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<h2>SL Paper 2</h2><div class="specification">
<p>The rate of change of the height <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>h</mi><mo>)</mo></math> of a ball above horizontal ground, measured in metres, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> seconds after it has been thrown and until it hits the ground, can be modelled by the equation</p>
<p style="padding-left: 60px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>h</mi></mrow><mrow><mo>d</mo><mi>t</mi></mrow></mfrac><mo>=</mo><mn>11</mn><mo>.</mo><mn>4</mn><mo>-</mo><mn>9</mn><mo>.</mo><mn>8</mn><mi>t</mi></math></p>
<p>The height of the ball when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>2</mn><mo> </mo><mtext>m</mtext></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for the height <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> of the ball at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> at which the ball hits the ground.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence write down the domain of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math>.</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 <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math>.</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 style="color:#999;font-size:90%;font-style:italic;">* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mo>∫</mo><mfenced><mrow><mn>11</mn><mo>.</mo><mn>4</mn><mo>-</mo><mn>9</mn><mo>.</mo><mn>8</mn><mi>t</mi></mrow></mfenced><mtext>d</mtext><mi>t</mi></math> <strong>M1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>11</mn><mo>.</mo><mn>4</mn><mi>t</mi><mo>-</mo><mn>4</mn><mo>.</mo><mn>9</mn><msup><mi>t</mi><mn>2</mn></msup><mo> </mo><mfenced><mrow><mo>+</mo><mi>c</mi></mrow></mfenced></math> <strong>A1</strong><strong>A1</strong></p>
<p>When <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn><mo>,</mo><mo> </mo><mi>h</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>2</mn></math> <strong>(M1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>2</mn></math> <strong>(A1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>h</mi><mo>=</mo></mrow></mfenced><mn>1</mn><mo>.</mo><mn>2</mn><mo>+</mo><mn>11</mn><mo>.</mo><mn>4</mn><mi>t</mi><mo>-</mo><mn>4</mn><mo>.</mo><mn>9</mn><msup><mi>t</mi><mn>2</mn></msup></math> <strong>A1</strong></p>
<p> </p>
<p><strong>[6 marks]</strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>43</mn><mo> </mo><mfenced><mrow><mn>2</mn><mo>.</mo><mn>42741</mn><mo>…</mo></mrow></mfenced></math> seconds <strong>(M1)A1</strong> </p>
<p> </p>
<p><strong>[2 marks]</strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mn>2</mn><mo>.</mo><mn>43</mn></math> <strong>A1</strong> </p>
<p> </p>
<p><strong>Note:</strong> Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>t</mi><mo><</mo><mn>2</mn><mo>.</mo><mn>43</mn></math>.</p>
<p> </p>
<p><strong>[1 mark]</strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Maximum value is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>83061</mn><mo>…</mo></math> <strong>(M1)</strong></p>
<p>Range is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>h</mi><mo>≤</mo><mn>7</mn><mo>.</mo><mn>83</mn></math> <strong>A1A1</strong> </p>
<p> </p>
<p><strong>Note:</strong> Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>h</mi><mo><</mo><mn>7</mn><mo>.</mo><mn>83</mn></math>.</p>
<p> </p>
<p><strong>[3 marks]</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>A water container is made in the shape of a cylinder with internal height <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span> cm and internal base radius <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> cm.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-07_om_08.31.01.png" alt="N16/5/MATSD/SP2/ENG/TZ0/06"></p>
<p>The water container has no top. The inner surfaces of the container are to be coated with a water-resistant material.</p>
</div>
<div class="specification">
<p>The volume of the water container is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.5{\text{ }}{{\text{m}}^3}">
<mn>0.5</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</math></span>.</p>
</div>
<div class="specification">
<p>The water container is designed so that the area to be coated is minimized.</p>
</div>
<div class="specification">
<p>One can of water-resistant material coats a surface area of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2000{\text{ c}}{{\text{m}}^2}">
<mn>2000</mn>
<mrow>
<mtext> c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down a formula for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A"> <mi>A</mi> </math></span>, the surface area to be coated.</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>Express this volume in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{c}}{{\text{m}}^3}"> <mrow> <mtext>c</mtext> </mrow> <mrow> <msup> <mrow> <mtext>m</mtext> </mrow> <mn>3</mn> </msup> </mrow> </math></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>Write down, in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span>, an equation for the volume of this water container.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \pi {r^2} + \frac{{1\,000\,000}}{r}"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mi>r</mi> </mfrac> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{d}}A}}{{{\text{d}}r}}"> <mfrac> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>A</mi> </mrow> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>r</mi> </mrow> </mfrac> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using your answer to part (e), find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span> which minimizes <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A"> <mi>A</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of this minimum area.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the least number of cans of water-resistant material that will coat the area in part (g).</p>
<div class="marks">[3]</div>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(A = ){\text{ }}\pi {r^2} + 2\pi rh"> <mo stretchy="false">(</mo> <mi>A</mi> <mo>=</mo> <mo stretchy="false">)</mo> <mrow> <mtext> </mtext> </mrow> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mi>h</mi> </math></span> <strong><em>(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for either <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi {r^2}"> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </math></span> <strong>OR</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi rh"> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mi>h</mi> </math></span> seen. Award <strong><em>(A1) </em></strong>for two correct terms added together.</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="500\,000"> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </math></span> <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Units <strong>not </strong>required.</p>
<p> </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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="500\,000 = \pi {r^2}h"> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mi>h</mi> </math></span> <strong><em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(A1)</em>(ft) </strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi {r^2}h"> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mi>h</mi> </math></span> equating to their part (b).</p>
<p>Do not accept unless <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="V = \pi {r^2}h"> <mi>V</mi> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mi>h</mi> </math></span> is explicitly defined as their part (b).</p>
<p> </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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \pi {r^2} + 2\pi r\left( {\frac{{500\,000}}{{\pi {r^2}}}} \right)"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </math></span> <strong><em>(A1)</em>(ft)<em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1)</em>(ft) </strong>for their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{{500\,000}}{{\pi {r^2}}}}"> <mrow> <mfrac> <mrow> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> </mrow> </math></span> seen.</p>
<p>Award <strong><em>(M1) </em></strong>for correctly substituting <strong>only</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{{500\,000}}{{\pi {r^2}}}}"> <mrow> <mfrac> <mrow> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> </mrow> </math></span> into a <strong>correct </strong>part (a).</p>
<p>Award <strong><em>(A1)</em>(ft)<em>(M1) </em></strong>for rearranging part (c) to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi rh = \frac{{500\,000}}{r}"> <mi>π</mi> <mi>r</mi> <mi>h</mi> <mo>=</mo> <mfrac> <mrow> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mi>r</mi> </mfrac> </math></span> and substituting for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi rh"> <mi>π</mi> <mi>r</mi> <mi>h</mi> </math></span> in expression for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A"> <mi>A</mi> </math></span>.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \pi {r^2} + \frac{{1\,000\,000}}{r}"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mi>r</mi> </mfrac> </math></span> <strong><em>(AG)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>The conclusion, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \pi {r^2} + \frac{{1\,000\,000}}{r}"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mi>r</mi> </mfrac> </math></span>, must be consistent with their working seen for the <strong><em>(A1) </em></strong>to be awarded.</p>
<p>Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{10^6}"> <mrow> <msup> <mn>10</mn> <mn>6</mn> </msup> </mrow> </math></span> as equivalent to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{1\,000\,000}"> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> </math></span>.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi r - \frac{{{\text{1}}\,{\text{000}}\,{\text{000}}}}{{{r^2}}}"> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mo>−</mo> <mfrac> <mrow> <mrow> <mtext>1</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>000</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>000</mtext> </mrow> </mrow> <mrow> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> </math></span> <strong><em>(A1)(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi r"> <mn>2</mn> <mi>π</mi> <mi>r</mi> </math></span>, <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{{{r^2}}}"> <mfrac> <mn>1</mn> <mrow> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> </math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{r^{ - 2}}"> <mrow> <msup> <mi>r</mi> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </math></span>, <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - {\text{1}}\,{\text{000}}\,{\text{000}}"> <mo>−</mo> <mrow> <mtext>1</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>000</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>000</mtext> </mrow> </math></span>.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi r - \frac{{1\,000\,000}}{{{r^2}}} = 0"> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mo>−</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> <mo>=</mo> <mn>0</mn> </math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for equating their part (e) to zero.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{r^3} = \frac{{1\,000\,000}}{{2\pi }}"> <mrow> <msup> <mi>r</mi> <mn>3</mn> </msup> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </math></span> <strong>OR</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = \sqrt[3]{{\frac{{1\,000\,000}}{{2\pi }}}}"> <mi>r</mi> <mo>=</mo> <mroot> <mrow> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </mrow> <mn>3</mn> </mroot> </math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for isolating <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span>.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>sketch of derivative function <strong><em>(M1)</em></strong></p>
<p>with its zero indicated <strong><em>(M1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(r = ){\text{ }}54.2{\text{ }}({\text{cm}}){\text{ }}(54.1926 \ldots )"> <mo stretchy="false">(</mo> <mi>r</mi> <mo>=</mo> <mo stretchy="false">)</mo> <mrow> <mtext> </mtext> </mrow> <mn>54.2</mn> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mrow> <mtext>cm</mtext> </mrow> <mo stretchy="false">)</mo> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mn>54.1926</mn> <mo>…</mo> <mo stretchy="false">)</mo> </math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi {(54.1926 \ldots )^2} + \frac{{1\,000\,000}}{{(54.1926 \ldots )}}"> <mi>π</mi> <mrow> <mo stretchy="false">(</mo> <mn>54.1926</mn> <mo>…</mo> <msup> <mo stretchy="false">)</mo> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mo stretchy="false">(</mo> <mn>54.1926</mn> <mo>…</mo> <mo stretchy="false">)</mo> </mrow> </mfrac> </math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution of their part (f) into the given equation.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 27\,700{\text{ }}({\text{c}}{{\text{m}}^2}){\text{ }}(27\,679.0 \ldots )"> <mo>=</mo> <mn>27</mn> <mspace width="thinmathspace"></mspace> <mn>700</mn> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mrow> <mtext>c</mtext> </mrow> <mrow> <msup> <mrow> <mtext>m</mtext> </mrow> <mn>2</mn> </msup> </mrow> <mo stretchy="false">)</mo> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mn>27</mn> <mspace width="thinmathspace"></mspace> <mn>679.0</mn> <mo>…</mo> <mo stretchy="false">)</mo> </math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{27\,679.0 \ldots }}{{2000}}"> <mfrac> <mrow> <mn>27</mn> <mspace width="thinmathspace"></mspace> <mn>679.0</mn> <mo>…</mo> </mrow> <mrow> <mn>2000</mn> </mrow> </mfrac> </math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for dividing their part (g) by 2000.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 13.8395 \ldots "> <mo>=</mo> <mn>13.8395</mn> <mo>…</mo> </math></span> <strong><em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Notes: </strong>Follow through from part (g).</p>
<p> </p>
<p>14 (cans) <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Final <strong><em>(A1) </em></strong>awarded for rounding up their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="13.8395 \ldots "> <mn>13.8395</mn> <mo>…</mo> </math></span> to the next integer.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>The cross-sectional view of a tunnel is shown on the axes below. The line <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>[</mo><mtext>AB</mtext><mo>]</mo></math> represents a vertical wall located at the left side of the tunnel. The height, in metres, of the tunnel above the horizontal ground is modelled by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>1</mn><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>8</mn><msup><mi>x</mi><mn>2</mn></msup><mo>,</mo><mo> </mo><mn>2</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mn>8</mn></math>, relative to an origin <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math>.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">Point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> has coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>2</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>)</mo></math>, point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> has coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>2</mn><mo>,</mo><mo> </mo><mn>2</mn><mo>.</mo><mn>4</mn><mo>)</mo></math>, and point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> has coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>8</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>)</mo></math>.</p>
</div>
<div class="specification">
<p>When <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>4</mn></math> the height of the tunnel is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>4</mn><mo> </mo><mtext>m</mtext></math> and when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>6</mn></math> the height of the tunnel is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>2</mn><mo> </mo><mtext>m</mtext></math>. These points are shown as <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext></math> on the diagram, respectively.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>y</mi></mrow><mrow><mo>d</mo><mi>x</mi></mrow></mfrac></math>.</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>Hence find the maximum height of the tunnel.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the trapezoidal rule, with three intervals, to estimate the cross-sectional area of the tunnel.</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>Write down the integral which can be used to find the cross-sectional area of the tunnel.</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>Hence find the cross-sectional area of the tunnel.</p>
<div class="marks">[2]</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>evidence of power rule (at least one correct term seen) <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>y</mi></mrow><mrow><mo>d</mo><mi>x</mi></mrow></mfrac><mo>=</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn><mo>.</mo><mn>6</mn><mi>x</mi></math> <em><strong>A1</strong></em></p>
<p><strong><br></strong><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>0</mn><mo>.</mo><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn><mo>.</mo><mn>6</mn><mi>x</mi><mo>=</mo><mn>0</mn></math> <em><strong>M1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>5</mn><mo>.</mo><mn>33</mn><mo> </mo><mfenced><mrow><mn>5</mn><mo>.</mo><mn>33333</mn><mo>…</mo><mo>,</mo><mo> </mo><mfrac><mn>16</mn><mn>3</mn></mfrac></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>×</mo><mn>5</mn><mo>.</mo><mn>33333</mn><msup><mo>…</mo><mn>3</mn></msup><mo>+</mo><mn>0</mn><mo>.</mo><mn>8</mn><mo>×</mo><mn>5</mn><mo>.</mo><mn>33333</mn><msup><mo>…</mo><mn>2</mn></msup></math> <em><strong>(M1)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>M1</strong></em> for substituting their zero for <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>y</mi></mrow><mrow><mo>d</mo><mi>x</mi></mrow></mfrac><mo> </mo><mfenced><mrow><mn>5</mn><mo>.</mo><mn>333</mn><mo>…</mo></mrow></mfenced></math> into <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>59</mn><mo> </mo><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><mfenced><mrow><mn>7</mn><mo>.</mo><mn>58519</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M0A0M0A0</strong></em> for an unsupported <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>59</mn></math>. <br>Award at most <em><strong>M0A0M1A0</strong></em> if only the last two lines in the solution are seen. <br>Award at most <em><strong>M1A0M1A1</strong></em> if their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>5</mn><mo>.</mo><mn>33</mn></math> is not seen.</p>
<p><strong><br></strong><em><strong>[6 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>2</mn><mfenced><mrow><mfenced><mrow><mn>2</mn><mo>.</mo><mn>4</mn><mo>+</mo><mn>0</mn></mrow></mfenced><mo>+</mo><mn>2</mn><mfenced><mrow><mn>6</mn><mo>.</mo><mn>4</mn><mo>+</mo><mn>7</mn><mo>.</mo><mn>2</mn></mrow></mfenced></mrow></mfenced></math> <em><strong>(A1)(M1)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>A1</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>2</mn></math> seen. Award <em><strong>M1</strong></em> for correct substitution into the trapezoidal rule (the zero can be omitted in working).</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>29</mn><mo>.</mo><mn>6</mn><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup></math> <em><strong>A1</strong></em></p>
<p><strong><br></strong><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><msubsup><mo>∫</mo><mn>2</mn><mn>8</mn></msubsup><mo>-</mo><mn>0</mn><mo>.</mo><mn>1</mn><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>0</mn><mo>.</mo><mn>8</mn><msup><mi>x</mi><mn>2</mn></msup><mo> </mo><mo>d</mo><mi>x</mi></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><msubsup><mo>∫</mo><mn>2</mn><mn>8</mn></msubsup><mi>y</mi><mo> </mo><mo>d</mo><mi>x</mi></math> <em><strong>A1A1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>A1</strong></em> for a correct integral, <em><strong>A</strong><strong>1</strong></em> for correct limits in the correct location. Award at most <em><strong>A0A1</strong></em> if <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>d</mtext><mi>x</mi></math> is omitted.</p>
<p><strong><br></strong><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mn>32</mn><mo>.</mo><mn>4</mn><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup></math> <em><strong>A2</strong></em></p>
<p><strong><br>Note:</strong> As per the marking instructions, <em><strong>FT</strong></em> from their integral in part (c)(i). Award at most <em><strong>A1FTA0</strong></em> if their area is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>></mo><mn>48</mn></math>, this is outside the constraints of the question (a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>×</mo><mn>8</mn></math> rectangle).</p>
<p><strong><br></strong><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Hyungmin designs a concrete bird bath. The bird bath is supported by a pedestal. This is shown in the diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAfsAAAFWCAYAAABuCTTiAAAgAElEQVR4Ae2d+3MUZ3rv859AFT9BFXXWJ9mE7IVNqlLnsOQcytmqOD7ZX5LY1NpJNsfJyWYv4uBcnLUNWJi7DQjJ3MGGGe43wSCuQkJIAiEJgcXNQrvHpFxYlTiUS/Wc+r4zz+hVq3ume6Znpi/frpKmpy9vv+/n6env+zzvpX9DuJAACZAACZAACSSawG8kunQsHAmQAAmQAAmQgFDseROQAAmQAAmQQMIJUOwTbmAWjwRIgARIgAQo9rwHSIAESIAESCDhBCj2CTcwi0cCJEACJEACFHveAyRAAiRAAiSQcAIU+4QbmMUjARIgARIgAYo97wESIAESIAESSDgBin3CDczikQAJNIDA1z2y+huzZc6s78vqngkR+VrGMz+WObNmy5xXMjLegCzF/5KTMjHSIQebm2StYVqiRBMjkjvQLH+zpke+LnFYNHfV5l6h2EfT2swVCZBAnAlQ7MO33gymXpeYkJ7m75uK1W82U+yVEsVeSfCTBEiABMIi4FuYwrpgCtLxzZRi73Y3UOzdqHAbCZAACfgm8ExG2tfK0rkI28+W+a+slbOD7T7D+NPPzZ/fLNmecZksXh/h69Oy+pUF+WaARU2yo2dEup3e63hGlqKZ4BtvSfb0W7IY67N+KG0jX4mIIw3sm/uqrM70yHjhQl/3NMtvmvNXSm7Qvt5yyY48E5kYkbPNr8p8k+4SWba9q3huMavFlceSfeUFmTPrBVl6oFN6Ms0Wn03SPf68eKRZKYTdleGcWUtkWWtORiYKmdOymWvnOc/5RrP0zIjR63ULx5jjtSkFV3omI7n9UyxnzZPFTa2SQ/lKLchfa1OBKdL2OG9yfFpZ58xaIEubT0+Vw1yjnM29wviwYU7ampbk7wOvPHiUg2LvAYabSYAESKA8gecylnmjIIC2wOi6Co3bA7zEuXPfkOxYXhAnxzLyeqEiYdr8IWBzX5alf5YX/2Ko2k0Q5y6X3LNJcU3DCOECeT3z0FQsimJvC6quL3pDlmllQ7fNWijLcp97IHITXWUyW+YsaZURrc1MDEjbjLQLxy5aKz0QfLeyBRb7ZzLc+pqHrX4gq3u+8CjLF9LT/IOCwFplAAfNnznT+7j5r2VkzJTXj83d7hXxtuHc16RtuExlRYRz43tYl5tJgARIoDyBZzlZZoR4nixe3p73dCfHpXuNesAlxH5yWNqWzJM5s6aEZkqU9byvZKT1hwWP/i3JGY/4uYzn1HOfLTPFfp4sbu4SdAucnJiQfxdNY2q7TD6U7GvTKwtTYr9AlrYOyASiAT1ri97s/Fd2yDCEd6JLVi9Cvq1rzyBlif2iQmRAbKH7sWTH4ZZr3lCBmRKtyfF2edNcw8pzlWH8yZFWedFUVLR8ADQmueUFT3macFsFKl7XqtwUGcyTF1uHTWVpKv0l8mZuLL+tWI7Cub5s7ib2n0uuaaGYSIGxDfI3VXmZ35STcnJPz96yKVdJgARIIAiBqQe8ilfh7GIlQEXb7QFeOBah38MZyWZaZFlBROeo11wUhylRyZ+lD39LcIver4bunSV5LuM9JySbOWCFgmeLCkVR7AvRAHO2m9CJnzZxFXtHvot5LPDyLN+kPMstz3vh6sEX86JMneXT7275syoVdlQBp8ywlaZT+LQqRvmw/F7JZjJyZFpTSwn7OpIzX0vZ3G3kRrHsjsiCRllsm7ldj569BxVuJgESIAEfBFwFEucVH84qTG5iMOWZFcPz+vDWIXvFdCyv0uTLRdBUSGc8+CdlYnhHsc3ceS2NDBTLouLqWg5sdLm2yZP9T8X+BVmaeTy1o1iegtgXvysn+9BCH4JZ5Y+dOgtrbvlz21Y4q5gHR16tRCfHu2RHsa3cEtxi1GIq/dJDK33Y3E3s1bbF+8PKg9nmqGxaeddVevZKgp8kQAIkEJDAlGfv8KZneIszxX7qXHRGO5D3FIvCUxA/T8+3hGdvizXKY6WxuKlFsofRKW9KnBoq9lbeNByeN0GEPPtp9wQ6+B2WbGbvVCc/Eymw7OuMHFjn+7K5m9jPuJ+sRH2uUux9guJhJEACJDCDgCVWwdrsLTErdsaz2+LV07XCz4t8ttk7xb4oFFOd8abaxKeaARri2cegzX6qH8VUW7zY/Q8K4m4LubbZS7HzIZozBuULbZooaXOr4lCcgGmqclfsO2H1N9CmmBn3p7WBYm/B4CoJkAAJBCNgdzpzhlbxXUV75gN8SkTs8xbK4kUYsjYVtnc9rlRvfKfYT2tz1mvNk/+26A9Mm7gKRWPEHlH3qQ5/ziaGab3dixWrQhmc5SwazqogmRC32sC7t7zdSbKYTHGl1HlTFSiREscVKmqutpzltPnMe8UMnfRqirE6Nhaz7LJCsXeBwk0kQAIk4J/A9HHT/sfZo8PcrqlOeWb8/GMZK0yrqyLsHCNv0h8ZmzlLnLbruojg9Dbnwhj5scK4/EIbf8PEHqDLjbM3xngu412bpvoeePWeR8vF+BVZWxzONzXaoeJx9mZ8fuuUrVCJWNQkbbkRM+qheK+4jrPPSE9xXgE/NncTe1zBOc6+MKdDuTkCCpmj2BetxBUSIAESiBqBqbb1OcXQr+0Ne3cqi1pJmJ/GEqDYN5Y/r04CJEACJQhMH+s+I8xtVwBKpMJdJECx5z1AAiRAApEmgNBvZqr3t2mH9piuNdLlYOYaSYBi30j6vDYJkAAJkAAJ1IEAxb4OkHkJEiABEiABEmgkAYp9I+nz2iRAAiRAAiRQBwIU+zpA5iVIgARIgARIoJEEKPaNpM9rkwAJkAAJkEAdCFDs6wCZlyABEiABEiCBRhKg2DeSfkKv/W//9m8yMjJS1R/S4EICJEACJBAOAYp9OBwbnsp//Md/uIrrmTNnzLuX8f5l+2/Txk3S9ItflPybMYGHGd+rc2tH97NcuXbu2DGNhXK5cuWKK8OGG5cZIAESIIEqCVDsqwQY1ulOb1gFSD+dAvb73/ue+BHjl196yVPQNW2vz0q9888++6xqLEijkuv39fW5CrldRidL/e6XKY7Tc/TTTh8VLDvvqIhxIQESIIFGEqDY14i+Ld62d63igM9S4vKXr78+TVCc3qibF1qjoqQ6WbeICdjb4g7b2HZFBcurImZXFFa8+24xHbuCwCaMVN9yLDwJ1IQAxT4gVvvhrw98PLTxsIdAuz3kbe/aFm1bsMPwhgMWhYfXiYDt5dsVP7spxavip5UIHKv3m6bHiEGdDMjLkEACCFDsHUZUj1y9N30gu3lr6n3bHpo+iCneDrD86puA3kN2k4RWKEvdh1oh0EokKwO+kfNAEkg8gVSKvQq6elluXrmGW1XI7TBr4u8KFjDyBNwiTBoFcEaXtFKKyIDex6wIRN7EzCAJhEog0WKvoo6HnHro9oNQw+saWodHRY881PuLiTWQAO5njQ7o/W83F2iFFvc/KwENNBQvTQJ1IJAYsYdII3ypnaXshxo8Hg1xUtDrcFfxEpEnYFcEEL2y+5toJQCVZFQW2GEw8uZkBkmgLIFYij0ePngIqbCrt66euj6k6KWXtT8PIIFpBLTSjN8QKslaaXZWANgMMA0bv5BA5AnEQuwh7vDa4Z3bHZTwMFJh58Mn8vcaMxhTAqUq1/hN4rdJ7z+mxmW2U0MgkmIP4Ybnbos7PAuEG9G2SI89NfcnCxpRAmgGUO9fI2toCkC0Db9dLiRAAtEiEBmxh8DDQ4Cg2w8PPFAo7tG6aZibWhB4LNlXXsjf+3OXS+7ZVzLes0uWLZon85ty8qwWlwwxTYg/hF7b/lE5R2Wdwh8iZCZFAlUQaLjY4yGBh4IKPMQeos+wfBVW5akxJfC55JoWyvymdhnr2SVr20/LtiUL5fXMQ5mMUYkQ0kcEzin8rLTHyIjMauIINEzsIeja/o6HAh4OFPjE3V8sUBACz3KybO48WfzTJlm2pksmgpwb0WMh/IjO6W8d/WxQwedCAiRQXwJ1F3uE9fSHD4+eP/z6GpxXiy6ByZFWeRFvFly0Vnom4uTL+2OK3z7EHlE8ir4/ZjyKBMIiUDexh9eu7fH4ZO/dsEzIdJJB4CsZaf2hzJm1UJblPk9GkTxKgQq+ij7a+bmQAAnUnkBdxB5Cj1A9Ou3Qk6+9UXmFOBLIt9fPWdIqI8lz6l0NgqY77cjnegA3kgAJhEagLmKPWjzEnm3yodmNCSWNQKG9/sXW4Vh1xqvWDOi0B8Gnh18tSZ5PAqUJ1Fzs0U6HHzPD9qUNwb3pJpBvr09+CN/Nyoj2oR2fzwg3OtxGAuEQqLnY68Qb4WSXqZAACSSRgI7ISWLZWCYSiAIBin0UrJCyPOicCn4+gcbtuFLI3I63t/HcKQI2F6/1qaOnr3kdb2+ffsbUN/sYXUcbPhcSIIHaEKi52COMjx8zO+bVxoBxTBX3g5/F73F+0uIx0SUAkYetGcaPro2Ys/gTqLnYAxE66H3vu9/ltLfxv19CKYFfEfd7XCiZYiINIYDJtWDnttbWhlyfFyWBtBCoi9ijFz466X3nW98yM+WlBS7L6U7Ar4j7Pc79KtwadQLozwMbv/E3/5sjdaJuLOYv9gTqIvZK6f/83d+ZH/fPf/YzhvUVSgo//Yq43+NSiDDWRdapslH53759e6zLwsyTQFwI1FXsAWVgYED+8Pvfz4v+T3/Gt2LF5U4JMZ9+RdzvcSFmjUnVkICKPOz6i5//XMbGxmp4NSZNAiRgE6i72OvF9+/fL7/zzW8a0X/pj//YTKrBDjpKJ9mffkXc73HJphXv0mHSHEyY83sLv2d+6//rT16W7u7ueBeKuSeBGBJomNiDFdry/+kf/9E8BNCmj4e7jrfl6zBjeDf5zLJfEfd7nM/L8rA6EVCB1xde/c8//B/yO7/1Tdm/b1+dcsDLkAAJOAnUROwRrkPnG/3DsDv7z5kJfRMe2vAg/vqQwCfejIf9nGrXSS2+3/2KuN/j4ksiGTlHRA6/efxWtdL+2o9+JD/9yT+YCjxG47DyngxbsxTxJVAzsceD2u0PP3y3BWKOcB/OwTFo28f4W6xrOvD6cQzEnyF/N4rx2AZ7+ln8HucnLR4THgFb3LViDlvhbZb4zSJMj+0Qfk6UEx53pkQC1RCoidgjQ/ZDQMUaP/5yIo0IgNuDAtt16l1ND8fpAwb7ucSDgNrPz2c8SpTcXKISrr89/NbUc4ftUBHHb1J/e3aFna+xTu49wZLFk0DNxB5hPefDPMibrfAQwfnw5t1CgHjAwGvAQ8WuWGgFQB9C5SoX8TQbc00C4RPA7wxRM/x2nL8r/A4Rpsdvzu33iPNQEcAf1rmQAAlEi0DNxB7FtEX4+/99UeCwHh4qGsbHA6jU4vRA8HCyKxtIBw8rrQS4PbBKpc994RGAXbg0joAt6vhN6G9Mfy+2sKvX7pVbVKZRMcC5SAu/Qy4kQALRI1BTsbe9ezxg8ODAgwR/QcQW3gQ8BlQeyj18nIhxHe0wiIeSsxKA7xqOZEXASa823yn2teFqp4rfCf5wTyOihnvcrnzDBrj38ZvAMfDGg/wmca1qfpd2XrlOAiRQewI1FXtkHw8YPEzsBd/xsHFut49xrsODUA8ED69qPQitfCAPXg9DVDBwTX0g4lh9iDrzx+/+CVDs/bNyO1KjWCrmuC9xn+rvA3z1z67MQpxxTrVNW2H/Ft3KyG0kQALhEqi52OPh4ibMEFs8nIJ66/VoG8TDDPnWiICGOp2eER6o2OasEOA8nI8/LjMJUOxnMsEWW8T13rOF3O3+UzHHPYpj9d6rVtDdcyjmGrAfrhs0EuCVJreTAAnUnkDNxb5cETQUGMRbx0NR2wnx6VaZKHfdavbbD2U8YPGnFQI370q9LOzTPz0Pn1oxwGetHtLVlDfsc9Mi9lpphF1RSbVtrveB1/2iUSXsx28D56pn3ohKJIQdAg/bIS9cSIAE4kWg4WIPXHgoQrThuQTpyYuHHs7BgxEPwqgtdqXA9tTsioE+QLVC4PxUz03FQR/8KhzqyYGF/kW9whAHsddmHmWKT9xjyh2f2vyjtilnSz3OFnCkg3ter1Pvimu53wzyg3LCZsh31O+tcuXhfhJIK4FIiL3C1xB9EG89aQ8jW2Sc3iCEwRYMrKOi46wgeH13VhzstJyVCFvU7HW3yoUKld9P5M/vsaWOsytQdh6d63blyi4z1t1C4178cKzzfOe17PzGPcyNskS5Mq3PDX6SAAmUJxApsUd2Id54OAf11vFggpjhPDyA07zYFQZbfJyeqS1UqGA5hczte5DKhZdohrW9VOXFzjvuJ7us9rodGrdZpdmD1d8g7BSk4p3m3xzLTgJRJxA5sVdg6lXgoR3kwYsHOR5SEIK4e1bKgp8kUC8CGl1DpQ7rXEiABJJBILJiD7waog/qraNygEoCRB/haaTDhQRIwJsAfzPebLiHBJJAINJir4DhocNTD+qtI0SLigLaHREp4EICJDCTAH8nM5lwCwkkjUAsxF6ha4gen369dXgsaHeEl4+2W7/n6TX5SQJJJYBKtEbAgvymksqD5SKBJBOIldjDEBpuDOqtsy0yybcxyxaUgFacg0bLgl6Hx5MACUSDQOzEXrFp6DGItw6vHsdrL2NUHLiQQJoIoDkLAh+0H0yaGLGsJJBEArEVexgD4o0QfdCew9rTH+eh0sClvgRQ2eJSXwL4rXBynPoy59VIIEoEYi32ClJD9BB+v946Hn4aygw6vE+vy8/KCFDsK+NW6Vl25RYTEXEhARJIH4FEiD3Mpp5LUG9de/pDgCD+XGpPgGJfe8a4gka+wJuT49SHOa9CAlElkBixV8DqxQT11iH0qCigPRNpcKkdAYp97dhqyvDgcT+jIysnx1Eq/CSB9BJInNjDlHaIPoi3rj39IUacjKd2PwqKfe3Y8h6uHVumTAJxJpBIsVeDaIg+qLeuPf2DDu/T6/KzNAGKfWk+le7lfVspOZ5HAsknkGixV/PpQzCIt872TqUX/ifFPlymWqkF1yCRrHBzwdRIgASiTCAVYg8DaHgzqLeO9k6cg/ZPtn2GcytT7MPhiFQg7uDJyXHCY8qUSCCJBFIj9mo87bgUpHey9vTHQzVoxz+9Lj9JIEwC2hE16OiTMPPAtEiABOJDIHViD9NoiD6ot84HbHxu7KTmlBXPpFqW5SKB2hJIpdgrUg3RB/XWGTpVgvysJwG9X4NWUuuZR16LBEggmgRSLfYwiXpKQcOh7BTlvKEnpKf5+6b9eM7c5ZJ7Nuk8gN8rJKCRKDQjBWl+qvByPI0ESCCBBFIv9mpThOjRySloRyft6R+0459eN1mfz2Us84bMX9IqI9T6UEyrfUx4f4WCk4mQQGoJUOwdptcQfZAhTNrTH55XkOF9jksn4Otjyb6yQF5sHRZqfXXm5D1VHT+eTQIkMJ0AxX46D/MNIXq04wf1ptCmiuYAnJfKYXrPcrJs7kJZlvvcherUJlSKuHgTQEUT91HQyaC8U+QeEiCBtBOg2Je4AzREH8RbT3P76uRIq7w468eSHf+6BFUx7folD0jpznr0A8nb6IfSNvKVN+XJYWlbMk/mN+XkmfdR7ntMhW9eiejOVzLS+kOZE0pTz6RMjJyW1cv3FpuN8uUrX+F0zzy3kkByCVDsy9hWw6lBvfX0DdP7WsYzPy48xJ/LeM8uWbZonsyZNVNY6NlPv+lQQdTmI0SUIPq1WnyJfTUXr6vYfy65poXTKg4U+2qMx3OTTIBi79O6GqIP0htae/pD3IIO7/OZrQgdln/wzm9ql7Ge9bK0KSMjIwdk6ayZXhbFfsps9a4UUuyn2HONBNJEgGIfwNoaokd7KnpJ+120pz/OC9Lxz2/6kTjOhH4XyJ+veEf+5q8zMjYp8nVPs/wmPXtX89gVQVQgEUGqx5IX+5dldSYjq19ZUBgq+aqsbh+RCc2AM4xf8NYXN60vnpMP8SOC40hnf7MsnesnjL9SsqfXytK5s00e5r+yVs6OTG80mBzvkWzzqzJ/Vv6YObOWyLLWnIxMoPtnwasv7stXKvPlWyBLm1uLeZ0zC99PF87TQvKTBNJFgGJfgb3VGwvqrWuoNujwvgqyWPdT8g/Z2TJn7huSHXsuIt5ts2n37DVKhMpfvTtyTtnpVVnbNS6TgnbvjCxb9IIsbu7KC76r2MO2r0nb8DORyV/LyKdfyETPWlkMAc4M58+bGJZs0xKZM8uH2M+aLfNf2STd47hXnslIZrksnvUDWd3zRf7eneiS1YsWytI1V2S8MLRjcrxd3rTzqYJvtf8Xy7douWQLlYeZ59X958ELkkDDCVDsKzSBemZBvXXtAwDBg/gjnfgvk/Ist1zmz1ogr2ce5ofdOQXDKmRaxV4jQyj/po2bGmJ79XyLdjJ2KdhPJ0Ny2s549rMdHfa02cbRic9vm32xUqg3hp2eIz96yIwKZMG7nyH2zqYj74pnMWmukEDCCVDsqzSw9qAO6q1rT/+gw/uqzG6NTi/Mnmc9dMU89J0P3fzl0yj2UbF3XuxndprMby/Yy4/Ye4m6OfeFCnrjFwRZKxzmVkHUocNUirOZA9JmogazrQ55AcV+Wto1+ikwWRKIKAGKfUiG0RB9EG8dXj7aaxvp6YVS/BkPePX0X5O2zA5p09BsKBeLVyIayXn55T+VRv3ZxMIS+3w6LuH6GfeCfXWse3nZDrGfGJA206dgnixuaskLfq5fejBsryjaFHsnXX4nAS8CFHsvMhVsLz7YX3pJ0K7vd2lkG67fPJY8boYXXxiGZ7fnlkwgmTu1Ahg06lNLGmGJfT5yUyux//f8WHyPUD/FvpZ3CNNOKgGKfQ0sqyHboJPxoB0XXn49e2fXoPipT1KbdmBLCH6Ulmnh+mLGHG3kfsL4hc5xMybe8QrvF6/l8OCL2+02+5keuzls8qFkX1tAz77IjCsk4J8Axd4/q0BHaog+aI9r7emP81Bp4BIfAtppEyIfdKRGvUqZF/vZMqfYW31SJoZ3yNK5JTpXGgF3dtATmRzLyOtzF8jS1oEKeuMjPJ8pDId7JsOtr8n8oievzUBL5M3cWKHD57h0rykMwyuG8e0mga9kYuJrca/MeFUw6kWd1yGBxhOg2NfYBhqiD+KtQzQ0BBxV0agxttglH5dKWl4MKxlnP1PsxQzbO22NZ18iyw7sl9VL/HTQKzPOfnJcerY3yWIdRz/3VVl9ICfdmSaZXxR7kfywOszUmG9S+NpM2ezsGEqxj90PihkOnQDFPnSkMxNUjy+otx7lcPDMUqZzC2xrN7/gOxcSIAESiBoBir3TIoWQJUKx+T/nMCV73vcF0yb9cCbl/K7eX1BvHV4+KgpJeQsauCZh0ahN0KaaJJSdZSABEogXAYr9NHs9l7HMG9b0nPaYXhw4mZ81bNFbksPMX5Njklv+g6mZx6al5f7FDtEH6bylPf0hlEE6/rnnorFb4y722h8jCbZo7J3Aq5MACdSLAMXeJo0pOpf8s+SeFebntPdh3fRS/oPp72s3kQCn9+88ceZ3DdEHHZalPf3jPBlPnMU+Cfxn3o3cQgIkkHQCFPuihbUHcGESj5z1YpDCMfnOTU5hxzChPygxY1jxAq4rGqIP4q0jOqCT8eAzbu3EcRR7VM7Q/IK8w2ZxY+5683EjCZBAaghQ7NXUhbHFeJjn/+yhQTjIq0evx5hgTdfHp4bog3rrcW0zjpvYQ9yR56BRGB+m5yEkQAIkUBcCFHsnZgz5Odwiyxblh/MU3wTm8oat/KnVi71mAa/NRWevIN46PExEBSBGQTv+6XXr/RkXsUeHSgg8bBKkf0W9efJ6JEACJFCOAMXei5DpfLek5Gxd+VPDE3ukpyH6oD28tac/zov6ZDxRF/s4VqC8bmNuJwESIAEQoNiXug9M5zudoKN2YXy3LCBEj7B+UG89DiHnKIu9XWlCpIULCZAACSSBAMW+lBVNO/6fSdvIV+Yo00HPmr0rv3FY2krOGFbqAqX3qYcZ1FvXnv4QVYafSzPWvRpRAbMgzSh6Pj9JgARIIMoEKPalrPMsJ28uz8kzPSbEoXeapJ9P9Tbh5UPI/S4cJuaPlHZ0RCQF61xIgARIIGkEKPYFi06O98iRwz0yXhhiPzl+RdY2NecnzylavfpJdYpJVbCiIfog3rr29IfHGmR4XwXZi90pZBM7kzHDJEACFRKg2BfATb1QY7bMMS/d6Ci8kctJ9rmMd22SpXMxRG+JLNveVawgOI+sxXcd7x10mJ729Kf3mrcKox61uDuZJgmQQFQJUOyjapky+VKxCuKts11aTDMIhtOxP0OZG4y7SYAEEkWAYh9jc2oYOqi3rn0A0PEvTT3OtRmEk+PE+KZn1kmABCoiQLGvCFu0TtIOZkF6kWtPf3i4QYf3VVt6XLOei125ifocBPXkwmuRAAmkhwDFPiG21hB9UG8dQljvWeLqJfaNrNAk5LZiMUiABBJCgGKfEENqMdSLDeqt1zPEXQ+x10mJglZ+lCM/SYAESCBJBCj2SbJmoSzq0VYyGQ8qCRBjiD/SqcVSS7HXCAeuEaRZoxblZJokQAIkEBUCFPuoWKIG+dAQfdAOadrTP+jwPr9FqJXY28MLUXYuJEACJEACeQIU+xTcCRqiD+Kto6c/PGMIc5DhfX5whi32OiqhFnn1Ux4eQwIkQAJRJ0Cxj7qFQsqfCmJQb117+qNJIKypZMMUe1RgkDdEL+jNh3SzMBkSIIHEEaDYJ86kpQukIfog3jrawTdt3GS8fHj7qDhUs4Qh9nzZTzUW4LkkQAJpI0CxT5vFRYxYQ7SDeuva0z9ox78wEaPioc0SQV8MFGY+mBYJkAAJxIkAxT5O1go5rxqiD9JrHWKLqAC886DD+6rNfhQqG9WWgeeTAAmQQCMIUOwbQT1C19QQfVBvvZ5h9EZWMCJkKmaFBEiABComQLGvGF2yTlSvOai3/pOf/IMs+OZvmw5yqACEvSD68HsLF8pv/9Y3ZefOXU7x5soAACAASURBVGEnz/RIgARIIBUEKPapMLO/Qtrt4WgX97Ps2btPVq5qlh/96EehDtNDXnTo3y9+0ST/d/k/SmfnNT9Z4jEkQAIkQAIOAhR7BxB+nXoNrJ/JeCD2W7Zuk3v3RmXH9p2y8NvfkT/545eqGgZnRgws/J780Yt/JOfOnTdp/9M/v0Wx581JAiRAAhUSoNhXCC4Np+kY9lLD9Gyx//TT+zI4OCxNv1hWHKYHD925eA2907kAsH/NmrUyNHRHRkcfUOydAPmdBEiABAISoNgHBJa2w1WAvSbjcYo9xPn+/Ydy4vhJ+e63vyO/v3DmZDxuYq/D6f7iz/9COju7TBpIh2KftjuO5SUBEqgFAYp9LagmME2djAeT69jeupfYQ6iHh0dk3dp1M4bp2WJv9+rf1tIqDx8+lgcPHlHsE3gPsUgkQAKNI0Cxbxz72F1ZO83Zk/GUEnuINsT7QsdF+cGLfyS/t/B7gkoDxB5p6Xj9v33jb+XWrdvy6NFnFPvY3RXMMAmQQBwIUOzjYKWI5RHD4RDWxzC9rS0txQ56aLNH2B1D5NDermIPEX/8eExaW9uM0EPs/+Sll+R73/2u7Nu7Tz777InZT7GPmKGZHRIggcQQoNgnxpT1LYh65v/1v3xD/v7vf2I60UHsr17pNIK+efOWGWIPUe/puSGv/sUr8ubyN2VwcEjGxp5Q7OtrOl6NBEgghQQo9ik0ephFfq95tXznW9+Wv/rLv5IrV67KX//VXxux//bvfsu02SOMr549xB7iPj7+K/P35Mm4b7F/592VcvLU6TCzzrRIgARIIDUEKPapMXVtCrpz124Txv/ggw+LIXqE6fG3ZfNW0wYfhthjLD/6B3AhARIgARIIToBiH5wZz7AIrFu/UT7avlN6enrld775zWmC/53f/ZbcuXM3FM+eYm9B5yoJkAAJBCRAsQ8IjIdPJ4CZ7Q4fOSY/++nPpgm9eveYHCcsz3737r3TL85vJEACJEACvghQ7H1h4kFeBCD2a9etdxV6FfybNwdMb/tq2uzh2aPJgAsJkAAJkEBwAhT74Mx4hkVAPXvMja9D73K5DsHf+fMXpKPjgoQl9mgy4EICJEACJBCcAMU+ODOeYRFwE3vMnoc/5zj7ajx7NBXgWlxIgARIgASCE6DYB2fGMwoExsbGjABfuHi5OM5e58an2PM2IQESIIHoEKDYR8cWscuJin3ntS6KfeysxwyTAAmkiQDFPk3WDrms9RT7s+fOmyjC06dPQy4FkyMBEiCB5BOg2CffxjUrYW9fnxHg/psDNffsET1Amz0qGFxIgARIgASCEaDYB+PFoy0CnZ3XjADfvTdKsbe4cJUESIAEokaAYh81i8QoP+c7Ouom9oNDd8y1UMHgQgIkQAIkEIwAxT4YLx5tEcBc9Rs2bJJ6ePa4BsL4FHvLAFwlARIgAZ8EKPY+QfGwmQTMS3C2tNRN7N95ZwXffDfTDNxCAiRAAmUJUOzLIuIBXgRWrHxP9uzZVzexx5S5nB/fyxrcTgIkQALeBCj23my4pwwBM3ve4aN1FXtOmVvGKNxNAiRAAi4EKPYuULipPAGMd4fYnzh5um5izylzy9uFR5AACZCAGwGKvRsVbitLQCfUuXr1Wt3F/ssvvyybPx5AAiRAAiQwRYBiP8WCawEIFCfU6b9VN7Hv7OTEOgFMxENJgARIoEiAYl9EwZUgBHRCnZGRe3UT+56eXtN0gIoGFxIgARIgAf8EKPb+WfFIi8CePXtl/YZNUk+xv3v3U461t2zAVRIgARLwS4Bi75cUj5tGAL3iN29pqbvYYxIfVDS4kAAJkAAJ+CdAsffPikdaBNAT/9Dho3UX+y1bWoTD7yxDcJUESIAEfBCg2PuAxEOmE9Ce+O3t5+ou9ocPHzWh/Ok54jcSIAESIIFSBCj2pehwnyuBoaEhI7jd3T11F/sLFy6Za/NVt66m4UYSIAEScCVAsXfFwo2lCOjb7u7cuVt3sb9+/YYRe/bIL2Uh7iMBEiCB6QQo9tN58JsPArt27zWd8xoh9uj9j/4CJ0+d9pFTHkICJEACJAACFHveB4EJQGw//uSgNErsMQpga0tr4HzzBBIgARJIKwGKfVotX2G5dU78M+3nGib2n3xy0Hj3FRaBp5EACZBA6ghQ7FNn8uoKrNPkdnX3NEzsOzouspNedWbk2SRAAikjQLFPmcGrLS7ayt9+Z4UM37nbMLHv67tpxB5T9nIhARIgARIoT4BiX54Rj7AIYEKbto92NFTs0VegefUazqRn2YWrJEACJFCKAMW+FB3um0YAr5ZF57xjx082XOx379nHdvtp1uEXEiABEvAmQLH3ZsM9DgLaXn+t63rDxR4dBFHx4OQ6DiPxKwmQAAm4EKDYu0DhJncCmewh014/NDzScLHvLbTbY4IfLiRAAiRAAqUJUOxL8+Fei8CKlasEE+pEQezRQRCv2N3ass3KYdJXP5dc00KZs6RVRibDLOukTIycltXL9wZLd3JY2pa8IC+2Dkuo2QmzaEyLBEjAEKDY80bwRWB0dNSEzU+fORsZscfEPgjloy9BOpZaiX2F6VLs03HbsZSJIECxT4QZa18IDLmDsN68ORAZsUffAeQpPfPkVyjKZW+PCtOl2JclywNIICoEKPZRsUTE84EQfmvbdhkauhMZsUdzQnPz+9KyLSJT5z7LybK58+TFlna5tuZVmT9rtsyZNU8WN+2SnvHn0yw8Od4lO5qWyJziMa2SG3nmOKZHss2azgJZ2twqq19Z4AjjP5fxnl2ybNG8QlpLZFlrTkYmrMD6xIjkWptksbkW8mQfUxD64r6Fsiz3ucnH5Lh9fed5IkKxn2YvfiGBKBOg2EfZOhHJWzGEf7o9cmL/8ccHohPKN2IPUVwgS9dckXHo7cSwZCHqi9ZKT0GAJ8cy8vpc6xh5JsOtr8n8uW9IdqxQKZjoktWLXpDFTZmCcD+TkczyvGAX2+yfy1jmDZk/91VZ2zWebzefGJC2VxbI/NcyMmb0/gvpaf6BzH9lhwzr9cfb5c1Fdlu7i2dvrr9wqhzQ9sJ5i5u7ZAL3JsU+Ir9QZoMEyhOg2JdnlPojTpw8ZXrhmxB+xDz7Gzf6jNhHYja9gthPCW3h1jHb1WN2EVZzWH77/KacPJNJeZZbLvPnLpfcM8tDF8e5GklwdpCzr+dLkB3pel7/Kxlp/eFUZMFX2qn/+RAACUSCAMU+EmaIbiaeP39uxHTnrj0yODgcOc8ezQrr12+Ul1/+04b8TbOcl/gaUZwnRsjNMbPz69NOLgipEfhfe/S6t8W2UCGYpZUIKzH7epL37OfMbZJsV06yuZG8V24dLs5KRHEfeul3SDaTkWzmgLRps4NGFij2RVJcIYGoE6DYR91CDc4fPGZ0grva2RVZsT99ut3kEc0NDV3KiL0ZMvcF2vUR6vf4g9h/MShtS+ZNedDFQrmJvUc6s+wKxTMZyWWmxNr0I7D7CDg9ezQ/5JsD8n0OWvKCn+uXHnj2GnGg2BctwxUSiDoBin3ULdTg/K1bv0EwH/7tweHIij0iDng5z67dexpLq4zYT3n288qMTXcRX1MyN7H/obSNfBWg3OjQl8l39FPRnuHZa5TB6kNgrlDIl55HsQ/AnYeSQGMJUOwbyz/SVx8aGjIe88lTZyIv9pnsYZPXp0+fNo6pV4jebNdwe14wZ7Tra7jdhMiDtNkvkNczD6dPalPo3Oc92Y02AWhFwVm5cH4vIJ18KNnXFtCzb9wdxiuTQMUEKPYVo0v+ies3bJT3mt+XgdtDkRf76z29RuxPnDjVOMMUxN4MbcsM59vGZ/SOF3HrjZ/vaf8DWd3zRT7/BWGd6kXvtze+o/d/wfue6tU/NUJgqsJhRwy+komJ5/kOgrOWyJu5sXxFYnJcunU4IT37xt1jvDIJVEiAYl8huKSfhhfMoK3+yNHjsRB7NDOgEyHy3LAZ9Qph/MVNLXJw2vj409PHvQs6vuWsNvTZMv+VZsn2FIbP6c01MSJni+nkx+tnm192tOWjPb7VGmeP8fiZaeP6Z46XdzsGw/EwVr/QxDA5Lj3brbH5c1+V1Qdy0p1pmholwDC+WoqfJBB5AhT7yJuoMRlE+zfawfv6bsZG7Luv3zBij9n+GrIUxN47fN6QXPGiJEACJCAUe94EMwioV3/wYFYGBgZjI/Zobti5c3fjvHuK/Yx7iRtIgASiQYBiHw07RCoX6tX39vbHTuy7u3sa591T7CN1HzMzJEACUwQo9lMsuCYi6tUfOJiVW7dux07sEYnY0UjvnncRCZAACUSQAMU+gkZpZJbUq7/R2x9bsde34Z04cbKRKHltEiABEogMAYp9ZEzR+IzouHp49Tdv3Y6t2CPvO3bsalzbfeNNyRyQAAmQwDQCFPtpONL9BXPMowd+z42+2It957VuI/aZTDbdRmXpSYAESECEvfF5F+QJqFd//PhJ6b85EHuxRxm2F7x79EPgQgIkQAJpJkDPPs3Wt8qOOfBXvbfajKtPithjVj1EKnbv2WuVlKskQAIkkD4CFPv02XxGifXNdseOn0yU2Pf135JPPjlowvn07meYnRtIgARSRIBinyJjuxUV76tfsfI9Wbtug/T23Uyc2F+/fsN49y0trW7F5zYSIAESSAUBin0qzOxdSPXqz547n0ixx3S/Hxe8e/RL4EICJEACaSRAsU+j1Qtlxgtj3l2xSjZ9sFkwrj6Jnj3EHuVCf4R16zem2NosOgmQQJoJUOxTbH28MAZviWs/m0u82B89dsKUtbevL8UWZ9FJgATSSoBin1LLw6uH0G/dus2Mq0+6Z4/ywbtH/wT0U+BCAiRAAmkiQLFPk7WtsmIqWYj95ctXUyP2J0+dMWVGPwUuJEACJJAmAhT7NFm7UNanT58a0Wv7aIf09PSmRuwxM+CmTR/Su0/hPc8ik0DaCVDsU3gHYJIZePWX4NWnTOzb28/Ru0/hPc8ik0DaCVDsU3YH6Cts4dVjhrm0iT3Ku3HTh2YUAtvuU3bzs7gkkGICFPuUGV+9+ouXrqRW7M/Qu0/ZXc/ikgAJUOxTdA+oV9/atl26r99IrdgjokHvPkU3PotKAiTAt96l6R5Qr/7CxcupF3t692m681lWEiABevYpuQd0XD28+q7untSLPSIb9O5TcvOzmCRAAvTs03IP6Gx5HRcuUex7ek1l5/SZs+yZn5YfAMtJAiknQM8+BTeA7dVf67pOsS+IPSIc769ZZ974l4LbgEUkARJIMQGKfQqMb7/ZjmLfazomIowPsT90+Kjx7vlGvBT8EFhEEkgxAYp9Coy/YuUq2bDxA4HQU+yniz14rFzVLHzffQp+CCwiCaSYAMU+4caHx4rZ8rKHjlDsb/SZSYQw9E49e4j9nr37DSNMI8yFBEiABJJIgGKfRKtaZdq1a4/xXDuvdVPsPcT+fMdFI/boxMiFBEiABJJIgGKfRKsWyqQd87bv2CUU+37zwh9Ml+v07MHmw81bzRS6Cb4dWDQSIIEUE6DYJ9j45zs6jMeaO3+BYt9bWuyPHD1uWLGjXoJ/ECwaCaSYAMU+wcZft36DrH5/rVzt7KLYlxF7MPrl2+9KJpNN8B3BopEACaSVAMU+oZbXd9bv//gAxb7vptzwIfbbWtuMd8+34SX0R8FikUCKCVDsE2r83r4+I1znch0Ue59ir6H80dHRhN4VLBYJkEBaCVDsE2p50wt/ZbNcvtJJsfcp9leuXjMVJPbKT+iPgsUigRQToNgn1PgYW//R9p0U+76b0htA7Ndv2CTo68CFBEiABJJEgGKfJGsWyqLvrT90+BjFPqDY796zj+32CfxNsEgkkHYCFPsE3gFTc+F3UOwDiv3xE6eM2KPCxIUESIAEkkKAYp8US1rlQJszhpFdutxJsQ8o9ngFMJpAUGHiQgIkQAJJIUCxT4olrXLs3Llb0PZMsb8lfQHFHh0aUVFiJz3rhuIqCZBA7AlQ7GNvwpkFWLFilbRsa6PY91cm9qgoYTQDFxIgARJICgGKfVIsaZUDYehdu/dS7KsQe7xPgAsJkAAJJIUAxT4plrTKQbG/Lf03B6SvQrHHkEUw5EICJEACSSFAsU+KJa1yUOyrE/tdu/PD7yykXCUBEiCBWBOg2MfafO6Zp9hT7N3vDG4lARJIKwGKfQItT7GvTuw/+HCrrF3HWfQS+NNgkUggtQQo9gk0PcW+OrFHb3wMX+RCAiRAAkkhQLFPiiWtcmze0sJx9lV00Fu5slmy2UMWUa6SAAmQQLwJUOzjbT/X3EOoVq58j0PvKuiNzxn0XG8pbiQBEog5AYp9zA3oln19l/3Zc5wbP+gMeoePHDPD7vhOe7c7i9tIgATiSoBiH1fLlcj306dPjWDt23+Ac+MHnC4XMw+iz8Pz589LEOYuEiABEogXAYp9vOzlO7d4J/vq99dS7AOKPebFz2SyvjnzQBIgARKIAwGKfRysVEEez3d0GA/1XK5DrnZ2See1brnWdd38dXX3SPf1G3K9p1d68HejT2709ktv303z4hjMPnfz1m25deu2DAwMysDtIbk9OCyDg8MyNHRHhoZHZPjOXblz566MjNyTu/dG5d69Ufn00/syOvpA7t9/aP4ePHgkDx8+lkePPpPHj8fks8+eyNjYExkf/5X5e/Jk3HzHduzHcTge52kaSA9p4xp3735qrofr4vrIB/KDfCF/yCfyi7xXMoNeJnvYMBsaGqqAOE8hARIggegSoNhH1zZV5ezLL780woWwNMX+pqnMoFKDyg0qOajsoNKDChAqQmCEIXcrVq6qijtPJgESIIEoEqDYR9EqIeXpxImTRvBz5y/Qs+/tNxEML7E/cfK0YcX32Id08zEZEiCBSBGg2EfKHOFmRr37DzdvpdiXEfuVq5qNV8+OeeHeg0yNBEggGgQo9tGwQ81yoW33J0+dYZu9Rxg/e+gI2+prdgcyYRIggSgQoNhHwQo1zAM8VbRDv79mHcXeRewvX+kU9MBfv35jDa3ApEmABEigsQQo9o3lX5er6yQ7hw4fZW98Rwe9vfs+Nl792NhYXWzBi5AACZBAIwhQ7BtBvQHXXLd+o6BdGp4sh97le+NfuHjZCP3uPXsbYBFekgRIgATqR4BiXz/WDb0Spn/FzHDwZCn2ebHfsnWbYYKOjFxIgARIIMkEKPZJtq6jbPBg0T4Njzbtk+qcaT9nhP7kqdMOSvxKAiRAAskjQLFPnk09S4R2aXj3rW3bUy/2Gzd9KO+uWMU58D3vFu4gARJIEgGKfZKs6aMsOtHOxUtXUjtd7pGjx02lhxPo+LhheAgJkEAiCFDsE2FG/4XQiXbg2aZ1bvxV762Wdes20Kv3f9vwSBIggZgToNjH3ICVZF8n2kG7ddpehKNePV92U8mdw3NIgATiSoBiH1fLVZFvTLSD9mp492kTe3j1nECnipuHp5IACcSSAMU+lmarPtNor0ZnvXZ49yl5xS29+urvG6ZAAiQQTwIU+3jabVquR0buTvvu5wu8+3feXSlvv/2utJ/NJf599qdOt8u/vPVL01bvhw+PIQESIIEkEaDYx9yajx49kq6u7opKcTCTNd49PPyPtu8073Tv67sp/TcH5Oat23Lr1m0ZGBiUgdtDcntwWAYHh2Vo6I4MDY/I8J27cufOXRkZuSd3743KvXuj8umn92V09IHcv//Q/D148EgePnwsjx59Jo8fj8lnnz2RsbEnMj7+K/P35Mm4+Y7t2I/jcDzO0zSQHtLGNe7e/dRcD9fF9ZEP5Af5Qv6QT+QXeUcZ+vpvSS7XIZs+2Fws56XLlytixZNIgARIIM4EKPZxtp6I7N69R/7zP/+zolJoz/zm1WuKYtjS0irouBd3sT9+4pR88OEWU66331khaKtHPwUuJEACJJBGAhT7GFv917/+f3Ly1KmqSqDj7jGr3vYduwTCCE//veb3Zd++j+Xq1Wux8ezPnjsvO3fuLpYBZfnkk4NyLtdhysRx9VXdKjyZBEggxgQo9jE2XiablWfPnlVVAp1V7+ixE9Lbd1OuX78h8Irx4hyIPv4gmjt37ZHTp9vlxo2+yITxr3Vdl2PHT5oZAbWSgvxua/3IlAFhfDRLoBKD7VGeAx92rKTvRVXG58kkQAKpIUCxj6mpIQ4I4YexQNjXrttgxN5us+/qui7owQ7xtMUU65u3tAhemXv2bE46r3XVtM0e7fK4xtlzOfnkQMZcWysidmXk5KkzRtztNnuUB/nNZLJhoKpZGmFU3GqWOSZMAiQQewIU+ypNiFB6I5aOCxdC8wR1kp2rnV1GLL066F26dMV40m0f7ZD1GzYVPX9beLe2tAr+0AQAr/v48ZNy4sQpuXjxsvT29ktfX7/0998yf339N813pHvi5ClzHI7ft/8TkwbmAbDT1nVce/eefSb9a9e6S3bQQzQC50V5Eh1U3CD2XEiABEigVgQo9lWSRW94/NV7WbNmXWiXfPr0qRFEiLPt2fvpjY82fbT3HzlyTA4ezBqRhthjWJ+Kc9BPnKuVhoOZQyZtePaYAAi9/4P0xt+zd7/JB4YaRnVBxa1RlcaoMmG+SIAEwiVAsQ+B582btyruEV/J5XE9CESYC3qqo207qNj7HXp3a2DQ07PHcLlaDb1D8wRGGER1wUiKsJpjolpG5osESKDxBCj2IdkgbPEtlS149dV2zHOmj3fdY3harcS+UePsEVVAM0VUF8yRgMobFxIgARKoJQGKfUh0Ib71eGgj3OvHE0R+goSGdfrcJIl97vwFE8IfHR0NycrhJ7Nla0v4iTJFEiABEnAQoNg7gFTzFUOngghsJddCRy4/Q7SC9u5GBzZ4wehI59VBL24z6KnYY3ihLuhfUekkRJpGWJ+wYz0jQmHlm+mQAAnEjwDFPmSbISxbKzFBuv/6y3fK5hgVjqC9u3W8fS7XkRixxzA9VGDsznlgWOn0wmXBBzwAXn3YzTEBs8DDSYAEUkKAYh+yoWspJmgm8CPilYhIksXeaWJUhhoxgsLOB0TeT3OMfQ7XSYAESKBSAhT7SsmVOA9C4ifUXiIJ110Q8XLNBLi2nwqB8wJJFnvbs9dyo+LUSK8a0xzX4h7R8vGTBEiABGwCFHubRojrYYfzIUx+QviVePUodlra7G0TN6q9HNGfMOdJsMvEdRIgARJwI0Cxd6MS0rYwxQSVh3IvvanUq0dxdRa9JPXGv3jpimmz95o9D6JbjxEUztsJ1yxnS/scRGqQVy4kQAIkUCkBin2l5HycF2Y4H159uRB+pV49ioKJZzABTZLEHi/CQQe9k6dOe1oLNsJfPZcg8yRUU4GrZ5l4LRIggWgToNjX2D7w7qv1yiDy5UL4EIVKO3zpe+0xtWzSxB6VmBVl3mMfdpNLqVsKzTFBQviwaSP7FpQqC/eRAAnEhwDFvsa2gtBXG85HyLdc2BdefaUeqk6ogznukyb2eLEOvHuvUL6av1obaTrlPmFHv00HsGe98lUu39xPAiQQbwIU+zrYDw/3SoUY2YNXX+p87AviLdpFRk91zIu/6YPNM15x6+dFOH7nxm/UdLmovGAa4PXrN9rFnrGO6IlfEZ5xcoANsKXfSA+8er/HBsgCDyUBEkghAYp9nYxeyXA4ZA0i9PNfLCuZS3j1lQoV2rPh+Z49dz6xYo+3+aGMvX19JTmCYS1D5hhq57epBXmhV1/SXNxJAiQQgADFPgCsag6F913JuGq0J5cSCIhTucqAV74xZzxE8KPtO+VGb39ixb6376bpfIgIBl7nW2qppcCiwue3UhYkAlCqPNxHAiRAAiBAsa/jfVCJd4/wfCmBQJrl2vPdigjRg/ghxH2t63rixb7jwiV5+50Vsm79xmnT5zrZoPJUirfzeL/fEY7/8d+84Sssj+tXcq/4zQuPIwESSB8Bin0dbY6HeBAhgfBAILxCyyogXvu9igahX7HyPSN+HR0XpedGX+LFHpGLk6fOmEgGeui7zaqnvGCjoEz1XK9PpFkqQmOfB68+7Ovb6XOdBEggfQQo9nW2ud8HPrIFgSjV8Q4hZ7TXB1lU6H/59rtyHkLf05sasUel5sjR40bwt7ZsKyn4lURLStkBdvdT0cMx9OpLkeQ+EiCBSghQ7CuhVsU5EOhSPevtpCEQpUQHbfV+BETTtIUer3+9DqFPmdijvH4Ev9I+Fsra/tQIjJ+e9ajclZs8yU6b6yRAAiTghwDF3g+lEI9BeNav5wYx9+rUB5HHfj8CguwjbI3QPTz6c7kO6b5+I7Vij0rO4SPH8iH9bW2eHj4qZn75lrpFYCs/ER1UMIJGakpdl/tIgARIQAlQ7JVEHT/hvZUTEXh3pTp0QRT8Vhog9Ahbo+f9qdPt0tXdk3qxR2Xn0OGjhsnuPXtdrY+KGUZDVLtA6P2kA5t6Ve6qzQPPJwESSDcBin0D7I8Hf7nwO47xaq+HCKEi4FcYWra1GVGDuKHnPcW+11R2wGHvvo8NG6/582GHajrLoVJXqpOl3n7w6tExjwsJkAAJ1IIAxb4WVMukCfEoF9bFfi/PHe34fsfWnziRn1DmkwMZI/QU+17TfAHPHmIPHttaPzKC7zbpDsS6VL+JMqY2FTI/Ig5b+/H+y12P+0mABEjAjQDF3o1KHbZ5ee166VKd77DPqyKg5+MT4oXQPcbTd17rptjf6DMdEtFmb4s92PzLW780rMbGxmyEZh1t95V697BTucqCRmrKNe3MyBg3kAAJkIBPAhR7n6DCPgyeu1evfG2vd+uVjdC9nxA+et5D6N95d6X5xBhzeLH07Gd69oh6gNVb//q2rFi5SvAWQHuBCPupXNnn6DoqZuWaW1AZqDR9vQ4/SYAESKAUAYp9KTo13Adv0Stsi/Z8CLrbAlHw2qfHo0PeuvUbTM/7M+3nZOWqZrOO+e8p9tPFXjvpbdj4gYAVRB99HJwLuAf1vLXS5kzL/o40USHwmdMBRwAADvJJREFUqvjZx3KdBEiABColQLGvlFyV5+Hh7uXNYbvbECwVhnLt/ZlM1ojWocPH5PKVTiNiGHKHPwg+O+jlw/gq9O+vWScXL12RK1evyf6PDxh2eO2vvUC4UUELsuB4NzvaaaBi56dN3z6H6yRAAiQQlADFPiixkI6HeHi122O7W0VAPX6viACyZr/c5tLlTiP2Vzu7pP1szog9PNd9+z9J9dA7tNHv2rXHiDqE/tLlqwJGEHtUjtZv2GT2oSnEXspVsuxjsQ6hL1dBgNCXO8aZLr+TAAmQQFACFPugxEI83iscj+1ugg6xwT63tnxky0ycs2KVmTwHU+HaYg+Bg5AhXA3BX7N2vfH40zaDHmbPw8t/wKC1bbthAja22J8912EqRpibwF5gk3Lt73o8ojCwVanwPPbhmEo7/+m1+EkCJEAC5QhQ7MsRquF+twe9CoCbSKBtF39ey8FC+P7osRPGW3WKvXbQO3AwW/TyN2360Hj9SX/FLZioyOPz+IlTxaF3TrEHN0Q/UCGww/kQZbeIi5s9tCOl2z7dhrS8ojt6DD9JgARIIAwCFPswKFaYBh70TlHXUL3T29NKgFcoGUPGIE5bW1pN+zNC015ijzZ7eLJon0Y7Ps6DAGYPHTHb+28OyM1bt+XWrdsyMDAoA7eH5PbgsAwODsvQ0B0ZGh6R4Tt35c6duzIyck/u3huVe/dG5dNP78vo6AO5f/+h+Xvw4JE8fPhYHj36TB4/HpPPPnsiY2NPZHz8V+bvyZNx8x3bsR/H4Xicp2kgPaSNa9y9+6m5Hq6L6yMfyA/yhfwhn8gv8o4yoIx79u4vijzKijK7Db2zPXtwAz+8DhfDFu3e+eXa4PVWQA/7Useq5+8WwdE0+EkCJEACYRGg2IdFsoJ0IAZOsUf7LTx+56LbvcQBIWe0/2Lee3Q2Kyf2Ojf+tWvdkskeLgoihB+90TF3fFfX9diJ/dWr10ze167bYCoxKA/W4dnjrXdotvAr9vpK3OMnThbNARH3E8qHbUuNr/eq1BUvxBUSIAESCJEAxT5EmEGTgiA4xRvb3EK72O7VBjw0NGSEbcfOPXLh4uVAYm+32aOisH3HLvOee4gk/t5rft+EtLEPx0bNs79xo09On26Xnbv2mLza+YZXf/HiZentuylopggq9qg0IVKCNNW7h9CXEnG9B2CrUpUC2NjNzno+P0mABEggTAIU+zBpBkwLAu7siQ0BwHbngrZ6N48fxyHcjDfadVy4XJXYQxT7+m6aEDg68x08mDVpq4Dis7n5fdm8pcW8RKaj46LAk65HGH9w6I50dnbJ2bM5c23k4e13VhS9d+Ttw81bzetrkXeE8fv6b5nyVCP2OvZevXuE38uJtDa5OJti1KbYDls6K3q6n58kQAIkEDYBin3YRAOk5yb2EAFnBUDFwU1k1Kv/+OODoYq9s80eXm42e1ja2rZL8+o100RWKwNbt24znnAmc0iOHTshx46flPb2cyYiAA+8t7df+vr6pb//lvnr60flot9sx/4TJ07J8eMnzXn79n1s0lLPWq+hnxget2v3XnPspUtXXNvswxB7REq2bJ3u3aO5BKLvtcB+pTpSIjIAO3tVBrzS5XYSIAESqJQAxb5SciGc5xR77bTlFHvt2e3WOQ/jxSE+mCwnTM/eKfZuHfSuXOmUCxcumTZy9PBXsdcpelWYK/lc/f7aotgfOXLMXAOe/fXrN0zHQD8d9MIS+9Nn8jPr6ZvxYDdnXwv7doCd3KIzegzshT8uJEACJFAvAhT7epF2uY5T7DX8i85b9gLxd/P40Y4MId3Wul3Od1yqu9j77Y2Ptv5ynv2tgcHQe+OHJfaoRG36YLPpmY+5DGCPUiF4CLmzwqb21Cl0/bT76zn8JAESIIFqCVDsqyVYxfleYu/0GjEeG2Lv7PB1vqPDiP3JU+2RFvtGDb0LU+wPZg4b1mg2gdB7jbfX6IzTVnqbaAjfa78ex08SIAESCJMAxT5MmgHTQhu87QGqB+8Ue1QKIPbO7XjZDdrPc+cvUuxdxtmHKfaInMBjx8RFsINXmB77YCuvWQ5hc+wv1eYf8Dbi4SRAAiRQlgDFviyi2h3g9NZV7J0dtyAyONZeNIS/a/c+ir3HpDphi/3mLdtMKB+C7tXmrja0baXr2tHSq6Kgx/GTBEiABMImQLEPm2iA9CDgtrfuJRQ4zin22gv/6LGTFPs6ib2+EQ+zFTrtoWYvNQWuTqQDO3MhARIggXoSoNjXk7Z1Le2oZYu9vujGOsysQlic3iB6hqNz3rncBYp9ncQefSPAvLevz1PsYSenrdSeal+21ysRfpIACdSLAMW+XqQd19G2XTtkD5FweoxaKXAKyI6du8w0sBR777nxww7jo28ExB4dI2Enu6Km5sV2L89dm2PYXq+0+EkCJFAvAhT7epF2XAc9up3C7ib2Wilwij1e0IJZ5Cj29RV7zLO/e/deV7HXnvhuw/K0vd6rrd9xe/ArCZAACYRKgGIfKk7/icH7cz74S4m9c1w2PEzMY0+xr7/Yb9+x01XstWLm5vEjdI/KndvESP7vGh5JAiRAApURoNhXxq3qsyDsTm+9lNg7Q8MU+/KvuK1FGB+evZfYawc8N7GH/UqF+Ku+oZgACZAACZQgQLEvAaeWu+DVO711in2477Ovt9iroLvdN2pbt4qA2/HcRgIkQAJhEqDYh0kzQFrw8pxtuyoIdjIaGnZ69mizh5fJMH79w/h4HwHs5xRunenQtp+ua+c8u0Om7uMnCZAACdSaAMW+1oRd0lcBd4pFELFnb/zGhPHRfIJhj25iD/s5+2Go+XE8/riQAAmQQCMIUOwbQF174juHYAURewgOhIWeff08+/az583Qu87Oa55iDxs6F6/hk87j+J0ESIAEakWAYl8rsiXSRbjXzQMMIvY6g1720FFOqlOnSXV0Br379x+4ij3eYe8m9hrJcdtX4jbhLhIgARIIjQDFPjSU/hOC0LsNwQoi9njVqrbb80U4w3K7xi/COXvuvKxY+Z6gvV7F29n+jjC9m101kuPsd+H/juGRJEACJFAdAYp9dfwCn62Tq7g9+LWDly0iKizOnvu4MKZtRRvy7j37+da7Gov9lq3bDGvMi682cRofYu9mV2zz2udMg99JgARIoBYEKPa1oFoiTZ1cBYLhXFQUnPsg9F7zqWM2Nwj+xx8flI4Ll+XCxcty8dIVuXT5qly63CmXr3TK1c4u6bzWLde6rpu/ru4e6b5+Q6739EoP/m70yY3efuntuyl9fTel/+aA3Lx1W27dui0DA4MycHvIeM6Dg8MyNHRHhoZHZPjOXblz566MjNyTu/dG5d69Ufn00/syOvpA7t9/aP4ePHgkDx8+lri/z/7jTzKGMabJxaKeum2/UpU4L7va53OdBEiABGpJgGJfS7ouaUO4vXplVyIKCOer1wlRotgPmooKKixhjLNv+2iHEXq8x14X2MnZ50K9fexzLvoCHGclznkcv5MACZBArQhQ7GtF1iNdtMuvWbPOda96jPgMskDwt7bkw8xbW1old/4CPfsqxf58x0VZt36jEfrjJ05OMwfE29nZrpTYa18Miv00jPxCAiRQRwIU+zrCxqUw3A5DsdyWUoLhdry9DYIPUUJIHx3Jjh0/yTB+/y3TLIHmCTRToLkCzRZovkAzBpoz0LSBJg40dVy5es00exw4eEh++fa7hiWG2TkXiDf6V9hLKdup2NvHc50ESIAE6kmAYl9P2mWupeOxnUJS5rRpu0dHR2XFilVGqNZv2CTnch1ss/cp9idOnhYwQ4Vp3foNgs54bguG2DnD9RR7N1LcRgIkEBUCFPuoWKKQD7TnO0PEQbMILx+T7kC08Let9SM5eeoMO+h5ePZHj52QDRs/MKwwnBHePBi6LfoaW7z0xl4o9jYNrpMACUSNAMU+YhaB0Du9xkqz+OWXX04T/ffXrJNDh4+acHXae+MjbH/gYFZWrmr2JfJqAxV1fNqLbnezHcP4NimukwAJNIIAxb4R1Ot8TYg+ho2tWJkP76M9Gr3MEbZO09A7tM8fOXq8OHohH67fWNKTd5pKO1E6t1PsnUT4nQRIIEoEKPZRskYd8oJpdjOZbDHED8FDD36EsuHtJm2c/cWLlyV76Ihs+mBzscwI1aOZA/0bgi5eUx1T7IOS5PEkQAL1JECxryftCF0LbdIQ/mz2kJl2V9v3V723Wnbs2CWHjxyTK1c6YzepzoULl0zeW7a1ydvvrCgKPDrcVSrwttkwbNJtSlyKvU2J6yRAAlEjQLGPmkUalB/0PEfHtN178jPyqfjj88PNW2Xnrj2SzR6WS5evmGFsjZ5BD8PmMEsg8oT56nVMvOYbww8RwcCUwk+fPg2Nqte0txT70BAzIRIggRoQoNjXAGoSkoRAwvNHW/+u3XvM2H0VUv1sXr1GtmxpkT1798uRI8fk6NHjcvnyVenGdLzdPXL9+g0zja7f6XKHh0fMGHich/PPn79gmheQ9kfbd5q2dlxTr6+f5gU1u/eYygryjD4KtVhU0PHpXHQfO+g5yfA7CZBAFAhQ7KNghZjkAaF/RAAgqIgCoAnAzatWEQ7zEzME4j0ACMXj2sgD8uI1RK4WSCHk8Owx/M656BwJbi8sYm98Jy1+JwESqDcBin29iSf8evCqIcL6h05wEGc/f3qOftZTyP2YBW31zjnx7fO85kig2NuUuE4CJNAIAhT7RlDnNWNJADPnlZrd0EvsMQEPogJuEYFYgmCmSYAEYkeAYh87kzHDjSCgYfpSLymC2Hu95KgReeY1SYAESEAJUOyVBD9JoAQBnUzH6yVGOBVCD8HnQgIkQAJRI0Cxj5pFmJ9IEkBve7fx9XZm2TZv0+A6CZBAlAhQ7KNkDeYl1gTQng/P3m1oXqwLxsyTAAnEngDFPvYmZAGiQkCH5lHso2IR5oMESEAJUOyVBD9JoEoC6HUPz95tYp0qk+bpJEACJFAVAYp9Vfh4MglMEUDnPbTb07OfYsI1EiCBaBCg2EfDDswFCZAACZAACdSMAMW+ZmiZMAmQAAmQAAlEgwDFPhp2YC5IgARIgARIoGYEKPY1Q8uESYAESIAESCAaBP4/jN6J1mqNfLgAAAAASUVORK5CYII="></p>
