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<h2>SL Paper 2</h2><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>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>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>4</mn><mo>-</mo><msup><mi>x</mi><mn>3</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>ln</mi><mo> </mo><mi>x</mi></math>, for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mn>0</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>f</mi><mo>∘</mo><mi>g</mi></mrow></mfenced><mfenced><mi>x</mi></mfenced></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>Solve the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>f</mi><mo>∘</mo><mi>g</mi></mrow></mfenced><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>x</mi></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>Hence or otherwise, given that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mrow><mn>2</mn><mi>a</mi></mrow></mfenced><mo>=</mo><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mrow><mn>2</mn><mi>a</mi></mrow></mfenced></math>, find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p 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 form composite (in any order) <strong><em>(M1)</em></strong></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mrow><mi>ln</mi><mo> </mo><mi>x</mi></mrow></mfenced><mo> </mo><mo>,</mo><mo> </mo><mi>g</mi><mfenced><mrow><mn>4</mn><mo>-</mo><msup><mi>x</mi><mn>3</mn></msup></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>f</mi><mo>∘</mo><mi>g</mi></mrow></mfenced><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>4</mn><mo>-</mo><msup><mfenced><mrow><mi>ln</mi><mo> </mo><mi>x</mi></mrow></mfenced><mn>3</mn></msup></math> <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>valid approach using GDC <strong><em>(M1)</em></strong></p>
<p>eg <img src="data:image/png;base64,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"> , <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo>.</mo><mn>85</mn><mo>,</mo><mo> </mo><mn>2</mn><mo>.</mo><mn>85</mn></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>85056</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>85</mn></math> <em><strong>A1 N2</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><strong>METHOD 1 – (using properties of functions)</strong></p>
<p>recognizing inverse relationship <strong><em>(M1)</em></strong></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mrow><mi>g</mi><mfenced><mrow><mn>2</mn><mi>a</mi></mrow></mfenced></mrow></mfenced><mo>=</mo><mi>f</mi><mfenced><mrow><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mrow><mn>2</mn><mi>a</mi></mrow></mfenced></mrow></mfenced><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mn>2</mn><mi>a</mi></mrow></mfenced></math></p>
<p>equating <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>a</mi></math> to their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> from (i) <strong><em>(A1)</em></strong></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>a</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>85056</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>42528</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>43</mn></math> <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><strong>METHOD 2 – (finding inverse)</strong></p>
<p>interchanging <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> (seen anywhere) <strong><em>(M1)</em></strong></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>4</mn><mo>-</mo><msup><mi>y</mi><mn>3</mn></msup><mo> </mo><mo>,</mo><mo> </mo><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mi>x</mi></mfenced><mo>=</mo><mroot><mrow><mn>4</mn><mo>-</mo><mi>x</mi></mrow><mn>3</mn></mroot></math></p>
<p>correct working <strong><em>(A1)</em></strong></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mrow><mn>4</mn><mo>-</mo><mn>2</mn><mi>a</mi></mrow><mn>3</mn></mroot><mo>=</mo><mi>ln</mi><mfenced><mrow><mn>2</mn><mi>a</mi></mrow></mfenced></math>, sketch showing intersection of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mrow><mn>2</mn><mi>x</mi></mrow></mfenced></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mrow><mn>2</mn><mi>x</mi></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>42528</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>43</mn></math> <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[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>
<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>Urvashi wants to model the height of a moving object. She collects the following data showing the height, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span> metres, of the object at time <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> seconds.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">She believes the height can be modeled by a quadratic function, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h\left( t \right) = a{t^2} + bt + c">
<mi>h</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>a</mi>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>b</mi>
<mi>t</mi>
<mo>+</mo>
<mi>c</mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a{\text{,}}\,\,b{\text{,}}\,\,c \in \mathbb{R}">
<mi>a</mi>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>b</mi>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>c</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>.</p>
</div>
<div class="specification">
<p>Hence find</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="4a + 2b + c = 34">
<mn>4</mn>
<mi>a</mi>
<mo>+</mo>
<mn>2</mn>
<mi>b</mi>
<mo>+</mo>
<mi>c</mi>
<mo>=</mo>
<mn>34</mn>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down two more equations for <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="c">
<mi>c</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>Solve this system of three equations to find the value of <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="c">
<mi>c</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>when the height of the object is zero.</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>the maximum height of the object.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 2{\text{,}}\,\,h = 34 \Rightarrow \,\,34 = a{2^2} + 2b + c">
<mi>t</mi>
<mo>=</mo>
<mn>2</mn>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>h</mi>
<mo>=</mo>
<mn>34</mn>
<mo stretchy="false">⇒</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>34</mn>
<mo>=</mo>
<mi>a</mi>
<mrow>
<msup>
<mn>2</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mi>b</mi>
<mo>+</mo>
<mi>c</mi>
</math></span> <em><strong>M1 </strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" \Rightarrow {\text{ }}34 = 4a + 2b + c">
<mo stretchy="false">⇒</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>34</mn>
<mo>=</mo>
<mn>4</mn>
<mi>a</mi>
<mo>+</mo>
<mn>2</mn>
<mi>b</mi>
<mo>+</mo>
<mi>c</mi>
</math></span> <em><strong>AG</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>attempt to substitute either (5, 38) or (7, 24) <em><strong>M1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="25a + 5b + c = 38">
<mn>25</mn>
<mi>a</mi>
<mo>+</mo>
<mn>5</mn>
<mi>b</mi>
<mo>+</mo>
<mi>c</mi>
<mo>=</mo>
<mn>38</mn>
</math></span> <em><strong>A</strong><strong>1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="49a + 7b + c = 24">
<mn>49</mn>
<mi>a</mi>
<mo>+</mo>
<mn>7</mn>
<mi>b</mi>
<mo>+</mo>
<mi>c</mi>
<mo>=</mo>
<mn>24</mn>
</math></span> <em><strong>A</strong><strong>1 </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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = - \frac{5}{3}{\text{,}}\,\,b = 13{\text{,}}\,\,c = \frac{{44}}{3}">
<mi>a</mi>
<mo>=</mo>
<mo>−</mo>
<mfrac>
<mn>5</mn>
<mn>3</mn>
</mfrac>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>b</mi>
<mo>=</mo>
<mn>13</mn>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>c</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>44</mn>
</mrow>
<mn>3</mn>
</mfrac>
</math></span> <em><strong>M1A1A1A1</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - \frac{5}{3}{t^2} + 13t + \frac{{44}}{3} = 0">
<mo>−</mo>
<mfrac>
<mn>5</mn>
<mn>3</mn>
</mfrac>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>13</mn>
<mi>t</mi>
<mo>+</mo>
<mfrac>
<mrow>
<mn>44</mn>
</mrow>
<mn>3</mn>
</mfrac>
<mo>=</mo>
<mn>0</mn>
</math></span> <em><strong>M1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 8.8">
<mi>t</mi>
<mo>=</mo>
<mn>8.8</mn>
</math></span> seconds <em><strong>M1A1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to find maximum height, e.g. sketch of graph <em><strong>M1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h = 40.0">
<mi>h</mi>
<mo>=</mo>
<mn>40.0</mn>
</math></span> metres <em><strong>A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A wind turbine is designed so that the rotation of the blades generates electricity. The turbine is built on horizontal ground and is made up of a vertical tower and three blades.</p>
<p>The point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> is on the base of the tower directly below point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> at the top of the tower. The height of the tower, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext></math>, is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn><mo> </mo><mtext>m</mtext></math>. The blades of the turbine are centred at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> and are each of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mo> </mo><mtext>m</mtext></math>. This is shown in the following diagram.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAd0AAAGrCAYAAACFRk2yAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAECaSURBVHhe7d0LXFVlvjfwX4ynGjHylikpqcWYUEZOMpUe0zGVg8m7k0pzxLDUqXQYYZjxQjody1vjSEN5edWSvOck7eMkk7f0NGqGSmhJeTBFRh28ZA6Cli+zz7v+i2fpBrlsYO21b7/v58PH/ay92Wwu8uP5r2f9nxv+VwMiIiJyuyD1LxEREbkZQ5eIiMgiDF0iIiKLMHSJiIgswtAlIiKyCEOXiIjIIgxdIiIiizB0iYiILMLQJSISxXaMDmuPsLDxsBeXawf+Dvvobtp4INJzSyseQ7VwoLRgBzKnr0CufPlqVIKCHZmYnpmHWh/mVcq1H4/x2s9Ce0Sl5zbqdTN0iYio8Yo3YEK/EZiWdVYdqI6E1xT0G/kysr5zqGOBhaFLRFStDrAtPYiiok1I7t5MHSNqHIYuEQWgKyjOXYW0mC56ybDr6Axs+/pbdZ+huvJy5fe7+r4FJep+jaMYuSvSEKPfPxhp9kMoUKXJsNF2FGsPKc+dhyh9/Da2Zb6ArvI8aTugP0ul95e3aIxO34KCUpkZXitzyvvu2JaB0V3lMV0QM20bih3a69u76NqxNLt6v+o4l0y34Svn50pbhdziK+pxQj5vO9JHR1d87KqPkdJ89Hhsltvn58HWuboyrHy8CYhOsuuj8+lx6Oz8tZXP2z5PvQZ50752K/Zqn1PF3dUrQcHV113Ta9eUFmBHptPXNCYNmTsKcO2kgQvf12o4inNhT39e//5VfOxM7KjjfRi6RBRgHCjNXYRE20SsyC/Tj5Rtfh2jRv6+IjRq4ShYjbFO7yf0942bix0lkg4XkPunF2FLexf5+r2fY0XSM/jVojx9dJ3Nv8eoaR9Cnu2m1iFoiu9RsPw3Tu8vTmFz+ijEzfqkIpQN2vuOHPU6NusvpQz5mS8hcexYJMa/du3Yion4zfsF2mdcu/Ppz2Kg83Np7/eLN3erj2d8vcYjffMp/YjxGFvf38J+qkrANYj6uiXNU69BaF+7tCfQ9yU7TlX7CThQsmMu4q6+bqFeV+Ii5Bp/bDiKYE/9BUZOc/qa5r+LaSNHYdaOc/qw7u9rNUr34k+JzyApfZP2UYV87JcxMm5qrV8Thi4RBZjz2Ld+nf4LOHjALGzJL0JRYQ6WJz5QcXeNSpH34RrkIRSxGbtRWHQChXveQmywdlfZNyg8rf2iLcnD+sV7tQOhGDB9E/LlMTnpiEZN5zkfQOLyHO25vsZHz/wETcrz8eEb/629sHhk7DmKoqKj2JMRD/1DfFGI05V+/xvv+yXsyT20sfZLf/O3iK5yLG/nVzijP74WwY9j+pb8yh9vYy6OyFTVUYD3X5mvfb20zyl1HXIKT6AofxsyErSvV9l6TJ6vhXNbG5bmvIUB8lwtU2A/egJ5yd3RRMZXNUFb2xvIybDpo5bJG3BUle4dBXa8kq593YIHInX9Pu31FyF/21tIiAhGWfZczP+kIhwru4Qjn3+mfYbBiJq+Tf9+FOV/gGTtfZC/Duv3ndceowXzJ0sxOVv7Y+G6z7EQK+Z9iAKHC9/X61zBqa0rsVj7IYpIfLfia1KUjy3TH0dw2UdY9N4Bp1l0ZQxdIgos5UX4fGOhdiMSY196Al2aab8Gg0LR56XnK0KjRs3QPXmT9st1K37T/AA22N/G1OcmIluf5pzDdxfL4ThdiC9k3HIYXhoRqb2H9tRtH8VLL/SXB12vZV/YeoVqv4iboW1b7dFNuiM5T/sFvnc8mudkw575n3guaX3FTKroPC46h25UPBJ6y/uG4O4H7tOD8tqx5uj26L+jpf7AugUPGYYhXUK0Wzci9KG+6FlxWOf45lNk5WmvQD6nlx5BW0mNZl1g+1XF16ss62Pk1jQbdMn3+GbXFi30tA8xdhxe6tFWe/3aVyT8cfxK/7oVImvLl5Vn+bomuKVFa+1f7Q+LaXGITXsb9q0ncffM/9aCcydm9JH7ruB04Tf616/S52j7E76SkN6QiPCgur+v1yvB/+zdrz2v9odO5rOI7ijl5Qj016sW2rHth/CPGr4kDF0iClDh6BR6s7qtaR2GyFpTyjhfGoF+I19EUtLvK5UjhePieRTJjQc7I/TqNK+J9tSdqw/AsJa4xfm3sKMYezOeR9eIvhiZNB5JziXRqto0V+8bhKYhzXFTpWP1U1Harl71n5PG+HqVnceFS40J3XJc/E5msi3xYKfbnGbH175uZacvaPPaqm5G+Mg/Yn3qQO0PDint/l77nozHONuD6BjzGnbo53WN567tc6z7+3q9y7hwupZzt1X/QHLC0CWiwBIUjBZhMi8swLFT31ccE+eKcEgqkjVxHMNHr6Zjc1koBiTPxXz7PhQe3YBkPU1bo8UtTRB0S0uEyXDfUZy6OkEq1576KKp96ioh6fjmI7w6dxPKggci+Y2lsOccxVF7SkVgVw1oi1T/OWmMr1dwSzRv2pgXZsxYz2PfsbNOi6+ufd2Cb29efWAGtUWPpLe1WetR5NiXIiNjLpIHhAL5i/Cifk7aeG7gh3Ml1QS3xoXv6/V+jOa3y6y5JQZkfKrNkqW87PSWl4Lu1b2bhqFLRIElqBU63nebduMQFi/4AIdlwY3jFHYseLv2hVRnvsJOKbPiDkQ+GoPB3VvizM5sbHJK06DbO+I+yfPza7Fg5SH9vJ6j+L+xYNEW/f7alePMoX16mRV33o9HBwxA9zbnsNO+vfrAtkhQu0j0lfOk8jkt2F2xmrj0MOxvVny9gof8HN1DtCgxZr7nj6LoXHUlWXFt9nr+UBEq5qA3ol23nyFCji2ejwV7i+GQxVsFH+JN/evWEUP63wuJuEoch5EZJ6uNozE6swDNusfAZovBo5F36HdXzI5vxO0d76o4R521FlmHZXYqC8MyKlYyd52GHQVf1vl9vV4z3BF+p/bveWxe9G7FrFoWbL0gq7u7IC7zsPZRqsfQJaIA0xq9x6XqC2XKNk9G/4gwhHWMxsjMz9X9NWjTFb2i5Nf3XqTb7tV+uXZG9MhFqvyrzv2FPITEiY9q41PYPG0gIrRf7B2jX8ep9h31R9WuCdpEPogouZn/OmxVX1ctJUu3anY/npmUoIWi9jnNfbri/GVEPySt0F5XcDxmjXukSiDakRTdse7OTZvHI1q/ZOgSmkU9iUmykK1sE+bGP4iOYWGI6DdeL/MGx6ZiXO+K2WolQeF48pVxFa9Lfa3Dwu6FTRZkaUGdMKIX5OxwSO/RmBWrzX7LPsS0/hHaY7Tntr2ufd+CETF2MB4Mv7fu7+t1bkb4kxPUoq1FGBndWftePYIkfcFWDJ4b0KnGcGXoElHACQqNxSur5uirY0XwgN9h2fL/rH0hVVAXjFy8DKlSvhQRz2KG/W/YMl1CthDbD57UZjcV5xntM57VZ24Vq3GXYvrj4TKqU1D4cCxe/zIG6C9LC4WEObDvycZ0CYXz+3HwmFM53DI3om2f3yHT/lZF6VanXtv2P8AWemPFoSb34pkl1157W/wL1b3aJlHDsUQ/DyukaKyFmixke2UJ7Bkp6v3FA0iY8QG2L7AhtNqkCtJmty9UeV0a7fsyffkyTNYXUmmCwmCbuwrLp6vviZDyfcYaZP66B5q59H2tRrMe+HXmGmQkG5+L9rTyc7Th1Wtfk2rc8L8adZuIiBqjPBfpD8Yh/bwWSskr8X6y9ktdStev/FKfscplMvuuu5SGAglDl4jINOewI82GkSvkkqSqeiDZvgzJ3ZurMQUilpeJiEzTGn0mL6tcytQED0hBhn0hfs3ADXic6RIREVmEM10iIiKLMHSJiIgswtAlIiKyCEOXiIjIIgxdIiIiizB0iYiILMLQJSIisghDl4iIyCIMXSIiIoswdImIiCzCNpBEPur8+fP49ttvcfx4Ibp2jcAdd1Rs3k1E3ouhS+Rjdu/ejRUrViA//xB69uyFDh06YPv27bgj1GlPUU36G2+oW0DyhAnqVmV1Pcb5flHXY1z5OESBjKFL5CMOHDiAGTNm4O6778bQoUNx//33q3uArVu3YPHiJVi3bp064jkFBQVYtmwZVq5cro+3bduO8HDXNnEn8ncMXSIvJ2XkuXPn4siRI3roVg2wy5cvIyZmIJYufduj4VY1bA0MXaJruJCKyItJKfmJJ2yIiIjAu+++W214ZWZmYtiwZzwabPKHwejRz18XuERUGWe6RF5q4cKFWLt2Ta0zWJldSth99NEm/PjHP1ZHPUNm3BkZGZg//011pMLhwwUef21E3oKhS+RlJLxSUlL02/Pmzas1sJ5++mmMHTsGjz3WXx3xLHntffv2QYsWLXDo0Jf6saKiE/q/RMTyMpFXOXnypH5+tlu3bvpMt7bAtdvtaNWqldcErpCZ7hNPDEFW1geYOXO2OkpEBs50ibyEBO7w4c9g6tSpdQapnEOVc72rV6/xmutzZXV1UtKvKpW6pfzNRVRE1zB0ibyALJgaNuxprF27Do888og6WrM5c+boYTtixAh1xLOMFdQZGW9WupSJiCpjeZnIwyRwJ0+e5HLgyowyO3sj4uPj1RHPkxXUsbGDGLhEdeBMl8iDjMB1tUwsM8pnn30WEyZMcCmgreBNK6iJvB1nukQeUt/AFZs2bdI7UnlL4MofAWlpaXpZmYFLVDfOdIk8oCGBK4unoqK6IS/vIFq2bKmOetbKlSv1BWATJ05UR4ioNgxdIosZi6Y+/fSzeq08njJlCqKjo2Gz2dQRzzLKyh98YPeaPwKIvB3Ly0QWkqAyVinXJ3AlqKX38sCBA9URzzLKynJ5EwOXyHUMXSKLSBlWZoaurlI2SMBJKVpCzlvOm65fv14/t+xNjTmIfAFDl8gCRuOLWbNm13sRlAScN12OI7P1JUsWIzU1VR0hIlfxnC6RmxmX+cTFxdW7mYUR1t5y3tT4XLyp3zORL+FMl8iNJKRk84K+ffs2qHvUa6+9huTkFK85b8qyMlHjMHSJ3Eg2ABAvvvii/m99bN26Bd9++61XrVZmWZmocVheJnIT2SXo4MGDdW7PVx2ZIUsv49r20rUSy8pE5uBMl8gN5BIf2YB+xowZDVpxbPQy9pYdelhWJjIHZ7pEJpMybL9+fevd/MJgNJ3wll7GxuthEwyixuNMl8hEztfiNiRwhdF0whsCV8rKbIJBZB6GLpFJJKBktfGYMWMbvCGB3W5Hq1atvKaMa2ywwLIykTlYXiYyiWws/89//hMzZ85UR+pHNjR44gmb1yye8rZrhIn8AWe6RCaQGer+/fv1MmxDLVmyRJ8le8viKZm1s6xMZC6GLlEjHThwAOnp87S39Aafh5XnyM7eiPj4eHXEs+SPiBYtWrCsTGQylpeJGqExPZUNxjWwEyZM8IrN6eVzevjhnzV49TUR1YwzXaIGMmPhlDAWK3lD4Ar5nDIy3mLgErkBQ5eogaSBhZRgG9JT2SCLp5KSxmPcuHHqiGdJWVl4S+tJIn/D8jJRA0jHKdnjtrENLKZMmYLo6GivCDmWlYncjzNdonqScJLAlUt7GhO4snjqyJEjGDhwoDriWSwrE7kfQ5eoHuQ8bnJysr7dXmMu7ZHnSUr6ld7tyRs6T7GsTGQNhi5RPchWfbLoqbHhJBsI9OzZC/fff7864jkyc5fzyi+//LI6QkTuwnO6RC4y6zyucZmRt3R6kr1+pcTNWS6R+3GmS+QCs87jivnz5+vlaW8IXJaViazFmS5RHeT8a0pKiimzwa1bt2Dx4iVYt26dOuI5XK1MZD3OdInqIOdf5XrcxgauhPerr76qb2zvDbhamch6DF2iWshlPUuWLEZqaqo60nDSTCM2dpBXbGggM27BsjKRtVheJqqBzExjYgZqs8E3G73KuKCgQN/cvrGLsMxgbCG4evUaznKJLMbQJaqBdIuKiIhoVJtHg6wQjo8f4hW79nhTFyyiQMPyMlE1pPwq3aLM2GrPWCHsDYFrfF4MXCLP4EyXqAozV/UapVy51MjT53K96bUQBSqGLlEVZjaLmDNnjh7cZpSoG8vMcjkRNQzLy0ROpBRsxuVBQhZPZWdvNKVE3VhmlsuJqOE40yVSjBXGZrRnlJXPzz77LCZMmODxzelZVibyHpzpEmkkJGXHn6lTp5rSnnHTpk36xgieDlwxd+5cjBkzloFL5AUYukQa6TolIWnGCmOZWcquPePGjVNHPIdlZSLvwvIyBTyzG1d4y3WwLCsTeR/OdCmgGWVl6TplRuBK20iZWcrqZ09jWZnI+zB0KaBJWfmnP/2pKZvJS4AnJf1KD3FPt3pkWZnIO7G8TAHL7LLyypUrkZ+fj5kzZ6ojnsGyMpH3YuhSQDIu6ZFZqRmzXKOLVV7eQY9vTs8mGETei+VlCkhmlpXF/Pnz9b1pPR24xjlllpWJvBNDlwKOlJVlj9ykpCR1pHG8ZRMB45yybJLv6XPKRFQ9lpcpoJhdVpbnkz13veH8qTf1eSai6nGmSwHFaIJhVlk5MzMTsbGDPB64Ula+rs+z4xR2TBuMsKh5yC1Xx3RXULx3EUZ3bY+wsC6ISVuF3OIr6j4icieGLgUMWewkZeXU1FR1pHGkTL127RqMGTNGHfEMo6xc+VrjKzi1YQ5ezPxcjQ0OlOYuQmL8RoQuzEFh4XZM+tFa/OKVbJxyqIcQkdswdClgvPbaa6b1Vhbz5s0z9fkaKiMjQ59tO8/eHaeyMf2VL3HnT4LVEcVRgPdfmY/jCb9Bap9QBAWFondCPMKz52L+J+fUg4jIXRi6FBCMLfvM6K0s5PmEWc/XUEZZudKisNJDWD7Nji7vpOOFjjepgxUc33yKrLyb0LPHXQhRx4LuehhDos4ia8uXKFHHiMg9GLrk98zegECeLz19HlJSUtQRz6i+rHwBuUv+gJ29fosx3VuoYwYHSk8eRQHaITLM6b6gpmje5iaUfVGI0ywxE7kVQ5f8nvQglmtoZWWvGZYsWYJhw57x+OKp68vKcr52JRZ8l4DXRkaimTp6jQOXLpxHmRpdp+g8LjJ0idyKoUt+bffu3aZeQyuLp6Scm5iYqI54RnVlZUfxdry+AHjpd33RtiH/s8Na4hb+RiByK/4XI78l5dfJkyfpzSLMItf3zpo126PNJ6ovK5fjzJ4PkLl5NmwRYQgLk8uBHkbS5vPA+Xmwde6G0fZ/oE3kg4jS5rrnSr5X76cpP4tj+84j+L6OuJ2/EYjciv/FyG/JNbRmloFl8ZRc4/vII4+oI55R3WploAna2t5CUdEJp7dPkTGgJdAyBfajB7HU1qHaRVOOYwex/XxHDOl/79XFVUTkHgxd8kvGNbRmlYHNXozVUNWuVq6PoE4Y8FwMkLUWWYe12C09jA2Z61EQm4pxvVurBxGRuzB0yS+ZXQaWxVgzZ842bTFWQ1RfVq6vGxFqexUbZrXB2v4RCIuIwyI8jw1z4xDK3wZEbsfey+R3pAyck5Nj2r62MruU88LvvvuuR8/lLly4ECUlJZg4caI6QkS+hqFLfsXYwH316jWmzEpldmnmBgkNZfaG+0TkGSwokV+RMnBycoppZWCzN0hoCAl+Cf3GlZWJyBswdMlvSBlYrskdOHCgOtI4skHClCmTTNsgoaHM3nCfiDyHoUt+QWaDct5VZoRmzQbnz5+vzS7f8uiGBsaG+57eyYiIzMHQJb+wadMmU8vAZneyagijrOwNOxkRkTm4kIp8niyeiorqhry8g6aEk4RdTMxALF36tkf7K69cuRL5+fmmrcImIs/jTJd8nrGhgVmzQelkJR2fPBm4RlnZ0+eTichcDF3yabJ4ateunaYtnjI6WXnyHCrLykT+i6FLPk0WT5nZeWrevHkeDzvjMiVPb5BPROZj6JLPMnsDgq1bt+j/ejLsWFYm8m9cSEU+yezOU8bzeXLxlJSVpfvV2LFjOMsl8lOc6ZJPkjKwbNtnVuepJUuWmLoNYEOwrEzk/xi65HNkVvrXv2ajV69e6kjjSElXtsszaxvAhmBZmSgwMHTJ58gipzlz5mhBma2ONI6sFDZzMVZ9cbUyUeBg6JJP6to1Avv371ejhjN7MVZDGN20WFYm8n9cSEU+KyysPYqKTqhR/RmdrD799DOPbU4vmyoMH/4MPvjAzlkuUQDgTJcClnSymjlztscCV7z22mssKxMFEIYu+SRZeDRo0GA1qj+jk1V8fLw6Yj0pbQuWlYkCB0OXfNKlS5fQokULNaofWbgknaw8uSm8lJWTksbj5ZdfVkeIKBAwdMknHTt2DBEREWpUP8b1sJ7cFF7KyrJJgydL20RkPYYu+aScnBx07txZjVwnM8wpUyZ59HpYo6zsyb16icgzuHqZfNKjj/Zu0IrfKVOmIDo62mOBJ6H/8MM/8+iKaSLyHM50yefIIqrbb29b78DdvXs3jhw5Yto2gA3BsjJRYGPoks/57LPPEBcXp0aukcVTkydP0hdQeWrxFMvKRMTQJZ+zYcMG3HfffWrkmszMTMTGDvLYhgZcrUxEgqFLPkXC6/Tp4nqtPJZy9Nq1azBmzBh1xHosKxORYOiST9m+fbu+BV99yDaAyckpHuv6xLIyERlMDt2/wz66G8Ki5iG3XB26jiuPcUGxHaPD2iMqPReNeRryLVJars/mBFu3btH/9eRqZZaVicjAmS65h/qjSDYluP4tGqPT/4wdBSXqwa6RMrFwtbQsi6deffVVpKSkqCPWY1mZiJwxdMk92tqwtOgItk1/VBvYkJFTqO8IVFSUj23LRgCLkzEybirsp65UPN4FW7duxfDhw9WobhkZGXop2lOLpzw9yyYi7+Oe0P3hELalP4+u+qymC2LSViG3uKZfrg6UFuxAZtpgp5nQYKSt2Itih3qI/pgtSB8dfe3+NZ+i8qZuV1CcuwppMV3UY2Q2tQUFpVefhCzXBLc0r9ofOQTh/cZi4kQtjMs+wjubj2nf3brJrHXWrBno3bu3OlI7mRVnZ29EYmKiOmIt2TZQZtksKxORM/eEbtkmvHO4D+z5RSjMWYDo/dNhS1yE3GoC0HFqA1Ljfom1P5qAnEJtJlS4D+tT2yArLRlvfnLO6THjsen2KdimP+cE/GiTHfn6vUIL5dxFSLT9Cadjl+nPU5gzC6GbxiMudQNOMXe9zI24veNdCFYjV8hG7+PG/crlxVBpaWn6lnmeuiZXtg2UxVssKxORM/eEbnA8Zk0fii7NghDUti9+N3McIvLXYf2+8+oBhu/xzeY/I7vsQQxL6Im28mqC2uKn//HvCEchNn5ehHLjMRiKSRPjEK6eM3XS0Gu/tB0FeP+V+ciPegkTxz+iP4/xGGTPxXwV3uQNpGqxAXNmv4ey4Bg8N6CTSz+Eq1evxpAhQ9SodrJaWDY08NSWeVJW9nTnKyLyTu4J3fAHENn2RjUIQrO7u+GnwUaIOrsZ4YmrUFS0ED1PbtF/Wdqz5mFs3MvIU48AzuLQzi+Ant1xT4jxcoMQck939FQjnPkKO/PK0LJvN3S6+hkZj6nu45K17EiK7qjK/mGI6DceK/JvQ8LCqbCFGj8nNZP2jcKVc7NS1k1Pn6fNisepI9Yyysqe7HxFRN7LPaHbpjlucX7mpiFofZO6XYWjeBumxfRAv5Gv4sNj32uvKBwjFv4nBqj7UX4Wx66bIWtahyFSVRodFy/gjPbv+fQ4dL56Xlh7ix6PzRUPIY9yXkh1FDn2t5A84ApWjIzF6MxDKFWPqsmKFSswYcIENaqdlHXHjBnrsbKu8fE9tXiLiLybe0K3qkslOPeDul3JOXzy5u+ReTwGGXt2YmnyMNhsg9H7jh/pIaprchs6Pail65kLuOh8bvZcEQ6pLA66pTnaIBhR07ehUP/FXvktL7k7mlQ8lDzuRrTtbkPyvNeREHwKm6fNxPsF2h9bNZAFUd9++61L1+YeOHAAu3btRHx8vDpiLaOs7KmPT0Tezz2huysXX5cYCelASe7HyCrriEEPhFUJv8u4cLqkSjnagdKTR1FxRaa4DZG97tN++x7FyasLsbTn/DoXu9QIbbqiVxSQl/UpvnEKZkdBJuLCuiAu87D2HuSLli1bhrFj627fKKubpaSbkfGmR8q6LCsTkSvcE7pl72H2nA365TqO4u2YO/s9IDYV43q3Vg8w3IKwyLu0tPwvfJh3QRvLZT9rKhbZaKMfzpXgEm7GXQOeQizewYspq3DY6TnlMbqgThjwXAyC8xZgzlu79UuNHMW78dacBciLGIdXngy3aEpPlZXi1LGT6vY1juK9WDHnj1ihfQODY5/CgLtuVvdUJrNcmbn27NlLHamZrG6WxVP16clsJpaVicgV7smiCBsG4m30iwhDx+iXkPPTOdgwNw6h13205ug+ZjYyEsqRbrsXYWGdET0lH+G/nYXkqGCUfVGI01qABoXGYe4GbcaDN9Fff8438K+BNkSoZ5GSZajtD9hu/zVuzx6F6I7ttceMQvbtv4Y98wV0b8bItZzekepe2NL3agPnhVTyvXkCaVltkPzG6hp+LirILFcuu6lr5mi0WkxNTVVHrMWyMhG56ob/1ajbRF5DZrmjRz+Pjz7aVGfoTpkyBdHR0R7p/CRl5SeesGHp0rc5yyWiOnEKSF7J1VmuXE7kyWtiWVYmovowfaYrvwTPnLm69hiRkZHqVu3at2/PBSgBTBZCnThxAocOHUJhYSE2btyobzxf26U/8j4xMQM9NsuUsvLixUvw7rvv8meXiFxieuiOHz8Od98djo4dO6K0tBT5+deaNdZm5crl6lbtBg0ajBYtqvbzvV6HDh3Qrl07NapZmzZtcNttt6lRzZo2bcqWfm4g5dnly9/FvHl/xEMPPaz/kSYBVlT0d+TkfKZ/D3/729+hV6/rF1OtXLlSP587ceJEdcQ6LCsTUUOYHrry139BwRG8+OKL6oi5jO3d6nL8eKEW+lfXN9fo8OHD+Oc//6lGNZMS5p49FZ2RatOpU2eXVtsKOQ/pik6dOumhXxdfqxbs3LkTqam/wX/8x3/ogRsSEqLuuUa+7itXrsC9996L1167djmOcc73gw/slmxOLx9PNsOXDQzkj685c+bo/44YMUI9goiobqaHrqdLfp4mMyBp5lCXS5cu4dixY2pUu5ycHHWrdq5WCx566BH98pq6uFotaNYsGHfe2VGNauZcLZDATUlJ1maxv9X+WOigH6vJDz/8gL/+NRtnz57F/PkL9OCVP+rkPK5Vi6ckdPv166vfTklJ1U+jsKxMRPVleugKYxayevUalmS9kJRkJfTr4mq14B//+Af+/ve/q1HNqlYL3nprgUulfcOqVavQtm1b7Y+Gn2H9+iwsXLhQ3eN+zqErevd+VJvtvs6fbyKqF7eErpCZwOTJk/Tt1Ty12wt5p9GjR+MnPwnHv/+7a3vjGmTGO3Hi73DDDTdgxYqVllZS5LTJc8+NUqNrMjLe4ib1ROQyt10yJL1yZaYrMxK5jlJmV0RSft+8+SNER/9MHamspKQEJ05UP2u+6aabEBsbi65dIyw/dVHdjF/K9LIQj4jIVW69TldKb1IClAVDw4c/o9+WX7oUuL7++mvExdn0AK1q48YPMWbM8/jNb1L0DlMSwFU98EB3nDt3Vo08Q8J27dp1WLdunUsbMRARGSxpjiHlN+ksJOQyC1n5KefIKPDIud+wsOsXTskiKbl0qLy8HJcvl6G4uBirVq1U914j54APHLi227KVGLZE1FhuO6dbE1ndLM3pV69erY+HDx+O3r17W3LZB1WWXGWP2vQ33lC3rr/PUNdjnO8X1T2mXWi7q+dz1733nv5vTZ4eOlTdqlDd46163VUfQ0RUX5aHrjPZ/1QWXM2aNUNvehEfPwTdu/+UAWyRp59+Gq1atbJ0FfCf//xnHDt29LpFVFJKnjAhCRcvXtRmu/8PN954E557bnS17R2HDn1K3yeZiMjXeLT3smzDJtdbHj5cgISEBOzfn6uXnyUMpNuQhDK5h91u1y/f2bjxL/rKXKv85Cc/wb59+9ToGmmMMWXKywgP/4n2R1drDB4chz59+qh7r5HLjn7+88fUiIjIt3h0plsTCdsvvvgCu3bt0kNhxIiR+mIsaRHIlnuNZzQwkRmnkC5aruzmU1/Vnbf//vvvMWpUImbMmFltB6q62O0f4MEHe+Cpp55SR4iIfIdXhq4zWe0sK14liA8ePKiHsJSie/bsic6dO+POO+9kg4J6knKylPSdzZw52+WWhhKmRkct5/7azs0vamuHeeXKFT18f/GLX6gjrpHFVr///TRs2/YxT0EQkU/y+tCtynk3GmmPuGvXTn3GJrPhiIgItG17u96SkDPi6sn10g8/XP01snl5ByuFmfEHz9GjR/VgNb7WxqYTRu9oYycpOT/sShjK9zAubrD2FqfPWl0hjTFmzZqJsrIyLFuWye8vEfkknwvd6kg4yKUoMvOSDQz279+vz7iMHsMSDsZuQoG+haCcyzV6OUuvZvljxRAVFaV/faSqsH37dv1raJT2ZdOF1q1bm1ZVCAtrrz/XE08MqbMzlcxwZdMDmTn36NEDb7zxhn7ZDhGRr/GL0K2JlEHlF7bs7ytB89133+nlaSFhcuutt6JLly5XA9nVmZq/kOCTVcASsh999BHmz3/z6ipy6frkrrK9fF+MHXumTZuqVy6efPIpffbq3DRDvncyu16zZrUWtBkYMmSIflw6nMkfAmy/SES+xq9DtyYyM5adgIyG/sb2fsYuPcYM2QhlYZRQ/WmmLKErn6sYO3aMZZdrSeguW7YMM2fO1Mey49D69eu1tz/r54LvuecefVehqKju6Nevn76y3fl1GSXyTz/9jOfzicinBGTo1sXYhceYJTsvFjLOawqjNOsczlW3ufPWc4/GYirpsGR1d6WqoessKSlJm2V3RWJiYq1/3EiZXJqsWHmNMRFRYzF0G8hY0CWc98Z1DmjhvMdtdSt6jcVIzoxZdVVmlb/lGmjjcixPNJmoLXTlPtkW0pVLmKzeU5eIqLEYuhZyDmpDdXvWGuXu6ri6UX1Nl+zIpTp/+9t/45NPdmqz83CvC10hvbmlclBXmLLMTES+hqHrx4xz184kdIOCgvTZtLGQymp1ha687qiobtddwlQdlpmJyJd4tA0kuZcElpxTdn677777aixfW0XOlct58JrI6548OQ3v1bEZgpDZsFwzLCVzIiJvx9Aly8niNGPhWU1kIdXatWv0EnJdUlNTsWTJYvbqJiKvx9AlrySLqJKTUzB//nx1pGYyM87IeBNJSb/SS9NERN6KoUteS1YmyyVacg64LrJj1ZgxY5GWlqaOEBF5H4YueS2Z7c6aNVvvXuUKY8MGLqoiIm/F0CWvJo07ZAX27t0VuxfVZcYMafixxuXHExFZiaFLXm/ChAn6JgeukPO7q1evwbBhT7tUliYishJDlywnm0/IrkWuktmu9MKWa3JdIY0ypL2ldLZyZfUzEZFVGLrkEU2bNlW3XCM7DM2d+we9q5crJKhl9fPw4c+4/D5ERO7G0CWfIO0zZQYr3adcJY0zhg17BikpKQxeIvIKDF3yGYMHxyEpaXy9rsWVTRG6devG4CUir8DQJZ/RrFkzl9tDOnMOXp7jJSJPYuiSTxk6dKjL7SGdSfD27NlTP8fLVc1E5CkMXbLckSNH6r2QyiCXBLnaHrIqaZ4hzTZkVbOrK6GJiMzE0CXL7dmzu1H739anPWRVsqpZruOVBVlPP/203kRDzvWy7ExEVmDoks+R9pBTp051uT1kVRL40ipSmm787W9/0zfzHz58OHbu3KkeQUTkHgxd8kmPPda/Xu0hqyOz3okTJ+ob+ScnJyM7O1vdQ0TkHgxd8ln1aQ9ZF7mmV841s2czEbkTQ5d8Vn3bQ9ZFtgWUEOf1vETkLgxd8mmjRo1Cevo8U4JS9uSVEK9P1ysiovpg6JKlZMXxoEGD1ajxwsPD0bNnL9OCcty4cXqI16frFRGRqxi6ZLkWLVqoW+ZITU2td3vImsjKZunXXN+uV0RErmDoks+ThhkNaQ9Zk8TExAZ1vSIiqgtDl/xCQ9tDVkeuA25o1ysiotowdMkvNKY9ZHWk65VcQsQ+zURkJoYu+YQ2bdrg8OHDalS9xrSHrEpmu3IdsFxGRERkFoYuWers2bO49dZb1ch1t912G/75z3+qUfUa2x6yKrkOWLBhBhGZhaFLljpz5gy6dOmiRuYzoz2ksxkzZmDy5ElsmEFEpmDokt8xsz2k2dcBE1FgY+iS3zG7PaSZXa+IKLAxdMkvmRmUMtuVhhnr169XR4iIGoahS37J7LKwXAc8ZcoktockokZh6JLfkvaQZvVRNrvrFREFJoYuWSonJwedOnVSI/eSoDSzj7LR9YqzXSJqKIYuWa5p06bqlvuZGZRG16slS5aoI0RE9cPQJb9mBOXcuXPVkcaRrlfZ2RvZHpKIGoShS37P7PaQEuLLli1TR4iIXMfQJb9ntIc0KyjNDHEiCiwMXQoI0h5Sdg0yoz0kZ7tE1FAMXbKUBJ+VC6mcmdkeklv/EVFDMHTJUnv27MYdd9yhRtYy2kNu3bpFHWk4Y+s/znaJqD4YuhRQpD3kq6++akp7SAlxznaJqD4YuhRQzG4PydkuEdUHQ5cCjpntITnbJaL6YOhSwDG7PSRnu0TkKoYuBSQz20NytktErmLokmUklAYNGqxG9SOXGUmwmcXs9pCc7RKRKxi6ZKkWLVqoW/UjlxnJ5UZmMrOzFGe7ROQKhi4FLLPbQ44dO4azXSKqFUOXApqZ7SHlUiT2ZCai2jB0KeCZ1R6SPZmJqC4MXQp4cj62VatWprSH5A5ERFQbhi5Z5uzZs7j11lvVyLukpKSY0h7SmO1u3bpVHSEiuoahS5Y5c+YMunTpokbexcz2kDLbNesaYCLyLwxdImXcuHGmtIeU2a6ZHa+IyH8wdIkUuRbYrLCUjlezZs3gbJeIKmHoEjkxKyyl49XkyWn45JNP1BEiIoYuUSUSlhkZb5nSHjIuLk4vV5uxdy8R+QeGLlEVZl32I+Vqo2EGEZFg6JJlcnJy0KlTJzXyXmY2uRg1ahQWL16iRkQU6Bi6ZCnZLcgX2Gw2U9pDyqVIwow2k0Tk+xi6RDUwqz2kPM+KFSvUiIgCGUOXqAZmtYeU58nPP8TWkETE0CWqjVntIdkakogEQ5eoFma1h+zduzebZRARQ5esIwuTfGUhlTMz2kOyWQYRCYYuWWbPnt36tau+xqz2kI899pge3kQUuBi6RC4woz2klKojIiJ5+RBRAGPoks8YNGiwx1YAm9UeMiEhgZcPEQUwhi75jBYtWqhbnmFGe0jj8qGTJ0+qI0QUSBi6RC4yqz3kmDFjsWHDBjUiokDC0CWqBzPaQ8bGxurnh7n7EFHgYeiSJaQkK+dk/UFj20PK+eERI0Zy9yGiAMTQJct4+pysWcxoD/n4449j/fosNSKiQMHQJWqAxraH5IIqosDE0CVqADPaQ3JBFVHgYegSNZDRHrKhs11ZULV27RouqCIKIAxdogYy2kNmZmaqI/UjC6qkQ9Xnn3+ujhCRv2PokiXOnj2LW2+9VY38R2PbQ0qHqg8//FCNiMjfMXTJEmfOnEGXLl3UyH8Y7SGXLFmijtTPAw88gJUrl3PLP6IAwdAlaiRpD5mdvbFB7SGly5Vs+Zebu18dISJ/xtAlaqTGtoeUy4d4zS5RYGDoEpnAaA954MABdcR1999/P6/ZJQoQDF0ik0h7yBkzZqhR/cgq6O3bt6sREfkrhi6RSYz2kA3ZDEHel40yiPwfQ5cskZOTg06dOqmR/5L2kJMnT6p3wwspMZ8+XcwSM5GfY+iSZZo2bapu+a/GtIdkiZnI/zF0iUzW0PaQLDET+T+GLpHJGtoe0igxs1EGkf9i6JLPkDaS0k7SFzS0PaSENRtlEPkvhi75DGkjKe0kfUFD20PKbJeNMoj8F0OXLLFr186AWEjlrCHtIaUX88aNf+F2f0R+iqFLljh27Kh+rjOQNKQ9pLzPiBEjud0fkZ9i6BK5UUPaQ0ZHRzeonSQReT+GLpGb1bc9ZI8ePXi9LpGfYugSuZlcfytcbQ8pZXheOkTknxi6RBaQmW592kPGxg7C119/rUZE5C8YuuR2XIlb//aQcnkUz+sS+R+GLrndiRMn9BW5gW7UqFEut4eMjIzEwYMH1YiI/AVDl8giMtt1tT2kPFau1yUi/8LQJbJQfdpDDho0uF6NNYjI+zF0iSwk7SFnzpztUnvIjh074vjxQjUiIn/A0CWyWHx8vEvtIWUxVWlpmRoRkT9g6BJZzNX2kJ06dUJOTo4aEZE/YOiS20mJtEOHDmpEQjZDqKs9ZKBtEEEUCBi65KQEBdsyMLpre4SFaW8xaViRWwyHurfCFRTvXaQe0wUxaauQW3xF3Vc9KZG2a9dOjUjIbLeu9pDt27fHypXL1YiI/AFDl5QrOGWfirjx+ehlz0dRUT62DPsWM20v4k+5F9RjHCjNXYTE+I0IXZiDwsLtmPSjtfjFK9k4VTmZyQV1tYeUYCYi/8LQpQqOY9j8zke4aexYjOgSoh0IQZeRyZgYlY/0V+wokFB1FOD9V+bjeMJvkNonFEFBoeidEI/w7LmY/8k5/WmofurbHpKIfBtDlyqc+Qo786qslA26Ez2HPAgUHMXJUgcc33yKrLyb0LPHXVokq4fc9TCGRJ1F1pYvUaKOkevq2x6SiHwbQ5cqNG2O24OBH86V4JI6dFXZeVy4VI7Sk0dRgHaIDGuh7tAENUXzNjeh7ItCnGaJuUHq0x6SiHwbQ5cqhNyL/kM6omzFHzHHfhil2iFHcS7+urMACG6J5k2BSxfOo8arRovO42INoVtaKs9GNampPSRDmMj/MHRJaY0+k99GRgKwIqkfIsIGY+qa/0L25lMIHvJzdA+p40clrCVuqeEh+fn5egP/xvLn61araw/JjSKI/A9Dl65p1gW2GX9BUdEJ7e2/MPGBm3AcPTA2PgohaII2kQ8iSpvrniv5Xr2Dpvwsju07j+D7OuJ2N/80+fN1q9W1hzx06BCvbybyMwxdqoYDpYdXIeXF93Bn8hSM6d5cP1rdoinHsYPYfr4jhvS/9+riKmoYaQ+5Zs0q2Gz/B8nJE/DOO+9cvayIiPwDQ5cqKy3AjsypeLL/m8CLy5D56x5opu5CUCcMeC4GyFqLrMNa7JYexobM9SiITcW43q3Vg6ihPvtsj15e3rv3M7z//p/xxRcHONMl8jMMXapQnov0qPYIi3gcsws6Y5x9AxYnPYK2lX5CbkSo7VVsmNUGa/tHaI+NwyI8jw1z4xDKn6RGe++9dfjXv8px+fIlfP/9JZSXl+Pbb79V9xKRP+CvSqrQpDuS8+Rc7mF8NON5DO7etoYfjhCE26bjI/28rzzWhvBm/DEyQ1hYGIKCfoSbb/4xmjS5ETfccIO6h4j8BX9bktvt2rUTrVq1UiOqyS9/+Uu0aNFSC9x/w7/9278hIeFZ/XIiIvIfDF1yu2PHjuqrc6l28jUaPXqMGgE9evRQt4jIXzB0ibyEbGo/d+7ragR2qSLyQwxdIi9RdVN7qRBU7VKlkxXmWfOubcGob7GYiR0F32DHtD9gRwn7cRJ5K4YukReQ7f2q2ztXulTJDNjgKN6GaU8+jpGLv0WvhduRry9o+wKZ8c3x+ZxnMDLzOC5cYugSeSuGLpGXyMh4S39zvi1vly6pLShK9+JPiS8h83gMMt75PRL7hKtrqG9E2+42JL8xH8kRP9KPEJF3YuiSW/GcpGuk85TNZtPfhHFb3u6//37tiAMl+/6CxfllCB7yBH4eeqP+uEqa3Y+hL9yFixfL1QEi8jYMXXIrNu03y3nkbvkYZait5aY0L0lCQvjNakxE3oahS+QTLuPCael4HYzWIQxVIl/F0CXyKVV2eSIin8LQJfIJtyGy133av2fxReG34PpkIt/E0CXyCTfjrgFPITa4DHlzFmDDqSvquLMrKN7xNjJzL6gxEXkbhi6RjwgKjcUrC19ARNl6JD33n8j8Sy6KjSlvaQG2pf8WrxQ+hCfV/sdE5H0YuuRWx48Xck9Y09yItn1eRnbOBmQMLMaccXGI7ljRlarrhL/g4qOTsSAx8tr+x0TkdRi65FalpWVo166dGpEZgtp2hy35bXyld6OqePtqaQpsNW7HSETegv9HyWc0bdoUR44cUSMiIt/D0CWfcccdd2DPnt1qRETkexi6REREFmHoEhERWYShS25VWlqqbhEREUOX3Co/Px+RkZFqREQU2Bi6REREFmHoEhERWYShS0REZBGGLhERkUUYukRERBZh6JJb7dq1E61atVIjIqLAxtAltzp27ChatmypRkREgY2hS0REZBGGLhERkUUYukRERBZh6BIREVmEoUtuc/nyZXWLiIgEQ5fc5sSJExgxYqQaERERQ5eIiMgiDF0iIiKLMHTJ5/BcMRH5KoYu+RQ5RyzniomIfBFDl4iIyCIMXXKb48cL0aFDBzUiIiKGLrlNaWkZ2rVrp0ZERMTQJSIisghDl4iIyCIMXSIiIoswdImIiCzC0CW3KS0tVbeIiEgwdMlt8vPzERkZqUZERMTQJSIisghDl4iIyCIMXSIiIoswdImIiCzC0CUiIrIIQ5fcZteunWjVqpUakTlKkZs+EGFh7RE22o5idZSIfANDl9zm2LGjaNmypRqROZqhe/J/Ydv0xxDVqyvaqKNE5BsYukS+xnEcu7K+Rd9ud/A/MJGP4f9ZIl9T+g8UFD2AB+5uqg4Qka9g6BL5FAdKcj9G1oPdcU9IKQrs0xAT1gUx6XvBpptE3o+hS+RTruB0YRHCe7XDd5nT8ccLQ7HW/ksUv/s3/E+5eggReS2GLrnF5cuX1S1zdejQAcePF6pRANLP5/4D9323HSsxCnMT78LZg/tx/sHOCG2iHkNEXouhS25x4sQJjBgxUo3M065dO5SWlqlRADrzFXbmHULW4XswbmQkmukh/AVXMhP5CIYukc9woOTrXOxCD4wd2weh8r9XFlUV3IchPe/kf2YiH8D/p0Q+4xKOfP457kyegjHdm2tjtagqvD963nVzxUOIyKsxdIl8heMkDm4HBj7aFc30AxLCnwH3BaNo+Vrkljr0o0TkvRi6RL5CzucWOF+f+x2KDv0DZfu/wMWesejejP+dibwd/5cS+Yq2Niz9ajr6hBj/bTvAtvQgij6aDlt4iDpGRN6MoUtuIZf1yOU9RER0DUOX3EIu65HLe4iI6BqGLhERkUUYukRERBZh6BIREVmEoUtERGQRhi65RWkpN5ojIqqKoUtukZ+fj8jISDUiIiLB0CUiIrIIQ5eIiMgiDF0iIiKLMHSJiIgswtAlIiKyCEOX3GLXrp1o1aqVGhERkWDoklscO3YULVu2VCNz8RpgIvJVDF3yKXLtr1wDTETkixi6REREFmHoEhERWYShS0REZBGGLpnu8uXL6hYRETlj6JLpTpw4gREjRqoREREZGLpEREQWYegSERFZhKFLRERkEYYuERGRRRi6REREFmHokumOHy9Ehw4d1IiIiAwMXTJdaWkZ2rVrp0ZERGRg6BIREVmEoUtERGQRhi4REZFFGLpEREQWYeiS6UpLS9UtIiJyxtAl0+Xn5yMyMlKNiIjIwNAlIiKyCEOXiIjIIgxd8imtWrXCrl071YiIyLcwdMmntGzZEseOHVUjIiLfEpihW2zH6LD2iErPRbk6RERE5G6c6ZLppPwrZWAiIqqMoUumk/KvlIGJiKiyxoduaQG2pT+PrmHtERbWBTFpbyF9dDTCouYhV2q3eilXOz46ETHqMXGZh+FACQp2ZCItpot2TI5HY3S6HbnFVyqet9oS8N9hH91NPXe59pDx2vslIt3u/DyDkWY/jGvtGRzaS9xS8ZqM+9d8ihPqXiIiIqs0LnQdRbCn/gKjNt2BWdvyUVS4HZN+tAnpm0+pBxjKkL/rZgzbko/CnCxMj7lDC8ypiBu5AKeHZSG/6IR2fBZCN02ELXERcksd6v1csRXpi46ix5t7tY+fg+WJwIqk5zFrxzn9XsepDUiNG49Nt0/Btvwi7eNMwI822ZGv30tERGSdRoWu45uP8U72jUiYlARbeIj2bKHok/obJASrBzjrGYOYLiEIahuJqKb7MH/yeiB2CqaPjEQz7e6gtn3xu5njEJE/H6+8X6DNT13VsdLH750QjygUYuPnRdoM+Xt8s/nPyMZQTJoYh/BmQfrHSZ00FNW9RCIiIndqROhqgbZrC/K0iOtxT3N1TBNyL/oP6agG17SMDENrddtxuhBflAUj/KGuaHv1FQSh2d3d8NPgMhQU/MOpPFyXYLQOuVnd1p7lluZoo24DZ3Fo5xda4HfHPSHGBwpCyD3d0VONiIiIrNKI0C3Hxe8qSriV3YyQ1rXPIx0Xz6MIN6FN86aVX0DTELS+CSg7fQGX1KFGKT+LY/vOq4GT1mGI5Doft7h8+bK6RUREVTUidJvglhYyd/0OFy46X+36PUrOlanb1Qu6pSXC8APOXLhUuYx8qQTnftDmrrc3R1N1qFGa3IZOD2rpeuYCLjp/oHNFOFRNFgeClStXqgVl7fWxcVve7Ha7fqwxTpw4gREjRqoRuWrhwoVu/b4QkXdoROjejLt69kcUjqPgpFMxuPQYPt9/Vg2qF3R7R9wnZeQ9X6H4ahg6UHrkIPZL2Tm8nX6e9zol32Dvrvqk5W2I7HUfUHAUJ68uznKg5Otc7FKjQBMfH49OnTqr0TVybODAgWpEVhs6dGi135eHHnoENptNjYjI1zUidLV3vuvneC72ClbMzoC9oETLs1PY8fp0pOfXPtNFyCMYNyseyJ6JacsP6edvHcXb8fqU+ciPGIdXngxHUJuu6BUVjPOLF2PlYXnuYuzNXIGsOp66Mu0PgwFPIRbv4MWUVTisBa98nLmz30O9nsaP/PjHP8bUqVPV6JpZs2br95FnyHXNyckpanRNWlqaukVE/qBRoYugMNjmrsKygScxuV8Ewjr2xex/9URCRF1rg29EqO1VbFj+Em5fOwQRYe3RMXoyTg2cA3vmC+jeTHtZQV0wcvEypPbMxbT+8txx+L//egBD6nzuyoJC4zB3wzKMxZvoHxGmfZw38K+BNkSo+wPRY4/1x6BBg9UIejn4kUceUSPrFRQU4OTJk2oUuGRGKzNbg3xf7r//fjUiIn9ww/9q1G2TSAOLQUjCdOQstaGtOkreRYKuX7+++u1t27YjPDxcv91Y8rzLli3DzJkz1ZGayaKrhIQRyMn5TB8nJDyLGTNm6LdrI+c5i4r8s73JgQMHMHjwIP12Xt5BdvYi8jONmOk6ULJjGrpKJ6nMihIxpMuUfQkWbb4ZsY93d7p0h7yNhOy4cb/C5MlppgVufS1f/q4euD/88L3+tmLFu9i9e7e6NzDJzFZmuDNnzmbgEvmhxs10HcXI3bAaCybPw2bjJGnEs5g+KRFP9gnXF0MZqzGJqpIfPYfDoc14y3DDDTegadNm+r/kH/y1GkHUGG4oLxO5ZseO7Rg5MgHl5eUICgrS31hSJSJ/xtAlj1q3bh02bKi4DjUpaQKio6P120RE/oihS0REZJHGXTJERERELmPoEhERWYShS0REZBGGLhERkUUYukRERBZh6JKHncOOtF4Ii8lA7tWdoIiI/BNDlzzKcWon1mYVAvnrsH5fgG5yTEQBg6FLHvQ9vtlsR2HPxxCBQmRt+RIl6h4iIn/E0CXPKdmDzDn/D8N+OxkvxIaiLOsDfHzqirqTiMj/MHTJQxwoyf0YGx99CgPCw/HzYTEILvsI72w+pt1DROSfGLrkGY4CZM3bhUHDeiE0KAgh3X+OIcFlyMv6FN8wdYnITzF0yQMcKM3bhLVIQGLv1hWHQqIQP7YHkLcUmZ+cqzhGRORnuOEBeYBcJmTDyBWFalxZcMJKfDajD0LUmIjIX3CmS5ZzFHyIeVk/x/Ivi/SNzq++FW7D9KhglGV9jNwS1piJyP8wdMlapYewfM4CFI21oVdIlR+/oLsQ81x/oOw9zJ6zAQVslkFEfoblZbJOeS7SH4xDutEDY8BbyFlqQ1t9UI5i+wREJ1VsaF/BhoycN2Br20SNiYh8G0OXiIjIIiwvExERWYShS0REZBGGLhERkUUYukRERJYA/j888ew9E+3FTAAAAABJRU5ErkJggg=="></p>
<p>The end of one of the blades of the turbine is represented by point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> on the diagram. Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> be the height of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> above the ground, measured in metres, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> varies as the blade rotates.</p>
</div>
<div class="specification">
<p>Find the</p>
</div>
<div class="specification">
<p>The blades of the turbine complete <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math> rotations per minute under normal conditions, moving at a constant rate.</p>
</div>
<div class="specification">
<p>The height, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math>, of point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> can be modelled by the following function. Time, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>, is measured from the instant when the blade <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[BC]</mtext></math> first passes <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[AB]</mtext></math> and is measured in seconds.</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mn>90</mn><mo>-</mo><mn>40</mn><mo> </mo><mi>cos</mi><mfenced><mrow><mn>72</mn><mi>t</mi><mo>°</mo></mrow></mfenced><mo>,</mo><mo> </mo><mi>t</mi><mo>≥</mo><mn>0</mn></math></p>
</div>
<div class="specification">
<p>Looking through his window, Tim has a partial view of the rotating wind turbine. The position of his window means that he cannot see any part of the wind turbine that is <strong>more than</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mn mathvariant="bold">100</mn><mo mathvariant="bold"> </mo><mtext mathvariant="bold">m</mtext></math> above the ground. This is illustrated in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAeIAAAFQCAYAAABj633dAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAACa3SURBVHhe7d0JeJTV3ffxn6kFJBGRJUWIkUBSSnBh0ZQK8taVFK2NUOtSgmDBarFUqK1AlLZuAV8EilsfsRoJWuxbaB4VHpG1KH0sSMAl0TRoMBACKgQipEIxfedMzmiALDPJJPd9z3w/15WL+5wZJkDC/HLOfc7/nPQfHwEAAEfE2F8BAIADCGIAABxEEAMA4CCCGAAABzV5sdb27du1c+cO7d692/YAABB9unXrpt69k3XGGWfYntCEHMQmgFeufFV79+61PQAAoHPnzrrqqu+HHMghBfGqVav05pubbAsAABxv6NChvo+LbKtxQQcxIQwAQHDOP/8CXXbZZbbVsKAWa23atIkQBgAgSCYz3377bdtqWKNBfPDgQa1evcq2AABAMNauXaMjR47YVv0aDeI33njDXgEAgGD961//0ltvvWVb9Ws0iAsK3rVXAAAgFFu3brFX9WswiM0WJZPoAAAgdCZHG5uebjCIg5nbBgAA9Wus7kaD25fKy8v17LM5ttWwSy8Nbpk2AOc9//zz/q0V8fHxtid0hw4d0gsvLNbIkaPUsWNH2wtEj2AXMt9009gGi3yELYinTp1mrwC43fTp0zVu3DilpKTYntDNmjVLPXr00OjRo20PEF1mzsy2Vw1rLIgbXawFAMczK0GXL1+mUaNG2R4ATUUQA1GooqLCXoXOLOB84IEHlJ09U6eccortBdBUBDEQhZYte6nJ09IrVqxQcnKyLrzwQtsDoDkIYiDK7Nu3T0lJvWwrNOb3Tpp0u+68807bA6C5CGIgyrz//vsaMmSobYVm9uzZmj//UXXq1Mn2AGgughiIMmahVVpamm0F7+9//7u2bdum4cOH2x4A4UAQA1Fm7dq16tevn20FxyzQmjZtqrKysligBYQZQQxEEXOPd8+e3SEv1FqyZIlGjLhS5513nu0BEC4EMRBF8vM36/rrb7Ct4JSVlWnBgic1YcIE2wMgnAhiIIosWbI05G1H999/vyZPnsICLaCFEMRAlDDT0oWFBSFNL69atdJfsD4jI8P2AAg3gtg1jmp33u1KTByuufkHbd/xgnlOMHYob/y5Suw/R/lHbRci3vr160OaljYLtO677z5/FS0ALYcgBlzH/qCUmFDnR9/xc7R0XbFC/VHMnLgUyrR0Tk6OP7ibczAEgMYRxIDrnKmMp97W9tX3q7866Yr5/6vS0p2+j1IVrn5Gt2ix7hjzY92ZV6pq+zsaU1xc7P812Glp8/zFi/+ksWPH2h4ALYUgdp0KFayep/F97QgoPUu5+bvrf8M9WKx1OVlK/3LE1EfpWc8pf/cR+wQf33NWz/2J+tZ6fNPOw/bBGtW7Nyk36/v2Ncyoa75WF1faR+GEmFM76tjTgmMUl3K5fnHXz3wBvUvLn16jD4JM4lWrVunGG2+0rcaZ/cL33HMPe4aBVkAQu84uvfr0Tg3NK1Tp9o1amPa2sjJu0+/z99vHa6kuVd6dP9aYxado6sYPfSOmD7VxyWQlLL1LP37k7/LHqH3OuBU9lL3avOZaTf3aBuUWHvK/hN/BTfr92NF6cM+VWmJex/d5n+i+UuOuvkd5u2oFOlwh5hs9dU6sbQTBLNLKzn5Aw4YNsz0Ny8vLU+fOnXXZZZfbHgAtiSB2ne4akT1dY/p08H11uuu7v56hyamFenLJ1ppgraX6gzV6evkB9b/+Wg3r1sbX00bdBl2soSmxOrQsX9uOBp7TRplTJykjxb7mnb9U5pdv5J+r+C/zNLfwfN1111hdYF4n8Bwt0bTHbKDDHQ4WKW/Ww8o95Ps+ufkS9Q7if7BZpDVtWlZQ249MaM+dO0dTpkyxPQBaGkHsOika3C/+qy9MXJIGDOr6ZbDWFpMyVi+Wvqfnh+zRi75RTF7eYs29JVMztgZGu0f1ccGb2qr+uuBbHW2fT4feumBI4E35ExW8/o7UaZDOTWpn+3zsc+r6vGhN+/TqpO98ecsgMfVSTcrdotjMh/RQRmKj/4HNymcTrJdddpntadiCBQs0YcItLNACWhFB7Dqnq+OpJ9tro506dKlnHrJ6l9bN+IFSL71R017+UNW+5yaNfkD3XhEI2c+1q6Rmkc6xTldivzNqLqurtP/jw773+znK6GXf7P0f39GkV/fVPAcOqr1Ya6e2b3xR8ycPl3JH69vjc1V0sOGbxFu2bPGftBRMsJrDIJYvX6ZRo0bZHgCtgSB2vc9V+Wmt+7lfqlbl+j/otpw9GjH/7yp4aopGZmQoY1iiZILVr526J5k34Art/6z2sLZCpQXlNZcx7dUxvq3U/36t3l7zZn/Mx9YpGlj75wI4KqbbQGVMnqUnMnvq0Kv361d/KW5w5fS8efN03XXX2Vb9zMjZ7BfOzp7JAi2glRHErrNVm96vtTCr8l2tXLpdsVcOVPIxgVitqv37dOj4qeyD5SouDgT3yYrvd7766yMVl9XadVr5gTZtCIx2u6rf0HN8n3alNnzwue3zqS5SztV9lHh1joqD3SMDVzHHFhrBbFlasWKFkpOTQy5/CaD5CGLX2a7cmfOVZ7YOmann2Q8rV6OUPfFCdbDPqBGjuMRvKlVvavHL7/iLO/i3IPkX8vgah/ersqpaMb0v0c0jjij3truVU1TrNb8cZLdT7yuu1YjYv2nWrBxtMtueqndr06MPadbWVE3+bYZS+C5xQLUO7irVTtv6ku9rk587VzNzt0ux6br5iqR6/xOb0fAdd9xhW/UzC7QmTbpdEydOtD0AWhNvsa4zQJnDD+sPl6YqsWeaxmwcoPkv3qeM7mZVdG2+IB44Vo/Mv06ae41SExPUM+1evZ9ym+ZPHiId+kDb9/hCNSZRGbOf0zO3/FuzLjevebFmfjFEmalf3XeO6Z6hx9f+VdO/sUyj0nr5nnO+Ri3vpul5T+gXA2st8kIrMZW1+is14yEVHr9Yy/e1ychaqYTJc7Wwzu+LGoHRcDAj3NmzZ2v+/EfVo0cP2wOgNZ30Hx97fYLy8nI9+2yObTVs6tRp9gqA0370ox/5R8ONBbFZoGXuDT/77LPcGwZCNHNmtr1q2E03jdUZZ9gFsnVgRAxEmGBHw2aB1qRJP/dX0SKEAecQxC5i7tWZGr/1fZgD2oG6mFANfJ+YEe7Pf367faR+S5Ys8W9tCuVYRADhx9S0i/z5z3/W448/5hvJDLE9x9q2bZveeKNmtNOQpKRe/jfYYKSlpdmrhvXr189eNSwhIYHRVSsyo9+nnlrgPzf4iivS9cUXR3X06Bf629/WasCAgfrVr36toUNP/F4wP9TdeOMN+utf8zjwH2iicE1NE8QuYkbEt956qz+Qm8O8jjnMvTFVVVUqKSmxrfodPHhQhYWFttWwRYsW2quGDR58oX+7TGPOPPPMBr+BA+LiYnXWWT1tq37t27ePiEVJZgR8991ZKigo0KhRP/QX7Gjbtq19tIb5we2ll170/dvE6b777j/m7z19+nT/D2Ec+A80HUEcoaLlDdKMyMwPAo356KPtvh8E6ipocizzvbpjxw7bql+wswrG6NFj7FXDgp1VSEpK8v8g0JjGZhVMCE+c+DN17dpV3/veiBMC+HivvrpCr7zyP/rLX5b6w9iMnp98ckGzf+ADoh1BHKHMaPaaazL8FY4oruAcE3Y7d56wi/cEwc4qGBs3brRXDWtsVqFbt266+OJLfD+sXWN7Gvfaa+tVWPiennjiCaWnD9dTT/2RetJAMxHEESxw/84U3x89erTtBWq2G02efIdmzPhNoyPh45l7yWakfeaZibrrrrtsL4CmYvtSBDPTh2YRjbkve9ttt/lXwgLG0qVLdcMNN4YcwkZ6err+8Y9/aNKkSbYHgBsQxC5lVrI++OCDGjVqpMaP/4l/StFMWyO6PfNM3VPKn3zyiaZMmazrrrtWd9zxC3/7eAkJZ8pMgPF9BLgLQexyl112uV55ZYV/WsPcO541axYj5Chlvu5Dh15U52h4wYIntXPnDh0+/Ll27SrT1Kl1Tz2fc845QS2SA9B6CGIPMPf1zCpqE8h9+vTxV0IyJQzN6ldGN9Hl1FOPPfoj4K23turIkcP697+P+H89ePAz+8ix4uPj/VueALgHQewhgUA2205MGG/enK/+/c/130cmlKPDZ59V2qtjnXdef7Vp01Zf/3ob/69xcafaR4718ccfB12cBUDrIIg9ypQlNCtfi4qKlZmZeUwo5+XlUQ4zApl7w6+//poOHz5se75iVtibe8Bt27bzb2+aOXOWfeRYZgFgMHuZAbQeti9FELP39Z///Ke/7OHatWu1Z89ujRhxpQYNGqi+fVM55s6jaq8J+MMfntC3vtVXZ599tu0JnrmHvGjRIv33f79oewA0B/uI0SgzVZ2fv9k/Wt68ebM/mE0NalMJylR5+uY3v0ldaAcEqooFqobVrgp2fOWv4+uGm9XQJSUf6u677wl5C5MJ8R/8IEMjR460PQCagyBGyEwwv//++/rwww/9U5SmgpOp+Txo0CD/IjATzqa2M4cAhIf59zYBaypvmapagZAN1NkO1NGuXSe7c+fOjf7733bbrf7p5R/+8Frb0zhTWWvVqlUaP36Cf6EfgOYjiBEWZtrTjLJqh7Nh6iwHgsIs7gkmIKJd4Aed1157TcuXL/P31Z6B6NKlS1huD/z617/2j4p79eoVVK1pE8J//etSPfro47rmmh9o69a3+VoCYUAQo8WYQDGnN5ltLoFp0w0bXve/+V955fd1+umn+8MlMJKLlBONmsLclzf/NkuWLNWyZS9p4sSft/g9eXMwyA033KCcnGe+PH2prnvGdZ2+ZBbymdG5KRYDoHkIYrS6wEEIZgRttsEcH9KB+5mnnXaaf6rbCGyVibRzis2/xYoVKzR37hz/3/mqq67SgAEDWuXvaIJ43LhxdhX163r66T/6t69ddNEwtWnTRjExMXr33Xf9q6ePP4/Y/Llvuukm3XHHHRwqAjQTQQzXCSxCCgR17XOMA1PetRcf1T5ruPYRgW6fBg8cymH+HhMnTmz12YDExIQTppdNwObk5Oidd97W5MlTGvw3NLcjTNlUUyCGxXpA0xHE8KTAtLdR+6zhoqIiHThwwH99/Mrh2ucC1x5tB9R1zm9LTZcHQtjJYypNEJeWnnhEownjYI84NNuYzN+FU5iApiOIETWOr619fInGwBT58QJT5nUJ3OsO1fbt23XzzeP8NcCdUl8QG2aKes2atY3eA2aKGmg+ghhopuMDPhhmRfTNN99sW85oKIgNsz0pmIANTFGbIzdZRQ2EjiAGolRjQWwqq82bN89fk7wxZora3MdnFTUQunAFMbWmgQhjRsJmsZaZpm7M6NGjVVFR4d/WBMAZBDHgIWaxm1l53pgpU6bovvvu898Lbszdd9/t34bVlKl6AM1HEAMeYlacB7Z/NcSsmjbPM3udG2NWl5tV4OZ+cTDBDSC8CGIgQpk9zmaka0bRjTHT2ddff4N/JA2gdRHEQIQyI10Tri+88ILtaZg5y9p44okn/L8CaB0EMRDBrrvuOmVnPxDUqNiYM2eOFi/+U1ALvQCEB0EMRDCzP3j+/Ec1e/Zs29MwU/Ly+ef/5F/oZbZBAWh5BDEQ4YYNG6Z169YGvSo6sHhr2rSp/jKYAFoWQQx4iCnvmZqaalvBMSutzQEbzzzzjO1pnFm8ZcLY1NUmjIGWRRADHmPOFw5V797J/sM0QpluJoyB1kEQA1HC1J82pS9DQRgDLY8gBqJEKKUvawuE8Xe+820WcAEtgCAGokgopS9rM2G8evVa/wIuc1AEFbiA8CGIgSgSSunL45nfa45MNKc1mbOMGR0D4UEQAx5ijiaNi4u1raYJpfTl8cy+ZHNkYlZWlnJzc/1HMg4e/G3fSJljUIGmIogBD9mxY4fOOqunbTVNqKUv63Leeef5S2Gac5EfffQx3+h4A9PVQBMRxEAUCrX0ZUPOP/98f7Dn5OTYHgChIIiBKBRq6cvGmGA3NarZ4gSEjiAGIlxCQoIWLVpoW18ZPny4Nmx4PejSlw0xwT558hQ99thjtgdAsAhiIMKZgxzqYvpNeIZS+rIhJthN9a633nrL9gAIBkEMRLGMjIyQS1/WxwS7qd71wAMP2B4AwSCIAQ8xU8xmqjmcmlL6sj5Nrd4FRDOCGPCY+qaamyrc4dnU6l1AtCKIAYQ1PE0FrhEjrmxS9S4gGhHEAJpV+rIuEyZM0KRJt4dlnzIQ6QhiAH6B0pfhGBWb7UzTpmU1q3oXEC0IYgB+gdKX4aqQNXbsWH+Rj3DsUwYiGUEMeISZ5k1K6mVbLSOcpS/DvU8ZiFQEMeARe/fu9d/HbUmB0pcLFiywPc0TzupdQKQiiAEcw4Tn8uXLwhKeZlScnT1Tc+bMsT0AjkcQAzhGuKeUzT5lM5oPR/UuIBIRxABOECh9Ga660eGs3gVEGoIYQJ3CWTc6UL2LUTFwIoIYQJ3CHZ6mepcZFVP6EjgWQQx4REFBgVJTU22rdZjwnDZtathKXyYnJ1P6EjgOQQx4SFxcnL1qHeEufTlu3LiwVe8CIgVBDKBB4Sx9Ge5gByIBQQygQeEufcmoGDgWQQygUeEsfckxicCxCGIgCgwefKHKyspsK3ThLn1pjklkVAzUIIgBjygvL1dcXKxthcasVq6qqrKtpgln6UsT7Ga6m1ExQBADnrFjxw6ddVZP22p94S59aaa7GRUDBDGAEISz9CWjYqAGQQwgJOEsfcmoGCCIAYTIlL40wlH6klExQBADaAIzIg5X6UtGxYh2BDGAkIWzQhajYkQ7ghjwiEWLFiohIcG2nBfOCllXX301o2JELYIY8BCzhcgtzKg4XKUvTRlNalAjWhHEAJosnKUvqUGNaEUQA2gyc3/3wQdnhqX0JSczIVoRxACaZdSoUWErfWlGxc8//7xtAdGBIAbQLOEsfWlGxaYudjj2KANeQRADHmDuwSYl9bIt9zEHQoSr9OVVV12lefPm2RYQ+QhiwAP27t3rv3/qVmZUHK7Sl+Gs3AV4AUEMICzCGaAm1F9++WXbAiIbQQwgbMJV+tKE+oYNr4dlARjgdgQxgLAJ5xakcJ59DLgZQQwgrMJVmMMsADOj4nAUCwHcjCAGEFbhKn1pFoCZ13nhhRdsDxCZCGLAAwoKCpSammpbTVNVVWWvWl64Sl8GXoeyl4hkBDHgEXFxcfYqdGlpaSopKbGtlheu0pfmdSZO/DllLxHRCGIALSJcpS9Hjhzpv+cMRCqCGECLCFfpS3PPOTW1HwU+ELEIYgAtJlylLzMzM5Wbm2tbQGQhiAG0mHCVvjQFPgoLCyjwgYhEEAMeUF5erri4WNvylnCVvjTT3KtWrbItIHIQxIAH7NixQ2ed1dO2vCccpS+HDRvGViZEJIIYQIsLR+lLtjIhUhHEAFpFOEpfmq1Mzz//vG0BkYEgBtAqAqUvlyxZYntCZ17DaO4qbMBNCGIArcaUrJw+fWqzSl/ecssEvfLKK7YFeB9BDKDVBEpfNucgB3Ov+bHHHuFUJkQMghjwgEWLFiohIcG2vM2Uvly8+E9N3hNs9iZPm5al9evX2x7A2whiwCNMAEWCcJS+NHuTWbSFSEEQA2h1gdKXTR0Vn3feef5fqbSFSEAQA2h1gdKXWVlZtid0N954I5W2EBEIYgCOaG7pS1Npy9xrptIWvI4gBuAYU/py3rx5TQpTswLbHI+4ZcsW2wN4E0EMuJzZppOU1Mu2Iosp0JGcnNzkspXmeMSXX37ZtgBvIogBl9u7d69/72ykak7pywEDBvi3drGnGF5GEANwVHNKX5pFX+YgiPz8zbYH8B6CGIgC8fHxKioqsi33aU7py/T0dF+IL7UtwHsIYiAKdO3aVQcOHLAt92lO6Uuzp7iwsIDpaXgWQQzAFZpT+tJMbTM9Da8iiAG4QnNKX5o9yUxPw6sIYsDlCgoKlJqaaluRzZS+3LDh9ZBHxUxPw8sIYsAD4uLi7FVkM6Pi7OyZTSp9OWLElUxPw5MIYgCu0tTSlxdddJHWrFlrW4B3EMQAXMeMiEMtfRko7kHtaXgNQQzAdcw931BLX5pp7dGjx1B7Gp5DEANwpaaUvrzkkov11ltv2RbgDQQx4HLl5eWKi4u1rehhSl+aBVihlL7s2zdVa9dynxjeQhADLrdjxw6ddVZP24ouEyZMCKn0ZY8ePbRnz26VlZXZHsD9CGIArmVKX06blhVS6Uszin7vvULbAtyPIAbgamPHjg2p9OWgQQO1eXO+bQHuRxADcLVQS1+a+8SbN1PYA95BEANwvVBKXwbuE1PuEl5BEANwvVBLXw4ZMtS/yA3wAoIYcDlTLSohIcG2olcopS/T0tJUUlJiW4C7EcSAB5gRIYIvfZmUlKSNGzfaFuBuBDEAzwi29GWXLl20bds22wLcjSAG4CnBlL40C7beeCO005sApxDEQJSoqKiwV94WbOnLpKRerJyGJxDEQBQw4bVs2Uu25X3BlL40K6f37t1rW4B7EcSAi5mgMSM7HKsppS8BtyKIARczIzozssOJQi19CbgVQQzAk0ItfQm4FUEMwLNCKX0JuBVBDMCzQi19CbgRQQzA0+orfWkKerRv3962APciiAF4XqD0ZYBZbW5OYDKFPQC3I4gBFysoKFBqaqptoT6m9KU5GOOnP71Fv/vd7/zbmq6//gb7KOBuBDHgcnFxcfYK9THlLles+B8tX75MCxb8l7KzH+DEKngGQQzA87Zs2aLKykp9/nmVL5QPqbq6Wq+9tt4+CrgbQQzA82JjY3XSSScpJuZrvo8Y/3VsLDMJ8AaCGIDnmXvEaWnfVtu27dSuXXuddlpHjR8/3j4KuBtBDCAi5OYu0uLFf9Yjjzym9etfY8U0PIMgBlysvLxccXGxtoWGmOIeZk9xRkaG/1AIwCsIYsDFduzYobPO6mlbaL5KFa/7f5o7Pk2JiQk1H+lZyllXpF3r/q9mrPvUPg9oPQQxgOhQvUvrZvxYl45ZqE+HPqTVhaUqLd2p7Tmj1HHLQ77+XO3a/y/7ZKD1EMQAosB+5f9+osbk7NGI+Y/pvrHfVUpczdtfTLeBypj8sJ6bfI6/DbQ2ghhA5KvcqiVPbpJi03X9JQl1vPF1VP/rrlfiZ1Wqtj1AayGIAUS4alXmr9HSQ74cHnmJBnao+20vpvv3NSOzD2+KaHV8zwGIcNWq2r9PvhxW2y4dxHlMcBuCGHCxRYsWhq1m8uDBF6qsrMy2otPhTytVZa8BtyCIAZcz+2PDITk5WVVV0RhDJyu+3/nq77s69M527eEmMFyGIAYQ8WJ6X6KbR3SXtj6uh18srXNBVvXudZqfk6+Dtg20FoIYQOSLSdTVv83W2NQDWj5pou7JWa783Ufsg5UqXj1fP/vtDg3/YX9xVARaG0EMICrEdLtU9y7/m/LmX6w9s25RRlqvmspafSfr5c+G6rePZ6qP3VsMtCa+6wBEj5huGpgxRU+9t9NfVcv/8d4fNTljoLrxbgiH8K0HuNS+ffuUlNTLtgBEKoIYcKm9e/dqyJChtgUgUhHEAAA4iCAGAMBBBDEAAA4iiAEAcBBBDLhUdJajBKIPQQy4VElJiVJTU20LQKQiiAEXi4uj4CIQ6QhiAAAcRBADAOAgghgAAAcRxAAAOIggBlyqqKhI8fHxtgUgUhHEgEsdOHBAXbt2tS0AkYogBqLEaaedpk8++cS2ALgFQQxEiT59+ujjjz+2LQBuQRADAOAgghgAAAcRxIBLVVRU2CsAkYwgBlxq2bKXlJKSYlsAIhVBDACAgwhiAAAcRBADAOAgghgAAAcRxAAAOIggBlyorKxMgwdfaFsAIhlBDLhQVVWVkpOTbQtAJCOIAQBwEEEMAICDCGIAABxEEAMA4CCCGHAhs1gLQHQgiAEXKikpUVpamm0BiGQEMQAADiKIAQBwEEEMAICDCGIgSiQlJWnjxo22BcAtCGIgSrRv395eAXATghhwoaKiIsXHx9sWgEhGEAMudODAAXXt2tW2AEQyghgAAAcRxAAAOIggBgDAQQQxAAAOIogBF6qoqLBXACIdQQy40LJlLyklJcW2AEQyghgAAAcRxAAAOIggBgDAQQQxAAAOIogBAHAQQQy4TFlZmQYPvtC2AEQ6ghhwmaqqKiUnJ9sWgEhHEAMA4CCCGAAABxHEAAA4iCAGAMBBBDHgMmaxVkto3769tm3bZlsA3IIgBlympKREaWlpthU+PXr00Btv/N22ALgFQQwAgIMIYgAAHEQQAwDgIIIYAAAHEcQAADiIIAZcpqioSPHx8bYFINIRxIDLHDhwQF27drUtAJGOIAYAwEEEMQAADiKIAQBwEEEMAICDCGLAZSoqKuwVgGhAEAMus2zZS0pJSbEtAJGOIAYAwEEEMQAADiKIAQBwEEEMAICDCGIAABxEEAMuUlZWpsGDL7QtANGAIAZcpKqqSsnJybYFIBoQxEAUufLK76u4uNi2ALgBQQxEkdNPP91eAXALghgAAAcRxAAAOIggBlzELNYCEF0IYsBFSkpKlJaWZlsAogFBDACAgwhiAAAcRBAjRDuUN/5cJfafo/yjtgsA0GQEMQAADiKIAQBwEEHsqEoVr56v8X0TlJjo+0jP0tNzf6K+icM1N/+g73E7DZw+VuPT+9Q85+ocFVdX62DxOuVkfb+mz/fRd/wc5eXvVrX/deuaPj6q3Xm3+55rX3t3nsYnnquxcxcr98vX6aP0rDwVH6x5Fb+DxVrt/zMFHn9Om3Yetg8i3IqKihQfH29bAKIBQeyYI9qVd4+uHrdS38hercLSD7Vx6in689wVOmSf8aXCQun6pSrc/qZevDddSbtf1J1Xj9asPT/SysJSlW7fqCe6r9WkjNv0+/z99jcFY5/WzH1O718wu+bzL8yUcm/X1dnrfT8i+FSXKu/OH2vcih7KXl3o+zxrNfVrG5RbeMKfEGFy4MABde3a1bYARAOC2CnVJXr16VekzF/qrow+ilMbdfvurZqa2dM+obY0XeUbEcfFdFP//ifr9cdma7lGKfve69QnzvcljOmu7/56hianFmrub30j2loD2sbE1v78w67V9f1jdWhZvrb5RtLVH6zR08vbKHPqJGWkdKj5PHf+Upmx9jcDAJqNIHZI9Qf/q6Vb22rIBb3lizirkwZefolOyLlOvZTY5eSa6+q92v7OJ1LKAPXr1qamz4hL0oBBvpFU8Ycqqz213Ii2XTqovb1WTHt1jG9rG0f1ccGb2qr+uuBbHW2fT4feumBIJ9sAADQXQeyQ6s/2qdRefyVG7Tt0VCAK61R9SBWlh6T4jjr1mK9eO3Xo4ovwQ/u0vyqEIXG9PteukrqOyztdif3OsNcAgOYiiB0Sc2onJeqwPt5fZRdYGdWqqtzv621ATKxOT/QF7sf79dkxefu5Kj/1BXRsJ3VsH44vazt1T0rx/Vqh/Z/V3jBcodKCcnsNAGgugtghMb2/o5H9peLicpn10TUqtW3LOycu1qotprN6nmOmoLeoYPcR2+lzsERbNpsp617qYe4bn2C/3t+01V4H42TF9ztf/fWRisu++hOq8gNt2rDPNhBuFRUV9gpAtCCInRKTpCtuTpdyH9asvCJfGB/R7nWPavrcTfYJ9emiYRPv1Agt0bQZL6jI3A+u3qV1D92ruYWpmvzbDKXEdFW/oedI+xbr8UUFNa+96S9atHS7fY3gxPS+RDePOKLc2+5WTlFlzeeZ/bByWTTdYpYte0kpKWYmAkC0IIgd00bdM+7Ti89crj3TLlVqYi+lzfxMwzMH2MfrF9P9as1+cZHu+safdXlqohJ7pum2XRdrft4T+sVAs7CqnVLGPKwld56jDTOG+1/74v/6TBeObPy1jxGTqIzZz+mZW/6tWZen+j7PxZr5xRBlprJsGgDC5aT/+NjrE5SXl+vZZ3Nsq2FTp06zV2g6U3TjDqVNkuZvnKeMbnalNKKGKaxSWrrTthq2bt1ajRmT6b8ePjxd8+c/olNOOcXfrs/06dM1btw4Rt1AGMycmW2vGnbTTWN1xhn1L3JlROyUynXK6msqYuXWTC/LVMt6WY/8YaViR1ymtHhCGPUrKyvzh/AXXxzV4cOfa8WKVzRv3jz7aP3OPPNMffRRaLcoALQsRsSOOaLd+cv1p8cf1NxXd9m+Acq895ca+8NhSrELrswICahPVdVBVVdXq1279vra176mk046yT4CLwt2VgTOCteImCAGPGjfvn3q3/9cfwgfPfpvtWnTVllZd+unP73VPgNAS2NqGohinTp10sKFuYqP/4Y/hH/ykwkaM+Ym+ygALyGIAY/67ncvVn7+Fv805m9+85tGF2oBcCeCGAAABxHEAAA4iCAGAMBBBDEAAA4iiAEAcBBBDACAgwhiwLOqVbluhvomXqO5+fttHwCvIYgBr6reqTWLX9EhbdKTS7aq0nYD8BaCGPCo6g/W6OntqboiNVaHlq5RfqU5PASA1xDEgCd9qvU5udL1U/SbW9MVe+gVLV6zU0Qx4D0EMeBFle9q5bKzdfMV39KZl1yjkbG7tPzpNfqAJAY8hyAGPOdzFS9doKVXXqNLureROpyty0f2lLau1IYPPrfPAeAVBDHgNQff0cuLv667xg5WB39HJ50/6kdK1d80K+cNFm0BHkMQA55Srco3X9KThas049JkJSYm+D4SlZrxkAp9j7JoC/AeghjwkupiLZ2zQSMXbvUff/jVxzatvvf/+JJ4jVbm77NPBuAFBDHgGZUqWjhXs0qv1KihXWxfQDulpF+rK7RduTPnK6+YCWrAKwhiwBMOKn/utbp8xss6tG+OMnrdrrzdR+1jPrvzND7tdr1qrguf1qRLh2p83g7/QwDc7aT/+NjrE5SXl+vZZ3Nsq2FTp06zVwAARL6ZM7PtVcNuummszjjjDNs6ESNiAAAcRBADAOCgsE1NAwCAEzE1DQCAg9q0aWOv6tZgEHfu3NleAQCApmgsSxsMYpPiPXok2BYAAAjF2WefY6/q1+jUdFpamr0CAAChGDRokL2qX6NB3KdPH0bFAACEKDk5ucFFWgFBLdYaMWKETjnlFNsCAAANMZmZnv4922pYUEFsbjSPHp1JGAMA0AiTlSYz4+LibE/DGtxHfLy9e/dq+fLlKivbaXsAAECAuZV7zTXXBB3CRkhBHFBUVKSNGzcSyAAA+Jj7weecc65/XVWomhTEAUeOHPGPkgEAiFbm9m1jRTsa0qwgBgAAzRPUYi0AANAyCGIAABwj/X93S+yOY6tMHQAAAABJRU5ErkJggg=="></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>maximum value 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">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>minimum value 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">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the time, in seconds, it takes for the blade <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[BC]</mtext></math> to make one complete rotation under these conditions.</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>Calculate the angle, in degrees, that the blade <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[BC]</mtext></math> turns through in one second.</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>Write down the amplitude of the function.</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 period of the function.</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 function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mn>5</mn></math>, clearly labelling the coordinates of the maximum and minimum points.</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 height of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> above the ground when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2</mn></math>.</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 time, in seconds, that point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> is above a height of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo> </mo><mtext>m</mtext></math>, during each complete rotation.</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>At any given instant, find the probability that point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> is visible from Tim’s window.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The wind speed increases. The blades rotate at twice the speed, but still at a constant rate.</p>
