGLbxRCNKCaCVkF7K070nt2SwHJNXtK1m9+9LX7ec75s7n+Tn9n0vcMzG+o5RRVHkke/fLcrhGDZzXXFJQdHupk5X5Fg+fXDdbinK4Zi81w+f6bg/0NP2iaUoh2Ne2H749PX7Az0XPtq9bjnHvFhpvdjj9ihG6iVKuTjG6WVgKUdHR7UeDoChRXj9WI/7x9uCIAgRriQgS4M9PYOSP4set5ig11gPZIReopRLYYReopQAeoPreaWaKIoo5RLR3UuUEkCf0MvUIddUQimXjtZeopQAeoZepgJKmVj09TKmUsq/Puj4xsFfaOsYkGLYASJLj2472xz8ZXJYAAAsEXqZXChlMtDUyxjnlLLU8+nOLZXH2ro6LnxYnr9mp/+o9Ug8Pwstb29+qdrGd4juqaSMG8B40MtkQSmTh45exrH6Kv/stGzI3d8+KiuKoshj3/3htys3N/wQ+cJBM/e/fvN3K0o+uO5CKQESCb1MPJQy2dK9l/Hup5Qfnd2RsXL72Z/UPrqd5nxu2Z4Il56V/3b90NbM5/Y5Hk0metQARodeJhJKmRrp28tFHdEjP+s4tJJZXckPqh+ZGTxbxTEv7G//OfiWs2POg88zK0ub+xa6hnt8l6QFAAW9TBSUMpXSsZdLOPZVnupqWM1wL1pvqQusHhdfywUVlNxw4Nz21VzGa9avzjfV76vaub+hpSvCq4jEf0laAFDQy6VDKVMvvXq59LNE5JHWPctY7qUPhQkSv0mxuSy8l/IwX5XBcqtMlub/uSH877fHqtYw3Jpa/lGEmWJ8l6QFAAW9XAqUUivp0svEnU8piS21a5icon2NfOul803ml1dxHGNq6guaAXoEax4TcA1atYINXU/C7zCul3QGAAW9XByUUlv672USXnlgynWLb7JZbcdOX755xpzDchuO90wHTRxJL/PmpoWzY+1vr2CytzT3e0PvDb0EiBt6GR9SSlxTSVt67mXyX6NnZpjfs4LJD792nlds3sKwqw93+c8j8QjWPCantOWvYQuy6CVA3NDLWKGU+qHPXqbm1ezkkW/f+m32esu3Ea6dN919fMNyrrhZ9E0nyYFCJcfvSmF3g14CxA29XBhKqTd662XKXvdVlno+3blhs4UX517cJ/CqtJ4R56H1TPGRLvLCBuOCdeua3V8PRzgxBL0EiBt6OR+UUp/008sUlVKWBnu6nGferyp67Q+nbwWfGRl0VVpF/qXvbN3ml3YfO/PVuY/rKt882xfhZfPiviQtACjoZTQopZ7poZcpvZbI5E83vu8SAi89GyD0qrTkI8LtKDcHgEVCL0OhlPqnbS9x1S0AY0Iv56CU6UKrXqKUAEaGXioKSpluUt9LlBIAjN5LlDIdpbKXExMTKCUAKEbuJUqZvlLTy4mJCQfPry8oQCkBQDFmL1HKdJfsXqKUABDOWL1EKemQvF6ilAAQjVF6iVLSJBm9RCkBYH709xKlpE9ie4lSAkAsaO4lSkmrRPUSpQSA2NHZS5SSbkvvJUoJAPGirZcopREspZcoJQAsDj29RCmNY3G9RCkBYClo6CVKaTTx9hKlBIClS+9eopTGFHsv/aXUwyXAACCtpWsvUUojiyV+KCUAJFb69RKlhPkTiFICQDKkUy9HR0ePNDSglBAthCglACRPevSSXH0QpQQiPIcoJQAkm957iVJCuMAoopQAkBr67SVKCdGQNKKUAJBKOu0lSgnzMNfVkT3ZKCUApIxOe4k3vM3/hlICQIrpsZcAAAB6g14CAAAsTMNePum5LIzI2n1/rcnSYI8Qolt0T0W65cAPrRccfNv3fSOe1A9Uj6bcYnfogyf86PYY+PcJAJJMs17Kw3z1sleb+p5pNQCtPetrejVst1y+xekOvtms1Huq6jlOvUHO5vorw6iCMuUWb357rGoNw3IZRbvf+8Bm/aDBXFG0anleieXTrmH8VwEACadVL5+JzTsyGe6Fw10GDebELdvvXrU0nXHwPHk7c3jbiqwDznFv6M2Ka46397o9U+5evr4oh2PWVPMPEUxFURQXX8mw3Cqr4Muj7Bn54cNXVnIZpcfvjms7NACgj0a9nLhl25CX9xuOy6prH53VZgxakp/dOPXxrbGA7Ek9x0pyzc7gp3l5SvjY0vpYvZk803eymGEz/6V1JHVD1bHQXiqK4hlp3beCYcMeSQCApdKkl7NjzoP5+89f+/hVjlm94+wAZkvKdPfxDS+FLcaGmepq+E20GMged+/l01/3SB5poNPR/Ef7BcHlkRVlVhrodNjtn7f3jFC2kBuhl7Nj7W+vYNgV+9rHNBwYANBIi17KDx1VZTZhXH50dkcGy/3uZN8MXc/jcZOn7x7fGL4YG367wbPbmbV7WodCHy95yNmwoyCD5Zht1uaGqrI3KssK85iczQ1Xeq8eNhW9VlGSn8nkFB+7TdWrP4T1UpbuntyWxzFFhzqMfCQZACRF6nspz/Sd3GKyizOyIg+11a7lmMKGricpH4auRFyMDTczzO/JfeWPvZMRWzB+4/BGjim0XBAlWfE/tuq7A+e2rw6eiqU/0suM/Jd/X1FZXlFZ/lrRKo7L2Frf+qOEWgJAoqW+l09uHDapR6zIz7qOvMCwufvbR438BBfbYqw89udDG6rsf5GifF4SrIUcU+tweWJ4lwqklzlvt/1tSvG4ReF6W9P+ogyWe+6ND68/pmg7AUAXUt1LeaR1z7K8orLyyvKKyvKKyrLCPIblMqrPPZpO8Uh0I7bFWNnlPLDr0HfzZMCovQzZf+k8+DzDcs+Z23GqKgAkVIp7OTXQUrWl6d7M3EemH52tzmSyi4M+aCgxLMbKv/Ta397b0jc57/2gl4riOySKYwptQrSJOADAYqS2lxO3bBt2hUwl5ZHWPctYbu2RG88MuSa74GIsiaW9x79PTpYGen56GnY79FJRFEUebX8zi+WYMrs4738XAABxSmUvZ4Zb33x+Jz8cmkW305xv1NPwIy7GTjxoPbK79njHiEeRf+m173q+yNVi5xcAAAD6SURBVNysvqwB33L0zZKqSDFALxVZ+rHt4NZMJmdzww9jxvtlAoCkSlUv5RHh9KHXn+O4ddW209cfzB3h+fSB8+T+TTkcw3KrTJaTzgeRD/6kVcTF2J/b973AMRvrO34SW2rXhF3KKvOfWgZC93U+fXDdbinK4Zi81w+f6bg/0NP2iaUoh2Ne2H749PX7Az0XPtq9bjnHvFhpvdjjpiCZTx90XPzsYOkKhuUYLm/Ta/594Znrth+0d7koO9MUAHQA1yfR1tMHHf/TMRC6uCpLgz09gzgpAgBAP9BLAACAhaGXAAAAC0MvAQAAFoZeAgAALAy9BAAAWNj/B8YVduKP0vd+AAAAAElFTkSuQmCC" alt></span></p>
</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">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the length of AG.</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 angle that AG makes with the floor.</span></p>
<div class="marks">[2]</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>\({\text{A}}{{\text{C}}^2} = {7.2^2} + {9.6^2}\) <em><strong>(M1)</strong></em></span> </p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in Pythagoras Theorem.</span></p>
<p> </p>
<p><span><span>\({\text{AC}} = 12{\text{ m}}\) </span><span> <em><strong>(A1) (C2)</strong></em></span></span></p>
<p><span><span><em><strong>[2 marks]</strong></em></span></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{A}}{{\text{G}}^2} = {12^2} + {3.5^2}\) <em><strong>(M1)</strong></em></span> </p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in Pythagoras Theorem.</span></p>
<p> </p>
<p><span>\({\text{AG}} = 12.5{\text{ m}}\) <em><strong>(A1)</strong></em><strong>(ft) </strong><em><strong> (C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their answer to part (a).</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>\(\tan \theta = \frac{{3.5}}{{12}}\) or \(\sin \theta = \frac{{3.5}}{{12.5}}\) or \(\cos \theta = \frac{{12}}{{12.5}}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitutions in trig ratio.</span></p>
<p> </p>
<p><span>\(\theta = {16.3^ \circ }\) <em><strong>(A1)</strong></em><strong>(ft) </strong><em><strong> (C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Follow through from parts (a) and/or part (b) where appropriate. Award <em><strong>(M1)(A0)</strong></em> for use of radians (0.284).</span></p>
<p><em><strong><span>[2 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-size: medium; font-family: times new roman,times;">Question 7 was surprisingly difficult for many candidates, especially part b. Many candidates did not recognize that <strong>ACG</strong> was a right angled triangle and tried to use the law of cosines to find angle A. Although correct substitution and manipulation provided the correct answer, many candidates attempting this method made arithmetical errors.</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;">Question 7 was surprisingly difficult for many candidates, especially part b. Many candidates did not recognize that <strong>ACG</strong> was a right angled triangle and tried to use the law of cosines to find angle A. Although correct substitution and manipulation provided the correct answer, many candidates attempting this method made arithmetical errors.</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;">Question 7 was surprisingly difficult for many candidates, especially part b. Many candidates did not recognize that <strong>ACG</strong> was a right angled triangle and tried to use the law of cosines to find angle A. Although correct substitution and manipulation provided the correct answer, many candidates attempting this method made arithmetical errors.</span></p>
<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;">Let \(f(x) = {x^4}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down \(f'(x)\).</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>Point \({\text{P}}(2,6)\) lies on the graph of \(f\).</span></p>
<p><span>Find the gradient of the tangent to the graph of \(y = f(x)\) at \({\text{P}}\).</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>Point \({\text{P}}(2,16)\) lies on the graph of \(f\).</span></p>
<p><span>Find the equation of the normal to the graph at \({\text{P}}\). Give your answer in the form \(ax + by + d = 0\), where \(a\), \(b\) and \(d\) are integers.</span></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><span>\(\left( {f'(x) = } \right)\) \(4{x^3}\) <strong><em>(A1) (C1)</em></strong></span></p>
<p> </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>\(4 \times {2^3}\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substituting 2 into their derivative.</span></p>
<p> </p>
<p><span>\( = 32\) <em><strong>(A1)</strong></em><strong>(ft) <em>(C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Follow through from their part (a).</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>\(y - 16 = - \frac{1}{{32}}(x - 2)\) <strong>or</strong> \(y = - \frac{1}{{32}}x + \frac{{257}}{{16}}\) <strong><em>(M1)(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for their gradient of the normal seen, <strong><em>(M1) </em></strong>for point substituted into equation of a straight line in only \(x\) and \(y\) (with any constant ‘\(c\)’ eliminated).</span></p>
<p> </p>
<p><span>\(x + 32y - 514 = 0\) <strong>or </strong>any integer multiple <strong><em>(A1)</em>(ft) <em>(C3)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Follow through from their part (b).</span></p>
<p> </p>
<p><span><strong><em>[3 marks]</em></strong></span></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>Emily’s kite ABCD is hanging in a tree. The plane ABCDE is vertical.</p>
<p>Emily stands at point E at some distance from the tree, such that EAD is a straight line and angle BED = 7°. Emily knows BD = 1.2 metres and angle BDA = 53°, as shown in the diagram</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_18.18.28.png" alt="N17/5/MATSD/SP1/ENG/TZ0/10"></p>
</div>
<div class="specification">
<p>T is a point at the base of the tree. ET is a horizontal line. The angle of elevation of A from E is 41°.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the length of EB.</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>Write down the angle of elevation of B from E.</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>Find the vertical height of B above the ground.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>Units are required in parts (a) and (c).</strong></p>
<p>\(\frac{{{\text{EB}}}}{{\sin 53{\rm{^\circ }}}} = \frac{{1.2}}{{\sin 7{\rm{^\circ }}}}\) <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substitution into sine formula, <strong><em>(A1) </em></strong>for correct substitution.</p>
<p> </p>
<p>\(({\text{EB}} = ){\text{ }}7.86{\text{ m}}\)\(\,\,\,\)<strong>OR</strong>\(\,\,\,\)\(786{\text{ cm }}(7.86385 \ldots {\text{ m}}\)\(\,\,\,\)<strong>OR</strong>\(\,\,\,\)\(786.385 \ldots {\text{ cm}})\) <strong><em>(A1) (C3)</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>34° <strong><em>(A1) (C1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>Units are required in parts (a) and (c).</strong></p>
<p>\(\sin 34^\circ = \frac{{{\text{height}}}}{{7.86385 \ldots }}\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into a trigonometric ratio.</p>
<p> </p>
<p>\(({\text{height}} = ){\text{ }}4.40{\text{ m}}\)\(\,\,\,\)<strong>OR</strong>\(\,\,\,\)\(440{\text{ cm }}(4.39741 \ldots {\text{ m}}\)\(\,\,\,\)<strong>OR</strong>\(\,\,\,\)\(439.741 \ldots {\text{ cm}})\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Accept “BT” used for height. Follow through from parts (a) and (b). Use of 7.86 gives an answer of 4.39525….</p>
<p> </p>
<p><strong><em>[2 marks]</em></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 class="p1">A cuboid has a rectangular base of width \(x\)<span class="s1"><em> </em>cm </span>and length <span class="s1">2\(x\) cm </span>. The height of the cuboid is \(h\) <span class="s1">cm </span>. The total length of the edges of the cuboid is \(72\)<span class="s1"> cm</span>.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-20_om_08.27.58.png" alt></p>
<p class="p1">The volume, \(V\), of the cuboid can be expressed as \(V = a{x^2} - 6{x^3}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of \(a\).</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">Find the value of \(x\) that makes the volume a maximum.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(72 = 12x + 4h\;\;\;\)(or equivalent) <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 a correct equation obtained from the total length of the edges.</p>
<p class="p2"> </p>
<p class="p1">\(V = 2{x^2}(18 - 3x)\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1">\((a = ){\text{ }}36\) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C3)</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\frac{{{\text{d}}V}}{{{\text{d}}x}} = 72x - 18{x^2}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1">\(72x - 18{x^2} = 0\;\;\;\)<strong>OR</strong>\(\;\;\;\frac{{{\text{d}}V}}{{{\text{d}}x}} = 0\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Notes:<span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1) </em></strong>for<span class="Apple-converted-space"> </span>\( - 18{x^2}\)<span class="Apple-converted-space"> </span>seen. Award <strong><em>(M1) </em></strong>for equating derivative to zero.</p>
<p class="p2"> </p>
<p class="p1">\((x = ){\text{ 4}}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C3)</em></strong></p>
<p class="p1"><strong>Note: </strong>Follow through from part (a).</p>
<p class="p2"> </p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">Sketch of \(V\) with visible maximum <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">Sketch with \(x \geqslant 0,{\text{ }}V \geqslant 0\) and indication of maximum (e.g. coordinates) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)</strong></p>
<p class="p1">\((x = ){\text{ 4}}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C3)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: </strong>Follow through from part (a).</p>
<p class="p1">Award <strong><em>(M1)(A1)(A0) </em></strong>for \((4,{\text{ }}192)\).</p>
<p class="p1">Award <strong><em>(C3) </em></strong>for \(x = 4,{\text{ }}y = 192\).</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>The model in this question seemed to be too difficult for the vast majority of the candidates, and therefore was a strong discriminator between grade 6 and grade 7 candidates. An attempt to find an equation for the volume of the cube often started with <em>V</em> = <em>x</em> x 2<em>x</em> x <em>h</em> . Many struggled to translate the total length of the edges into a correct equation, and consequently were unable to substitute <em>h</em>. Some tried to write <em>x</em> in terms of <em>h</em> and got lost, others tried to work backwards from the expression given in the question.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>As very few found a value for <em>a</em>, often part (b) was not attempted. When a derivative was calculated this was usually done correctly.</p>
<div class="question_part_label">b.</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 angle BAC \( = 30^\circ \), BC \( = 6.7\) cm and AC \( = 13.4\) cm.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"> </span></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 size of angle ACB.</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>Nadia makes an accurate drawing of triangle ABC. She measures angle BAC and finds it to be 29°.</span></p>
<p><span>Calculate the percentage error in Nadia’s measurement of angle BAC.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{\sin {\text{A}}{\operatorname{\hat B}}{\text{C}}}}{{13.4}} = \frac{{\sin 30^\circ }}{{6.7}}\)</span><span> <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 substitution.</span></p>
<p><br><span>\({\text{A}}{\operatorname{\hat B}}{\text{C}}\)</span><span> = 90° </span><span> <em><strong>(A1)</strong></em></span></p>
<p><span>\({\text{A}}{\operatorname{\hat C}}{\text{B}}\)</span><span><span> =</span> 60° <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C4)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span><strong>Note:</strong> Radians give no solution, award maximum <em><strong>(M1)(A1)(A0)</strong></em>.</span></p>
<p><span> </span></p>
<p><em><strong><span>[4 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{29 - 30}}{{30}} \times 100\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into correct formula.</span></p>
<p><br><span>% error = −33.3 % <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Percentage symbol not required. Accept positive answer.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</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;">Use of cosine rule was common. The assumption of a right angle in the given diagram was minimal.</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;"><span style="font-size: medium; font-family: times new roman,times;">The incorrect denominator was often seen in the error formula.</span></span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Consider \(f:x \mapsto {x^2} - 4\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \(f ′(x)\).</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>Let <em>L</em> be the line with equation <em>y</em> = 3<em>x</em> + 2.</span></p>
<p><span>Write down the gradient of a line parallel to <em>L</em>.</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>Let <em>L</em> be the line with equation <em>y</em> = 3<em>x</em> + 2.</span></p>
<p><span>Let P be a point on the curve of <em>f</em>. At P, the tangent to the curve is parallel to <em>L</em>. Find the coordinates of P.</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>\(2x\) <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>3 <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(2x = 3\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note: <em>(M1)</em></strong> for equating their (a) to their (b).</span></p>
<p><br><span>\(x =1.5\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>\(y = (1.5)^2 - 4\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note: <em>(M1)</em></strong> for substituting their <em>x</em> in <em>f</em> (<em>x</em>). </span></p>
<p><br><span>(1.5, −1.75) (accept <em>x</em> = 1.5, <em>y</em> = −1.75) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C4)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Missing coordinate brackets receive <em><strong>(A0)</strong></em> if this is the first time it occurs.</span></p>
<p><span> </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-size: medium; font-family: times new roman,times;">This question was generally answered well in parts (a) and (b).</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 generally answered well in parts (a) and (b).</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 part proved to be difficult as candidates did not realise that to find the value of the <em>x</em> coordinate they needed to equate their answers to the first two parts. They did not understand that the first derivative is the gradient of the function. Some found the value of <em>x</em>, but did not substitute it back into the function to find the value of <em>y</em>.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The number of apartments in a housing development has been increasing by a constant amount every year.</p>
<p class="p1">At the end of the first year the number of apartments was 150, and at the end of the sixth year the number of apartments was 600.</p>
<p class="p1">The number of apartments, \(y\), can be determined by the equation \(y = mt + n\), where \(t\)<em> </em>is the time, in years.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of \(m\).</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">State what \(m\) represents <strong>in this context</strong>.</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">Find the value of \(n\).</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">State what \(n\) represents <strong>in this context</strong>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\frac{{600 - 150}}{{6 - 1}}\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p2"><strong>OR</strong></p>
<p class="p2">\(600 = 150 + (6 - 1)m\) <strong><em>(M1)</em></strong></p>
<p class="p2"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into gradient formula or arithmetic sequence formula.</p>
<p class="p2"> </p>
<p class="p2">\( = 90\) <strong><em>(A1) (C2)</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">the annual rate of growth of the number of apartments <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C1)</em></strong></p>
<p class="p2"><strong>Note: </strong>Do not accept common difference.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(150 = 90 \times (1) + n\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution of their gradient and one of the given points into the equation of a straight line.</p>
<p class="p2"> </p>
<p class="p1">\(n = 60\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C2)</em></strong></p>
<p class="p2"><strong>Note: </strong>Follow through from part (a).</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">the initial number of apartments <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C1)</em></strong></p>
<p class="p2"><strong>Note: </strong>Do not accept “first number in the sequence”.</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">In the following diagram, <span class="s1">ABCD </span>is the square base of a right pyramid with vertex <span class="s1">V</span>. The centre of the base is <span class="s1">O</span>. The diagonal of the base, <span class="s1">AC</span>, is <span class="s1">8 cm </span>long. The sloping edges are 10 cm <span class="s2">long.</span></p>
