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</div><h2>SL Paper 1</h2><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A liquid is heated so that after \(20\) seconds of heating its temperature, \(T\) , is \({25^ \circ }{\text{C}}\) and after \(50\) seconds of heating its temperature is \({37^ \circ }{\text{C}}\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The temperature of the liquid at time \(t\) can be modelled by \(T = at + b\) , where \(t\) is the time in seconds after the start of heating.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Using this model one equation that can be formed is \(20a + b = 25\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using the model, write down a second equation in \(a\) and \(b\) .</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>Using your graphic display calculator or otherwise, find the value of \(a\) and of \(b\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use the model to predict the temperature of the liquid \(60{\text{ seconds}}\) after the start of heating.</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>\(50a + b = 37\) <em><strong>(A1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(50a + b\) , <em><strong>(A1)</strong></em> for \(= 37\) .</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(a = 0.4\), \(b = 17\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span></p>
<p> </p>
<p><span>Notes: Award <em><strong>(M1)</strong></em> for attempt to solve their equations if this is done analytically. If the GDC is used, award <strong>(ft)</strong> even if no working seen.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(T = 0.4(60) + 17\) <em><strong>(M1)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of their values and \(60\) into equation for \(T\).</span></p>
<p> </p>
<p><span>\(T = 41{\text{ }}{{\text{(}}^ \circ }{\text{C}})\) <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 part (b).</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;">A plumber in Australia charges 90 AUD per hour for work, plus a fixed cost. His total charge is represented by the cost function <em>C</em> = 60 + 90<em>t</em>, where<em> t</em> is in hours.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the fixed cost.</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>It takes \(3 \frac{1}{2}\) hours to complete a job for Paula. Find the total cost.</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>Steve received a bill for 510 AUD. Calculate the time it took the plumber to complete the job.</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>AUD 60 <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>C</em> = 60 + 90(3.5) = AUD 375 <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 correct substitution of 3.5.</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> </p>
<p><span><strong><em>Note: Unit penalty (UP) applies in this part</em></strong></span></p>
<p> </p>
<p><span> </span></p>
<p><span>510 = 60 + 90<em>t</em> <em><strong>(M1)(A1)</strong></em></span></p>
<p><span><em><strong>(UP) </strong></em> <em>t</em> = 5h (hours, hrs) <em><strong>(A1)</strong></em> <em><strong>(C3)<br></strong></em><br></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for setting formula = to any number.</span></p>
<p><span><em><strong>(A1)</strong></em> for 510 seen.</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;">The majority of candidates answered this question correctly. Some gave an answer of 150 AUD.</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 answered this question correctly.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The majority of candidates answered this question correctly. Very few lost a unit penalty mark in this part.</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 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="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the two functions, \(f\) and \(g\), where</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;"> \(f(x) = \frac{5}{{{x^2} + 1}}\)</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;"> \(g(x) = {(x - 2)^2}\)</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Sketch the graphs of \(y = f(x)\) and \(y = g(x)\) on the axes below. Indicate clearly the points where each graph intersects the <em>y-</em>axis.</span></p>
<div>
<br><span><img src="images/Schermafbeelding_2014-09-03_om_07.24.03.png" alt></span>
</div>
<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>Use your graphic display calculator to solve \(f(x) = g(x)\).</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><img src="images/Schermafbeelding_2014-09-03_om_07.27.59.png" alt></span></p>
<p><span>\(f(x)\): a smooth curve symmetrical about <em>y</em>-axis, \(f(x) > 0\) <strong><em>(A1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>If the graph crosses the <em>x</em>-axis award <strong><em>(A0)</em></strong>.</span></p>
<p> </p>
<p><span>Intercept at their numbered \(y = 5\) <strong><em>(A1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Accept clear scale marks instead of a number.</span></p>
<p> </p>
<p><span>\(g(x)\): a smooth parabola with axis of symmetry at about \(x = 2\) (the 2 does not need to be numbered) and \(g(x) \geqslant 0\) <strong><em>(A1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Right hand side must not be higher than the maximum of \(f(x)\) at \(x = 4\).</span></p>
<p><span> Accept the quadratic correctly drawn beyond \(x = 4\).</span></p>
<p> </p>
<p><span>Intercept at their numbered \(y = 4\) <strong><em>(A1) (C4)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Accept clear scale marks instead of a number.</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>\(–0.195, 2.76\) \((–0.194808…, 2.761377…)\) <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft) <em>(C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A0)(A1)</em>(ft) </strong>if both coordinates are given.</span></p>
<p><span> Follow through only if \(f(x) = \frac{5}{{{x^2}}} + 1\) is sketched; the solutions are \(–0.841, 3.22\) \((–0.840913…, 3.217747...)\)</span></p>
<p> </p>
<p><span><strong><em>[2 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;">
<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;">Many candidates attempted this question but relatively few were awarded the full six marks. Although they were asked to indicate clearly where the graph met the axes, many did not do this. Some entered the functions incorrectly into their calculator. A common error in part (b) was to give ordered pairs and therefore were not awarded the final mark.</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;">Many candidates attempted this question but relatively few were awarded the full six marks. Although they were asked to indicate clearly where the graph met the axes, many did not do this. Some entered the functions incorrectly into their calculator. A common error in part (b) was to give ordered pairs and therefore were not awarded the final mark.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A quadratic function \(f\) is given by \(f(x) = a{x^2} + bx + c\). The points \((0,{\text{ }}5)\) and \(( - 4,{\text{ }}5)\) lie on the graph of \(y = f(x)\).</p>
</div>
<div class="specification">
<p>The \(y\)-coordinate of the minimum of the graph is 3.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of the axis of symmetry of the graph of \(y = f(x)\).</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 value of \(c\).</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 value of \(a\) and of \(b\).</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>\(x = - 2\) <strong><em>(A1)(A1) (C2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for \(x = \) (a constant) and <strong><em>(A1) </em></strong>for \( - 2\).</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>\((c = ){\text{ }}5\) <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>\( - \frac{b}{{2a}} = - 2\)</p>
<p>\(a{( - 2)^2} - 2b + 5 = 3\) or equivalent</p>
<p>\(a{( - 4)^2} - 4b + 5 = 5\) or equivalent</p>
<p>\(2a( - 2) + b = 0\) or equivalent <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for two of the above equations.</p>
<p> </p>
<p>\(a = 0.5\) <strong><em>(A1)</em>(ft)</strong></p>
<p>\(b = 2\) <strong><em>(A1)</em>(ft) <em>(C3)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award at most <strong><em>(M1)(A1)</em>(ft)<em>(A0) </em></strong>if the answers are reversed.</p>
<p>Follow through from parts (a) and (b).</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>Maria owns a cheese factory. The amount of cheese, in kilograms, Maria sells in one week, \(Q\), is given by</p>
<p style="text-align: center;">\(Q = 882 - 45p\),</p>
<p>where \(p\) is the price of a kilogram of cheese in euros (EUR).</p>
</div>
<div class="specification">
<p>Maria earns \((p - 6.80){\text{ EUR}}\) for each kilogram of cheese sold.</p>
</div>
<div class="specification">
<p>To calculate her weekly profit \(W\), in EUR, Maria multiplies the amount of cheese she sells by the amount she earns per kilogram.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down how many kilograms of cheese Maria sells in one week if the price of a kilogram of cheese is 8 EUR.</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 how much Maria earns in one week, from selling cheese, if the price of a kilogram of cheese is 8 EUR.</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 an expression for \(W\) in terms of \(p\).</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>Find the price, \(p\), that will give Maria the highest weekly profit.</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>522 (kg) <strong><em>(A1) (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>\(522(8 - 6.80)\) or equivalent <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for multiplying their answer to part (a) by \((8 - 6.80)\).</p>
<p> </p>
<p>626 (EUR) (626.40) <strong><em>(A1)</em>(ft) <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>\((W = ){\text{ }}(882 - 45p)(p - 6.80)\) <strong><em>(A1)</em></strong></p>
<p><strong>OR</strong></p>
<p>\((W = ) - 45{p^2} + 1188p - 5997.6\) <strong><em>(A1) (C1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>sketch of \(W\) with some indication of the maximum <strong><em>(M1)</em></strong></p>
<p><strong>OR</strong></p>
<p>\( - 90p + 1188 = 0\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for equating the correct derivative of their part (c) to zero.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>\((p = ){\text{ }}\frac{{ - 1188}}{{2 \times ( - 45)}}\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into the formula for axis of symmetry.</p>
<p> </p>
<p>\((p = ){\text{ }}13.2{\text{ (EUR)}}\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from their part (c), if the value of \(p\) is such that \(6.80 < p < 19.6\).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></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 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 a trial for a new drug, scientists found that the amount of the drug in the bloodstream decreased over time, according to the model</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;">\[D(t) = 1.2 \times {(0.87)^t},{\text{ }}t \geqslant 0\]</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;">where \(D\) is the amount of the drug in the bloodstream in mg per litre \({\text{(mg}}\,{{\text{l}}^{ - 1}}{\text{)}}\) and \(t\) is the time in hours.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the amount of the drug in the bloodstream at \(t = 0\).</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 amount of the drug in the bloodstream after 3 hours.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to determine the time it takes for the amount of the drug in the bloodstream to decrease to </span><span><span><span>\(0.333{\text{ mg}}{{\text{1}}^{ - 1}}\).</span></span></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>\(1.2{\text{ (mg}}\,{{\text{l}}^{ - 1}}{\text{)}}\) <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>\(1.2 \times {(0.87)^3}\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into given formula.</span></p>
<p> </p>
<p><span>\( = {\text{0.790 (mg}}\,{{\text{l}}^{ - 1}}{\text{) (0.790203}} \ldots {\text{)}}\) <strong><em>(A1) (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>\(1.2 \times {0.87^t} = 0.333\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for setting up the equation.</span></p>
<p><br><br><img src="images/low_down_graph.jpg" alt> <span><strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Some indication of scale is to be shown, for example the window used on the calculator.</span></p>
<p><span> Accept alternative methods.</span></p>
<p> </p>
<p><span>\(9.21\) (hours) (\(9.20519…\), 9 hours 12 minutes, 9:12) <strong><em>(A1) (C3)</em></strong></span></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><span style="font-size: medium; font-family: times new roman,times;">The number of bacteria in a colony is modelled by the function </span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">\(N(t) = 800 \times 3^{0.5t}, {\text{ }} t \geqslant 0\), </span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">where \(N\) is the number of bacteria and \(t\) is the time in hours.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of bacteria in the colony at time \(t = 0\).</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 number of bacteria present at 2 hours and 30 minutes. Give your answer correct to the nearest hundred bacteria.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the time, in hours, for the number of bacteria to reach 5500.</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>800 <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>\(800 \times {3^{(0.5 \times 2.5)}}\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted formula.</span></p>
<p><br><span>\( = 3158.57\)... <em><strong>(A1)</strong></em></span></p>
<p><span>\(= 3200\) <em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Final <em><strong>(A1)</strong></em> is given for correctly rounding <strong><em>their</em></strong> answer. This may be awarded regardless of a preceding <em><strong>(A0)</strong></em>.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(5500 = 800 \times {3^{(0.5 \times t)}}\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for equating function to 5500. Accept correct alternative methods.</span></p>
<p><br><span>\(= 3.51{\text{ hours}}\) (3.50968...) <em><strong>(A1)</strong></em> <em><strong>(C2)</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;">
[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>A company sells fruit juices in cylindrical cans, each of which has a volume of \(340\,{\text{c}}{{\text{m}}^3}\). The surface area of a can is \(A\,{\text{c}}{{\text{m}}^2}\) and is given by the formula</p>
<p>\(A = 2\pi {r^2} + \frac{{680}}{r}\) ,</p>
<p>where \(r\) is the radius of the can, in \({\text{cm}}\).</p>
<p>To reduce the cost of a can, its surface area must be minimized.</p>
<p>Find \(\frac{{{\text{d}}A}}{{{\text{d}}r}}\)</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 value of \(r\) that minimizes the surface area of a can.</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>\(\left( {\frac{{{\text{d}}A}}{{{\text{d}}r}}} \right) = 4\pi r - \frac{{680}}{{{r^2}}}\) <em><strong>(A1)(A1)(A1) (C3)</strong></em></p>
<p><strong>Note: </strong>Award <em><strong>(A1)</strong></em> for \(4\pi r\) (accept \(12.6r\)), <em><strong>(A1)</strong></em> for \( - 680\), <em><strong>(A1)</strong></em> for \(\frac{1}{{{r^2}}}\) or \({r^{ - 2}}\)</p>
<p>Award at most <em><strong>(A1)(A1)(A0)</strong></em> if additional terms are seen.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(4\pi r - \frac{{680}}{{{r^2}}} = 0\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for equating their \(\frac{{{\text{d}}A}}{{{\text{d}}r}}\) to zero.</p>
<p>\(4\pi {r^3} - 680 = 0\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for initial correct rearrangement of the equation. This may be assumed if \({r^3} = \frac{{680}}{{4\pi }}\) or \(r = \sqrt[3]{{\frac{{680}}{{4\pi }}}}\) seen.</p>
<p><strong>OR</strong></p>
<p>sketch of \(A\) with some indication of minimum point <em><strong>(M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for sketch of \(A\), <em><strong>(M1)</strong></em> for indication of minimum point.</p>
<p><strong>OR</strong></p>
<p>sketch of \(\frac{{{\text{d}}A}}{{{\text{d}}r}}\) with some indication of zero <em><strong>(M1)(M1)</strong></em></p>
<p><strong>Note: </strong>Award <em><strong>(M1)</strong></em> for sketch of \(\frac{{{\text{d}}A}}{{{\text{d}}r}}\), <em><strong>(M1)</strong></em> for indication of zero.</p>
<p>\((r = )\,\,3.78\,({\text{cm}})\,\,\,\,\,(3.78239...)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong> </em> </p>
<p><strong>Note:</strong> Follow through 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;">
<p>Question 15: Optimization<br>Many candidates were able to differentiate in part (a), but then were unable to relate this to part (b). However, it seemed that many more had not studied the calculus at all.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 15: Optimization<br>Many candidates were able to differentiate in part (a), but then were unable to relate this to part (b). However, it seemed that many more had not studied the calculus at all.</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;">Given the function \(f (x) = 2 \times 3^x\) for −2 \( \leqslant \) <em>x</em> \( \leqslant \) 5,</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>find the range of \(f\).</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 value of \(x\) given that \(f (x) =162\).</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>\(f (-2) = 2 \times 3^{-2}\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(= \frac{{2}}{{9}}(0.222)\) <em><strong>(A1)</strong></em></span></p>
<p><span>\(f (5) = 2 \times 3^5\)</span></p>
<p><span>\(= 486\) <em><strong>(A1)</strong></em></span></p>
<p><span>\({\text{Range }}\frac{2}{9} \leqslant f(x) \leqslant 486\) <strong>OR</strong> \(\left[ {\frac{2}{9},{\text{ }}486} \right]\) </span><span><em><strong>(A1)</strong></em> <em><strong>(C4)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of –2 or 5 into \(f (x)\), </span><span><em><strong>(A1)(A1)</strong></em> for each correct end point.</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>\(2 \times 3^x = 162\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(x = 4\) <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">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;">Part (a) proved to be difficult to gain the maximum marks as, although candidates could find the end points, they did not seem to be able to identify the range of the function. Many students gave a list of values for the range, which indicates that this concept was not understood well.</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 part (b).</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A potato is placed in an oven heated to a temperature of 200<span class="s1">°</span>C.</p>
<p class="p1">The temperature of the potato, in <span class="s1">°</span>C, is modelled by the function \(p(t) = 200 - 190{(0.97)^t}\), where \(t\) is the time, in minutes, that the potato has been in the oven.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down the temperature of the potato at the moment it is placed in the oven.</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 temperature of the potato half an hour after it has been placed in the oven.</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">After the potato has been in the oven for \(k\) minutes, its temperature is 40<span class="s1">°</span>C.</p>
<p class="p1">Find the value of \(k\).</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"><strong><em>For parts (a) and (b) only, the first time a correct answer has incorrect or missing units, the final (A1) is not awarded.</em></strong></p>
<p class="p2">\(200 - 190{(0.97)^0}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p2"><span class="s1"><strong>Note: </strong>Award <strong><em>(M1) </em></strong></span>for correct substitution.</p>
<p class="p2"> </p>
<p class="p2">\( = 10\,^\circ {\text{C}}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(A1) <span class="Apple-converted-space"> </span>(C2)</em></strong></span></p>
<p class="p1"><strong>Note: </strong>Units are required.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong><em>For parts (a) and (b) only, the first time a correct answer has incorrect or missing units, the final (A1) is not awarded.</em></strong></p>
<p class="p2">\(200 - 190{(0.97)^{30}}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p2"><span class="s1"><strong>Note:<span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong></span>for correct substitution.</p>
<p class="p4"> </p>
<p class="p2">\( = 124^\circ {\text{C }}(123.808 \ldots ^\circ {\text{C}})\) <span class="s1"><strong><em>(A1) (C2)</em></strong></span></p>
<p class="p1"><strong>Note:<span class="Apple-converted-space"> </span></strong>Units are required, unless already omitted in part (a).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(200 - 190{(0.97)^k} = 40\) <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.</p>
<p class="p2"> </p>
<p class="p1">\(k = 5.64{\text{ (minutes) }}(5.64198 \ldots )\) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C2)</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>Sejah placed a baking tin, that contained cake mix, in a preheated oven in order to bake a cake. The temperature in the centre of the cake mix, \(T\), in degrees Celsius (°C) is given by</p>
<p>\[T(t) = 150 - a \times {(1.1)^{ - t}}\]</p>
<p>where \(t\) is the time, in minutes, since the baking tin was placed in the oven. The graph of \(T\) is shown in the following diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_18.27.39.png" alt="N17/5/MATSD/SP1/ENG/TZ0/12"></p>
</div>
<div class="specification">
<p>The temperature in the centre of the cake mix was 18 °C when placed in the oven.</p>
</div>
<div class="specification">
<p>The baking tin is removed from the oven 15 minutes after the temperature in the centre of the cake mix has reached 130 °C.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down what the value of 150 represents in the context of the question.</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 value of \(a\).</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 total time that the baking tin is in the oven.</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>the temperature in the oven <strong><em>(A1)</em></strong></p>
<p><strong>OR</strong></p>
<p>the maximum possible temperature of the cake mix <strong><em>(A1) (C1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A0) </em></strong>for “the maximum temperature”.</p>
<p> </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>\(18 = 150 - a( \times 1.1^\circ )\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution of 18 and 0. Substitution of 0 can be implied.</p>
<p> </p>
<p>\((a) = 132\) <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>\(150-132 \times {1.1^{ - t}} = 130\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substituting their <em>a </em>and equating to 130. Accept an inequality.</p>
<p>Award <strong><em>(M1) </em></strong>for a sketch of the horizontal line on the graph.</p>
<p> </p>
<p>\(t = 19.8{\text{ }}(19.7992 \ldots )\) <strong><em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from part (b).</p>
<p> </p>
<p>34.8 (minutes) (34.7992…, 34 minutes 48 seconds) <strong><em>(A1)</em>(ft) <em>(C3)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award the final <strong><em>(A1) </em></strong>for adding 15 minutes to their \(t\) value.</p>
<p>In part (c), award <strong><em>(C2) </em></strong>for a final answer of 19.8 with no working.</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>Consider the function \(f\left( x \right) = \frac{{{x^4}}}{4}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <em>f'</em>(<em>x</em>)</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 gradient of the graph of <em>f</em> at \(x = - \frac{1}{2}\).</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>Find the <em>x</em>-coordinate of the point at which the <strong>normal</strong> to the graph of <em>f</em> has gradient \({ - \frac{1}{8}}\).</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><em>x</em><sup>3</sup> <em><strong>(A1) (C1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A0)</strong></em> for \(\frac{{4{x^3}}}{4}\) and not simplified to <em>x</em><sup>3</sup>.</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>\({\left( { - \frac{1}{2}} \right)^3}\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of \({ - \frac{1}{2}}\) into their derivative.</p>
<p>\({ - \frac{1}{8}}\) (−0.125) <em><strong> (A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note:</strong> Follow through from their 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><em>x</em><sup>3</sup> = 8 <em><strong>(A1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for 8 seen maybe seen as part of an equation <em>y</em> = 8<em>x</em> + <em>c</em>, <em><strong>(M1)</strong></em> for equating their derivative to 8.</p>
<p>(<em>x</em> =) 2 <em><strong>(A1) (C3)</strong></em></p>
<p><strong>Note:</strong> Do not accept (2, 4).</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</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;">Shiyun bought a car in 1999. The value of the car \(V\) , in USD, is depreciating according to the exponential model</span><br><span style="font-family: times new roman,times; font-size: medium;">\[V = 25000 \times {1.5^{ - 0.2t}}{\text{, }}t \geqslant 0\]</span><br><span style="font-family: times new roman,times; font-size: medium;">where \(t\) is the time, in years, that Shiyun has owned the car.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of the car when Shiyun bought it.</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 value of the car three years after Shiyun bought it. Give your answer correct to <strong>two decimal places</strong>.</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 time for the car to depreciate to half of its value since Shiyun bought it.</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>\(25000{\text{ USD}}\) <em><strong>(A1)</strong></em> <em><strong>(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>\(25000 \times {1.5^{ - 0.6}}\) <em><strong>(M1)</strong></em></span><br><span>\(19601.32{\text{ USD}}\) <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">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(12500 = 25000 \times {1.5^{ - 0.2t}}\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(M1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <strong><em>(A1)</em>(ft)</strong> for \(12 500\) seen. Follow through from their answer to part (a). Award <em><strong>(M1)</strong></em> for equating their half value to \(25000 \times {1.5^{ - 0.2t}}\) . Allow the use of an inequality.</span></p>
<p><span><strong>OR</strong></span></p>
<p><span>Graphical method (sketch):</span></p>
<p><span><strong><em>(A1)</em>(ft)</strong> for \(y =12 500\) seen on the sketch. Follow through from their answer to part (a). <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span><em><strong>(M1)</strong></em> for the exponent model and an indication of their intersection with their horizontal line. <em><strong>(M1)</strong></em></span></p>
<p><span><span>\(8.55\) </span> <span><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></span></span></p>