<p>At any given instant, find the probability that Tim can see point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> from his window. Justify your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>maximum <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>130</mn></math> metres <strong><em>A1</em></strong></p>
<p> </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>minimum <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>50</mn></math> metres <strong><em>A1</em></strong></p>
<p> </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><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>60</mn><mo>÷</mo><mn>12</mn><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mn>5</mn><mo> </mo><mtext>seconds</mtext></math> <strong><em>A1</em></strong></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><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>360</mn><mo>÷</mo><mn>5</mn></math> <em><strong>(M1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>360</mn></math> divided by their time for one revolution.<br><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>72</mn><mo>°</mo></math> <strong><em>A1</em></strong></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>(amplitude =) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn></math> <strong><em>A1</em></strong></p>
<p> </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>(period <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>360</mn><mn>72</mn></mfrac><mo>=</mo></math>) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> <strong><em>A1</em></strong></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 src="data:image/png;base64,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"></p>
<p>Maximum point labelled with correct coordinates. <strong><em>A1</em></strong></p>
<p>At least one minimum point labelled. Coordinates seen for any minimum points must be correct. <strong><em>A1</em></strong></p>
<p>Correct shape with an attempt at symmetry and “concave up" evident as it approaches the minimum points. Graph must be drawn in the given domain. <strong><em>A1</em></strong></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><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>90</mn><mo>-</mo><mn>40</mn><mo> </mo><mi>cos</mi><mfenced><mrow><mn>144</mn><mo>°</mo></mrow></mfenced></math> <strong><em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>h</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>122</mn><mo> </mo><mtext>m</mtext><mo> </mo><mo> </mo><mfenced><mrow><mn>122</mn><mo>.</mo><mn>3606</mn><mo>…</mo></mrow></mfenced></math> <strong><em>A1</em></strong></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>evidence of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>100</mn></math> on graph <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo>=</mo><mn>90</mn><mo>-</mo><mn>40</mn><mo> </mo><mi>cos</mi><mfenced><mrow><mn>72</mn><mi>t</mi></mrow></mfenced></math> <strong><em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>55</mn><mo> </mo><mo>(</mo><mn>3</mn><mo>.</mo><mn>54892</mn><mo>.</mo><mo>.</mo><mo>.</mo><mo>)</mo></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>45</mn><mo> </mo><mo>(</mo><mn>1</mn><mo>.</mo><mn>45107</mn><mo>.</mo><mo>.</mo><mo>.</mo><mo>)</mo></math> or equivalent <strong><em>(A1)</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>A1</strong></em> for either <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>-coordinate seen.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>2</mn><mo>.</mo><mn>10</mn></math> seconds <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo>.</mo><mn>09784</mn><mo>…</mo></mrow></mfenced></math> <strong><em>A1</em></strong></p>
<p> </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><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>-</mo><mn>2</mn><mo>.</mo><mn>09784</mn><mo>…</mo></math> <strong><em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mfenced><mrow><mn>2</mn><mo>.</mo><mn>902153</mn><mo>…</mo></mrow></mfenced><mn>5</mn></mfrac></math> <strong><em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>580</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>580430</mn><mo>…</mo></mrow></mfenced></math> <strong><em>A1</em></strong></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>changing the frequency/dilation of the graph will not change the proportion of time that point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> is visible. <strong><em>A1</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>580</mn><mo> </mo><mo> </mo><mo>(</mo><mn>0</mn><mo>.</mo><mn>580430</mn><mo>.</mo><mo>.</mo><mo>.</mo><mo>)</mo></math> <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>correct calculation of relevant found values</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mfenced><mrow><mn>2</mn><mo>.</mo><mn>902153</mn><mo>…</mo></mrow></mfenced><mo>/</mo><mn>2</mn></mrow><mrow><mn>5</mn><mo>/</mo><mn>2</mn></mrow></mfrac></math> <strong><em>A1</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>580</mn><mo> </mo><mo> </mo><mo>(</mo><mn>0</mn><mo>.</mo><mn>580430</mn><mo>.</mo><mo>.</mo><mo>.</mo><mo>)</mo></math> <strong><em>A1</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>A0A1</strong> </em>for an unsupported correct probability.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">f.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Judging by the responses in parts (a), (b) and (c), transferring and interpreting the information from a diagram is a skill that requires further nurturing. The amplitude should be expressed as a positive value. Overall, the sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced></math> reflected the correct general shape. Common flaws included a lack of symmetry about the mean, 'concave up' not evident as the curve approached the minimum points, and the curve being drawn beyond the given domain. At least one correct pair of coordinates was seen, though some gave their answers inaccurately, suggesting they found an approximate solution using the "trace" feature in their GDC. Most were able to find the height of point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2</mn></math> and make an attempt to find a time at which point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> is at a height of <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>100</mn><mo> </mo><mi mathvariant="normal">m</mi></math>. It was pleasing to see a number of candidates draw <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>100</mn></math> on their sketch, which would no doubt have assisted the candidates in visualizing the solution. Part (f) proved to be a high-grade discriminator, with few attaining full marks. Premature rounding in part (f)(i) resulted in an inaccurate final answer. It is recommended that candidates retrieve and use unrounded values from previous calculations in their GDC. Though many recognized the probability was independent of the speed of rotation, most were not able to support their answer through a correct calculation or written explanation.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Judging by the responses in parts (a), (b) and (c), transferring and interpreting the information from a diagram is a skill that requires further nurturing. The amplitude should be expressed as a positive value. Overall, the sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced></math> reflected the correct general shape. Common flaws included a lack of symmetry about the mean, 'concave up' not evident as the curve approached the minimum points, and the curve being drawn beyond the given domain. At least one correct pair of coordinates was seen, though some gave their answers inaccurately, suggesting they found an approximate solution using the "trace" feature in their GDC. Most were able to find the height of point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2</mn></math> and make an attempt to find a time at which point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> is at a height of <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>100</mn><mo> </mo><mi mathvariant="normal">m</mi></math>. It was pleasing to see a number of candidates draw <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>100</mn></math> on their sketch, which would no doubt have assisted the candidates in visualizing the solution. Part (f) proved to be a high-grade discriminator, with few attaining full marks. Premature rounding in part (f)(i) resulted in an inaccurate final answer. It is recommended that candidates retrieve and use unrounded values from previous calculations in their GDC. Though many recognized the probability was independent of the speed of rotation, most were not able to support their answer through a correct calculation or written explanation.</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Judging by the responses in parts (a), (b) and (c), transferring and interpreting the information from a diagram is a skill that requires further nurturing. The amplitude should be expressed as a positive value. Overall, the sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced></math> reflected the correct general shape. Common flaws included a lack of symmetry about the mean, 'concave up' not evident as the curve approached the minimum points, and the curve being drawn beyond the given domain. At least one correct pair of coordinates was seen, though some gave their answers inaccurately, suggesting they found an approximate solution using the "trace" feature in their GDC. Most were able to find the height of point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2</mn></math> and make an attempt to find a time at which point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> is at a height of <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>100</mn><mo> </mo><mi mathvariant="normal">m</mi></math>. It was pleasing to see a number of candidates draw <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>100</mn></math> on their sketch, which would no doubt have assisted the candidates in visualizing the solution. Part (f) proved to be a high-grade discriminator, with few attaining full marks. Premature rounding in part (f)(i) resulted in an inaccurate final answer. It is recommended that candidates retrieve and use unrounded values from previous calculations in their GDC. Though many recognized the probability was independent of the speed of rotation, most were not able to support their answer through a correct calculation or written explanation.</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Judging by the responses in parts (a), (b) and (c), transferring and interpreting the information from a diagram is a skill that requires further nurturing. The amplitude should be expressed as a positive value. Overall, the sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced></math> reflected the correct general shape. Common flaws included a lack of symmetry about the mean, 'concave up' not evident as the curve approached the minimum points, and the curve being drawn beyond the given domain. At least one correct pair of coordinates was seen, though some gave their answers inaccurately, suggesting they found an approximate solution using the "trace" feature in their GDC. Most were able to find the height of point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2</mn></math> and make an attempt to find a time at which point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> is at a height of <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>100</mn><mo> </mo><mi mathvariant="normal">m</mi></math>. It was pleasing to see a number of candidates draw <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>100</mn></math> on their sketch, which would no doubt have assisted the candidates in visualizing the solution. Part (f) proved to be a high-grade discriminator, with few attaining full marks. Premature rounding in part (f)(i) resulted in an inaccurate final answer. It is recommended that candidates retrieve and use unrounded values from previous calculations in their GDC. Though many recognized the probability was independent of the speed of rotation, most were not able to support their answer through a correct calculation or written explanation.</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Judging by the responses in parts (a), (b) and (c), transferring and interpreting the information from a diagram is a skill that requires further nurturing. The amplitude should be expressed as a positive value. Overall, the sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced></math> reflected the correct general shape. Common flaws included a lack of symmetry about the mean, 'concave up' not evident as the curve approached the minimum points, and the curve being drawn beyond the given domain. At least one correct pair of coordinates was seen, though some gave their answers inaccurately, suggesting they found an approximate solution using the "trace" feature in their GDC. Most were able to find the height of point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2</mn></math> and make an attempt to find a time at which point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> is at a height of <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>100</mn><mo> </mo><mi mathvariant="normal">m</mi></math>. It was pleasing to see a number of candidates draw <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>100</mn></math> on their sketch, which would no doubt have assisted the candidates in visualizing the solution. Part (f) proved to be a high-grade discriminator, with few attaining full marks. Premature rounding in part (f)(i) resulted in an inaccurate final answer. It is recommended that candidates retrieve and use unrounded values from previous calculations in their GDC. Though many recognized the probability was independent of the speed of rotation, most were not able to support their answer through a correct calculation or written explanation.</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Judging by the responses in parts (a), (b) and (c), transferring and interpreting the information from a diagram is a skill that requires further nurturing. The amplitude should be expressed as a positive value. Overall, the sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced></math> reflected the correct general shape. Common flaws included a lack of symmetry about the mean, 'concave up' not evident as the curve approached the minimum points, and the curve being drawn beyond the given domain. At least one correct pair of coordinates was seen, though some gave their answers inaccurately, suggesting they found an approximate solution using the "trace" feature in their GDC. Most were able to find the height of point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2</mn></math> and make an attempt to find a time at which point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> is at a height of <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>100</mn><mo> </mo><mi mathvariant="normal">m</mi></math>. It was pleasing to see a number of candidates draw <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>100</mn></math> on their sketch, which would no doubt have assisted the candidates in visualizing the solution. Part (f) proved to be a high-grade discriminator, with few attaining full marks. Premature rounding in part (f)(i) resulted in an inaccurate final answer. It is recommended that candidates retrieve and use unrounded values from previous calculations in their GDC. Though many recognized the probability was independent of the speed of rotation, most were not able to support their answer through a correct calculation or written explanation.</p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Judging by the responses in parts (a), (b) and (c), transferring and interpreting the information from a diagram is a skill that requires further nurturing. The amplitude should be expressed as a positive value. Overall, the sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced></math> reflected the correct general shape. Common flaws included a lack of symmetry about the mean, 'concave up' not evident as the curve approached the minimum points, and the curve being drawn beyond the given domain. At least one correct pair of coordinates was seen, though some gave their answers inaccurately, suggesting they found an approximate solution using the "trace" feature in their GDC. Most were able to find the height of point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2</mn></math> and make an attempt to find a time at which point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> is at a height of <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>100</mn><mo> </mo><mi mathvariant="normal">m</mi></math>. It was pleasing to see a number of candidates draw <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>100</mn></math> on their sketch, which would no doubt have assisted the candidates in visualizing the solution. Part (f) proved to be a high-grade discriminator, with few attaining full marks. Premature rounding in part (f)(i) resulted in an inaccurate final answer. It is recommended that candidates retrieve and use unrounded values from previous calculations in their GDC. Though many recognized the probability was independent of the speed of rotation, most were not able to support their answer through a correct calculation or written explanation.</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Judging by the responses in parts (a), (b) and (c), transferring and interpreting the information from a diagram is a skill that requires further nurturing. The amplitude should be expressed as a positive value. Overall, the sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced></math> reflected the correct general shape. Common flaws included a lack of symmetry about the mean, 'concave up' not evident as the curve approached the minimum points, and the curve being drawn beyond the given domain. At least one correct pair of coordinates was seen, though some gave their answers inaccurately, suggesting they found an approximate solution using the "trace" feature in their GDC. Most were able to find the height of point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2</mn></math> and make an attempt to find a time at which point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> is at a height of <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>100</mn><mo> </mo><mi mathvariant="normal">m</mi></math>. It was pleasing to see a number of candidates draw <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>100</mn></math> on their sketch, which would no doubt have assisted the candidates in visualizing the solution. Part (f) proved to be a high-grade discriminator, with few attaining full marks. Premature rounding in part (f)(i) resulted in an inaccurate final answer. It is recommended that candidates retrieve and use unrounded values from previous calculations in their GDC. Though many recognized the probability was independent of the speed of rotation, most were not able to support their answer through a correct calculation or written explanation.</p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Judging by the responses in parts (a), (b) and (c), transferring and interpreting the information from a diagram is a skill that requires further nurturing. The amplitude should be expressed as a positive value. Overall, the sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced></math> reflected the correct general shape. Common flaws included a lack of symmetry about the mean, 'concave up' not evident as the curve approached the minimum points, and the curve being drawn beyond the given domain. At least one correct pair of coordinates was seen, though some gave their answers inaccurately, suggesting they found an approximate solution using the "trace" feature in their GDC. Most were able to find the height of point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2</mn></math> and make an attempt to find a time at which point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> is at a height of <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>100</mn><mo> </mo><mi mathvariant="normal">m</mi></math>. It was pleasing to see a number of candidates draw <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>100</mn></math> on their sketch, which would no doubt have assisted the candidates in visualizing the solution. Part (f) proved to be a high-grade discriminator, with few attaining full marks. Premature rounding in part (f)(i) resulted in an inaccurate final answer. It is recommended that candidates retrieve and use unrounded values from previous calculations in their GDC. Though many recognized the probability was independent of the speed of rotation, most were not able to support their answer through a correct calculation or written explanation.</p>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Judging by the responses in parts (a), (b) and (c), transferring and interpreting the information from a diagram is a skill that requires further nurturing. The amplitude should be expressed as a positive value. Overall, the sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced></math> reflected the correct general shape. Common flaws included a lack of symmetry about the mean, 'concave up' not evident as the curve approached the minimum points, and the curve being drawn beyond the given domain. At least one correct pair of coordinates was seen, though some gave their answers inaccurately, suggesting they found an approximate solution using the "trace" feature in their GDC. Most were able to find the height of point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2</mn></math> and make an attempt to find a time at which point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> is at a height of <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>100</mn><mo> </mo><mi mathvariant="normal">m</mi></math>. It was pleasing to see a number of candidates draw <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>100</mn></math> on their sketch, which would no doubt have assisted the candidates in visualizing the solution. Part (f) proved to be a high-grade discriminator, with few attaining full marks. Premature rounding in part (f)(i) resulted in an inaccurate final answer. It is recommended that candidates retrieve and use unrounded values from previous calculations in their GDC. Though many recognized the probability was independent of the speed of rotation, most were not able to support their answer through a correct calculation or written explanation.</p>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Judging by the responses in parts (a), (b) and (c), transferring and interpreting the information from a diagram is a skill that requires further nurturing. The amplitude should be expressed as a positive value. Overall, the sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced></math> reflected the correct general shape. Common flaws included a lack of symmetry about the mean, 'concave up' not evident as the curve approached the minimum points, and the curve being drawn beyond the given domain. At least one correct pair of coordinates was seen, though some gave their answers inaccurately, suggesting they found an approximate solution using the "trace" feature in their GDC. Most were able to find the height of point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2</mn></math> and make an attempt to find a time at which point <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">C</mi></math> is at a height of <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mn>100</mn><mo> </mo><mi mathvariant="normal">m</mi></math>. It was pleasing to see a number of candidates draw <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>100</mn></math> on their sketch, which would no doubt have assisted the candidates in visualizing the solution. Part (f) proved to be a high-grade discriminator, with few attaining full marks. Premature rounding in part (f)(i) resulted in an inaccurate final answer. It is recommended that candidates retrieve and use unrounded values from previous calculations in their GDC. Though many recognized the probability was independent of the speed of rotation, most were not able to support their answer through a correct calculation or written explanation.</p>
<div class="question_part_label">f.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The Texas Star is a Ferris wheel at the state fair in Dallas. The Ferris wheel has a diameter of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>61</mn><mo>.</mo><mn>8</mn><mo> </mo><mtext>m</mtext></math>. To begin the ride, a passenger gets into a chair at the lowest point on the wheel, which is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>7</mn><mo> </mo><mtext>m</mtext></math> above the ground, as shown in the following diagram. A ride consists of multiple revolutions, and the Ferris wheel makes <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>5</mn></math> revolutions per minute.</p>
<p style="text-align: center;"><img 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"></p>
<p>The height of a chair above the ground, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math>, measured in metres, during a ride on the Ferris wheel can be modelled by the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mo>−</mo><mi>a</mi><mo> </mo><mi>cos</mi><mo>(</mo><mi>b</mi><mi>t</mi><mo>)</mo><mo>+</mo><mi>d</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> is the time, in seconds, since a passenger began their ride.</p>
</div>
<div class="specification">
<p>Calculate the value of</p>
</div>
<div class="specification">
<p>A ride on the Ferris wheel lasts for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math> minutes in total.</p>
</div>
<div class="specification">
<p>For exactly one ride on the Ferris wheel, suggest</p>
</div>
<div class="specification">
<p>Big Tex is a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mo>.</mo><mn>7</mn></math> metre-tall cowboy statue that stands on the horizontal ground next to the Ferris wheel.</p>
<p style="text-align: center;"><img 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tWoUqVKVgUcBNqrr4aICKYjXfAQa7js2rUxQvC6S9gHH1Dk55/LLdeBH2zXrl2ofv2GVKFCBbmaPRDMiPCuXh0tBHtmIMh//vlnOnLkyCPC1ZORZ4ZhGOYhXKPKMD5Mu3btRcQT0UIIyuyijBBpS5d+K6KYjoCIolYiVUtg2o/H5YhIBXi+eN7WRCrA64XniNcPUefXXsuI2DIMwzD6wBFVhjE47kRUgRlqI7WKqHoaV15TjqgyDMO4DkdUGYZhGIZhGEPCQpVhDM7du3fF77Nnz4jfjoImHlvWToxrXLt2Tf7lHGx/xTAM4zwsVBnGoKAxCNOWXnqpDRUpUoRWrlzlsAcprotOczbB1xbYfaGhCq+vI+D9Wrp0qWjYCg6uLq2wHLsuwzAMwzWqDGMoEHXbuXMnRUZOo2LFitOAAW+LxqUDBw6IbnYIHnvWSIj4QUzBhgrjRh2xafI2ZqlRhfBs27aNcDxwxC7M0h0Bjgt4HxcvXkyJiUeFl2y7du2ybeRiGIZhWKgyjCFAw9SqVato5szpNHJkOLVq1SpL45R6md9++02uPOTcuV/Iz89PEU4Zoge+n23atDGFSAVmEaoAYnXlypUPjP+vXbtKd+7coRIlSoptS1B6Yc0LFv6tmNIF71pX/GIZhmFyCixUGUYD1M58V6hW7XkhMrt37+6yuPzpyBH66aefqGu3bnLFXJhJqGZmxvTp1LZtW6rggtCE6I2NjRXlARcvXqTTp0/J/ziHs44QDMMwZoGFKsNogCpUEQ0tUaKEXLUPbIsQURs+fLhccY0///yTRii3MWXqVPr73/8uV82DWYXqjRs36NNPPqEJEyfKFddBPTIi6hgB6ygYNYuoLAtVhmF8FRaqDKMBrnqdujKbPjuWffstPffcc/RctWpyxTyYVaju27uXzqem0iuvvCJXXMcVv1VX9zuGYRizwF3/DOMjQKQi/c/ox549eygoMFBuMQzDMFrDQpVhfISKlSrRjz/+KMoAGM+DtP+pU6fo2YAAucIwDMNoDQtVhvERUJtavnx5Svr5Z7nCeJKfT5ygevXqmbImmGEYxiywUGUYDfn111/lX/ZRJxX5+/uJ31pQv359Tv/rBNL+KLfQGmcmWKn7W/78+cVvhmEYX4OFKsNoAIQCzN9HjhxBhw4dEk0utn5wmfDwcHHdmjVrid9aUKlyZU7/64Ca9ke5hVbUqVNH/MZ+YW2fyfyDCVfDh38k/Ftv374trsswDONrcNc/w7gBfDAXLFhAy5Z9S71796H58+c5NZN/2bLl1LBhQ7mlDfD1bNasmam6/83W9e8p31qIT0wgcxRMKsN+t3DhAuV63ahPnz6mGfLAMAzjCCxUGcZFNm/eRBMmTKB27drT22+/LUZhQrieO+eYvdBTTz3lkfGZWlom6YXZhKonrcCQ+r9y5Yrcss0zzzwjhCmu891334kTpjFjxlCrVi/KSzAMw5gbFqoM4yQYfzlz5kw6efIkTZo0yXD+lVqa0OuFmYSqkYcroCRg2rRp4u/Ro0dTqVKlxN8MwzBmhWtUGcZBEC2FKXuDBvXELP3ly5cb0mT9ySefpGLFitFJRbQw2gNXBaN2+2N/nD17thjF2717N1qyZInYbxmGYcwKC1WGcQBEqnr37k3x8fF08OBhTSZJeRJ0/x9NTJRbjJagNtUT3f5agv1z9epoSlT2Aey32H8ZhmHMCKf+mRzHqFGjaMmSRXLLOZwZb+lNzJb+N0vq38hpf2tAoGLEqitoNdqXYRjGHVioMjkOCFXUl3bv3l2u2AeRVIhbswhVgO7/tm3bUgUTzIA3i1BFt//27dtp8JAhcsXYqEJ15MhwKlGihFy1T2joYBaqDMMYAhaqTI4DQhVERESI346A2lR8eZtJqG7cuFHUJ5qh+98sQhXd/hUqVKDa0vPU6KhCdcuWbU7VUwcEPMNClWEYQ8A1qgzjo9SoUUNYVTHagLQ/hilgqALDMAyjDyxUGcZHefrpp8nf35+7/zUC3f7ly5cXrgoMwzCMPrBQZRgfpkbNmtz9rxGnkpOFmwLDMAyjHyxUmRxHgQIFRDOVM9y8eVP+ZS6Q/j9+7JjcYtwBZRRmS/tj+hlAyYKjsO8qwzBGgoUqk+N44YUXaM+e3cIY3ZEvZcxfnzt3DvXo0UuumAek/8Gvv/4qfjOugfIJDFEwW9ofI3rr128o9t9Dhw7J1ezBKNYFCxaIv4OCgsRvhmEYb8Jd/0yOZMiQIfSf/6yWW/bBl31kZKQpR1Ki+x+0bt1a/DYiRu/6/89//kOlSpY0Tbe/JRj5iylVp08nyxX7vPhiG/r666/lFsMwjPdgocrkKBBBjYqKojNnzlD//v3pl19+kf/Jyr179ygmZh01bdKUunbrRvny5ZP/MReIps5TRMfwESPkivEwulAdM3o0/eOjj0zbSIX9fuHChXTwwAFq2aoVPf744/I/WYGN1YwZM6hQoUI0ZswY0+73DMP4BixUmRwDIksTJ06kMmXKUGhoqENfwBCyc/79bwp9//0HaXQzMnXKFOr31luGfQ5GFqpI+2/YsME0Jv/WwMlKxKRJNCo83KF9AMIWJQDbtm0zbSaBYRjfgGtUmRyBmv5s1KgRDR8+3OEo0bPPPkut27Sh75YtEz6aZgXd/wcOHJBbjDPANcHM3qnYbxFRf/PNNx0+UcHnY+DAgWJ6Gz43GBzAMAzjDVioMj4PmqEaNKhHkydPoR49eshVx0HzVX4/P9qxY4dcMR/lypalAwkJcotxBnT7wz3BrKxetYpKly7tUn0tJlPhc9O//1vic8QwDKM3LFQZn2bz5k00cuQIMUKyYcOGctV5XnvtNfrvzp2mNc/HvH9YbHH3v3Pg/cbQBLOWffx05AgdPXqUXu3USa44Dz43S5d+Kz5HS5YskasMwzD6wEKV8VlgPzVhwgTxJevMnHNroImmd+/eoiHFrCUAiKhx+t85kPZH2YQZwUnJd999RwPeeYf+/ve/y1XXQI0qPkdxcXHic8UwDKMXLFQZnwRfpocPH6YNG2I1awRBVPKFJk3om2++kSvmIigwkNP/ToJhCWZN+6OuGvXVqLPWAnyOpk2bJj5XU6dO5cEADMPoAnf9M6YAKcdEB0aB/vXXX8rljoq/AwOD6LHHHqOIiAixrQWIps6dM4eeDw4Wtatmw6g2S0bs+jeDrVd2wDv35xMnNHcqGDVqlNXPmD0ClZMkV+rDGYZhOKLKmAKI1Li4XXIre/ClWa1adfFz+vRpReAukv/RBqRQ3+jalTbGxpqy3hPpfwgYxj4okzBj2h91tain7tW7t1zRDnye8LlSP2OOiFR8bh05yWQYhrEGR1QZU4BIDnAmOhodHU2hoYMpJeWcXNEOdIJv2bKFPggLc7v+T0+M6glqxIiq0b1nrYGI/8QJE0Q9NUpVtCYg4BmKipoh3AAcxZXPLsMwjApHVBnGBRCZhOUPrH/MBMTLxYsX6caNG3KFsYYaLTdbtz/qp7FvekKkMgzDeAMWqgzjIrD8OXv2rLAAMhOc/rePGdP+//3vf+n2rVvUtm1bucIwDGN+WKgyjIsg5d/9zTeFBZCZ6lXR/b9nzx65xVgD7ggYkmAWsP+tWrlS1E+bqRSFYRjGHixUGZ8FBveexnLEqll4NiCATp06xen/bIDow75jlvS5KyNS9eTatWvyL4ZhGOdhocqYAghCdBw7OsYRs/3nzp1DgwZ5vmlItamCJZAZQMStXr16nP7PBqT9UR5hFtwZkeos9es3pMjIaeLz5Qj4vMbErKUWLZrLFYZhGOfgrn/GFMBcfOjQoeJLD1+WFSpUkP/JCiI4uFzZsuXENB2tDP9tgejkp5984rFua61BXe327dsN0/1vpK5/dPt37tzZNO8jSk9GjxmjS8ofArV79250+nQytW/fgQoVKiT/k5WTJ0/Snj27xeUwKCBfvnzyPwzDMI7DEVXGFOBLDl92nTq9RmlpF+j+/fvyP1nBlycsdFavjtZFpAKzjVitWKkSp/+tgNfDLGl/PFatRqQ6Cj5P+Fzh82VLpILr169RkyZNWaQyDOMWHFFlTIM6FtXIX3z/+c9/6MqVK9SvXz+5YlyWffstPffcc/RctWpyxXsYJaIKf9zzqan0yiuvyBXjMmP6dENPSFOzINWrV6eBAwfKVYZhGOfgiCpjCmDev23bNsNHZ2ANBIsgWAUZHYjUn376SW4xAG4IcEUwOmo9tJHH+KpZEJxc4iSTYRjGFVioMoYHDRlo4IiMjDR8ChEpWFgEwSrI6JZVSP//+OOPpihV0AOk0jEMwehp/19++cVjI1K1Bp/XSZMm0bJl3zrcCMkwDGMJC1XG0CQlJVHXrl10a4rSAlgEwSoIlkFGFoFq93/Szz/LlZwNXBCM3u2P/WnOv/8t6qFRF20GChcuLD6/I0eOoEOHDslVhmEYx2ChyhgWdBj37/8WLVu23DQiVQWCxwwjVjn9/xAzpP3NOiIVn9/Jk6dQaOgQh62tGIZhAAtVxpCgEWPixIkUFjaUGjZsKFfNBUasHj161NAjVjn9nwHS/nBBwDAEo4JGr18vXTLtiFR8jseMGaN8psPE55thGMYRWKgyhmTChAmiWzgkJESumA+k1mEdZOQRq3iM5cuXz/Hpf6T9UQahl82Ts2D/QTS131tvGfYxOkKrVi9S8+bNhRsAwzCMI7BQZQzHkiVLhGl/nz595Ip5McOI1fr16+f49D/S/iiDMCKIdht5RKqzqFZV7ATAMIwjsFBlDAU6gzH6FJ3CRu/wdxSjj1itVLlyjk7/q2l/lEEYkQ0bNtDTRYuaaqyrPWBbxU4ADMM4Ahv+M7owatQo+Vf2oG7tp5+OUNWqgeTv7y/WAgMDqUePHuJvMwMxZOQRqzCPb9asmdfM/71p+I8aYkSUu3brJleMg94jUj0NsiWJiYnib3zeDxxIoBo1ajp0UhoRESH/YhgmJ8ERVUYXlixZJGZ/2wJfVnXq1H0gUuPidj34UjM7Rh+xivT/qeRkuZWzgEg1YtrfGyNSPQ0+z/hcA3zeGzZsZFek4riB4wfDMDkTjqgyuhAQ8IyYD+5Mc5QahfWlSIpRR6yqEd8JEyfKFX3xVkQVJw0jhg+nKVOnGk4MIsqNsozWrVvLFfPjymcaU+lCQwdTSso5ucIwTE6CI6oMoyNGHbGKiG+xYsXoZFKSXMkZwO3AiN3+aj2zL4lUhmEYV2ChyjA6AkFk1BGrSP8f9ZFSC0cxYtrfTCNSGYZhPA0LVYbRGaOOWEWaGabyOQW89nA7MFK3Px4TRqS+8cYbphmRyjAM40lYqDK6cfPmTfmXY9hrvjIzRhyxmtPS/0j7Y9iBkdL+6ohUb7kv6AE8kp3B2eMGwzC+BQtVRhfq128o/FEdnfONBoo9e3ZTixbN5YrvYcQRq4iq5pT0P9L+KHcwCmYfkeoIdevWpZiYtbR58ya5Ypsk5aQJx40ePXrJFYZhchosVBldiIyMFL8bNKgnHADs/aDLt3TpMlS5chVxPV8EkTyjjVitUaNGjkj/q2l/CHMj4CsjUu1RoXx5Kl++AvXr19fq5z7zT8uWGSeqgwYNEr8Zhsl5sD0VoxtXr16lnTt3imgpsGVVVbRoUXryiSeEiHuhSROf7n6GA8Chgwdp8JAhcsW7TJ0yhTp37qzrYAK97akQxd6+fbshXnOI5s+VE7mWLVv61PQpS/Acd+zYIZrE4Cd8SRHmly5dkv/NinqM6NHjTWrUqLHPTKljGMZ5WKgyunLo0CEKDR1CGzbEOvTlA3/PRQsXir/RBe2rDSZG8syENRKmBr3yyityxfPoLVThZ1uqZElDCEOjeutqBaLF3y1bRvn9/EQToSMRY+x/bdu2oaio6fT888/LVYZhciKc+md0A18+mOGPLx9HIyQQpoh6QcTBkN5I9ZxaAhGOaBOsibwN0v/Hjx2TW74JyhuMkPbH/ozHAgHni+C5RSif+eeDg4UQd7SsAccHHCdwUovjBsMwORcWqoxurFy5kipUqOBShASRRrWeExEopBJ9CQhypERhTeTt5wb7LGA0n1etgKsB3A28HZ33xRGpKtiHl337LW3ZsoVGhYfTCy+8IP/jODhOtGvXXhGsUXKFYZicCAtVRhfU7t1hw4bJFed59tlnafSYMSJNipo+XxNSqAlFKhpNNd6mRs2adODAAbnlW8DVwAjd/ihpQf019mtfAlmBiRMmiL8/CAt7cOLjCqGhobR+fYw4fjAMkzNhocrowrRp02iMIjILFy4sV1wDkSekENF4gpSir3WoqyNWvf28kP4/kJAgt3wLI6T9fXVEKhoD1YEFXbt1cztSjBIAHDfCw8O5BIBhcigsVBmPo3bwtmr1ovitBYg8IqWI1OK8efN8phQAX+wYsYqoqjcjxr6a/jdC2t8XR6SijAENgXCvCH3/fU0HFuC4gZKh2NhYucIwTE6ChSrjUWBJFRk5jYYOHSpXtANiCqnFp556SqQajdCIpAVGGbHqi+l/pP29GU3F++lrI1Ih/tHoiNcVjY/upPqzAz6q8FbG8YRhmJwFC1XGo8ydO5e6du1GFT3kyYkIJGyU1EYkNaVqdhAxfrpoUdqwYYNc0Z9yZcv6XPofaX+UNXgLXxqRCtGNxsaFCxeKz58nyxhKlSpFERFT6LPPPpMrDMPkFFioMh4DDRBohOjTp49c8RxoRPrHRx/RzydOiBQkUpFmB1FVCCtvWXLhNcWcdV9J/yPy5+/v75GInyPgvfSVEanYJ+bOmSMaG9HgqMdwCAyhiIvbxY1VDJPDYKHKeAy1gUqvqTKq5yo8G33BcxXRYtWSy1vCG9E/X0n/I+2PcgZvAGHnKyNSIbhd8UZ1FxxHJk+eIhqrGIbJObBQZTzC7t27RbRFywYqR4Fnoyrw4OVo5kYrWBfBwkidzqU3QYGBPpP+xxADb6T9sf9hMhMi5N6K5moBnoe73qju0rBhQ1GTvnnzJrnCMIyvwyNUGacZNWqU/Ms69+/fp02bNlLt2nUe+WIOVERPjx495JbnwRfr6lWr6OzZsyKSZWaR4M0Rq2NGjxZlFZ5s/vH0CFVENNGcNnzECLmiH74wIhWNiqgBDwoKolc7ddI1KrxkyRJKTEyUW0TXr1+jrVu3UseOr1Du3LnlqnUiIiLkXwzDmBWOqDJOs2TJIjp58qTcygq+PF56qd0jwhC1ZZZfNnqAL1N4Oaqeq/B4NCveHLGK9D9qf80Myhe8kfZHXSxS5WYekaq1N6qz4LiB44dKwYKFqFOnzjZFKo5POE4xDGN+OKLKOE1AwDMUFTWDQkJC5Ip91CistyIciKgh/Zrfz0+IBjPWCaLmFuUMaF7R8/FDbMF9APW/nsLTEdWpU6boHlVHXTFqpVGGYsbpU3j8askJvH29lZFw5dgB72bYWaWknJMrDMOYFY6oMjkCfMm+PWDAA89ViC+zAUsjRDf1HrGKju6LFy+a1klBdS3QW2iZeUSqHt6oDMMwjsBClckxIAqpeq7C+9GMnquwNoLFEdLJemLm9D/S/lWqVpVb+qCWmZhtRKqe3qgMwzCOwEKVyXFk9lxVI25mAGIbKWy9R6yWL1eO9uzZI7fMBVwL4F6gF6gj3hgba7oRqdif9PZGZRiGsQcLVUYX0NxQoEABueV9LD1Xo774wlSeq0jD6j1itWKlSnTq1CnTpf8hvjC0QC/RhffDjCNSveWN6ijXrl2TfzEMk9Ngoco4Tdmy5Sg2Npb++OMPuWIbeKru2bObatXyjtm6LczquYpUvJ4jViFc6tWrZ7r0P9L+eK30AnZosHAyy4hU7O/e9ka1B2ztYmLW0qFDh+SKbXBcWrp0KdWv31CuMAxjZrjrn3EaCM+uXbsIwdqoUWO5ah1EQvAl0759BzGpSq8pVc6CL2yzea7iMaMxDNE7PYQRos7bt2/3SPe/p7r+0e2P0Zt6RFQRlYTg+yAszHARSWuo3qgQ8qh9NupjhvBs27YNnT6dTD169JKr2QMrK1x27doYev755+UqwzBmhSOqjNNgOsyWLduoXbv2YvvChVTli+G0+DszhQoVooiIKYYWqQBf0mbzXMVj1nPEqtnS/3iceqX9UWJgphGplt6oaDA08mPGcWP16mgaOTL70ak4/qjHIByXcHxikcowvgFHVBm3UKMdX331NVX0keYLiA4zea7CvQApeU/6nKogTfzcc89pHsH1REQVEc7zqalCiHkSRLbRhIT6TiOmzi2BeFe9UdHsZaY6WltcvXqVXn01hDZsiDX0CTHDMM7DEVUfBOLR0fpRd0GaDel/XxGpwGyeq6qFkB52WxCpP/30k9wyNnAp0KPbH3XCOKkxukjN7I3qKyIVFC5cWERSUTvPMIxvwULVx0hSvozgf3junD4TWebMmUt9+/aVW74Doqhm8lzVa8Qq0v8//vij4ZvOEDnEkAJPp/0h/ow+IhXvleqNilIRX/VG7dSpE0VGTpNbDMP4CixUfQREUJcsWUItWzYXHfZ6gKYq4EvR1MxA6JjBcxXRMdQbou7QkyISAh7d/0k//yxXjAneL093+0MMq8b4Ri0Pwf76eWTkA29UM07JchQchwIDgx4clxiG8Q1YqPoAahR11KgRckUf1q1bRx988IHc8l3M4rmq14hVM6T/kfbHkAJPoo5I1cuj1VlUb1Q0CBrRG9UT9OzZkxYvXiy3GIbxBViompzsoqhnz56Rf3mG8+fPi/rUGjVqyBXfxwyeq3qMWA0oXdrQ6X9EOuFOgDIFT2HkEal4X+bNm/fAG1VPH1lvA0cSRI9x8s4wjG/AQtXklCtXzqqx9c2bt+RfnmHNmjX09tsDclyHLVKnSKECpFSNVgqAqJmnR6wiwly+fHnDpv+R9kd5gqciiOqI1De6dpUrxgGPDQ2AaASEn6sZ/IC1pnv37rR582a5xTCM2WGhanIQQVi+fDlNnBihfDkVkaueBfWwy5Z9S+3atZMrOQsIINVzFaUARvNc1WPEav369Q2b/kfaH+UJngCvp+o/ajQRiIY/s3ijepImTZrQ5MmTdHM+YRjGs7BQ9RFQLzpz5ixhdO3I9BZ3wFhKWFLBEiYng5Rq6Pvv06GDB0Wq1UipcDw2T45YhcWREdP/eDyeTPsbcUQqSh3Q6IdIMhr/zDK+1VPguDRo0BBRmsQwjPlhoeoDqDOwEV1F52tERISIKngKNCu8/PLLcitno3quPvPMM4bzXEVUFbWqnnhMavr/l5QUuWIMUI7gqbQ/XkuM2H21Uye54n3Q2Oer3qjugFptWOcxDGN+WKj6AGjuGTDgbbmVgaeinWiiSkw8KkQxkwFEEZpqjOa5iseF5i88JkTdtAbp/6OJiXLLGKAcwRNpf9T7GmlEKiLH8EYVn30f9kZ1FXV8KjdVMYz5YaFqctTue6Ti9WDbtm2iiYrJiuq5imELRvFcRfMXLJTUsZlagiieJ90FnAXiDeUIWqf9cbsYqdupc2dD1KXmJG9Ud+jYsSM3VTGMD8BC1eTo3X0/d+4cat68udxiMoPUKzwrVc9VIwg5NdqmddMXnmuxYsUMU+7gqbS/kUakYn/Kad6oroJmTzR9clMVw5ibv/1PQf7NmAwcgCtXrkgHDx7WJNWPiS5oysoORHKOHDlCLVq0kCsPGTRoEJUqVUpuMQBWQUu/+YZKly4t6hq9KSqQ+kctI9LEWkbgIJzOp6aKLnN3CPvgA4r8/HO55RrwtkXaX8tmIohwlE4gcunN9w9RXWE5dumSKD/IibZTtkBmaebMmXLrIVu3bqUqVapQyZIl5UpWUG/PpUwMY1w4ompikPJHd6tW9aiXlC/BJUsWya2s4Msxs0i9du2auM7t27flCqMCQQgvS4BUrafn8NsC0U9PjFg1SvpfTftjGIFWGGVEKnuj2gfHHxyHcDyyBMcrWyIV18Fxj2EYA4OIKmNOXn/99f8dPHhQbrnP6tWr//fss6XklmP8/PPP4jr4zWTP3vj4/40OD//fzp075Yp3iI6O/t+3S5fKLW2YMnny/5LcfP8/eP99+ZdrHDl8+H/To6Lkljbg9mJjY+WWd8D9Y7/B82Oyx9XjEK6D4x7DMMaFI6omRe1mVbtbGWOT2XPVE134jgDbHlgsaRkFrVGzpte7/9HtDxcCrfD2iFT2RmUYhsmAhapJQTcruloZ82DpuYp6UW80ISGFrfWI1Ro1ang1/a+m/VGGoAXeHpHK3qgMwzAPYaFqQnL6CFMzA6GY2XNVy5pRR4BghtUSLJe0uG/cnr+/v9e6/zF0AMMHtBB0eD28NSIV983eqAzDMI/CQtWEYIRpYGCQIUaYqk1UZ8+eEb8Zx7D0XJ07Z47unquwWoLlklYjVpH+Tz59Wm7pC8oOtEr7e2tEKnujug4EPqzJnIVtqxjGHLBQNSGon+vZs6fc0o6iRYuK35s3bxK/7YED/ZdffkmlSj1DRw4foTGjRwuLIKQu9Y4SmhFve65qOWIV6f8DCQlyS1/wHLRI++N2vDEiFffL3qjOgeMLjjM43owYPlzUKINVyomGowJ0wYIF4nfZsmXFb4ZhjAn7qJqMq1evUnBwdTpxIskjJv8DBw6kmJi11L59BypUqJBctQ7ssU6fTqZly5YLH0I0gKD5Y8+ePXTq1Clhvg5fS0wK4i9f23jLc1X1CUV0193U+dQpU1z2+HTVRxWPH1Fh1HK6AyKaOFlAw5teKX+ILdQK3751S9TD6l1qYDbUyClEKWqSq1WvTtWrVRMnKdh3lyxZQqNGjVCEZzm7k/pOnjypHKd2U48evSgiIkKuMgxjRFiomgxEO/fvT6Dhw4fLFW1BNAICdOvWbWL7+vVr9MMPP9BLL2Wthy1QoIDoIrfmPKCK1sNHjtCRw4dZtDoAvoiRekZUr/ubb+qW/kWdLN4rd8Uebge4UlvpqlBFTWepkiWFq4Kr4HVH+QUi23pNn8KJCWph8bjxGeLPhHXU4wiEJcSpveMIhpYg4/Tbb7/JlYfA/L+aImzVE4IWLZpTq1Yvir8ZhjEuLFRNBiKeSPvrNUkFUQrQo0cP8dsVMkdC8GVToUKFB5EQ5lGQCoYAa92mjW7CCVZI7go1RCXnff01DR8xQq44jqtCFeUm7kaDIbBRK4y0ux7g/v67c6doqEOtMvMonsrMaHEsYxhGf7hG1UQg7Y+0POoB9SIuLk5EIdwBXy5oTunarRtNmTpVfOkgQvLx2LFCIEGY4cuJycAbnqtIPcOSyZ3pWWqkSq/GMKT94TbgjkjFbUA0ol7X0+B9tPRGZZH6ELw2OA7g9cFxAceHZs2aieMFjhs4frgbdYbgXbNmjdxiGMYscETVRHg67Z8ZlAFUrlyRUlLOyRVtyRxphcUQurc50poBXp8dO3boFn1DcwqskdyZa49IMGqnnU3/uxJRdfW+VCCO4Feq52urZ5Tc6OCE5uyZMyJyevHiRXGCFhQY6NH3omnTJrR6dbQhHFMYhnGMx8YpyL8Zg/P99yvEl5xetYt79+6lvHnziW5kT5A7d24qWqyYiJagTg9fHqeSk2nF999T4tGjlCtXLno8Tx7y8/OT18hZ4PWBeA9Q3m80PN2/f18MC8C6J8B7cUkRDMePHXPZnin3Y4+JWsDGjW03s2QmdsMGsQ84wzdLllBISIjL+wcamZAtqFO3rlzRHpxsYH/etm2b8EZ1NzthdiBOkaXBa4Ja0ieUE9KGDRrQa6+/TlWqVKHCTz0lL+kZMNcf+wvbfzGMeeCIqklQo5ue6va3xuzZs6lEiRJCDOgNUrLwx0Q6EOld+HSi5CGndkYj+rdixQqPd4hDWMHPEycnrjYooW7U2e55ZyOq2D9WrlzpUj0sgEhCaQUmhbmbUs4OtWZXbycHo4HXAd7PsC+7efOmLpHT7NA7K8UwjPuwUDUJhw4dEp6lEI960aVLF4pUREupUqXkindg0foQCCzUkr7yyisuC0l7QFjA13NUeLhLr7ErKXlnhao7DgNqx70nrajwPq1ShDRqXz31PhkZS3EK8JmtWrWq1yOZ58+fp+7du9GOHTvlCsMwRoeFqknQO7qp+rV6qj7VVSAyjh07ZrgvQD3Rw3PVnYgjTiyc9TZ1Vqi66tmqRcTYFrj9nOqNapYTStSpLl36rddPwBmGcQyuUTUJn376qbDP0avJCNEQT9anugq8W1G3iRrIypUrU1paGm3auFHUOP7++++iRtLTdW7eBq9BHUVkoZYUzxuCFWtagtv86ehRSk1NFbWDzoDXf+3atVS7dm2HRa4zNapqtA6NSc6C2siCBQu6dF17QKhNj4oS1mtvvPFGjmgIxHP+765dol4YVlLPBgSIk2m8vvicGrG+HHWq+LxwnSrDmAMWqiYA6apFixZSaOj7csXzoNscowWdFSl6gi9BVbSiSeXy5cuikScniFY0VKHhqaDyhbto4UJ6/PHHhbjUksDAQDGiEs1czr6OeP3v3b1LJR2MWjkjVNGMg+wC3ntnQKQPArevcsKndUMaShFgfQQHAXgce6rhzQhYilOcKOI40f7llw0tTi25c+cPSkw8Jk72GIYxPixUTUB8/I9UsmQpXQ+sKDVAHeRTJhF6mUXrrVu3KE75MkVkz5dFKzr18Xy3bN4sIqB4DbQqBYDYUh0HnImOArze27dvp7r16skV2zgjVBEVbdeunVOCCFFYCPo+fftqak2E250/bx5duXKF3hs0iEqULCn/4zugnAHRe5wEfv3116IsKLBqVeqoHB9eaNJEnCAZXZxa8tdf6eJ5vP7663KFYRgjwzWqJmDq1KnClkqvaVQgIOAZw9WnugK65T0x5caIeGriEW7XlRGrzkyNcrRGFcLQ2elXEFqeGJHqy96oeM182eMYxzc9HVQYhnEdjqiagPDwUTR48GDdDqpJSUl05cpVevnll+WKeYEYRfoZkT0IfZyX7dq1i75fvpyuX7smLlOgYEGfSNVCTKgRUESRkZLV4nnhduPj4+nPu3edKi9wJv3vaEQVaX/UmDpTkoJI4B937mjWiAgR54veqJaR04ULFtD9v/4SjYrwOEXkFO+jr5zc/frrZbFfmyVjxDA5GRaqBgf1qbt2xVGvXr3kiudBxzdSeb5Ww2VNtB4/flx8KfuKaEV5Q6NGjUQU7Mc9e6hsuXKapGVxO3AaqFixosONW/fv3RMnBY6k/x0VqhCITZs2dbiMA/WUqB19++23NRFZiOjOnjVLiOV33n3X9BOOkHE4cvgwbYiNFe9vnjx5RMYBjgX4/PuSOLXkwoUL9Ntvvxm6Bp9hmAxYqBoc1Kc++WRGl7dewAfzueeCqFw555pVzIQqWtGQ1Lx5c1FTiTQnRCs63f+6f5/8n3jClF/SENqwBUIEFH6hRRRR50hU0xYQu0WfflrUeUIIOyLmIfoRucZJgb3X0RGhCpGIkyhE+BwBImyWIipRCqFF7SjuG68nareR7jfrCY0qTletWiV+8ufPL/YXiNPg4GBR92zmkzVHwOABRMSN5mrCMExWuEbV4KA+tVatmtSq1YtyxX3QDLFzZ/aG13PnzhVpf3RWZyYoKEhE1XwVX6vNU2s6kbLXwnMVLgCga7du4rc9cHnYNdnzLHWkRhW1spjQBqHoCPPmzRMjZ10ZCmAJ9gmze6Na1mpjrj4+x75aq23J7t27hR1VZnAMRIlMWFiYXMmKNybyMQyTFRaqBscT06FQg9qyZXO55RxRUTNyzAHcUrQePXqUihUrZkrRiuexetUq8RxQU+mOfyRuyxnDfDQcofvfXiOWI0J1xvTpIurqSKOYOwMLLEHpgHA9UJ4r7ttMog4nKShtwesAcYrn4K3Rpd5i1KhRtGTJIrnlHL7QTMowvgALVQOjzvfX+oCpCtUtW7Y5FR1Fp2xOEqqZgWhRJ+9AtKKLHDVuZomwadWlDgHk6IhVCNsRw4fTlKlTbYo8e0IVEcFPP/mEJkycKFeyR6sRqZ5yUfAkeG+MMlffCECogoiICPHbEaKjoyk0dDALVYYxCLnkb8aAnDt3jnr00K+JirENvuyRdoZYQnQN6cOoL74Q4zwhaiASjAzqcSHeEGFDdBLizxUg/jp17kzfLVsmhKgtIE5hCYbItDsgbe1IBBePB01BeJ9cFal4H/H64D5hr2V0kYfHi/0P+yH2R5zgdlbeH+yneB1yqkhlGMY3YKFqYJCqxXQgxnhYilaIAogDM4hWiDek4VG+gAglosSugIhsfj8/McHMHqiFRPmEO6C2EpFBe6DEAfW4johaayDqjPcR0XK8TkYt8UDUWBWnqEEG/d56i8UpwzA+BwtVA3PixAkqV66c3GKMiqVohVgAEA+qaIWoMBpoMEJKG/WXcHmwFxm1xptvvilS4/bELhp20Jjmyn0ARH5RY2lPfKEk4+zZs6JpzFnw2ND4hdII1PEa0cAfrzPeKwxSQNQYYH/D8AO8n+6UOTAMwxgVFqoGZv/+/ZrPb7fk9u3b8i9GKyAWIBogHlTRClEBcQGR4WoE0xNA+I0eM0aM/8TkJmejwEjrq2LXVhmBu+l/R9L+eOx4fbsr4tnZhidcFw1iAK+HO81mWmMpTleuXCmGfqB8g8Wp41yTHskMw5gTFqoGZs+e3Zp2+6uoDVSIHjkKGrCAv795Znp7G0vRCnEBkQGxYSTRClHXr18/kepGgxSiks4AsYupRStWrJAr1nEn/Y+0f3kbmQVEQ1EviyYxZ0Um3AGQ6oeLASy3nBW5nsBSnG7YsIFKlSzJ4tRFUDoVE7NWDE5xlNjYWCpbljNZDGMUuOvfoEAYTps2jWbPni1XtGXJkiU0atQIql+/IXXv3l2uWgclCDNnThcH7w0bYnk+tpsggnf2zJkHnpZG6czG43LVcxXNR7Zm6SPi+vHYsdl2/2fX9W/vegDlFWg8hOB2FIhbo3ij4rH48lx9b4KGx1dfzXAp6dq1m1VvaBW4JGCKGQIEOdndhGGMBgtVgwKjakR7hg8fLle0BzYsiB4g4mALCNR27dqLMZRmHxlpNCDEVCP2U6dOiRS5N43YIZpc8VyFyEVk0tZ1IGabNWsm3Acyk51QRYT35MmT2Q4YQPQRpQfozndU1KnXQSQY41i99TqzONUHRFNxYr5+fQydPp0sV63Tvn0H6tmzp5imxjCMMWChalAgIoGeZ/WbN2+ipKSTNHDgQLnC6ImRRKsrnqsQlVu2bKEPwsKsPl5bojM7oWpL3OL1gnOBoz6nEIdwKfCWN2pmcYr3F1O7WJx6D28cZxmGcQ6uUTUoSLcXLVpUbunDzZu3bKbGGM8CsYIyANgi/XP8eCFiIGpgmI+OdIhHiB09cMVzFY8dZQOIyFoDgsyZ7n9cDoIdQt0aqItFVNQRwYmILxrGUCKgpzcqXjcIdIxzxfuI9xMnHyhlgGDHa8Yi1bsg5c8wjHF5bJyC/JsxEOvXr6dGjRrRU089JVc8Dxo40HxgpK7nnAoikiVLlRKCsXnz5pT7sceEyFm4YAGlpqbSX/fvk/8TT3g00urn50d169Wj67/9Rt8uXUoByn5R2M7+CFEZu2ED5ZWP3xI8VqTdiz79dJbbwXUwRMGS48eOUZ48eSg4OFiuPARlMed++UUMHsidO7dctQ6E4qKFC6lR48Yicubp6DTE6ZHDh2mVItjxkz9/fqpRo4aohcVzKVqsmN3HzOjDY8rnatOmTaKZjmEYY8JC1aD07dubwsNH0+OPPy5XPI83xDFjH4gaiBtVtObLm1fMcEfdHYRfrly5PCpaUT8JkYq6zt9//53Kli2brdDCOqKqsOSqpjxeiF1L8FhPJSeL0bOWWBOqW7duFdFHPHdLEB3F7b/Vv7/NaCQisiu+/16MFO3Tt694PJ7CUpyiuQuvQ926dVmcGhw0Wx08eJCFKsMYGK5RNSCemvFvjy5dulBkZKRHLLEY7bGseUTzUzFFDHmyIQf352inPCKeKBt4e8CARwS0WleK4QiWZK5RxX0hVZ652x/r8DyFsLDlrYohCxCzrjgYOAoEM04Y8DyN5N7AOI63jrUMwzgOC1UD4mlrquwICHiGD9gmBtHVo4mJItUN0Qq7KEQutbZegghdtXKlmExlSyyiLvOZZ54R3p+WoOYV0VNLQZdZqKIeFwI8c+MVanVBdi4AAI9vY2ysmBZm6/G5AsQpIrQHEhJEbSOLU/PDxz2GMTYsVA0IhOr8+fMpIiJCrugDH7B9B0vR6u/vTzVq1hR1klqJVgg2e56ravQ0c4c9HtP51FQhJFUyC1UIUqT9Lbv9IV5jYmKydRXA/aHBSmtvVBanvg2OeydOJLE/NMMYFK5RNSCICBUoUICqV68uVzwPvAaPHk2k119/Xa4wZgbNSoimtmjRgooXK0apFy6Ibvy98fFidC5KAzLXjzoDrltHEWyYrQ9RiWln2GctgZhUa1tr1679QFyinha1o3hsKpY1qkjvo2ks5NVXH1xHFcaoNbXm5QthPmvWLFGHigYrd0sfUDoAhwK1xhVuGO3ataOXO3QQr6u9pjLGPPz662VRh821+QxjTFioGhDUvaHbOXPDiSdBjV1KSgo3FfgglqK1cuXKlJaWRv+3fj3F7dolROv/0tNdEl5oDsLtoosfXfVo/EOE1RLc7v3794U3LCK6AOITghkCWr1fS6GKbn9ER2E9pTJ/3jzRtZ+5IQqiFk1XmCiEyG2dunVdblqC2P2v8pp8s2SJsIdTxSm8ZCFk3BH2jHGB9y/2TRaqDGNM2EfVgFy4cEH+xTDagnQ4akYxN77fW2+JtZUrV4q58rAng1hzFqTn4U2anecqpj8hHY9MgQpKEVCaYA3UpqIpTAVd9PkVkZh58ACirO56o+L5qnP18Tog/ctz9RmGYYwD16gakFGjRlHfvn1FOlUvDh06JCYR6V0XyxgDreowISox+emNN954pL4Ut285YvXw4cO0XNnf/p43L129ckVeikRaH1He3n36iGgthKS1Eamoc4XAdGZyFkAE9peUlEeaziCKS5cpw6I0hwKbN9Rx83QqhjEmLFQNiDeEKo8SZFQgKs+eOSPS9Za2S88GBFhtYsoM6jvn/Pvf4npI56vXgTCEkC1YqBClnD1L5StUoADlNi0FKKKxKEE5dfIkBZQuTannz1MfRbSqghlCE7W2qI3t/uabDg2nwHV4rj6THXzsYxhjw0LVgGDW/tChQ1moMl4HwvHnEyeEaMU4U8ynRzc+JlDZEq0Qh/Bc/fXSJVFigGglBPCnn34q9usqikjMbWOYxf179+i4cr+IqA77xz/E9Z3xRmVxyjgKH/sYxtiwUDUg3rCJ4oM1Yw9XRCuiqBCsHTp0oM2bN4vaVHirOgrqT1GO0PiFF+iH3btteqNmFqd4fBUqVGBxytiEj30MY2xYqBoQFqqM0REp+rNnHxGF2YlWWJ+hyQod+2XLlZOrjnM6OZmOHDlCg4cMyTI1zdWIL8Oo8LGPYYwNC1UD4kmhisaBRCvd1qdOnRS/y5evIH5bgxutGGvYS7Pv2LGD4uPjqXHjxvIazrNr1y4xOx8OAixOGWdB3X92pKamKj/nqXbtrJH6wMBA6tGjh9xiGMYbsFA1IJ4Uqjhgx8XtokaNHBcNJ0+eVETBbt2jvIz5sCZaL126RDVr1RId9q6Cpq6E/fupaNGiDxq8ypcrx+KUcQgcU+vXbyhKQRxFPU7yCTrDeBcWqgbE00IVOHPwRWosNHQwC1XGKSBaUaMKM35MmXKX6NWr6bXXXhOm/gzjDDimRkXNcCq978qxkmEY7WHDf4OBOf/t23eQWwxjXhDpRBT1qSJF5Ip74HYKFSoktxiGYZicAAtVA8JfxoyvcCEtjYoVLSq33AO3g9tjGIZhcg6c+jcYiKjOnz/fY+kmd1L/nTu9JlcYxnECg4JEs5O7oO418ehRucUwjrNy1QpO/TOMSWGhajD0EKrXrl2j2bNnyxX7cI0q4yow6f9u2TJq5EbHv0rcrl30RteuDk2jYhhLXKlRxeAVZLdYqDKMd+HUfw4DdisxMWvFbH9HuHr1KkVGTuO6WcYlMMcfPqqYNOUOuD5uB7fHMM6Cjv+lS5fSH3/8IVdss3v3bnGcbNGiuVxhGMZbcETVYHg6oooDddu2bej06WQhPu3Vwy5Zskj83rJlm64jXRlzgk7/X1JS6Ghiouj4RzPVH3fuUJkyZZyaSJUZTKg6dfIk/e1vf6ObN28Ke6og5aSrAu+TjAPgxLxDh/ZUtmw5u9Z8yDhBpOL4OG3aNMqXL5/8D8Mw3oCFqsHwtFAFEKsrV658xPj/2LFj5OeXnwICSsuVDJBm7dixY5aJQAyjYs/wH/P6Fy9eTK1atbI53z87EE3dvGUL9ezRQwhTS8N/1VMVovXZgAD2VGWyBcdWjPFFOYol169fE8fChg0byRUSwyXatGnDIpVhDAALVYOhh1C1Bo8RZJzBnji15NdffxUjVBFdxax/Z8GsfwjSD4cNy3LbPKWKcRdvHXMZhnEMFqoGg4UqY1Qyi1NVFAaULp1FQKog/f/NN99Qx1deEYIzb968TolVXOfOnTtUpWpV+mH3bnrjjTfouWrV5H8fhUUr4wo49qGchEelMowxYaFqMNAwEhYWRsuXL5cr+sBClbGGq+IPonb1qlV09uxZ6vfWW/T000+L25qsnID5+flRjRo1qPBTT8lLZwVNUwcOHKBbt27RyFGjhBBGynbOv/8tUv1t27a1ef+4rxTlvjOLahatTGb42McwxoaFqgHx5AjV7OCDNaPibmRSFZRBQUH0aqdOD64zd84cunfvnhCqiceO0RP+/qIGuojF5KrLly+L6/9+8yYFVq1KFy9dorJly9Lrr78u/m9NANvDmTIFJufBxz6GMTYsVA0IC1VGbyzFqdqgVL5cOacjkP/9739pY2xslhT96dOnKeqLL6hDx46iQQUNUmnK/fyqCNGbt27JSxH5KyL26aJFqXixYqLxCo9r86ZNNGbs2EdEpVpS8Oabb4rH6igsWpnM8LGPYYwNC1UD4g2hCt9AiIzhw4fLFcbXQZMT0usQqJbd865YPkFQLlq4UPwNU/7Mkc5JEycKKzRXm6muX79Oo8LD5UoGePwYJpBfEbcQrM6m9FXReio5+YGVFovWnAcLVYYxNixUDYg3hCp3vuYMVHEK8aeVHynspxYqIvWFJk2odevWcvUhq1atoj0//EAdOnRwyZ4Kdmpr16yhl9q1y3L7EJsbNmwQQnPAO++4NbUKz8PS/xWCFbW0jpQXMOYF0/qQAXj++eflCsMwRoKFqgFp2rQJrV4dTYULF5YrnoeFqu9iKU4BOui1MMu3FIm9e/e2ensQf/PmzaPKiuiD8HMVPHaUCgwZMsSqcLQnlp3FUrT6+/uLSDCLVt8EQrVv37480IRhDAoLVQPijQMnhCqmsMyePVuuMGYGQiv59OkH4lRroeVI2h1C9p/jxlF6ejq1b9/epWiqCmpa18XE0JNPPEHD/vEPq/dnr/zAVVTRevzYMbHNotW3YKHKMMaGhaoB8daB0xslB4x26BUFxO2jkalT5870wgsvyNWsIJKaduGCmGrmTjRVBbW0KSkp4nPRtVs3uZqV7Bq6tMBT0WnGe3gjg8UwjOOwUDUg3qqZYqFqPvRMUSNC6qg1FMQiDPrhg9r2pZfk6kNQd/rH7dtyKytoZsocgUVUNSYmhnLlykXdu3e3KUKzs8jSEk/U+zL6w8c9hjE2LFQNiLe6UDmyYHy81anujPCDgIuYNEl0+VdVhNszzzwj//MQ2ENdunTpgYfqaeX5lC1XTvx9Wbk+rmMtCouo6rXr1+nK5csU+v77NsWyM8LaXVi0mhcWqgxjbB4bpyD/ZgzC8ePHxe8qVaqI33qBOlU0vTxlY2IQoz8QXKiP3Lp1Ky1csEDUYsIMH2NJ0TxUslQpj0QMVRAdXf7ddyLK36JlS8qdO7f8T1bwWGfPmiWiuhcuXKCatWrJ/zxKgiLoUN7SokULql27toiUho8eLf4uWaIE/bBnjzD6z8xTirCFyH0+OFg4CdStV0/+Jyt4nIi65lVem1kzZ4pBA6VLl5b/1RbcNjxZGzduLJ7Dvbt3afv27bR27Vr6/fffRTS4QMGCNl87Rn9wzLty5Sq9/PLLcoVhGKORS/5mDETRokXpxIkTcktfbttIxzL6AcH305EjtOzbb2nE8OFC9FSoUIH+OX48DR4yRETsPO31CUE8Y/p0OnTwoIheOlLvCRcAiEGUI6AMwRpI+0PIZWcl9WxAgIiqQtxZA1Oy1MamjRs3it+2wGsFD1Y8D9TN4rX1JHhfcJ94n/7x0UdUqmRJ8f7hfcT7iffV04+BcRxE/hmGMS4cUTUgd+7cEROCWrZsKVf0AREwCFW9I7lMBhCGSOurkdM8efIIURby6qu6RE4tQe3rrFmzRES0W/fuImJoDwiwTYpwDFIeM4Qm0v7WOPfLL0IcBAcHyxWiWEXgYn4/QNQRpQDp//ufVTGONZzINWnalLZs3kwBiuAtbCcLgMePKGxqaqoQi45cRwvwfuF9Q+S3YcOGhEqrXbt20ffLl9P1a9fEZTjS6j0OHEig+/f/ojrKiQXDMMaEa1QNyPnz5yksLIyWK19mngKTqFAjaEl8fLz4XbduXfE7O3iCi3ZAnLozV19rEOmz541qDTyPTz/5hPr07Utff/UVNWrUKFshiNGlrZSTMMsIbdgHH1Dk55/LLWVfVC6zb9++bKOymKR1RBHG3bp2Ff6po8eMcfj1ggjX0nPVFfA6W45yVd/3gNKlPR4pz0mo9f7Zkd0xD1ktnFgwDON9WKgaFE8X+MNZYMmSRXLLObjxwD2MJk5VHPFGzQ6UCCBiiXT9XkVg2rKtQr0rShgsBVlmoYrH8q9//YteeeUVuZKVuF27qI4iMDBe9cqVK9SvXz/5H/vgPfCE56orZBatqHXlUa7agOOoK/To0YuHnzCMQWChalA83YEPoQqcORgjOhEaOpiFqgtYilPLufqox/SmOFVRvVEhUPHYnAF1onhubw8YIAz+mzZrlq3AwnM/dfIkfThsmFzJILNQBRMmTBCRruxu66oiTuPi4mjEyJFCdEIo2xLI1vCk56orsGjVFgjVqKgZTmWBXDk2MgzjObiZyqA0atRYRIkY84KoIETc1ClTRFr8fGqqqMOcMHGiiBQire5tkQphhJrNLVu2iIYjZ0UqbKv+u3Mn9erdm2LWrRO2UrYEFV6TwGxqVzNTtWpVMTAgO1BaULBQIdq/b5+Iiq5auVLcvjNA2A545x367rvvxOuA18ObYH+AYMZAgylTp4r9BfsN9h9ErXFCgZMehmGYnAILVYOCjuizZ8/ILcYsWIrTqC++EB3unTt3fkScGgWIzIkTJlC+/Pnpg7Awp9PfEHXwVkU0EiA6iUlNtjh37pzDYjj4+efp3Pnzcss6GIqxadMmIY4RDZ739ddOi0181lDjCj6PjHRa7HoKiFbsL9hvsP9YilbsX9jPjPJYGYZhPAULVYNSokQJSku7KLcYI2MpTiGUgFHFqQpEpSoy8RhdieyiVACiExHA2NhYMdo0X7588r9ZUW2pHBXE9myqAAQqoriI5uKxwBoLJv/OguePKCacNjCsAK+P0bAUrdi/8HriZIhFK8MwvgwLVYMCs/PExES5xRgNdI7/5z//eUScYvrR8BEjRCe5EcUpQNpY9UaFx6erdZlIQf966ZKI8kEgJezfT9Xs3BbS+Nl18VsD4rH6889T2kXbJ2yI4kJY4rlhatbRo0eFVZYrQOzq6bnqKplFK8B+yKKVYRhfg4WqQcFoybi4XXJLewoUKCBuH1EZR8Dlli5dSu3bd5ArOQ9VnI4ZPZpWrlwpooeW4tSbneOOAPGGtDEac2BG72pzDkQQoql47hCTq1atEt67mWfzZwYeplWd9OhFwxns2myB9wHRXER18XjUmlNXxRreRzSGYUIbSiPwvhsZiFbsf9gP8Z4AVbRifzX64/ck9es3FPuFo1y9elUcF7MbRsEwjP5w17+BQcfqiRNJNtOproLRgS1bNhcH8u7du8vV7IFI3bNnN61dGyPqAnMK+JLHlCV1rj5EHsaDGl2UWoKooOqNChHnzpcwbgt1nEiRI/qIOteZM2YoJzDtbQpVpO8haNEgZK3MwFrXP0CUdHJEhBgXawvc/vr162nohx+K9wYRVkRFIcjdAe+/tz1XXQVC/cCBA3QgIYFu3rwp3i8If6NG+z3B5s2bqF+/vg4d5/AazZ07h06fTqYffviRSpUqJf/DMIw3YaFqYGCTgnnoiBZ5gkOHDtGXX35JMTFr5Ur24ED/gSImfN0EG0IM9kCnkpMfiFMz2wNBrCC69nTRok57o1oDETpLz1LM9c+fP794fWwBW6rkU6eEkLRGdkIVIKqJkwN7k6RgkXVHef/eUcQ4QIkDHpe7AhNi2Sieq66iila8Rpb2aDlBtEKszpkzV5xo2wMZo6FDh3rsmMswjPOwUDUws2fPVg6YFahVqxflij542sPVaKji1Ne8KyG0XfVGtQZKB5BSV6dAYfv7FSsejD61BaJ6sJtq3qKFXHkUW0IVjVKpFy6IoQi2QFQ1Zv16GjRokIgaQ2Ci1MGZCVu2QJTWSJ6rroLXJbOnb/ly5bw+cEJPUMpUuXJF9oRmGBPAs/4NzG+/XaekpJO6z6FGWQC+6IsXLy5XfA+I0+PHjj2Yq48v7+rVq9Nrr7+u+1x9rcFzW7RokRDeoe+/r0l0CK/PnDlzROmAegKDbXiiOiLmDx86RC936CBm7lvDctZ/ZnL97W+0VxHdaDC0Ra7HHhOXRTMVPjN4/zDTH6l7jHR1d54+HAXwWsKv9dwvvwhhZ8YZ/XhdsH/XrVePateuLZwYdu3aRd8vX07Xr10TlylQsKApn5ujnDlzhtLT/ydKWBiGMTbcTGVgSpcuQ4cPH5Zb+oFpQKdPn5ZbvgPEFqKAMHYfMXy4EHKI0qFuErWMiCyZOYIKVG9UNAK54o2aHUh9Q8Cr9a0oG7l3756whrIHXve7TthSZQbRUDgMONL4hyg4XALUBiJcF+8rIstagOeP1xUYyXPVVbC/4/XB/o+xthUqVKDt27eLzwc+J/i84MTH18DJjKODJxiG8S4cUTUwEBvvvfcuvfvuQHrcTke1luCLCRY3vhBtgEg6ooh9NPLgJ0+ePEKcotYwODiYihYr5jORI7xn8BBFarqJIiq1el64XdSldpPNKNg/YN2EaByGBdgj9fx5KqUI2qCgILmSFVsRVXAxLY3u37/v0IlE3rx5aeeOHeI1AIjE/rhnD/2piGVERd0FrytS/3n//nch4PHZ1OJ2vY1lpLV58+aU+7HHxMkcMg5qpDVvvnw+UR6AWmt8/t1pLGQYRh84ompwUNyPaT56goP3kiWL5Jb5gDhFfSaaaT4eO5ZOnjxJzZo1E5FTmLpDZPjCl60Kni+eK+oO3fFGtYbliFQV1DbmU8SgveYmFVdsqTKD+lZ7NlUqiPIigouoL8B77eqIVVsgEonSCtVzFe+Dr4DXDPuROsoVJ3cQrfg8+cIo1/XrY3zi5IJxjvsJ0yg44BnhqPPoTwcKX7Cdkm6my0v+QtH9q1NA8DRKuC+XnCEtmvpbvR/LnzYUmXBTXkEvblDSli8pcu0vctsR0ulm0iaKjNxAaXJFb1ioGhzU1iFNpSeoQUSXv6PCwAhYilPLufq+Kk5VtPJGtQYip+r0KvV2sYboJ4SjI6DBCfsR6jndAab+iKo6CgYLrFmzRm5leKO6OmLVFrhdeK5CHON98EXP0syiFSd9OPkzq2iFVypg+6mcSmFqHfWDaKTL+Emm+JXt6eLUHtRx8k5FyoFnKeSrw5RycCjVdCUxVTyEvnpw++coOXqocq+Z7zeWwmr6yyvoRNpWmtp3Fh39S247xHnaPPVDijx6R27rDwtVg4NpP/Hx8XJLP2rVqkXHjhl7MhaiY0hLw9jcUpxaji71RXEKILaQvkQXPhqcPOHxaTkiVWV3XBwVLFTI4WjqFUUUIELv7vsAoYxGrKtXrsgV28BWDFHfHTt2yJWMCKirI1ZtgeeG1x/uAmjcwj6ppRg2EplFKz5v+Nzh82cW0Xr8+HFq1Kix3GKYPFS8zmvUo1MZurVqKyXcUKOqjFFgoWpwvJWGr1WrpnAcMBqW4hRzztFgY/S5+lqD1wCNPKgbhVWUJ+rsIDjUEakqECCbNm0StamOgvrUBhp578JLFTZVjoKoL6K/lqLR3RGrtsC+h9ILlOrMnTPH9I1W9oBoxXNWR7lailYjj3JNTk4WDaMMk4WK5aiUP2RR5tS/TH/3ryvT9h0ofN6n1L/qMxQcmUCuVAeA9LS9tDi8w4NygKr9o2hLUsaJXnpqNL2r3H7Vd6MpVWpna2uPkJ5GCYvDqe2D8oK61D9ykyhpEGUPdQfTRrpKG0MbPHxuN5No+wLL61SmtuHfUELaXdRKUGRwAwrdeJVo42CqK8oVjlkpi7hPadGDletaljPcpbSEbyi8beUsj8VZWKgaHDUND8soPalaNZC2bdsmt7yLpThV5+rnNHGqAgEZMWmSaHSD6b4nIsZ4vS1HpKpsVkQqUtzOTEq7pIhddJJrQeXKlZ0SPoj6IvqLKLAKno86YtUTkT9EfvG+PB8cLE6k8H7lFCxFKz6fOInEa2A00Rqn7A+2GvuYnIYiqPauoCUxz9H4TztRRSuqKD11DQ3rOJhii42iLYkpdCb+A3ps+Ve08Za8gCvc3Etf9OlBERfb08r4ZEo5E0+zS26ivh3HUHTqXcpVsh2NndyZaH0EjV+TQunpKbRmfAStp840eWw7Kpnlcd6hpEUfUkh4IrWJ/olSUlIocdMQojl9RUnD7ZpD6WD8DGqtliCgrCFXCkUPe5N6LctHI/AYRBlEGD2zaji9OX033chdk8IO/kBRrQsTtZ5B8Q6XKyjCPuFL6hPyBV1sN5/iz5xTXrPJVDJ2MHUctsa6yLYBC1UTgA5cvetUUb918WLag3ouvUGtH1LbluLUcq5+ThKnAFFBNOxs2bKFRoWHizS2JxD3o7zeqOe0tJOCqIPhPWpFHQXXeSx3bs0ssvCe3/z9d4dsqlQw7hdRYMuoKiLQrdu0eTBtyhO88MILQhDj/YLNk6+WAmRHZtEKsF95W7Ri38EkPp48lZOREcUHEcRyVLfzRNr45z3lmHVbkViZuUOnNn6vCMQ3aMTwjlTRPxflKt6cho14g6y7QjuCIipXfE6RibVp+PA+VKd4HkWNlaRmwz6knrSSRs5URCLloZIdP6TJ7RSt+uVSil70CY1cT9Ru8ofUsaRy+Sz8Skd3HSHyq0Y1KqCnIBf5V+5JXx07R8cmNSNr3Qvpp7bSvPW/UXDX16kJHgPKIGo1p8YV/ehWTAKddDlUnEQrxs2kxOD3aPjghlRcUZrqa0brP6OZOy/LCzoGC1UTgC9bb9SptmvXXtRz6YUqTseMHk0rV64UkTtLcaqV4DEbnvJGtcaGDRvEuNXMQjg2NpYCg4KciqamXbjgcNOVoyCqitt1FEQ4EQXGdCtLICQBRJOngCC29FzF+5gTgWjF5xefY3yegSpa8XnXswHt559/ph49esktJmeSuakphRK3zKCepXfRZ70m05rUu/JykvSzFLdqH1GjmlTlSVUy5aIna7agTi4rVSkqC9ei6mXzyjWFJ8tTnUaFH4rEXAHU8cP3KDhxBn0wNlr5Uh5FYzsGZCPcilHdl5uT3615NHDo57QqeqfdNHuuin1oTcoxWtroIq2Jjqbo6GUUOaAnjT3oTqhY4dIx2qXcRuHm1ansgwervGZValIjOkMxB1LkmmOwUDUBqM1DnaozkSQtQJ2qavHjKSzFKUQShBAsf3K6OFWBkFI77xGh8kSqXwV1m0hVI5pqCQRWwv79VEURic5w7vx5ClZOsrQETX6XnIzGIQqMaHDmVD8st2C95UkBifcLjUco1cD7iMeRk8Hn2VK04vOOk1J8/vUQrbt37+b6VCYTuci/Ykdln3xDEXnbaF38RbkuSb9F11KsCLf8T1IRVw/H6bfp+qU/ia5Oo5ByamQXP7Ie1IJc5RtQp2Ao4pLUtG1NEZ20Th4qGTKB1iyaQcOLbaMPQrtTy8AAqtp/GkUnpFmJFCukp9L2sa9QYMvuNHJdsnKZvFS2xyQaj1S/G6T/fp0uKb+vRnakcg+em/IjamSdh4WqCcDBHH6qiAboCepUly37Vm5pA1KgEESW4rRUyZKiCQX2SixOM4Co8pQ3qjVwf6qDQGYxvH79eqpSpQrldmLoBGypLiuC8tmAALmiDQGlS9PZM2fklmPg84NUL6LCliDaik59CEhPp+Z92XPVVSxFK14bvE84HnhStKLunutTmayo0T4r5PKjQgGKULx0nX63VHu3b9BlVw8bufJTwaLKcTZ4Im05o0Z2LX4e2GLdpdQ1s2iqiHCm0vqR/8oa8X2EJ6lisxDqM2mtcjuJtGXRROp07t8U+uYs2pnFzSCdbuz8kgYuuEjtonbT0a+GUqeQEAppohyzIaLdINcTBako+VHw+C10JvNzU34OhtWUl3QMFqomoU2bNnTEA53KtkCdarFixd32U1XFqTq6FCMaLcUpvsRVn07Gs96o2ZF5RKoKoo2nk5OpXLlycsUxMMa0UqVKmkeA1VT+ReX2nQE2b4gKZ66NRFoa+59WI1ZtAWHm656rrqKKVuzvOC7g+KCKVq1GuaLeHnX3XJ/KZEURbccTKE4ResUKZipvylWaGnWqTZSUTOcfpNLT6ebJw7Tf5Qz50xTUuBrRwU0Ud+qOXFNIP0ELOlamgI4LKAl3dWM3zRy5kqjdDIqLm0HtaAN9+d0hcmxMAERrDxry7otEt07RmYuZBW463b5+lW5RRaofVPShGLx5gZKSnH1i1+n43oPyb4WiValxsPL0Vv1Apyz0cXrSAuoYUJk6LjghVxyDhapJqKN8mVoamOsFGrlc8VO1Jk7R/Y154ixOrYPXDJEkT3qjWkOt07R2f+vWrqXq1as7FU0FsLZCmt4TYEa7s804ePyICmOMbmZgq4THq0eHPoQ7Xuec4LnqKjgu4PigilYcN3D8wHHEHdGakLBf1N0zTGbS07bRZ1O+o1vB/alPkyJyVSUvlW/9uiISv6MpU9eIuk9c/pNRM8l1p3F5m347aOrUBbQXVlDpabR3xic09WAghY0LoYq5rlPC11/Q4ltNafiHbenZZ5vRgAGBlBgZQXMTrsvbsSA9haLfrUsBbcdStLS4opsnaMO6eOWgWY+ql1AbsK7SvtNpdP3Uafq9VCUKpH20bN0RIX6FXdbUfyn3qWz8eZ1u3LZQmfuSKfV6CiWlFcgQ2VeX0awlR5XrSdeEVRaZrlxlqXW/tuR3cBZNnbGb0pSbSU/bTTOmzqKDgYNo3GvOnSz+7X8K8m/G4DRt2oSWLv3WoxNVRo0aJf/K4LffrhOKzatVqy5XrAPx0LFjR5GqxtSaH3/8kerVqydGL2IqkSdrK30BCC80mMCQHl6fer1eiJgi9Q1BkPnEAYLg+xUrHvFSdRQI7g8//NDhMo6wDz6gyM8/l1u2wWP+6quvnH5cKEeIWb+eBg0alCVyjNcftl9wVNCr9ATp/xXK63v71i0x4lWv+zUreL1wfMEI31OnTj1yfPn+++8pMdG2bIDFH+z+0JRoSUREhPyL8XXgJVo7ZJoi1TJTklqHTaLhb7cUXf3KUYai+7en0H19KHof0vDwUd1Cc6eGU+TGVOX/NahnWCDtj/yG0sLW0L6wmmRrgFXG/S6g2lEx9FXIw2MPhOE308dT+OIDGQuBvWlSxBB6s2ZRup0wg14LmakcHJfQirA6JEyhbu6lyNd6UCQNougVg6mmeKwPSU9LoDXfzqSRkbGUERP1o8CeYyliyOtUE139QgyHU6/PlP/79aNFPw6lUlun0ZDQeVJ0K89r/ECqc20hhUbmpvFbvqY+FXMpQnQeje41kTbeKkM9F0XTpCb3H94O7qX1+/SPYjtp3OK7FBa9UlpYwUf1e5o+ajwtThSXevSxOAELVRMxe/ZsKlGiBIWEhMgV7UHBM3xbnfG+jIvbRf5+flSpUmUWpy6ASB5Sz2hiQiRJLxCVgpsAGrWs1cDif5WrVBGpameAoIBLxZgxY+SKfZwRqmDUyJHU6sUXRV2jM0Do3L59mwa+955ceQjeB9hJoVNfz30XDVYbY2NFs5ye77+Zwb6b9PPP9NNPP4mT4pRfUujy5ctOTZzCCfWePbtFzRzDOA3m+dcdS5RJfDLaw0LVRKAD/8svvxSC1VNAqEZFzXBKDCMKe0X5koiaPp3FqRPgyxYC1VsRNaRR8+XPLwRSZrCvrVq5ktq+9JJccRyIQT9/f3rttdfkin2cFaoLFyygxx9/nMo6WTsLUPvYs0cPq168aHRCxM3aa+JJECVequwLekfUfQF8jkKHDKGnihRxKjoaHR1NoaGDWagydrhM28NDqNeq52h89CfUp/KTIqUePXkYha4qR1FbPqUQq76mjFZwjaqJgJ9qYuJRr5nw2wJfEvzl6jhopFG9UdFgo7dIRfTw7NmzVtPn+OJHPbSrNj6esKXKjCs2VSqI+KMO2BqIauO1QdmDnrDnquvguIPjD8N4hiLUZEgURQ24R1NfDMywWQrsSF9SZ1q0ZgKLVB1goWoyunbtJpoCGPOCBho00qChxtPeqNZAPaa1EakqqAHMlzevGEHqLJ6ypcqMKzZVKihluHv3rlWPYLwenhyxagvcN3uuMozxyFW8JoWEfU3HHlgsnaANk/pQs4rcEKwHLFRNRsOGDWnlyqydy4zxgUC09Ea1lnr2NIiWfrdsWZYRqSr4f+yGDS5PlIItVfXnn/e4+HbVpkqlRs2a2bpoILoJqy5Pjli1BepU2XOVYRgmAxaqJkNN/7vrbaolaEooUKCA3GKsgVRy1Bdf0PPBwbp5o1oD9Zn5/fyybdrZHRdHBQsVcimaCmDzFBQYKLc8iys2VSrFihUTUeMdO3bIlUdRrbo8OWLVFjiJYM9V57h27Zr8yzFu3nTMjZJhGO/CQtWEIP2PCSueAB3/kZHTHBbCaEhA56w6O515FEQo0bSkeqN683WC2EH9ZeYRqSqI3G3atIlq164tV5wHtZUYWaoHENvnzrneCIOoMaLHeI+soceIVVsgKs2eq46BeuqYmLW0efMmuWIbHN/mzp3Dc/8Zj2CkQJIvwELVhLRq1cpj5v+TJk0Svxs0qPdwPq+NH3TNYrwrShKYR0G0D40xYPSYMVm8O/UEIlSti80uLb9ZEamI4Dlr+aRy9coV8vPz0y1ajKjjvbt3XU6NI2qM6DGiyNbA84B1lx4jVm2BEhGUikCUz50zx+Uosi+DyX04DvXr19fqcSrzD45vAJ66DKMl8Ovt3r2b3GK0gO2pTEqXLl0oPDxclAJoDVwFdu7cKbcecvjwIUpOPv2IdVXRokVZpFoBjTCwd9LbGzU7UBuLkazZTbuC2Pt47Fjq0LGjy0IVnpYlS5Sg9i+/LFccx1l7KhUYvUOsumJTBfC8d2zfTh+PG5etgMfwgiuKCO/Xr59c8R7suWqb3bt306VLl+QWSjdiqXjx4lS9etbjZJMmTcQAAIbREnw3DxjwNrVq9aJcYdyFhapJQcr9woULNHDgQLnief744w+qXLkinTiR5LKY8XUQefOmN6o1IG7QmIPa2OyA4Lt+/bqwbnIVlKN0ef11l5rEXBWqqP1F3W2jxo4bvWfmQEKCEDOdOneWK4+C9xSRcXTjG0EcIqLqjSlmZkM9Xh08eJgFqcFRgyP+/n5iaIOj3y/qiUlQUBBV9EJzambwvYxhJzztTFs49W9SEA2YPHmSOBjrBQ4egwYNEZOomKx42xvVGqivRAQOojk7cJmE/fupSuXKcsV5sB+ikUpvJwNMQEM9GGyxXAU1tRDz2ZUQQAjCygsnIEZIu2O/Ys9V+xw4cEDUoLJINTYQqa++GiJ6I5KSTlLbtm2EALUFPvOIXK5bt04Iw5Ytm1u1m9MTPA+UwnE5ifY8Nk5B/s2YCIjGu3fv0f3796hcufJy1fPkypWLli37jl52Ib3ry6DRBXXDqAFFKUTu3LYmP+sDIoGR06aJOsuyZcvK1awsW7ZMRBSfLlpUrjgPbKIg0IODg+WKc6CpydnZ/QCvc+LRo5RX+Tz4+4tp2E6DCVfwVb2QliYiM9ZA7W0R5fmhnKNOnTpef39x/xh7W7BAAWGjheeACCvzEEzww3HKm7XhjH0Q+Lh8+QotXryEGjRoIMqTXnqpjfLedRDHlMzgpBhlb6+++qoQhch0PP10UVq9erVXv5cmTJhA/fu/7fKgFCZ7OKJqYvDFjjNQPYEIM5o9ljdBhM3b3qjZsXrVKiG8rM3xV0E07nRysnKy41qNpwr2B1e9V92lRo0alOrm/lhNeY0QVbYVMUXaH2IepQZGAe+t6rmK/dDVxjJfA9EtCCDsG4yxgS/4u++++yDdX6pUKeXkebmIkiKVbpk1RKQVwYDq1as/0ivRuXNn4fqgZ4bREjwu2DSiqY/RHhaqJgaNVHrWqKq8/fYAj7kOmAmjeKNaQx2RihpGW6xbu1Yc9HM//rhccY2LaWm62VJlBmLNsoHGFfD8q1SpQqsUcW8Lb41YtQVKAbD/oVmOPVczWL9+vbDx41p6YwNhCYFZqVIluZIBAiI//PAjnThxQtQZq24Nixcvpg8++CDL9x7eZ5R5oNxDb/AcRo4cIaK8vL95BhaqjNO0a9dOOeP91mtnr94GKXWjeKNaA1FBWyNSVSC2MEnK1Y55Fb1tqTIDoYbUvbvRRESVEV22VfOJ19NbI1btYem5CqcCb1pqeRt4pHbs2FFuMUbl559/FgLTmsBDZHX48OFyZGnGD8o5snOZadHCO3WqK1euVL4T23vEgYfJgIUq4zRoTkBnpjfOXr0NRKBRvFGtAXGCEanoYLfXzIW0mjtd/iqpFy54PcWKkahXLl+WW66BqCrKFxBltoW3R6zaAqUn2C9hp5VTPVeRhg0MDBJChzE2eK8gMLWgatVAEUDRE3im4qTo7bffliuMJ2ChyrgEitY/d8FOyMygMzxi0iRRvN+1WzdD2gKpI1LtRXkRebh3754w+HcXiKHKbjgGaEHVKlUoNTVVbrkO0ueIMttLn3t7xKothEtBv36iJAX7K0oVchLoBO/Zs6fcYowMLO0gMLUAJybFihXXtX9i2rRpNEY5MWRnCc/CQpVxCTX9gjNKXwdRynnz5omGlVHh4YY1Wrc3IlUFzwc1xlp0p6L84+bvv3u9iUwLmyoVRJnhhGAPb49YtQdOVrC/btmyRZSq5IRSAOwD3ERlDlRBqWXku3nz5rRXpxMzZKQAG/t7HhaqjMt0797dbvOJ2TGiN6o1UC9pb0Sqyp49eyhf3rxihKi7IMXs7WgqwHNGQ8aVq1fliusgyoxos716N6OMWLWFpecq9mNf91zFCVhY2FBuajEBx44lCmGpJQigxMbGyi3PAVcJ+L4OHTpUrjCehIUq4zKw4pg5c7r40PoiSOuq4g8jK42Y6ldBvSTqJu1FNiGo4FmqlZUUoiK1atWSW94lWAObKhXUvDribAHHAUTY0bxmVLDfolRFFdUoYfFFcBzCEBQMQ2GMz9at2zRvQMLJqh42VZ999plwvzHCNKycAAtVxmUQtRg5Mlx0QPsSqLk0qjeqNVThkd0cf0t2x8VRwUKFNImmgrNnzlCAQYzmK1SoQCkaRQyLFSsmos47duyQK9kDP2NM5TJ6Laive65iBCeOR1wv6B0gDlEKpv7YCmDgskuWLMpSopH5Nmz9WLt9Z2yqLG/LmbpWZFpQXgLvVkYfeNY/4xY4WGD83YYNsT6RboNlE4R36zZtDGc7ZQ2kchElgwCxV5YAYTJl8mRq9eKLmrxXmEZ16uRJ+nDYMLniOq7O+s8MpsOg9lYLqyzYbsUpwv7jcePsRtNxcoPGJdSEGrU8xBJkC1Bfi2yB0U/EHAECB6M3ly79lrv9vQCEXvfu3YTbQiHlRBhAzKG5Cel9pOQR7VSPOxnz8CfRa6+9TomJicIsf8+ejLGpEJqZ2bPnBwoOrkF5lZNHFdz+6dPJ9Mwzz1Ljxi+I6XslSpSg3367Trdv/5HFaxWPEfWruG+I5PbtOzzyWOG7a8+XHPsZPjPwTGU7Kv1goco4DSxFLA3WN26MpYIFCznUnGM5TcRIICWOSU4wye/+5pumGLuIx4y6Q6R0bU2fUsH4z7S0NJHW1oKffvqJnlFEwUvt2skV19FKqK5YsYJu3bwpuve1ANHqOrVrU/MWLeRK9iCiivpf1DIbuUxEBfXXKG1B6QKiwkZ8zDgRRqTUHhAfp06dpG7dussVoqJFi2brucloy9SpU6lWrZpZGosgDlGLiulTSMlDhMKOat++/XTixHF65ZUQMT0PJ73du3elLVu2ZUmn4/uma9cu1L//ABo7dqxczQDCsXbtmtSvX39FOFYnTGrEZxC3vW3bduHTiuvDXQBYE83A0ROdJUuWCGEdEREhVxg9YKHKOM2oUaPEGakrwLTZaCAaNu/rr8WsdExyMoPIAOjkBqg/tAeiqR8rB/kOHTtqFvmGFVb//v01EfVaCVWIr++WL1e+DO0LS0fA67Zj+3aHoqoA7hBovENNsxnAyQ7qa2/fukVvdO1quGgw0rIYpekKEEUsKPQBU6NOnEiyeWyBGERKHid/0dGrqUSJkvTiiy+KyCQiqqNHj1LerynK+9ZDXiMDfKbGjRsr9s39+x9N6UMIN2hQT/m8txLDAM6dO0dHjx6lxYsX0d698SJqil6KOsrJmL1IO65fsWKFbLv41ajx6tXRXF6iM1yjyrgEvgQsJ4bY+4mKmiGvaSxw0MQYVCN7o1oD0TtHRqSqoBM2MChIM5GKL517d+8aLvL8bEAAXVZOPLSwqQIoIYALQMy6dXLFNuqIVXs+rEYB+7sZPFcRabN2XMnux1r6mPEMOJmAILR3bMH/Ec3EtKkffthD06dPF8IQx2CY5oOEhAQhGGH9hFpQ3DZGPIOwsA/FtvqDyyCVX6ZMWZEpwqhV+JrevHmTxo79WAhn3BayeI6Ug+CxocErOyZOnCgcJVik6g8LVSZHgkiZ6o2K+k6jeqNaAxFgR0akqqCONWH/fqqioY1U2oULhrClygxeD6T1YNqvFVWqVhVfpo40H+H+MWIVKXVHLm8UcqLnKuNdIB4RvYRw/e9/d9HBg4dFjSjqTAF6BebPny8sEENCOomUO7bVHwhSMH36DPr666/FCQqEKSKyiNI6e1J+69YtKlCggNx6lM2bNwkrPqOWrvk6LFSZHAeiXZ9+8omIlBnZG9UaEBCOjkhVWb9+PVWpUkWMCNWKS4pYNootVWbwuNCFrxX4wkPdnKP+jEYesWoL7E85yXOV0QZ8NhITj4oopzsgUonbghjED8o21J+oqKhHtvEDQYrLQZRq0UCHiWbWGmiRPUKT5qRJk+QKozcsVJkcA0SepTcq7JzMkupXcXREqgrExunkZCpXrpxc0QYj2VJlpqzyXLWyqVKpVq2aiEojmu0IqlUYIrFmAp+HnOC5ymjL5MlTqH//t0QdpxlBJPbatWtWm+8gkuEIwJ6p3oOFKpMjgMCYO2eOKLY3gzeqNRAJRg2hvRGplqxbu1bUeGkZTUWHLqLRWlhAeQJEBv0UMa9l6h2vH6LSzkxiw4jVjbGxpoxMGs1z1dETBBU052SXxmW0BwIPYg7NRu5GVvUE0VKI1MOHD4v61szguaxfH0N9+vSRK4w3YKHKOE1gYKDo+nfm7Blp07JltY3qOQrEHRqm0DCCxhGjCixbQCg4OiJVBZ6wqNVEhFFLIBqwDxgZTN5CHa2WICqN6LSjwtMMI1ZtAcE/eMgQYfWFUhlvNIipUSykZR0F4gKenLBLYvQD9aVqZBXiz5bhvxGAbRWOp/g8Q6RmrmmFiIVfKp6Ts/WujLawPRXjNKrJP8BZtFr8nh1Lly4VXxzz5s3P1vrDE0AcmM0bNTsQ1YJgcGT6lArqDCtXqSKin1qCEayDBg/WtLZXK3sqFa1tqlQwrez27ds08L335Ip9nLERMyp4Pb3luQrvylGjRjywGrLFBeXkBGNUcVLsK0NIzAa+H9AIhfcBk8I6duyoSQ2pFkB8wtx/zpy5YtuWcT9OeNC0hXpYxruwUGVcAtFUfIFg1r898AXTs2dPq/U/ngJnyUu/+cZ03qjWQJ0gUrCIbjkKrF1g8N/2pZfkijYgsgtf0YjJk+WKNmgtVAFus5Py3mtZ9gBQJ9yzRw+Hy0dwwvR5ZKSwQDOTu0Rm8Dy85bkKKyJkZWAab49Bg4aIRhujiKOcCgQrGjlhPYUJVRCs9erV073WE4/j+PHj4jiK7yvsH6jx1/P7iHEPFqqMR4CIhZiF9Yje4ICE2kCYrptZGAAIbkdHpKpAUHzyySdUs0YNzWb6qyD1/XiePPT666/LFW3whFBduGCBaDzTOqKMOucTyhff6DFj5Ip9UC5hphGrtkApDQQraqW98flCWhnYG3fJGAecOB85coQWLlwgpkbB5xaTDDH2tEiRIpqdVCBiis/n2bNnCFOqMJEK2by3336HGjSoTzVr1mIfVBPCQpXxCDhgYCTdV199rdsZNKJ9GKFp1Ck7zqJG4tq3b+/QiFSVHTt20N74eGrUuLFc0Y64XbtE6teZx+MInhCq8T/+SLt/+EFEcbRmw//9n7AIc2betxoZN8uIVVtAeHtjmhtPBzIv+E6AKf+ePfFi/zl9+rQYfavO7K9btx6VK1f+wcx+FWznz59fbpEQoTdv3pJbGeNzr1+/RgeVz9a5c78IEYwyLwwTKF26DG3evFn8rWfZGaMtj41TkH8zjGY8/vjjysHiGWGq//LLL8tVz4EaulmzZgkbIQgIMzZMZWbF999TwYIFqUXLlnLFPhC3X3/1FdWsWZPyWRzctQDTnvClgJOA3Llzy1VtQN0rBLCWPKHsAxCUqNPVGtw2hGfTpk3lin0g6n46epRSU1OFg4CZgasCxlKi/hs1uDgZ1aPLfsqUKfTaa69RjRo15ApjFs6cOUNXrlylbt26UfHixcVnAOUwffv2FcftXcpJ8NChHyonPXno7t2Hk+V+VE44Mb8fQhQ/+fLlpzx58sj/EjVWTsjv3r1L6el/UUzM/4njCPZNiF6MM8Zl0YyH+2LMCUdUGY/SpUsXGjDgbY+dzUKYIYL43507RQenGW2nrIH0KqYEwYDdmWjVtq1bae++fQ77rDoDbKmST52ioR9+KFe0wxMRVYCGMogarUsgAKLLderWdUqsYn/FY/KlfRXuEmiewZADZ5r9nAVd2p8r+wiaurhJynygzhjTpDLP8sf7OnLkCFq69Fu3SgAsbaYs9w+1+XfHjp1yhTEbbE/FeBRM88BUD6R9tAbpI7N7o1oDz+s///mPwyNSVVD6sGnTJqpdu7Zc0ZbU8+dNF8nC403V2KZKBRZYiARDfDoK3k+IVLONWLUFykDw+YMjgqc8V3H8gJhBlzaLVHMCR4bixYvJrQwgXrUQqQBep4UKFaKhQ4cKcaqCEhGUFjDmhYUq41GQEmzXrj0tWLBArmiDL3ijWgOiByNSW7dp43SN7WZFpKJxyFNf5JcuXdK8NtXTVK5cWQh/T4AobUHli3F3XJxccQycUJlxxKot8Pmz9FxFlFVLVq5cSY0aNXaqJpgxFmgMRc0ogPXTqFGjhJODFiIV4LgHK6lGjRqJCCpEsBoggfOMmQYRMI/CQpXxOG+//TYtW/atJgcKCDnUxCEtPuCddzyS4vYmKGNwZkSqCqJYqJmsUrWqXNEW3D7qwMzWoAZRiLn/nojoAwgnRLGdiaoCs45YtQeeFz6XKAVAVsDZ18UaaKCCj+qwYcPkCmNG7ty5I9L8cGvAUAB0/SNdr7WNGEoL0MSLeno09MKB5m9/k/9kTAkLVcbjIPUyZswYqyPqnAFn5OiCB6jdNLOBvzXQEIZaWzSLOAsiE4FBQR6Lpl65fJlq1DTnpJ/g4GC6cuWK3NIWRBIRxY5xYnKSCprSzDpi1Rb4XMK6C685Pq/uRrQnTpxIUVEzuMvf5Ny58wcdPXpUeGpjGENISMbQGE+ATB6iq4jWglOnOPVvZlioMrqgNlMhHeMKiDzBTxSdm5jwY3Z7n8wgYqmOSHW2jAFCJ2H/fqpSubJc0R50qlc1aac6akmdGffrLIhiY/90tjYT0Wkzj1i1BT6fKMnB5xX+sSjVcYXNmzeJ354UNYxt1DS9Zd2nK1SrVp1at35RGO3bO6FG5BU/2YEMCSKl9kC0FhHWY8eOCvHKmBMWqoxujB49mkJDBzslGvDlD4sr+E/C9N7sBv7ZAf9X1C260hCG6S+wetF6ApMKbKnwnlWsVEmumAsIyYtpaXJLe/Cliy9BRLWdBTW/QUFBYtSvL4LPK4YcoFQHn2NnBDmEERox0RzDeAeIRaTpr127Jso53AHeqGlpF+VW9uBYs3jxYvGT3XcF9onExESHAh/uCmzG+7BQZXQDZ7dI4SGV5whIhaMxA6lVmKSb3cA/OxCNw5ACZ2yOVBBNxbSocuXKyRXtuaIc6JHONWsUGxFq+H5e9VD6H8AHElFtV9LcMMyHH6mrUUejg88tSnXgaQlrLkdLHT777DN6++0BHAnzEoikqh35cG/B7H53RB+M+yEu7bFX+RyUKVOGqlevLiZLZQaPAWUl8Od25OQQ+xuGADDmhYUqoytqCs/WmTCiLhs3bnyQCkeDhq+l+lVwEEWdIuoVXXmO69auFQd0T0VTAWypYKptZjxpUwXw+iOqvcqFyKhIk7/1lhhL6imHAm+D54iRxmqpAz7ftkDK/+TJk9S5c2e5wujN/PnzRW8BAgyoD46ImEJz586V/3WeSpUq0ZIli+w2NqrfERkC81HPVYDH8sEHHwgRjSydPRAVRuMWY17Y8J/RBdQ44SDlCikp5+RfvgUEOZpNUMfnSkkDLIC+X7FC84lOmUH39ocffujRiLanDP9V8KWHVGLz5s3livagRCImJoYGDR7sUqMfIuu+MmI1OwICnpF/OQciYmiOYfQBUcvMJvkQmO6OxZ46dapwNEGdqi1UMWurlhWXcaR5tGnTJppZYDHegYUqowsQqoiQdO/eXa7YB/YiELe+KlRhswXQHOYKSKNiPChKIzwFaoTxPiCy4kk8LVTBqJEjqdWLL3rMGQHA9P727ds08L335IpzoI4TKXJEH30RCFWITmciXEuXLqUKFSqwUNWRQ4cOiZrUzK85MmE4Hrj6XiC6iRNG2FLpgd73x3gGTv0zuoEvG6R1HP3x5XQN6hFRl4j6RFfAF8m9e/c8KlJB2oULomveF4D5P56PJ4HhfdrFi6K+2hXefPNNsW+4en0zgM+1tc97dj84bjD6cvr0aatZgTZt2lBc3C6XPbERSUV9KY5feoCRu7DDYswNC1WG0Rl1RGp3RZS4kuJFycCaNWt0EfLnzp+nYB+ZBlSrVi26pEMN6HPPPUfLli2TW86B/cHXRqwy5gONT9YamZCNmDx5ihhl6yqoL0Vzlr1aVXdBnTOyE/bKDBjjw0KVYXQEIlMdkerqwII9e/ZQvrx5xQhPT4Kay8uKsHs2IECumJuA0qXp7JkzcstzIMqNaLerUSNfHLHKmAscm/bs2W21y18VfrZ8Tm2B6yNKrvVYbUtgawVrM0earRjjw0KVYXTE1RGpKhC6sRs26JKORwobnbq+0tijTpG6qDwvT4MpXoh6u4qvjlhlzAE661FLnJCwX648CqKiSKu7CmreMVbbVbFrC0Rqw8LClJ+h3EDlI7BQZXQDptHOgKL9+vV9J23jzohUld1xcVSwUCGPR1MBZuQjXe5LBAYG6mIBVaxYMRH1xomJq/jqiNULTtYJowmT0Z++ffuKqKS1FL0aFXVVaKKEAJ34sJjSUqzisWIYANw9UN/M+AaPjVOQfzOMx/j9998pKupzyps3HxUsWFCklGz9IJI0depk6tmzF9XxgWlUqDecNWuWqD8sUbKkXHUO3AbSwY1feIEe96BvqgpOFNq1by/M8j0NosSettkCeRXxuH37dl0adPyV1w11fni/cufOLVcdB6970aefFu95o0aNXLoNo4HPP4zjMSDhr7/SrX72LX+WL19Oy5YtpVGjwl0ulWFcA/WdaJq6c+eO8AjOzM8//0xPPvkElStXXq44BzIcyBy8995AcTyDH7Q7IN3/7rvvUv369WngwIFylfEF2J6K0Q146M2cOV1u2QepJ6SIPGknpBewHULaWU3pusKqlSspLS1NpJU9jV62VCp62FOp6GFTpYITrjq1a1PzFi3kivO4a2NmJNSIV0zMWrlin5Ejw1l4eAkIVYxQ3bAh9pHPC6Kgw4d/RBs3bnL7cwSBqU4rxL7hrEcr9ilMqMJ47nnz5lOrVi/K/zC+AgtVRldwUILPZHZ8q3wpnzhxgj755BOfqS/SwsgdwvHjsWOpQ8eOuggs+IH6+fu7VabgDHoK1YULFogITlkPjp1Vwfu2Y/t2+njcOJffe3cHQxgRCKDIyGlUvHgJ6mZDgOfPn5/rDL0MPEifeOIJMSUKDYLo2P/99xuKoKxEUVFR8lLuA4/WiIhJoi6+SZOMcdJnbDQ/ItN25MgR+s9/VlObNi/RsGHDRG0t43uwUGUMhRpxQRrIF6IoqC/EyMjQ9993a7LT999/T9evXxfWR3qwdetWeqNLF9GBrgd6ClVM9Nq8ZQvVq1dPrniWAwkJiiArTp3cGAeKutqoL75wez8yCkuWLKG4uDiaNm2aT2RMfBmUYPTr14/u3v1TlKOgSQkjid2dUqXy6aef0LffLqXLly8rJyXPUP36DcQ+UaBAAeF9bI2bN29SYmIipaf/RampF2j79q1ivVGjxjRz5iwWrD4GC1XGcODAiPF98OszsweeVpEwiN1ZM2dSu3btPDrTXwW2VJhZP2XqVN06/vUUqmp0ussbb8gVz4KTr7Vr1tA/x48XdXmu4isjVpE2RhMNj7U0D4iqIhOGUcoq7k6pAps2baJ//eszsS+4Ky7xOVu/PkY5qV/hso8xY0y4658xHDhg4cDVtWsXUSpgVlYrYq906dJup2vXr18vmhn0EKkAtlTBwcE+Y0uVGT1tqgCiQ4g6oY7OHWBpBmszd5wEvA0+zxCpiMSxSDUPOFnu2LGj3MoAXfVwZHBnylTJkiUpMfGoEJnugs9ZfPxe4ezB+BYsVBlDgi+xZcuWU/fu3UwpVt0dkaqCL4jTyclUTod6ShW83r4yNjU7atasqYtNlQq63BP273f7PjFiFRZnZhyxCjGCzzMyJe6mixljoE6ZcpWgoCB699336P33Q90Wq5hEtXdvPP3jH/+QK4yvwEKVMSxI+7/99gDREarFGbdeuDsi1ZJ1a9eKel29oqngYloaVfFxofqcIhzPnzsntzwP3j9ExVFS4Q7Yn8w4YhWfX9Sed+3azdTlPDmZs2ezNjap76U7XqijRo0Sk9xWrlwpV5wHJ9f9+vWl0aN9wyWGeRQWqoyhQacphBq+5MyAFiNSVdD0gzS8Ht3pKlevXBENE+7UUpoBNCTdvXtXV7GHqDii4+4a+KsjVlesWCFXjA+M48uUKcM2UyYFx7L9+xPk1qMgooopVc4GE3B51Ll26dJF+SzeEy4QrpYRjB//T+EU0KdPL1FPa+aSMSYrLFQZw9OnTx/xGwcgo+PuiFRLcBDXq8tfJfXCBdHRmxOAH+2Vy5flludBVBUlFYiSu0vTpk3p9q1bphixis8tptKFhobKFcZstGrVSjQqWROjKOPAAA1Ha7DRLIt9Aq4BsCKE0P2///s/GjDgHeVE5l2nBS8cJC5duqT8/oYOHjwsrLRQYoJIrZZTrxjvwUKVMTxI5cDG5vDhw4YWq1qMSFVBZAHpMDT96AnKFrKzhPE1qlapQqmpqXJLHyopry2i5O7WmKIEwAwjViEi8LllGypzAzEK66fsxCjGrSIimp3IhG8ujmkQj3B0AatXR9Pw4cMf1Cu/8847YvSwM96suN0vvvicxowZK7bRiIssHAYUvPzyyyLSi4gtTvrxg8fgrBBmvA8LVcYUqGJ12bJvRdG80UDKH3WDqB90N22O21qzZg3VrVtXrugDDuCY76+Xd6q3qVipkkgRwo5LTxAl18I+B+ULr7zyCi395huxzxgNRLPmzp1Do0ePZpHqA9gSoxCb7dq1f0TI4nIILDRt2oTCw8Ppu+++oxYtmgsRiRIQa3ZUbdu+pPz//xw6xuP2+/btI0qV0BxpCfY31M9iBC/uW+XLL78UkVyIVqOBYxGENB4bpjjiNQoIeEb8ndNhH1XGFOBMfMmSRXLLOVJSPN80o8WIVBWUD+yNj6dGjRvLFX04d+6cSCf3lqUWeqKnj6ol0/71LypXvryI5OjJhv/7PzEA4Pnnn5crrqPniFV8cboCxiG747fJGAMIT3VKVWaQ0g8Ori7S7xCRSL9DvL799tsOe6RCqE2ePJnOnj1NMTH/Z/N6EHC4PD5DiMw6CqKwCHp4a6gMXpuff/6ZTp8+LUofMH0LI4XLli0notaw1ypevBiVLl1GeNdC4Of0zw4LVcYUQKjCs6979+5yxT4wo4a49bRQ1dKIHZGxf44bpxywGlHhp56Sq/rw448/UsMGDaiuThObLPGWUN22dSsdO3ZM1KvqCTxcMf5xzJgxcsV1sM/oNWIVQhWi05lo/9KlS0UNIwtV82MpRq2JSAjZP/+8Q6tXr3ZpYAtEXOXKFalXr97066+X6d///rf8z6MgWj9kyCDl+6CHIlSrOz3fH/eDBl0cZ62Jbk8CgQ1x2qZNGypatKjIjGRn14bnie8XZ4S4L8Kpf8Y04MsOJtOO/uiROkdNJ+oEUS/orkgFu+PiqGChQrqLVJATbKkyA5sqNGLoDSK4+fLm1cS8H/sdrNBgiaaHNyw+V9Y+b9n94HPL+AYQpyNHZqTxrfHGG2+IdHtQ0HMu2ZAhZd++fQfldrpSSspZqyl6iOVhwz6kL76YLk6uq1Z13uAf94MmLpSmICqrF6jZRmkYBD0+G3iNshOpAI+tVi19T6KNCAtVhnERRLLmff21qBPUYv46rJIwUrB27dpyRT9yii1VZrxhU6UCB4DYDRs0qS+FfRAs0WCNZsR6VcZ3gAsLegWsWUBByH700XD6+ecTImrpCohynjp1iiZOnEQREZNEqt4SRCSbNWsmUuQXL6a5POEMjzUqajqFhg4R4ldr8Pzx2FFvC4GKrOCKFd8LBwVHwGOaPHkS1axZS67kXFioMoyLaDUiVWWzIlJR5+qNxpOcZEuVGb1tqlQQNUf0HFF0LfCFEauM8cHxKSxsKM2cOVOuPApS2hBpCxYskCvOgSluKNuqVasWhYS8KkbuqqIXEdbjx48pAnay8vu4qIF1B9S3YqjMZ599Jlecx5ogRQMZShhQCwv/WX9/fxFtbtOmLR09elReM3twm2gCi4iYYrNON6fAQpVhXABm/DjguDsiVQURPdQieSv1npNsqTLjDZsqFXxRIoquVRQU1mhmHbHKmAeI0bi4XVminQBC9h//+IhiYzc8EJjO+JlWqlTpQeMsRN9ff6UL0YsIbmjoYCFSgVZp8c6dOwufX3tOAM4I0qVLvxW9EUjxo74UaX581itWrEAXLlyQt2gdPE/Uz2JAht71s0aFhSpjGtBM5Qw4IKCTUmsg6lCjNeCddzSpSwWwdQkMCvJKNBUH4Ju//55jbKky4y2bKoBSC0TRY9atkyvugdvz9IjVmzdvyr8cA5/bAgUKyC3GF8BxCo2A8+fPlyuPAmGWK9djD5qhunbt8kC02gO3jTpVtXYUkdvZs2dShw7t6eOP/0lBynESoPzAlfrUzOD+YKEG6y0IUS0EaXblCOjkP3Dg0QlfSPHj/lRbKrgl4EQgpzdQWcJClTEF8N/bs2e3OCDYqyfC/3GQQX0PZotrjVYjUlVg2J6wfz9V8VJEM00R9Dk1mgpwsoEozhUP1Kk5AqLoiKZrJSw9OWIVHf+jRo0Qny97wgPiH59XfG61mNTGGAt02uMkJLto6bBhw2jVqofz+505CUedKlwxQMmSJWn79p30/fcr6a233hJran2sM/WpEL7Z2VHhdiC8W7ZsLgQpBHhS0kkhSOEfi+EEzgjS7Hjqqafo8uUrYgIXBDBcNDAAAfeHE0B8TuAzi9tnHsL2VIxpwEEC4tNRcFaOM2Ato5QbN26kn0+coMFDhsgV9/lSeV54jJha5A3QOduqZUvRAe8tvGVPpRKvvAb79u3T3aZK5UBCAj1dtCi9/vrrcsU9UEowd84cej44WFORCHGKtCR8Hx0FXeI84983gUjF9Cd0+lvjtdc6U506dYUdE47fjgJRCXP+7K6DEyVENp2NOmI/RLQyOyGI/VvL7wtL1M8ORDjqcPPnz++1ngSzwUKVMRU4kz52LFE5+7wlV7KCiOqcOf+m3r37aPoFibo/pFT/8dFHmnXHI5o6c8YMRVS3F7PgvcHy776jf44f79WOf28LVZRz/Otf/xIODt4AZQfr16+noR9+qImDBMBzivriC1GiolX0HyBFOWXKZDGb3Vajh7+/n0jNutqVzZgDHGN79uxp1Y4KKe333htINWrUpE8++USu2gbXmTt3Li1btjRbD2yI44UL59PMmbOdssHCxL+PPvoHrV27zqYtlNbge2vixInib62DJzkBFqqMTwKxiq5JraaPIEI1ccIEUf+nZS3n7FmzRP1e2XLa19I6AoznT508SR8OGyZXvIO3hSqYoLy/8Aj1lmBHpP6Osp9h5rlW7Nu7l7Zs2UIfhIVpUk+NCNe2bdsoMjKSBSgjgLDs3/8tkbK2JsCGD/+I7t//S5wI2gLHbNT+o/YUrgJonMpOqOJkCT0I2BcBjvVIxdsDNaB4jCtXrsj28WoBXhOcKMKjGf0HiYlHxXPilL5rcI0q45Mg0oMz18OHD4taIHv1dPb45ptvhA2VliIVzgFpilD0lkgFOJjCj5DJ8DVFva63KKfsB6eTk0WUXSuwz8JCDVZq7oDPD77k8XlCVoFFKqOCyCRGf1rO+bekf/+3RRYsO7BvoWkJE6+AozWaJUqUECUHHygnuTDvx3EeAtEW69fHiE569C7gxNRdcH8of4Bwxv136dJF1J1COK+TDZKINnPdqXuwUGV8FpwtQ6wi7YnaIHtNWNmBRhfMwG/btq1c0YbVysHtueeek1veAfP9vVmbaiSCn3+ezskmDW+A0g+I5XVrHa//dARYqJ09e1ZEV11Bra377bffOG3JWAUNR+iatxYQgJD96acjWY6/uCwEXtu2bURqHGNZkf1ydv9C6h8nT8iGILKLEyprx3rcR7FixUUQA0ML0AiGWld74HFCkOKymQUpPg/4fgBwAUCmAVFgCGiMDIY4xePjz4x7sFBlfBocIHDwQwkAuivVblFHQcRx1cqVmo1IVUGzAOoSUUzvLXAAvnf3rqb1i2bm2YAAuqy8396wqVJBQx2i7Fr6oLozYhWfFwgJfH7wxctfuIw1IEYRpVypHCszo4pXy3pmRCFRRgVj/6+++lo0RbljbI/9EqIQkUs4mCA6izIVS+GMkzV1nC8uD1HZr19fIT5xOUtBmp0tFbAUpLgPd1wAGMdgocrkCCBWJ0+eQg0a1HPYfBp1qRiR+qbyJa9VgwvA7aKoHxEAb5LTbakyo9pUQSh6E0TZly1bJre0wZURq/icwNMRtj1a1Hkzvg0EHKzLMkczYdaP2f8AQhDRSDRDIV2Pkx8tm5pUwYroLMBJlipEUS9qecyFqMTlUOsKMepJWyrGPVioMjkGpGC2bNkmRvLhjNkeWo9IVdmzZw/ly5tXjND0Jpd+/VWMKWQegtfjV+ULzZsgyn7v3r0Hhuda4cyIVXy543OCWejwy2QYeyAiGhU1Q2SucJKDyCREKWqujx79SUQoUbuJmlKkxj3ZdY/HgpMrGPIjagvBGh//o/zvQ9TLQYziB8IZ2xCkeHzuRHkZ7eCufybHgdoiV4DZOQ5k7oBo1j/HjRNeet4WqkawpVIxQtc/QGrcmzZVKnBjgOE5opnu4ur+/uqrnemLL76QWwzjGCgXUQMBnTp1EoIP+yBELDxMHS0fwXUgHq2BEykAQekIiOR+9NFHwiLLkwKZ8QwsVJkcBw6AEJ3OpN6XLl0q6pvcFarbtm6lvfv2eX1Sj1FsqVSMIlSBt22qVOJ27aI6yuNo2rSpXHENb+7vDAOwD544keRUjbOWQhUgoot0PgtV88GpfyZHgi9tHOQc/VGL8N0BIzI3bdpEtWvXliveA5HDml6awmR0vG1TpYLHEbthg8M1pbbwxv7OMCo4UYLDCMO4AgtVhtEJjF81ysi882xLlS3etqlSQWlIwUKFaHdcnFxhGIbJebBQZRgdQDQVqdwqVavKFe+Bx3L37l1NnQx8CQx1gE2VpbWNt0CHMaLwWkRVGYZhzAgLVYbRAUxtCQwKMkQ09crly1SD0/42CQ4OpitXrsgt74E6WUThY+SUG4ZhmJwGC1Umx1G2bDnhnecM165dk385D+xZEvbvpyoG8SxNTU2lqlWqyC3GGqgPdXY4hKdAFB7TbxAJdwXs7ydOnJBbDMMw5oKFKpPjwASVyZMnOTQ+D+ByMTFrneqatgTRsCqKMMSITG+DqUsQYBUrVZIrjDUgDi+mpckt74IoPDqVs5ulbg/s7zNnTndqf1+yZBFPLGMYxhCwUGVyHJjz3L59BzE+DxYo9n4yLlfGJaGKaOqZM2eoXLlycsW7XLl6VQgQLcfB+iJIufv5+dFVA6T/QbVq1URU3tkRqAATgwIDg5za3/H5wOeEYRjG27CPKpMjQaPMgQMHxFg9exQsWIDOnTtPc+fOEQbszkzqmT1rFhUoUIDKGkSoHkhIEGnt5i1ayBVjYCQfVRVEwlMvXBAjTY3AzydO0J0//6R33nlHrtgH0VH4wvbu3Uc5WSpL16//Jv+TPUWLFhVT3BhGKzAzH3P42UeVcQUWqgzjIJhughGA8JgcNGiQ3XnPPx05Qt+vWEFt27aVK94HvpyDBg82XMe/EYXqSeX9Xv7999S8eXO54l1QthETEyPeP3tpecxb/+yzz+jkyZNipjp/OTPexJbozA4WqowKp/4ZxkFwgMOMapQANGhQTxwsbVkYrVb+b5RoHGBbKueATRXm/hvBpgqgxrl69eq0bu1auWId7JfBwdXFfrpw4UL+YmYYxtSwUGUYJ8FZ/MGDhyk+Pp569+5Nhw4dkv95CNYQAYO1kFFgWyrnMYpNlQpKSNIuXhTR+swg4t+lSxexX/7ww49iPzWCHRrDuAr2aWs/yBgwOQdO/TOMG+zevZs+//xzunTpIiUnnxJr+fLlpw4vdxApY0wXMgoYOIAyBCNOpDJi6h/E//gj7f7hB6pXr55c8T4YRblHeUzfr1guV4gaNGhIaWlpNHnyFK4vZQwH0vg4uXf0pO/OnTs0bdq/qESJknLlUU6cOE4vvfQSNW3aTK7YJn/+/DRz5kxO/ZsUFqoM4yZIDffp05vwSerevbsQErdv3aIXmjSRl/A+iO6uWrWKpkydasiOf6MKVZRLTI6IoI6vvCJXjMH/rV9PAaVLU5EiRSg0dLCYpY5GP46gMkYEQrV+/Yaivt8Rzp49I0Rldo2rOOZWrlxR7PeOgFptiFX0GLBQNR8sVBlGA1CoDz7++GP657hx1KhRI0NFUy9evEgXUlNp4HvvyRVjYVShCiZOmEA1atQw1PsJ26yEAwfoo48+Ur54y1NU1AynGksYRk8gVNeujREjgR3BkcYnZxq0IGwbNmxA06fPoMaNG8tVxixwjSrDaMjuuDgqWKiQoUQNSD1/nmrVqiW3GGeASIVNlZHA/pUvb17as2ePXGEYY4OIpqtMnjyZ2rRp7XJjIzINsAm8c8cYjZGMc7BQZRiNQHJi06ZNVLt2bbliHFJ++cUwXq5mo/rzz4tyDqMBP1zYjaEmmmF8FfQBLFgwjxISEmjYsGFylclJsFBlGI3IlSuX6PI3Wp0g6iwxZYltqVwDnqX37t41jE2VCqKqiN7Xq2ucRi+G0Ro0B/bp049KlCjxoMSKyVmwUGUYDfD39xcNVJgRbzTSLlwQ0TfGdSpXrixeR6OB6D0mSf35559yhWGMye3bt+VfzjNy5Ejavn2H3SEr2YGTzN9++43y5uVmQzPCzVQMowGwPsmTJ4+hDP5Vtm7dSm906SIM7I2KkZupAHxLN2/ZYiibKhWMxc2bLx/169dPrjCMsXC26//YsWM0bty4bJuvuOs/Z8FClWHc5JdffqFZilBt166dmB5kJIxuS6VidKGK8omPx46lLm+8IVeMA760165ZQ/8cP56efPJJucowxsGej2rLls1py5ZtcivDpWTatGnUq5d1IRobu4HatGlDQUEPAwNrlM8AxGirVq3kykPYR9XccOqfYdwkZt06qlKliuFEKsAUo0qVKhlapJoBCEDUH+ML1GigJjowKEj58o6VKwxjPAoXLixEorWfsmXL0VNPPfVgGxZS06dPl9fMyrvvDqSQkFcfuQ2IYIhUyzX1x9WSAcYYsFBlGDdANPXMmTNUzqAd9ZhVz7ZU2hAYGEi//vqr3DIWVSpXpoT9+8X+yDBmo1GjxnT8+HG5lQHEJbyBrf1YKwlYsmSRELuM78FClWHcYN3atVS9enVDRlNBSkoK21JpBEbPGlUIYv9DVH/9+vVyhWHMQ4sWzenQoUNyy3lw3fbtO4ioLeN7sFBlGBdBgw1S60YVgqirzJs3L9tSaQRsqu7++afhbKpUENU/nZzMUVXGdNSsWYsmT57k8mdrw4YN1LlzJ7nF+BosVBnGRVZHRxuyy18FdkrPBgTILUYLApTX04g2VQBRVUT3EeVnGDOBSOjIkeEu1VmfP3+e1q+PEeUDjG/CXf8M4wJINa1auZLavvSSXDEemzdtosYvvEDNmzeXK9kTrYhuV4CHJwy53UWrrn9Msbl06ZLccg7UvtkDX6SwzjGiTZUKokuvv/aaKFVgGCPgyFz+q1evUnBwdfrhhx+dan7CEIC6deva/fzictz1b05YqDKMk8Bc/ZNPPqGaNWoYbqa/impLNewf/3DooI8vEleAj2FERITcch2thCq+jNBU4Qr2vkhBYmIizZ0zx5A2VSoY93ri+HEaPWaMXGEY7+KIUAU4YcbJIKypHJnwN3v2bDp8+LD4bQ8WquaFhSrDOMmOHTtob3w8NWps3FQTxMruuDi6o4jqDL/BIJsHaHyRREXNcCiqqKKOM3RUqKqXt8bRoz894oloCbrte/ToIbds4+xjAvhyDA0dbPOLNCkpSXmMR0XENj09XdjnFCtWTP7XeGz4v/+jTp07Z2uYzjB64qhQBar4tCdWcblly76l1aujHWqiYqFqXrhGlWGcANHU2A0bDD+SFHVbSE+/++67dPPmTTGRBV8WOFhDmEF46Q0inZgQY43sRGpc3C4RxdQbvD54nfB64XXD63fhwgV68803lfe+CqUqr6+RQSoUBug8WpUxGwMHDhS11m3bthEnhplBiQA+lxCzjopUxtxwRJVhnGDb1q20d98+euGFF+SKMfkPRJYiriwnFeEAD6/C5ORkRQDGUUzMWmHp0qhRI+XAP8LjEVU9o7auRFQjIqY88rrgyxIRSdg+WX4Zwkt1xowZyhdpW7liTOJ27aI6imBt2rSpXGEY7+BMRFUFfQCTJk0Sf3fs2JGKFy9GW7duEyevYWFDRabIkfIAFRwbOKJqTjiiyjAOArunTZs2Ue3ateWKMbl65Qr5+/tnGacJsYXGJ6TRkTY7cSKJhg4dKi7LkHgd8HrgdcHrg8gOXq/MERvYfd27e1fsD0YGUX9E/zmqypgRnCQuX75cZDP27o2nYcOG0csvv0wbNsSKk11nRCpjblioMoyDbNy4UYzRNPoBMvXCBapRo4bcyh48D0QXnIlwWnLt2jVRVmAk3Hk8eB3wejjy/taoWZOuXL4st4wJGv0KFiokapUZxqxAsNapU5f+9jcSJ44sUHMeLFRNzy8U3b86BQRPo4T7cskuNyhpy5cUudbCGPzmCYoO7yBSNAEBjSl8u7G/hPUG0TOkUqsYvDYVIDVduXJlueU4J06ckH/ZBzWwSJEjPZexzzwjIpBIr+EH6XTLH3dqYiE+cf3Nmzc9cpvqfeF+1ccQHx8vamFR5uAouA5mjTtD1SpVKDU1VW4ZF0T/kQUwevSXYWyBOnXM8jfqsA3Gs3CNqumBUG1Pofv6UPS+oVQzt1y2RVo09a87ligqhr4KeVZZSKcb28dRvV5bqdOiaJrUrEjG5ZgHfP/993T9+nVDG/wDHMjXrlnjtNXTkiVLFNE3QthNoRHHFhCOc+fOEX9bNjOoYvT27dt0+vRp8TdAExKmJUHYvvvue0JYOgqEKHxLkcbGZKgSJUrI/5AiLstS/vz5xd9q3RkEdIMG9YTwRB2bPVRh62ztLNLpI4YPp06dOhl2fK7KgYQEKl68uHABYBhvgJNIZ2tULWnatAk9/3wwDRkyxOUaUxxLuEbVnLBQNT1aCNX7ytIHVDc0icKiV1JYTa5ZtAQia9bMmdSuXTvDixLYUt2+dYt69+kjVxwHUcrIyGmKyEyWK9mDZqPRo0c7ZcyNuk+MSVy7NsYh2yREUPv16ysm1jgjbiGYYW0DYWwPVdC6Uv4w7V//onLlyxvapgqoJy//HD8+S90yw+iBO0IV+2/lyhXFcQAnqq6WKrFQNS8sVA2NKiBvUtjnNelo+Ce08ZayHNibJkUMoTdrFqdc1oTqzSTavmIBTRm7kDKMffwosOdYihjyOlVPnUG1Q6bRg8Ro4d4U1nUfRc46KhcUWs+g+K86kn/STlqx4F80dvEBsezXeihNfq87dbS833M1qTX9QBsTlQcWPJYW9j5MvcPOUs9xTejip19kPF6/NjRs0UfU5kYsfTpYfQ79KGr6MAqpaPwvzi8VgYW6qEoupNP15scff6SGDRpQXQNOTkI6HnZZe/ZktZzJDghiR82/9QYOEIj2ol7V6Pz0009UsGBBev311+UKw+iHO0IVJ57z58+nFi2aK3+fdOqk1RIWquaFa1RNwWaKDE+kxtGJlHImnhbVPUzhIQPpi4Tr8v8WpKdQ9LA3qdeyfDQiPlk5OCRT/MowembVcHpz+m66XXMoHYyfoYjLwtQ66gdKOTiJwkbEUHwUzlKDKCz6OKV8FUJFU9fQsI49aOrFLrQpMUXc7+yS2yg08/3C47LrKko8s4/WjH+JKj2GxQO0ePmf1GObcv+Jqyms9C76rHNLCvk2D72jrJ2JX0h96DsK/XAVJaWLWzEsiKaeOXOGypVzrobRW1xMSzNsHS1KBBYuXEjz5s0XqXZ7P8uWLTesSAUYUerquFa9qaKcZCXs3y/2Z4YxE2fPnhFlP6VLl+H9N4fCQtUUlKR2k0dRr8pPKu9YSWr20VgKC0ykOSsPUuYWifRTW2ne+t8ouOvr1KR4HmUlDxWv1ZwaV/SjWzEJdNKhhqvLtHPmZ7SeOtPk8W9QZX9lN7G438hx0RYCsy693LYy+ecqTsHBJUjoVCpDPUe8S81w//7V6OWusHMqQ516vEZ1lLVcxetRSJsyRAf30dFLDneAeYV1a9cKP02jp/wBbKn8/PwMnd6F6GzV6kWRvrP3Y/QOX9hU3TWBTRXA/gs/2PXr18sVhjEHiKIi5Q/HFVfHIzPmhoWqKahI9YOKPnyz/MtSjVpPWxWeuSr2oTUpx2hpo4u0RnRHL6PIAT1p7EHk2x0k/QqdOfKrcrc1KEiIXYm8X0pKpvM3pVItXI4CimQujPWjIk/mlX/npicKFlJ+B1OdKgUzlkzCT0eOUNrFi1TWJNFUR22pGO0wg02VCrICp5OTOSrFmArsrxgBjZPW+vUbioZJJmfBQtUUFKKCT1iKwbz0ZBE/+Xcm0lNp+9hXKLBldxq5LpnSlcuW7TGJxrd2Ysxc+i26lqII26IF6YlH9hB5v7eu0vXbBs/Za8BqRegbvcvfEthSVefZ7rpSIzjYFDZVAFFVZAeQJWAYvXHVWgpRVERTQYUKFeiySU4MGe1goWpK7tCNy9YipOl0Y+eXNHDBRWoXtZuOfjWUOiGN2iSA6JIT02ly+VGhAEWQXrpOvz+iR+X9+hWmgvl9e9eBP+j9e/ceHCCNDr4Ebv7+u6jlYvTj2YAAEeHBvmIGkB1AlgDZAobRC9jewZHEWfDZgjOHWgIE6zxL6zsmZ8BC1RQcpL3HLRqYbvxEm1adIb/2NanCI1n3dLp9/SrdylwqcPMCJSU5kfrP9RSVqYYU/wE6mnZXLircPE0H9qMkoByVQt2qjwKPzDVr1tj1EzUSaRcuuGTyz7jH3//+d6pUqZIQf2YBWQJYkTGM0UH0tFGjxnKLqGjRosL7mMlZsFA1BWdo8ZQoik66kZHa/+xftBiNToMa0qNtM7nIP6ASBdI+WrbuCGGYZHraXlo8Vbk8dOqf1+nGg5T9Vdp3Oo2unzpFaVmy+EWoyaBh1I5W0six39EJ1KPifj8ZT5GJgRQ2LoQq+vCes2fPHsqXN68YQWkWLv36K9WqVUtuMXqC1/1Xk3T/A2QJ7t27J7IGDGNkED21DBiULl2aTp48KbecIy5uFz1lomM68xAWqqagJLWu9Rt92TKQAsrUpYGpL9L8NRMopKRFo5NAEao1+9D0qDeIIl+lwIBnqEzd8XS84kCKCmtEdOsUnbl4VzktrU/vDGtDfyqXqf7yQjquNkZZkKtkR/pszRIaXmw5vRgYIO+3OUVFz6b3a5qrKcoZEE2N3bBBTEIyE2fPnKEA5SDO6A/S6Skma1DClz+yBtjfGcaoYKwzoqgqGDDijA+zJRhkok7RY8wFG/4bGp4YpTcwcd+7bx+98MILcsX4XLx4kU6dPEkfDhsmVxi9mTBhghB/Zpr8FLdrF9VRHnPTpk3lCsN4Bkylq1ixgrCmcwaY+w8dOvQRk35ra47g7hhXxnuwUDU0LFT1BH6YUyZPFvPj8/z973LV+KCJqkGDBvRSu3ZyhdGbFStW0OFDh8j/iSfkivHBfnP//n36eNw4UWvLMJ5CrYmGP7IzWBOXU6dOFYEE+Cw7ijqGlYWqOWGhamiyClV8cBmGYRhzkZNFkitCFaNTw8PDafny5XIlA1dvC2NYIyIi5ApjJliomgxOXzAMw5iLnH7c3r17N/33v/+l4cOHyxX7oNnvu+++yyIus1u3BQtVc8PNVAzDMAzDeAyMG/7tt9/klmNk7vhXKVKkiNOd/xiGUqBAAbnFmA0WqgzDMAzDeJRr167Jvxwjc8e/iiud/5cuXWKfaROTg4Qq6j0HU0BAG4pMgMMowzAMwzCeBh36MTHOje49c+aMiMRao337DiKd7yg3b/J3vpnhiCrDMAzDMB7HmXn/ELbZjbAuVKgQ3b59W27ZJzExkYKCguQWYzZYqDIMwzAM41Gcmfd/9epV8Vud8Z8Z1K46M/Pf2bIDxli4LlRvJtGWyLeoasAzFBBQmdqGz6DI/nUpIHgaJdx/mGbv37+N6HgMCHiTFiTdEdfbviCc2oo15afqWxQZnfBwjGdaNPVX1oMjE+i+XCL6haL7V890232U6y2g8LaV5e13oPDoE2JsaAY3KGlLFPWvKu+nbTh9u/es/B/DMAzDMHqBZiY0NTnClStXhLC1xYULF+Rf9kF01tkBAYxxcE2opqdQ9LA3qW9sKZq8JZFSzmyjEY/FUuTGVHkBlaMURz1oU+JJil8zitqWvSSu12vqFeq6SbleSjLFzy5LsaHdqM8Xey1EpiNspsgvk6nO9L3K/cfToj5Ei0PfosnbLyv/u0up0WOoY99NVGzyFkrE/Yx4gmIXH8i4KsMwDMMwulGrVk3q2rWLDCzZ/mnZsrnNLv06derQ5MmTrF7X2k/9+o4PB2CMh0tCNf3UVpq3Pg/1HBFKIRWfVG6lJDUb9iH19JMXeEBhavRyM6rsn5eKB1el/Lu+opHridpNHkW9KmPUYB4q3mwwRYQFUmLk57QCEVeHKfPI/Tfp2ZmC6QzFHEih++mnaeO8DUQ9P6ThIZXJX9zPuzSiZxl5XYZhGIZh9ALjU+Elq/rJqn9n/lH/Z8tzFZ3/mS9v7Uf9X+ahAYy5cEGo3qFTcZvooCIL61QpKNcUnnyOXuyUWQiWoKCAQvLvu3TxzCm6RRWpflBRizt+kirUqEZ+dJaSzjsTU/WjIk/mlX8rT+SJgvTAyOLSMdp18O/UqE555dZVClKVOsHyb4ZhGIZhGMbouCBU79Pv15Bez0xeerJIlpCqBer1ClHBJ3JnLAlyUf4nC9Lf6QZdvO54R6At7qcm0z7590NyU5GAclRYbjEMwzAMwzDGxgWhmpueKFRE+X2Nrv/+sN0JkdYbl2/Jv62R3fXS6faN6/QnPUnFClrv8HOW3CXLUW3lFi9dv63cusp9upySTBm9hAzDMAzDMIzRcUGo5qXyjV6k4Myp+pun6cB+Wx19eahYmfLkR0m05+glCwF5g04eOEK3qDRVLOUv1zJx4xTtjXNCYhatSo2DMd/3gkWD1nU6vveg/JthGIZhGL2Jjo4Wv601PeHHGVTTf2u3gx/GN3BBqCpXKt+C+rW7S4unRFF00g2i9FTa/sl4iky0FVHNRU826U+T2xGtHxlBi04o16O7lLZ9Bo2KTKTAsA/otYp5pcj0o6tz5tASXCY9jfYuWEyrbN10ZnKVpdb92hIt/oiGLjiqiFXcz5c0ZfEZeQGGYRiGYbxBVNSMLI1P+NmyZZtdW6rM4PJa3RZjTFwSqpQrgEI++4bmtzlPI1sGUkCZ5jTlr0bUM9BWjaqCvN6i4U/RsheV6wWUo7oDT1ObqG9pwft1SMRTc1WmXnPm07BGCTQWlynTkf79Vw3qZO+2HyEPlQyZQGvm9yCa2oYCcT9Tfqc2PWvI/zMMwzAMwzBG52//U5B/uwlM+dtTKI2n+K9CqLhcZbQF6QycLTIMwzDmgI/bD0HqPzY2lqZNm5Zl8tTs2bPpl19+oYiICLliG6T+w8PDaeHChVlua/PmTbR16zaHb4sxLi5EVNPpxvaxVDWgLvUXaXVwg5Ki59KXG/NSu5drPrSJYhiGYRiGkWDmPiZFDR06VAhN9QciFSb+LVo0l5e0z1NPPUUXL6ZluS2I1H79+tKzzz4rL8mYGdciqulplLBmKc0aOY02qrWjgb1p/Ig+9FqziiKFz4XMDMMwDMMw7pOTI/Iapv4ZhmEYhmEYRjtca6ZiGIZhGIZhGA/DQpVhGIZhGIYxJCxUGYZhGIZhGEPCQpVhGIZhGIYxJCxUGYZhGIZhGEPCQpVhGIZhGIYxJCxUGYZhGIZhGEPCQpVhGIZhGIYxJCxUGYZhGIZhGANC9P8XVnRMoNuC6AAAAABJRU5ErkJggg=="></p>
<p style="text-align: center;"><sup><br>[Source: Aline Escobar., n.d. Cowboy. [image online] Available at: <a href="https://thenounproject.com/search/?q=cowboy&i=1080130">https://thenounproject.com/search/?q=cowboy&i=1080130</a><br>This file is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) <br><a href="https://creativecommons.org/licenses/by-sa/3.0/deed.en">https://creativecommons.org/licenses/by-sa/3.0/deed.en</a> [Accessed 13/05/2021]. Source adapted.]</sup></p>
</div>
<div class="specification">
<p>There is a plan to relocate the Texas Star Ferris wheel onto a taller platform which will increase the maximum height of the Ferris wheel to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>65</mn><mo>.</mo><mn>2</mn><mo> </mo><mtext>m</mtext></math>. This will change the value of one parameter, <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> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>, found in part (a).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></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><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</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><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the number of revolutions of the Ferris wheel per ride.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>an appropriate domain for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo></math>.</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>an appropriate range for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo></math>.</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>By considering the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo></math>, determine the length of time during one revolution of the Ferris wheel for which the chair is higher than the cowboy statue.</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>Identify which parameter will change.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the new value of the parameter identified in part (e)(i).</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>an attempt to find the amplitude <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>61</mn><mo>.</mo><mn>8</mn></mrow><mn>2</mn></mfrac></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>64</mn><mo>.</mo><mn>5</mn><mo>-</mo><mn>2</mn><mo>.</mo><mn>7</mn></mrow><mn>2</mn></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>a</mi><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mn>30</mn><mo>.</mo><mn>9</mn><mo> </mo><mtext>m</mtext></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Accept an answer of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>a</mi><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mo>-</mo><mn>30</mn><mo>.</mo><mn>9</mn><mo> </mo><mtext>m</mtext></math>.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(period <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>60</mn><mrow><mn>1</mn><mo>.</mo><mn>5</mn></mrow></mfrac><mo>=</mo></math>) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mo> </mo><mfenced><mtext>s</mtext></mfenced></math> <em><strong>(A1)</strong></em></p>
<p>(<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>b</mi><mo>=</mo></mrow></mfenced><mo> </mo><mfrac><mrow><mn>360</mn><mo>°</mo></mrow><mn>40</mn></mfrac></math>)</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>b</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>9</mn></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Accept an answer of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>b</mi><mo>=</mo></mrow></mfenced><mo> </mo><mo>-</mo><mn>9</mn></math>.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>d</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>30</mn><mo>.</mo><mn>9</mn><mo>+</mo><mn>2</mn><mo>.</mo><mn>7</mn></math> <strong>OR</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>64</mn><mo>.</mo><mn>5</mn><mo>+</mo><mn>2</mn><mo>.</mo><mn>7</mn></mrow><mn>2</mn></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>d</mi><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mn>33</mn><mo>.</mo><mn>6</mn><mo> </mo><mtext>m</mtext></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>5</mn></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>12</mn><mo>×</mo><mn>60</mn></mrow><mn>40</mn></mfrac></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math> (revolutions per ride) <em><strong>A1</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><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mn>720</mn></math> <em><strong>A1</strong></em></p>