<p class="p1" style="text-align: center;"><span class="s2"><img src="images/Schermafbeelding_2015-12-20_om_17.33.52.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down the length of \({\text{AO}}\).</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">Find the size of the angle that the sloping edge \({\text{VA}}\)<span class="s1"> </span>makes with the base of the pyramid.</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">Hence, or otherwise, find the area of the triangle \({\text{CAV}}\).</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 class="p1">\({\text{AO}} = 4{\text{ (cm)}}\) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C1)</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\cos {\rm{O\hat AV}} = \frac{4}{{10}}\) <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 correct trigonometric ratio.</p>
<p class="p2"> </p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">\(\cos {\rm{O\hat AV}} = \frac{{{{10}^2} + {8^2} - {{10}^2}}}{{2 \times 10 \times 8}}\;\;\;\)<strong>OR</strong>\(\;\;\;\frac{{{{10}^2} + {4^2} - {{(9.16515 \ldots )}^2}}}{{2 \times 10 \times 4}}\) <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 into the cosine rule formula.</p>
<p class="p2"> </p>
<p class="p1">\({\rm{O\hat AV}} = 66.4^\circ \;\;\;(66.4218 \ldots )\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C2)</em></strong></p>
<p class="p1"><strong>Notes: </strong>Follow through from their answer to part (a).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\({\text{area}} = \frac{{8 \times 10 \times \sin (66.4218 \ldots ^\circ)}}{2}\;\;\;\)<strong>OR</strong>\(\;\;\;\frac{1}{2} \times 8 \times \sqrt {{{10}^2} - {4^{\text{2}}}} \)</p>
<p class="p1"><strong>OR</strong>\(\;\;\;\frac{1}{2} \times 10 \times 10 \times \sin (47.1563 \ldots ^\circ )\) <span class="Apple-converted-space"> </span><strong><em>(M1)(A1)</em>(ft)</strong></p>
<p class="p1"><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for substitution into the area formula, <strong><em>(A1)</em>(ft) </strong>for correct substitutions. Follow through from their answer to part (b) and/or part (a).</p>
<p class="p2"> </p>
<p class="p1">\({\text{area}} = 36.7{\text{ c}}{{\text{m}}^2}\;\;\;(36.6606 \ldots {\text{ c}}{{\text{m}}^2})\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C3)</em></strong></p>
<p class="p1"><strong>Notes:<span class="Apple-converted-space"> </span></strong>Accept an answer of \(8\sqrt {21} {\text{ c}}{{\text{m}}^2}\) which is the exact answer.</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;">The surface of a red carpet is shown below. The dimensions of the carpet are in metres.</span></p>
<div style="text-align: center;"><img src="images/Schermafbeelding_2014-09-02_om_14.31.51.png" alt></div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down an expression for the area, \(A\), in \({{\text{m}}^2}\), of the carpet.</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>The area of the carpet is \({\text{10 }}{{\text{m}}^2}\).</span></p>
<p><span>Calculate the value of \(x\).</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 area of the carpet is \({\text{10 }}{{\text{m}}^2}\).</span></p>
<p><span>Hence, write down the value of the length and of the width of the carpet, in metres.</span></p>
<div class="marks">[2]</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>\(2x(x - 4)\) <strong>or</strong> \(2{x^2} - 8x\) <strong><em>(A1) (C1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A0) </em></strong>for \(x - 4 \times 2x\).</span></p>
<p> </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>\(2x(x - 4) = 10\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for equating their answer in part (a) to \(10\).</span></p>
<p> </p>
<p><span>\({x^2} - 4x - 5 = 0\) <strong><em>(M1)</em></strong></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>Sketch of \(y = 2{x^2} - 8x\) and \(y = 10\) <strong><em>(M1)</em></strong></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>Using GDC solver \(x = 5\) and \(x = - 1\) <strong><em>(M1)</em></strong></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>\(2(x + 1)(x - 5)\) <strong><em>(M1)</em></strong></span></p>
<p><span>\(x = 5{\text{ (m)}}\) <strong><em>(A1)</em>(ft) <em>(C3)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Follow through from their answer to part (a).</span></p>
<p><span> Award at most <strong><em>(M1)(M1)(A0) </em></strong>if both \(5\) and \(-1\) are given as final answer.</span></p>
<p><span> Final <strong><em>(A1)</em>(ft) </strong>is awarded for choosing only the positive solution(s).</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>\(2 \times 5 = 10{\text{ (m)}}\) <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span>\(5 - 4 = 1{\text{ (m)}}\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Follow through from their answer to part (b).</span></p>
<p><span> Do not accept negative answers.</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></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><span style="font-family: times new roman,times; font-size: medium;">\(75\) metal spherical cannon balls, each of diameter \(10{\text{ cm}}\), were excavated from a Napoleonic War battlefield.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the total volume of all \(75\) metal cannon balls excavated.</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 cannon balls are to be melted down to form a sculpture in the shape of a cone. The base radius of the cone is \(20{\text{ cm}}\).</span></p>
<p><span>Calculate the height of the cone, assuming that no metal is wasted.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(75 \times \frac{4}{3}\pi \times {5^3}\)</span><span> <em><strong>(M1)(M1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted formula of a sphere. Award <em><strong>(M1)</strong></em> for multiplying their volume by \(75\). If \(r = 10\) is used, award <strong><em>(M0)(M1)(A1)</em>(ft)</strong> for the answer 314000 cm<sup>3</sup> .</span></p>
<p> </p>
<p><span>\(39300{\text{ c}}{{\text{m}}^3}\) . <em><strong>(A1) (C3)</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{1}{3}\pi \times {20^2} \times h = 39300\) <em><strong>(M1)(M1)</strong></em> <br></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted formula of a cone. Award <em><strong>(M1)</strong></em> for equating their volume to their answer to part (a).</span></p>
<p> </p>
<p><span>\(h = 93.8{\text{ cm}}\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></span></p>
<p><span><strong>Notes:</strong> Accept the exact value of \(93.75\) . Follow through from their part (a).</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</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 well as some candidates reading the diameter given as the radius, there was much confusion between the area and volume of a sphere and, although there was some recovery when multiplying by \(75\), two of the three marks were invariably lost. Recovery was possible in part (b) and many successful attempts were seen to calculate the height of the cone.</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 well as some candidates reading the diameter given as the radius, there was much confusion between the area and volume of a sphere and, although there was some recovery when multiplying by \(75\), two of the three marks were invariably lost. Recovery was possible in part (b) and many successful attempts were seen to calculate the height of the cone.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A balloon in the shape of a sphere is filled with helium until the radius is <span class="s1">6 cm</span>.</p>
</div>
<div class="specification">
<p class="p1">The volume of the balloon is increased by <span class="s1">40%</span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the volume of the balloon.</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">Calculate the radius of the balloon following this increase.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>Units are required in parts (a) and (b).</strong></p>
<p class="p1"><span class="Apple-converted-space">\(\frac{4}{3}\pi \times {6^3}\) </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 volume of sphere formula.</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\( = 905{\text{ c}}{{\text{m}}^3}{\text{ }}(288\pi {\text{ c}}{{\text{m}}^3},{\text{ }}904.778 \ldots {\text{ c}}{{\text{m}}^3})\) </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C2)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Answers derived from the use of approximations of \(\pi \) (<span class="s1">3.14</span>; <span class="s1">22/7</span>) are awarded <strong><em>(A0)</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"><strong>Units are required in parts (a) and (b).</strong></p>
<p class="p1">\(\frac{{140}}{{100}} \times 904.778 \ldots = \frac{4}{3}\pi {r^3}\) <strong>OR</strong> \(\frac{{140}}{{100}} \times 288\pi = \frac{4}{3}\pi {r^3}\) <strong>OR</strong> \(1266.69 \ldots = \frac{4}{3}\pi {r^3}\) <strong><em>(M1)(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 multiplying their part (a) by <span class="s1">1.4 </span>or equivalent, <strong><em>(M1) </em></strong>for equating to the volume of a sphere formula.</p>
<p class="p2"> </p>
<p class="p1">\({r^3} = \frac{{3 \times 1266.69 \ldots }}{{4\pi }}\) <strong>OR</strong> \(r = \sqrt[3]{{\frac{{3 \times 1266.69 \ldots }}{{4\pi }}}}\) <strong>OR</strong> \(r = \sqrt[3]{{(1.4) \times {6^3}}}\) <strong>OR</strong> \({r^3} = 302.4\) <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 isolating \(r\).</p>
<p class="p2"> </p>
<p class="p1">\((r = ){\text{ }}6.71{\text{ cm }}(6.71213 \ldots )\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C4)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Follow through from part (a).</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</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>
<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;">Günter is at Berlin Tegel Airport watching the planes take off. He observes a plane that is at an angle of elevation of \(20^\circ\) from where he is standing at point \({\text{G}}\). The plane is at a height of 350 metres. This information is shown in the following diagram.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><br><img src="images/Schermafbeelding_2014-09-02_om_14.52.24.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the horizontal distance, \({\text{GH}}\), of the plane from Günter. <strong>Give your answer to the nearest metre.</strong></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 plane took off from a point \({\text{T}}\), which is \(250\) metres from where Günter is standing, as shown in the following diagram.</span></p>
<div>
<br><img src="images/Schermafbeelding_2014-09-02_om_14.54.36.png" alt>
</div>
<div>
<p><span>Using your answer from part (a), calculate the angle \({\text{ATH}}\), the takeoff angle of the plane.</span></p>
</div>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{350}}{{\tan 20^\circ }}\) <strong><em>(M1)</em></strong></span></p>
<p><span>\( = {\text{961.617}} \ldots \) <strong><em>(A1)</em></strong></span></p>
<p><span>\( = 962{\text{ (m)}}\) <strong><em>(A1)</em>(ft) <em>(C3)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into correct formula, <strong><em>(A1) </em></strong>for correct answer, <strong><em>(A1)</em>(ft) </strong>for correct rounding to the nearest metre.</span></p>
<p><span> Award <strong><em>(M0)(A0)(A0) </em></strong>for \(961\) without working.</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>\({\text{961.617}} \ldots - 250 = {\text{711.617}} \ldots \) <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span>\({\tan ^{ - 1}}\left( {\frac{{350}}{{{\text{711.617}} \ldots }}} \right)\) <strong><em>(M1)</em></strong></span></p>
<p><span>\( = {\text{26.2}}^\circ {\text{ (26.1896}} \ldots {\text{)}}\) <strong><em>(A1)</em>(ft) <em>(C3)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Accept \(26.1774…\) from use of 3 sf answer \(962\) from part (a). Follow through from their answer to part (a).</span></p>
<p><span> Accept alternative methods.</span></p>
<p> </p>
<p><span><strong><em>[3 marks] </em></strong></span></p>
<div class="question_part_label">b.</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>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A child’s toy consists of a hemisphere with a right circular cone on top. The height of the cone is \(12{\text{ cm}}\) and the radius of its base is \(5{\text{ cm}}\) . The toy is painted red.</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 length, \(l\), of the slant height of the cone.</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>Calculate the area that is painted red.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\sqrt {{5^2} + {{12}^2}} \) <em><strong>(M1)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in Pythagoras Formula.</span></p>
<p> </p>
<p><span><span>=\(13{\text{ (cm)}}\) </span> <span><em><strong>(A1) (C2)</strong></em></span></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{Area}} = 2\pi {(5)^2} + \pi (5)(13)\) <em><strong>(M1)(M1)(M1)</strong></em></span></p>
<p> </p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for surface area of hemisphere, <em><strong>(M1)</strong></em> for surface of cone, <em><strong>(M1)</strong></em> for addition of two surface areas. Follow through from their answer to part (a).</span></p>
<p> </p>
<p><span>\( = 361{\text{ c}}{{\text{m}}^2}\) (\(361.283 \ldots \)) <em><strong>(A1)</strong></em><strong>(ft) </strong><em><strong> (C4)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> The answer is \( 361{\text{ c}}{{\text{m}}^2}\) , the units are required.</span></p>
<div class="question_part_label">b.</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>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The diagram below shows the line PQ, whose equation is <em>x</em> + 2<em>y</em> = 12. The line intercepts the axes at P and Q respectively.</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>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the coordinates of P and of Q.</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>A second line with equation <em>x</em> − <em>y</em> = 3 intersects the line PQ at the point A. Find the coordinates of A.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(0 + 2y = 12\) or \(x + 2(0) = 12\) <em><strong>(M1)</strong></em></span></p>
<p><span>P(0, 6) (accept \(x = 0\), \(y = 6\)) <em><strong>(A1)</strong></em></span></p>
<p><span>Q(12, 0) (accept \(x = 12\), \(y = 0\)) <em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for setting either value to zero.</span></p>
<p><span>Missing coordinate brackets receive <em><strong>(A0)</strong></em> the first time this occurs.</span></p>
<p><span>Award <em><strong>(A0)(A1)</strong></em><strong>(ft)</strong> for P(0, 12) and Q(6, 0).</span></p>
<p><span> </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><span>\(x + 2(x - 3) = 12\) <em><strong>(M1)</strong></em></span></p>
<p><span>(6, 3) (accept \(x = 6\), \(y = 3\)) <em><strong>(A1)(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><br><span><strong>Note: <em>(A1)</em></strong> for each correct coordinate</span>.</p>
<p><span>Missing coordinate brackets receive <em><strong>(A0)(A1)</strong></em> if this is the first</span> <span>time it occurs.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">b.</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;">Most candidates could find the <em>x</em> and <em>y</em> intercepts but many wrote the coordinates the wrong way around. A number of candidates did not label their coordinates as <em>P</em> and <em>Q</em> or did not include parentheses.</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;">In this part many had trouble recognising the need to solve the two simultaneous equations.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The mid-point, M, of the line joining A(<em>s</em> , 8) to B(−2, <em>t</em>) has coordinates M(2, 3).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the values of <em>s</em> and <em>t</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>Find the equation of the straight line perpendicular to AB, passing through the point M.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(s = 6\) <em><strong>(A1)</strong></em></span></p>
<p><span>\(t = - 2\) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></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>\({\text{gradient of AB}} = \frac{{ - 2 - 8}}{{ - 2 - 6}} = \frac{{ - 10}}{{ - 8}} = \frac{5}{4}\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><em><strong>(A1)</strong> for gradient of AM or BM</em> \( = \frac{5}{4}\)</span></p>
<p><span>\({\text{Perpendicular gradient}} = - \frac{4}{5}\)</span><span><span> <em><strong>(A1)</strong></em><strong>(ft)</strong></span></span></p>
<p><span><span>Equation of perpendicular bisector is</span></span></p>
<p><span><span>\(y = - \frac{4}{5}x + c\)</span></span></p>
<p><span><span>\(3 = - \frac{4}{5}(2) + c\) <em><strong>(M1)</strong></em></span></span></p>
<p><span><span>\(c = 4.6\)</span></span></p>
<p><span><span>\(y = -0.8x + 4.6\)</span></span></p>
<p><span><span><em>or</em> \(5y = -4x + 23\) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C4)</strong></em></span></span></p>
<p><span><span><em><strong>[4 marks]</strong></em></span></span></p>
<p> </p>
<div class="question_part_label">b.</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;">(a) It was surprising how many errors were made in finding the values for <em>s</em> and <em>t</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;">(b) The candidates had difficulty in finding the equation of a straight line. They could find the gradient of the line AB and a number could give the gradient of the perpendicular line but most did not substitute the correct midpoint to find the equation of the line.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The diagram shows points A(2, 8), B(14, 4) and C(4, 2). M is the midpoint of AC.</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>Write down the coordinates of M.</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>Calculate the gradient of the line AB.</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 the line parallel to AB that passes through M.</span></p>
<div class="marks">[2]</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>\(\left( {\frac{{2 + 4}}{2},\frac{{8 + 2}}{2}} \right)\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for a correct substitution into the midpoint formula.</span></p>
<p><span> </span></p>
<p><span>\( = (3, 5)\) <em><strong>(A1) (C2)</strong></em></span></p>
<p><span><span><strong>Note:</strong> Brackets must be present for final</span> <em><strong>(A1)</strong></em> to be awarded.</span></p>
<p><span><strong>Note:</strong> Accept \(x = 3\), \(y = 5\) .</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>\(\frac{{8 - 4}}{{2 - 14}}\) <em><strong>(M1)</strong></em><strong> <br></strong></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted formula.</span></p>
<p> </p>
<p><span><span>\( = - \frac{1}{3}\) \(\left( {\frac{{ - 4}}{{12}}, - 0.333} \right)\) \(( - 0.333333 \ldots )\)</span><span> <em><strong>(A1) (C2)</strong></em></span></span></p>
<p><span><span><em><strong>[2 marks]<br></strong></em></span></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\((y - 5) = - \frac{1}{3}(x - 3)\) <strong><em>(M1)(A1)</em>(ft)<br></strong></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>\(5 = - \frac{1}{3}(3) + c\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(y = - \frac{1}{3}x + 6\) <em><strong>(A1)</strong></em><strong>(ft) </strong><em><strong> (C2)</strong></em></span></p>
<p><span><span><strong>Notes:</strong> Award</span><span> <em><strong>(M1)</strong></em> for substitution of their gradient into equation of line with their values from (a) correctly substituted.</span></span></p>