<p><span><span><em><strong>[3 marks]<br></strong></em></span></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;">A substituted value of \(t = 1\) in part (a) saw many incorrect answers of \(23052.70\) for this part of the question. Part (b) was better attempted with many correct answers seen. Many candidates picked up the first two marks of part (c) equating a correct expression to half their answer found in part (a). Many though did not seem to know the correct process of using their GDC to find the required answer. Much <em>trial and improvement</em> was seen here with varying degrees of success.</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 substituted value of \(t = 1\) in part (a) saw many incorrect answers of \(23052.70\) for this part of the question. Part (b) was better attempted with many correct answers seen. Many candidates picked up the first two marks of part (c) equating a correct expression to half their answer found in part (a). Many though did not seem to know the correct process of using their GDC to find the required answer. Much <em>trial and improvement</em> was seen here with varying degrees of success.</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;">A substituted value of \(t = 1\) in part (a) saw many incorrect answers of \(23052.70\) for this part of the question. Part (b) was better attempted with many correct answers seen. Many candidates picked up the first two marks of part (c) equating a correct expression to half their answer found in part (a). Many though did not seem to know the correct process of using their GDC to find the required answer. Much <em>trial and improvement</em> was seen here with varying degrees of success.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider the quadratic function, \(f(x) = px(q - x)\), where \(p\) and \(q\) are positive integers.</p>
<p class="p2"><span class="s1">The graph of \(y = f(x)\) </span>passes through the point \((6,{\text{ }}0)\)<span class="s1">.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the value of \(q\).</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 vertex of the function is \((3,{\text{ }}27)\)<span class="s1">.</span></p>
<p class="p2">Find the value 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 class="p1">The vertex of the function is \((3,{\text{ }}27)\)<span class="s1">.</span></p>
<p class="p1">Write down the range of \(f\).</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>\(0 = p(6)(q - 6)\) <strong><em>(M1)</em></strong></p>
<p>\(q = 6\) <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>OR</strong></p>
<p>\(f(x) = - p{x^2} + pqx\)</p>
<p>\(3 = \frac{{ - pq}}{{ - 2p}}\) <strong><em>(M1)</em></strong></p>
<p>\(q = 6\) <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>OR</strong></p>
<p>\(f(x) = - p{x^2} + pqx\)</p>
<p>\(f'(x) = pq - 2px\) <strong><em>(M1)</em></strong></p>
<p>\(pq - 2p(3) = 0\)</p>
<p>\(q = 6\) <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">\(27 = p(3)(6 - 3)\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution of the vertex <span class="s1">\((3,{\text{ }}27)\) </span><strong>and </strong><em>their</em> \(q\) into or equivalent \(f(x) = px(q - x)\) or equivalent.</p>
<p class="p2"> </p>
<p class="p1">\(p = 3\) <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 part (a).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(y \leqslant 27\;\;\;\left( {f(x) \leqslant 27} \right)\) <span class="Apple-converted-space"> </span><strong><em>(A1)(A1) <span class="Apple-converted-space"> </span>(C2)</em></strong></p>
<p class="p1"><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for \(y \leqslant {\text{ }}\left( {{\text{or }}f(x) \leqslant } \right)\), <strong><em>(A1) </em></strong>for \(27\)<span class="s1"> </span>as part of an inequality.</p>
<p class="p1">Accept alternative notation: \(( - \infty ,{\text{ }}27],{\text{ }}] - \infty ,{\text{ }}27]\).</p>
<p class="p1">Award <strong><em>(A0)(A1) </em></strong>for \([27,{\text{ }}- \infty )\).</p>
<p class="p1">Award <strong><em>(A0)(A0) </em></strong>for \(( - \infty ,{\text{ }}\infty )\).</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>This question was left unanswered by many candidates. For candidates who attempted the question, one method mark was often awarded for a correct equation resulting from substitution of the point (6, 0). Many were unable to find the value of <em>q</em>, and therefore did not continue to find the value of <em>p</em>.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many were unable to find the value of <em>q</em>, and therefore did not continue to find the value of <em>p</em>.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Part (c) was poorly attempted, although the range was independent of the values of <em>p</em> and <em>q</em>. The most common error was confusion between domain and range, resulting in an answer of (-∞, ∞).</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 sketch of the function \(f(x) = 5{x^3} - 3{x^5} + 1\) is shown for \( - 1.5 \leqslant x \leqslant 1.5\) and \( - 6 \leqslant y \leqslant 6\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down \(f'(x)\) .</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 tangent to the graph of \(y = f(x)\) at \((1{\text{, }}3)\) .</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 coordinates of the second point where this tangent intersects the graph of \(y = f(x)\) .</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>\(f'(x) = 15{x^2} - 15{x^4}\) <em><strong>(A1)(A1) (C2)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award a maximum of <em><strong>(A1)(A0)</strong></em> if extra terms seen.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(f'(1) = 0\) <em><strong>(M1)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for \(f'(x) = 0\) .</span></p>
<p> </p>
<p><span>\(y = 3\) <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>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(( - 1.38{\text{, }}3)\) \(( - 1.38481 \ldots {\text{, }}3)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Follow through from their answer to parts (a) and (b).</span></p>
<p><span><strong>Note:</strong> Accept \(x = - 1.38\), \(y = 3\) (\(x = - 1.38481 \ldots\) , \(y = 3\)) .</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;">A function <em>f</em> (<em>x</em>) = <em>p</em>×2<em><sup>x</sup></em> + <em>q</em> is defined by the mapping diagram below.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of</span></p>
<p><span>(i) <em>p</em> ;</span></p>
<p><span>(ii) <em>q</em> .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of <em>r </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>Find the value of <em>s </em>.</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>(i) 2<em>p</em> + <em>q</em> = 11 and 4<em>p</em> + <em>q</em> = 17 <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for either two correct equations or a correct equation in one unknown equivalent to 2<em>p</em> = 6 .</span></p>
<p> </p>
<p><span><em>p</em> = 3 <em><strong>(A1)</strong></em></span></p>
<p> </p>
<p><span>(ii) <em>q</em> = 5 <em><strong>(A1)</strong> <strong>(C3)</strong></em></span></p>
<p><span><strong>Notes:</strong> If only one value of <em>p</em> and <em>q</em> is correct and no working shown, award <em><strong>(M0)(A1)(A0)</strong></em>.</span></p>
<p><span> </span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>r</em> = 8 <strong><em>(A1)</em>(ft)</strong> <em><strong>(C1)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their answers for <em>p</em> and <em>q</em> irrespective of whether working is seen.</span></p>
<p><span><em><strong>[1 mark]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>3 × 2<em><sup>s</sup></em> + 5 = 197 <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for setting the correct equation.</span></p>
<p> </p>
<p><span><em>s</em> = 6 <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their values of <em>p</em> and <em>q</em>.</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;">Candidates both understood how to interpret a mapping diagram correctly and did very well on this question or the question was very poorly answered or not answered at all. Writing down two simultaneous equations in part (a) proved to be elusive to many and this prevented further work on this question. Candidates who were able to find values of <em>p</em> and <em>q</em> (correct or otherwise) invariably made a good attempt at finding the value of <em>s</em> in part (c).</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 both understood how to interpret a mapping diagram correctly and did very well on this question or the question was very poorly answered or not answered at all. Writing down two simultaneous equations in part (a) proved to be elusive to many and this prevented further work on this question. Candidates who were able to find values of <em>p</em> and <em>q</em> (correct or otherwise) invariably made a good attempt at finding the value of <em>s</em> in part (c).</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 both understood how to interpret a mapping diagram correctly and did very well on this question or the question was very poorly answered or not answered at all. Writing down two simultaneous equations in part (a) proved to be elusive to many and this prevented further work on this question. Candidates who were able to find values of <em>p</em> and <em>q</em> (correct or otherwise) invariably made a good attempt at finding the value of <em>s</em> in part (c).</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The number of fish, \(N\), in a pond is decreasing according to the model</p>
<p class="p1">\[N(t) = a{b^{ - t}} + 40,\;\;\;t \geqslant 0\]</p>
<p class="p2"><span class="s1">where \(a\) and \(b\) are positive constants, and \(t\) </span>is the time in months since the number of fish in the pond was first counted.</p>
<p class="p2">At the beginning \(840\) <span class="s1">fish were counted.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of \(a\).</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">After \(4\)<span class="s1"> </span>months \(90\)<span class="s1"> </span>fish were counted.</p>
<p class="p1">Find the value of \(b\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The number of fish in the pond will <strong>not </strong>decrease below \(p\).</p>
<p class="p1">Write down the value of \(p\).</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 class="p1">\(a{b^0} + 40 = 840\) <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 substituting \(t = 0\) and equating to \(840\).</p>
<p class="p1"> </p>
<p class="p1">\(a = 800\) <span class="Apple-converted-space"> </span><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">\(800{b^{ - 4}} + 40 = 90\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution of their \(a\)<span class="s1"><em> </em></span>(from part (a)) <strong>and </strong><span class="s1">\(4\) </span>in the formula of the function and equating to \(90\).</p>
<p class="p2"> </p>
<p class="p1">\({b^4} = 16\;\;\;\)<strong>OR</strong>\(\;\;\;\frac{1}{{{b^4}}} = \frac{1}{{16}}\;\;\;\)<strong>OR</strong>\(\;\;\;b = \sqrt[4]{{16}}\;\;\;\)<strong>OR</strong>\(\;\;\;b = {16^{\frac{1}{4}}}\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p3"><span class="s2"><strong>Notes: </strong>Award second <strong><em>(M1) </em></strong></span>for correctly rearranging their equation and eliminating the negative index (see above examples).</p>
<p class="p3">Accept \(\frac{{800}}{{50}}\) <span class="s2">in place of \(16\)</span><span class="s2">.</span></p>
<p class="p2"> </p>
<p class="p1"><strong>OR</strong></p>
<p class="p1"><img src="data:image/png;base64,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" alt> <span class="Apple-converted-space"> </span><strong><em>(M1)(M1)</em></strong></p>
<p class="p1"><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for a decreasing exponential and a horizontal line that are both in the first quadrant, and <strong><em>(M1) </em></strong>for their graphs intersecting.</p>
<p class="p1">For graphs drawn in both first and second quadrants award at most <strong><em>(M1)(M0)</em></strong>.</p>
<p class="p2"> </p>
<p class="p1">\(b = 2\) <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>Note: </strong>Follow through from their answer to part (a) only if \(a\) is positive.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="s1">\(40\) </span><strong><em>(A1) (C1) </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>The size of a computer screen is the length of its diagonal. Zuzana buys a rectangular computer screen with a size of 68 cm, a height of \(y\) cm and a width of \(x\) cm, as shown in the diagram.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="images/Schermafbeelding_2018-02-12_om_18.05.15.png" alt="N17/5/MATSD/SP1/ENG/TZ0/06"></p>
</div>
<div class="specification">
<p>The ratio between the height and the width of the screen is 3:4.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use this information to write down an equation involving \(x\) 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>Use this ratio to write down \(y\) in terms of \(x\).</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 value of \(x\) and of \(y\)<em>.</em></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>\({x^2} + {y^2} = {68^2}\) (or 4624 or equivalent) <strong><em>(A1) (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>\(\frac{y}{x} = \frac{3}{4}\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for a correct equation.</p>
<p> </p>
<p>\(y = \frac{3}{4}x{\text{ }}(y = 0.75x)\) <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>\({x^2} + {\left( {\frac{3}{4}x} \right)^2} = {68^2}{\text{ }}\left( {{\text{or }}{x^2} + \frac{9}{{16}}{x^2} = 4624{\text{ or equivalent}}} \right)\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution of their expression for \(y\) into their answer to part (a). Accept correct substitution of \(x\) in terms of \(y\).</p>
<p> </p>
<p>\(x = 54.4{\text{ (cm), }}y = 40.8{\text{ (cm)}}\) <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft) <em>(C3)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from parts (a) and (b) as long as \(x > 0\) and \(y > 0\).</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 class="p1">Gabriella purchases a new car.</p>
<p class="p1">The car’s value in dollars, \(V\), is modelled by the function</p>
<p class="p1">\[V(t) = 12870 - k{(1.1)^t},{\text{ }}t \geqslant 0\]</p>
<p class="p1">where \(t\) is the number of years since the car was purchased and \(k\) is a constant.</p>
</div>
<div class="specification">
<p class="p1">After two years, the car’s value is <span class="s1">$9143.20</span>.</p>
</div>
<div class="specification">
<p class="p1">This model is defined for \(0 \leqslant t \leqslant n\). At \(n\) years the car’s value will be zero dollars.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down, and simplify, an expression for the car’s value when Gabriella <span class="s1">purchased it.</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">Find the value of \(k\).</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 value of \(n\).</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="Apple-converted-space">\(12870 - k{(1.1)^0}\) </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for correct substitution into \(V(t)\).</p>
<p class="p2"> </p>
<p class="p3"><span class="Apple-converted-space">\( = 12870 - k\) </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C2)</em></strong></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Accept \(12870 - 3080\) <strong>OR</strong> 9790 for a final answer.</p>
<p class="p2"> </p>
<p class="p4"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(9143.20 = 12870 - k{(1.1)^2}\) </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for correct substitution into \(V(t)\).</p>
<p class="p2"> </p>
<p class="p3"><span class="Apple-converted-space">\((k = ){\text{ }}3080\) </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C2)</em></strong></p>
<p class="p4"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(12870 - 3080{(1.1)^n} = 0\) </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for correct substitution into \(V(t)\).</p>
<p class="p2"> </p>
<p class="p3"><strong>OR</strong></p>
<p class="p3"><img src="images/Schermafbeelding_2017-03-07_om_07.33.35.png" alt="N16/5/MATSD/SP1/ENG/TZ0/15.c/M"> <strong><em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for a correctly shaped curve with some indication of scale on the vertical axis.</p>
<p class="p2"> </p>
<p class="p3"><span class="Apple-converted-space">\((n = ){\text{ }}15.0{\text{ }}(15.0033 \ldots )\) </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C2)</em></strong></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Follow through from part (b).</p>
<p class="p2"> </p>
<p class="p3"><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="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Factorise the expression \({x^2} - 3x - 10\).</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>A function is defined as \(f(x) = 1 + {x^3}\) for \(x \in \mathbb{Z}{\text{, }} {- 3} \leqslant x \leqslant 3\).</span></p>
<p><span>(i) List the elements of the domain of \(f(x)\).</span></p>
<p><span>(ii) Write down the range of \(f(x)\).</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>\((x - 5)(x + 2)\) <em><strong>(A1)(A1) (C2)</strong></em></span></p>
<p><span><strong>Note: </strong>Award <em><strong>(A1)</strong></em> for \((x + 5)(x - 2)\), <em><strong>(A0)</strong></em> otherwise. If equation is equated to zero and solved by factorizing award <em><strong>(A1)</strong></em> for both correct factors, followed by <em><strong>(A0)</strong></em>.</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>(i) \( - 3\), \( - 2\), \( - 1\), \(0\), \(1\), \(2\), \(3\) <em><strong>(A1)(A1) (C2)</strong></em></span></p>
<p><span><strong><br>Note: </strong>Award <em><strong>(A2)</strong></em> for all correct answers seen and no others. Award <em><strong>(A1)</strong></em> for 3 correct answers seen.</span></p>
<p><br><span>(ii) \( - 26\), \( - 7\), 0,1, 2, 9, 28 <em><strong>(A1)(A1) (C2)</strong></em></span></p>
<p><span><strong><br>Note: </strong>Award <em><strong>(A2)</strong></em> for all correct answers seen and no others. Award <em><strong>(A1)</strong></em> for 3 correct answers seen. If domain and range are interchanged award <em><strong>(A0)</strong></em> for (b)(i) and <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong> for (b)(ii).</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;">It was surprising how many candidates could not factorise this expression. Of those that could some went on to find the zeros of a quadratic equation which was not what the question was asking. Some confused domain and range and many did not write down all the values when they did know domain and range.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">It was surprising how many candidates could not factorise this expression. Of those that could some went on to find the zeros of a quadratic equation which was not what the question was asking. Some confused domain and range and many did not write down all the values when they did know domain and range.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the quadratic function \(f\left( x \right) = a{x^2} + bx + 22\).</p>
<p>The equation of the line of symmetry of the graph \(y = f\left( x \right){\text{ is }}x = 1.75\).</p>
</div>
<div class="specification">
<p>The graph intersects the <em>x</em>-axis at the point (−2 , 0).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using only this information, write down an equation in terms of <em>a</em> and <em>b</em>.</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>Using this information, write down a second equation in terms of <em>a</em> and <em>b</em>.</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>Hence find the value of <em>a</em> and of <em>b</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The graph intersects the <em>x</em>-axis at a second point, P.</p>
<p>Find the <em>x</em>-coordinate of P.</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>\(1.75 = \frac{{ - b}}{{2a}}\) (or equivalent) <em><strong>(A1) (C1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(f\left( x \right) = {\left( {1.75} \right)^2}a + 1.75b\) or for \(y = {\left( {1.75} \right)^2}a + 1.75b + 22\) or for \(f\left( {1.75} \right) = {\left( {1.75} \right)^2}a + 1.75b + 22\).</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>\({\left( { - 2} \right)^2} \times a + \left( { - 2} \right) \times b + 22 = 0\) (or equivalent) <em><strong>(A1) (C1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \({\left( { - 2} \right)^2} \times a + \left( { - 2} \right) \times b + 22 = 0\) seen.</p>
<p>Award <em><strong>(A0)</strong></em> for \(y = {\left( { - 2} \right)^2} \times a + \left( { - 2} \right) \times b + 22\).</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>a</em> = −2, <em>b</em> = 7 <em><strong>(A1)</strong></em><strong>(ft)</strong><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).<br>Accept answers(s) embedded as a coordinate pair.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>−2<em>x</em><sup>2</sup> + 7<em>x</em> + 22 = 0 <em><strong> (M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of <em>a</em> and <em>b</em> into equation and setting to zero. Follow through from part (c).</p>
<p>(<em>x </em>=) 5.5 <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><strong>OR</strong></p>
<p><em>x</em>-coordinate = 1.75 + (1.75 − (−2)) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct use of axis of symmetry and given intercept.</p>
<p>(<em>x </em>=) 5.5 <em><strong>(A1) (C2)</strong></em></p>
<p><em><strong>[2 marks]</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;">
[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="question" style="padding-left: 20px; padding-right: 20px;">
<p>The golden ratio, \(r\) , was considered by the Ancient Greeks to be the perfect ratio between the lengths of two adjacent sides of a rectangle. The exact value of \(r\) is \(\frac{{1 + \sqrt 5 }}{2}\).</p>
<p>Write down the value of \(r\)</p>
<p>i) correct to \(5\) significant figures;</p>
<p>ii) correct to \(2\) decimal places.</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>Phidias is designing rectangular windows with adjacent sides of length \(x\) metres and \(y\) metres. The area of each window is \(1\,{{\text{m}}^2}\).</p>
<p>Write down an equation to describe this information.</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>Phidias designs the windows so that the ratio between the longer side, \(y\) , and the shorter side, \(x\) , is the golden ratio, \(r\).</p>
<p>Write down an equation in \(y\) , \(x\) and \(r\) to describe this information.</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>Find the value of \(x\) .</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>i) \(1.6180\) <em><strong>(A1)</strong></em></p>
<p>ii) \(1.62\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (a)(i).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(xy = 1\) <em><strong>(A1) (C1)</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{y}{x} = r\) <strong>OR</strong> \(\frac{y}{x} = \frac{{1 + \sqrt 5 }}{2}\) <strong>OR</strong> equivalent <em><strong>(A1) (C1)</strong></em></p>
<p><strong>Note:</strong> Accept \(\frac{y}{x} = \) their part (a)(i) or (a)(ii).</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\({x^2}r = 1\) or eqivalent <em><strong>(M1)</strong></em></p>
<p>\(x = 0.786\,\,\,(0.78615...)\) <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 substituting their part (c) into their equation from part (b). Follow through from parts (a), (b) and (c). Use of \(r = 1.62\) gives \(0.785674...\)</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 13: Golden ratio<br>This question was partially answered by all but the best candidates. Parts (a) and (b) yielded the most success. Only the best candidates were successful in part (d).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 13: Golden ratio<br>This question was partially answered by all but the best candidates. Parts (a) and (b) yielded the most success. Only the best candidates were successful in part (d).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 13: Golden ratio<br>This question was partially answered by all but the best candidates. Parts (a) and (b) yielded the most success. Only the best candidates were successful in part (d).</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 13: Golden ratio<br>This question was partially answered by all but the best candidates. Parts (a) and (b) yielded the most success. Only the best candidates were successful in part (d).</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 graph of the quadratic function \(f (x) = c + bx − x^2\) intersects the <em>y</em>-axis at point A(0, 5) and has its vertex at point B(2, 9).</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 value of <em>c</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>b</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>Find the <em>x</em>-intercepts of the graph of <em>f</em> .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down \(f (x)\) in the form \(f (x) = −(x − p) (x + q)\).</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>5 <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>\(\frac{{ - b}}{{2( - 1)}} = 2\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in axis of symmetry formula.</span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span>\(y = 5 + bx - x^2\)</span></p>
<p><span>\(9 = 5 + b (2) - (2)^2\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of 9 and 2 into their quadratic equation.</span></p>
<p><br><span>\((b =) 4\) <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 (a).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>5, −1 <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> Follow through from parts (a) and (b), irrespective of working shown.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(f (x) = -(x - 5)(x + 1)\) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C1)</strong></em></span></p>
<p><br><span><strong>Notes:</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-size: medium; font-family: times new roman,times;">Many candidates did not see the connection between the <em>x</em>-intercepts and the factored form of a quadratic function. The syllabus explicitly sates that the graphs of quadratics should be linked to solutions of quadratic equations by factorizing and vice versa. This was one of the most challenging questions for candidates.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Many candidates did not see the connection between the <em>x</em>-intercepts and the factored form of a quadratic function. The syllabus explicitly sates that the graphs of quadratics should be linked to solutions of quadratic equations by factorizing and vice versa. This was one of the most challenging questions for candidates.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Many candidates did not see the connection between the <em>x</em>-intercepts and the factored form of a quadratic function. The syllabus explicitly sates that the graphs of quadratics should be linked to solutions of quadratic equations by factorizing and vice versa. This was one of the most challenging questions for candidates.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Many candidates did not see the connection between the <em>x</em>-intercepts and the factored form of a quadratic function. The syllabus explicitly sates that the graphs of quadratics should be linked to solutions of quadratic equations by factorizing and vice versa. This was one of the most challenging questions for candidates.</span></p>
<div class="question_part_label">d.</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 style="text-align: left;"><span style="font-size: medium; font-family: times new roman,times;">A quadratic function, \(f(x) = a{x^2} + bx\), is represented by the mapping diagram below.</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>Use the mapping diagram to write down <strong>two</strong> equations in terms of <em>a</em> and<em> b</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 value of</span><span> <em>a</em>.</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>Find the value of <em>b</em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the <em>x</em>-coordinate of the vertex of the graph of <em>f </em>(<em>x</em>).</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>4<em>a</em> + 2<em>b</em> = 20</span></p>
<p><span><em>a </em>+ <em>b</em> = 8 <em><strong> </strong></em><em><strong>(A1)</strong></em></span></p>