<p> </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><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>7</mn><mo>≤</mo><mi>h</mi><mo>≤</mo><mn>64</mn><mo>.</mo><mn>5</mn></math> <em><strong>A1A1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>A1</strong> </em>for correct endpoints of domain and <em><strong>A1</strong> </em>for correct endpoints of range. Award <em><strong>A1</strong> </em>for correct direction of both inequalities.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>16</mn><mo>.</mo><mn>7</mn></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mn>16</mn><mo>.</mo><mn>7</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>31596</mn><mo>…</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>33</mn><mo>.</mo><mn>6840</mn><mo>…</mo></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>27</mn><mo>.</mo><mn>4</mn><mo> </mo><mfenced><mtext>s</mtext></mfenced><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>27</mn><mo>.</mo><mn>3680</mn><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">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>+</mo><mn>30</mn><mo>.</mo><mn>9</mn><mo>=</mo><mn>65</mn><mo>.</mo><mn>2</mn></math> <em><strong>(A1)</strong></em></p>
<p><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>65</mn><mo>.</mo><mn>2</mn><mo>-</mo><mfenced><mrow><mn>61</mn><mo>.</mo><mn>8</mn><mo>+</mo><mn>2</mn><mo>.</mo><mn>7</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>7</mn></math> <em><strong>(A1)</strong></em></p>
<p><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>4</mn></math> (new platform height) <em><strong>(A1)</strong></em></p>
<p><br><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>d</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>34</mn><mo>.</mo><mn>3</mn><mo> </mo><mtext>m</mtext></math> <em><strong>A1</strong></em></p>
<p> </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;">
<p>Overall, this question was not well answered. Part (a) proved to be problematic for most candidates – hardly any candidates determined all three parameters correctly. The value of b was rarely found. Most candidates were able to find the number of revolutions in part (b). Only a small number of candidates were able to determine the domain and range in part (c) correctly. In part (d), a number of candidates understood that they needed to solve the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>.</mo><mn>67</mn></math>, and gained the method mark, but very few candidates gained all three marks. In part (e), determining the parameter which would change proved challenging, and few were able to determine correctly how the parameter d would change.</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">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.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.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>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>A pan, in which to cook a pizza, is in the shape of a cylinder. The pan has a diameter of 35 cm and a height of 0.5 cm.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_11.14.51.png" alt="M17/5/MATSD/SP2/ENG/TZ1/04"></p>
</div>
<div class="specification">
<p>A chef had enough pizza dough to exactly fill the pan. The dough was in the shape of a sphere.</p>
</div>
<div class="specification">
<p>The pizza was cooked in a hot oven. Once taken out of the oven, the pizza was placed in a dining room.</p>
<p>The temperature, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P">
<mi>P</mi>
</math></span>, of the pizza, in degrees Celsius, °C, can be modelled by</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="P(t) = a{(2.06)^{ - t}} + 19,{\text{ }}t \geqslant 0">
<mi>P</mi>
<mo stretchy="false">(</mo>
<mi>t</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>a</mi>
<mrow>
<mo stretchy="false">(</mo>
<mn>2.06</mn>
<msup>
<mo stretchy="false">)</mo>
<mrow>
<mo>−<!-- − --></mo>
<mi>t</mi>
</mrow>
</msup>
</mrow>
<mo>+</mo>
<mn>19</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>t</mi>
<mo>⩾<!-- ⩾ --></mo>
<mn>0</mn>
</math></span></p>
<p>where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> is a constant and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> is the time, in minutes, since the pizza was taken out of the oven.</p>
<p>When the pizza was taken out of the oven its temperature was 230 °C.</p>
</div>
<div class="specification">
<p>The pizza can be eaten once its temperature drops to 45 °C.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the volume of this pan.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the radius of the sphere in cm, correct to one decimal place.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <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">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the temperature that the pizza will be 5 minutes after it is taken out of the oven.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, to the nearest second, the time since the pizza was taken out of the oven until it can be eaten.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In the context of this model, state what the value of 19 represents.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p 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="(V = ){\text{ }}\pi \times {{\text{(17.5)}}^2} \times 0.5">
<mo stretchy="false">(</mo>
<mi>V</mi>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>π</mi>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mtext>(17.5)</mtext>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>0.5</mn>
</math></span> <strong><em>(A1)(M1)</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Award <strong><em>(A1) </em></strong>for 17.5 (or equivalent) seen.</p>
<p>Award <strong><em>(M1) </em></strong>for correct substitutions into volume of a cylinder formula.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 481{\text{ c}}{{\text{m}}^3}{\text{ }}(481.056 \ldots {\text{ c}}{{\text{m}}^3},{\text{ }}153.125\pi {\text{ c}}{{\text{m}}^3})">
<mo>=</mo>
<mn>481</mn>
<mrow>
<mtext> c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>481.056</mn>
<mo>…</mo>
<mrow>
<mtext> c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>153.125</mn>
<mi>π</mi>
<mrow>
<mtext> c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)(G2)</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{4}{3} \times \pi \times {r^3} = 481.056 \ldots ">
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
<mo>×</mo>
<mi>π</mi>
<mo>×</mo>
<mrow>
<msup>
<mi>r</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>=</mo>
<mn>481.056</mn>
<mo>…</mo>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for equating <strong>their </strong>answer to part (a) to the volume of sphere.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{r^3} = \frac{{3 \times 481.056 \ldots }}{{4\pi }}{\text{ }}( = 114.843 \ldots )">
<mrow>
<msup>
<mi>r</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>3</mn>
<mo>×</mo>
<mn>481.056</mn>
<mo>…</mo>
</mrow>
<mrow>
<mn>4</mn>
<mi>π</mi>
</mrow>
</mfrac>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mo>=</mo>
<mn>114.843</mn>
<mo>…</mo>
<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 correctly rearranging so <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{r^3}">
<mrow>
<msup>
<mi>r</mi>
<mn>3</mn>
</msup>
</mrow>
</math></span> is the subject.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = 4.86074 \ldots {\text{ (cm)}}">
<mi>r</mi>
<mo>=</mo>
<mn>4.86074</mn>
<mo>…</mo>
<mrow>
<mtext> (cm)</mtext>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for correct unrounded answer seen. Follow through from part (a).</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 4.9{\text{ (cm)}}">
<mo>=</mo>
<mn>4.9</mn>
<mrow>
<mtext> (cm)</mtext>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> The final <strong><em>(A1)</em>(ft) </strong>is awarded for rounding their unrounded answer to one decimal place.</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="230 = a{(2.06)^0} + 19">
<mn>230</mn>
<mo>=</mo>
<mi>a</mi>
<mrow>
<mo stretchy="false">(</mo>
<mn>2.06</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>0</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>19</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 211">
<mi>a</mi>
<mo>=</mo>
<mn>211</mn>
</math></span> <strong><em>(A1)(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(P = ){\text{ }}211 \times {(2.06)^{ - 5}} + 19">
<mo stretchy="false">(</mo>
<mi>P</mi>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>211</mn>
<mo>×</mo>
<mrow>
<mo stretchy="false">(</mo>
<mn>2.06</mn>
<msup>
<mo stretchy="false">)</mo>
<mrow>
<mo>−</mo>
<mn>5</mn>
</mrow>
</msup>
</mrow>
<mo>+</mo>
<mn>19</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution into the function, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P(t)">
<mi>P</mi>
<mo stretchy="false">(</mo>
<mi>t</mi>
<mo stretchy="false">)</mo>
</math></span>. Follow through from part (c). The negative sign in the exponent is required for correct substitution.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 24.7">
<mo>=</mo>
<mn>24.7</mn>
</math></span> (°C) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(24.6878 \ldots ">
<mo stretchy="false">(</mo>
<mn>24.6878</mn>
<mo>…</mo>
</math></span> (°C)) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="45 = 211 \times {(2.06)^{ - t}} + 19">
<mn>45</mn>
<mo>=</mo>
<mn>211</mn>
<mo>×</mo>
<mrow>
<mo stretchy="false">(</mo>
<mn>2.06</mn>
<msup>
<mo stretchy="false">)</mo>
<mrow>
<mo>−</mo>
<mi>t</mi>
</mrow>
</msup>
</mrow>
<mo>+</mo>
<mn>19</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for equating 45 to the exponential equation and for correct substitution (follow through for their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> in part (c)).</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(t = ){\text{ }}2.89711 \ldots ">
<mo stretchy="false">(</mo>
<mi>t</mi>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>2.89711</mn>
<mo>…</mo>
</math></span> <strong><em>(A1)</em>(ft)<em>(G1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="174{\text{ (seconds) }}\left( {173.826 \ldots {\text{ (seconds)}}} \right)">
<mn>174</mn>
<mrow>
<mtext> (seconds) </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>173.826</mn>
<mo>…</mo>
<mrow>
<mtext> (seconds)</mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award final <strong><em>(A1)</em>(ft) </strong>for converting their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{2.89711}} \ldots ">
<mrow>
<mtext>2.89711</mtext>
</mrow>
<mo>…</mo>
</math></span> minutes into seconds.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the temperature of the (dining) room <strong><em>(A1)</em></strong></p>
<p><strong>OR</strong></p>
<p>the lowest final temperature to which the pizza will cool <strong><em>(A1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>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 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7pUtuQJHIqJQVhIKFza0NvnSCyEfJ2pGyKEniRsE5LS0KdPhNM+adowSCQWDWlYuk/dEEuJSSp/dfVNsMVu+g5wrhcgNxYkEovGyNB5pydwpeQKcnJyMHL4cKdnwQCQWAj5GlA3RAg90dtGH4hGcLAKgU4+GUsXKBILHQlrPqkbYg01ydiwlbH+b8wYyfhrb0dJLOxNmMqXJAH25rHT8afRr4/zrl9hHDgSC2MilhxTN8QSWpLKm5dfiLJrlRjQr6+k/LansyQWQuhSN0QIPVHbJiWdQrdAf3TpFihqP1vSORKLlqRN15IMgZhDRzB6zDiaX9EgYsoG+063W63V4nJBPjKzc+Dm6obw/mFo38bbfA7UDTGflYRyssV5D0R/h7179kvIa/u76tQti7lz38TKNWvg4uKG0tKrGPv3CYiNrXuRjFnoqRtiFiapZTqV9CuUShf0H+jci90Yx81pWxbbt2/HsSNxSE0+q3/0WKFUYsrTT+D3jN/RxrOtMSs6dhICcbHHERoaBm9vC1qZTsDGaVsWSUnxqK2t0QsFi3UH7w64VlaGsopK80JP3RDzOEksV1xcHKKcfL1NUyFzWrEIDemJzMxMfPTxGj2X76L3YcyYMfAP8NOfa3KHuiFN4pFiIptfcerUKUye9JQU3berz07bDZn67LP45uudmPvma/gjLwdBXbrialEpvvz8P3YFToWLm8C2XbvQ2b8zevbqKW5HHeCd04pFK6US3+4/iPHjH8IXa9cjJFiFYydOoW2DdRaLr15FUkJCo2EpKChoNI0SpEkg7kgsht9PD46Zip7TigWDkavOQ/sOHTB9+jRs27ID99//AI79/DP8A/x5VrnZOXj22WdNcePPabU1jaZRgvQIlJffQHziaSz+4F/Sc74FPL6L4ziuBa4jukuo1WqMGjUSccdP8uKwfv0GvPDCLISFhuLMmQS0btOa9/nGnzeAu/9i4D9TWC2AzHMZGNg/Ek6K0ICJHA7i489i4MD+KCm5Bm/v9nKokk3r4LQtiw8/+BB/u6+7vhUxe/ZMVNfcwJzX3sKZM2cQNbxuzcW2bRq/hdqmjdPis+mXUCyFRR/YhxHDhpFQNBIQp70bcunSFbi5uRhgefLxKXD3cMMNTZXBeTqQPwE2m/fbffswfuKj8q+slTV0WrF4+OFRiI+Px40bf+rRXSurhLubO/pF0mPJeihOspN57jfkFxbg74Npyf/GQu607ejpM2ejsKgUDwy7H7Nnzsb1qkr8cvg49u/9Hr4dOjTGi87LlMDxE4cQ5B+Ee+77m0xrKLxaTjvAqUN3tfgq0tJS4NGuHcJ797boKcP0zEz07NGDBjh1MCX8OWjQEAyPGoIPPqQ7IY2F0enFojEw5pxPz0xFzx4RJBbmwBJxHnVuPv7213vwW9YfCA4JErGnjnXNaccsHIudri4mAnu+2orw8HDco+omJrdE5wuJhehCQg61JAF2F+TwkRiMHj3Coi5oS/oolmuRWAiKhOFkLUFFkbFDCFwuLMapEwl4avJ0h1xfShclsRAUrVuCrMnY8QQ2bvg3IiIi0L1Hd8c7I3IPSCxEHiByz34E2PJ53x2IxqQpk+x3ERmVTGIhJJi0+I0Qeg63zczORo46Bw+NHO9wX6TgAImFkCjR4jdC6DncdtfuHRjcfyDdLjUzEk47g9NMPpRNpgTYilgbN2zEli07ZFpD21eLWhZCmFI3RAg9h9p+990BuLq50lqbFkSBxMICWHdkpW7IHUikcmLr9q0YN/5hWsHbgoBRN8QCWJRVHgR+U6tx9OhRZK//XR4VaqFaUMtCCGjqhgih5zDbj//1Lzzw4DD8LZDeY2pJEEgsLKFlnJe6IcZERH9cWlqKw8eO4OknnjR4Z4zoHReBg9QNEUEQ7OUC+8dIS0rBb3k5uJBXgIqq61DcUqBd+/boFhiIoCAVwsOd681b27ZuhbZai0mTJtsLu2zLJbEQEloRdkPYg1E5GRlY/8UG7Ni5DQooERAQwAuDX8eOuFGjQd6FNH4JuaKiItRCi9Ejx+DpZ5/B/QMHGrwKQQgaMdqy26Ubvvgcc15/U78gsxj9FKtPJBZCIiOybkhhQSFef/N1HDjwHYYMHIyvd+5BRGQk/HxNr/zFxCIzPR37vvsO48ePRedOHTFh4hQsWjBflqIRc/gICguLMGUqvW3Mqq89exUAbdYROJeRwl6jYJ2xja12bNvCdezoww0cOJj75dgxi0svKbnGrfvsUy4kJJTr3Lkz9/7SJVxFWZnF5YjVQHPrFhcWEc699dYcsbooer/E8U0XPSbTDp47d87hYsH+CebPn8+5urpwi95fwrFjIRuz//ijj7iugV25rl27ct/u3S24TCH+2Mp2947dnLu7O3fp0iVbFel05ZBYCAi5o1sWVZVV3KSnJnPt2rXjfv7pRwE1udOUlf3WG29xrm6u3KgH/87997/n78wkkTP/u3WLi+zfn3t+5kyJeCxON+nWqVWdN8cbsYHMV155AbGHY3H0558xYuQomzrF3si2YuUKpKSew01tFfr2680/S2HTi7RQYZs3b0V2ZiYWL1nSQleU6WXEqWHS8MqR3ZA33nqL8/Lx4s4kJLQIrGUrl/PN+IfHjZNUK4ONuwQHq7hFixa1CCc5X4RaFkJ+BBxwN6RWq8X6DRux/t9r8dXOr9Cvb18hNTDbdt4bc5GcnIyCwiK+lREbG2u2rSMzbtu2C8XFVzH7xRcd6YY8ri1nJbR33RwxZpGQksT/wq/69DN7V89k+fxYxltvcEoXJTfnjbdEPfj5x+9/8Ky27dhhsi500jIC9N4QAZqfnp6Onj17tth7Q0pLr+P++wejf2QfbN66XYDnwk0PHjyIWbNmITg4GJs2bUZgoPiW0X/iyYnIzyvkx3TYGAxtwghQN0QIvxbuhixftgzVN6uxcuVKIV7bxHbs2LE4ffostFoN3y3Zs2e/Tcq1VSE7d25H9IFD+OzTT2i2pq2gWtYQodwNCbRkN+To0aN80//Y0aMNXXD4PpuXsWDBIs7V3ZWbM+dVjnVTHL1dvHCRn1i2YMECR7siq+tTN0SA6rZkN6Rnr+4ID++D7Q7ufjSG63hsLCY+MRHdAoPw9VdfIdBBj3+zFbvHjn8IGo0GR4/H0YuDGguYFeepG2IFNL1JC3VDVq5cheKi6/hk1af6S4ttJ2r4cJw9mwpf7/bo3bs3Nm/e5BAXly5bjpS0NGzfvpOEwtYRkFU7qYUr0xLdkMtXrnCdO3XiPv10dQvXzvrLLVu+nJ9+/tz06dyly1esL8gCSzZL84sv/8Nf94cfDlpgSVnNJUDTvetJsWcGvvnmG27ZymUc6/Oas7XEpKz5CxZwKlWw5B7qSkpI4FTBIfwzJj/99JNdb7EyodixYwfn6urKfbpunTmhozxWEHB6sWADdAsXLuDuj7qf++HgD1zJlctmY7R3y+L3P87zv5QHD/5gtk9iyshmT86f/zY/MDt50iSOPdlqj23Hrl38fIply5bZo3gqs56AU4tFpaaMmzZ9Gjd44ECrvsj2FotX57zMRYRHiOIOg5D/mDNnzvD1YA+8fbTqI5vVR6Op4t5fspRvUSz7iIRCSIzMsXVasWBN1zfeepv/RWK/4NZs9uyGnD9/kW9VfPf9t9a4Jjob1oL7dPVqzqujT92j7998I6hrdf78Be7/Rv0f/3zMt9/Kg5HogmbkkNOKxYlffuHXonj5xReNkJh/aK+WBROyl1+dw0X2ibRrX9/8mtouZ0lJCbd82VLOzdWNCwoK5BYuXMixc+ZsTHDKSkq4hQsX8Y/lDx7Yn/v999/NMaU8NiDgtGIxadJkvi/92bp13FOTJ3ORkZHctKeeMntwk7G3l1iwvj5b9WrLl9tsEGJxFsHu8nz88cf8ylxs4Z4Hhz3ILVw4n/vxx6PcxQt1C9Qw0WSTvDLSMrnPPv+MjxPrytyrupf78j//sVl3RpyExOeVU07Kqq6+iXv/ei+qKjVYsWIFnpr8FE78egoTJ0yAn58fElJ+RZtWnjgZdxKPPvoov6gtW/i24aaAAlptDUrKrjHBbZgkeP+DxYvx5ZYdyP49yynmChw+cgQ/HI7BmbjTyFFno+xamQFDpYsSQYFBiIyMxJgx4zBx4gSDdDpoGQJOJxbsEe/q6lvw8PLA0IEP4OjxI3rSn21Yi5dnvYRv9n2LCY88CvbgVlJSAp+u1WqhVNYJhm4/Lz8fs55/3qZiwVagjugTgZfeeAmvzX5d75uz7NzQaKC5Xo7LZdeA2mpA0QpdO3eBa5vWTiGcYo6z4c+lmD21kW8KpRLsn11bo4WPb3uDUgdFDuaPc7LTgUcehbd3e4wcOdIgT8OD9MzUhoc22T9x6hQKCwvxxGNTbFKe1App6+qKtn6u6ODnKzXXZe+vU073dlEq0alTR5SVaQwC7NfBG+7t3NHe2/TS+QaZ7XSwYsVKzHh2Bnw7OM4HO1WNipU4AacUi1ZKJUYMH4GMrESwZq9uq6jUALVAZHik7lQzn39pJt2y5NTUczj16wk89/wsywwpNxFoAQJOKRaM6wcfrkBFWSW2ff65HvPBmIN4eNzD6Degn/5c0zu3mk62MHXHrl2ICItAcPf7LLSk7ETA/gScbsxCh7RbN38c/eUYXnr+eSSmpcHVxQXtvb2x7rPPdFla9JOt1v3Vzu145913aSCvRcnTxcwl4LRiwQD1690XZxOTcf3qdbi1b+vQf9J9e/ZAU6PBc9OnmRs7ykcEWpSAU4uFjnT7DoZ3RXTnm/+0zZgFu527e9cujBs1Gq1a0VqRzXOnHI4g4LRjFraBbZsxi+vl5Yg9fhwTJj5hG7eoFCJgBwIkFkKg1t4txFpvu/ubb+DVwQsPjmp8Toc+M+0QAQcRILEQAt4Gy+qxLsimjZswY9qzDh0zEYKBbJ2DAImFg+OsVudDnZtt83eVOrhadHkZEiCxEBJUG3RDfo6LgW8HX0T07S3EE7IlAnYnQGIBgHUFrNps0A35ZvtOTHr8ceqCWBUAMmpJAiQWANjDZVZtAlsWarUaJ079iiefmWrV5cmICLQkARKLetpWtS4EtiwO7N+L0NBQ3Bv4t5aMOV2LCFhFgMSiHptVrQuBLYsjJ05gcNRQ6oJY9dUlo5YmYGX7u6XdFOn1BLQs2CI3x48cwY8//SzSypFbRMCQALUshAxwCmhZ7Nr9DTr6dELU0KGGEaEjIiBSAiQWQgY4BbQsoqOj8dDYh0T6tSC3iMCdBEgs6plYNcBpZcuitLQUiYnxeGDYsDsjQmeIgEgJkFjUB8aqAU4rWxbZ2dkouXYNw4dGifRrQW4RgTsJkFjcycT8M1a2LGIORWP4Aw+ggy+ts2k+bMrpaAIkFkIGOK1sWXz11R6MffQRR8eerk8ELCJAYiFkgNOKlkXmuSxcuHQBwwbSeIVF31TK7HACJBb1IbBqgNPClgW7xtmEM+japQvuDQp0ePDJASJgCQESi3paVg1wWtiyYNeIjY3FkCFRaN2Gls+z5ItKeR1PgMRCSAwsbFmwFbyjD0Vj3JjRQq5KtkTAIQRILIQMcFrYskg4Hce/OnHEyFEOCTZdlAgIIUBiIWSA08KWxaHDhxEeFgZPz7ZCYka2RMAhBEgs6rFbNcBpQcuCdUESziRhwNAhDgk0XZQICCVAYlFP0KoBTgtaFrXVtxB/9iyGD6FZm0K/tGTvGAIkFkK4W9CySEpJgrZGg2H0PIgQ4mTrQAIkFkIGOC1oWURHH0BU1Ai6ZerALztdWhgBEgshA5wWtCxijxzH/VH3C4sWWRMBBxIgsaiH/2f5DezZswc3/7xpfjjMbFkUFV+FOk+NQZEDzC+bchIBkREgsagPyLKPlmPq1KmoqqkwP0RmtizUOdnQaKrQp0+E+WVTTiIgMgIkFgBOx8dj69ZNULoooNC6mB8iM1sWZ8+eRXhYBNp6eppfNuUkAiIj4PRiwRbOXb50GZ6eMZsPjba21vwQmdmyiImJwaiR9NJj88FSTnVJJhcAABibSURBVDEScGqxYBOxlixfigUL3oaPp7fl8TGjZcHE6JcTv2AEiYXlfMlCVAScWixiYo5AUatEvwGDoEXdKwyVCguQmNGySMvMhKurG4KDVKIKPDlDBCwl4LTvDSm9WoyN2zdg15e7eGbK+tedWtQNMaNlcfrUKahUQfDoYEXLxdJoUn4iYEcCTikW7DmNeXPfwaIFi/STpLQmSGRlZOH95UvhWqsAWLoW0CoVQE0NlC5KXCtp/s5JUnwyP7jZytr3qdox+FQ0EbCEgIl/EUvMpZk3JuZH5F7Mx6+/nsGZX8/wj40nnD4JjaYGO3ZsQUhYGD8geffdreDl5oEabS1Y50TpWt9FcXXjK67xqGkWQHxiHN5b/EGz+SgDERA7gbs4juPE7qSt/VvxrxVYvWa1QbGaKg3KKsrQqVMnjB41Gps2bzJIN3WQnpmKnj0i0BjCvLx83HvvPSgpuQZv7/amiqBzREAyBCwYzZNMnZp1dO68uSgqKjL4W7T4Pbh7uCHrXJZZQlF3kb80ea2Yw4cQHBxMQtEkJUqUCgGnFAtTwakf3zSV1MS5W02kAfxkrHCatdkkJEqUDAESi/pQtVYq4e7qbrPAsUHUzPR0DBgSbrMyqSAi4EgCJBb19KdPm47UrFR4drDN2EJleTnUubkIC+7nyPjStYmAzQg45d0QU/TY0vyWL8/f+JgFG9wsu1aG/v37mLocnSMCkiNALQtBIWt8zOLEL8cQ2SeSHh4TxJeMxUSAxMJO0Th9+ixGjKKHx+yEl4p1AAESCztAZ4Obx0/GIjQ01A6lU5FEwDEESCwEcTc9ZnExPx+VVZUICwkTVDoZEwExESCxEBQN02MWOdk5cFe68Q+QCSqejImAiAiQWAgJRiOPqJ/LzkBwSLAVd1eEOEO2RMC+BEgshPBt5BH1hNO/YsAAWpxXCFqyFR8BEgs7xCT2+HEMjRphh5KpSCLgOAIkFkLYm+iG5GRk8U+vRvShwU0haMlWfARILITExEQ35Fx2Jrp27Qqfdj5CSiZbIiA6AiQWNg5JSloSArsFQdHK9G1VG1+OiiMCLUaAxEIIahPdkMz0XIT1CgMtoycELNmKkQCJhZComOiGZGQkondELyGlki0RECUBEgsbhqW8vBwXzl9Ev4j+NiyViiIC4iBAYiEkDkbdkF9//RXuHu4I7dldSKlkSwRESYDEQkhYjLohx2OPo28/WuxGCFKyFS8BEgsbxiYtMx3hISE2LJGKIgLiIUBiISQWDboh7LH0vFw1wvrQylhCkJKteAmQWAiJTYNuSNnVUhQWFSJYRe80FYKUbMVLgMTCRrEpKCxEZUUVQqkbYiOiVIzYCJBYCIlIg25IenoSvzJWW09PISWSLREQLQESCyGhadANSUnJxNChQ4WURrZEQNQESCxsFJ7Y2CMIDaM1N22Ek4oRIQESCyFBqe+G3PzzJnLUOQgPpbePCcFJtuImQGIhJD713RC1OhdKhQKBgUFCSiNbIiBqAiQWNgiPOi8HXj5e8PJqZ4PSqAgiIE4CJBZC4lLfDWGreQf4B9ICvUJYkq3oCZBYCAlRfTckOzsbYaG0jJ4QlGQrfgIkFjaIUUpKCnr17WmDkqgIIiBeAk4tFgcORGPihIl4MGoEXpg5E2yg0qKtvhuSm6tG1OBhFplSZiIgNQJOKxYbN2/G7BdnQFNTg2pFFTZu+RJDhgyAOjff/Bg2mJT11+5/M9+OchIBCRJwSrGorr6J+LjjOJeahe+/34+Tsafx6SfrcOVKCRa/+67FYQwODgEtz2sxNjKQGAGnFAuNRos5b7wBb+/2+nDNnj0Dnbt0Qlpmkv5cszv13RD/gEAolMpms1MGIiBlAk75Dff0bAtPzzsHJP39/BFiyZvP67shYSE0GUvK/wTku3kEnLJlYQrNjfJyZOdkY+bMZ00lN3KurvOhCqbVsRoBRKdlRMApWxam4rdl22aMGDEKffrdfqFx6dVipKVnmsrOn8vLq7t7EhpGcywahUQJsiFAYgGgsKAQ3x+Ixte79xi8HCg7W42JEyc0GuyaGi2fFk4TshplRAnyIXAXx3GcfKpjeU1Y92PWrFl4a/7b6NXTspcDbd68GdOnT4eTI7QcOllIkoBTj1mwR8vnLliAV996w2KhYNFOT0+XZNDJaSJgDQGnFov3l76PJx6fhH69++rZ5arViI2L0x83tZOcmNxUMqURAVkRcMoxC9aimDXrecQcjkHCmXQouWpo72qF//2vGulpSTgbn9hskNnS/2q1utl8lIEIyIWAU4rFz8d+hkZbixHDR0BbywYp3erj6Ya+M2YgKLj5eRNs6f+KqjK5fA+oHkSgWQJOP8DZLKFGMiQnp6JPnwg+lQY4G4FEp2VFwKnHLIREkj1pShsRcCYCJBZWRpuNV3Ts3NFKazIjAtIjQGJhZczSU9LQu9ftuyhWFkNmREAyBEgsrAxVSnoawsPrxiysLILMiICkCJBYWBEu/j0hOTlQqbpZYU0mRECaBEgsrIhbenYOXF1dENiN3phuBT4ykSgBEgsrApefp0bHTp3g6uJqhTWZEAFpEiCxsCJu7D0hfr7+aNuexMIKfGQiUQIkFlYELr8gH6qgAEDRygprMiEC0iRAYmFF3NQ5anQLVAG11VZYkwkRkCYBEgsr4paXr0Z4OHtjOq3pbQU+MpEoARILCwPHFsu5cOES+vHL792y0JqyEwHpEiCxsDB2aZmZcHd3R7duAdSysJAdZZc2ARILC+OXlJAAVbBufgW1LCzER9klTIDEwsLgZWVlITCg+fUuLCyWshMB0RMgsbAwRBcvXmwwzZsGOC3ER9klTIDEwoLgsaX0CgoL0C2IuiEWYKOsMiFAYmFBICvLy1FcWEzPhFjAjLLKhwCJhQWx1FTV4FrFNaiCOtVbUTfEAnyUVeIESCwsCKBancPn7hL4t3oruhtiAT7KKnECJBYWBJDN3AxWBRu84tACc8pKBCRNgMTCgvBlpmcjPCK0gQV1QxrAoF2ZEyCxsCDAOepcBAc3FAvqhliAj7JKnACJhQUBPHcuESHBIRZYUFYiIB8CJBZmxrK0tBRXrl1DQAB7JkS3UTdER4I+5U+AxMLMGBcWFEEJJTp08L1tUVt7e5/2iIDMCZBYmBngKyUl/CK9Pj4+ty0U/7u9T3tEQOYESCzMDHBeXg48PLzh6dnWTAvKRgTkRYDEwsx45uXl477uDe+EAKi920xrykYEpE+AxMLMGOapcxGiCjTMTd0QQx50JGsCJBZmhjc9OxOhYUa3TallYSY9yiYHAiQWZkSRPZqeo86BymBCFgBqWZhBj7JYQ2D/gQNITky0xtRuNiQWZqC9mJ/P5woJDjbMTS0LQx50ZDMCMYdj0H/wQDzx5JO4WnzVZuUKKYjEwgx6anUu2rVrB3d3N8Pc1LIw5EFHNiOw4bN1+OnHn5CTk40ePbtj8Yf/QnX1TZuVb01BJBZmUMvKSoWfnx9wt9GMTWpZmEGPslhLYPjw4UhOTMa77y7AhvVrEBYajv3R0WDdYkdsSkdctLlrXr96vbksLZauUALnL1yEn1dnaP68iaqa24G6Uf4n70f59euovX26xXyjC8mfAPv+PTXpaTw8+hH888PF+MfYsRgxbBg+W7sRwSEtu3D0XRzHcWJCHn3we7z4yiuoqqqCUqGEVlsDKBQO3S8ru8Yj8nBvB4XydmNMU6NB2bUydOpUv3KWQgFtjQZKpQvvt9LFlY6Jh1XfB5P/k1qgrPIaNJoafjbxkg+X4c05r5vMao+TomtZHPnpGFRBKrz7zjt19VW4ALU1jttXuOCll2Zh8NCBeOLxp3lf2BMhCoUL2GI406dNx86dO/WxUSpcoK2tgaM/mX88twafTz89EU8/MwMjh490uH/N8dm+/Svk5WVj8Xv/EgXPxvxlnIuKCjF91jR8seoTdAsItIm/7CdJ9z2rra3hv2/R0fuwdu1adO7cGfPmvYXnn5+p/961xI7oxKJWWQ3vDr6IGj68Jerf7DVY/7C8vByDBg5BVNQQg/zeme78MetbSmHz9PREUKAKUvA3Li4OVZoqDDViLkbOanUe/589dMhQdAvsZnMXszKysGjpIkR/dwDTnpmOD5Z8CG/v9ja/TnMF3m5TN5ezhdIV2la3WxItdM3GLnPzz5tYOO8dsHeFHI4+gtdeew3snJS3WgcNjlnFTNeitMq45YxcFFq+m1xTo7HpRdmP1OuvvY4+/SNQVlyKpIQUrF+33iFCwSomOrFgLQuwprMIttfnvoaTJ+N4T77c9gWul1/HwvffF4Fn1rugUIquMdl4ZUTyPWjcwbqUWr7rqbXp93bDho3o3uM+sPkWu3buwc+xsejeo3tzrtg1XXxiUfMXUbQsEhMT8fm6LzB0+HB06dIFrVq1xowZM/HxR8uRmqGbWWd0K9WuoRJeuFZq629IpGWh+ydyaTD4LTRahQX5ePnlV5GUkIRHHh4ntDib2IvuZ0apUNhUoa2ltG3LNnh4eKCyopxf0ZuVE6oKgbuHG3Zv241eK/oCkNYanIytpLoh1gbPEXZaQGvD++eLP/jAEbVo8po6UWwyU4smulaLomWRnJwIj/btcfXqFf1Sesq2reHVwRcpKdktisRWF2MtC6WrOLp4ZtVJIt0QXiRE97NrFmGLMolOLLRVfxFFy6KgMB9tXF1QUnwdgaq6yS8uSiVa31KgqDivHrK0uiHM6VqthJYClEg3hM0HghaorRXdv5NFYtBcZtHp4eOTH0NlRWVzfts9vaamFq1bA+cvncdT/v7667GbNbd/m6XVDZn/9nyEhYfr6yLmnVGjRqJfv35idlHvm5dXO6xcuQKdOnrpz9l7h93ST0vNQHZ2Gtq5e2H8I2P5Sx6OjcVvOZl44ZkZULq62tQN0YkFu1ctho3NSSgvvw6tVouAgLpFb7R/3sStW7fg0bFLvYvSallMmfK0GNCa5cOAAYPMyieGTG09PfHiiy+3uCsdvBVYcygGB6KjcenyJRw+fAgLFyxCYWER/t+IUVCpVDb1Sd7tJgGo2EM7l6+UoORaGQI6deRL0mhrUFFRAZVK19KQVstCAA4yFRmBVkolAgN74tPP1oE9drB5yw5cyr+ClHMZ+C0jw+ZCwaovOrG4UV5uMH3aUTEaPnwI64RCqVSga2Bdy6KsrAyVZZUYHjWq3i1ptSyY03u+/hpsPEbMW3FxIT7597/x7ry5+HrPHoc/mt0UK8Zy1eo1eO+9d7D/uwNNZbVLGpvJOXjwYOzYugnTnpnKv4fXz+DdNja8LHuQTAxbRVkZt3vXt1zXwK6cV7t2DneppOQa17lzZ65jRx+9L59/sY4LDFRxFRWV/LlzGSnsITx9uph3jh09xg0cPJD399SJM6J1NSUthevYsSPXNSiQ8+now/sbGRnJsXiIbUvPyuIi+/ThHnjgQS44OJj39dVX57S4mwvmz+fuvVdl9+uK5puu0VRxJVcuc+PGPcb5+HjZveLmXGDJ0iW8WPyW9QeXlJDAhYSFcOzLrNvOZWRIRiwuXrjErf7sY9GLxcP/eJg78csvnObWLa6srIJ7YdZs3uc5b7T8P6EuzqY+mX9vz5/PXbp8hU+uqqziHpv8MOfq6sJVVFaYMrHLOXbdh8c9xrm6uXLn/3veLtfQFSqabgibIckeIAsK1I0H2LD5ZGVRBRcvIyoqCj/GxiAlPQ3Hfj6GXj17NShNOmMW/gF+6BVS57tY756yLujUKc9gyNChfHOavaNl5cqP4e7ujiNHjjTg7vhdNmaw4O234efbgXemdZvWeOzhyXB1dYPSeJEkO7r7ny//gw9XfMAPxCenJvPPLsWfjrfLFUV3N6RGRN/kzNRkTJg4Ea+++KJd4Ld0oboZFkrUP/Lf0g40cz12V8F4ajP7J+zTpz9at27VjHXLJzN/G25XLl/CG3PeQGsb37JseA22fzYxEbt37EZYWAhCQ0PB1oaNCIvAf778ErkX/osZ054zNrHJsWhaFrrasNneYtkys7Px17/e24Q70hvg5CsjkZmRzFd+PkFaEiZNmtxEHByflJOdi4L8Irzzzjy7O6NQ1CLzXCq8fH30yw18+OFiuLm44Yl/TAK77W+PTXQtCwXE4RJ7azq7++HnZ/RiIYMoSKcbYuC2RGZGMp+PHo9FgL8/Hps0xqAKYjlgd27ef/9DbN++jb+FeePGdazfsMGu7vXt3Q8/xRp2y0aMHAX2Z89NRL/jddWsZfNmRbCxt6a7urvCu30T7zaV6oK9EmlZsFbFmuXLsGXLFrRpZZ9fS6FfNV9ff6xbtxa/HDuGsIhwfP7FFzgQ3fK3UIXWwxx7u/6Mv/LKa/jjj994P7TaujkLdZ+toNHcgKurK3p074kVK1fofVWIZOoHmxHXzt0D7byamMIr1VcBSKBlwYRi0T/fwdRpz6F3X/aEr7g35uO2zdsR1r07YmNiMW6MOB4rtyU1u4rFJ6tW6h/iZqPH7Atg/GlcmVp+5UHjsy1/XFiUz/f9XNu0bvmL2/uKIm9ZsMfod23eClWgCk8++aS9adis/B4hdQOOShfRNdhtUke71oqtysTEgf2xzdSn7pyuNmIZs8hX56FL5656n3X+GXxKtRsi8pbFnr37UVlTg2dnzNDjZj808WeT9Mdi3blaehWTJ4t7MNZadnYVC2ucuvW/m3XL/1tjbEObq9dL4efv13SJEuuGsIfi2Faju4fadO0ckrp580YsWPgWrhbl471338U/572DeXPfxAODBqG2ptohPpm6aGnpdcx78zXEHK4baGStocXvfYBx4x9BLwl0m0zVqblzdu2GNHfxhulsIdxfz5zB73+ch6+vHzZs3IhRI0ejWzfHTNLKzs7FoCEDGrp4576EWhZnE1Px9d6vEaQKwr59u+Hh7obefXvfWScHnjkZF4dlH30EhdIFu/ftu+2JQoGOXj4YNEQ8T6JW1WgQHXMEazduRLAqCL5+ARjxwDBs/Pzz237LbE80LxlizUy2sZkLDW9IGndTWop/UFAgPvjgQzzxxBONXjI9MxU9e0SwKfON5hFLAvvlY3//Uyr5T10XUSz+6fxg3wPmp6mFhR31XdD5ZvzJfuA0VRqwFcg8vD2b7rIaG0vwWDQti4ZfBDHM1btw8aJ+7c1G4yqhlgX752N/fMBFvMI3/z0QsX8Nvwtsdin7c5ZNdGMWYgCfn18AbY0WquDgpt2R2JhF05WhVCLQNAESCxN8srOz4ePjhbZt25hIbXBKQi2LBl7TLhGwigCJhQlsuXlq+PsHmEgxOkUtCyMgdChnAiQWJqLLXnTr4+VjIsXolIRbFmwQkTYiYAkBEgsTtAryChEQKO+Wham7DSZQ0CkioCdAYqFHcXvnyrUSBPiZIRYSblncri3tEQHzCJBYGHFi9/mLiwrh5etrlGLiUKJjFtQFMRFLOtUsARILI0Q11TfBHk+/z5x3Lki0ZUFdEKOg06FZBEgsGmBiv7g1mhpUVJahc6fODVIa2ZVoy6KR2tBpItAkARKLBnjYL25JUTE0mhoEmjPAKcGWBXVBGgScdi0iIJrp3hZ5baPMarUam7duQnHJdfQN64Fp055D3sWLaOfVDsaLsZq8pARbFtQFMRlJOmkGAacVi9jY45g48VEEBASg+GoxvtzwBTZu34p/jBmHkOAQM9CxV5LfbV4+ykUEZEDAKbsh7I7H+rVr8fPROCQnp/IDmi+8/CJSziTh/SVLEBQUZF5oJdiyoG6IeaGlXHcScEqxqCi9jmdmz0CvnqF6IqtWfQJ3Nw/+AbJuQU2t6K03kWTLgrohDeJHuxYRcEqx6ODbAaNHjDQAxR6NjugTzp/za2/GHAuWU2ItC2pVGIScDiwk4JRiYYoR65qkpKTwSff8taupLHeek9iYBbUq7gwhnTGfgNMOcBoj2rdnL/z8OuL6dRf+nassPSsjC6tXf8xnZctWGitr2bVrULoQQmOWdCxPAvRNr39F3tp/r8EPP8Tw7wrx6ODNR5utguTZoe7Ft8bhZ+BY2sEZM42TRHnMuiDUshBlaCTjlGjW4LQFsVy1Gq+/+RqUChfUsuXuFS58a8B4/423F2DIoLrFX1n346UXZ+LRMf/AqLEP2cINKoMIyJKArMTC0gixX9s1a9biHlUgHhknvzdIWcqD8hOBpggYd8Obyiu7tE1bt6JjRw8DobhRXo7ExGTZ1ZXuhMgupC1eIadtWSxf9hHWff4pRo0aAwV7/wB7+U61BgkJKdixZQt69urV4sGgCxIBMRNwSrE4Hnscc+fNNRmXAP9u2Lt/j8k0qZ6kwU2pRk5cfjulWIgrBOQNEZAGAaces5BGiMhLIiAOAiQW4oiD3byggU27oXW6gqkb4nQhpwoTAesIUMvCOm5kRQScjgCJhcxDTt0QmQe4Bav3/wHye1pFwP9oUgAAAABJRU5ErkJggg=="><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>At Grande Anse Beach the height of the water in metres is modelled by the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h(t) = p\cos (q \times t) + r">
<mi>h</mi>
<mo stretchy="false">(</mo>
<mi>t</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>p</mi>
<mi>cos</mi>
<mo><!-- --></mo>
<mo stretchy="false">(</mo>
<mi>q</mi>
<mo>×<!-- × --></mo>
<mi>t</mi>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mi>r</mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> is the number of hours after 21:00 hours on 10 December 2017. The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span> , for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 72">
<mn>0</mn>
<mo>⩽<!-- ⩽ --></mo>
<mi>t</mi>
<mo>⩽<!-- ⩽ --></mo>
<mn>72</mn>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-14_om_10.10.26.png" alt="M17/5/MATME/SP2/ENG/TZ1/08"></p>
<p>The point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}(6.25,{\text{ }}0.6)">
<mrow>
<mtext>A</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>6.25</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.6</mn>
<mo stretchy="false">)</mo>
</math></span> represents the first low tide and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}(12.5,{\text{ }}1.5)">
<mrow>
<mtext>B</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>12.5</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>1.5</mn>
<mo stretchy="false">)</mo>
</math></span> represents the next high tide.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>How much time is there between the first low tide and the next high tide?</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the difference in height between low tide and high tide.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the 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.i.</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="q"> <mi>q</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>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>There are two high tides on 12 December 2017. At what time does the second high tide occur?</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>attempt to find the difference of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-values of A and 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="6.25 - 12.5{\text{ }}"> <mn>6.25</mn> <mo>−</mo> <mn>12.5</mn> <mrow> <mtext> </mtext> </mrow> </math></span></p>
<p>6.25 (hours), (6 hours 15 minutes) <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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to find the difference of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y"> <mi>y</mi> </math></span>-values of A and 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="1.5 - 0.6"> <mn>1.5</mn> <mo>−</mo> <mn>0.6</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.9{\text{ (m)}}"> <mn>0.9</mn> <mrow> <mtext> (m)</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>valid approach <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{{{\text{max}} - {\text{min}}}}{2},{\text{ }}0.9 \div 2"> <mfrac> <mrow> <mrow> <mtext>max</mtext> </mrow> <mo>−</mo> <mrow> <mtext>min</mtext> </mrow> </mrow> <mn>2</mn> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>0.9</mn> <mo>÷</mo> <mn>2</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = 0.45"> <mi>p</mi> <mo>=</mo> <mn>0.45</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">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>period <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 12.5"> <mo>=</mo> <mn>12.5</mn> </math></span> (seen anywhere) <strong><em>(A1)</em></strong></p>
<p>valid approach (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="{\text{period}} = \frac{{2\pi }}{b},{\text{ }}q = \frac{{2\pi }}{{{\text{period}}}},{\text{ }}\frac{{2\pi }}{{12.5}}"> <mrow> <mtext>period</mtext> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> </mrow> <mi>b</mi> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>q</mi> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> </mrow> <mrow> <mrow> <mtext>period</mtext> </mrow> </mrow> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> </mrow> <mrow> <mn>12.5</mn> </mrow> </mfrac> </math></span></p>
<p>0.502654</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q = \frac{{4\pi }}{{25}},{\text{ 0.503 }}\left( {{\text{or }} - \frac{{4\pi }}{{25}},{\text{ }} - 0.503} \right)"> <mi>q</mi> <mo>=</mo> <mfrac> <mrow> <mn>4</mn> <mi>π</mi> </mrow> <mrow> <mn>25</mn> </mrow> </mfrac> <mo>,</mo> <mrow> <mtext> 0.503 </mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mrow> <mtext>or </mtext> </mrow> <mo>−</mo> <mfrac> <mrow> <mn>4</mn> <mi>π</mi> </mrow> <mrow> <mn>25</mn> </mrow> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mo>−</mo> <mn>0.503</mn> </mrow> <mo>)</mo> </mrow> </math></span> <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>attempt to use a coordinate to make an equation <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="p\cos (6.25q) + r = 0.6,{\text{ }}p\cos (12.5q) + r = 1.5"> <mi>p</mi> <mi>cos</mi> <mo></mo> <mo stretchy="false">(</mo> <mn>6.25</mn> <mi>q</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>r</mi> <mo>=</mo> <mn>0.6</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>p</mi> <mi>cos</mi> <mo></mo> <mo stretchy="false">(</mo> <mn>12.5</mn> <mi>q</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>r</mi> <mo>=</mo> <mn>1.5</mn> </math></span></p>
<p>correct substitution <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="0.45\cos (6.25q) + 1.05 = 0.6,{\text{ }}0.45\cos (12.5q) + 1.05 = 1.5"> <mn>0.45</mn> <mi>cos</mi> <mo></mo> <mo stretchy="false">(</mo> <mn>6.25</mn> <mi>q</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mn>1.05</mn> <mo>=</mo> <mn>0.6</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>0.45</mn> <mi>cos</mi> <mo></mo> <mo stretchy="false">(</mo> <mn>12.5</mn> <mi>q</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mn>1.05</mn> <mo>=</mo> <mn>1.5</mn> </math></span></p>
<p>0.502654</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q = \frac{{4\pi }}{{25}},{\text{ }}0.503{\text{ }}\left( {{\text{or }} - \frac{{4\pi }}{{25}},{\text{ }} - 0.503} \right)"> <mi>q</mi> <mo>=</mo> <mfrac> <mrow> <mn>4</mn> <mi>π</mi> </mrow> <mrow> <mn>25</mn> </mrow> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>0.503</mn> <mrow> <mtext> </mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mrow> <mtext>or </mtext> </mrow> <mo>−</mo> <mfrac> <mrow> <mn>4</mn> <mi>π</mi> </mrow> <mrow> <mn>25</mn> </mrow> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mo>−</mo> <mn>0.503</mn> </mrow> <mo>)</mo> </mrow> </math></span> <strong><em>A1</em></strong> <strong><em>N2</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>valid method to find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</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="\frac{{{\text{max}} + {\text{min}}}}{2},{\text{ }}0.6 + 0.45"> <mfrac> <mrow> <mrow> <mtext>max</mtext> </mrow> <mo>+</mo> <mrow> <mtext>min</mtext> </mrow> </mrow> <mn>2</mn> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>0.6</mn> <mo>+</mo> <mn>0.45</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = 1.05"> <mi>r</mi> <mo>=</mo> <mn>1.05</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">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>attempt to find start or end <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span>-values for 12 December <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 + 24,{\text{ }}t = 27,{\text{ }}t = 51"> <mn>3</mn> <mo>+</mo> <mn>24</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>t</mi> <mo>=</mo> <mn>27</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>t</mi> <mo>=</mo> <mn>51</mn> </math></span></p>
<p>finds <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span>-value for second max <strong><em>(A1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 50"> <mi>t</mi> <mo>=</mo> <mn>50</mn> </math></span></p>
<p>23:00 (or 11 pm) <strong><em>A1</em></strong> <strong><em>N3</em></strong></p>
<p><strong>METHOD 2 </strong></p>
<p>valid approach to list either the times of high tides after 21:00 or the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span>-values of high tides after 21:00, showing at least two times <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="{\text{21:00}} + 12.5,{\text{ 21:00}} + 25,{\text{ }}12.5 + 12.5,{\text{ }}25 + 12.5"> <mrow> <mtext>21:00</mtext> </mrow> <mo>+</mo> <mn>12.5</mn> <mo>,</mo> <mrow> <mtext> 21:00</mtext> </mrow> <mo>+</mo> <mn>25</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>12.5</mn> <mo>+</mo> <mn>12.5</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>25</mn> <mo>+</mo> <mn>12.5</mn> </math></span></p>
<p>correct time of first high tide on 12 December <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>10:30 (or 10:30 am) </p>
<p>time of second high tide = 23:00 <strong><em>A1</em></strong> <strong><em>N3</em></strong></p>
<p><strong>METHOD 3</strong></p>
<p>attempt to set <strong>their</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span> equal to 1.5 <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="h(t) = 1.5,{\text{ }}0.45\cos \left( {\frac{{4\pi }}{{25}}t} \right) + 1.05 = 1.5"> <mi>h</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>1.5</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>0.45</mn> <mi>cos</mi> <mo></mo> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>4</mn> <mi>π</mi> </mrow> <mrow> <mn>25</mn> </mrow> </mfrac> <mi>t</mi> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mn>1.05</mn> <mo>=</mo> <mn>1.5</mn> </math></span></p>
<p>correct working to find second max <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="0.503t = 8\pi ,{\text{ }}t = 50"> <mn>0.503</mn> <mi>t</mi> <mo>=</mo> <mn>8</mn> <mi>π</mi> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>t</mi> <mo>=</mo> <mn>50</mn> </math></span></p>
<p>23:00 (or 11 pm) <strong><em>A1</em></strong> <strong><em>N3</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.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.</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) = {x^2} - 1">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mn>1</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x) = {x^2} - 2">
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mn>2</mn>
</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>.</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="(f \circ g)(x) = {x^4} - 4{x^2} + 3">
<mo stretchy="false">(</mo>
<mi>f</mi>
<mo>∘</mo>
<mi>g</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>4</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</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>On the following grid, sketch the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(f \circ g)(x)">
<mo stretchy="false">(</mo>
<mi>f</mi>
<mo>∘</mo>
<mi>g</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant x \leqslant 2.25">
<mn>0</mn>
<mo>⩽</mo>
<mi>x</mi>
<mo>⩽</mo>
<mn>2.25</mn>
</math></span>.</p>
<p><img src="images/Schermafbeelding_2017-08-15_om_08.00.33.png" alt="M17/5/MATME/SP2/ENG/TZ2/06.b"></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(f \circ g)(x) = k">
<mo stretchy="false">(</mo>
<mi>f</mi>
<mo>∘</mo>
<mi>g</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>k</mi>
</math></span> has exactly two solutions, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant x \leqslant 2.25">
<mn>0</mn>
<mo>⩽</mo>
<mi>x</mi>
<mo>⩽</mo>
<mn>2.25</mn>
</math></span>. Find the possible values 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">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 form composite in either order <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^2} - 2),{\text{ }}{({x^2} - 1)^2} - 2">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>1</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>2</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="({x^4} - 4{x^2} + 4) - 1">
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>4</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>4</mn>
<mo stretchy="false">)</mo>
<mo>−</mo>
<mn>1</mn>
</math></span> <strong><em>A1</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(f \circ g)(x) = {x^4} - 4{x^2} + 3">
<mo stretchy="false">(</mo>
<mi>f</mi>
<mo>∘</mo>
<mi>g</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>4</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
</math></span> <strong><em>AG</em></strong> <strong><em>N0</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><img src="images/Schermafbeelding_2017-08-15_om_08.05.50.png" alt="M17/5/MATME/SP2/ENG/TZ2/06.b/M"> <strong><em>A1</em></strong></p>
<p><strong><em>A1A1</em></strong> <strong><em>N3</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>A1 </em></strong>for approximately correct shape which changes from concave down to concave up. Only if this <strong><em>A1 </em></strong>is awarded, award the following:</p>
<p><strong><em>A1 </em></strong>for left hand endpoint in circle <strong>and </strong>right hand endpoint in oval,</p>
<p><strong><em>A1 </em></strong>for minimum in oval.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>evidence of identifying max/min as relevant points <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 = 0,{\text{ }}1.41421,{\text{ }}y = - 1,{\text{ }}3">
<mi>x</mi>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>1.41421</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>y</mi>
<mo>=</mo>
<mo>−</mo>
<mn>1</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>3</mn>
</math></span></p>
<p>correct interval (inclusion/exclusion of endpoints must be correct) <strong><em>A2</em></strong> <strong><em>N3</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=" - 1 < k \leqslant 3,{\text{ }}\left] { - 1,{\text{ 3}}} \right],{\text{ }}( - 1,{\text{ }}3]">
<mo>−</mo>
<mn>1</mn>
<mo><</mo>
<mi>k</mi>
<mo>⩽</mo>
<mn>3</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>]</mo>
<mrow>
<mo>−</mo>
<mn>1</mn>
<mo>,</mo>
<mrow>
<mtext> 3</mtext>
</mrow>
</mrow>
<mo>]</mo>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>1</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>3</mn>
<mo stretchy="false">]</mo>
</math></span></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = 0.3{x^3} + \frac{{10}}{x} + {2^{ - x}}">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.3</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>+</mo>
<mfrac>
<mrow>
<mn>10</mn>
</mrow>
<mi>x</mi>
</mfrac>
<mo>+</mo>
<mrow>
<msup>
<mn>2</mn>
<mrow>
<mo>−<!-- − --></mo>
<mi>x</mi>
</mrow>
</msup>
</mrow>
</math></span>.</p>
</div>
<div class="specification">
<p>Consider a second function, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x) = 2x - 3">
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>2</mn>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mn>3</mn>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate <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>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</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="y = f(x)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 7 \leqslant x \leqslant 4">
<mo>−</mo>
<mn>7</mn>
<mo>⩽</mo>
<mi>x</mi>
<mo>⩽</mo>
<mn>4</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 30 \leqslant y \leqslant 30">
<mo>−</mo>
<mn>30</mn>
<mo>⩽</mo>
<mi>y</mi>
<mo>⩽</mo>
<mn>30</mn>
</math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation of the vertical asymptote.</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 the coordinates of the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-intercept.</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>Write down the possible 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="x < 0">
<mi>x</mi>
<mo><</mo>
<mn>0</mn>
</math></span> and <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>.</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 solution of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = g(x)">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>g</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">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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.3{(1)^3} + \frac{{10}}{1} + {2^{ - 1}}">
<mn>0.3</mn>
<mrow>
<mo stretchy="false">(</mo>
<mn>1</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>3</mn>
</msup>
</mrow>
<mo>+</mo>
<mfrac>
<mrow>
<mn>10</mn>
</mrow>
<mn>1</mn>
</mfrac>
<mo>+</mo>
<mrow>
<msup>
<mn>2</mn>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution into function.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 10.8">
<mo>=</mo>
<mn>10.8</mn>
</math></span> <strong><em>(A1)(G2)</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><img src="images/Schermafbeelding_2017-08-16_om_14.01.31.png" alt="M17/5/MATSD/SP2/ENG/TZ1/03.b/M"> <strong><em>(A1)(A1)(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for indication of correct window and labelled axes.</p>
<p>Award <strong><em>(A1) </em></strong>for correct shape and position for <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> (with the local maximum, local minimum and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-intercept in relative approximate location in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{3}}^{{\text{rd}}}}">
<mrow>
<msup>
<mrow>
<mtext>3</mtext>
</mrow>
<mrow>
<mrow>
<mtext>rd</mtext>
</mrow>
</mrow>
</msup>
</mrow>
</math></span> quadrant).</p>
<p>Award <strong><em>(A1) </em></strong>for correct shape and position for <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> (with the local minimum in relative approximate location in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{1}}^{{\text{st}}}}">
<mrow>
<msup>
<mrow>
<mtext>1</mtext>
</mrow>
<mrow>
<mrow>
<mtext>st</mtext>
</mrow>
</mrow>
</msup>
</mrow>
</math></span> quadrant).</p>
<p>Award <strong><em>(A1) </em></strong>for smooth curve with indication of asymptote (graph should not touch <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-axis and should not curve away from the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-axis). The asymptote is only assessed in this mark.</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><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> <strong><em>(A2)</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="x = {\text{(a constant)}}">
<mi>x</mi>
<mo>=</mo>
<mrow>
<mtext>(a constant)</mtext>
</mrow>
</math></span>” and <strong><em>(A1) </em></strong>for “<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{(a constant)}} = 0">