<p style="text-align: left;">The interior of the bird bath is in the shape of a cone with radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>, height <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> and a constant slant height of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn><mo> </mo><mtext>cm</mtext></math>.</p>
</div>
<div class="specification">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> be the volume of the bird bath.</p>
</div>
<div class="specification">
<p>Hyungmin wants the bird bath to have maximum volume.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an equation in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> 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>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mfrac><mrow><mn>2500</mn><mtext>π</mtext><mi>h</mi></mrow><mn>3</mn></mfrac><mo>-</mo><mfrac><mrow><mtext>π</mtext><msup><mi>h</mi><mn>3</mn></msup></mrow><mn>3</mn></mfrac></math>.</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 <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mtext>d</mtext><mi>V</mi></mrow><mrow><mtext>d</mtext><mi>h</mi></mrow></mfrac></math>.</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>Using your answer to <strong>part (c)</strong>, find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> for which <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> is a maximum.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the maximum volume of the bird bath.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>To prevent leaks, a sealant is applied to the interior surface of the bird bath.</p>
<p>Find the surface area to be covered by the sealant, given that the bird bath has maximum volume.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>h</mi><mn>2</mn></msup><mo>+</mo><msup><mi>r</mi><mn>2</mn></msup><mo>=</mo><msup><mn>50</mn><mn>2</mn></msup></math> (or equivalent)<strong> </strong> <strong><em>(A1)</em></strong></p>
<p><em><strong><br></strong></em><strong>Note:</strong> Accept equivalent expressions such as <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><msqrt><mn>2500</mn><mo>-</mo><msup><mi>h</mi><mn>2</mn></msup></msqrt></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><msqrt><mn>2500</mn><mo>-</mo><msup><mi>r</mi><mn>2</mn></msup></msqrt></math>. Award <em><strong>(A0)</strong></em> for a final answer of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>±</mo><msqrt><mn>2500</mn><mo>-</mo><msup><mi>h</mi><mn>2</mn></msup></msqrt></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>±</mo><msqrt><mn>2500</mn><mo>-</mo><msup><mi>r</mi><mn>2</mn></msup></msqrt></math>, or any further incorrect working.</p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>×</mo><mi mathvariant="normal">π</mi><mo>×</mo><mfenced><mrow><mn>2500</mn><mo>-</mo><msup><mi>h</mi><mn>2</mn></msup></mrow></mfenced><mo>×</mo><mi>h</mi></math> <strong>OR</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>×</mo><mi mathvariant="normal">π</mi><mo>×</mo><msup><mfenced><msqrt><mn>2500</mn><mo>-</mo><msup><mi>h</mi><mn>2</mn></msup></msqrt></mfenced><mn>2</mn></msup><mo>×</mo><mi>h</mi></math><strong> </strong> <strong><em>(M1)</em></strong></p>
<p><em><strong><br></strong></em><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in the volume of cone formula.</p>
<p><br><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mfrac><mrow><mn>2500</mn><mtext>π</mtext><mi>h</mi></mrow><mn>3</mn></mfrac><mo>-</mo><mfrac><mrow><mtext>π</mtext><msup><mi>h</mi><mn>3</mn></msup></mrow><mn>3</mn></mfrac></math> </strong> <strong><em>(AG)</em></strong></p>
<p><em><strong><br></strong></em><strong>Note:</strong> The final line must be seen, with no incorrect working, for the <em><strong>(M1)</strong></em> to be awarded.</p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mrow><mtext>d</mtext><mi>V</mi></mrow><mrow><mtext>d</mtext><mi>h</mi></mrow></mfrac><mo>=</mo></mrow></mfenced><mo> </mo><mfrac><mrow><mn>2500</mn><mi mathvariant="normal">π</mi></mrow><mn>3</mn></mfrac><mo>-</mo><mtext>π</mtext><msup><mi>h</mi><mn>2</mn></msup></math><strong> </strong> <strong><em>(A1)(A1)</em></strong></p>
<p><em><strong><br></strong></em><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2500</mn><mi mathvariant="normal">π</mi></mrow><mn>3</mn></mfrac></math>, <em><strong>(A1) </strong></em>for <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mtext>π</mtext><msup><mi>h</mi><mn>2</mn></msup></math>. Award at most <em><strong>(A1)(A0)</strong></em> if extra terms are seen. Award <em><strong>(A0)</strong></em> for the term <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mrow><mn>3</mn><mtext>π</mtext><msup><mi>h</mi><mn>2</mn></msup></mrow><mn>3</mn></mfrac></math>.</p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>=</mo><mfrac><mrow><mn>2500</mn><mi mathvariant="normal">π</mi></mrow><mn>3</mn></mfrac><mo>-</mo><mtext>π</mtext><msup><mi>h</mi><mn>2</mn></msup></math><strong> </strong> <strong><em>(M1)</em></strong></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for equating <strong>their</strong> derivative to zero. Follow through from part (c).</p>
<p><br><strong>OR</strong></p>
<p>sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mtext>d</mtext><mi>V</mi></mrow><mrow><mtext>d</mtext><mi>h</mi></mrow></mfrac></math><strong> </strong> <strong><em>(M1)</em></strong></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for a labelled sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mtext>d</mtext><mi>V</mi></mrow><mrow><mtext>d</mtext><mi>h</mi></mrow></mfrac></math> with the curve/axes correctly labelled <em>or</em> the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-intercept explicitly indicated.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>h</mi><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mn>28</mn><mo>.</mo><mn>9</mn><mo> </mo><mfenced><mtext>cm</mtext></mfenced><mo> </mo><mo> </mo><mfenced><mrow><msqrt><mfrac><mn>2500</mn><mn>3</mn></mfrac></msqrt><mo>,</mo><mo> </mo><mfrac><mn>50</mn><msqrt><mn>3</mn></msqrt></mfrac><mo>,</mo><mo> </mo><mfrac><mrow><mn>50</mn><msqrt><mn>3</mn></msqrt></mrow><mn>3</mn></mfrac><mo>,</mo><mo> </mo><mn>28</mn><mo>.</mo><mn>8675</mn><mo>…</mo></mrow></mfenced></math> <strong><em>(A1)</em>(ft)</strong></p>
<p><br><strong>Note:</strong> An unsupported <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>28</mn><mo>.</mo><mn>9</mn><mo> </mo><mtext>cm</mtext></math> is awarded no marks. Graphing the <strong>function</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mfenced><mi>h</mi></mfenced></math> is not an acceptable method and <em><strong>(M0)(A0)</strong></em> should be awarded. Follow through from part (c). Given the restraints of the question, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>≥</mo><mn>50</mn></math> is not possible.</p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>V</mi><mo>=</mo></mrow></mfenced><mo> </mo><mfrac><mrow><mn>2500</mn><mo>×</mo><mi mathvariant="normal">π</mi><mo>×</mo><mn>28</mn><mo>.</mo><mn>8675</mn><mo>…</mo></mrow><mn>3</mn></mfrac><mo>-</mo><mfrac><mrow><mi mathvariant="normal">π</mi><msup><mfenced><mrow><mn>28</mn><mo>.</mo><mn>8675</mn><mo>…</mo></mrow></mfenced><mn>3</mn></msup></mrow><mn>3</mn></mfrac></math><strong> </strong> <strong><em>(M1)</em></strong></p>
<p><strong>OR</strong></p>
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>3</mn></mfrac><mi mathvariant="normal">π</mi><msup><mfenced><mrow><mn>40</mn><mo>.</mo><mn>828</mn><mo>…</mo></mrow></mfenced><mn>2</mn></msup><mo>×</mo><mn>28</mn><mo>.</mo><mn>8675</mn><mo>…</mo></math> </strong> <strong><em>(M1)</em></strong></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting their <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>28</mn><mo>.</mo><mn>8675</mn><mo>…</mo></math> in the volume formula.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>V</mi><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mn>50400</mn><mo> </mo><mfenced><msup><mtext>cm</mtext><mn>3</mn></msup></mfenced><mo> </mo><mo> </mo><mfenced><mrow><mn>50383</mn><mo>.</mo><mn>3</mn><mo>…</mo></mrow></mfenced></math> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><br><strong>Note:</strong> Follow through from part (d).</p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>S</mi><mo>=</mo></mrow></mfenced><mo> </mo><mi mathvariant="normal">π</mi><mo>×</mo><msqrt><mn>2500</mn><mo>-</mo><msup><mfenced><mrow><mn>28</mn><mo>.</mo><mn>8675</mn><mo>…</mo></mrow></mfenced><mn>2</mn></msup></msqrt><mo>×</mo><mn>50</mn></math><strong> </strong> <strong><em>(A1)</em>(ft)</strong><strong><em>(M1)</em></strong></p>
<p><strong><br>Note:</strong> Award <em><strong>(A1)</strong></em> for their correct radius seen <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>40</mn><mo>.</mo><mn>8248</mn><mo>…</mo><mo>,</mo><mo> </mo><msqrt><mn>2500</mn><mo>-</mo><msup><mfenced><mrow><mn>28</mn><mo>.</mo><mn>8675</mn><mo>…</mo></mrow></mfenced><mn>2</mn></msup></msqrt></mrow></mfenced></math>. <br>Award <em><strong>(M1)</strong></em> for correctly substituted curved surface area formula for a cone.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>S</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>6410</mn><mo> </mo><mfenced><msup><mtext>cm</mtext><mn>2</mn></msup></mfenced><mo> </mo><mo> </mo><mfenced><mrow><mn>6412</mn><mo>.</mo><mn>74</mn><mo>…</mo></mrow></mfenced></math> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><br><strong>Note:</strong> Follow through from parts (a) and (d).</p>
<p><em><strong><br>[3 marks]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>A function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = (2x + 2)(5 - {x^2})">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mn>5</mn>
<mo>−<!-- − --></mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo stretchy="false">)</mo>
</math></span>.</p>
</div>
<div class="specification">
<p>The graph of the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x) = {5^x} + 6x - 6">
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mrow>
<msup>
<mn>5</mn>
<mi>x</mi>
</msup>
</mrow>
<mo>+</mo>
<mn>6</mn>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mn>6</mn>
</math></span> intersects the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <strong>exact </strong>value of each of the zeros of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></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>Expand the expression for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x)">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></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>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’(x)">
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your answer to part (b)(ii) to find the values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> for which <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> is increasing.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><strong>Draw </strong>the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 3 \leqslant x \leqslant 3">
<mo>−</mo>
<mn>3</mn>
<mo>⩽</mo>
<mi>x</mi>
<mo>⩽</mo>
<mn>3</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 40 \leqslant y \leqslant 20">
<mo>−</mo>
<mn>40</mn>
<mo>⩽</mo>
<mi>y</mi>
<mo>⩽</mo>
<mn>20</mn>
</math></span>. Use a scale of 2 cm to represent 1 unit on the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis and 1 cm to represent 5 units on the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-axis.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the coordinates of the point of intersection.</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 style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 1,{\text{ }}\sqrt 5 ,{\text{ }} - \sqrt 5 ">
<mo>−</mo>
<mn>1</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<msqrt>
<mn>5</mn>
</msqrt>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>−</mo>
<msqrt>
<mn>5</mn>
</msqrt>
</math></span> <strong><em>(A1)(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for –1 and each exact value seen. Award at most <strong><em>(A1)(A0)(A1) </em></strong>for use of 2.23606… instead of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt 5 ">
<msqrt>
<mn>5</mn>
</msqrt>
</math></span>.</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="10x - 2{x^3} + 10 - 2{x^2}">
<mn>10</mn>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>10</mn>
<mo>−</mo>
<mn>2</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>The expansion may be seen in part (b)(ii).</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="10 - 6{x^2} - 4x">
<mn>10</mn>
<mo>−</mo>
<mn>6</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>4</mn>
<mi>x</mi>
</math></span> <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Notes: </strong>Follow through from part (b)(i). Award <strong><em>(A1)</em>(ft) </strong>for each correct term. Award at most <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)<em>(A0) </em></strong>if extra terms are seen.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="10 - 6{x^2} - 4x > 0">
<mn>10</mn>
<mo>−</mo>
<mn>6</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>4</mn>
<mi>x</mi>
<mo>></mo>
<mn>0</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’(x) > 0">
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>></mo>
<mn>0</mn>
</math></span>. Accept equality or weak inequality.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 1.67 < x < 1{\text{ }}\left( { - \frac{5}{3} < x < 1,{\text{ }} - 1.66666 \ldots < x < 1} \right)">
<mo>−</mo>
<mn>1.67</mn>
<mo><</mo>
<mi>x</mi>
<mo><</mo>
<mn>1</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mfrac>
<mn>5</mn>
<mn>3</mn>
</mfrac>
<mo><</mo>
<mi>x</mi>
<mo><</mo>
<mn>1</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>−</mo>
<mn>1.66666</mn>
<mo>…</mo>
<mo><</mo>
<mi>x</mi>
<mo><</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(A1)</em>(ft) </strong>for correct endpoints, <strong><em>(A1)</em>(ft) </strong>for correct weak or strict inequalities. Follow through from part (b)(ii). Do not award any marks if there is no answer in part (b)(ii).</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2018-02-14_om_06.23.51.png" alt="N17/5/MATSD/SP2/ENG/TZ0/05.d/M"> <strong><em>(A1)(A1)</em>(ft)<em>(A1)</em>(ft)<em>(A1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for correct scale; axes labelled and drawn with a ruler.</p>
<p>Award <strong><em>(A1)</em>(ft) </strong>for their correct <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-intercepts in approximately correct location.</p>
<p>Award <strong><em>(A1) </em></strong>for correct minimum and maximum points in approximately correct location.</p>
<p>Award <strong><em>(A1) </em></strong>for a smooth continuous curve with approximate correct shape. The curve should be in the given domain.</p>
<p>Follow through from part (a) for the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-intercepts.</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(1.49,{\text{ }}13.9){\text{ }}\left( {(1.48702 \ldots ,{\text{ }}13.8714 \ldots )} \right)">
<mo stretchy="false">(</mo>
<mn>1.49</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>13.9</mn>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mo stretchy="false">(</mo>
<mn>1.48702</mn>
<mo>…</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>13.8714</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(G1)</em>(ft)<em>(G1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(G1) </em></strong>for 1.49 and <strong><em>(G1) </em></strong>for 13.9 written as a coordinate pair. Award at most <strong><em>(G0)(G1) </em></strong>if parentheses are missing. Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 1.49">
<mi>x</mi>
<mo>=</mo>
<mn>1.49</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 13.9">
<mi>y</mi>
<mo>=</mo>
<mn>13.9</mn>
</math></span>. Follow through from part (b)(i).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.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>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>In a company it is found that 25 % of the employees encountered traffic on their way to work. From those who encountered traffic the probability of being late for work is 80 %.</p>
<p>From those who did not encounter traffic, the probability of being late for work is 15 %.</p>
<p>The tree diagram illustrates the information.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>The company investigates the different means of transport used by their employees in the past year to travel to work. It was found that the three most common means of transport used to travel to work were public transportation (<em>P </em>), car (<em>C </em>) and bicycle (<em>B </em>).</p>
<p>The company finds that 20 employees travelled by car, 28 travelled by bicycle and 19 travelled by public transportation in the last year.</p>
<p>Some of the information is shown in the Venn diagram.</p>
<p style="text-align: center;"><img 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ES62aHew2pcXl6eCsQ6i3IjTfxR+lUpqrOoUffHjRsn6ViiLln6NXK2mg7WKYu4ngbeNYFy6CSFau2XmWANjrGIMenF4NDQTkwot2zZQmPHjnWg8inU9Ye9qCudp8pXV9Oe7BmUd7MzuiVM4xAMb6q9fJh2HJxAv8xRSFIq0EXZMBuQ66IiiaEoKTcNoDt8YTpYfT6Gsj6NBt8iTVANlaEnMcYixqQXAxOTyl7FCghEZ4jQToSUG3pROhFdN3Y2+cfdfO20yMYK7d+/n+677z6DJdbTgTX/QX2WPkaZOnVk2ENn23Su+zAa/2gqHfnwL1TXquuOUGPtCTqSM4HuGni9QTz0JZenc15cnWNiUjkmQqGQtP3Euc2636NbCkvopRkZmqc+KpuoKhoMKuEsX3+IUOOBP9BbvWbTLzJ76M5m2LBh9MEHH+hOry1hb8qeM58mvrOI5q87Kim7I3UfUen60zRv6WQa5NBThLGIfYSeXJ2zw6xKaTxlR5lmlwGDNhhWOhIaPhYl/g2iqqHZkeKjC0VfGjFwbK79kyhZd6TFUDQ6Z23fUQejddFWIg6SfFcU5+NUZhLXHjKpLSczY2NMxjuzz8yyrMxLyREOcb2295UbYuPtDGdwtoXG/fTKPWPo/77xR1r+2wr6+1//nIbonPaYVWf4BJo9e7Zu5X+kbjf9y1vX0z8+Kkt9EWo89kd6Y895zVWEtIC6wDGdPSGFug0aT8+uP4LdEiTef5mmZzpraIl2Y0zCdMNrgYlJZY9CvwQPjbaFSCOdC52iitDX9Pf/Z6ZuXYyZ9YUXRRj2aQ8Rajy+lQqnTqN58+6l1O/BQBGf79ENt79FlKpPeQyzDdQpmQOMLTE2vRau81qDrGgPJAVYHNuqX+o+jl4Oh61oju48jx07RiNHjtScPvL5Nnom+yF6o92SOxEZUB6np6fT3r17NdfHawkgOWKMqt8e5H4EWGJS0UfwzuilTlfR5JhRTp06RQMGDIh5L97FlJsnUym2omAKpPzsmKlbedynTx9CnZI93HbbbVRdXe0pGNjtiYrulE//kN28qkjiySiYfjU1NdkrOXaCZDt3GZ3E9+JtL4xPZT+yxKRipGIK07dvXxUxvRtFtpWxdTqrAs5Ro0Z5dluGiuZLUTA2YcbhpcDEpKI36+vrCdOGZA5Y/YLNjNsC3KCcP699Vc9t7TBSHy+OTSYmFSPi4sWLKmJxFEbAGQTgTRXKby8FJiYVvWm7qYCKOtkdBbolN4Zbb73Vc4pfrThj7yDc8XgpsLmAyt50m25FZbVNi3by5EkaPXq0rvygn4pnCIk3vt5NwdjM29ho/+5+XUBwItUIMDGphoojxkNAJh8YPMKR25kzZ6QTij/55BMpWTz9FKYh8hsfNjk9e/aUSBBK3f79++smrXj15XvuRoCJyd3949ragYiwsbm8vJx27dolEQvIB1skYPMFv9Q4cgnHfGsJIClMGyGhwXgS3gxAWsgbXg2GDh3KRKUF0ASNy3ZMKjpOaWOhIonnosBW5sqVK9K2HBDGggULpL1qEydObCUjqxoNz6FVVVVUWVkpkSDKgU0ZHMaBuOTfVpWfCPkm+hhV1p+JScWoU4KmIomnokCKgUthLAJAcsH2HPgCckrvBgdx8MUEsqyrq6Px48dTYWGhY/VxQ2cn+hhV1p+JScWoUoKmIoknouBEGDi8x+512AthO8ovf/lLV7Xtd7/7neSP6NNPP5X8kE+dOlXz9NFVDdJZmUQfo8r6s7mAyoEgWz6rjJ7Q0UBI8OkNKQmncWC6BKW0G/djffvttxJZvvvuuxLmOKUWZ65h+schcRFgYlLRd5i+xFvuVpFFQkTBlO3xxx+XCAlt3rZtm/ojmhxqoWyVDyU7Tk/Bse0IIKgNGzZ4+lBIGXL0G14cXgpMTF7qTZ1tgTS4dOlSmjZtmnRmXkeElAgW8NEEBdMFOOyHBOj1ABMLLwUmJhW96WXr4oMHD0oPb/fu3aXleSzzxwpudUiG6WYsB34gqGXLltGaNWskCdDv93t2ege3PD166PefHqu/nb7GdkwqesCL1sWQkpYvXy7pjzZu3KjK35S8k1+rbZIKiHVFkfV+8VYH77jjDtq8ebN0zNGECRMkosI1L4UvvviChgwZ4qUmOXYKUEKBmJaW5im3Elhuf+SRR6Q+wEOr1gme23byq/V4AOLKz8+XSOmJJ56w9bBMOwY6XJ54zS0PT+VUjJzevXtL2ytURHV9FOhbMPXBsv/8+fM12f7AqttNPraxSohpttoASQnGoTB/gJJflrjUpndrPCi/sXXHS4GJSUVvYoMp9nwl+hI0Vqnmzp0rrTB2pEuKBwd8bMNpnhkh8vlWmpX6U3rj+De6s8MDqVbakwuB9LR27VrpUAUoxu06zVcu3+z/IFds2dG7Cdrs+piVHxOTSiSxfI6NqYkaYNuDI6hgLa13EOOtLG8BMYRD5DRt+82i2IcTaMgYe/T0+CBHETAtWLJkibS1JZHJCfsVMTa9FpiYVPYoXH4cPnxYZWx3RQMpYfqyYsUK3aSEFoHQ4DnAmORYTwdKiunD3sPIZwAm1AGSglaJKbpISI1YAMC+O6xOJmLAmLT1vEObQGJiUgk0Ol92+q4yiSuiRZNSvNUrtZWFRTg21OoLOB58A62gaTRvvDGdCOpQVFSkrxpRqcaMGSOR05133pmQXiAhBeO4dK8FJiaVPYo3s3FpQWVhJkUzm5RQLZwrp/sst8YgrV5BNOcXI+kGg21EHfSccRerWJAT3LfAwDSRpnWQGrGx2mvmD+gjJqZYI7WDa5AWgsFgB3fdddkKUkILQQZweaJ9RaueDqzeRDQn35RThWGdbhYxoV2y5IRpXaKQk1lSo7tG7tXaMDFp6BWs4mzZskVDCmeiwiQAK3Avv/yyJnMANbWFcSX2ZVVUVKiJ3hIHU7g/UCBtLs3LNG6hDH0Qjio329AT5ATndlCMaydeDXCYFBU6NoxJLwYmJg29Ch9EUCIbU/5qKFBHVCyhwyQA+jCzH1y5OlOmTNE2nWsM0tqAj57K62+KiI5pF+pgRYDEBE+ZixYtsiJ70/LEGMR2HIxJTwZhQyDCydDeCCtXrhSBQMCVjWlqahKjRo0S5eXlltYP5aBPL1y4oKKcZnGprFD4iKQ0SNfuk1MqQs0qshJCaCtbXZ7KWChj9uzZYv369cpbrvmNMYix6JWg5AhbGENZaCKDGQqFRG5uriubUFBQYNtgLSoqMkDQMllNEaWhrzVhuWPHDoGyrQ4gXZA8+tuNAWPQrXXTg5eSI3gqp1EOlu1m3OZKY+fOndJy96xZszS2SF/0hx9+WNJj6UutP9Vrr71GDzzwgP4MVKbENBg2Tlipc5u+SR578lhU2aSEisbEpKO7YGkLl7NuCdA3LFy4UNqcaoatkpp2yQ+F/JCoSWM0jlyWXcvjUIZjJRYE5aYgnxrjpjqZXhc9YpfWNEoxTWt6N8Z3kyiNKZwT+hDosuyc1qIsq/VnyrEm6+3cMm1CPTDFRL28FJQcwRKTTqqH1ATjNqcDls6xEmfVKlW89kGiQJAlmXhxjd6Ty5DLNJqf2vSQQLGnDo7m3BAw5mDSYJdk7FSbmZh0Io8HBIQgPzA6szGcbPHixYSPUwMVBI1la6sDynBqsyr21PXp08fxLUkYb/jgLD+vByYmAz1s10PZURVhqwRdj106l1j1AEGjDlbuI4RiH8Rgt7QU3V709UsvveSoIhxSG+rh1EsoGg+rvzMxGUDYjoeyo+phpQgPihtOx0AdUBcrDE/RTij29UlLl+n4e8tpemoXwrllXVKn0yvvHafGjkCNcx3kCw+e77zzTpxY1t0C8TtNzta1LkbOdijQlIotO8q0q4yamhoNxobm1QoGdlB6uyVA+W6FfRHy1GdI+K2oDTwlfL6ZorTqkgRTc3inKMz+sfCXndMFm1OKZ9mmCmPNq0HJEWxgaUJPO0ESbloVBITy6lVlZaUJiF7NAnnpXoFqrhKlOT7h85eJq7SEPL8WodIpimvaqouXgd2W/06tumpDxlhsJTHxVC6GFKn1EvZX4cw1K/Us0XWCwh1ivWxLFH3Pqe/Qe+CoJDj7N2NKhykc8kKeunQqKb1pwB2pVLf/EH3aGGmBpZFqQ0306Phh1F0nUJi2YoO0XUE2nHVi1dWuNsYsxxjPqUutZEN1qRIrljyls0Pcxj4uu+151PYGpnRmTDGRh74pnFzTZtEQLBHZRMKXv05UNXwtwmXFwl9SLsIq9+XJOSn/Q1o1UzJU5i//tnNMyWU69V/JESwxxaRr7RfhdnbHjh2Sm1YrtzBAGoGHA7fuKsebHdKjEakCkifyMLa9JoW6ZT5Fmz5eRfe/N4NuvyGNZlRPohfnjiGfwVGPE2b+/Oc/ax8kGlJgDMH9CsaUXh/tGopzX1Q7GFLJhnaU6VQZeMtDorEqQCIxJkmgZmdEID+9ZZf/g6I4eFGI5rD4uCRf8gKQXhwU3xlogKys1SPVIQ30SuZIns2iIbRNFBe/KPzZPkGUIwrLaoVBganVw4GV1tfGJUYDHehAUiVHsPLb5E7AYAUxGSeP2BUzcxrRXBsQM30kfP4/iJ0li1tXr2KXrO0qVrAw2LQQDOKClMyZJjWLhqp1YuaTAVELJmquFWWFOYKohYi1NaddbKwW6iHedhnFuCC/3KwkvhjFOnqJickG+K0iJ/nBNa8J50SZP1MQZYiZgWrDkoSyXlqkH7ltpj3s0qpcusgprYpq10URLH5QkAb/T8o2yb9RTyvMI7Dih5dPMpESMGVikkeWxf9Nf9CEkJapzZXE9PtFUgsf/Cd1NjWTsTJ1Gf5SmfD7fApiammvCcQE4lA+TGox6SieFiLvKI9Eva7EkqdyFvak/MCZJQVA72DONEdudIsRIikfYPm+Of9Bph2Rk4yRuYSLerdIR1EGlqLhiCjNzzZNOsSU3az+SGZSQm8xMZnzrKnOxcwHD51npogPHdOTM+eJedlKQ0TVzVMdEUp7JTmZiU3MijSHRXCdXzIZAHbkyxfFO0OiIWZk7RfRJnyMBkiKSmyM5plo6ZmYHOgxPIBGFeJQJpu62tdcLQJP+kWg9pJkDU2+QlFW+5EoKdx2VVlsAU6yVIC2yKSEqV6iBkhLRm224kmTiYqLnnozMelBzYQ0skIc5KJH6sFb1ZTpzndBUZxOgrILRSCEzRqyIaJPZPsDItRgdDE9PlggJ0l6IbJsVSt+Dcy7a0TPhLQgNb3jwbxWuCMnJTEZNDVzn12WW2uEbRUrVqyQzkN75JFHNB+qeOzYMXO2oFyXSc+eECTeX0qTB2FjBgwR59L7IkzvvzyZBnWzdkhUVlZKGOBcOHy30hjV6rGAPs3NzdXclzhQE2Pg1ltvlcaEri03VjfO4fytHYUON85txWMAwpoXlsP9+vUj7INSG06dOkUDBgxQG9118fAwPv7445LV+kcffUT4nDlzhubMmaP5wXZT47Bf8fz586qrhD5H32MMYCwwKXUAnR2CnFJMs6NMt5ch650gzqs5nw0Y6pkCugEH2WQgljkArqFtse65oe6d1QH1VlN39DH6GjZK6HsO1yKg5AiWmDogbKsvY/8TpnYZGRk0YcKEuJ4J5OlOor1dZSkJx6pj/xu8MCgDrtXU1EgO2CBRIU0ihW7dulE4HI5bZUhJ6GP09ebNm5Nz71tchGLcvJa3rPmlZENrSkncXGXpCW9TrFgpA64ZXf1R5mnlb0h28mqTGmlCrgviYtkcaRNFOozXN7iHPoWCO1a/yu3m/+3tmFhiikHWdl+C9LR27VrJfSz8OuMDp/OJFiDZQTIaO3asVPV33303ppTUUbsgPSENAvJAXrK02FEaN15H36EPcVgmXAKjb93kO8uNmCnr1AVsrbxo9m/4W7ahGLOr7Uh+eBDhVxo+tOFjeurUqfTll19SMBik+fPnO1KnzgqFK5a3335bOnATdYZC26irDuS5evVq2rZtm6QknjRpEuF0XLcF9FfXruA7URoAAAxbSURBVF2l8Y2jtDZt2kR79uyRjljCaSaJNv12Ct92HGGHGMlTOe0oYyoDmx9MBbKyssRvfvMbVUpy7SXpTwEDQ2xkRf9i+qVGia+1NOSJvFEGyjJrC4jWenQUH/2EuqGf8IGiP1GmoR21yYnrSo5gicmpV4SGcktKSujAgQPS27ioqEia5sBRnBNvYyind+/e3aqsx7L33XffbXldIJl88MEH9Nprr0nKZiy1jx492pEpEupSUVFBe/fupQULFkg9CZssJ4/R0jCcXBlVKTExMbmym66tFHQtCJgaRD8Q8D+Na1jtgW2MFUQFIjp9+rRkDAmvlKmpqZLeaNy4cYana9e2Uv2vaHLEilheXp5E1v3797esTtAbHT16VJpm4zTc6BeEPJVT3wKOqUSAiUmJSAL8lokperkdb+1QKESHDx+WJAk8LCCq2267jYYMGUJpaWmS7qN3796qdDOysr26uprOnj0rPYTQlSDgwR85ciQNHTrUsgdfbzdAFwX9Gz7QR33yySeSwhlkfdNNN7UapapRPiMvGEs2NTXRyZMnCdb2MGyVsYVkOGzYMBo8ePA1LwHlQ6W3LcmcTokhS0wJMBpiEVOsaoNcQCyNjY20b98+KQrIBQ9rZwGk1rNnT2mbBKQiPNhqSa2zvO28L5MLpBtIU7Auh/9wkEtnYdSoUdKCA+JhmggbJVjbd0Zqyoeqs3L4fnsElBgyMbXHyHVX1BKT6yqeJBVSPlRJ0mxTm6nEkO2YTIXXmsz69u0rTSusyZ1zNYIAptQczEeAicl8TE3PEYdb1tfXm54vZ2gcAWyngRElB3MRYGIyF0/OjRFgBExAgInJBBCtzgKmAMXFxVYXw/nrQACLDfCrxMFcBJiYzMXTktxk+yTWZ1gCr6FMsQKKVUwO5iLAxGQunpblhuV86DM4uAsBmGXAZoyDuQgwMZmLp2W5wRUtpg0c3IUAbMdg78XBXASYmMzF07LcMF2QrbMtK4Qz1oQAptbbt293nTW8pka4NDITk0s7RlktWGLv2rVLeZl/O4gAtgSxqYA1HcCW39bgakmusI7FPi5ZGW5JIZypagSwqRkhPz9fdRqOGBsBtvyOjUtCXMXbGd4FOLgDAbhhwaZeDuYjwBKT+ZhaliOc2kPPBF9EHJxFAJuFb7zxRvbMalI3sMRkEpBOZAO3I/L0wYnyucw2BOBmBT6ZOFiDACu/rcHVklzhRxurc/AtnRCh8Tjt3rqJXpk+np7bHetQyCtUt/9Vmp7ahbp0SaV7nttKxxsjCdE0HEklH7qQEBVOsEoyMSVYh8FZXHl5uftrHTlGb/zjQlofeJEKNlyIUd8INVa+QztpMv0+LKg5vIV+cnYRZf92D12OEdtNlzCNg38nuDfmYA0CTEzW4GpZrjgtBNM5129PSRlCM99+i36/aC7lxEIjcpqCl0bQo1k+wiBM8f1vmjX9H4je3EXBy+6WmuB8D9M4Xh2N1bHmXGNiMgdH23LBEUY4IinhV+dSbqPs7H4SKV0F7wqdrT5Ng+flUVZ3dw9LvBgeeOAB2/o8GQty9whIxh5R0ebc3FxveRuALuqNf6KiEzNo07ws6qYCA6eiyPo9PhHF2h5gYrIWX0tyHzNmjJSv/JBYUogtmUbo8u75lHrDYLp31ou04aP36aMT7tYw4UBLHFnFwVoEmJisxdey3GFtjIcksUMKdR+3lMLiWwoHN5Cf1tFD2fNp6+dXXNks2JBBv4TTUjhYiwATk7X4WpY7zpPDQ+KNjb3fJ1/mo/Tivy6hnLp99HHInVITVuKef/55VnpbNqrbMmZiasMiob5hRQgPiZc8W6YM/DH9LOdvXNkPsrSEFwIH6xFgYrIeY8tKgE3TuXPn6MMPP7SsDFszbgxT6LM76UeDu9tarJrC/H4/LVmyhKUlNWCZEIeJyQQQncxi8eLFNHfuXPfbNSlAiny+lWaljqfn1u+nOpgtRT6n3S+tprPzf0E5N39fEdvZn9ijiJCTE9Miy9nKebV0YUMgwl5HDlYhUFBQINavX29V9jrzPSfK/JkCfd/6ySkVoeaW7BqOiNL8jNZ7vvxiEQiGhXxbZ6GmJ7tw4YIYNWqUCIVCpufNGbYhoOQI9i7ggTcOtkhMmDCBNm7c2Olx1h5orq1NwBQOp6CwRwdrYWfvAtbi60jusAaH/gMPkeu3qjiCkL5CZTczs2bN0pcBp9KNAOuYdEPnroTQfwwaNIiWL1/uroolaG1qa2tp4cKFtGzZMlZ4O9CHPJVzAHSrioS0BFcckJ5YUasfZeA4Z84cgmkAVj45WI+AcirHxGQ95raWgDc9Tu6Fo3xIUBy0I7B06VKqr6+XpCXtqTmFHgSUxMRTOT0oujgNnMnBX9O0adMIJMVBGwKrVq2iU6dO0QsvvKAtIcc2FQEmJlPhdEdm2OSLVSR8WBmuvk9gqAqXJosWLepEr9RIB165h/CWb/e55zl6Y/dxalRfLMeMgQATUwxQvHAJm3zvu+8+SVfC5NR5j4KUYKi6detWFQdYdqPMZ8voUlkh+SiT/GXnpEMJREMVBbIO0qx7H6Jntp4md7u76xwTJ2MwMTmJvsVlQ2LC0eJQ5DI5dQy2NlJS5pNGg29p8SDVbQjlzfoZ5dBRemP7AfpCGZV/q0aAiUk1VIkZkckpfr/pJ6WvKLhjJ9XlTKC7Bl7fUkiEGmtP0BHyUc7YodQ3ftF8Nw4CTExxwPHKLZmcYErACvG2XoU+Sf30rS2d9O2vp6kicIDS7x9OaXiKInV0YGsJPT1tHQ32r6KVPx0U5TZYkZZ/do5A224V674p98FYVxLnHA+BQCAg7fuqrKyMF83z95qamsTKlStFbm6uqKmp0dXe5lCpyIneByh9f1AUBy/qyi/ZEyk5giWmzrnbMzFgLAjL8CeeeEJS8nqmYRoagn2F0LkdOnSINm/erELRHSvzb+hE+bu0k56kQPg7ErIHzuwKKnj2X2h3nTs9cMZqiVuvMTG5tWcsqhdMCbDyhGlMsu2tg490bHaGa9y1a9d2YhIQrwMaqTZ0kignizL6XkdE8MD5c1rw6xnk27OYpv1zuevPxovXOjfcY2JyQy/YXAcYYUJa6NGjh7SFJfEPNYgPIFYkYc0NSXHNmjUEUwpD4fJh2vFmlH5JyiyFuv6wF3Ulorqz9fTfhgrgxExMSToG4Jp3/vz50oOKBxYPLqY5XgtYdZOP8t67dy+ZcexS5Gw1HazLpIdG9CfIS1dDPR16fw99xityMiDG/tuhdFMqtuwok8tQj4CsDIZDNCjI8TvRA5TacKCHNpmq7G+uFoGZGYJ8haLs0lW3ds3hj8U6f47k9M6Xv05UNbjN3Z37e1PJEba4llQW6n6YkrOG8NKIhxmrVeXl5QkJAjxOYsUNY85skv0uWCzS263EtXjozPaL0m1BEWZO0jVulBzB3gWMCZyeTI3pj3z6SkFBAY0YMcKAotgeiGCftW3bNnr66adp5cqVNHXqVIIDPQ6JgYDSuwATU2L0myO1BEFt375dOr8ORpqTJk1y3cMeXUcotZmQHBkqhgtlYjIMYfJlIEsjMDHA3rspU6bQyJEjHSMprCLCtUt0fWACAIU+h8REgIkpMfvNFbXGsntFRQVhdWvBggU0e/ZsySZo9OjRknM6q4gBq4VVVVVSuZiupaamSp4lx40bp9NA0hVwciWiEGBiigKDvxpDAJLL4cOH6YMPPiAcnw2igkQF4sjIyKCuXbtqIg4QX01NjXSI5xdffEH79u2TppGoZV5eniSlDR06VFOexlrIqe1CgInJLqSTrByZVI4ePUrhcJjOnDlDOFYbOiqE3NzcDl39yop2xAO59ezZkyCF9e3bl/r3789ElARjiYkpCTrZjU0ESXUUevfu7Zi+qqM68XV7EWBishdvLo0RYARUIKAkJt6SogI0jsIIMAL2IsDEZC/eXBojwAioQICJSQVIHIURYATsRYCJyV68uTRGgBFQgQATkwqQOAojwAjYiwATk714c2mMACOgAgEmJhUgcRRGgBGwFwEmJnvx5tIYAUZABQJMTCpA4iiMACNgLwJMTPbizaUxAoyACgSYmFSAxFEYAUbAXgSYmOzFm0tjBBgBFQgwMakAiaMwAoyAvQi0HYtlcbnYPcyBEWAEGAE1CNhCTELgNB0OjAAjwAioQ4Cncupw4liMACNgIwJMTDaCzUUxAoyAOgSYmNThxLEYAUbARgT+P9Z+4pS1sdvsAAAAAElFTkSuQmCC"></p>
</div>
<div class="specification">
<p>There are 54 employees in the company.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <em>a</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <em>b</em>.</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>Use the tree diagram to find the probability that an employee encountered traffic and was late for work.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the tree diagram to find the probability that an employee was late for work.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the tree diagram to find the probability that an employee encountered traffic given that they were late for work.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>x</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>y</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of employees who, in the last year, did not travel to work by car, bicycle or public transportation.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n\left( {\left( {C \cup B} \right) \cap P'} \right)"> <mi>n</mi> <mrow> <mo>(</mo> <mrow> <mrow> <mo>(</mo> <mrow> <mi>C</mi> <mo>∪</mo> <mi>B</mi> </mrow> <mo>)</mo> </mrow> <mo>∩</mo> <msup> <mi>P</mi> <mo>′</mo> </msup> </mrow> <mo>)</mo> </mrow> </math></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><em>a</em> = 0.2 <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>b</em> = 0.85 <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.25 × 0.8 <em><strong>(M1)</strong></em></p>
<p><strong>Note</strong>: Award <em><strong>(M1)</strong></em> for a correct product.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.2\,\,\,\left( {\,\frac{1}{5},\,\,\,20\% } \right)">
<mo>=</mo>
<mn>0.2</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mn>1</mn>
<mn>5</mn>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>20</mn>
<mi mathvariant="normal">%</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)(G2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.25 × 0.8 + 0.75 × 0.15 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for their (0.25 × 0.8) and (0.75 × 0.15), <em><strong>(M1)</strong></em> for adding two products.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.313\,\,\,\left( {0.3125,\,\,\,\frac{5}{{16}},\,\,\,31.3\% } \right)"> <mo>=</mo> <mn>0.313</mn> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mn>0.3125</mn> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mfrac> <mn>5</mn> <mrow> <mn>16</mn> </mrow> </mfrac> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>31.3</mn> <mi mathvariant="normal">%</mi> </mrow> <mo>)</mo> </mrow> </math></span> <em><strong>(A1)</strong></em><strong>(ft)<em>(G3)</em></strong></p>
<p><strong>Note:</strong> Award the final <em><strong>(A1)</strong></em><strong>(ft)</strong> only if answer does not exceed 1. Follow through from part (b)(i).</p>
<p><strong><em>[3 marks]</em></strong></p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.25 \times 0.8}}{{0.25 \times 0.8 + 0.75 \times 0.15}}"> <mfrac> <mrow> <mn>0.25</mn> <mo>×</mo> <mn>0.8</mn> </mrow> <mrow> <mn>0.25</mn> <mo>×</mo> <mn>0.8</mn> <mo>+</mo> <mn>0.75</mn> <mo>×</mo> <mn>0.15</mn> </mrow> </mfrac> </math></span> <strong><em>(A1)</em>(ft)</strong><strong><em>(A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for a correct numerator (their part (b)(i)), <strong><em>(A1)</em>(ft)</strong> for a correct denominator (their part (b)(ii)). Follow through from parts (b)(i) and (b)(ii).</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.64\,\,\,\left( {\frac{{16}}{{25}},\,\,64{\text{% }}} \right)"> <mo>=</mo> <mn>0.64</mn> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>16</mn> </mrow> <mrow> <mn>25</mn> </mrow> </mfrac> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>64</mn> <mrow> <mtext>% </mtext> </mrow> </mrow> <mo>)</mo> </mrow> </math></span> <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p><strong>Note:</strong> Award final <strong><em>(A1)</em>(ft)</strong> only if answer does not exceed 1.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(<em>x</em> =) 3 <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 Mark]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(<em>y</em> =) 10 <em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Following through from part (c)(i) but only if their <em>x</em> is less than or equal to 13.</p>
<p><em><strong>[1 Mark]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>54 − (10 + 3 + 4 + 2 + 6 + 8 + 13) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for subtracting their correct sum from 54. Follow through from their part (c).</p>
<p>= 8 <em><strong>(A1)</strong></em><strong>(ft)<em>(G2)</em></strong></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> only if their sum does not exceed 54. Follow through from their part (c).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>6 + 8 + 13 <em><strong>(M1)</strong></em></p>
<p><strong>Note</strong>: Award (M1) for summing 6, 8 and 13.</p>
<p>27 <em><strong>(A1)(G2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[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.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">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Sila High School has 110 students. They each take exactly one language class from a choice of English, Spanish or Chinese. The following table shows the number of female and male students in the three different language classes.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>A <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
<mrow>
<msup>
<mi>χ<!-- χ --></mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> test was carried out at the 5 % significance level to analyse the relationship between gender and student choice of language class.</p>
</div>
<div class="specification">
<p>Use your graphic display calculator to write down</p>
</div>
<div class="specification">
<p>The critical value at the 5 % significance level for this test is 5.99.</p>
</div>
<div class="specification">
<p>One student is chosen at random from this school.</p>
</div>
<div class="specification">
<p>Another student is chosen at random from this school.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the null hypothesis, H<sub>0 </sub>, for this test.</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>State the number of degrees of freedom.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the expected frequency of female students who chose to take the Chinese class.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State whether or not H<sub>0</sub> should be rejected. Justify your statement.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the student does not take the Spanish class.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that neither of the two students take the Spanish class.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that at least one of the two students is female.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>(H<sub>0</sub>:) (choice of) language is independent of gender <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Accept “there is no association between language (choice) and gender”. Accept “language (choice) is not dependent on gender”. Do not accept “not related” or “not correlated” or “not influenced”.</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>2 <em><strong>(AG)</strong></em></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>16.4 (16.4181…) <em><strong>(G1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(we) reject the null hypothesis <strong><em>(A1)</em>(ft)</strong></p>
<p>8.68507… > 5.99 <strong><em>(R1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from part (c)(ii). Accept “do not accept” in place of “reject.” Do not award <strong><em>(A1)</em>(ft)<em>(R0)</em></strong>.</p>
<p><strong>OR</strong></p>
<p>(we) reject the null hypothesis <em><strong>(A1)</strong></em></p>
<p>0.0130034 < 0.05 <em><strong>(R1)</strong></em></p>
<p><strong>Note:</strong> Accept “do not accept” in place of “reject.” Do not award <strong><em>(A1)</em>(ft)<em>(R0)</em></strong>.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{88}}{{110}}\,\,\,\left( {\frac{4}{5}{\text{,}}\,\,0.8{\text{,}}\,\,80{\text{% }}} \right)">
<mfrac>
<mrow>
<mn>88</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>4</mn>
<mn>5</mn>
</mfrac>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>0.8</mn>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>80</mn>
<mrow>
<mtext>% </mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em></strong><strong><em>(A1)</em></strong><strong><em>(G2)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em></strong> for correct numerator, <strong><em>(A1)</em></strong> for correct denominator.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{88}}{{110}} \times \frac{{87}}{{109}}">
<mfrac>
<mrow>
<mn>88</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>87</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)</em></strong><strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for multiplying two fractions. Award <strong><em>(M1)</em></strong> for multiplying their correct fractions.</p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{{46}}{{110}}} \right)\left( {\frac{{45}}{{109}}} \right) + 2\left( {\frac{{46}}{{110}}} \right)\left( {\frac{{42}}{{109}}} \right) + \left( {\frac{{42}}{{110}}} \right)\left( {\frac{{41}}{{109}}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>46</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>45</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>46</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>42</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>42</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>41</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(M1)</em></strong><strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for correct products; <strong><em>(M1)</em></strong> for adding 4 products.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.639\,\,\,\left( {0.638532 \ldots {\text{,}}\,\,\frac{{348}}{{545}}{\text{,}}\,\,63.9{\text{% }}} \right)">
<mn>0.639</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.638532</mn>
<mo>…</mo>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mrow>
<mn>348</mn>
</mrow>
<mrow>
<mn>545</mn>
</mrow>
</mfrac>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>63.9</mn>
<mrow>
<mtext>% </mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p><strong>Note:</strong> Follow through from their answer to part (e)(i).</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1 - \frac{{67}}{{110}} \times \frac{{66}}{{109}}">
<mn>1</mn>
<mo>−</mo>
<mfrac>
<mrow>
<mn>67</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>66</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)</em></strong><strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for multiplying two correct fractions. Award <strong><em>(M1)</em></strong> for subtracting their product of two fractions from 1.</p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{43}}{{110}} \times \frac{{42}}{{109}} + \frac{{43}}{{110}} \times \frac{{67}}{{109}} + \frac{{67}}{{110}} \times \frac{{43}}{{109}}">
<mfrac>
<mrow>
<mn>43</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>42</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<mn>43</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>67</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<mn>67</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>43</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)</em></strong><strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for correct products; <strong><em>(M1)</em></strong> for adding three products.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.631\,\,\,\left( {0.631192 \ldots {\text{,}}\,\,63.1{\text{% ,}}\,\,\frac{{344}}{{545}}} \right)">
<mn>0.631</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.631192</mn>
<mo>…</mo>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>63.1</mn>
<mrow>
<mtext>% ,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mrow>
<mn>344</mn>
</mrow>
<mrow>
<mn>545</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)</strong></em><em><strong>(G2)</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">e.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{1}{3}{x^3} + \frac{3}{4}{x^2} - x - 1">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>+</mo>
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mn>1</mn>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'\left( x \right)">
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the gradient of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 2">
<mi>x</mi>
<mo>=</mo>
<mn>2</mn>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of the tangent line to the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 2">
<mi>x</mi>
<mo>=</mo>
<mn>2</mn>
</math></span>. Give the equation in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="ax + by + d = 0">
<mi>a</mi>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
<mi>y</mi>
<mo>+</mo>
<mi>d</mi>
<mo>=</mo>
<mn>0</mn>
</math></span> where, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span>, and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d \in \mathbb{Z}">
<mi>d</mi>
<mo>∈</mo>
<mrow>
<mi mathvariant="double-struck">Z</mi>
</mrow>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^2} + \frac{3}{2}x - 1">
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
<mi>x</mi>
<mo>−</mo>
<mn>1</mn>
</math></span> <strong><em>(A1)(A1)(A1)</em></strong></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for each correct term. Award at most <em><strong>(A1)(A1)(A0)</strong></em> if there are extra terms.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{2^2} + \frac{3}{2} \times 2 - 1">
<mrow>
<msup>
<mn>2</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
<mo>×</mo>
<mn>2</mn>
<mo>−</mo>
<mn>1</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of 2 in their derivative of the function.</p>
<p>6 <strong><em>(A1)</em>(ft)</strong><strong><em>(G2)</em></strong></p>
<p><strong>Note:</strong> Follow through from part (d).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{8}{3} = 6\left( 2 \right) + c">
<mfrac>
<mn>8</mn>
<mn>3</mn>
</mfrac>
<mo>=</mo>
<mn>6</mn>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>c</mi>
</math></span> <strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for 2, their part (a) and their part (e) substituted into equation of a straight line.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c = - \frac{{28}}{3}">
<mi>c</mi>
<mo>=</mo>
<mo>−</mo>
<mfrac>
<mrow>
<mn>28</mn>
</mrow>
<mn>3</mn>
</mfrac>
</math></span></p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {y - \frac{8}{3}} \right) = 6\left( {x - 2} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mi>y</mi>
<mo>−</mo>
<mfrac>
<mn>8</mn>
<mn>3</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>6</mn>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for 2, their part (a) and their part (e) substituted into equation of a straight line.</p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 6x - \frac{{28}}{3}\,\,\left( {y = 6x - 9.33333 \ldots } \right)">
<mi>y</mi>
<mo>=</mo>
<mn>6</mn>
<mi>x</mi>
<mo>−</mo>
<mfrac>
<mrow>
<mn>28</mn>
</mrow>
<mn>3</mn>
</mfrac>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mi>y</mi>
<mo>=</mo>
<mn>6</mn>
<mi>x</mi>
<mo>−</mo>
<mn>9.33333</mn>
<mo>…</mo>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their answer to (e) and intercept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - \frac{{28}}{3}">
<mo>−</mo>
<mfrac>
<mrow>
<mn>28</mn>
</mrow>
<mn>3</mn>
</mfrac>
</math></span> substituted in the gradient-intercept line equation.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 18x + 3y + 28 = 0">
<mo>−</mo>
<mn>18</mn>
<mi>x</mi>
<mo>+</mo>
<mn>3</mn>
<mi>y</mi>
<mo>+</mo>
<mn>28</mn>
<mo>=</mo>
<mn>0</mn>
</math></span> (accept integer multiples) <strong><em>(A1)</em>(ft)</strong><strong><em>(G2)</em></strong></p>
<p><strong>Note:</strong> Follow through from parts (a) and (e).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = a\sin bx + c">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>a</mi>
<mi>sin</mi>
<mo><!-- --></mo>
<mi>b</mi>
<mi>x</mi>
<mo>+</mo>
<mi>c</mi>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant x \leqslant 12">
<mn>0</mn>
<mo>⩽<!-- ⩽ --></mo>
<mi>x</mi>
<mo>⩽<!-- ⩽ --></mo>
<mn>12</mn>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-03_om_16.53.31.png" alt="N16/5/MATME/SP2/ENG/TZ0/10"></p>
<p style="text-align: center;">The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> has a minimum point at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(3,{\text{ }}5)">
<mo stretchy="false">(</mo>
<mn>3</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>5</mn>
<mo stretchy="false">)</mo>
</math></span> and a maximum point at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(9,{\text{ }}17)">
<mo stretchy="false">(</mo>
<mn>9</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>17</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
</div>
<div class="specification">
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> is obtained from the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> by a translation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} k \\ 0 \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mi>k</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>. The maximum point on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> has coordinates <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(11.5,{\text{ }}17)">
<mo stretchy="false">(</mo>
<mn>11.5</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>17</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
</div>
<div class="specification">
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> changes from concave-up to concave-down when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = w">
<mi>x</mi>
<mo>=</mo>
<mi>w</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c">
<mi>c</mi>
</math></span>.</p>
<p>(ii) Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b = \frac{\pi }{6}">
<mi>b</mi>
<mo>=</mo>
<mfrac>
<mi>π</mi>
<mn>6</mn>
</mfrac>
</math></span>.</p>
<p>(iii) Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span>.</p>
<p>(ii) Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x)">
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></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>(i) Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
<mi>w</mi>
</math></span>.</p>
<p>(ii) Hence or otherwise, find the maximum positive rate of change of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>(i) valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{5 + 17}}{2}">
<mfrac>
<mrow>
<mn>5</mn>
<mo>+</mo>
<mn>17</mn>
</mrow>
<mn>2</mn>
</mfrac>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c = 11">
<mi>c</mi>
<mo>=</mo>
<mn>11</mn>
</math></span> <strong><em>A1 N2</em></strong></p>
<p>(ii) valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span>period is 12, per <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{2\pi }}{b},{\text{ }}9 - 3">
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
<mi>b</mi>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>9</mn>
<mo>−</mo>
<mn>3</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b = \frac{{2\pi }}{{12}}">
<mi>b</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
<mrow>
<mn>12</mn>
</mrow>
</mfrac>
</math></span> <strong><em>A1</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b = \frac{\pi }{6}">
<mi>b</mi>
<mo>=</mo>
<mfrac>
<mi>π</mi>
<mn>6</mn>
</mfrac>
</math></span> <strong><em>AG N0</em></strong></p>
<p>(iii) <strong>METHOD 1</strong></p>
<p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="5 = a\sin \left( {\frac{\pi }{6} \times 3} \right) + 11">
<mn>5</mn>
<mo>=</mo>
<mi>a</mi>
<mi>sin</mi>
<mo></mo>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mi>π</mi>
<mn>6</mn>
</mfrac>
<mo>×</mo>
<mn>3</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>11</mn>