<p><span><em>a</em> – b = –4 <em><strong> (A1) (C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award<em><strong> (A1)(A1)</strong> </em>for any two of the given or equivalent equations.</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><em>a</em> = 2 <em><strong> (A1)</strong></em><strong>(ft)</strong></span></p>
<p><em><strong><span>[1 mark]</span></strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>b</em> = 6 <strong><em> (A1)</em>(ft)<em> (C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note:</strong> Follow through from their (a).</span></p>
<p> </p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(x = - \frac{6}{{2(2)}}\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in correct formula.</span></p>
<p> </p>
<p><span>\( = -1.5\) <em><strong>(A1)</strong></em><strong>(ft) </strong><em><strong> (C2)</strong></em></span></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;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates attempted this question but very few of them completed it entirely. A number of students wrote incorrect equations in part (a), which shows that the mapping diagram was poorly understood and read. Part (c) proved to be difficult for many who didn’t know how to find the <em>x</em>-coordinate of the vertex of the graph of the function. Some students gave the two coordinates instead of the <em>x</em>-coordinate only.</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 attempted this question but very few of them completed it entirely. A number</span> <span style="font-family: times new roman,times; font-size: medium;">of students wrote incorrect equations in part (a), which shows that the mapping diagram was </span><span style="font-family: times new roman,times; font-size: medium;">poorly understood and read. Part (c) proved to be difficult for many who didn’t know how to </span><span style="font-family: times new roman,times; font-size: medium;">find the <em>x</em>-coordinate of the vertex of the graph of the function. Some students gave the two </span><span style="font-family: times new roman,times; font-size: medium;">coordinates instead of the <em>x</em>-coordinate only.</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;">Most candidates attempted this question but very few of them completed it entirely. A numberof students wrote incorrect equations in part (a), which shows that the mapping diagram was poorly understood and read. Part (c) proved to be difficult for many who didn’t know how to find the <em>x</em>-coordinate of the vertex of the graph of the function. Some students gave the two coordinates instead of the <em>x</em>-coordinate only.</span></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates attempted this question but very few of them completed it entirely. A number</span> <span style="font-family: times new roman,times; font-size: medium;">of students wrote incorrect equations in part (a), which shows that the mapping diagram was </span><span style="font-family: times new roman,times; font-size: medium;">poorly understood and read. Part (c) proved to be difficult for many who didn’t know how to </span><span style="font-family: times new roman,times; font-size: medium;">find the <em>x</em>-coordinate of the vertex of the graph of the function. Some students gave the two </span><span style="font-family: times new roman,times; font-size: medium;">coordinates instead of the <em>x</em>-coordinate only.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">An iron bar is heated. Its length, \(L\), in millimetres can be modelled by a linear function, \(L = mT + c\), where \(T\) <span class="s1">is the temperature measured in degrees Celsius (°C)</span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">At <span class="s1">150°</span><span class="s1">C </span>the length of the iron bar is <span class="s1">180 mm</span>.</p>
<p class="p1">Write down an equation that shows this information.</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">At <span class="s1">210°</span><span class="s1">C </span>the length of the iron bar is <span class="s1">181.5 mm</span>.</p>
<p class="p1">Write down an equation that shows this second piece of information.</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">At <span class="s1">210°</span><span class="s1">C </span>the length of the iron bar is <span class="s1">181.5 mm</span>.</p>
<p class="p1">Hence, find the length of the iron bar at <span class="s1">40°</span><span class="s1">C</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 class="p1">\(180 = 150m + c\;\;\;\)(or equivalent) <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">\(181.5 = 210m + c\;\;\;\)(or equivalent) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C1)</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(m = 0.25,{\text{ }}c = 176.25\) <span class="Apple-converted-space"> </span><strong><em>(A1)(A1)</em>(ft)</strong></p>
<p class="p1"><strong>Note: </strong>Follow through from part (a) and part (b), irrespective of working shown.</p>
<p class="p2"> </p>
<p class="p1">\(L = 0.025(4) + 176.25\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Note:<span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for substitution of their \(m\), their \(c\) and <span class="s1">40 </span>into equation.</p>
<p class="p2"> </p>
<p class="p1">\(L = 177\;\;\;(177.25){\text{ (mm)}}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C4)</em></strong></p>
<p class="p1"><strong>Note: </strong>Follow through, within <strong>part (c)</strong>, from their \(m\) and \(c\) only if working shown.</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>The equations in part (a) and (b) were given correctly by the vast majority of the candidates.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The equations in part (a) and (b) were given correctly by the vast majority of the candidates.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Part (c) was in most cases either completely correct or awarded no marks at all. Only few were able to find the values of <em>m</em> and<em> c</em>, and therefore the length at 40<strong>°</strong>C. Part (c) was often left open or answered incorrectly. A common answer was <em>L = 40m + c</em> . Very few partial correct responses were given. Some candidates managed a correct 3 sf answer by intelligent guessing. As the question was not structured asking for the m and c values explicitly, not many candidates made an attempt to find those values. Very few seemed to realize they could find those values using their GDC. An attempt to use simultaneous equations was the most common approach.</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;">Consider the quadratic function <em>y</em> = <em>f</em> (<em>x</em>) , where <em>f</em> (<em>x</em>) = 5 − <em>x</em> + <em>ax</em><sup>2</sup>.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>It is given that <em>f</em> (2) = −5 . Find the value of <em>a</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 axis of symmetry of the graph of <em>y</em> = <em>f</em> (<em>x</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>Write down the range of this quadratic function.</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>−5 = 5 − (2) + <em>a</em>(2)<sup>2</sup> <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in equation.</span></p>
<p> </p>
<p><span>(<em>a</em> =) −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>\(x = - \frac{1}{4}\) (–0.25) <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Follow through from their part (a). Award <em><strong>(A1)(A0)</strong></em><strong>(ft)</strong> for “ <em>x</em> = constant”. Award <em><strong>(A0)(A1)</strong></em><strong>(ft)</strong> for \(y = - \frac{1}{4}\).</span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>f</em> (<em>x</em>) ≤ 5.125 <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for <em>f</em> (<em>x</em>) ≤ (accept <em>y</em>). Do not accept strict inequality. Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for 5.125 (accept 5.13). Accept other correct notation, for example, (−∞, 5.125]. Follow through from their answer to part (b).</span></p>
<p><span><em><strong>[2 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;">This question proved to be quite a discriminator with a significant number of candidates achieving, at most, one or two marks in part (a). Part (b) was tested in the May 2012 series of examinations but the same errors were prevalent here as they were then. A number of candidates simply wrote the equation of the axis of symmetry in terms of <em>y</em> rather than <em>x</em> or just wrote down a numerical value rather than an equation. Expressions for the required range in part (c) fared little better with again much confusion between the variables <em>x</em> and <em>y</em>. A strict inequality was required at the turning point and a mark was lost where this was not indicated. Alternative forms for the range such as (–∞, 5.125] were, of course, accepted.</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 proved to be quite a discriminator with a significant number of candidates achieving, at most, one or two marks in part (a). Part (b) was tested in the May 2012 series of examinations but the same errors were prevalent here as they were then. A number of candidates simply wrote the equation of the axis of symmetry in terms of <em>y</em> rather than <em>x</em> or just wrote down a numerical value rather than an equation. Expressions for the required range in part (c) fared little better with again much confusion between the variables <em>x</em> and <em>y</em>. A strict inequality was required at the turning point and a mark was lost where this was not indicated. Alternative forms for the range such as (–∞ , 5.125] were, of course, accepted.</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 proved to be quite a discriminator with a significant number of candidates achieving, at most, one or two marks in part (a). Part (b) was tested in the May 2012 series of examinations but the same errors were prevalent here as they were then. A number of candidates simply wrote the equation of the axis of symmetry in terms of <em>y</em> rather than <em>x</em> or just wrote down a numerical value rather than an equation. Expressions for the required range in part (c) fared little better with again much confusion between the variables <em>x</em> and <em>y</em>. A strict inequality was required at the turning point and a mark was lost where this was not indicated. Alternative forms for the range such as (–∞ , 5.125] were, of course, accepted.</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 following is the graph of the quadratic function <em>y</em> = <em>f</em> (<em>x</em>).</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 solutions to the equation <em>f</em> (<em>x</em>) = 0.</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 equation of the axis of symmetry of the graph of <em>f</em> (<em>x</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>The equation <em>f</em> (<em>x</em>) = 12 has two solutions. One of these solutions is <em>x</em> = 6. Use the symmetry of the graph to find the other solution.</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 minimum value for <em>y</em> is – 4. Write down the range of <em>f</em> (<em>x</em>).</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><em>x</em> = 0, <em>x</em> = 4 <em><strong> (A1)(A1) (C2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Accept 0 and 4.</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><em>x</em> = 2 <em><strong>(A1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<address>
<br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <em>x</em> = constant, <em><strong>(A1)</strong></em> for 2.</span>
</address><address><span> </span></address><address><em><strong><span>[2 marks]</span></strong></em></address>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>x</em> = –2 <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Accept –2.</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>\(y \geqslant -4{\text{ }}(f(x) \geqslant -4)\) <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Accept alternative notations.</span></p>
<p><span>Award <em><strong>(A0)</strong></em> for use of strict inequality.</span></p>
<p><span> </span></p>
<p><em><strong><span>[1 mark]</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;">A number of candidates left out this question which indicated that this topic was either entirely unfamiliar, that this topic of the syllabus had perhaps not been taught, or was barely familiar. A few candidates wrote down coordinate pairs when asked for a solution to the equation. A number of candidates wrote down the formula for the equation of the axis of symmetry without being able to substitute values for <em>a</em> and <em>b</em>. When given the minimum value of the graph a small number of candidates could identify the range of the function correctly. Overall this question proved to be difficult with its demands for reading and interpreting the graph, and dealing with additional information about the quadratic function given in the different parts.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">A number of candidates left out this question which indicated that this topic was either entirely unfamiliar, that this topic of the syllabus had perhaps not been taught, or was barely familiar. A few candidates wrote down coordinate pairs when asked for a solution to the equation. A number of candidates wrote down the formula for the equation of the axis of symmetry without being able to substitute values for <em>a</em> and <em>b</em>. When given the minimum value of the graph a small number of candidates could identify the range of the function correctly. Overall this question proved to be difficult with its demands for reading and interpreting the graph, and dealing with additional information about the quadratic function given in the different parts.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">A number of candidates left out this question which indicated that this topic was either entirely unfamiliar, that this topic of the syllabus had perhaps not been taught, or was barely familiar. A few candidates wrote down coordinate pairs when asked for a solution to the equation. A number of candidates wrote down the formula for the equation of the axis of symmetry without being able to substitute values for <em>a</em> and <em>b</em>. When given the minimum value of the graph a small number of candidates could identify the range of the function correctly. Overall this question proved to be difficult with its demands for reading and interpreting the graph, and dealing with additional information about the quadratic function given in the different parts.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">A number of candidates left out this question which indicated that this topic was either entirely unfamiliar, that this topic of the syllabus had perhaps not been taught, or was barely familiar. A few candidates wrote down coordinate pairs when asked for a solution to the equation. A number of candidates wrote down the formula for the equation of the axis of symmetry without being able to substitute values for <em>a</em> and <em>b</em>. When given the minimum value of the graph a small number of candidates could identify the range of the function correctly. Overall this question proved to be difficult with its demands for reading and interpreting the graph, and dealing with additional information about the quadratic function given in the different parts.</span></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;">A quadratic curve with equation <em>y</em> = <em>ax</em> (<em>x</em> − <em>b</em>) is shown in the following diagram.</span></p>
<p style="text-align: center;"><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The <em>x</em>-intercepts are at (0, 0) and (6, 0), and the vertex V is at (<em>h</em>, 8).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of <em>h</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 curve.</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>\(\frac{{0 + 6}}{2} = 3\) \(h = 3\) <em><strong>(M1)(A1) (C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for any correct method.</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>\(y = ax(x - 6)\) <em><strong>(A1)</strong></em></span></p>
<p><span>\(8 = 3a(- 3)\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>\(a = - \frac{8}{9}\) </span><span> <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>\(y = - \frac{8}{9} x (x - 6)\) </span><span><em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for correct substitution of \(b = 6\) into equation.</span></p>
<p><span>Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for substitution of their point V into the equation.</span></p>
<p><br><em><strong><span>OR</span></strong></em></p>
<p><span>\(y = a(x - 3)^2 + 8\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for correct substitution of their <em>h</em> into the equation.</span></p>
<p><br><span>\(0 = a(6 - 3)^2 + 8\) <em><strong>OR</strong></em> \(0 = a(0 - 3)^2 + 8\) <em><strong>(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct substitution of an <em>x</em> intercept.</span></p>
<p><br><span>\(a = - \frac{8}{9}\) </span><em><strong><span>(A1)</span></strong></em><strong><span>(ft)</span></strong></p>
<p><span>\(y = - \frac{8}{9}(x - 3)^2 + 8\)<em><strong> </strong></em></span><span><em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C4)</strong></em></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;">Most candidates successfully found <em>h</em> but very few could find the equation of the curve.</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;">This question appeared to be the most difficult question on the paper.</span></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>Factorise the expression \({x^2} - kx\) .</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>Hence solve the equation \({x^2} - kx = 0\) .</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 below shows the graph of the function \(f(x) = {x^2} - kx\) for a particular value of \(k\).<br></span></p>
<p><br><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Write down the value of \(k\) for this function.</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 diagram below shows the graph of the function \(f(x) = {x^2} - kx\) for a particular value of \(k\).<br></span></p>
<p><br><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Find the minimum value of the function \(y = f(x)\) .</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>\(x(x - k)\) <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>\(x = 0\) <strong>or</strong> \(x = k\) <em><strong>(A1) (C1)</strong></em></span></p>
<p><span><strong>Note:</strong> Both correct answers only.</span></p>
<p><span><em><strong>[1 mark]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(k = 3\) <em><strong>(A1) (C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{Vertex at }}x = \frac{{ - ( - 3)}}{{2(1)}}\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note: <em>(M1)</em></strong> for correct substitution in formula.</span></p>
<p><br><span>\(x = 1.5\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>\(y = - 2.25\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>\(f'(x) = 2x - 3\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note: <em>(M1)</em></strong> for correct differentiation.</span></p>
<p><br><span>\(x = 1.5\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span><br><span>\(y = - 2.25\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>OR</strong></span></p>
<p><span><em>for finding the midpoint of their 0 and 3</em> <em><strong>(M1)</strong></em></span><br><span>\(x = 1.5\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span><br><span>\(y = - 2.25\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Note: </strong>If final answer is given as \((1.5{\text{, }}{- 2.25})\) award a maximum of <em><strong>(M1)(A1)(A0)</strong></em></span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">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 poorly answered by all but the best candidates. The links between the parts were not made. The idea of the line of symmetry for the graph was seldom investigated. The “minimum value of the function” was often incorrectly given as a coordinate pair.</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 all but the best candidates. The links between the parts were not made. The idea of the line of symmetry for the graph was seldom investigated. The “minimum value of the function” was often incorrectly given as a coordinate pair.</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 poorly answered by all but the best candidates. The links between the parts were not made. The idea of the line of symmetry for the graph was seldom investigated. The “minimum value of the function” was often incorrectly given as a coordinate pair.</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 poorly answered by all but the best candidates. The links between the parts were not made. The idea of the line of symmetry for the graph was seldom investigated. The “minimum value of the function” was often incorrectly given as a coordinate pair.</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;">Consider the graph of the function \(y = f(x)\) defined below.</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;">Write down <strong>all</strong> the labelled points on the curve</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>that are local maximum points;</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>where the function attains its least value;</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>where the function attains its greatest value;</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>where the gradient of the tangent to the curve is positive;</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>where \(f(x) > 0\) and \(f'(x) < 0\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>B, F <em><strong>(C1)</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span>H </span><span> <em><strong>(C1)</strong></em></span></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span>F </span><span> <em><strong>(C1)</strong></em></span></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span>A, E </span><span> <em><strong>(C1)</strong></em></span></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span>C </span><span> <em><strong>(C2)</strong></em></span></span></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Consider the function \(f(x) = a{x^2} + c\).</p>
<p>Find \(f'(x)\)</p>
<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>Point \({\text{A}}( - 2,\,5)\) lies on the graph of \(y = f(x)\) . The gradient of the tangent to this graph at \({\text{A}}\) is \( - 6\) .</p>
<p>Find the value of \(a\) .</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 value of \(c\) .</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>\(2ax\) <em><strong>(A1) (C1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(2ax\). Award <em><strong>(A0)</strong></em> if other terms are seen.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(2a( - 2) = - 6\) <em><strong>(M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of \(x = - 2\) in their gradient function, <em><strong>(M1)</strong> </em>for equating their gradient function to \( - 6\) . Follow through from part (a).</p>
<p>\((a = )1.5\,\,\,\left( {\frac{3}{2}} \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\({\text{their }}1.5 \times {( - 2)^2} + c = 5\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of their \(a\) and point \({\text{A}}\). Follow through from part (b).</p>
<p>\((c = ) - 1\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</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>Question 11: Equation of tangent<br>Part (a) was generally well answered.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>In part (b), many candidates substituted the value of the function, rather than its gradient; this was usually correctly followed through into part (c).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>In part (b), many candidates substituted the value of the function, rather than its gradient; this was usually correctly followed through into part (c).</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram shows part of the graph of a function \(y = f(x)\). The graph passes through point \({\text{A}}(1,{\text{ }}3)\).</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_06.22.37.png" alt="M17/5/MATSD/SP1/ENG/TZ2/13"></p>
</div>
<div class="specification">
<p>The tangent to the graph of \(y = f(x)\) at A has equation \(y = - 2x + 5\). Let \(N\) be the normal to the graph of \(y = f(x)\) at A.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of \(f(1)\).</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 equation of \(N\). Give your answer in the form \(ax + by + d = 0\) where \(a\), \(b\), \(d \in \mathbb{Z}\).</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>Draw the line \(N\) on the diagram above.</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)</em></strong> <strong><em>(C1)</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Accept \(y = 3\)</p>
<p> </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>\(3 = 0.5(1) + c\)\(\,\,\,\)<strong>OR</strong>\(\,\,\,\)\(y - 3 = 0.5(x - 1)\) <strong><em>(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for correct gradient, <strong><em>(A1) </em></strong>for correct substitution of \({\text{A}}(1,{\text{ }}3)\) in the equation of line.</p>
<p> </p>
<p>\(x - 2y + 5 = 0\) or any integer multiple <strong><em>(A1)</em>(ft)</strong> <strong><em>(C3)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em>(ft) </strong>for their equation correctly rearranged in the indicated form.</p>
<p>The candidate’s answer <strong>must </strong>be an equation for this mark.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2017-08-16_om_08.26.38.png" alt="M17/5/MATSD/SP1/ENG/TZ2/13.c/M"> <strong><em>(M1)(A1)</em>(ft)</strong> <strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>M1) </em></strong>for a straight line, with positive gradient, passing through \((1,{\text{ }}3)\), <strong><em>(A1)</em>(ft) </strong>for line (or extension of their line) passing approximately through 2.5 or their intercept with the \(y\)-axis.</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;">Water has a lower boiling point at higher altitudes. The relationship between the boiling point of water (<em>T</em>) and the height above sea level (<em>h</em>) can be described by the model \(T = -0.0034h +100\) where <em>T</em> is measured in degrees Celsius (</span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">°</span>C) and <em>h</em> is measured in metres from sea level.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the boiling point of water at sea level.</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>Use the model to calculate the boiling point of water at a height of 1.37 km above sea level.</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>Water boils at the top of Mt. Everest at 70 </span><span><span>°</span>C.</span></p>
<p><span>Use the model to calculate the height above sea level of Mt. Everest.<br></span></p>
<p><span> </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>100 °C <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>\(<em>T</em> = -0.0034 \times 1370 + 100\) <em><strong>(A1)(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <strong><em>(A1)</em></strong> for 1370 seen, <em><strong>(M1)</strong></em> for substitution of their <em>h</em> into</span> <span>the equation.</span></p>
<p><br><span>95.3 °C (95.342) <em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><span><strong>Notes:</strong> If their <em>h</em> is incorrect award at most <em><strong>(A0)(M1)(A0)</strong></em>. If their <em>h</em> = 1.37</span> <span>award at most <em><strong>(A0)(M1)(A1)</strong></em><strong>(ft)</strong>.</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>\(70 = -0.0034h + 100\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted equation.</span></p>