<mrow>
<mtext>(a constant)</mtext>
</mrow>
<mo>=</mo>
<mn>0</mn>
</math></span>”.</p>
<p>The answer must be an equation.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="( - 6.18,{\text{ }}0){\text{ }}( - 6.17516 \ldots ,{\text{ }}0)">
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>6.18</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0</mn>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>6.17516</mn>
<mo>…</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for each correct coordinate. Award <strong><em>(A0)(A1) </em></strong>if parentheses are missing.</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=" - 4.99 < x < - 2.47{\text{ }}( - 4.98688 \ldots < x < - 2.46635 \ldots )">
<mo>−</mo>
<mn>4.99</mn>
<mo><</mo>
<mi>x</mi>
<mo><</mo>
<mo>−</mo>
<mn>2.47</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>4.98688</mn>
<mo>…</mo>
<mo><</mo>
<mi>x</mi>
<mo><</mo>
<mo>−</mo>
<mn>2.46635</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for both correct end points, <strong><em>(A1) </em></strong>for strict inequalities used with 2 endpoints.</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.3{x^3} + \frac{{10}}{x} + {2^{ - x}} = 2x - 3">
<mn>0.3</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>+</mo>
<mfrac>
<mrow>
<mn>10</mn>
</mrow>
<mi>x</mi>
</mfrac>
<mo>+</mo>
<mrow>
<msup>
<mn>2</mn>
<mrow>
<mo>−</mo>
<mi>x</mi>
</mrow>
</msup>
</mrow>
<mo>=</mo>
<mn>2</mn>
<mi>x</mi>
<mo>−</mo>
<mn>3</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for equating the expressions for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> or for the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 2x - 3">
<mi>y</mi>
<mo>=</mo>
<mn>2</mn>
<mi>x</mi>
<mo>−</mo>
<mn>3</mn>
</math></span> sketched (positive gradient, negative <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-intercept) on their graph from part (a).</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(x = ){\text{ }} - 1.34{\text{ }}( - 1.33650 \ldots )">
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>−</mo>
<mn>1.34</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>1.33650</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)(G2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award a maximum of <strong><em>(M1)(A0) </em></strong>or <strong><em>(G1) </em></strong>for coordinate pair seen as final answer.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>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>The diagram shows the straight line <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>1</mn></msub></math>. Points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mfenced><mrow><mo>-</mo><mn>9</mn><mo>,</mo><mo> </mo><mo>-</mo><mn>1</mn></mrow></mfenced></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext><mfenced><mrow><mo>-</mo><mn>3</mn><mo>,</mo><mo> </mo><mn>2</mn></mrow></mfenced></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> are points on <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>1</mn></msub></math>.</p>
<p style="text-align: center;"><img 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6DpwDfbso2XVYmXV4kBMKnH5T/DYPfL0OvthIPBWRhdXl15OVyOzsL3g/8bXlz9LqmZmwyB2gUEvtqJ7YAAAQKbFWgi8KXWsl1aML6L98NfwsF2/+oyML3prdWm+W/pwTyRQDkCAl85tbQSAgQ6IlBX4Eu7ZduR4lomgZoEBL6aYA1LgACBugQ2HfiyadnWBWpcAh0QEPg6UGRLJECgLIFNBL5sW7ZlldJqCDQmIPA1Rm1HBAgQ2IzAXQOflu1m/I1CIEcBgS/HqpkzAQKdFlg18D1//vzGvWyTPcu201W1eAL1Cgh89foanQABAhsXWCbwxZbtycnJjXvZtnlh5I0jGJAAgZUEBL6VuDyZAAEC7QssCnzv3r2bXB9vb2/v6pIkh4eHIY0LI7fvZgYEuiwg8HW5+tZOgECWArOBT8s2yzKaNIFGBQS+RrntjAABAusLxMCnZbu+oxEIdElA4OtSta2VAIGsBaYt2xj4pl/7+/tatllX1eQJNCMg8DXjbC8ECBC4s8BsyzaGveFwmN69bO+8Qi8kQKBuAYGvbmHjEyBA4A4Ci1q2o9Fo8u7eHYb0EgIEOiwg8HW4+JZOgEBaAtOW7fWzbKct27ht+ojv8HkQIEBgFQF/a6yi5bkECBCoQWC2ZRsvjHxby1bgq6EIhiRQuIDAV3iBLY8AgTQFbmvZVs1Y4KsSsp0AgVkBgW9WxM8ECBCoSWDZlm3V7gW+KiHbCRCYFRD4ZkX8TIAAgQ0LrNqyrdq9wFclZDsBArMCAt+siJ8JECCwAYE3b97MvZdtPMt23YfAt66g1xPonoDA172aWzEBAjUJxJZtvG9t1Vm26+5e4FtX0OsJdE9A4Oteza2YAIENC8SW7fHx8dXdL6rOsl139wLfuoJeT6B7AgJf92puxQQIbEBg2rKN4S4GsK2trUno20TLtmp6Al+VkO0ECMwKCHyzIn4mQIDAAoGmWrYLdn/1a4HvisI3BAgsKSDwLQnlaQQIdFeg6ZZtlbTAVyVkOwECswIC36yInwkQIBBCmG3ZxpAVP6cXw1/bD4Gv7QrYP4H8BAS+/GpmxgQI1CQwr2Ubz7iNZ97Gbak8BL5UKmEeBPIREPjyqZWZEiBQk8C8lu3JycnkXb6adrnWsALfWnxeTKCTAgJfJ8tu0QQIpNyyraqOwFclZDsBArMCAt+siJ8JEChWIJeWbVUBBL4qIdsJEJgVEPhmRfxMgEBxArm1bKsKIPBVCdlOgMCsgMA3K+JnAgSKEMi5ZVtVAIGvSsh2AgRmBQS+WRE/EyCQrUApLduqAgh8VUK2EyAwKyDwzYr4mQCB7ATi7cziNfLi7c1iGIq3O0v5LNt1gQW+dQW9nkD3BAS+7tXciglkKfDy5cswHA7D9F61sWUbf57eyzaGoFQujFw3sMBXt7DxCZQnIPCVV1MrIlCcQDzpIoac6dfXX3999X2KF0auuwACX93CxidQnoDAV15NrYhAcQLffvvtVcCLYec3v/lN0S3bqgIKfFVCthMgMCsg8M2K+JkAgSQE5rVsp+/wHR4eJjHHtiYh8LUlb78E8hUQ+PKtnZkTKE5gepbt/v7+1Tt6sWX7j3/8I0zf5Yuf2Yuf5+vyQ+DrcvWtncDdBAS+u7l5FQECGxSYPcs2nm0bz7LterBbRCzwLZLxewIEFgkIfItk/J4AgVoF5rVsY6s2nqCx2mMc3p49Dv2rkzoehMHo/S1DvA+jwYOrdxB7O4MwGt/y9AQ3CXwJFsWUCCQuIPAlXiDTI1CSwKKW7enpaYjb1nqMfwrDh1+GXq8fto+ehctFg709Cwf9eMZvVTBcNED7vxf42q+BGRDITUDgy61i5ksgQ4FmWravw9nBg7C7ux16/T+G4asPc6Q+hFfDg7C7+4fQF/jm+PgVAQKlCgh8pVbWugi0LLC5lu2yC4mB71H4y49/Dw/7/bAzeBF+1am9fBaOdp+EH4cHAt+yrJ5HgEARAgJfEWW0CAJpCNTasq1c4qfANxj9dzg7uBd6/cfh7O31yPfp3b1Hw/8Xfp585k9Lt5LUEwgQKEZA4CumlBZCoD2BZlq2VeubBr73YTwahJ3ezLt84xdh8PDP4fzy4+eTPAS+KlHbCRAoR0DgK6eWVkKgUYHmW7ZVy/sl8IUQv78XettPwvllfJcvnsn7Xfhq0uadntUr8FWJ2k6AQDkCAl85tbQSAo0IPH36NMTLp8QzReNXvDDyRs6yXXv21wPfOFyePwnbvXvh4Ox1CPHdva+++9ziFfjWpjYAAQLZCQh82ZXMhAk0LxAvgHx8fBziBZFjyEvzwsjXA198U+/zZVp2/hKe/Th9dy/aCXzNH0H2SIBA2wICX9sVsH8CiQrElm185y7eymz6bt7dLozc1AJnAt9VsOvNnMAh8DVVEfshQCAdAYEvnVqYCYEkBNJt2VbwTN7Re3jzLhuxlbvzxcyFmAW+CkmbCRAoUEDgK7ColkRgVYE8WraLVjUNcJ8+UxjfjewfnIW3k6d/CK9+GIQfphdhvrrLxi/PdWu1Ra5+T4BASQICX0nVtBYCKwgsatnGd/g80haIodaDAAECqwj4W2MVLc8lUIDAbMs2fkYvflYvBkCPPAQEvjzqZJYEUhIQ+FKqhrkQqElgXss2nnUbf++Rn4DAl1/NzJhA2wICX9sVsH8CNQlo2dYEm8CwAl8CRTAFApkJCHyZFcx0CVQJaNlWCeW/XeDLv4ZWQKBpAYGvaXH7I1CDgJZtDagJDynwJVwcUyOQqIDAl2hhTItAlYCWbZVQudsFvnJra2UE6hIQ+OqSNS6BmgS0bGuCzWhYgS+jYpkqgUQEBL5ECmEaBG4TiC3bk5OTG/eydZbtbWJlbxP4yq6v1RGoQ0Dgq0PVmAQ2IPDu3bvJ9fH29vZu3MvWhZE3gJv5EAJf5gU0fQItCAh8LaDbJYHbBJ4/fx4ODw+vQp4LI9+m1c1tAl83627VBNYREPjW0fNaAhsS0LLdEGRHhhH4OlJoy8xSIHZn4p/R+DGc+H0qD4EvlUqYR+cEtGw7V/KNLVjg2xilgQjUIjAcDiehL3ZoYtcmhYfAl0IVzKFTAvNatvEvB/ey7dRhsNZiBb61+LyYQCMCsXOzv78/CX7xYzptv9sn8DVSdjvpusCilu1oNOo6jfXfQUDguwOalxBoSeD09HRyhYWtra3JiXgtTSMIfG3J22/xAvNatvH/9uJZtm3/n17x+IUvUOArvMCWV5xA7OBMT8aL/w600dFZO/DFv3h8MXAMOAYcA44Bx4BjwDGw3DEQ3+1r+rF24Gt6wvZHIEUBLdsUq1LunOI/qh4ECOQlcL2128b1VP2tkdfxYrYJCWjZJlSMjk1F4OtYwS03a4FUTt4Q+LI+jEy+DQFn2bahbp/XBQS+6xq+J5CuQEqXZxH40j1OzCwhAS3bhIpR+lTGF+H8+4OwHT8f3d8NT55dhPHMmgW+GRA/EkhMIF6BIV6DL/5ZTeUCzAJfYgeJ6aQjEFu28XMW1+9l6yzbdOpT5kx+DudHfwjbj38MF+MQxhc/hsfbfwhH5z/fWK7Ad4PDDwSSEoj/dsQ/o/HfjpQuvSXwJXWYmEwKArFle3x8fHX2efy/NBdGTqEy5c9hPBqEnf7jcPZ2+p7eOLw9exz6O4Mwmv4qhMmxWb6GFRLIV2Bx0PsYLoaPPv/70g/bR8/CZfgQLp79a9jt90Lvi6Nw/rGedQt89bgaNTOBeE2k+Lb79C34eMp8DH2L/9BmtkDTzUDgfRgNHoTeTLgLb8/CQf9BGIzeX63BO3xXFL4hkKfA+KcwfPhl6PUPwvDHfw0Hg3+Gy5pXIvDVDGz4dAW0bNOtTSdnNn4RBjv90D84C2+vA0wCXz/sDF5cfZZP4LsO5HsCOQp8fve+1wv9h8Pw6to7+HWtRuCrS9a4yQpo2SZbmm5PbE6wm4DM+b3A1+1DxeoLEZjzZ7vOlQl8deoaOxmB2ZZt/AdTyzaZ8phIFFj0l/+c3wt8DhkC+QuMXw3Dw/i5vdmPcdS0NIGvJljDti8wr2Ubz5pyL9v2a2MGcwS0dOeg+BWBQgXiZ/gePQoHf9oJvRsnatW3XoGvPlsjtyQwr2UbT8ho42bVLRHYbZYCn07amP0M3+TM3Z6TNrIsqUkTmCvwIbwaHoRHw5/Cx3hmfu9eODgbhfMn/zsMX32Y+4pN/FLg24SiMVoXWNSyjeHPg0AuAi7LkkulzJPAXQQuw/nRduj1dsLB8MWns3Ivn4Wj7X7obT8Ow9GN07XusoNbXyPw3cpjY8oCWrYpV8fc7ibgwst3c/MqAgSqBAS+KiHbkxPQsk2uJCa0SYHxRXj2ZDf0463Vtg/C9+durbZJXmMR6KqAwNfVymew7nj/2ngB5HhG4jfffBP++te/Xl0YeXqWrZZtBoU0xY0LOEt346QGJFC8gMBXfInzXeC33357dXuz+A9c/HKWbb71NPPNCQh8m7M0EoGuCAh8Xal0RuucbdlOw14809aDAAH30nUMECCwuoDAt7qZV9QgEM+yHQ6HN1q219/hi63d2OL1IEBA4HMMECCwuoDAt7qZV2xIYHqW7f7+/lXrdrZlG0PeaDRyDb0NmRumDAEt3TLqaBUEmhQQ+JrUtq+JQAxw8bZm0xMy7t+/H1a5MPKn29HcvBAtWgJdEhD4ulRtayWwGQGBbzOORqkQmNeyjaFv9bNsP92NoNfrh53BizCu2K/NBEoUEPhKrKo1EahXQOCr17fToy/Tsl0ZKF6V/OG/hKM/3WvshtMrz9ELCNQsIPDVDGx4AgUKCHwFFrXtJc22bGPrdpWW7eL5j8Pbs+/CV4P/Cj+fPQ79yf0HXy9+ui0EChUQ+AotrGURqFFA4KsRt0tDz2vZHh4e3qFle4va+EUYfPVdOHs7DuHtWTjo98LsjeZvebVNBIoREPiKKaWFEGhMQOBrjLq8HS1q2Z6enoa4bdOP8ej78PDo2acbTofPn+XrP/4UADe9M+MRSFhA4Eu4OKZGIFEBgS/RwqQ8rUUt23qvk/c6nB08CoPR+yua8WgQdnpfhofDn5y8caXimy4ICHxdqLI1EtisgMC3Wc9iR2ukZXub3ucWbvyH7ldfO4MwcrrubXq2FSYg8BVWUMsh0ICAwNcAcq67aLplu9gptm8fhYOz2RM0PoRXwz+Gfs81+Rbb2VKigMBXYlWtiUC9AgJfvb5Zjt5Oy/YWqsmlWL6f/y7e5J0/1+S7Rc+mAgUEvgKLakkEahYQ+GoGzmX41lu2i6DGr8LZ453FZ+PGM3d3+qHX2wmPz175LN8iR78vSkDgK6qcFkOgEQGBrxHmdHfy9OnTMHsv27rOsl1Z4SrMff7c3uxn9Wa391ymZWVjL8hSQODLsmwmTaBVAYGvVf52dh7Ppr1+L9vphZHrPcu2nbXaK4ESBQS+EqtqTQTqFRD46vVNZvTYso3v3N2/f//qLNeNXxg5mdWaCIGyBQS+sutrdQTqEBD46lBNaMzYso3BLv4DEb/29vYmwa+OCyMntGxTIVC0gMBXdHktjkAtAgJfLaztDqpl266/vROoW0Dgq1vY+ATKExD4Cqmplm0hhbQMAksICHxLIHkKAQI3BAS+Gxz5/TDbso2f0Yuf1YsB0IMAgTIFBL4y62pVBOoUEPjq1K1p7Hkt23jWrbNsawI3LIHEBAS+xApiOgQyEBD4MihSnOKilm18h8+DAIFuCQh83aq31RLYhIDAtwnFGsfQsq0R19AEMhUQ+DItnGkTaFFA4GsRf9GutWwXyfg9AQJRQOBzHBAgsKqAwLeqWE3P17KtCdawBAoUEPgKLKolEahZQOCrGbhqeC3bKiHbCRCYFRD4ZkX8TIBAlYDAVyVUw3Yt2xpQDUmgQwICX4eKbakENiQg8G0IsmqYeCuzeH28eGuz+Jd1/Iq3PHOWbZWc7QQIzAoIfLMifiZAoEpA4KsSWnP78+fPb9zL1oWR1wT1cgIEnLThGCBAYGUBgW9lsuoXxJbtyclJ2NramvzFHHDRgc4AAARBSURBVP/rwsjVbp5BgMByAt7hW87JswgQ+EVA4PvFYq3vtGzX4vNiAgRWEBD4VsDyVAIEJgIC35oHgpbtmoBeToDAygIC38pkXkCg8wIC3x0OgUUt29FodIfRvIQAAQKrCQh8q3l5NgECIQh8Sx4F81q2+/v7k7Ns4zYPAgQINCUg8DUlbT8EyhEQ+CpqOa9lOxwOQ7wzhgcBAgTaEBD42lC3TwJ5Cwh8c+qnZTsHxa8IEEhGQOBLphQmQiAbAYHvc6m0bLM5Zk2UQOcFBL7OHwIACKws0PnAp2W78jHjBQQItCwg8LVcALsnkKFAJwOflm2GR6opEyBwJSDwXVH4hgCBJQU6E/i0bJc8IjyNAIHkBQS+5EtkggSSEyg+8MWWbbytWfwLMn7Fe9k6yza549CECBBYQUDgWwHLUwkQmAgUGfjiJVPivWxjuIt/MU7vZevCyI56AgRKEBD4SqiiNRBoVqCYwBdbtk+fPg17e3tX7+a5MHKzB5O9ESDQjIDA14yzvRAoSSD7wKdlW9LhaC0ECCwjIPAto+Q5BAhcF8gy8GnZXi+h7wkQ6JqAwNe1ilsvgfUFsgl881q2sX0b27hxmwcBAgS6IiDwdaXS1klgcwLJB755Ldt4QoZ72W7uIDASAQJ5CQh8edXLbAmkIJBk4Jtt2ca/3OKlVWL48yBAgEDXBQS+rh8B1k9gdYEkA19s08a/0LRsVy+oVxAgUL6AwFd+ja2QwKYFkgx88TN5WrabLrXxCBAoRUDgK6WS1kGgOYEkA19zy7cnAgQI5Ccg8OVXMzMm0LaAwNd2BeyfAAECKwoIfCuCeToBAkHgcxAQIEAgMwGBL7OCmS6BBAQEvgSKYAoECBBYRUDgW0XLcwkQiAICn+OAAAECmQkIfJkVzHQJJCAg8CVQBFMgQIDAKgIC3ypankuAQBQQ+BwHBAgQyExA4MusYKZLIAEBgS+BIpgCAQIEVhEQ+FbR8lwCBKKAwOc4IECAQGYCAl9mBTNdAgkICHwJFMEUCBAgsIqAwLeKlucSIBAFBD7HAQECBDITEPgyK5jpEkhAQOBLoAimQIAAgVUEBL5VtDyXAIEoIPA5DggQIJCZgMCXWcFMl0ACAgJfAkUwBQIECKwiIPCtouW5BAhEAYHPcUCAAIHMBAS+zApmugQSEBD4EiiCKRAgQGAVAYFvFS3PJUAgCgh8jgMCBAhkJiDwZVYw0yWQgIDAl0ARTIEAAQKrCAh8q2h5LgECUUDgcxwQIEAgMwGBL7OCmS6BBAQEvgSKYAoECBBYRUDgW0XLcwkQiAICn+OAAAECBAgQIFC4gMBXeIEtjwABAgQIECAg8DkGCBAgQIAAAQKFCwh8hRfY8ggQIECAAAECAp9jgAABAgQIECBQuIDAV3iBLY8AAQIECBAgIPA5BggQIECAAAEChQsIfIUX2PIIECBAgAABAv8fzUDIMo7qA/YAAAAASUVORK5CYII="></p>
</div>
<div class="specification">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext></math> is the midpoint of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AC</mtext></math>.</p>
</div>
<div class="specification">
<p>Line <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>2</mn></msub></math> is perpendicular to <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>1</mn></msub></math> and passes through point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext></math>.</p>
</div>
<div class="specification">
<p>The point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>N</mtext><mfenced><mrow><mi>k</mi><mo>,</mo><mo> </mo><mn>4</mn></mrow></mfenced></math> is on <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>2</mn></msub></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the gradient of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>1</mn></msub></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>Find the coordinates of point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></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 the equation of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>2</mn></msub></math>. Give your answer in the form <math xmlns="http://www.w3.org/1998/Math/MathML"><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>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mo> </mo><mi>b</mi><mo>,</mo><mo> </mo><mi>d</mi><mo>∈</mo><mi mathvariant="normal">ℤ</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>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">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the distance between points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>N</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>Given that the length of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AM</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>45</mn></msqrt></math>, find the area of triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ANC</mtext></math>.</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><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mo>-</mo><mfenced><mrow><mo>-</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mo>-</mo><mn>3</mn><mo>-</mo><mfenced><mrow><mo>-</mo><mn>9</mn></mrow></mfenced></mrow></mfrac></math> <strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award<em><strong> (M1)</strong></em> for correct substitution into the gradient formula.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo> </mo><mfenced><mrow><mfrac><mn>3</mn><mn>6</mn></mfrac><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></mfenced></math> <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><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>=</mo><mfrac><mrow><mo>-</mo><mn>9</mn><mo>+</mo><mi>x</mi></mrow><mn>2</mn></mfrac><mo> </mo><mfenced><mrow><mo>-</mo><mn>6</mn><mo>+</mo><mn>9</mn><mo>=</mo><mi>x</mi></mrow></mfenced></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>=</mo><mfrac><mrow><mo>-</mo><mn>1</mn><mo>+</mo><mi>y</mi></mrow><mn>2</mn></mfrac><mo> </mo><mfenced><mrow><mn>4</mn><mo>+</mo><mn>1</mn><mo>=</mo><mi>y</mi></mrow></mfenced></math> <strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award<em><strong> (M1)</strong></em> for correct substitution into the midpoint formula for both coordinates.</p>
<p><strong>OR</strong></p>
<p style="padding-left:60px;"><img src="data:image/png;base64,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"> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for a sketch showing the horizontal displacement from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math> and the vertical displacement is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math> <strong>and</strong> the coordinates at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext></math>.</p>
<p><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>+</mo><mn>6</mn><mo>=</mo><mn>3</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>+</mo><mn>3</mn><mo>=</mo><mn>5</mn></math> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct equations seen.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>3</mn><mo>,</mo><mo> </mo><mn>5</mn></mrow></mfenced></math> <em><strong>(A1)(G1)(G1)</strong></em></p>
<p><strong>Note:</strong> Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>3</mn><mo>,</mo><mo> </mo><mi>y</mi><mo>=</mo><mn>5</mn></math>. Award at most <em><strong>(M1)(A0)</strong></em> or <em><strong>(G1)(G0)</strong></em> if parentheses are missing.</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>gradient of the normal <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>-</mo><mn>2</mn></math> <strong><em>(A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from their gradient from part (a).</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>-</mo><mn>2</mn><mo>=</mo><mo>-</mo><mn>2</mn><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math> <strong>OR</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>=</mo><mo>-</mo><mn>2</mn><mfenced><mrow><mo>-</mo><mn>3</mn></mrow></mfenced><mo>+</mo><mi>c</mi></math> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext></math> and their gradient of normal into straight line formula.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mn>4</mn><mo>=</mo><mn>0</mn></math> (accept integer multiples) <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></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><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mfenced><mi>k</mi></mfenced><mo>+</mo><mn>4</mn><mo>+</mo><mn>4</mn><mo>=</mo><mn>0</mn></math> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>4</mn></math> into their equation of normal line or substitution of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>k</mi><mo>,</mo><mo> </mo><mn>4</mn></mrow></mfenced></math> into equation of gradient of normal.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mo>-</mo><mn>4</mn></math> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><strong>Note:</strong> Follow through from 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><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><msup><mfenced><mrow><mo>-</mo><mn>4</mn><mo>+</mo><mn>3</mn></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mn>4</mn><mo>-</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></msqrt></math> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituting point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext></math> and their <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>N</mtext></math> into distance formula.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>5</mn></msqrt><mo> </mo><mfenced><mrow><mn>2</mn><mo>.</mo><mn>24</mn><mo>,</mo><mo> </mo><mn>2</mn><mo>.</mo><mn>23606</mn><mo>…</mo></mrow></mfenced></math> <strong><em>(A1)</em>(ft)</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><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mfenced><mrow><mn>2</mn><mo>×</mo><msqrt><mn>45</mn></msqrt></mrow></mfenced><mo>×</mo><msqrt><mn>5</mn></msqrt></math> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their correct substitution into area of a triangle formula. Award <em><strong>(M0)</strong></em> for <em><strong>their</strong> </em><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mfenced><msqrt><mn>45</mn></msqrt></mfenced><mo>×</mo><msqrt><mn>5</mn></msqrt></math> without any evidence of multiplication by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> to find length <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AC</mtext></math>. Accept any other correct method to find the area.</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><strong>Note:</strong> Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>.</mo><mn>02637</mn><mo>…</mo></math> from use of a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math> sf value for <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>5</mn></msqrt></math>. Follow through from part (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">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>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = 2\,{\text{sin}}\left( {3x} \right) + 4">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>2</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>sin</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>3</mn>
<mi>x</mi>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>4</mn>
</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>.</p>
</div>
<div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right) = 5f\left( {2x} \right)">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>5</mn>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mi>x</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
</div>
<div class="specification">
<p>The function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> can be written in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right) = 10\,{\text{sin}}\left( {bx} \right) + c">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>10</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>sin</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>b</mi>
<mi>x</mi>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>c</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The range of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span> ≤ <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> ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m"> <mi>m</mi> </math></span>. Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m"> <mi>m</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>Find the range of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g"> <mi>g</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>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b"> <mi>b</mi> </math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c"> <mi>c</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the period of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g"> <mi>g</mi> </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>The equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right) = 12"> <mi>g</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>12</mn> </math></span> has two solutions where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi "> <mi>π</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="{\frac{{4\pi }}{3}}"> <mrow> <mfrac> <mrow> <mn>4</mn> <mi>π</mi> </mrow> <mn>3</mn> </mfrac> </mrow> </math></span>. Find both solutions.</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>valid attempt to find range <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <img src="data:image/png;base64,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">, max = 6 min = 2,</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\,{\text{sin}}\left( {3 \times \frac{\pi }{6}} \right) + 4"> <mn>2</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>sin</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mn>3</mn> <mo>×</mo> <mfrac> <mi>π</mi> <mn>6</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mn>4</mn> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\,{\text{sin}}\left( {3 \times \frac{\pi }{2}} \right) + 4"> <mn>2</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>sin</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mn>3</mn> <mo>×</mo> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mn>4</mn> </math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\left( 1 \right) + 4"> <mn>2</mn> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>+</mo> <mn>4</mn> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\left( { - 1} \right) + 4"> <mn>2</mn> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mn>4</mn> </math></span>,</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 2"> <mi>k</mi> <mo>=</mo> <mn>2</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m = 6"> <mi>m</mi> <mo>=</mo> <mn>6</mn> </math></span> <em><strong> A1A1 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>10 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y"> <mi>y</mi> </math></span> ≤ 30 <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>evidence of substitution (may be seen in part (b)) <em><strong>(M1)</strong></em></p>
<p>eg <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="5\left( {2\,{\text{sin}}\left( {{\text{3}}\left( {2x} \right)} \right) + 4} \right)"> <mn>5</mn> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>sin</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mrow> <mtext>3</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mi>x</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mn>4</mn> </mrow> <mo>)</mo> </mrow> </math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{3}}\left( {2x} \right)}"> <mrow> <mrow> <mtext>3</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mi>x</mi> </mrow> <mo>)</mo> </mrow> </mrow> </math></span> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b = 6"> <mi>b</mi> <mo>=</mo> <mn>6</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c = 20"> <mi>c</mi> <mo>=</mo> <mn>20</mn> </math></span> (accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="10\,{\text{sin}}\left( {6x} \right) + 20"> <mn>10</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>sin</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mn>6</mn> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mn>20</mn> </math></span> ) <em><strong>A1A1 N3</strong></em></p>
<p><strong>Note:</strong> If no working shown, award <em><strong>N2</strong></em> for one correct value.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct working <em><strong>(A1)</strong></em></p>
<p><em>eg </em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2\pi }}{b}"> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> </mrow> <mi>b</mi> </mfrac> </math></span></p>
<p>1.04719</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2\pi }}{6}\,\,\,\left( { = \frac{\pi }{3}} \right)"> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> </mrow> <mn>6</mn> </mfrac> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mo>=</mo> <mfrac> <mi>π</mi> <mn>3</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </math></span>, 1.05 <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg </em> <img src="data:image/png;base64,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">, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{si}}{{\text{n}}^{ - 1}}\left( { - \frac{8}{{10}}} \right){\text{, }}6x = - 0.927{\text{, }} - 0.154549{\text{, }}x = 0.678147"> <mrow> <mtext>si</mtext> </mrow> <mrow> <msup> <mrow> <mtext>n</mtext> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mfrac> <mn>8</mn> <mrow> <mn>10</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow> <mtext>, </mtext> </mrow> <mn>6</mn> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mn>0.927</mn> <mrow> <mtext>, </mtext> </mrow> <mo>−</mo> <mn>0.154549</mn> <mrow> <mtext>, </mtext> </mrow> <mi>x</mi> <mo>=</mo> <mn>0.678147</mn> </math></span></p>
<p><strong>Note:</strong> Award <em><strong>M1</strong></em> for any correct value for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6x"> <mn>6</mn> <mi>x</mi> </math></span> which lies outside the domain of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span>.</p>
<p>3.81974, 4.03424</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 3.82"> <mi>x</mi> <mo>=</mo> <mn>3.82</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 4.03"> <mi>x</mi> <mo>=</mo> <mn>4.03</mn> </math></span> (do not accept answers in degrees) <em><strong>A1A1 N3</strong></em></p>
<p><em><strong>[3 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.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 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>The diagram below shows a circular clockface with centre <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math>. The clock’s minute hand has a length of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mtext>cm</mtext></math>. The clock’s hour hand has a length of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo> </mo><mtext>cm</mtext></math>.</p>
<p>At <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>:</mo><mn>00</mn></math> pm the endpoint of the minute hand is at point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and the endpoint of the hour hand is at point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
<p> </p>
</div>
<div class="specification">
<p>Between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>:</mo><mn>00</mn></math> pm and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>:</mo><mn>13</mn></math> pm, the endpoint of the <strong>minute hand</strong> rotates through an angle, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math>, from point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> to point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math>. This is illustrated in the diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>A <strong>second</strong> clock is illustrated in the diagram below. The clock face has radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mtext>cm</mtext></math> with minute and hour hands both of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mtext>cm</mtext></math>. The time shown is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>:</mo><mn>00</mn></math> am. The bottom of the clock face is located <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo> </mo><mtext>cm</mtext></math> above a horizontal bookshelf.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>The height, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> centimetres, of the endpoint of the minute hand above the bookshelf is modelled by the function</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>θ</mi></mfenced><mo>=</mo><mn>10</mn><mo> </mo><mi>cos</mi><mo> </mo><mi>θ</mi><mo>+</mo><mn>13</mn><mo>,</mo><mo> </mo><mi>θ</mi><mo>≥</mo><mn>0</mn><mo>,</mo></math></p>
<p>where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math> is the angle rotated by the minute hand from <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>:</mo><mn>00</mn></math> am.</p>
</div>
<div class="specification">
<p>The height, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math> centimetres, of the endpoint of the <strong>hour hand</strong> above the bookshelf is modelled by the function</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mi>θ</mi></mfenced><mo>=</mo><mo>-</mo><mn>10</mn><mo> </mo><mi>cos</mi><mfenced><mfrac><mi>θ</mi><mn>12</mn></mfrac></mfenced><mo>+</mo><mn>13</mn><mo>,</mo><mo> </mo><mi>θ</mi><mo>≥</mo><mn>0</mn><mo>,</mo></math></p>
<p>where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math> is the angle in degrees rotated by the minute hand from <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>:</mo><mn>00</mn></math> am.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the size of angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mtext>O</mtext><mo>^</mo></mover><mtext>B</mtext></math> in degrees.</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 distance between points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></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 the size of angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math> in degrees.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the length of arc <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AC</mtext></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>Calculate the area of the shaded sector, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AOC</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>Write down the height of the endpoint of the minute hand above the bookshelf at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>:</mo><mn>00</mn></math> am.</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>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>=</mo><mn>160</mn><mo>°</mo></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>Write down the amplitude of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>θ</mi><mo>)</mo></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">h.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The endpoints of the minute hand and hour hand meet when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>=</mo><mi>k</mi></math>.</p>
<p>Find the smallest possible 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">i.</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"><mn>4</mn><mo>×</mo><mfrac><mrow><mn>360</mn><mo>°</mo></mrow><mn>12</mn></mfrac></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>×</mo><mn>30</mn><mo>°</mo></math> <em><strong>(M1)</strong></em></p>
<p><em><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>120</mn><mo>°</mo></math> A1</strong></em></p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>substitution in cosine rule <em><strong>(M1)</strong></em></p>
<p><em><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>AB</mtext><mn>2</mn></msup><mo>=</mo><msup><mn>10</mn><mn>2</mn></msup><mo>+</mo><msup><mn>6</mn><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>×</mo><mn>10</mn><mo>×</mo><mn>6</mn><mo>×</mo><mi>cos</mi><mfenced><mrow><mn>120</mn><mo>°</mo></mrow></mfenced></math> (A1)</strong></em></p>
<p><em><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext><mo>=</mo><mn>14</mn></math> </strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>cm</mtext></math><em><strong> A1</strong></em></p>
<p><br><strong>Note:</strong> Follow through marks in part (b) are contingent on working seen.</p>
<p><em><strong><br>[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>θ</mi><mo>=</mo><mn>13</mn><mo>×</mo><mn>6</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>78</mn><mo>°</mo></math><em><strong> A1</strong></em></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>substitution into the formula for arc length <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mfrac><mn>78</mn><mn>360</mn></mfrac><mo>×</mo><mn>2</mn><mo>×</mo><mi mathvariant="normal">π</mi><mo>×</mo><mn>10</mn></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mfrac><mrow><mn>13</mn><mi mathvariant="normal">π</mi></mrow><mn>30</mn></mfrac><mo>×</mo><mn>10</mn></math></p>
<p><em><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>13</mn><mo>.</mo><mn>6</mn><mo> </mo><mtext>cm</mtext><mo> </mo><mo> </mo><mfenced><mrow><mn>13</mn><mo>.</mo><mn>6135</mn><mo>…</mo><mo>,</mo><mo> </mo><mn>4</mn><mo>.</mo><mn>33</mn><mi mathvariant="normal">π</mi><mo>,</mo><mo> </mo><mfrac><mrow><mn>13</mn><mi mathvariant="normal">π</mi></mrow><mn>3</mn></mfrac></mrow></mfenced></math> A1</strong></em></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>substitution into the area of a sector <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfrac><mn>78</mn><mn>360</mn></mfrac><mo>×</mo><mi mathvariant="normal">π</mi><mo>×</mo><msup><mn>10</mn><mn>2</mn></msup></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mfrac><mrow><mn>13</mn><mi mathvariant="normal">π</mi></mrow><mn>30</mn></mfrac><mo>×</mo><msup><mn>10</mn><mn>2</mn></msup></math></p>
<p><em><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>68</mn><mo>.</mo><mn>1</mn><mo> </mo><msup><mtext>cm</mtext><mn>2</mn></msup><mo> </mo><mo> </mo><mfenced><mrow><mn>68</mn><mo>.</mo><mn>0678</mn><mo>…</mo><mo>,</mo><mo> </mo><mn>21</mn><mo>.</mo><mn>7</mn><mi mathvariant="normal">π</mi><mo>,</mo><mo> </mo><mfrac><mrow><mn>65</mn><mi mathvariant="normal">π</mi></mrow><mn>3</mn></mfrac></mrow></mfenced></math> A1</strong></em></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"><mn>23</mn></math><em><strong> A1</strong></em></p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution<em><strong> (M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>10</mn><mo> </mo><mi>cos</mi><mfenced><mrow><mn>160</mn><mo>°</mo></mrow></mfenced><mo>+</mo><mn>13</mn></math></p>
<p><em><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>3</mn><mo>.</mo><mn>60</mn><mo> </mo><mtext>cm</mtext><mo> </mo><mo> </mo><mfenced><mrow><mn>3</mn><mo>.</mo><mn>60307</mn><mo>…</mo></mrow></mfenced></math> A1</strong></em></p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math><em><strong> A1</strong></em></p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">h.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>×</mo><mi>cos</mi><mfenced><mi>θ</mi></mfenced><mo>+</mo><mn>13</mn><mo>=</mo><mo>-</mo><mn>10</mn><mo>×</mo><mi>cos</mi><mfenced><mfrac><mi>θ</mi><mn>12</mn></mfrac></mfenced><mo>+</mo><mn>13</mn></math> <em><strong>(M1)</strong></em></p>
<p><br><strong>OR</strong></p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALIAAAB2CAYAAABs88nKAAAgAElEQVR4Ae19aZhV1Zlu8uT+uDd9//Wfvn3TnTi0SYyKCBFURGMLOEbBCQVFUFCEGHFoFcVWFNNRUVDAARwQcIIqUAaBiKIgUyEto4CMVafm6dTZ8/j2835rn6pTBYGa61TV3rg8u87Ze6+1vvXub33T+tZPEB8xBboABX7SBfoQdyGmAGIgxyDoEhSIgdwlhjHuRD0gF+UXgqXwaLoUoSi/OC4xDbIAAwqbaYzyM/M4LpDTFxcS1PlFcYlpkAUYaAaQ9+/Zh5yPF2Huu3Oxc8dOlJeVo7w8LjEN2h8DZaVlKCspQ2F+QqSFNJM9KUcuSRRj1fKVmPgfj2PZ0mUoKCiA4zhwXTcuMQ06BAO6riPRNCAXoaSwBLmLcvHs5GfhOi5830cYhpniSHweU6DdKEDs2baNxFFyZOpsdSWzEQ1kZAK5FDk5uXjuuecyr4vPYwp0CAWOBXKd8SGzQTGQM6kRn2cdBWIgZ92QxA1qDgViIDeHavE9WUeBZgI5gdJEORbnLMSzz05GGDhAGCAIAgRhAD90leIXBkAAIPABsMRHTIFGUoCGgyAUXBFbCD0EIQ0KqhBnHjEXugBxF4SwTRNFR5pgfisoKER5IoElCz/DhIfmYM/+EHt/9JBIQFkvAlbqSsVB6Kj2xBaNRo5gfJlQgAYwMkGCGF4EaIKbzJHAdWFbHhIFHvbtD/DDjwEO7ddQkn+08XbkwoJClCWK8VluAr89fT/O7mGgR48Urr5Cx/sfmMjJNXH4kAePYA48hOTIwpXjQYop0EgKkPEJJw5BZuiHPgLfh2n6+H67hcW5Fma9ZuCaqwycc3YKZ/eowtAby1BWXBWFT9Rx5swaG1gtilFSWIjc3M3449VfYMpzKUx80sAl/Q307Z/Er36tY9gtOhYv17B7jwOfogdfrPiIKdBoClCcUL4JL3SgWS527THw6vQkbrrRwIUXV2PAFSk88GAKkyfreObZGrz+RiWKEyWN58hF+QllR164EM8/OwVh6MCxQmz/zsS2rTaW5GgYdoeGC/paGHiZhVkzUqhKuvBdTgtsXICQMo/8U58QX0rsUGn0OHexC0OlTEXgpewbwg89eE6A3TtdjLvbxHVXaXj8MQsffqhjS56FPT9Y0HRiKUQYhHAsG4UiI9c5Q+gYyTwacOT6DhEFTPVACt2+G6I0YeBva0yc36sKv/k3DZdeWo2/felA00I4joswCMDGizxP/IoMHSuEmUTvVuciD0eKXBDC82wUFYZ4+y0DA/9QjYGDqvH+Ag2llQ58j+IqRY46vDTTatEQyGHEZQlmFl8q8TwXu/f4+OhjC7fdnsLF/VK4/0865i8wkdJo2aDsrAT6EOxEtxq6uLMZFCBjI1cLvQC252L9Bg/jxtVg2PAavPqqiaNHXJhmgMD3EPrkwIprCzcmRz7GRd0cz55wVAKyrsjbErLSAI4LlFYEeOstG5cPSqLnOQ4WLjZguA5CMZ+ECOHGYnTGwHa3U5/mWYqbToBdPxgYOyaFue96KKsKYNsErWKSVADJLH0Y8GnNiI7WAXKtfENNU4GZlQXwRM4RE5xvw3N95BdbGDlKQ/9LbHySY0EzPZGXQ9gxkNOj0g0/yWXLKhx8uc7EhHEO3p6jw7I9MbMJloTrKnuymsUJ/LopvJWAfHLKiwRBLTQIkF/o4J6RNTjjLA33j2foXQg/CMS6IVOF2A35Qlgnf3B8RaejgIwxOauICPQ3hDCMEE9OTGLQwBq8v6AGNSm3Sf1qRyBzSiDHVs6Sg4c93D48iVNO0XDHiEoxbFNJFBlb5CUCue6Na1Kv4ouzmwJikQjg0s/gO6hJhnh1ZhX+PN7Fss9NmLaJ0KsTGxrTmQ4AMi0WSlgvrvSx6m8BzjvPwNVXV2Dffht+oCwaIvjHbu3GjGHnu4bcWJQ1C9WVLl54ycDYsTXY/aMHVxxoyu3clI61G5CV7EyljjJxJLCHLnzHwboNBi7so+OO2zUcyPfgSewGuXOdeaUpnYqvzW4KyMQc2NBSAd5408Sf7k/i4BEbnk+A07RG5a4dRYvcKLCeb0O6/F0Sih6o7MaUl5XVjdMLTS4uNm7w0PPsJEbeaWI3ObPHTtUpj+pFoLAfixt/l8bZ+gPHTIYucoYFHsrKPMycYWHMvSns3W3TiaeUfgI4ck03pTst4siLcxfjyiuvxOOPP45du3ZJ9FtTKhdvCMWM0IVte/jiby569y7DzUNNJAoc+D6DRdixdNBIfU21SXXFF3ccBQhM2n8D5V8wDB+vvFyDRx7TsGMXZ+goWrIFLWwRkHNzczF27Fh89dVXKCsrazqQBaDqLQ1CcmEfG7c5+H1vA7fdWoXqanJkOk3UJwUTOk7io3NRgCALYAABxcYA02ZouGuUiz2HAniRvsRrWnK0CMgtXbMnsjIijitTT4DACzD1lSROOcPCRx/r0E3K0140NfGjabJTS4gT39s6FCDz8cmCvABb8hzccrOOWW9Y0A0OOmPZyZwobDb/6FAgB/T8ieSfBirfWB9FFS7G35vCWedYeP9dD7oVabG1gRnN73B8Z/tTQBwagYOdP7gYf4+G3CUGTMtF6DJeIgpVaBlDbiUXdWvRJs15Ax8llTYeerAG/fpY+HItubJyppAo8ZHFFCAgKQmGDIdX8Y0cO8MK8PAEC1Nf0uH5LUTtcbrfoRy5YXtETAodMcFwuVTedx4uvMDCjTcYKEg4spyFAdbxkcUUkBk2bcUioAMYZoCZs0xcNSiJ/QfaJjgsu4CsbDTRcpYQtuVj9hwLZ55p48mnDVRVp23QilBZPJzdt2lpUyx1mcCD4wb4OMfAoMt0fLHGg+/Z8FqfIWepaBGtDGBEnKHbmPu+hX79Tbz0Ai0b6be9DajRfeHXej2n/kaHBuihdbF2nYfrrzewYpUNx2a0IyPXmuZ+bkzjsoojK+FK6a/Ucxm6FwQ+bCPAww/7+H1vE9u+t2rjMcSpEuO5MePchtc0cFpxYUXgw6fTo8TBhIcdjB2jo7DYkuAg8di1gXSYZUA+lt6y5MUPsWKlg4svTWL47SkUFlHOUgsSZWHrsbfF37QbBTKBrJxbXGNH5jPjNQd/uKwCe7ZzvCzlqRVza+tzn6wHMhvI6YhLv9+bb+Of/8nAhws9SZwIar+0Q8ZHx1FAMMn/cX5UMTRc5XHwYIDBt1Rh2VKC2BbGoyxOMo+2enuzH8iyBMoHQVtW6WPCQxp6/DaJz5ZYME1DRI9Wp0r8wMZTQIAcmUfDUBZP7NpjY9TIasx504auE8gMLeAjVSIfdd74KhpzZdYDmXIyPT9eyNUmPgoTBu6+uwpnnaljxUofrtsGAldjKBdfoygQcWSZOQPgwD4H199QjZmzXGhJmkyjsFxZypSOMZebWpWCWQ9kNpDWderBPGe8ckVliIGXaxhzn4niYhc+xY90mgGRwVqVRvHDTkCBdBorpnnQDA9vvKnh7rtNHEkoBxaXuckYimm1GwO5IQ1p1mHClzdmmeh5roVp02340bIZZYZWwG94X/x321CAYQZMYUX594u1DgZfW4Mv13pwoxgKWTTaFrJEg+5kPUdu0F7RKZiKK1kdYPQ9Ls49z8LK5SpyjmvAaOWQXGHH3Bh/0RYUIIBD38P+QxZuvbUGk54yUV2tVgFRJBSOLYpgW9Re98xOB2TClIZ2eojyvrdx4YUarhzgYMdONYUpESSOx6gb4rY9o0WiotzFY4+aGH23jeIyX+X7k1ADzo52pOi1dTsabr3QnLwWbdvGek8nULmCgFOW5Xj46BMTZ53j4LXXXKR0RlKpaa7uJkI/BnYdPVpwpriIyLzUWiQ63A3w5VcmbrjBxsJcU+JkxJEl45BeFMEb2/bodBxZQCm2ZZp1PNRUhpg82cEZp6ewMY8Khi0gr2MDtGrEMcytAiMBslq+r8DqI5UMce1VKfz1BQYHtXylR3Pb2QmBnF7/RUcJxQkf+3f4uGxgCvfclxLzjyggwoUjTtz2DKG59O9U98kKnchBxXgKroCe8WYKY8ZY2JynS042hox3xNFCIOdgypQpssSJD2Jp+4PG9cjALvUFsAwfK5Za+N1ZLmbMcRE4qi1iiJfg2LZvVXeogUCmMs1FwX5oYOO3Ps7vVY5lK60oDzYFv9YPCGoMbVsE5CWLl6Bfv34YPnw48vLyJFt9Yypt0TWRXVkit2WqI1Ed6Ckfg6+rwb8PSGHrVldhXWKXuXC1PV6wFvWqU9wckVsYVkGJj4cmGLISujpJkY6Jd2xZ0tQRnWkRkJkOYOLEiSguLoZltVN6K6EmSZUGJ7mEg8APcOCIg2uuDnDdDZUoq2TeMK4UI4HT13YEibtOnSRjEFqwTB+vztZw6xADhw8yTIAKtieJKDuK1C0CcksXn7bWECtLhg/TcfHyNAen/8rG088YSBm67MET0McfHy2mAC1CTLz92acmBlxqY9EiTXJhE0RkGEoRb3E1zXpA1wCycGmV/Lmo1Mf4sRZ6nG1i+25OeWkXabPoE98UUUDAGgaorvBwx3AfT0w04UlUWx03joHcQriQyJIrjpnOQw+7frBx3TU27hljoKqKXqaOUUBa2K2suV3oy9aEwP4DIYYM0ZCXpxKuqG3naOKkhYilY8S4LsGRVSYiYpmLaDxYjo8ln3rodZ6JHbvUbkBZg4pO2hACxXMDPPJQBf7ygg3bjYAss2EavwRyx0Qjdg0gNwRHGKKwwMWll1i44koNiXxfbWLJJTjREvXY2deQaMf5WzJBqRx8hhFg2TIdN95oYMMmrnQnTbNnpuuyQHZ9D489pOMXv3Dw4QfMsOAAzPYoG1kyBiBylhxn/OKvIgowEbdEt4XYts3BJRfr+GihDzdaAMyow2w5uiSQ6QihmFFYFOLyQSmMvsvE3n0qwJseqZCgzp4xyBYsHNMOBmfRtFlZGWD6KyZGjuW+iaQjlWi1fdgxN3XQF10SyMpZ4sJ1XWz4xsXVV9qY+LgJ3SKHUStOJDFiBxG9s1QrOocbYOUaD1cONLH2G0u2yFCpztQq92zpS5cEsooJoBjho6o6wKMPu/jFL3TMnZeC59PrpzKm12rZ9RSWbBma9m4Hg7AY05amCjctd7Frp4mL+2t4caojGYO4j6K4qSW6rWMsFMejTJcFMqOzuGDVCwzsO2Rj2O0erhxgYu8BB6HPQTNqh0wsRmkwH49K3eA7iaOQWArSRtmGmQn16Uc9jBlZgYoqV+iZraTookAmV4nyKksq/xCfr9Bx9m90THrSQ1WVkvHYeZb4SHNhprlSNnluTJSzyMeIO1PYv4emNgK5Y0xrjRmfLgpk8hc1VRKn5DCuF+DFF0388v9pWLzUgeuS66SBTDBzUu2+oJYJSTKeqgW+e/Z6uKx/Bd54K4Dt2JIGi2Gz2Xp0SSArZU+tvKbdmIXevaNHXfS/1MUll9pYt7ZSAo0UR+Ywktt0YyALktVMdTjfwfh7TLww3URpARf7KotPNmdC7ZpAPg7boPE+cDxs+t5Av4ssTHneRkWNI6GHypLRvTmykih8WI4rCQf/eJWDLeu42kbFsNTu43Ic2mbDV90GyAw/JGANy8czz+g4r2eA9z+gh6pOC+/Occu08FAB5iLewdd4eHeuBtfhd4znTm9GlA2QPX4buhGQ6VLl1Onh4BEfQ4e7GHydgYMHmcFITZ3dEchKtKIe4UPTHfzlOQs3Ddawd2+0kFd23crUJ44PpI7+ttsAWfwgssd1AE338NFCA7/vYWDikxbKKxVnporYXQ/HcbH4Ux8DLk5h4wYuVIj030jioj+UJVuPFgI5B0899RSSySQcJ9vjfunRo5WCFqYQhunjqadMnPIrF6u+sOD56fy9Sj1UcnO2DlvL28X+SaqxyFJxKOHipiEa3n7HFCU4oJ1dcKuWimU3jDm0LchrsXjxEvTq1QsDBgzAt99+2/R99lo+Hs1/QggUlNj44+Bq9O2t4RC1c9nwnTJzoKxxsJv//Cy/k6Y0le7Kh2mHGD9Ww8SJBkor1U5bQoMs70Nm81oEZC51euyxx1BQUADTNDuVc0E4kh9g2SoTvXoa+M8pBgqLKBdSS4+2S+vC+TCUNcKHrgX4ZKGF4TdZWLPWhulSwWOwEGWKznO0GMjPPfdc5+ltRkvZcQLW8UNMnGjj1H+xMG++oTZ0F7mQCk7GDV3slEANQxNb/9vGZX11LGTydNkFgJGBnS8RZDcGslpRQu5TVu7gqis03HG7ie170lMuB7OLoTejO1y6X5108fxfTYwfp2O/hLmSG0fRgVnsxcvoRu1ptwUyE4kwTJEB9tTYv1prYtAgC88+7cH16ZLNduW1dgxPeiIKLpza1TGypW7gY8duF3/4dwNr1uidfp1BtwUyma3kuxAFz0V5jYeHHzTxuzNq8HGOCc+jbfmkGOkUFxC4KvSSVhsfTL9bWO7izjtTeP55G1WpaCvlTtGb4zeyWwNZRd+S8wZwQw97f3Rx000BrrnGRqKspjaoiETqzIfseSdvrlrh5Tgepk1zMPhGWyWyYVRbRyVtayXCdlsgi/zLwY0KOZXvB8jNsdDjTBsz37TgutyNKB0h10oU74DHqEhA9tWRYPlvNhi47eYkVq624QVpmbgDGtaKVXZfIEvYJtM80YXFPL60HfsiUjz9Fw3n9bCwcyc3c1GriGtXnXQGDVBmEOUAYnOp0DKmhFaaIiZYuc3D5P+0UFNFPYGmRpodWxFVHfCobgzkY6ktiyr9ALt/9NGvj45ht+nYvtOReHLal6kckmBZf0gb+XIqMxpFJ+bBKyux8dcXDDz6iIYfdvuw/Ug2DhlQn/W9OmEDYyBnkEcUIUbDuT6Wf+bhjNNMjL3XQmEZbau0cBAcGTdk7WlkBxaxiZnxbDhGiDdmOxgz2kTiqMrvwf+r6LbOb2qMgZwJRgnpVLZUyzbx2VIHvc81MXW6LYFGAvTOgGThxCr+gAPsuS7Wb2KyGh2rl3oIJF8FX0wCOFre1Cle0MzBqn8eAzmDHkpepHLHqThASULHXSMt/NvpLhZ+4sN0XclTlHFLdp4KJ2Y/6G4Hdmz3cc1VFp55qkrECYoZtTHG4sWknsDSeY8YyBljp9LTqmmWhCHn+u47D7feouOyS3UsXW7BsVU+B8rT3F8uG2MSZOYQmd7D9h0e/jxew7NTNFQn2V7OOAQyrRhpkYJo7txCcgzkDCA3POU4+6GNvYddjB7jYNDlBiqqyK0V1+bv2Wh/FS+zvIgunp6kYehQC4UVpmyPwPYKkBt2tpP/HQP5BAMoDCvk4ssQ78+zccZpOh76Dx0pzZSl8YxXkN0dTvCM9vqJA1lXLNiuj3kfm7jich3LllpwZV8V7nmnHEDt1a72qicG8okozZmXcmbooibpSXRc/34m/nyfjqP55HBq+dSJHtFev3EgefCzWnMlQH7kGA3fbLDg2WnFjuIQL8qeLJqtRZ+WAXlRDhjGmSZiazUqa54jQObYc1lJANsKsWSJg9/+WsOou3WUlDoIMvNjCFds5wVBIubyZVMg5oLRWa+bGHi5jW83JAW0slYRpnL+iJWicyt2x8NHi4C8aNGirg3kBhQjsZI1Ht55x8N5PXQ8+ICOomLl/ZON3ZnVqL2dJoJgla/YNF3MftPEHXfqWLXagePSm8e4464H3AZDI8zUtm0kjiZQlF+EovwmbOGbBrLa1UdNbQ0r6Cp/E8QstFJoNR5yljjofZ6Ju+5KojLJ31S6AbqC29UAQCAHHmwnxIzXdAwdZmLDBh8O5fdIsYuBXIfCn9SdQhBfUlgKbk/2yCOPYPv27bIAlQPd5Q+a3BBCMzy897aNnr1MjBppoLTIQ+jTjU0O2H6mLNZnaBZmv2Pi2iEprP3KhMMUVyLbZ38+itbCC7HXbI5MIN96662YOXMmDh482HVl5QxqSwyzBBL5YLbK994x0ad3EhMetFFUphwp7flC226I9+Z5uO0WDevWmXD8KLWBssFFbvWuz2BaBOScnBxMnjxZEmpTvOgOh6hykWIlaQU0H7k5Ls7pkZS4jEQizQ253J4cmhe3gDaizCmFUz1PcXzKvn7gyMLRGwbX4OtvLHgOnTUqEIgDKwW0rNAgrpwhtCOnl+RJ06QvkW+kwblcx6ZLIB2fx943+Bc9RLyhkl+5we8Nr+ffvC4t9oDtZZ+i9tb7ZEQiM+OHCP0oG6gvxn2V4paY88g8lInUME0kjiRQdJQycp2cnInL44oW2bJhZGZD2+uchOfBQUjqFubMtnHGKTYenJCCYTiRB1gNRLPNXVIFwePKhowy2FyC5Qc4eMjAzJkpDLvZwKqVKpVByL09GEchWyMwq5IqHl+kdOx8wKelRQ4i9O8X/kSspLEjsfdsU0ZhFhD+54UMhk2Dvd4lmZfLOVVPj+AURTRUN0tcdF1bSFdHABzAqyiDtXQ1zJUrYH2+vLYYK1fAXLES1ufLYKxaAX3tFygVENcpelT6Mo8YyJnUyDgXPAcBkjUuPl5k4uJ+Ju4cYWLBAhMpnQE6jAVW4Z9p8GfcfsJTtYJFWR3SoKystvHWHBPXX2/gumsNLF1uw/JMtfe27AfN6xtwWAEMObLKc0flkJL+yf6llUXpg+cj8AJZfMAFCLWFOoO8QAE8S4NVVQqrsuKExa4oh7VmDYz7H4B15wgYo+6GMeoumKNG1S8j1d/WLTcjdcGFMPpeCKNPZukLs09v6H37wvp9P1SPGYPKREk9i0UM5BNCrO5HxSXJlwI4NpP/meh9noZT/7+OJycZyC/xZLN5uS7i4nV3n/gsfQ+nVtsDqmoCLPjAx/k9K/HY4zoKCmy4pgoxJZcW9imcrT6S+RyPscfVlQiqKxBUVwONKH5VNYIDPyLM24Rw8yYEW7Yg2JJXr/h53yLcvBXBd1tgT5+Kqp7nI9mz50nKuajpeS60PhdA73sR9Av7QL/gAhgEa1T0C/pB79MfxgXnIzlsOMz9u6H/eAD6gYO1RTtwENqBwzD4/Y8HkDx0GPn5JShswJUzqVyPIxfmF6E0UYacRYsxhQ6RYyaPjLknS38TSS5iXTKDN7PJSjZUIKLcx1Rc274PJMbhootqcM9oC2u/NpAo1KBT5JDp98RTr9BT5EjO/CGOFrr46BMLTzxSjQcuWIvvZm1E6edfw1r/Nez138Ba/w3sb9fBXr8O9roNsNevr1cs/r1qOawJE2Dfdy+M8eNh3jfupMUdOw760NtQOeQGlA8egnJ+NigVgwejfMh1KB0yGMkHHoQ1axbMGTNOWIwZs2AvW4Hw6GGgqAR+cSmC4iKEx5Ri+Q7llfDSsnKGDC0WooB6gSNhBJZlopAyssjHjZCRC/NLUFxYio9zc/Ffk59ieLaYpCjNdZoiMhplSg+BoSPQkgi1VKsUT6+Cl6rG3Nk1+OU/l+CW0z/Hs7fNxZaX5sOYtwDG/HnQ5s+HPv+DjMK/50Kb9wG0eR/Jdal5H0CftwAr730Xt//DHNz9v2Zgxz/2hXXaKTBPPRX6af8K7bTToZ/2q5OUX0L/9W9QeevNqLrjdtQMuw3J4XecvIwYAWvO2wiP5iMoKUVQVCyAI+hqS2kCYVEhwuJiBDVVCHxbbdHABa0nKqJJRvJ2Jsts5jlnnSab3wjkkkQZ1uR8ivdHj4O16gtYK1d1umJ/vhL6nNlIPfIojPvugzZ+HFJ/Gt/ioo+7H9p4Pu9PyDllDPJOvQFTL3oCa3rfgq//79VY/rNBWP3TgVj100G1ZfVPr8Dqnw7Cip9diuU/G4jV//sypPpfC3vg5bAGDoQ5YBDy+tyAIxOnIDXzXWgzZyE1azb0ma/LOf/+eyU181WYs9+FoyfFOkDrx4mUvPRvSi5XO2ARKJSx0+JO+lMYV/S9RNbRKtKIQkGez2itg89qMpBLjxSjIFGGI58uxqHf/hrJHuegukfPTleS5/SCcc0QmNOnoWb+fGjvvQ/9vbktLtrc95Au9rvzoH21FtMmLcWGDzdg62eHMKT3Npz1f/4bZ/58a2353c+34qyff4ezfr4VN/fajYXTd6Nmz36YBw7C3b8P3r7v8fxzn2P16n3wGMFGs1NktoosZOJQPO55CG6RKYtPZWmTr0xwZIonKspaQROiypVMgKZBXvsZxWSLiz6aj4/bhijiOf1bWpLrUCAn8hMoSpRj5aIleHfsGDibNsDduKlTFWfjRjgbN8HbtRdeqgaB5SC0WewWF98xEVg2PCclz/U9G9NeWYcd2/LheDZ+2GNh02Ybm7dkFgubtrA42PODi2SNSk/AQHgmIvcCH6/N2oQ33vwOQWDLxo0qroM88cT/CDKHkXoRpxTTV3198FhLh4Bc2XCpbIrFQ0AbnUff0eyWtoakP4+xmjSoi+8DTXAEdWvx5GZx5IQoe6XIWZgrQUOt1prWej0b85w0SxAiK/vnyVSwRv8uttlo6owM/9NeWY/vtx9RzoiIi9UfcMXt1HSr7KlyzmdB7XWyPe8oXn99qzgHPDCuOArPPIlCLcpjpCzxUqm3vjn4uE+Q/qbpJDeyXekHqE8BY+13kR34JPTnI9Mg7lAgUytkrEV3doicZKzq/xyGmD5tHbZvPypACBnQ06gRJDAU4mgd2bMjgTfe3CQrumVDc3kIIREfzeLIMZCbCBwC+eU8bP++IAIyuWljnhHxrcjCsntHPt58PU88YpSPaTdWTpPGPKtrXxMDuT3GNwzx6rRvsP17cmRiWcm0J61a0K72vuNC2MMHi7D0052i6PniZqaHLj5IgRjI7YADErlaU3vYUdsXIDeGI4tYoYJqZFmVz2TcBgKPsRWMbGB6gsY8qB062cFVxEDu4AGIq28dCsRAbh06xk/pYAp0GiCzoe21pKor15XuW3vgLl0XP9v6IDa4IZNas5fFYZz5+fmYM2eORJK1NVHo6pw7d664PNu6Lg7y4sWLUVRU1NZViWy+YcMGrF27ts3rYgX79u3DggULpN62rpB7PaCrTZgAAAGqSURBVBIfpUWlTQ3jLEHuolxMemISqquqUVVV1aZl/fr1GDp0KMrLy9u0HvaDoBoxYoR8VldXg6Ut+pd+Ntc9bt68uc3qyWz766+/junTp7dLXStWrMCYMWPapa79+/dj5MiRqCqvQtHRQhQeLayNgst8ieqHcR4tREmiGJ8vXYERw+7A1Jem4sUXX2yz8tJLL+GJJ57AwIED26wOtp/1sLzwwgu44oor5DP9XWv3L/3cqVOn4sYbb8SkSZNq62/tutLPY52jR4/GqFGj8PLLL7cpLVnnww8/jGuvvbZd6nr++eeF+ZSXlqMon0BmOCfBXJiJYzQAsor5PPzjIWzdlIe8zW1YtuQhb0setmzegk0bN7VtXel+bNkqdW3dshV56ZL+rTU/o75Jv6LzNqXl5jxs3rRZivStNftynGfVjhlpeJzfW/u7bVu3oahAgTcN4hMCOX1RcQGDlxUbZ7B9XGIadBwGCiP8NQHI9Xh1/EdMgU5EgXqiRSdqd9zUmAL1KBADuR454j86KwViIHfWkYvbXY8CMZDrkSP+o7NSIAZyZx25uN31KPA/49aai1aR0YkAAAAASUVORK5CYII="> <em><strong>(M1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1</strong></em> for equating the functions. Accept a sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>θ</mi></mfenced></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mi>θ</mi></mfenced></math> with point(s) of intersection marked.</p>