<p><span>Accept correct equivalent forms of the equation of the line. Follow through from their parts (a) and (b).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></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-size: medium; font-family: times new roman,times;">Overall, there was a very good response to parts (a) and (b) with only a few candidates giving an incorrect expression for the gradient in part (b). <br></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;">Overall, there was a very good response to parts (a) and (b) with only a few candidates giving an incorrect expression for the gradient in part (b). Occasionally, the final mark in part (b) was lost because the negative sign was dropped by some candidates. <br></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 able candidates recognized they needed to do something with the equation \(y = mx + c\) in part (c). Weaker candidates clearly showed a lack of understanding of an equation of a line and either simply gave a numerical answer for this part of the question or tried to use the coordinates of \(M\) into what they believed was the required equation of the straight line. A popular incorrect answer seen was \(y = 3x + 5\) .</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;">Line <em>L</em> is given by the equation 3<em>y</em> + 2<em>x</em> = 9 and point P has coordinates (6 , –5).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Explain why point P is not on the line <em>L</em>.</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 gradient of line <em>L</em>.</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>(i) Write down the gradient of a line perpendicular to line <em>L</em>.</span></p>
<p><span>(ii) Find the equation of the line perpendicular to <em>L</em> and passing through point P.</span></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><span>3 × (–5) + 2 × 6 ≠ 9 <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><span><strong>Note:</strong> Also accept 3 × (–5) + 2<em>x</em> = 9 gives <em>x</em> =12 ≠ 6 or 3<em>y</em> + 2 × (6) = 9 gives <em>y</em> = –1 ≠ –5.</span></p>
<p><span><em><strong>[1 mark]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>3<em>y</em> = –2<em>x</em> + 9 <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for 3<em>y</em> = –2<em>x</em> + 9 or \(y = \frac{{ - 2}}{3}x + 3\) or \(y = \frac{{( - 2x + 9)}}{3}\).</span></p>
<p><span> </span></p>
<p><span>\({\text{gradient}} = - \frac{2}{3}( - 0.667)( - 0.666666...)\) <em><strong>(A1) (C2)</strong></em><br></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>(i) gradient of perpendicular line \( = \frac{3}{2}(1.5)\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Note:</strong> Follow through from their answer to part (b).</span></p>
<p> </p>
<p><span>(ii) \(y = \frac{3}{2}x + c\)</span></p>
<p><span>\( - 5 = \frac{3}{2} \times 6 + c\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution of their perpendicular gradient and the point (6, –5) into the equation of their line.</span></p>
<p> </p>
<p><span>\(y = \frac{3}{2}x - 14\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Note:</strong> Follow through from their perpendicular gradient. Accept equivalent forms.</span></p>
<p> </p>
<p><strong><span>OR</span></strong></p>
<p><span>\(y + 5 = \frac{3}{2}(x - 6)\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong> <em><strong>(C3)</strong></em><br></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for substitution of their perpendicular gradient and the point (6, –5) into the equation of their line. Follow through from their perpendicular gradient.</span></p>
<p><span> </span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></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-size: medium; font-family: times new roman,times;">In part (a), the word <em>'explain'</em> required more than simply stating that '<em>I put the coordinates into my GDC and it did not work</em>'. A written statement, showing the substitution of one or both of the coordinates leading to an inequality was required for this first mark. It was pleasing to see that many scripts showed correct methodology for calculating the gradient of <em>L</em> and the gradient of a line perpendicular to <em>L</em>. The correct equation of the line perpendicular to <em>L</em> passing through P proved to be more elusive as poor arithmetic spoilt what could have been excellent work. In particular \( - 5 = \frac{3}{2} \times 6 + c\) leading to \(c = ( \pm )4\) proved to be a popular but erroneous calculation.</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;">In part (a), the word <em>'explain'</em> required more than simply stating that '<em>I put the coordinates into my GDC and it did not work</em>'. A written statement, showing the substitution of one or both of the coordinates leading to an inequality was required for this first mark. It was pleasing to see that many scripts showed correct methodology for calculating the gradient of <em>L</em> and the gradient of a line perpendicular to <em>L</em>. The correct equation of the line perpendicular to <em>L</em> passing through P proved to be more elusive as poor arithmetic spoilt what could have been excellent work. In particular \( - 5 = \frac{3}{2} \times 6 + c\) leading to \(c = ( \pm )4\) proved to be a popular but erroneous calculation.</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;">In part (a), the word <em>'explain'</em> required more than simply stating that '<em>I put the coordinates into my GDC and it did not work</em>'. A written statement, showing the substitution of one or both of the coordinates leading to an inequality was required for this first mark. It was pleasing to see that many scripts showed correct methodology for calculating the gradient of <em>L</em> and the gradient of a line perpendicular to <em>L</em>. The correct equation of the line perpendicular to <em>L</em> passing through P proved to be more elusive as poor arithmetic spoilt what could have been excellent work. In particular \( - 5 = \frac{3}{2} \times 6 + c\) leading to \(c = ( \pm )4\) proved to be a popular but erroneous calculation.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A lampshade, in the shape of a cone, has a wireframe consisting of a circular ring and four straight pieces of equal length, attached to the ring at points A, B, C and D.</p>
<p>The ring has its centre at point O and its radius is 20 centimetres. The straight pieces meet at point V, which is vertically above O, and the angle they make with the base of the lampshade is 60°.</p>
<p>This information is shown in the following diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_17.16.13.png" alt="M17/5/MATSD/SP1/ENG/TZ2/03"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the length of one of the straight pieces in the wireframe.</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>Find the total length of wire needed to construct this wireframe. Give your answer in centimetres correct to the nearest millimetre.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(\cos 60^\circ = \frac{{20}}{b}\)\(\,\,\,\)<strong>OR</strong>\(\,\,\,\)\(b = \frac{{20}}{{\cos 60^\circ }}\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution into a correct trig. ratio.</p>
<p>\((b = ){\text{ 40 (cm)}}\) <strong><em>(A1)</em></strong> <strong><em>(C2)</em></strong></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>\(4 \times 40 + 2\pi (20)\) <strong><em>(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution in the circumference of the circle formula, <strong><em>(M1) </em></strong>for adding 4 times their answer to part (a) to their circumference of the circle.</p>
<p> </p>
<p>285.6637… <strong><em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (a). This <strong><em>(A1) </em></strong>may be implied by a correct rounded answer.</p>
<p> </p>
<p>285.7 (cm) <strong><em>(A1)</em>(ft)</strong> <strong><em>(C4)</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Award <strong><em>(A1)</em>(ft) </strong>for rounding their answer (consistent with their method) to the nearest millimetre, irrespective of unrounded answer seen.</p>
<p>The final <strong><em>(A1)(</em>ft) </strong>is not dependent on any of the previous <strong><em>M </em></strong>marks. It is for rounding their unrounded answer correctly.</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</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>
<br><hr><br><div class="specification">
<p class="p1">A building company has many rectangular construction sites, of varying widths, along a road.</p>
<p class="p1">The area, \(A\), of each site is given by the function</p>
<p class="p1">\[A(x) = x(200 - x)\]</p>
<p class="p1">where \(x\) is the <strong>width </strong>of the site in metres and \(20 \leqslant x \leqslant 180\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Site <span class="s1">S </span>has a width of \(20\)<span class="s1"> m</span>. Write down the area of <span class="s1">S</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 class="p1">Site <span class="s1">T </span>has the same area as site <span class="s1">S</span>, but a different width. Find the width of <span class="s1">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 class="p1">When the width of the construction site is \(b\) metres, the site has a maximum area.</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>Write down the value of \(b\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Write down the maximum area.</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 range of \(A(x)\) is \(m \leqslant A(x) \leqslant n\).</p>
<p class="p1">Hence write down the value of \(m\) and of \(n\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(3600{\text{ (}}{{\text{m}}^2})\) <span class="Apple-converted-space"> </span><strong><em>(A1)(C1)</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(x(200 - x) = 3600\) <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 setting up an equation, equating to their \(3600\).</p>
<p class="p2"> </p>
<p class="p1">\(180{\text{ (m)}}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C2)</em></strong></p>
<p class="p1"><strong>Note: </strong>Follow through from their answer to part (a).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>\(100{\text{ (m)}}\) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C1)</em></strong></p>
<p class="p1"> </p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\(10\,000{\text{ (}}{{\text{m}}^2})\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(C1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Follow through from their answer to part (c)(i).</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(m = 3600\;\;\;\)<strong>and</strong>\(\;\;\;n = 10\,000\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C1)</em></strong></p>
<p class="p1"><strong>Notes:<span class="Apple-converted-space"> </span></strong>Follow through from part (a) and part (c)(ii), but only if their \(m\) is less than their \(n\). Accept the answer \(3600 \leqslant A \leqslant 10\,000\).</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"><span class="s1">The distance \(d\) </span>from a point \({\text{P}}(x,{\text{ }}y)\) to the point \({\text{A}}(1,{\text{ }} - 2)\) <span class="s1">is given by \(d = \sqrt {{{(x - 1)}^2} + {{(y + 2)}^2}} \)</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the distance from \({\text{P}}(100,{\text{ }}200)\) to \({\text{A}}\)<span class="s1">. Give your answer correct to two decimal places.</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 class="p1">Write down your answer to <strong>part (a) </strong>correct to three significant figures.</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">Write down your answer to <strong>part (b) </strong>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">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\sqrt {{{(100 - 1)}^2} + {{(200 + 2)}^2}} \) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">\(\sqrt {50605} \;\;\;( = 224.955 \ldots )\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(M1)(A1) </em></strong>if \(\sqrt {50605} \) seen.</p>
<p class="p2"> </p>
<p class="p1">\({\text{224.96}}\) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C3)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for their answer given correct to <span class="s1">2 </span>decimal places.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="s1">\(225\) <span class="Apple-converted-space"> </span></span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Follow through from their part (a).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(2.25 \times {10^2}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C2)</em></strong></p>
<p class="p1"><strong>Notes: </strong>Award <strong><em>(A1)(A0) </em></strong>for \(2.25\) and an incorrect index value.</p>
<p class="p1">Award <strong><em>(A0)(A0) </em></strong>for answers such as \(22.5 \times {10^1}\).</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;">The diagram shows the points M(<em>a</em>, 18) and B(24, 10) . The straight line BM intersects the <em>y</em>-axis at A(0, 26). M is the midpoint of the line segment AB.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><br><img src="images/Schermafbeelding_2014-09-20_om_13.24.23.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of \(a\).</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 gradient of the line AB.</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>Decide whether triangle OAM is a right-angled triangle. Justify your answer.</span></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><span>12 <strong><em>(A1) (C1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for \(\left( {12,18} \right)\).</span></p>
<p> </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>\(\frac{{26 - 10}}{{0 - 24}}\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Accept \(\frac{{26 - 18}}{{0 - 12}}\) or \(\frac{{18 - 10}}{{12 - 24}}\) (or equivalent).</span></p>
<p> </p>
<p><span>\( = - \frac{2}{3}{\text{ }}\left( { - \frac{{16}}{{24}},{\text{ }} - 0.666666 \ldots } \right)\) <strong><em>(A1) (C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>If either of the alternative fractions is used, follow through from their answer to part (a).</span></p>
<p><span> The answer is now <strong>(<em>A1</em>)(ft)</strong>.</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>gradient of \({\text{OM}} = \frac{3}{2}\) <strong><em>(A1)</em>(ft)</strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Follow through from their answer to part (b).</span></p>
<p> </p>
<p><span>\( - \frac{2}{3} \times \frac{3}{2}\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for multiplying their gradients.</span></p>
<p> </p>
<p><span>Since the product is \(-1\), OAM is a right-angled triangle <strong><em>(R1)</em>(ft)</strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award the final <strong><em>(R1) </em></strong>only if their conclusion is consistent with their answer for the product of the gradients.</span></p>
<p><span> The statement that OAM is a right-angled triangle without justification is awarded no marks.</span></p>
<p> </p>
<p><span><strong>OR</strong></span></p>
<p><span>\({(26 - 18)^2} + {12^2}\) and \({12^2} + {18^2}\) <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span>\(\left( {{{(26 - 18)}^2} + {{12}^2}} \right) + ({12^2} + {18^2}) = {26^2}\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>This method can also be applied to triangle OMB.</span></p>
<p><span> Follow through from (a).</span></p>
<p> </p>
<p><span>Hence a right angled triangle <strong><em>(R1)</em>(ft)</strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award the final <strong><em>(R1) </em></strong>only if their conclusion is consistent with their <strong><em>(M1) </em></strong>mark.</span></p>
<p> </p>
<p><span><strong>OR</strong></span></p>
<p><span>\(OA = OB = 26\) (cm) an isosceles triangle <strong><em>(A1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for \(OA = 26\) (cm) and \(OB = 26\) (cm).</span></p>
<p> </p>
<p><span>Line drawn from vertex to midpoint of base is perpendicular to the base <strong><em>(M1)</em></strong></span></p>
<p><span>Conclusion <strong><em>(R1) (C3)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award, at most <strong><em>(A1)(M0)(R0) </em></strong>for stating that OAB is an isosceles triangle without any calculations.</span></p>
<p> </p>
<p><span><strong><em>[3 marks]</em></strong></span></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>The equation of line \({L_1}\) is \(y = - \frac{2}{3}x - 2\).</p>
</div>
<div class="specification">
<p>Point P lies on \({L_1}\) and has \(x\)-coordinate \( - 6\).</p>
</div>
<div class="specification">
<p>The line \({L_2}\) is perpendicular to \({L_1}\) and intersects \({L_1}\) when \(x = - 6\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the gradient of \({L_1}\).</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 \(y\)-coordinate of P.</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>Determine the equation of \({L_2}\). Give your answer in the form \(ax + by + d = 0\), where \(a\), \(b\) and \(d\) are integers.</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>\( - \frac{2}{3}\) <strong><em>(A1)</em></strong> <strong><em>(C1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(y = - \frac{2}{3}( - 6) - 2\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correctly substituting \( - 6\) into the formula for \({L_1}\).</p>
<p> </p>
<p>\((y = ){\text{ }}2\) <strong><em>(A1)</em></strong> <strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A0)(A1) </em></strong>for \(( - 6,{\text{ }}2)\) with or without working.</p>
<p> </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>gradient of \({L_2}\) is \(\frac{3}{2}\) <strong><em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from part (a).</p>
<p> </p>
<p>\(2 = \frac{3}{2}( - 6) + c\)\(\,\,\,\)<strong>OR</strong>\(\,\,\,\)\(y - 2 = \frac{3}{2}\left( {x - ( - 6)} \right)\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for substituting their part (b), their gradient and \( - 6\) into equation of a straight line.</p>
<p> </p>
<p>\(3x - 2y + 22 = 0\) <strong><em>(A1)</em>(ft)</strong> <strong><em>(C3)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from parts (a) and (b). Accept any integer multiple.</p>
<p>Award <strong><em>(A1)(M1)(A0)</em></strong> for \(y = \frac{3}{2}x + 11\).</p>
<p> </p>
<p><strong><em>[3 marks]</em></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 child’s wooden toy consists of a hemisphere, of radius 9 cm , attached to a cone with the same base radius. O is the centre of the base of the cone and V is vertically above O.</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 OVB is \({27.9^ \circ }\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">Diagram not to scale.</span></em></strong></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><br><img src="images/Schermafbeelding_2014-09-20_om_08.21.27.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate OV, the height of the cone.</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>Calculate the volume of wood used to make the toy.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\tan 27.9^\circ = \frac{9}{{{\text{OV}}}}\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution in trig formula.</span></p>
<p> </p>
<p><span>\({\text{OV}} = 17.0\left( {{\text{cm}}} \right)\left( {16.9980 \ldots } \right)\) <strong><em>(A1) (C2)</em></strong></span></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>\(\frac{{\pi {{(9)}^2}(16.9980 \ldots )}}{3} + \frac{1}{2} \times \frac{{4\pi {{(9)}^3}}}{3}\) <strong><em>(M1)(M1)(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correctly substituted volume of the cone, <strong><em>(M1) </em></strong>for correctly substituted volume of a sphere divided by two (hemisphere), <strong><em>(M1) </em></strong>for adding the correctly substituted volume of the cone to <em>either </em>a correctly substituted sphere <em>or </em>hemisphere.</span></p>
<p> </p>
<p><span>\( = 2970{\text{ c}}{{\text{m}}^3}{\text{ (2968.63}} \ldots {\text{)}}\) <strong><em>(A1)</em>(ft) <em>(C4)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>The answer is \(2970{\text{ c}}{{\text{m}}^3}\), the units are required.</span></p>
<p> </p>