<p><br><span><em>h</em> = 8820 m (8823.52...) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Note:</strong> The answer is 8820 m (or 8.82 km.) units are required.</span></p>
<p><span><em><strong>[2 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;">The majority of the candidates showed they were able to substitute values into the model. The most common mistake was to neglect converting 1.37 km into metres. Some candidates did not appreciate the practical considerations of this question; Mount Everest will never be less than one metre high. It is important to remind students to check their answers in terms of the context of the information given.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The majority of the candidates showed they were able to substitute values into the model. The most common mistake was to neglect converting 1.37 km into metres. Some candidates did not appreciate the practical considerations of this question; Mount Everest will never be less than one metre high. It is important to remind students to check their answers in terms of the context of the information given.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The majority of the candidates showed they were able to substitute values into the model. The most common mistake was to neglect converting 1.37 km into metres. Some candidates did not appreciate the practical considerations of this question; Mount Everest will never be less than one metre high. It is important to remind students to check their answers in terms of the context of the information given.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p>Consider the following graphs of quadratic functions.</p>
<p><img src="images/Schermafbeelding_2017-08-16_om_06.31.16.png" alt="M17/5/MATSD/SP1/ENG/TZ2/15"></p>
<p>The equation of each of the quadratic functions can be written in the form \(y = a{x^2} + bx + c\), where \(a \ne 0\).</p>
<p>Each of the sets of conditions for the constants \(a\), \(b\) and \(c\), in the table below, corresponds to one of the graphs above.</p>
<p>Write down the number of the corresponding graph next to each set of conditions.</p>
<p> <img src="images/Schermafbeelding_2017-08-16_om_06.39.22.png" alt="M17/5/MATSD/SP1/ENG/TZ2/15_02"></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><img src="images/Schermafbeelding_2017-08-16_om_08.45.18.png" alt="M17/5/MATSD/SP1/ENG/TZ2/15/M"> <strong><em>(A1)(A1)(A1)(A1)(A1)(A1)</em></strong> <strong><em>(C6)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for each correct entry.</p>
<p> </p>
<p><strong><em>[6 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>The following function models the growth of a bacteria population in an experiment,</p>
<p style="text-align: center;"><em>P</em>(<em>t</em>) = <em>A</em> × 2<sup><em>t</em></sup>, <em>t</em> ≥ 0</p>
<p>where <em>A</em> is a constant and t is the time, in hours, since the experiment began.</p>
<p>Four hours after the experiment began, the bacteria population is 6400.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>A</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>Interpret what <em>A</em> represents in this context.</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 time since the experiment began for the bacteria population to be equal to 40<em>A</em>.</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>6400 = <em>A</em> × 2<sup>4</sup> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of 4 and 6400 in equation.</p>
<p>(<em>A</em> =) 400 <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>the initial population <strong>OR</strong> the population at the start of experiment <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>40<em>A</em> = <em>A</em> × 2<em><sup>t</sup></em> <strong>OR</strong> 40 × 400 = 400 × 2<em><sup>t</sup></em> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into equation. Follow through with their<em> A</em> from part (a).</p>
<p>40 = 2<em><sup>t</sup></em> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for simplifying.</p>
<p>5.32 (5.32192…) (hours) <strong>OR </strong> 5 hours 19.3 (19.3156…) minutes <em><strong>(A1) (C3)</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<p> </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;">Consider the function \(f(x) = p{(0.5)^x} + q\) where <em>p</em> and <em>q</em> are constants. The graph of <em>f</em> (<em>x</em>) passes through the points \((0,\,6)\) and \((1,\,4)\) and is shown below.</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down two equations relating <em>p</em> and <em>q</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 value of <em>p</em> and of <em>q</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>Write down the equation of the horizontal asymptote to the graph of <em>f</em> (<em>x</em>).</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>p</em> + <em>q</em> = 6 <em><strong>(A1)</strong></em><br></span></p>
<p><span>0.5<em>p</em> + <em>q</em> = 4 <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><br><strong>Note:</strong> Accept correct equivalent forms of the equations.</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><em>p</em> = 4, <em>q</em> = 2 <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> If both answers are incorrect, award <em><strong>(M1)</strong></em> for attempt at solving</span> <span>simultaneous equations.</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><em>y</em> = 2 <em><strong>(A1)(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> for “<em>y</em> = a constant”, <em><strong>(A1)</strong></em><strong>(ft)</strong> for 2. Follow through from their value for <em>q</em> as long as their constant is greater than 2 and less than 6.</span></p>
<p><span>An equation must be seen for any marks to be awarded.</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;">A significant number of candidates found it difficult to identify and write two equations that relate<em> p</em> and <em>q</em>. Many of those who wrote the equations were unable to solve them or use their GDC to find the values of <em>p</em> and <em>q</em> in part b). Although the question in part c) was quite standard, there were many errors in the responses. Many students wrote <em>x</em> = 2 or only 2 instead of <em>y</em> = 2.</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 significant number of candidates found it difficult to identify and write two equations that relate<em> p</em> and <em>q</em>. Many of those who wrote the equations were unable to solve them or use their GDC to find the values of <em>p</em> and <em>q</em> in part b). Although the question in part c) was quite standard, there were many errors in the responses. Many students wrote <em>x</em> = 2 or only 2 instead of <em>y</em> = 2.</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;">A significant number of candidates found it difficult to identify and write two equations that relate<em> p</em> and <em>q</em>. Many of those who wrote the equations were unable to solve them or use their GDC to find the values of <em>p</em> and <em>q</em> in part b). Although the question in part c) was quite standard, there were many errors in the responses. Many students wrote <em>x</em> = 2 or only 2 instead of <em>y</em> = 2.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A population of mosquitoes decreases exponentially. The size of the population, \(P\) , after \(t\) days is modelled by</p>
<p>\(P = 3200 \times {2^{ - t}} + 50\) , where \(t \geqslant 0\) .</p>
<p>Write down the <strong>exact</strong> size of the initial population.</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 the population after \(4\) days.</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 time it will take for the size of the population to decrease to \(60\).</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>The population will stabilize when it reaches a size of \(k\) .</p>
<p>Write down the value of \(k\) .</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>\(3250\) <em><strong>(A1) (C1)</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(3200 \times {2^{ - 4}} + 50\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting \(t\) into exponential equation.</p>
<p>\( = 250\) <em><strong>(A1) (C2)</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(3200 \times {2^{ - t}} + 50 = 60\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award<em> <strong>(M1)</strong></em> for setting up the equation used in part (b).</p>
<p><strong>OR</strong></p>
<p><img src="data:image/png;base64,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" alt></p>
<p><em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award<em><strong> (M1)</strong></em> for a decreasing exponential graph intersecting a horizontal line.</p>
<p>\((t = )\,\,8.32\,\,(8.32192...)\) (days) <em><strong>(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> Accept a final answer of “\(8\) days, \(7\) hours and \(44\) minutes”, or equivalent. Award<strong> (M0)(A0)</strong> for an answer of \(8\) days with no working</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(50\) <em><strong>(A1) (C1)</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>Question 13: Exponential model.</p>
<p>Most candidates were able to correctly substitute values into the given exponential model but only the stronger ones found a correct answer. It was expected that candidates would use their calculator to solve the exponential equation rather than use logarithms which is not in the syllabus. The concept of the population stabilizing (horizontal asymptote) was not widely understood.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 13: Exponential model.<br>Most candidates were able to correctly substitute values into the given exponential model but only the stronger ones found a correct answer. It was expected that candidates would use their calculator to solve the exponential equation rather than use logarithms which is not in the syllabus. The concept of the population stabilizing (horizontal asymptote) was not widely understood.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 13: Exponential model.</p>
<p>Most candidates were able to correctly substitute values into the given exponential model but only the stronger ones found a correct answer. It was expected that candidates would use their calculator to solve the exponential equation rather than use logarithms which is not in the syllabus. The concept of the population stabilizing (horizontal asymptote) was not widely understood.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 13: Exponential model.</p>
<p>Most candidates were able to correctly substitute values into the given exponential model but only the stronger ones found a correct answer. It was expected that candidates would use their calculator to solve the exponential equation rather than use logarithms which is not in the syllabus. The concept of the population stabilizing (horizontal asymptote) was not widely understood.</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 function \(g(x)\) is defined as \(g(x) = 16 + k({c^{ - x}})\) where \(c > 0\) .</span><br><span style="font-size: medium; font-family: times new roman,times;">The graph of the function \(g\) is drawn below on the domain \(x \geqslant 0\) .</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAgoAAAEqCAIAAAD75++pAAATPklEQVR4nO3d728TZ4LA8f4njghC3GlX9IQqVVstVhC7d90rJ+jp3EgndbvqtayjpuUQsJVTigrSFWdPSVcC+y6qmnadtmqgmtDdcHuZnoJus7NwwtUAArVDGxUySq7JTrrFx0Bj4+dePMQNyRNiOx7PD38/8ptSx3na0nx55nmemYcEAAArPOT3AAAAQUQeAAAK5AEAoEAeAAAKK/NwZyb/m7f7Dh0cuFAQQoj5/EDq0PCnt5s+MgCAj5Szh9s3hrs3P9yXLwohCtYH+zue12aaPC4AgK/UF5eK+b6tse6RmaIQ5dsX3zqsXS83eVwAAF+tsvYwoz0X23NyakEsWO8fft9aoA4A0FpWycPs6IsbHu/Pz3z2XubDSbe5QwIA+G+VPBTz/Q9v2/d67y/PXC82d0AAgCBYJQ+liyce2/JE+g/zXFUCgJakzkO5cCHz6oeTLDkAQKtS5aE4pf8ql79ZavpgAABBcV8eSp8N7t64I/HCG+PTd/waEAAgCO6fPRSnPzl7ebbINSUAaHXccwkAoFBDHvSxsc8//9y7oQAAgqPaPDiO0x5r60p2eToaAEBAVJuHnlTq73c/ufNvnzBN09MBAQCCoKo8WJbVEY//4uDB4Q8+6EwkXJfbbABAxFWVh85EwjCMnlTKsqyeVGpE07weFgDAX2vnQdf1rmRSCCHzYNt2RzzuOI73YwMA+GaNPLiu2xGPW5YlFvMghMhmstlMthmjAwD4ZI08mKZZKUElD67r9qRSng8NAOCfGs49VPIAAIg88gAAUCAPAAAF8gAAUCAPAAAF8gAAUCAPAAAF8gAAUCAPAAAF8gAAUCAPAAAF8gAAUCAPAAAF8gAAUCAPAAAF8gAAUCAPAAAF8gAAUCAPAAAF8gAAUKgtD6ZpejcUAEBw1JaHbCbr3VAAAMFRWx464nHXdb0bDQAgIGrLQ3uszTAM70YDAAiImi8u9abT3o0GABAQNS9Nt8faHMfxbkAAgCCoeWNrbzqt67p3AwIABEHNeTBNszOR8G5AAIAgqOdYXGciwfk4AIi2evIwlMtxAAIAoq2ePDiOwwEIAIi2Ou+51JVMcgACACKszjwYhtGTSnkzJACA/+rMg+u6HfE4ByAAIKrqv6F3NpMdyuU8GBIAwH/158G27Y54vPEjAgAEwLoeB8QCNQBE1bryoOs6C9QAEEnrygML1AAQVet91jQL1AAQSevNAwvUABBJ682DYIEaAKKoAXngBDUARE8D8sACNQBETwPyIFigBoDIaUweuMU3AERMY/Ig/y4L1AAQGQ3Lg2EYPIMaACKjYXkQPIMaACKkkXkY0TSeQQ0A0dDIPLiu2x5rY4crAERAI/Mg2OEKAFHR4DzIWzCxwxUAwq7BeRDscAWASGh8HkzTZIcrAIRd4/MghOhMJEzTrHdIAAD/eZIHHjIKAGHnSR7kPVxt2653VAAAn3mSB8EROQAIOa/y4DgOR+QAILy8yoPgiBwAhJmHeeCIHACEl4d5kF8yomk1DgkA4D9v82BZVkc8XtuIAAAB4G0eBPfYAIBw8jwP3GMDAMLI8zwIIToTCSYQABAuzcgDj6EGgNBpRh4EEwgACJsm5YEJBACES5PyIIToTCTW8+UAgGZqXh64yzcAhEjz8iDv8s0EAgBCoXl5EEKMaBoTCAAIhabmgQkEAIRFU/MgWIEAgJBodh4EW5gAIAx8yINhGEwgACDgfMiDYAIBAIHnTx44RA0AAedPHgR3YQKAYPMtD0wgACDIfMuDYAIBAAHmZx4sy+pMJFzXbeBnAgAaws88yM8c0bTGfiYAYP18zoNlWR3xOBMIAAgan/MghMhmskO5XMM/FgCwHv7nwXGc9lib4zgN/2QAQN38z4MQYiiX602nvfhkAEB9ApEHbvQNAEETiDwInhQEAAETlDwITskBQJAEKA+mabLJFQACIkB5EJySA4DACFYebNvuiMfZ5AoAvgtWHgSbXAEgGAKXBza5AkAQBC4PgkdBAEAABDEPgjVqAPBbQPPAGjUA+CugeRBCDOVynKMGAL8ENw9yjdo0zaZ9RwBARXDzIIQwTZOnjQKALwKdB/lNeVgQADRf0PPgOA7HIACg+YKeByGErutdyWTzvy8AtLIQ5EEI0ZVMcgwCAJopHHmwbbs91mbbti/fHQBaUDjyIIQY0TQuMQFA04QmD4JLTADQRGHKA5eYAKBpwpQHwSUmAGiWkOVBcIkJAJoifHngEhMANEH48iAWD8pxLyYA8E4o8yC4FxMAeCyseZD3YuJ23wDgkbDmQQhhmmZHPM4lJgDwQojzIITIZrI8UQ4AvBDuPLiuyz5XAPBCuPMghLBtmwdCAEDDhT4PQghd13nmKAA0VhTyIIToTadZhACABopIHuQihK7rfg8EACIiInkQLEIAQENFJw9CCMMwOAkBAA0RqTwIIbKZLHf8BoD1i1oehBBdyWQ2k/V7FAAQbhHMg+u6HfG4YRh+DwQAQiyCeRCLz4QIy2gBIICimQexuEztOI7fAwGAUIpsHoQQQ7kcTw0CgPpEOQ+C09QAUK+I50GepmYjEwDUKuJ5EGxkAoC6RD8PYvF+GxQCAKrXEnkQi08etW3b74EAQDi0Sh7E4lZXCgEA1WihPAghdF3nMAQAVKO18iAW79nHYQgAeLCWy4OgEABQhVbMg6AQALCWFs2DPC7HkyEAYDUtmgfBgWoAeKDWzYOgEACwupbOg6AQALCKVs+DoBAAoEIehFgsRE8qxV4mAJDIwz2VvUwUAgAEeVjKdd3edJpCAIAgDytxYg4ABHlQkoXg3q4AWhl5UBvK5bj7N4BWRh5WJZ8P0VL/yABQQR4exDCM9lgbTyEF0ILIwxrkc6o5NAeg1ZCHtdm2LY9Vs50JQOsgD1VxXbcnlWLDK4DWQR5qkM1k2c4EoEWQh9qwWA2gRZCHmrFYDaAVkId6VO7f5ziO32MBAE+Qh/rJk9Wmafo9EABoPPKwLqZpdsTjQ7mc3wMBgAYjD+vlOA4XmgBED3loDHmhiR1NACKDPDSMZVlyRxNH5wBEAHloJPm8uc5Egn9RAMKOPDSerutyvZppBIDwIg+ecBynJ5ViGgEgvMiDh5hGAAgv8uAtOY3g9ByA0CEPzSBPz/WkUpyNABAW5KFJXNeVZyNGNM3vsQDA2shDU8kHz7FkDSD4yIMPDMPgWhOAgCMP/pDXmtpjbSOaxr4mAAFEHvxU2dfEggSAoCEP/rMsS56h445+AIKDPASFYRidiQSr1gACgjwEi4xEVzLJv2oA/iIPQUQkAPiOPARX5XITaxIAmo88BB2RAOAL8hAOhmFUtsByTgJAE5CHMLEsqzedbo+1ZTNZTlwD8BR5CB/HcbKZrLwtB1ecAHiEPISV67qVZYkRTWMyAaCxyEPoWZaVzWTbY2296TQPHQLQKOQhIlzX1XVdTiaGcjkmEwDWiTxEjZxMdMTjXcmkYRhscwJQH/IQTXJlQm5z4qITgDqQh4hzHEfX9a5ksiMez2aydAJAlchDq1jZCa47AXgA8tByKp2Q151YnwCgRB5al+yEXJ/oSiZHNM22bb8HBSAoyAOE67qmacr9Tp2JBJeeAAjygGVs2x7RNHnpSU4p+I8OtCbyADU5pRjK5ToTCblKoes6vwGA1kEesDbHcQzDyGaynYmEvBUgswog8sgDalNJhbwA1ZNKDeVyrFUA0UMeUD95AWpE03pSqfZYW2ci0ZtOM7EAmq9c+Fw/fWGuvPLvzH9yeswqlOr4TPKAhrFte+nEoiuZzGayrFgAHisXp/+r99B7V1ZpQLlw6deH/vW3k/9X6+eSB3jFsixd1yu1qMwtTNPkhrJAo5QLn2Se2nfy+u0HvWf6t/+c6Ds3X9scgjygSSzLMgxjKJeTV6Iq6xZyesHSBVCXW9bgM1t6xr9Z421fnz+2c0ffhZr+NyMP8IfjOJZljWhaNpOVwZB7orKZrFy94Ag3Qu7OTP43b/cdOjhwoSCEEPP5gdSh4U8f9If81ZS/sc7829HXjvUfe/VQX07TtJHT56cWykIIcetc+tGtz2lT8n0Lk3rmtf17Xnwrf7NULlw5dWTvS/e++91vxl/9/sb9Z2aL1X9b8oCgkMHQdV3OMOR5i65kUu6jlZMMmoFQuX1juHvzw335ohCiYH2wv+N5babWzyjPnUs/+f3nT90olkX5y5NPb9n0N93HsuNTd4UQonTx+LbY4/35wndvv/nH3u2PPDP40XD/m9roR2fy0zIIpasDfx3b9sr4XPXfmTwg0CzLkpuj5CSjIx6XyxiVeYZpmlybQmAV831bY90jM0UhyrcvvnVYu67YW/Rgs6Mvblj8sV7+8uTTWzbvH5tf/PgZrbs9lhi4uvT3/8183872jd3LVyNmtOdif7lr8NO7VX9n8oDwsW1bzjPkntrKYoacasgFcDnb4HcsfDajPRfbc3JqQSxY7x9+31pYWoevLw0f7+/rW/E6fvLi19+9a37swMbtRybmhSgvfPHeM3/xZO+5yv5VmYefvTt5Z8nHlubHXt78vaMTt+4v0Yz2XKxtq5zJVIc8IDpkD2Q25GxDbppaVo7KnINLVfDc7OiLGx7vz8989l7mw8n65rh3pn+f+fnTe48dO3xg/7+8c256yc/30vzYy5vvv7gkil+c2r9z24ZlUwqZh79aXKWoCnlAS5DlMAxD5kHOOeTyRuVqldxJtbQfXLbCehXz/Q9v2/d67y/PXF/xx/Y7c5aZVzCtuSWzgfKfr7x94KW3rxRUl6XuWoO7YnJuId2+cfrEO5eMgR89ukezps/+7vziZtbSxePbYjv78zerHzt5AO5drZKLHEv7UZl8LE2IXPOQL8MwZEWYiECtdPHEY1ueSP9hXvHDvbqLS3evvfvUlvbY1p88ve/ov5+amLx53yfdvfbuU4/sGvz0rnCvDiQ2Pbb74KlrC+KbfN+uTT98tn/cXmxSaXZ036YdJy59W8PaB3kAqiITUrl4tbQiSycilR26lVflzZXlEIrSOsqFC5lXP5xcqHlBevHLr5z8RU/mf65N5sdHBvteefYnWzf8Q/+F+SVvKc1PvL7jp8M3yqJcmLpszd3rQfFPX9pL5hvl/x07sHvv6FRN4yAPQIPJHbrLLmdVlkOURamsjii7sux6F4EJjeKU/qtc/mY99zsSQsg/8m9+YXT2u1+Zn3jtyQNjX933rvLcufSel8emV//RXypcfHPv0Y+ni7VVijwAgbDsR//SK13LZiqrBWa1zChjo5zQkJ9GKX02uHvjjsQLb4xP31n73asqL0wO/3z7z9Lv/sfEhXz+3Mcnjx8+2D+u+Clf/Cr/6zcyv7dVu5LuzOY/6D1xttY2CPIARIzyB/3K2CgnNNXkp5oULXstXa1Z87VyklSlYMWsOP3J2cuztf9EVn3UnJWfGDv90djEJ/ctWS9XKtjTf1Z8w1v2ZC1HpZcgDwDqVOUP7qWrNWu+qulNfTGr71X3eBr4qqmvy17ruf0leQAANdd165vKNFZNffUnD0uLuuZfLv2VBv5lNd86kuMM6bA9GmdIhx2WcYZ02GEZZ/OHXTdmDwAABfIAAFAgDwAABfIAAFAgDwAABfIAAFAgDwAABfIAAFAgDwAABfIAAFAgDwAABfIAAFAgDwAABfIAAFAgDwAABfIAAFAgDwAABfIAAFAgDwAABfIAAFAgDwAABfIAAFAgDwAABfIAAFAgDwAABfIAAFAgDwAABfIAAFAgDwAABfIAAFAgDwAABfIAAFAgDwAABfIAABHXm06bplnrV5EHAIg4wzA64vGeVMpxnOq/ijwAQPS5rjuiae2xtqFcznXdar6EPABAq3Acpzed7ojHdV1f880PyZ7w4sWLF6+Weq35x31mDwDQKizL6kwkupLJan6Yr5qHcuH6+bHRsfPXC+V7v0IeACCkHMfpSaU64nHDMKr8EmUeysXpj48muk/858T4wEudRz6eLpYFeQCAcKp1UVpS5aF8fWTPD3583PxWCPGteWLH9r2jU2XyAADhNJTL1bSlVVLk4a41uCu2/cjEvBBCiPmJ17a3/92gdZc8AEAElBcm9cxr+/e8+Fb+ZqlcuHLqyN6XBi4UVrxvZR6KM1p3eywxcFXOQdyrA4n2DfvOzJbIAwBEQ/nmH3u3P/LM4EfD/W9qox+dyU8XV7xnZR5uXTq+qz3WPTIj3yxr0T0yUyQPABAVN/N9O9s3dp+8fnu1d6zMg3t1ILEkDwtTw3vIAwBES2l+7OXN3zs6cau82jtW5qE0O7pvU+wf37ZkUgr5vsfbN748Ns/FJQCIiuIXp/bv3Lahso6goFiaLt8YfmZDZWl6brxn26afDt8oszQNANFw+8bpE+9cMgZ+9OgezZo++7vz86WVb1JubP1q/JUf/+DYuVtCiFvn0o/uPDoxy8ZWAAg/9+pAYtNjuw+eurYgvsn37dr0w2f7x+2V69JitVPT5dn/7n3q2SO59wYO/NPedy/Lg9PkAQDCrlyYumzN3etB8U9f2oXVFh9Wv+dSuTB16aI1d6fyC+QBAFoHt+QDACjUkAfbtmu6XwcAILxqyAMAoHX8PwNglVmgNIKiAAAAAElFTkSuQmCC" alt></span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The graph of \(g\) intersects the <em>y</em>-axis at (0, 80) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of \(k\) .</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 graph passes through the point (2, 48) . </span></p>
<p><span>Find the value of \(c\) .</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 graph passes through the point (2, 48) . </span></p>
<p><span>Write down the equation of the horizontal asymptote to the graph of \(y = g(x)\) .</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>\(80 = 16 + k({c^0})\)</span><span> <em><strong>(M1)</strong></em></span></span></p>
<p><span>\(k = 64\) <em><strong>(A1) (C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(48 = 16 + 64({c^{ - 2}})\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution of their \(k\) and (2, 48) into the equation for \(g(x)\).</span></p>
<p> </p>
<p><span>\(c = \sqrt 2 \) (\(1.41\)) (\(1.41421 \ldots \)) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></span></p>
<p><span><strong>Notes:</strong> Award <strong><em>(M1)(A1)</em>(ft)</strong> for \(c = \pm \sqrt 2 \) . Follow through from their answer to part (a).</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>\(y = 16\) <em><strong>(A1)(A1) (C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(y = \) a constant, <em><strong>(A1)</strong></em> for \(16\).</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 was perhaps the most difficult question on the paper. Being the last question some candidates may have felt that they were under pressure to complete and many scripts showed no attempt at an answer to this question. The response by the upper quartile of candidates was quite encouraging with many achieving at least 4 of the 6 marks available. For the rest, many fell at the first hurdle and were unable to obtain a value of \(k\). This, in turn, led to problems in finding \(c\). For a large number of candidates the only mark that they achieved was identifying that the asymptote was a linear equation in \(y\).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This was perhaps the most difficult question on the paper. Being the last question some candidates may have felt that they were under pressure to complete and many scripts showed no attempt at an answer to this question. The response by the upper quartile of candidates was quite encouraging with many achieving at least 4 of the 6 marks available. For the rest, many fell at the first hurdle and were unable to obtain a value of \(k\). This, in turn, led to problems in finding \(c\). For a large number of candidates the only mark that they achieved was identifying that the asymptote was a linear equation in \(y\).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This was perhaps the most difficult question on the paper. Being the last question some candidates may have felt that they were under pressure to complete and many scripts showed no attempt at an answer to this question. The response by the upper quartile of candidates was quite encouraging with many achieving at least 4 of the 6 marks available. For the rest, many fell at the first hurdle and were unable to obtain a value of \(k\). This, in turn, led to problems in finding \(c\). For a large number of candidates the only mark that they achieved was identifying that the asymptote was a linear equation in \(y\).</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;">Consider the function \(f(x) = 1.25 - {a^{ - x}}\) , where a is a positive constant and \(x \geqslant 0\). The diagram shows a sketch of the graph of \(f\) . The graph intersects the \(y\)-axis at point A and the line \(L\) is its horizontal asymptote.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the \(y\)-coordinate of A .</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 \((2{\text{, }}1)\) lies on the graph of \(y = f(x)\) . Calculate the value of \(a\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The point \((2{\text{, }}1)\) lies on the graph of \(y = f(x)\) . Write down the equation of \(L\) .</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>\(y = 1.25 - {a^0}\) \(1.25 - 1\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(= 0.25\) <em><strong>(A1) (C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)(A1)</strong></em> for \((0{\text{, }}0.25)\) .</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>\(1 = 1.25 - {a^{ - 2}}\) <em><strong>(M1)</strong></em></span><br><span>\(a = 2\) <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">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(y = 1.25\) <em><strong>(A1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(y =\) “a constant”, <em><strong>(A1)</strong></em> for \(1.25\).</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;">Very few candidates showed working and subsequently lost marks due to this. Many candidates seemed to forget that \({a^0} = 1\) and not \(0\).</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;">Very few candidates showed working and subsequently lost marks due to this. Many candidates seemed to forget that \({a^0} = 1\) and not \(0\).</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;">Very few candidates showed working and subsequently lost marks due to this. Many candidates seemed to forget that \({a^0} = 1\) and not \(0\).</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the graph of the function \(f\left( x \right) = \frac{3}{x} - 2,\,\,\,x \ne 0\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation of the vertical asymptote.</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 equation of the horizontal asymptote.</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 value of <em>x</em> for which <em>f</em>(<em>x</em>) = 0 .</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><em>x</em> = 0 <em><strong>(A1)(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <em>x </em>= “a constant” <em><strong>(A1)</strong></em> for = 0. Award <em><strong>(A0)(A0)</strong></em> for an answer of “0”.</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><em>f</em>(<em>x</em>) = −2 (<em>y</em> = −2) <em><strong>(</strong><strong>A1)(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for y = “a constant” <em><strong>(A1)</strong></em> for = −2. Award <em><strong>(A0)(A0)</strong></em> for an answer of “−2”.</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>\(\frac{3}{x} - 2 = 0\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for equating <em>f</em>(<em>x</em>) to 0.</p>
<p>\(\left( {x = } \right)\frac{3}{2}\,\,\,\,\,\left( {1.5} \right)\) <em><strong> (A1) (C2)</strong></em></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>A population of \(200\) rabbits was introduced to an island. One week later the number of rabbits was \(210\). The number of rabbits, \(N\) , can be modelled by the function</p>
<p>\[N(t) = 200 \times {b^t},\,\,t \geqslant 0\,,\]</p>
<p>where \(t\) is the time, in weeks, since the rabbits were introduced to the island.</p>
<p>Find the value of \(b\) .</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 number of rabbits on the island after 10 weeks.</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>An ecologist estimates that the island has enough food to support a maximum population of 1000 rabbits.</p>
<p>Calculate the number of weeks it takes for the rabbit population to reach this maximum.</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>\(210 = 200 \times {b^1}\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into equation.</p>
<p>\((b = )\,\,1.05\) <em><strong>(A1) (C2)</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(200 \times {1.05^{10}}\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into formula. Follow through from part (a).</p>
<p>\( = 325\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note: </strong>The answer must be an integer.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(200 \times {1.05^t} = 1000\) <em><strong>(M1)</strong></em></p>
<p>\(t = 33.0\,\,\,(32.9869...)\) <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 setting up the equation. Accept alternative methods such as \(t = \frac{{\log \,(5)}}{{\log \,(1.05)}}\) , or a sketch of \(y = 200 \times {1.05^t}\) and \(y = 1000\) with indication of point of intersection. Follow through from (a).</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 14: Exponential Function<br>This question was well-answered by the majority of candidates.<br>Part (a) was generally accessible, unless subtraction was used in the rearrangement of the formula.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Part (b) required an integer value.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Part (c) saw good use of the GDC – with many sketch graphs being shown on paper (this is to be encouraged) – as well as attempts using logarithms. Use of the GDC is to be encouraged as its efficient use is a mandatory part of the course. Logarithms are not discouraged – but they are not a necessary component of the course and it is easy to construct equations that are not accessible to solution by logarithms.</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 rumour spreads through a group of teenagers according to the exponential model</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;">\(N = 2 \times {(1.81)^{0.7t}}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">where <em>N</em> is the number of teenagers who have heard the rumour <em>t</em> hours after it is first started.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number of teenagers who started the rumour.</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 number of teenagers who have heard the rumour five hours after it is first started.</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>Determine the length of time it would take for 150 teenagers to have heard the rumour. <strong>Give your answer correct to the nearest minute.</strong></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><em>N</em> = 2 × (1.81)<sup>0.7×0</sup> <em><strong>(M1)</strong></em></span><br><span><em>N</em> = 2 <em><strong>(A1) (C2)</strong></em></span></p>
<p> </p>