<p> </p>
<p><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mn>196</mn><mo>°</mo><mo> </mo><mo> </mo><mfenced><mrow><mn>196</mn><mo>.</mo><mn>363</mn><mo>…</mo></mrow></mfenced></math><em><strong> A1</strong></em></p>
<p><br><strong>Note:</strong> The answer <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>166</mn><mo>.</mo><mn>153</mn><mo>…</mo></math> is incorrect but the correct method is implicit. Award <em><strong>(M1)A0</strong></em>.</p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">i.</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>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">i.</div>
</div>
<br><hr><br><div class="specification">
<p>Boris recorded the number of daylight hours on the first day of each month in a northern hemisphere town.</p>
<p>This data was plotted onto a scatter diagram. The points were then joined by a smooth curve, with minimum point <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>8</mn><mo>)</mo></math> and maximum point <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>6</mn><mo>,</mo><mo> </mo><mn>16</mn><mo>)</mo></math> as shown in the following diagram.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>Let the curve in the diagram be <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> is the time, measured in months, since Boris first recorded these values.</p>
<p>Boris thinks that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo></math> might be modelled by a quadratic function.</p>
</div>
<div class="specification">
<p>Paula thinks that a better model is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>a</mi><mo> </mo><mi>cos</mi><mo>(</mo><mi>b</mi><mi>t</mi><mo>)</mo><mo>+</mo><mi>d</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>≥</mo><mn>0</mn></math>, for specific values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mo> </mo><mi>b</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>.</p>
</div>
<div class="specification">
<p>For Paula’s model, use the diagram to write down</p>
</div>
<div class="specification">
<p>The true maximum number of daylight hours was <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn></math> hours and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn></math> minutes.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down one reason why a quadratic function would not be a good model for the number of hours of daylight per day, across a number of years.</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>the amplitude.</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>the period.</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>the equation of the principal axis.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence or otherwise find the equation of this model in the form:</p>
<p style="text-align:center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>a</mi><mo> </mo><mi>cos</mi><mo>(</mo><mi>b</mi><mi>t</mi><mo>)</mo><mo>+</mo><mi>d</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>For the first year of the model, find the length of time when there are more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> hours and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math> minutes of daylight per day.</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>Calculate the percentage error in the maximum number of daylight hours Boris recorded in the diagram.</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><strong>EITHER<br></strong>annual cycle for daylight length <em><strong>R1</strong></em></p>
<p><strong>OR<br></strong>there is a minimum length for daylight (cannot be negative) <em><strong>R1</strong></em></p>
<p><strong>OR<br></strong>a quadratic could not have a maximum and a minimum or equivalent <em><strong>R1</strong></em></p>
<p><br><strong>Note:</strong> Do not accept “Paula's model is better”.</p>
<p><br><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></strong> <em><strong>A1</strong></em></p>
<p><br><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math></strong> <em><strong>A1</strong></em></p>
<p><br><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>12</mn></math></strong> <em><strong>A1A1</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>A1</strong></em> “<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo></math> (a constant)” and <em><strong>A1</strong> </em>for that constant being <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math>.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mo>-</mo><mn>4</mn><mo> </mo><mi>cos</mi><mo>(</mo><mn>30</mn><mi>t</mi><mo>)</mo><mo>+</mo><mn>12</mn></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mo>-</mo><mn>4</mn><mo> </mo><mi>cos</mi><mo>(</mo><mo>-</mo><mn>30</mn><mi>t</mi><mo>)</mo><mo>+</mo><mn>12</mn></math> <em><strong>A1A1A1</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>A1</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>30</mn></math> (or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>-</mo><mn>30</mn></math>), <em><strong>A1</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>-</mo><mn>4</mn></math>, and <em><strong>A1</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>12</mn></math>. Award at most <em><strong>A1A1A0</strong></em> if extra terms are seen or form is incorrect. Award at most <em><strong>A1A1A0</strong></em> if <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> is used instead of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>.</p>
<p> </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><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>.</mo><mn>5</mn><mo>=</mo><mo>-</mo><mn>4</mn><mo> </mo><mi>cos</mi><mo>(</mo><mn>30</mn><mi>t</mi><mo>)</mo><mo>+</mo><mn>12</mn></math> <em><strong>(M1)</strong></em></p>
<p><br><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>t</mi><mn>1</mn></msub><mo>=</mo><mn>2</mn><mo>.</mo><mn>26585</mn><mo>…</mo><mo>,</mo><mo> </mo><mo> </mo><msub><mi>t</mi><mn>2</mn></msub><mo>=</mo><mn>9</mn><mo>.</mo><mn>73414</mn><mo>…</mo></math> <em><strong>(A1)(A1)</strong></em></p>
<p><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>t</mi><mn>1</mn></msub><mo>=</mo><mfrac><mn>1</mn><mn>30</mn></mfrac><msup><mi>cos</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfrac><mn>3</mn><mn>8</mn></mfrac></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>t</mi><mn>2</mn></msub><mo>=</mo><mn>12</mn><mo>-</mo><msub><mi>t</mi><mn>1</mn></msub></math> <em><strong>(A1)</strong></em></p>
<p><br><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>.</mo><mn>73414</mn><mo>…</mo><mo>-</mo><mn>2</mn><mo>.</mo><mn>26585</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>47</mn><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>7</mn><mo>.</mo><mn>46828</mn><mo>…</mo></mrow></mfenced></math> months (<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>622356</mn><mo>…</mo></math> years) <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>M1A1A1A0</strong></em> for an unsupported answer of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>46</mn></math>. If there is only one intersection point, award <em><strong>M1A1A0A0</strong></em>.</p>
<p> </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><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|" close="|"><mfrac><mrow><mn>16</mn><mo>-</mo><mfenced><mrow><mn>16</mn><mo>+</mo><mstyle displaystyle="true"><mfrac><mn>14</mn><mn>60</mn></mfrac></mstyle></mrow></mfenced></mrow><mrow><mn>16</mn><mo>+</mo><mstyle displaystyle="true"><mfrac><mn>14</mn><mn>60</mn></mfrac></mstyle></mrow></mfrac></mfenced><mo>×</mo><mn>100</mn><mo>%</mo></math> <em><strong>(M1)(M1)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>M1</strong> </em>for correct values and absolute value signs, <em><strong>M1</strong> </em>for <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>×</mo><mn>100</mn></math>.</p>
<p> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1</mn><mo>.</mo><mn>44</mn><mo>%</mo><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>1</mn><mo>.</mo><mn>43737</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">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Part (a) indicated a lack of understanding of quadratic functions and the cyclical nature of daylight hours. Some candidates seemed to understand the limitations of a quadratic model but were not always able to use appropriate mathematical language to explain the limitations clearly.</p>
<p>In part (b), many candidates struggled to write down the amplitude, period, and equation of the principal axis.</p>
<p>In part (c), very few candidates recognized that it would be a negative cosine graph here and most did not know how to find the “<em>b</em>” value even if they had originally found the period in part (b). Some candidates used the regression features in their GDC to find the equation of the model; this is outside the SL syllabus but is a valid approach and earned full credit.</p>
<p>In part (d), very few candidates were awarded “follow through” marks in this part. Some substituted 10.5 into their equation rather that equate their equation to 10.5 and attempt to solve it using their GDC to graph the equations or using the “solver” function.</p>
<p>Part (e) was perhaps the best answered part in this question. However, due to premature rounding, many candidates did not gain full marks. A common error was to write the true number of daylight hours as 16.14.</p>
<p> </p>
<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>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The 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>In the month before their IB Diploma examinations, eight male students recorded the number of hours they spent on social media.</p>
<p>For each student, the number of hours spent on social media (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>) and the number of IB Diploma points obtained (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>) are shown in the following table.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-07_om_07.43.52.png" alt="N16/5/MATSD/SP2/ENG/TZ0/01"></p>
</div>
<div class="specification">
<p>Use your graphic display calculator to find</p>
</div>
<div class="specification">
<p>Ten female students also recorded the number of hours they spent on social media in the month before their IB Diploma examinations. Each of these female students spent between 3 and 30 hours on social media.</p>
<p>The equation of the regression line <em>y </em>on <em>x </em>for these ten female students is</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="y = - \frac{2}{3}x + \frac{{125}}{3}.">
<mi>y</mi>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
<mi>x</mi>
<mo>+</mo>
<mfrac>
<mrow>
<mn>125</mn>
</mrow>
<mn>3</mn>
</mfrac>
<mo>.</mo>
</math></span></p>
<p>An eleventh girl spent 34 hours on social media in the month before her IB Diploma examinations.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On graph paper, draw a scatter diagram for these data. Use a scale of 2 cm to represent 5 hours on the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis and 2 cm to represent 10 points 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">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar x}">
<mrow>
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</mrow>
</math></span>, the mean number of hours spent on social media;</p>
<p>(ii) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar y}">
<mrow>
<mrow>
<mover>
<mi>y</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</mrow>
</math></span>, the mean number of IB Diploma points.</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>Plot the point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(\bar x,{\text{ }}\bar y)">
<mo stretchy="false">(</mo>
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mover>
<mi>y</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo stretchy="false">)</mo>
</math></span> on your scatter diagram and label this point M.</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 the equation of the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> for these eight male students.</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>Draw the regression line, from part (e), on your scatter diagram.</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>Use the given equation of the regression line to estimate the number of IB Diploma points that this girl obtained.</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>Write down a reason why this estimate is not reliable.</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 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="images/Schermafbeelding_2017-03-07_om_08.41.53.png" alt="N16/5/MATSD/SP2/ENG/TZ0/01.a/M"> <strong><em>(A4)</em></strong></p>
<p> </p>
<p><strong>Notes</strong>: Award <strong><em>(A1) </em></strong>for correct scale and labelled axes.</p>
<p>Award <strong><em>(A3) </em></strong>for 7 or 8 points correctly plotted,</p>
<p><strong><em>(A2) </em></strong>for 5 or 6 points correctly plotted,</p>
<p><strong><em>(A1) </em></strong>for 3 or 4 points correctly plotted.</p>
<p>Award at most <strong><em>(A0)(A3) </em></strong>if axes reversed.</p>
<p>Accept <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> sufficient for labelling.</p>
<p>If graph paper is not used, award <strong><em>(A0)</em></strong>.</p>
<p>If an inconsistent scale is used, award <strong><em>(A0)</em></strong><em>. </em>Candidates’ points should be read from this scale <strong>where possible </strong>and awarded accordingly.</p>
<p>A scale which is too small to be meaningful (ie mm instead of cm) earns <strong><em>(A0) </em></strong>for plotted points.</p>
<p> </p>
<p><strong><em>[4 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="\bar x = 21">
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo>=</mo>
<mn>21</mn>
</math></span> <strong><em>(A1)</em></strong></p>
<p>(ii) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar y = 31">
<mrow>
<mover>
<mi>y</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo>=</mo>
<mn>31</mn>
</math></span> <strong><em>(A1)</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(\bar x,{\text{ }}\bar y)">
<mo stretchy="false">(</mo>
<mrow>
<mover>
<mi>x</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mover>
<mi>y</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
<mo stretchy="false">)</mo>
</math></span> correctly plotted on graph <strong><em>(A1)</em>(ft)</strong></p>
<p>this point labelled M <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from parts (b)(i) and (b)(ii).</p>
<p>Only accept M for labelling.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = - 0.761x + 47.0{\text{ }}(y = - 0.760638 \ldots x + 46.9734 \ldots )">
<mi>y</mi>
<mo>=</mo>
<mo>−</mo>
<mn>0.761</mn>
<mi>x</mi>
<mo>+</mo>
<mn>47.0</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>y</mi>
<mo>=</mo>
<mo>−</mo>
<mn>0.760638</mn>
<mo>…</mo>
<mi>x</mi>
<mo>+</mo>
<mn>46.9734</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)(A1)(G2)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 0.761x">
<mo>−</mo>
<mn>0.761</mn>
<mi>x</mi>
</math></span> and <strong><em>(A1)</em></strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" + 47.0">
<mo>+</mo>
<mn>47.0</mn>
</math></span>. Award a maximum of <strong><em>(A1)(A0) </em></strong>if answer is not an equation.</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>line on graph <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(A1)</em>(ft) </strong>for <strong>straight line </strong>that passes through their M, <strong><em>(A1)</em>(ft) </strong>for line (extrapolated if necessary) that passes through <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(0,{\text{ }}47.0)">
<mo stretchy="false">(</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>47.0</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<p>If M is not plotted or labelled, follow through from part (e).</p>
<p> </p>
<p><strong><em>[2 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="y = - \frac{2}{3}(34) + \frac{{125}}{3}">
<mi>y</mi>
<mo>=</mo>
<mo>−</mo>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
<mo stretchy="false">(</mo>
<mn>34</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mfrac>
<mrow>
<mn>125</mn>
</mrow>
<mn>3</mn>
</mfrac>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution.</p>
<p> </p>
<p>19 (points) <strong><em>(A1)(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>extrapolation <strong><em>(R1)</em></strong></p>
<p><strong>OR</strong></p>
<p>34 hours is outside the given range of data <strong><em>(R1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Do not accept ‘outlier’.</p>
<p> </p>
<p><strong><em>[1 mark]</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">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 braking distance of a vehicle is defined as the distance travelled from where the brakes are applied to the point where the vehicle comes to a complete stop.</p>
<p>The speed, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s\,{\text{m}}\,{{\text{s}}^{ - 1}}">
<mi>s</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>
</math></span>, and braking distance, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d\,{\text{m}}">
<mi>d</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>m</mtext>
</mrow>
</math></span>, of a truck were recorded. This information is summarized in the following table.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAawAAABMCAYAAAAx+4OaAAAcMUlEQVR4Ae2dC3BT15nH/xKUsMQ8lpYN15DiYhVIazdp7IUmYRqBi5yUSeLiAFkaZCIvJdOEdNYTyzFNtqSlUJDHCSnshHSk2GZKw+N6SPMoNpUxHRJqV6Jp7a4jYxiTGF2yUGJbDm/p7Jyr19XL8gPbkvk049G9557Hd37n3Pvd7zvfkVWMMQb6EAEiQASIABFIcALqBJePxCMCRIAIEAEiIBMghUUTgQgQASJABJKCwFi/lCqVyn9I30SACBABIkAERpxA+IpVQGFxycIvjri0JAARSAAC/GWO7o34A0Gc4jPiOYhTfE6xGJFLMD47ykEEiAARIAIJQIAUVgIMAolABIgAESAC8QmQworPiHIQASJABIhAAhAghZUAg0AiEAEiQASIQHwCpLDiM6IcRIAIEAEikAAESGElwCCQCESACBABIhCfACms+IySMMcVtFpWyOGzKtUKWFqvJGEfSGQiQASIQCiBkH1YoZfoLHkJjMccw1voStNgXk5b8naDJCcCRIAIKAiQhaWAQYdEgAgQASKQuARIYSXu2JBkRIAIEAEioCAwSIV1DZK9GmUFmb71EhVUqlyUWOrQ2uNRNJM4hzfsZdCoVFBpymC/kThyDUQS/vMlsf6SvGsDwXFLlPFIjagsyZXHPbVgJxqla7dEv29OJ/nz6n0cKCtAqkqF1JI6dN+cipOgFg96WutRfaAMBZoNqOuO/nxO9Pk1CIV1DVLdFqzKzkdxVbNiwGqxrTAHcx/ZDnuCKi2FsKP2kBYnR+HQ9jSifNXP4ci1wM2uwl5wASWrdtJ91peh9khofGUtsh7Zi/a0p1DvcsO5dTEm9aXsKMjjaa3AEy+/CfG5YlRditGhJJhfA1dYntP4w9ZdqAcg6CvQ4nKDsatwWjdCy3nUm7BhXyui6/EYwCi5XwT4D7LG+utXRZQ5CQhcQeu+MpTPL8ILi2dAjXEQFj+Dl+YfoPss7uh1wl6+FnkfzcdB+2/w/ONazEkZ+KMvbnMJmEE9x4B3f7sLP9u0PIZ0yTG/Bj5qni9w8ZQkd35CZgY08gQYB0G7Eqt1AgAJTQ4nengOqRoFsvuqEJa6dxUuxFyUVDZCCtFq3Wits6BkUarP3RXNxcjN2zpYfK4RlSoVi0osqGsNM/B7WnHYZ/6rVJkoKKtBa9et4CzjYe1PYHLOFkjYj8K5C1FSdyHGRKXkpCDgacexvSeQOTcVKQGBpyI790E07f0QbSH3UCADHcCDHvubeL48DTs2r8V8YRwxiUYgWeYX8328/13Ef9aHb3cLM+sExssBOmY0i8zq6Ipe0CkyvZyP5w3/E5jW1MBccsmrrEN8hgkRecAEfQVrcbnlXO4OkRmE8HrAIBiYucUng7udiYaMKO35yqWbmO16dHF7T+1iDrGUaWUZM5je9Fu2f7vITkSp67rNxNIDfTEws/UdZtL7ZNJuZFanizmtG311hfYxRAa3kzWU6xVc0ple/CQkC50MHYF+3xtDIIrbYWY6ZDGj9byidjfrspYyAcuZ2XFZkT4yh4nAKaLn8nMqnWmNb7D9Jt89JOiZqdbhe+ZElBjyhJHjdJk5zMsZhFJm7fI+S/2dTbT5FYvRwC0s9Rys2L4Fem5Mga9b5SNn7mR4LZk9eNsuRXEHCtCW1sLpZmBuJxrK9RAgob78IBr5ImD3Mbz27E5IggHmli6vu8vVBLM+A1LVr/Fm40UAF1D/2mZYpAzozU1wyW6xLrSYDRAkC15804ZueNBdvwvPWvjamg6l1g64GYPbeQzl+oxo7xd9TvO0HsD6/AqMM7fAzez41b0nsdMOTI+yaDQ261m8b/ab4I042p6Gp998F6IhA6jfiCdXPYLHn/wEq4/vh1EApKpS/CTCjcr78mvkFV3GJsdlMNYFR+1/IXNMn0WmjElPwIOejjY0YTbmzgzaV0nfrWHogKftQ+ytTcf8b9yNB4oq4WRdaNk0FuW6Irxu7xwGCZKhieSZXwNXWFAjZV4B3rTbcNBs9K5byWPTjKriHyIvW4enLM1el2BgzB7F+vWLIPBW1QLmFxZgtew9PI4TJy/hxskTELmXUbKg8C6u/FRQTcxEoRzUYcfumr+j+8YZnBDtAJpRVZiJibKrcTLuKrRALrr7j7B1X8G59jb5HPp1WC/7/HmT96Gw4BHIOjYgU/8OPK6LOMXdnUcb0NozFsLi9Sh/Lgt3RK1mLCZOmeq78gAee3geUtRfxqy7viKnSY7ZKKx7BYbvLMCCJemyG/XUxS/CFL0HX3RehIRj2G1+H609KZiz5Bk8/9idUVukRCJABPwEfA9iIQu5P8j2PncwCfPWFGOT7gSKN1SjlVypflhJ8T0IheXtn1rIwmOGrTjCLR2XA1bxDRi1XCU0o+rFPV7LyY8iXYNZ0xSmyITJmDbBf/EGzp9pwyn/aZRv6Vwnvjh/Bk29ZrqIzi+uwXXxvFyDMH0Kbg/UpcaEyVMRaDKQ3veDsd9ejm0GbvGtwV2P/AJ1Ugq+nTULAwK5ZCkenhcvTmksBJ0BJi1Qvy0fc+c8hbLDrWEvAn2Xn3ImIwE1UmZqkInTcHTIq8LJ2IkRkPla8MVV2bo6DQtXLgSa2tBBkczcekia+TWg5yy4y61ug7yXIeS36lLmYPGytfhlWRG4vQDJazkF5sqpRvzttOJ37S514XwgxFKN26dM9Vo/6SbYrkeJgKtcBuH2KZgum0hamGyuKFFyr2OZMB4Tp06Tm5U+ase5wFuUB5e6LiLQZECwfhyoZ2HZ9t/JbkrZrffqsaHfy5EyH89b7bBVGKGVqlCsy8czEdZrP/pAWZOOgFpzP1bqbguT2/dA1j2EhZrxYdfoFBiH6WkaCFIb2s9F2a+WqcHMWyxaMNasSJb5NUCFpcak7O953XnYjxd/aQ5uYOxpRtVrlV5LSbgP935dac/43VoegO+LMFdiN/fjyflSgnWeqsRrVV53okc6jA1yxGC2N9Jt0reQuzqLx82j/DURH/M3JM9Z1G3wbaaUNwOOh2bhQ9Dx0andi4r6s7KbzSMdh7nyHa+rMNbI9ZLuaa3B2/yHZFMyYNhphkkrQBJP4ORwBB6qBWQVbIXVWYtS7T9RtfkQHMPRbi886NIwEpCtghlet3ig2R50OM5Ct/J+aAZ4JweqGpUH/udUCz5o/kzhaiduEcOdLPPLHyUSKyrDfz3yO3ZEH68LyGB6c5M3EqfXKMEMZhDbmTdmpYu1mA2KaLhgJGAwStDNXC0VTH/TogQ/YaI+nQHxIu+8EVnp+h2swXmVMV8UomC0shixkYwxX1SOzGMdE508lPA8sxqzvNGLOjNz8I4rIi4j67vOnAe3M5NoY045rzf6UTCIrCM00CdyiCjlphDo/71xU5qNrMTVwEzapazU2sHc7Ko3wlRbzmy+6NnIAsObkjCcQrrte04FIoivMmfDDqbXjRy3keMUO0pQRpZA8ysWI+5Skz+xMvivR/++ypy2d5jZqAsJHxf0JrbfqggbDSisdWy/7Rir8OePGl7axRxWMzNq/SHzPHT8EHOE3JRu5nJYQ9oV9OWsNjys3uVgtf5QVq5ATYfYP6xbvKHmgbD2viqsy6ztyDHW0nLIF5oeTa5QSqFh7WBI38TEt9aFsEo3vcXekhWmXzmHK87rzHnkT8zR1cJEmZvAtMYqZuNKkz7DQmBg98bQiOZ2HmPl8taIxJsHicQplH4Xc9SW+15yR57biHDqsjJjyEu+wHTmFp+hEKSVKPMrFiMVF5Wbhzwiz3cYYS0OOoFvHE7NRxXWQXTuwDJBEXgx6MpvRgUXUFeyBjW5Fdi62BvBdzNqpTpGB4EhvTdGByK5F8Spb4NJnOJzisWIPN98J/zH76FSTMOCufEi9uKDphxEgAgQASIwNARIYXk+Re2rf8E9e36KvBn0sy1DM82oViJABIjA4AkMj0tw8HJSDURgxAjEck+MmEAJ2jBx6tvAEKf4nGIxIgsrPjvKQQSIABEgAglAgBRWAgwCiUAEiAARIALxCZDCis+IchABIkAEiEACECCFlQCDQCIQASJABIhAfAKksOIzohxEgAgQASKQAARIYSXAIJAIRIAIEAEiEJ8AKaz4jCgHESACRIAIJACBkH1YCSAPiUAEiAARIAJEQCYQ/nOBIT/qF36RmBEBIjDEv7M5igDH2uw5irp4U7pCnOJjjMWIXILx2VEOIkAEiAARSAACpLASYBBIBCJABIgAEYhPgBRWfEaUgwgQASJABBKAACmsBBgEEoEIEAEiQATiEyCFFZ8R5SACRIAIEIEEIEAKKwEGgUQgAkSACBCB+ARIYcVnRDmIABEgAkQgAQiQwkqAQSARiAARIAJEID4BUljxGVEOIkAEiAARSAACpLASYBBIBCJABIgAEYhPYOAK64YdZRoV+E9oRP6lYlHJbtila/El6GsOqRoFcltPo1q6EaPUp6gu0ECl0qCg+tMYeYYv+Ya9DBous6YMdlnkQcjX04q6A2V4+hU7YvV++Ho2HC11o7XubRwoK0BqQTWk4WgyCdrwSI2oLMmV77nUgp1ovJn3WBL0P6qI/N6o3oOyglyU1F2IkqUbrYdfQUGq71m1qASVdgmeKDlHf9I1SPb3vfeVSoXUkjp0Kzqd6PNr4ApL0cnIQwn12/TIXrUT9p5bc1pEMhlMSg/sr69DzvJi/NE9mHqSpewNSNVGzM3Jw/Liw8h88Bu4I1lEH0o5expRvurncORa4GZXYS+4gJJb/R7zfAzLEy+iUtyC4qp/RqF/DWff3o33sBQ7nQzM7UTDo+dQmr0W5fbOKPlHcZJHQuMra5H1yF60pz2Fepcbzq2LMcnf5WSYX8z3AeA/7Nv3dRszpYMB65jovB5Sxt0hMoPAr2Uxo/V8yLUBnzhFpkf09gZc5xAXvG4zsXQuc7qJ2UIR9bNlF7OZtIyPUbrJxgZVVT9bHrHs7nYmGjIYsJyZHZdHTAzecL/vjSGR9jJzmJczwWhlXYH6zzOr8X6mM7cwdyBt5A5GkpPbYWa6aM8b92l25MgnoXzcLcysE8JYDh+3keH0ObOZljJBv4M1OK9G6Wxiza9YjIbEwlLP+HcsXZIOoBPnOi979bffpad5GdU1L2OR7N5bAUvrFQAe9LTWoKwgM+heTC1AWbUdUkwD7RqkOl89qYWwfMwN2yguN3+7qqdxwP5nVHMXk9x2Jgpe+SC0/p5WHA5cz0VJZSM+bQx36/lfR8K+Q8pmoqCsBq1d4c67KPKBu74sKFmUGuz7ohJY6lrRIzfBy9yD7OJ6+exUcTa+pFqEMrv3KkLa5S4P3na1wh2raPPAn2GvLgu4RqK5lDySXcFIBRUfh8N+WXx95i4YS4lvDFVQhcgbxmWgp5/Z8balGUifj7tnjx9oLaOnnKcdx/aeQObcVKQEejUV2bkPomnvh2iLeZ8EMt+aB+qvQau9EyEPOvVXkHZP6i3Ew4Me+5t4vjwNOzavxXxhXGTfk2V++VVtLI3mvx7xHdPCcjNXSwXTcwtLeIaJHT5tHrCQuJXk+xNKmbXLzYIWmeKanCeDGcR279tRoDy36L5gTutGppXzLGUm2+c+8T5hoj6dAelML37iTQuUC6+bnwvBt9PAG70yXwZbpc9jQjwrKWpZRT0BCytcPjdz2cp9/VDkD+mXv4zyupaZbC7GemlXMIisQ37tjlZeUZfOzBz+13NXAzNpheD4yHLwvIpxiNlmBtObm5grYqL0NeEqc9qqmFFuX8eKjKtk7qEWhaKuwPzj8qUzvfkQqzXpvWMFHSu1drDrzlpW6u+PYGDmlqBtoqgp7mG/7424NfY/Q3QLws26rKVMSAArlPdoJDlF5xOLM7dMdcFnS6xsQ5Q+7JxkizKdaY1vsP3+e0TQM1OtI3C/Ruc3cvMrFqOQF49ItduXlF3IT/1S0DpQjcHEu9agCnqUH/wp8maEa3MBWlMDXIzB3boB35l0DW01b8EiBdOZux2iIQNAM46evhC2OHodnc2/xQtPbkQ9dCi17kJR1pQ+CCpAaxThcLkRrF9C7dH/xWfcxmuzYhd/o5fr7ICby+csx6xPGuIs+HvQXb8Lz0aUPYZyPe9Db59LcBz5PbjtJBit6GIMjH0Om2kpgPdQvKEarZ47sazyI9hMWrmidJMN19kRPJ+VEpRZWw4b7xe7ig7xGQgApKOncS78rVtbCtHRFZIPtY1o/oxbglfQuq8MxfUSoN0Iq/OqnM9p3QgtmmF5dhfqu28E+iroK9Ait+mGq6UCeqEZVS/uQWN3eKO99d9/jVvLW7AquwSN91XCeX07vvnREUjIwurcbwV97P7s/HtsForeN0Mnp53C4aPncOfTu/AXuf+12PLkCix5vBRnV1dCNGYBkgWFPzmA1oGIp2x3RI496OloQxNmY+7MoH01IqKMhka7/46ajx7Cj3Vhltdo6FuUPnjaPsTe2nTM/8bdeKCoEk7WhZZNY1GuK8Lr8jpe8syvm6CwohDiSVIVTDurYYuIYlqI1Y9+S3ZrqFNSMAHjMcewD4y1Y8+iC6itPgBL6Y+QLysA4NL5LlwKacKCQt2PUCUBgmEdntHOCDX3Q/IqTxZideH3MSdFDahn4L6lDyguXkHbsUOo5Sm6lVjjq1Mt5OCFl9bICkCROezwGs61t3mVmn4d1i/2yqMW7kNhwSNxyo7D9Nnf9CqYbTmYV1CGA9V1OPP1l+F0M7AaA+b0MkLqOQbUcMW657voqD2IastLeDJ/p1eWSxfRdUn5dBagW61H3hy+xDoOM+5bjCUhPTmP5qMnAKRDv96AxbLbYByExT/DEa5InZuxeNIVnDxxXK5fqlqDuyaOgcr/gsLD+KRa1NguhtTalxPP2XfxIn8BEdbgpRdyIIy9HVOmTwDiPKDVE6dgutxAOpY8thjzUsbjjllp4CUhdeOrhRXYaViE+xZke8U4dREuJZK+CEd5RhmBTtjf+D2mbX4KWfxZMOo/PmUkZCH3B9kQ5C5Pwrw1xdikO+F7KU4eCDdhxNZBdF7nERvBP1cLRKMOUtWzyHv1WEjYJAQN0qYrrS4Pej6uREHqbUjNXor8/OUo3CarDpnihGmTvQ+gKEwliwW/+2tfI32mYspE/z9YHotpszTgq2zezw24Lp6XD4V70jA9QEWNCZOnxmw/ouz0KbjdVyPQl7LjMCPvp3inwghuP0lVxVien4/8vGykjslFSfXHvnWsQKWhBz3NsBRkYkxqNvJ4ucJtsrUmZ5owFZMnBDoCYAKmT7k9qNynzUJmEABw4/9w+oNTofVHnH2OM029bRdQrFlGlI2VcAH1r232WthFeZg/SQ10n0TD4VOA7iEs1Ax0/eoBPPbwPMV6T6z2kyFdjZSZGmTiNBwdvrXLZBA74WTkazlvYd/U/8TTffLKJFwHBiCQ4oVaWVqdhoUrFwJNbeBTKlnml/KJpuzO4I5T5uHRFUtkhSCJJ3BSGXsQ/iD1tGLfT0pRxV2CxjcgHrTB6XYFXGCRgnDX4XF0WEshBNxmkbn6lzIWE6dOk4tIH7UrXGkeXOq6GGbhhdc8mLIA1AKyCrbiCHPD5TgCURSx36SHgFpsy/9v7JODUsLb5OfchfdzFFY1A1ojzOJ7sDmv4rrNpFDE0crFSBv7b5j9ANdgl3Cu84swN6y/zL9gynSv+9XrmlS8pMgvLG2oXHanP3Pfvrl7ZrcdgN/y9qDb9kfsloD0JXdj9tDM0L7JlkC51Jr7sVJ3W5hEvofRoBR7WJWj+NRz9hB+07wQLxkyRsmLTF8Gaxymp2kgSG1oPxdlX2ymBjNT1EiW+TU0jwPPWfxJPAz5ff2B2Uj1GzbR+PY44Wji/qQvY/YCHfIey8Idnx2H+J4jWm4Aj2L9D7MxQ7sOO/g6V+0r2HrwTIwHbIwqIpLHQ7PwIe96SO1eVNSflevzSFb86hcVcdawYpU9DnPlO72X9ZxBdSGPjEzFog1WuDRaLFu2DMv+4zE8zBeiev30oMNxWs4hzF6A3LzvI+uO80HuvZaNdnEaMh68l9t5qN29F/WyK9dv/fLoQx7ROQHZuTrZhXmq/H9QJUdmKqM1N6Cun2tYN06egMiH329599jwhsw8C/n33o4m+2DHNlpfkzBNfiOegd01f1d4LPgcOAvdyvuhGZo7OQlBRRfZI9Vh+77xeGK1X1nxuX0AlvpoG42j15GcqWpMyv4eVgst+KD5M8VzMmzuJMn8ugnTPDzoQgXVmJnI2cLdekthem5x7+s4KelY8LA3wMKSn4YxKhXGpBbgKL4ml4tcw/JNG/Wd0P3Y4A0I+HU1/jrIDcpqTQ7WyYEetdiSM9MnRxHOfHVB7/JzIylq2YUo4tZPb59AHyTUb9EhdYx3J/6YmfmwyGt0TyBXdokFrbhgWLsacxd8R5ZNsuRjJi/LuR+9Bi1XdhFrWL0Jwq+Nx5wVz8PEC9dvRE7qbYr1KQHa0rV4WDMBk+avwiYeTMKDGO6aDJXqNqTm8ACYDOg3rfK69KJtL4jXPL/ukWA/3ozzn3INdhUdNX8D5sZeGPe4OnEupF6lRXwRnS5u2t+Aq9O3rtZvJiGVj/CJd3yKGsvxqzr+QsVfFHbiF42PY/OKOUFX7whLmXjN8y0z1Shd9SSKinIC95h37XUfkHoLBLFMWojndjyIPzz7c1T4XzIb96LyI+XcSZL55Y/cjBVG6L8e8R0SVqwIk/aFQgt6ExNtzuCGPX94eSDEO1ij29nAKow6Xzi1jhkrGpizw7dR2Bf6zvzlQzYqezfDBcPT/SHc0cLaQzc4Bzb16kXm9IvicgRDo31hn5/3dfOvsiwymN50iP3DuiVs43AU+ZibuRxWZg70n7PUMaPZyhwuf7w5Y27nMVau5xtp+XVfKL/byWwVRl9YvMC0xipmc7b5Qvv9m7ajtckYC4xfKBe308ZEf+grb4tzEG3MGRSFMZeDWc3+dn15FCGyjMVo089Z+R0Ik/eNe5cvtF5bykRHL2HoAfn9c0/LTKLZt7ncl5a+iYlvrQsN01eOt1KOXo77fW/0UtdgLwXngX+8o20CHWwrAys/Mpx4iHpW6BgrtmrE3jIDBkW+gfV4YKVGhlMXc9SWe7cbIfbcSZT5FYuRiiPnb0X89wB9h4n3kjQMEvHf/ZuXXYxTyIBBfBe/WTYLanTCXvYksovfA/QinJXL4lpbwyBqkjRxAXUla1CTW4Gti7+SJDJHF/NWvzeiU4lMJU6RTKKlEKdoVELTYjG6CS7B0IaS9Wzs3O/iadmX1gy/a1Kl+levsuJKjK+tJWvnhl1uvj7wHirFNCyYG/ilsmGXghokAkRgdBEgheUfz5T5KNrzDkQ5Qs+fCG8EnlXEdtniUqTTYWwCnk9R++pfcM+eaBvHYxejK0SACBCB3giQS7A3OnSNCJC7vM9zIJYbp88V3CIZiVP8gY7FiCys+OwoBxEgAkSACCQAAVJYCTAIJAIRIAJEgAjEJ0AKKz4jykEEiAARIAIJQIAUVgIMAolABIgAESAC8QmQworPiHIQASJABIhAAhAghZUAg0AiEAEiQASIQHwCIWHt8bNTDiJABIgAESACw0Mg/NeXAr+jHn5heMShVogAESACRIAI9I0AuQT7xolyEQEiQASIwAgTIIU1wgNAzRMBIkAEiEDfCPw/3S6NeCozvX0AAAAASUVORK5CYII="></p>
<p>This information was used to create Model A, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d">
<mi>d</mi>
</math></span> is a function of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s">
<mi>s</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s">
<mi>s</mi>
</math></span> ≥ 0.</p>
<p style="text-align: center;">Model A: <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d\left( s \right) = p{s^2} + qs">
<mi>d</mi>
<mrow>
<mo>(</mo>
<mi>s</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>p</mi>
<mrow>
<msup>
<mi>s</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>q</mi>
<mi>s</mi>
</math></span>, where <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="q \in \mathbb{Z}">
<mi>q</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">Z</mi>
</mrow>
</math></span></p>
<p>At a speed of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6\,{\text{m}}\,{{\text{s}}^{ - 1}}">
<mn>6</mn>
<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>
</math></span>, Model A can be represented by the equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6p + q = 2">
<mn>6</mn>
<mi>p</mi>
<mo>+</mo>
<mi>q</mi>
<mo>=</mo>
<mn>2</mn>
</math></span>.</p>
</div>
<div class="specification">
<p>Additional data was used to create Model B, <strong>a revised model</strong> for the braking distance of a truck.</p>
<p style="text-align: center;">Model B: <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d\left( s \right) = 0.95{s^2} - 3.92s">
<mi>d</mi>
<mrow>
<mo>(</mo>
<mi>s</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0.95</mn>
<mrow>
<msup>
<mi>s</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mn>3.92</mn>
<mi>s</mi>
</math></span></p>
</div>
<div class="specification">
<p>The actual braking distance at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="20\,{\text{m}}\,{{\text{s}}^{ - 1}}">
<mn>20</mn>
<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>
</math></span> is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="320\,{\text{m}}">
<mn>320</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>m</mtext>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down a second equation to represent Model A, when the speed is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="10\,{\text{m}}\,{{\text{s}}^{ - 1}}">
<mn>10</mn>
<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>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
<mi>q</mi>
</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>Find the coordinates of the vertex of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = d\left( s \right)">
<mi>y</mi>
<mo>=</mo>
<mi>d</mi>
<mrow>
<mo>(</mo>
<mi>s</mi>
<mo>)</mo>
</mrow>
</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>Using the values in the table and your answer to part (b), sketch the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = d\left( s \right)">
<mi>y</mi>
<mo>=</mo>
<mi>d</mi>
<mrow>
<mo>(</mo>
<mi>s</mi>
<mo>)</mo>
</mrow>
</math></span> for 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s">
<mi>s</mi>
</math></span> ≤ 10 and −10 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d">
<mi>d</mi>
</math></span> ≤ 60, clearly showing the vertex.</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>Hence, identify why Model A may not be appropriate at lower speeds.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use Model B to calculate an estimate for the braking distance at a speed of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="20\,{\text{m}}\,{{\text{s}}^{ - 1}}">
<mn>20</mn>
<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>
</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>Calculate the percentage error in the estimate in part (e).</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>It is found that once a driver realizes the need to stop their vehicle, 1.6 seconds will elapse, on average, before the brakes are engaged. During this reaction time, the vehicle will continue to travel at its original speed.</p>
<p>A truck approaches an intersection with speed <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s\,{\text{m}}\,{{\text{s}}^{ - 1}}">
<mi>s</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>
</math></span>. The driver notices the intersection’s traffic lights are red and they must stop the vehicle within a distance of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="330\,{\text{m}}">
<mn>330</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>m</mtext>
</mrow>
</math></span>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>Using model B and taking reaction time into account, calculate the maximum possible speed of the truck if it is to stop before the intersection.</p>
<div class="marks">[3]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="text-align: left;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p{\left( {10} \right)^2} + q\left( {10} \right) = 60">
<mi>p</mi>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>10</mn>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>q</mi>
<mrow>
<mo>(</mo>
<mrow>
<mn>10</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>60</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="10p + q = 6\left( {100p + 10q = 60} \right)">
<mn>10</mn>
<mi>p</mi>
<mo>+</mo>
<mi>q</mi>
<mo>=</mo>
<mn>6</mn>
<mrow>
<mo>(</mo>
<mrow>
<mn>100</mn>
<mi>p</mi>
<mo>+</mo>
<mn>10</mn>
<mi>q</mi>
<mo>=</mo>
<mn>60</mn>
</mrow>
<mo>)</mo>
</mrow>
</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">a.i.</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 = 1">
<mi>p</mi>
<mo>=</mo>
<mn>1</mn>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q = - 4">
<mi>q</mi>
<mo>=</mo>
<mo>−</mo>
<mn>4</mn>
</math></span> <em><strong>A1A1</strong></em></p>
<p style="text-align: left;"><strong>Note:</strong> If <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
<mi>q</mi>
</math></span> are both incorrect then award <em><strong>M1A0</strong> </em>for an attempt to solve simultaneous equations.</p>
<p style="text-align: left;"><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align: left;">(2, −4) <em><strong>A1A1</strong></em></p>
<p style="text-align: left;"><strong>Note:</strong> Award <em><strong>A1</strong> </em>for each correct coordinate.<br>Award <em><strong>A0A1</strong> </em>if parentheses are missing.</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;"><img 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"> <em><strong>A3</strong></em></p>
<p style="text-align: left;"><strong>Note:</strong> Award <em><strong>A1</strong> </em>for smooth quadratic curve on labelled axes and within correct window.<br>Award <em><strong>A1</strong> </em>for the curve passing through (0, 0) and (10, 60). Award <em><strong>A1</strong> </em>for the curve passing through their vertex. Follow through from part (b).</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;">the graph indicates there are negative stopping distances (for low speeds) <em><strong>R1</strong></em></p>
<p style="text-align: left;"><strong>Note:</strong> Award <em><strong>R1</strong></em> for identifying that a feature of their graph results in negative stopping distances (vertex, range of stopping distances…).</p>
<p style="text-align: left;"><em><strong>[1 mark]</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="0.95 \times {20^2} - 3.92 \times 20">
<mn>0.95</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>20</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>3.92</mn>
<mo>×</mo>
<mn>20</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=" = 302\,\left( {\text{m}} \right)\,\,\left( {301.6 \ldots } \right)">
<mo>=</mo>
<mn>302</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mtext>m</mtext>
</mrow>
<mo>)</mo>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>301.6</mn>
<mo>…</mo>
</mrow>
<mo>)</mo>
</mrow>
</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">e.</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="\left| {\frac{{301.6 - 320}}{{320}}} \right| \times 100">
<mrow>
<mo>|</mo>
<mrow>
<mfrac>
<mrow>
<mn>301.6</mn>
<mo>−</mo>
<mn>320</mn>
</mrow>
<mrow>
<mn>320</mn>
</mrow>
</mfrac>
</mrow>
<mo>|</mo>
</mrow>
<mo>×</mo>
<mn>100</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=" = 5.75">
<mo>=</mo>
<mn>5.75</mn>
</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">f.</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="330 = 1.6 \times s + 0.95 \times {s^2} - 3.92 \times s">
<mn>330</mn>
<mo>=</mo>
<mn>1.6</mn>
<mo>×</mo>
<mi>s</mi>
<mo>+</mo>
<mn>0.95</mn>
<mo>×</mo>
<mrow>
<msup>
<mi>s</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>3.92</mn>
<mo>×</mo>
<mi>s</mi>
</math></span> <em><strong>M1A1</strong></em></p>
<p style="text-align: left;"><strong>Note:</strong> Award <em><strong>M1</strong> </em>for an attempt to find an expression including stopping distance (model B) and reaction distance, equated to 330. Award <em><strong>A1</strong> </em>for a completely correct equation.</p>
<p style="text-align: left;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="19.9\left( {{\text{m}}\,{{\text{s}}^{ - 1}}} \right)\,\,\left( {19.8988 \ldots } \right)">
<mn>19.9</mn>
<mrow>
<mo>(</mo>
<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>
</mrow>
<mo>)</mo>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>19.8988</mn>
<mo>…</mo>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>A1</strong></em></p>