</math></span>, substitution of points</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = - 6">
<mi>a</mi>
<mo>=</mo>
<mo>−</mo>
<mn>6</mn>
</math></span> <strong><em>A1 N2</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{17 - 5}}{2}">
<mfrac>
<mrow>
<mn>17</mn>
<mo>−</mo>
<mn>5</mn>
</mrow>
<mn>2</mn>
</mfrac>
</math></span>, amplitude is 6</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = - 6">
<mi>a</mi>
<mo>=</mo>
<mo>−</mo>
<mn>6</mn>
</math></span> <strong><em>A1 N2</em></strong></p>
<p><strong><em>[6 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 2.5">
<mi>k</mi>
<mo>=</mo>
<mn>2.5</mn>
</math></span> <strong><em>A1 N1</em></strong></p>
<p>(ii) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x) = - 6\sin \left( {\frac{\pi }{6}(x - 2.5)} \right) + 11">
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mo>−</mo>
<mn>6</mn>
<mi>sin</mi>
<mo></mo>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mi>π</mi>
<mn>6</mn>
</mfrac>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>−</mo>
<mn>2.5</mn>
<mo stretchy="false">)</mo>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>11</mn>
</math></span> <strong><em>A2 N2</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) <strong>METHOD 1 </strong>Using <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span></p>
<p>recognizing that a point of inflexion is required <strong><em>M1</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span>sketch, recognizing change in concavity</p>
<p>evidence of valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g''(x) = 0">
<msup>
<mi>g</mi>
<mo>″</mo>
</msup>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0</mn>
</math></span>, sketch, coordinates of max/min on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{g'}">
<mrow>
<msup>
<mi>g</mi>
<mo>′</mo>
</msup>
</mrow>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w = 8.5">
<mi>w</mi>
<mo>=</mo>
<mn>8.5</mn>
</math></span> (exact) <strong><em>A1 N2</em></strong></p>
<p><strong>METHOD 2 </strong>Using <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span></p>
<p>recognizing that a point of inflexion is required <strong><em>M1</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span>sketch, recognizing change in concavity</p>
<p>evidence of valid approach involving translation <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = w - k">
<mi>x</mi>
<mo>=</mo>
<mi>w</mi>
<mo>−</mo>
<mi>k</mi>
</math></span>, sketch, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6 + 2.5">
<mn>6</mn>
<mo>+</mo>
<mn>2.5</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w = 8.5">
<mi>w</mi>
<mo>=</mo>
<mn>8.5</mn>
</math></span> (exact) <strong><em>A1 N2</em></strong></p>
<p>(ii) valid approach involving the derivative of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> (seen anywhere) <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g'(w),{\text{ }} - \pi \cos \left( {\frac{\pi }{6}x} \right)">
<msup>
<mi>g</mi>
<mo>′</mo>
</msup>
<mo stretchy="false">(</mo>
<mi>w</mi>
<mo stretchy="false">)</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>−</mo>
<mi>π</mi>
<mi>cos</mi>
<mo></mo>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mi>π</mi>
<mn>6</mn>
</mfrac>
<mi>x</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, max on derivative, sketch of derivative</p>
<p>attempt to find max value on derivative <strong><em>M1</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - \pi \cos \left( {\frac{\pi }{6}(8.5 - 2.5)} \right),{\text{ }}f'(6)">
<mo>−</mo>
<mi>π</mi>
<mi>cos</mi>
<mo></mo>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mi>π</mi>
<mn>6</mn>
</mfrac>
<mo stretchy="false">(</mo>
<mn>8.5</mn>
<mo>−</mo>
<mn>2.5</mn>
<mo stretchy="false">)</mo>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mo stretchy="false">(</mo>
<mn>6</mn>
<mo stretchy="false">)</mo>
</math></span>, dot on max of sketch</p>
<p>3.14159</p>
<p>max rate of change <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \pi ">
<mo>=</mo>
<mi>π</mi>
</math></span> (exact), 3.14 <strong><em>A1 N2</em></strong></p>
<p><strong><em>[6 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>A hollow chocolate box is manufactured in the form of a right prism with a regular hexagonal base. The height of the prism is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo> </mo><mtext>cm</mtext></math>, and the top and base of the prism have sides of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo> </mo><mtext>cm</mtext></math>.</p>
<p style="text-align: center;"><img 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Sim56EhGJ2zGlbhcZl0buzZJ4EuhFS3jPSPBIGjBNShc2v3KL1jx9n4qdbE/pd/+b/HMuEoCHRAwL2Q6mRkcfoOWpJzE5lw1s5Bikz3rETWzlJKhsAxAu6FVLfkiEaPOZej7gkgpPcsav5lkwQZn65JnbJqE3AtpIpGdTW7ZznAOYCascms3TkycbYhpG18Le5/9Vf/k4lebfBTaiUCroX0yHKAc9zoROeoxNqmV4OxaEBdn4u3LoQfP34XIa2LntIqE3AtpFo1JccEEYS0cquiOAhcLndDMjZbmlu7NImRCbgVUlt+LAd8hDQHRfKAQDoBPfJikwRNTNOPZk8I9EXArZDqoe4jywHO4VdeZ8dZ5/JlGwQgME9At9JtkiBCOs+IreMQcCmkEj3d1s2VdGVMggAE6hCwSYK2EANCWoc7pbQj4FJIdSs255gKQtqugVFyPAI6d3UOW0JIjQSfoxJwJ6QllgPUzEFSbAIWHcWmUKf2t4+sIaR1uFNKOwLuhFTjKhpfyZl4hjQnzT7zYsJZHb/NPbKGkNZhTyntCLgS0ulMv3ZIKHlEAghpHa9qbsPtJEGEtA57SmlHwJWQ6oSzmX7tkFDyiAQQ0vJe1TPfc5MEEdLy7CmhLQE3Qmoz/Vh9pm2DGLV0hLS8Z8X4NhpVqQhpefaU0JaAGyHVyaYTkQSBEgQQ0hJU7/O0xenn5iMgpPec+GtMAm6EVLeEWDRhzEbmoVYIaVkvaEhGgjmXENI5KmwbiYALIdXtoLmxlVygiXRzkew3H4S0nO9skuBcNKpSEdJy7MnZBwEXQjo30y8nHhZkyEmzz7x0scazpGV8p2h0bZIgQlqGO7n6IdBcSHMvBziHFiGdo8I2CJwnoChU59faRQpCep4zOfgm0FxIdctNL94umRDSknTJOzIBieRaNCo2CGnkFhKj7k2F1F78uzS2kssFCGkukuQDgXsCOm9vlwO8//X+L4T0ngV/jUmgqZCuzfTLiRshzUmTvCDwOQGNO6dM5ENIaTGjE2gmpDbTb21sJRd8hDQXSfKBwD0BTRLUakZbCSHdIsTvvRNoJqRbM/1ygi35aE1OO8mrHAF1+KWHEMpZ7y/nPY+sIaT+/IdFeQk0EVIbW6kRjebFRW69EuA50ryeE0+JaUpCSFMosU/PBJoIqU6slLGVnsFiuy8CCGk+f9hygKk5IqSppNivVwJNhDRlpl+vQLHbJwGENJ9fxFLimJoQ0lRS7NcrgepCmjrTr1eg2O2TAEKaxy8ajtGF8J7xZoQ0D3ty8UugupCWXg7QL2osa0kAIc1DX5ME33nnh7syQ0h34WLnDglUFdKlF/+W5rbn6rm0LeTfhgBCep770UfWENLz7MnBN4GqQqrOLHWmX05suhVFik0AIT3vfwni1nKAc6UgpHNU2DYSgWpCajP9WkSHLMgwUpM9VhctR9mi7R2z1t9RYqcLUnHcmxDSvcTYvzcC1YT00aPXds30ywkSIc1Jk7wiEtCLJRTVH0kI6RFqHNMTgSpCamMrrSIChLSnJomtHglokqDuKh1JCOkRahzTE4EqQlpzOcA5+AjpHBW2QSCNwJ7lAOdyREjnqLBtJALFhVRRqISs5XKACOlITZa61CZw9pE1hLS2xyivNoHiQqqT6MhMv5wgENKcNMkrEgHdzj370geENFKLiVnXokJqM/2Ojq3kcklrIc9VD/I5TkCdecu7Isctb3ukJhiJ3ZmEkJ6hx7E9ECgqpCwH2EMTiGEjz5Hu97Meddm7HOBcKQjpHBW2jUTgkJCmzr598cWvNVmAYSQHUZc8BBDS/Rx1J+dsNKpSEdL97DmiLwK7hVRRZupamxqb1BVtjpOxL6xY640AQrrPI/bIWo7b4QjpPvbs3R+BXUJqY54SyJQVTrSfxkfViWnCgtbaJUGgBQGEdB91XSznmluAkO5jz979EdglpDq5JI76p45pK2k/S/Ysmo5LEWE7jk8I5CCAkKZTtAvmHNGoSkVI09mzZ58EkoXUbvWYkOpzK8KcCqnw6ATVSaXbvbraTR1rPYtWIk6KTQAhTfe/ztGUC+XUHBHSVFLs1yuBZCHViTUVUf299XzZrZAaJImy1t6VoGoNz9JpyY7S5ZK/HwIIabovdF7mfGQNIU1nz559EkgSUp1UtyJq33WSLKUtAVO+r7zy8p0g5zxxb+3ZsuN2f76PRyDXbcrxyFzXSHdvdE7mTAhpTprk5ZFAkpDeGp4qTKn76eTVVbCihhIdXqodt/XkOwSiETi7HOAcL4R0jgrbRiLgQkgF1MZPJXqa1JRz/BQhHanJUpdSBDTnYWu45kjZCOkRahzTEwE3QmrQFJEqMlWEmmuSEEJqdPmEwDIBnXe5zrlpKQjplAZ/j0jAnZAaZI2Z6upY4zVnx08RUqPKJwTmCegc08VrzjtBVhJCaiT4HJWAWyE14JrVqxNcs3yPjp8ipEaTTwjME8i1HOBc7gjpHBW2jUTAvZAKtq6SbTEInZR7r5pL3K4aqRFEqIsuxFgIZN7TukDVxebe82o+t4dbEdKHTNgyFoEuhNSQqyPUOE6JmYVWBp9jElC7OTtEMCaZy93iKLmWA5xjhJDOUWHbSAS6ElIDb7ML6RyNCJ9bBGgr84QUhSoaPTpsMp/r9VaE9JoH38Yj0KWQmht0gmr8tOZyg1Y2n30RQEjn/aVzSLe9SyaEtCRd8vZAoGshFUBdSUtIJag6YUkQmCOAkD6komhU503pW94I6UP2bBmLQPdCau5QZ6DOUuOnW4vp2zF8xiGAkD70tSbhiUvphJCWJkz+rQkMI6QGUp2DxFQdhM3SJFI1OnE/EdKHvq910YmQPmTPlrEIDCekco9uWenk1SQKe2xmLLdRm70EdPu/5ISavfa03t8uOGvYgZDWoEwZLQkMKaQGVB2nJlJIUGu8rs3K5RMC3gkoQq/1fDVC6r01YN9ZAkMLqcGRkNZ4XZuVxycEPBOw5QBr2YiQ1iJNOa0IhBFSAdYVuGYp6mqc23ytmhzltiag9i9xq5UQ0lqkKacVgVBCKsgaP7VxU53g+k6CQBQCuoDUxWTNdo+QRmldcesZTkjN1epQdGWuTqXWWJGVzScEWhHQpCv9q5kQ0pq0KasFgbBCarA1XqTHAHK8rs3y5NMfAW7lf754SenlAOc8j5DOUWHbSARCCGlKJ6qTXdEpj0mM1Lzv66K7D6VX8LkvzedfauO1o1GRQEh9tgesykcghJCm4tK4kToaCapO/prjSKk2st8xAtGFVG1Z7doWKTlG8dhRCOkxbhzVDwGEdMZXvK5tBkrnm6ILqZ6jFoMWCSFtQZ0yaxJASFdoT1/X1uJKfsU0ftpJILqQah5Aq1vbCOnOxsru3RFASDdcplti6ghs/JTbvRvAnP4cWUhrLgc4536EdI4K20YigJAmelMTlqbjp4mHsZsTApGFVDPSWz7ipfOGJTqdnAiYUYRACCHNOTak22PKr9abM4p4PWCmUYXUHu9q6fKo7Fsyp+y6BEIIqZ6dy51YbjA30bL5KSKKeFteIqZbqy0TQtqSPmXXIICQnqBs46cSai07GLGjPoGPQwsT0AQ5je23bpcIaWFHk31zAghpBhdo/FSva1OnxVhQBqBkcYiABFO3cnW3RFHo7//+i5fHj989lFfOgxDSnDTJyyMBhDSjV9SJ8bq2jEDJapaAIk21NYmlJvJIqHQRpzsj+lsXdfrtj//4f1x++ct/n82j5kaEtCZtympBACEtQF1RqTo2dWgpyxMWMIEsByAwjS7VlnSRJrFU25I4aThBbU37zbUzLwLmxY4BmgRVcEoAIS3kGN1m43VtheAOlK0E0KJLtReJjkWXEk6LLnW7VvvtSV4EzIsde9ixLwT2EAghpHpUpVVSR2mdY8tn+VrV30u5e0Uot90qXytl6ZbrXHSpW7T6TfvNRZdH7PEiYF7sOMKQYyCQQiCEkKaAKL3PdLnB1p166bp6zL9GZ27RpW63WnSpizjdjlV0KRsklhZdlp5NW6POKb72YkeKrewDgSMEigmpxEKdB+magDpS3bpTBJIr8rgugW9zBHJ25prsY9GlTfaRWNpkH4sutU/LNZpz1nmOaeo2L3ak2st+ENhLoKiQ6gQiPSSgSESdrQRVwlo6MnloQbwteztz+UQXg4ou5SMdb9GlPvVd222yj0cf7q1zqVbhxY5S9SNfCCCkDduAohXroBW9kMoRWOrMUx8laR1dHiGzVOcjeZ05xosdZ+rAsRBYI4CQrtGp9JvGzCzKaXkrsFJ1qxejaFHDDFqcwKJLfdetWOO+9ShJdaMzFOhFwLzYkQEpWUBglkAIIfV42+3WG7JRnbyNn/Zg820dWn+3yT7iaJN97FGS55776uXb3/6zO8Y22ae1vaXL9yJgXuwozZv84xIIIaTqTHtJEoPp+Gkvdte0U2OXEkMJ5tyjJBJR/ab9bEKX2oD9XdPWlmV5ETAvdrT0BWWPTSCEkOoWXm/JZj3r1qP+jpYsusz1KElEhl4EzIsd0c4h6luPAEJaj/WhkhR5KZpSZzRiRKUxYXuURNGl6qkLH6uzPUoiIWT8eF8T8iJgXuzYR4+9IZBOACFNZ9VsTxs/lcDotmVv46eyV0LY86MkzZx/omAvAubFjhMoORQCqwQQ0lU8vn5URKpOSdGaIlVvaRpdKpKUrRJ//dPfFl32+CiJN9Yp9ngRMC92pDBjHwgcIYCQHqHW+BhFdxo71SMctcf+LLq0yT7qJCM8StLY5YeK9yJgXuw4BJGDIJBAACFNgOR1F90qVXSqscXc46c22UezXy26VFmKLiWcKlO/KbqsLeZe/eHNLi8C5sUOb/7BnnEIhBBSdfijJkWIGjeVwKmee8dPJYIWXaY+StIjy5HbwJI/vAiYFzuWOLEdAmcJhBDSs5B6OF7jk+qwdMv3dvzUosvpoyTT6FLHSWh03KjRpS40oiUvAubFjmj+p771CCCk9VhXKUm3WiWm3/zmHz6d7CPRVGdmk30kltEeJUFIqzS/2UIQ0lksbByIAEI6kDOnVZFwSDD33uqd5jHS3whpO28ipO3YU3IdAghpHc7VS4koHGuQI/LwImBe7FhrH/wGgTMEENIz9BwfG1E41twRkYcXAfNix1r74DcInCEQQkhHnUCz5viIwgGPawJeBMyLHdd0+AaBfASGF1KJqE7kaAkhvfa4JlxFS14EzIsd0fxPfesRQEjrsa5aEkJ6jTvipCsvAubFjusWwTcI5COAkOZj6SonhNSVO5oY40XAvNjRxAkUGoIAQjqomxHSQR27o1peBMyLHTvQsSsEdhFASHfh6mdnhLQfX5Wy1IuAebGjFGfyhQBCOmgbQEgHdeyOankRMC927EDHrhDYRQAh3YWrn50R0n58VcpSLwLmxY5SnMkXAsMLqWZrav3ZaAkhvfa41h+OlrwImBc7ovmf+tYjMLyQ1kPpqySE9NofEXl4ETAvdly3CL5BIB8BhDQfS1c5RRSONQdE5OFFwLzYsdY++A0CZwggpGfoOT42onCsuSMiDy8C5sWOtfbBbxA4QwAhPUPP8bERhWPNHRF5eBEwL3astQ9+g8AZAgjpGXqOj40oHGvuiMjDi4B5sWOtffAbBM4QGF5INWv3gw/eP8Ooy2MjCseaoyLy8CJgXuxYax/8BoEzBIYXUt7+cqZ5jHOsOvNoyYuAebEjmv+pbz0CCGk91lVLihiBVQXcQWFeBMyLHR24DBM7JYCQduq4LbMR0i1C4//uRcC82DG+x6lhKwIIaSvyhctFSAsD7iB7LwLmxY4OXIaJnRJASDt13JbZCOkWofF/9yJgXuwY3+PUsBUBhLQV+cLlIqSFAXeQvRcB82JHBy7DxE4JIKSdOm7LbIT0mtAnn/zmekOAb14EzIsdAVxOFRsRGF5IxTViJ4qQXp9REXl4ETAvdly3CL5BIB+BEEKaD1c/OUUUjjXvROThRcC82LHWPvgNAmcIIKRn6Dk+NqJwrLkjIg8vAubFjrX2wRanUfYAACAASURBVG8QOEMAIT1Dz/GxEYVjzR0ReXgRMC92rLUPfoPAGQII6Rl6jo+NKBxr7ojIw4uAebFjrX3wGwTOEEBIz9BzfGxE4VhzR0QeXgTMix1r7YPfIHCGwPBCqhm7b7315hlGXR4bUTjWHBWRhxcB82LHWvvgNwicITC8kPL2lzPNY5xjI15MeREwL3aM05qpiTcCCKk3j2SyJ2IElgndMNl4ETAvdgzjWCrijgBC6s4leQxCSPNw7DkXLwLmxY6efYntvgkgpL79c9g6hPQwumEO9CJgXuwYxrFUxB0BhNSdS/IYhJDm4dhzLl4EzIsdPfsS230TQEh9++ewdQjpYXTDHOhFwLzYMYxjqYg7AsML6ZMnTy6PHr3mDnxpgxDSa8Iffviz6w0BvnkRMC92BHA5VWxEYHghbcS1ebEI6bULIvLwImBe7LhuEXyDQD4CCGk+lq5yiigcaw6IyMOLgHmxY6198BsEzhBASM/Qc3xsROFYc0dEHl4EzIsda+2D3yBwhgBCeoae42MjCseaOyLy8CJgXuxYax/8BoEzBBDSM/QcHxtRONbcEZGHFwHzYsda++A3CJwhEEJIP/vsszOMujw2onCsOSoiDy8C5sWOtfbBbxA4Q2B4IdWi9Tz+cqaJjHEsQtrOjwhpO/aUXIdACCHViRwtRRSONR/zHOkanbK/IaRl+ZJ7ewIIaXsfFLEAIS2CtatMvQiYFzu6ch7GdkUAIe3KXenGIqTprEbd86WXvn7Ryl6tE0La2gOUX5oAQlqacKP8EdJG4B0V66UNIKSOGgWmFCGAkBbB2j5TL51oexJxLfDSBhDSuG0wSs0R0kE97aUTHRRvF9Xy0gYQ0i6aC0aeIDC8kH7yyW8u7733oxOI+jzUSyfqhd5bb73pxZRqdnhpAwhpNZdTUCMCwwtpI67Ni/XSiTYH8YUBEXl4qTNC6uUswI5SBBDSUmQb5+ulE22M4WnxEXl4qTNC+rQZ8segBBDSQR3rpRP1gjciDy91Rki9nAXYUYoAQlqKbMN8NS78/PPPNbTAX9FeRKUmGS91Rkhrep2yWhBASFtQL1ym1hdW50W6J+BFVO4tKv+XlzojpOV9TQltCQwvpHrziyK0SAkhfehtL6Ly0LJyW7zUGSEt52Ny9kFgeCGNKCoR67x1OkW81Y2QbrUKfodAHgIIaR6OrnJBSB+6g3fSPmRSawsRaS3SlNOKAELainzBchHSgnA7ytpLRPrKKy9f1CZJEBiVAEI6oGcR0gGdeqBKXoTUix0HEHIIBJIIIKRJmPraCSHty1+lrPUiYF7sKMWZfCGAkA7YBhDSAZ16oEpeBMyLHQcQcggEkgggpEmY+toJIe3LX6Ws9SJgXuwoxZl8ITC8kGq25kcf/SKUpxHSh+6OuECFFwHzYsfDVsEWCOQhMLyQ5sHUVy4I6UN/RezMvdTZix0PWwVbIJCHAEKah6OrXBDSh+6I2Jl7qbMXOx62CrZAIA8BhDQPR1e5IKQP3RGxM/dSZy92PGwVbIFAHgIIaR6OrnJBSB+6I2Jn7qXOXux42CrYAoE8BIoJ6QcfvH95660381hJLrsIIKQPcUXszL3U2YsdD1sFWyCQh0AxIX3vvR9d9K910ptfmLXb2gvty4/YmXupsxc72rdCLBiVwPBCGjE6i1jnrROUx1+2CJX7HSEtx5acfRBASH34IasVCGlWnN1m5kXAvNjRrSMx3D2Bp0L6jW/8wUUN/o03Xt80OuXE8HJrN6KoRKzzZqMNuEPKeVoDixc7atSVMmISeCqkqv73vveXlx//+J83SaScGAjpJsZiOyCkxdB2lXHKeVqjQl7sqFFXyohJ4KmQfvrpp3cR6ccff7xJIuXEQEg3MRbbASEthrarjFPO0xoV8mJHjbpSRkwCT4X05z//t8urr34riULKiYGQJqEsshNCWgRrd5mmnKc1KuXFjhp1pYyYBJ4KqcZGHz9+96KIVIKqxv+Tn/zrLJWUEwMhnUVXZSNC+hCzXl4QLaWcpzWYeLGjRl0pIyaBp0L6wgvPXxSVapz017/+z9Xx0pQTw4uQyq16ljRSQkivvf3kyZMLj79cM6n5LaW/qGkPZUEgN4E7IZVwSkgtItV4qb5r+1xKOTE8CelcHUbehpBeezcqj5Tz9JpUmW9e7ChTO3KFwOVyJ6SaqavHX+xWriJTfV9KKScGQrpEr/z2qMKxRDYqj5TzdIlZzu1e7MhZJ/KCwJTAnZDqdq7+WbLxUvt++5lyYiCkt9TqfY8qHEuEo/JIOU+XmOXc7sWOnHUiLwhMCXzJHnux27h2W1dRqm2bHqC/U04MhPSWWr3vUYVjiXBUHinn6RKznNu92JGzTuQFgSmBL90+9iLxVMN/++0fTPe7+jvlxEBIr5BV/RJVOJYgR+WRcp4uMcu53YsdOetEXhCYEng6a3e6cevvlBPDi5DqzS8ffvizrSoN9XtU4VhyYlQeKefpErOc273YkbNO5AWBKYHhhdSLoE+hl/47qnAscdUzpHo/brTkRcC82BHN/9S3HgGEtB7raiUhpNVQuy7Ii4B5scO1szCuawIIadfumzceIZ3nEm2rFwHzYkc0/1PfegQQ0nqsq5WEkFZD7bogLwLmxQ7XzsK4rgkgpF27b954hHSeS7StXgTMix3R/E996xFASOuxrlYSQloNteuCvAiYFztcOwvjuiYwvJBqtma0GZsI6cNzUkyiJS8C5sWOaP6nvvUIDC+k9VD6KQkhvfZFVB5eBMyLHdetgm8QyEcAIc3H0k1OUYVjyQFReXgRMC92LLUPtkPgLAGE9CxBh8dHFY4lV0Tl4UXAvNix1D7YDoGzBBDSswQdHh9VOJZcEZWHFwHzYsdS+2A7BM4SQEjPEnR4fFThWHJFVB5eBMyLHUvtg+0QOEsAIT1L0OHxUYVjyRVReXgRMC92LLUPtkPgLIHhhVSPvmjh+kgpqnAs+TgqDy8C5sWOpfbBdgicJTC8kPL2l7NNpP/j9fYXvU4vWvIiYF7siOZ/6luPAEJaj3W1kqJGYNUAd1KQFwHzYkcnbsPMDgkgpB06bctkhHSLUIzfvQiYFztieJ1atiCAkLagXrhMhLQw4E6y9yJgXuzoxG2Y2SEBhLRDp22ZjJBuEYrxuxcB82JHDK9TyxYEENIW1AuXiZAWBtxJ9l4EzIsdnbgNMzskMLyQarZmtBmbCOn1mfjJJ78J9wiUCHgRMC92XLcKvkEgH4HhhTQfqn5yQkivfRWVhxcB82LHdavgGwTyEUBI87F0k1NU4VhyQFQeXgTMix1L7YPtEDhLACE9S9Dh8VGFY8kVUXl4ETAvdiy1D7ZD4CwBhPQsQYfHRxWOJVdE5eFFwLzYsdQ+2A6BswQQ0rMEHR4fVTiWXBGVhxcB82LHUvtgOwTOEhheSLXOqmZtRkpRhWPJx1F5eBEwL3YstQ+2Q+AsgeGFlEXrzzaR/o9HSNv6ECFty5/SyxNASMszrl5CVOFYAx3troRYeBEwL3astQ9+g8AZAgjpGXpOj0VInTqmslleBMyLHZXxU1wgAgjpgM5GSAd06oEqeREwL3YcQMghEEgigJAmYeprJ4S0L3+VstaLgHmxoxRn8oUAQjpgG0BIB3TqgSp5ETAvdhxAyCEQSCKAkCZh6msnhLQvf5Wy1ouAebGjFGfyhcDwQvrkyZOL/kVKCOm1t+X/R49eu94Y4JsXAfNiRwCXU8VGBIYX0kZcmxaLkF7jj8rDi4B5seO6VfANAvkIIKT5WLrJKapwLDkgKg8vAubFjqX2wXYInCWAkJ4l6PD4qMJx6wotDykWP/jB/7783u997fbn4b97ETAvdgzvcCrYjABC2gx9uYIR0svlnXd+eLeyz3e+8+eX11///uWll/7b5aWXvn756KNflAPvLGcvAubFDmfuwZyBCCCkAznTqjKikFp0+eGHP7to/WQJ5CuvvHz3afXe+tSxElMdHyF5ETAvdkTwOXVsQ2B4IWXWbpuGlbNUCaA6YwmnZt9KCBVZ6oJhb5Ig61+E5EXAvNgRwefUsQ2B4YWUt7+0aVhbpUoELbqUOEokFS2S8hHwImBe7MhHlpwgcE0AIb3mMcQ3z7d2FUmqY51GlxLUI9FlTmcpSh3teWMvAubFjpzthbwgMCWAkE5pDPJ3bSFVeRJIRf+KLjV++fzzz3VFU69Zk82yfZRXrnkRMC92dNUgMbYrAghpV+5KM7aWkCqCUyepW7ISIAmpRZc9jkPKZpvtq7r0WIdpC/EiYF7smLLhbwjkJICQ5qTpJK8zQipxtOjyrbfevBNIdYSjRGkpLlJdLarWhUGvyYuAebGjVz9it38CCKl/H+228IiQSjzU4U2jyw8+eP9u7LL3yGw3wC8OEMeeH5fxImBe7DjaDjgOAlsEENItQh3+bkKq6FJ/6zalRZcaB4wUXXboviwm6+LHi4B5sSMLWDKBwAyB4YVUHUq0iOqXv/z3y7PP/tbTyTMa97PoEhGdOQsG3GQXUx6qhpB68AI2lCQwvJCWhFczbwmgRZcSRhvD03jmbfLUid7aNsp3Rfuex089tQGEdJRWTz2WCCCkS2Qcbdc4nT2aIRHVrVp1lEvRpadO1BHGrKaIvY0nS1S9JU9tACH11jqwJzcBhDQ30YT8LLrU7VaLLtUp54pwPHWiCTi63UVDBrqo0UWOxqA9DSF4agMIabdNHMMTCSCkiaBy7aYVfdSx6NasOl+LLnNGNZ460VzcPOejCyP5UoIqf3pIntoAQuqhRWBDSQII6Um6ikLUaSm6VCcqgVR0qUizVfLUibZi0KJc4z43bl3bHrOldrlz5SGkc1TYNhKB4YVUt0tLdWyKQm6jS5WVM7o80tg8daJH7OeY8wQ8tQGE9Lw/ycE3geGFVFFi6u02iy4lvhZd6lasBLOnJDFXZEyKSwAhjet7al6fAEL6BXPditWV8/StJBIkdUi9pT0XD73VrVd71Y5yTSZLYYCQplBiHwjkITC8kP7d3/3N5U//9E/u3kpiIpkHnd9cEFJ/vtHtfo2dqw3WuDhDSP21ASwal8DwQvrCC89fvvvdv3j6VpJxXXlfM4T0noW3vzQpTbN79bq5peeAc9iMkOagSB4QSCMwtJCqM1EUEC0hpL49rrF4G0qQr0o8f4qQ+m4DWDcWgaGFVBNuFAFESwhpHx5XRKrItMQsb4S0jzaAlWMQGFpINdu2xNW+d9cjpN49VN4+L0IqOzQuTILAyASGFtKRHbdWN4R0jU6M3zwJKY9ixWhzkWuJkA7ofYS0f6faSllH76ggpP23AWrQDwGEtB9fJVuKkCajcrujxk1tuckjK3MhpG5di2EDEkBIB3QqQjqOU7WIg2aeS1T3TEpCSMdpA9TEPwGE1L+PdluIkO5G5voA3d6VT+11bSnGIqQplNgHAnkIDCek6myOjivlQdo+F4S0vQ9KWKDHZeTblIUcENISHiBPCMwTGEpIdRuMGYKXu85WHS4pLgGENK7vqXl9AkMJqcaSai4MXt9daSUSkaZxGnkvhHRk71I3bwSKCakWQ6i5qpBNyvAGuIU9CGkL6m3L1JKD+mfDGghpW39QeiwCxYRUt1h1MtdKKo9o9HPaCGmtVuenHI2b6hzQHAGdBwipH99gyfgEhhBSdRpMMrpvrAjpPYtof+lc0BDHN7/5hy6W5vMi6NHaAfWtS2AIIdVtZIkH6XMCCCkt4R/+4f9cnn32t+4WxW9JAyFtSZ+yaxEYQkhTHgeoBdRDOQipBy+0tUEC9u1v/1nVeQpzNUZI56iwbTQCQwjpaE45Wx+E9CzB/o/3ImBe7Ojfo9TAMwGE1LN3DtqGkB4EN9BhXgTMix0DuZaqOCSAkDp0ylmTENKzBPs/fkvA9I5QzS0oPSyyZUf/pKkBBC4XhHTAVoCQDujUnVXaEjA9byoh1Wx3tZdSacuOUuWSLwRqEuhWSHWC7nkbRk2orctCSFt7oH35qQJm++mRmSOva9uqqeW/tR+/Q6BnAt0KaakTv2dnmu0IqZGI+7lXwGxlsEePXssKba8dWQsnMwhUItClkNpJX4lRd8UgpN25LLvBRwRMt3t1XM50xI6c5ZMXBGoQ6FJINVGC5QCXmwdCuswmyi9eBMyLHVH8Tj3bEOhOSHVi6rYuaZkAQrrMJsovuQXMFsPfyy+3HXvLZ38I1CDQnZBqYW4JBWmZAEK6zCbKL7kFTLN7de7tfVwmtx1R/Ec9+yLQlZDqJGZx+u0GhpBuMxp9j9wCpohUr2l75pkv313Ipkaoue0Y3W/Ur08CXQmpHndhbHS7oSGk24xG36OUgOlidvq6ti2OpezYKpffIVCTQFdCWhNMz2UhpD17L4/tpQVM+WuuwtbjMqXtyEOLXCBwjgBCeo6fy6MRUpduqWpULQHbGjOtZUdVuBQGgRsCCOkNkBG+IqQjePFcHbwImBc7ztHkaAisE0BI1/l0+StC2qXbshrdUsCmCzu0tCMrUDKDwAoBhHQFTq8/IaS9ei6f3S0FTEKq8VNNSvrgg/fvPvPVjJwg4I+AeyHVQtpbExr8YW1rEULalr+H0lsKqdVf7fCrX/3K5Xd/9wXbxCcEhiTgXkh1ZcsjL/vaHkK6j9eIe3sQUnF9/fXvX/76r//XiIipEwSeEnAtpOoMWA7wqa+S/0BIk1ENu6MHIdUtXi3gsDWzd1gnULEwBFwLqY2xhPFGpooipJlAdpyNByFVO9TLw0kQGJ2AWyHVKkYsB3is+SGkx7iNdFRrIVU0qvNXdpAgMDoBt0KqK1kJAmk/AYR0P7PRjmgtpJrXoDtKJAhEIOBWSBlbOd78ENLj7EY5srWQam6DZtyTIBCBgFshZYLC8eaHkB5nN8qRLYVU0SiTBEdpSdQjhYBbIU0xnn3mCSCk81wibW0ppLqlyyNrkVobdUVIB2wDCOmATt1ZpVZCqnI1yYgEgUgEENIBvY2QDujUnVVqJaSKRtX+SBCIRAAhHdDbCOmATt1ZpRZCqnkNPLK201HsPgQBV0KqBa5J5wkgpOcZ9p5DCyHVI2vvvPPD3tFhPwR2E3AjpJoqz0y/3f6bPQAhncUSamNtIVU0yiNroZoYlZ0QcCOkzPSbeOXknwjpSYADHF5bSNXmWA5wgIZDFQ4RcCGkOukZWznkv9mDENJZLKE21hRSWw5Qy3qSIBCRgAsh1ftG1fmT8hBASPNw7DmXmkLKy7t7binYnoNAcyG1sRVd1ZLyEEBI83DsOZeaQqq5DSqPBIGoBJoLqcZVGFvJ2/wQ0rw8e8ytlpCyHGCPrQObcxNoLqS6LcS6unndipDm5dljbrWEVNEoywH22EKwOSeB5kKaszLk9TkBhJSWUENIVQaPrNHWIHC5IKQDtgKEdECn7qxSDSHVI2ssorLTMew+JAGEdEC3IqQDOnVnlUoLqR514ZG1nU5h92EJIKQDuhYhHdCpO6tUWkg1QVDtjAQBCHBrd8g2gJAO6dZdlSoppPbIGpMEd7mEnQcm0CQi1diKTnRSGQIIaRmuPeVaUki1MD2PrPXUGrC1NIHqQqoTnBf/lnUrQlqWbw+5lxJSWw6QaLSHVoCNtQhUF1Je/FvetQhpecbeSyglpGpbOodJEIDAPYGqQqqrWGb63cMv9RdCWopsP/mWElKdv8qbBAEI3BOoKqQaV+HFv/fwS/2FkJYi20++JYRUKxi98srL/UDAUghUIlBNSJnpV8mjl8vdYwkSU1JcAiWElOUA47Ynar5OoJqQagUUZvqtOyPXr0SkuUj2m09uIf3oo1+wHGC/zQHLCxOoJqS8Jq2wJyfZI6QTGEH/zC2kmmDE4vRBGxPV3iRQTUg3LWGHbAQQ0mwou80op5AqLyYJdtsUMLwCAYS0AuTaRSCktYn7Ky+nkLIcoD//YpEvAklCqvGRZ5758uw/ddpzidWL5qjU2YaQ1uHsuZRcQmqTBBma8extbGtNIElIZaSE8VZMNYtv6QRDSNu5FiFtx95LybmEVNEokwS9eBU7vBJIFlK7Mp2KqSLVpSQh/elPf8rD20uACm5HSAvC7STrHEKqi2Sd7zr3SRCAwDKBZCFVFlpMwYRUQrmW9Lse3ubFv2uUyvyGkJbh2lOuOYRU7ejRo9d6qja2QqAJgV1CqitUzd6TmOrFvmvp1Ve/dfmd3/mvi7d+147lt3MEENJz/EY4+qyQ2rmufEgQgMA6gV1CqqxSF1Z44YXnL6+//v310vm1CAGEtAjWrjI9K6R6ZnTrrlNXQDAWAgUJ7BZS2bI0wWhq53e/+xd3kas69ZT9p8fy9zkCCOk5fiMcfVZINZFwbQ7ECIyoAwRyETgkpKmFa5KCrmp1O5hVUVKpnd8PIT3PsPcc1AaOviBC56qElAQBCKQRKCqkZoKujnViavIRYy5GpdwnQlqObS85n2kDuvjlwrcXT2OnBwJVhNQqqpNb0ameS2NKvVHJ/3mmE81vDTm2IHC0DehCV+coCQIQSCdQVUhllsZLJaQ6WXWyM36a7qzUPY92oqn5s59/AkfbgKJRHUuCAATSCVQXUjNNj8/opNUtX24jGZU8n0c70Tylk4sHAkfagO4S6QKXi1sPHsSGngg0E1KDZO85lKhuPZtqx/C5TuBIJ7qeI7/2RuBIG2A5wN68jL1eCDQXUoHQFbBOfBs/5Yr4XPM40omeK5GjvRHY2wYUjbIcoDcvYk8vBFwIqcHSyTwdP7XtfO4jsLcT3Zc7e/dAYG8b0P4690gQgMB+Aq6E1MzXzEE9KqPxUx6XMSrpn7pNzsP06bxG3HOPkOoOkO4GMbQyYkugTjUIuBRSq7gmIekElzDwuIxR2f4ULy5AtjmNvMceIdWyn2ozJAhA4BgB10KqKtn4qcZvtFIL46fbjkZItxmNvsceIeXOz+itgfqVJuBeSA2AIlK90kkRKq9mMyrznwjpPJdIW1OFlOUAI7UK6lqKQDdCagB0y5LlBo3G/CdCOs8l0tZUIeU57kitgrqWItCdkBoIRaWKThWlMn5qVD7/REiveUT8liKkdlEakQ91hkBOAt0KqSBovFTjpho/VcfB+OnnTQMhzXmK9JlXipCqnWg/EgQgcI5A10JqVVdEqk5BESrLDV7uWDBr11pHzM8tIdWjLjpfuPiM2T6odV4CQwipIZkuNxhZSIhIrUXE/dwSUi2+QDQat31Q87wEhhJSQ6MOQlfb6iwijp8ipNYS4n6uCanOCZYDjNs2qHl+AkMKqTDpltV0ucFIt7AQ0vwnSm85rgmp5hWwHGBvHsVezwSGFVKDPn1dW5Rl8xBS837czyUh1QWl7tZEvFMTtzVQ89IEhhdSA2gPnktkRl9TFCE1r8f9XBJSbVf7IEEAAvkIhBFSIdPVuDoSGz8d9XYvQprvBOk1pyUhZTnAXj2K3Z4JhBJSc4Rua4283CBCap6O+zknpLoro7cqkSAAgbwEQgqpIdQjMiO+rg0hNQ/H/ZwTUpYDjNseqHlZAqGF1NDqSl23eyVAI0zCQEjNs3E/b4XUnrGOS4SaQ6AcAYT0C7Y2fjrC69oQ0nInTC853wqp2gSrfvXiPezsjQBCeuMxRaTqdBSh9trxIKQ3Tg34dSqkGsJQex51cl1A91JlZwQQ0gWHqPPp9XVtCOmCUwNtngopywEGcjxVbUIAId3A3uPr2hDSDacG+NmEVHdYNFxBNBrA6VSxGQGENAG9OqGeXteGkCY4dfBdTEgVjbIc4ODOpnrNCSCkO1wwXW7Q8/gpQrrDqYPuKiF9/Pjdu7HREWaiD+omqjUIAYT0gCPtUQKvguXVrgOoOeQgAQmp2oEWHiFBAAJlCSCkJ/iqs7LlBj1d9SOkJ5w6yKGKRn/7t5+9RH4v7yCupBodEEBITzpJ46cag5KgSlg9JITUgxfq26ChBwmn2uEf/dF/v5t1Xt8KSoRAPAIIaSafqwOTgOmRmdava0NIMznVaTZqaxqjl2Dq1q2WudTMXF3MyfeaGKffPN0lcYoSsyCQhQBCmgXjfSbq4CSm6tBava4NIb33R69/SQQtupQwyqcSSgmmhFMCKrFUe9N+JAhAoB0BhLQAe93uVSfXarlBhLSAUwtlKRHUHQyLLuW7aXRpiylov1YXZoWqTrYQGIYAQlrQlYoqWryuDSEt6NQDWevCSkKoxT0sutRdC4su5a9pdKn9SRCAQD8EENIKvlInWvN1bQhpBafOFKGI0aJLRZIWXUow9bdFl9qH6HIGIJsg0CkBhLSi4zSeZRNCSk4EQUjLOXUaXSqKFGuLLm1sXNsVfeoCiuiynC/IGQJeCCCklT2hjrX0coMI6XmnKmKUEEoULbq0yT7ia5N9FF1qPxIEIBCXAELayPeKSNUhq3NWpJozIaTpNCWC4m/R5dyjJBZdlryLkG4xe0IAAt4IIKSNPaKOXLcE1YHnimwQ0munSgDFVmJpk30suuRRkmtWfIMABPYTQEj3MytyRM7XtUUVUomlTfZZW6hA+xFdFmnGZAqBkAQQUkdu1/ipxuMULSl6OjpRZWQhteiSR0kcNVxMgUBwAgipwwagiS4SQ93yPTJ+OoKQTh8lUXSpOukxkttHSRRd8iiJw0aMSRAIRAAhdexs3aa0RyokGKmpFyFVxK16Kbq0yT6qr8TS6q3tNtnnaISeyo39IAABCBwhgJAeoVb5GImJbvfqtm+KmHgT0rlHSabR5fRREqLLyo2L4iAAgdMEENLTCOtkoLHB6fjpWqkthNSiy7lHSSy61IxZiy6Z7LPmQX6DAAR6IoCQ9uSty+XuVqiEUuKkW79zqaSQ2mQfRclrj5KwUMGcZ9gGAQiMSAAh7dSrivx0u1eieRvd5RBSjV1adMmjJJ02EsyGAASqEEBIq2AuU4hupyoy1HijokMbP00VUosup4+STBcqUD7KX4K6Z7JTmdqSKwQgAAGfBBBSn37ZZZUEUVGjRFCieCukEsHpQgX6nZD/oAAAAIlJREFUXeJrEa3GXiWY2o/JPrvQszMEIACBC0I6UCOQEGrJu6985b88fW0bj5IM5GCqAgEIuCSAkLp0yzmjdCtWESjR5TmOHA0BCEAghQBCmkKJfSAAAQhAAAILBBDSBTBshgAEIAABCKQQQEhTKLEPBCAAAQhAYIEAQroAhs0QgAAEIACBFAL/H18XfI8kOP9KAAAAAElFTkSuQmCC"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mo> </mo><mn>60</mn><mo>°</mo><mo>=</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></math>, show that the area of the base of the box is equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><msqrt><mn>3</mn></msqrt><msup><mi>x</mi><mn>2</mn></msup></mrow><mn>2</mn></mfrac></math>.</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>Given that the total external surface area of the box is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1200</mn><mo> </mo><msup><mtext>cm</mtext><mn>2</mn></msup></math>, show that the volume of the box may be expressed as <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mn>300</mn><msqrt><mn>3</mn></msqrt><mi>x</mi><mo>-</mo><mfrac><mn>9</mn><mn>4</mn></mfrac><msup><mi>x</mi><mn>3</mn></msup></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mn>300</mn><msqrt><mn>3</mn></msqrt><mi>x</mi><mo>-</mo><mfrac><mn>9</mn><mn>4</mn></mfrac><msup><mi>x</mi><mn>3</mn></msup></math>, for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mn>16</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>V</mi></mrow><mrow><mo>d</mo><mi>x</mi></mrow></mfrac></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> which maximizes the volume of the box.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, or otherwise, find the maximum possible volume of the box.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The box will contain spherical chocolates. The production manager assumes that they can calculate the exact number of chocolates in each box by dividing the volume of the box by the volume of a single chocolate and then rounding down to the nearest integer.</p>
<p>Explain why the production manager is incorrect.</p>
<div class="marks">[1]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>evidence of splitting diagram into equilateral triangles <strong><em>M1</em></strong></p>
<p>area <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>6</mn><mfenced><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mi>x</mi><mn>2</mn></msup><mo> </mo><mi>sin</mi><mo> </mo><mn>60</mn><mo>°</mo></mrow></mfenced></math> <strong><em>A1</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>3</mn><msqrt><mn>3</mn></msqrt><msup><mi>x</mi><mn>2</mn></msup></mrow><mn>2</mn></mfrac></math> <strong><em>AG</em></strong></p>
<p><br><strong>Note:</strong> The <em><strong>AG</strong></em> line must be seen for the final <em><strong>A1</strong></em> to be awarded.</p>
<p><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>total surface area of prism <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1200</mn><mo>=</mo><mn>2</mn><mfenced><mrow><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></mrow></mfenced><mo>+</mo><mn>6</mn><mi>x</mi><mi>h</mi></math> <strong><em>M1A1</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>M1</strong></em> for expressing total surface areas as a sum of areas of rectangles and hexagons, and <em><strong>A1</strong></em> for a correctly substituted formula, equated to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1200</mn></math>.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mfrac><mrow><mn>400</mn><mo>-</mo><msqrt><mn>3</mn></msqrt><msup><mi>x</mi><mn>2</mn></msup></mrow><mrow><mn>2</mn><mi>x</mi></mrow></mfrac></math> <strong><em>A1</em></strong></p>
<p>volume of prism <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>3</mn><msqrt><mn>3</mn></msqrt></mrow><mn>2</mn></mfrac><msup><mi>x</mi><mn>2</mn></msup><mo>×</mo><mi>h</mi></math> <strong><em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>3</mn><msqrt><mn>3</mn></msqrt></mrow><mn>2</mn></mfrac><msup><mi>x</mi><mn>2</mn></msup><mfenced><mfrac><mrow><mn>400</mn><mo>-</mo><msqrt><mn>3</mn></msqrt><msup><mi>x</mi><mn>2</mn></msup></mrow><mrow><mn>2</mn><mi>x</mi></mrow></mfrac></mfenced></math> <strong><em>A1</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>300</mn><msqrt><mn>3</mn></msqrt><mi>x</mi><mo>-</mo><mfrac><mn>9</mn><mn>4</mn></mfrac><msup><mi>x</mi><mn>3</mn></msup></math> <strong><em>AG</em></strong></p>
<p><br><strong>Note:</strong> The <em><strong>AG</strong></em> line must be seen for the final <em><strong>A1</strong></em> to be awarded.</p>
<p><br><em><strong>[5 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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"> <strong><em>A1A1</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>A1</em></strong> for correct shape, <strong><em>A1</em></strong> for roots in correct place with some indication of scale (indicated by a labelled point).</p>
<p><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>V</mi></mrow><mrow><mo>d</mo><mi>x</mi></mrow></mfrac><mo>=</mo><mn>300</mn><msqrt><mn>3</mn></msqrt><mo>-</mo><mfrac><mn>27</mn><mn>4</mn></mfrac><msup><mi>x</mi><mn>2</mn></msup></math> <strong><em>A1A1</em></strong></p>
<p><strong><br>Note:</strong> Award <strong><em>A1</em></strong> for a correct term.</p>
<p><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>from the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>V</mi></mrow><mrow><mo>d</mo><mi>x</mi></mrow></mfrac></math> <strong>OR </strong> solving <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>V</mi></mrow><mrow><mo>d</mo><mi>x</mi></mrow></mfrac><mo>=</mo><mn>0</mn></math> <strong><em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>8</mn><mo>.</mo><mn>88</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>8</mn><mo>.</mo><mn>877382</mn><mo>…</mo></mrow></mfenced></math> <strong><em>A1</em></strong></p>
<p><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>from the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> <strong>OR </strong> substituting their value for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> into <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> <strong><em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mtext>max</mtext></msub><mo>=</mo><mn>3040</mn><mo> </mo><msup><mtext>cm</mtext><mn>3</mn></msup><mtext> </mtext><mfenced><mrow><mn>3039</mn><mo>.</mo><mn>34</mn><mo>…</mo></mrow></mfenced></math> <strong><em>A1</em></strong></p>
<p><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong><br>wasted space / spheres do not pack densely (tesselate) <strong><em>A1</em></strong><br><br><strong>OR</strong><br>the model uses exterior values / assumes infinite thinness of materials and hence the modelled volume is not the true volume <strong><em>A1</em></strong></p>
<p><br><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{{27}}{{{x^2}}} - 16x,\,\,\,x \ne 0">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>27</mn>
</mrow>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>−<!-- − --></mo>
<mn>16</mn>
<mi>x</mi>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>≠<!-- ≠ --></mo>
<mn>0</mn>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of <em>y</em> = <em>f </em>(<em>x</em>), for −4 ≤ <em>x</em> ≤ 3 and −50 ≤ <em>y</em> ≤ 100.</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>Use your graphic display calculator to find the zero of <em>f </em>(<em>x</em>).</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>Use your graphic display calculator to find the coordinates of the local minimum point.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to find the equation of the tangent to the graph of <em>y</em> = <em>f </em>(<em>x</em>) at the point (–2, 38.75).</p>
<p>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">b.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><img src="data:image/png;base64,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"><em><strong>(A1)(A1)(A1)(A1)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for axis labels and some indication of scale; accept <em>y</em> or <em>f</em>(<em>x</em>).</p>
<p>Use of graph paper is not required. If no scale is given, assume the given window for zero and minimum point.</p>
<p>Award <em><strong>(A1)</strong></em> for smooth curve with correct general shape.</p>
<p>Award <em><strong>(A1)</strong></em> for <em>x</em>-intercept closer to <em>y</em>-axis than to end of sketch.</p>
<p>Award <em><strong>(A1)</strong></em> for correct local minimum with <em>x</em>-coordinate closer to <em>y</em>-axis than end of sketch and <em>y</em>-coordinate less than half way to top of sketch.</p>
<p>Award at most <em><strong>(A1)</strong></em><em><strong>(A0)</strong></em><em><strong>(A1)</strong></em><em><strong>(A1)</strong></em> if the sketch intersects the <em>y</em>-axis or if the sketch curves away from the <em>y</em>-axis as<em> x</em> approaches zero.</p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>1.19 (1.19055…) <em><strong> (A1)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Accept an answer of (1.19, 0).</p>
<p>Do not follow through from an incorrect sketch.</p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(−1.5, 36) <em><strong>(A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A0)(A1)</strong></em> if parentheses are omitted.</p>
<p>Accept <em>x</em> = −1.5, <em>y</em> = 36.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>y</em> = −9.25<em>x</em> + 20.3 (<em>y</em> = −9.25<em>x</em> + 20.25) <em><strong>(A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for −9.25<em>x</em>, award <em><strong>(A1)</strong></em> for +20.25, award a maximum of <em><strong>(A0)(A1)</strong></em> if answer is not an equation.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.iii.</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">b.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider a function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced></math>, for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≥</mo><mn>0</mn></math>. The derivative of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mrow><mn>6</mn><mi>x</mi></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfrac></math>.</p>
</div>
<div class="specification">
<p>The graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is concave-down when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mi>n</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>''</mo><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mrow><mn>24</mn><mo>-</mo><mn>6</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><msup><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced><mn>2</mn></msup></mfrac></math>.</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>Find the least value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math>.</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 <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∫</mo><mfrac><mrow><mn>6</mn><mi>x</mi></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfrac><mtext>d</mtext><mi>x</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> be the region enclosed by the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math>, the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis and the lines <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>1</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>3</mn></math>. The area of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>19</mn><mo>.</mo><mn>6</mn></math>, correct to three significant figures.</p>
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced></math>.</p>
<div class="marks">[7]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><strong>METHOD 1</strong></p>
<p>evidence of choosing the quotient rule<em><strong> (M1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>v</mi><mi>u</mi><mo>'</mo><mo>-</mo><mi>u</mi><mi>v</mi><mo>'</mo></mrow><msup><mi>v</mi><mn>2</mn></msup></mfrac></math></p>
<p>derivative of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mi>x</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math> (must be seen in rule)<em><strong> (A1)</strong></em></p>
<p>derivative of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>x</mi></math> (must be seen in rule)<em><strong> (A1)</strong></em></p>
<p>correct substitution into the quotient rule <em><strong>A1</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>6</mn><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mn>6</mn><mi>x</mi></mrow></mfenced><mfenced><mrow><mn>2</mn><mi>x</mi></mrow></mfenced></mrow><msup><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced><mn>2</mn></msup></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>''</mo><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mrow><mn>24</mn><mo>-</mo><mn>6</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><msup><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced><mn>2</mn></msup></mfrac></math> <em><strong>AG N0</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>evidence of choosing the product rule<em><strong> (M1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>u</mi><mo>'</mo><mo>+</mo><mi>u</mi><mi>v</mi><mo>'</mo></math></p>
<p>derivative of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mi>x</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math> (must be seen in rule)<em><strong> (A1)</strong></em></p>
<p>derivative of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mi>x</mi><msup><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced><mrow><mo>-</mo><mn>2</mn></mrow></msup></math> (must be seen in rule)<em><strong> (A1)</strong></em></p>
<p>correct substitution into the product rule <em><strong>A1</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><msup><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>+</mo><mfenced><mrow><mo>-</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mn>6</mn><mi>x</mi></mrow></mfenced><mfenced><mrow><mn>2</mn><mi>x</mi></mrow></mfenced><msup><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced><mrow><mo>-</mo><mn>2</mn></mrow></msup></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>''</mo><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mrow><mn>24</mn><mo>-</mo><mn>6</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><msup><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced><mn>2</mn></msup></mfrac></math> <em><strong>AG N0</strong></em></p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1 </strong>(2<sup>nd</sup> derivative) <em><strong>(M1)</strong></em></p>
<p>valid approach</p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>''</mo><mo><</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>24</mn><mo>-</mo><mn>6</mn><msup><mi>x</mi><mn>2</mn></msup><mo><</mo><mn>0</mn><mo> </mo><mo>,</mo><mo> </mo><mi>n</mi><mo>=</mo><mo>±</mo><mn>2</mn><mo>,</mo><mo> </mo><mi>x</mi><mo>=</mo><mn>2</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>2</mn></math> (exact) <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><strong>METHOD 2 </strong>(1<sup>st</sup> derivative)</p>
<p>valid attempt to find local maximum on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo></math> <em><strong>(M1)</strong></em></p>
<p>eg sketch with max indicated, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo>,</mo><mo> </mo><mn>1</mn><mo>.</mo><mn>5</mn></mrow></mfenced><mo>,</mo><mo> </mo><mi>x</mi><mo>=</mo><mn>2</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>2</mn></math> (exact) <em><strong>A1 N2</strong></em></p>
<p> </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>evidence of valid approach using substitution or inspection <em><strong>(M1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∫</mo><mn>3</mn><mfenced><mrow><mn>2</mn><mi>x</mi></mrow></mfenced><mfrac><mn>1</mn><mi>u</mi></mfrac><mtext>d</mtext><mi>x</mi><mo> </mo><mo>,</mo><mo> </mo><mi>u</mi><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo> </mo><mo>,</mo><mo> </mo><mtext>d</mtext><mi>u</mi><mo>=</mo><mn>2</mn><mi>x</mi><mo> </mo><mtext>d</mtext><mi>x</mi><mo> </mo><mo>,</mo><mo> </mo><mo>∫</mo><mn>3</mn><mo>×</mo><mfenced><mfrac><mn>1</mn><mi>u</mi></mfrac></mfenced><mtext>d</mtext><mi>u</mi></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∫</mo><mfrac><mrow><mn>6</mn><mi>x</mi></mrow><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced></mfrac><mtext>d</mtext><mi>x</mi><mo>=</mo><mn>3</mn><mo> </mo><mi>ln</mi><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced><mo>+</mo><mi>c</mi></math> <em><strong>A2 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing that area <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><msubsup><mo>∫</mo><mn>1</mn><mn>3</mn></msubsup><mi>f</mi><mfenced><mi>x</mi></mfenced><mtext>d</mtext><mi>x</mi></math> (seen anywhere) <em><strong>(M1)</strong></em></p>
<p>recognizing that <strong>their</strong> answer to (c) is their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> (accept absence of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>) <em><strong>(M1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>3</mn><mo> </mo><mi>ln</mi><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced><mo>+</mo><mi>c</mi><mo> </mo><mo>,</mo><mo> </mo><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>3</mn><mo> </mo><mi>ln</mi><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced></math></p>
<p>correct value for <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mo>∫</mo><mn>1</mn><mn>3</mn></msubsup><mn>3</mn><mo> </mo><mi>ln</mi><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced><mtext>d</mtext><mi>x</mi></math> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>.</mo><mn>4859</mn></math></p>
<p>correct integration for <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mo>∫</mo><mn>1</mn><mn>3</mn></msubsup><mi>c</mi><mo> </mo><mtext>d</mtext><mi>x</mi></math> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mfenced open="[" close="]"><mrow><mi>c</mi><mi>x</mi></mrow></mfenced><mn>1</mn><mn>3</mn></msubsup><mo> </mo><mo>,</mo><mo> </mo><mn>2</mn><mi>c</mi></math></p>
<p>adding <strong>their</strong> integrated expressions <strong>and</strong> equating to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>19</mn><mo>.</mo><mn>6</mn></math> (do not accept an expression which involves an integral) <em><strong>(M1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>.</mo><mn>4859</mn><mo>+</mo><mn>2</mn><mi>c</mi><mo>=</mo><mn>19</mn><mo>.</mo><mn>6</mn><mo> </mo><mo>,</mo><mo> </mo><mn>2</mn><mi>c</mi><mo>=</mo><mn>7</mn><mo>.</mo><mn>114</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>3</mn><mo>.</mo><mn>55700</mn></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>3</mn><mo> </mo><mi>ln</mi><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced><mo>+</mo><mn>3</mn><mo>.</mo><mn>56</mn></math> <em><strong>A1 N4</strong></em></p>
<p><em><strong>[7 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="specification">
<p>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{{48}}{x} + k{x^2} - 58">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>48</mn>
</mrow>
<mi>x</mi>
</mfrac>
<mo>+</mo>
<mi>k</mi>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mn>58</mn>
</math></span>, where <em>x</em> > 0 and <em>k</em> is a constant.</p>
<p>The graph of the function passes through the point with coordinates (4 , 2).</p>
</div>
<div class="specification">
<p>P is the minimum point of the graph of <em>f </em>(<em>x</em>).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>k</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>Using your value of <em>k</em> , find <em>f</em> ′(<em>x</em>).</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><strong>Use your answer</strong> to part (b) to show that the minimum value of <em>f</em>(<em>x</em>) is −22 .</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of <em>y</em> = <em>f</em> (<em>x</em>) for 0 < <em>x</em> ≤ 6 and −30 ≤ <em>y</em> ≤ 60.<br>Clearly indicate the minimum point P and the <em>x</em>-intercepts on your graph.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{48}}{4} + k \times {4^2} - 58 = 2">
<mfrac>
<mrow>
<mn>48</mn>
</mrow>
<mn>4</mn>
</mfrac>
<mo>+</mo>
<mi>k</mi>
<mo>×</mo>
<mrow>
<msup>
<mn>4</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>58</mn>
<mo>=</mo>
<mn>2</mn>
</math></span> <em><strong>(M1)</strong></em><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of <em>x</em> = 4 and <em>y</em> = 2 into the function.</p>
<p><em>k</em> = 3 <em><strong>(A1) (G2)</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{ - 48}}{{{x^2}}} + 6x">
<mfrac>
<mrow>
<mo>−</mo>
<mn>48</mn>
</mrow>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>+</mo>
<mn>6</mn>
<mi>x</mi>
</math></span> <strong><em>(A1)(A1)(A1)</em>(ft)<em> (G3)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em></strong> for −48 , (A1) for <em>x</em><sup>−2</sup>, <strong><em>(A1)</em>(ft)</strong> for their 6<em>x</em>. Follow through from part (a). Award at most <strong><em>(A1)(A1)(A0)</em></strong> if additional terms are seen.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{ - 48}}{{{x^2}}} + 6x = 0">
<mfrac>
<mrow>
<mo>−</mo>
<mn>48</mn>
</mrow>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>+</mo>
<mn>6</mn>
<mi>x</mi>
<mo>=</mo>
<mn>0</mn>
</math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for equating their part (b) to zero.</p>
<p><em>x</em> = 2 <em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from part (b). Award (<em><strong>M1)(A1)</strong></em> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{ - 48}}{{{{\left( 2 \right)}^2}}} + 6\left( 2 \right) = 0">
<mfrac>
<mrow>
<mo>−</mo>
<mn>48</mn>
</mrow>
<mrow>
<mrow>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>+</mo>
<mn>6</mn>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0</mn>
</math></span> seen.</p>
<p>Award <em><strong>(M0)(A0)</strong></em> for <em>x</em> = 2 seen either from a graphical method or without working.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{48}}{2} + 3 \times {2^2} - 58\,\,\,\left( { = - 22} \right)">
<mfrac>
<mrow>
<mn>48</mn>
</mrow>
<mn>2</mn>
</mfrac>
<mo>+</mo>
<mn>3</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>2</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>58</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mo>=</mo>
<mo>−</mo>
<mn>22</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting their 2 into their function, but only if the final answer is −22. Substitution of the known result invalidates the process; award <em><strong>(M0)(A0)(M0)</strong></em>.</p>
<p>−22 <em><strong>(AG)</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"><em><strong>(A1)(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct window. Axes must be labelled.<br><em><strong>(A1)</strong></em><strong>(ft)</strong> for a smooth curve with correct shape and zeros in approximately correct positions relative to each other.<br><em><strong>(A1)</strong></em><strong>(ft)</strong> for point P indicated in approximately the correct position. Follow through from their <em>x</em>-coordinate in part (c). <em><strong>(A1)</strong></em><strong>(ft)</strong> for two <em>x</em>-intercepts identified on the graph and curve reflecting asymptotic properties.</p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[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">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A company performs an experiment on the efficiency of a liquid that is used to detect a nut allergy.</p>
<p>A group of 60 people took part in the experiment. In this group 26 are allergic to nuts. One person from the group is chosen at random.</p>
</div>
<div class="specification">
<p>A second person is chosen from the group.</p>
</div>
<div class="specification">
<p>When the liquid is added to a person’s blood sample, it is expected to turn blue if the person is allergic to nuts and to turn red if the person is not allergic to nuts.</p>
<p>The company claims that the probability that the test result is correct is 98% for people who are allergic to nuts and 95% for people who are not allergic to nuts.</p>
<p>It is known that 6 in every 1000 adults are allergic to nuts.</p>
<p>This information can be represented in a tree diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-13_om_14.31.34.png" alt="N17/5/MATSD/SP2/ENG/TZ0/04.c.d.e.f.g"></p>
</div>
<div class="specification">
<p>An adult, who was not part of the original group of 60, is chosen at random and tested using this liquid.</p>
</div>
<div class="specification">
<p>The liquid is used in an office to identify employees who might be allergic to nuts. The liquid turned blue for <strong>38 </strong><strong>employees</strong>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this person is <strong>not </strong>allergic to nuts.</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 probability that both people chosen are <strong>not </strong>allergic to nuts.</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><strong>Copy </strong>and complete the tree diagram.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this adult is allergic to nuts and the liquid turns blue.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the liquid turns blue.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the tested adult is allergic to nuts given that the liquid turned blue.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the number of employees, from this 38, who are allergic to nuts.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{34}}{{60}}{\text{ }}\left( {\frac{{17}}{{30}},{\text{ }}0.567,{\text{ }}0.566666 \ldots ,{\text{ }}56.7\% } \right)">
<mfrac>
<mrow>
<mn>34</mn>
</mrow>
<mrow>
<mn>60</mn>
</mrow>
</mfrac>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>17</mn>
</mrow>
<mrow>
<mn>30</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.567</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.566666</mn>
<mo>…</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>56.7</mn>
<mi mathvariant="normal">%</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for correct numerator, <strong><em>(A1) </em></strong>for correct denominator.</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{34}}{{60}} \times \frac{{33}}{{59}}">
<mfrac>
<mrow>
<mn>34</mn>
</mrow>
<mrow>
<mn>60</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>33</mn>
</mrow>
<mrow>
<mn>59</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for their correct product.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.317{\text{ }}\left( {\frac{{187}}{{590}},{\text{ }}0.316949 \ldots ,{\text{ }}31.7\% } \right)">