<p><span><strong>Notes:</strong> Award<em><strong> (M1)</strong></em> for correct substitution of<em> t</em> = 0.</span><br><span>Award<em><strong> (A1)</strong></em> for correct answer.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>16.0 (3 s.f) <em><strong>(A1) (C1)</strong></em></span></p>
<p><span> </span></p>
<p><span><strong>Note:</strong> Accept 16 and 15.</span></p>
<p><span> </span></p>
<p><em><strong><span>[1 mark]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>150 = 2 × (1.81)<sup>0.7<em>t</em></sup> <em><strong>(M1)</strong></em></span></p>
<p><span><em>t</em> = 10.39... h <em><strong>(A1)</strong></em></span></p>
<p><span><em>t</em> = 624 minutes <em><strong> (A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></span></p>
<p><span> </span></p>
<p><span><strong>Notes:</strong> Accept 10 hours 24 minutes. Accept alternative methods.</span></p>
<p><span>Award last <strong><em>(A1)</em>(ft)</strong> for correct rounding to the nearest minute of their </span><span>answer.</span></p>
<p><span>Unrounded answer must be seen so that the follow through can be</span> <span>awarded.</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;">Parts (a) and (b) were confidently answered with many candidates correctly finding the number who started the rumour and also the number involved after 5 hours. A common mistake was to let <em>t</em> = 0 but not evaluate the expression correctly.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Parts (a) and (b) were confidently answered with many candidates correctly finding the number who started the rumour and also the number involved after 5 hours. A common mistake was to let <em>t</em> = 0 but not evaluate the expression correctly.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Very few candidates could answer part (c). With the working shown, it was obvious candidates could correctly state the equation, but could not use their calculators to find the value of<em> t</em>.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Jashanti is saving money to buy a car. The price of the car, in US Dollars (USD), can be modelled by the equation</p>
<p>\[P = 8500{\text{ }}{(0.95)^t}.\]</p>
<p>Jashanti’s savings, in USD, can be modelled by the equation</p>
<p>\[S = 400t + 2000.\]</p>
<p>In both equations \(t\) is the time in months since Jashanti started saving for the car.</p>
</div>
<div class="specification">
<p>Jashanti does not want to wait too long and wants to buy the car two months after she started saving. She decides to ask her parents for the extra money that she needs.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the amount of money Jashanti saves per month.</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>Use your graphic display calculator to find how long it will take for Jashanti to have saved enough money to buy 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>Calculate how much extra money Jashanti needs.</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>400 (USD) <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>\(8500{\text{ }}{(0.95)^t} = 400 \times t + 2000\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for equating \(8500{(0.95)^t}\) to \(400 \times t + 2000\) or for comparing the difference between the two expressions to zero or for showing a sketch of both functions.</p>
<p> </p>
<p>\((t = ){\text{ }}8.64{\text{ (months) }}\left( {8.6414 \ldots {\text{ (months)}}} \right)\) <strong><em>(A1)</em></strong> <strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept 9 months.</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>\(8500{(0.95)^2} - (400 \times 2 + 2000)\) <strong><em>(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution of \(t = 2\) into equation for \(P\), <strong><em>(M1) </em></strong>for finding the difference between a value/expression for \(P\) and a value/expression for \(S\). The first <strong><em>(M1) </em></strong>is implied if 7671.25 seen.</p>
<p> </p>
<p>4870 (USD) (4871.25) <strong><em>(A1)</em></strong> <strong><em>(C3)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept 4871.3.</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><span style="font-size: medium; font-family: times new roman,times;">The \(x\)-coordinate of the minimum point of the quadratic function \(f(x) = 2{x^2} + kx + 4\) is \(x =1.25\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Find the value of \(k\) .</span></p>
<p><span>(ii) Calculate the \(y\)-coordinate of this minimum point.</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>Sketch the graph of \(y = f(x)\) for the domain \( - 1 \leqslant x \leqslant 3\).</span></p>
<p><span><img src="data:image/png;base64,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" alt></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) \(1.25 = - \frac{k}{{2(2)}}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong> OR</strong></span></p>
<p><span>\(f'(x) = 4x + k = 0\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for setting the gradient function to zero.</span></p>
<p><span> </span></p>
<p><span>\(k = - 5\) <em><strong>(A1) (C2)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span>(ii) \(2{(1.25)^2} - 5(1.25) + 4\) <em><strong>(M1)</strong></em></span></p>
<p><span>\( = 0.875\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></span></p>
<p><span><strong>Note:</strong> Follow through from their \(k\).</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><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZgAAAGyCAIAAABWbkVSAAAbDElEQVR4nO3d329U553H8ecPmBtfcoGEhJB8ESmKqrlIhFZwAaJCYqpICNFWFqlmBWh3RWh1QFnFJep6Um0dtXKmKZsqVndQo3XSHGU3bBZPG9LijEC7dTpeBSuddmEFU7zF3dliGQYHm3P24uBh8M/58Z3zfc4579dVYjueE8Pn42ee8zzPMT4ARJzRvgAA6BZF1rq56bFvD+zaYcxTx87/wfN9f+nz0X3bdhz/YMbTvjQg2Siy9nhzl3PP9qUOj93wfN+/e+2Dl3f/xdnpJe3LApKNImvX/NTIfpM65s4s+r7vz338yncv39O+JiDhKLJ2eV9Mvf6cefrE+B99f6k2/v3vT97RviQg6Siy9t2dGNxqtg1dWXgw/ZPvfHCLCTJAG0XWgVvnj/abQz8tf/TD1xmOARagyDpwvzJ60PQ9s2eweJvhGGABiqwD3t2JM1v7jo7duK99JQB8nyLryFJt/O/+2r2+qH0dAAIUWdu82YvffbU4s8i7SsAWFFmLvMWZT37y5r/99lb57dfevTq/xhLYSqVSLBbDvzIAFFmLHs5NvNJvtqSP/XTNFqvX65lMxhhTrVbDvzgg4SgyGa7rptNpY4zjONrXAiQORSagVqul02nXdY0xxphyuax9RUCyUGQC8vl8JpOp1+vGmOCfta8ISBaKrFvVatUYUyqVfN83xjRGZ9rXBSQIRdYt13Ub82LGmBUfARACikxSUGQAQkbwJFFkgAqCJ4kiA1QQPEkUGaCC4EmiyAAVBE8SRQaoIHiSKDJABcGTRJEBKgieJIoMUEHwJFFkgAqCtz7vTqX02Z+eOAh2YebSG8d27zDGmNRzR0Z+teKcWIoMUEHw1uLNXf949NT+frN9ePLxyfxL/3d5+MCBkyPn3h176zsD6S3GbN0z8mnzY8YpMkAFwVvtwcyVD8cvvz+0e8sTRfbwd+e+Pjh++9G/e7cvnOxPma1nJu4+HpRRZIAKgreem+7A9uYi826+99Lo9IPHX1CbGHzWmKPuzOMxG0UGqCB461lZZKvMTw7vMk8PTy4wIgOUEbz1bFZk3u/PZbY/O/wfzJEB6gjeejYuMu9BZTTTf/L8zIPmj5pVQrlUIOlI2no2LDLv1vjJ5188f2PFJ2kuQAXBW88GRbZw6/zgN/5han7Vs8YpMkAFwVvPekW2ND/15vEzP1+xFDZAkQEqCN561iyypfmrheN/9c61B40Wu3ftw59Pf/HoXykyQAXBW8/qIvMWb51/8akvn3rrXfeR98Z+9M3DTTcuKTJABcFbzbt//RO3MHigz5jUvlNv/ezDqVnP973ZX57ZvXXVbcnnz07fbfyXFBmgguBJosgAFQRPEkUGqCB4kigyQAXBk0SRASoIniSKDFBB8CRRZIAKgieJIgNUEDxJFBmgguBJosgAFQRPEkUGqCB4kigyQAXBk0SRASoIniSKDFAhFrxyuVytVqW+W0RRZIAKseC5rpvP56W+W0RRZIAKseDV6/V0Ol2r1aS+YRRRZIAKyeAxKKPIABWSwWNQRpEBKoSDl/BBGUUGqBAOXsIHZRQZoEI+eEkelFFkgAr54NVqNWNMMgdlFBmgoifBy+fzyRyUUWSAip4EL7GDMooMUNGr4CVzUEaRASp6FbxkDsooMkBFD4OXwEEZRQao6GHwEjgoo8gAFb0NXtIGZRQZoKK3wUvaoIwiA1T0PHj5fL5QKPT6VSxBkQEqeh68arWaTqfr9XqvX8gGFBmgIozgOY7jum4IL6SOIgNUhBG8SqWSyWRCeCF1FBmgIqTgZbPZUqkUzmsposgAFSEFr1QqJWFQRpEBKsILXiaTKZfLob2cCooMUBFe8EqlkuM4ob2cCooMUBFe8IJTsCuVSmivGD6KDFARavBc183lcmG+YsgoMkBFqMGL/aNJKDJARdjBi/c2cooMUBF28OK9jZwiA1QoBC+fz8d1xxJFBqhQCF6Mt5FTZIAKneA5jlMsFlVeuqcoMkCFTvDiuo2cIgNUqAUvk8nEbxs5RQaoUAteLLeRU2SACs3gZTKZmO1YosgAFZrBKxaLMdtGTpEBKpSDF7NBGUUGqFAOXszO9qHIABX6wYvToIwiA1ToBy9OgzKKDFBhRfBiMyijyAAVVgQvNoMyigxQYUvw4jEoo8gAFbYELx6DMooMUGFR8GIwKKPIABUWBS8Guy8pMkCFXcGL+pEYFBmgwq7gRX1QRpEBKqwLXqQHZRQZoMK64EV6UEaRASpsDF50B2UUGaDCxuBFd1BGkQEqLA1eRAdlFBmgwtLgRXRQRpEBKuwNXhQHZRQZoMLe4EVxUEaRASqsDl7kBmUUGaDC6uBFblBGkQEqbA9etAZlFBmgwvbgRWtQRpEBKiIQvAgNyigyQEUEghehQRlFBqiIRvCiMiijyAAV0QheVAZlFBmgIjLBi8SgjCIDVEQmeJEYlFFkgIooBc/+QRlFBqiIUvDsf/YlRQaoiFjwLH/2JUUGqIhY8CwflFFkgIroBc/mQRlFBqiIXvBsHpRRZICKSAbP2kEZRQaoiGTwrF1TRpEBKqIaPDvXlFFkgIqoBq9cLmcymXq9rn0hT6DIABURDp7jOK7ral/FEygyQEWEg1epVNLptFWDMooMUBHt4OXz+UKhoH0Vj1FkgIpoB69WqxljarWa9oU8QpEBKiIfvEKhkM/nta/iEYoMUBH54NXr9XQ6bcn6WIoMUBGH4Lmua8mmJYoMUBGH4NXr9UwmUy6XtS+EIgN0xCR4lmxaosgAFfEJng2bligyIFAsFsN8ufgEz4b1sRQZ4C+HMcxXjFXw1DctUWSAr/H2KFbBU18fS5EBrutms9mQXzRuwSsUCopLMSgyJJzWus64BU93fSxFhoTL5/MqO21iGLxisai1FIMiQ5JVq9V0Oq0ytxPP4GUymZDv/gYoMiSZ4t22eAZPaykGRYbE0l2UHtvg5XK58I8qo8iQTOrbBGMbPJWlGBQZkkn94IY4By/8Hy5FhgRSX7/px7vIwl+KQZEhgVSmcVaIefBCnoCkyJA0Nuxx9mNfZL7vZ7PZ0JZiUGRIGq2lTivEP3hh/sagyJAoxWIx/G2Va0pE8HK5nPi2CW/+xuTFfzl3tjAx86DxQYoMyVGr1Sx6XIb2BYQh+IlXq1WR7+bNf/7+0NfSzx4bOT81u+g1f4oiQ3LYMMffkJTgCS3F8BZnfv7t3dt2HPnHq/NLqz9NkSEhyuWyDXP8DQkKXveHvXmzvzyze2tqzw9+PbdGi/kUGZIhWMevfrJ8swQFr+vfIXcmh/cZ89zpi7e9db6CIkMSqK/jXy1Zwetqd35t/ESfMakDp773twO7dphU+uDLhSszC81fQpEh9qrVqvo6/tWSFbwu9lJ4C1dy24zpOzh8YXp20Zu/MXH2yI7UireZFBliT/3JGGtKXPA6PQt7ccY9asy2Q2P/vfy+8sEt93ifefrE+B8bX2RWkblowA7BVhl75vgbEpe0TjdgLs2e/5uU2T7g3mx8yLt+LmPM9uHJxeWP0FyIMd1z5DeWxOB1tgFzafrsTtO38+xnj99JzrgDJvXMyFTjIxQZYiyfz+dyOe2rWFtCg9fJ+/wvyiPP9aUOj91Yfm/5sDK61+wcnPjfxpdQZIirYKufbXP8DQkNXkd/Kou3x0/3m725KzXP933/XmX0a/0vjF178HgxBkWGuArz8IUOJDd4HY2TF2YuvXFsz56DzneGXnxhYPBn00+u76fIEEsqz9xtS3KDF8xcyp4yTpEhfmS3KvdIooNXLpdl7yVTZIgfx3Hs2Ry+nqQHT/YPiSJDzFi7cGyFpAdP9kwligxxYvPCsRUInuQplxQZ4iSXy1m7cGwFguf7vp/NZkW2j1FkiA1LnirSIoLn+8sb+ru/L0ORIR4sPHFsYwTvEZEjligyxEOnZyuoIXiPdf9gK4oMMVCtVm3ejbQmgvdY97vJKDLEgNSUcZgI3hMKhUI3t2koMkSd/buR1kTwntDlviWKDJEWHKFs+W6kNRG8lbp5RglFhkiLxG6kNRG8NXS8DpAiQ3RF9E1lgOCtIXiD2cEiGooMERXc6Yrim8oAwVtbZ3cwKTJEUbD81eZzEzdF8NZVKBTaHWlTZIiiCO2pXA/B20i7C2ooMkROqVSK0J7K9RC8jQRLnFs/xoQiQ7TIHmOliOBtolgstn6wHEWGaMlmsxFdb7ECwdtc6zMIFBkiJNLrLVYgeJtrfTUGRYaosPw5le0ieC1p8U+dIkMkdLxS0loEr1WtrMagyBAJMVhvsQLBa8OmqzEoMtivrftXUUHw2rDpagyKDJaTOtXdNgSvPRuvHqTIYLMYbEVaD8FrWz6fX+84c4oMNovf1FgDwWtbvV5fb7KMIoO1Yjk11kDwOrHeZBlFBjtF/ZSeTRG8DgWTZStWllFksFD8Vo2tRvA6t3plGUUGCzmOk8/nta+itwheV1bsuaXIYJtgQ2Vcp8YaCF5XglNQGk9doshgldhPjTUQvG4FT10KJssoMtgjCVNjDQRPQGOyjCKDPbLZbOynxhoInozgLw1FBkvk8/nYnDXWCoInIxjGU2SwQTyO4W8LwRNTqVRiuR0X0RLXbeEbo8gkGWOScKsb1krUBH8zikySMSbG+3Jhv0RN8DejyCQZY4It5fF4Mg2iJWkT/M0oMknBZH+wpTyBw3soSuAEfzOKTFLjrmWwSjZpE67QkswJ/mYUmaTm5RfxPv4J9kjsBH8zikzSinVkG5wlC4gI5mSTOcHfjCKTtKLImPhHr3GXPECRSVq9sj84HiPhw370SHCbkukLnyKTteYWpeQcpYIwFYvFJN+mXIEik7TeXksm/iErWGzBb8cGikzSBpvGk7xYEbKChYqN4zzhU2SyNigy7i5BBLOua6LIJG18jA9dhi7xV2g9FJmkTc8j4y8iuuE4Dost1kSRSWrlYEW6DJ1hscUGKDJJLZ4QG+wpocvQOlpsYxSZpNaPug5uPLHoH63I5/Ms39kYRSaprTP7Oe0HrWDJWCsoMkntPnyELsPGaLEWUWSSOniKEl2G9dBiraPIJHX2OLjg8UuVSkX8ehBd5XKZvxWto8gkdfxcS373ohnj9HZRZJK6eUAvXYYALdYBikxSl08ap8sQHPpEi7WLIpPUZZH5dFmylUolYwwt1gGKTFL3Reb7fqFQoMsSKPgdRot1hiKTJFJkPiu5k4eReJcoMklSReazty5JaLHuUWSSBIvMX+4y/n7HGy0mgiKTJFtkvu/n83n+lscYf75SKDJJ4kXmLz8sh7/r8cOIWxBFJqkXRebz7iN2gsM1mQMVRJFJ6lGR+dybj5FqtZrJZDhWUxZFJql3RebTZbEQLNx3XVf7QuKGIpPU0yLzl3fh8cs8oli43zsUmaReF5nP9EpksWGjpygySSEUWYDb9hFSr9dzuRw3KHuKIpMUWpH5vE+JiFqtls1mHcdhBN1TFJmkMIvMZ8rMesHUPs/KCgFFJinkIvObpsxqtVrIL42NBSuZGTKHgyKTFH6RBYKJZM53t0S9Xg/OL2FSLDQUmSStIvOXV5mxQEkdt5VVUGSSFIvM9/1qtZrNZnO5HBHSEkyKMWsZPopMkm6R+ct3+nlTE756vR68wS+Xy9rXkkQUmST1IgsUi0VjDG8zQ1OpVDKZjOM43HLRYkXwYsOSIvOX32ayfCkEruum0+lisah9IYlmS/DiwZ4i85fvnXE3s3eC3xYs2beBRcGLAauKLFAul9PpNHcAxPH+3SrWBS/SLCwyf/kOAIszpTAQs5CNwYsuO4sswIR09+r1uuu6DMQsZG/wosjmIvOblgi4rss7zXbxm8BmVgcvciwvskC1WnUch20ArWv8AuDWpLUiELwIiUSRBSqViuM4mUyGibONBXu/crkcAzGbRSZ4kRChIguUy+VMJkOdralUKgXvJVm/Yr+IBc9ykSuyAIldgR9I5EQyeNaKaJEFSK/PDyGyIhw8C0W6yALBhpukJblWqwXT+Un7H4+NyAfPKjEoMn95tVRCUl0qlYJ7uPl8ngWu0RWH4NkjHkUWiHedNYZg2Wy2VCqxqi7q4hM8G8SpyBqCaaMg8NrX0q16vc4QLJZiGDxFsSyyQFBnwYqqKA5hqtVqcBYIQ7BYim3wVMS4yAK1Wq1YLOZyOWNMNpt1XdfyQU21Wi0Wi0EFFwoFFrXGVcyDF7LYF1lDvV4vl8vBs4KCt2n2DHOC8goO/AiGkBw/HXtJCV44klNkzYLicBynMUwL/+bA6vIqFouWjxYhKInB651kFllDMEwrFArZbNYY4zhOoVAol8s9GqlRXmhIdPDEJbzImgWl5rpuY6TmOE4+n3ddt1gsViqV1kdtwReXSiXXdQuFguM4wW3HTCYTvKVl5gsETxJFtp6gjIrFouu6uVzOcZxg1NYQLFhrlFTzp4ISzOVyruu6rlsulyuVCuWFZgRPEkXWsVqtVlnG20O0i+BJosgAFQRPEkUGqCB4kigyQAXBk0SRASoIniSKDFBB8CRRZIAKgieJIgNUEDxJFBmgguBJosgAFQRPEkUGqCB4kigyQIVY8Miwzw8BWBZyFigySfwQgABFFmH8EIBAx1moVqvpdNp13fZerrMXW+MbkWF+CMCybrIQPFA1k8m0/rAFikwSPwQg0GUWarVa8LAux3FaOURTJngGAHpm0y5jBCHJMCIDhNRqteCBD4VCYdMvJnjtWpqvnM8dPjDw8qtDJ7568PS70/NLjc9RZICIYrEYPBa+xYfUELz2eLcvnOx/6sjYfy36vu/VruT27Tjy08p9L/gsRQZ0qV6vBwOxtm5cEry23Jkc3mf6vjVeezQKW5o+u9P0v+DeCJqMIgO6FEzzt/sAGoLXjrsTg1uNyZy77j3xkdThsaDJKDJAhXTwvDuV0md/8jb/wihamj6705gtpy7ONT708PPRvVsaYzSKDIm3MDv59un9/cYYY/oP5D6aWQyjDuSC581d/3j01P5+s314clHsu9pkqTb+rT6z4v/vpjuw3ZiDo5X7PkWGpPPuX/3x4cOvvnfp3yd//ct/Or0vZbZ95dzvHnb7XW9NvPm9lweeS6W+MjI1581/NvbinlTqUBC6gFTwHsxc+XD88vtDu7fEt8gWZ9yjZu0i2zU8Oe9TZEg47w//+uroVOM+fjAVM+DOiHzvGfdIqm/nGxc+/vvhd8q/mSh+2jzWkw3eTXdge3yL7OHcxZe2rF1kmbPT93yKDGi2cGVom8SILPDw89G9W1LbDwxNzK5+s0qRteFhZXSvMVsHJ+42PuT9/lxmK3NkwCoLt86/lHnxvcbipK7NTQ7vMdtyVxbW+IYUWTvuXR56KmUOjd1s/CQXrgxte3wfkyIDfN9bnJ06P3IsnUrtOPSDSzMLMt918bp77EuN+egVKLK2/PnK0C6z5aWLc48Gyw8ro3tZRwY082anPnTHRr93Yn+/MSa15/Wpe90PyuZ/O3rmtffeGEjtOOLe8Pwv7vz5iW9KkbXHm/ng+I7mlf17UwfevMrKfmC1xZvjp3cZ8+zgxObHV6zDW5z5tPjxp5/94oevvH998eHno3u39B175ze/+NFrxZvNNdNq8I6m1tuXvm9kqjFlFP8i8/2l+co/Dx1+/sjLrw6deH730TcvN42cKTKg2cPK6F6zfcC92ek3WLh27usp88yR0f+c93zfv3dt7PiOx//6GCMySRQZ8IQZd8DsGZ6c2/wru0ORSaLIgCZLtXFna2a08qDni/spMkkUGRLt4e/OfWWb2fHVnFuefTB345PRF48MX5S6a7khqeB5969/4hYGD/QZk9p36q2ffTi1xqK12KPIkGwLM1feHjrxjYGBY6dyZ8cmrs2H1QIETxJFBqggeJIoMkAFwZNEkQEqCJ4kigxQQfAkUWSACoIniSIDVBA8SRQZoILgSaLIABUETxJFBqggeJIoMkAFwZNEkQEqCJ4kigxQQfAkUWSACoIniSIDVBA8SRQZoILgSaLIABUETxJFBqggeJIoMkAFwZNEkQEqCJ4kigxQQfAkUWSACoIniSIDVBA8SRQZoILgSaLIABUETxJFBqggeJIoMkAFwZNEkQEqCJ4kigxQQfAkUWSACoIniSIDVBA8SRQZoILgSaLIABUETxJFBqggeJIoMkAFwZNEkQEqCJ4kigxQQfAkUWSACoIniSIDVBA8SRQZoILgSaLIABUETxJFBqggeJIoMkAFwZNEkQEqCJ4kigxQQfAkUWSACoIniSIDVBA8SRQZoILgSaLIABUETxJFBqggeJIoMkAFwZNEkQEqCJ4kigxQQfAkUWSACoIniSIDVBA8SRQZoILgSaLIABUETxJFBqggeJIoMkAFwZNEkQEqCJ4kigxQQfAkUWSACoIniSIDVBA8SRQZoILgSaLIABUETxJFBqggeJIoMkAFwZNEkQEqCJ4kigxQQfAkUWSACoIniSIDVBA8SRQZoILgSaLIABUETxJFBqggeJIoMkAFwZNEkQEqCJ4kigxQQfAkUWSACoIniSIDVBA8SRQZoILgSaLIABUETxJFBqggeJIoMkAFwZNEkQEqCJ4kigxQQfAkUWSACoIniSIDVBA8SRQZoILgSaLIABUETxJFBqggeJIoMkAFwZNEkQEqCJ4kigxQQfAkUWSACoIniSIDVBA8SRQZoILgSaLIABUETxJFBqggeJIoMkAFwZNEkQEqCJ4kigxQQfAkUWSACoIniSIDVBA8SRQZoILgSaLIABUEr1Pe/M3Jjz849+aPJ255yx+jyAAVBK993p3K+7lD6d1HR85PzS40f4YiA1QQvDYtVj/69pdTO/5y9Oodb9UnKTJABcFrh/c/l858OZXKDP+6trrFfIoMUELwWufdm3ztWZPqP/3R2jVGkQFKCF7r/jh+4mljtu0/NTQ4sHu72fKlgy+PXrm12PQVFBmgguC1bOHK0DZj+g4PX7j6p8Wl+RuXzh55xjz5NpMiA1QQvJbNuAPGmENjN5d7y7vlvtBn+k6M15a/xKyidK1AspC0JrPnj6ZWd1Fg38iFt4+mjBlwZxpf7/3+XGar2T48ufz2kuYCVBC8li19dnZnn9l5dnqp8aGb7sB288zI1NIG/xmAnqPIWjc/NbLfpL4xduOLRx94+Pno3q39g5fmVC8LAEXWBu/2hZP9W57NXZ7zfN/3HlRGM/3Hx67d074uIOkosrZ4izO/ev3Y/l0Hvzk0dHJg4JV3ptdY3w8gZBQZgMijyABEHkUGIPL+H32Ruv1CEu7TAAAAAElFTkSuQmCC" alt><span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span></span></p>
<p> </p>
<p><span><span><strong>Notes:</strong> Award</span><span> <strong><em>(A1)</em>(ft)</strong> for a curve with correct concavity consistent with their \(k\) passing through (0, 4).</span></span></p>
<p><span><strong><em>(A1)</em>(ft)</strong> for minimum in approximately the correct place. Follow through from their 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 not answered well at all except by the more able. Indeed, of the lower quartile of candidates, the maximum mark achieved was only 1. Of those that did make a successful attempt at the question, very few used the fact that \(1.25 = - \frac{k}{{2(2)}}\) preferring instead to differentiate and equate to zero. But such candidates were in the minority as substituting \(x = 1.25\) into the given quadratic and equating to zero produced the popular, but erroneous, answer of \(- 5.7\). Recovery was possible for the next two marks if this incorrect value had been seen to be substituted into the correct quadratic, along with \(x = 1.25\) to arrive at an answer of \(0\). This would have given (M1)(A1)(ft). However, candidates who had an answer of \(k = - 5.7\) in part (a)(i), invariably showed no working in part (ii) and consequently earned no marks here. Irrespective of incorrect working in part (a), the quadratic function clearly passes through (0, 4) and has a minimum at \(x = 1.25\). Using this information, a minority of candidates picked up at least one of the two marks in part (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 not answered well at all except by the more able. Indeed, of the lower quartile of candidates, the maximum mark achieved was only 1. Of those that did make a successful attempt at the question, very few used the fact that \(1.25 = - \frac{k}{{2(2)}}\) preferring instead to differentiate and equate to zero. But such candidates were in the minority as substituting \(x = 1.25\) into the given quadratic and equating to zero produced the popular, but erroneous, answer of \(- 5.7\). Recovery was possible for the next two marks if this incorrect value had been seen to be substituted into the correct quadratic, along with \(x = 1.25\) to arrive at an answer of \(0\). This would have given (M1)(A1)(ft). However, candidates who had an answer of \(k = - 5.7\) in part (a)(i), invariably showed no working in part (ii) and consequently earned no marks here. Irrespective of incorrect working in part (a), the quadratic function clearly passes through (0, 4) and has a minimum at \(x = 1.25\). Using this information, a minority of candidates picked up at least one of the two marks in part (b).</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 part of the graph of \(y = 2^{-x} + 3 \), and its horizontal asymptote.</span> <span style="font-family: times new roman,times; font-size: medium;">The graph passes through the points (0, </span><span style="font-family: times new roman,times; font-size: medium;"><em><span style="font-family: times new roman,times; font-size: medium;">a</span></em>) and (</span><span style="font-family: times new roman,times; font-size: medium;"><em><span style="font-family: times new roman,times; font-size: medium;">b</span></em>, 3.5).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of</span></p>
<p><span>(i) <em>a</em> ;</span></p>
<p><span>(ii) <em>b</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>Write down the equation of the horizontal asymptote to this graph.</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<sup>0</sup> + 3 <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution.</span></p>
<p><br><span>= 4 <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span> </span></p>
<p><span>(ii) 3.5 = 2<sup>−</sup><em><sup>b</sup></em> + 3 <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution.</span></p>
<p><br><span><em>b</em> = 1 <em><strong>(A1) </strong> <strong>(C2)</strong></em></span></p>
<p><br><span><em><strong>[4 marks]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>y</em> = 3 <em><strong>(A1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> <em>y</em> = constant (other than 3) award <em><strong>(A1)(A0)</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;">Most candidates answered parts (a) i and ii correctly, however a large number of candidates could not find the correct equation for part (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;">Most candidates answered parts (a) i and ii correctly, however a large number of candidates could not find the correct equation for part (b).</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;">In an experiment it is found that a culture of bacteria triples in number every four hours. There are \(200\) bacteria at the start of the experiment.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the 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>Calculate how many bacteria there will be after one day.</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 how long it will take for there to be two million bacteria.</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>\(a = 1800\) <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>\(200 \times {3^6}{\text{ (or }}16200 \times 9{\text{) }} = 145800\) <em><strong>(M1)(A1) (C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(200 \times {3^n} = 2 \times {10^6}\) (where \(n\) is each \(4\) hour interval) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note: </strong>Award <em><strong>(M1)</strong></em> for attempting to set up the equation or writing a list of numbers.</span></p>
<p><br><span>\({3^n} = {10^4}\)</span></p>
<p><span>\(n = 8.38{\text{ }}(8.383613097)\) <em>correct answer only</em> <em><strong>(A1)</strong></em></span></p>
<p><span>\({\text{Time}} = 33.5{\text{ hours}}\) <em>(accept</em> \(34\)<em>,</em> \(35\)<em> or</em> \(36\) <em>if previous <strong>A</strong> mark awarded)</em> <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C3)</strong></em></span></p>
<p><br><span><strong>Note: <em>(A1)</em>(ft)</strong> for correctly multiplying their answer by \(4\). If \(34\), \(35\) or \(36\) seen, or \(32 - 36\) seen, award <em><strong>(M1)(A0)(A0)</strong></em>.</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-family: times new roman,times; font-size: medium;">Parts (a) and (b) were answered well with most candidates attempting and gaining marks. Very few candidates gained maximum marks for part (c) with most using a list to find the number of hours rather than the 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;">Parts (a) and (b) were answered well with most candidates attempting and gaining marks. Very few candidates gained maximum marks for part (c) with most using a list to find the number of hours rather than the 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;">Parts (a) and (b) were answered well with most candidates attempting and gaining marks. Very few candidates gained maximum marks for part (c) with most using a list to find the number of hours rather than the 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 diagram below shows the graph of a quadratic function. The graph passes through the points (6, 0) and (<em>p</em>, 0). The maximum point has coordinates (0.5, 30.25).</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>Calculate the value of <em>p</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>Given that the quadratic function has an equation \(y = -x^2 + bx + c\) where \(b,{\text{ }}c \in \mathbb{Z}\), find \(b\) and \(c\).</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>\(\frac{{(p + 6)}}{2} = 0.5\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(p = -5\) <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>\(\frac{{ - b}}{{2( - 1)}} = 0.5\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(b = 1\) <em><strong>(A1)</strong></em></span></p>
<p><span>\(- 0.5^2 + 0.5 + c = 30.25\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(c = 30\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Note:</strong> Follow through from their value of <em>b</em>.</span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span>\(y = (6 - x) (5 + x)\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(= 30 + x - x^2\) <em><strong>(A1)</strong></em></span></p>
<p><span>\(b = 1,{\text{ }}c = 30\) <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong> <em><strong>(C4)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from their value of <em>p</em> in part (a).</span></p>
<p><span> </span></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-size: medium; font-family: times new roman,times;">This question was one of the most difficult in this paper. Many students left this question blank, showed incorrect working or gave answers without any preceding working.</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 one of the most difficult in this paper. Many students left this question blank, showed incorrect working or gave answers without any preceding working.</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 number of cells, <em>C</em>, in a culture is given by the equation \(C = p \times 2^{0.5t} + q\), where <em>t</em> is the time in hours measured from 12:00 on Monday and <em>p</em> and <em>q</em> are constants.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The number of cells in the culture at 12:00 on Monday is 47.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The number of cells in the culture at 16:00 on Monday is 53.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use the above information to </span><span>write down two equations in <em>p</em> and <em>q</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>Use the above information to </span><span>calculate the value of <em>p</em> and of <em>q</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>Use the above information to </span><span>find the number of cells in the culture at 22:00 on Monday.</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>p</em> + <em>q</em> = 47 <em><strong>(A1)</strong></em></span></p>
<p><span>4<em>p</em> + <em>q</em> = 53 <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>Reasonable attempt to solve their equations <em><strong>(M1)</strong></em></span></p>
<p><span><em>p</em> = 2, <em>q</em> = 45 <em><strong>(A1) </strong> <strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Accept only the answers </span><span><span><em>p</em> = 2, <em>q</em> = 45</span>.</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><em>C</em> = 2 × 2<sup>0.5(10)</sup> + 45 <em><strong>(M1)</strong></em></span></p>
<p><span><em>C</em> = 109 <em><strong>(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 substitution of 10 into the formula with their values of <em>p</em> and <em>q</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;">Concern was expressed about the wording of the question; answers were given great leeway by examiners and suggestions for wording are welcome. The 24 hour clock method of describing time is the norm in IB examinations. It should be recognised that the purpose of this question was to discriminate at the grade 6/7 level.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The concept of the zero index was not understood by many.</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;">Concern was expressed about the wording of the question; answers were given great leeway by examiners and suggestions for wording are welcome. The 24 hour clock method of describing time is the norm in IB examinations. It should be recognised that the purpose of this question was to discriminate at the grade 6/7 level.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The use of the GDC was (as always) expected in solving the simultaneous equations.</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;">Concern was expressed about the wording of the question; answers were given great leeway by examiners and suggestions for wording are welcome. The 24 hour clock method of describing time is the norm in IB examinations. It should be recognised that the purpose of this question was to discriminate at the grade 6/7 level.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Working was required for follow through in this part.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The graph of a quadratic function has \(y\)-intercept 10 and <strong>one </strong>of its \(x\)-intercepts is 1.</p>
<p>The \(x\)-coordinate of the vertex of the graph is 3.</p>
<p>The equation of the quadratic function is in the form \(y = a{x^2} + bx + c\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of \(c\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(a\) and of \(b\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the second \(x\)-intercept of the function.</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>10 <strong><em>(A1)</em></strong> <strong><em>(C1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept \((0,{\text{ }}10)\).</p>
<p> </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>\(3 = \frac{{ - b}}{{2a}}\)</p>
<p>\(0 = a{(1)^2} + b(1) + c\)</p>
<p>\(10 = a{(6)^2} + b(6) + c\)</p>
<p>\(0 = a{(5)^2} + b(5) + c\) <strong><em>(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for each of the above equations, provided they are not equivalent, up to a maximum of <strong><em>(M1)(M1)</em></strong>. Accept equations that substitute their 10 for \(c\).</p>
<p> </p>
<p><strong>OR</strong></p>