<p><span><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">b.</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>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A shipping container is a cuboid with dimensions \({\text{16 m}}\), \({\text{1}}\frac{{\text{3}}}{{\text{4}}}{\text{ m}}\) and \({\text{2}}\frac{{\text{2}}}{{\text{3}}}{\text{ m}}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the <strong>exact</strong> volume of the container. Give your answer as a fraction.</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>Jim estimates the dimensions of the container as 15 m, 2 m and 3 m and uses these to estimate the volume of the container.</span></p>
<p><span>Calculate the percentage error in Jim’s estimated volume of the container.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(V = 16 \times 1\frac{3}{4} \times 2\frac{2}{3}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in volume formula. Accept decimal substitution of \(2.66\) or better.</span></p>
<p><span> </span></p>
<p><span>\( = 74.6666{\text{ }} \ldots \) <em><strong>(A1)</strong></em></span><br><span>\( = {\text{74}}\frac{{\text{2}}}{{\text{3}}}{\text{ }}{{\text{m}}^{\text{3}}}{\text{ }}\left( {\frac{{{\text{224}}}}{{\text{3}}}{\text{ }}{{\text{m}}^{\text{3}}}} \right)\) <em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><span><strong>Note:</strong> Correct answer only.</span></p>
<p><span> </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><span>\({\text{% error}} = \frac{{\left( {90 - 74\frac{2}{3}} \right) \times 100}}{{74\frac{2}{3}}}\) <em><strong>(A1)(M1)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(90\) seen, or inferred in numerator, <em><strong>(M1)</strong></em> for correct substitution into percentage error formula.</span></p>
<p><span> </span></p>
<p><span>\( = 20.5\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span><strong>Note:</strong> Accept \( - 20.5\).</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">b.</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 well answered by the majority of candidates. Candidates encountered difficulty in part (a) with using fractions finding the exact volume. Nearly all candidates could use the formula for volume and most could achieve at least 2 marks in this first part. Most candidates could find the percentage error correctly using the formula once they found the estimate for the volume. Very few candidates substituted the formula incorrectly, or had an incorrect denominator.</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 well answered by the majority of candidates. Candidates encountered difficulty in part (a) with using fractions finding the exact volume. Nearly all candidates could use the formula for volume and most could achieve at least 2 marks in this first part. Most candidates could find the percentage error correctly using the formula once they found the estimate for the volume. Very few candidates substituted the formula incorrectly, or had an incorrect denominator.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A race track is made up of a rectangular shape \(750{\text{ m}}\) by \(500{\text{ m}}\) with semi-circles at each end as shown in the diagram.</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;">Michael drives around the track once at an average speed of \(140{\text{ km}}{{\text{h}}^{ - 1}}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the distance that Michael travels.</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><span>Calculate how long Michael takes in</span> <span><strong>seconds</strong>.</span></span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><em>Unit penalty <strong>(UP)</strong> may apply in this question.</em></span></p>
<p><span>\({\text{Distance}} = \pi \times 500 + 2 \times 750\) <em><strong>(M1)</strong></em></span></p>
<p><span><em><strong>(UP)</strong></em> \( = 3070{\text{ m}}\) <em><strong>(A1) (C2)</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> may apply in this question.</em></span></p>
<p><span>\({\text{140 km}}{{\text{h}}^{ - 1}} = \frac{{140 \times 1000}}{{60 \times 60}}{\text{ m}}{{\text{s}}^{ - 1}}\) <em><strong>(M1)</strong></em><br></span></p>
<p><span>\( = 38.9{\text{ m}}{{\text{s}}^{ - 1}}\) <em><strong>(A1)</strong></em><br></span></p>
<p><span>\({\text{Time}} = \frac{{3070}}{{38.889}}\) <em><strong>(M1)</strong></em><br></span></p>
<p><span><em><strong>(UP)</strong></em> \( = 78.9{\text{ seconds}}\) <em>(accept</em> \(79.0\)<em> seconds) </em> <strong><em>(A1)</em>(ft) <em> (C4)</em></strong><em><br></em></span></p>
<p><span><strong><em>[4 marks]<br></em></strong></span></p>
<div class="question_part_label">b.</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;">Candidates generally answered part (a) well. A usual mistake was taking \(500\) as the radius. Some candidates worked out the area rather than the circumference. A good number of candidates correctly answered part (b). Others seemed to get lost in the conversion with multiplication by \(3600\) and not multiplying by \(1000\) being common errors. Again follow through marks could be awarded from the candidate’s answer to part (a) provided working was shown.</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;">Candidates generally answered part (a) well. A usual mistake was taking \(500\) as the radius. Some candidates worked out the area rather than the circumference. A good number of candidates correctly answered part (b). Others seemed to get lost in the conversion with multiplication by \(3600\) and not multiplying by \(1000\) being common errors. Again follow through marks could be awarded from the candidate’s answer to part (a) provided working was shown.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagram shows the straight lines \({L_1}\) and \({L_2}\) . The equation of \({L_2}\) is \(y = x\) .</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</span><br><span>(i) the gradient of \({L_1}\) ;</span><br><span>(ii) the equation of \({L_1}\) .</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 shaded triangle.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(\frac{{0 - 2}}{{6 - 0}}\) <em><strong>(M1)</strong></em></span><br><span>\( = - \frac{1}{3}{\text{ }}\left( { - \frac{2}{6}{\text{, }} - 0.333} \right)\) <em><strong>(A1) (C2)</strong></em></span></p>
<p><br><span>(ii) \(y = - \frac{1}{3}x + 2\) <em><strong>(A1)</strong></em><strong>(ft) </strong><em><strong> (C1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Follow through from their gradient in part (a)(i). Accept equivalent forms for the equation of a line.</span></p>
<p> </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><span>\({\text{area}} = \frac{{6 \times 1.5}}{2}\) <em><strong>(A1)(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(1.5\) seen, <em><strong>(M1)</strong></em> for use of triangle formula with \(6\) seen.</span></p>
<p> </p>
<p><span><span>\( = 4.5\) </span><span> <em><strong>(A1) (C3)</strong></em></span></span></p>
<p><span><span><em><strong>[2 marks]</strong></em></span></span></p>
<div class="question_part_label">b.</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;">In this question, many candidates did not use the \(x\) and \(y\) intercepts to find the slope and attempted to read ordered pairs from the graph.</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;">Part b proved difficult for many candidates, often using trigonometry rather than the more straight forward area of the triangle.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The diagram shows quadrilateral ABCD in which AB = 13 m , AD = 6 m and DC = 10 m. Angle ADC =120° and angle ABC = 40 °.</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 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>Calculate the size of angle ACB.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>AC<sup>2</sup> = 6<sup>2</sup> + 10<sup>2</sup> – 2×10×6×cos120° <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>AC = 14 (m) <em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><span><em><strong>[3 marks]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{14}}{{\sin 40}} = \frac{{13}}{{\operatorname{sinACB} }}\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution in sine formula, <em><strong>(A1)</strong></em> for correct substitutions.</span></p>
<p> </p>
<p><span>Angle ACB = 36.6° (36.6463...) <strong><em>(A1)</em>(ft)</strong> <em><strong>(C3)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their (a).</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</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;">In part (a), candidates seemed to be well drilled in the use of the cosine rule and AC = 14 m proved to be a popular, and correct, answer seen. The most popular incorrect answer seemed to be 11.7 m. This seems to have been arrived at by simple Pythagoras on triangle DCA – clearly, a totally incorrect method. Not as many candidates then went on to find the required angle in part (b). Some simply continued with using triangle DCA and found angle DCA. Indeed, some candidates even found angle DCB rather than the required angle ACB. In most cases, correct or otherwise, the sine rule was used and credit was awarded for this process.</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;">In part (a), candidates seemed to be well drilled in the use of the cosine rule and AC = 14 m proved to be a popular, and correct, answer seen. The most popular incorrect answer seemed to be 11.7 m. This seems to have been arrived at by simple Pythagoras on triangle DCA – clearly, a totally incorrect method. Not as many candidates then went on to find the required angle in part (b). Some simply continued with using triangle DCA and found angle DCA. Indeed, some candidates even found angle DCB rather than the required angle ACB. In most cases, correct or otherwise, the sine rule was used and credit was awarded for this process.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">In a television show there is a transparent box completely filled with identical cubes. Participants have to estimate the number of cubes in the box. The box is 50 cm wide, 100 cm long and 40 cm tall.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the volume of the box.</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>Joaquin estimates the volume of one cube to be 500 cm<sup>3</sup>. He uses this value to estimate the number of cubes in the box.</span></p>
<p><span>Find Joaquin’s estimated number of cubes in the box.</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 actual number of cubes in the box is 350.</span></p>
<p><span>Find the percentage error in Joaquin’s estimated number of cubes in the box.</span></p>
<div class="marks">[2]</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>\(50 \times 100 \times 40 = 200\,000{\text{ c}}{{\text{m}}^3}\) <em><strong>(M1)(A1) (C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in the volume 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>\(\frac{{200\,000}}{{500}} = 400\) <em><strong> (M1)(A1)</strong></em><strong>(ft) </strong><em><strong> (C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for dividing their answer to part (a) by 500.</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>\(\frac{{400 - 350}}{{350}} \times 100 = 14.3{\text{ }}\% \) <em><strong> (M1)(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span></p>
<p><span><br><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in the percentage error formula.</span></p>
<p><span>Award <em><strong>(A1)</strong></em> for answer, follow through from part (b).</span></p>
<p><span>Accept –14.3 %.</span></p>
<p><span>% sign not necessary.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 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;">This question proved to be the one that most candidates answered correctly. Many received full marks and the only error seen was incorrect substitution in the percentage error formula.</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 proved to be the one that most candidates answered correctly. Many received full marks and the only error seen was incorrect substitution in the percentage error formula.</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 proved to be the one that most candidates answered correctly. Many received full marks and the only error seen was incorrect substitution in the percentage error formula.</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;">The equation of a curve is given as \(y = 2x^{2} - 5x + 4\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\)</span><span>.</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 equation of the line <em>L</em> is \(6x + 2y = -1\).</span></p>
<p><span>Find the <em>x</em>-coordinate of the point on the curve \(y = 2x^2 - 5x + 4\) where the tangent is parallel to <em>L</em>.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 4x - 5\)</span><span> <em><strong>(A1)(A1) </strong> <strong>(C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for each correct term. Award <em><strong>(A1)(A0)</strong></em> if any other terms are given.<br></span></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>\(y = - 3x - \frac{1}{2}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for rearrangement of equation</span></p>
<p><br><span>gradient of line is –3 <em><strong>(A1)</strong></em></span></p>
<p><span>\(4x - 5 = -3\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for equating their gradient to their derivative from part (a).</span> <span>If \(4x - 5 = -3\) is seen with no working award <em><strong>(M1)(A1)(M1)</strong></em>.</span></p>
<p><span> </span></p>
<p><span>\(x = \frac{1}{2}\) </span><span> <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C4)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their part (a). If answer is given as (0.5, 2) with no</span> <span>working award the final <em><strong>(A1)</strong></em> only.</span></p>
<p><span><em><strong>[4 marks]</strong></em></span></p>
<div class="question_part_label">b.</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 derivative of the function was correctly found by most candidates. Rearranging the equation of the line to find the gradient was also successfully performed. Most candidates could not find the <em>x</em>-coordinate of the point on the curve whose tangent was parallel to a given line. To most candidates, part (b) appeared to be disconnected to part (a).</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 derivative of the function was correctly found by most candidates. Rearranging the equation of the line to find the gradient was also successfully performed. Most candidates could not find the <em>x</em>-coordinate of the point on the curve whose tangent was parallel to a given line. To most candidates, part (b) appeared to be disconnected to part (a).</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The volume of a sphere is \(V{\text{ = }}\sqrt {\frac{{{S^3}}}{{36\pi }}} \), where \(S\) is its surface area.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The surface area of a sphere is 500 cm<sup>2</sup> .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>Calculate the volume of the sphere. Give your answer correct to <strong>two decimal</strong></span> <span><strong>places</strong>.</span></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 your answer to (a) correct to the nearest integer.</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>Write down your answer to (b) in the form \(a \times {10^n}\), where \(1 \leqslant a < 10\) and \(n \in \mathbb{Z}\).</span></p>
<div class="marks">[2]</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>\(V{\text{ = }}\sqrt {\frac{{{500^3}}}{{36\pi }}} \) <em><strong>(M1)</strong></em></span><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong> </em>correct substitution into formula.</span></p>
<p><br><span><em>V</em> = 1051.305 … <em><strong>(A1)</strong></em></span><br><span><em>V</em> = 1051.31 cm<sup>3</sup> <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C3)</strong></em></span></p>
<p><span><span><strong>Note:</strong> Award last <strong><em>(A1)</em>(ft)</strong> for correct rounding to 2 decimal places of</span> <span>their answer. Unrounded answer must be seen so that the follow</span> <span>through can be awarded.</span></span></p>
<p><span><span> </span></span></p>
<p><em><strong><span><span>[3 marks]</span></span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>1051 <strong><em>(A1)</em>(ft)</strong></span></p>
<p><em><span><strong>[1 mark]</strong></span></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span> \(1.051 \times {10^3}\)</span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span><br><br><span><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for 1.051 (accept 1.05)<em><strong> (A1)</strong></em> for </span><span> \( \times {10^3}\).</span></span></p>
<p><span><span> </span></span></p>
<p><em><strong><span><span>[2 marks]</span></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;">This question was well answered by many of the candidates. A significant number of candidates lost two marks in part (a) for not using the calculator correctly and omitting brackets in the denominator when entering the volume expression in their GDC. Also, those students who did not show the unrounded answer in the working box could not be awarded the last mark in part a). Follow through marks were awarded for parts (b) and (c) which most candidates gained.</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 well answered by many of the candidates. A significant number of candidates lost two marks in part (a) for not using the calculator correctly and omitting brackets in the denominator when entering the volume expression in their GDC. Also, those students who did not show the unrounded answer in the working box could not be awarded the last mark in part (a). Follow through marks were awarded for parts (b) and (c) which most candidates gained.</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 well answered by many of the candidates. A significant number of candidates lost two marks in part (a) for not using the calculator correctly and omitting brackets in the denominator when entering the volume expression in their GDC. Also, those students who did not show the unrounded answer in the working box could not be awarded the last mark in part a). Follow through marks were awarded for parts (b) and (c) which most candidates gained.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The four points A(−6, −11) , B(−2, 7) , C(4, 9) and D(6, 3) define the vertices of a kite.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-02_om_19.53.36.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the distance between points \({\text{B}}\) and \({\text{D}}\).</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 distance between points \({\text{A}}\) and \({\text{C}}\) is \(\sqrt {500} \).</p>
<p class="p1">Calculate the area of the kite \({\text{ABCD}}\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\({\text{BD}} = \sqrt {\left( {{4^2} + {8^2}} \right)} \) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p2"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into the distance formula.</p>
<p class="p4"> </p>
<p class="p4">\( = 8.94\left( {8.94427 \ldots ,{\text{ }}\sqrt {80} ,{\text{ }}4\sqrt 5 } \right)\) <strong><em>(A1) (C2)</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Area \({\text{ABCD}} = 2 \times \left( {0.5 \times \frac{{{\text{their BD}}}}{2} \times \sqrt {500} } \right)\) <span class="Apple-converted-space"> </span><strong><em>(M1)(M1)(M1)</em></strong></p>
<p class="p2"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for dividing their BD by 2, <strong><em>(M1) </em></strong>for <strong>correct </strong>substitution into the area of triangle formula, <strong><em>(M1) </em></strong>for adding two triangles (or multiplied by 2).</p>
<p class="p1">Accept alternative methods:</p>
<p class="p1">Area of kite \( = 0.5 \times \sqrt {500} \times \) their part (a).</p>
<p class="p1">Award <strong><em>(M1) </em></strong>for stating kite formula.</p>
<p class="p1">Award <strong><em>(M1) </em></strong>for correctly substituting in \(\sqrt {500} \).</p>
<p class="p1">Award <strong><em>(M1) </em></strong>for correctly substituting in their part (a).</p>
<p class="p2"> </p>
<p class="p1">\( = 100\) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C4)</em></strong></p>
<p class="p2"><strong>Note: </strong>Accept 99.9522 if 3 sf answer is used from part (a).</p>