<mo>=</mo>
<mn>0.317</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>187</mn>
</mrow>
<mrow>
<mn>590</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.316949</mn>
<mo>…</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>31.7</mn>
<mi mathvariant="normal">%</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)<em>(G2)</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><img src="images/Schermafbeelding_2018-02-14_om_05.54.09.png" alt="N17/5/MATSD/SP2/ENG/TZ0/04.c/M"> <strong><em>(A1)(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for each correct pair of branches.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.006 \times 0.98">
<mn>0.006</mn>
<mo>×</mo>
<mn>0.98</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for multiplying 0.006 by 0.98.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.00588{\text{ }}\left( {\frac{{147}}{{25000}},{\text{ }}0.588\% } \right)">
<mo>=</mo>
<mn>0.00588</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>147</mn>
</mrow>
<mrow>
<mn>25000</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.588</mn>
<mi mathvariant="normal">%</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.006 \times 0.98 + 0.994 \times 0.05{\text{ }}(0.00588 + 0.994 \times 0.05)">
<mn>0.006</mn>
<mo>×</mo>
<mn>0.98</mn>
<mo>+</mo>
<mn>0.994</mn>
<mo>×</mo>
<mn>0.05</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>0.00588</mn>
<mo>+</mo>
<mn>0.994</mn>
<mo>×</mo>
<mn>0.05</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em>(ft)<em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1)</em>(ft) </strong>for their two correct products, <strong><em>(M1) </em></strong>for adding two products.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.0556{\text{ }}\left( {0.05558,{\text{ }}5.56\% ,{\text{ }}\frac{{2779}}{{50000}}} \right)">
<mo>=</mo>
<mn>0.0556</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.05558</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>5.56</mn>
<mi mathvariant="normal">%</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mfrac>
<mrow>
<mn>2779</mn>
</mrow>
<mrow>
<mn>50000</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from parts (c) and (d).</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.006 \times 0.98}}{{0.05558}}">
<mfrac>
<mrow>
<mn>0.006</mn>
<mo>×</mo>
<mn>0.98</mn>
</mrow>
<mrow>
<mn>0.05558</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for their correct numerator, <strong><em>(M1) </em></strong>for their correct denominator.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.106{\text{ }}\left( {0.105793 \ldots ,{\text{ }}10.6\% ,{\text{ }}\frac{{42}}{{397}}} \right)">
<mo>=</mo>
<mn>0.106</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.105793</mn>
<mo>…</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>10.6</mn>
<mi mathvariant="normal">%</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mfrac>
<mrow>
<mn>42</mn>
</mrow>
<mrow>
<mn>397</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from parts (d) and (e).</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.105793 \ldots \times 38">
<mn>0.105793</mn>
<mo>…</mo>
<mo>×</mo>
<mn>38</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for multiplying 38 by their answer to part (f).</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 4.02{\text{ }}(4.02015 \ldots )">
<mo>=</mo>
<mn>4.02</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>4.02015</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Follow through from part (f). Use of 3 sf result from part (f) results in an answer of 4.03 (4.028).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>All lengths in this question are in metres.</strong></p>
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = - 0.8{x^2} + 0.5">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mn>0.8</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>0.5</mn>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 0.5 \leqslant x \leqslant 0.5">
<mo>−<!-- − --></mo>
<mn>0.5</mn>
<mo>⩽<!-- ⩽ --></mo>
<mi>x</mi>
<mo>⩽<!-- ⩽ --></mo>
<mn>0.5</mn>
</math></span>. Mark uses <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x)">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span> as a model to create a barrel. The region enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>, the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis, the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - 0.5">
<mi>x</mi>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mn>0.5</mn>
</math></span> and the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0.5">
<mi>x</mi>
<mo>=</mo>
<mn>0.5</mn>
</math></span> is rotated 360° about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis. This is shown in the following diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-03_om_15.49.19.png" alt="N16/5/MATME/SP2/ENG/TZ0/06"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the model to find the volume of the barrel.</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>The empty barrel is being filled with water. The volume <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="V{\text{ }}{{\text{m}}^3}">
<mi>V</mi>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</math></span> of water in the barrel after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> minutes is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="V = 0.8(1 - {{\text{e}}^{ - 0.1t}})">
<mi>V</mi>
<mo>=</mo>
<mn>0.8</mn>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>−</mo>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mn>0.1</mn>
<mi>t</mi>
</mrow>
</msup>
</mrow>
<mo stretchy="false">)</mo>
</math></span>. How long will it take for the barrel to be half-full?</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 style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>attempt to substitute correct limits or the function into the formula involving</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{y^2}">
<mrow>
<msup>
<mi>y</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi \int_{ - 0.5}^{0.5} {{y^2}{\text{d}}x,{\text{ }}\pi \int {{{( - 0.8{x^2} + 0.5)}^2}{\text{d}}x} } ">
<mi>π</mi>
<msubsup>
<mo>∫</mo>
<mrow>
<mo>−</mo>
<mn>0.5</mn>
</mrow>
<mrow>
<mn>0.5</mn>
</mrow>
</msubsup>
<mrow>
<mrow>
<msup>
<mi>y</mi>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>π</mi>
<mo>∫</mo>
<mrow>
<mrow>
<msup>
<mrow>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>0.8</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>0.5</mn>
<mo stretchy="false">)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
</mrow>
</mrow>
</math></span></p>
<p>0.601091</p>
<p>volume <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.601{\text{ }}({{\text{m}}^3})">
<mo>=</mo>
<mn>0.601</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<mo stretchy="false">)</mo>
</math></span> <strong><em>A2 N3</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to equate half <strong>their </strong>volume to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="V">
<mi>V</mi>
</math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.30055 = 0.8(1 - {{\text{e}}^{ - 0.1t}})">
<mn>0.30055</mn>
<mo>=</mo>
<mn>0.8</mn>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>−</mo>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mn>0.1</mn>
<mi>t</mi>
</mrow>
</msup>
</mrow>
<mo stretchy="false">)</mo>
</math></span>, graph</p>
<p>4.71104</p>
<p>4.71 (minutes) <strong><em>A2 N3</em></strong></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>A box of chocolates is to have a ribbon tied around it as shown in the diagram below.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The box is in the shape of a cuboid with a height of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math> cm. The length and width of the box are <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> cm.</p>
<p style="text-align: left;">After going around the box an extra <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> cm of ribbon is needed to form the bow.</p>
</div>
<div class="specification">
<p>The volume of the box is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>450</mn><msup><mtext> cm</mtext><mn>3</mn></msup></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for the total length of the ribbon <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>.</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>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mn>2</mn><mi>x</mi><mo>+</mo><mfrac><mn>300</mn><mi>x</mi></mfrac><mo>+</mo><mn>22</mn></math></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 <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>L</mi></mrow><mrow><mo>d</mo><mi>x</mi></mrow></mfrac></math></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Solve <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>L</mi></mrow><mrow><mo>d</mo><mi>x</mi></mrow></mfrac><mo>=</mo><mn>0</mn></math></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence or otherwise find the minimum length of ribbon required.</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 style="color:#999;font-size:90%;font-style:italic;">* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>2</mn><mi>y</mi><mo>+</mo><mn>12</mn><mo>+</mo><mn>10</mn><mo>=</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>2</mn><mi>y</mi><mo>+</mo><mn>22</mn></math> <strong>A1A1</strong></p>
<p> </p>
<p><strong>Note: A1</strong> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>x</mi><mo>+</mo><mn>2</mn><mi>y</mi></math> and <strong>A1</strong> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>+</mo><mn>10</mn></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>22</mn></math>.</p>
<p> </p>
<p><strong>[2 marks]</strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mn>3</mn><mi>x</mi><mi>y</mi><mo>=</mo><mn>450</mn></math> <strong>A1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mn>150</mn><mi>x</mi></mfrac></math> <strong>A1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>2</mn><mfenced><mfrac><mn>150</mn><mi>x</mi></mfrac></mfenced><mo>+</mo><mn>22</mn></math> <strong>M1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mn>2</mn><mi>x</mi><mo>+</mo><mfrac><mn>300</mn><mi>x</mi></mfrac><mo>+</mo><mn>22</mn></math> <strong>AG</strong></p>
<p> </p>
<p><strong>[3 marks]</strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>300</mn><msup><mi>x</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>+</mo><mn>22</mn></math> <strong>(M1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>L</mi></mrow><mrow><mo>d</mo><mi>x</mi></mrow></mfrac><mo>=</mo><mn>2</mn><mo>-</mo><mfrac><mn>300</mn><msup><mi>x</mi><mn>2</mn></msup></mfrac></math> <strong>A1</strong><strong>A1</strong></p>
<p> </p>
<p><strong>Note: A1</strong> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> (and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math>), <strong>A1</strong> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>300</mn><msup><mi>x</mi><mn>2</mn></msup></mfrac></math>.</p>
<p> </p>
<p><strong>[3 marks]</strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>300</mn><msup><mi>x</mi><mn>2</mn></msup></mfrac><mo>=</mo><mn>2</mn></math> <strong>(M1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><msqrt><mn>150</mn></msqrt><mo>=</mo><mn>12</mn><mo>.</mo><mn>2</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>12</mn><mo>.</mo><mn>2474</mn><mo>…</mo></mrow></mfenced></math> <strong>A1</strong></p>
<p> </p>
<p><strong>[2 marks]</strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mn>2</mn><msqrt><mn>150</mn></msqrt><mo>+</mo><mfrac><mn>300</mn><msqrt><mn>150</mn></msqrt></mfrac><mo>+</mo><mn>22</mn><mo>=</mo><mn>71</mn><mo>.</mo><mn>0</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>70</mn><mo>.</mo><mn>9897</mn><mo>…</mo></mrow></mfenced><mo> </mo><mtext>cm</mtext></math> <strong>(M1)A1</strong></p>
<p> </p>
<p><strong>[2 marks]</strong></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the curve <em>y</em> = 2<em>x</em><sup>3</sup> − 9<em>x</em><sup>2</sup> + 12<em>x</em> + 2, for −1 < <em>x</em> < 3</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the curve for −1 < <em>x</em> < 3 and −2 < <em>y</em> < 12.</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>A teacher asks her students to make some observations about the curve.</p>
<p>Three students responded.<br><strong>Nadia</strong> said <em>“The x-intercept of the curve is between −1 and zero”.</em><br><strong>Rick</strong> said <em>“The curve is decreasing when x < 1 ”.</em><br><strong>Paula</strong> said <em>“The gradient of the curve is less than zero between x = 1 and x = 2 ”.</em></p>
<p>State the name of the student who made an <strong>incorrect</strong> observation.</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 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{dy}}}}{{{\text{dx}}}}">
<mfrac>
<mrow>
<mrow>
<mtext>dy</mtext>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>dx</mtext>
</mrow>
</mrow>
</mfrac>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <em>y</em> = 2<em>x</em><sup>3</sup> − 9<em>x</em><sup>2</sup> + 12<em>x</em> + 2 = <em>k</em> has <strong>three</strong> solutions, find the possible values of <em>k</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><img src="data:image/png;base64,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"><em><strong>(A1)(A1)(A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct window (condone a window which is slightly off) and axes labels. An indication of window is necessary. −1 to 3 on the <em>x</em>-axis and −2 to 12 on the <em>y</em>-axis and a graph in that window.<br><em><strong>(A1)</strong></em> for correct shape (curve having cubic shape and must be smooth).<br><em><strong>(A1)</strong></em> for both stationary points in the 1<sup>st</sup> quadrant with approximate correct position,<br><em><strong>(A1)</strong></em> for intercepts (negative <em>x</em>-intercept and positive <em>y</em> intercept) with approximate correct position.</p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Rick <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A0)</strong></em> if extra names stated.</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>6<em>x</em><sup>2</sup> − 18<em>x</em> + 12 <strong><em>(A1)(A1)(A1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em></strong> for each correct term. Award at most <strong><em>(A1)(A1)(A0)</em></strong> if extra terms seen.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>6 < <em>k</em> < 7 <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for an inequality with 6, award <em><strong>(A1)</strong></em><strong>(ft)</strong> for an inequality with 7 from their part (c) provided it is greater than 6, <em><strong>(A1)</strong></em> for their correct strict inequalities. Accept ]6, 7[ or (6, 7).</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = - {x^4} + a{x^2} + 5">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>a</mi>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>5</mn>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> is a constant. Part of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f(x)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span> is shown below.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_17.47.40.png" alt="M17/5/MATSD/SP2/ENG/TZ2/06"></p>
</div>
<div class="specification">
<p>It is known that at the point where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 2">
<mi>x</mi>
<mo>=</mo>
<mn>2</mn>
</math></span> the tangent to the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f(x)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span> is horizontal.</p>
</div>
<div class="specification">
<p>There are two other points on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f(x)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span> at which the tangent is horizontal.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-intercept of the graph.</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 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'(x)">
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></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>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 8">
<mi>a</mi>
<mo>=</mo>
<mn>8</mn>
</math></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>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(2)">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-coordinates of these two points;</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the intervals where the gradient of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f(x)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span> is positive.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the range of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x)">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of possible solutions to the equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = 5">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>5</mn>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = m">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>m</mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m \in \mathbb{R}">
<mi>m</mi>
<mo>∈</mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>, has four solutions. Find the possible values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>5 <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept an answer of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(0,{\text{ }}5)">
<mo stretchy="false">(</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>5</mn>
<mo stretchy="false">)</mo>
</math></span>.</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {f'(x) = } \right) - 4{x^3} + 2ax">
<mrow>
<mo>(</mo>
<mrow>
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
</mrow>
<mo>)</mo>
</mrow>
<mo>−</mo>
<mn>4</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mi>a</mi>
<mi>x</mi>
</math></span> <strong><em>(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 4{x^3}">
<mo>−</mo>
<mn>4</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
</math></span> and <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" + 2ax">
<mo>+</mo>
<mn>2</mn>
<mi>a</mi>
<mi>x</mi>
</math></span>. Award at most <strong><em>(A1)(A0) </em></strong>if extra terms are seen.</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 4 \times {2^3} + 2a \times 2 = 0">
<mo>−</mo>
<mn>4</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>2</mn>
<mn>3</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mi>a</mi>
<mo>×</mo>
<mn>2</mn>
<mo>=</mo>
<mn>0</mn>
</math></span> <strong><em>(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for substitution of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 2">
<mi>x</mi>
<mo>=</mo>
<mn>2</mn>
</math></span> into their derivative, <strong><em>(M1) </em></strong>for equating their derivative, written in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span>, to 0 leading to a correct answer (note, the 8 does not need to be seen).</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 8">
<mi>a</mi>
<mo>=</mo>
<mn>8</mn>
</math></span> <strong><em>(AG)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {f(2) = } \right) - {2^4} + 8 \times {2^2} + 5">
<mrow>
<mo>(</mo>
<mrow>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
</mrow>
<mo>)</mo>
</mrow>
<mo>−</mo>
<mrow>
<msup>
<mn>2</mn>
<mn>4</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>8</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>2</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>5</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 2">
<mi>x</mi>
<mo>=</mo>
<mn>2</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 8">
<mi>a</mi>
<mo>=</mo>
<mn>8</mn>
</math></span> into the formula of the function.</p>
<p> </p>
<p>21 <strong><em>(A1)(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(x = ){\text{ }} - 2,{\text{ }}(x = ){\text{ 0}}">
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>−</mo>
<mn>2</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> 0</mtext>
</mrow>
</math></span> <strong><em>(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for each correct solution. Award at most <strong><em>(A0)(A1)</em>(ft) </strong>if answers are given as <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="( - 2{\text{ }},21)">
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>2</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo>,</mo>
<mn>21</mn>
<mo stretchy="false">)</mo>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(0,{\text{ }}5)">
<mo stretchy="false">(</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>5</mn>
<mo stretchy="false">)</mo>
</math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="( - 2,{\text{ }}0)">
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>2</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0</mn>
<mo stretchy="false">)</mo>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(0,{\text{ }}0)">
<mo stretchy="false">(</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x < - 2,{\text{ }}0 < x < 2">
<mi>x</mi>
<mo><</mo>
<mo>−</mo>
<mn>2</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0</mn>
<mo><</mo>
<mi>x</mi>
<mo><</mo>
<mn>2</mn>
</math></span> <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em>(ft) </strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x < - 2">
<mi>x</mi>
<mo><</mo>
<mo>−</mo>
<mn>2</mn>
</math></span>, follow through from part (d)(i) provided their value is negative.</p>
<p>Award <strong><em>(A1)</em>(ft) </strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 < x < 2">
<mn>0</mn>
<mo><</mo>
<mi>x</mi>
<mo><</mo>
<mn>2</mn>
</math></span>, follow through only from their 0 from part (d)(i); 2 must be the upper limit.</p>
<p>Accept interval notation.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y \leqslant 21">
<mi>y</mi>
<mo>⩽</mo>
<mn>21</mn>
</math></span> <strong><em>(A1)</em>(ft)<em>(A1)</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Award <strong><em>(A1)</em>(ft) </strong>for 21 seen in an interval or an inequality, <strong><em>(A1) </em></strong>for “<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y \leqslant ">
<mi>y</mi>
<mo>⩽</mo>
</math></span>”.</p>
<p>Accept interval notation.</p>
<p>Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - \infty < y \leqslant 21">
<mo>−</mo>
<mi mathvariant="normal">∞</mi>
<mo><</mo>
<mi>y</mi>
<mo>⩽</mo>
<mn>21</mn>
</math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) \leqslant 21">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>⩽</mo>
<mn>21</mn>
</math></span>.</p>
<p>Follow through from their answer to part (c)(ii). Award at most <strong><em>(A1)</em>(ft)<em>(A0) </em></strong>if <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> is seen instead of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>. Do not award the second <strong><em>(A1) </em></strong>if a (finite) lower limit is seen.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>3 (solutions) <strong><em>(A1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="5 < m < 21">
<mn>5</mn>
<mo><</mo>
<mi>m</mi>
<mo><</mo>
<mn>21</mn>
</math></span> or equivalent <strong><em>(A1)</em>(ft)<em>(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em>(ft) </strong>for 5 and 21 seen in an interval or an inequality, <strong><em>(A1) </em></strong>for correct strict inequalities. Follow through from their answers to parts (a) and (c)(ii).</p>
<p>Accept interval notation.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>A theatre set designer is designing a piece of flat scenery in the shape of a hill. The scenery is formed by a curve between two vertical edges of unequal height. One edge is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> metres high and the other is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> metre high. The width of the scenery is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math> metres.</p>
<p>A coordinate system is formed with the origin at the foot of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> metres high edge. In this coordinate system the highest point of the cross‐section is at <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo>,</mo><mo> </mo><mn>3</mn><mo>.</mo><mn>5</mn></mrow></mfenced></math>.</p>
<p style="text-align: center;"><img 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"></p>
<p>A set designer wishes to work out an approximate value for the area of the scenery <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>A</mi><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup><mo> </mo><mo>)</mo></math>.</p>
</div>
<div class="specification">
<p>In order to obtain a more accurate measure for the area the designer decides to model the curved edge with the polynomial <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>a</mi><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mi>b</mi><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>c</mi><mi>x</mi><mo>+</mo><mi>d</mi><mo> </mo><mo> </mo><mi>a</mi><mo>,</mo><mo> </mo><mi>b</mi><mo>,</mo><mo> </mo><mi>c</mi><mo>,</mo><mo> </mo><mi>d</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> metres is the height of the curved edge a horizontal distance <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo> </mo><mtext>m</mtext></math> from the origin.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo><</mo><mn>21</mn></math>.</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>By dividing the area between the curve and the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>‐axis into two trapezoids of unequal width show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>></mo><mn>14</mn><mo>.</mo><mn>5</mn></math>, justifying the direction of the inequality.</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 value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>.</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>Use differentiation to show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mi>a</mi><mo>+</mo><mn>4</mn><mi>b</mi><mo>+</mo><mi>c</mi><mo>=</mo><mn>0</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine two other linear equations in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find an expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>x</mi></mfenced></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the expression found in (f) to calculate a value for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color:#999;font-size:90%;font-style:italic;">* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.</p>
<p>The area <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> is less than the rectangle containing the cross-section which is equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>×</mo><mn>3</mn><mo>.</mo><mn>5</mn><mo>=</mo><mn>21</mn></math> <strong>R1</strong></p>
<p> </p>
<p><strong>Note:</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>×</mo><mn>3</mn><mo>.</mo><mn>5</mn><mo>=</mo><mn>21</mn></math> is not sufficient for <strong>R1</strong>.</p>
<p> </p>
<p><strong>[1 mark]</strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>2</mn><mo>×</mo><mfenced><mrow><mn>2</mn><mo>+</mo><mn>3</mn><mo>.</mo><mn>5</mn></mrow></mfenced><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>4</mn><mo>×</mo><mfenced><mrow><mn>3</mn><mo>.</mo><mn>5</mn><mo>+</mo><mn>1</mn></mrow></mfenced></math> <strong>(M1)(A1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>14</mn><mo>.</mo><mn>5</mn></math> <strong>A1</strong></p>
<p>This is an underestimate as the trapezoids are enclosed by (are under) the curve. <strong>R1</strong></p>
<p> </p>
<p><strong>Note:</strong> This can be shown in a diagram.</p>
<p> </p>
<p><strong>[4 marks]</strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mn>0</mn></mfenced><mo>=</mo><mn>2</mn><mo>⇒</mo><mi>d</mi><mo>=</mo><mn>2</mn></math> <strong>A1</strong></p>
<p> </p>
<p><strong>[1 mark]</strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>'</mo><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>3</mn><mi>a</mi><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>b</mi><mi>x</mi><mo>+</mo><mi>c</mi></math> <strong>A1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>'</mo><mfenced><mn>2</mn></mfenced><mo>=</mo><mn>0</mn></math> <strong>M1</strong></p>
<p>hence <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mi>a</mi><mo>+</mo><mn>4</mn><mi>b</mi><mo>+</mo><mi>c</mi><mo>=</mo><mn>0</mn></math> <strong>AG</strong></p>
<p> </p>
<p><strong>[2 marks]</strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Substitute the points <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo>,</mo><mo> </mo><mn>3</mn><mo>.</mo><mn>5</mn></mrow></mfenced></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>6</mn><mo>,</mo><mo> </mo><mn>1</mn></mrow></mfenced></math> <strong>(M1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mi>a</mi><mo>+</mo><mn>4</mn><mi>b</mi><mo>+</mo><mn>2</mn><mi>c</mi><mo>+</mo><mn>2</mn><mo>=</mo><mn>3</mn><mo>.</mo><mn>5</mn><mo> </mo><mfenced><mrow><mn>8</mn><mi>a</mi><mo>+</mo><mn>4</mn><mi>b</mi><mo>+</mo><mn>2</mn><mi>c</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>5</mn></mrow></mfenced></math></p>
<p>and</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>216</mn><mi>a</mi><mo>+</mo><mn>36</mn><mi>b</mi><mo>+</mo><mn>6</mn><mi>c</mi><mo>+</mo><mn>2</mn><mo>=</mo><mn>1</mn><mo> </mo><mfenced><mrow><mn>216</mn><mi>a</mi><mo>+</mo><mn>36</mn><mi>b</mi><mo>+</mo><mn>6</mn><mi>c</mi><mo>=</mo><mo>-</mo><mn>1</mn></mrow></mfenced></math> <strong>A1</strong><strong>A1</strong></p>
<p> </p>
<p><strong>[3 marks]</strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Solve on a GDC <strong>(M1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>0365</mn><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>0</mn><mo>.</mo><mn>521</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn><mo>.</mo><mn>65</mn><mi>x</mi><mo>+</mo><mn>2</mn></math> <strong>A2</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>h</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>0364583</mn><mo>…</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>0</mn><mo>.</mo><mn>520833</mn><mo>…</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn><mo>.</mo><mn>64583</mn><mo>…</mo><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></math></p>
<p> </p>
<p><strong>[3 marks]</strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mo>∫</mo><mn>0</mn><mn>6</mn></msubsup><mn>0</mn><mo>.</mo><mn>0364583</mn><mo>…</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>0</mn><mo>.</mo><mn>520833</mn><mo>…</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn><mo>.</mo><mn>64583</mn><mo>…</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo> </mo><mtext>d</mtext><mi>x</mi></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>15</mn><mo>.</mo><mn>9</mn><mo> </mo><mfenced><mrow><mn>15</mn><mo>.</mo><mn>9374</mn><mo>…</mo></mrow></mfenced><mo> </mo><mfenced><msup><mtext>m</mtext><mn>2</mn></msup></mfenced></math> <strong>(M1)A1</strong></p>
<p> </p>
<p><strong>Note:</strong> Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mo>.</mo><mn>0</mn><mo> </mo><mo>(</mo><mn>16</mn><mo>.</mo><mn>014</mn><mo>)</mo></math> from the three significant figure answer to part (g).</p>
<p> </p>
<p><strong>[2 marks]</strong></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>The Happy Straw Company manufactures drinking straws.</p>
<p>The straws are packaged in small closed rectangular boxes, each with length 8 cm, width 4 cm and height 3 cm. The information is shown in the diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAicAAADbCAYAAAC2nzGWAAAgAElEQVR4Ae3dDXSU1b3v8V+iSxFzkNK0mhheFtgEKAhIAO8NrkaQgFgPGApaKqBEy7kcFIskVI+2p9ZqSVx61NZVFaKCxx6xyYJ6e5UIIesoXsAEAaOQiMqbGayImKaK9Jq5a4/OMJnMSzKZl+eZ5ztrsTLzvOxn788e4z/Ps/97p7ndbrd4IYAAAggggAACFhFIt0g9qAYCCCCAAAIIIOARIDjhi4AAAggggAAClhIgOLFUd1AZBBBAAAEEECA44TuAAAIIIIAAApYSIDixVHdQmW4LtNZqRXaa0tL8/k2tVHO7KemYalfkd9yXNkeVzSe7fRlOQAABBBBInEAa2TqJw+ZK8RJoV2vtXRo6eb/ubVqjhbm9Ol7IBDBDr9eue2v10sKhIiLvyMMnBBBAwGoC/J62Wo9QHwQQQAABBBwuQHDi8C8AzUcAAQQQQCB2Aq1qrn1eDywYefqR+uUrVLmhQa4T21Rdd6xLlyI46RITByGAAAIIIIBAWIG2RlUuKFDer3eq34Iq/c3tlpnn1f1iiQZ9sk5zv7VE2z3jAcOW4tl5ZuRDOAIBuwi8oJK8F1QStLpZKgq6nY0IIIAAAj0WaD+o6qU/Vsmhhap/canGZvjd+8jI1aSFv1Ze3y+16MAxtSsz4tg/v7N7XDUKQCDJArO1uumLryN1b8Rufn62WWVZSa4al0cAAQRSVqBdrXWPa0nl2Sq7e17HwMTX5rN04czFuvnbXQs7uHPig+MNAggggAACCHRf4LjqN9bIlVWkqfn9Qp+enqsZM0Lv9t/TtRDG/wzeI4AAAggggAACXoHWPdq4tsH7KeDnSTVXzjk9ONYzJ1Xk+aYITgIY+YgAAggggAACsRLopdyF6+T+23ZVFGYpq2yzPnOv6zwfVcDlCE4CQPiIAAIIIIAAAt0QyMhW3sgsybVfB46eCn5i7z7qd1bwXcG2EpwEU2GbfQQ809efofMm3y+XTLbOOUoLnL7+vMkqd7lUUzJMZzB9vX36lpoigIA9BNIHaeK1EyW9prV/3qO2GNSa6etjgEgRCCCAAAIIOFqgbYceuHqmSusuUUX9s1o+tm9HjvZ9qrxyku4a/az2rZykPh33dvrEnZNOJGxAAAEEEEAAgW4JZIzXsuee0R2FO1Waf61WVNaquc0741qrmuteV1OIJz7BrsOdk2AqbEMAAQQQQACB7gu0u9Tw4hZtqb5fpWsafednza/QI8WXq+Dqscrqwm0RghMfHW8QQAABBBBAwAoCTMJmhV6gDnEROH78uI4d69oiU3GpAIUigAACDhDo37+/zjnnnJi2lOAkppwUlkyB9957T6+88opqa2v1zjvv6O23305mdbg2Aggg4AiBCy64QC6XK6ZtJTiJKSeFJVLgjTfe0KZNm7RlyxZPMPLhhx96Lj9u3DhNnz7dE5w8+uijKipiyb9E9gvXQgCB1BH4/PPPtWfPHr366qtatWpVh4ZdfPHF+uKLL/Tuu+922B6LDwQnsVCkjIQI1NTUeIIRc1fkrbfe0qFDhzzXNcHI4sWLlZ+fr+HDhysnJ8ezvaKiQtnZ2crNzU1I/bgIAgggYHcB8zh87969evPNN7V79+4OAUleXp4yMzM1dOhQDRs2TL1799auXbsITuze6dS/ewLeYMTcIamrq/OdPGPGDJWWlmrMmDEaOHCgLxjxHcAbBBBAAIEuCRw5ckQHDx70BCPmTvSGDRt855nfsVOmTPEFI74dCXjDnZMEIHOJyAImWjfjRTZv3qyGhgbt3LnTd5IJRszjGfMfionW+/ULs+ql7yzeIIAAAggECphgxNx9rq+v1/r162X++DMvM6g1IyMjacFIYD0JTgJF+JwQATN41fzHYYIR8zxz+/btvuvedNNNWrp0qczzTHMbMdajwH0X4g0CCCCQ4gLNzc1qbGzUvn37OgQjWVlZMv/MH3/mMY25C22lF8GJlXojhesSLpPGPKIpKyvT4MGDYxqMmHLPP//8FFalaQgggEBHAW8wsm3bNplxd96X+UPv3HPP1XXXXecJRKwWjHjr6f3JJGxeCX7GVMA/k6alpaVDWq8JGi699FKNGDGCwaoxVacwBBBwkoDJlGlqagqaTWPuPJ955pme37Hmcfh3vvOduNCYAbFPPPGE3G53TMvnzklMOZ1bmBm8asaKbN26tVMmzdy5cztl0jhXipYjgAAC0Ql4M2nMnejA1F4TjBQUFPgGr5pMGju/CE7s3HtJrLs3k+b111/3BCTeqpjnl4sWLSIY8YLwEwEEEIhSwBuMmLTeUJk0AwYM8KX1RnkZS55GcGLJbrFWpbyZNObOSLC0XjJprNVf1AYBBOwp4J9Js2PHjg5pvebRTLLSepOhSXCSDHWLX9MbjITKpLnxxhs9mTQmYiet1+KdSfUQQMCyAmbw6oEDB4Km9ZoxIlbNpEkEKMFJIpQtfg3/TBqT1msGWHlfZvCqmX3Vjmm95j98M5shAZS3N/mJAALJFIiUSePkYCSwXwhOAkUc8NmbSWOeYwYukJdKmTQmda6qqkrFxcUO6FWaiAACVhLwz6Qx84z4p/UOGTJEl1xySdwzaazk0d26EJx0V8yGx3uDEZNJY9K+/BfIM5k0ZgIe0npt2LFUGQEELCPgH4yEy6Qxj8PjldZrGYwYVITgJAaIVivCP5Pm8OHDERfIs1r9qQ8CCCBgdYFImTSplNabjL4gOEmGegyvaf4DMdPAmzSzYJk0ZjZA1qSJIThFIYCAIwW8mTRm3EiotF7var2OBIpxowlOYgwa7+K6kkljnmeyQF68e4LyEUAglQW8wUiwBfK8mTTeOUZS2SFZbSM4SZZ8F6/rn0lz6NChTgvk2TWTpovN5zAEEEAgIQKhMmnM4nh9+/Z1dFpvQjog4CIEJwEgyf7oH4wEy6QxC+SZwatmeWtW6w3fW7Fe6yH81diLAAJ2ETCDV814PJNFE2yBPDJpkt+TBCdJ7gNvJs2WLVs8ab3+mTTTp0/XPffcQyZNkvuIyyOAgL0FupJJY/7gi+cCefYWTHztCU4SbO7NpDF3Rd566y0yaRLsz+UQQCD1BfwzaXbv3q1Vq1b5Gm3mPyKTxsdh2TcEJ3HuGm8wEiyTxkx4ZjJpBg4cqJycnDjXhOIRQACB1BQwg1cPHjyocAvkkUljr74nOIlhf/ln0phF8nbu3Okr3UxLzAJ5Pg7eIIAAAlELhMukycjIcNQCeVEjWvxEgpMedJAZvGrSzEItkLd06VJbrknTAxJORQABBGIu4M2k2bdvn9avX++Z08lcxGTSmH+sSRNz8qQXeDo4ad+nyisnqaTGFaZSY1W2+WWtnJQZ5pjU3dWVTJrBgwfLPNMkkyb534O0tDTW1kl+N1ADBLot4A1GgmXSnHvuuTKTS5rH4eYfr9QUOB2cpA/Vwo0tuqG5UlfmPabRnYKQVu2r/JXWpKZD0Fb5Z9K0tLTo7bff9h1nxouQSePj4A0CCCAQlUCkTBrSeqNitf1Jp4OTiE3po6E/mq3808MoIp5htwPM4FUzVsQskBeYSWMWyMvPz9fw4cMZvGq3jqW+CCBgGQFvJo25Ex1ugTyT1tu7d2/L1JuKJFagy8FJe/NGvagfqLiwV2JrGMereTNpXn/9dU9A4r2UeX65aNEighEvCD8RQACBKAW8wUi4TBrvNPAEI1Eip+BpXQxOTsnV+I5OjPiBbQm8mTTmzkiwtF4yaWzbtVQcAQQsJOCfSbNjxw5t2LDBVztzN2TKlCkirddHwpsQAiGCkwaVT/6OyjucNFurm/5Xhy1W/uANRkJl0tx4442eTBoTsffr18/KTaFuCCCAgGUFzODVAwcOeDIX/TNpzIyr3gXyTDDC4FXLdqElKxYiOAnMyjGDYR/Tdks24etK+WfS7NmzR01NTb7amsGrLJDn43DMG/MdyMx0ZmaZYzqZhiZcIFImDWm9Ce+SlLxgiOAksK19lDtxjE7/7z5wf+I/ezNpzHPMYAvkXXrppaxJk/husdQVc3NzLVUfKoOA3QT8M2nMInkVFRW+JgwZMkRk0vg4eBNjgS4GJ1J67lTNiPHFu1OcNxgxmTS7du2S/wJ5JpPG3DY0q/XyP6TuqHIsAgggcFrAPxgJl0ljHoebRza8EIiXQJeDk68r0K62N7eqaUiBxvZJj1edPOX6Z9KYpa0PHTrk2T5u3DjPIxrSeuPKT+EIIOAAgUiZNCyQ54AvgUWb2I3g5JRcO57UXeuH6aH7YhuYmP9AzDTwmzZtCppJY2YDNAvkmZHeDF616DeJaiGAgOUFvJk0ZtyI+X3rn0ljfseSSWP5LnRMBU8HJwHT19d0ytYxJl8PlO3TQ56uZNKY55kEIz2E5nQEEHC0gDcYMX/8hcqk8c4x4mgoGm85gTS32+2Od638M2nM45nt20/n/dx000267LLLWCAv3p3gwPLLyso8C4KZW9O8EHCCQKhMGrM4Xt++fT1j8kjrdcI3IXFtNGNAn3jiCcU6lDh95ySGbfEPRoJl0pj/aZjBqyYPngXyYghPUR0ETGaBydrihUAqCpjBq2Y8nsmiCbZAHpk0qdjrzmlTTIITbybNli1bPGm9/pk006dPZ4E853yfaCkCCMRJoCuZNOYPPvM4nEyaOHUCxSZMIKrgxJtJY+6KBC6QZyY7I5MmYf3HhRBAIEUF/DNpdu/erVWrVvlampeXJzJpfBy8SUGBLgcnaWlp+t73vqd33323E4OZEXD8+PGeuUbMzra2Npk1Fcw/XggkU8Dc7uaFgJ0EWlpayKSxU4dR17gIdGlArAkyTABy9OjRuFSCQhFAAAEEvhYwj2YyMjKUk5PDAnl8KSwvkNQBsWaUtzcwifWIXMvLU0HbClRXVzNrsG17z5kVN3eoTTbNNddc40wAWo3ANwJdfqyDGAJ2EyguLrZblakvAggggIAkghO+BggggIBVBU42af2vHlbNZ2EqOOx6/fuS/6nvpoU5hl0I2EyA4MRmHUZ1EUDAQQK98jTz/t9rWtOf9auH92rC0iWamZfhA3B/tk9/XrNfn37p1nd7EZ34YHhje4HYLpJjew4agAACCNhHIO28Ifof475lnwpTUwS6KMCdky5CcRgCCCBgKQH3cR06crYGXFqg71qqYlQGgZ4LcOek54aUYFEBk61j1hrhhUDqCbj15eG9avo87kujpR4dLbKFAHdObNFNVDIagVmzZqmqqsqz2Fk053MOAtYSOKSah8tU46vUABUtHeX7xBsEUkmA4CSVepO2IIBACguYYMQ7INatLz96Uw2tKdxcmuZoAYITR3c/jUcAAXsKpOns7w5SzikydOzZf9Q6kgDBSSQh9iOAAAJWFEjrpwH9rVgx6oRAzwUYENtzQ0pAAAEEEEAAgRgKEJzEEJOirCVQWlqq888/31qVojYIIIAAAhEFCE4iEnGAXQXKy8tVUFBg1+pTbwQkM339Hf+qZQ9v1Gf6Oltn8R0b1HSSFGK+HvYRaHdt1UMLRsosbJl2+Z2qbo48kpsxJ/bpX2qKAAJOE/BMX/+YZjqt3bQ3dQTadmt9zRm67qm39LOnXNrx8M81s/C36rvvXk3qE/r+SOg9qUNDSxBAAAEEEEAg4QIn9V79F5ow71JlmWgjPUvjSxZonmq0sf542NoQnITlYScCCCCAAAIIRCfQS0MKL9WFfpFG+9ED2pX3E80Z3y9skTzWCcvDTgQQQAABBBDouUCrmmv/pNXPuLTiuVKNzfCLWIIUHn5vkBPYhIBdBFhbxy49RT0RQCClBVprtSL7POVNLlH5mv/Wxv/7vtoiNJjgJAIQu+0rYNbWaWxstG8DqDkCCCCQCgJ9Jmlli1tftWzX02VS+azZWlp9UO1h2kZwEgaHXQgggAACCCAQG4H0rPFacP/DWl30iV7a/l7YuycEJ7ExpxQEEEAAAQQQiCSQPkgTr50Y6SgRnEQk4gAEEEAAAQQQiI1Am440faYrJwxRRpgCCU7C4LALAQQQQAABBKIUaD+o6pJ8Xb5irRpcpySdkqv291p5dK5Ki/qHvTtCcBKlOachgAACCCCAQBiB9G9peMEoNZXPV3722UrLvln/eeKHevqpBRoaIZWYeU7CuLLL3gJuN+uP2LsHqT0CCNhboI+GLlytloWru90M7px0m4wTEEAAAQQQQCCeAgQn8dSlbAQQQAABBBDotgDBSbfJOAEBBBBAAAEE4ilAcBJPXcpGAAEEEEAAgW4LEJx0m4wT7CLQ3Nys48fDL8ttl7ZQTwQQQMBJAgQnTupth7U1Ly9PdXV1Dms1zUUAAQTsL0BwYv8+pAUIIIAAAgiklADBSUp1J41BAAEEEEDA/gIEJ/bvQ1qAAAIIIIBASgkQnKRUd9IYBBBAAAEE7C9AcGL/PqQFCCCAAAIIpJQAa+ukVHfSGH+BpqYmZWZm+m/iPQIIIICADQQITmzQSVQxOoHc3NzoTuQsBBBAAIGkCvBYJ6n8XBwBBBBAAAEEAgUITgJF+IwAAggggAACSRUgOEkqPxdHAAEEEEAAgUABgpNAET4jgAACCCCAQFIFCE6Sys/F4ymQlpam6urqeF6CshFAAAEE4iBAcBIHVIpEAAEEEEAAgegFCE6it+NMBBBAAAEEEIiDAMFJHFApEgEEEEAAAQSiFyA4id6OMxFAAAEEEEAgDgIEJ3FApUgEEEAAAQQQiF6A4CR6O860uEBVVZVGjBhh8VpSPQQQQACBQAHW1gkU4XPKCBQXF6dMW2gIAggg4CQB7pw4qbdpKwIIIIAAAjYQIDixQSdRRQQQQAABBJwkQHDipN6mrQgggAACCNhAgODEBp1EFRFAAAEEEHCSAMGJk3rbYW0tKyvT1q1bHdZqmosAAgjYX4DgxP59SAtCCFRUVOijjz4KsZfNCCCAAAJWFSA4sWrPUC8EEEAAAQQcKkBw4tCOp9kIIIAAAghYVYDgxKo9Q70QQAABBBBwqADBiUM7nmYjgAACCCBgVQGCE6v2DPXqsUBpaanOP//8HpdDAQgggAACiRVgbZ3EenO1BAqUl5cn8GpcCgEEEEAgVgLcOYmVJOUggAACCCCAQEwECE5iwkghCCCAAAIIIBArAYKTWElSDgIIIIAAAgjERIDgJCaMFIIAAggggAACsRIgOImVJOVYTqC6ulrNzc2WqxcVQgABBBAIL0BwEt6HvTYWmDVrlhobG23cAqqOAAIIOFOA4MSZ/U6rEUAAAQQQsKwAwYllu4aKIYAAAggg4EwBghNn9jutRgABBBBAwLICBCeW7RqnVeyYalfkKy0tLcS/qVpRWa3a5lanwdBeBBBAwHECBCeO63KrNjhTk1bWy/3ZZpVlZalo9V595XbL7fn3mZo2XyutXaLJeQVaUNmoti40g7V1uoDEIQgggIAFBQhOLNgpVClQoI9yJy3UyhdrtHq+tKbk5/pDw4nAgzp9NmvrFBQUdNrOBgQQQAABawsQnFi7f6idv0DGCN1w36+0MOsvKr2zWs3t/jt5jwACCCCQKgIEJ6nSkw5pR3rWcBWMzJJqXtZr+086pNU0EwEEEHCWAMGJs/rb/q1Nz9Sg0dmS3lfTka6MPLF/k2kBAggg4DQBghOn9TjtRQABBBBAwOICBCcW7yCqFyDQfkwHdrVIGqy8nIyAnR0/mnV1jh8/3nEjnxBAAAEELC9AcGL5LqKC/gLtrne09S2XshZep6kX9fLf1el9Xl6e6urqOm1nAwIIIICAtQUITqzdP9TOX6CtUU/f+UtVuq7SssWTdCHfXn8d3iOAAAIpI8Cv95TpylRuSKuaayu14uoilazJ1h2bH9eysX1TucG0DQEEEHC0wJmObj2Nt5CAmb5+miaXN3xdp5JhOqPEr3pZ81XxyCrVP3eFxmad5beDtwgggAACqSZAcJJqPWrb9nwzff1K2zaAiiOAAAIIxEiAxzoxgqQYBBBAAAEEEPAXOCVXw//Rnx5YoGzvoq6Xr1Dlhga5/l+zNmxoVqiJvglO/B15n1ICZtHA4uLilGoTjUEAAQRsIdDu0o6HbtbYq5/XgcG3quGrbxZy3XybRn21RT8fUKjHPgkVmkhpbvMbPMLLzBdh0jLNqwuHRyiN3QjER+CLL77QOeec4ys8LS3N9z7wTbDvcbjjzfndPccOx5t2hWu3HdoQrv6p0G+PPfZY4NfX83nx4sVBt5uNwc6x0/Gp0IZgfWDaZad+CNaGUPXv+LvilD6sXqZxsw5oWf2zWt4pgaFdbQ0Pa9a6UXph5ST1CfJNZsxJEBQ22UPABM2NjY3atm2bKioqVFVVxZ0Se3QdtUQAAZsInDhxQp988omOHDmiffv2da3Wra/pkSW/l8o266edAhNTRLoyxs7THQf3hyyPOychadhhVYHf/e53uuWWW3zVmzFjhq644gpNnDhRo0eP9m3nDQJ2EzB3gaZMmaJrrrnGblWnvikiYIIRl8ulgwcPavfu3Z6fpmmjRo3SrFmz9P3vf18jRoxQbm5uiBafVHPlfOWVvKai1bV6aeFQRTN+hDsnIXjZnFwB77Tz/fr161SR7OxsPfPMM7r44os9jxv9H+V0OpgNCCCAAAIhBf7617+qpaVFH3zwgczdaBOUmJf5Q++nP/2p8vPzNXz4cOXk5IQso+OONh1pel9StkYPyowqMDHlEZx0VOVTkgRMMLJ37169+eab2rRpkzZs2KDf/OY3uvPOOzvViEGunUjYgAACCHRJwD8YeeWVV3znTJs2TcuXL9eYMWM0cODAbgQjviJi+obgJKacFBaNQOBjmtLSUs/4kfHjx0dTHOcggAACCEj6xz/+oY8++sgzXuS9997T1q1bfS7z5s3To48+6glGhg0bpmB3qX0Hd+tNhnLyBksyd0+ifxGcRG/Hmd0QMLcLzSvYc8qioiJt3Lixm7cOu3FxDkUAAQQcIPD3v/9dR48e1ccff6xgwYh5TBP/x+G9dNHEaSpSidZu3KN/mxQ8GydSdxCcRBJif1QCgZk0ppCbbrpJTz75ZKfyTMASLGjpdCAbEEAAAQR8At5gxJtJYwawel+33Xabli1b5hm82r9//w7TLHiPidfP9Nx/1oqysZpc/qCemHNJkFRiSe0uNfz335RXmKuMIBUhOAmCwqaeCVRXV3tGdZtSTCaN/63DnpXM2QgggIBzBUJl0hiR22+/Xb/4xS8iZNIkyi5Tk+5+WquP/lgl+dfq49UrVDKnULkZJm+nXW3Ndap67XNNmDM9aGBiaklwkqi+SqHrmMnOmpqaZKL2goKCTi0zY0XMwNYBAwbE8Dlmp8uwAQEEEEhpATN41cwxEiytt6SkRBMmTLDu4/CMEVr4VI1GFf9vrfuP65VX4vq6rwrLtPq2ObryhknKCpNjzDwnKf3Vjk3jgmXSmJLHjRunHTt2xOYilIIAAp7ZepnnxLlfhHCZNFdddZXn8Xf30nrta8mdE/v2XcJqblJ8zQRn5uXNpAk/CU/CqsaFEEAAAVsK+GfSmEnP/NN6p0+f3uFxeOwyaexDRXBin76KW03NYKp33nnHMwHPkiVLOl3nkksu8TzGYdBqJxo2IIAAAl0SMI/BP/3005BpvUws2ZGR4KSjhyM+mTEjL730km9NGm+jzWOaYMGJmYGVwMSrxE8EEEAgskCkTJrEpPVGrqdVjyA4sWrPxLFehw8f9mTTBGbSOPHWYRyZKRoBBBwk4M2kMeNGzAJ5gWm91smksUenEJzYo5+6XEtvJs2ePXs8K/aWl5d3OtfcBTEjwAlGOtGwAQEEEOiSgDcYCZZJYxbIM797Bw0axF3nLml2PojgpLOJ7baYbJrnnnvOE6mvWrXKV38z6ZkZTxJswSYCEx8TbxBAAIGIAuEyaaJbIC/iJR19AMFJCnS/GRNyyy23kEmTAn1JExBAIPkC3kyaY8eOeVbr9c+kMQvk+U8syR968ekvgpP4uMasVG8mTX19vdavXy8z+2rgnRATnLjd7phdk4IQQAABJwl4gxHz+zbYmjQmk2bIkCGK7QJ5ThLuflsJTrpvFvczzLiRhx56yBOMvPHGG57rmUyamTNnqnfv3nG/PhdAAAEEUlnAP5PGBCT+q/UuWLBAZNIkv/cJTpLcByYQMXc+/F/m8wcffKD58+d7gpSBAwd2ulvifzzvEUAAAQRCC5jBqyYJwAQiwTJpvAvkMWVCaMNE7yE4SaC4fybNq6++KjN41axBM3r06E61CLZ6b6eD2IAAAggg0EkgUiYNab2dyCy3geAkQV1y8803e4IR7+VMJo15jpmZmendxE8EEEAAgSgE/DNpmpubPQvlmWLMH35k0kQBaoFTCE5i2Akmpdc8kgl8TGMuMWrUKFVVVWnw4MHKy8sLekwMq0JRCCCAQMoK+AcjgZk0y5cv15gxY8TjcHt3P8FJD/rPP5PGrM67YcMGTwBSXFzcqdRg08J3OogNCCCAAAIdBCJl0pDW24ErZT4QnETZlf6PabyZNIsXL1Z+fn6UJXIaAggggIA3k+bjjz8OmtZLJo0zviMEJ2H62Ty7NK9gI7hvuOEGzZ49W8OHDyeTJowhuxBAAIFwAt5gJFImTf/+/eP7OLz9oKpvnqXHC57VSwuHKj1cpdkXdwGCk2+I/TNpGhsbVVFR4dljbhkGC04KCgri3jlcAAEEEEg1gVCZNKadt99+u5KTSXNKH66v0JLKFo3kV7slvnIEJ990wy9/+UtfQOLNpLn44os1YMAAS3QUlUAAAQTsKGAGr5o5RoItkFdSUqIJEyYk+Q50u9oa/qA7t56tKVnSUTsip2CdHROcmEyavXv36txzzw06r4gJSObOnUsmTQp+yWkSAggkTiBSJo25E22px+Ft9frDI9Kt903Tuj/+keAkcV+VsFdK2eDEm0ljxo1s2rTJk0ljJEpLS4MGJ8Ee3YSVYycCCCDgcAH/TBqXyyX/tN7p06fbYIG8E2r4w3PSrf+usf+0U+sc3k545d4AAAfVSURBVJ9Wan7KBie1tbUyayT4Z9IMGjQo6PgRK3UIdUEAAQSsKmAGr3766aeeaeBDLZBnHofbYy4n8zhnjR7RXP1+bF+p1arqzqyXbYMTc0fEDFxta2vzrEET2H0//OEPdfjwYTJpAmH4jAACCHRRIFImja3Tetvq9WTVQN1373hldNGDwxInYJvgxIwZqaur07Zt23wDVw2TGStiFsgLfPXr10/mHy8EEEAAga4JeDNpzLiRYAvkJSeTpmt1795RJ9TwZK0G/usyXUjOcPfoEnR0mtvtdke6lrlLYW7TmVcXDo9UXFT7a2pqNHXqVE8wctlll2nIkCEaNmwYAUhUmpyEAAJWFEhLS9OUKVN0zTXXJKR63mAkWCbNrFmzPJk0Kfk4vLVWK4ZOVrkrFPNsrW5ao4W5vUIdwPY4C1jizok3k8as0GtewaZ6NwHJ559/Ht9JeOKMTfEIIIBAMgXCZdI4aoG8PpO0ssWtlf6d4QlYrteue2uZhM3fJUnvkxacmLsx5m6IfyaNMTDZNMFewRbTC3Yc2xBAAAEEJG8mzbFjx/TBBx90yKSZNm2aDTJp6EUnCyQtODHoa9asUWFhoWexvBEjRpBJ4+RvIm1HAIEeCXiDETONQqhMGh6H94iYkxMoEJfgxJtJYwZUrV+/XmbF3sCXmVck2PbA4/iMAAIIINBZwD+TxgQkW7du9R1kplGwdSaNryUJfON51NOSwAtyqXACMQtOzLiR3/72tx0yaWbMmOHJpDH7yJwJ1w3sQwABBMILmMGrZhr4SAvkMaFkeEf22kOg28GJWSAv1PgPMzmPWShvzJgxZNLYo/+pJQIIWFQgUiZN6qT1WrQDqFZSBbqdSpzU2nJxBBBAIMUFBg4c6GmhSe81r9GjR2v27NnKz8+31po0Kd4PNC+5Al26c5KZmZncWnJ1BBBAwCEC5u703Xff7bkDbQKVnJwch7ScZiJwWqBLd05OH847BBBAAAEEEEAgvgJM3BtfX0pHAAEEEEAAgW4KEJx0E4zDEUAAAQQQQCC+AgQn8fWldAQQQAABBBDopgDBSTfBOBwBBBBAAAEE4isQITg5pQ+rlyh7aqWa2+NbEUpHIDYC7Wpr3qgHFoyUWeE1LW2kFjywUc1tfIFj40spPRNoV2vtncr2fDfN9zPwn/m+Pq/a5taeXYazEbC5QPjgpP19bXy8Wq6al/Xa/pM2byrVd4JA+4frtbRwud76wR/1N7db7q9e1oLjD6rw13Xi170TvgFWb2O6+ky6Ty3uj7W5bKxUtFpNX7nlNt9V95dqqS/TBX/5mSYX/kyV+/jGWr03qV/8BMIEJ+1qe7NGWy+/VcuyXtPzrx0Qf3vGryMoORYCJ7V/43+pUldrwY+GK8MUmX6hCm+4ViPXblJ9K9/gWChTRrwEzlLW2Hm6//F7VeSq1F1P1RNQx4uaci0vECY4Oa4d695RQfFPdNW8bNXctUZ1/HK3fIc6u4Jn6YJBFynLtUc73/X+1dmutiP79d68K5TfJ8zX3dlwtB4BBBCwlEDI39btzX/Wg5qjH+VeqPypRcpy1Whj/XFLVZ7KINBRIF19xs/UssKdKr36ds9t8XbXZj2wcYCeu22i+nQ8mE8IWE6g3bVDa1c/r5qshbr3xny+s5brISqUKIEQwclJ7X+tSYVzLlEfpatP4XzdW9SitRv3cJsxUT3DdaITyBivZc+9oAen7FDJsPN0xg2Hdf39/6LxWWdFVx5nIRBPgZoS5Z1xelDsGdkTdEP5Jyp7dqUWDiWcjic9ZVtbIHhw0vq6Vlfn6Z/H9P269umDNPHaiXKtrdamD09Zu0XUzvEC6f/0bQ0cuUAVZUVSzV1adNcrcjHcxPHfC0sCdBoQW6WK+V+qfPLlWlDZqDZLVppKIRB/gSDBSbta6zdp7V/8I/pzlFfyguSq1uMb32dgbPz7hStEK9DWqMqlT0k/vlXLV76ols2LpPsXaO6DO/hFH60p5yVIwAyILdbyp17Q6qJPtKbkHq1rJksyQfhcxmICnYOT9mb96cEz9exnX32T3vZNmttXB1S18Nuqef517eevUIt1I9X5WuCkmtfdo5IjeRrheYxzlrIm3a0X60ul0gf4Rc/XxB4C6ZkaNDpb0vtqOsK9E3t0GrWMtUBAcPJN+nDxXBUGZjak99cVP7laWcx5Eus+oLyYCbTpSNP7AaWlK+N7ozQ+K2AzHxGwqkD733Xi2JeSBisvx5MQb9WaUi8E4ibQITgxmQ33LX9emYMy1WGH5/Lpysi5SCP1gkoWrVSti7EncesVCo5SoJ/Gz/mJCmse0m+e9j6vb9W+P/2nqq68TlMv6hVluZyGQGIE2l0Nqn7wF1pS+YkK77hZV/KdTQw8V7GcQJrbTE0oqb25UlfmlajGU8UsFa2u1UsLh/qClI77zUFjVbb5Za2clGm5RlEhJwuckqvhef3H8hUqr3NJGqH5FQ/o3/5linIzOofcTpai7ckQMNPX36Whk++X+XYGfRWWafVtc3Tl1WOVxVc2KBEbU1/AF5ykflNpIQIIIIAAAgjYQYC43A69RB0RQAABBBBwkADBiYM6m6YigAACCCBgBwGCEzv0EnVEAAEEEEDAQQIEJw7qbJqKAAIIIICAHQQITuzQS9QRAQQQQAABBwkQnDios2kqAggggAACdhD4/70ALe9ln9iTAAAAAElFTkSuQmCC"></p>
</div>
<div class="specification">
<p>Each week, the Happy Straw Company sells <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> boxes of straws. It is known that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{d}}P}}{{{\text{d}}x}} = - 2x + 220">
<mfrac>
<mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>P</mi>
</mrow>
<mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mn>2</mn>
<mi>x</mi>
<mo>+</mo>
<mn>220</mn>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> ≥ 0, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P">
<mi>P</mi>
</math></span> is the weekly profit, in dollars, from the sale of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> thousand boxes.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the surface area of the box in cm<sup>2</sup>.</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 length AG.</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 boxes that should be sold each week to maximize the profit.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P\left( x \right)">
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the least number of boxes which must be sold each week in order to make a profit.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="text-align: left;">2(8 × 4 + 3 × 4 + 3 × 8) <em><strong>M1</strong></em></p>
<p style="text-align: left;">= 136 (cm<sup>2</sup>) <em><strong>A1</strong></em></p>
<p style="text-align: left;"><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align: left;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {{8^2} + {4^2} + {3^2}} ">
<msqrt>
<mrow>
<msup>
<mn>8</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mrow>
<msup>
<mn>4</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mrow>
<msup>
<mn>3</mn>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</math></span> <em><strong>M1</strong></em></p>
<p style="text-align: left;">(AG =) 9.43 (cm) (9.4339…, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {89} ">
<msqrt>
<mn>89</mn>
</msqrt>
</math></span>) <em><strong>A1</strong></em></p>
<p style="text-align: left;"><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align: left;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 2x + 220 = 0">
<mo>−</mo>
<mn>2</mn>
<mi>x</mi>
<mo>+</mo>
<mn>220</mn>
<mo>=</mo>
<mn>0</mn>
</math></span> <em><strong>M1</strong></em></p>
<p style="text-align: left;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 110">
<mi>x</mi>
<mo>=</mo>
<mn>110</mn>
</math></span> <em><strong>A1</strong></em></p>