<p style="text-align: left;"><em><strong>[3 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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<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{{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 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 src="data:image/png;base64,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"> <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>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,iVBORw0KGgoAAAANSUhEUgAAAVEAAACRCAYAAAB66YtCAAAgAElEQVR4Ae2dC3zU1Zn3H0IIk5AEkDshxshSjAhyEwGxZfHGa5W12ura1t5ct+vr68d1rXWtbbVaa2+uH2tdF/HSalvrraLr62utpWrR9YIoIiIiRW5yDbkSQhjD+/me8IPDMJPMTCbJf5L/+Xz+c27Pec5znpnzm+dc/7327du3z0IXaqCHaoCff69evVzrm5ubnU+ccO/evdvUyieffGJ79+61Pn362IoVK2zjxo124okn2qBBg1xZ8nNycg7U0SbDbkogmJFuaaZ0L/3LzzYV5GSbwPHkff6Z52zz5s3xssK0UANxNUAHVidWBwfsAM89e/YkBaAwFtDCQ2AZjUZdnfACGLIVHOIqrh2J0oN0j754cPoO2sG+y4p2CxDtMu2FFWe1BtRxATuF6+vrbceOHWm1Cx4A6K5du1x5+GKJ4ofuIFACnPz5CFTRjR/ONl11CxBtjO7ONr2H8naxBui0Ak6AjjBPTU2NG9UoLxkxI5GI5ebmOtKmpiarra11YdJS4ZNMXdlMwx+M/lDQC2HFQxDt4m927+6o5ea0/Ii7WJSw+izSgIaSEpmO3dDQYJWVlc5Xelu+5kWhgwfWLA6AYK40tp62+HXHfEASXeDQcV1dnZs2QV/ZDKC0J+st0T3MS+WbNTS3zEN1xx9g2KbMa8DvvFiMdGTAjgfwa2xsTLpSFpZwAwcOtJKSEuvXr5+LM6ynntC1aABdoNf169fbxx9/bLt373Z6R9/SYTbqKuvNt75mVlfZaHnZqP1Q5i7RAJ1ZIMoQU4tDCEMYIKWDJ+vy8vIOWFOAhAC4oKAgtEL3KxFrHQt0+/btTj+FhYXOMuXPS99HsvoOGl3WgygKzS20cDgftF9WwOWh4+Lo3ACnOrKG3nT4ZJxAGPrVq1fbiy++6AD1+OOPtyOOOCIZFj2CBksT6xMQZfsXT35+vms7uteccjYqI+uH8yg9khMJh/PZ+OvrYpkZRmr4LhCVSCwwJesAiE2bNtlrr71mixcvdmD617/+1aqqqg4snCTLqzvSMUfM/ll8rPPBgwdbcXGxA079mWXzvGjWgyhzojmWa80pzGF1xx9q2KbUNaCFH3wNK/F5WPhIxmHFAqIrV660999/31idZwFl3bp19vbbb7uVevh3V6c/n9Z85obZNgaAHnXUUW7uWFMo0rfANBv1lPUgypxo3/75Vl+XvOWQjV9UKHNmNaDOG8uVzp3K1iSmA9jS9N577zmQmDFjhhUVFdkZZ5xh77zzjm3bts0Ba2w9PSkOeI4YMcJZoCy6oWP077vYuJ8X9HCgQHTPnt22dfvWlHVWWFBoW3dsS7lcWKBnaoAOyzBe85/SAukAKAtFyTroH3roIWdpzZs3zz73uc+5oiNHjrRvfOMb1r9//8MAI1ne3YWOuc/hw4e7OeK+ffse0IesT/Qegmimvu3efeyxR36fMreiSMS2VlalXC4s0LM1QMelI6sT4wOgdHQszGQcQ3UWS6ZNm+YerFAAY9GiRc4iZQElFVBOps5so8HyRAcawiO/AJRwNgMo8gfKEnUC5UbwUnIFRUWWF+0WGw1Sanc84j3RqK1atTpeVpgWRwMCUbLozFiWPMxtJuM+/PBDw+osKytzli3zoyycMA/IQgrWbraDRDJ6aIsGPccCJ3rpDroJFIhyniHHUp+ELy4eYE05LadE2voyu3v+m4tft72W/B7H7q6PRO1Th8b3gU7DfC4hScZx8Q2WK/seme/DEmX4CphyHLQ7gEQyemiLprsAZrx2BgpEc3JzraE+dRBtwPpavipe+3pU2jtLl1p9U5UdN3ZCj2p3qo0VgFLODxMXoCYLooBDeXm5m+9jVZ450CFDhrhTOVizTAvE1pGqvN2Bvjv/mQQKRPmxVFZtSOk3U1NVZd/59r/ZYw8ttIcefzilst2J+O0l79jL//OGfWbOGd2pWR3WlkTAps6e7HC+tLTUxo0b5/Y9AphYpAzvsVDhkaieDmtYgBmjC+aQeWL1EhsPcDMOEy1wIFpcMMDqUtjzee8Dv7KtW7fb2AmTbMUby+z5Rc8f1sjunrB0yVJbtf4D+8Y/fcX67r9NqLu3ORPta63jMhxPxmGFDhs2zO0NBRxYQBkwYICzaDn+Kcs2ES9kaE2OROU6Iz2ebPHSOLVFW/0/ntg2qVysr3boz0vxbPIDB6L9hw20+qrkVtrZEP3yolfswi9daLubKu3LX/uyvf3WMnv+2eey6Ttol6w1NXWW37+fXXDu561v35ZjdO1i2AMK02F5sBxZRJJl5Hf8WCtSnd9Xj+gZ+gOW8CINn8tI3n33XbfApCF9LA/igLX4+LyDEPavrkMe9KQ0tQX5q6urneXNKS/p1tcptKSjI1boedr6cwlC+5OVIXBL2sMHllptfa2NsBFttuGB3/zGRleU2Zcv+qq99eZbtnNntX3rqquMFeqe4ADQSCTXKsaM7QnN7ZQ2CgTw1fn9iuOlaQEJsPSt0UcffdSBJOfo2erEnKnPlzCAix9Ep6vrJBvAx4NDDwAoNzJx2ID2YYHHOtHHpnenePAs0SMi1pTkDTpLX19i53/+H90QdsbJJ9nq1S2LSz1hSMuc21133hFanxnujQCaHgCxLYdlJnpoARSOe7JP9MEHH7Rbb73VWaTcCgXw4Hy+2WCRIbcsS+kD6xvLEyuUPHYlaD8s9Pw59AQARR+BA1EuV66rb/sGnd27dtvO6p02depU972OLR9ta9as0Xfc7f2tO3bYZZdf3u3b2ZkNBAzp+Bpu+sBBXjyndIb/0HOb07Jly+zll1920wUfffSRAxrAViAaj0+Q05Bbj+RUnJuquEOVXQmk6RpA6NCHrHOV645+4IbzOZE8q9/R8nqF1hT+0fqPbN68cw+QlJSUWkNtoxvK9wRLdOL48QfaHgYyowFZlAApj+ZMBZSxtZAOHWChMENgzopTtqKiwsaPH+/mR6ETHwGQH4e34rH1dHUcuWJlUzvZE8s+Wf54BJqiJY6j7d3ZxbRuuy358VDr1etf7IaPu2ZeMS/J1eUNmzbY3LmnHvhuRpSMsMqaSmvcFW40P6CUMJCyBgAAOr3AEcBrzUEvECXMFifmQGfNmuVuLDr77LNt1KhRbj5UYCKQgS9l26qjtfo7Iw95JbNkZbgOgPKHAaAqXfOoWN78keBUtjNk7Yo6YkB0vwgjjrCh/eJndYaQu/a2vC2xtbpOP/V0dzOMT1PUP9927kzvTY0+nzDcczVAh48FUQFEIq2oDKDBvODYsWPts5/9rDuxRJjN96T7YKKwrDXFE9XRFel+uwnzSF7kwfpEbtJ4CNNO6NAFcf1xdIX8nVXnIUjZvPFOu+t7A23C7d+0f+5/SFZnyWPN0WZriiZ3bjlWqElTTrTFLy2OTc76+Nbt2+2l517K+nZkSwPo/Dw+iLQmeyyYACRjxoxxPDg/j9UmC83nkyx/v0xnhpHPl9EPI4fyAUyBJukAKuCpnQex5TqzDZ1Rl4eUG23pA/faA1+5xR48r8y6arI0vyjfGuuTf0mYr6Qxo8vttTfeNBaduourrKqym266yY4oGdJdmhTodghAETJe5xdw+I2gDMNXwJT5Qbb+kMa2H268Jw6oUNa35OLx9/l2ZjieLMhMO3D4xGmj74gLLNU2fNKgRy+0vzs7DytH2dTvbLCubm5hpNAqd7a9sBT7pXAX6bPPLLI777zd3ntnuS166c+xJFkXZ7/r/DvvtClTJtlx4yqyTv6gC0xHj3WAgj8kJQ4Q4AgLDGPLydIEjAActgBxETFbmygvgIGHAEu8BFSxPDsrzo4C5GM+F8cKO38GsXIlitMOHjnpgrgfVn538w//FXVxC9m43DuJ/XmxYi5b9pb95JZbXPKbK16Pzc7a+IRx4+2U00/PWvmzWXABnw8eAKCAUj5tFDBCCwiz8RzABKB0+snnExS90Eb6HPLr2GY8AA2KvEGU4+DfR0CkY59oNCf1nQFlZeU2dNRQ14qSYaX2yquvBqRF6YvBVq3Tzv6s5fcLj3Omr8X0SzLPh5OlFQuCAk5oACPo8bFwWUzCB0Q5ngxAUZ4yfrlYnulLm15JyYKP/MjM8Ft/IOlx7VmlAgmi+3JSN5CHDRthF553oY0eVWblo8ts0XOLusUiU0/Y8xrELgeoaC4PoIsHdrFAQxkegIiLmRnKwoOTPfGu1oM2Ee/O0Inqpx08Gnp/8MEHB6YwOkOObK8jcCCKQnn5XDrukksvtvGTp1jF2HF29Xe+bc8ves6WLFmaDqsuK8PVfj3l7H+XKTmJigEYDW8FdLFACo2AlDzNC+IzvwiYMqTHEgVEVZ5yOJVNQpwOI0FWyUMlvFiPI8VBkK3DGp1hxoEE0T17k7tVPFYXRxQfYRXjx9qAoQPcefprrr7Wnnn2Kff+71jaIMbZynTfA/eZfdLVy3tB1E7nygSwAHw+wMSTALCBRkN+ASlWHQDKZnS2ObHAFOu6GqgAdWSXv3PnTluxYoU7YYWsbbU9tj09NR44EGUkzw336bhoc9QGFBRb9fqWN38yl3jOWefabbfdbmwVCrJjd8Hvf/M7+/uTTgsvFQnIF9UWiAp8JK4sTYEjgFpcXOwA1B/OC5xiffHpLJ/6kRU5sbq5kelvf/ubO65KnuTrLHmytZ7AgSiK1I8xVaUWFBRabUO1NXnbLSZMnGDzzjrTfnbrTwINpM//5UUbOnKoTZwavtoj1e+9I+gBEICFxZZEYMLvFGvT/70CSmxpIk0gCh8fRCWvwFbxzvRpk+Z8kRP5sJa5ZFrvhu9MebK5ruCBaE5u2ieW+vcvchdTDRg+2NasPXij09Rp0+yLF3zVfnLTzbZh07pAfl8DC4vt3PO+EEjZeqpQ/v5O6QBwFGgKKAEkPQCjv6rPcB4+ShMffJVR2M/r6DCyUz+OfaHIyBn/OXPmOEBlOgJwDV3bGgiclnJyohbZy3s/03Q5OXbqzFm25JVD94pOGF9h137vOluw4H57+umn02TeccVmzpoZvtqj49R7GGcBIRmAhR8nDYAB+AQkgKNAT+BDGVmTKs9iEvsusfIojxWKtQqdLD/iOOgAL/ipvMvopA/2s9I+9oWymwAQJU56V8jTSc3OeDWBA9Hm5lyri6Z+YkmaYX9epLDQ3lyxXEkHfF7ZcN13v2sb1q21xx999EB6GOiZGvDBMJ4GAJK2wCQ2H54AEUCpE0CAEotLbHXCCZBjy8aToSPT1D58wF9bnLparo5sc0fwDhyI5vTtY/UN6V1AgoKGDx1u+RxDa47Pg32Xl152uVXX19rjTz7RETpNiWcqL+VLiXFInLYGAEJZhwKaeMyUJ3r5gCRAytl50lhc2rVrl1VWVrq4P7SHLgSteNrNnrTAgSj3iYJ/u9N9T9L+hf3caF6r3wLvZdrw0cYuBVL2D958ww3hvtBWv6muyRSIJlO7LEtoKQdIAozc+s5wHjBlKM8WItGILyAauuzWQOC+QWZDmRdlrigdN2TgENtUXW21TS233CfigUX6r1dcbmtXrLZnumCOlA3N37vuezZv3lnhXGiiL6mT02VJUq1ANBkrUSAaS8twnhVvwJThPdaoAFa08ju5qWF1GdRA4EDU7RHNzUl7w/mIwYOtctNWO3J0iW3bvLlNVV3+7X+zpUvfsWefffYAbd2uOmtOE8QPMGklgAV6++232ze+9hWbOXNWK5RhVldoQGCazlCbMlo4Yp6Rs/N6hQar4Hz3vvUZgmhXfMOZrTNwIOrAK9r2WxYTqWHAkCG2dtMamzx+kq1evToR2YF0LNLvfv879uqrr7gjoktef91uuv5629uBp4bWrd9oJ0yfbhMmTz4gRxgIlgZkiSYjVSzY+iDJMB6gZKsTVikb2mNdCKSxGsmueOBAlAOP3OSUrnMb7msbrKy8zF5//dBtTq3xvPbaa+3e+xfYLbf+zC6/6mprjppxDLMjHHeDnnfOOR3BOuSZIQ0Aoj4Y+mzJ8x2WJ0DIsJ7hOvmAJ772Ww4dOtSFP/74Y7cS7pcPw9mtgcCBKOqMNjdZXt/0rn9jw320od5Gjiix+sb6pL+dVStX2/qN621M2WgrzI3YNddeYytWrki6fEiYfRqIBUO1gPREeaLxfQBUIKr5Uc3ps70JkGV7HftCeS+971Ktyy8bhoOhgcCBKMP55pzWV9bbUl1ubsTyIxEriBTYpnUb2iK3d5a+Y7fedqvd91/32DnnzrOvfeUbNmXK8Tbn07PbLJsMAefig352P5l2dDcafxgNmAGAAkHaypymvxlewIqFqjB0AkLSeeCLBcpCEjyIs8hUVFTkTgNt2bLlQHlZrpnWLXxpi+RjPraqquowEM90vT2RX+BAlIWlpsYGa8eZJWtsanDf5fSZn7ZXXmn7xXVjJxxrd997rw0bMcI+3rLF8orzLC9SkJHFJd73dNstt9nmgB437Yk/+kRtFqjiCwh9sFQ50SkuGtIFooAn25tIIx9QZZWeRaZVq1apqMsXeB9IbGcglh9TC1jAbLEC2EOXWQ0EDkRpXl4kt13vetpd17LRvmLMaFu3aVObGmNxiWfdunX2yuJX7L577rFN67fYc88932bZtggeWfiYHTd1gh133MS2SMP8TtaAwI9qAbtYEOQ4JKCI82lF7zKS+ADU4M28KA+XHgvoGOrDm3gmnHgJzOEJiGKJcslIpurJhKzdhUfgQJThfJ7ltssS7VPUsjB1xJAhtmPLNtu9qy6p72vo4KF2/fXXu2HX5Vdebq8vXWLvr2x7hT8Rc1b6t27abKfNnZuIJEwPkAYEpAJTrEaBkUCUvFSdyvDeJY4lb9++3R0B1ZBb9abKNx69ZBf4QwNQ84fA7Uy0KXSZ1UDgQJTm1Tc2tssSZYUeh3VZNrrcVicxLwo9948yb6Wy11x9ld1+589taxL7TV0h74P9gM8vet6++vWvh5vpPb0EOQhQ6kFOFoIERn56qm0AxHAAHHOjDOs//PBDZxUy50odokmVdzx6+GFxYoHi0w4uGOHtoxxBDV1mNRBIEOWl9wBgui636WDZk046yV5+8cW0WPXtm28/veXn9u/f/7at25DaFXpbPt5ip8+da8OGhO+LT0v5nVBIFiJVAZIAjh6sROYxfRpfJOhTdZTBGp0wYYL99a9/dYtO7QHn1uoHnAFRLVwB0topoJ0DrZUP85LXQOBAlMOehdZiSSbfjBjKyMH5pbHHHmsb1m4w3l2UjsMyvfHGH9vtt91lmza0vdKvOsaMHWOTJ4ab6aWPbPAFaPiAqe98MI2X79PGhgEyHDzYdH/UUUfZ1q1b3WIPC1CydmPLpRvXHwBDd+0OgJfk9tuSbh1huYMaCByI8n6hggEFByVMI9RQf3AvHhbt2IoKW746/T2fpSNK7NJLL7Y7598ZblVK4/vIliKAix4NiQEenNKJ60m1XfAE1JibLCkpsffff98t+KTKpzV6yUZdPALM2PTWeIR5qWkgcCDa3BS13gdH46m1Zj91Xt6hluzsOZ+2xS+0vdWptcrGjBlj55/zRfv1gvvDW5daU1QW5QEscoCNgEe+hvY+DWHS/bLKT+TDjzJYiNTDsHr8+PH2zjvvOGs01upNxCfZdOpAPtWpIT3pepLlFdK1rYHggWjUbB8XkLTDxRYvKyuzLR9vs92Nje3gau79RyXlJXbP/LvaxScsHEwNADC+i/eGTll0Pq3CyoMHYfZmCpBJE/gCoscee6y7X5SN92w/EuhBw/5STQHE8hQP1SF5SWeuMxFIJkpX+dBPXwPtQ6v0601Ykjd25rKy1B7XfHizpkyaZG8uXdIerq7sBV+4wCyaYw899NAhvFiNf/TRPxySFkaySwMAlhygxG30gCDOBzPi/mq6ACqWhq1MmvMUmEJDePjw4e51HGvWrHGb4LWSTj5hANHnR1hyuICZA1rkxAG6WjCCPzLhIycP8dB1jAYOR5uOqSclro1N7bMY41V25plz7be/eyReVsppl11xmW3btsPuvf9+V3bDhg123XXX2OSpk1LmFRYIrgYAM4GXL2UiQBKYihaAY3tRPMCF5jOf+Yzx2+HhyjzqAvhYfMLHCUhVpw+IgCZ1QEO+yqj+0O8cDQQORLnBKb9v3/a1PnL4hc6DhgyxfsUR936l9jFvKX3FFZdbU0O93XHHnXbnXXfY1Vdfa6PLyzPBOuQREA1wwkcgKoCUH09EQMwHMkCO3R1YoziVhSd5TDOxyMSe0W3btrmyADd0lIFOlqbK4ysNOurDx0lWFwk/Ok0DwQPRglzbXde+87319YeDKBq94tLLbf6C+RlT7pcvvsSeX/SMDR9WYkNLSzPGN2TUtRoQ2DFXqUUZXyLlx4KWQA1agA4QZnM76YAm9DzwFBCeffbZjm7t2rVuLhTwFJACkL7lSVlZn9ShfaykM52ERfvRRx/5oobhTtBA4EDUevexhvr0h/N7olGL7ImvudLSUndX6epV6R/lFGeOpz718ON2zRXXWZ/cPHvstw8qK/SzTAMCN8QG8OQL+BI1h3KxjjQBJCDM0Bwg5AEUyYMGAGTOlfcvcZJox44dBy4Rp14cYCvAphxxePDgJDf18CZRePAyvNB1rgYCB6IMfBosfRCtr6mywpLBCbX4zUsvszvn39XuG5q4berTp86ymbNn2j998xKrra4+MEeasPIwI1AaEGBKKMXlA1wKi8b3W8uDjtV9zqwDmAAfIIiViaMsq/QA4bhx41ycYT00pKu8AJl0HsqpXsrisF7ZWN+/f393Isolhh+dpoHAgajl5lqEd8+nuR1p9ao1dvzYcQkVyDHM0aPLbXESV+QlZLI/o7SkzIXY0M9rmOsra+3eBQvaKhbmZ4EGZO3hC7QkdmycdAGaHwZEZYFSBhpAUbwBS6zOYcOGuUub2RK1ceNGVwY+gKYc5cXDr4s0QJRpA1b84RW6ztVA4EA0n0n4dryobvP2zVZaVpJQi1iQ55//j7bwqaczvmn+im9d4d5n/9DDh25/SihMmBFYDQBOOPkSNDZOukBNPjQ8zInik84DeAJ4pGGRClABWqaaGPq/++67DljhixWLk0UMnepwGfs/4Acgc7kJT+g6VwOBA1HmNNkmyjuO0nE7tm2zvDZ+SFijR5aX2vLXl6ZcBbfUP/HEEwnLXXXlVbZm9Rp7e8k7CWnCjGBowAckAV2sZAAUIKZ8vwx5OOX5ZUkjH5/yAkwtBgGiPGyBwh155JFubpQ7bdmAD73yZJECwr5l7NevOnwZwnDnaCBwIOpub4qapfuuupqqJuufxJ2Jn5s7z55Z9EzK1ujLr71m0abWEf6Sb37Tfv/IA1ZTk9w9pp3zVYe1+BrwwQ0wYlgNWAmMACtADjpOEJEuJ/BSHJ80pePDizlKWaOUJ408eGI5ij8Wp4bjbHnihifliSdlCOtR3JdXc6m+XGG44zUQOBBVk9O1RBuba8y9u16MEvjcM2rNObZ+7ZoEFIcn86qPF55/wU4//dTDM70ULN1TT59rD/zuPi81DAZJAwIjXyYBFgCKxQiQ4RhG85APePH4zuclHvjwwOk1IQzlWUnH2ly0aJHx5k/y4AcYlpeXG1c3LlmyxIEvZf2jpwAy9JILOSUbYQG1L1sY7ngNBBZE0206r6znx5qM+/y8z9tTjz+ZtDX6yMJHbOas6dZ/4MA22c+ZPdvqKnfZkleTf21zm0xDgoxqQKAIU0AIRxq/H+YnOUWEE4C6iDcHqriA04/Dj+E4AClA1sLRn/70J3vzzTftV7/6lb311lvuBXICZ+4bnTdvnt14440OcJFDVjKWJrx4qFNWKGWJC1AlR+h3jgYCCaLRnINDp1TVwFCef/tk3LETj7Wapnpb9e57rZIzT/vr+++1wkihnT6ndStUjLCGL73sUrvngXvC6/OklID5PvgRVhyQYljNPk4cgKi8RE0QCJIvUANEGcITBwhffvlle/DBBx24XnjhhXb++efbypUr3d2iACIgyBQAFimvWH7ttdecDNomBR+sUGhVH/xVRyLZwvSO1UAgQXRA8QBraEj+nfG+ioYOHmn1dTV+Uqvhq6+82v7ztttat0Y/2WuzZs+28847L6mpAlVIR+A46M0339TuG6TEM/QzpwEfGAWi+FiirHJjiQJQsc4vpzxADSdwgwbwA/T4U9+0aZN7yydDeEBw+fLl7j5RLikRgFIX9LyHiZNMDOu5oITyDOVZcFq/fv0By5U6AF5Z0dQNr9B1rgYCCaJDhgyzhv1WQKrqKCkZZnX1LcOwZMpytvmzF5xnt97204TkvCZkdPnohPmtZXCe/qwzz7Q7/uM2i8ZYyFu3bm4dvFtjHOa1SwMCPZgQBpAEjliigCjgJatPlfl0SpPv8ySN4TfgBw9OE1GWe2mhYyvTe++9Z6NHj3ZTB5rnBBTZOH/ccce5PZ8M+//2t785axUA5pXH0MIL8NQj2WNlkGyh33EaCCSIDsgrdv+26TSbH399dWpW7NlnnmWNu5rs1dcPnb9kO1Mm3Jw5p1p+vwL74Y9/bCxO4TZv3mzfu/56q03ztSWZkKun8gBoBDbyBULoBCBjOM8QPNayE710p7h80hXWQhJAx+r70UcfbZ/61KecpctRz2OOOcYtJDGExwqFXvOoLCBxyxPWsKxWphd4yR1//JI3HshLttDvHA0EEkQLhhTZhi1b0tIAW6Si1voWpHiMr77qKvvdgvutcvt2l82FDo/94ZGMWYr/fNllNnDIQLv5JzcbFuj3v/t9NyfG0C10na8BAZ1fM2k8sgYBKh7RylcZAZjS5SufslizgHFFRYV7QR0gyWLRiSeeaF/4whfce+hZTML6pLweAJMTSKeccoqzQpctW+asTtIAeBy0gK/kkLyqP/Q7RwOBBNGjhg+3bWm8phiV7cnvY3v2JriBpBWd8u/+xYsvsp/dequbv5x/5wKbOmFau9466lcHuF9x2RU2bfo0+4cz/pfNO3XR+okAACAASURBVHeezfn0bEfyxMKnfNIw3EUaEIABRgzFsSBjgQkaOcDRjyvd5wMNPABmTiWddtppbr4TUNUqu4BQQ3N8XnGMgw7rFcfL7RjKq07KqQx1AKakha5zNRBIEC0oKrJmS2+CvGTAYOPUUjpu+vSZDuT+zyXftNmnzrKx4yrSYdNqmQ9XrrWyinG2ZUu1W6R64qGHbeO61F7H3GoFYWabGhCoQcgQmjhOgATgYTEypNacJgAFHTQCKsV9fprbhI5VdrY1cc3d0qVL3TwoccAT3qqTOHUCjtQjB5DDe86cOXbWWWe5Ka4f/ehHbn4VGqxcHOWwXLnJifbIIQvTAZrb9dMVDv32a+CgxtvPK2McCvZP6qfDcMDAgbZh3aZ0iroy555zru3aVWeLXnzRvUyMRaVMOK7Oe3f1avto3Rp7+KHf2h233WH33nu/PbfoWXvg17/NRBUhjwxrAHBiszvDb0Au1pEGyLHYg8UJ6AG+gBer8WxpeuWVV9wrkpkTZbUeeq6rY0Hp3HPPdaBMOQ3JFYYG8GOHBzy5wBmwZX705z//uZ1xxhk2Y8YMB/IAJzIC7siL3MRJF6iShox+Wmx7wnh6GggkiNKUpt3pLerkRyKWV9BylVh6KjG76Etftccff9RuvukWu/qaq91Efrq8VI59o1gmv/jFL1zS1/75a/aZE2fYT3/xHxmbMlBdoZ8ZDWBNYjkCZIAPAAgYyRHHAY6AH/QAKIuGgCf5gB+WJAtJgJiAjsuTeU8XQ/WxY8ceqAMLla1MrMgzTwqA8gCKnK9n2omhPntIAVpOOHFzE3IBxAA7cuCoCxmI4/OQBq3A1RGGH+3SQCCH85HciO1pbBnupNO6vmkcvGdDvVbOqfO8875gc2bPsauuvipjl4kU7b9sglX/+XfcZRdfcak9/NAzh9SbTnvDMpnXAIADOFZXVx8AI2oBgASk0ACaABdWIg6QAqAAvokTJzqQPOqoo9zKPNubAE1W5SdPnuzu/uQOUfaCMhwH7CjPEBy+ACYykE6d1MdK/tSpU23mzJnulSJ/+ctf3FYpyiAHD1MQlMdRRr7AFD90mdNAILWZW5TvflTuRqc02lq5rTalUoDaffMX2JvL3jyk3OxTZ9stN91sv1/4O1uwYEHGVupXrlhpw8pK7NKvf9Muufgf7ZZbfnBIvWGk6zUA+ABizDP685S+ZACbhuGki45tSAAoly1jQWJdClwBWICR4TxWJItNWJ5YrxpuY/kyaikpKTmwEq96AEBW5wHh448/3vHl/fVvvPGGm0Lw5QNQkZG6KU+bQgD1NZSZcCBB1FlseTnWuH9PZapNLR1bYps3bU662PLlK+yEE0+0WTNnHVaGF9z94IYfWmEkYtd959/T3r/qM66YMMEuuvBLbmFp2vTpVlI22h56OJwX9XXU1WHAhq1HbHUDhGId4MQDUMnag4ZygCTgCAhDg2Xo89BCEkP86dOnuz2kWKLMrcKP4fnf/d3fuXR4UxYfvli48GTuk21Sc+fOdWmcwX/11Vfde5Z8sKQsVqnqpyxgHbrMaaD3DTfccEPm2GWO09I33rBjx41zP8RUuTY3RK1ud7WVlCT38riRI0fayJEjElaTm5Nj448/3oYPGW7X//u1Nqx0lJWOGpWQvq0M+Plu/JQp9offP2aDBgyyYSPCm8l93XRVGNDRO4sYhjM/GesAJCxLfBzgJdADEAE9rEwWlbSwJABkDhVa5lz11k/AljKar0QGAA9ghpYwNAAtFi5DeICaTfzIx9QAp6CwVAFq6hBgywKlfkBV0w+xbQrjqWvg0N6cevkOK1HQv3/aRz/7FUasMdr2JSQ1KR4tnTBxgv3XfffZY08vtP/40c+sqrIqI+3n/nIuK7nvgbvDO0gzotH2MwF0AD7AUENpAAgwA8QEbNSEtcpKOg4ABLywYkkjT4AGKPIAcrrijsMWvBKEhSYAVfUBmNQLL+oj7+2337Y//vGPbi5UgCtAPeGEE9zdDhgE999/v/33f/+3A1XqEYACnvCM94fQfo31XA6BtUTf+2ClRfIibliU6tezbftWa6ztZWXl8a1Ftht9vGmTrV67xoYOG26xlmFr9fXJ62NnzDnV6vbstrv/6y7rk5drI0aWWB9vf15r5RPlYVEURApt0V/+ZBMmTU5JpkQ8w/T0NQDYsKi0evVqt9UN4AFAeeQUhhagBECZ/5QVSjpbnQBNLEesTEARUIMe2g8++MBYHFqxYoUrx7FlTiUJ+KgDa5bVfk4tYX2++OKLbr6UN4UCtoA1AA/oMw0we/Zsd9kJV+5hmULDghS84QeYAr6hy4wGAguiWz/62GprG+2YijEpt7S6tsYqt22z0WMOvzSExaoP3n3PVq370E46cbr1zWt5j02qlYw++mibPmOGPbfoz/bkEwttT7TJjhxZaoBsum74qBJ745U3bNOWjVbxqbHWK2bYny7fsFzqGgCUACze5c6pIUAQAOIhD4tSQIfPozzyAUmAiiE24KltUliQACmOMgAtw3EsUuZFubCZRSamEOAH0HLTPduZWKziYpKqqiqXx7wrvKlHoChAZ0fAhAkTHB1/BFx4Ag/agZWM/GoPZYgjt9qEfMR9H/rQHa6BwILotsrtVlu13Y497rjDpW4jZV9Ob3vzrdds0sTJh1FWba+0nTt22IknzUobQMUU62TGidPt+EmTbPmyd+2B+39tn/Taa2Xlo9OyJLGIJ54wxZ567Amrqa2xsccco6pCv5M1AIAwFOa+T1bZNQT2gQTAwcojTSBKGEBTnJuXAFSAS0CMJcg+UECTdFbzAVl8aAFSQA+rEodFiUXLohJX5+3cudMYtgOi0COrZKBe6icNyxSePDjAmdNT8AK0fTlVHh8HsCoMLx6c0lwk/HAaCCyIVtdX27q1G2zipIkpf1X98vPtlZf/atOmTT+kLFZocXGRjRhVkhbIHcLMixT262cTJx5v02ZOd1tN5t92t/XONystLUt5mA+QnjjrJHv4d7+3uvpdNnZsy7lpr7ow2EkaACDZ1I4FKBAVOApMBDbE9UAj4AHwSGc4DQ+G3oAZV9wJODXEZ9hPGuUBO6YHGIIz5CdM/vvvv+/Ake1NDOfhjQw4wvKxLAFY6oQnD2HahEUKuDNfS11Ys9CKl9ok4IRGfEWjulxGD/8I7MISt8g3NCV/L2js9zigeOghSVu3b7WbbvjhIWmZjgwaONAuufgS++Xdv7Cqqhr7p4svtkWLXjDmYFNxXFZy4w9vtJdefcFeemlxKkVD2gxpAJAAtLTQA7AIVKiCfOIADA9hgEt0xHmwNAEoHPkMxQFFzVMKlFQOsAW02UPKeXuADotz1KhRDlCxILGMsURlcfpNFh+sXuoljnxsm2Jv6cknn+yG+SxUMdVAHWyPwjImDad24VMeufUoH191uUI9+COwIOqGLlu3pv3V9Ot/cEsK19vdcvMtduUVl6XNL5WC+f3y7aIvXWT33H2Pvb1suV16yb/Yopdesrq6qpQA9eYbf2xPLVxo761amUr1IW0GNAC4YaEx9AZABIo+a9IAMgEhdACLwIU8LEDyycMBnkwTsD8US1IAizXKAx3++PHjD6z6A6D0B/hwNR4r8Vio1E8aVip14fABTclBXFYmtAzxsWK5ho/pgm3btrn9pYsXL3ZTCFjJTDNQHr445mWZy0V2HHzIJ47f011gz84XFhdaQwo31Md+kb2bD56f37ppu3GfJxvnO9MBpv925eXO+lhw/732zCNP2YDSQTb3tDNs/LgK69O7T6uvG8Eivfbaa+wHN11vV1xxpY0enfoiW2e2t7vVBVgASAzBATcBldpJvoAMHwc9jxwAxhwngAOgsuADKMIPYASkASvAiDAOEKUuaJkOOPbYY511KsCSHICbD6DIIAAFqPkT8IGQhTJkxjrGyuboKBv2mSNl5Z83kEIzbdo0dyE0QA0/pgEoh6MO6sWRp3SX0EM/Ajsnajm97dk//dk+8+mTU55X5Lt84S+LbNXfVtvYYypsxMhhNmTQoC77ivkRnjRjpp1+5uk2ZNBg+9Pzz9hTT/5f+yTabMNHDHc/9kTCFfTrZ5865libf/d8O27ccWkdPkjEO0xvWwO854jjlwyzZQ36pQSigAmgwiOH9cbQ/d5773XbmAA/VtfxebRaDsBSHtCjPKCNz6IWYIjFSv2UgU7ABUBCp7jqhR+/OfIoz0OYbXS0AUcZ6HiwTrkEhTP5TB2wmr9w4UI3d8t0BvUCuqqLegXesXVLhp7kB9YSxQobYAUW/YR/55YvPtkvhgWkW2/7iR0xYKiNLh1t02dOS7Zoh9OxXYZn6/bttuiF5+0H111vg48cahd+4UJ3ciWeALyn6Yuf/7LdNf8uu/rfv2O6yCQebZiWWQ1gPXJ+HrABRHwHgAhElAeoYjGSjlXHXCOLOISx+JgTBRCZ6wQcKQdIqZxAmTRAlZV1fFmh5AvMkIU4spFPGQEccfIATYE/aVi70DNnKlrocAAvQ3zmT5kfZVENC5U9rMiMBc2Zf+ZjcVjTtFNtd4k98COwIMp3kTc416INUbOWtyEk/fU01tVZXc0uO/LIQlu5ckWgQFSNGDZkiAPOs848y1YsW2kLFsy32upqO/nkv7fT5861/v2LROr8iVMn2JZtH9vPfvgjt+h0SGYY6RANAC5YYFhyAI/vyBOAAk6EeUjnAVi0uR0QBjzZcwogAYoAGz5ltAAEwBEnj1vsAXCAjk3/WuACKAEvnECRsACRfECQOGEfcKGjLvIoqzzJTN3IBA1WK/OvgD3HX5krZWcAl53AHzDlaj7ANQRR93UE8yPaFE3q+Gas9E1NUSvuP8g+3rjRKuu321MLn7JmLNo+vSynOdf27L+rtBf77PeZ5TA537uPu6WJt4w21kctN9Js1pxru6L11i+v0CIWseZI1Jrqo7Z5+2ZjG9XJM062stHllheJWFG/gwtZyLMrGrV++yfmuUs0kSvqV+RAHmuZq/j+/Pyzdt33vmU12+vt3HM/bzNnzzIAFzf3zLlWtavKbr/tNrviyisTsQzTM6QBQIX5SaxIhtgCHkAHUAVsCEMnR5gH4AU4AZxzzjnH0TO3yXwkIAYNc4viRXn4CyQBM6xF6mFagMUezctSFh440ngoq7BeI0JZySfAhI50rE7qog3URZw/DKVTDjCn/QAquwKwTnkAVuZ52YaFjJSBlntOmRogrDbiS1bJi/yxwEt9OMkLjeIu4G3hUjzWpywPvGknjjBp6AY5xD+2bHvivfbBNaBu/vz5NuWEKTZ18tSkJGQY/z+LF1tpWamNGjnS6hsajW1HHeEAvOWrltnqVWts66ZtBnBbn2b3irycPc3WnPuJNTeywpljUWt2P7bSo452YDxocKEVFRZYYVF/t7BUU19rXCZdXFhshQMHOvDdtXu3vfw/L9tLzy6y2miDWY7ZlHFTrLSszBY++Qcbc3S5nTDjZJs+bXKri1Md0faexPPpp592liC3yLPQA/AIiAAYug+gRKcXAGI5AjAAKVfa4ZMHGAE4dGysTsARJ8AQuJBPmHqg4wFwiZMnYBJAUL9o8AEMeAP8hKGjfngShxc8CCO/eAKoagM8qY8y0NJWfBxWMdY1YAov6oReVix8qB/eDP3RAVY1bYeP2unXr/bi66G8HpWhLuX7PnKJVnxpC22jHeQhP3IhH+mZcolNpEzV0A4+I4ePtK1bdibFYXdjoy18/Amz3GZ3dphCmXq1RzwBWHmfNnm6e+Llx6bVVFVZQ2OjNTQ2OAuFdr29fIU1NTRZ8dBia6xvtKraaivKi9jmyu02pnyMezvo7DNPtQEFhbatutrWrV5jzzyz0LZv2WxPPP2kVX//u3bRRV+1Uz5zmo0+5igrHXmks4pjpwJiZQnjyWuA4SrDWQGKSqoT0pEBEOKEAS4sQfZgYpnx0HnJo1PHOtJxdHKc4i6y/4M8AQH5qks0ygc8cAJ3AIdy0OshjrwAO4CCz4PcACJhLG/Ckgme1MsjQOUPgflawBT9UE7bo5CDYb92FrCdi/sAAFLmgbFUeZBJ/AA2+AO0pKm9ft2E4S0doM94MvpASz6PdE95+GfSZZZbJiUzs6PKS23JW28lxXX5u+9aWUmZTZkVnEUkX/D+AwdafyWUKxDfx6LmbafVVZVuimHnlp0YojZmzFgbf8I4q6xutMqGGnvxhS32/57/o3247kPra31s++4aG5I/0ErLS9x8VT93qUnEigcOsfJRw23QkGFWXFBsxYMGpvxKEmRiy3hrUxPxW5PdqQxjV61adQBE1WkBAMJ0aFk2xAU+WF9YYXRY8nHkCxwEakqHTyJHnkBA9JKDuPJFo3qUjs8jWuQBxHDIwyNal+gNqxUHeLFAAUZAkzCWKOAJL1b12cUAb/jxR8IcMItpbOhnOoI2M/wHSIcOHXpg+I8Fi54EzEwryPGHQL4AU7pGXurB0V4efSek8adAGnx5kF/WtP5spC/Vla4faBAdPqzE1qx+LKm2TZua3JA/KWZdTMTOBH6UPInc2NJye+TRR+3iS75uxcUDbMe2ltvR+bHW1dTZx9u2WM3WGttUv9U2bX7JcnOarSkasfqmnbZ9wyYbOGSEjRlb7hY/CiMF1n/QQBtTNsYKBxRa0cAii1juAcBsiDZa5fZKe+jhh2x0abmNHjPWPjWm3KxPb9tTt9tq6+vde4QSyZrN6YAonY5O6Ds6rDoxnRQHgJKO1YUFiqMz01np9OrshKHDwQP+xNWpRYcPrR7i0OP7Tvm+Dy/x82ljw5SRLKqPOniUh08bscp5mNYgzXeUpR2kUy8gyQ1SLEDxShTO/DPFwbYttnaxyZ/bqfi9Asw8WMCUY16V+gBP6sPiBVipg8taSNO2LwCcOtE9D98T0yks4MEPYGdXARYuvMmnLr5X3SngtyOdcKDnRLF+rvrX/22//OXd6bQtLBNHA0wrAHqc4lr30UZbt3WtfbB8tVXVVFlV5VZraOxl/QcWWMkRw214WYmxT3Vg8QDLLeDf3GxXY73VVlXZuvVrbfX76+yCC86z0tISO+vMeXFqy/4kgIF9nlOmTHF7PDVUBngAGnw6r0CLNMrgsJoYMisvFng6QjsADUBBnT44ks6DE+jg8wBYovVlEpjSHngKWGkXeqCsaAhTJ3UQpt2AGSAH6OFUv3zJQpyHeuCHpcvCFZYsYUAPEObh3lXqBxSxannYBQHIAr6kMwrAEuaeVkCa4b0AVm8TYI4bgM2EC7QlikVWmDfYDWkJh679GnDTCgMHOit34uRDb7nypxE+WrvBlq9cYTsqt1tTZaWt215tAwcV2+DCYrfI9Yuf/dL9SO+//16bdPyk9gsWUA4AA50WixJgwDrC0ekFPAIX4kqDFhpZqdCQRxphfAGPwEhp8Cct1pGvPD9fPOGLo04/n7Afh0btED98+ACWPAAagKQ/AHQgBy/yASbqUhspT7spT1ntgxVP6pQsSiNOeepRHpY8uxg4mECbBOJ8Bzh2CAhU2QGBxQmdwJ25WUCVOwbgjRxYz1xqzdSMFrnUnvb6wUcmthqFrlM04E8jjJ8w0c7+h7MPqbemps4aGurd4lXfvn2s+IgBVl5aZmvXrHVnwQ8h7kYRrC6BqJpFp5XlJYChs+NIl6UGMPiOuMqRrnwBiGiVrrjvx+YRB6CVLt8vExtGfuh8WsLIJrCnDG2CFoD089VG0gFTHFYnugC49GeixS3SKS9e5EtvoiWfh/KaFyWOoxyyUB9DcfaoUq9AmzzC1Md8LeWYryWNqRWmAfgOsVBZDIMmU8P5wIOo/n2cJsOPLtUAq/48DLV+85sHbE/NHjv7vLPt6IqKLpWrIyun09LZ6bACC+qjUwMk+AIBwr7D2hJQkC5A8MPwpxx5Ph/xIt1/xJ9yPOIlmtbylacyivu8SEMO+Ek24oRVh+j9uORVWeK0H1pZmn69aqt4QU+afHjLqW7pG7CWVav6oNGwXYAKdvBgqb7++utuLpbFPt5pxSJWplzgQTQ3GrGm3XXWt6hlvydDznBon6mvPzU+vFr6kd//wTZt2GBfuugCKy1rY5tBauxTpqbj4PwOR1zprTGMLROvnDo0nZeOqSEoYXVo6uKBHx1adVOWR3mtyeLnqbzSkimvMrFtaq2sQCxeu1U3/GhnrFN9pEMDSPpppCtOefLloI+V06cXnXzxUTnJzXdAnp+P9S+LF0sTUMUSZcjP8B/rlmOtDO2ZS6VsPFlUd7L+wdYlW6KT6SIDcqy+vtH446DzVu6stgnHj+9kKcLq0ACHF1jRP/9LF7T6R8YfHUdvWcDatHaDrd681nZu3GHRnJZN6c3RZuu1r5dZrtm+Xvusd6/elrN7nzXnNlmu5dqMOXNsasx8LfWrw+jb8OPqDKT56aL1fWhF45fz6yAfECSfBwCVpYNlQ4elI6pTi594AB6xAOTT+PLE8lCdPo3KSl75ookX9+tX+Xj08eoTXTy/NXrJEa/9rfFCB8hIecnaWj2xOlNZ1c+oge1V69evd8DKHa1MAagevkvRUpbvM10XeBAdUDzEautr7YjoEHv6sWfsnC+fk3RbuQw5E/sa2cjPRShsiI82t0y806maok3uflBOJNnelvmwuvoGq6+ut6q6KjeUaGpiE3PLhHhh7mCrj+6wwsIBLo3N93U1NWZNZo05TZYDqrBZOtpsOXm51sQZ67x9lr+nt9VFd1tDc5NZfY415rRcVg1dU3Ou5RXkWF5uxCL7t800Iltj1NHBk4ezVNBbJM8KCwrN+ubawEi+NTRGbd/ePVbd1GA59U3WqJMczVE2hVqEIWpByw8st7HZGnOa7dlnn7P8SJ7tqW9yhxuaolGrbai14rxCi+Y0W04zCyxmR4wY4a7vm1gxzgom97OCwkKL5EZadAj//Y40Vv+VFInE/1micxw/fjpDvE4WL031yKfTYMmIVr54i446AFKGj1rAQAa26DCvxr2elPWdAIA0wjyySH262HAsn9h8xaFTHfLJ88OiVTp5epSXTH2xZVTW99viI7mSoROt+FNGj9JiaZQe66Nz5k51DJUwZdkxwIo9oImFrD9HVvTTdfF/rSly0xAbnzU87l1qy2/as9vqa+utaf8pnih3KdLJc3OcX9fI/FKTbdm2yZ56+El7b81qa2iqtU2VG6xhf2dq5jzz/r7IK5J778uxov6FzFiZ5eZZHp1gf1vYlUc4LzfXGpoINbp6cizPmqzJcpqarSk3p6X6aPSAgptzzPKaIu4sfV5xgStf2Jxvn/TLteK8AsvbDzAAAZdNFeUXWfGAQhsxaqzbR1mQGzkA5PWN9caN/Y2NDS4tL7cF0HJzDv0amKbPAaz3AzZN4Asv4JRHXq7l77+HVOfz8aN1ux29o83JdaDUr2/LeX79mfC9NO7abdHaBmuwlj110AMS3N9qvfsYJfw/Hng372m55zKnbx/X/v0qRSgX9F/1x0FGP36ANgMBf34xlh2dhicZR8f0h5jxytDhmE/TKjNhymHZcLPR5z73ObdwQWf0O7YAU2niA2i35hh+YuG25qgfRx1YUnqwuuDPQ57q8mUQX6WxwKKw8mJ9FmbEKzZPcerjaa+jbclYg5qXli78etUe/vyQG5+5U82fQkt5bXsiDg1W8zXXXOOzSimc9D7Rb337Wy2McyJmzY3uR0jnx+oB93KbzfIKI5YPaPTJN9u7x/b23ufsoKZP9ljfPn1tL7re94k17ay1xtxcK470t7xIjg0acoTryABEc1PUAUVen76Wn5Nni199yZa9tdyuu/57VlpS4iwZMMfhDvXsd+H1cNJE9/UBMhwdiA6jR+BBZ6bjiy6RJgArQAQnHvL9NOrh4QgjG8XhLwuGi0UAWN86hpZOKZ8wTvN0LtKOD+r364O/HoCAMH8OrDojA440wv5DOlMRokkkEm2lfGtO/KFRGF9h6kDutsBY8sEHeh6+E/n6fgSI4i/ZREscffMHAw0GArrhN0GbsUyh9eujDHTpukNNoFa4/PynPz8k139vkG+5HELUzgjHyh5/8mE7/4vnW3c6kdROtfTY4o888sghbacjqMOqUwEidJrWnDqkyuMLhBTGhxednzDDd95RxDvd1TnprAJslSMPXuKHHMmAkWRqS27Jo/rwcfh+WGnSi/LEvy0dqXxsOZWXHwtIopfv0ymcjA9fAah80nyw8+sgz3cCUY1e4EGbNQIRT8r4fHweyYaTBtFYhh0FnH49/Ot+9eKL7a033vCTw3AP1QDvHYp1gISAk7BALJYuXpzOI5CRT5o6FWl0No4vMmfG5m2OMAokGRr65fxwLJ949aeTJrCQjMgnQCCPdAGFaOSrPugo05ZTe1qjg1esTK3Rt5YXT07o/TpUXrTyfRpfHnQBjdrLnxC4ou9Q/Nrjpw2i7ak02bKcLBgxZIS9VHVwESLZsiFd99MAJ1hiHR2Ezs6TrPM7HOX9jujzIJ2tMWPGjHFHC/k9ajiv+vyhuvj4PBRWx1Y8XT9eHUqTL9lUh+qO9ZWfyAd4xDMRDenJ0LRWXnmST3Hx9vkLDJUXS6u4LG14+nzhJX6k+3GVTdUPNIjSGP5JGqN1qbYrpO+GGlDHaO8PX50IFSmsjiafPMLsMwREGc4LVPBlycQCViK1q55E+X69ydLAs636xTfWly4T1UU6VpvKJaKL1654aYnKK516VFdr5f32ih4efrrPU23wh/WEVV9rdYlPW37gQbStBoT5PUcDmg+kw7Tnx08HEiD62oOn+JLPsI8bgFhUYvVcw0B8eDDvBhipjM8r1XAyPHwagUAy9VDOL0sZyrflkgHa1uTw60ymvnhAmEhG8ZMPnV8fccnm0+gPMJW6Esmg9OTHQCrRQT43xS/8w8LDuEfyIsY+xNCFGsCCYGTS3g5Ap6IziQ9h0gBpHuI8DN1xrMJDSxrA4qfHdtzO+paoF5niPeT5TzyZ4n20vQAABFRJREFU/PxE4XjlYtMoGyuD+Pm0SmvN9+nbCouP6iYe68jjN6Pvi3zNkcbSticeCBAFQG//z1/aMRXj4rdFm0Hj54apoQZS0oA6F4W01Yk0LEuuXiONzha6UAPJaKDLQRQAve+B+TZ1yiQ7pmJMXJlDSzSuWsLENDUgS5Ti3HUJgAKcL774ontPPFentbXxPc2qw2LdUANdCqJcaHHnHXdZRcVEO3XOqQnVG3uiJyFhmBFqIEkNMDRnbpPN29xPuXjxYgec3H4OyJIeulADyWigy8YsAOh99zxg02ZOsxNnTk8oa2NT4yHHEBMShhmhBlLQAHNo7PPEf+2115zPqyy4+RwQTWZRJYXqQtJurIEuA9E///EvdtJJM2zCxAmtqpeFJf90VKvEYWaogSQ1AFAyB8pt52xfqqiocBvqWUTS4hLD/NCFGmhLA10GoqeceXqr16n5gnMRR+hCDWRSAwAoL0rjxWm80pcTSbpjEisUkA1dqIFkNNBlIBperJzM1xPSdJQG2ETPbUynnHKKewskc6Da2sQQP1yd7yjNdz++XQaiyarSLSqFlmiy6grpktAAVijzoZMmTXI3nVOEOBYoAMpwPgTRJBQZkjgNBB5EufIuxNDw15pJDbD5mkt6eeRiN2STDpgCrFpkYoivYT5gG7pQA2ggK0C0qSmcEw1/rpnVQCogmAptZqUMuWWDBoK//OhdvJwNCg1lDDUQaqBnaSD4IPpJy6spetbXErY21ECogWzRQOBBlPnQmFcQZYtuQzlDDYQa6AEaCDyIsqoUHvvsAb/EsImhBrJUA4EH0XCjfZb+skKxQw30EA0EHkTzeANouDjfQ36OYTNDDWSfBgIPotYn33inPO8zD12ogVADoQaCpoHAgyjvk99ds8vCi8mC9tPpOfKwT5QjoWy0J4zPCafQhRpAA4EHUYTs0z8//LZCDXSZBuJttgdUQxdqAA1kBYj2/iQ8Yhf+XLtOA1yJp2vxwmOfXfc9BLXmrADRPn37BFV/oVzdWAOyQHV+HgDFAiVdoNqNmx82LUkNZAWI7t0TnlpK8vsMyTKoAYEoNzrpVicuJcHpUpIMVheyylINZAWI9uodDuez9PfVLcT2LVGBaGiJdouvNiONyAoQzUhLQyahBlLUgG+J8v5yHCCqeVH5KbINybuZBrICRPPCd4B3s59ddjUHqxNA1ZyowFN+drUmlDbTGsgKEK3bVZfpdof8Qg2kpAEN37VflMIhiKakwm5LnBUgGs0P94l2219gwBvmAyVDeR4AlXQN9wPehFC8DtZAVoCo1dSFr03u4B9CyL51DQCYACiWqKzSEERb11lPyc0KEO1XVGS7dodD+p7yowzbGWogmzTQa58/XskmyUNZQw2EGgg1EAANZIUlGgA9hSKEGgg1EGogrgZCEI2rljAx1ECogVADyWkgBNHk9BRShRoINRBqIK4GQhCNq5YwMdRAqIFQA8lp4P8DetOlT2wp5wQAAAAASUVORK5CYII="></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>The depth of water in a port is modelled by the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d(t) = p\cos qt + 7.5">
<mi>d</mi>
<mo stretchy="false">(</mo>
<mi>t</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>p</mi>
<mi>cos</mi>
<mo><!-- --></mo>
<mi>q</mi>
<mi>t</mi>
<mo>+</mo>
<mn>7.5</mn>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 12">
<mn>0</mn>
<mo>⩽<!-- ⩽ --></mo>
<mi>t</mi>
<mo>⩽<!-- ⩽ --></mo>
<mn>12</mn>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> is the number of hours after high tide.</p>
<p>At high tide, the depth is 9.7 metres.</p>
<p>At low tide, which is 7 hours later, the depth is 5.3 metres.</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>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
<mi>q</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>Use the model to find the depth of the water 10 hours after high tide.</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 <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{{{\text{max}} - {\text{min}}}}{2}">
<mfrac>
<mrow>
<mrow>
<mtext>max</mtext>
</mrow>
<mo>−</mo>
<mrow>
<mtext>min</mtext>
</mrow>
</mrow>
<mn>2</mn>
</mfrac>
</math></span>, sketch of graph, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="9.7 = p\cos (0) + 7.5">
<mn>9.7</mn>
<mo>=</mo>
<mi>p</mi>
<mi>cos</mi>
<mo></mo>
<mo stretchy="false">(</mo>
<mn>0</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>7.5</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = 2.2">
<mi>p</mi>
<mo>=</mo>
<mn>2.2</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>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="B = \frac{{2\pi }}{{{\text{period}}}}">
<mi>B</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
<mrow>
<mrow>
<mtext>period</mtext>
</mrow>
</mrow>
</mfrac>
</math></span>, period is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="14,{\text{ }}\frac{{360}}{{14}},{\text{ }}5.3 = 2.2\cos 7q + 7.5">
<mn>14</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mfrac>
<mrow>
<mn>360</mn>
</mrow>
<mrow>
<mn>14</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>5.3</mn>
<mo>=</mo>
<mn>2.2</mn>
<mi>cos</mi>
<mo></mo>
<mn>7</mn>
<mi>q</mi>
<mo>+</mo>
<mn>7.5</mn>
</math></span></p>
<p>0.448798</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q = \frac{{2\pi }}{{14}}{\text{ }}\left( {\frac{\pi }{7}} \right)">
<mi>q</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
<mrow>
<mn>14</mn>
</mrow>
</mfrac>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mi>π</mi>
<mn>7</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, (do not accept degrees) <strong><em>A1</em></strong> <strong><em>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>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="d(10),{\text{ }}2.2\cos \left( {\frac{{20\pi }}{{14}}} \right) + 7.5">
<mi>d</mi>
<mo stretchy="false">(</mo>
<mn>10</mn>
<mo stretchy="false">)</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>2.2</mn>
<mi>cos</mi>
<mo></mo>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>20</mn>
<mi>π</mi>
</mrow>
<mrow>
<mn>14</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>7.5</mn>
</math></span></p>
<p>7.01045</p>
<p>7.01 (m) <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>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>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = {x^2} + 2x + 1">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mi>x</mi>
<mo>+</mo>
<mn>1</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x) = x - 5">
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mn>5</mn>
</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>.</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(8)">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mn>8</mn>
<mo stretchy="false">)</mo>
</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 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(g \circ f)(x)">
<mo stretchy="false">(</mo>
<mi>g</mi>
<mo>∘</mo>
<mi>f</mi>
<mo stretchy="false">)</mo>
<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>Solve <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(g \circ f)(x) = 0">
<mo stretchy="false">(</mo>
<mi>g</mi>
<mo>∘</mo>
<mi>f</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0</mn>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p 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 <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> <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="{8^2} + 2 \times 8 + 1">
<mrow>
<msup>
<mn>8</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mo>×</mo>
<mn>8</mn>
<mo>+</mo>
<mn>1</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(8) = 81">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mn>8</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>81</mn>
</math></span> <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 form composition (in any order) <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 - 5),{\text{ }}g\left( {f(x)} \right),{\text{ }}\left( {{x^2} + 2x + 1} \right) - 5">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>−</mo>
<mn>5</mn>
<mo stretchy="false">)</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>g</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mi>x</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>−</mo>
<mn>5</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(g \circ f)(x) = {x^2} + 2x - 4">
<mo stretchy="false">(</mo>
<mi>g</mi>
<mo>∘</mo>
<mi>f</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mi>x</mi>
<mo>−</mo>
<mn>4</mn>
</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>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="x = \frac{{ - 2 \pm \sqrt {20} }}{2}">
<mi>x</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mo>−</mo>
<mn>2</mn>
<mo>±</mo>
<msqrt>
<mn>20</mn>
</msqrt>
</mrow>
<mn>2</mn>
</mfrac>
</math></span>, <img src="images/Schermafbeelding_2017-03-03_om_17.12.57.png" alt="N16/5/MATME/SP2/ENG/TZ0/01.c/M"></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1.23606,{\text{ }} - 3.23606">
<mn>1.23606</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>−</mo>
<mn>3.23606</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 1.24,{\text{ }}x = - 3.24">
<mi>x</mi>
<mo>=</mo>
<mn>1.24</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>x</mi>
<mo>=</mo>
<mo>−</mo>
<mn>3.24</mn>
</math></span> <strong><em>A1A1 N3</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>+</mo><mfrac><mn>50</mn><mi>x</mi></mfrac><mo>,</mo><mo> </mo><mo> </mo><mi>x</mi><mo>≠</mo><mn>0</mn><mo>.</mo></math></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mn>1</mn></mfenced></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>Solve <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>0</mn></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>The graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> has a local minimum at point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>.</p>
<p>Find the coordinates of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>.</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>attempt to substitute <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>1</mn></math> <em><strong>(M1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mn>1</mn></mfenced><mo>,</mo><mo> </mo><msup><mn>1</mn><mn>2</mn></msup><mo>+</mo><mn>1</mn><mo>+</mo><mfrac><mn>50</mn><mn>1</mn></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>52</mn></math> (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><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>.</mo><mn>04932</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>.</mo><mn>05</mn></math> <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><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo>.</mo><mn>76649</mn><mo>,</mo><mo> </mo><mn>28</mn><mo>.</mo><mn>4934</mn></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mfenced><mrow><mn>2</mn><mo>.</mo><mn>77</mn><mo>,</mo><mo> </mo><mn>28</mn><mo>.</mo><mn>5</mn></mrow></mfenced></math> <em><strong>A1A1 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>The following diagram shows a water wheel with 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>10</mn></math> metres. Water flows into buckets, turning the wheel clockwise at a constant speed.</p>
<p><br>The height, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> metres, of the top of a bucket above the ground <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> seconds after it passes through point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> is modelled by the function</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mn>13</mn><mo>+</mo><mn>8</mn><mo> </mo><mi>cos</mi><mfenced><mrow><mfrac><mi mathvariant="normal">π</mi><mn>18</mn></mfrac><mi>t</mi></mrow></mfenced><mo>-</mo><mn>6</mn><mo> </mo><mi>sin</mi><mfenced><mrow><mfrac><mi mathvariant="normal">π</mi><mn>18</mn></mfrac><mi>t</mi></mrow></mfenced></math>, for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>≥</mo><mn>0</mn></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>A bucket moves around to point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> which is at a height of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>06</mn></math> metres above the ground. It takes <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math> seconds for the top of this bucket to go from point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> to point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>.</p>
</div>
<div class="specification">
<p>The chord <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>[</mo><mtext>AB</mtext><mo>]</mo></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>17</mn><mo>.</mo><mn>0</mn></math> metres, correct to three significant figures.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the height of point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> above the ground.</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>Calculate the number of seconds it takes for the water wheel to complete one rotation.</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>Hence find the number of rotations the water wheel makes in one hour.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</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>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mtext>O</mtext><mo>^</mo></mover><mtext>B</mtext></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>Determine the rate of change of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> when the top of the bucket is at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mn>0</mn></mfenced><mo>,</mo><mo> </mo><mn>13</mn><mo>+</mo><mn>8</mn><mo> </mo><mi>cos</mi><mfenced><mrow><mfrac><mi mathvariant="normal">π</mi><mn>18</mn></mfrac><mo>×</mo><mn>0</mn></mrow></mfenced><mo>-</mo><mn>6</mn><mo> </mo><mi>sin</mi><mfenced><mrow><mfrac><mi mathvariant="normal">π</mi><mn>18</mn></mfrac><mo>×</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mo> </mo><mn>13</mn><mo>+</mo><mn>8</mn><mo>×</mo><mn>1</mn><mo>-</mo><mn>6</mn><mo>×</mo><mn>0</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>21</mn></math> (metres) <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach to find the period (seen anywhere) <em><strong>(M1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>36</mn><mo>,</mo><mo> </mo><mn>21</mn></mrow></mfenced></math>, attempt to find two consecutive max/min, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn><mo>.</mo><mn>3130</mn><mo>-</mo><mn>14</mn><mo>.</mo><mn>3130</mn></math></p>
<p> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi></mrow><mstyle displaystyle="true"><mfrac bevelled="true"><mi mathvariant="normal">π</mi><mn>18</mn></mfrac></mstyle></mfrac><mo>,</mo><mo> </mo><mi>b</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi></mrow><mtext>period</mtext></mfrac><mo>,</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>36</mn></math> (seconds) (exact) <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct approach <em><strong>(A1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>60</mn><mo>×</mo><mn>60</mn></mrow><mn>36</mn></mfrac><mo>,</mo><mo> </mo><mn>1</mn><mo>.</mo><mn>6666</mn></math> rotations per minute</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn></math> (rotations) <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution into equation (accept the use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>) <em><strong>(A1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>06</mn><mo>=</mo><mn>13</mn><mo>+</mo><mn>8</mn><mo> </mo><mi>cos</mi><mfenced><mrow><mfrac><mi mathvariant="normal">π</mi><mn>18</mn></mfrac><mo>×</mo><mi>k</mi></mrow></mfenced><mo>-</mo><mn>6</mn><mo> </mo><mi>sin</mi><mfenced><mrow><mfrac><mi mathvariant="normal">π</mi><mn>18</mn></mfrac><mo>×</mo><mi>k</mi></mrow></mfenced></math></p>
<p>valid attempt to solve their equation <em><strong>(M1)</strong></em></p>
<p>eg <img src="data:image/png;base64,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"></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn><mo>.</mo><mn>6510</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn><mo>.</mo><mn>7</mn></math> <em><strong>A1 N3</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><strong>METHOD 1</strong></p>
<p>evidence of choosing the cosine rule or sine rule <em><strong>(M1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>AB</mtext><mn>2</mn></msup><mo>=</mo><msup><mtext>OA</mtext><mn>2</mn></msup><mo>+</mo><msup><mtext>OB</mtext><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>×</mo><mtext>OA</mtext><mo>×</mo><mtext>OB</mtext><mo> </mo><mi>cos</mi><mfenced><mrow><mtext>A</mtext><mover><mtext>O</mtext><mo>^</mo></mover><mtext>B</mtext></mrow></mfenced><mo>,</mo><mo> </mo><mfrac><mrow><mi>sin</mi><mfenced><mrow><mtext>A</mtext><mover><mtext>O</mtext><mo>^</mo></mover><mtext>B</mtext></mrow></mfenced></mrow><mtext>AB</mtext></mfrac><mo>=</mo><mfrac><mrow><mi>sin</mi><mfenced><mrow><mtext>O</mtext><mover><mtext>A</mtext><mo>^</mo></mover><mtext>B</mtext></mrow></mfenced></mrow><mtext>OB</mtext></mfrac></math></p>
<p>correct working <em><strong>(A1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cos</mi><mfenced><mrow><mtext>A</mtext><mover><mtext>O</mtext><mo>^</mo></mover><mtext>B</mtext></mrow></mfenced><mo>=</mo><mfrac><mrow><msup><mn>10</mn><mn>2</mn></msup><mo>+</mo><msup><mn>10</mn><mn>2</mn></msup><mo>-</mo><mn>17</mn><mo>.</mo><msup><mn>0</mn><mn>2</mn></msup></mrow><mrow><mn>2</mn><mo>×</mo><mn>10</mn><mo>×</mo><mn>10</mn></mrow></mfrac><mo>,</mo><mo> </mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>445</mn><mo>,</mo><mo> </mo><mfrac><mrow><mi>sin</mi><mfenced><mrow><mtext>A</mtext><mover><mtext>O</mtext><mo>^</mo></mover><mtext>B</mtext></mrow></mfenced></mrow><mrow><mn>17</mn><mo>.</mo><mn>0</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>sin</mi><mfenced><mrow><mstyle displaystyle="true"><mfrac><mi mathvariant="normal">π</mi><mn>2</mn></mfrac></mstyle><mo>-</mo><mstyle displaystyle="true"><mfrac><mn>1</mn><mn>2</mn></mfrac></mstyle><mtext>A</mtext><mover><mtext>O</mtext><mo>^</mo></mover><mtext>B</mtext></mrow></mfenced></mrow><mn>10</mn></mfrac><mo>,</mo></math></p>
<p> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>sin</mi><mfenced><mstyle displaystyle="true"><mtext>O</mtext><mover><mtext>A</mtext><mo>^</mo></mover><mtext>B</mtext></mstyle></mfenced></mrow><mn>10</mn></mfrac><mo>=</mo><mfrac><mrow><mi>sin</mi><mfenced><mstyle displaystyle="true"><mi mathvariant="normal">π</mi><mo>-</mo><mn>2</mn><mo>×</mo><mtext>O</mtext><mover><mtext>A</mtext><mo>^</mo></mover><mtext>B</mtext></mstyle></mfenced></mrow><mrow><mn>17</mn><mo>.</mo><mn>0</mn></mrow></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>03197</mn><mo> </mo><mo>,</mo><mo> </mo><mn>116</mn><mo>.</mo><mn>423</mn><mo>°</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>03</mn><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>116</mn><mo>°</mo></mrow></mfenced></math> <em><strong>A1 N3</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>attempt to find the half central angle <em><strong>(M1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mfenced><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mtext>A</mtext><mover><mtext>O</mtext><mo>^</mo></mover><mtext>B</mtext></mrow></mfenced><mo>=</mo><mfrac><mrow><mstyle displaystyle="true"><mfrac><mn>1</mn><mn>2</mn></mfrac></mstyle><mtext>AB</mtext></mrow><mtext>OA</mtext></mfrac></math></p>
<p>correct working <em><strong>(A1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>×</mo><msup><mi>sin</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mfrac><mrow><mn>8</mn><mo>.</mo><mn>5</mn></mrow><mn>10</mn></mfrac></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>03197</mn><mo> </mo><mo>,</mo><mo> </mo><mn>116</mn><mo>.</mo><mn>423</mn><mo>°</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>03</mn><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>116</mn><mo>°</mo></mrow></mfenced></math> <em><strong>A1 N3</strong></em></p>
<p> </p>
<p><strong>METHOD 3</strong></p>
<p>valid approach to find fraction of period <em><strong>(M1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>k</mi><mn>36</mn></mfrac><mo>,</mo><mo> </mo><mfrac><mrow><mn>11</mn><mo>.</mo><mn>6510</mn></mrow><mn>36</mn></mfrac></math></p>
<p>correct approach to find angle <em><strong>(A1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>k</mi><mn>36</mn></mfrac><mo>×</mo><mn>2</mn><mi mathvariant="normal">π</mi></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>03348</mn><mo>,</mo><mo> </mo><mn>116</mn><mo>.</mo><mn>510</mn><mo>°</mo></math> (<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>04203</mn></math> using <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn><mo>.</mo><mn>7</mn></math>)</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>03</mn><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>117</mn><mo>°</mo></mrow></mfenced></math> <em><strong>A1 N3</strong></em></p>
<p> </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 rate of change is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>'</mo></math> <em><strong>(M1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>'</mo><mfenced><mi>k</mi></mfenced><mo>,</mo><mo> </mo><mi>h</mi><mo>'</mo><mfenced><mrow><mn>11</mn><mo>.</mo><mn>6510</mn></mrow></mfenced><mo> </mo><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>782024</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>0</mn><mo>.</mo><mn>782024</mn></math> (<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>0</mn><mo>.</mo><mn>768662</mn></math> from <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo> </mo><mtext>sf</mtext></math> )</p>
<p>rate of change is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>0</mn><mo>.</mo><mn>782</mn><mo> </mo><mfenced><msup><mtext>ms</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></mfenced></math> <em><strong>A1 N2</strong></em></p>
<p>(<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>0</mn><mo>.</mo><mn>769</mn><mo> </mo><mfenced><msup><mtext>ms</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></mfenced></math> from <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo> </mo><mtext>sf</mtext></math> )</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Scott purchases food for his dog in large bags and feeds the dog the same amount of dog food each day. The amount of dog food left in the bag at the end of each day can be modelled by an arithmetic sequence.</p>
<p>On a particular day, Scott opened a new bag of dog food and fed his dog. By the end of the third day there were <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>115</mn><mo>.</mo><mn>5</mn></math> cups of dog food remaining in the bag and at the end of the eighth day there were <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>108</mn></math> cups of dog food remaining in the bag.</p>
</div>
<div class="specification">
<p>Find the number of cups of dog food</p>
</div>
<div class="specification">
<p>In <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2021</mn></math>, Scott spent <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>625</mn></math> on dog food. Scott expects that the amount he spends on dog food will increase at an annual rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>4</mn><mo>%</mo></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>fed to the dog per day.</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>remaining in the bag at the end of the first day.</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>Calculate the number of days that Scott can feed his dog with one bag of food.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the amount that Scott expects to spend on dog food in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2025</mn></math>. Round your answer to the nearest dollar.</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>Calculate the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><munderover><mtext>Σ</mtext><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mn>10</mn></munderover><mfenced><mrow><mn>625</mn><mo>×</mo><mn>1</mn><mo>.</mo><msup><mn>064</mn><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced></msup></mrow></mfenced></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe what the value in part (d)(i) represents in this context.</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>Comment on the appropriateness of modelling this scenario with a geometric sequence.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>115</mn><mo>.</mo><mn>5</mn><mo>=</mo><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><mfenced><mrow><mn>3</mn><mo>-</mo><mn>1</mn></mrow></mfenced><mo>×</mo><mi>d</mi><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>115</mn><mo>.</mo><mn>5</mn><mo>=</mo><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><mn>2</mn><mi>d</mi></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>108</mn><mo>=</mo><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><mfenced><mrow><mn>8</mn><mo>-</mo><mn>1</mn></mrow></mfenced><mo>×</mo><mi>d</mi><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>108</mn><mo>=</mo><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><mn>7</mn><mi>d</mi></mrow></mfenced></math> <em><strong>(M1)(A1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1</strong> </em>for attempting to use the arithmetic sequence term formula, <em><strong>A1</strong> </em>for both equations correct. Working for <em><strong>M1</strong> </em>and <em><strong>A1</strong> </em>can be found in parts (i) or (ii).</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>d</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>.</mo><mn>5</mn></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>5</mn></math> (cups/day) <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Answer must be written as a positive value to award <em><strong>A1</strong></em>.</p>
<p><br><em><strong>OR</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>d</mi><mo>=</mo></mrow></mfenced><mo> </mo><mfrac><mrow><mn>115</mn><mo>.</mo><mn>5</mn><mo>-</mo><mn>108</mn></mrow><mn>5</mn></mfrac></math> <em><strong>(M1)(A1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1</strong> </em>for attempting a calculation using the difference between term <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math> and term <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math>; <em><strong>A1</strong> </em>for a correct substitution.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>d</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>1</mn><mo>.</mo><mn>5</mn></math> (cups/day) <em><strong>A1</strong></em></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><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msub><mi>u</mi><mn>1</mn></msub><mo>=</mo></mrow></mfenced><mo> </mo><mn>118</mn><mo>.</mo><mn>5</mn></math> (cups) <em><strong>A1</strong></em></p>
<p> </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>attempting to substitute their values into the term formula for arithmetic sequence equated to zero <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>=</mo><mn>118</mn><mo>.</mo><mn>5</mn><mo>+</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>×</mo><mfenced><mrow><mo>-</mo><mn>1</mn><mo>.</mo><mn>5</mn></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>n</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>80</mn></math> days <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Follow through from part (a) only if their answer is positive.</p>
<p><em><strong><br>[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><msub><mi>t</mi><mn>5</mn></msub><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mn>625</mn><mo>×</mo><mn>1</mn><mo>.</mo><msup><mn>064</mn><mfenced><mrow><mn>5</mn><mo>-</mo><mn>1</mn></mrow></mfenced></msup></math> <em><strong>(M1)(A1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1</strong> </em>for attempting to use the geometric sequence term formula; <em><strong>A1</strong> </em>for a correct substitution</p>