<div class="question_part_label">b.</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>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The diagram below represents a rectangular flag with dimensions 150 cm by 92 cm. The flag is divided into three regions A, B and C.</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>Write down the total area of the flag.</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>Write down the value of <em>y</em>.</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 areas of regions A, B, and C are equal.</span></p>
<p><span>Write down the area of region A.</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>Using your answers to <strong>parts (b) and (c)</strong>, find the value of <em>x</em>.</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><em><strong>Units are required in this question for full marks to be awarded.</strong></em><br></span></p>
<p><span>13800 cm<sup>2</sup> <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>75 <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><strong><em>Units are required in this question for full marks to be awarded.</em></strong><br></span></p>
<p><span>4600 cm<sup>2</sup> <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C1)</strong></em></span></p>
<p><span><br><strong>Notes:</strong> Units are required unless already penalized in part (a). Follow through from their part (a).<br></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(0.5(x + 92) \times 75 = 4600\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><strong><span>OR</span></strong></p>
<p><span>\(0.5 \times 150 \times (92 - x) = 4600\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution into area formula, <em><strong>(A1)</strong></em><strong>(ft)</strong> for their correct</span> <span>substitution.</span></p>
<p><br><span>(= 30.7 (cm)(30.6666...(cm)) </span><span><em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C3)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from their parts (b) and (c).</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><span style="font-family: times new roman,times; font-size: medium;">In the diagram, \({\text{AD}} = 4{\text{ m}}\), \({\text{AB}} = 9{\text{ m}}\), \({\text{BC}} = 10{\text{ m}}\), \({\text{B}}\hat {\text{D}}{\text{A}} = {90^ \circ }\) and \({\text{D}}\hat {\text{B}}{\text{C}} = {100^ \circ }\) .</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 \({\text{A}}\hat {\text{B}}{\text{C}}\).</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 AC.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\sin {\text{A}}\hat {\text{B}}{\text{D}} = \frac{4}{9}\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(100 + {\text{their }}({\text{A}}\hat {\text{B}}{\text{D}})\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(126\% \) <em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><span><strong>Notes:</strong> Accept an equivalent trigonometrical equation involving angle ABD for the first <strong><em>(M1)</em></strong>. </span></p>
<p><span>Radians used gives \(100\% \) . Award at most <em><strong>(M1)(M1)(A0)</strong></em> if working shown. </span></p>
<p><span>\({\text{BD}} = 8{\text{ m}}\) leading to \(127\% \) . Award at most <em><strong>(M1)(M1)(A0)</strong></em> (premature rounding).</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>\({\text{A}}{{\text{C}}^2} = {10^2} + {9^2} - 2 \times 10 \times 9 \times \cos (126.38 \ldots )\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for substituted cosine formula. Award <em><strong>(A1)</strong></em> for correct substitution using their answer to part (a).</span><br><br></p>
<p><span>\({\text{AC}} = 17.0{\text{ m}}\) <strong><em>(A1)</em>(ft)</strong> <em><strong>(C3)</strong></em></span></p>
<p><span><strong>Notes:</strong> Accept \(16.9{\text{ m}}\) for using \(126\). Follow through from their answer to part (a). Radians used gives \(5.08\). Award at most <strong><em>(M1)(A1)(A0)</em>(ft)</strong> if working shown.</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</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;">Although many candidates were able to calculate the size of angle ABD correctly, a significant number then simply stopped, failing to add on \(100\% \) and consequently losing the last two marks in part (a). Recovery was seen on many scripts in part (b) as candidates seemed to be well drilled in the use of the cosine rule and much correct working was seen. Indeed, despite many incorrect final answers of \(26.4\% \) seen in part (a), many used the correct angle of \(126\% \) in part (b).</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;">Although many candidates were able to calculate the size of angle ABD correctly, a significant number then simply stopped, failing to add on \(100\% \) and consequently losing the last two marks in part (a). Recovery was seen on many scripts in part (b) as candidates seemed to be well drilled in the use of the cosine rule and much correct working was seen. Indeed, despite many incorrect final answers of \(26.4\% \) seen in part (a), many used the correct angle of \(126\% \) in part (b).</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The diagram shows a right triangular prism, ABCDEF, in which the face ABCD is a square.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">AF = 8 cm, BF = 9.5 cm, and angle BAF is 90°.</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 length 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>M is the midpoint of EF .</span></p>
<p><span>Calculate the length of BM .</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>M is the midpoint of EF .</span></span></p>
<p><span>Find the size of the angle between BM and the face ADEF .</span></p>
<div class="marks">[2]</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>9.5<sup>2</sup> = 8<sup>2</sup> + AB<sup>2</sup> <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into Pythagoras’ theorem.</span></p>
<p> </p>
<p><span>AB = 5.12 (cm) (5.12347…) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></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>\({\text{BM = }}\sqrt {{{9.5}^2} + {{\left( {\frac{{5.12347...}}{2}} \right)}^2}} \) <em><strong>(M1)</strong></em> </span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into Pythagoras’ theorem.</span></p>
<p><span> </span></p>
<p><span>= 9.84 (cm) (9.83933…) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Accept alternative methods. Follow through from their answer to part<em><strong><br></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>sin \({\text{A}}\hat {\rm M}{\text{B = }}\frac{{5.12347...}}{{9.83933...}}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for a correctly substituted trigonometrical equation using \({\text{A}}\hat {\rm M}{\text{B}}\) .</span></p>
<p><br><span>= 31.4 (31.3801...) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> If radians used, the answer will be 0.5476… award <em><strong>(M1)(A0)</strong></em><strong>(ft)</strong>. Degree symbol ° not required. Follow through from their answers to part (a) and to part (b).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></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-size: medium; font-family: times new roman,times;">This seemed to be a good discriminatory question enabling the majority of candidates to at least score well on part (a). Challenges arose for candidates who were then required to see the problem in three dimensions for the remainder of the question. Indeed, a significant number of candidates correctly identified the required lengths for part (b) and, provided they used Pythagoras correctly, were able to pick up the marks in this part of the question. However, in part (c), invariably the wrong triangle was chosen with triangles BFM and BAF proving to be the most popular, but incorrect triangles, chosen.</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 seemed to be a good discriminatory question enabling the majority of candidates to at least score well on part (a). Challenges arose for candidates who were then required to see the problem in three dimensions for the remainder of the question. Indeed, a significant number of candidates correctly identified the required lengths for part (b) and, provided they used Pythagoras correctly, were able to pick up the marks in this part of the question. However, in part (c), invariably the wrong triangle was chosen with triangles BFM and BAF proving to be the most popular, but incorrect triangles, chosen.</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 seemed to be a good discriminatory question enabling the majority of candidates to at least score well on part (a). Challenges arose for candidates who were then required to see the problem in three dimensions for the remainder of the question. Indeed, a significant number of candidates correctly identified the required lengths for part (b) and, provided they used Pythagoras correctly, were able to pick up the marks in this part of the question. However, in part (c), invariably the wrong triangle was chosen with triangles BFM and BAF proving to be the most popular, but incorrect triangles, chosen.</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;">Tennis balls are sold in cylindrical tubes that contain four balls. The radius of each tennis ball is 3.15 cm and the radius of the tube is 3.2 cm. The length of the tube is 26 cm.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the volume of one tennis ball.</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>Calculate the volume of the empty space in the tube when four tennis balls have been placed in it.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><em><strong>Unit penalty (UP) applies</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span>\({\text{Volume of tennis ball}} = \frac{{4}}{{3}} \pi 3.15^3\) </span><em><strong><span>(M1)</span></strong></em></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into correct formula.</span></p>
<p><br><span><em><strong>(UP) </strong></em> Volume of tennis ball = 131 cm<sup>3</sup> <em><strong>(A1) </strong> <strong>(C2)</strong></em></span></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><em><strong>Unit penalty (UP) applies</strong></em></span></p>
<p><span> </span></p>
<p><span>\({\text{Volume of empty space}} = \pi 3.2^2 \times 26 - 4 \times 130.9\) <em><strong>(M1)(M1)(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into cylinder formula, <em><strong>(M1)</strong></em> 4 × their (a), </span><span><em><strong>(M1)</strong></em> for subtracting appropriate volumes.</span></p>
<p><br><span><em><strong>(UP)</strong></em> Volume of empty space = 313 cm<sup>3</sup> <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C4)</strong></em></span></p>
<p><span><strong>Note:</strong> Accept 312 cm<sup>3</sup> with use of 131.</span></p>
<p><em><strong><span> </span></strong></em></p>
<p><em><strong><span>[4 marks]</span></strong></em></p>
<div class="question_part_label">b.</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 poorly answered by many but perfectly well by many others, there being little in between. Volume seemed to be little understood and this part of the course is perhaps overlooked. A (candidate drawn) diagram helped visualise the situation and this, in general, is to be encouraged.</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 poorly answered by many but perfectly well by many others, there being little in between. Volume seemed to be little understood and this part of the course is perhaps overlooked. A (candidate drawn) diagram helped visualise the situation and this, in general, is to be encouraged. Many found (b) difficult due to it not being broken up into “one stage” parts in the question. Practice in multi-stage questions is recommended.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Consider the statement<em> p</em>:</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">“If a quadrilateral is a square then the four sides of the quadrilateral are equal”.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the inverse of statement <em>p</em> in words.</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>Write down the converse of statement <em>p</em> in words.</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>Determine whether the converse of statement <em>p</em> is always true. Give an example to justify your answer.</span></p>
<div class="marks">[2]</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>If a quadrilateral is not a square (then) the four sides of the quadrilateral are not equal. <em><strong>(A1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for “if…(then)”, <em><strong>(A1)</strong></em> for the correct phrases in the correct order.</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>If the four sides of the quadrilateral are equal (then) the quadrilateral is a square. <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for “if…(then)”, <em><strong>(A1)</strong></em><strong>(ft)</strong> for the correct phrases in the correct order.</span></p>
<p><span> </span></p>
<p><span><strong>Note:</strong> Follow through in (b) if the inverse and converse in (a) and (b) are correct and reversed.</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>The converse is not always true, for example a rhombus (diamond) is a quadrilateral with four equal sides, but it is not a square. <em><strong>(A1)(R1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Do not award <em><strong>(A1)(R0)</strong></em>.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 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-size: medium; font-family: times new roman,times;">There was confusion among some students about which was the inverse and converse of the given statement.</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;">There was confusion among some students about which was the inverse and converse of the given statement.</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;">There was confusion among some students about which was the inverse and converse of the given statement. Part (c) was poorly done with very few students able to provide an example that shows that the converse is not always true.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagram shows a pyramid \({\text{VABCD}}\) which has a square base of length \(10{\text{ cm}}\) and edges of length \(13{\text{ cm}}\). \({\text{M}}\) is the midpoint of the side \({\text{BC}}\).</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 length of \({\text{VM}}\).</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>Calculate the vertical height of the pyramid.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><em>Unit penalty<strong> (UP) </strong>applies in this question.</em></span></p>
<p><span><span>\({\text{VM}}^{2} = {13^2} - {5^2}\) </span> <span><em><strong>(M1)</strong></em></span></span></p>
<p><span><strong>UP</strong> \( = 12{\text{ cm}}\) <em><strong>(A1)</strong></em> <em><strong>(C2)</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> applies in this question.</em></span></p>
<p><span>\({h^2} = {12^2} - {5^2}\) <em>(or equivalent)</em> <em><strong>(M1)</strong></em></span></p>
<p><span><strong>UP</strong> \( = 10.9{\text{ cm}}\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">b.</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 poorly answered by many of the candidates. Pythagoras was improperly applied and candidates were unable to identify right angled triangles.</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 poorly answered by many of the candidates. Pythagoras was improperly applied and candidates were unable to identify right angled triangles.</span></p>
<div class="question_part_label">b.</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 average radius of the orbit of the Earth around the Sun is 150 million kilometres.</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_14.06.16_1.png" alt></span></p>
</div>
<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 average radius of the orbit of the Earth around the Sun is 150 million kilometres.</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_14.06.16.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down this radius, in kilometres, in the form \(a \times {10^k}\), where \(1 \leqslant a < 10,{\text{ }}k \in \mathbb{Z}\).</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 Earth travels around the Sun in one orbit. It takes one year for the Earth to complete one orbit.</span></p>
<p><span>Calculate the distance, in kilometres, the Earth travels around the Sun in one orbit, assuming that the orbit is a circle.</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>Today is Anna’s 17th birthday.</span></p>
<p><span>Calculate the total distance that Anna has travelled around the Sun, since she was born.</span></p>
<div class="marks">[2]</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>\(1.5 \times {10^8}{\text{ (km)}}\) <strong><em>(A2) (C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(A2) </em></strong>for the correct answer.</span></p>
<p><span> Award <strong><em>(A1)(A0) </em></strong>for 1.5 and an incorrect index.</span></p>
<p><span> Award <strong><em>(A0)(A0) </em></strong>for answers of the form \(15 \times {10^7}\).</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>\(2\pi 1.5 \times {10^8}\) <strong><em>(M1)</em></strong></span></p>
<p><span>\( = 942\,000\,000{\text{ (km) (942}}\,{\text{477}}\,{\text{796.1}} \ldots {\text{, }}3 \times {10^8}\pi ,{\text{ }}9.42 \times {10^8})\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into correct formula. Follow through from part (a).</span></p>
<p><span> Do not accept calculator notation \(9.42{\text{E}}8\).</span></p>
<p><span> Do not accept use of \(\frac{{22}}{7}\) or\( 3.14\) for \(\pi\).</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>\(17 \times 942\,000\,000\) <strong><em>(M1)</em></strong></span></p>
<p><span>\( = 1.60 \times {10^{10}}{\text{ (km) }}\left( {{\text{1.60221}} \ldots \times {{10}^{10}}{\text{, 1.6014}} \times {{10}^{10}},{\text{ 16}}\,{\text{022}}\,{\text{122}}\,{\text{530, }}(5.1 \times {{10}^9})\pi } \right)\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Follow through from part (b).</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></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="question" style="padding-left: 20px; padding-right: 20px;">
<p>When Bermuda \({\text{(B)}}\), Puerto Rico \({\text{(P)}}\), and Miami \({\text{(M)}}\) are joined on a map using straight lines, a triangle is formed. This triangle is known as the Bermuda triangle.</p>