<p style="text-align: left;">110 000 (boxes) <em><strong>A1</strong></em></p>
<p style="text-align: left;"><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align: left;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P\left( x \right) = \int { - 2x + 220} \,{\text{d}}x">
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mo>∫</mo>
<mrow>
<mo>−</mo>
<mn>2</mn>
<mi>x</mi>
<mo>+</mo>
<mn>220</mn>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
</math></span> <em><strong>M1</strong></em></p>
<p style="text-align: left;"><strong>Note:</strong> Award <em><strong>M1</strong> </em>for evidence of integration.</p>
<p style="text-align: left;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P\left( x \right) = - {x^2} + 220x + c">
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mo>−</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>220</mn>
<mi>x</mi>
<mo>+</mo>
<mi>c</mi>
</math></span> <em><strong>A1</strong></em><em><strong>A1</strong></em></p>
<p style="text-align: left;"><strong>Note:</strong> Award <em><strong>A1</strong> </em>for either <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - {x^2}">
<mo>−</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="220x">
<mn>220</mn>
<mi>x</mi>
</math></span> award <em><strong>A1</strong> </em>for both correct terms and constant of integration.</p>
<p style="text-align: left;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1700 = - {\left( {20} \right)^2} + 220\left( {20} \right) + c">
<mn>1700</mn>
<mo>=</mo>
<mo>−</mo>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>20</mn>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>220</mn>
<mrow>
<mo>(</mo>
<mrow>
<mn>20</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>c</mi>
</math></span> <em><strong>M1</strong></em></p>
<p style="text-align: left;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c = - 2300">
<mi>c</mi>
<mo>=</mo>
<mo>−</mo>
<mn>2300</mn>
</math></span></p>
<p style="text-align: left;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P\left( x \right) = - {x^2} + 220x - 2300">
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mo>−</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>220</mn>
<mi>x</mi>
<mo>−</mo>
<mn>2300</mn>
</math></span> <em><strong>A1</strong></em></p>
<p style="text-align: left;"><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align: left;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - {x^2} + 220x - 2300 = 0">
<mo>−</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>220</mn>
<mi>x</mi>
<mo>−</mo>
<mn>2300</mn>
<mo>=</mo>
<mn>0</mn>
</math></span> <em><strong>M1</strong></em></p>
<p style="text-align: left;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 11.005">
<mi>x</mi>
<mo>=</mo>
<mn>11.005</mn>
</math></span> <em><strong>A1</strong></em></p>
<p style="text-align: left;">11 006 (boxes) <em><strong>A1</strong></em></p>
<p style="text-align: left;"><strong>Note:</strong> Award <em><strong>M1</strong></em> for their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P\left( x \right) = 0">
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0</mn>
</math></span>, award <em><strong>A1</strong> </em>for their correct solution to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>.<br>Award the final <em><strong>A1</strong> </em>for expressing their solution to the minimum number of boxes. Do not accept 11 005, the nearest integer, nor 11 000, the answer expressed to 3 significant figures, as these will not satisfy the demand of the question.</p>
<p style="text-align: left;"><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A cafe makes <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> litres of coffee each morning. The cafe’s profit each morning, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math>, measured in dollars, is modelled by the following equation</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mfrac><mi>x</mi><mn>10</mn></mfrac><mfenced><mrow><msup><mi>k</mi><mn>2</mn></msup><mo>-</mo><mfrac><mn>3</mn><mn>100</mn></mfrac><msup><mi>x</mi><mn>2</mn></msup></mrow></mfenced></math></p>
<p>where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math> is a positive constant.</p>
</div>
<div class="specification">
<p>The cafe’s manager knows that the cafe makes a profit of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>426</mn></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math> litres of coffee are made in a morning.</p>
</div>
<div class="specification">
<p>The manager of the cafe wishes to serve as many customers as possible.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>C</mi></mrow><mrow><mo>d</mo><mi>x</mi></mrow></mfrac></math> in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>.</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>Hence find the maximum value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math> in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>. Give your answer in the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><msup><mi>k</mi><mn>3</mn></msup></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> is a constant.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>.</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>Use the model to find how much coffee the cafe should make each morning to maximize its profit.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math> against <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>, labelling the maximum point and the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-intercepts with their coordinates.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the maximum amount of coffee the cafe can make that will not result in a loss of money for the morning.</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>attempt to expand given expression <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mfrac><mrow><mi>x</mi><msup><mi>k</mi><mn>2</mn></msup></mrow><mn>10</mn></mfrac><mo>-</mo><mfrac><mrow><mn>3</mn><msup><mi>x</mi><mn>3</mn></msup></mrow><mn>1000</mn></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>C</mi></mrow><mrow><mo>d</mo><mi>x</mi></mrow></mfrac><mo>=</mo><mfrac><msup><mi>k</mi><mn>2</mn></msup><mn>10</mn></mfrac><mo>-</mo><mfrac><mrow><mn>9</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><mn>1000</mn></mfrac></math> <em><strong>M1A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1</strong> </em>for power rule correctly applied to at least one term and <em><strong>A1</strong> </em>for correct answer.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>equating their <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>C</mi></mrow><mrow><mo>d</mo><mi>x</mi></mrow></mfrac></math> to zero <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msup><mi>k</mi><mn>2</mn></msup><mn>10</mn></mfrac><mo>-</mo><mfrac><mrow><mn>9</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><mn>1000</mn></mfrac><mo>=</mo><mn>0</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mfrac><mrow><mn>100</mn><msup><mi>k</mi><mn>2</mn></msup></mrow><mn>9</mn></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mfrac><mrow><mn>10</mn><mi>k</mi></mrow><mn>3</mn></mfrac></math> <em><strong>(A1)</strong></em></p>
<p>substituting their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> back into given expression <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>C</mi><mtext>max</mtext></msub><mo>=</mo><mfrac><mrow><mn>10</mn><mi>k</mi></mrow><mn>30</mn></mfrac><mfenced><mrow><msup><mi>k</mi><mn>2</mn></msup><mo>-</mo><mfrac><mrow><mn>300</mn><msup><mi>k</mi><mn>2</mn></msup></mrow><mn>900</mn></mfrac></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>C</mi><mtext>max</mtext></msub><mo>=</mo><mfrac><mrow><mn>2</mn><msup><mi>k</mi><mn>3</mn></msup></mrow><mn>9</mn></mfrac><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>222</mn><mo>…</mo><msup><mi>k</mi><mn>3</mn></msup></mrow></mfenced></math> <em><strong>A1</strong></em> </p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>substituting <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math> into given expression and equating to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>426</mn></math> <em><strong>M1</strong></em> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>426</mn><mo>=</mo><mfrac><mn>20</mn><mn>10</mn></mfrac><mfenced><mrow><msup><mi>k</mi><mn>2</mn></msup><mo>-</mo><mfrac><mn>3</mn><mn>100</mn></mfrac><msup><mfenced><mn>20</mn></mfenced><mn>2</mn></msup></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mn>15</mn></math> <em><strong>A1</strong></em> </p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math> <em><strong>A1</strong></em> </p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img 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5YBA4yw1N0dbi7OsLezp4mqWYiCS+Z8fLahR7dufPmWjd7eaNGiBU11yECtW7fCZukPxJHDh/nyOCRrUHDJ2O7dfrC2mg7LKVMxddpUlVzNQRmVLKmFlWtWw9fHF//995+oksxEwSVT586dh72tHRYuWYLBg/+iqQ6ZTLtcOYwaPQrmI0fh7t17okoyC73aZejgwUP8gmCzUSPx++/tRJVktp69eqFRk8YwMzXFixcvRJVkBgouGfn8WYFdu3Zj3OgxGDxkKN+sgmSdXDlzwt5+HooWLYYx0v+Tt2/DxRmS0Si4ZCIoKBgzplth8cKFWOq+HKPHmIszJCvlz58PK9esQqlSpWAybBiePn0mzpCMRMElA08CA9G3Tx8EPg2E7/Zt/JMtGtNSHgULFIDbQjeU09bG4L/+QkhIiDhDMgq9+pVcoBRaxv2MULt2HSxbvlz6C59fnCHKhP0hmTV7FoqXKIGxY8bSNmgZjIJLiX38GIOZVjPQSK8J5i+Yz7slRHmxlTccnRzx8MED+Pn5iyrJCBRcSupjTAwWzJ+P6OhoODgsoNCSCW2pu+i2aBGWSDcarM84FFxKiF13aDvHFtt8fWEvtbSUeddo8q3ffmuI3xo1gp2tLa2gmkEouJQMu/7N2toGe/z84LHSE+V1dcUZIhd8RYnR5ti/dx82bNgoqiQ9UXApETYQb2oyAo8ePMAG701o2LChOEPkhnUZFy1djGVLlmKz92ZaxyudUXApCRZa/fr0RdFixeG5aiUqV64kzhC5atmyJWztbTF71iwcO3ZcVEl6oOBSArGxsXB2dEL9Bg1gP88OefLkEWeI3LVp0wamZiMx2dKSr0xL0gcFVxZjXYgli5fiyZMncHJ2ooF4FcPGu4YPHwZdXV0+dkmD9emDgisLsdDy+tcLKz08YC11J2iZZdWUN68GHBwdcOXiRaxcuYrGu9IBBVcWYpMU2VytWXNmo27dOqJKVBFb6NFy6lQsW7KEuozpgIIrC3z48AGLFi3CfHt7LF66FN26dxNniCrr2bMHhpuYYJ70/538GgquTMbmadnYzIL3xk1Yv3Ej2rZtQ0stqwn2/9lspBlCQ8OwZSvtFvQrKLgyERuYdVjgiIP792OFpyftd6iGWHgNGz4cjvPn4+WrV6JK0oqCKxOxuTzrvf6F68KFqFmzhqgSdcOWJaparRpsZlrjU2ysqJK0oODKJJGRkZhnZ4f5jo5o0aK5qBJ1xKa8WNtY4/SpU9i7Z4+okrSg4MoEbDB+suVk1K5TB507dxJVos4qVaqEf8xGYu7suQgOfi2qJLUouDKBk5Mz/rvwHyZZWtJAPOHY6+DvYUOhrV0O8+fNo7ldaUTBlYHYKphTJk/ByePH8e86L74fHyHxcufODUdn9kftAlavXkPhlQYUXBkkOvoDRo0chZs3bsBrw3pUqVJZnCHkC11dHdhJLS5nBwdcvnxFVMmPUHBlAHbRtIuLC65euQon6b5okSLiDCHfatpUDz1694b1jJm0Vn0qUXBlAG/vzfDesBFLli2l5WlIqowdOxZBQa9w6tQpUSHfQ8GVzq5duw57W1vYzJ7Nl/AlJDWKFy+GseMtsGH9BlEh30PBlc5cpa7hoCFD0K17V1EhJHX69u2NZ0+f4fqNm6JCUkLBlU7i14pn+x5OmjSRpj2QNGN7Mw4fYQKradMQFhYmqiQ5FFzpgIXWtKnTcPL4CcyeO0dUCUk7Q8MuyJUrFxbMX0DTI76DgusXsRfXxg2bsMffH86uLtAsVEicISTtcuTIgYmTJmHXjh3UZfwOCq5fdOLESTjMnw8HJydaDJCkiyZNGsOwW3fMsbFBTEyMqJLEKLh+waNHjzF5kiUGDDSGvr6+qBLy6/4xM8Xt27dx5MhRUSGJUXD9pKioKEycMAE1ataA5WRLZM9Og/Ek/bDNNUzNzGBva4d376JElcSj4PoJbEFAG+tZeBMWBgdHR/5pECHpzdh4gPRai4W3t7eokHj0jvsJmzdvwY3r17BqzRoULUqX85CMUahQIdja28PD3R1XrlwVVcJQcKXRw4eP4LnCQwqt1bT0MslwbNHJzgYGcaulfvokqoSCKw3Cw8MxwcICffr2hZYWLVFDMh6byDziH1MEBgbi0qVLokoouFKJjWs5Ojjh7Zs3GPiXsagSkvFKSn8kR5iOgK+Pr6gQCq5UYJNM2YoPO3fswOKlS/hlPYRkpr79+uLcuXO07I1AwZUKd+7e5dtJsWkP1atXF1VCMo+mpiaa6unBY4WnqKg3Cq4fCAt7g9EjzdG+Q0cMMB5AF0+TLNPJwADrvLwQGhoqKuqLgus7Xr9+jdGjzPkk05nWM0SVkKyhp9eEvxbZBdhszFWdUXClgC2/zLYUYxwcHZAvXz7+34RkFXYBto2NDfz9/PjmwuqMgisFe/z38I0u2IoPbDcWQpSBto422uvrY6Wnp1ove0PBlQzW2vJYsYLPWtbSKiGqhGQ9NsY6ecpkXL92HUePBoiq+qHg+gr7K7Z8+QqU09ZGu3ZtRZUQ5VGiRAn07NUTHu4r1HY2PQXXV9g1YSuWLcNwk+GiQohyidsFe5j0Wr2M8+fPi6p6oeBKhO3QM8rMDJOnTUWDBg1ElRDlU6ZMaYwZOxYzrWbg7du3oqo+KLiE58+fw0T6K2Y0wBhGRv1FlRDlNWjwILDh+XVe6+IKaoSCS7CxtkGFChVhMmI4TTIlsqChoYFxFuOx0nMlIt+9E1X1oPbBxQbj3d1X4Mqly1jg5EBTH4is/N6uHd9M9uSJE6KiHtQ+uG7fuYPlS5diqtV0lCtbVlQJkYe8efPC+K+/cFzNJqSqdXBFR0djwngLdDbowvezI0SO2JjsqVOnEBEZKSqqT62Da9++/XgfFYUJEy1o3XgiW2x4o379+tjrv0dUVJ/avltfvHiBVZ6eWOHpgaJFi4oqIfLUq3cvLFq4CKGh6rF1v1oGF+8iWkxAF0NDVK5cWVQJka9mzZqhdJnSWOjmphbXMKplcLGPj588fox+/Wm+FlENbAqP0YABvLvI9kZQdWoXXJcuXcayJUswe+5cFCpUUFQJkb/OnTuhgPSaZsuMqzq1Cq7IyEhMnzoVPXv3xu+/txNVQlQDG6QfNmwY1q9bx1/rqkxtgouv+rBsOZ9hbDHBQlQJUS36HTsgSnqNBwQcExXVpDbBtXHjJmzftg2eKz1RuHBhUSVEtRQrWhTjLSbAydERERERoqp61CK4Tp78H+zmzIGLmxuqVKkiqoSopp69eiCP1G1U5YuvVT64Pnz4AOsZMzBg4ED89ltDUSVEdbGLr7v37ImtW7eKiupR+eDautWHX8813mI8zY4nauOvvwYiMjwCZ8+dExXVotLvZLZ2/GZvb8ywtubhRYi6YLtSdevRHcdUdF16lQ0u9ini6tVroK1dDo0bNxJVQtRH7z59cPrUaXGkWlQ2uJ48CeQTTQcYD6SFAYlaqlq1CiC99B89eiwqqkMlgysoKBijzc3Rs1cvNG2qJ6qEqB8DAwM+NSJWxXa+Vrngio39DBtraxQqpIlJlpY0IE/UWoeOHXD40CHcv3dfVFSDyr2rt2/fLvXrT2GO7Rzkzp1LVAlRT6VLl0azFi2wZs0aUVENKhVcYWFhcFrgABNTU5TX1RVVQtQXXzXCyAj79uzB69evRVX+VCa4Pkt9eOuZ1tDR1eEXmtKAPCFxmjVrivwFCuDw4SOiIn8qE1w3b97E0SNHMGXaNOoiEpIIm9PVX2p1/bt2LZ/bqApUIrjYnK1Vnqt4F7FevbqiSgiJ16tXTwQ+foIzZ86KirypRHAdO3YcT589hYmJCXURCUmGlpYWunQ1hKeHh6jIm+yD6+HDhxg/ZiwsJkyAhkYeUSWEJMb+oLP3yJnTp1Xi+kXZB9eCeQtQo2YNWvmBkB8oVqwo2uvrY+3q1aIiX7IOri1btvK/IHbz5iFnzpyiSghJiWHXrvz6xeDgYFGRJ9kGV0hIKFycnGDyjyl0dLRFlRDyPa1bt+KfMh4+Iu+pEbIMLjZni13Wo62jg+HDac4WIamVK1cuDB46FKs8V/L3kVzJLrj4cjWrVuPqlatwcHTg/yMIIanXtash3oSF4fq166IiP7ILrqNHjsLV2RkLFy+Suog6okoISS02NYIt7Xzo8GFRkR9ZBRfbOn+evT36Ghmhbt06okoISStjY2OcOvk/cSQ/sgquHdt3IHv2HJg82VJUCCE/o2zZsoiJ+YiXL1+JirzIKrg2bdyIaVbT+Y69hJCflyNHdlSvUQPHjx8XFXmRTXD5+PiicJEiaNWqpagQQn5Fy5YtsXHDBnEkL7IIrtDQUDg5OMBogJGoEEJ+VeMmTXDr5k1ck+Gni0ofXOHh4TAzNUPrNm3wx59/iioh5FexS4DY+2qdl5eoyIdSBxebIOfg4IiIiHBY21gjB60fT0i6YfsxmJqZYffOnVKvJkxU5UGpkyAgIADbfXywwNGRNnQlJAM0qF8PFSpWxPr160VFHpQ2uFgXcZ6dPfoZDUCtWjVFlRCS3jobGODg/v2IiYkRFeWnlMHFuojOzi7Ili07LCdPomsRCclAbKmb27duy2rjWKUMrsuXr2CLtzesZs6gOVuEZLBKlSqiYaNG8PPzExXlp3TBFRQUxFc0nWhpiZYtW4gqISSjsB6NyQgTbFy/gS8XJQdKF1weKzzQpKkeBg8eJCqEkIzWlG1hlj8/DuzfLyrKTamCi21YybYYmzxlMm2dT0gmyquhAf0O+rLpLipNOrABeVcXV7Rq3RrFihUTVUJIZunXvz/Onj6Nx4+fiIryUprgCgg4hh3btmHI0CGiQgjJTNra5fiF1367d4uK8lKK4HoXFYW5c+agv7Gx9Muj9eMJyQpsw5nf//gDhw8dVvplnbM8uPhlPfMXIHeuXJgwwYLmbBGShbp2747r168hNEy5LwHK8uDy9fHFwQMH4OzqCg0NDVElhGSFCuV10aZdOxw6eFBUlFOWBteVK1cwy9qG74tYo0Z1USWEZKXevXrhfydOiiPllGXB9eHDB1hNs0KnLgZo0YImmhKiLPSaNsW9+/fFkXLKsuDy9FyJsNBQTJ48mS8jSwhRDgULFuBTkh4/CRQV5ZMlifHy5Ut4uLvDcuoUvpgZIUS5NGjQAFu8N4sj5ZMlweXltY5PNO0idRMJIcqndp06OBZwFDGfPomKcsn04Lpz5y6OBwRg1pzZNPWBECXVqNFvePToEa5dvSYqyiVTg+v9+/cYbW6OQYMHo2iRIqJKCFE2RaT3ZxdDQ2z29hYV5ZKpweXq6obPn2LRqXNnUSGEKCu2Oc3+ffsQEREhKsoj04KLLQ64Yd06WFnPRP78+USVEKKsGjSoj+zZsuHixUuiojwyJbj4nK3p0/na1rShKyHywLqLtevWxQkl3O06U4LLw8MTb9+8geVkWmeLELlgH54ZGnbFvr17RUV5ZHiK3L9/Hx7L3WE5ZTLN2SJEZtr93g5vpEbH+fMXREU5ZGhwsfXjzUz/weChQ9GlSxdRJYTIReHCmnzO5TYfHygUClHNehkWXJ8+fcKkiZYoX6ECxo4bI6qEEDnh3cWuXXHo0GE+Vq0sMiy4zp07j6tXLmO6lRVy5MghqoQQuWndpjWio9/jrPSeVhYZFlyrVq7EhEmToKurIyqEEDliG2mwlVGVaUnnDAmuixcv4+WLF+jXr6+oEELkrHnz5nwjjffR0aKStdI9uKKjP2CWtTXfMYStYU0IkT+2RldwcDAePXwkKlkr3YPLY8UKhLx+je49eogKIUTuypYtg8qVq+D8uXOikrXSLbjYR6X+/nuwaeNGuCx0Q4EC+cUZQojcsYnjRsYDsHbtWsTGxopq6rANcdJ7KkW6BRfbRNJq6lRMmDiRL4lBCFEtbdu15b2pJ0/StmHs1KnTYD3TGtHpOD6WLsEVExODmVYz0FhPT+oidhdVQogqKV6sGCpVqsTX1EuL9u3b4/ixY3wyenDwa1H9NekSXNt8t+H69euYZjWdrkUkREWx+ZiNGjfB7Vu3RCV1/vzzD+z290d26esNDQxw4MBBfPqUtu7m1345ZV68fIn59vMwboIFdHVozhYhqsywW1fcunlTHKUeW8pqydIl6Nu/P8aam8PUxATPnj8XZ9Pul4PLa81q1KhVE0b9+4kKIURV1aheje/+8zNb9LMNny0sxmPTli2IiIxEd8OuWLVytTibNtkUYrg/uVF/1qRb7+Uljr715PFjPlBXrXp1lChRQlQJIars0sWLqFW7NnLlyiUqafc5NhYXpe/DlnOvVbuOFGbefIZ+cpLbm+K7wRUV9R7v3r0TR9/y9PBAwUKaNEOeEJJq7MO8LVu2wtN9OW/0TJ0+Hb/91lCc/Vaag+tH3FzdoKlZGEOGDhYVQghJ2Z27dzHbZhauXb0KE1NTmJqO+OEVNskFF30ESAjJcKxhtH37DvTp0ZMH0bYdOzBq1MifviyQgosQkqHYcNM8+3mwt7XFDBsbrFm7FhUqlBdnfw4FFyEkQ40ZMw579+zBkmXL0Lt3L+TI8euxQ8FFCMlQM2ZYYceuXel6KSAFFyEkQ5Uvr8vXrk9PvxRc7BIAusSHkKzHJnTeunVbHMUNhkdKtefPX/xwNQc2mTTq/Xu+UAKbqpAasbGf8ebNWzx99kxUUo89nxcvXvKxr8SzGU6ePMX3qkiNHDYS8d9JhEdE8B+kWLFiogLpF/EOHz/GIHfu3Py4iV4T1Ktfj/93arEnHRUVlfA9mNchIQgJDYVmoUKiQghJLbbqwtYtW9GqVSvkzJlDCoQozJwxE9ev3+CrOSxf7o6iRYtCW1tbfEUcFhpHjwbA2ckJz549h4ZGHpQpU+aHn/QdOXwErq5uiIx6h/z58qJ06dLizI+xcJ0lRU70hw/Yt+8AX9+Lra7KZMueDcuXuUsttPLQ1PySBamex3Xx0iVcuPAfBhoP4NP0WdDwJxoRyVtZ+fLnw5gxo5E/f+rX3GLfn63X5e/nL/0Si0BXenJ//z00ocXm5bUehaUna9Cli1T79okSQr718eNHjBs7jm+2zLpkzOzZc6CRR0OqTeLHF85fwEgzM/jt3cNXeIi3b99+LHRzg9tCN1SuXFlUv+/4iZNYumgx3D3cUSiNDQ22S5ChgSHGjh8HA4POvNavbz/+nh806C9+HPj0GWZMt8LCRW4J3z9V87jYKg9ea//FYOkbsdBigWNna8+bkHNt52D2nFkIfxuORYuWJAm7HwkIOAbHBQtgZ28rfY/ZPLW9vNYlfI+BAwfg7r17OKckKywSIgfr1q2XGgLFEkKL2evvjxJaXy7BK1mqFO+WPZdCIV6o1MOZZ2cHJ2fnVIfWhQsXYP7PPxgzbmyaQ4thlxCGvQlDp04dRQXQ19fHsiVLeSuR0S5XFk2b6mHa1GnfvR4ySXBFSC2qSRMmwVR6cvHXIbGdqL03buAfY7LWEUu/fv37YaXHCikdn/LH/MhHKfTmzJqF9tKT1NTU5N9DX789li5eLP2bEfwxrMZaYOwyop+5gJMQdfPqVRCWLFqETp07iUocHd3y0vvTA6+CgvjxDakxUkJLCxUrVeTH7P01dcpUsMttqlevxms/EvbmDSzGjUdV6WuaNGksqmnznxR8LCQTj4tXrVYNwUGv8OjRl7XsO3TsiEMHDvBGVEqSBJeT1NctUqSI9M0riQpw5vQZFCteHOXKlRMV9ovR4QF09sxZUfm+QwcP4bH0xJq3aCEqQP2GDXn/20/qOsYrXLgwH/vat2+fqBBCUuKzdSu/WLlqtaqiEmeu7VwULFgQPbt1h6uLGy5fvoJ169ejQIEC/PzZs+cQcOQIypQtC1e3hbyryS7fY4PtKVkv9Y5ePH+Olq1a8WGjCeMtsGmTd5qWcQ4MDPxm4qlWyZL8/r7U24rHHlNWWxuLv9OrSwgu1try3rCRD7Yn3sD18ePH/AfOly+fqAD58ubjTUW2OkRqXLt2jd+Xk35R8cqWKcPvT586ze/j1apVC4vcFqXpF0KIOtq7dx80pT/2JaSGRWKs4bF+00bkyaOBFe7LebexdOlS4iywf99e/v5q2rSpFFpj8PewYXwf1GFDh/Ixs+Ts2rUb+fLnR0OpwTF+/Dg0bdacL9VuZ2cvHvFjkRHhUm4knRYR/0FAfM8rXp26dXE84CjCwsJEJamE4Lpz9w5iYj6iZu3aohKHLTuRR2oFJbeERUo/5NfYx7JMoUIF+X1iX68+UVJK4CdPHic0cwkhyXv44D6Kl9ASR1+wEJg6eQpmz52Ljp06w3bOHHis8Exovdy9e196P+dG48ZxXb66detg8JAhuHrlCq5ejWtkfO2R9G+xTxxbtWrJu3p9+vbmvabdO3bi7duUW2qJ5cjx7aeV8Q2Ur/NFW2rksHMpLfWcEFxsA1emePGk62olN6LPfgHslto5XMl9j8+KuHGsrz961SysyT99CJb674SQlL2PihvQToy9L+fOmSt1tyqiZcvmmDN3Dm8lubo4J4wZZc+RnX9yn3hKUuMmTfjY1/MUViVlyy6z1l1iLVq2RFTUu29aSykpUrQoQkNCxFGc8PBwfl+yVFyXMR7LBZazKc3rSkieTzFxD/g6ZNiYF5tzkbh19VFqmbG5I0WKJP1BUsJaUUxYoj50fH9aRyfp3BLWTVVIv8CPHz+ICiEkOcVLlED42zfiKE5ISCj2+PujoVjfii2Z7ODkhJzS++rixUu8Vk/qhrHWDJvmFI9NUYq7L8rvv1ajZi0EvXqVJEhYNuTOkwcaefOKyvfp6uriSWCgOIrz/OlTnjksaBNjmcPmdeVN4XsnBFd8+ib+YZjyFcrzRI3/uJKJlrqPrKarm7orvOuLSaqJn3R8Cy/xgD3DZuSyllxqfxmEqCs2DhQuddM+fPjSqGATUFlrJXFrjDUOtKXQiJ93+ceff/B7NiQTj3XJ2CePderEDRWxIZw3ibqAXbsa4pUUXM8SzZQPDgrmY+JFpQBjWGMkPDzl1lez5s1x88aNJFly584dVKtRI8kYHBMY+JSHVqmvWmLxEoKrQsW4xHvxImlTsa70y3n75g2ePf/yhB88eMiTt269uvz4/fvo7z7hJlIzlH1Ee+7MGVGB9APc5J9qNGrUSFTisL8geTQ0oFUy6Q9CCEmqTZs2vKEREvql+8U+mR88dCjWea1DWFhca+zKlSusD4m2bdvw43r16qFP//7YuXMX71qylY69N3nD2sYmYX7WgvkLMKCfUcJeiH379UWVKlWxYoUHf++zS4lOnDiOmdLXsIZGaGgYOrTX5wP8KX2w1qJFc9Rv0ABeXl783w1+/RqHDx/GjJkzvxnjun37Nlq2bp3kQ8HEEi75YRdB+vn5IbvUbGP7oMVjzUHWN/X18eUJHxQUhCWLl/JJaA0bNuC/OIOOnbDC3Z23zpKbzMZ+MNaHZk+YNQmj3kdhw/r1mG5lhYoVK4hHxfHz28M/xWTLQSc3NkYIiVNOuxz8pG5hRanRUaVKFVEFGjduJJ3T5qFw8+Yt/h6dOGkify/HY5cHvQkLw6lTp/Dw4SN062bIP2WMf8/FxHxC2bLl+JLK7P3LgsVQanWxgGLTKYKDgzHKfJT0mLL8a1gQsU8A2TWPHTp2SPbDPIZly8sXL3HmzFmpAfQAI0eaoXbtWuJsnLt372HNqlVY4OCA4sWLJ5sDSS758ZHCiU3n373XP8nC9ewc20qIzXZnCchmuxYsGDcnhJ1j+yq+l5KZTXSztbPl9eSwX+ChQ4f5LPzOnTvza6O+NnjQYFjPskHFCkkDjRDyLXY94vRp07Fl6+YUwyKzsCxYvnwFTE1NeNj9LCurGahWrRoGDjTmofXD4GIz3EeammHQkMFo3boVf0BqsdBjrbY//ojrP/+M169DYGdrC0cnx1/6wQlRF+x9u337Tj62ZWjYRVQzH5vytHHjJjRr1lRqQSWdUpUWrGFz+dIljLcYnxBYPwwuhg3AsQRns29LlfrxOFOM1N/du2cvv36xn1E//unFz2AfxS5Y4ICePXugatWkM4EJId/HrkBhrZTEV71kJjYWxqZM5P6FVt+x4ycQEhKCroaGSLxKaqqCi3krhdCqVavRt1+fhBnuKfnw8SNiPsagQIHUrxTxNb4sx1Zf6RdflffPCSFpxwbFE1/1Ijds0D+5JXVSHVwM29uffSSaeF2cjMJm57MWV1qWySGEqIc0BRchhCiD5IKLRsAJIbKT0OIihBC5oBYXIURmgP8D08PNJ/cOn/kAAAAASUVORK5CYII="> <em><strong>A1A1A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A1</strong> </em>for graph drawn for positive <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> indicating an increasing and then decreasing function, <em><strong>A1</strong> </em>for maximum labelled and <em><strong>A1</strong> </em>for graph passing through the origin and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>86</mn><mo>.</mo><mn>6</mn></math>, marked on the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis or whose coordinates are given.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>setting their expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math> to zero <strong>OR</strong> choosing correct <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-intercept on their graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mtext>max</mtext></msub><mo>=</mo><mn>86</mn><mo>.</mo><mn>6</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>86</mn><mo>.</mo><mn>6025</mn><mo>…</mo></mrow></mfenced></math> litres <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A sector of a circle, centre <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math> and radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>5</mn><mo> </mo><mtext>m</mtext></math>, is shown in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>A square field with side <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo> </mo><mtext>m</mtext></math> has a goat tied to a post in the centre by a rope such that the goat can reach all parts of the field up to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>5</mn><mo> </mo><mtext>m</mtext></math> from the post.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p style="text-align: center;"><sup>[Source: mynamepong, n.d. Goat [image online] Available at: <a href="https://thenounproject.com/term/goat/1761571/">https://thenounproject.com/term/goat/1761571/</a></sup><br><sup>This file is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)</sup><br><sup><a href="https://creativecommons.org/licenses/by-sa/3.0/deed.en">https://creativecommons.org/licenses/by-sa/3.0/deed.en</a> [Accessed 22 April 2010] Source adapted.]</sup></p>
</div>
<div class="specification">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> be the volume of grass eaten by the goat, in cubic metres, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> be the length of time, in hours, that the goat has been in the field.</p>
<p>The goat eats grass at the rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>V</mi></mrow><mrow><mo>d</mo><mi>t</mi></mrow></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>3</mn><mo> </mo><mi>t</mi><msup><mtext>e</mtext><mrow><mo>-</mo><mi>t</mi></mrow></msup></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AÔB</mtext></math>.</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>Find the area of the shaded segment.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of a circle with radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>5</mn><mo> </mo><mtext>m</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of the field that can be reached by the goat.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> at which the goat is eating grass at the greatest rate.</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><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mtext>AÔB</mtext><mo>=</mo></mrow></mfenced><mo> </mo><mtext>arccos</mtext><mfenced><mfrac><mn>4</mn><mrow><mn>4</mn><mo>.</mo><mn>5</mn></mrow></mfrac></mfenced><mo>=</mo><mn>27</mn><mo>.</mo><mn>266</mn><mo>…</mo></math> <em><strong>(M1)(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AÔB</mtext><mo>=</mo><mn>54</mn><mo>.</mo><mn>532</mn><mo>…</mo><mo>≈</mo><mn>54</mn><mo>.</mo><mn>5</mn><mo>°</mo></math> (<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>951764</mn><mo>…</mo><mo>≈</mo><mn>0</mn><mo>.</mo><mn>952</mn></math> radians) <em><strong>A1</strong> </em></p>
<p> </p>
<p><strong>Note:</strong> Other methods may be seen; award <em><strong>(M1)(A1)</strong></em> for use of a correct trigonometric method to find an appropriate angle and then <em><strong>A1</strong> </em>for the correct answer.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>finding area of triangle</p>
<p><strong>EITHER</strong></p>
<p>area of triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>4</mn><mo>.</mo><msup><mn>5</mn><mn>2</mn></msup><mo>×</mo><mi>sin</mi><mfenced><mrow><mn>54</mn><mo>.</mo><mn>532</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1</strong> </em>for correct substitution into formula.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>8</mn><mo>.</mo><mn>24621</mn><mo>…</mo><mo>≈</mo><mn>8</mn><mo>.</mo><mn>25</mn><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup></math> <em><strong>(A1)</strong></em></p>
<p><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext><mo>=</mo><mn>2</mn><mo>×</mo><msqrt><mn>4</mn><mo>.</mo><msup><mn>5</mn><mn>2</mn></msup><mo>-</mo><msup><mn>4</mn><mn>2</mn></msup></msqrt><mo>=</mo><mn>4</mn><mo>.</mo><mn>1231</mn><mo>…</mo></math></p>
<p>area triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>4</mn><mo>.</mo><mn>1231</mn><mo>…</mo><mo>×</mo><mn>4</mn></mrow><mn>2</mn></mfrac></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>8</mn><mo>.</mo><mn>24621</mn><mo>…</mo><mo>≈</mo><mn>8</mn><mo>.</mo><mn>25</mn><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup></math> <em><strong>(A1)</strong></em></p>
<p> </p>
<p>finding area of sector</p>
<p><strong>EITHER</strong></p>
<p>area of sector <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>54</mn><mo>.</mo><mn>532</mn><mo>…</mo></mrow><mn>360</mn></mfrac><mo>×</mo><mi mathvariant="normal">π</mi><mo>×</mo><mn>4</mn><mo>.</mo><msup><mn>5</mn><mn>2</mn></msup></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>9</mn><mo>.</mo><mn>63661</mn><mo>…</mo><mo>≈</mo><mn>9</mn><mo>.</mo><mn>64</mn><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup></math> <em><strong>(A1)</strong></em></p>
<p><strong>OR</strong></p>
<p>area of sector <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>0</mn><mo>.</mo><mn>9517641</mn><mo>…</mo><mo>×</mo><mn>4</mn><mo>.</mo><msup><mn>5</mn><mn>2</mn></msup></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>9</mn><mo>.</mo><mn>63661</mn><mo>…</mo><mo>≈</mo><mn>9</mn><mo>.</mo><mn>64</mn><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup></math> <em><strong>(A1)</strong></em></p>
<p> </p>
<p><strong>THEN</strong></p>
<p>area of segment <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>9</mn><mo>.</mo><mn>63661</mn><mo>…</mo><mo>-</mo><mn>8</mn><mo>.</mo><mn>24621</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1</mn><mo>.</mo><mn>39</mn><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup><mo> </mo><mo> </mo><mfenced><mrow><mn>1</mn><mo>.</mo><mn>39040</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong> </em></p>
<p> </p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</mi><mo>×</mo><mn>4</mn><mo>.</mo><msup><mn>5</mn><mn>2</mn></msup></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>63</mn><mo>.</mo><mn>6</mn><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>63</mn><mo>.</mo><mn>6172</mn><mo>…</mo><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup></mrow></mfenced></math> <em><strong>A1</strong> </em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p style="padding-left:90px;"><img src="data:image/png;base64,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"></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>39040</mn><mo>.</mo><mo>.</mo><mo>.</mo><mo> </mo><mo> </mo><mo> </mo><mo>(</mo><mn>5</mn><mo>.</mo><mn>56160</mn><mo>)</mo></math> <em><strong>(A1)</strong></em></p>
<p>subtraction of four segments from area of circle <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>58</mn><mo>.</mo><mn>1</mn><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>58</mn><mo>.</mo><mn>055</mn><mo>…</mo><mo> </mo></mrow></mfenced></math> <em><strong>A1</strong> </em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mfenced><mrow><mn>0</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>4</mn><mo>.</mo><msup><mn>5</mn><mn>2</mn></msup><mo>×</mo><mi>sin</mi><mo> </mo><mn>54</mn><mo>.</mo><mn>532</mn><mo>…</mo></mrow></mfenced><mo>+</mo><mn>4</mn><mfenced><mrow><mfrac><mrow><mn>35</mn><mo>.</mo><mn>4679</mn></mrow><mn>360</mn></mfrac><mo>×</mo><mi mathvariant="normal">π</mi><mo>×</mo><mn>4</mn><mo>.</mo><msup><mn>5</mn><mn>2</mn></msup></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo> </mo><mo> </mo><mn>32</mn><mo>.</mo><mn>9845</mn><mo>…</mo><mo>+</mo><mn>25</mn><mo>.</mo><mn>0707</mn></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>58</mn><mo>.</mo><mn>1</mn><mo> </mo><msup><mtext>m</mtext><mn>2</mn></msup><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>58</mn><mo>.</mo><mn>055</mn><mo>…</mo><mo> </mo></mrow></mfenced></math> <em><strong>A1</strong> </em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>V</mi></mrow><mrow><mo>d</mo><mi>t</mi></mrow></mfrac></math> <strong>OR</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>V</mi></mrow><mrow><mo>d</mo><mi>t</mi></mrow></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>110363</mn><mo>…</mo></math> <strong>OR </strong>attempt to find where <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mo>d</mo><mn>2</mn></msup><mi>V</mi></mrow><mrow><mo>d</mo><msup><mi>t</mi><mn>2</mn></msup></mrow></mfrac><mo>=</mo><mn>0</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>1</mn></math> hour <em><strong>A1</strong> </em></p>
<p> </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>Part (a)(i) proved to be difficult for many candidates. About half of the candidates managed to correctly find the angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mi>O</mi><mo>^</mo></mover><mi>B</mi></math>. A variety of methods were used: cosine to find half of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mi>O</mi><mo>^</mo></mover><mi>B</mi></math> then double it; sine to find angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mi>O</mi><mo>^</mo></mover><mi>B</mi></math> , then find half of A<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mi>O</mi><mo>^</mo></mover><mi>B</mi></math> and double it; Pythagoras to find half of AB and then sine rule to find half of angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mi>O</mi><mo>^</mo></mover><mi>B</mi></math> then double it; Pythagoras to find half of AB, then double it and use cosine rule to find angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mi>O</mi><mo>^</mo></mover><mi>B</mi></math> . Many candidates lost a mark here due to premature rounding of an intermediate value and hence the final answer was not correct (to three significant figures).</p>
<p>In part (a)(ii) very few candidates managed to find the correct area of the shaded segment and include the correct units. Some only found the area of the triangle or the area of the sector and then stopped.</p>
<p>In part (b)(i), nearly all candidates managed to find the area of a circle.</p>
<p>In part (b)(ii), finding the area of the field reached by the goat proved troublesome for most of the candidates. It appeared as if the candidates did not fully understand the problem. Very few candidates realized the connection to part (a)(ii).</p>
<p>Part (c) was accessed by only a handful of candidates. The candidates could simply have graphed the function on their GDC to find the greatest value, but most did not realize this.</p>
<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.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><strong>All lengths in this question are in metres.</strong></p>
<p> </p>
<p>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \sqrt {\frac{{4 - {x^2}}}{8}} ">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msqrt>
<mfrac>
<mrow>
<mn>4</mn>
<mo>−<!-- − --></mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mn>8</mn>
</mfrac>
</msqrt>
</math></span>, for −2 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> ≤ 2. In the following diagram, the shaded region is enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> and the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">A container can be modelled by rotating this region by 360˚ about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis.</p>
</div>
<div class="specification">
<p>Water can flow in and out of the container.</p>
<p>The volume of water in the container is given by the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( t \right)">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</math></span>, for 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> ≤ 4 , where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> is measured in hours and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( t \right)">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</math></span> is measured in m<sup>3</sup>. The rate of change of the volume of water in the container is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g'\left( t \right) = 0.9 - 2.5\,{\text{cos}}\left( {0.4{t^2}} \right)">
<msup>
<mi>g</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0.9</mn>
<mo>−<!-- − --></mo>
<mn>2.5</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>cos</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.4</mn>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
</div>
<div class="specification">
<p>The volume of water in the container is increasing only when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> < <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> < <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
<mi>q</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the volume of the container.</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 value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
<mi>q</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>During the interval <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> < <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> < <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
<mi>q</mi>
</math></span>, he volume of water in the container increases by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> m<sup>3</sup>. Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>When <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> = 0, the volume of water in the container is 2.3 m<sup>3</sup>. It is known that the container is never completely full of water during the 4 hour period.</p>
<p> </p>
<p>Find the minimum volume of empty space in the container during the 4 hour period.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>attempt to substitute correct limits or the function into formula involving <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^2}">
<mrow>
<msup>
<mi>f</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi \int_{ - 2}^2 {{y^2}\,{\text{d}}y} ">
<mi>π</mi>
<msubsup>
<mo>∫</mo>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mn>2</mn>
</msubsup>
<mrow>
<mrow>
<msup>
<mi>y</mi>
<mn>2</mn>
</msup>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>y</mi>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi {\int {\left( {\sqrt {\frac{{4 - {x^2}}}{8}} } \right)} ^2}{\text{d}}x">
<mi>π</mi>
<mrow>
<mo>∫</mo>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<msqrt>
<mfrac>
<mrow>
<mn>4</mn>
<mo>−</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mn>8</mn>
</mfrac>
</msqrt>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
</math></span></p>
<p>4.18879</p>
<p>volume = 4.19, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{4}{3}\pi ">
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
<mi>π</mi>
</math></span> (exact) (m<sup>3</sup>) <em><strong>A2 N3</strong></em></p>
<p><strong>Note:</strong> If candidates have their GDC incorrectly set in degrees, award <strong><em>M</em></strong> marks where appropriate, but no <em><strong>A</strong></em> marks may be awarded. Answers from degrees are <em>p</em> = 13.1243 and <em>q</em> = 26.9768 in (b)(i) and 12.3130 or 28.3505 in (b)(ii).</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<p> </p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing the volume increases when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{g'}">
<mrow>
<msup>
<mi>g</mi>
<mo>′</mo>
</msup>
</mrow>
</math></span> is positive <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g'\left( t \right)">
<msup>
<mi>g</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</math></span> > 0, sketch of graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{g'}">
<mrow>
<msup>
<mi>g</mi>
<mo>′</mo>
</msup>
</mrow>
</math></span> indicating correct interval</p>
<p>1.73387, 3.56393</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> = 1.73, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> = 3.56 <em><strong>A1A1 N3</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<p> </p>
<p> </p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach to find change in volume <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( q \right) - g\left( p \right)">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>q</mi>
<mo>)</mo>
</mrow>
<mo>−</mo>
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>p</mi>
<mo>)</mo>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_p^q {g'\left( t \right){\text{d}}t} ">
<msubsup>
<mo>∫</mo>
<mi>p</mi>
<mi>q</mi>
</msubsup>
<mrow>
<msup>
<mi>g</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
</mrow>
</math></span></p>
<p>3.74541</p>
<p>total amount = 3.75 (m<sup>3</sup>) <em><strong>A2 N3</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>Note:</strong> There may be slight differences in the final answer, depending on which values candidates carry through from previous parts. Accept answers that are consistent with correct working.</p>
<p> </p>
<p>recognizing when the volume of water is a maximum <em><strong>(M1)</strong></em></p>
<p><em>eg</em> maximum when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = q">
<mi>t</mi>
<mo>=</mo>
<mi>q</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^q {g'\left( t \right){\text{d}}t} ">
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mi>q</mi>
</msubsup>
<mrow>
<msup>
<mi>g</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
</mrow>
</math></span></p>
<p>valid approach to find maximum volume of water <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.3 + \int_0^q {g'\left( t \right){\text{d}}t} ">
<mn>2.3</mn>
<mo>+</mo>
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mi>q</mi>
</msubsup>
<mrow>
<msup>
<mi>g</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.3 + \int_0^p {g'\left( t \right){\text{d}}t} + 3.74541">
<mn>2.3</mn>
<mo>+</mo>
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mi>p</mi>
</msubsup>
<mrow>
<msup>
<mi>g</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
</mrow>
<mo>+</mo>
<mn>3.74541</mn>
</math></span>, 3.85745</p>
<p>correct expression for the difference between volume of container and maximum value <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="4.18879 - \left( {2.3 + \int_0^q {g'\left( t \right){\text{d}}t} } \right)">
<mn>4.18879</mn>
<mo>−</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>2.3</mn>
<mo>+</mo>
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mi>q</mi>
</msubsup>
<mrow>
<msup>
<mi>g</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, 4.19 − 3.85745</p>
<p>0.331334</p>
<p>0.331 (m<sup>3</sup>) <em><strong>A2 N3</strong></em></p>
<p> </p>
<p><em><strong>[5 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.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>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x) = {x^3} + k{x^2} - 15x + 5">
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>k</mi>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mn>15</mn>
<mi>x</mi>
<mo>+</mo>
<mn>5</mn>
</math></span>.</p>
</div>
<div class="specification">
<p>The tangent to the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = g(x)">
<mi>y</mi>
<mo>=</mo>
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 2">
<mi>x</mi>
<mo>=</mo>
<mn>2</mn>
</math></span> is parallel to the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 21x + 7">
<mi>y</mi>
<mo>=</mo>
<mn>21</mn>
<mi>x</mi>
<mo>+</mo>
<mn>7</mn>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g'(x)">
<msup>
<mi>g</mi>
<mo>′</mo>
</msup>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></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>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 6">
<mi>k</mi>
<mo>=</mo>
<mn>6</mn>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of the tangent to the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = g(x)">
<mi>y</mi>
<mo>=</mo>
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 2">
<mi>x</mi>
<mo>=</mo>
<mn>2</mn>
</math></span>. Give your answer in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = mx + c">
<mi>y</mi>
<mo>=</mo>
<mi>m</mi>
<mi>x</mi>
<mo>+</mo>
<mi>c</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your answer to part (a) and the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span>, to find the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-coordinates of the stationary points of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = g(x)">
<mi>y</mi>
<mo>=</mo>
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g’( - 1)">
<msup>
<mi>g</mi>
<mo>′</mo>
</msup>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence justify that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> is decreasing at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - 1">
<mi>x</mi>
<mo>=</mo>
<mo>−</mo>
<mn>1</mn>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-coordinate of the local minimum.</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 style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3{x^2} + 2kx - 15">
<mn>3</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mi>k</mi>
<mi>x</mi>
<mo>−</mo>
<mn>15</mn>
</math></span> <strong><em>(A1)(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3{x^2}">
<mn>3</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span>, <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2kx">
<mn>2</mn>
<mi>k</mi>
<mi>x</mi>
</math></span> and <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 15">
<mo>−</mo>
<mn>15</mn>
</math></span>. Award at most <strong><em>(A1)(A1)(A0) </em></strong>if additional terms are 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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="21 = 3{(2)^2} + 2k(2) - 15">
<mn>21</mn>
<mo>=</mo>
<mn>3</mn>
<mrow>
<mo stretchy="false">(</mo>
<mn>2</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mi>k</mi>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
<mo>−</mo>
<mn>15</mn>
</math></span> <strong><em>(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for equating their derivative to 21. Award <strong><em>(M1) </em></strong>for substituting 2 into their derivative. The second <strong><em>(M1) </em></strong>should only be awarded if correct working leads to the final answer of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 6">
<mi>k</mi>
<mo>=</mo>
<mn>6</mn>
</math></span>.</p>
<p>Substituting in the known value, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 6">
<mi>k</mi>
<mo>=</mo>
<mn>6</mn>
</math></span>, invalidates the process; award <strong><em>(M0)(M0)</em></strong>.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 6">
<mi>k</mi>
<mo>=</mo>
<mn>6</mn>
</math></span> <strong><em>(AG)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(2) = {(2)^3} + (6){(2)^2} - 15(2) + 5{\text{ }}( = 7)">
<mi>g</mi>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mrow>
<mo stretchy="false">(</mo>
<mn>2</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>3</mn>
</msup>
</mrow>
<mo>+</mo>
<mo stretchy="false">(</mo>
<mn>6</mn>
<mo stretchy="false">)</mo>
<mrow>
<mo stretchy="false">(</mo>
<mn>2</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>15</mn>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>5</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mo>=</mo>
<mn>7</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for substituting 2 into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span>.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="7 = 21(2) + c">
<mn>7</mn>
<mo>=</mo>
<mn>21</mn>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mi>c</mi>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution of 21, 2 and their 7 into gradient intercept form.</p>
<p> </p>
<p><strong>OR</strong></p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y - 7 = 21(x - 2)">
<mi>y</mi>
<mo>−</mo>
<mn>7</mn>
<mo>=</mo>
<mn>21</mn>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution of 21, 2 and their 7 into gradient point form.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 21x - 35">
<mi>y</mi>
<mo>=</mo>
<mn>21</mn>
<mi>x</mi>
<mo>−</mo>
<mn>35</mn>
</math></span> <strong><em>(A1)</em></strong> <strong><em>(G2)</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3{x^2} + 12x - 15 = 0">
<mn>3</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>12</mn>
<mi>x</mi>
<mo>−</mo>
<mn>15</mn>
<mo>=</mo>
<mn>0</mn>
</math></span> (or equivalent) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for equating their part (a) (with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 6">
<mi>k</mi>
<mo>=</mo>
<mn>6</mn>
</math></span> substituted) to zero.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - 5,{\text{ }}x = 1">
<mi>x</mi>
<mo>=</mo>
<mo>−</mo>
<mn>5</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>x</mi>
<mo>=</mo>
<mn>1</mn>
</math></span> <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (a).</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3{( - 1)^2} + 12( - 1) - 15">
<mn>3</mn>
<mrow>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>1</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>12</mn>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mo>−</mo>
<mn>15</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for substituting <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 1">
<mo>−</mo>
<mn>1</mn>
</math></span> into their derivative, with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 6">
<mi>k</mi>
<mo>=</mo>
<mn>6</mn>
</math></span> substituted. Follow through from part (a).</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = - 24">
<mo>=</mo>
<mo>−</mo>
<mn>24</mn>
</math></span> <strong><em>(A1)</em>(ft)</strong> <strong><em>(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g’( - 1) < 0">
<msup>
<mi>g</mi>
<mo>′</mo>
</msup>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mo><</mo>
<mn>0</mn>
</math></span> (therefore <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> is decreasing when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - 1">
<mi>x</mi>
<mo>=</mo>
<mo>−</mo>
<mn>1</mn>
</math></span>) <strong><em>(R1)</em></strong></p>
<p><strong><em>[1 marks]</em></strong></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(1) = {(1)^3} + (6){(1)^2} - 15(1) + 5">
<mi>g</mi>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mrow>
<mo stretchy="false">(</mo>
<mn>1</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>3</mn>
</msup>
</mrow>
<mo>+</mo>
<mo stretchy="false">(</mo>
<mn>6</mn>
<mo stretchy="false">)</mo>
<mrow>
<mo stretchy="false">(</mo>
<mn>1</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>15</mn>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>5</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correctly substituting 6 and their 1 into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span>.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = - 3">
<mo>=</mo>
<mo>−</mo>
<mn>3</mn>
</math></span> <strong><em>(A1)</em>(ft)</strong> <strong><em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award, at most, (<strong><em>M1)(A0) </em></strong>or <strong><em>(G1) </em></strong>if answer is given as a coordinate pair. Follow through from part (c).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.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>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = - 0.5{x^4} + 3{x^2} + 2x">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mn>0.5</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mi>x</mi>
</math></span>. The following diagram shows part of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_06.09.00.png" alt="M17/5/MATME/SP2/ENG/TZ2/08"></p>
<p> </p>
<p>There are <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-intercepts at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0">
<mi>x</mi>
<mo>=</mo>
<mn>0</mn>
</math></span> and at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = p">
<mi>x</mi>
<mo>=</mo>
<mi>p</mi>