<p>sketch graph showing given information: intercepts \((1,{\text{ }}0)\) and \((0,{\text{ }}10)\) and line \(x = 3\) <strong><em>(M1)</em></strong></p>
<p>\(y = a(x - 1)(x - 5)\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for \((x - 1)(x - 5)\) seen.</p>
<p> </p>
<p>\(a = 2\) <strong><em>(A1)</em>(ft)</strong></p>
<p>\(b = - 12\) <strong><em>(A1)</em>(ft)</strong> <strong><em>(C4)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (a).</p>
<p>If it is not clear which is \(a\) and which is \(b\) award at most <strong><em>(A0)(A1)(ft)</em></strong>.</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>5 <strong><em>(A1)</em></strong> <strong><em>(C1)</em></strong></p>
<p><strong><em>[1 mark]</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;">The amount of electrical charge, <em>C</em>, stored in a mobile phone battery is modelled by \(C(t) = 2.5 - {2^{ - t}}\), where <em>t</em>, in hours, is the time for which the battery is being charged.</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_2014-09-20_om_13.45.23.png" alt><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"> </p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the amount of electrical charge in the battery at \(t = 0\).</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 line \(L\) is the horizontal asymptote to the graph.</span></p>
<p><span>Write down 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>To download a game to the mobile phone, an electrical charge of 2.4 units is needed.</span></p>
<p><span>Find the time taken to reach this charge. Give your answer correct to the nearest minute.</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>\(1.5\) <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>\(C = 2.5\) (accept \(y = 2.5\)) <strong><em>(A1)(A1) (C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for \(C{\text{ (or }}y) = \) a positive constant, <strong><em>(A1) </em></strong>for the constant \(= 2.5\).</span></p>
<p><span> Answer must be an equation.</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>\(2.4 = 2.5 - {2^{ - t}}\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for setting the equation equal to 2.4 or for a horizontal line drawn at approximately \(C = 2.4\).</span></p>
<p><span> Allow \(x\) instead of \(t\).</span></p>
<p> </p>
<p><span><strong>OR</strong></span></p>
<p><span>\( - t\ln (2) = \ln (0.1)\) <strong><em>(M1)</em></strong></span></p>
<p><span>\(t = 3.32192 \ldots \) <strong><em>(A1)</em></strong></span></p>
<p><span>\(t = 3{\text{ hours and 19 minutes (199 minutes)}}\) <strong><em>(A1)</em>(ft) <em>(C3)</em></strong></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award the final <strong><em>(A1)</em>(ft) </strong>for correct conversion of <strong>their </strong>time in hours to the nearest minute.</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 function \(f\) is of the form \(f(x) = ax + b + \frac{c}{x}\), where \(a\) , \(b\) and \(c\) are positive integers.</p>
<p>Part of the graph of \(y = f(x)\) is shown on the axes below. The graph of the function has its local maximum at \(( - 2,{\text{ }} - 2)\) and its local minimum at \((2,{\text{ }}6)\).</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_11.28.21.png" alt="M17/5/MATSD/SP1/ENG/TZ1/12"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the domain of the function.</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>Draw the line \(y = - 6\) on the axes.</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>Write down the number of solutions to \(f(x) = - 6\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the range of values of \(k\) for which \(f(x) = k\) has no solution.</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>\((x \in \mathbb{R}),{\text{ }}x \ne 0\) <strong><em>(A2)</em></strong> <strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept equivalent notation. Award <strong><em>(A1)(A0) </em></strong>for \(y \ne 0\).</p>
<p>Award <strong><em>(A1) </em></strong>for a clear statement that demonstrates understanding of the meaning of domain. For example, \({\text{D}}:( - \infty ,{\text{ }}0) \cup (1,{\text{ }}\infty )\) should be awarded <strong><em>(A1)(A0)</em></strong>.</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><img src="images/Schermafbeelding_2017-08-15_om_15.32.51.png" alt="M17/5/MATSD/SP1/ENG/TZ1/21.b.i/M"> <strong><em>(A1)</em></strong> <strong><em>(C1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> The command term “Draw” states: “A ruler (straight edge) should be used for straight lines”; do not accept a freehand \(y = - 6\) line.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>2 <strong><em>(A1)</em>(ft)</strong> <strong><em>(C1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (b)(i).</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\( - 2 < k < 6\) <strong><em>(A1)(A1)</em></strong> <strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for both end points correct and <strong><em>(A1) </em></strong>for correct <strong>strict </strong>inequalities.</p>
<p>Award at most <strong><em>(A1)(A0) </em></strong>if the stated variable is different from \(k\) or \(y\) for example \( - 2 < x < 6\) is <strong><em>(A1)(A0)</em></strong>.</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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</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 computer virus spreads according to the exponential model</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;">\[N = 200 \times {(1.9)^{0.85t}},{\text{ }}t \geqslant 0\]</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;">where \(N\) is the number of computers infected, and \(t\) is the time, in hours, after the initial infection.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the number of computers infected after \(6\) hours.</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 time for the number of infected computers to be greater than \({\text{1}}\,{\text{000}}\,{\text{000}}\).</span></p>
<p><span>Give your answer correct to the nearest hour.</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>\(200 \times {(1.9)^{0.85 \times 6}}\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into given formula.</span></p>
<p> </p>
<p><span>\( = 5280\) <strong><em>(A1) (C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Accept \(5281\) or \(5300\) but no other answer.</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>\(1\,000\,000 < 200 \times {(1.9)^{0.85t}}\) <strong><em>(M1)(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for setting up the inequality (accept an equation), and <strong><em>(M1) </em></strong>for \({\text{1}}\,{\text{000}}\,{\text{000}}\) seen in the inequality or equation.</span></p>
<p> </p>
<p><span>\(t = 15.6\) \((15.6113…)\) <strong><em>(A1)</em></strong></span></p>
<p><span>\(16\) hours <strong><em>(A1)</em>(ft) <em>(C4)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>The final <strong><em>(A1)</em>(ft) </strong>is for rounding <strong>up </strong>their answer to the nearest hour.</span></p>
<p><span> Award <strong><em>(C3) </em></strong>for an answer of \(15.6\) with no working.</span></p>
<p><span> Accept \({\text{1}}\,{\text{000}}\,{\text{001}}\) in an equation.</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;">
<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 answered very well, although some candidates were not awarded the final mark because the answer was not an integer number of computers. In part (b), some candidates neglected to give their answer correct to the nearest hour and lost the final mark.</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 answered very well, although some candidates were not awarded the final mark because the answer was not an integer number of computers. In part (b), some candidates neglected to give their answer correct to the nearest hour and lost the final mark.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Passengers of Flyaway Airlines can purchase tickets for either Business Class or Economy Class.</p>
<p class="p2">On one particular flight there were <span class="s1">154 </span><span class="s2">passengers.</span></p>
<p class="p2">Let \(x\) be the number of Business Class passengers and \(y\) be the number of Economy Class passengers on this flight.</p>
</div>
<div class="specification">
<p class="p1">On this flight, the cost of a ticket for each Business Class passenger was <span class="s1">320 </span>euros and the cost of a ticket for each Economy Class passenger was <span class="s1">85 </span>euros. The total amount that Flyaway Airlines received for these tickets was \({\text{14}}\,{\text{970 euros}}\).</p>
</div>
<div class="specification">
<p class="p1">The airline’s finance officer wrote down the total amount received by the airline for these tickets as \({\text{14}}\,{\text{270 euros}}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Use the above information to write down an equation in \(x\) <span class="s1">and \(y\).</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">Use the information about the cost of tickets to write down a second equation <span class="s1">in \(x\) and \(y\).</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 class="p1">Find the value of \(x\) <span class="s1">and the value of \(y\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the percentage error.</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"><span class="Apple-converted-space">\(x + y = 154\) </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C1)</em></strong></p>
<p class="p1"><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(320x + 85y = 14\,970\) </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C1)</em></strong></p>
<p class="p1"><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(x = 8,{\text{ }}y = 146\) </span><strong><em>(A1)</em>(ft)<em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C2)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Follow through from parts (a) and (b) irrespective of working seen, <strong>but only </strong>if both values are positive integers.</p>
<p class="p1">Award <strong><em>(M1)(A0) </em></strong>for a reasonable attempt to solve simultaneous equations algebraically, leading to at least one incorrect or missing value.</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(\left| {\frac{{14270 - 14970}}{{14970}}} \right| \times {\text{ }}100\) </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 percentage error formula.</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\( = 4.68(\% ){\text{ }}(4.67601 \ldots ){\text{ }}\) </span><strong><em>(A1) (C2)</em></strong></p>
<p class="p1"><strong><em>[2 marks]</em></strong></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;">The graph of <em>y </em>= 2<em>x</em><sup>2</sup> \( - \) <em>rx </em>+ <em>q</em> is shown for \( - 5 \leqslant x \leqslant 7\).</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The graph cuts the <em>y</em> axis at (0, 4).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of <em>q</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 axis of symmetry is <em>x</em> = 2.5.</span></p>
<p><span>Find the value of <em>r</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>The axis of symmetry is <em>x</em> = 2.5.</p>
<p><span>Write down the minimum value of <em>y</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><span><span>The axis of symmetry is <em>x</em> = 2.5.</span>x</span></span></p>
<p><span><span>Write down the range of</span> <span><em>y</em>.</span></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><em>q</em> = 4 <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>\(2.5 = \frac{r}{4}\) <em><strong> (M1)</strong></em></span></p>
<p><span><em>r</em> = 10 <em><strong> (A1) (C2)</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>–8.5 <em><strong>(A1)</strong></em><strong>(ft)</strong><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>\(-8.5 \leqslant y \leqslant 104\) <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> </span></p>
<p><span><strong>Notes:</strong> Award <strong><em>(A1)</em>(ft)</strong> for their answer to part (c) with correct inequality signs,</span> <span><strong><em>(A1)</em>(ft)</strong> for 104. Follow through from their values of <em>q</em> and <em>r</em>.</span></p>
<p><span>Accept 104 ±2 if read from graph.</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-size: medium; font-family: times new roman,times;">This question was not well answered with few candidates gaining full marks. Many candidates could find the value of <em>q</em> but not<em> r</em>. Although many found the minimum value of <em>y</em>, they could not find the maximum value of the function or express the range correctly.</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 not well answered with few candidates gaining full marks. Many candidates could find the value of <em>q</em> but not<em> r</em>. Although many found the minimum value of <em>y</em>, they could not find the maximum value of the function or express the range correctly.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was not well answered with few candidates gaining full marks. Many candidates could find the value of <em>q</em> but not<em> r</em>. Although many found the minimum value of <em>y</em>, they could not find the maximum value of the function or express the range correctly.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was not well answered with few candidates gaining full marks. Many candidates could find the value of <em>q</em> but not<em> r</em>. Although many found the minimum value of <em>y</em>, they could not find the maximum value of the function or express the range correctly.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A function \(f\) is given by \(f(x) = 4{x^3} + \frac{3}{{{x^2}}} - 3,{\text{ }}x \ne 0\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the derivative of \(f\).</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 point on the graph of \(f\) at which the gradient of the tangent is equal to 6.</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>\(12{x^2} - \frac{6}{{{x^3}}}\) or equivalent <strong><em>(A1)(A1)(A1) (C3)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for \(12{x^2}\), <strong><em>(A1) </em></strong>for \( - 6\) and <strong><em>(A1) </em></strong>for \(\frac{1}{{{x^3}}}\) or \({x^{ - 3}}\). Award at most <strong><em>(A1)(A1)(A0) </em></strong>if additional terms seen.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(12{x^2} - \frac{6}{{{x^3}}} = 6\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for equating their derivative to 6.</p>
<p> </p>
<p>\((1,{\text{ }}4)\)\(\,\,\,\)<strong>OR</strong>\(\,\,\,\)\(x = 1,{\text{ }}y = 4\) <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft) <em>(C3)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>A frequent wrong answer seen in scripts is \((1,{\text{ }}6)\) for this answer with correct working award <strong><em>(M1)(A0)(A1) </em></strong>and if there is no working award <strong><em>(C1)</em></strong>.</p>
<p> </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><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,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" 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 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;">Part of the graph of the quadratic function <em>f</em> is given in the diagram below.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">On this graph one of the <em>x</em>-intercepts is the point (5, 0). The <em>x</em>-coordinate of the maximum point is 3.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The function <em>f</em> is given by \( f (x) = -x^2 + bx + c \), where \(b,c \in \mathbb{Z}\)</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>b</em> ;</span></p>
<p><span>(ii) <em>c</em> .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The domain of <em>f</em> is 0 </span><span><span><span>≤</span></span> </span><em><span> x </span></em><span><span>≤</span></span><span> 6.</span></p>
<p><span>Find the range of <em>f</em> .</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>(i) \(3 = \frac{{-b}}{{-2}}\) </span><em><strong><span>(M1)</span></strong></em></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in formula.</span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span>\(-1 + b + c = 0\)</span></p>
<p><span>\(-25+5b + c = 0\)</span></p>
<p><span>\(-24 + 4b = 0\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for setting up 2 correct simultaneous equations.</span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span>\(-2x + b = 0\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct derivative of \(f (x)\) equated to zero.</span></p>
<p><br><span>\(b = 6\) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span>(ii) \(0 = -(5)^2 + 6 \times 5 + c\)</span></p>
<p><span>\(c =-5\) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C1)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their value for <em>b</em>.</span></p>
<p><span> </span></p>
<p><span><strong>Note:</strong> Alternatively candidates may answer part (a) using the method below,</span> <span>and not as two separate parts.</span></p>
<p><span><br>\( (x - 5)(-x +1)\) <em><strong>(M1)</strong></em><br></span></p>
<p><span>\(-x^2 +6x - 5\) <em><strong>(A1)</strong></em><br></span></p>
<p><span>\(b = 6{\text{ }} c = -5\) <em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em><br></span></p>
<p><br><span><em><strong>[3 marks]</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>–5 ≤ <em>y</em> ≤ 4 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><span><strong>Notes:</strong> Accept [</span><span>–5, 4]. </span><span>Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for –5, <em><strong>(A1)</strong></em><strong>(ft)</strong> for 4. <em><strong>(A1)</strong></em> for inequalities in the</span> <span>correct direction or brackets with values in the correct order or a </span><span>clear word statement of the range.</span> <span>Follow through from their part (a).</span></p>
<p><span><em><strong>[3 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;">Question 11 proved to be the most problematic of the whole paper. Many candidates attempted this question but were not able to set up a system of equations to find the value of <em>b</em> or use the formula \(x = \frac{-b}{2a}\). From the working seen, many candidates did not understand the non-standard notation for the domain, with a number believing it to be a coordinate pair. This was taken into careful consideration by the senior examiners when setting the grade boundaries for this paper.</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 11 proved to be the most problematic of the whole paper. Many candidates attempted this question but were not able to set up a system of equations to find the value of <em>b</em> or use the formula \(x = \frac{-b}{2a}\). From the working seen, many candidates did not understand the non-standard notation for the domain, with a number believing it to be a coordinate pair. This was taken into careful consideration by the senior examiners when setting the grade boundaries for this paper.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>In an experiment, a number of fruit flies are placed in a container. The population of fruit flies, <em>P</em> , increases and can be modelled by the function</p>
<p>\[P\left( t \right) = 12 \times {3^{0.498t}},\,\,t \geqslant 0,\]</p>
<p>where <em>t</em> is the number of days since the fruit flies were placed in the container.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of fruit flies which were placed in the container.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of fruit flies that are in the container after 6 days.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The maximum capacity of the container is 8000 fruit flies.</p>
<p>Find the number of days until the container reaches its maximum capacity.</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>\(12 \times {3^{0.498 \times 0}}\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting zero into the equation.</p>
<p>= 12 <em><strong>(A1) (C2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(12 \times {3^{0.498 \times 6}}\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting 6 into the equation.</p>
<p>320 <em><strong>(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> Accept an answer of 319.756… or 319.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(8000 = 12 \times {3^{0.498 \times t}}\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for equating equation to 8000.<br>Award <em><strong>(M1)</strong></em> for a sketch of P(<em>t</em>) intersecting with the straight line <em>y</em> = 8000.</p>
<p>= 11.9 (11.8848…) <em><strong>(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> Accept an answer of 11 or 12.</p>
<p><em><strong>[2 marks]</strong></em></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;">
[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="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>On the grid below sketch the graph of the function \(f(x) = 2{(1.6)^x}\) for the domain \(0 \leqslant x \leqslant 3\) .</span></p>
<p><span><img src="data:image/png;base64,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" alt></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 coordinates of the \(y\)-intercept of the graph of \(y = f(x)\) .</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>On the grid draw the graph of the function \(g(x) = 5 - 2x\) for the domain \(0 \leqslant x \leqslant 3\).</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>Use your graphic display calculator to solve \(f(x) = g(x)\) .</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><img 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" alt></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> correct endpoints, <em><strong>(A1)</strong></em> for smooth curve. <em><strong>(A1)(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>\((0{\text{, }}2)\) <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Accept \(x = 0\), \(y = 2\)</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Straight line in the given domain <em><strong>(A1)</strong></em></span><br><span>Axes intercepts in the correct positions <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(x = 0.943\) (\(0.94259 \ldots \)) <em><strong>(A1) (C1)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(A0)</strong></em> if \(y\)-coordinate given.</span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The graph of the quadratic function \(f(x) = c + bx - {x^2}\) intersects the \(x\)-axis at the point \({\text{A}}( - 1,{\text{ }}0)\) and has its vertex at the point \({\text{B}}(3,{\text{ }}16)\).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2017-03-06_om_09.57.03.png" alt="N16/5/MATSD/SP1/ENG/TZ0/09"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down the equation of the axis of symmetry for this graph.</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 value of \(b\).</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">Write down the range of \(f(x)\).</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="Apple-converted-space">\(x = 3\) </span><strong><em>(A1)(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>Award <strong><em>(A1) </em></strong>for \(x = \) constant, <strong><em>(A1) </em></strong>for the constant being <span class="s1">3</span>.</p>
<p class="p1">The answer must be an equation.</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(\frac{{ - b}}{{2( - 1)}} = 3\) </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 axis of symmetry formula.</p>
<p class="p1"> </p>
<p class="p1"><strong>OR</strong></p>
<p class="p1"><span class="Apple-converted-space">\(b - 2x = 0\) </span><strong><em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for correctly differentiating and equating to zero.</p>
<p class="p2"> </p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">\(c + b( - 1) - {( - 1)^2} = 0\) (or equivalent)</p>
<p class="p1">\(c + b(3) - {(3)^2} = 16\) (or equivalent) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for correct substitution of \(( - 1,{\text{ }}0)\) and \((3,{\text{ }}16)\) in the original quadratic function.</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\((b = ){\text{ }}6\) </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>Note: <span class="Apple-converted-space"> </span></strong>Follow through from part (a).</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="s1">\(( - \infty ,{\text{ 16]}}\)<strong> OR</strong></span> \(] - \infty ,{\text{ }}16]\) <span class="Apple-converted-space"> </span><span class="s2"><strong><em>(A1)(A1)</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1) </em></strong>for two correct interval endpoints, <strong><em>(A1) </em></strong>for left endpoint excluded <strong>and </strong>right endpoint included.</p>
<p class="p4"> </p>
<p class="p3"><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 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 graph of the quadratic function \(f(x) = a{x^2} + bx + c\) intersects the <em>y</em>-axis at point A (0, 5) and has its vertex at point B (4, 13).</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_14.11.23.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of \(c\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>By using the coordinates of the vertex, B, or otherwise, write down <strong>two </strong>equations in \(a\) and \(b\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of \(a\) and of \(b\).</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>5 <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><em>at least one of the following equations required</em></span></p>
<p><span>\(a{(4)^2} + 4b + 5 = 13\)</span></p>
<p><span>\(4 = - \frac{b}{{2a}}\)</span></p>
<p><span>\(a{(8)^2} + 8b + 5 = 5\) <strong><em>(A2)(A1) (C3)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A2)(A0) </em></strong>for one correct equation, or its equivalent, and <strong><em>(C3) </em></strong>for any two correct equations.</span></p>
<p><span> Follow through from part (a).</span></p>
<p><span> The equation \(a{(0)^2} + b(0) = 5\) earns no marks.</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>\(a = - \frac{1}{2},{\text{ }}b = 4\) <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft) <em>(C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Follow through from their equations in part (b), but only if their equations lead to unique solutions for \(a\) and \(b\).</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="specification">
<p class="p1">Consider the functions \(f(x) = x + 1\) and \(g(x) = {3^x} - 2\).</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 \(x\)-intercept of the graph of \(y = {\text{ }}f(x)\);</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>the \(y\)-intercept of the graph of \(y = {\text{ }}g(x)\).</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">Solve \(f(x) = g(x)\).</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">Write down the interval for the values of \(x\) for which \(f(x) > g(x)\).</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>\(( - 1,{\text{ }}0)\) <strong><em>(A1)</em></strong></p>
<p class="p1"><strong>Note:<span class="Apple-converted-space"> </span></strong>Accept \( - 1\).</p>
<p class="p2"> </p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\((0,{\text{ }} - 1)\) <span class="Apple-converted-space"> </span><strong><em>(A1) (C2)</em></strong></p>
<p class="p1"><strong>Note: </strong>Accept \( - 1\).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\((x = ){\text{ }} - 2.96{\text{ }}( - 2.96135 \ldots )\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1">\((x = ){\text{ }}1.34{\text{ }}(1.33508 \ldots )\) <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 class="p1">\( - 2.96 < x < 1.34\;\;\;{\mathbf{OR}}\;\;\;\left] { - 2.96,{\text{ }}1.34} \right[\;\;\;{\mathbf{OR}}\;\;\;( - 2.96,{\text{ }}1.34)\) <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 both correct endpoints of the interval, <strong><em>(A1) </em></strong>for correct strict inequalities (or correct open interval notation).</p>