<p>According to the map, the distance \({\text{MB}}\) is \(1650\,{\text{km}}\), the distance \({\text{MP}}\) is \(1500\,{\text{km}}\) and angle \({\text{BMP}}\) is \(57^\circ \).</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAdMAAAE/CAYAAAAdeClUAAAgAElEQVR4Ae2dCVgV5ffHv6CZEi6AKSoKKKDgjqIi/tMMNbTS1NzQpFJzqdxKKzU19WduqW1WUmFuaS64koqK5pJSJJqQgAGKgSVuEbnC/3kHBi5wL9wLd5/vPI8xd+Zdzvmc6Z77LueMTW5ubi54kAAJkAAJkAAJlJuAbblrsiIJkAAJkAAJkIBEgM6UDwIJkAAJkAAJVJAAnWkFAbI6CZAACZAACdCZ8hkgARIgARIggQoSoDOtIEBWJwESIAESIAE6Uz4DJEACJEACJFBBAnSmFQTI6iRAAiRAAiRAZ8pngARIgARIgAQqSIDOtIIAWZ0ESIAESIAE6Ez5DJAACZAACZBABQnQmVYQIKuTAAmQAAmQAJ0pnwESIAESIAESqCABOtMKAmR1EjA/AtcQNbMrPNzc1f/zGY0V244iMSvH/EQvU6IsxCzvLenVfnkMHojyGeEYI+n6BnZkSFfKbIUFihHISkTUtuWY+FE+02K3Cz/eRmLU91jx+ueIsUjUadgxyhcebr4YE55WqJYezuhM9QCRTZCAeRGojW7zjyDp7DcYameHlnN+QEJKMpLEvz9OYvM7dXFgykgMmLQBFyzSoZoXbcuXJgsxqydi1JSPcPxh6do8iPkKQ0Om4ZNj/5VeUIF3KytQZ6pMAsolYOsM3xEzseJhCoLmrMa6n5/GvG61LZuHcz98mdLPsnWg9BZPgCNTizchFSABayWQg6zEA1gxyj9vulpMTx9MwO3i6qqd5i1WV0wDi/rhMchQnd3OSsSh5aPRSpom7otZa6ORFr0c7cXntsvzpzLlqcHeWBq+DXOCmsPDrTmeD7sAqakibYipdX+MWR6OmIx7eZI+iMGKtuJ6b6yIiinaX/gFZOE2Eg9+jDE+okxz9Jm5obBucV3xABnhb+TxGLUJMTHhRfh8HJ2RJ1NBvfxpWZmh1H4YohJlikK3JzBoZbxU4+bKAWgm5IzJKmgh7ySv32b9P8JNceHGRxjk4Y6CqXYI3kexvYClOzyCZmJNVCKKt1S0YVEvCmtm9lVZkuiLWWFRJZYhcjJisEO1fel5KNZ+WbYo2nnhJzHNHTYTfaTnQFvZC6uLM45Mi/LgJxKwcgL3kBGzDd9u+hV2ge9geHtHs9U358+dmNZ3MvZn54uYHYlPXonUSt4SdUUtUX/Sb0jAJnzSrxFscy5hx1svYmpERn6bZ7Fx1hu4EuiGfDdYrK94fD5pav61Rmjh5qSmDXE7A4dWTsZPCcAPn/ZD/YJW4vFJyICCT8BZbJw0DQ9+dsSedVHIUzMbF9bNQAjq49j8bqihUrrEaeTbGKSKIzsSK1/4DzUOhGKkZ1UAt3EhbDpemPNDftuiBdH+XIxatwuvbfsKk3xLtFqOCznIurABU56fhUOyrUQr8esxL2Q7Nk8Mw6bJfrBX13LWLwh9YwI+iVeteBYb50xAzA2VelnR+OilkKLlpOfhNySs0GRP0WExW6gbPpZ4DmTZD+L4nFB8GNJcvezF9FHXdLEi/EgCJGC5BLJxbs7T8JJ/cbs1RZf+M7AxdSA++nAYmtqb61fANRz9bHmeI/UehdCfLiAp5QKOfT8d3e3KssYdXNy/Bfuz7dB04mackdaKj2BZkLP05Xo6+Zo0esu5eAhhkiNtheFhx6V15YSf5qPRlbMqzqdYX95TsPm3i0j6IwLTOziioA35esoFHF3RD0LE7J+Si46CAdgFzsMeUf+3zXjNW5Q6i++3VcXUfbFISvkVmyfmebfsPb8iqcwNPq0wdMUPkn4JJ5ajp8QlDsfPX5OEzknchrclR+qM7nN253M4jtCRrQDE4JMZaxGTVR99Q49i80RvqU6tiVvxe8peTPIt7voqw7nfR/h92xuoJUo6vIHNScn4ebIvKuckYuu0hZIjLdBP2CpsFJoK573yA4TGSOPZYjCBBwnHsE44UrsXEXr2IpJSLuLMtin59VZia+IdAHeQuGVlniNVfRak9jOw/92vcPR2js62yBMmB7ePfoVZERmFthEy7JuH7nYZOLR4M36+rTqVUUKFggvm+n9SgYA8IQESqAgBNRuQVryB7vgWozpNwJoL8nRfRfowQN2cTKSeE07BAd1fHYluzlUAVIGz30AM69+ojA6rwjNkneScvuqaiYPh27DmvdcLRqD3Mm8jG3dw8XgkzomWWj+P4CfqQ3wZ2jo/iSnTB0rOsGQndmg5uCfaiB8gtnawt7OFrWcItqckI+GbAPwZuRM7wt7H6Enhec747k3czlb9Im6EvsOfzvsBY++NJ3q6Sl3Y9R+M55uKMWgttOraJc9Zley85JXWz+PF55pKoybb+u3Rq7ODShlV/V7FWy/mj65s66Pb1MkYKhxvfASOJqiOCFWq63Cac/EkwmNFOwGYOn1g/g+0KnDu9ireGi5sFYN1R/7I23ldrF1bZ3d0kH55iOfxVazYthMHL3linvTjaV3+CPsa4o7FlXwWus3AHvFDKW4uutXQ1RayINlI+jVasld25Cz0adEEHm5N0KZX/ig7OwoHY67LhUv9y2neUvHwJglYGQGxAanfZHze3AEDeszFvGkd0Xl7CDzN7Wd1zr+4cUl8QddG3VpiylI+qqKG02PyBw1/NUw75peu4lQDdniAf27kfUnatXRD3QL9bWFXoxaE6y7pZmrnTe2q9pp1HmsmjcK8SHmqWOXmo7VQw66gYQCPwamGqi55ZfPkUamn7enjtVC9oPlaaNjcGSiQo1C/Wt1awb2gnBge14DTo0LBDMRdugn4SmNNbXstUS7nnxu4LK46tENLd1X9Cm118/wlXIMvxNyA6mFbvzfeW5cNpxkLsDE+Ep9Mkeet7dB0+AKsePs5eFb9C8m/3JCcqWrdEuc62UKufROXz6uxnXwb/+DqTTE6LvtQRVx2aZYgARKwCgK2dd3QQowIEpNxxRzDY2wfg0MjIeA1/JaSqbKp5g5uZ/5bug0Kph3FF/IsLPt4K479ca5gKjOvcmVUd8hbL84+l4KrBQPIHGTfvqlhzbS4MxTTjwvzHKl3MGatWIXNP10onAotXUoD3y3U72bUWSQX6Cec6G1k3hXdO8OnUcUcqWjFtroDGoqTG7/gXLKq4ym0Va3mjaB+z3gVOPsOw7yI80j6bT9CVyzHsg/fQHe7vLXjaVsSkVO5DtzbiVH3Xfx981+VZ0EVYXltURU1natLDeVNceeHkMmhZCkx+LKfi2pHGs/pTDWi4Q0SsF4COVk3kSnU83RHA3NcN7V1Refn20rjw3ObtuCotDP2HjKit2DDtkulGyYrHUmJYlxZA67tA/Hss76o89cp7NyfqlKvKpoEBKKluBK7HeuP/pm3jppxGB8u2qJmVKpSteA0C1eSpDEZ7Nzao8dzT8O3zjUc2xGVt+O1oJwpTlT1+wJLvj2ft6s2509ELVuOjQKPdxCe8BI/WCp22DbxR7/Wop3jWLZoS37s8j1kRH2BJeuErXwxvGtjNbtd7+HP8Ml5O6mDFiAqyxXd+vVD334D0Ker6hi2Nny6+BR7FsTsw7r8HdDDsSbxWjlt4QjfwG7StP7N1auxXlr2ELIvyNvZ6zMbUVwzrdgDwtokYJ0ExG7ecHz03iLsz26F4ZN7oolZ/qSuiiY9B+ZtqokPxahOTeEhNk+9sKjojlF1RrJvjPbSl3EG9k/qKm2+8ur0Bk6ivvSlmbdmCtg26Y4QaVPSWawLCcgvNxOXGrTSsGZavLMa8GrvK5XNjpiMJxq7w6NxAEaduI+mwreUWDMtXt+wn209+2GWtKEpA4fmPIM2YhOakG/NWcnBvbZgBHylH1Iqo1iNoTF5shaOQlVCY2w9MWD2WDQV7q5g3bEpuoSE4gLEJrC3MUrtVHIV1A8chpfFRqwCGwsZu+atb9v1REhPd9iiKjwHTszbsFVQTl7XtEPTkS+hV5M65bSFLWq0H4Spgc5A9g+Y16t13nMmye6M7tMGoX0N7f4H0a6UYW3O1kmABPRKID+dYKuXsDFb/W7eA84ipeAXeK9b3sYbvXavp8Zs6z+HxTu+xGvii04cdoF47autCM3feaqxG9tGeHb2R5gzXOxaFUcrDJ0XhjVfTUAn8YW/7TBixGjDthH6LvkWX04MzHOeUvvfYvn4DtKaaX7lUv5UQf3npiNsXrDkSCAcx/AF2Lz2E4wRm4F02LxSSicVuFULvpO/QUTY4kKGkoyzEXrgG0wqcHBV0eTpCZgoc0Y1QO12IfED5GnMmJLPC3aoi4e4A1vY+07ApgNrsERmKaQWU99h4ZrDYkQZez9M+j4coXNkhuKi4DgboTvmom99sXqdV+6Nb9ZimWr7wl4r1uKr2U/B2bYCtrBvjpErvi0qQ/6zoG1YjBDRJjc3NzdPWv6XBEiABJRD4EHMcnSSkhA4o6ccq4ibiFn+CgatjAECl+NYaL8Sm2aUQ4ia6kKAzlQXWixLAiRgPQSyorHihWKJAAq0U3WwBRd5QgIaCdCZakTDGyRAAtZOQKSo27VxFWatjCzcdCSmJ6ePxIBunlplvrF2RtRPOwJ0ptpxYikSsEgCn6/6HIMGD4Kjo/mmDbRIsBSaBIoR4AakYkD4kQSshYBwpEsXLUJmphQEYy1qUQ8SMEsCdKZmaRYKRQLlJ/Dff/9hwvjx2LzpO/h17IC48+fL3xhrkgAJaEWAzlQrTCxEApZBQDjSN6dORXxcHNauX48mHh7Iyir9JViWoRmlJAHzJkBnat72oXQkoDWBK1eu4OWQEKm8cKQNGjSAn58f4uPz3lWpdUMsSAIkoDMBOlOdkbECCZgfAeFIRwQHw9HJCUuXLZMcqZDyMXt7XExKMj+BKREJWBkBOlMrMyjVUR6B2NhYyZF2DgiQHGm1aiKDTd7h6uqK6FOn5Y/8SwIkYCACdKYGAstmScAYBE6ePIkBffth0OAhmL9gAVQdqejfxSXvjReJiYnGEId9kIBiCdCZKtb0VNzSCQhHOmLoMLw5fTrGjhurVh3ZuWZnl3w7p9oKvEgCJFAuAnSm5cLGSiRgWgIihlQ40rUbN2h0pLKEQ4KHISU5Wf7IvyRAAgYgQGdqAKhskgQMSUBOxiAcqb+/f5ld1axZEwkJCWWWYwESIIHyE6AzLT871iQBoxIQMaQzZ8yQkjFs3RGulSMVAnp5eeHWrVtGlZWdkYDSCNCZKs3i1NciCcjJGE4cPy4lY2jdurXWeri5u+O79Ru0Ls+CJEACuhOgM9WdGWuQgFEJiBhSkdXoemam5EhFMgZdDjs7O6m4cMg8SIAEDEOAztQwXNkqCeiFgJyMQTT2dVhYQTIGXRr39PSUiqelpelSjWVJgAR0IEBnqgMsFiUBYxIQsaEiq5G3j0+JZAy6ytHIzRWpqam6VmN5EiABLQnQmWoJisVIwJgERAxpUI+eUjKGTz/7rEQyBl1lEdmR/mXCe12xsTwJaE2AzlRrVCxIAsYhoE0yBl0l8fb2RnR0tK7VWJ4ESEBLAnSmWoJiMRIwBoH169ZJyRiWrVheZjIGXeSxt7fHjRs3dKnCsiRAAjoQsMnNzc3VoTyLkgAJGIiArskYdBFDrL+KaeOkFGZC0oUby5KAtgQ4MtWWFMuRgIEIiJCVJYsXS8kYtM1qpKsocniM2B3MgwRIQP8EKuu/SbZIAiSgLQE5GUN8XFy5Yki17UeOTWXCe22JsRwJ6EaAI1PdeLE0CeiNwPXr16VkDIZ2pLLAvXoHIe78efkj/5IACeiRAJ2pHmGyKRLQloCYbh3Yv79UfE9ERLmSMWjbl1zOwcEBWQyPkXHwLwnolQCdqV5xsjESKJuAnNVIH8kYyu6tsISfnx/i4+MLL/CMBEhAbwToTPWGkg2RQNkEpBjS4GApGcPSZcsqnIyh7B4LSzxmbw+RKJ8HCZCA/gnQmeqfKVskAbUE5GQMgwYPkWJIq1WrpracoS66urriUgpTChqKL9tVNgE6U2Xbn9obicCO8HApGcPc+fP0moxBF/FdXFyk4iLmlAcJkIB+CdCZ6pcnWyOBEgREMoapkyZDxJAGDx9e4r6xLsgj4WvXrhmrS/ZDAoohwDhTxZiaihqbgIghXRO2BksXLZIcqb+/v7FFKNHfkOBh+Ovq1RLXeYEESKBiBOhMK8aPtUlALQHVZAxHjh8zSuiLWkGKXXRxaYiEhIRiV/mRBEigogQ4zVtRgqxPAsUIqDrStevXm40jFWLWq+eMW7duFZOYH0mABCpKgM60ogRZnwRUCIgY0pdDQqQrW7ZtMytHKoRyc3fHd+s3qEjMUxIgAX0QoDPVB0W2QQIA5GQMjk5OEDGkjo6OZsdFTngvUhnyIAES0B8BOlP9sWRLCiYQGxuLEcHB6BwQIDlSeeesuSHx9PSURMrMzDQ30SgPCVg0ATpTizYfhTcHAiIZw4C+/aSsRvMXLDBqVqPy6O/XsQNSU5m8oTzsWIcENBGgM9VEhtdJQAsCkZGRUjKGN6dPN1kyBi3ELFKkiYcH/mXC+yJM+IEEKkqAzrSiBFlfsQREMoaxo0ZLMaRjx421GA7e3t6Ijo62GHkpKAlYAgE6U0uwEmU0OwLCkZpTMgZdANnb2+NiUpIuVViWBEigDAJM2lAGIN4mAVUCqjGkEQf2Q97Qo1rG3M99mjdH9KnT5i4m5SMBiyLAkalFmYvCmpKAqiMVyRgs0ZEKfk5OThJGEcrDgwRIQD8E6Ez1w5GtWDkB4XjenDpV0tLcshrpil6Of83Ozta1KsuTAAloIEBnqgEML5OATEBOxiA+i2QMDRo0kG9Z7N9evYMQd/68xcpPwUnA3AjQmZqbRSiPWREQ7/4UyRi8fXzMOhmDrtAcHByQnp6hazWWJwES0ECAzlQDGF4mAZGMIahHTykZw6effWb2yRh0sZifnx/S0i7rUoVlSYAESiFAZ1oKHN5SLgHhSEcMHQZLSsagi7Xq1K2LE8eP61KFZUmABEohwNCYUuDwljIJyDGkn4euRmBgoFVCqF27Ni6lMKWgVRqXSpmEAEemJsHOTs2VgOxI127cYLWOVLB3cXGRTCDWhHmQAAlUnACdacUZsgUrICBiSJcsXozNm77D1h3h8Pf3twKtNKsg3mrTyM0V165d01yId0iABLQmwGlerVGxoLUSKJ6MwRpCX7SxlXhd3F9Xr2pTlGVIgATKIMCRaRmAeNu6CYiXZItkDPFxcbD0ZAy6WsrFpSESEhJ0rcbyJEACagjQmaqBwkvKICCSMQzs319Sdk9EhFUkY9DFcvXqOSMlJUWXKixLAiSggQCdqQYwvGzdBOSsRtaWjEEXq7m5u2Pf3ghdqrAsCZCABgJ0phrA8LL1EhAxpF0DukjJGER6QLEZR4mHCI8Rh5jq5kECJFAxAnSmFePH2hZGoHgyBqU6UmE2eaNVZmamhVmR4pKA+RGgMzU/m1AiAxHYER4uZTVatmI5xo4ba6BeLKtZv44dkJrK5A2WZTVKa44EGBpjjlahTHonoJqMwdpjSHWB18TDA1czmPBeF2YsSwLqCNCZqqPCa1ZDQMSQrglbg6WLFkFkNaIjLWpab29vxMfHF73ITyRAAjoToDPVGRkrWAoB1WQMR44fK1gjtBT5jSFnXWdn7N61yxhdsQ8SsGoCXDO1avMqVzlVR6q0ZAy6WN3V1RXRp07rUoVlSYAE1BCgM1UDhZcsm4CIIe0TFCQpsWXbNo5ISzGnk5OTdFcw40ECJFB+AnSm5WfHmmZIoHgyBkdHRzOU0nxEkvkw4b352ISSWCYBOlPLtBulVkNAiiENDkZQ795QcjIGNWhKvdSrdxBSkpNLLcObJEACpROgMy2dD+9aCAE5GcOgwUPw1rRpis1qVB5zubm5IT2d4THlYcc6JCAToDOVSfCvxRKIjIyUkjHMnT+PyRjKYUUvLy+kpV0uR01WIQESkAkwNEYmwb8WSYDJGCputjp16+LE8eMVb4gtkICCCXBkqmDjW7rqdKT6saBIeH8pJRUinIgHCZBA+QhwZFo+bqxlQgKqMaQRB/bD09PThNJYftcyv7S0NLK0fHNSAxMR4MjURODZbfkIqDpSkYxBdgTla421ZAKN3FzB8BiZBv+SgO4E6Ex1Z8YaJiIgYkhfDgmRemdWI/0aoXNAAP66elW/jbI1ElAQATpTBRnbklWVkzE4OjlJMaTyuzgtWSdzkt3FpSGio6PNSSTKQgIWRYDO1KLMZe7C5uDOzb+QcS0LD/QoamJiIkYEB0OMnpiMQY9gVZqqV88ZN27cULnCUxIgAV0I0JnqQotlSyFwF+mHF+OFdh3RpX13BC8+jPQHuaWU1+6WSMYQ1KMnRDKG+QsWMBmDdth0LuXTvDn27Y3QuR4rkAAJ5BGgM+WToBcCuekReH/ar2jz9vuY/oIzznz2BsYsPFQhhypnNXpz+nQmY9CLlTQ3YmdnJ928fv265kK8QwIkoJEAQ2M0ouEN7Qnk4t6lZPw3YQ7eC/HGIw+6w7PG63j1qzmY26gOlr7YEvY22rcmSsoxpJ+HrkZgYKBulVlaZwLyGnRmZibk5Pc6N8IKJKBgAhyZKtj4FVU9N+sCdi4ehz5P9MXoxT+jTauGeEQ0WrkBur2zAisGVUHk7PF4a0sS7uvQmexI127cQEeqA7eKFvXr2AFx589XtBnWJwFFEqAzVaTZ9aH0bZxbMwfTd/+JqriIE7+cxcE9pwqndSs3wtPvrcB7vYADb0/BjC/DsHLlfqSXsowqYkhnzpiBzZu+w9Yd4fD399eHoGxDSwJNPDyQlZWlZWkWIwESUCVAZ6pKg+daEMjFg6vJSL15EceO+GHNnm3Yemg/Ql/xRIKY1l3/G7LyHaaNfUuMmD8LAx1/R9QvNnjyxSdRT8N0r5yMQeSIFTGkrVu31kIWFtEnAT8/P8THx+uzSbZFAoohQGeqGFPrSdHcy9gzezheWrgVfwU9jXbVK+VP636ET0ZUl6Z139wYjztSd7l4+CAXTr0XYs2y4WjlIE0ClxBEbHp5c+pUXM/MlBypvH5XoiAvGJTAY/b2uJiUZNA+2DgJWCsBOlNrtaze9crFgwcP8N+v2/HJD3/i0qbNOJqcgevytG1lFwROXyRN60bOmoGl++NxOe4n/JLZCmNm9Ye3fSW1EolkDAP795fufR0WBjpStZiMctHV1RXRp04bpS92QgLWRoDO1NosWm59cnEn+QSOJKlbM7uL9KjVWLE/Bf9UeRKhcT8i9JUWuPLtbMz69lzRad2lH+L15okIGzMGC05XhVczZ9SsrH5uV85q5O3jw2QM5bab/io6OTlJjYkkGTxIgAR0I0Bnqhsv6y2dexn7Fk3CmImfICr9bqGeuf8gee8SjFlRBX2f9kCdFq3gaueislv3NczckVyQ8cimuje6P/0UBiz5AktHtoWDBkcqYki7BnSRkjEwq1EhblOeySEx2dnZphSDfZOARRKgM7VIs+lb6FzcTzyKH/6uh3q/f4FXX/0SMf88lDrJvRqPn8+l4G9/bzRSfVoKduvmYPfUqfjg8BU8yP0PmemX8J/fNCx4wUdjbGnxZAzVqlXTt0Jsr5wEhgQPQ0pycjlrsxoJKJeA6tejcikoXvMcZNu2w7vrN2Fj6KvwOr8SY9/ciLish7Bx7oDne7SAo301FM/wIe3W/WARXm2WiLBRwzB09BIcuNEAfn71S5SVEa9ftw4jhg7DshXLmdVIhmJGf2vWrIn09AwzkoiikIBlEKAztQw7GVjKSqjp4Y2GVauiXrdxWCSCQ/e9j9cWHUT6gwe4dukKXBo4Qt0WIhsHf0x4dzBqeHXB4KkTMdinJtSvkOZlNZo9cxZEMoa+/foZWCc2Xx4CXl5eSEu7XJ6qrEMCiiZgk5ubK+/HVDQIKq9CIPcmzq56DS8sjoXXqA8x12sbxnzzAEHd2sCjsTtcG7mgQQNn1KlVFdkJP+HAyQw06j8Y3eo9qtJI4amIIf3k448RsXcvFixcyGQMhWjM7kyegk9K4VSv2RmHApk1ATpTszaPoYR7gKxrmch6UBn2tR1hr26T0IMriFoo8usmorqTE+o+noULv2cWE8gFgXM+wsLhbTRuNJKTMcTHxTGGtBg9c/wodvKKt/Sci4/jG3rM0UCUyWwJ0JmarWkMI1huVhy2vj8P35xLQ1J8Gh46dMDQiePxysAucCseC3o/CVtefwlv/2CLZ1Z8g/nd7HAt/U9cuRyDHYv2wGbsAswaqHmjER2pYWxo6FY93NwRcWA/PD09Dd0V2ycBqyHANVOrMaU2ioh8uh8huttS7Ig4gtiTm/B+j/+weU4Ieg2ehx0Jt1Fkzv8RDwxY+hne6yV27L6JFb8+hEuzZmjRtisGfvBpqTt2RQxpn6AgSag9ERFMxqCNecykTCM3V6SmppqJNBSDBCyDAJ2pZdhJP1I+TMOpHbfh4e6IyrBF1XodMOx/3+D7Ob1R8/waTB06ExsTiiZtsLFvgWFz5iCkYMfuUkT8XafUHbtMxqAfc5mqlc4BAfiXCe9NhZ/9WigBOlMLNVz5xH6A+9m/49CplMJXolV2QquR/0PY3N5wzNyFuZO/xKkbeTGmeX3YoHK97pii5Y5daQNLcDCCevdmVqPyGcnktby9vREdHW1yOSgACVgSATpTS7KWzrI+RFbqJWTKc7eVnOHpXw3Rn25A1N8PCluzqQmfF9/Dh6PaAuc/xzufnMANuY4olXsNZ87WxYdfv4eB3ppDX+SdoIMGD8Fb06ZxA0shYYs6s7e3x40bNyxKZgpLAqYmQGdqagsYrP+7SD+8BEO7v4vdSXnvcAGc0L5PL9T+eyNmLdlf+O5RIYNNXQRMmoVJHexwKWwNIlJUUgraPI7O40ZrDH0R1XeEh0vJGObOn8dkDAazqXEa9mneHPv2RhinM/ZCAlZCgM7USgxZRI3c20gMX4gxo75AQrNmqFdVvlsJDgFD8Ua3Wri2+T28E1aYpF6UsLFvg5fmvI52OO0b3TEAACAASURBVIVdJ9OKbkaSm1Dz9/NVn2PqpMlSMobg4cPVlOAlSyJgZ2cniSvWvnmQAAloR4DOVDtOFlTqAf6OXIzgSeuQ3u41fBH6Fno2LPCmwCMeeGH2dPRwuolj8ydjXsSlgiT1gA2qej+DUQNqIfHqLaiunGoCIBzp0kWLJEfq7++vqRivWxAB+TV4THhvQUajqCYnQGdqchPoW4BKeKxGTTzSfCK+/HqSmqlZGzzi3h9L1s5BoFMqto4Pxmthv+LGg/xFUhtHePu1QkOHx1DawyFiSCeMH4/Nm77DkePHmNVI32Y0cXu9egch7vx5E0vB7knAcgiU9n1pOVpQUhUCNrDz9kP3nEqofC8Vx7//FO9NGIRuTTzQPmg03lt9EMlZgL3PUCxdtxADvG8ics5wDJj8JQ6cTUb65RhEHKyNMb0aa3SmTMaggttKTx0cHJDF8BgrtS7VMgQBZkAyBFWjtvkQWWfDsftBDwzxrZHf81848NZQvBN5GTdv3C8mTSU49pqDsGVD4WNfCbl3/sSv+3cgfOdu7I1MgX2XoXh9xuvor2HXrlhHe3PKFDg6OeHdGTOYjKEYXWv5KDaUifCY+QsWWItK1IMEDEqg+Fu1DNoZG9c3gVzcTw7H7K018PYc2ZGKPhzRIqAF/vn+DrqMn4px/TqiWSNnPPbgbyTHRiJ0/oeYuNobOye3Q7Wq9eH73Djp3/tliMdkDGUAsqLbj9nb48Tx41akEVUhAcMS4DSvYfkatvXcDESt2o8mA/zxeJH3nlVG3bb9MW/TFoRO64+OXg1Qs2olVLZ3hmdAMBZ8MQNNtv+I+LuqwaSlixobG4sRwcEQ2XGWLlvGGNLScVn8XVdXV1xKYUpBizckFTAaATpTo6E2QEc3f8OBAw3R2uOxEo3bunbFoI711Lyk2waVG7ZHoPtlXC6S6ahEEwUXRDKGAX37QSRjENN+1apVK7jHE+sk4OLiIikm3iLDgwRIoGwCdKZlMzLbEg+Sf8MhPIZqVeRhqXi12lVkZIjXq5Uy6sy9g3/v1Ec9B3Wv+y6qrpzV6M3p05mMoSgaq/4k/2BieIxVm5nK6ZEAnakeYRq3qYf4J/Mv/Hs7DVfFCFO8f3TxSHRr3wldOnVEt8FzsTX+lprEC3eRfnAzwpt3hPejshNWL7mIIR0xdJgUQzp23Fj1hXjVagkMCR6GlGS+JNxqDUzF9EqAG5D0itOYjVVCdac6eOzhAZz74woa/Pw+Vt1+Am8veQoX923E15FrMH34ddzd+D8M87KXnO3xsNXYGHEYBy49gU/2dkL1UsRlMoZS4CjkVs2aNZGQkKAQbakmCVSMAJ1pxfiZtHYlh7rwRDzWrXwXvzUaiVULe8BRDDYHDsGwyJUYP/ZLzPuwO55c1Q91Lx/BpwvXIaHdS1iy/nUEPq7e9CKGdMH8+dJOzq07wtG6dWuT6sjOTUfAy8uLb48xHX72bGEEOM1r7gbLisaq9zYj8U7JNVAb1w54tlNNZJ9IgMMTLfIcqdDHxg4Ne0zBlx8PQ80DP+LMtYewdR+Cr3+JRtSGd/GcVw2om+CVkzGIkIi169fTkZr7s2Fg+dzc3fHd+g0G7oXNk4B1EKAzNWs7PsDfRzfjo2/nYcqSQ0Xf8iLktnVDj1eeRW38jR/CduJslmo23UdRL3AQXmycguR08QYYW1St5QD7yurcKCAlY5g6FdczMyVHKudnNWs8FM6gBOSE9+JHFg8SIIHSCdCZls7HtHdzUnDwwH08H+iMhK8mYewnP+OfIgPUynj8ydGYPagxHp5ehknvhyNR1aE+Yo9addrCx00l0b0ajeRkDOLW12FhzGqkhpESL3l6ekpqp6WlKVF96kwCOhGoNGfOnDk61WBh4xH4NxP3fPpi+PAgtPz3FMJWbUeiox+6ta6LgmgY25rw8G+Hx9NOY9e2jdhwOB1VHWugRtV7uHJ4J35s/ByGtq+jJt40Tw0RR/hySAi8fXyYjMF4lrWYnkRoVOMmTdC4cWOLkZmCkoApCNCZmoK6tn1WcUI9xyqAbQ24dWwFp8Rd+Cr0KG636Ir/a1KjIBG9TZU6aNmjD55q5oDci/uwetVX2HAwFY92GImpL/jATv3MLuRkDKNfHYvZc2bjkUce0VYyllMIgTNnzuDxxx9Hs2bNFKIx1SSB8hFgovvycTNJrdyss/hqwsv44FgjvLRmFd7tUlftRiJthGMyBm0oscz6desQHx/PhPd8FEigDAJcMy0DkDndtrFviZAPFiGkWSK+mfg+1sapS8pQtsTiC1IkY/g8dDWzGpWNS9El7O3tcTEpSdEMqDwJaEOAzlQbSmZTxgaV63XH25/PwzPYh/dHzMfOy3d0kk4kY5g9c5aU1SgwMFCnuiysPAI+zZsj+tRp5SlOjUlARwLqI/d1bITFjUlAJKp/FvPXZuHOiDmYNvZR3BjVFP9l+WDI8HZw0LA+KsIbPvn4Y0Ts3Ss5Un9/f2MKzb4slICTk5MkudjxzXApCzUixTYKAY5MjYJZ351Ugr3PEMxbFoIG53dg62/10W+ob6mO9M2pU/Mc6fr1oCPVtz2stz1HR0dJOSa8t14bUzP9EKAz1Q9HE7Rig6rVaqPjnG/x7TvdUU9DMobr169DONL4uDgmYzCBlayhy169gxB3/rw1qEIdSMBgBOhMDYbWwA3n3sYV2x6YMbItHDQ4UjE1N7B/f0mQPRERnKYzsEmstXkHBwekp2dYq3rUiwT0QoDOVC8YTdCIjQOa+TWBvYY1UjmrEZMxmMA2Vtaln58f0tIuW5lWVIcE9EuAzlS/PM2iNSmGNDgYgwYPYVYjs7CIZQtRp25d6S1Clq0FpScBwxKgMzUsX6O3LidjEI5UvNC7WrVqRpeBHVoXgdq1a+NSSqp1KUVtSEDPBOhM9QzUlM3tCA+XkjHMnT+PyRhMaQgr69vFxUXSSORx5kECJKCeAJ2pei4Wd1UkY5g6abIUQxo8fLjFyU+BzZeAPLtx7do18xWSkpGAiQkwaYOJDVDR7kUyhjVha7B00SImY6goTNbXSGBI8DD8dfWqxvu8QQJKJ0BnasFPgHCkcgzpkePHGPpiwbY0d9FdXBoiISHB3MWkfCRgMgKc5jUZ+op1rOpI165fT0daMZysXQaBevWccevWrTJK8TYJKJcAnakF2l7EkIoXeotjy7ZtdKQWaENLE9nN3R3frd9gaWJTXhIwGgE6U6Oh1k9HcjIGRycnKYZUzp2qn9bZCgmoJyDCY8Qh0lPyIAESKEmAzrQkE7O9EhsbixHBwegcEMBkDGZrJesUTH5jTGZmpnUqSK1IoIIE6EwrCNBY1UUyhgF9+0lZjeYvWMBkDMYCz34KCPh17IDUVCZvKADCExJQIUBnqgLDXE8jIyOlZAxvTp/OZAzmaiQFyNXEwwNXM5jwXgGmporlIMDQmHJAM2YVkYyBMaTGJM6+NBHw9vZGfHy8ptu8TgKKJsCRqRmbn47UjI2jQNHqOjvjYlKSAjWnyiRQNgGOTMtmZPQSqjGkEQf2w9PT0+gysEMSKE7A1dUV0adOF7/MzyRAAgA4MjWzx0DVkYpkDHSkZmYgBYvj5OQkaS/Cs3iQAAkUJUBnWpSHST+JLymRHlAczGpkUlOwczUE5JhmJrxXA4eXFE+AztRMHgE5GYMQZ+myZcxqZCZ2oRhFCfTqHYSU5OSiF/mJBEiA07zm8AyI90SKZAzePj5MxmAOBqEMGgm4ubkhPZ3hMRoB8YZiCXBkamLTi2QMQT16SskYPv3sMyZjMLE92H3pBLy8vJCWdrn0QrxLAgokQGdqQqMLRzpi6DAwGYMJjcCudSJQp25dnDh+XKc6LEwCSiBAZ2oiK4sYUuFIPw9dzaxGJrIBu9WdgEh4fyklFWLXOQ8SIIFCAnSmhSyMdqaajCEwMNBo/bIjEqgoARcXF6mJtLS0ijbF+iRgVQToTI1oTvFrfsnixdi86Tts3REOf39/I/bOrkig4gSqVauGRm6uYHhMxVmyBesiwAxIRrJn8WQM8iutjNQ9uyEBvREQrwD86+pVvbXHhkjAGghwZGoEK4oXKotkDPFxcUzGYATe7MKwBFxcGiIhIcGwnbB1ErAwAnSmBjaYSMYwsH9/qZc9ERFMxmBg3mze8ATq1XNGSkqK4TtiDyRgQQToTA1oLDmrEZMxGBAymzY6ATd3d+zbG2H0ftkhCZgzATpTA1lHxJB2DegiJWMQ6QHFxg0eJGANBER4jDjE8gUPEiCBPAJ0pgZ4EoonY6AjNQBkNmkyAvLmuczMTJPJwI5JwNwI0Jnq2SI7wsOlZAzLVixnMgY9s2Vz5kPAr2MHpKammo9AlIQETEyAoTF6NIBqMgbGkOoRLJsyOwJNPDxwNYMJ783OMBTIZAQ4MtUDehFDSkeqB5BswmII+Pn5IT4+3mLkpaAkYGgCHJlWkLBqMoYjx48x9KWCPFndMgg8Zm+Pi0lJliEspSQBIxDgyLQCkFUd6dr16+lIK8CSVS2LgKurK6JPnbYsoSktCRiQAJ1pOeGKGNI+QUFS7S3bttGRlpMjq1kmAScnJ0lw8WJ7HiRAAgCnecvxFDAZQzmgsYpVEXB0dJT0yc7Otiq9qAwJlJcAR6Y6kpNiSIODEdS7N5iMQUd4LG5VBIYED0NKcrJV6URlSKC8BOhMdSAnJ2MYNHgI3po2jVmNdGDHotZHoGbNmkhPZ3iM9VmWGpWHAJ2pltQiIyOlZAxz589jMgYtmbGYdRPw8vJCWtpl61aS2pGAlgToTLUAJWJIx44ajbUbNyB4+HAtarAICVg/gTp16+K79RusX1FqSAJaEKAzLQMSkzGUAYi3FUtATngvQsR4kIDSCXA3r4YnQDWGNOLAfnh6emooycskoEwC8v8TaWlp/P9DmY8AtVYhwJGpCgz5VNWRimQM8peGfJ9/SYAE8gg0cnPFtWvXiIMEFE+AzrTYIyBiSF8OCZGuMqtRMTj8SALFCHQOCMBfV68Wu8qPJKA8AnSmKjaXkzE4OjlJMaTyextVivCUBEhAhYCLS0NER0erXOEpCSiTAJ1pvt1FWrQRwcEQv7SZjEGZ/zNQa90J1KvnjBs3buhekTVIwMoI0JkCEMkYgnr0hEjGMH/BAiZjsLKHnOoYjoBP8+bYtzfCcB2wZRKwEAKKd6bfb94sJWOYOGUykzFYyENLMc2HgJ2dnSTM9evXzUcoSkICJiCg6NCYt6dPx5ZNm9HYowkeeaSKCfCzSxKwbALyvoLMzEzIye8tWyNKTwLlI6DYkansSBcuXoQdu3bh3LmzWL9uXfkoshYJKJhAr95BiDt/XsEEqDoJKPAVbCKGdETwcJyNPYPPV3+JwB49pOfg3RkzpA1ILVq2ROvWrflskAAJaEnAwcEBWVlZWpZmMRKwTgKKGpkKR9r32WcRf/48Nm7eXOBIhWnFdNXylSsxeeJEcP3HOh92amUYAn5+foiPjzdM42yVBCyEgGKc6Z9//oneTwfh77/+xs69e9CuXbsSJhIj0ldGjcKsmTNL3OMFEiAB9QQes7fHiePH1d/kVRJQCAFFONOLFy+ix5Pdcf/+PRw6EoUmTZpoNK/8Vpgd4eEay/AGCZBAIQFXV1dcSkktvMAzElAgAat3pufPn8dzvfugQUMXHDh4EGJ9p6xDrJ9OnTQZIiMSDxIggdIJuLi4SAVE4hMeJKBUAlbtTHfu3Im+fZ5BOz8/acdutWrVtLKzWD9dtmI5Vn32mVblWYgElExA/v8qOztbyRiou8IJWK0zFY50yhsT8dzz/fDturU6ZzXq2asXLiYlSdmRFP6MUH0SKJPAkOBhSElOLrMcC5CAtRKwSmf6/ty5kiN9dfw4fLh8eblsJ35tv/3uu/hoxYpy1WclElASgZo1ayIhIUFJKlNXEihCwOqcqUjG8O03YZg97328NW1aEWV1/SB29zbx8AA3I+lKjuWVRsDLywu3bt1SmtrUlwQKCFiNMxUxpK+89BK2bdmCDz9aiREjRhQoWZGTkSEhWLliBUT7PEiABNQTcHN3x3frN6i/yaskoAACVuFM5WQMJ44dl5IxPPfcc3oznaenp/RatuOMo9MbUzZkfQTkhPf80Wl9tqVG2hGweGcq3qUoshpduZyG3T9EqE3GoB0KzaXE6PSr1as1F+AdElA4AfGjUxxpaWkKJ0H1lUrAop2pSMbQpZM/bt28hWM/nSw1GUNFDCx/UcTGxlakGdYlAasm0MjNFampTN5g1UamchoJWKwzFY5UTsYQ9eNRrZIxaKSgxY1XRo/G/n37tCjJIiSgTAKdAwLwLxPeK9P41BoW6UxFDGlQz55o0aqVTskYKmLvgIAAfPHZKibBrwhE1rVqAt7e3oiOjrZqHakcCWgiYHHOVE7GIJIqbPp+s87JGDSBKOu6iDsVcasxMTFlFeV9ElAkAXt7e4g9DDxIQIkELMqZrly5UkrG8OJLIfjEBKn+hAPfvm2bEp8T6kwCZRLwad4c+/ZGlFmOBUjAGglUthSlRDKGLZs24+0Z72LU6NEmEVskcRBfFuJ9p46OjiaRgZ2SgLkSkMNjxAsiRH5rHiSgJAIWMTKdMnmy5EhFMgZTOVL5oRBTvRcuXJA/8i8JkEA+AdmBMuE9HwklEjBrZyoCwHsGBmL3zp3YtHUL9JmMQb2x7yEjagH6uDVHn9kHkZFTslRbX18c+/HHkjd4hQRIAL16ByHu/HmSIAHFETBbZypnNRLJGCL279ciGUMObkfNRis3d3jI//qGIVF2iLejMMtH5Z5cxq05ng+7AKlYTjL2bXXFij9+wQr3E9h38U6JB0LsWIzYu7fEdV4gARKAFKKWnp5BFCSgOAJm6UxFDGnnjp2kZAw79+7RLhlDThoOb9qPwjcq2qHl8/5oImmYg9sxh7Gj8KaKoduiX4BrXoyQrTt6DUjFpMbtMCm5M3o1qapSLu9UnsoS66Y8SIAEihLw8/NDWtrlohf5iQQUQMDsNiDJyRjqODtjW/h2LZMx5CDrzA6EOS1ETEo31ChhuOuI+bU2PvrpAro5Vym8K0arL6Wgc4HTrALnbjOwJ2VGYRk1ZyI4/fLly9yEpIYNLymbQJ26dXGCeayV/RAoVHuzGplGHjiAZ54OgoeXJ/b+EKGlIxWWu46ft23BuXXLsSQsHFGJt4uaMycHDfqOLOpIcQeJ29bgt2fl0WvRKqV9Er+++SLk0gjxnlIJ1K5dG5dSmFJQqfZXst5m40xFMoaxo8egS9cndM5qlJO4GyvXXQJwFhvnTMaoHiMwK/wCsmTL2taBZ+Ni49WcVJzYVRshPd11TgMlfn3zRcgyXP4lgUICLi4u0ofExMTCizwjAQUQMAtn+v3mzVIyhoGDB2F1aKjO2G09Q7A9JRkJP23FijnBaCqc6qR3ERpzU2NbORdPYrd3HzxZX2XaV2PpojfEr2++CLkoE34iAUFAZAoTx7Vr1wiEBBRFwOTOVCRjeGfadCkZwweLFlUIvq2zL54JmY9dP4ViuPfv+HrbGRSb8M1v/w4uHo9Bs8AWatZXyxZB/Prmi5DL5sQSyiQwJHgY/rp6VZnKU2vFEjCpM5WzGuk7GYOt85OYMn0gsO0wYm7LsTEqNpameB/HU77ly2Ik//pWaZGnJEAC+QRcXBpyGYRPg+IIaHCm1xA1s6v6eE11iHIuYE3f5vnlVeI21ZUFIMeQbtuyBZ+v/tIAyRhsYd/AHU083dHAvqSKeVO8/wffGiXvaRC5xGW/jh0g0qbxIAESKEqgXj1nLoMURcJPCiCgwZvURrf5R5BwYjl62gGI3YU9ZzStP+bg9tENWBabDbSejYg/zmN7SFONm3pkR5qUkIjtO3cisEcPA2DOQdaVa2g9+Rl4ltCwYlO8srBNPDzAtGkyDf4lgUICbu7uXAYpxMEzhRAo4WpU9ba1rwUnz27oLtYfV0fhTzUzphDJErb+iU5POqtWVXsuYkh7PPUU/v7rb4hkDM2bN1dbTreL95AR8wN2x2TkZTHCPWREf4UlR9ti7BO1SzZVwSnekg3yCgmQgCoBOeE9E5uoUuG5tRMo1ZlKylfuiCGjewIRW3CgRHo9kSxhF/Y0fg59GpS+K1ZOxiDaPHQkSrusRtrSv/0LVvX3h5ebO1qN+hQn/+2G6e89BWc12uVcjMapLk+jfQWmeLUVi+VIQIkEPD09JbUzMzOVqD51VigBNe6mOImqaNi9L/raHceyNT8V3R2bk4aD36Sjz+B2qFm8mspnMbU7fOgw3L17Fw8fPMS899+HSNAgrlf8kLMWJSMpJRlnQyfj+W6esNfQsK3ncHw22U/jfQ3VeJkESEAHAmJPQWoqkzfogIxFLZyAFs4UQI1OeHFaALLXhWJ7YmHy95yLR7GvcV88VUasptj9evL0KezYsxv9Bw5AfFyclKChpbeP9FaY9+fOxc8//2zhKCk+CZCATEDsKfg3qyBtinyZf0nAaglo50xRFZ79R2Go3a/YvPtcfmahazi65jQ6PtNS61GeWCN9a9o0ROzbJ40ixU5evw4dsH/fPgwZ+IK0G3hg/wH48ssvIaaFeZAACVgmAfF2pejoaMsUnlKTQDkIaJ/ovkYbPD+6GTau3o2fX2mHJ67uxqfoj688xZtVyvcLVOzklXfziinf3bt2Yf/+/Vj1yadY/L+FqGZXDR06dsTTQUF4KjCQieXLYWBWIQFTELC3t8fFpCRTdM0+ScAkBLQcmQrZaqHN4BHoiS1Yue0YotbE4JmRncqVQUidpmIq+IVBeekEfz0bi6MnjuP1SZOQlfUv3psxEx1828G/Q0dMmTxZj+ut6iTR7pp4M4a8a1G7GixFAsoh4NO8OaJPnVaOwtRU8QS0H5kCsK3fBYP618aoOSMxafg3OCaNSg3DsH79+hgzZoz0T/Rw/vx57N2zB4cOHsTO7eFSp409mqDL//0fevfpg/bt2xtGEA2tijdjyO821VCEl0lAsQScnJwk3UViE/5/otjHQFGKl+pMc7Juoujm9tp4YuRLaLluF7r2b6O3Uak2xMV6q7zmKsqL3cCHDx+W1lu//SZMaqKNry96Pt0LTz31lH5Db4oJqJ9dyMUa5UcSsCICjo55qTqZ2MSKjEpVSiVgk5ubm1uyhEgnOACjpNeaibuNMDRsK+Z1qw3kXMLuVXHwHfc06tvm4HbUXHQJ+RbZBY3YoeWcbdhaShakgqJ6OlFdb/35dDT+uX3boOut4vVSa8LCMH/BAj1pwGZIwPoITBg/Hj179kTffv2sTzlqRALFCGhwpsVKWdjHP//8E7t378bBA5E4e+YM7t+/j8fr1IF/QGf07t0bAV26FLwqqjyqnTx5Esd+/FHamVye+qxDAkogsGTxYlSvXgNjx41VgrrUUeEErNKZFrepvN4qHOD5c79Jtyuy3rp+3TqI3Yr8xV2cND+TQCGBHeHhUngMZ3AKmfDMegmUumZqLWprWm89fOgwyrPeGh8fL+08thY+1IMEDEGgTt26ELveeZCAEggoYmRamiHl9dYjUVE4fuy4VuutHm7uOB3zC+NeSwPLe4onIPYWBPXoiXPxcRVaVlE8SAKwCAKKd6bFrSSvt/545AjEZqbi663ujRtj5rvvYuOmTcWr8jMJkIAKAfFDVaQMjTiwH3Lye5XbPCUBqyJAZ1qGOTWtt44MCZGyM/FLogyAvK1oAt27dcOChQvh7++vaA5U3voJ0JnqaGMR3/rHH38gNjYW+/ZGSLWHBA9DtyefhMhHygB1HYGyuFUTmDljBvz8/LhZz6qtTOUEAUVsQNKnqeVcwqJNMY115swZxJ6JxVerV0vp0xq5uSKod2+09fWFr68v11X1CZ9tWRwBF5eGSEhIsDi5KTAJ6EqAI1NdiZVS/vr164iJicGvMTGI2LsXIuWgeK9j125PonWb1mjTpg03YpTCj7esj4AIjxEvr/j0s8+sTzlqRAIqBOhMVWDo+1TkJf05OlqKtftu/Qap+V69g9C5c2e0aNkSrVu31neXbI8EzIqAWA4Z0Lef9MpFsxKMwpCAngnQmeoZaGnNiVCB06dO4cSJE0XWW8WaUns/P663lgaP9yySgPhB2TWgC0PJLNJ6FFoXAnSmutDSY1mx3irWkk6eOIkjUYe53qpHtmzKvAiIuGyGx5iXTSiN/gnQmeqfablaFOutFy5ckHL+cr21XAhZyUwJDB08GK+MHo3AwEAzlZBikUDFCdCZVpyhQVoQ02MibWHU4cPgeqtBELNRIxEQ4TEibCx4+HAj9chuSMD4BOhMjc+8XD1yvbVc2FjJDAiIF0OIH4ZMeG8GxqAIBiNAZ2owtIZrmOuthmPLlvVPIDIyUorDZgpO/bNli+ZDgM7UfGxRbkm43lpudKxoBAJywvuklGQj9MYuSMA0BOhMTcPdoL1yvdWgeNm4jgTEj70Ovu1w5Pgxhn/pyI7FLYcAnanl2KrcknK9tdzoWFFPBER4zNYd4UxUoieebMb8CNCZmp9NDCoR11sNipeNayDAhPcawPCy1RCgM7UaU5ZPEa63lo8ba+lGYMnixahevQbGjhurW0WWJgELIUBnaiGGMpaYXG81Fmll9SMS3kdHRzM8RllmV5S2dKaKMrfuynK9VXdmrFGSwMmTJzFi6DAmvC+JhleshACdqZUY0hhqcL3VGJStsw85POZcfBxfQ2idJla8VnSmin8Eyg+A663lZ6fEmkx4r0SrK0dnOlPl2BrAA2SlJSIu6SKSEhPxBzphwmh/OOiJAddb9QTSSpvp3q0bFixcCH9/fyvVkGopmQCdqZKsn3sbSadP49fdH+OdtfHwmBGOPaN9UMlADLjeaiCwFtosw2Ms1HAUWysCdKZaYbKmQneRsmEcAt/NwJhNGzCtY62Syj24hIiFi3CwSnv8X8fW8GnmBXdne1QuWVLrK2Wtt4q3ijRo0EDr9ljQ8gh8vupzpKVdKB/QmAAADxdJREFU5o5eyzMdJdaCQEW+H7VonkXMj8AtJP56AbALRAfvGiXFy72BmE/exextp3H9xl6ErxJF7OE9/gt8+1ZnONiUrKLNlWrVqknZb1q3bi3FGqqut/5v/nxcSkmFX8cO6NrtSbRu0xpNmzaFo6OjNk2zjIUQqFfPGefOnbUQaSkmCehGgCNT3XhZfuns45jXcTg2PPkpjq7sjceLOMcsJG54D++lDcRnb/kCly4i/nwMTv/yEJ1fG4EODoaaEAbKWm/18vLiLlALf/rkHb1MeG/hhqT4agnQmarFYq0Xc3Hv7Co8+9wqOP4vHBuGNUGhL72L9MPLMWZUKNLbvYRZc8ahj4+j2qnd3Kw/cHTLOnz19SacQke88uZ0jH+2KewLG6swwNLWW32aN4enp2eF+2ADxiUgfjB1DeiC0zG/cNbBuOjZmxEIcJrXCJDNp4u7SI05gYvwwcC29VUcKYDcu8h6WA9dnnTH15GhmPrsLzgX+jHefrJBEYeam3UOa6eOx4Ibg/Dt1hh863AFWyZMxfxqn2Fhj3pF26yA4sJZin/Bw4dDXm/97dw5fLdxI6JPnUYjN1cE9e6Ntr6+4HprBUAbsaq8Jp6ZmUlnakTu7Mo4BGyN0w17MQsCuX8j7uTvQAN/tGtctahINjXgGTgS01fvQGToBLSrcRZhY+Zh8x//FZbL/Rsnlr+N9/fVxri3R6Lj448ClRuiU2BdbFm8Hb/dyy0oK0avR8Lex4tPNEfTJ17G4p0XkFV4u6CcNifyeqtwrOIF02JkI0IsRK5Xsd4qRjtDBw+G2OAiMu2I9Vge5klArIvHnT9vnsJRKhKoAAE60wrAs7iqN3/H8UOZsHuyDTwe1TAna2OHhoGvY8WCwah9PxKffn8W2ZKiubgXvwNLw+JQqdswDGgrb16yQeVHqgCJP+PclXt5JaXR60iM2euACVtjcOHQTDTe8zbmR6ajnP60CGqxMUnEKoqk6YeioqT3ZL4yejT++ee2lLJOvDtzwvjxWL9uHWJjY6WRbZEG+MFkBJp4eCArK8tk/bNjEjAUATpTQ5E1u3ZzkR13CvvvO6N7Zy9UL1W+R1EvcBBe9LTF1cR03JbK3sKZXdtw7qEzggYFwKXAFz/EnWzx5ZiBv27cB3QYvYqy537Yjg2rP8byRV/hSMb9UqXSdFNMHwYGBuKtadOk3K8RB/ajZ8+eOHHiBAb07YeW3j4QMY4i2bpYi+VhOgJ+fn6Ij483nQDsmQQMRIBrpgYCa37NZuH306eRBW908HYqe22zihMauNqjUrUqeUkd7l7EiZ0JwCPPo5dfHZX6/yAl7iIAR1SpbKMyel2scfTa0v3RPDw2DnBvWRWb3/oQGx++iNBx+tktLK+39u3Xj+utZvYgPmZvj4tJSWYmFcUhgYoToDOtOEMzbyEX/8WH45Pvj+L09jig5hh41K+iIvNdXEtMwZ16HnCxV3Fm9zJxJbUauk9ogdpif9KfF3DqykOgY1t411Z5bO5dQdypdKBSe7jXu4MzX+eNXp8pbfQqO1NUhn31asBD4JHAjmheXf8TJfJ6q4hvFWuucnxr7JlYab2V8a0qj4IRTl1dXaUNZEboil2QgFEJqHwrGrVfdmY0Ajao5v083nr3KaQNHIS42BjsX7AGmJwfN5r9M1b1H4ldnWch9INhaOXwCJB7C3Ebv8L2JpPwZZ+G0ij0wY2rEBOktTo1U5niBXJSf8WBxPtA65bwsE/BnjJHr6oOMxd3k84gKtsebTo1Re2CqWPDwZHXW+U1Vzm+9deYGGm9VfTcq3cQOnfujBYtW4Lxrfq1hZOTk9SgmG5neJN+2bI10xKgMzUtf+P1XrkGXHz8pX89VXu1a40h817E2bnz8ELfH/DsE41w+9cE2PaeiK9XPIGGj6h6OAf4utdRCZXJxoWo/TiHmugwuAsaZ5zWYvSaP8UryXAXl87+jHT44MXioTqqMhrwXKy3qq65ii95sdt0//79mD1zltTzkOBhEGt9jG+tuCHkrFbZ2Xnb2ireIlsgAfMgQGdqHnYwoRT28Oz3HjY//RouJV/CdTjA5e0GeNy+6KNRuWFTBFQCVAJlgP/ise+7n4HHh2NMkDtyk3eVPXp1UplKzk1HbFQc0ODFvFCd3HSc2PQjstzboFXzxnAuJoMxIHG91fCUxY+TlORkKb2k4XtjDyRgHAJFvzGN0yd7MUMCNlUd4ertCFdNstVuge49HkPYzX+RA8AWd3B59xp8cbEenlkxAl1EqsFkUbn00WsT1Vnem0k4ffwG7AaLUB3gwc3buJWwEZM+24MX+rRCTXtXdGpTEzf+voabj7bHoCBPFIuO1SStXq5zvVUvGEs0UrNmTaSnZ5S4zgskYMkE6Ewt2XrGlN2mIXpNGY+IN9djm/ezcE6PQujiBPT636eY39c9b+pXi9FroS/Nwe3YY/jhfn30bF8dSVsXYMnXf6Lj6FmImtYG9araIjfrMmK2LMWEOXtQ/aVF8Lj7A3ZEnMWtmq3Qd9RIPO1VQ2VXseFhcL1VP4zFOnR0dLR+GmMrJGAmBJib10wMYRli5OBOeiwO7/8JybkN0Drg/9DR06FwDTX3EnaMC0ZYp1BsDWmaN3r9fhp6vhWLXivCsLRfvtOVlP0HMcuDMWjluTzVPadg844J8LUrdLdim+/fe6ehy/j98HjhdbzWry3q5l7AppnvY2ulCdgcPgLVzx7DibhbqOXTBU91dtdrfmBdbaK63rpvb4RUneutJSmKRBoi/pcJ70uy4RXLJUBnarm2M0PJc3En4TtMejMegTPyR68LDqLW5KWYP7RFUUeXcwFrnu+PeRiDD4JO4e0PgOkRoRjtbaei1w0cf38gRq71xccnFiLocTGRkoWY5YMwaOU/aNvLH62aOuPR9J+w+ft0+C35Bh+94IFHVFow1alqPuHdu3Yxn7CKIcSPjqAePXEuPo5vAlLhwlPLJsBpXsu2n5lJb4OqXoOx4ou80evZ3KYYvWFU0dFrvsS5qb/gh9i7qDexC57pUx97lryDsJ3nEOzdEQXu9N4lxP54GfB9pTC2NfcGLv/+F9BgON75aCJ8RVrEnAuom9Af89YdQ8oAD3iqDm5NRIjrrZrByyExaWlpDI/RjIl3LIwAnamFGcz8xbVF1XptETSyrXpRc68j8edEJB/bgxg0wKC2rqjq4oJhA+phXOgWHHm5Xf4IVI5hBTxmtEFDOUJHzi8sbVrKv3j/Jq6mZAN+tWCAvA/q9dDxKtdbiwITb/1JTU2lMy2KhZ8smIAZ/Ia3YHoUXXcCNo/BoWYOHjq2x6BAJyQcPIyz16qjY++esL9/AN/uSUReht57uHLmFOLQDE+3a5iX0hByfmEndG7fpCC/cM6leJy8ZYeWXbxRR3eJTFJDNbZVrB0qLZ9w54AA/MuE9yZ59tipYQhwZGoYrmxVI4FHUdvLH0Hi38hJeJB1DTdxC79ffIAO3pVx6OMv8X3LUWiJSzj4/Uk8tOuLNh6P5bf2Ly6e+RVZaIUnWsv5ge/iUvRRnEMTvNaqPiz116HS4lvFO2jFjl6RP5kHCVgDATpTa7Cixepgg8r2j0u5f2u/MhcdXpmFrIw/EBcTh0uPVIKj/zPo/m8SDu07i+ZBzVCjSip+2vc74DUJbRvJmZRuIfHXC4BdoIrTtVggkuBKWG+1t7fHjRs3LNtQlJ4EVAhwN68KDJ6aI4EHyLp6A3f+jcX332zC7t2HcaH+a/g2bCz8H68Km9tRmNXpJWzp8yVOLOkBB3NUQc8yqeYT/uKzVVLr4qXbzzz7rMXkE5Z39DI8Rs8PB5szGQE6U5OhZ8flIvAgCxl/xOG3v2uhCU5g7TfrsT4yCY+N+w4np3eEPF4tV9sWWkldfKtI1i/e6Wqu+YTFD4KuAV2kF7uL9WMeJGDpBOhMLd2CipY/Fw+yriI54XfEnb2A++2GYmDLGoomoi6+VQB5dfw4tPX1hVirNBfn5eHmLm28kkNlFG04Km/xBOhMLd6EVIAENBNQfX/rkajDBckjBg0egtZtWqNp06aQ3+SiuRXD3Jkwfrw0euYmJMPwZavGJUBnalze7I0ETEpAdb01Yu9eyC9HN8V668wZM6SRsnhpOw8SsHQCdKaWbkHKTwIVICCvt4owle/Wb5BaMtZ6647wcCk8Zv6CBRXQgFVJwDwI0Jmahx0oBQmYnIDqeuuJEycgJ+s31HprZGQk/jd/Pg5FRZlcdwpAAhUlQGdaUYKsTwJWSsDQ660Mj7HSB0ehatGZKtTwVJsEdCWg7/VWMRJu6e3DHb26GoLlzZIAnalZmoVCkYD5E9DHeqsIj9m6IxytW7c2f4UpIQmUQoDOtBQ4vEUCJKAdgfKut4odvX5+fszRqx1mljJjAnSmZmwcikYClkpA2/XWz1d9jn/+uY23pk2zVFUpNwlIBOhM+SCQAAkYnICm9VZHJyc4ODiA4TEGNwE7MDABOlMDA2bzJEACJQkUX29lwvuSjHjFsgjQmVqWvSgtCVg9gZzEMAzoMRfnSmjqjO4Tp2DYM73QzVPZOZhLoOEFkxOw1HcpmxwcBSABEjAMAVvPEGxPiUfEnACg9WxE/JGMpJSLOHNgOurun4NRfadjzYXbhumcrZJAOQnQmZYTHKuRAAkYk4At7D37Ye5Hb6Fl9g9YtjYGdKfG5M++yiJAZ1oWId4nARIwGwK2dd3Qwg7IPpeCqzlmIxYFIQHQmfIhIAESsBgCOVdT8Fs2YNfSDXX57WUxdlOCoHwclWBl6kgClkog8RROJOZN6OZknMSni77AOfji5f5twC1IlmpU65S7snWqRa1IgASsgkD2D5jX6wfMy1fGLvANLNs2FM/61rIK9aiE9RCgM7UeW1ITErA+AmI37/YQeHIOzfpsa2Ua8RG1MoNSHRIgARIgAeMToDM1PnP2SAIkQAIkYGUE6EytzKBUhwSsg8Ad/HPjP+DeP/gnmzEw1mFT69aC6QSt277UjgQsjkDJdIJ2aDlnG7aGNGUsn8VZUzkC05kqx9bUlARIgARIwEAEOM1rILBslgRIgARIQDkE6EyVY2tqSgIkQAIkYCACdKYGAstmSYAESIAElEOAzlQ5tqamJEACJEACBiJAZ2ogsGyWBEiABEhAOQToTJVja2pKAiRAAiRgIAL/D/7Mer2WyIH7AAAAAElFTkSuQmCC" alt></p>
<p>Calculate the distance from Bermuda to Puerto Rico, \({\text{BP}}\).</p>
<p> </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 area of the Bermuda triangle.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\({\text{B}}{{\text{P}}^2} = {1650^2} + {1500^2} - 2 \times 1650 \times 1500\,\cos \,(57^\circ )\) <em><strong>(M1)(A1)</strong></em></p>
<p>\(1510\,({\text{km}})\,\,\,\left( {1508.81...\,({\text{km}})} \right)\) <em><strong>(A1) (C3)</strong></em></p>
<p><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for substitution in the cosine rule formula, <em><strong>(A1)</strong></em> for correct substitution.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{1}{2} \times 1650 \times 1500 \times \sin \,57^\circ \) <em><strong>(M1)(A1)</strong></em></p>
<p>\( = 1\,040\,000\,({\text{k}}{{\text{m}}^2})\,\,\,\left( {1\,037\,854.82...\,({\text{k}}{{\text{m}}^2})} \right)\) <em><strong>(A1) (C3)</strong></em></p>
<p>Note: Award <em><strong>(M1)</strong></em> for substitution in the area of triangle formula, <em><strong>(A1)</strong></em> for correct substitution.</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Question 6: Non-right angle trigonometry.<br>Instead of using the law of cosines weaker candidates substituted into Pythagoras’ theorem and likewise used \(A = \frac{1}{2}bh\) instead of \(A = \frac{1}{2}ab\sin C\). Those that did select the correct formula almost always made correct substitutions but were not always able to calculate the correct answer.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 6: Non-right angle trigonometry. Instead of using the law of cosines weaker candidates substituted into Pythagoras’ theorem and likewise used \(A = \frac{1}{2}bh\) instead of \(A = \frac{1}{2}ab\sin C\). Those that did select the correct formula almost always made correct substitutions but were not always able to calculate the correct answer.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Assume that the Earth is a sphere with a radius, \(r\) , of \(6.38 \times {10^3}\,{\text{km}}\) .</p>
<p><img 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" alt></p>
<p>i) Calculate the surface area of the Earth in \({\text{k}}{{\text{m}}^2}\).</p>
<p>ii) Write down your answer to part (a)(i) in the form \(a \times {10^k}\) , where \(1 \leqslant a < 10\) and \(k \in \mathbb{Z}\) .</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>The surface area of the Earth that is covered by water is approximately \(3.61 \times {10^8}{\text{k}}{{\text{m}}^2}\) .</p>
<p>Calculate the percentage of the surface area of the Earth that is covered by water.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>i) \(4\pi {(6.38 \times {10^3})^2}\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into the surface area of a sphere formula.</p>
<p>\( = 512\,000\,000\,\,\,(511506576,\,\,162\,817\,600\pi )\) <em><strong>(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> Award at most <em><strong>(M1)(A0)</strong></em> for use of \(3.14\) for \(\pi \), which will give an answer of \(511\,247\,264\).</p>
<p> </p>
<p>ii) \(5.12 \times {10^8}\,\,\,(5.11506... \times {10^8},\,\,1.628176\pi \times {10^8})\) <em><strong>(A1)</strong></em><strong>(ft)<em>(A1)</em><strong>(ft)<em> (C2)</em></strong></strong></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(5.12\) and <em><strong>(A1)</strong></em> for \( \times {10^8}\).<br>Award <em><strong>(A0)(A0)</strong></em> for answers of the type: \(5.12 \times {10^7}\).<br>Follow through from part (a)(i).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{3.61 \times {{10}^8}}}{{5.11506...\,\, \times {{10}^8}}} \times 100\) <strong>OR</strong> \(\frac{{3.61}}{{5.11506...\,}} \times 100\) <strong>OR</strong> \(0.705758... \times 100\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution. Multiplication by \(100\) must be seen.</p>
<p>\( = 70.6\,(\% )\,\,\,\,(70.5758...\,(\% ))\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (a). Accept the use of \(3\) sf answers, which gives a final answer of \(70.5\,(\% )\,\,\,\,(70.5758...\,(\% ))\) .</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Question 1: Surface area of a sphere; scientific notation and percentage.<br>The weakest candidates were unable to square a number given in scientific notation or write the answer in scientific notation. Weaker candidates used the area of a circle formula rather than the surface area of a sphere. Premature rounding caused some candidates to obtain an incorrect final answer. Many candidates confused percentage of a quantity with percentage error or found the reciprocal of the correct answer. Overall this question was well attempted.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 1: Surface area of a sphere; scientific notation and percentage.<br>The weakest candidates were unable to square a number given in scientific notation or write the answer in scientific notation. Weaker candidates used the area of a circle formula rather than the surface area of a sphere. Premature rounding caused some candidates to obtain an incorrect final answer. Many candidates confused percentage of a quantity with percentage error or found the reciprocal of the correct answer. Overall this question was well attempted.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The right pyramid shown in the diagram has a square base with sides of length 40 cm. The height of the pyramid is also 40 cm.</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="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the length of OB.</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>Find the size of angle OBP.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em><strong><span>Note: Unit penalty (UP) applies in this part</span></strong></em></p>
<p><span> </span></p>
<p><span>\({\rm{PB}} = \frac{1}{2}\sqrt {{{40}^2} + {{40}^2}} = \sqrt {800} = 28.28(28.3)\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitutions, <em><strong>(A1)</strong></em> for correct answer.<br><br></span></p>
<p><span><em><strong>(UP)</strong></em> \({\rm{OB}} = \sqrt {{{40}^2} + {{28.28}^2}} = 49.0{\text{ cm }}\left( {\sqrt {2400} {\text{ cm}}} \right)\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong> <em><strong>(C4)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution, can <strong>(ft)</strong> from any answer to PB.</span></p>
<p><span> </span></p>
<p><em><strong><span>[4 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\sin ^{ - 1}}\left( {\frac{{40}}{{49}}} \right)\)</span></p>
<p><em><strong><span>OR</span></strong></em></p>
<p><span>\({\cos ^{ - 1}}\left( {\frac{{28.28}}{{49}}} \right)\)</span></p>
<p><em><strong><span>OR</span></strong></em></p>
<p><span>\({\tan ^{ - 1}}\left( {\frac{{40}}{{28.28}}} \right)\) <em><strong>(M1)</strong></em></span></p>
<p><span>= 54.7 (54.8) <em><strong>(A1)</strong></em><strong>(ft)</strong> <strong><em>(C2)</em></strong></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for any correct trig. ratio.</span></p>
<p><span>In radians = 0.616, award <em><strong>(M1)(A0)</strong></em>.</span></p>
<p><br><span><strong>Note:</strong> Common error: (a) \(OB = \sqrt {40^2 + 20^2} = 44.7 {\text{ cm}}\). Award <em><strong>(M0)(A0)(M1)</strong></em>, <em><strong>(A1)</strong></em><strong>(ft)</strong>, and (b) angle OBP = 63.4° (63.5</span><span><span>°</span>) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong>.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</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 well answered by many candidates although a number lost an accuracy</span> <span style="font-size: medium; font-family: times new roman,times;">penalty or a unit penalty in this question. A very common error was assuming <em>PB</em> to be </span><span style="font-size: medium; font-family: times new roman,times;">20 cm. The mark-scheme allowed for follow through marks to be awarded in this case. Most </span><span style="font-size: medium; font-family: times new roman,times;">candidates could find the angle and very few did not use right angled trigonometry.</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 well answered by many candidates although a number lost an accuracy</span> <span style="font-size: medium; font-family: times new roman,times;">penalty or a unit penalty in this question. A very common error was assuming <em>PB</em> to be </span><span style="font-size: medium; font-family: times new roman,times;">20 cm. The mark-scheme allowed for follow through marks to be awarded in this case. Most </span><span style="font-size: medium; font-family: times new roman,times;">candidates could find the angle and very few did not use right angled trigonometry.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A snack container has a cylindrical shape. The diameter of the base is \(7.84\,{\text{cm}}\). The height of the container is \(23.4\,{\text{cm}}\). This is shown in the following diagram.</p>
<p><img 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" alt></p>
<p>Write down the radius, in \({\text{cm}}\), of the base of the container.</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>Calculate the area of the base of the container.</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>Dan is going to paint the curved surface and the base of the snack container.</p>
<p>Calculate the area to be painted.</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>\(3.92\,({\text{cm}})\) <em><strong>(A1) (C1)</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\pi \times {3.92^2}\) <em><strong>(M1)</strong></em></p>
<p>\( = 48.3\,{\text{c}}{{\text{m}}^2}\,\,\,(15.3664\,\pi \,{\text{c}}{{\text{m}}^2},\,\,48.2749...\,{\text{c}}{{\text{m}}^2})\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in area of circle formula. Follow through from their part (a). The answer is<strong> \(48.3\,{\text{c}}{{\text{m}}^2}\)</strong>, units are required.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(2 \times \pi \times 3.92 \times 23.4 + 48.3\) <em><strong> (M1)(M1)</strong></em></p>
<p>\(625\,{\text{c}}{{\text{m}}^2}\,\,\,(624.618...\,{\text{c}}{{\text{m}}^2})\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></p>
<p><strong>Note: </strong>Award <em><strong>(M1)</strong></em> for correct substitution in curved surface area formula, <em><strong>(M1)</strong></em> for adding their answer to part (b). Follow through from their parts (a) and (b). The answer is <strong>\(625\,{\text{c}}{{\text{m}}^2}\)</strong>, units are required.</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>Question 11: Cylinder base area and curved surface area.</p>
<p>In responses to this question, units were sometimes missing or the wrong units were given. The question explicitly asked for the base and curved surface area but many gave both the top and bottom as well as the curved surface area, or omitted the ends.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 11: Cylinder base area and curved surface area.</p>
<p>In responses to this question, units were sometimes missing or the wrong units were given. The question explicitly asked for the base and curved surface area but many gave both the top and bottom as well as the curved surface area, or omitted the ends.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 11: Cylinder base area and curved surface area.</p>
<p>In responses to this question, units were sometimes missing or the wrong units were given. The question explicitly asked for the base and curved surface area but many gave both the top and bottom as well as the curved surface area, or omitted the ends.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the functions \(f\left( x \right) = {x^4} - 2\) and \(g\left( x \right) = {x^3} - 4{x^2} + 2x + 6\)</p>
<p>The functions intersect at points P and Q. Part of the graph of \(y = f\left( x \right)\) and part of the graph of \(y = g\left( x \right)\) are shown on the diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the range of <em>f</em>.</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>Write down the <em>x</em>-coordinate of P and the <em>x</em>-coordinate of Q.</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>Write down the values of <em>x</em> for which \(f\left( x \right) > g\left( x \right)\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(\left[ { - 2,\,\,\infty } \right[{\text{ or }}\left[ { - 2,\,\,\infty } \right)\) <strong>OR</strong> \(f\left( x \right) \geqslant - 2{\text{ or }}y \geqslant - 2\) <strong>OR</strong> \( - 2 \leqslant f\left( x \right) < \infty \) <em><strong>(A1)(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for −2 and <em><strong>(A1)</strong></em> for completely correct mathematical notation, including weak inequalities. Accept \(f \geqslant - 2\).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>–1 and 1.52 (1.51839…) <em><strong>(A1)(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for −1 and <em><strong>(A1)</strong></em> for 1.52 (1.51839).</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>\(x < - 1,\,\,\,x > 1.52\) <strong>OR</strong> \(\left( { - \infty ,\,\, - 1} \right) \cup \left( {1.52,\,\,\infty } \right)\). <strong><em>(A1)</em>(ft)</strong><strong><em>(A1)</em>(ft)</strong> <em><strong>(C2)</strong></em></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for <strong>both</strong> critical values in inequality or range statements such as \(x < - 1,\,\,\left( { - \infty ,\,\, - 1} \right),\,\,x > 1.52\,{\text{ or }}\left( {1.52,\,\,\infty } \right)\).</p>
<p>Award the second <strong><em>(A1)</em>(ft)</strong> for correct strict inequality statements used with their critical values. If an incorrect use of strict and weak inequalities has already been penalized in (a), condone weak inequalities for this second mark and award <strong><em>(A1)</em>(ft)</strong>.</p>
<p><em><strong>[2 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.</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><span style="font-family: times new roman,times; font-size: medium;">José stands 1.38 kilometres from a vertical cliff.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Express this distance in metres.</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>José estimates the angle between the horizontal and the top of the cliff as 28.3° and uses it to find the height of the cliff.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span><span>Find the height of the cliff according to José’s calculation.<strong> Express your answer in metres, to the nearest whole metre.</strong></span></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>José estimates the angle between the horizontal and the top of the cliff as 28.3° and uses it to find the height of the cliff.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>The actual height of the cliff is 718 metres. Calculate the percentage error made by José when calculating the height of the cliff.</span></p>
<div class="marks">[2]</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>1380 (m) <em><strong>(A1) (C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(1380\tan 28.3\) <em><strong> (M1)</strong></em></span></p>