</math></span>. There is a maximum at A where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = a">
<mi>x</mi>
<mo>=</mo>
<mi>a</mi>
</math></span>, and a point of inflexion at B where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = b">
<mi>x</mi>
<mo>=</mo>
<mi>b</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></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>Write down the coordinates of A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the rate of change of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> at A.</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 coordinates of B.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the the rate of change of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> at B.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="R">
<mi>R</mi>
</math></span> be the region enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> , the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis, the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = b">
<mi>x</mi>
<mo>=</mo>
<mi>b</mi>
</math></span> and the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = a">
<mi>x</mi>
<mo>=</mo>
<mi>a</mi>
</math></span>. The region <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="R">
<mi>R</mi>
</math></span> is rotated 360° about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis. Find the volume of the solid formed.</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 style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>evidence of valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = 0,{\text{ }}y = 0">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>y</mi>
<mo>=</mo>
<mn>0</mn>
</math></span></p>
<p>2.73205</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = 2.73">
<mi>p</mi>
<mo>=</mo>
<mn>2.73</mn>
</math></span> <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>1.87938, 8.11721</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(1.88,{\text{ }}8.12)">
<mo stretchy="false">(</mo>
<mn>1.88</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>8.12</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>A2</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>rate of change is 0 (do not accept decimals) <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p><strong><em>[1 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1 (using GDC)</strong></p>
<p>valid approach <strong><em>M1</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’’ = 0">
<msup>
<mi>f</mi>
<mo>″</mo>
</msup>
<mo>=</mo>
<mn>0</mn>
</math></span>, max/min on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’,{\text{ }}x = - 1">
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>x</mi>
<mo>=</mo>
<mo>−</mo>
<mn>1</mn>
</math></span></p>
<p>sketch of either <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’">
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
</math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’’">
<msup>
<mi>f</mi>
<mo>″</mo>
</msup>
</math></span>, with max/min or root (respectively) <strong><em>(A1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 1">
<mi>x</mi>
<mo>=</mo>
<mn>1</mn>
</math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p>Substituting <strong>their</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> value into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(1)">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 4.5">
<mi>y</mi>
<mo>=</mo>
<mn>4.5</mn>
</math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p><strong>METHOD 2 (analytical)</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’’ = - 6{x^2} + 6">
<msup>
<mi>f</mi>
<mo>″</mo>
</msup>
<mo>=</mo>
<mo>−</mo>
<mn>6</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>6</mn>
</math></span> <strong><em>A1</em></strong></p>
<p>setting <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’’ = 0">
<msup>
<mi>f</mi>
<mo>″</mo>
</msup>
<mo>=</mo>
<mn>0</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 1">
<mi>x</mi>
<mo>=</mo>
<mn>1</mn>
</math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p>substituting <strong>their</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> value into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(1)">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 4.5">
<mi>y</mi>
<mo>=</mo>
<mn>4.5</mn>
</math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing rate of change is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’">
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
</math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y’,{\text{ }}f’(1)">
<msup>
<mi>y</mi>
<mo>′</mo>
</msup>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
</math></span></p>
<p>rate of change is 6 <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to substitute either limits or the function into formula <strong><em>(M1)</em></strong></p>
<p>involving <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^2}">
<mrow>
<msup>
<mi>f</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> (accept absence of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi ">
<mi>π</mi>
</math></span> and/or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{d}}x">
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
</math></span>)</p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi \int {{{( - 0.5{x^4} + 3{x^2} + 2x)}^2}{\text{d}}x,{\text{ }}\int_1^{1.88} {{f^2}} } ">
<mi>π</mi>
<mo>∫</mo>
<mrow>
<mrow>
<msup>
<mrow>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>0.5</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mi>x</mi>
<mo stretchy="false">)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<msubsup>
<mo>∫</mo>
<mn>1</mn>
<mrow>
<mn>1.88</mn>
</mrow>
</msubsup>
<mrow>
<mrow>
<msup>
<mi>f</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mrow>
</math></span></p>
<p>128.890</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{volume}} = 129">
<mrow>
<mtext>volume</mtext>
</mrow>
<mo>=</mo>
<mn>129</mn>
</math></span> <strong><em>A2</em></strong> <strong><em>N3</em></strong></p>
<p><strong><em>[3 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.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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</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>The Maxwell Ohm Company is designing a portable Bluetooth speaker. The speaker is in the shape of a cylinder with a hemisphere at each end of the cylinder.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The dimensions of the speaker, in centimetres, are illustrated in the following diagram where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> is the radius of the hemisphere, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math> is the length of the cylinder, with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>></mo><mn>0</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>≥</mo><mn>0</mn></math>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The Maxwell Ohm Company has decided that the speaker will have a surface area of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>300</mn><mo> </mo><msup><mtext>cm</mtext><mn>2</mn></msup></math>.</p>
</div>
<div class="specification">
<p>The quality of sound from the speaker will improve as <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> increases.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math>, the volume (cm<sup>3</sup>) of the speaker, in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</mi></math>.</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 an equation for the surface area of the speaker in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</mi></math>.</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>Given the design constraint that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mfrac><mrow><mn>150</mn><mo>-</mo><mn>2</mn><mi mathvariant="normal">π</mi><msup><mi>r</mi><mn>2</mn></msup></mrow><mrow><mi mathvariant="normal">π</mi><mi>r</mi></mrow></mfrac></math>, show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mn>150</mn><mi>r</mi><mo>-</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi><msup><mi>r</mi><mn>3</mn></msup></mrow><mn>3</mn></mfrac></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mtext>d</mtext><mi>V</mi></mrow><mrow><mtext>d</mtext><mi>r</mi></mrow></mfrac></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using your answer to part (d), show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> is a maximum when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> is equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mn>75</mn><mi mathvariant="normal">π</mi></mfrac></msqrt><mo> </mo><mtext>cm</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the length of the <strong>cylinder</strong> for which <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> is a maximum.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the maximum value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your answer to part (f) to identify the shape of the speaker with the best quality of sound.</p>
<div class="marks">[1]</div>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>V</mi><mo>=</mo></mrow></mfenced><mo> </mo><mfrac><mrow><mn>4</mn><mtext>π</mtext><msup><mi>r</mi><mn>3</mn></msup></mrow><mn>3</mn></mfrac><mo>+</mo><mi mathvariant="normal">π</mi><msup><mi>r</mi><mn>2</mn></msup><mi>l</mi></math> (or equivalent) <em><strong>(A1)</strong></em><em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for either the volume of a hemisphere formula multiplied by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> or the volume of a cylinder formula, and <em><strong>(A1)</strong></em> for completely correct expression. Accept equivalent expressions. Award at most <em><strong>(A1)(A0)</strong></em> if <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> is used instead of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math>.</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><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>300</mn><mo>=</mo><mn>4</mn><mi mathvariant="normal">π</mi><msup><mi>r</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi mathvariant="normal">π</mi><mi>r</mi><mi>l</mi></math> <em><strong>(A1)</strong></em><em><strong>(A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for the surface area of a hemisphere multiplied by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math>. Award <em><strong>(A1)</strong></em> for the surface area of a cylinder. Award <em><strong>(A1)</strong></em> for the addition of their formulas equated to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>300</mn></math>. Award at most <em><strong>(A1)(A1)(A0)</strong></em> if <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> is used instead of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math>, unless already penalized in part (a).</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mfrac><mrow><mn>4</mn><mi mathvariant="normal">π</mi><msup><mi>r</mi><mn>3</mn></msup></mrow><mn>3</mn></mfrac><mo>+</mo><mi mathvariant="normal">π</mi><msup><mi>r</mi><mn>2</mn></msup><mo> </mo><mfenced><mfrac><mrow><mn>150</mn><mo>-</mo><mn>2</mn><mi mathvariant="normal">π</mi><msup><mi>r</mi><mn>2</mn></msup></mrow><mrow><mi mathvariant="normal">π</mi><mi>r</mi></mrow></mfrac></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their correctly substituted formula for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math>.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mfrac><mrow><mn>4</mn><mi mathvariant="normal">π</mi><msup><mi>r</mi><mn>3</mn></msup></mrow><mn>3</mn></mfrac><mo>+</mo><mn>150</mn><mi>r</mi><mo>-</mo><mn>2</mn><mi mathvariant="normal">π</mi><msup><mi>r</mi><mn>3</mn></msup><mo> </mo></math> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct expansion of brackets and simplification of the cylinder expression in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> leading to the final answer.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mn>150</mn><mi>r</mi><mo>-</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi><msup><mi>r</mi><mn>3</mn></msup></mrow><mn>3</mn></mfrac></math> <em><strong>(AG)</strong></em></p>
<p><strong>Note:</strong> The final line must be seen, with no incorrect working, for the second <em><strong>(M1)</strong></em> to be awarded.</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><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mrow><mtext>d</mtext><mi>V</mi></mrow><mrow><mtext>d</mtext><mi>r</mi></mrow></mfrac><mo>=</mo></mrow></mfenced><mn>150</mn><mo>-</mo><mn>2</mn><mi mathvariant="normal">π</mi><msup><mi>r</mi><mn>2</mn></msup></math> <em><strong>(A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>150</mn></math>. Award <em><strong>(A1)</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mi mathvariant="normal">π</mi><msup><mi>r</mi><mn>2</mn></msup></math>. Award maximum <em><strong>(A1)(A0)</strong></em> if extra terms seen.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>150</mn><mo>-</mo><mn>2</mn><mi mathvariant="normal">π</mi><msup><mi>r</mi><mn>2</mn></msup><mo>=</mo><mn>0</mn></math> <strong>OR</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mtext>d</mtext><mi>V</mi></mrow><mrow><mtext>d</mtext><mi>r</mi></mrow></mfrac><mo>=</mo><mn>0</mn></math> <strong>OR</strong> sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mtext>d</mtext><mi>V</mi></mrow><mrow><mtext>d</mtext><mi>r</mi></mrow></mfrac></math>with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-intercept indicated <em><strong>(M1)</strong></em></p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASAAAAEACAYAAAATL6u2AAAdg0lEQVR4Ae2dDUyVV5rHjSGENYR12Ya5cVg/aohhGIYylFCXZdXW2o7rOMahDCGUvaJWrTUMYY1xXcIwxDVoaa1pDMsSxxKGYVhX6xjXEMOyjHUscW8YYq2EIS7rWGoYi/cSSnWt+W/Oa8Wvey/vvTzv5/3fxHjv+573PM/5PYd/zns+Z4EfEiABErCIwCyL7NIsCZAACYACxEpAAiRgGQEKkGXoaZgESIACxDpAAiRgGQFdAnT77l0MDQ1hcmJyylG/34+BgaGp3/xCAiRAApESmFaAzp07D++mTYiLn42jLUen8t9VvRsJ8fFQQsQPCZAACURDYFoBUpmqFtCitDS8tePNKRsj10ew8sW/faxVNHWTX0iABEhABwFdAqTyeXHZyyguKp7KUolSbU3d1G9+IQESIIFICegWICU++blLp/KvranB4MDg1G9+IQESIIFICegWoMrKSix6dqGWf5/Ph7bWtkhtMT0JkAAJPEZAtwDt27tX63QeGxtD1c5dWr/QYznxBwmQAAlESEC3AB1tbcWsWbOwc+duTHLkK0LMTE4CJBCMgG4B6uk+h/jEORgYuPxUPqpD+sbo6FPXeYEESIAEwhHQLUDNjYfR2XkmaF7vv/8ekpKSMHztetD7vEgCJEACwQjoEqCunm6cPHEy2PMYvDqMv5rnQfIzc1FYuDZoGl4kARIggWAEwgrQj364Do2N/4qPfvvbYM9i9E9fYPnLy3HqxH+gfKMXW9/6KX5e97OgaXmRBEiABJ4kEFaAhv5n+Mn0j/0uKynGwQMNGJ8Yh3djGe7dvYu83Dx0dXU9lo4/SIAESCAYgbACFOyBB9eOHz+Ol1atwD0Afv84vGXl2q1P+i5j8ZJnuUbsASj+TwIkEJJA1AJ05thx9H16fya0EqBSb+mUkdajrbg+MjL1m19IgARIIBiBqAXo0cyUAJVvLHv0Er+TAAmQwLQERARI9QGVffMKNq1FJiABEiCBbwiICNCTr2CkSwIkQAJ6CIgJkNfr1WOPaUiABEhgioCYAD3aCT2VO7+QAAmQQBgCYgLEFlAYyrxFAiQQlICYALEFFJQvL5IACYQhICZAbAGFocxbJEACQQmICRBbQEH58iIJkEAYAmICxBZQGMq8RQIkEJSAmACtWf8SfL0+XLl8BdeuXdP+jY7eCGqUF0mABEhAERAToOTkJMxNTNQOMFRbtz76Lyl5rrahfXZ2JtauXovyTV7s2lWFg4cOoq2lBWq3xctDlzB68yajQgIkEEMERAQoEAhgw+ubMXnnzv1/tycxeXsStwIB/O/1YfT1XULv7z5G55kz6OjoQNO/NGF/w3uo/IcqbN26FUU/fg2vvPIycnNzkZ71PbzwfC5+tH4NKip2YP+BBvy6vQ2+Ph8+//zzGAoNi0oC7icgIkBqKUbZxhJRWn39l9DU3Iw3d+zA3yxfjpRnnsGs2bORnJKCspIyHH7/ffgu9uLGjRGe0CFKnpmRgHkERARI25DM4MWoSuRU/9KJjmPYUVGBJenpiIuP07aCzc3Lxc5dVbhw4Txu356kIJlXf2iJBGZEQESAtBZQqWwLSE+p1EkcZ093ou6f61CwYoXW/6T2pl5XuB51tdUYuHSZYqQHJNOQgEUExATIDvsB+f1+nDh5Cm9uewM52fmaIGVlZKJyVxV8/+2zCDHNkgAJhCIgJkAPtmQNZcjs6+qsMrUr49v792utoz+f+2dYunQpDh0+jGvD19gyMjsgtEcCQQiICVCZBa9gQcoT8tKlTwawb/9+pC7waEdMLysowL76fdy7OiQx3iAB4wmICZAdXsH04jp3rgc7q3YifXGaJkaFxUVob23F5MSk3iyYjgRIQICAmADZ7RVML5vOzk4UF5doo2lqiL+upgYX+/r5iqYXINORwAwIiAmQ3V/BpmOkZmEfPXIUuTm5SExMQEFBAY53HNOOHJruWd4nARKIjoCYADnpFSwcKtV53XfRh4pdO7XXM/Watqu6GiM3eO59OG68RwLREBATIKe+goWDNjY2hgMNDcjKytLE6Od1e9lpHQ4Y75FAhATEBKhsc3GEpp2V/Mzp00j/7hJtKUh9Qz1bRM4KH721KQExAXJjC+jJmH355ZdoamrEvNSFSJ47FxUVlVCzsfkhARKIjoCMAI2NTZ0NH50bznpKDde3d3RAzbJOSkpCVVUlhoevOasQ9JYEbEBARoDUanibT0Q0grXqsG5paUFWdo7WR1S1cyeFyAjQzNO1BMQEqNwb22fDnzp5Elk5GZoQ1eyp5quZa/9kWDBJAiICdGssAO/G1yX9cmRed27fQa/vIjZv3oq0Z5/Fa6+9hv/6zx6oviN+SIAEniYgIkBqO45Y6IR+Gl/oK+MTfhx+/z2tjyg9PQMfnjzJ2dWhcfFOjBIQE6BYfwULVX9GR0eh+oYSEhLw8sqX0f9Jf6ikvE4CMUdATIBisRM6ktoyODCItet+gLjZs1HfsD+SR5mWBFxLQEyAvBtjuxNabw3pOtuJBQsW4KVVK3B18Krex5iOBFxJQE6ADN4T2k30Pxv+I5YtX6b1D1XX1mr7WLupfCwLCeglICZAfAXTi/xhuuYjzfB4UrQJjWdOn3l4g99IIEYIiAiQOhXDLavhzY672sfau2kT4uPjsW3LNoyMjJjtAu2RgGUERARIDcOXlrEPaCZR7DnXjbT0JUhJ9eD0hx9yyH4mMPmsYwiICRDnAc085qo1VFdXq82mXr96Da5zfdnMoTIHWxMQFCB3b8dhZhQv9vdj6Yp8rX+orbWNrSEz4dOWqQRkBCjGVsObFaHdVXu01lB5aZl2xJBZdmmHBMwiICNAfnZCGxWwPp8PGTmZSPF48OGx40aZYb4kYAkBMQEqjcHtOMyKmNp/qKa6DrNmz9ZGytRWsfyQgBsIiAkQZ0IbXx16zvVg0eI0ZGVmYPDKZeMN0gIJGExAToA4E9rgUN3PXrWGSkqKsXhxGgavDuPe3bum2KUREjCCgIgABcYn4N3AeUBGBChUnh988AEWLF6AN9/aBrW0gx8ScCIBEQHycxTMktirrT7WF67T1pS1tDZzuN6SKNDoTAjICFCM7gk9E/BSz6p9qQ8eeBdzEudoHdRqMiM/JOAUAmICxA3JrA15d3cP0hYvRF5eHi598qm1ztA6CegkICZAHAXTSdzAZCPXR7B69atISpoLdZCiah3xQwJ2JiAnQBwFs0WclejUVNdoM6ira6opQraICp0IRUBMgLgfUCjE1lxvO96K5KRnsH5NIY+RtiYEtKqDgJgAsQ9IB22Tk6h9qDMy0pGTm42Bfk5cNBk/zekgICZA7APSQduCJGrZxtrVa7Sh+jOnTvGVzIIY0GRoAjICxHlAoQnb4I7qF6qurUZCfALerj9gA4/oAgncJyAjQGoe0GbuB2T3StXS2qq1hDZt3wq1pIMfErCagJgAcUdEq0Opz3732S6kzvNg2Yv5CAQC+h5iKhIwiAAFyCCwds5WLWLNzcnBa+vXs0/IzoGKAd/EBIjD8M6qLapz+vmlL8C70cvXMWeFzlXeiglQudfrKjCxUJiBgQHtdUyNkl2/PsKtPWIh6DYro5gAsRPaZpHV6Y5avqG2fM3KzsQwT+HQSY3JpAiICNCtsQC8bAFJxcT0fCYmJlDzj/+EBanz8c7Bg7hz+47pPtBgbBIQESDuB+SOynPx9z4kp6Rg9epV7BdyR0htXwoZAVKnYni5I6Lto63DwatDV5G+JB35+XkYvXlTxxNMQgLRExATII6CRR8Euz2p+oWycjK1dWTsF7JbdNzlj5gAcS2YuyqGGqbPy82Dx+OBWtTKDwkYQUBOgLgfkBHxsTRPtVxj1apXNRG60NtrqS807k4CYgJU6i11JyGWCsUlpUhOmYuuzi7SIAFRAmICVL6RndCikbFZZpWVbyE+cQ66uyhCNguNo92RESBux+HoSqDXeSVCSUlJaG9r0/sI05FAWAIyAsRh+LCQ3XRzb90+rSXU1t7qpmKxLBYREBMgDsNbFEELzO7dW69ten/8WIcF1mnSTQTEBIjD8G6qFtOXZd++A4iLi8PHH388fWKmIIEQBOQEiMPwIRC79/Lb7xxEamoq1BHR/JBANATEBIhLMaLB7/xntm3fipycLKjZ0/yQQKQExASIfUCRondHerWSXu2umJWTxZaQO0JqainEBIh9QKbGzVbG/H7/fRHKyIT6zg8J6CUgI0CcB6SXt2vTqX6gJd+soqcIuTbM4gUTEaDA+AS8GzgTWjw6Dstw9E9foMy7CekZ38G58791mPd01woCIgLk94+Dx/JYET572jxQ34CkxDk4deK0PR2kV7YhICZA7IS2TUxt4ciePTXasg0uYLVFOGzrhJgA8VQM28bYEsfUcdBq7VhCQgK6u3ss8YFG7U9ATIB4Kob9g22Fh5u3bILHk4KLvX1WmKdNmxMQEyD2Adk80ha5p1pCRcVFWLxoPndWtCgGdjYrI0AchrdzjC33Te2suHq12lkxBepYaH5I4AEBGQHyj4Od0A+Q8v9gBMbHJ/HyimXIzMzWlm3cu3s3WDJeizECYgLEtWAxVnOiKK620X1ODvLyczhjOgp+bnxETIC4FMON1UO+TMPXriMzMwfqPPoxLtuQB+ywHOUEiNtxOCz01rk7PHRV6w8qLS3lCazWhcEWlsUEiMPwtoinY5z4dOCydgx0dXU11EgZP7FJQEyAOAwfmxVoJqXuPntW29q1ob4B977+eiZZ8VmHEpARIA7DOzT81rvd0tKChMQ4nP/oI+udoQemE5ARIA7Dmx44Nxl8+51D+P73n2N/kJuCqrMsYgLEYXidxJksKIGidT9GSXEZ+4OC0nHvRREBujUWgHfj6+6lxJIZTuCzG58jN/d5/OQnP0EgEDDcHg3Yg4CIAHE/IHsE0+leqImKWTnZWLVyJV/HnB5Mnf4LClCxTpNMRgKhCaiJiotS56OwuBiTX30VOiHvuIKAoACVuwIIC2E9gb7+fiQnJaKmuhr3rHeHHhhIQEyASr2lBrrJrGONwIlTpxE3ezZafs0z6N0cezEBKt/ITendXFGsKNvhw+8jIT4BZ06fscI8bZpAQEaAOBHRhFDFpokdFZX39xEaGIxNAC4vtYwA+cfBeUAurykWFm/NmtXIyEjHTZ5Bb2EUjDEtJkDckMyYADFXQBuez87EsoICDs+7rEKICRD3A3JZzbBZcYaHryFl3jxU7tqtecYdFW0WoCjdkRMg7gcUZQj4mF4C3We7tNXzTU2Neh9hOpsTEBMgDsPbPNIuce/+yFg8us52uaREsV0MMQHyer2xTZKlN43Ajl27keLxYGBgyDSbNGQMATEBYgvImAAx16cJqB0UVxUUIDcvB2M3bz6dgFccQ0BMgNgCckzMXeGoGhlLW7wQZaWl3MLDwREVEyC2gBxcCxzqev8n/UhKSsLeur0OLQHdFhMgtoBYmawg0Np+DAkJcTh+5rQV5mlzhgREBCgwPoHXy0tm6AofJ4HoCPyy7Zf4y7+YiwvnL0SXAZ+yjICIAGkbknEUzLIg0jBwvOMYMp/L5Exph1UGMQFiH5DDIu9Cd1e/8qq2hxDPGXNOcMUEiH1Azgm6Wz3tv/SpNlO6taXFrUV0XbnEBIgtINfVDUcWSB1yqEbGzvt8jvQ/1pwWEyC2gGKt6ti3vOvXFyInMwt+v9++TtIzjYCYALEFxBplFwI3b97AosVpKCoq5CRFuwQlhB9iAsQWUAjCvGwJgT6fT3sVO3TwkCX2aVQfATEBYgtIH3CmMo/A0ZYj2rnzXZ1cOW8e9cgsiQkQW0CRgWdqcwiUb96mvY6NcjtXc4BHaEVMgNgCipA8k5tCYHJiEvn5eVixchknKZpCPDIjYgLEFlBk4JnaPAJXh65q/UH7arlo1Tzq+iyJCRBbQPqAM5U1BD48eRJxCXE8Y8wa/CGtigkQW0AhGfOGTQhUVVVoZ4ypDe75sQcBMQFiC8geAaUXoQmo/iDVF/TSqhWcHxQak6l3xASILSBT40ZjURIYHBhEckoK2B8UJUDhx0QE6NZYAGVlG4RdY3YkYAyB3310Ht/+tgfvHXzPGAPMVTcBEQFS+wHxFUw3cya0AYGenvPfrJxvtYE3seuCmADxFSx2K5FTS15XV6sNz7NT2roIigkQW0DWBZGWoyegOqULCgrYKR09whk9KSZAbAHNKA582CICg1eHtaH5PVW7LPIgts2KCRBbQLFdkZxc+s7OTm2S4tmzZ51cDEf6LiZAbAE5Mv50+hsCFdt3wOPxIBAIkImJBMQEiC0gE6NGU+IE1CTFrJylOLC/XjxvZhiagJgAsQUUGjLvOIOAOmk1/TtLMMrz5k0LmJgAsQVkWsxoyEACm/5+A7Zs2W6gBWb9KAExAWIL6FGs/O5UAoN/+APi4mej5SiP9jEjhmICxBaQGeGiDTMI1NbWIMXjAScoGk9bTIDYAjI+WLRgDgF1smpBwVKsWrmKExQNRi4mQGwBGRwpZm8qAbVqXh1w2NTUZKrdWDMmJkBsAcVa1XF/eZubm7QFqz6esmpYsMUEiC0gw2LEjC0icO/uXaxbuxY52dm4e/euRV6426yIAAXGJ+Atf93dpFi6mCTgn5jA8heX4+9+uBZffvllTDIwstAiAsT9gIwMEfO2moB21HPqfFRtr2KntHAwxASIfUDCkWF2tiLQ1d2tLVg9feq0rfxyujNiAsQ+IKdXBfo/HYEtW7dqp6z6/f7pkvK+TgJiAsQWkE7iTOZYAmrBakZGOraUefkqJhRFMQFiC0goIszG1gS6u3u0pRonTx63tZ9OcU5MgNgCckrI6edMCai9pFNSPbjOAw5nihJiAsQW0IxjwQwcQkC9imVnZ6PE63WIx/Z1U0yA2AKyb5DpmTyB3os+JCXOQWsHj/WZCV0xAWILaCZh4LNOJFC1e4+2of3o6KgT3beFz2ICxBaQLeJJJ0wkoK2az89H0Zr1HBWLkruYALEFFGUE+JijCfh6L2oTFNva2h1dDqucFxMgtoCsCiHtWk3g4IEGJCcnY2ho0GpXHGdfTIDYAnJc7OmwEIHbtyeRm5uHkpJiqBX0/OgnICZAbAHph86U7iOgTtRISpqLtna+ikUSXTEBYgsoEuxM60YCO6t2YlHqfIxPTLixeIaUSUyA2AIyJD7M1GEEsrIzse/t/Q7z2jp3RQTo1lgAZWUbrCsFLZOATQhcGfwDnvvedzF8bdgmHtnbDREB4oZk9g4yvTOXwP76eixdupRzg3RgFxMgvoLpoM0kMUFg9E9faJvZNzY2x0R5Z1JIMQFiJ/RMwsBn3UagubFRO9ZnYGCIQ/NhgismQGwBhaHMWzFHQC3TyM1firXr11GAwkRfTIDYAgpDmbdiksDg0JDWCmpu4qtYqAogJkBsAYVCzOuxTKC6rg7znknBDa6YD1oNxASILaCgfHkxxgmopRk5OTkoLFwX4ySCF19MgNgCCg6YV0mgt/eCto90V1cXYTxBQEyA2AJ6gix/ksAjBB4s0+CRPo9AAeT2hGYL6HGw/EUCjxIYGxvDvEULsXPXHu0yV83fp8MW0KO1hN9JwEACp0+e1F7FLlzoNdCKs7IWEyC2gJwVeHprDYHS4iLk5uRymcY3+MUEiH1A1lRoWnUWgZGbo9rcoEMN7zrLcYO8FRMgtoAMihCzdR2BB8s0hoevxfwsaTEBYgvIdX8nLJBBBNQyjbzcXKwrLjTIgnOyFRGgwPgEvOWvO6fU9JQELCbw2fAfseDZVNTX7bPYE2vNiwgQ9wOyNoi07kwC3d092pE+Ped6nFkAAa/FBIh9QALRYBYxR2DLlu3IyshErE5QFBMg9gHF3N8OCyxAYOT6CJJTUvD2vnqB3JyXhZgAsQXkvODTY3sQ6Oho13ZQvDQ4ZA+HTPRCTIDYAjIxajTlKgLaGfMFBSgsir1RMTEBYgvIVX8TLIzJBLSDDRPn4Fh7m8mWrTUnJkBsAVkbSFp3PoGKyiqkpadj7OZN5xdGZwnEBIgtIJ3EmYwEQhCYnJjEosVpUFt3xMpHTIDYAoqVKsNyGkng+LFjU6dpGGnHLnmLCRBbQHYJKf1wMgHVIb1qxQqsWbcG//f117YtyvhXX2HrNi8GBwZn5KOYALEFNKM48GESmCLQ5/NpraCLH388dc2OX1qOHkVa+rNQK/ujnUgpJkBsAdmxitAnpxJQHdIbyjfZfrW82umxxOtFbn4eLp47HzFuMQEqWleEq1ev8h8ZsA7MsA4MDw/jyuUrSJ0/D30Xfbbnqfw9cuQIFs2fj4qKSqjOdL0fMQHKzkrHG2+UP/1va5BrwdKFu7ZZIA+7+KHKaRdf7OIHmdz/u9n+eD1/4YW/RrLH8/jfVPkjafR8V387etKFS/Po31+IdKUlpUhISEDa4oUYuXFdr/4Ibkq/sUy3USYkARKYnsDAlQFtD+me85G/2kyfu1yKcxcuIDMjE9u2bIt4q1mxFlBZWblciZgTCZCARsBbXIr83PyI/7DNwKdetcrLvMjIyIDqOI/mIyJAt8YC2LTRG419PkMCJBCGwNgXY8h6PhNVVVVhUpl/a/LOHfy0shK/+c0pTE7eidoBEQFSG5J52QKKOgh8kATCEfD1XUZCXBw6OzvDJXPkPTEB4jwgR8afTjuEwI4dFViyJB2Tfr9tPe739WPPnt0oKizC9ZERzc/zPh/WrVuPzrNng/pNAQqKhRdJwF4E1ES/FI8HdQfsvYe02mAtae5cVFfvwaVPB7Fm9avaOWhq0mKwj5gAlXMULBhfXiMBMQLNTUe0GdKjo6NieRqRUUVFBXLzctHwXj1u3w4/J0hGgMbG2AdkRCSZJwk8QUCdqlpaZu8pL51nuxA3ezYuXJh++oCMAPnHUe61N5Qn4sifJOBIAl1dXdr2rb29F2zr/7Xha5g1axZa249N66OYAJWVlkxrjAlIgARmTkDNvcnOs+f58mo1f21tLbKyc1C1Y+u0hRUTIC/7gKaFzQQkIEFAHemcmJCAllb7bd/aeaYTF/t82LqpHDnZS7Xith1pCVlsOQHiPKCQkHmDBKQJ1O7di9R5nqi3wZD0R80DXLlsGd58YxMam45oWZ84eUpbRrJz50/R92noPYPEBIjzgCRDyrxIIDwBNbqkFn7W1OwJn9CEu/cANDc2ov3f2x+z9u7BQ+i/fPmxa0/+EBMgDsM/iZa/ScBYAs1H7g/Lq7k3Tv3ICBCH4Z0af/rtcAIFBQVYvfoVx5ZCRoD84+ArmGPrAB13MAE11yY+Ph5237IjFGIxAeIrWCjEvE4CxhLYsnkLcrKzI9qJ0FiP9OcuI0B8BdNPnClJQJiAWvip1l+1NDcL52x8diICFBifgHcDZ0IbHy5aIIHgBH71b7/CM9/6Fn7f3x88gU2viggQ9wOyaXTpVkwRULsnrli5zJa7J4YKhJgAcSlGKMS8TgLmEBi8Oqytlu/oeHw+jjnWo7MiJkDlXm7JGl0I+BQJyBGoqa3VJiiq87qc8BEToLKNXIzqhIDTR3cTuHnzBpJTPDj4ToMjCiomQNwT2hHxppMxQKCttVV7FVOLVu3+kREgNQzPVzC7x5r+xQgBdVyO2g5jx7Ydti+xjAD5x1G2udj2haWDJBArBH5z6v5q9M8++6OtiywmQHwFs3Wc6VwMEnhl7Q/ws7o6W5ecAmTr8NA5EoieQO9FH77/3HPRZ2DCk2ICxHlAJkSLJkggQgKrVq5CR5t95wWJCVD55tII0TA5CZCA0QR+8YujSE/PsO1CVTEBYh+Q0VWJ+ZNA5AQCgQA8nhQcang38odNeEJMgPgKZkK0aIIEoiDQ1NiI5Gfmwo4HGooJEM8Fi6Jm8BESMIGAdqxz6kLs22e/Y53FBIhLMUyoSTRBAlESaG9rR1LiHNhtdrSYALEPKMqawcdIwAQC6sDAPXt2Y/jadROs6TchIkD6zTElCZAACTwkQAF6yILfSIAETCZAATIZOM2RAAk8JEABesiC30iABEwmQAEyGTjNkQAJPCRAAXrIgt9IgARMJkABMhk4zZEACTwkQAF6yILfSIAETCZAATIZOM2RAAk8JEABesiC30iABEwm8P+wkFeAU6EnXwAAAABJRU5ErkJggg=="></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for equating their derivative to zero or a sketch of their derivative with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-intercept indicated.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><msqrt><mfrac><mn>150</mn><mrow><mn>2</mn><mi mathvariant="normal">π</mi></mrow></mfrac></msqrt></math> <strong>OR</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>r</mi><mn>2</mn></msup><mo>=</mo><mfrac><mn>150</mn><mrow><mn>2</mn><mi mathvariant="normal">π</mi></mrow></mfrac></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><msqrt><mfrac><mn>75</mn><mi mathvariant="normal">π</mi></mfrac></msqrt></math> <em><strong>(AG)</strong></em></p>
<p><strong>Note:</strong> The <em><strong>(AG)</strong></em> line must be seen for the preceding <em><strong>(A1)</strong></em> to be awarded.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>l</mi><mo>=</mo></mrow></mfenced><mfrac><mrow><mn>150</mn><mo>-</mo><mn>2</mn><mi mathvariant="normal">π</mi><msup><mfenced><msqrt><mstyle displaystyle="true"><mfrac><mn>75</mn><mi mathvariant="normal">π</mi></mfrac></mstyle></msqrt></mfenced><mn>2</mn></msup></mrow><mrow><mi mathvariant="normal">π</mi><mfenced><msqrt><mfrac><mn>75</mn><mi mathvariant="normal">π</mi></mfrac></msqrt></mfenced></mrow></mfrac></math> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <strong>(M1)</strong> for correct substitution in the given formula for the length of the cylinder.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>l</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>0</mn><mo> </mo><mfenced><mtext>cm</mtext></mfenced></math> <em><strong>(A1)(G2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)(A1)</strong></em> for correct substitution of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math> sf approximation <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>89</mn></math> leading to a correct answer of zero.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mn>150</mn><mfenced><msqrt><mfrac><mn>75</mn><mi mathvariant="normal">π</mi></mfrac></msqrt></mfenced><mo>-</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi><msup><mfenced><msqrt><mstyle displaystyle="true"><mfrac><mn>75</mn><mi mathvariant="normal">π</mi></mfrac></mstyle></msqrt></mfenced><mn>3</mn></msup></mrow><mn>3</mn></mfrac></math> <em><strong>OR</strong></em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mfrac><mrow><mn>4</mn><mi mathvariant="normal">π</mi><msup><mfenced><msqrt><mstyle displaystyle="true"><mfrac><mn>75</mn><mi mathvariant="normal">π</mi></mfrac></mstyle></msqrt></mfenced><mn>3</mn></msup></mrow><mn>3</mn></mfrac></math> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in the formula for the volume of the speaker or the volume of a sphere.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>489</mn><mo> </mo><mfenced><mrow><mn>488</mn><mo>.</mo><mn>602</mn><mo>…</mo><mo>,</mo><mo> </mo><mn>100</mn><msqrt><mfrac><mn>75</mn><mi mathvariant="normal">π</mi></mfrac></msqrt></mrow></mfenced><mo> </mo><mfenced><msup><mtext>cm</mtext><mn>3</mn></msup></mfenced></math> <em><strong>(A1)(G2)</strong></em></p>
<p><strong>Note:</strong> Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>489</mn><mo>.</mo><mn>795</mn><mo>…</mo></math> from use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math> sf value of <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mn>75</mn><mi mathvariant="normal">π</mi></mfrac></msqrt></math>. Award <strong><em>(M1)(A1)</em>(ft)</strong> for correct substitution in their volume of speaker. Follow through from parts (a) and (f).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>sphere (spherical) <strong><em>(A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Question requires the use of part (f) so if there is no answer to part (f), part (h) is awarded <em><strong>(A0)</strong></em>. Follow through from their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>></mo><mn>0</mn></math>.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>The graph of the quadratic function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>8</mn></mrow></mfenced></math> intersects the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-axis at <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>,</mo><mo> </mo><mi>c</mi></mrow></mfenced></math>.</p>
</div>
<div class="specification">
<p>The vertex of the function is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>3</mn><mo>,</mo><mo> </mo><mo>-</mo><mn>12</mn><mo>.</mo><mn>5</mn></mrow></mfenced></math>.</p>
</div>
<div class="specification">
<p>The equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>12</mn></math> has two solutions. The first solution is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mn>10</mn></math>.</p>
</div>
<div class="specification">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> be the tangent at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mn>3</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>.</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 for the axis of symmetry of the graph.</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><strong>Use the symmetry</strong> of the graph to show that the second solution is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>4</mn></math>.</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>Write down the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-intercepts of the graph.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On graph paper, draw the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>f</mi><mfenced><mi>x</mi></mfenced></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>10</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mn>4</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>14</mn><mo>≤</mo><mi>y</mi><mo>≤</mo><mn>14</mn></math>. Use a scale of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mtext>cm</mtext></math> to represent <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> unit on the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mtext>cm</mtext></math> to represent <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> units on the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-axis.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the tangent <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> on your graph.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>a</mi></mfenced><mo>=</mo><mn>5</mn><mo>.</mo><mn>5</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mfenced><mi>a</mi></mfenced><mo>=</mo><mo>-</mo><mn>6</mn></math>, state whether the function, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math>, is increasing or decreasing at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>a</mi></math>. Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mfenced><mrow><mn>0</mn><mo>-</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mn>0</mn><mo>+</mo><mn>8</mn></mrow></mfenced></math> <strong>OR</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mfenced><mrow><msup><mn>0</mn><mn>2</mn></msup><mo>+</mo><mn>6</mn><mfenced><mn>0</mn></mfenced><mo>-</mo><mn>16</mn></mrow></mfenced></math> (or equivalent) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for evaluating <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mn>0</mn></mfenced></math>.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>c</mi><mo>=</mo></mrow></mfenced><mo> </mo><mo>-</mo><mn>8</mn></math> <em><strong>(A1)</strong></em><strong><em>(G2)</em></strong></p>
<p><strong>Note</strong>: Award<em><strong> (G2)</strong></em> if <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>,</mo><mo> </mo><mo>-</mo><mn>8</mn></mrow></mfenced></math> seen.</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><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mn>3</mn></math> <em><strong>(A1)</strong></em><em><strong>(A1)</strong></em></p>
<p><strong>Note</strong>: Award<em><strong> (A1)</strong></em> for “<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo></math> constant”, <em><strong>(A1)</strong></em> for the constant being <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math>. The answer must be an equation.</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><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>3</mn><mo>-</mo><mo>-</mo><mn>10</mn></mrow></mfenced><mo>+</mo><mo>-</mo><mn>3</mn></math> <em><strong>(M1)</strong></em></p>
<p><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>8</mn><mo>-</mo><mo>-</mo><mn>10</mn></mrow></mfenced><mo>+</mo><mn>2</mn></math> <em><strong>(M1)</strong></em></p>
<p><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>10</mn><mo>+</mo><mi>x</mi></mrow><mn>2</mn></mfrac><mo>=</mo><mo>-</mo><mn>3</mn></math> <em><strong>(M1)</strong></em></p>
<p><strong>OR</strong></p>
<p>diagram showing axis of symmetry and given points (<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-values labels, <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>10</mn></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math>, are sufficient) <strong>and</strong> an indication that the horizontal distances between the axis of symmetry and the given points are <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math>. <em><strong>(M1)</strong></em></p>
<p><img src="data:image/png;base64,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"></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct working using the symmetry between <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mn>10</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mn>3</mn></math>. Award <em><strong>(M0)</strong></em> if candidate has used <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mn>10</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>4</mn></math> to show the axis of symmetry is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mn>3</mn></math>. Award <em><strong>(M0)</strong></em> if candidate solved <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>12</mn></math> or evaluated <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mrow><mo>-</mo><mn>10</mn></mrow></mfenced></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mn>4</mn></mfenced></math>.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>4</mn></math> <em><strong>(AG)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> <em><strong>(A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mn>8</mn><mo>,</mo><mo> </mo><mi>y</mi><mo>=</mo><mn>0</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>2</mn><mo>,</mo><mo> </mo><mi>y</mi><mo>=</mo><mn>0</mn></math><strong> or</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>8</mn><mo>,</mo><mo> </mo><mn>0</mn></mrow></mfenced></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo>,</mo><mo> </mo><mn>0</mn></mrow></mfenced></math>, award at most <em><strong>(A0)(A1)</strong></em> if parentheses are omitted.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img 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"> <em><strong>(A1)(A1)</strong></em><em><strong>(A1)(A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for labelled axes with correct scale, correct window. Award <em><strong>(A1)</strong></em> for the vertex, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>3</mn><mo>,</mo><mo> </mo><mo>-</mo><mn>12</mn><mo>.</mo><mn>5</mn></mrow></mfenced></math>, in correct location.<br>Award <em><strong>(A1)</strong></em> for a smooth continuous curve symmetric about their vertex. Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for the curve passing through their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> intercepts in correct location. Follow through from their parts (a) and (d).</p>
<p><strong>If graph paper is not used:</strong><br>Award at most <strong><em>(A0)(A0)(A1)(A1)</em>(ft)</strong>. Their graph should go through their <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> for the last <strong><em>(A1)</em>(ft)</strong> to be awarded.</p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>12</mn><mo>.</mo><mn>5</mn></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>0</mn><mi>x</mi><mo>-</mo><mn>12</mn><mo>.</mo><mn>5</mn></math> <em><strong>(A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(</strong><strong>A1)</strong></em> for "<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo></math> constant", <em><strong>(A1)</strong></em> for the constant being <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>12</mn><mo>.</mo><mn>5</mn></math>. The answer must be an equation.</p>
<p> <em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>tangent to the graph drawn at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mn>3</mn></math><strong> </strong> <em><strong>(A1)</strong></em><strong>(</strong><strong>ft)</strong></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for a horizontal straight-line tangent to curve at approximately <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mn>3</mn></math>. Award <em><strong>(A0)</strong></em> if a ruler is not used. Follow through from their part (e).</p>
<p> <em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">f.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>decreasing <em><strong> (A1)</strong></em></p>
<p>gradient (of tangent line) is negative (at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>a</mi></math>) <strong>OR</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mfenced><mi>a</mi></mfenced><mo><</mo><mn>0</mn></math> <em><strong> (R1)</strong></em></p>
<p><strong>Note:</strong> Do not accept "gradient (of tangent line) is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn></math>". Do not award <em><strong>(A1)(R0)</strong></em>.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{{16}}{x}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>16</mn>
</mrow>
<mi>x</mi>
</mfrac>
</math></span>. The line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span> is tangent to the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 8">
<mi>x</mi>
<mo>=</mo>
<mn>8</mn>
</math></span>.</p>
</div>
<div class="specification">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span> can be expressed in the form <em><strong>r</strong></em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \left( {\begin{array}{*{20}{c}} 8 \\ 2 \end{array}} \right) + t">
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>8</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>2</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>t</mi>
</math></span><em><strong>u</strong></em>.</p>
</div>
<div class="specification">
<p>The direction vector of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = x">
<mi>y</mi>
<mo>=</mo>
<mi>x</mi>
</math></span> is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 1 \\ 1 \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the gradient of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L"> <mi>L</mi> </math></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>Find <em><strong>u</strong></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 acute angle between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = x"> <mi>y</mi> <mo>=</mo> <mi>x</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L"> <mi>L</mi> </math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {f \circ f} \right)\left( x \right)"> <mrow> <mo>(</mo> <mrow> <mi>f</mi> <mo>∘</mo> <mi>f</mi> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, write down <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^{ - 1}}\left( x \right)"> <mrow> <msup> <mi>f</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence or otherwise, find the obtuse angle formed by the tangent line to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 8"> <mi>x</mi> <mo>=</mo> <mn>8</mn> </math></span> and the tangent line to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 2"> <mi>x</mi> <mo>=</mo> <mn>2</mn> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>attempt to find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'\left( 8 \right)"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </math></span> <em><strong>(M1)</strong></em></p>
<p><em>eg </em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'\left( x \right)"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{y'}"> <mrow> <msup> <mi>y</mi> <mo>′</mo> </msup> </mrow> </math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 16{x^{ - 2}}"> <mo>−</mo> <mn>16</mn> <mrow> <msup> <mi>x</mi> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </math></span></p>
<p>−0.25 (exact) <em><strong>A1 N2</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><strong>u</strong></em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \left( {\begin{array}{*{20}{c}} 4 \\ { - 1} \end{array}} \right)"> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>4</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span> or any scalar multiple <em><strong>A2 N2</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>correct scalar product and magnitudes <em><strong>(A1)(A1)(A1)</strong></em></p>
<p>scalar product <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 1 \times 4 + 1 \times - 1\,\,\,\left( { = 3} \right)"> <mo>=</mo> <mn>1</mn> <mo>×</mo> <mn>4</mn> <mo>+</mo> <mn>1</mn> <mo>×</mo> <mo>−</mo> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mo>=</mo> <mn>3</mn> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p>magnitudes <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \sqrt {{1^2} + {1^2}} "> <mo>=</mo> <msqrt> <mrow> <msup> <mn>1</mn> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mn>1</mn> <mn>2</mn> </msup> </mrow> </msqrt> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {{4^2} + {{\left( { - 1} \right)}^2}} "> <msqrt> <mrow> <msup> <mn>4</mn> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </math></span> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( { = \sqrt 2 {\text{,}}\,\,\sqrt {17} } \right)"> <mrow> <mo>(</mo> <mrow> <mo>=</mo> <msqrt> <mn>2</mn> </msqrt> <mrow> <mtext>,</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <msqrt> <mn>17</mn> </msqrt> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p>substitution of their values into correct formula <em><strong> (M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4 - 1}}{{\sqrt {{1^2} + {1^2}} \sqrt {{4^2} + {{\left( { - 1} \right)}^2}} }}"> <mfrac> <mrow> <mn>4</mn> <mo>−</mo> <mn>1</mn> </mrow> <mrow> <msqrt> <mrow> <msup> <mn>1</mn> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mn>1</mn> <mn>2</mn> </msup> </mrow> </msqrt> <msqrt> <mrow> <msup> <mn>4</mn> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> </mfrac> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{ - 3}}{{\sqrt 2 \sqrt {17} }}"> <mfrac> <mrow> <mo>−</mo> <mn>3</mn> </mrow> <mrow> <msqrt> <mn>2</mn> </msqrt> <msqrt> <mn>17</mn> </msqrt> </mrow> </mfrac> </math></span>, 2.1112, 120.96° </p>
<p>1.03037 , 59.0362°</p>
<p>angle = 1.03 , 59.0° <em><strong>A1 N4</strong></em></p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">attempt to form composite <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {f \circ f} \right)\left( x \right)"> <mrow> <mo>(</mo> <mrow> <mi>f</mi> <mo>∘</mo> <mi>f</mi> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span> <strong><em><span style="font-family: 'Verdana',sans-serif;">(M1)</span></em></strong></span></p>
<p><em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">eg </span></em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( {f\left( x \right)} \right)"> <mi>f</mi> <mrow> <mo>(</mo> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( {\frac{{16}}{x}} \right)"> <mi>f</mi> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>16</mn> </mrow> <mi>x</mi> </mfrac> </mrow> <mo>)</mo> </mrow> </math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{16}}{{f\left( x \right)}}"> <mfrac> <mrow> <mn>16</mn> </mrow> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </math></span></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">correct working <strong><em><span style="font-family: 'Verdana',sans-serif;">(A1)</span></em></strong></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{16}}{{\frac{{16}}{x}}}"> <mfrac> <mrow> <mn>16</mn> </mrow> <mrow> <mfrac> <mrow> <mn>16</mn> </mrow> <mi>x</mi> </mfrac> </mrow> </mfrac> </math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="16 \times \frac{x}{{16}}"> <mn>16</mn> <mo>×</mo> <mfrac> <mi>x</mi> <mrow> <mn>16</mn> </mrow> </mfrac> </math></span></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {f \circ f} \right)\left( x \right) = x"> <mrow> <mo>(</mo> <mrow> <mi>f</mi> <mo>∘</mo> <mi>f</mi> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>x</mi> </math></span> <strong><em><span style="font-family: 'Verdana',sans-serif;">A1 N2</span></em></strong></span></p>
<p><strong><em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[3 marks]</span></em></strong></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: Verdana, sans-serif;font-size: 10.5pt;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^{ - 1}}\left( x \right) = \frac{{16}}{x}"> <mrow> <msup> <mi>f</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>16</mn> </mrow> <mi>x</mi> </mfrac> </math></span> (accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = \frac{{16}}{x}"> <mi>y</mi> <mo>=</mo> <mfrac> <mrow> <mn>16</mn> </mrow> <mi>x</mi> </mfrac> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{16}}{x}"> <mfrac> <mrow> <mn>16</mn> </mrow> <mi>x</mi> </mfrac> </math></span>) </span><strong style="font-family: Verdana, sans-serif;font-size: 10.5pt;"><em>A1 N1</em></strong></p>
<p style="text-align: left;"><strong>Note:</strong> Award <em><strong>A0</strong></em> in part (ii) if part (i) is incorrect.<br>Award <em><strong>A0</strong></em> in part (ii) if the candidate has found <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^{ - 1}}\left( x \right) = \frac{{16}}{x}"> <mrow> <msup> <mi>f</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>16</mn> </mrow> <mi>x</mi> </mfrac> </math></span> by interchanging <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y"> <mi>y</mi> </math></span>.</p>
<p><strong><em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[1 mark]</span></em></strong></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>recognition of symmetry about <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = x"> <mi>y</mi> <mo>=</mo> <mi>x</mi> </math></span> <em><strong>(M1)</strong></em></p>
<p><em>eg</em> (2, 8) ⇔ (8, 2) <img src="data:image/png;base64,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"></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">evidence of doubling <strong>their</strong> angle <strong><em> (M1)</em></strong><br></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2 \times 1.03"> <mn>2</mn> <mo>×</mo> <mn>1.03</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2 \times 59.0"> <mn>2</mn> <mo>×</mo> <mn>59.0</mn> </math></span></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">2.06075, 118.072°</span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">2.06 (radians) (118 degrees) <em><strong>A1 N2</strong></em></span></p>
<p> </p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><strong>METHOD 2</strong><br></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">finding direction vector for tangent line at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 2"> <mi>x</mi> <mo>=</mo> <mn>2</mn> </math></span> <em><strong>(A1)</strong></em><br></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} { - 1} \\ 4 \end{array}} \right)"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>4</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 1 \\ { - 4} \end{array}} \right)"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">substitution of <strong>their</strong> values into correct formula (must be from vectors) <em><strong>(M1)</strong></em><br></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{ - 4 - 4}}{{\sqrt {{1^2} + {4^2}} \sqrt {{4^2} + {{\left( { - 1} \right)}^2}} }}"> <mfrac> <mrow> <mo>−</mo> <mn>4</mn> <mo>−</mo> <mn>4</mn> </mrow> <mrow> <msqrt> <mrow> <msup> <mn>1</mn> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mn>4</mn> <mn>2</mn> </msup> </mrow> </msqrt> <msqrt> <mrow> <msup> <mn>4</mn> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> </mfrac> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{8}{{\sqrt {17} \sqrt {17} }}"> <mfrac> <mn>8</mn> <mrow> <msqrt> <mn>17</mn> </msqrt> <msqrt> <mn>17</mn> </msqrt> </mrow> </mfrac> </math></span></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">2.06075, 118.072°</span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">2.06 (radians) (118 degrees) <em><strong>A1 N2</strong></em></span></p>