<p class="p1">Follow through from part (b).</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 quadratic function \(f:x \mapsto a{x^2} + b\), where \(a\) and \(b \in \mathbb{R}\) and \(x \geqslant 0\), is represented by the mapping diagram.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><br><span style="font-family: 'times new roman', times; font-size: medium;"><img src="images/Schermafbeelding_2014-09-03_om_08.19.32.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using the mapping diagram, write down two equations in terms of \(a\) and \(b\).</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>Solve the equations to find the value of</span></p>
<p><span>(i) \(a\);</span></p>
<p><span>(ii) \(b\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of \(c\).</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>\(a{(1)^2} + b = - 9\) <strong><em>(A1)</em></strong></span></p>
<p><span>\(a{(3)^2} + b = 119\) <strong><em>(A1) (C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Accept equivalent forms of the equations.</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>(i) \(a = 16\) <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span>(ii) \(b = - 25\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Follow through from part (a) irrespective of whether working is seen.</span></p>
<p><span> If working is seen follow through from part (i) to part (ii).</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>\(16{c^2} - 25 = 171\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct quadratic with their \(a\) and \(b\) substituted.</span></p>
<p> </p>
<p><span>\(c = 3.5\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Accept \(x\) instead of \(c\).</span></p>
<p><span> Follow through from part (b).</span></p>
<p><span> Award <strong><em>(A1) </em></strong>only, for an answer of \( \pm 3.5\) with or without working.</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 answered reasonably well with many candidates able to write down the two equations and solve them for a and b. Errors such as mistaking the equation given for \(3{a^2} + b = 119\) meant that marks were lost even though the candidates appeared to know what they needed to do. Most candidates who were able to set up the equation in part (c) solved it correctly. Follow through marks were awarded to many candidates for correct working with their substituted values from part (b).</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 answered reasonably well with many candidates able to write down the two equations and solve them for a and b. Errors such as mistaking the equation given for \(3{a^2} + b = 119\) meant that marks were lost even though the candidates appeared to know what they needed to do. Most candidates who were able to set up the equation in part (c) solved it correctly. Follow through marks were awarded to many candidates for correct working with their substituted values from part (b).</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 answered reasonably well with many candidates able to write down the two equations and solve them for a and b. Errors such as mistaking the equation given for \(3{a^2} + b = 119\) meant that marks were lost even though the candidates appeared to know what they needed to do. Most candidates who were able to set up the equation in part (c) solved it correctly. Follow through marks were awarded to many candidates for correct working with their substituted values from part (b).</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the straight lines <em>L</em><sub>1</sub> and <em>L</em><sub>2 </sub>. <em>R</em> is the point of intersection of these lines.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">The equation of line <em>L</em><sub>1</sub> is <em>y</em> = <em>ax</em> + 5.</p>
</div>
<div class="specification">
<p>The equation of line <em>L</em><sub>2</sub> is <em>y</em> = −2<em>x</em> + 3.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>a</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>Find the coordinates of <em>R</em>.</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>Line <em>L</em><sub>3</sub> is parallel to line <em>L</em><sub>2</sub> and passes through the point (2, 3).</p>
<p>Find the equation of line <em>L</em><sub>3</sub>. Give your answer in the form <em>y</em> = <em>mx</em> + <em>c</em>.</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>0 = 10<em>a</em> + 5 <em><strong>(M1)</strong></em></p>
<p>Note: Award <em><strong>(M1)</strong></em> for correctly substituting any point from <em>L</em><sub>1</sub> into the equation.</p>
<p><strong>OR</strong></p>
<p>\(\frac{{0 - 5}}{{10 - 0}}\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituting any two points on <em>L</em><sub>1</sub> into the gradient formula.</p>
<p>\( - \frac{5}{{10}}\left( { - \frac{1}{2},\,\, - 0.5} \right)\) <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>\(\left( { - 1.33,\,\,5.67} \right)\,\,\left( {\left( { - \frac{4}{3},\,\,\frac{{17}}{{13}}} \right),\,\,\left( { - 1\frac{1}{3},\,\,5\frac{2}{3}} \right),\,\,\left( { - 1.33333 \ldots ,\,\,5.66666 \ldots } \right)} \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note: </strong>Award <em><strong>(A1)</strong></em> for <em>x</em>-coordinate and <em><strong>(A1)</strong></em> for <em>y</em>-coordinate. Follow through from their part (a). Award <em><strong>(A1)</strong></em><em><strong>(A0)</strong></em> if brackets are missing. Accept <em>x</em> = −1.33, <em>y</em> = 5.67.</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>3 = −2(2) + <em>c</em> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituting –2 and the given point into the equation of a line.</p>
<p><em>y</em> = −2<em>x</em> + 7 <em><strong>(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A0)</strong></em> if the equation is not written in the form <em>y</em> = <em>mx</em> + <em>c</em>.</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-size: medium; font-family: times new roman,times;">The graph of a quadratic function \(y = f (x)\) is given 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 equation of the axis of symmetry.</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 coordinates of the minimum point.</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 range of \(f (x)\).</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> = 3 <em><strong>(A1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for “ <em>x</em> = ” <em><strong>(A1)</strong></em> for 3.</span></p>
<p><span>The mark for <em>x</em> = is not awarded unless a constant is seen on the other side </span><span>of the equation.</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>(3, −14) (Accept <em>x</em> = 3, <em>y</em> = −14) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)(A0)</strong></em> for missing coordinate brackets.</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><em>y</em> ≥ −14 <em><strong>(A1)(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> for y </span><span><span>≥</span> , <em><strong>(A1)</strong></em><strong>(ft)</strong> for –14.</span></p>
<p><span> Accept alternative notation for intervals.</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;">The lack of the answer, “<em> x</em> = 3 ”, expressed as an equation 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-size: medium; font-family: times new roman,times;"><span style="font-size: medium; font-family: times new roman,times;">Misreading the <em>y</em> coordinate was the common error.</span></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;"><span style="font-size: medium; font-family: times new roman,times;"><span style="font-size: medium; font-family: times new roman,times;">This part proved challenging for many; there was confusion between domain and range</span> <span style="font-size: medium; font-family: times new roman,times;">for many, the incorrect inequality also was a common error. It is the accepted practice in </span><span style="font-size: medium; font-family: times new roman,times;">examinations that if a domain is not specified, then it is taken as the real numbers.</span></span></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 small manufacturing company makes and sells \(x\) machines each month. The monthly cost \(C\) , in dollars, of making \(x\) machines is given by</span><br><span style="font-family: times new roman,times; font-size: medium;">\[C(x) = 2600 + 0.4{x^2}{\text{.}}\]</span><span style="font-family: times new roman,times; font-size: medium;">The monthly income \(I\) , in dollars, obtained by selling \(x\) machines is given by</span><br><span style="font-family: times new roman,times; font-size: medium;">\[I(x) = 150x - 0.6{x^2}{\text{.}}\]</span><span style="font-family: times new roman,times; font-size: medium;">\(P(x)\) is the monthly profit obtained by selling \(x\) machines.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \(P(x)\) .</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 number of machines that should be made and sold each month to maximize \(P(x)\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>Use your answer to part (b) to find the selling price of</span> <span><strong>each machine</strong> in order to maximize \(P(x)\) .</span></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>\(P(x) = I(x) - C(x)\) <em><strong>(M1)</strong></em></span><br><span>\( = - {x^2} + 150x - 2600\) <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>\( - 2x + 150 = 0\) <em><strong>(M1)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for setting \(P'(x) = 0\) .</span></p>
<p> </p>
<p><span><strong>OR</strong></span></p>
<p> </p>
<p><span>Award <em><strong>(M1)</strong></em> for sketch of \(P(x)\) and maximum point identified. <em><strong>(M1)</strong></em></span><br><span>\(x = 75\) <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>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{7875}}{{75}}\) <em><strong>(M1)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for \(7875\) seen.</span></p>
<p> </p>
<p><span>\( = 105\) <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 (b).</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>Consider the function \(f(x) = {x^3} - 3{x^2} + 2x + 2\) . Part of the graph of \(f\) is shown below.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAcMAAAGCCAYAAACcgqgXAAAgAElEQVR4Ae3dC1xUdd4/8E+zbau+WB/FXhtKj4Iw+uQFlDSXSwaJlre8VGpZK5ZkWeslK9rU1MzHlLz2V+sRDdO8ZYDhPQzWVCptBLVaHRB0w2hfRS5Laj77DP/X79ggwgBnZs6ZOZcPr5cFZ37nd3l/D/Pl/Oac37mpurq6GvyiAAUoQAEKmFjAYuKxc+gUoAAFKEABSYDJkAcCBShAAQqYXoDJ0PSHAAEoQAEKUIDJkMcABShAAQqYXoDJ0PSHQFMA/0Z51mSEh4QiPKQrBi89iippFwcq82Yjoss07LhwtalK+DoFKEABTQswGWo6PFro3M0IGr4CRWf3YlYkcDrvK3znEP2yIOC/+mJkh4u4+LO0QQudZR8oQAEKeCTAZOgRmwl3sgSje3wH4PxP+Nevuc/yh9sRGtIL3dveYkIQDpkCFDCSAJOhkaKp6lhuxu9bBwI/leDvP/wbwFVc+GgDbPcNRY8AHkaq0rNyClBAdQG+i6lObJQGbsbvWwVeH0xVIT483gcpD7SHq4MoPz//ell+RwEKUEDjAq7exzTeZXbPPwIWtGjVGi1QhJK/FyNvySdoP/E+tHNxBFVUVODxRx6F3W73T1fZKgUoQAE3BVy8lblZA4ubRMCCFi1b4Rb8hBPvpOHTvo9jaDvXnxVu27pNMlmfnm4SGw6TAhTQuwCTod4j6MP+W37fGv8J4Oa4JEyLb+dyelScFb65cKHUqy3vb+LZoQ/jw6YoQAHPBZgMPbcz4Z43o+241/Han7oioIHRi7PC3n3ukl59ISUFPDtsAIqbKUABTQkwGWoqHBruTNVRrFxvwZQXExDUwFHjPCucPHWqNJBRo0dBnB0WFhZqeGDsGgUoQAHgZiJQoEGBqqNY9vAr+H70M2hX9CNiX34SnRu5jcJ5VhgdHS1VGRgYCHF2+MG2bYiMjGywGb5AAQpQwN8CTIb+joCW23f8jB/PXcCJoit4+LlxiGokEYph9Evsh6EPDL1hROOSxqGgoOCGbfyBAhSggNYEbuLDfbUWEmP0R6xlWlRaYozBcBQUoIDhBRr49Mfw4+YAKUABClCAAjUCTIY1FPyGAhSgAAXMKsBkaNbIc9wUoAAFKFAjwGRYQ8FvKEABClDArAJMhmaNPMdNAQpQgAI1AkyGNRT8hgIUoAAFzCrAZGjWyHPcFKAABShQI8BkWEPBbyhAAQpQwKwCTIamiXwl7AfewlNdQiFuiA8fOBMbbeVw1Bu/A5V5sxEhyjj/DUuHvX7BentyAwUoQAG9CjAZ6jVybvX7Ki5kb8Je3I8lX5eg6Gw+tgz8HotGPosVtos31uT4Frlb9+NSzdYW6D4iGmE8UmpE+A0FKGA8Aa5NaryY1h+RowxF/zEEz/a9/dozCC1B6PXcC5h+YCQWZxTgiah4tJT2cqCqYAfS2yyArdS5rX513EIBClDAaAJMhkaLqKvxWELRt2+dFyxt0KH7rXU2VuBYxnac3JiD1PCL6Bd7L+Kt19JknYL8kQIUoIChBDj5ZahwujuYVojr1bHmQb0O+04s33gewAlsnjMNE/o/jllZp1HlbrUsTwEKUEBnAkyGOguYYt2tPIUDJxMxIfHXqVMAFmsSMktLcOazD7Fszlh0Fklx6itIq/u5omKdYEUUoAAFtCHARzhpIw4+7sVF2JbOx8F7ZmBqVKsG23aUH8Br4ycj486VOPT69c8QxVWmcr74CCc5SixDAQpoQYDJUAtR8GkfHKiyrcXCEzFISepaM0XqugviNou5iJsErPhsNuJbyp9I4PMMXYtyKwUooE0BXkCjzbio1ivHhf149ys5iVB0wYKA4FCEWYHgJp5yr1qHWTEFKEABHwjI/1PfB51hE+oKOMrzsHJ7Mzw81nlG6EDV6QysP/hDAw07UFX2AyKnDYGVR0oDRtxMAQoYQYBnhkaIYpNjcKDK/hEWTp6Bzd9cwvIltXeIxayPBwG4inLbJziGHhgUFQSL+Pnoeqw82BPPzqx7C0bt/fk9BShAAf0L8O99/cewyRE4LnyEl4ZNkxJhvcKRiYgJa3Ztc+WXWD0yGp1CQhExYSXyf45Hyqv9EMSjpB4bN1CAAsYS4AU0xoqnZkbDC2g0Ewp2hAIUkCHAv/llILEIBShAAQoYW4DJ0Njx5egoQAEKUECGAJOhDCQWoQAFKEABYwswGRo7vhwdBShAAQrIEGAylIHEIhSgAAUoYGwBJkNjx5ejowAFKEABGQJMhjKQWIQCFKAABYwtwGRo7PhydBSgAAUoIEOAyVAGEotQgAIUoICxBZgMjR1fjo4CFKAABWQIMBnKQGIRClCAAhQwtgCTobHjy9FRgAIUoIAMASZDGUgsQgEKUIACxhZgMjR2fDk6ClCAAhSQIcBkKAOJRShAAQpQwNgCTIbGji9HRwEKUIACMgSYDGUgsQgFKEABChhbgMnQ2PHl6ChAAQpQQIYAk6EMJBahAAUoQAFjCzAZGju+HB0FKEABCsgQYDKUgcQiFKAABShgbAEmQ2PHl6OjAAUoQAEZAkyGMpBYhAIUoAAFjC3AZGjs+HJ0FKAABSggQ4DJUAYSi1CAAhSggLEFmAyNHV+OjgIUoAAFZAgwGcpAYhEKUIACFDC2AJOhsePL0VGAAhSggAwBJkMZSCxCAQpQgALGFmAyNHZ8OToKUIACFJAhwGQoA8kYRSphP/AWnuoSivCQUIQPnImNtnI46g7OUQ7bhpkYLMp0ScZbR12UqbsPf6YABSigcwEmQ50HUF73r+JC9ibsxf1Y8nUJis7mY8vA77Fo5LNYYbtYq4qLsC2fhllFCVh7tgRnPhmDH1+dVqdMreL8lgIUoIBBBJgMDRLIRofhKEPRfwzBs/2sCBAFLUHo9dwLmB75N6zLKEDlrzs77FmYt6YTXpyegCCLKJaA51M6Yd3cLNjrnUI22iJfpAAFKKArASZDXYXLw85aQtG37+24IdiWNujQ/dZaFV5B8eEcnLSGIjjAWdKCllEJGGbPwZHiK7XK8lsKUIACxhJwvusZa1QcjUyBVojr1fHa2aLjHI5kHkeL7iG4rd5RcRxZh8/V/3xRZissRgEKUEDrAvXe9rTeYfZPIYHKUzhwMhETEn89Y6z6DkV2ICy87bXkqFAzrIYCFNCOQFlZGS5fvqydDmmoJzdrqC/sis8ELsK2dhfazJ6BqJopUfmNi6tR+UUBCuhP4IXnn8eTyclITEzUX+dV7jGTocrA2qvegSrbB8hsnYSUqFbXuxfQFuFWYEfRd6hCZ7S8/kq974pKS+ptq7uBCbOuCH+mgH8FxFnh0c+/wJtLlvi3IxptndOkGg2MWt1yXNiPd7+KQUpS1xunQy0dEDOiZ71mHd+X4tSlnhge2+HGC3DqleQGClBAywLffPMNeve5C8HBwVrupt/6xmToN3rfN+woz8PK7c3w8FhnInSg6nQG1h/8AUAzhMUmIiwjF7ZK530UDlSVlaA4MhExYc1832G2SAEKKCaQmZGBe+ITFKvPaBUxGRotoi7H40CVPQuzxz+L5UvGI67jr6vQhIShx30ZQFvp7kNYrMMxK/kMUhfnotwBOMpzsWThGTwxezisPFJcynIjBfQgIC6a2bd7D6JjovXQXb/0kW9xfmH3baOOCx/hpWHTsPmbS/UbvuGsrxWipizF3DZbMKBjKDqNz0X4/KWYXPuzxfo1cAsFKKBxgYKCAqmHkZGRGu+p/7p3U3V1dbX/mmfLRhUQF9DIudDGqOPnuCigJYHURYuk7rz40kta6pam+sIzQ02Fg52hAAUooLzAO6tWI+7uu5Wv2EA1MhkaKJgcCgUoQIG6AoWFhdKmHj161H2JP9cSYDKshcFvKUABChhNIP9IPu4bNBDNmzc32tAUHQ+ToaKcrIwCFKCAtgS2bd2CESNHaqtTGuwNk6EGg8IuUYACFFBCQKw6c770HKKiopSoztB1MBkaOrwcHAUoYGaBvNxcaYo0MDDQzAyyxs5kKIuJhShAAQroT2BndjZiYmL013E/9JjJ0A/obJICFKCA2gIVFRXSwtzxCVyCTY41k6EcJZahAAUooDMBm82G9iEduDC3zLgxGcqEYjEKUIACehIQC3OPGj1GT132a1+ZDP3Kz8YpQAEKKC8gpki5MLd7rkyG7nmxNAUoQAHNCzinSLkwt/xQMRnKt2JJClCAAroQOG6zcYrUzUgxGboJxuIUoAAFtCwgnl0oFubmswvdixKToXteLE0BClBA0wJ8dqFn4WEy9MyNe1GAAhTQpMChTz/FxEnPaLJvWu4Uk6GWo8O+UYACFHBDwDlFymcXuoH2a1EmQ/fNuAcFKEABTQo4p0j57EL3w8Nk6L4Z96AABSigSQHnFCmfXeh+eJgM3TfjHhSgAAU0J8ApUu9CwmTonR/3pgAFKKAJAU6RehcGJkPv/Lg3BShAAU0IFBYUSleRcorUs3AwGXrmxr0oQAEKaEpg29Yt4FWknoeEydBzO+5JAQpQQBMChYWFOF96DryK1PNwMBl6bsc9KUABCmhCIP9IPqdIvYwEk6GXgNydAhSggD8FxFWknCL1PgJMht4bsgYKUIACfhMQV5FyitR7fiZD7w1ZAwUoQAG/CfBGe2XomQyVcWQtFKAABXwuwBvtlSNnMlTOkjVRgAIU8KmAmCJtH9KBV5EqoM5kqACifqqohD0vG5lLk9FrZh4qXXbcgcq82YgICUW489+wdNgdLgtzIwUo4EeBXTt3Sk+054323geBydB7Q53UcAX29BQs2LgJs5fn4GpDvXZ8i9yt+3Gp5vUW6D4iGmE8UmpE+A0FtCBQUVGBLe9v4hPtFQrGzQrVw2o0L9AM1qTVWPen01g/YiQWu+yvA1UFO5DeZgFspfFo6bIMN1KAAloQsNls0hRpZGSkFrqj+z7w733dh1DJAVTgWMZ2nNy4FKnpWcizu55IVbJF1kUBCngmkJmRIU2RerY396orwGRYV8TEPzvsO7F843kAJ7B5zjRM6P84ZmWdRpWJTTh0CmhRoKysDPt278HQB4ZqsXu67BOToS7Dpk6nLdYkZJaW4MxnH2LZnLHoLJLi1FeQZruoToOslQIU8EggLzcXvfvcheDgYI/25071BfiZYX0T02+xBEVhSFIUBt2fgNfGT8a6jAI8EXX9M0RxlSm/KEAB/wnszM7GkKE8K1QyAkyGSmoarC5LUAKeT3kIGZNyYXupL+JbXptIKCotaXKkTJhNErEABTwSEFOkRz//AitXr/Zof+7kWoDJ0LULt0oCFgQEhyLMCgQHcEadBwUFtCCQ/VE27hs0EIGBgVrojmH6wHc4w4RSjYE4UFX2AyKnDYGVR4oawKyTAm4LiCdUjBg50u39uEPjAnyLa9zHRK9eRbltL3baynFtsZmrKD+6FqkHe+LpvreayIFDpYB2BfLz86UnVMTGxmq3kzrtGZOhTgPnfrd/XWat4/2YV3gJlzaOR1TIY1hvv3K9qsovsXpkNDqFhCJiwkrk/xyPlFf7IYhHyXUjfkcBPwrwCRXq4d9UXV1drV71rNmsAuICGjkX2pjVh+OmgLsC4gkV3e/ogg2bNyE6Otrd3Vm+CQH+zd8EEF+mAAUooAWBw4cPS8uvMRGqEw0mQ3VcWSsFKEABRQW4/JqinPUqYzKsR8INFKAABbQl4Fx+rV9iP211zEC9YTI0UDA5FApQwJgCzuXXrFarMQeogVExGWogCOwCBShAgcYE1qal4cnk5MaK8DUvBZgMvQTk7hSgAAXUFCgsLJTuLYyKilKzGdPXzWRo+kOAABSggJYF9u/bh4mTnuHyayoHiclQZWBWTwEKUMBTgYqKCryzajXi7r7b0yq4n0wBJkOZUCxGAQpQwNcCnx48yHsLfYTOZOgjaDZDAQpQwF2BLZs348kJE9zdjeU9EGAy9ACNu1CAAhRQW0BcOCOeWzhw0CC1m2L9AJgMeRhQgAIU0KCAuHBmzNhHeeGMj2LDZOgjaDZDAQpQQK6AWJRbXDgzeMgQubuwnJcCTIZeAnJ3ClCAAkoLcFFupUWbro/JsGkjlqAABSjgU4G1a9bwwhmfivMzQx9zszkKUIACjQvwwpnGfdR6lWeGasmyXgpQgAIeCPDCGQ/QFNjlZgXqYBUUoAAFKKCAgHPFmQ93ZClQG6twR4Bnhu5osSwFKEABFQX27N6N3n3uQmRkpIqtsGpXAkyGrlS4jQIUoICPBcTtFOJRTWMeecTHLbM5IcBkyOOAAhSggAYECgoKpEc1DbjvPg30xnxdYDI0X8w5YgpQQIMCK5YtwwspKWjevLkGe2f8LjEZGj/GHCEFKKBxAbvdLq1DOmr0KI331LjdYzI0bmw5MgpQQCcCWZmZXIfUz7HirRV+DgCbpwAFzC3A2ym0EX+eGWojDuwFBShgUgHeTqGNwDMZaiMO7AUFKGBCAd5OoZ2gMxlqJxbsCQUoYDIB8XQK8cXbKfwfeCZD/8eAPaAABUwqIJ5OMWr0GN5OoYH4MxlqIAjsAgUoYD6B/Px83k6hobAzGWooGOp3pRL2vGxkLk1Gr5l5qHTVoKMctg0zMTgkFOFdkvHW0XI4XJXjNgpQwCuBXTt3SjfZBwYGelUPd1ZGgMlQGUcd1HIF9vQULNi4CbOX5+Cqyx5fhG35NMwqSsDasyU488kY/PjqNKywXXRZmhspQAHPBMRN9lve34R+if08q4B7KS7AZKg4qVYrbAZr0mqs+585mB7ZwmUnHfYszFvTCS9OT0CQBbAEJeD5lE5YNzcLdp4eujTjRgp4IrA+PV26yd5qtXqyO/dRQYDJUAVUfVZ5BcWHc3DSGorgAOdhYUHLqAQMs+fgSPEVfQ6LvaaAxgTETfbirHBcUpLGembu7jjf9cytwNEDjnM4knkcLbqH4LZ6R8VxZB0+x88OeZxQQAGBbVu3Sc8s5FmhApgKVsHl2BTE1HVVVd+hyA6EjWiLAF0PhJ2ngHYFxFnhmwsXYsPmTdrtpEl7xmRo0sB7M+zwkFBvdue+FDCtgHPptejoaNMaaHXgTIZajYyv+xXQFuFWYEfRd6hCZ7RspP2i0pJGXr32EhNmk0QsYDIB59Jr8xcsMNnI9THcep8O6aPb7KXiApYOiBnRs161ju9LcepSTwyP7QAeLPV4uIECsgX279snle3Ro4fsfVjQdwJ8f/OdtcZbaoaw2ESEZeTCVum8j8KBqrISFEcmIiasmcb7z+5RQLsC4qxw+bJlmDJ1Kpde02iYmAw1Ghh/dMtiHY5ZyWeQujgX5Q7AUZ6LJQvP4InZw2HlkeKPkLBNgwg4zwq5ILd2A8q3OO3GRuGeOVCZNxsRHe/HvMJLuLRxPKJCHsN6e+37B1shaspSzG2zBQM6hqLT+FyEz1+KyVGtFO4Lq6OAeQR4VqiPWN9UXV1drY+uspd6EhAX0Mi50EZPY2JfKeCJwI6sLGmKdNeePZwi9QTQR/vwzNBH0GyGAhQwnwDPCvUTcyZD/cSKPaUABXQmwM8K9RMwJkP9xIo9pQAFdCQgVpsRV5C+MnMmp0d1EDcmQx0EiV2kAAX0JyDWIL3tttuQmJiov86bsMdcgcaEQeeQKUABdQW4Bqm6vmrUzjNDNVRZJwUoYGoB55MpuAapfg4DnhnqJ1bsKQUooAOBsrIyPplCB3Gq20WeGdYV4c8UoAAFvBBYvWqV9BR7nhV6geiHXXlm6Ad0NkkBChhTICcnR3qKfdbObGMO0MCj4pmhgYPLoVGAAr4VePH56egQGoJu3br5tmG25rUAzwy9JmQFFKAABYC0NWvwr8pKfJiZQQ4dCvDMUIdBY5cpQAFtCfz0009YvCgVCf36oWNYmLY6x97IEmAylMXEQhSgAAUaFlj85pv4P8f/YdGbqQ0X4iuaFmAy1HR42DkKUEDrAmeLi6WLZkaNGYPWrVtrvbvsXwMCfIRTAzDc7J0AH+HknR/31o/A8AeGobioCCe//ko/nWZP6wnwApp6JNxAAQpQQJ6AuJXi1IkTeDttjbwdWEqzAjwz1Gxo9N0xnhnqO37svTyBnhGRCGobhD379snbgaU0K8AzQ82Ghh2jAAW0LDBzxgzeSqHlALnZN15A4yYYi1OAAhQQF81s27JFWnaNt1IY43jgNKkx4qi5UXCaVHMhYYcUFOiXkIB/fP8PXjSjoKm/q+I0qb8jwPYpQAFdCXzwwQc4V1LKi2Z0FbWmO8tp0qaNWIICFKCAJCBWmpnx8svSSjN8gr2xDgomQ2PFk6OhAAVUFHh15iypdq40oyKyn6rmNKmf4NksBSigLwFxT+GeXbuwIHURV5rRV+hk9ZZnhrKYWIgCFDCzgJgenTZ5CrpFRODhhx82M4Vhx85kaNjQcmAUoIBSAmJ69JdfruDd9elKVcl6NCbAaVKNBYTdoQAFtCWQnZ3N6VFthUSV3vDMUBVWVkoBChhBQEyPTp86ldOjRghmE2NgMmwCiC9TgALmFRg/Lgm/sfyG06MmOAQ4TWqCIHOIFKCA+wKpqak1T6Tgcwrd99PbHjwz1FvEVO+vA5V5sxEREgqxpJr0b1g67A7VG2YDFNCMwJdffol3Vq6S1h7lzfWaCYuqHWEyVJVXh5U7vkXu1v24VNP1Fug+IhphPFJqRPiNsQXE54STJj6NoHZt8fr8+cYeLEdXI8Bp0hoKfgM4UFWwA+ltFsBWGo+WJKGACQWm/HkyfvqpAnv37zfh6M07ZP69b97Yuxh5BY5lbMfJjUuRmp6FPHulizLcRAHjCqStWYMjhw5h/htvgI9mMm6cXY2Mj3BypWLSbQ57Oh7sPxcna8YfgUeWLULK8M4IqNkm7xs+wkmeE0tpR0B8Tjj6wYcwcPBgvLXy/2mnY+yJTwSYDH3CrK9GHOU27N6bgdVz3sdpROG5jLWYGtXKrUEwGbrFxcJ+FhCfE/aNjcMfbvsDDuTm+rk3bN4fAkyG/lDXSZuO8gN4bfxkZNy5Eodev/4Zokh0cr6KSkvkFGMZCvhdQDys9+/nz+PzY8e4CLffo+GfDjAZ+sddJ62K2yzmIm4SsOKz2YhvKf8jZp4Z6iTE7Cb+9Njj+Cz/CDZv24Y777yTIiYV4NWkJg28vGFbEBAcijArEBwgPxHKq5ulKOB/AecFMy/PeIWJ0P/h8GsP+A7nV36tN+5AVdkPiJw2BFYeKVoPFvvnpoB4PuEb8/9bumBmQnKym3uzuNEE+BZntIh6PJ6rKLftxU5bOa4tNnMV5UfXIvVgTzzd91aPa+WOFNCigLhydNLEiYiJi+OVo1oMkB/6xGToB3TNNln5JVaPjEankFBETFiJ/J/jkfJqPwTxKNFsyNgx9wWKi4vxyKhRaN06EO9t3OB+BdzDkAK8gMaQYfX/oHgBjf9jwB7UFxC3UNzff4D0wt6P9/PK0fpEpt3CC2hMG3oOnALmEnAmwkuXLuHg4UNMhOYKf5OjZTJskogFKEABvQs4E6FYc1TcQsFHMuk9osr3n58GKW/KGilAAQ0J1E2EvJdQQ8HRUFeYDDUUDHaFAhRQVoCJUFlPI9fGZGjk6HJsFDCxABOhiYPvwdD5maEHaNxFOYGzxcU4W1IC8cZVWFAgVXzlyhUct9kabeSWW25B127d0KxZM6lc5//6L7Rt21b617Vr10b35YvGF3Amwsp//pPLrBk/3IqMkMlQEUZWIkdArPhx/PhxnCw8gbKyb3GupPSG3TqEhtT83DMqqibR1Wys9c3Fn36qSZi//PILtry/qdarwG9/+1u0uz0YXbp0RfuQDujZs6e03BYvnLiByZA/iBvqnfcRHvnic14sY8goKz8o3meovClrBCDuM9z64XZkZmQg/8iRmsTXvEULhIWHo1v3bojs0UM6k4uLi1PMTLwRirMCkXT/efGi1PY/vv8HLl+6JLXhTJLRMTHo88c/QrTNBKkYv98rOnToEJ4YN066oZ73Efo9HLrqAJOhrsKl/c5+8MEHyN7xkfS0cNFbkfz+GBONAffdhzujovz29PDLly/j8OHDNWemp//2N/z4ww8S6O9btkT3iAj0vacvRJLkNKv2jzNXPRSLbou1RsUSa8vfWsE/clwhcVuDAkyGDdLwBbkC4nO/pUuWIi83VzoDa3PrrVKi2X8gx2/JT07fnQlS9PvLY8dQXFQEx/85pAQupmlFcrz33ns1PQY54zRDGfEYpiOHDvEp9WYItkpjZDJUCdYM1YqzwLdXrZKmQMUZ4LARw/HEE09IyUOvy7GJadZPPvkEhz89hFMnTkhhFGOLT0hA3/h7MGTIEDRv3twM4dXFGMUfYo+MHgNxM/1LL78MPn1CF2HTZCeZDDUZFm13SkxHLV+6TDoLFBe9PD1pEh5++OEbOq3XZHjDIACIi37EmaP4V37hO+lla+dOuDcxEQ+OHMmzxrpgPvxZ/DE24+WXpc8HV73zNp9H6EN7IzbFZGjEqKo0ptpJUHwuM2funAaTgVGSYW1KcWHOzp078fG+/Tj6+ef43//9X2lKVZw1Drj/PgwdOrR2cX6vkoCIw6szZ2HPrl38fFAlYzNWy2Roxqi7OWZxdjRt8hTpTLCpJOis2ojJ0Dk25//FlKq4WlYkR3ExjuU3FojPGvsPGIAHH3qIF3A4oRT8v/NY/OWXK5j/xhv1ZiQUbIpVmUyAydBkAXdnuOLzmGcnTYL99BmIqcGVq1Y1eCZYt14zJMPaYxZWu3bvxoGPc2o+a+wWEYHYu+M4nVobysPva58Niqn5NWlpso9FD5vkbiYTYDI0WcDlDnfmjBnYtmULfve7Zli6YjkSExPl7iqVM1syrI1Tezr1s/wj0hWq4grbu/r0QdIT4/nZVm0sGd9v2LABixa8AXE2yItkZICxiEcCTIYesRl3JzH1N2ni09K035ixj+L1+fM9GqyZk2FdMDG1tyMzq+bWE3Hjf+8+fTB02AOc5quLVetn4bZg/nzpamXeO1gLht+qIoPd4B8AABsCSURBVMBkqAqrPit9/bXXkL7uXQS1a4v3NmzwahqKydD1MfDVV19h9+7d2L51W81N/2I6dcjQIRg0eDDatWvnekcTbRVTztOmTsVXJ09BTIn+ZcYMt2cmTMTFoSokwGSoEKSeqxHTeg+NHCn9Be7N2WBtAybD2hquv79w4QJ279qFndk78fVXp2qmU+++py+GjxghLRXnek9jbhWzEuKWHXHzvFgVaN781zGEV+gaM9gaHBWToQaD4ssuiamoSRMnSp8Npm94T7HPs5gM3Y/izuxs7Nu7D4c+/RT/qqy84epUI6+EI27Z2bxpk/THmPhsNXniU7x53v3Dh3t4KcBk6CWgnndPTU3FOytXQUzTvbs+XdFbAZgMvTsyxFThhxkZ0ko4zrNGcbbUq3dvaSWcfv366XpKVYyv9hJ+d/buLSVBdy/U8k6Ze1PgugCT4XUL03wnpkWn/HmyNB018dlJePHFFxUfO5OhsqTiaQy5YiWcTz6RzqBE7XpbYNy51J3z89K6S/gpK8baKOCeAJOhe166Ly0S4f39B0hrOa565x3VLkxgMlT3UBHT22KJuNqPxxI3/f9n+/bSkzfE47G6dOni1ydwiLO/w0eOSIsSiIc1i8doOdd55S0m6h4frN19ASZD9810u4f4y3zC+Cfw73//G0p+PugKhMnQlYp620RsRcL5/PPP8c3XX9esoypaFFdkBgffjvYd2kvPcBQLjcfGxiq64Lho/+zZsygsKMCpk6ekJ4A4nyEp2o+/914MGjRIsc+k1ZNkzWYVYDI0SeTFm5Xz6d++eOgpk6H/D6zaCUo8oupf//rXDUlS9FBMtQa2CZQ6e8cdXdCqdasmO37+3HmUlX0rlfv7+fPSVbDOncRtOR07hqF7ZAR69uyp2syDsz3+nwJKCTAZKiWp4Xp8nQgFBZOhdg8IMVUujgnxJaZaxdeVK1ekM0vphyb+8/vft0S37t2kUiEhIQgJDUVH8S8srIk9+TIFtCvAZKjd2CjSM+djbv4YHYP3Nm5QpE45lTAZylFiGQpQQCsCFq10hP1QXkD89S+e9+brRKj8SFgjBShAAXUFmAzV9fVb7c6pUSZCv4WADVOAAjoSYDLUUbDkdpWJUK4Uy1GAAhS4JsBkaLAjgYnQYAHlcChAAZ8IMBn6hNk3jTgT4R9uu82nF8v4ZnRshQIUoIB6AkyG6tn6tGZxuby4ob5160Bk79rl07bZGAUoQAG9CzAZ6j2CAJxLrImVZXxxQ70ByDgEClBARwKXL19Gfn4+xP/V+mIyVEvWh/WOH5ckrTUqllhr3bq1D1tmUxSgAAV8I7Bi2TIMHjgQO7KyVEmKTIa+iaNqrfz52edw6sQJbN62jes+qqbMiilAAX8KiPV0N2/divkLFmDL5s2qJEXFV6ARK4/wiwIUoAAFKKC2QPuQDpgydSqGDR/udVM3e11DnQrGjH0UvXv3VqRzdarWzY++WIpMXDk6+sGHEBMX5/MrR+X+wVNUWqKbmKnRUV8cB2r0W6k67XY7BvYfAB4HoaY2ENOaR48exevz5ytyaInjan16Ora8vwkxsbHo0rWrIvUqngwV6RUraVRAXDCT9PifpEfz+HK9UWen5Ly5yU2Yzjr5fwpQgAKNCdROguKka8/H+2G1Whvbxa3XmAzd4tJG4YdGjsQvv1zB9owMbXSIvaAABSigokBFRYU0y6BGEnR2mxfQOCV08v+ZM2bgXEmpdMEMrxzVSdDYTQpQwCuBwMBAaapZTLW6Phv8FjsmREmPjot4JgsXHICjPB9vTYhGeMggLLNVNdk+zwybJNJOgZycHGmefOKzk3jlqHbCwp5QgAJ+F7gdw9KOoZ9tJUaP3I6PCwJRmfEtBiw7jD8HyDvnk1fK7wNlB8TnhJMmTkS3iAi8+OKL+gRxlMO2YSYGh4QivEsy3jpaDoc+R8JeU4ACmhOwICBqBJ5K/BrzHstE+0kPobPMRCiGwmSouYC67pC4sf43lt/g3fXprgtofutF2JZPw6yiBKw9W4Izn4zBj69OwwrbRc33nB2kAAX0InArusR1AWLuQZ92t7jVacWT4R133AGxUDS/lBNITU2Vbqx/a/Uq3a4w47BnYd6aTnhxegKCLIAlKAHPp3TCurlZsPP0ULmDhTVRQGMCIh+IvODTryPH8bdK995YFE+GYx97DNHR0T4dt5EbE/cTvrNyFcRVVImJiTod6hUUH87BSWsogmumLSxoGZWAYfYcHCm+otNxsduNCYgLHeTchtNYHXxN/wIiH4i84Isvx4WP8X7R7bgXeThgq3CrScWToVutG7SwUm8AYlHaSROfRlC7tordsOoXcsc5HMk8jhbdQ3BbvSPuOLIOnzPkZ4dKHQd+iRkbVUyAx4FilI1XVPUVNqwqxwMvP49HR96CU6U/4t8XsjFvw2lZ7y/13poab42v+lJg1syZ0gLc723Y4MtmlW+r6jsU2YGw8LYIUL521qiCwM5de1WolVU6BejrlFDg/47TWD+sK8If3oZW40YjKuBWRCXGoHhOEiZtvxXJYzvLujhGxWRYCfuBt/BUl1Dp3o/wgTOx0WbWqwcdqLIfxI6MpXiq52zkyZjLFtOjWR9mIPnpp9ExLEyBI4ZV+E7A/Xj7rm/yWhoy+H55BRssxd9/4CrKj77963tgVwyemQV71bXPsbz3bRBemy84zmPHM/dgRLq8szS3BmHpjHE7vkLRnrkYZm0pXRfaMn4uTpTm438mR0vXKMipT6VkeBUXsjdhL+7Hkq9LUHQ2H1sGfo9FI5815dWDDvt7GP/fG7Bj5gp88kvTYRHTo+JBvR1CQ/R7G0XtYQa0RbgVKC76Dk3f+lp7R31+72689TnKxnrN33/AgaqCfcjBcLz9dQnOfJaG+8sX4sE3DqKyMTpDvnYVFz5aill7ftD06NRJho4yFP3HEDzbz3ptWswShF7PvYDpkX/DuowC0x0MFmsSPnj3LfzlpVhZB4OYHv355yqsSUuTVV7zhSwdEDOiZ71uOr4vxalLPTE8toOsaYx6FWh0g7vx1ugwPO8Wf/8BxznYKnvi0d5B0rFtCeqDcY8NADJyYZMxM+Q5vtb2dKDKtgZzPvsd/thCa327sT/qJENLKPr2vf3GNzhLG3TofuuNrfOnegLGnB5thrDYRITd8EbgQFVZCYojExET1qyeAzfoWIC//0A9g6v4vvQ8/jN5CHq1VOdtV5NHTNWXSFsFPD25P7R+w52Po9IKcb068iKKRo5acfWoYaZHa43TYh2OWclnkLo4F+XSuoG5WLLwDJ6YPRxWHx+FtbrFb30qYNLf/yo78tIXILXkMayd0ttE738XYVuzDZg0FlEBv/HpkeZJY757G6o8hQMnEzEhsc4Zoye9Nug+4ub6H3/4AYvefNOAI2yFqClLMbfNFgzoGIpO43MRPn8pJke1MuBYOaR6Aqb8/XegMm82IroNwIQ57+GTLw7i82KzfGIopkffx9sYhQk6+R330ULdF2FbuwttZs9AVM1N1/V+XUy94WxxMda8/bZ0c/2dd95pTAvx2fHkNTgx2ZjD46gaEjDr778F165qnIFy23asnDEf04dVAjkLMczNpcIaktXs9qov8e6O9pgzWz9nwrKTocOejgf7z8XJRvVjMevjNIyz1v4MSPyF8AEyWychRSd/ITQ6RHFPy4iRmFd4qZFiLdB9TgY+TJJ3f4uo6Plpz+N3v2uG6S+80Ei9fIkCehMw2O+/R/y3ICjqUcxdcRWn+r+LY2cqMaydka+fuAjbur+i/cTJaOe7uUePIlN7J9nJUFwhl1maVHtfWd87LuzHu1/FICWpqzHmyn+9p2WcrNHLK7QzO1tae/TttDW6XXtU3khZymwChvv99yKAlrBoDI98H0Ve1KGLXSsLkPn2SmxeshLT63Z4zv3oNMfVSVPdgr7/WdW87SjPw8rtzfDwWGcidKDqdAbWH9T2/Sa+DIO4p/AvKS/D2rmTjtce9aUY29KLAH//60RKrMR0vht6dRI3hhv4q2U85on7y0tr/TvxLh5pIWbM9uJM6cY6s4fasJB9Zuhed8UKHB9h4eQZ2PzNJSxfUntv8VfBoNobTP39/Ndfxy+/XMHKVatM7cDBG0mAv/+OC1l4LvFdtPnLTDw7tjeCcAF5i9Pw/ZS/oJ/RPy/U6aGsypmh48JHeGnYNCkR1nMx431llXmY1eUODJxzGLj0HiZEdJeWJSoqLsa2LVswaswYLrlW70DR8YYG4u3eA2X0O37+/gOWllb0ifkHNs8ahbiOoYh4aiv+OexNvG2Uj4v0e3g22PObqqurqxt8lS+oKvCnxx7HcZsNX3x5DM2bN1e1LV9XHh4Sysf3+Bqd7VGAAh4LqDRN6nF/TLNjTk4Ojhw6hAWpiwyXCE0TRA6UAhQwjADPDP0Uyn4JCVLLB3Jz/dQDdZvlmaG6vqydAhRQVkCVzwyV7aLxatuwYQPOlZRi7rx5xhscR2QIAT5vT90w0lddX09qZzL0RM3LfRYteAMxcXGIi4vzsibuTgEKUIACSggwGSqh6EYdb69+W7qVYs7cOW7sxaIU8K2A6R4+61te0NfH4DKaYzKUgaRUEXGD/batW5C6eDFvpVAKlfVQgAIUUECAyVABRLlV7N+3Tyo64L775O7CchSgAAUo4AMBJkMfIIsmxFnh8mXLMGXqVN5K4SNzNkMBClBArgCToVwpL8utT1+P2267DTwr9BKSu1OAAhRQQYA33auAWrfKiooKvLlwITZs3sSzwro4/JkCFKCABgR4ZuiDIGzbug29+9yF6OhoH7TGJihAAQpQwF0Bnhm6K+Zm+dpnhW7uyuIUoAAFKOAjAZ4ZqgzNs0KVgVk9BShAAQUEmAwVQGyoCudZ4eSpUxsqosHtDlTmzUZESCjE+qLSv2HpsJvl+UMajAi7RAEKqC/AZKiisS7PCh3fInfrflyqcWmB7iOiEcYjpUaE31CAAsYT4GeGKsXUeVYoriDVz5cDVQU7kN5mAWyl8Wipn46zpxSgAAW8EuDf+17xNbyzLs8KUYFjGdtxcuNSpKZnIc9e2fAA+QoFKEABAwnweYYqBFOcFd4Vdad0X6Gebqdw2NPxYP+5OFljEoFHli1CyvDOCKjZJu8bPs9QnhNLUYAC2hDgmaEKcdDnWSFgsSYhs7QEZz77EMvmjEVnnMDmqa8gzXZRBSVWSQEKUEA7AjwzVDgWej0rdMXgKD+A18ZPRsadK3Ho9eufIYqzPjlfRaUlcoqxDAUoQAG/CzAZKhwC8bzCv+blYvPWrQrX7H519ac9XdURi1kfp2GctZmLF8VtFnMRNwlY8dlsxLeUP5HAaVIXnNxEAQpoVoBXkyoYGufzCucvWKBgrZ5XdW3aM8nzCmBBQHAowqxAcID8ROhFg9yVAhSggF8E+A6nILvzeYU9evRQsFZ/VuVAVdkPiJw2BFYeKf4MBNumAAVUFuBbnELA+n9e4VWU2/Zip60c1xabuYryo2uRerAnnu57q0JKrIYCFKCANgWYDBWKy+HDh6WadP28wsovsXpkNDqFhCJiwkrk/xyPlFf7IYhHiUJHCauhAAW0KsALaBSKzCOjR+Oe+AQ8/czTCtWo72p4AY2+48feU8BsAvybX4GI5+fn4+jnX2DU6FEK1MYqKEABClDA1wJMhgqI79q5ExMnPYPAwEAFamMVFKAABSjgawHeWuGluN1ux5b3N2HPx/u9rIm7U4ACFKCAvwR4Zuil/IGcAxgz9lFYrVYva+LuFKAABSjgLwEmQy/knY9pGjxkiBe1cFcKUIACFPC3AJOhFxH49OBB9O5zF/T0ZAovhstdKUABChhWgMnQi9AuX7YMYx55xIsauCsFKEABCmhBgMnQwyiI2ynOl56Drm+y93Ds3I0CFKCA0QSYDD2M6MYNG/BCSgqaN2/uYQ3cjQIUoAAFtCLAZOhBJMTtFPt278HQB4Z6sDd3oQAFKEABrQkwGXoQkazMTOl2iuDgYA/25i4UoAAFKKA1ASZDNyMibqd4Z9Vq8HYKN+FYnAIUoICGBZgM3QwOb6dwE4zFKUABCuhAgMnQzSDxdgo3wVicAhSggA4EmAzdCJLzdoq7+/Z1Yy8WpQAFKEABrQswGboRIfF0CnE7BZ9O4QYai1KAAhTQgQCTocwgiQtnxNMp+iX2k7kHi1GAAhSggF4EmAxlRmrP7t3SOqR8OoVMMBajAAUooCMBJkOZwVqbloYnk5NllmYxClCAAhTQkwCToYxoOS+ciY2NlVGaRShAAQpQQG8CTIYyIua8cIbrkMrAYhEKUIACOhRgMmwiaLxwpgkgvkwBClDAAAJMhk0EkRfONAHElylAAQoYQIDJsIkg7szO5gN8mzDiyxSgAAX0LsBk2EgECwsLcfTzL8AVZxpB4ksUoAAFDCDAZNhIEPfv2yc9qokrzjSCxJcoQAEKGECAybCBIF6+fJmPamrAhpspQAEKGE2AybCBiB4+fBjtQzogOjq6gRLcTAEKUIACRhFgMmwgkpkZGRg1ekwDr3IzBShAAQoYSYDJ0EU0y8rKsG/3Hgx9YKiLV/W8qRL2vGxkLk1Gr5l5qHQ1FEc5bBtmYnBIKMK7JOOto+VwuCrHbRSgAAUMJMBk6CKYebm50qLcwcHBLl7V66YrsKenYMHGTZi9PAdXXQ7jImzLp2FWUQLWni3BmU/G4MdXp2GF7aLL0txIAQpQwCgCTIYuImnMewubwZq0Guv+Zw6mR7ZwMWrAYc/CvDWd8OL0BARZAEtQAp5P6YR1c7Ng5+mhSzNupAAFjCHAZFgnjua9t/AKig/n4KQ1FMEBzsPCgpZRCRhmz8GR4it1pPgjBShAAeMION/1jDMiL0eSfyTfnPcWOs7hSOZxtOgegtvqHRXHkXX4HD879PLY4u4UoIB2Beq97Wm3q+r3TNxb+ObChRg8ZIj6jWmtharvUGQHwsLbIkBrfWN/KEABCqgswGRYC7igoED6qUePHrW28lsKUIACFDC6wM1GH6A74zv06aeYOOkZ6OG5hQ57Oh7sPxcnGx1gLGZ9nIZx1maNlpJeDGiLcCuwo+g7VKEzWjayR3hIaCOv8iUKUIAC+hNgMvw1Zs7l1z7ckaWLKFqsScgsTVKur5YOiBnRE4uLbqzS8X0pTl3qieGxHeCcRigqLbmxkIufmDBdoHATBSigWQHn+5tmO+irjjmXX4uMjPRVkxprpxnCYhMRlpELW6XzPgoHqspKUByZiJgwGWeXGhsRu0MBClBArgCT4a9SXH4NsFiHY1byGaQuzkW5A3CU52LJwjN4YvZwWHmkyP2dYjkKUECHAnyLA1BRUSEtv9YvsZ8OQyi3yw5U5s1GRMf7Ma/wEi5tHI+okMew3l77/sFWiJqyFHPbbMGAjqHoND4X4fOXYnJUK7mNsBwFKEABXQrcVF1dXa3LnivY6R1ZWdiyeTM2b92qYK3mrkp8Zijns0VzK3H0FKCAVgR4ZghIiXDIUKMtyq2VQ4z9oAAFKKB9AdMnQ/GEiqOff4H4hATtR4s9pAAFKEABVQRMnwyN+YQKVY4VVkoBClDAsAKmT4biCRVPJicbNsAcGAUoQAEKNC1g6mRot9ulKdKoqKimpViCAhSgAAUMK2DqZHgg5wDuGzQQgYGBhg0wB0YBClCAAk0LmDoZbtu6BSNGjmxaiSUoQAEKUMDQAqZNhuIhvudLz4FTpIY+vjk4ClCAArIETJsMxUN8OUUq6xhhIQpQgAKGFzBtMuQUqeGPbQ6QAhSggGwBUyZDTpHKPj5YkAIUoIApBEyZDDlFaopjm4OkAAUoIFvAlMmQU6Syjw8WpAAFKGAKAdMlQ06RmuK45iApQAEKuCVgumR46uRJXkXq1iHCwhSgAAWML2C6ZCjWIuWN9sY/sDlCClCAAu4ImCoZOh/XdMcdd7hjxLIUoAAFKGBwAVMlQz6uyeBHM4dHAQpQwEMBUyVDMUXKJ9p7eKRwNwpQgAIGFjBNMnROkfKJ9gY+mjk0ClCAAh4KmCYZfvPNN+jd5y4EBwd7SMXdKEABClDAqAKmSYaZGRmcIjXqUcxxUYACFPBSwBTJsKKiAvt278Fdffp4ycXdKUABClDAiAKmSIY2mw3tQzrAarUaMYYcEwUoQAEKeClgimR43GbDqNFjvKTi7hSgAAUoYFQBwyfDy5cv451VqxEdE23UGHJcFKAABSjgpYDhk2FBQYFE1KlTJy+puDsFKEABChhVwPDJsLCgEBMnPYPmzZsbNYYcFwUoQAEKeClg+GQonl0Yd/fdXjJxdwpQgAIUMLKAoZOh89mFnTt3NnIMOTYKUIACFPBSwNDJMP9IPp9deMMBUgl7XjYylyaj18w8VN7wmvMHByrzZiMiJBThzn/D0mF3OF/n/ylAAQoYT+Bm4w3p+oj+mpeLJ5OTr28w9XdXYE9PwYJDF3Es5zPgsbGuNRzfInfrflyqebUFuo+IRpih/2yqGSy/oQAFTCpg2GToXJj7zSVLTBrausNuBmvSaqz702msHzESi+u+LP3sQFXBDqS3WQBbaTxauizDjRSgAAWMJ2DYv/ePHT3KhbndPl4rcCxjO05uXIrU9Czk2V1PpLpdLXegAAUooHEBwybD/fv3c2FuNw8+h30nlm88D+AENs+Zhgn9H8esrNOocrMeFqcABSigNwFDJkPnwtzdunfXWzz82l+LNQmZpSU489mHWDZnLDqLpDj1FaTZLvq1X2ycAhSggNoChkyGp0+flhbmjoyMVNvPkPVbgqIwJOl1ZH+Whsfu+BvWZRQ0cOWpIYfPQVGAAiYUMOQFNIc+/RQDBw0ydDgd9nQ82H8uTjY6yljM+jgN46zNGi3V0IuWoAQ8n/IQMiblwvZSX8S3vPa3k7jlgl8UoAAFjCRgyGT45IQJRoqRy7Fcm9JMcvmachstCAgORZgVCA64PolQVFrSZBNMmE0SsQAFKKAhAUMmw8DAQA0R67krDlSV/YDIaUmwXs+FsgYkJ2HKqoiFKEABCvhAwM23OB/0iE34SeAqym17sdNWjmuLzVxF+dG1SD3YE0/3vdVPfWKzFKAABXwjcFN1dXW1b5piK/4VEMuszUVc0nu1Vpep/ZniVZTnpeLJpDScBtAicTLmPjYE/eOtCPBvx9k6BShAAdUFmAxVJ2YDFKAABSigdQFOk2o9QuwfBShAAQqoLsBkqDoxG6AABShAAa0LMBlqPULsHwUoQAEKqC7w/wGdFlhxODyClAAAAABJRU5ErkJggg==" alt></p>