<p><span>\( = 743.05 \ldots \) .<em><strong> (A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>\( = 743\) (m) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <strong><em>(M1)</em> </strong>for correct substitution in tan formula or equivalent,</span> <span><em><strong>(A1)</strong></em><strong>(ft)</strong> for their 743.05 seen, <em><strong>(A1)</strong></em><strong>(ft)</strong> for their answer correct to </span><span>the nearest m.</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>\({\text{percentage error}} = \frac{{743.05 \ldots - 718}}{{718}} \times 100\) <em><strong> (M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in formula.</span></p>
<p><br><span>= 3.49 % (% <em>symbol not required</em>) <em><strong> (A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Accept 3.48 % for use of 743.</span></p>
<p><span>Accept negative answer.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 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-size: medium; font-family: times new roman,times;">This question was well answered by the majority of candidates although it was surprising to find some who could not express the given distance in metres. Where working was present, follow through marks could be awarded in the remainder of the question. Most candidates could give their answer correct to the nearest metre and find the percentage error correctly, using the formula. A common error was to use the calculated value in the denominator.</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 well answered by the majority of candidates although it was surprising to find some who could not express the given distance in metres. Where working was present, follow through marks could be awarded in the remainder of the question. Most candidates could give their answer correct to the nearest metre and find the percentage error correctly, using the formula. A common error was to use the calculated value in the denominator.</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 well answered by the majority of candidates although it was surprising to find some who could not express the given distance in metres. Where working was present, follow through marks could be awarded in the remainder of the question. Most candidates could give their answer correct to the nearest metre and find the percentage error correctly, using the formula. A common error was to use the calculated value in the denominator.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Fabián stands on top of a building, <span class="s1">T</span>, which is on a horizontal street.</p>
<p class="p1">He observes a car, <span class="s1">C</span>, on the street, at an angle of depression of <span class="s1">30°</span>. The base of the building is at <span class="s1">B</span>. The height of the building is <span class="s1">80 </span>metres.</p>
<p class="p1">The following diagram indicates the positions of <span class="s1">T</span>, <span class="s1">B </span>and <span class="s1">C.</span></p>
<p class="p1" style="text-align: center;"><span class="s1"><img src="images/Schermafbeelding_2015-12-20_om_09.20.36.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show, in the appropriate place on the diagram, <strong>the values </strong>of</p>
<p class="p1">(i) the height of the building;</p>
<p class="p1">(ii) the angle of depression.</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 distance, <span class="s1">BC</span>, from the base of the building to the car.</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">Fabián estimates that the distance from the base of the building to the car is <span class="s1">150 </span>metres. Calculate the percentage error of Fabián’s estimate.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="s1"><img 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" alt> <span class="Apple-converted-space"> </span></span><strong><em>(A1)(A1) <span class="Apple-converted-space"> </span>(C2)</em></strong></p>
<p class="p3"><strong>Notes:<span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1) </em></strong>for 80 m in the correct position on diagram.</p>
<p class="p3">Award <strong><em>(A1) </em></strong>for 30° in a correct position on diagram.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\tan 30^\circ = \frac{{80}}{{{\text{BC}}}}\;\;\;\)<strong>OR</strong>\(\;\;\;\tan 60^\circ = \frac{{{\text{BC}}}}{{80}}\;\;\;\)<strong>OR</strong>\(\;\;\;\frac{{80}}{{\sin 30^\circ }} = \frac{{{\text{BC}}}}{{\sin 60^\circ }}\) <strong><em>(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for a correct trigonometric or Pythagorean equation for BC with correctly substituted values.</p>
<p> </p>
<p>\(({\text{BC}} = ){\text{ 139 (m)}}\;\;\;\left( {138.564 \ldots {\text{ (m)}}} \right)\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></p>
<p><strong>Notes: </strong>Accept an answer of \(80\sqrt 3 \) which is the exact answer.</p>
<p>Follow through from part (a).</p>
<p>Do not penalize use of radians unless it leads to a negative answer.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\left| {\frac{{150 - 138.564 \ldots }}{{138.564 \ldots }}} \right| \times 100\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Notes:<span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for their correct substitution into the percentage error formula.</p>
<p class="p2"> </p>
<p class="p1">\( = 8.25(\% )\;\;\;(8.25317 \ldots \% )\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C2)</em></strong></p>
<p class="p1"><strong>Notes: </strong>Accept \(7.91(\%)\)<span class="s1"> (\(7.91366...\) </span>if \(139\)<span class="s1"> </span>is used.</p>
<p class="p3"><span class="s2">Accept \(8.23(\%)\) </span>(\(8.22510...\) <span class="s2">if \(138.6\)</span> <span class="s2">is used.</span></p>
<p class="p1">Follow through from their answer to part (b).</p>
<p class="p1">If answer to part (b) is \(46.2\)<span class="s1">, </span>answer to part (c) is \(225\%\), award <strong><em>(M1)(A1)</em>(ft) </strong>with or without working seen. If answer to part (b) is negative, award at most <strong><em>(M1)(A0)</em></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><span style="font-family: times new roman,times; font-size: medium;">The diagram shows a rectangular based right pyramid VABCD in which \({\text{AD}} = 20{\text{ cm}}\), \({\text{DC}} = 15{\text{ cm}}\) and the height of the pyramid, \({\text{VN}} = 30{\text{ cm}}\).</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</span><br><span>(i) the length of AC;</span><br><span>(ii) the length of VC.</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>Calculate the angle between VC and the base ABCD.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(\sqrt {{{15}^2} + {{20}^2}} \) <em><strong>(M1)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in Pythagoras Formula.</span></p>
<p> </p>
<p><span>\({\text{AC}} = 25{\text{ (cm)}}\) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span>(ii) \(\sqrt {{{12.5}^2} + {{30}^2}} \) <em><strong>(M1)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in Pythagoras Formula.</span></p>
<p> </p>
<p><span>\({\text{VC}} = 32.5{\text{ (cm)}}\) <strong><em>(A1)</em>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Follow through from their AC found in part (a).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\sin {\text{VCN}} = \frac{{30}}{{32.5}}\) <strong>OR</strong> \(\tan {\text{VCN}} = \frac{{30}}{{12.5}}\) <strong>OR</strong> \(\cos {\text{VCN}} = \frac{{12.5}}{{32.5}}\) <em><strong>(M1)</strong></em></span><br><span>\({ = 67.4^ \circ }\) (\(67.3801 \ldots \)) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Accept alternative methods. Follow through from part (a) and/or part (b).</span></p>
<div class="question_part_label">b.</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>
<br><hr><br><div class="specification">
<p>A park in the form of a triangle, ABC, is shown in the following diagram. AB is 79 km and BC is 62 km. Angle A\(\mathop {\text{B}}\limits^ \wedge \)C is 52°.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the length of side AC in km.</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 area of the park.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>(AC<sup>2</sup> =) 62<sup>2</sup> + 79<sup>2</sup> − 2 × 62 × 79 × cos(52°) <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting in the cosine rule formula, <em><strong>(A1)</strong></em> for correct substitution.</p>
<p>63.7 (63.6708…) (km) <em><strong> (A1) (C3)</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>\(\frac{1}{2}\) × 62 × 79 × sin(52°) <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting in the area of triangle formula, <em><strong>(A1)</strong></em> for correct substitution.</p>
<p>1930 km<sup>2</sup> (1929.83…km<sup>2</sup>) <em><strong>(A1) (C3)</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</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>
<br><hr><br><div class="specification">
<p>Julio is making a wooden pencil case in the shape of a large pencil. The pencil case consists of a cylinder attached to a cone, as shown.</p>
<p>The cylinder has a radius of <em>r</em> cm and a height of 12 cm.</p>
<p>The cone has a base radius of <em>r</em> cm and a height of 10 cm.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for the slant height of the cone <strong>in terms of <em>r</em></strong>.</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>The total external surface area of the pencil case rounded to 3 significant figures is 570 cm<sup>2</sup>.</p>
<p>Using your graphic display calculator, calculate the value of <em>r</em>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>(slant height<sup>2</sup> =) 10<sup>2</sup> + <em>r </em><sup>2</sup> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> For correct substitution of 10 and <em>r</em> into Pythagoras’ Theorem.</p>
<p>\(\sqrt {{{10}^2} + {r^2}} \) <em><strong>(A1) (C2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\pi {r^2} + 2\pi r \times 12 + \pi r\sqrt {100 + {r^2}} = 570\) <em><strong>(M1)(M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in curved surface area of cylinder and area of the base, <em><strong>(M1)</strong></em> for their correct substitution in curved surface area of cone, <em><strong>(M1)</strong></em> for adding their 3 surface areas and equating to 570. Follow through their part (a).</p>
<p>= 4.58 (4.58358...) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C4)</strong></em></p>
<p><strong>Note:</strong> Last line must be seen to award final <em><strong>(A1)</strong></em>. Follow through from part (a).</p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.</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>
<br><hr><br><div class="specification">
<p>A solid right circular cone has a base radius of 21 cm and a slant height of 35 cm.<br>A smaller right circular cone has a height of 12 cm and a slant height of 15 cm, and is removed from the top of the larger cone, as shown in the diagram.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the radius of the base of the cone which has been removed.</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 curved surface area of the cone which has been removed.</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>Calculate the curved surface area of the remaining solid.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(\sqrt {{{15}^2} - {{12}^2}} \) <em><strong> (M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into Pythagoras theorem.</p>
<p><strong>OR</strong></p>
<p>\(\frac{{{\text{radius}}}}{{21}} = \frac{{15}}{{35}}\) <em><strong> (M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for a correct equation.</p>
<p>= 9 (cm) <em><strong>(A1) (C2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\pi \times 9 \times 15\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their correct substitution into curved surface area of a cone formula.</p>
<p>\( = 424\,\,{\text{c}}{{\text{m}}^2}\,\,\,\,\,\left( {135\pi ,\,\,424.115...{\text{c}}{{\text{m}}^2}} \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note</strong>: Follow through from part (a).</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>\(\pi \times 21 \times 35 - 424.115...\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their correct substitution into curved surface area of a cone formula and for subtracting their part (b).</p>
<p>\( = 1880\,\,{\text{c}}{{\text{m}}^2}\,\,\,\,\,\left( {600\pi ,\,\,1884.95...{\text{c}}{{\text{m}}^2}} \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (b).</p>
<p><em><strong>[2 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.</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="question" style="padding-left: 20px; padding-right: 20px;">
<p>Temi’s sailing boat has a sail in the shape of a right-angled triangle, \({\text{ABC}}{\text{.}}\,\,\,{\text{BC}} = \,\,5.45{\text{m}}\),<br>angle \({\text{CAB}} = {76^{\text{o}}}\) and angle \({\text{ABC}} = {90^{\text{o}}}\).</p>
<p>Calculate \({\text{AC}}\), the height of Temi’s sail.</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><img 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" alt></p>
<p>William also has a sailing boat with a sail in the shape of a right-angled triangle, \({\text{TRS}}\).<br>\({\text{RS}}\,\,{\text{ = }}\,\,{\text{2}}{\text{.80m}}\). The area of William’s sail is \({\text{10}}{\text{.7}}\,{{\text{m}}^2}\).</p>
<p>Calculate \({\text{RT}}\), the height of William’s sail.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>Units are required in parts (a) and (b).</strong></p>
<p>\({\text{sin}}\,\,{76^{\text{o}}} = \,\,\frac{{5.45}}{{{\text{AC}}}}\) <em><strong>(M1)</strong></em></p>
<p><strong>Note: </strong>Award<em> <strong>(M1)</strong></em> for correct substitution into correct trig formula. </p>
<p>\({\text{AC}}\,\, = \,\,5.62{\text{m}}\,\,\,( = 5.61684...{\text{m}})\) <em><strong>(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> The answer is \(5.62{\text{m}}\), <strong>the units are required. </strong></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{1}{2}\,\, \times \,\,2.80\,\, \times \,\,{\text{RT}}\,\,{\text{ = }}\,\,{\text{10}}{\text{.7}}\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into area of a triangle formula or equivalent.</p>
<p>\({\text{RT}}\,\,{\text{ = }}\,\,{\text{7}}{\text{.64}}\,{\text{m (7}}{\text{.64285}}...{\text{m)}}\) <em><strong>(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> The answer is \({\text{7}}{\text{.64}}\,{\text{m}}\), <strong>the units are required.</strong></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Question 2: Trigonometry and area<br>The response to this question was mixed, with many fully correct attempts. Those failing to score 6 marks often either lost a mark due to the use of Pythagoras and premature rounding or due to an incorrect trigonometric ratio used in a right angled triangle. The use of sine and cosine rule often led to errors.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 2: Trigonometry and area<br>The response to this question was mixed, with many fully correct attempts. Those failing to score 6 marks often either lost a mark due to the use of Pythagoras and premature rounding or due to an incorrect trigonometric ratio used in a right angled triangle. The use of sine and cosine rule often led to errors.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>FreshWave brand tuna is sold in cans that are in the shape of a cuboid with length \(8\,{\text{cm}}\), width \({\text{5}}\,{\text{cm}}\) and height \({\text{3}}{\text{.5}}\,{\text{cm}}\). HappyFin brand tuna is sold in cans that are cylindrical with diameter \({\text{7}}\,{\text{cm}}\) and height \({\text{4}}\,{\text{cm}}\).</p>
<p><img 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" alt></p>
<p>Find the volume, in \({\text{c}}{{\text{m}}^3}\), of a can of</p>
<p>i) FreshWave tuna;</p>
<p>ii) HappyFin tuna.</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>The price of tuna per \({\text{c}}{{\text{m}}^3}\) is the same for each brand. A can of FreshWave tuna costs \(90\) cents.</p>
<p>Calculate the price, in cents, of a can of HappyFin tuna.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>i) \(8\,\, \times \,\,5\,\, \times \,3.5\) <em><strong>(M1)</strong></em></p>
<p>\( = 140\) <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in volume formula.</p>
<p> </p>
<p>ii) \(\pi \,\, \times \,\,{3.5^2}\,\, \times \,\,4\) <em><strong>(M1)</strong></em></p>
<p>\( = 154\,\,\,\,(153.938...,\,\,49\pi )\) <em><strong>(A1) (C4)</strong></em></p>
<p><strong>Note: </strong>Award<strong><em> (M1)</em> </strong>for correct substitution in volume formula.</p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{90\,\, \times \,\,{\text{their}}\,154}}{{{\text{their}}\,140}}\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for multiplying the given \(90\) by their part (a)(ii) and dividing by their part (a)(i). Follow through from (a). Accept correct alternative methods.</p>
<p>\( = 99\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note: </strong>Award a maximum of<em><strong> (M1)(A0)</strong></em> if the final answer is not an integer.</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Question 4: Volume<br>Part (a) was generally answered well, as was part (b); misreading of the question was the main problem.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 4: Volume<br>Part (a) was generally answered well, as was part (b); misreading of the question was the main problem. Part (c), though straightforward in concept, was not well understood by a number of candidates, and many did not give the answer as a number of cents as instructed in the question.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The planet Earth takes one year to revolve around the Sun. Assume that a year is 365 days and the path of the Earth around the Sun is the circumference of a circle of radius \(150000000{\text{ km}}\).</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 distance travelled by the Earth in <strong>one day</strong>.</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>Give your answer to part (a) in the form \(a \times {10^k}\) where \(1 \leqslant a \leqslant 10\) and \(k \in \mathbb{Z}\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(2\pi \frac{{150000000}}{{365}}\) <em><strong>(M1)(A1)(M1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for substitution in correct formula for circumference of circle.</span></p>
<p><span>Award <em><strong>(A1)</strong></em> for correct substitution.</span></p>
<p><span>Award <em><strong>(M1)</strong></em> for dividing their perimeter by \(365\).</span></p>
<p><span>Award <em><strong>(M0)(A0)(M1)</strong></em> for \(\frac{{150000000}}{{365}}\) .</span></p>
<p><span> </span></p>
<p><span>\(2580000{\text{ km}}\) <em><strong>(A1)</strong></em> <em><strong>(C4)</strong></em></span></p>
<p><span><em><strong>[4 marks]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(2.58 \times {10^6}\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <strong><em>(A1)</em>(ft)</strong> for \(2.58\), <strong><em>(A1)</em>(ft)</strong> for \({10^6}\) . </span><span>Follow through from their answer to part (a).</span> <span>The follow through for the index should be dependent not only on the answer to part (a), but also on the value of their mantissa.</span> <span>No <em><strong>(AP)</strong></em> penalty for first <em><strong>(A1)</strong></em> provided their value is to 3 sf or is all their digits from part (a).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</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 significant number of candidates simply divided \(150 000 000\) by \(365\) and consequently lost all but one method mark in part (a). Presumably these candidates assumed that the given value was the circumference rather than the radius. <br></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 significant number of candidates simply divided \(150 000 000\) by \(365\) and consequently lost all but one method mark in part (a). Presumably these candidates assumed that the given value was the circumference rather than the radius. Recovery in part (b) did, however, result in many getting both marks here. It was noted on some answers to part (b) that the index power was negative rather than positive suggesting a misunderstanding by candidates of standard form.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br>