<p> </p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><strong>METHOD 3</strong><br></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">using trigonometry to find an angle with the horizontal <em><strong>(M1)</strong></em><br></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{tan}}\,\theta = - \frac{1}{4}"> <mrow> <mtext>tan</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> <mo>=</mo> <mo>−</mo> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{tan}}\,\theta = - 4"> <mrow> <mtext>tan</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> <mo>=</mo> <mo>−</mo> <mn>4</mn> </math></span></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">finding both angles of rotation <em><strong> (A1)</strong></em><br></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\theta _1} = 0.244978{\text{, 14}}{\text{.0362}}^\circ "> <mrow> <msub> <mi>θ</mi> <mn>1</mn> </msub> </mrow> <mo>=</mo> <mn>0.244978</mn> <mrow> <mtext>, 14</mtext> </mrow> <msup> <mrow> <mtext>.0362</mtext> </mrow> <mo>∘</mo> </msup> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\theta _1} = 1.81577{\text{, 104}}{\text{.036}}^\circ "> <mrow> <msub> <mi>θ</mi> <mn>1</mn> </msub> </mrow> <mo>=</mo> <mn>1.81577</mn> <mrow> <mtext>, 104</mtext> </mrow> <msup> <mrow> <mtext>.036</mtext> </mrow> <mo>∘</mo> </msup> </math></span></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">2.06075, 118.072°</span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">2.06 (radians) (118 degrees) <em><strong>A1 N2</strong></em></span></p>
<p><strong><em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[3 marks]</span></em></strong></p>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = 4 - 2{{\text{e}}^x}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>4</mn>
<mo>−<!-- − --></mo>
<mn>2</mn>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mi>x</mi>
</msup>
</mrow>
</math></span>. The following diagram shows part of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>.</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 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-intercept of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></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>The region enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>, the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis and the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-axis is rotated 360º about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis. Find the volume of the solid formed.</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 style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = 0">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0</mn>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="4 - 2{{\text{e}}^x} = 0">
<mn>4</mn>
<mo>−</mo>
<mn>2</mn>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mi>x</mi>
</msup>
</mrow>
<mo>=</mo>
<mn>0</mn>
</math></span></p>
<p>0.693147</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> = ln 2 (exact), 0.693 <em><strong>A1 N2</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>attempt to substitute either their correct limits or the function into formula <em><strong>(M1)</strong></em></p>
<p>involving <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^2}">
<mrow>
<msup>
<mi>f</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^{0.693} {{f^2}} ">
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mrow>
<mn>0.693</mn>
</mrow>
</msubsup>
<mrow>
<mrow>
<msup>
<mi>f</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi {\int {\left( {4 - 2{{\text{e}}^x}} \right)} ^2}{\text{d}}x">
<mi>π</mi>
<mrow>
<mo>∫</mo>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>4</mn>
<mo>−</mo>
<mn>2</mn>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mi>x</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^{{\text{ln}}\,2} {{{\left( {4 - 2{{\text{e}}^x}} \right)}^2}} ">
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mrow>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mn>2</mn>
</mrow>
</msubsup>
<mrow>
<mrow>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>4</mn>
<mo>−</mo>
<mn>2</mn>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mi>x</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</math></span></p>
<p>3.42545</p>
<p>volume = 3.43 <em><strong>A2 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \,\,{\text{sin}}\,\left( {{e^x}} \right)">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>sin</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mi>e</mi>
<mi>x</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> for 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> ≤ 1.5. The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <em>x</em>-intercept of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></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>The region enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>, the<em> y</em>-axis and the <em>x</em>-axis is rotated 360° about the <em>x</em>-axis.</p>
<p>Find the volume of the solid formed.</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 style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>valid approach <em><strong>(M1)</strong></em><br><em>eg </em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = 0,\,\,\,\,{e^x} = 180">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mi>e</mi>
<mi>x</mi>
</msup>
</mrow>
<mo>=</mo>
<mn>180</mn>
</math></span> or 0…</p>
<p>1.14472</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = {\text{ln}}\,\pi ">
<mi>x</mi>
<mo>=</mo>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>π</mi>
</math></span> (exact), 1.14 <em><strong>A1 N2</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>attempt to substitute either their <strong>limits</strong> or the function into formula involving <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^2}">
<mrow>
<msup>
<mi>f</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span>. <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\int_0^{1.14} {{f^2},\,\,\pi \int {\left( {{\text{sin}}\,\left( {{e^x}} \right)} \right)} } ^2}dx,\,\,0.795135">
<mrow>
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mrow>
<mn>1.14</mn>
</mrow>
</msubsup>
<msup>
<mrow>
<mrow>
<msup>
<mi>f</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>π</mi>
<mo>∫</mo>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mtext>sin</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mi>e</mi>
<mi>x</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mi>d</mi>
<mi>x</mi>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>0.795135</mn>
</math></span></p>
<p>2.49799</p>
<p>volume = 2.50 <em><strong> A2 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <em>g</em>(<em>x</em>) = −(<em>x</em> − 1)<sup>2</sup> + 5.</p>
</div>
<div class="specification">
<p>Let <em>f</em>(<em>x</em>) = x<sup>2</sup>. The following diagram shows part of the graph of <em>f</em>.</p>
<p><img src="data:image/png;base64,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"></p>
<p>The graph of <em>g</em> intersects the graph of <em>f</em> at <em>x</em> = −1 and <em>x</em> = 2.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the coordinates of the vertex of the graph of <em>g</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>On the grid above, sketch the graph of g for −2 ≤ <em>x</em> ≤ 4.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of the region enclosed by the graphs of <em>f</em> and <em>g</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 style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>(1,5) (exact) <em><strong> A1 N1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img 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"> <em><strong> A1A1A1 N3</strong></em></p>
<p><strong>Note:</strong> The shape must be a concave-down parabola.<br>Only if the shape is correct, award the following for points in circles:<br><em><strong>A1</strong></em> for vertex,<br><em><strong>A1 </strong></em>for correct intersection points,<br><em><strong>A1 </strong></em>for correct endpoints.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>integrating and subtracting functions (in any order) <em><strong>(M1)</strong></em><br><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int {f - g} ">
<mo>∫</mo>
<mrow>
<mi>f</mi>
<mo>−</mo>
<mi>g</mi>
</mrow>
</math></span></p>
<p>correct substitution of limits or functions (accept missing d<em>x</em>, but do not accept any errors, including extra bits) <em><strong>(A1)</strong></em><br>eg <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_{ - 1}^2 {g - f,\,\,\int { - {{\left( {x - 1} \right)}^2}} } + 5 - {x^2}">
<msubsup>
<mo>∫</mo>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
<mn>2</mn>
</msubsup>
<mrow>
<mi>g</mi>
<mo>−</mo>
<mi>f</mi>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mo>∫</mo>
<mrow>
<mo>−</mo>
<mrow>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mrow>
<mo>+</mo>
<mn>5</mn>
<mo>−</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span></p>
<p>area = 9 (exact) <em><strong>A1 N2</strong></em></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>Haruka has an eco-friendly bag in the shape of a cuboid with width 12 cm, length 36 cm and height of 9 cm. The bag is made from five rectangular pieces of cloth and is open at the top.</p>
<p> </p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>Nanako decides to make her own eco-friendly bag in the shape of a cuboid such that the surface area is minimized.</p>
<p>The width of Nanako’s bag is <em>x </em>cm, its length is three times its width and its height is <em>y </em>cm.</p>
<p> </p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">The volume of Nanako’s bag is 3888 cm<sup>3</sup>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the area of cloth, in cm<sup>2</sup>, needed to make Haruka’s bag.</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 volume, in cm<sup>3</sup>, of the bag.</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>Use this value to write down, and simplify, the equation in<em> x</em> and <em>y</em> for the volume of Nanako’s bag.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down and simplify an expression in <em>x</em> and <em>y</em> for the area of cloth, <em>A</em>, used to make Nanako’s bag.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your answers to parts (c) and (d) to show that</p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = 3{x^2} + \frac{{10368}}{x}">
<mi>A</mi>
<mo>=</mo>
<mn>3</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mfrac>
<mrow>
<mn>10368</mn>
</mrow>
<mi>x</mi>
</mfrac>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{d}}A}}{{{\text{d}}x}}">
<mfrac>
<mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>A</mi>
</mrow>
<mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
</mrow>
</mfrac>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your answer to part (f) to show that the width of Nanako’s bag is 12 cm.</p>
<div class="marks">[3]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The cloth used to make Nanako’s bag costs 4 Japanese Yen (JPY) per cm<sup>2</sup>.</p>
<p>Find the cost of the cloth used to make Nanako’s bag.</p>
<div class="marks">[2]</div>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>36 × 12 + 2(9 ×12) + 2(9 × 36) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into surface area of cuboid formula.</p>
<p> </p>
<p>= 1300 (cm<sup>2</sup>) (1296 (cm<sup>2</sup>)) <em><strong>(A1)(G2)</strong></em></p>
<p> </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>36 × 9 ×12 <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into volume of cuboid formula.</p>
<p> </p>
<p>= 3890 (cm<sup>3</sup>) (3888 (cm<sup>3</sup>)) <em><strong>(A1)(G2)</strong></em></p>
<p> </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<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> × <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> × <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> = 3888 <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into volume of cuboid formula and equated to 3888.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span><sup>2</sup><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> = 1296 <em><strong>(A1)(G2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct fully simplified volume of cuboid.</p>
<p>Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = \frac{{1296}}{{{x^2}}}">
<mi>y</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>1296</mn>
</mrow>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span>.</p>
<p> </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>(<em>A</em> =) 3<em>x</em><sup>2</sup> + 2(<em>xy</em>) + 2(3<em>xy</em>) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into surface area of cuboid formula.</p>
<p> </p>
<p>(<em>A</em> =) 3<em>x</em><sup>2</sup> + 8<em>xy <strong>(A1)(G2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct simplified surface area of cuboid formula.</p>
<p> </p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = 3{x^2} + 8x\left( {\frac{{1296}}{{{x^2}}}} \right)">
<mi>A</mi>
<mo>=</mo>
<mn>3</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>8</mn>
<mi>x</mi>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>1296</mn>
</mrow>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(M1)</strong></em></p>
<p><strong>Note: </strong>Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for correct rearrangement of their part (c) seen (rearrangement may be seen in part(c)), award <em><strong>(M1)</strong></em> for substitution of their part (c) into their part (d) but only if this leads to the given answer, which must be shown.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = 3{x^2} + \frac{{10368}}{x}">
<mi>A</mi>
<mo>=</mo>
<mn>3</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mfrac>
<mrow>
<mn>10368</mn>
</mrow>
<mi>x</mi>
</mfrac>
</math></span> <em><strong>(AG)</strong></em> </p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{{{\text{d}}A}}{{{\text{d}}x}}} \right) = 6x - \frac{{10368}}{{{x^2}}}">
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>A</mi>
</mrow>
<mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>6</mn>
<mi>x</mi>
<mo>−</mo>
<mfrac>
<mrow>
<mn>10368</mn>
</mrow>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> <em><strong>(A1)</strong></em><em><strong>(A1)</strong></em><em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6x">
<mn>6</mn>
<mi>x</mi>
</math></span>, <em><strong>(A1)</strong></em> for −10368, <em><strong>(A1)</strong></em> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^{ - 2}}">
<mrow>
<msup>
<mi>x</mi>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
</msup>
</mrow>
</math></span>. Award a maximum of <em><strong>(A1)</strong></em><em><strong>(A1)</strong></em><em><strong>(A0)</strong></em> if any extra terms seen.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6x - \frac{{10368}}{{{x^2}}} = 0">
<mn>6</mn>
<mi>x</mi>
<mo>−</mo>
<mfrac>
<mrow>
<mn>10368</mn>
</mrow>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0</mn>
</math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for equating their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{{{\text{d}}A}}{{{\text{d}}x}}}">
<mrow>
<mfrac>
<mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>A</mi>
</mrow>
<mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
</mrow>
</mfrac>
</mrow>
</math></span> to zero.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6{x^3} = 10368">
<mn>6</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>=</mo>
<mn>10368</mn>
</math></span> <strong>OR</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6{x^3} - 10368 = 0">
<mn>6</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>10368</mn>
<mo>=</mo>
<mn>0</mn>
</math></span> <strong>OR </strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^3} - 1728 = 0">
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>1728</mn>
<mo>=</mo>
<mn>0</mn>
</math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly rearranging their equation so that fractions are removed.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = \sqrt[3]{{1728}}">
<mi>x</mi>
<mo>=</mo>
<mroot>
<mrow>
<mn>1728</mn>
</mrow>
<mn>3</mn>
</mroot>
</math></span> <em><strong>(A1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 12">
<mi>x</mi>
<mo>=</mo>
<mn>12</mn>
</math></span> (cm) <em><strong>(AG)</strong></em></p>
<p><strong>Note:</strong> The <em><strong>(AG)</strong></em> line must be seen for the final <em><strong>(A1)</strong></em> to be awarded. Substituting <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 12">
<mi>x</mi>
<mo>=</mo>
<mn>12</mn>
</math></span> invalidates the method, award a maximum of <em><strong>(M1)(M0)(A0)</strong></em>.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {3{{\left( {12} \right)}^2} + \frac{{10368}}{{12}}} \right) \times 4">
<mrow>
<mo>(</mo>
<mrow>
<mn>3</mn>
<mrow>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>12</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mfrac>
<mrow>
<mn>10368</mn>
</mrow>
<mrow>
<mn>12</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>×</mo>
<mn>4</mn>
</math></span> <em><strong>(M1)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting 12 into the area formula and for multiplying the area formula by 4.</p>
<p> </p>
<p>= 5180 (JPY) (5184 (JPY)) <em><strong>(A1)(G2)</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {x^2}{{\text{e}}^{3x}}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mn>3</mn>
<mi>x</mi>
</mrow>
</msup>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \in \mathbb{R}">
<mi>x</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'\left( x \right)"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></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>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> has a horizontal tangent line at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0"> <mi>x</mi> <mo>=</mo> <mn>0</mn> </math></span> and at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = a"> <mi>x</mi> <mo>=</mo> <mi>a</mi> </math></span>. Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a"> <mi>a</mi> </math></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 style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>choosing product rule <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="uv' + vu'"> <mi>u</mi> <msup> <mi>v</mi> <mo>′</mo> </msup> <mo>+</mo> <mi>v</mi> <msup> <mi>u</mi> <mo>′</mo> </msup> </math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\left( {{x^2}} \right)^\prime }\left( {{{\text{e}}^{3x}}} \right) + {\left( {{{\text{e}}^{3x}}} \right)^\prime }{x^2}"> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> </mrow> <mo>)</mo> </mrow> <mi mathvariant="normal">′</mi> </msup> </mrow> <mrow> <mo>(</mo> <mrow> <mrow> <msup> <mrow> <mtext>e</mtext> </mrow> <mrow> <mn>3</mn> <mi>x</mi> </mrow> </msup> </mrow> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mrow> <msup> <mrow> <mtext>e</mtext> </mrow> <mrow> <mn>3</mn> <mi>x</mi> </mrow> </msup> </mrow> </mrow> <mo>)</mo> </mrow> <mi mathvariant="normal">′</mi> </msup> </mrow> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> </math></span></p>
<p>correct derivatives (must be seen in the rule) <em><strong>A1A1</strong></em></p>
<p>eg <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2x"> <mn>2</mn> <mi>x</mi> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{3}}{{\text{e}}^{3x}}"> <mrow> <mtext>3</mtext> </mrow> <mrow> <msup> <mrow> <mtext>e</mtext> </mrow> <mrow> <mn>3</mn> <mi>x</mi> </mrow> </msup> </mrow> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'\left( x \right) = 2x{{\text{e}}^{3x}} + 3{x^2}{{\text{e}}^{3x}}"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>2</mn> <mi>x</mi> <mrow> <msup> <mrow> <mtext>e</mtext> </mrow> <mrow> <mn>3</mn> <mi>x</mi> </mrow> </msup> </mrow> <mo>+</mo> <mn>3</mn> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> <mrow> <msup> <mrow> <mtext>e</mtext> </mrow> <mrow> <mn>3</mn> <mi>x</mi> </mrow> </msup> </mrow> </math></span> <em><strong>A1 N4</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid method <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'\left( x \right) = 0"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </math></span>, <img src="data:image/png;base64,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">, <img src="data:image/png;base64,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"></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = - 0.667\left( { = - \frac{2}{3}} \right)"> <mi>a</mi> <mo>=</mo> <mo>−</mo> <mn>0.667</mn> <mrow> <mo>(</mo> <mrow> <mo>=</mo> <mo>−</mo> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </math></span> (accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - 0.667"> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mn>0.667</mn> </math></span>) <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</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>Let <em>f</em>(<em>x</em>) = ln <em>x</em> − 5<em>x</em> , for <em>x</em> > 0 .</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <em>f '</em>(<em>x</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 <em>f "</em>(<em>x</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>Solve<em> f '</em>(<em>x</em>)<em> = f "</em>(<em>x</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 style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'\left( x \right) = \frac{1}{x} - 5">
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mi>x</mi>
</mfrac>
<mo>−</mo>
<mn>5</mn>
</math></span> <em><strong>A1A1 N2</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>f "</em>(<em>x</em>) = −<em>x</em><sup>−2 </sup> <em><strong>A1 N1</strong></em></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><strong>METHOD 1 (using GDC)</strong></p>
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg </em><img src="data:image/png;base64,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"></p>
<p>0.558257</p>
<p><em>x</em> = 0.558 <em><strong>A1 N2</strong></em></p>
<p><strong>Note:</strong> Do not award <em><strong>A1</strong></em> if additional answers given.</p>
<p> </p>
<p><strong>METHOD 2 (analytical)</strong></p>
<p>attempt to solve their equation <em>f '(x) = f "</em>(<em>x</em>) (do not accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{x} - 5 = - \frac{1}{{{x^2}}}">
<mfrac>
<mn>1</mn>
<mi>x</mi>
</mfrac>
<mo>−</mo>
<mn>5</mn>
<mo>=</mo>
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span>) <em><strong>(M1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="5{x^2} - x - 1 = 0,\,\,\frac{{1 \pm \sqrt {21} }}{{10}},\,\,\frac{1}{x} = \frac{{ - 1 \pm \sqrt {21} }}{2},\,\, - 0.358">
<mn>5</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mi>x</mi>
<mo>−</mo>
<mn>1</mn>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mrow>
<mn>1</mn>
<mo>±</mo>
<msqrt>
<mn>21</mn>
</msqrt>
</mrow>
<mrow>
<mn>10</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mn>1</mn>
<mi>x</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mo>−</mo>
<mn>1</mn>
<mo>±</mo>
<msqrt>
<mn>21</mn>
</msqrt>
</mrow>
<mn>2</mn>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mo>−</mo>
<mn>0.358</mn>
</math></span></p>
<p>0.558257</p>
<p><em>x</em> = 0.558 <em><strong>A1 N2</strong></em></p>
<p><strong>Note:</strong> Do not award <em><strong>A1</strong></em> if additional answers given.</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><strong>In this question distance is in centimetres and time is in seconds.</strong></p>
<p>Particle A is moving along a straight line such that its displacement from a point P, after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> seconds, is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{s_{\text{A}}} = 15 - t - 6{t^3}{{\text{e}}^{ - 0.8t}}">
<mrow>
<msub>
<mi>s</mi>
<mrow>
<mtext>A</mtext>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mn>15</mn>
<mo>−<!-- − --></mo>
<mi>t</mi>
<mo>−<!-- − --></mo>
<mn>6</mn>
<mrow>
<msup>
<mi>t</mi>
<mn>3</mn>
</msup>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mo>−<!-- − --></mo>
<mn>0.8</mn>
<mi>t</mi>
</mrow>
</msup>
</mrow>
</math></span>, 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> ≤ 25. This is shown in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>Another particle, B, moves along the same line, starting at the same time as particle A. The velocity of particle B is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_{\text{B}}} = 8 - 2t">
<mrow>
<msub>
<mi>v</mi>
<mrow>
<mtext>B</mtext>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mn>8</mn>
<mo>−<!-- − --></mo>
<mn>2</mn>
<mi>t</mi>
</math></span>, 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> ≤ 25.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the initial displacement of particle A from point P.</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 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span> when particle A first reaches point 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>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span> when particle A first changes direction.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total distance travelled by particle A in the first 3 seconds.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that particles A and B start at the same point, find the displacement function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{s_{\text{B}}}"> <mrow> <msub> <mi>s</mi> <mrow> <mtext>B</mtext> </mrow> </msub> </mrow> </math></span> for particle B.</p>
<div class="marks">[5]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the other value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span> when particles A and B meet.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{s_{\text{A}}}\left( 0 \right){\text{,}}\,\,s\left( 0 \right){\text{,}}\,\,t = 0"> <mrow> <msub> <mi>s</mi> <mrow> <mtext>A</mtext> </mrow> </msub> </mrow> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mrow> <mtext>,</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mi>s</mi> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mrow> <mtext>,</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mi>t</mi> <mo>=</mo> <mn>0</mn> </math></span></p>
<p>15 (cm) <em><strong>A1 N2</strong></em></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>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{s_{\text{A}}} = 0{\text{,}}\,\,s = 0{\text{,}}\,\,6.79321{\text{,}}\,\,14.8651"> <mrow> <msub> <mi>s</mi> <mrow> <mtext>A</mtext> </mrow> </msub> </mrow> <mo>=</mo> <mn>0</mn> <mrow> <mtext>,</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mi>s</mi> <mo>=</mo> <mn>0</mn> <mrow> <mtext>,</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>6.79321</mn> <mrow> <mtext>,</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>14.8651</mn> </math></span></p>
<p>2.46941</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span> = 2.47 (seconds) <em><strong>A1 N2</strong></em></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>recognizing when change in direction occurs <em><strong>(M1)</strong></em></p>
<p><em>eg</em> slope of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s"> <mi>s</mi> </math></span> changes sign, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s' = 0"> <msup> <mi>s</mi> <mo>′</mo> </msup> <mo>=</mo> <mn>0</mn> </math></span>, minimum point, 10.0144, (4.08, −4.66)</p>
<p>4.07702</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span> = 4.08 (seconds) <em><strong>A1 N2</strong></em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1 (using displacement)</strong></p>
<p>correct displacement or distance from P at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 3"> <mi>t</mi> <mo>=</mo> <mn>3</mn> </math></span> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p><em>eg</em> −2.69630, 2.69630</p>
<p>valid approach <em><strong> (M1)</strong></em></p>
<p><em>eg</em> 15 + 2.69630, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s\left( 3 \right) - s\left( 0 \right)"> <mi>s</mi> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> <mo>−</mo> <mi>s</mi> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </math></span>, −17.6963</p>
<p>17.6963</p>
<p>17.7 (cm) <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><strong>METHOD 2 (using velocity)</strong></p>
<p>attempt to substitute either limits or the velocity function into distance formula involving <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| v \right|"> <mrow> <mo>|</mo> <mi>v</mi> <mo>|</mo> </mrow> </math></span> <em><strong> (M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^3 {\left| v \right|{\text{d}}t} "> <msubsup> <mo>∫</mo> <mn>0</mn> <mn>3</mn> </msubsup> <mrow> <mrow> <mo>|</mo> <mi>v</mi> <mo>|</mo> </mrow> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> </mrow> </math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int {\left| { - 1 - 18{t^2}{{\text{e}}^{ - 0.8t}} + 4.8{t^3}{{\text{e}}^{ - 0.8t}}} \right|} "> <mo>∫</mo> <mrow> <mrow> <mo>|</mo> <mrow> <mo>−</mo> <mn>1</mn> <mo>−</mo> <mn>18</mn> <mrow> <msup> <mi>t</mi> <mn>2</mn> </msup> </mrow> <mrow> <msup> <mrow> <mtext>e</mtext> </mrow> <mrow> <mo>−</mo> <mn>0.8</mn> <mi>t</mi> </mrow> </msup> </mrow> <mo>+</mo> <mn>4.8</mn> <mrow> <msup> <mi>t</mi> <mn>3</mn> </msup> </mrow> <mrow> <msup> <mrow> <mtext>e</mtext> </mrow> <mrow> <mo>−</mo> <mn>0.8</mn> <mi>t</mi> </mrow> </msup> </mrow> </mrow> <mo>|</mo> </mrow> </mrow> </math></span></p>
<p>17.6963</p>
<p>17.7 (cm) <em><strong>A1 N2</strong></em></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognize the need to integrate velocity <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int {v\left( t \right)} "> <mo>∫</mo> <mrow> <mi>v</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="8t - \frac{{2{t^2}}}{2} + c"> <mn>8</mn> <mi>t</mi> <mo>−</mo> <mfrac> <mrow> <mn>2</mn> <mrow> <msup> <mi>t</mi> <mn>2</mn> </msup> </mrow> </mrow> <mn>2</mn> </mfrac> <mo>+</mo> <mi>c</mi> </math></span> (accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span> instead of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span> and missing <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c"> <mi>c</mi> </math></span>) <em><strong>(A2)</strong></em></p>
<p>substituting initial condition into their integrated expression (must have <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c"> <mi>c</mi> </math></span>) <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="15 = 8\left( 0 \right) - \frac{{2{{\left( 0 \right)}^2}}}{2} + c"> <mn>15</mn> <mo>=</mo> <mn>8</mn> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>−</mo> <mfrac> <mrow> <mn>2</mn> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> </mrow> <mn>2</mn> </mfrac> <mo>+</mo> <mi>c</mi> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c = 15"> <mi>c</mi> <mo>=</mo> <mn>15</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{s_{\text{B}}}\left( t \right) = 8t - {t^2} + 15"> <mrow> <msub> <mi>s</mi> <mrow> <mtext>B</mtext> </mrow> </msub> </mrow> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>8</mn> <mi>t</mi> <mo>−</mo> <mrow> <msup> <mi>t</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mn>15</mn> </math></span> <em><strong>A1 N3</strong></em></p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{s_{\text{A}}} = {s_{\text{B}}}"> <mrow> <msub> <mi>s</mi> <mrow> <mtext>A</mtext> </mrow> </msub> </mrow> <mo>=</mo> <mrow> <msub> <mi>s</mi> <mrow> <mtext>B</mtext> </mrow> </msub> </mrow> </math></span>, sketch, (9.30404, 2.86710)</p>
<p>9.30404</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 9.30"> <mi>t</mi> <mo>=</mo> <mn>9.30</mn> </math></span> (seconds) <strong><em>A1 N2</em></strong></p>
<p><strong>Note:</strong> If candidates obtain <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{s_{\text{B}}}\left( t \right) = 8t - {t^2}"> <mrow> <msub> <mi>s</mi> <mrow> <mtext>B</mtext> </mrow> </msub> </mrow> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>8</mn> <mi>t</mi> <mo>−</mo> <mrow> <msup> <mi>t</mi> <mn>2</mn> </msup> </mrow> </math></span> in part (e)(i), there are 2 solutions for part (e)(ii), 1.32463 and 7.79009. Award the last <em><strong>A1</strong></em> in part (e)(ii) only if both solutions are given.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>Note: In this question, distance is in metres and time is in seconds.</strong></p>
<p>A particle P moves in a straight line for five seconds. Its acceleration at time <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 3{t^2} - 14t + 8">
<mi>a</mi>
<mo>=</mo>
<mn>3</mn>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mn>14</mn>
<mi>t</mi>
<mo>+</mo>
<mn>8</mn>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 5">
<mn>0</mn>
<mo>⩽<!-- ⩽ --></mo>
<mi>t</mi>
<mo>⩽<!-- ⩽ --></mo>
<mn>5</mn>
</math></span>.</p>
</div>
<div class="specification">
<p>When <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 0">
<mi>t</mi>
<mo>=</mo>
<mn>0</mn>
</math></span>, the velocity of P is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3{\text{ m}}\,{{\text{s}}^{ - 1}}">
<mn>3</mn>
<mrow>
<mtext> m</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mrow>
<mtext>s</mtext>
</mrow>
<mrow>
<mo>−<!-- − --></mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span> when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 0"> <mi>a</mi> <mo>=</mo> <mn>0</mn> </math></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>Hence or otherwise, find all possible values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span> for which the velocity of P is decreasing.</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 an expression for the velocity of P at time <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total distance travelled by P when its velocity is increasing.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = \frac{2}{3}{\text{ (exact), }}0.667,{\text{ }}t = 4"> <mi>t</mi> <mo>=</mo> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> <mrow> <mtext> (exact), </mtext> </mrow> <mn>0.667</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>t</mi> <mo>=</mo> <mn>4</mn> </math></span> <strong> <em>A1A1 N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v"> <mi>v</mi> </math></span> is decreasing when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a"> <mi>a</mi> </math></span> is negative <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a < 0,{\text{ }}3{t^2} - 14t + 8 \leqslant 0"> <mi>a</mi> <mo><</mo> <mn>0</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>3</mn> <mrow> <msup> <mi>t</mi> <mn>2</mn> </msup> </mrow> <mo>−</mo> <mn>14</mn> <mi>t</mi> <mo>+</mo> <mn>8</mn> <mo>⩽</mo> <mn>0</mn> </math></span>, sketch of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a"> <mi>a</mi> </math></span></p>
<p>correct interval <strong><em>A1 N2</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{2}{3} < t < 4"> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> <mo><</mo> <mi>t</mi> <mo><</mo> <mn>4</mn> </math></span></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>valid approach (do not accept a definite integral) <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v\int a "> <mi>v</mi> <mo>∫</mo> <mi>a</mi> </math></span></p>
<p>correct integration (accept missing <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c"> <mi>c</mi> </math></span>) <strong><em>(A1)(A1)(A1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{t^3} - 7{t^2} + 8t + c"> <mrow> <msup> <mi>t</mi> <mn>3</mn> </msup> </mrow> <mo>−</mo> <mn>7</mn> <mrow> <msup> <mi>t</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mn>8</mn> <mi>t</mi> <mo>+</mo> <mi>c</mi> </math></span></p>
<p>substituting <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 0,{\text{ }}v = 3"> <mi>t</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>v</mi> <mo>=</mo> <mn>3</mn> </math></span> , (must have <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c"> <mi>c</mi> </math></span>) <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3 = {0^3} - 7({0^2}) + 8(0) + c,{\text{ }}c = 3"> <mn>3</mn> <mo>=</mo> <mrow> <msup> <mn>0</mn> <mn>3</mn> </msup> </mrow> <mo>−</mo> <mn>7</mn> <mo stretchy="false">(</mo> <mrow> <msup> <mn>0</mn> <mn>2</mn> </msup> </mrow> <mo stretchy="false">)</mo> <mo>+</mo> <mn>8</mn> <mo stretchy="false">(</mo> <mn>0</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mi>c</mi> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>c</mi> <mo>=</mo> <mn>3</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = {t^3} - 7{t^2} + 8t + 3"> <mi>v</mi> <mo>=</mo> <mrow> <msup> <mi>t</mi> <mn>3</mn> </msup> </mrow> <mo>−</mo> <mn>7</mn> <mrow> <msup> <mi>t</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mn>8</mn> <mi>t</mi> <mo>+</mo> <mn>3</mn> </math></span> <strong><em>A1 N6</em></strong></p>
<p><strong><em>[6 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v"> <mi>v</mi> </math></span> increases outside the interval found in part (b) <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 < t < \frac{2}{3},{\text{ }}4 < t < 5"> <mn>0</mn> <mo><</mo> <mi>t</mi> <mo><</mo> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>4</mn> <mo><</mo> <mi>t</mi> <mo><</mo> <mn>5</mn> </math></span>, diagram</p>
<p>one correct substitution into distance formula <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^{\frac{2}{3}} {\left| v \right|,{\text{ }}\int_4^5 {\left| v \right|} ,{\text{ }}\int_{\frac{2}{3}}^4 {\left| v \right|} ,{\text{ }}\int_0^5 {\left| v \right|} } "> <msubsup> <mo>∫</mo> <mn>0</mn> <mrow> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> </mrow> </msubsup> <mrow> <mrow> <mo>|</mo> <mi>v</mi> <mo>|</mo> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <msubsup> <mo>∫</mo> <mn>4</mn> <mn>5</mn> </msubsup> <mrow> <mrow> <mo>|</mo> <mi>v</mi> <mo>|</mo> </mrow> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <msubsup> <mo>∫</mo> <mrow> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> </mrow> <mn>4</mn> </msubsup> <mrow> <mrow> <mo>|</mo> <mi>v</mi> <mo>|</mo> </mrow> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <msubsup> <mo>∫</mo> <mn>0</mn> <mn>5</mn> </msubsup> <mrow> <mrow> <mo>|</mo> <mi>v</mi> <mo>|</mo> </mrow> </mrow> </mrow> </math></span></p>
<p>one correct pair <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math>3.13580 and 11.0833, 20.9906 and 35.2097</p>
<p>14.2191 <strong><em>A1 N2</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d = 14.2{\text{ (m)}}"> <mi>d</mi> <mo>=</mo> <mn>14.2</mn> <mrow> <mtext> (m)</mtext> </mrow> </math></span></p>
<p><strong><em>[4 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>A particle P moves along a straight line. Its velocity <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_{\text{P}}}{\text{ m}}\,{{\text{s}}^{ - 1}}">
<mrow>
<msub>
<mi>v</mi>
<mrow>
<mtext>P</mtext>
</mrow>
</msub>
</mrow>
<mrow>
<mtext> m</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mrow>
<mtext>s</mtext>
</mrow>
<mrow>
<mo>−<!-- − --></mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</math></span> after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> seconds is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_{\text{P}}} = \sqrt t \sin \left( {\frac{\pi }{2}t} \right)">
<mrow>
<msub>
<mi>v</mi>
<mrow>
<mtext>P</mtext>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<msqrt>
<mi>t</mi>
</msqrt>
<mi>sin</mi>
<mo><!-- --></mo>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mi>π<!-- π --></mi>
<mn>2</mn>
</mfrac>
<mi>t</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 8">
<mn>0</mn>
<mo>⩽<!-- ⩽ --></mo>
<mi>t</mi>
<mo>⩽<!-- ⩽ --></mo>
<mn>8</mn>
</math></span>. The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_{\text{P}}}">
<mrow>
<msub>
<mi>v</mi>
<mrow>
<mtext>P</mtext>
</mrow>
</msub>
</mrow>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-14_om_10.04.21.png" alt="M17/5/MATME/SP2/ENG/TZ1/07"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the first value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span> at which P changes direction.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <strong>total </strong>distance travelled by P, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 8"> <mn>0</mn> <mo>⩽</mo> <mi>t</mi> <mo>⩽</mo> <mn>8</mn> </math></span>.</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>A second particle Q also moves along a straight line. Its velocity, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_{\text{Q}}}{\text{ m}}\,{{\text{s}}^{ - 1}}"> <mrow> <msub> <mi>v</mi> <mrow> <mtext>Q</mtext> </mrow> </msub> </mrow> <mrow> <mtext> m</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <msup> <mrow> <mtext>s</mtext> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></span> after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span> seconds is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_{\text{Q}}} = \sqrt t "> <mrow> <msub> <mi>v</mi> <mrow> <mtext>Q</mtext> </mrow> </msub> </mrow> <mo>=</mo> <msqrt> <mi>t</mi> </msqrt> </math></span> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 8"> <mn>0</mn> <mo>⩽</mo> <mi>t</mi> <mo>⩽</mo> <mn>8</mn> </math></span>. After <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span> seconds Q has travelled the same total distance as P.</p>
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></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 class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 2"> <mi>t</mi> <mo>=</mo> <mn>2</mn> </math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>substitution of limits or function into formula or correct sum <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^8 {\left| v \right|{\text{d}}t,{\text{ }}\int {\left| {{v_Q}} \right|{\text{d}}t,{\text{ }}\int_0^2 {v{\text{d}}t - \int_2^4 {v{\text{d}}t + \int_4^6 {v{\text{d}}t - \int_6^8 {v{\text{d}}t} } } } } } "> <msubsup> <mo>∫</mo> <mn>0</mn> <mn>8</mn> </msubsup> <mrow> <mrow> <mo>|</mo> <mi>v</mi> <mo>|</mo> </mrow> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mo>∫</mo> <mrow> <mrow> <mo>|</mo> <mrow> <mrow> <msub> <mi>v</mi> <mi>Q</mi> </msub> </mrow> </mrow> <mo>|</mo> </mrow> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <msubsup> <mo>∫</mo> <mn>0</mn> <mn>2</mn> </msubsup> <mrow> <mi>v</mi> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> <mo>−</mo> <msubsup> <mo>∫</mo> <mn>2</mn> <mn>4</mn> </msubsup> <mrow> <mi>v</mi> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> <mo>+</mo> <msubsup> <mo>∫</mo> <mn>4</mn> <mn>6</mn> </msubsup> <mrow> <mi>v</mi> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> <mo>−</mo> <msubsup> <mo>∫</mo> <mn>6</mn> <mn>8</mn> </msubsup> <mrow> <mi>v</mi> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </math></span></p>
<p>9.64782</p>
<p>distance <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 9.65{\text{ (metres)}}"> <mo>=</mo> <mn>9.65</mn> <mrow> <mtext> (metres)</mtext> </mrow> </math></span> <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct approach <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s = \int {\sqrt t ,{\text{ }}\int_0^k {\sqrt t } } {\text{d}}t,{\text{ }}\int_0^k {\left| {{v_{\text{Q}}}} \right|{\text{d}}t} "> <mi>s</mi> <mo>=</mo> <mo>∫</mo> <mrow> <msqrt> <mi>t</mi> </msqrt> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <msubsup> <mo>∫</mo> <mn>0</mn> <mi>k</mi> </msubsup> <mrow> <msqrt> <mi>t</mi> </msqrt> </mrow> </mrow> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <msubsup> <mo>∫</mo> <mn>0</mn> <mi>k</mi> </msubsup> <mrow> <mrow> <mo>|</mo> <mrow> <mrow> <msub> <mi>v</mi> <mrow> <mtext>Q</mtext> </mrow> </msub> </mrow> </mrow> <mo>|</mo> </mrow> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> </mrow> </math></span></p>
<p>correct integration <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int {\sqrt t = \frac{2}{3}{t^{\frac{3}{2}}} + c,{\text{ }}\left[ {\frac{2}{3}{x^{\frac{3}{2}}}} \right]_0^k,{\text{ }}\frac{2}{3}{k^{\frac{3}{2}}}} "> <mo>∫</mo> <mrow> <msqrt> <mi>t</mi> </msqrt> <mo>=</mo> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> <mrow> <msup> <mi>t</mi> <mrow> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </mrow> </msup> </mrow> <mo>+</mo> <mi>c</mi> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <msubsup> <mrow> <mo>[</mo> <mrow> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> <mrow> <msup> <mi>x</mi> <mrow> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </mrow> </msup> </mrow> </mrow> <mo>]</mo> </mrow> <mn>0</mn> <mi>k</mi> </msubsup> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> <mrow> <msup> <mi>k</mi> <mrow> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </mrow> </msup> </mrow> </mrow> </math></span></p>
<p>equating their expression to the distance travelled by their P <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{2}{3}{k^{\frac{3}{2}}} = 9.65,{\text{ }}\int_0^k {\sqrt t {\text{d}}t = 9.65} "> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> <mrow> <msup> <mi>k</mi> <mrow> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </mrow> </msup> </mrow> <mo>=</mo> <mn>9.65</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <msubsup> <mo>∫</mo> <mn>0</mn> <mi>k</mi> </msubsup> <mrow> <msqrt> <mi>t</mi> </msqrt> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> <mo>=</mo> <mn>9.65</mn> </mrow> </math></span></p>
<p>5.93855</p>
<p>5.94 (seconds) <strong><em>A1</em></strong> <strong><em>N3</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A particle P starts from a point A and moves along a horizontal straight line. Its velocity <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v{\text{ cm}}\,{{\text{s}}^{ - 1}}">
<mi>v</mi>
<mrow>
<mtext> cm</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mrow>
<mtext>s</mtext>
</mrow>
<mrow>
<mo>−<!-- − --></mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</math></span> after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> seconds is given by</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="v(t) = \left\{ {\begin{array}{*{20}{l}} { - 2t + 2,}&{{\text{for }}0 \leqslant t \leqslant 1} \\ {3\sqrt t + \frac{4}{{{t^2}}} - 7,}&{{\text{for }}1 \leqslant t \leqslant 12} \end{array}} \right.">
<mi>v</mi>
<mo stretchy="false">(</mo>
<mi>t</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mrow>
<mo>{</mo>
<mrow>
<mtable columnalign="left" rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mo>−<!-- − --></mo>
<mn>2</mn>
<mi>t</mi>
<mo>+</mo>
<mn>2</mn>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mrow>
<mtext>for </mtext>
</mrow>
<mn>0</mn>
<mo>⩽<!-- ⩽ --></mo>
<mi>t</mi>
<mo>⩽<!-- ⩽ --></mo>
<mn>1</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>3</mn>
<msqrt>
<mi>t</mi>
</msqrt>
<mo>+</mo>
<mfrac>
<mn>4</mn>
<mrow>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>−<!-- − --></mo>
<mn>7</mn>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mrow>
<mtext>for </mtext>
</mrow>
<mn>1</mn>
<mo>⩽<!-- ⩽ --></mo>
<mi>t</mi>
<mo>⩽<!-- ⩽ --></mo>
<mn>12</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
<mo fence="true" stretchy="true" symmetric="true"></mo>
</mrow>
</math></span></p>
<p>The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v">
<mi>v</mi>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-03_om_16.40.29.png" alt="N16/5/MATME/SP2/ENG/TZ0/09"></p>
</div>
<div class="specification">