<p>Find \(f'(x)\) .</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>There are two points at which the gradient of the graph of \(f\) is \(11\). Find the \(x\)-coordinates of these points.</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>\((f'(x) = )\,\,3{x^2} - 6x + 2\) <em><strong>(A1)(A1)(A1) (C3)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(3{x^2}\), <em><strong>(A1)</strong></em> for \( - 6x\) and <em><strong>(A1)</strong></em> for \( + 2\).<br>Award at most <em><strong>(A1)(A1)(A0)</strong></em> if there are extra terms present.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(11 = 3{x^2} - 6x + 2\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for equating their answer from part (a) to \(11\), this may be implied from \(0 = 3{x^2} - 6x - 9\) .</p>
<p>\((x = )\,\, - 1\,\,,\,\,\,\,(x = )\,\,3\) <em><strong>(A1)</strong></em><strong>(ft)<em>(A1)</em><strong>(ft) <em>(C3)</em></strong></strong></p>
<p><strong>Note: </strong>Follow through from part (a).<br>If final answer is given as coordinates, award at most <strong><em>(M1)(A0)(A1</em>)(ft)</strong> for \(( - 1,\,\, - 4)\) and \((3,\,\,8)\) .</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 15: Differential calculus.</p>
<p>Many candidates correctly differentiated the cubic equation. Most candidates were unable to use differential calculus to find the point where a cubic function had a specified gradient.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 15: Differential calculus.</p>
<p>Many candidates correctly differentiated the cubic equation. Most candidates were unable to use differential calculus to find the point where a cubic function had a specified gradient.</p>
<div class="question_part_label">b.</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>A factory produces shirts. The cost, <em>C</em>, in Fijian dollars (FJD), of producing<em> x</em> shirts can be modelled by</p>
<p style="text-align: center;"><em>C</em>(<em>x</em>) = (<em>x</em> − 75)<sup>2</sup> + 100.</p>
</div>
<div class="specification">
<p>The cost of production should not exceed 500 FJD. To do this the factory needs to produce at least 55 shirts and at most <em>s</em> shirts.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the cost of producing 70 shirts.</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 <em>s</em>.</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 number of shirts produced when the cost of production is lowest.</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>(70 − 75)<sup>2</sup> + 100 <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting in <em>x</em> = 70.</p>
<p>125 <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>(<em>s</em> − 75)<sup>2</sup> + 100 = 500 <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for equating <em>C</em>(<em>x</em>) to 500. Accept an inequality instead of =.</p>
<p><strong>OR</strong></p>
<p><img src="data:image/png;base64,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"> <em><strong>(M1)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for sketching correct graph(s).</p>
<p>(<em>s</em> =) 95 <em><strong>(A1) (C2)</strong></em></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><img 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"> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for an attempt at finding the minimum point using graph.</p>
<p><strong>OR</strong></p>
<p>\(\frac{{95 + 55}}{2}\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for attempting to find the mid-point between their part (b) and 55.</p>
<p><strong>OR</strong></p>
<p>(<em>C'</em>(<em>x</em>) =) 2<em>x</em> − 150 = 0 <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for an attempt at differentiation that is correctly equated to zero.</p>
<p>75 <em><strong>(A1) (C2)</strong></em></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 graph of the quadratic function \(f(x) = 3 + 4x - {x^2}\) intersects the \(y\)-axis at point A and has its vertex at point B .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the coordinates of B .</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>Another point, C , which lies on the graph of \(y = f(x)\) has the same \(y\)-coordinate as A .</span><br><span>(i) Plot and label C on the graph above.</span><br><span>(ii) Find the \(x\)-coordinate of C .</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>\(x = - \frac{4}{{ - 2}}\) <em><strong>(M1)</strong></em></span><br><span>\(x = 2\) <em><strong>(A1)</strong></em></span></p>
<p> <span><strong>OR</strong></span></p>
<p> <span>\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 4 - 2x\) <em><strong>(M1)</strong></em></span><br><span>\(x = 2\) <em><strong>(A1)</strong></em></span><br><span>\((2{\text{, }}7)\) or \(x = 2\), \(y = 7\) <em><strong>(A1) (C3)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)(A1)(A0)</strong></em> for 2, 7 without parentheses.</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>(i) C labelled in correct position on graph <em><strong>(A1) (C1)</strong></em></span><br><span><img src="data:image/png;base64,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" alt></span></p>
<p> </p>
<p><span>(ii) \(3 = 3 + 4x - {x^2}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of \(y = 3\) into quadratic.</span></p>
<p> </p>
<p><span>\((x = )4\) <em><strong>(A1) (C2)</strong></em></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>Using symmetry of graph \(x = 2 + 2\) . <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their \(x\)-coordinate of the vertex.</span></p>
<p> </p>
<p><span><span>\((x = )4\) </span> <span><strong><em>(A1)</em>(ft) <em>(C2)</em></strong></span></span></p>
<p> </p>
<p><span><span><strong><em>[3 marks]</em></strong></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 part b, the point C was sometimes not labelled or not shown on the graph provided. Candidates using their GDC to find the coordinates of the vertex needed to translate their calculator answer to the exact mathematical answer. Answers of \((1.9{\text{, }}7)\) or \((2.1{\text{, }}7)\) did not achieve the maximum number of marks. A common response in part c was to give \((4{\text{, }}3)\), with no working shown. This incurred a penalty of one mark. The correct answer to this question was \(x = 4\).</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;">In part b, the point C was sometimes not labelled or not shown on the graph provided. Candidates using their GDC to find the coordinates of the vertex needed to translate their calculator answer to the exact mathematical answer. Answers of \((1.9{\text{, }}7)\) or \((2.1{\text{, }}7)\) did not achieve the maximum number of marks.</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>Consider the numbers \(2\), \(\sqrt 3 \), \( - \frac{2}{3}\) and the sets \(\mathbb{N}\), \(\mathbb{Z}\), \(\mathbb{Q}\) and \(\mathbb{R}\).</span></p>
<p><span>Complete the table below by placing a tick in the appropriate box if the number is an element of the set, and a cross if it is not.<img src="data:image/png;base64,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" alt></span></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><span>A function \(f\) is given by \(f(x) = 2{x^2} - 3x{\text{, }}x \in \{ - 2{\text{, }}2{\text{, }}3\} \).</span></p>
<p><span>Write down the range of function \(f\).</span></p>
<div class="marks">[1]</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><img src="data:image/png;base64,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" alt><span> <em><strong>(A1)(A1)(A1) (C3)</strong></em></span></span></p>
<p><span><strong>Note:</strong> Accept any symbol for ticks. Do not penalise if the other boxes are left blank.<strong><br></strong></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>\({\text{Range}} = \{ 2{\text{, }}9{\text{, }}14\} \) <em><strong>(A1)</strong></em><strong>(ft) <em>(C1)</em></strong></span></p>
<p><span><strong>Note: </strong>Brackets not required.<em><strong><br></strong></em></span></p>
<p><span><em><strong>[1 mark]</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;">There was a lack of familiarity with number systems and mappings - it was surprising to see how few knew what a mapping diagram involved. Part (c) (range) was also poorly answered with many giving an interval although they had correctly worked out the values for the function.</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 was a lack of familiarity with number systems and mappings - it was surprising to see how few knew what a mapping diagram involved. Part (b) (range) was also poorly answered with many giving an interval although they had correctly worked out the values for the function.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p><span>The following curves are sketches of the graphs of the functions given below, but in a different order. Using your graphic display calculator, match the equations to the curves, writing your answers in the table below.</span></p>
<p><span>(the diagrams are not to scale)</span></p>
<p><img 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" 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" alt></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span>(i) B <em><strong>(A1)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span>(ii) D</span><span> <em><strong>(A1)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span>(iii) A</span><span> <em><strong>(A1)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span>(iv) E</span><span> <em><strong>(A1)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span>(v) C</span><span> <em><strong>(A1)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span>(vi) F</span><span> <em><strong>(A1) (C6)<br></strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span><em><strong>[6 marks]<br></strong></em></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">Nearly all the candidates scored 6 marks for this question.Without any working shown it was difficult to say where the errors might have arisen from the few candidates who did not score full marks. However, it was obvious that the candidates were using their GDC's to graph the functions.</span></p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;"><em>y</em> = <em>f</em> (<em>x</em>) is a quadratic function. The graph of <em>f</em> (<em>x</em>) intersects the <em>y</em>-axis at the point A(0, 6) and the <em>x</em>-axis at the point B(1, 0). The vertex of the graph is at the point C(2, –2).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the equation of the axis of symmetry.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Sketch the graph of <em>y</em> = <em>f</em> (<em>x</em>) on the axes below for 0 ≤ <em>x </em>≤ 4 . Mark clearly on the sketch the points A , B , and C.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The graph of <em>y</em> = <em>f</em> (<em>x</em>) intersects the <em>x</em>-axis for a second time at point D.</span></p>
<p><span>Write down the <em>x</em>-coordinate of point D.</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><em>x</em> = 2 <em><strong>(A1)(A1) </strong></em><em><strong>(C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(A1)(A0)</strong></em> for “<em> x</em> = constant” (other than 2). Award <em><strong>(A0)(A1)</strong></em> for <em>y</em> = 2. Award <em><strong>(A0)(A0)</strong></em> for only seeing 2. Award <em><strong>(A0)(A0)</strong></em> for 2 = –<em>b</em> / 2<em>a</em>.<em><strong><br></strong></em></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><img 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" alt></span></p>
<p><span><em><strong>(A1)</strong></em> for correctly plotting and labelling A, B and C</span></p>
<p><span><em><strong>(A1)</strong></em> for a smooth curve passing through the three given points</span></p>
<p><span><em><strong>(A1)</strong></em> for completing the symmetry of the curve over the <strong>domain given</strong>. <em><strong>(A3) </strong></em><em><strong>(C3)</strong></em></span></p>
<p><span><strong>Notes:</strong> For <em><strong>A</strong></em> marks to be awarded for the curve, each segment must be a </span><span>reasonable attempt at a continuous curve.</span> <span>If straight line segments are used, penalise once only in the last </span><span>two marks.</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>3 <em><strong>(A1)</strong></em><strong>(ft) </strong><em><strong>(C1)</strong></em></span></p>
<p><span><strong>Notes: <em>(A0)</em></strong> for coordinates. Accept <em>x</em> = 3 or D = 3 .</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; font-family: times new roman,times;">(a) Identifying '2' and leaving this as the answer was not sufficient for any marks in this part of the question as was simply leaving the equation \(2 + \frac{{ - b}}{{2a}}\). </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 (b) whilst much good work was seen by some candidates in sketching the correct curve, others failed to recognise the symmetry, joined the given points with straight lines or simply drew curved segments which were far from smooth. </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;">Part (c) required, for one mark, the writing down of the <em>x</em>-coordinate of the point D. A significant number of candidates, including very able candidates, lost this mark by writing down (3,0).</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 function \(f(x) = 5 - 3({2^{ - x}})\) is defined for \(x \geqslant 0\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>On the axes below sketch the graph of <em>f</em> (<em>x</em>) and show the behaviour of the curve as <em>x</em> increases.</span></p>
<p><span> </span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the coordinates of any intercepts with the axes.</span></p>
<p><span><img alt="onbekend.png"></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>Draw the line<em> y</em> = 5 on your sketch.</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>Write down the number of solutions to the equation</span> <span><em>f</em> (<em>x</em>) = 5 .</span></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><img 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" alt> <em><strong>(A1)(A1)(A1)</strong></em></span></p>
<p><span> </span></p>
<p><span><strong>Notes:</strong> Award<em><strong> (A1)</strong></em> for labels and scale on <em>y</em>-axis.</span><br><span>Award <em><strong>(A1)</strong></em> for smooth increasing curve in the given domain.</span><br><span>Award<em><strong> (A1)</strong></em> for asymptote implied (\({\text{gradient}} \to {\text{0}}\)).</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<p> </p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(0, 2) <em>accept</em> <em>x</em> = 0, <em>y</em> = 2 <strong><em> (A1) (C4)</em></strong></span></p>
<p><span><span><br> </span><strong>Note:</strong> If incorrect domain used and both (0, 2) and (\( - \)0.737, 0) seen award <strong><em>(A1)</em>(ft)</strong>.</span></p>
<p> </p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>line passing through (0, 5), parallel to <em>x</em> axis and not intersecting their graph. <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>zero <em><strong> (A1) (C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</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;">Most candidates attempted this question and many gained 3 or 4 marks. All made an attempt</span> <span style="font-family: times new roman,times; font-size: medium;">at sketching the graph which demanded that students used their GDC. Many candidates failed </span><span style="font-family: times new roman,times; font-size: medium;">to label their graphs and to give an indication of scale, and lost one mark in part (a). Some did </span><span style="font-family: times new roman,times; font-size: medium;">not pay attention to the domain and sketched the graph in a different region. A significant</span><span> </span><span style="font-family: times new roman,times; font-size: medium;">number could also write down the coordinates of the <em>y</em>-intercept, although some wrote only</span> <span style="font-family: times new roman,times; font-size: medium;"><em>y</em> = 2 instead of giving the two coordinates. Almost all could draw the line <em>y</em> = 5 </span><span style="font-family: times new roman,times; font-size: medium;">on the</span> <span style="font-family: times new roman,times; font-size: medium;">sketch but many could not find the answer for the number of solutions to the equation given </span><span style="font-family: times new roman,times; font-size: medium;">in part c). Some candidates lost time in an attempt to draw this graph accurately on graph</span> <span style="font-family: times new roman,times; font-size: medium;">paper, which was not the intended task. Most candidates attempted this question, which </span><span style="font-family: times new roman,times; font-size: medium;">clearly indicated that the time given for the paper was sufficient.</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;">Most candidates attempted this question and many gained 3 or 4 marks. All made an attemptat sketching the graph which demanded that students used their GDC. Many candidates failed to label their graphs and to give an indication of scale, and lost one mark in part (a). Some did not pay attention to the domain and sketched the graph in a different region. A significant<span style="font: 14.0px 'Helvetica Neue';"> </span>number could also write down the coordinates of the <em>y</em>-intercept, although some wrote only<em>y</em> = 2 instead of giving the two coordinates. Almost all could draw the line <em>y</em> = 5 on thesketch but many could not find the answer for the number of solutions to the equation given in part c). Some candidates lost time in an attempt to draw this graph accurately on graphpaper, which was not the intended task. Most candidates attempted this question, which clearly indicated that the time given for the paper was sufficient.</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;">Most candidates attempted this question and many gained 3 or 4 marks. All made an attemptat sketching the graph which demanded that students used their GDC. Many candidates failed to label their graphs and to give an indication of scale, and lost one mark in part (a). Some did not pay attention to the domain and sketched the graph in a different region. A significant<span style="font: 14.0px 'Helvetica Neue';"> </span>number could also write down the coordinates of the <em>y</em>-intercept, although some wrote only<em>y</em> = 2 instead of giving the two coordinates. Almost all could draw the line <em>y</em> = 5 on thesketch but many could not find the answer for the number of solutions to the equation given in part c). Some candidates lost time in an attempt to draw this graph accurately on graphpaper, which was not the intended task. Most candidates attempted this question, which clearly indicated that the time given for the paper was sufficient.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates attempted this question and many gained 3 or 4 marks. All made an attemptat sketching the graph which demanded that students used their GDC. Many candidates failed to label their graphs and to give an indication of scale, and lost one mark in part (a). Some did not pay attention to the domain and sketched the graph in a different region. A significant<span style="font: 14.0px 'Helvetica Neue';"> </span>number could also write down the coordinates of the <em>y</em>-intercept, although some wrote only<em>y</em> = 2 instead of giving the two coordinates. Almost all could draw the line <em>y</em> = 5 on thesketch but many could not find the answer for the number of solutions to the equation given in part c). Some candidates lost time in an attempt to draw this graph accurately on graphpaper, which was not the intended task. Most candidates attempted this question, which clearly indicated that the time given for the paper was sufficient.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Consider the curve \(y = 1 + \frac{1}{{2x}},\,\,x \ne 0.\)</p>
<p>For this curve, write down</p>
<p>i) the value of the \(x\)-intercept;</p>
<p>ii) the equation of the vertical asymptote.</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>Sketch the curve for \( - 2 \leqslant x \leqslant 4\) on the axes below.</p>
<p><img src="data:image/png;base64,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" alt></p>
<p> </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>i) \(\left( {x = } \right) - 0.5\,\,\left( { - \frac{1}{2}} \right)\) <em><strong>(A1)</strong></em></p>
<p>ii) \(x = 0\) <em><strong>(A1)(A1) (C3)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for “\(x = \)” and <em><strong>(A1)</strong></em> for “\(0\)” seen as part of an equation.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img 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" alt></p>
<p><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)(ft)(A1) (C3)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for correct \(x\)-intercept, <em><strong>(A1)</strong></em><strong>(ft)</strong> for asymptotic behaviour at \(y\)-axis, <em><strong>(A1)</strong></em> for approximately correct shape (cannot intersect the horizontal asymptote of \(y = 1\)). Follow through 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;">
<p>Question 8: Rational function.</p>
<p>Few candidates could find the \(x\)-intercept of the rational function. Many candidates did appreciate that the curve does not cross the asymptote. Often the candidates wrote down the equation of the horizontal asymptote rather than the equation of the vertical asymptote. The most frequent incorrect sketch was that of \(y = \frac{1}{2}x + 1\) suggesting that the candidate did not understand that the curve \(y = 1 + \frac{1}{{2x}}\) is not linear and had taken insufficient care in entering the function into the calculator. Some candidates that appreciated the shape of the curve did not earn marks on account of the poor quality of their sketches, which either crossed, or veered away from, the asymptotes.</p>
<div class="question_part_label">a.</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 8: Rational 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;">Few candidates could find the \(x\)-intercept of the rational function. Many candidates did appreciate that the curve does not cross the asymptote. Often the candidates wrote down the equation of the horizontal asymptote rather than the equation of the vertical asymptote. The most frequent incorrect sketch was that of \(y = \frac{1}{2}x + 1\) suggesting that the candidate did not understand that the curve \(y = 1 + \frac{1}{{2x}}\) is not linear and had taken insufficient care in entering the function into the calculator. Some candidates that appreciated the shape of the curve did not earn marks on account of the poor quality of their sketches, which either crossed, or veered away from, the asymptotes.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The axis of symmetry of the graph of a quadratic function has the equation <em>x</em> \( = - \frac{1}{2}\)</p>
<p class="p1">.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the axis of symmetry on the following axes.</p>
<p><img src="images/Schermafbeelding_2015-12-03_om_13.39.20.png" alt></p>
<p>The graph of the quadratic function intersects the <em>x</em>-axis at the point N(2, 0) . There is a second point, M, at which the graph of the quadratic function intersects the <em>x</em>-axis.</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">Draw the axis of symmetry on the following axes.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-03_om_12.01.55.png" alt></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 graph of the quadratic function intersects the \(x\)-axis at the point \({\text{N}}(2, 0)\). There is a second point, \({\text{M}}\), at which the graph of the quadratic function intersects the \(x\)-axis.</p>
<p class="p1">Clearly mark and label point \({\text{M}}\) on the axes.</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">(i) <span class="Apple-converted-space"> </span>Find the value of \(b\) and the value of \(c\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Draw the graph of the function on the axes.</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><img alt></p>
<p>vertical straight line which may be dotted passing through \(\left( { - \frac{1}{2},{\text{ }}0} \right)\) <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img 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" alt></p>
<p class="p1">vertical straight line which may be dotted passing through \(\left( { - \frac{1}{2},{\text{ }}0} \right)\) <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">point \({\text{M }}( - 3,{\text{ }}0)\) correctly marked on the \(x\)-axis <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>Note: </strong>Follow through from 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"> \(b = 1\)</span>, \(c = - 6\) <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong></p>
<p class="p1"><strong>Notes: </strong>Follow through from (b).</p>
<p class="p2"> </p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>smooth parabola passing through \({\text{M}}\) and \({\text{N}}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)</strong></p>
<p class="p2"><strong>Note: </strong>Follow through from their point \({\text{M}}\) from part (b).</p>
<p class="p1"> </p>
<p class="p1">parabola passing through \((0,{\text{ }} - 6)\) and symmetrical about \(x = - 0.5\) <strong><em>(A1)</em>(ft) <em>(C4)</em></strong></p>
<p class="p1"><strong>Note: </strong>Follow through from part (c)(i).</p>
<p class="p1">If parabola is not smooth and not concave up award at most <strong><em>(A1)(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">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>
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