<p>P is at rest when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 1">
<mi>t</mi>
<mo>=</mo>
<mn>1</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = p">
<mi>t</mi>
<mo>=</mo>
<mi>p</mi>
</math></span>.</p>
</div>
<div class="specification">
<p>When <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = q">
<mi>t</mi>
<mo>=</mo>
<mi>q</mi>
</math></span>, the acceleration of P is zero.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the initial velocity of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P"> <mi>P</mi> </math></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>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></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>(i) Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q"> <mi>q</mi> </math></span>.</p>
<p>(ii) Hence, find the <strong>speed </strong>of P when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = q"> <mi>t</mi> <mo>=</mo> <mi>q</mi> </math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) Find the total distance travelled by P between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 1"> <mi>t</mi> <mo>=</mo> <mn>1</mn> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = p"> <mi>t</mi> <mo>=</mo> <mi>p</mi> </math></span>.</p>
<p>(ii) Hence or otherwise, find the displacement of P from A when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = p"> <mi>t</mi> <mo>=</mo> <mi>p</mi> </math></span>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>valid attempt to substitute <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 0"> <mi>t</mi> <mo>=</mo> <mn>0</mn> </math></span> into the correct function <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 2(0) + 2"> <mo>−</mo> <mn>2</mn> <mo stretchy="false">(</mo> <mn>0</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mn>2</mn> </math></span></p>
<p>2 <strong><em>A1 N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = 0"> <mi>v</mi> <mo>=</mo> <mn>0</mn> </math></span> when P is at rest <strong><em>(M1)</em></strong></p>
<p>5.21834</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = 5.22{\text{ }}({\text{seconds}})"> <mi>p</mi> <mo>=</mo> <mn>5.22</mn> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mrow> <mtext>seconds</mtext> </mrow> <mo stretchy="false">)</mo> </math></span> <strong><em>A1 N2</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>(i) recognizing that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = v'"> <mi>a</mi> <mo>=</mo> <msup> <mi>v</mi> <mo>′</mo> </msup> </math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v' = 0"> <msup> <mi>v</mi> <mo>′</mo> </msup> <mo>=</mo> <mn>0</mn> </math></span>, minimum on graph</p>
<p>1.95343</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q = 1.95"> <mi>q</mi> <mo>=</mo> <mn>1.95</mn> </math></span> <strong><em>A1 N2</em></strong></p>
<p>(ii) valid approach to find <strong>their </strong>minimum <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v(q),{\text{ }} - 1.75879"> <mi>v</mi> <mo stretchy="false">(</mo> <mi>q</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mo>−</mo> <mn>1.75879</mn> </math></span>, reference to min on graph</p>
<p>1.75879</p>
<p>speed <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 1.76{\text{ }}(c\,{\text{m}}\,{{\text{s}}^{ - 1}})"> <mo>=</mo> <mn>1.76</mn> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mi>c</mi> <mspace width="thinmathspace"></mspace> <mrow> <mtext>m</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <msup> <mrow> <mtext>s</mtext> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mo stretchy="false">)</mo> </math></span> <strong><em>A1 N2</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) substitution of <strong>correct</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v(t)"> <mi>v</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </math></span> into distance formula, <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_1^p {\left| {3\sqrt t + \frac{4}{{{t^2}}} - 7} \right|{\text{d}}t,{\text{ }}\left| {\int {3\sqrt t + \frac{4}{{{t^2}}} - 7{\text{d}}t} } \right|} "> <msubsup> <mo>∫</mo> <mn>1</mn> <mi>p</mi> </msubsup> <mrow> <mrow> <mo>|</mo> <mrow> <mn>3</mn> <msqrt> <mi>t</mi> </msqrt> <mo>+</mo> <mfrac> <mn>4</mn> <mrow> <mrow> <msup> <mi>t</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> <mo>−</mo> <mn>7</mn> </mrow> <mo>|</mo> </mrow> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mrow> <mo>|</mo> <mrow> <mo>∫</mo> <mrow> <mn>3</mn> <msqrt> <mi>t</mi> </msqrt> <mo>+</mo> <mfrac> <mn>4</mn> <mrow> <mrow> <msup> <mi>t</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> <mo>−</mo> <mn>7</mn> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> </mrow> </mrow> <mo>|</mo> </mrow> </mrow> </math></span></p>
<p>4.45368</p>
<p>distance <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 4.45{\text{ }}({\text{cm}})"> <mo>=</mo> <mn>4.45</mn> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mrow> <mtext>cm</mtext> </mrow> <mo stretchy="false">)</mo> </math></span> <strong><em>A1 N2</em></strong></p>
<p>(ii) displacement from <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 1"> <mi>t</mi> <mo>=</mo> <mn>1</mn> </math></span> to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = p"> <mi>t</mi> <mo>=</mo> <mi>p</mi> </math></span> (seen anywhere) <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 4.45368,{\text{ }}\int_1^p {\left( {3\sqrt t + \frac{4}{{{t^2}}} - 7} \right){\text{d}}t} "> <mo>−</mo> <mn>4.45368</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <msubsup> <mo>∫</mo> <mn>1</mn> <mi>p</mi> </msubsup> <mrow> <mrow> <mo>(</mo> <mrow> <mn>3</mn> <msqrt> <mi>t</mi> </msqrt> <mo>+</mo> <mfrac> <mn>4</mn> <mrow> <mrow> <msup> <mi>t</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> <mo>−</mo> <mn>7</mn> </mrow> <mo>)</mo> </mrow> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> </mrow> </math></span></p>
<p>displacement from <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 0"> <mi>t</mi> <mo>=</mo> <mn>0</mn> </math></span> to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 1"> <mi>t</mi> <mo>=</mo> <mn>1</mn> </math></span> <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^1 {( - 2t + 2){\text{d}}t,{\text{ }}0.5 \times 1 \times 2,{\text{ 1}}} "> <msubsup> <mo>∫</mo> <mn>0</mn> <mn>1</mn> </msubsup> <mrow> <mo stretchy="false">(</mo> <mo>−</mo> <mn>2</mn> <mi>t</mi> <mo>+</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>0.5</mn> <mo>×</mo> <mn>1</mn> <mo>×</mo> <mn>2</mn> <mo>,</mo> <mrow> <mtext> 1</mtext> </mrow> </mrow> </math></span></p>
<p>valid approach to find displacement for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant p"> <mn>0</mn> <mo>⩽</mo> <mi>t</mi> <mo>⩽</mo> <mi>p</mi> </math></span> <strong><em>M1</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^1 {( - 2t + 2){\text{d}}t + \int_1^p {\left( {3\sqrt t + \frac{4}{{{t^2}}} - 7} \right){\text{d}}t,{\text{ }}\int_0^1 {( - 2t + 2){\text{d}}t - 4.45} } } "> <msubsup> <mo>∫</mo> <mn>0</mn> <mn>1</mn> </msubsup> <mrow> <mo stretchy="false">(</mo> <mo>−</mo> <mn>2</mn> <mi>t</mi> <mo>+</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> <mo>+</mo> <msubsup> <mo>∫</mo> <mn>1</mn> <mi>p</mi> </msubsup> <mrow> <mrow> <mo>(</mo> <mrow> <mn>3</mn> <msqrt> <mi>t</mi> </msqrt> <mo>+</mo> <mfrac> <mn>4</mn> <mrow> <mrow> <msup> <mi>t</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> <mo>−</mo> <mn>7</mn> </mrow> <mo>)</mo> </mrow> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <msubsup> <mo>∫</mo> <mn>0</mn> <mn>1</mn> </msubsup> <mrow> <mo stretchy="false">(</mo> <mo>−</mo> <mn>2</mn> <mi>t</mi> <mo>+</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> <mo>−</mo> <mn>4.45</mn> </mrow> </mrow> </mrow> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 3.45368"> <mo>−</mo> <mn>3.45368</mn> </math></span></p>
<p>displacement <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = - 3.45{\text{ }}({\text{cm}})"> <mo>=</mo> <mo>−</mo> <mn>3.45</mn> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mrow> <mtext>cm</mtext> </mrow> <mo stretchy="false">)</mo> </math></span> <strong><em>A1 N2</em></strong></p>
<p><strong><em>[6 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>A particle moves along a straight line so that its velocity, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v">
<mi>v</mi>
</math></span> m s<sup>−1</sup>, after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> seconds is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v\left( t \right) = {1.4^t} - 2.7">
<mi>v</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mn>1.4</mn>
<mi>t</mi>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mn>2.7</mn>
</math></span>, for 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> ≤ 5.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find when the particle is at rest.</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 acceleration of the particle when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 2">
<mi>t</mi>
<mo>=</mo>
<mn>2</mn>
</math></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>Find the total distance travelled by the particle.</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 style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>valid approach <em><strong> (M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v\left( t \right) = 0">
<mi>v</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0</mn>
</math></span>, sketch of graph</p>
<p>2.95195</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = {\text{lo}}{{\text{g}}_{1.4}}2.7">
<mi>t</mi>
<mo>=</mo>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mrow>
<mn>1.4</mn>
</mrow>
</msub>
</mrow>
<mn>2.7</mn>
</math></span> (exact), <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 2.95">
<mi>t</mi>
<mo>=</mo>
<mn>2.95</mn>
</math></span> (s) <em><strong>A1 N2</strong></em></p>
<p> </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>valid approach <em><strong> (M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a\left( t \right) = v'\left( t \right)">
<mi>a</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msup>
<mi>v</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v'\left( 2 \right)">
<msup>
<mi>v</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</math></span></p>
<p>0.659485</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a\left( 2 \right)">
<mi>a</mi>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</math></span> = 1.96 ln 1.4 (exact), <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a\left( 2 \right)">
<mi>a</mi>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</math></span> = 0.659 (m s<sup>−2</sup>) <em><strong>A1 N2</strong></em></p>
<p> </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>correct approach <em><strong> (A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^5 {\left| {v\left( t \right)} \right|} \,{\text{d}}t">
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mn>5</mn>
</msubsup>
<mrow>
<mrow>
<mo>|</mo>
<mrow>
<mi>v</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
<mo>|</mo>
</mrow>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^{2.95} {\left( { - v\left( t \right)} \right)} \,{\text{d}}t + \int_{295}^5 {v\left( t \right)} \,{\text{d}}t">
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mrow>
<mn>2.95</mn>
</mrow>
</msubsup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mi>v</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
<mo>+</mo>
<msubsup>
<mo>∫</mo>
<mrow>
<mn>295</mn>
</mrow>
<mn>5</mn>
</msubsup>
<mrow>
<mi>v</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
</math></span></p>
<p>5.3479</p>
<p>distance = 5.35 (m) <em><strong>A2 N3</strong></em></p>
<p> </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>The function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{1}{3}{x^3} + \frac{1}{2}{x^2} + kx + 5">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>k</mi>
<mi>x</mi>
<mo>+</mo>
<mn>5</mn>
</math></span> has a local maximum and a local minimum. The local maximum is at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - 3">
<mi>x</mi>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mn>3</mn>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = - 6">
<mi>k</mi>
<mo>=</mo>
<mo>−</mo>
<mn>6</mn>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of the local <strong>minimum</strong>.</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 interval where the gradient of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right)">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> is negative.</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>Determine the equation of the normal at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - 2">
<mi>x</mi>
<mo>=</mo>
<mo>−</mo>
<mn>2</mn>
</math></span> in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = mx + c">
<mi>y</mi>
<mo>=</mo>
<mi>m</mi>
<mi>x</mi>
<mo>+</mo>
<mi>c</mi>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^2} + x + k">
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>x</mi>
<mo>+</mo>
<mi>k</mi>
</math></span> <em><strong> (A1)(A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for each correct term. Award at most <em><strong>(A1)(A1)(A0)</strong></em> if additional terms are seen or for an answer <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^2} + x - 6">
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>x</mi>
<mo>−</mo>
<mn>6</mn>
</math></span>. If their derivative is seen in parts (b), (c) or (d) and not in part (a), award at most <em><strong>(A1)(A1)(A0)</strong></em>.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\left( { - 3} \right)^2} + \left( { - 3} \right) + k = 0">
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>k</mi>
<mo>=</mo>
<mn>0</mn>
</math></span> <strong> <em>(M1)</em><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - 3">
<mi>x</mi>
<mo>=</mo>
<mo>−</mo>
<mn>3</mn>
</math></span> into their derivative and <em><strong>(M1)</strong></em> for setting it equal to zero. Substituting <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = - 6">
<mi>k</mi>
<mo>=</mo>
<mo>−</mo>
<mn>6</mn>
</math></span> invalidates the process, award at most (<em><strong>A1)(A1)(A1)(M0)(M0)</strong></em>.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {k = } \right) - 6">
<mrow>
<mo>(</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
</mrow>
<mo>)</mo>
</mrow>
<mo>−</mo>
<mn>6</mn>
</math></span> <em><strong>(AG)</strong></em></p>
<p><strong>Note:</strong> For the final <em><strong>(M1)</strong></em> to be awarded, no incorrect working must be seen, and must lead to the conclusion <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = - 6">
<mi>k</mi>
<mo>=</mo>
<mo>−</mo>
<mn>6</mn>
</math></span>. The final <em><strong>(AG)</strong></em> must be seen.</p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(2, −2.33) <strong>OR </strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {2{\text{,}}\,\, - \frac{7}{3}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mo>−</mo>
<mfrac>
<mn>7</mn>
<mn>3</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong> (A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for each correct coordinate. Award <em><strong>(A0)(A1)</strong></em> if parentheses are missing. Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 2">
<mi>x</mi>
<mo>=</mo>
<mn>2</mn>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = - 2.33">
<mi>y</mi>
<mo>=</mo>
<mo>−</mo>
<mn>2.33</mn>
</math></span>. Award <em><strong>(M1)(A0)</strong></em> for their derivative, a quadratic expression with –6 substituted for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span>, equated to zero but leading to an incorrect answer.</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 3 < x < 2">
<mo>−</mo>
<mn>3</mn>
<mo><</mo>
<mi>x</mi>
<mo><</mo>
<mn>2</mn>
</math></span> <em><strong> (A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x > - 3">
<mi>x</mi>
<mo>></mo>
<mo>−</mo>
<mn>3</mn>
</math></span> , <em><strong>(A1)</strong></em><strong>(ft)</strong> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x < 2">
<mi>x</mi>
<mo><</mo>
<mn>2</mn>
</math></span>. Follow through for their "2" in part (b). It is possible to award <em><strong>(A0)(A1)</strong></em>. For <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 3 < y < 2">
<mo>−</mo>
<mn>3</mn>
<mo><</mo>
<mi>y</mi>
<mo><</mo>
<mn>2</mn>
</math></span> award <em><strong>(A1)(A0)</strong></em>. Accept equivalent notation such as (−3, 2). Award <em><strong>(A0)</strong><strong>(A1)</strong></em><strong>(ft)</strong> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 3 \leqslant x \leqslant 2">
<mo>−</mo>
<mn>3</mn>
<mo>⩽</mo>
<mi>x</mi>
<mo>⩽</mo>
<mn>2</mn>
</math></span>.</p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>−4 <em><strong> (A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for the gradient of the tangent seen. If an incorrect derivative was used in part (a), then working for their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'\left( { - 2} \right)">
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> must be seen. Follow through from their derivative in part (a).</p>
<p>gradient of normal is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{4}">
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
</math></span> <em><strong> (A1)</strong></em><strong>(ft)</strong> </p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for the negative reciprocal of their gradient of tangent. Follow through within this part. Award <em><strong>(G2)</strong></em> for an unsupported gradient of the normal.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{49}}{3}">
<mfrac>
<mrow>
<mn>49</mn>
</mrow>
<mn>3</mn>
</mfrac>
</math></span> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {f\left( { - 2} \right) = \frac{1}{3}{{\left( { - 2} \right)}^3} + \frac{1}{2}{{\left( { - 2} \right)}^2} - 6\left( { - 2} \right) + 5 = \frac{{49}}{3}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
<mrow>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mrow>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>6</mn>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>5</mn>
<mo>=</mo>
<mfrac>
<mrow>
<mn>49</mn>
</mrow>
<mn>3</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong> (A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{49}}{3}">
<mfrac>
<mrow>
<mn>49</mn>
</mrow>
<mn>3</mn>
</mfrac>
</math></span> (16.3333…) seen.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{49}}{3} = \frac{1}{4}\left( { - 2} \right) + c">
<mfrac>
<mrow>
<mn>49</mn>
</mrow>
<mn>3</mn>
</mfrac>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>c</mi>
</math></span> <strong>OR </strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y - \frac{{49}}{3} = \frac{1}{4}\left( {x - - 2} \right)">
<mi>y</mi>
<mo>−</mo>
<mfrac>
<mrow>
<mn>49</mn>
</mrow>
<mn>3</mn>
</mfrac>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting their normal gradient into equation of line formula.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = \frac{1}{4}x + \frac{{101}}{6}">
<mi>y</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
<mi>x</mi>
<mo>+</mo>
<mfrac>
<mrow>
<mn>101</mn>
</mrow>
<mn>6</mn>
</mfrac>
</math></span> <strong>OR </strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 0.25x + 16.8333 \ldots ">
<mi>y</mi>
<mo>=</mo>
<mn>0.25</mn>
<mi>x</mi>
<mo>+</mo>
<mn>16.8333</mn>
<mo>…</mo>
</math></span><strong> </strong> <em><strong>(A1)</strong></em><strong>(ft)<em>(G4)</em></strong></p>
<p><strong>Note:</strong> Award <em><strong>(G4)</strong></em> for the correct equation of line in correct form without any prior working. The final <em><strong>(A1)</strong></em><strong>(ft)</strong> is contingent on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = \frac{{49}}{3}">
<mi>y</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>49</mn>
</mrow>
<mn>3</mn>
</mfrac>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - 2">
<mi>x</mi>
<mo>=</mo>
<mo>−</mo>
<mn>2</mn>
</math></span>.</p>
<p><strong><em>[5 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>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f''\left( x \right) = \left( {{\text{cos}}\,2x} \right)\left( {{\text{sin}}\,6x} \right)">
<msup>
<mi>f</mi>
<mo>″</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mtext>cos</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mn>2</mn>
<mi>x</mi>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mtext>sin</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mn>6</mn>
<mi>x</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, for 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> ≤ 1.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f''}">
<mrow>
<msup>
<mi>f</mi>
<mo>″</mo>
</msup>
</mrow>
</math></span> on the grid below:</p>
<p><img src="data:image/png;base64,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"></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 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-coordinates of the points of inflexion of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></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>Hence find the values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> for which the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> is concave-down.</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 style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><img 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"> <em><strong>A1A1A1 N3</strong></em></p>
<p><strong>Note:</strong> Only if the shape is approximately correct with exactly 2 maximums and 1 minimum on the interval 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> ≤ 0, award the following:<br><em><strong>A1</strong></em> for correct domain with both endpoints within circle and oval.<br><em><strong>A1</strong></em> for passing through the other <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-intercepts within the circles.<br><em><strong>A1</strong></em> for passing through the three turning points within circles (ignore <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-intercepts and extrema outside of the domain).</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>evidence of reasoning (may be seen on graph) <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'' = 0">
<msup>
<mi>f</mi>
<mo>″</mo>
</msup>
<mo>=</mo>
<mn>0</mn>
</math></span>, (0.524, 0), (0.785, 0)</p>
<p>0.523598, 0.785398</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0.524\,\,\left( { = \frac{\pi }{6}} \right)">
<mi>x</mi>
<mo>=</mo>
<mn>0.524</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mo>=</mo>
<mfrac>
<mi>π</mi>
<mn>6</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0.785\,\,\left( { = \frac{\pi }{4}} \right)">
<mi>x</mi>
<mo>=</mo>
<mn>0.785</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mo>=</mo>
<mfrac>
<mi>π</mi>
<mn>4</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>A1A1 N3</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>M1A1A0</strong></em> if any solution outside domain (<em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0">
<mi>x</mi>
<mo>=</mo>
<mn>0</mn>
</math></span>) is also included.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.524 < x < 0.785\,\,\,\left( {\frac{\pi }{6} < x < \frac{\pi }{4}} \right)">
<mn>0.524</mn>
<mo><</mo>
<mi>x</mi>
<mo><</mo>
<mn>0.785</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mi>π</mi>
<mn>6</mn>
</mfrac>
<mo><</mo>
<mi>x</mi>
<mo><</mo>
<mfrac>
<mi>π</mi>
<mn>4</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>A2 N2</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>A1</strong></em> if any correct interval outside domain also included, unless additional solutions already penalized in (b).<br>Award<em><strong> A0</strong></em> if any incorrect intervals are also included.</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>The population of fish in a lake is modelled by the function</p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( t \right) = \frac{{1000}}{{1 + 24{{\text{e}}^{ - 0.2t}}}}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>1000</mn>
</mrow>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mn>24</mn>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mo>−<!-- − --></mo>
<mn>0.2</mn>
<mi>t</mi>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span>, 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> ≤ 30 , where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> is measured in months.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the population of fish at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> = 10.</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 rate at which the population of fish is increasing at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> = 10.</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 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> for which the population of fish is increasing most rapidly.</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 style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>(10)</p>
<p>235.402</p>
<p>235 (fish) (must be an integer) <em><strong>A1 N2</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>recognizing rate of change is derivative <em><strong>(M1)</strong></em></p>
<p><em>eg</em> rate = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f'}">
<mrow>
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
</mrow>
</math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f'}">
<mrow>
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
</mrow>
</math></span>(10) , sketch of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f'}">
<mrow>
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
</mrow>
</math></span> , 35 (fish per month)</p>
<p>35.9976</p>
<p>36.0 (fish per month) <em><strong>A1 N2</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>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> maximum of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f'}">
<mrow>
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
</mrow>
</math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f''}">
<mrow>
<msup>
<mi>f</mi>
<mo>″</mo>
</msup>
</mrow>
</math></span> = 0</p>
<p>15.890</p>
<p>15.9 (months) <em><strong>A1 N2</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>A particle P moves along a straight line. The velocity <em>v</em> m s<sup>−1</sup> of P after <em>t</em> seconds is given by <em>v</em> (<em>t</em>) = 7 cos <em>t</em> − 5<em>t </em><sup>cos <em>t</em></sup>, for 0 ≤ <em>t</em> ≤ 7.</p>
<p>The following diagram shows the graph of <em>v</em>.</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 initial velocity of P.</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 maximum speed of P.</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>Write down the number of times that the acceleration of P is 0 m s<sup>−2</sup> .</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the acceleration of P when it changes direction.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total distance travelled by P.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>initial velocity when <em>t</em> = 0 <em><strong>(M1)</strong></em></p>
<p>eg <em>v</em>(0)</p>
<p><em>v</em> = 17 (m s<sup>−1</sup>) <em><strong>A1 N2</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>recognizing maximum speed when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| v \right|"> <mrow> <mo>|</mo> <mi>v</mi> <mo>|</mo> </mrow> </math></span> is greatest <em><strong>(M1)</strong></em></p>
<p><em>eg</em> minimum, maximum, <em>v'</em> = 0</p>
<p>one correct coordinate for minimum <em><strong>(A1)</strong></em></p>
<p><em>eg</em> 6.37896, −24.6571</p>
<p>24.7 (ms<sup>−1</sup>) <em><strong>A1 N2</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing a = <em>v </em>′ <em><strong>(M1)</strong></em></p>
<p>eg <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = \frac{{{\text{d}}v}}{{{\text{d}}t}}"> <mi>a</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>v</mi> </mrow> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> </mrow> </mfrac> </math></span>, correct derivative of first term</p>
<p>identifying when a = 0 <em><strong>(M1)</strong></em></p>
<p><em>eg</em> turning points of <em>v</em>, <em>t</em>-intercepts of <em>v </em>′</p>
<p>3 <em><strong>A1 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing P changes direction when <em>v </em>= 0 <em><strong>(M1) </strong></em></p>
<p><em>t</em> = 0.863851 <em><strong>(A1) </strong></em></p>
<p>−9.24689</p>
<p><em>a</em> = −9.25 (ms<sup>−2</sup>) <em><strong> A2 N3</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution of limits or function into formula <em><strong>(A1)</strong></em><br><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^7 {\left| {\,v\,} \right|,\,\int_0^{0.8638} {v{\text{d}}t - \int_{0.8638}^7 {v{\text{d}}t} } ,\,\,\int {\left| {\,7\,{\text{cos}}\,x - 5{x^{{\text{cos}}\,x}}\,} \right|} \,dx,\,\,3.32 = 60.6} "> <msubsup> <mo>∫</mo> <mn>0</mn> <mn>7</mn> </msubsup> <mrow> <mrow> <mo>|</mo> <mrow> <mspace width="thinmathspace"></mspace> <mi>v</mi> <mspace width="thinmathspace"></mspace> </mrow> <mo>|</mo> </mrow> <mo>,</mo> <mspace width="thinmathspace"></mspace> <msubsup> <mo>∫</mo> <mn>0</mn> <mrow> <mn>0.8638</mn> </mrow> </msubsup> <mrow> <mi>v</mi> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> <mo>−</mo> <msubsup> <mo>∫</mo> <mrow> <mn>0.8638</mn> </mrow> <mn>7</mn> </msubsup> <mrow> <mi>v</mi> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> </mrow> </mrow> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mo>∫</mo> <mrow> <mrow> <mo>|</mo> <mrow> <mspace width="thinmathspace"></mspace> <mn>7</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>x</mi> <mo>−</mo> <mn>5</mn> <mrow> <msup> <mi>x</mi> <mrow> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>x</mi> </mrow> </msup> </mrow> <mspace width="thinmathspace"></mspace> </mrow> <mo>|</mo> </mrow> </mrow> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>x</mi> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>3.32</mn> <mo>=</mo> <mn>60.6</mn> </mrow> </math></span></p>
<p>63.8874</p>
<p>63.9 (metres) <em><strong>A2 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = 6 - \ln ({x^2} + 2)">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>6</mn>
<mo>−<!-- − --></mo>
<mi>ln</mi>
<mo><!-- --></mo>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \in \mathbb{R}">
<mi>x</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>. The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> passes through the point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(p,{\text{ }}4)">
<mo stretchy="false">(</mo>
<mi>p</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>4</mn>
<mo stretchy="false">)</mo>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p > 0">
<mi>p</mi>
<mo>></mo>
<mn>0</mn>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></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>The following diagram shows part of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>.</p>
<p><img src="images/Schermafbeelding_2018-02-12_om_13.30.18.png" alt="N17/5/MATME/SP2/ENG/TZ0/05.b"></p>
<p>The region enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>, the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis and the lines <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - p">
<mi>x</mi>
<mo>=</mo>
<mo>−</mo>
<mi>p</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = p">
<mi>x</mi>
<mo>=</mo>
<mi>p</mi>
</math></span> is rotated 360° about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis. Find the volume of the solid formed.</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 style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(p) = 4">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>p</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>4</mn>
</math></span>, intersection with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 4,{\text{ }} \pm 2.32">
<mi>y</mi>
<mo>=</mo>
<mn>4</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>±</mo>
<mn>2.32</mn>
</math></span></p>
<p>2.32143</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = \sqrt {{{\text{e}}^2} - 2} ">
<mi>p</mi>
<mo>=</mo>
<msqrt>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>2</mn>
</msqrt>
</math></span> (exact), 2.32 <strong><em>A1 N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to substitute <strong>either their</strong> limits <strong>or</strong> the function into volume formula (must involve <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^2}">
<mrow>
<msup>
<mi>f</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span>, accept reversed limits and absence of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi ">
<mi>π</mi>
</math></span> and/or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{d}}x">
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
</math></span>, but do not accept any other errors) <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_{ - 2.32}^{2.32} {{f^2},{\text{ }}\pi \int {{{\left( {6 - \ln ({x^2} + 2)} \right)}^2}{\text{d}}x,{\text{ 105.675}}} } ">
<msubsup>
<mo>∫</mo>
<mrow>
<mo>−</mo>
<mn>2.32</mn>
</mrow>
<mrow>
<mn>2.32</mn>
</mrow>
</msubsup>
<mrow>
<mrow>
<msup>
<mi>f</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>π</mi>
<mo>∫</mo>
<mrow>
<mrow>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>6</mn>
<mo>−</mo>
<mi>ln</mi>
<mo></mo>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
<mo>,</mo>
<mrow>
<mtext> 105.675</mtext>
</mrow>
</mrow>
</mrow>
</math></span></p>
<p>331.989</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{volume}} = 332">
<mrow>
<mtext>volume</mtext>
</mrow>
<mo>=</mo>
<mn>332</mn>
</math></span> <strong><em>A2 N3</em></strong></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="question">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = {({x^2} + 3)^7}">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>7</mn>
</msup>
</mrow>
</math></span>. Find the term in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^5}">
<mrow>
<msup>
<mi>x</mi>
<mn>5</mn>
</msup>
</mrow>
</math></span> in the expansion of the derivative, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’(x)">
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span>.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><strong>METHOD 1 </strong></p>
<p>derivative of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x)">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span> <strong><em>A2</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="7{({x^2} + 3)^6}(x2)">
<mn>7</mn>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>6</mn>
</msup>
</mrow>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mn>2</mn>
<mo stretchy="false">)</mo>
</math></span></p>
<p>recognizing need to find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^4}">
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
</math></span> term in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{({x^2} + 3)^6}">
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>6</mn>
</msup>
</mrow>
</math></span> (seen anywhere) <strong><em>R1</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="14x{\text{ (term in }}{x^4})">
<mn>14</mn>
<mi>x</mi>
<mrow>
<mtext> (term in </mtext>
</mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
<mo stretchy="false">)</mo>
</math></span></p>
<p>valid approach to find the terms in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{({x^2} + 3)^6}">
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>6</mn>
</msup>
</mrow>
</math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 6 \\ r \end{array}} \right){({x^2})^{6 - r}}{(3)^r},{\text{ }}{({x^2})^6}{(3)^0} + {({x^2})^5}{(3)^1} + \ldots ">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>6</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>r</mi>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<msup>
<mo stretchy="false">)</mo>
<mrow>
<mn>6</mn>
<mo>−</mo>
<mi>r</mi>
</mrow>
</msup>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mi>r</mi>
</msup>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<msup>
<mo stretchy="false">)</mo>
<mn>6</mn>
</msup>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>0</mn>
</msup>
</mrow>
<mo>+</mo>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<msup>
<mo stretchy="false">)</mo>
<mn>5</mn>
</msup>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>1</mn>
</msup>
</mrow>
<mo>+</mo>
<mo>…</mo>
</math></span>, Pascal’s triangle to 6th row</p>
<p>identifying correct term (may be indicated in expansion) <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{5th term, }}r = 2,{\text{ }}\left( {\begin{array}{*{20}{c}} 6 \\ 4 \end{array}} \right),{\text{ }}{({x^2})^2}{(3)^4}">
<mrow>
<mtext>5th term, </mtext>
</mrow>
<mi>r</mi>
<mo>=</mo>
<mn>2</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>6</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>4</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<msup>
<mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>4</mn>
</msup>
</mrow>
</math></span></p>
<p>correct working (may be seen in expansion) <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 6 \\ 4 \end{array}} \right){({x^2})^2}{(3)^4},{\text{ }}15 \times {3^4},{\text{ }}14x \times 15 \times 81{({x^2})^2}">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>6</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>4</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<msup>
<mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>4</mn>
</msup>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>15</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>3</mn>
<mn>4</mn>
</msup>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>14</mn>
<mi>x</mi>
<mo>×</mo>
<mn>15</mn>
<mo>×</mo>
<mn>81</mn>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<msup>
<mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
</mrow>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="17010{x^5}">
<mn>17010</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>5</mn>
</msup>
</mrow>
</math></span> <strong><em>A1</em></strong> <strong><em>N3</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>recognition of need to find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^6}">
<mrow>
<msup>
<mi>x</mi>
<mn>6</mn>
</msup>
</mrow>
</math></span> in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{({x^2} + 3)^7}">
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>7</mn>
</msup>
</mrow>
</math></span> (seen anywhere) <strong><em>R1 </em></strong></p>
<p>valid approach to find the terms in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{({x^2} + 3)^7}">
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>7</mn>
</msup>
</mrow>
</math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 7 \\ r \end{array}} \right){({x^2})^{7 - r}}{(3)^r},{\text{ }}{({x^2})^7}{(3)^0} + {({x^2})^6}{(3)^1} + \ldots ">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>7</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>r</mi>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<msup>
<mo stretchy="false">)</mo>
<mrow>
<mn>7</mn>
<mo>−</mo>
<mi>r</mi>
</mrow>
</msup>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mi>r</mi>
</msup>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<msup>
<mo stretchy="false">)</mo>
<mn>7</mn>
</msup>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>0</mn>
</msup>
</mrow>
<mo>+</mo>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<msup>
<mo stretchy="false">)</mo>
<mn>6</mn>
</msup>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>1</mn>
</msup>
</mrow>
<mo>+</mo>
<mo>…</mo>
</math></span>, Pascal’s triangle to 7th row</p>
<p>identifying correct term (may be indicated in expansion) <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span>6th term, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = 3,{\text{ }}\left( {\begin{array}{*{20}{c}} 7 \\ 3 \end{array}} \right),{\text{ (}}{{\text{x}}^2}{)^3}{(3)^4}">
<mi>r</mi>
<mo>=</mo>
<mn>3</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>7</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>3</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mrow>
<mtext> (</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>x</mtext>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<msup>
<mo stretchy="false">)</mo>
<mn>3</mn>
</msup>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>4</mn>
</msup>
</mrow>
</math></span></p>
<p>correct working (may be seen in expansion) <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 7 \\ 4 \end{array}} \right){{\text{(}}{{\text{x}}^2})^3}{(3)^4},{\text{ }}35 \times {3^4}">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>7</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>4</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mrow>
<mtext>(</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>x</mtext>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<msup>
<mo stretchy="false">)</mo>
<mn>3</mn>
</msup>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>4</mn>
</msup>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>35</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>3</mn>
<mn>4</mn>
</msup>
</mrow>
</math></span></p>
<p>correct term <strong><em>(A1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2835{x^6}">
<mn>2835</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>6</mn>
</msup>
</mrow>
</math></span></p>
<p>differentiating their term in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^6}">
<mrow>
<msup>
<mi>x</mi>
<mn>6</mn>
</msup>
</mrow>
</math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(2835{x^6})',{\text{ (6)(2835}}{{\text{x}}^5})">
<mo stretchy="false">(</mo>
<mn>2835</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>6</mn>
</msup>
</mrow>
<msup>
<mo stretchy="false">)</mo>
<mo>′</mo>
</msup>
<mo>,</mo>
<mrow>
<mtext> (6)(2835</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>x</mtext>
</mrow>
<mn>5</mn>
</msup>
</mrow>
<mo stretchy="false">)</mo>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="17010{x^5}">
<mn>17010</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>5</mn>
</msup>
</mrow>
</math></span> <strong><em>A1</em></strong> <strong><em>N3</em></strong></p>
<p><strong><em>[7 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p><strong>Note:</strong> <strong>In this question, distance is in metres and time is in seconds.</strong></p>
<p> </p>
<p>A particle moves along a horizontal line starting at a fixed point A. The velocity <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v"> <mi>v</mi> </math></span> of the particle, at time <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span>, is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v(t) = \frac{{2{t^2} - 4t}}{{{t^2} - 2t + 2}}"> <mi>v</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mrow> <msup> <mi>t</mi> <mn>2</mn> </msup> </mrow> <mo>−</mo> <mn>4</mn> <mi>t</mi> </mrow> <mrow> <mrow> <msup> <mi>t</mi> <mn>2</mn> </msup> </mrow> <mo>−</mo> <mn>2</mn> <mi>t</mi> <mo>+</mo> <mn>2</mn> </mrow> </mfrac> </math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 5"> <mn>0</mn> <mo>⩽</mo> <mi>t</mi> <mo>⩽</mo> <mn>5</mn> </math></span>. The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v"> <mi>v</mi> </math></span></p>
<p><img src="images/Schermafbeelding_2017-08-15_om_08.18.11.png" alt="M17/5/MATME/SP2/ENG/TZ2/07"></p>
<p>There are <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span>-intercepts at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(0,{\text{ }}0)"> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>0</mn> <mo stretchy="false">)</mo> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(2,{\text{ }}0)"> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>0</mn> <mo stretchy="false">)</mo> </math></span>.</p>
<p>Find the maximum distance of the particle from A during the time <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 5"> <mn>0</mn> <mo>⩽</mo> <mi>t</mi> <mo>⩽</mo> <mn>5</mn> </math></span> and justify your answer.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p><strong>METHOD 1 (displacement)</strong></p>
<p>recognizing <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s = \int {v{\text{d}}t} "> <mi>s</mi> <mo>=</mo> <mo>∫</mo> <mrow> <mi>v</mi> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> </mrow> </math></span> <strong><em>(M1)</em></strong></p>
<p>consideration of displacement at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 2"> <mi>t</mi> <mo>=</mo> <mn>2</mn> </math></span> <strong>and</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 5"> <mi>t</mi> <mo>=</mo> <mn>5</mn> </math></span> (seen anywhere) <strong><em>M1</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^2 v "> <msubsup> <mo>∫</mo> <mn>0</mn> <mn>2</mn> </msubsup> <mi>v</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^5 v "> <msubsup> <mo>∫</mo> <mn>0</mn> <mn>5</mn> </msubsup> <mi>v</mi> </math></span></p>
<p> </p>
<p><strong>Note:</strong> Must have both for any further marks.</p>
<p> </p>
<p>correct displacement at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 2"> <mi>t</mi> <mo>=</mo> <mn>2</mn> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 5"> <mi>t</mi> <mo>=</mo> <mn>5</mn> </math></span> (seen anywhere) <strong><em>A1A1</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 2.28318"> <mo>−</mo> <mn>2.28318</mn> </math></span> (accept 2.28318), 1.55513</p>
<p>valid reasoning comparing correct displacements <strong><em>R1</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| { - 2.28} \right| > \left| {1.56} \right|"> <mrow> <mo>|</mo> <mrow> <mo>−</mo> <mn>2.28</mn> </mrow> <mo>|</mo> </mrow> <mo>></mo> <mrow> <mo>|</mo> <mrow> <mn>1.56</mn> </mrow> <mo>|</mo> </mrow> </math></span>, more left than right</p>
<p>2.28 (m) <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Do not award the final <strong><em>A1 </em></strong>without the <strong><em>R1</em></strong><em>.</em></p>
<p> </p>
<p><strong>METHOD 2 (distance travelled)</strong></p>
<p>recognizing distance <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \int {\left| v \right|{\text{d}}t} "> <mo>=</mo> <mo>∫</mo> <mrow> <mrow> <mo>|</mo> <mi>v</mi> <mo>|</mo> </mrow> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> </mrow> </math></span> <strong><em>(M1)</em></strong></p>
<p>consideration of distance travelled from <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 0"> <mi>t</mi> <mo>=</mo> <mn>0</mn> </math></span> to 2 <strong>and</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 2"> <mi>t</mi> <mo>=</mo> <mn>2</mn> </math></span> to 5 (seen anywhere) <strong><em>M1</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^2 v "> <msubsup> <mo>∫</mo> <mn>0</mn> <mn>2</mn> </msubsup> <mi>v</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_2^5 v "> <msubsup> <mo>∫</mo> <mn>2</mn> <mn>5</mn> </msubsup> <mi>v</mi> </math></span></p>
<p> </p>
<p><strong>Note:</strong> Must have both for any further marks</p>
<p> </p>
<p>correct distances travelled (seen anywhere) <strong><em>A1A1</em></strong></p>
<p>2.28318, (accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 2.28318"> <mo>−</mo> <mn>2.28318</mn> </math></span>), 3.83832</p>
<p>valid reasoning comparing correct distance values <strong><em>R1</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3.84 - 2.28 < 2.28,{\text{ }}3.84 < 2 \times 2.28"> <mn>3.84</mn> <mo>−</mo> <mn>2.28</mn> <mo><</mo> <mn>2.28</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>3.84</mn> <mo><</mo> <mn>2</mn> <mo>×</mo> <mn>2.28</mn> </math></span></p>
<p>2.28 (m) <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Do not award the final <strong><em>A1 </em></strong>without the <strong><em>R1</em></strong>.</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>