<p> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>801</mn></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> The answer must be rounded to a whole number to award the final <em><strong>A1</strong></em>.</p>
<p><em><strong><br>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msub><mi>S</mi><mn>10</mn></msub><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mfenced><mo>$</mo></mfenced><mo> </mo><mn>8390</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>8394</mn><mo>.</mo><mn>39</mn><mo>…</mo></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p>the total cost (of dog food) <em><strong> R1</strong></em></p>
<p>for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> years beginning in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2021</mn></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> years before <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2031</mn></math> <em><strong> R1</strong></em></p>
<p><br><strong>OR</strong></p>
<p>the total cost (of dog food) <em><strong> R1</strong></em></p>
<p>from <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2021</mn></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2030</mn></math> (inclusive) <strong>OR</strong> from <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2021</mn></math> to (the start of) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2031</mn></math> <em><strong> R1</strong></em></p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong><br>According to the model, the cost of dog food per year will eventually be too high to keep a dog.</p>
<p><strong>OR</strong><br>The model does not necessarily consider changes in inflation rate.</p>
<p><strong>OR</strong><br>The model is appropriate as long as inflation increases at a similar rate.</p>
<p><strong>OR</strong><br>The model does not account for changes in the amount of food the dog eats as it ages/becomes ill/stops growing.</p>
<p><strong>OR</strong><br>The model is appropriate since dog food bags can only be bought in discrete quantities. <em><strong> R1</strong></em></p>
<p><em><strong><br></strong></em><strong>Note:</strong> Accept reasonable answers commenting on the appropriateness of the model for the specific scenario. There should be a reference to the given context. A reference to the geometric model must be clear: either “model” is mentioned specifically, or other mathematical terms such as “increasing” or “discrete quantities” are seen. Do not accept a contextual argument in isolation, e.g. “The dog will eventually die”.</p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Parts (a) and (b) were mostly well answered, but some candidates ignored the context and did not give the number of dog food cups per day as a positive number. Most candidates considered geometric sequence in part (c) correctly, and used the correct formula for the nth term, although they used an incorrect value for n at times. Some candidates used the finance application incorrectly. The sum in part (d) was calculated correctly by some candidates, although many seemed unfamiliar with sigma notation and with calculating summations using GDC. In part (d), most candidates interpreted correctly that the sum represented the cost of dog food for 10 years but did not identify the specific 10-year period. Part (e) was not answered well – often candidates made very general and abstract statements devoid of any contextual references.</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.</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>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {x^3} - 5{x^2} + 6x - 3 + \frac{1}{x}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mn>5</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>6</mn>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mn>3</mn>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mi>x</mi>
</mfrac>
</math></span>, <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></p>
</div>
<div class="specification">
<p>The function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {x^3} - 5{x^2} + 6x - 3 + \frac{1}{x}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mn>5</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>6</mn>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mn>3</mn>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mi>x</mi>
</mfrac>
</math></span>, <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>, models the path of a river, as shown on the following map, where both axes represent distance and are measured in kilometres. On the same map, the location of a highway is defined by the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right) = 0.5{\left( 3 \right)^{ - x}} + 1">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0.5</mn>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
<mrow>
<mo>−<!-- − --></mo>
<mi>x</mi>
</mrow>
</msup>
</mrow>
<mo>+</mo>
<mn>1</mn>
</math></span>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The origin, O(0, 0) , is the location of the centre of a town called Orangeton.</p>
<p>A straight footpath, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P">
<mi>P</mi>
</math></span>, is built to connect the centre of Orangeton to the river at the point where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = \frac{1}{2}">
<mi>x</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span>.</p>
</div>
<div class="specification">
<p>Bridges are located where the highway crosses the river.</p>
</div>
<div class="specification">
<p>A straight road is built from the centre of Orangeton, due north, to connect the town to the highway.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the domain 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.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the distance from the centre of Orangeton to the point at which the road meets the highway.</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>This straight road crosses the highway and then carries on due north.</p>
<p>State whether the straight road will ever cross the river. Justify your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>0 < <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="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span> <em><strong>(A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for both endpoints correct, <em><strong>(A1)</strong></em> for correct mathematical notation indicating an interval with two endpoints. Accept weak inequalities. Award at most <em><strong>(A1)</strong></em><em><strong>(A0)</strong></em> for incorrect notation such as 0 − 0.5 or a written description of the domain with correct endpoints. Award at most <em><strong>(A1)</strong></em><em><strong>(A0)</strong></em> for 0 < <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> < <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span>.</p>
<p><strong><em>[2 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="g\left( 0 \right) = 0.5{\left( 3 \right)^0} + 1">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0.5</mn>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
<mn>0</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>1</mn>
</math></span> <em><strong>(M1)</strong></em></p>
<p>1.5 (km) <em><strong>(A1)(G2)</strong></em></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>domain given as <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> (but equation of road is <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>) <em><strong> (R1)</strong></em></p>
<p><strong>OR</strong></p>
<p>(equation of road is <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>) the function of the river is asymptotic to <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> <em><strong> (R1)</strong></em></p>
<p>so it does not meet the river <em><strong> (A1)</strong></em></p>
<p><strong>Note:</strong> Award the <em><strong>(R1)</strong></em> for a correct mathematical statement about the equation of the river (and the equation of the road). Justification must be based on <strong>mathematical reasoning</strong>. Do not award <em><strong>(R0)</strong></em><em><strong>(A1)</strong></em>.</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">b.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><strong>Note: In this question, distance is in millimetres.</strong></p>
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = x + a\sin \left( {x - \frac{\pi }{2}} \right) + a">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>x</mi>
<mo>+</mo>
<mi>a</mi>
<mi>sin</mi>
<mo><!-- --></mo>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mfrac>
<mi>π<!-- π --></mi>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>a</mi>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \geqslant 0">
<mi>x</mi>
<mo>⩾<!-- ⩾ --></mo>
<mn>0</mn>
</math></span>.</p>
</div>
<div class="specification">
<p>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 origin. Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{P}}_k}">
<mrow>
<msub>
<mrow>
<mtext>P</mtext>
</mrow>
<mi>k</mi>
</msub>
</mrow>
</math></span> be any point on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-coordinate <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2k\pi ">
<mn>2</mn>
<mi>k</mi>
<mi>π<!-- π --></mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k \in \mathbb{N}">
<mi>k</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">N</mi>
</mrow>
</math></span>. A straight line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span> passes through all the points <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{P}}_k}">
<mrow>
<msub>
<mrow>
<mtext>P</mtext>
</mrow>
<mi>k</mi>
</msub>
</mrow>
</math></span>.</p>
</div>
<div class="specification">
<p>Diagram 1 shows a saw. The length of the toothed edge is the distance AB.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_15.10.11.png" alt="N17/5/MATME/SP2/ENG/TZ0/10.d_01"></p>
<p>The toothed edge of the saw can be modelled using the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> and the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span>. Diagram 2 represents this model.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_15.11.17.png" alt="N17/5/MATME/SP2/ENG/TZ0/10.d_02"></p>
<p>The shaded part on the graph is called a tooth. A tooth is represented by 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> and the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span>, between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{P}}_k}">
<mrow>
<msub>
<mrow>
<mtext>P</mtext>
</mrow>
<mi>k</mi>
</msub>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{P}}_{k + 1}}">
<mrow>
<msub>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</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="f(2\pi ) = 2\pi ">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mi>π</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>2</mn>
<mi>π</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>Find the coordinates of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{P}}_0}">
<mrow>
<msub>
<mrow>
<mtext>P</mtext>
</mrow>
<mn>0</mn>
</msub>
</mrow>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{P}}_1}">
<mrow>
<msub>
<mrow>
<mtext>P</mtext>
</mrow>
<mn>1</mn>
</msub>
</mrow>
</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>Find the equation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</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>Show that the distance between the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-coordinates of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{P}}_k}">
<mrow>
<msub>
<mrow>
<mtext>P</mtext>
</mrow>
<mi>k</mi>
</msub>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{P}}_{k + 1}}">
<mrow>
<msub>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</math></span> is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi ">
<mn>2</mn>
<mi>π</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A saw has a toothed edge which is 300 mm long. Find the number of complete teeth on this saw.</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>substituting <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 2\pi ">
<mi>x</mi>
<mo>=</mo>
<mn>2</mn>
<mi>π</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="2\pi + a\sin \left( {2\pi - \frac{\pi }{2}} \right) + a">
<mn>2</mn>
<mi>π</mi>
<mo>+</mo>
<mi>a</mi>
<mi>sin</mi>
<mo></mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mi>π</mi>
<mo>−</mo>
<mfrac>
<mi>π</mi>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>a</mi>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi + a\sin \left( {\frac{{3\pi }}{2}} \right) + a">
<mn>2</mn>
<mi>π</mi>
<mo>+</mo>
<mi>a</mi>
<mi>sin</mi>
<mo></mo>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>3</mn>
<mi>π</mi>
</mrow>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>a</mi>
</math></span> <strong><em>(A1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi - a + a">
<mn>2</mn>
<mi>π</mi>
<mo>−</mo>
<mi>a</mi>
<mo>+</mo>
<mi>a</mi>
</math></span> <strong><em>A1</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(2\pi ) = 2\pi ">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mi>π</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>2</mn>
<mi>π</mi>
</math></span> <strong><em>AG N0</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>substituting the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> <em>(<strong>M1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{P}}_0}(0,{\text{ }}0),{\text{ }}{{\text{P}}_1}(2\pi ,{\text{ }}2\pi )">
<mrow>
<msub>
<mrow>
<mtext>P</mtext>
</mrow>
<mn>0</mn>
</msub>
</mrow>
<mo stretchy="false">(</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0</mn>
<mo stretchy="false">)</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>P</mtext>
</mrow>
<mn>1</mn>
</msub>
</mrow>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mi>π</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>2</mn>
<mi>π</mi>
<mo stretchy="false">)</mo>
</math></span> <strong><em>A1A1 N3</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to find the gradient <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{{2\pi - 0}}{{2\pi - 0}},{\text{ }}m = 1">
<mfrac>
<mrow>
<mn>2</mn>
<mi>π</mi>
<mo>−</mo>
<mn>0</mn>
</mrow>
<mrow>
<mn>2</mn>
<mi>π</mi>
<mo>−</mo>
<mn>0</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>m</mi>
<mo>=</mo>
<mn>1</mn>
</math></span></p>
<p>correct working <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="\frac{{y - 2\pi }}{{x - 2\pi }} = 1,{\text{ }}b = 0,{\text{ }}y - 0 = 1(x - 0)">
<mfrac>
<mrow>
<mi>y</mi>
<mo>−</mo>
<mn>2</mn>
<mi>π</mi>
</mrow>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
<mi>π</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>b</mi>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>y</mi>
<mo>−</mo>
<mn>0</mn>
<mo>=</mo>
<mn>1</mn>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>−</mo>
<mn>0</mn>
<mo stretchy="false">)</mo>
</math></span></p>
<p><em>y = x</em> <strong><em>A1 N3</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>subtracting <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-coordinates of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{P}}_{k + 1}}">
<mrow>
<msub>
<mrow>
<mtext>P</mtext>
</mrow>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{P}}_k}">
<mrow>
<msub>
<mrow>
<mtext>P</mtext>
</mrow>
<mi>k</mi>
</msub>
</mrow>
</math></span> (in any order) <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="2(k + 1)\pi - 2k\pi ,{\text{ }}2k\pi - 2k\pi - 2\pi ">
<mn>2</mn>
<mo stretchy="false">(</mo>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mi>π</mi>
<mo>−</mo>
<mn>2</mn>
<mi>k</mi>
<mi>π</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>2</mn>
<mi>k</mi>
<mi>π</mi>
<mo>−</mo>
<mn>2</mn>
<mi>k</mi>
<mi>π</mi>
<mo>−</mo>
<mn>2</mn>
<mi>π</mi>
</math></span></p>
<p>correct working (must be in correct order) <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="2k\pi + 2\pi - 2k\pi ,{\text{ }}\left| {2k\pi - 2(k + 1)\pi } \right|">
<mn>2</mn>
<mi>k</mi>
<mi>π</mi>
<mo>+</mo>
<mn>2</mn>
<mi>π</mi>
<mo>−</mo>
<mn>2</mn>
<mi>k</mi>
<mi>π</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>|</mo>
<mrow>
<mn>2</mn>
<mi>k</mi>
<mi>π</mi>
<mo>−</mo>
<mn>2</mn>
<mo stretchy="false">(</mo>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
<mo stretchy="false">)</mo>
<mi>π</mi>
</mrow>
<mo>|</mo>
</mrow>
</math></span></p>
<p>distance is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi ">
<mn>2</mn>
<mi>π</mi>
</math></span> <strong><em>AG N0</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>recognizing the toothed-edge as the hypotenuse <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="{300^2} = {x^2} + {y^2}">
<mrow>
<msup>
<mn>300</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mrow>
<msup>
<mi>y</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span>, sketch</p>
<p>correct working (using their equation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span> <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="{300^2} = {x^2} + {x^2}">
<mrow>
<msup>
<mn>300</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = \frac{{300}}{{\sqrt 2 }}">
<mi>x</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>300</mn>
</mrow>
<mrow>
<msqrt>
<mn>2</mn>
</msqrt>
</mrow>
</mfrac>
</math></span> (exact), 212.132 <strong><em>(A1)</em></strong></p>
<p>dividing their value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi {\text{ }}\left( {{\text{do not accept }}\frac{{300}}{{2\pi }}} \right)">
<mn>2</mn>
<mi>π</mi>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mtext>do not accept </mtext>
</mrow>
<mfrac>
<mrow>
<mn>300</mn>
</mrow>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</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="\frac{{212.132}}{{2\pi }}">
<mfrac>
<mrow>
<mn>212.132</mn>
</mrow>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
</mfrac>
</math></span></p>
<p>33.7618 <strong><em>(A1)</em></strong></p>
<p>33 (teeth) <strong><em>A1 N2</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>vertical distance of a tooth is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi ">
<mn>2</mn>
<mi>π</mi>
</math></span> (may be seen anywhere) <strong><em>(A1)</em></strong></p>
<p>attempt to find the hypotenuse for one tooth <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^2} = {(2\pi )^2} + {(2\pi )^2}">
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mrow>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mi>π</mi>
<msup>
<mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mrow>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mi>π</mi>
<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="x = \sqrt {8{\pi ^2}} ">
<mi>x</mi>
<mo>=</mo>
<msqrt>
<mn>8</mn>
<mrow>
<msup>
<mi>π</mi>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</math></span> (exact), 8.88576 <strong><em>(A1)</em></strong></p>
<p>dividing 300 by their value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em></p>
<p>33.7618 <strong><em>(A1)</em></strong></p>
<p>33 (teeth) <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.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>
<br><hr><br><div class="specification">
<p>The Voronoi diagram below shows four supermarkets represented by points with coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mo>(</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext><mo>(</mo><mn>6</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext><mo>(</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>6</mn><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext><mo>(</mo><mn>2</mn><mo>,</mo><mo> </mo><mn>2</mn><mo>)</mo></math>. The vertices <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>X</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Y</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Z</mtext></math> are also shown. All distances are measured in kilometres.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>The equation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>(XY)</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>2</mn><mo>−</mo><mi>x</mi></math> and the equation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>(YZ)</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mi>x</mi><mo>+</mo><mn>3</mn><mo>.</mo><mn>5</mn></math>.</p>
</div>
<div class="specification">
<p>The coordinates of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Y</mtext></math> are <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mo> </mo><mn>3</mn><mo>)</mo></math> and the coordinates of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Z</mtext></math> are <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>7</mn><mo>,</mo><mo> </mo><mn>7</mn><mo>)</mo></math>.</p>
</div>
<div class="specification">
<p>A town planner believes that the larger the area of the Voronoi cell <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>XYZ</mtext></math>, the more people will shop at supermarket <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the midpoint of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[BD]</mtext></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>Find the equation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>(XZ)</mtext></math>.</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 coordinates of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>X</mtext></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>Determine the exact length of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[YZ]</mtext></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>Given that the exact length of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[XY]</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>32</mn></msqrt></math>, find the size of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>XŶZ</mtext></math> in degrees.</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>Hence find the area of triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>XYZ</mtext></math>.</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>State one criticism of this interpretation.</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><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mrow><mn>2</mn><mo>+</mo><mn>6</mn></mrow><mn>2</mn></mfrac><mo>,</mo><mo> </mo><mo> </mo><mfrac><mrow><mn>2</mn><mo>+</mo><mn>0</mn></mrow><mn>2</mn></mfrac></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>4</mn><mo>,</mo><mo> </mo><mn>1</mn></mrow></mfenced></math> <em><strong> A1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>A0</strong></em> if parentheses are omitted in the final answer.</p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to substitute values into gradient formula <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mrow><mn>0</mn><mo>-</mo><mn>2</mn></mrow><mrow><mn>6</mn><mo>-</mo><mn>2</mn></mrow></mfrac><mo>=</mo></mrow></mfenced><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math> <em><strong>(A1)</strong></em></p>
<p>therefore the gradient of perpendicular bisector is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> <em><strong>(M1)</strong></em></p>
<p>so <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>-</mo><mn>1</mn><mo>=</mo><mn>2</mn><mfenced><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mi>y</mi><mo>=</mo><mn>2</mn><mi>x</mi><mo>-</mo><mn>7</mn></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>identifying the correct equations to use: <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>2</mn><mo>-</mo><mi>x</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>2</mn><mi>x</mi><mo>-</mo><mn>7</mn></math></p>
<p>evidence of solving their correct equations or of finding intersection point graphically <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>3</mn><mo>,</mo><mo> </mo><mo>-</mo><mn>1</mn></mrow></mfenced></math> <em><strong> A1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Accept an answer expressed as “<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>3</mn><mo>,</mo><mo> </mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>1</mn></math>”.</p>
<p> </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>attempt to use distance formula <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>YZ</mtext><mo>=</mo><msqrt><msup><mfenced><mrow><mn>7</mn><mo>-</mo><mfenced><mrow><mo>-</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mn>7</mn><mo>-</mo><mn>3</mn></mrow></mfenced><mn>2</mn></msup></msqrt></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><msqrt><mn>80</mn></msqrt><mo> </mo><mo> </mo><mfenced><mrow><mn>4</mn><msqrt><mn>5</mn></msqrt></mrow></mfenced></math> <em><strong> A1</strong></em></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><strong>METHOD 1 (cosine rule)</strong></p>
<p>length of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>XZ</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>80</mn></msqrt><mo> </mo><mo> </mo><mfenced><mrow><mn>4</mn><msqrt><mn>5</mn></msqrt><mo>,</mo><mo> </mo><mn>8</mn><mo>.</mo><mn>94427</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><br><strong>Note:</strong> Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>.</mo><mn>94</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>.</mo><mn>9</mn></math>.</p>
<p><br>attempt to substitute into cosine rule <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cos</mi><mo> </mo><mtext>XŶZ</mtext><mo>=</mo><mfrac><mrow><mn>80</mn><mo>+</mo><mn>32</mn><mo>-</mo><mn>80</mn></mrow><mrow><mn>2</mn><mo>×</mo><msqrt><mn>80</mn></msqrt><msqrt><mn>32</mn></msqrt></mrow></mfrac><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mn>0</mn><mo>.</mo><mn>316227</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>A1</strong> </em>for correct substitution of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>XZ</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>YZ</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>32</mn></msqrt></math> values in the cos rule. Exact values do not need to be used in the substitution.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mtext>XŶZ</mtext><mo>=</mo></mrow></mfenced><mo> </mo><mn>71</mn><mo>.</mo><mn>6</mn><mo>°</mo><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>71</mn><mo>.</mo><mn>5650</mn><mo>…</mo><mo>°</mo></mrow></mfenced></math> <em><strong> A1</strong></em></p>
<p><br><strong>Note:</strong> Last <em><strong>A1</strong> </em>mark may be lost if prematurely rounded values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>XZ</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>YZ</mtext></math> and/or <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>XY</mtext></math> are used.</p>
<p> </p>
<p><strong>METHOD 2 (splitting isosceles triangle in half)</strong></p>
<p>length of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>XZ</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>80</mn></msqrt><mo> </mo><mo> </mo><mfenced><mrow><mn>4</mn><msqrt><mn>5</mn></msqrt><mo>,</mo><mo> </mo><mn>8</mn><mo>.</mo><mn>94427</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><br><strong>Note:</strong> Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>.</mo><mn>94</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>.</mo><mn>9</mn></math>.</p>
<p><br>required angle is <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>cos</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mfrac><msqrt><mn>32</mn></msqrt><mrow><mn>2</mn><msqrt><mn>80</mn></msqrt></mrow></mfrac></mfenced></math> <em><strong>(M1)(A1)</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>A1</strong> </em>for correct substitution of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>XZ</mtext></math> (or <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>YZ</mtext></math>), <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>32</mn></msqrt><mn>2</mn></mfrac></math> values in the cos rule. Exact values do not need to be used in the substitution.</p>
<p> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mtext>XŶZ</mtext><mo>=</mo></mrow></mfenced><mo> </mo><mn>71</mn><mo>.</mo><mn>6</mn><mo>°</mo><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>71</mn><mo>.</mo><mn>5650</mn><mo>…</mo><mo>°</mo></mrow></mfenced></math> <em><strong> A1</strong></em></p>
<p><br><strong>Note:</strong> Last <em><strong>A1</strong> </em>mark may be lost if prematurely rounded values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>XZ</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>YZ</mtext></math> and/or <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>XY</mtext></math> are used.</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>(area =) <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><msqrt><mn>80</mn></msqrt><msqrt><mn>32</mn></msqrt><mo> </mo><mi>sin</mi><mo> </mo><mn>71</mn><mo>.</mo><mn>5650</mn><mo>…</mo></math> <strong>OR </strong>(area =) <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><msqrt><mn>32</mn></msqrt><msqrt><mn>72</mn></msqrt></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>24</mn><mo> </mo><msup><mtext>km</mtext><mn>2</mn></msup></math> <em><strong> A1</strong></em></p>
<p> </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><em>Any sensible answer such as:</em></p>
<p>There might be factors other than proximity which influence shopping choices.</p>
<p>A larger area does not necessarily result in an increase in population.</p>
<p>The supermarkets might be specialized / have a particular clientele who visit even if other shops are closer.</p>
<p>Transport links might not be represented by Euclidean distances.</p>
<p>etc. <em><strong> R1</strong></em></p>
<p> </p>
<p><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;">
<p>Part (a) was answered very well and demonstrated that the candidates had good knowledge of the midpoint formula. Some candidates did not write the midpoint they found as a coordinate pair and lost a mark there. Part (b) was answered well. Most candidates were able to find the gradient of [BD] and then the gradient of the perpendicular [XZ] and its equation. Candidates who lost marks in (b) were able to collect follow through marks in parts (c), (d), and (e). In part (c), not all candidates were able to identify the correct equations that they needed to find the coordinates of point X. In part (d), many candidates overlooked the fact that the question called for the exact length of [YZ] – the majority of candidates gave the answer correct to three significant figures and hence lost a mark. In part (d) most candidates were able to correctly use the cosine rule. Marks were lost here if the candidates calculated the length of [XZ] incorrectly, or substituted the [XZ], [YZ] or [XY] values incorrectly. Often candidates used rounded [XZ], [YZ] or [XY] values prematurely, for which they lost the last mark. Part (f) was mostly well answered. If candidates found an angle in part (e), they were usually able to find the area in (f) correctly. Again, the contextual question in part (g) was challenging to many candidates. Some answers showed misconceptions about Voronoi diagrams, for example some candidates stated that “if the cell were larger, then some people living there will be much closer to supermarkets A, B, C than to supermarket D.” Many candidates offered explanations, which were long and unclear, which often did not address the issue they were asked to comment on, nor displayed a sound understanding of the topic.</p>
<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>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = 12\,\,{\text{cos}}\,x - 5\,\,{\text{sin}}\,x,\,\, - \pi \leqslant x \leqslant 2\pi ">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>12</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>cos</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mn>5</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>sin</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mo>−<!-- − --></mo>
<mi>π<!-- π --></mi>
<mo>⩽<!-- ⩽ --></mo>
<mi>x</mi>
<mo>⩽<!-- ⩽ --></mo>
<mn>2</mn>
<mi>π<!-- π --></mi>
</math></span>, be a periodic function with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = f\left( {x + 2\pi } \right)">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
<mi>π<!-- π --></mi>
</mrow>
<mo>)</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="f">
<mi>f</mi>
</math></span>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">There is a maximum point at A. The minimum value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> is −13 .</p>
</div>
<div class="specification">
<p>A ball on a spring is attached to a fixed point O. The ball is then pulled down and released, so that it moves back and forth vertically.</p>
<p style="text-align: center;"><img 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"></p>
<p>The distance, <em>d</em> centimetres, of the centre of the ball from O at time <em>t</em> seconds, is given by</p>
<p style="padding-left: 90px;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d\left( t \right) = f\left( t \right) + 17,\,\,0 \leqslant t \leqslant 5.">
<mi>d</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>17</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>0</mn>
<mo>⩽<!-- ⩽ --></mo>
<mi>t</mi>
<mo>⩽<!-- ⩽ --></mo>
<mn>5.</mn>
</math></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span>, write down the amplitude.</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>For the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span>, write down the period.</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>Hence, write <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> in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p\,\,{\text{cos}}\,\left( {x + r} \right)"> <mi>p</mi> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mi>x</mi> <mo>+</mo> <mi>r</mi> </mrow> <mo>)</mo> </mrow> </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 the maximum speed of the ball.</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 first time when the ball’s speed is changing at a rate of 2 cm s<sup>−2</sup>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p 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>−0.394791,13</p>
<p>A(−0.395, 13) <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>13 <em><strong>A1 N1</strong></em></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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{2\pi }"> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </math></span>, 6.28 <em><strong>A1 N1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> recognizing that amplitude is <em>p</em> or shift is <em>r</em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = 13\,\,{\text{cos}}\,\left( {x + 0.395} \right)"> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>13</mn> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mi>x</mi> <mo>+</mo> <mn>0.395</mn> </mrow> <mo>)</mo> </mrow> </math></span> (accept <em>p</em> = 13, <em>r</em> = 0.395) <em><strong>A1A1 N3</strong></em></p>
<p><strong>Note:</strong> Accept any value of <em>r</em> of the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.395 + 2\pi k,\,\,k \in \mathbb{Z}"> <mn>0.395</mn> <mo>+</mo> <mn>2</mn> <mi>π</mi> <mi>k</mi> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mi>k</mi> <mo>∈</mo> <mrow> <mi mathvariant="double-struck">Z</mi> </mrow> </math></span></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 need for <em>d </em>′(<em>t</em>) <em><strong>(M1)</strong></em></p>
<p><em>eg</em> −12 sin(<em>t</em>) − 5 cos(<em>t</em>)</p>
<p>correct approach (accept any variable for <em>t</em>) <em><strong>(A1)</strong></em></p>
<p><em>eg </em> −13 sin(<em>t + </em>0.395), sketch of <em>d</em>′, (1.18, −13), <em>t</em> = 4.32</p>
<p>maximum speed = 13 (cms<sup>−1</sup>) <em><strong>A1 N2</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing that acceleration is needed <em><strong>(M1)</strong></em></p>
<p><em>eg </em>a(<em>t</em>), <em>d "</em>(t)</p>
<p>correct equation (accept any variable for <em>t</em>) <em><strong> (A1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a\left( t \right) = - 2,\,\,\left| {\frac{{\text{d}}}{{{\text{d}}t}}\left( {d'\left( t \right)} \right)} \right| = 2,\,\, - 12\,\,{\text{cos}}\,\left( t \right) + 5\,\,{\text{sin}}\,\left( t \right) = - 2"> <mi>a</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>−</mo> <mn>2</mn> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>|</mo> <mrow> <mfrac> <mrow> <mtext>d</mtext> </mrow> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> </mrow> </mfrac> <mrow> <mo>(</mo> <mrow> <msup> <mi>d</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mo>|</mo> </mrow> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mo>−</mo> <mn>12</mn> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mn>5</mn> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mtext>sin</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>−</mo> <mn>2</mn> </math></span></p>
<p>valid attempt to solve <strong>their</strong> equation <em><strong>(M1)</strong></em></p>
<p><em>eg </em> sketch, 1.33</p>
<p>1.02154</p>
<p>1.02 <em><strong>A2 N3</strong></em></p>
<p><em><strong>[5 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.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>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 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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MdogoObCbQ8+zx458Zv7MKFCwtwhAsP6GmwivN58Ez63EVwaOXqEtLyDh1w0iqC43dGXmNw4nC14S6CIx+6BE56vqx6Bq5n8dG79FAkI+WNvypuJqINQ8qZWzxDOLzJYxF8MT3CjzwUyQj8zTffdH/USjtMi/RjehQe8qs+iUcYxvQIjniozuo9pGcxE7eiIjj5k2tVSKt0VGfL4GXtjvqCvkN6ZOLmmBLOcMIAhnLyjozSU1F5oAdgIb3SlPFfKeO4bMOIZUYIrPdK3PDC2NKD0JcvxOlWGryjFApAcX4oOMoTLaFweFYlLoJTcFQAwUWrEDgVkZ6Ej8MzMG5VEOJEJ1zhSUbB/ZA8cvv0PlwVgdCP1zNGBxnJh+L8EBlV+Xy5hEMcPCRjKIdoYnDBoCd9wiJ6X49K2w/hX6YHeFOeIX/xkB7Jr+L8EDrpwY/XM3AMNx8zKA2F4PBMGpQDzyGMd/hzi6cfCp/6UqYn1aeifNBjRE7x89PgGRlj/IUHTPlQnB/CV7r043kGxo0OwNG78HjnGflYtBSNDwcHWrXrMJ/iCQ6yijYMsSFc98UwKuGVShw+6gLTU6THqN11gPnp8IxiuGMXcJRYBpfRE++QP115CkBwPx3ikFVDwJCWd9FTaD7c50MBImMRXBWBtGKXeuyqCCEOMtBYyvRA5eNGBt3iwzvyS8ZQTt6RjcagsvNpgSODKnqMHrg/xyh6PyR9dBHSCwcelGcRfDE9Kg/wiV3wZQioTwLB8dPiOdSj+ADjJg8xPQpOKIPCs38JR4Y3hAuXdqM5RsX5ofRQRE/+kbGoPkFHPsGJXYKrrPx0eOamI4GcYX2BH3BoY/VJcHAkI8+xS/EKYzjLiVtWjxHGJHwvbhTnO3jH0lABxWDEoeCwwfu4NFa/AH0Yz1QSKqoKMIQTzz9f2eKLX9FDet59wxiDIx83ssTg0JNHwhgcOhnGGJw4KlmZnkLDGPKRUSnSEzLIMMZwiMMwFulRMi5WVqQRyqZ3aMljkR6VhyI9wgf55K4jvn4I/zI9omcavE8TPtOjLMunbxhDWt59wxiDw7uMP/ohD/ozj/EATl5iMOKAl6WB4UbOInpoF9OTbxiL+CzH8C2Gu2TDuBijO4Urk6FhjPFTAcVg8EHB4MQu4H6PMcQBTiUp6jGCT2Pq+TEW9xjRkfSIrtXYQl2HhjGE805DKKIHLuMboyUOWuoCacUu5KQxYhiLLt8whjjQw5+bZ+7wAuY3eMGFT6ihtmB+CBz6Mj3QbuiRFV20CeiLLhnGIj0gAzwoj9gFnHyCw8W7Lp65/cUXHy58aGN68vnIMCruXoc9w9jWMAXWM4x5xaYhURFVsf1KSJx6W4Sxio4ee4axt1Gt6s+PvWFURsPG4Dec5T6LJ8M/fygd8gGPxlr2z1X2z0YjvpseI+nDIzbHiKzAZVjL/uH5Z9a/Y5hH3skD/8CkFbugB6foHx4Z6EWU6Un/8MgcXsTBezHD6E85iAe00kORYQQuPWooLXo/JH3yCX7sQkYNpWPwxfQIX/XGYvTAkU9zjLz7svCsNEIY/IgjDzE9Cp8QPcbqi3Cgj8ElM2W9lDlG4Ych9YX6QBqxi7ICjhzhJRlVn4ATp0vwcCgtuPDFn7R8esGJI33KPISLl9IqggtvqeGye4y+ACvxLGWEQ+kYb5SDEmMw+FBRwYnBiWPYUkQPHMXLaMV4UIkw4GrQIQ5w6NWgQ7jSKJNRjQ1eMXriwSmDyzDG6IlDB2V6oJGUyYiugavswnSQTUPEEMY7dGVzteDAv0yPpCHDGEtDeSySkXgZxhg9cTHDKFzoka9IRuDkoUzPkqGIB2ktpoey+gg9ZVnGX3+CMjrKn0LlsywfwGS8ReeH6jHCy4/nmTjoyWdRnQYPnCIZQ55LNX5leMsyjAiA8CgBQVfiVsHTUJIkcbtwFPHFl4nGcKdw+RAW0SMLfmWEMRwqGP53zOnE4NDJxxDcGA7yq+cag2NQkCEGI47GDJwwhoMM7G1HGjE4ccDQRQwOPfAyGZRPQu6Qj+BFMoKPHvEHXUxPIW+9kwb1Qe9hSE+srCzBh75MxlOnTjkvCfEO84oO5SMYwsgXZb0UPSKr0lAofovVedye5K4jWj+EN3IW6Zl05EPo0/nP5KGs3aED6m1RGmfOnHF7PuoPV7yFDy0yIIvihCM9+K52gvmhjGaZsVsObNmGEQuvfyEycbc3mYOfbxiLeFI4KoAQBx5UgCI4+IKTZkjPO4Ug37gQLhqcpzGMMR2Ag1GhMob0egdGPvQehsDhoUoSwokvgyOD/Bgls8+DuDI9gus3Jp9Wz8qn3v0QGLdfkWNwjLf+YHy4ninHMj2qrEhLNH64mB4pP/SIYfTp/Gf2EcR9zI/zn9GjyjKUA/7kQfCwvghfetK7z59nZIRPEZypHQxjyF980EOZHsk/7aKovkkG5UN8CZGJG1gsDcmMHqmTZTKST+H7aeiZNPQnpjg/VG9zOcavDHdZhlGMwq7r3byre62hdNHRBqRB4aG8ovRQPDhFcJQLTgxO3lAuyo/BiQNe5GYieiqI/r1ifICVyajCVkGHPKAnD0Vw9KnNfqHlCnmoAobxel9Mj6SBnlR2olOIbGpIivPDMj0KDx0VlRU46AGDIfwwlB6LZASfPJSVFUPAMnedxeojcJV1rBwkQ1mdhp68hPnTuz/HqDg/RIdleqQsSL9MD4vVh8Xqk4bSRTogf+STsirCWUxGR7iCP8s2jFL6SskgfjKMd+PgjfK4Yxfp8K8UVjLhAqeSYNjUmAQjFNx31yFOMGhEr4ro0+sZHBlf0cJHtxo0eD78W9/kM72v29fffcdmZ6bt9Kk37eTJ1+31kyfttde5X3f3V197zfbvP2CvvPqyvX7yNbt44Zy98/V37N2v/6n92bvfsG9+k94q8075H4TyqvQJ1RAEk+yEfj5DuHggu/8n5NODA53/ByO46AnRkcpKcD+kIZNG0QUtdYG0YhfxMowxOHGhYfTxkFH1TXLH4Grw4OgSPiH1DX2HcgoH+rA+CUboG0bx90PVJ3BjF2VFPtBn7EIueCBHeEkOYCorPx3B0SNy8h7Lp/gD8+lJTzxIQ8Y7lEN4sfg7jVu2YbzThIrolPHQMMbwKcBYAYELHxQMTuwC7hvGEAc4lYSKKplCHArON4w+3KcPK7KPRxrKg9IhVKWAluNlb9y44b6BRS/HXnzROEPlwL6m7Wu1rNFouK+EsoRzcprWTFNrJfndTCYtTRuWpalladOyrGVTrSlr7Wtac39qB/YftKPPHXWGiTk00nn77bcX9ECpgDLeklF5kKzAJbNghMDJI7ou0gN0McPo80FHRfTgkUaZYYSWukBasQs5FzOMLL6oxxjygB7+3DxzhxcwX4+CC5+QXi+yxi7g0JfpgfrR82OMae/u4nqGsa0/KuH9MIykSeXnSFmOgMDwcnAQixO4L/GZZCNNrJVmliYtm8ia1kgzm0xSazRS25MdsD/KvmKfabzg7j9IjtmXRyZsLDtsjbRljbRpk2nTGs5wJtZM8jsjbDZdOmyMwXZqrHDSyKanp51MyBYaP/REHDKHMFQpPfYMY8+PkbrAraG03n2TRRwdmtgfiPDAUY9Rcfc6XLZhVOYU3o2A4kEY9hgFE3/eUY56W4pXCFw9RtES6uI5Nu/lw2UY1eBDeuCL9Rhj//C+PEoDw4ERevHYMTt86JDtT/dZYyqzZjppzWzCGbPRbJ9tTw/ab2Yv2X9MXrb/M33d/u7keRscess+1LhmH8qu2QebMzbQvGG1LL8r6ayt2zxkPz123n46mXH3YDZrfy+7bP8mPW0fzU7ax8ZfsK3JlA1l+2wsadlUY9KaaWaNLHVGuZW03HD85ZdO2MVLl+2b3/pWZxiDbsjDYoYxNpSWHqBfSo+R8vTLQGVFCA/SKIJDy428sQs68lA0hAS+2FCauhjrMULLvViPEdkYoYT5FD0haYQ9Rh9Ou0HOogvakN7HRY9+GuItHN7JB3fsElx54F2XeC1mGOGNDGp3IT18gIdDafH3Q9Hebbhsw0iCviAr9Rxz8A55oxzuMF7vFE4ZPBxKi46Qi0rizzH6cJ4pON8whnDRqyKGcIZNuKiwQkcvLU25U0vTcZtKEtuR7bffbxy3f7HnBfvH6SUbyK7bQHLD+lo3rZrOWj25abXJWesbPmPVxqxVsxvurqdzpruaztiaLaNWnbhmtWze3fX0htWzeaumt6yvdcP6R6/YwJ7zVslu2i82r9ivZm/ZJ9IT9mR2xEayI5ZlY9akR5pOWiNr2L79+5whY3sr3CqkZ/Ib5pF34n3DGOIAxzDSYEKY3ilHv7EpXiGNhDTUmBSvEFoaXBEcPBlG0YRhaBhDODLKYIQw3oGX1Udk8w1jEY+i+gS+DGOMljhoF9MjMsroxPiovGMw4oCXpUEHgPZdRC/DSL0osi+LyegI27ZJz3cTLsswkjEKEyWQmZW4qZzwo6FgJFiVhm+YBu9UIhpDLF3B5doQ4gAPXSNCHJSP8SSe5xDOO0YN4xbC4A8N6SMncOIIb9265YbJ7EnH8FhD5FaS2J80nrX/Z+KE/fLEGatOXLb62FWr7H7LKhNXrTY5Y7XGVRuYuGr1yVmrT05bffyK1YZOW31i2mqT19s3z9fcXZm4bGs3D1tl74VOXA0jyT15zQYnZqw2ejG/J6/awOS0VSdnrTI5Y5WJ6/Zz4xftfxx71T4+dtweHz9gSdqyljPeGPDUGXT2zmSvwnfeeaeTR+lDesAFhLJVfBgW6VF4lLPqhuL8EBhp+HH+M2UATlE5qqzKZOSPwHfX8fnzrLJWOYdw8qD6Gsqhd+qb6ktIzzv0wIUf4tBuyvxBpYeQTu/kn3wU6YG8waOsXQkObqgL3tEjHQqMtNL1Q3gX8RcecNLRexiq54+NWonrvhtGMojyUNxiDt5UojIFLgWuihoqVu8YT57Disg7N36M9CSQOcSBDodc4inEa1ev2dHnX7BkasothLTSCUvTMdvaOGT/YfKkfWTPaesfP2fV0UtW23Ohcw8Mn7IKxsuL03N9z0WrD71llQgMnMqe87Z2826r7D5dSF8dPmvVkbNW23Peu/P0kaUyctbWj5y26ugF+/mJ0/ZrE1+1z2bP22Q25XqSaTZhSTJl+6am7Pix4zYzM+PyLH0QoodYRRaO/EGl9zBUYxF+CCdeZRXCeKehAy+iB4f6UmQQgOOYzOJLjD9xyAiPEE6a3OS/SAbJBbxMBvneCj9Mi3aDH2MYr3d4U+dDgyU4ITLEyko4kkHvYQj/sjzgx3j48OHCdgUtMsA3zKfeVVZ6D2VQj3cljCI8lmUYlWhRl/hu4hkS0CMJ3XV8nlKGH+c/y1j5cf4zygXHj/Of6cpTSEXDLw0B2ZKfy6flGTgGgaED/+SsGreSMZtKUtuTtuw/Z6/a399zyurj01ZN562efs0qzXmruznCW1bLbll98rpVh07bYDLn3onz78HGnIMPNKYXxAunml23Bz49kvcQA1pwmG/E4NX3XHZDa4bXoiVkSF7be8mqI+dsQ3rDBh2PeRtIbtnPZlfs11qn7Q8nj9p4M7FmNu7mJik3Gig9AxoJelBjDHWEbrnRT9GnldBQDmVlpaF0yF/vqivIorgwpJGpQYUw3vkDDL+V9vFIIyaj6g9w0tC7T6tn5bMIB/qyobTOlRa/MHwvhtKLyUh7oH2HsuldeiorK3DK4OIlG3W34bIN40oLIH6xOUY/c+BRiVCQaAh1UbFihlFwcP3GqniFwGkk9AL8SurDKZjYYVg/+CFpf9+uX5+1Q4cOW9ZKLEmbbt7w6fSI/V/Nt+xn0qu2vjln9fGrVh27YAPpDas2b9hANm8D6c08zOadYawMn3FwBwPu384wnrV6MrswXjjprK3ZMuLSWUDXhrNIU91zyQb2XDY398j8Y9qWg3nI5k2rjV22Kr3J5qzV0vn8bs5YBVj6tjOof2foLft32Snbmh22VjpmGS5CzX128MABe6pcmnAAACAASURBVOWrr9j1mZmO0fB1iJ5DPYZwcHyDIbgf+obRj9czdUF1RXF+SBr0kkKjIxzgGEYdhsW7f/EOf6Xhw3nmJg/cqk+iF5xQIyCe/Us40oMPF4wQg4PhKbqQT8Y7hoMewQn/IIRb1q4kB4ZRacTk9A0j/HSByzvpw4N64cN9PN/4Kt4PJYufvg9f7vOyDeNyE1gMXxmigMt214GPFBjjCR81hiK432MMcaCnYGgskinEodDoGdFjFA7hO2+/bV898YqlrcwmWaxIpmxncsh+NTtt9eZVqyXvuMUPFkCYI6yOtY0S7+E9MW3V4TO50QphvCezVt99xurJ3O20LLakc7Z2y4hVJ65E4RhLDGN976XO4gzGUnJU4YFhHMV406vNDafgdRc3b9WRM1ZJ521DNmP/Mj1lX0hOWMYiUiNz0wZpM3HHAjDMptx8ffHs9xhDPfO+WEOgrPijK7o0nxVraNAgA0YHg1B09fwYcz3RriiP2IUeKV9wuHjXxTM3fzD0bPUuuPChpSxicOGQfllZ+TxX4rlnGNtapFCWaxgpLA76ae3bZ43GpGVpy55K9tuvZq9ZrTlnA423Xc+vls10DM+Pj2E8Z4PpjFWya7Zu35xVm3P2S83L9lvNl204yxdq+KPDJ5PFGv5M0Bd6xlj1DGNuNOgxYsRjF7rCYKhXG8NZrMeI0SniDz/qPIatyOggQ88wxjQfiUNZK32HPcYYf/UYYzDiFoP7PcYYj9Awhjh+jxEn6GePPmvN5pSxuvxMdsj+deNV20Bvb2I2d59pzlutmQ+F1eOqtXuM9Ow01BXMha7HeNrqaXyoXE9mrM6qdMFQOu8xjlpt4kqHv9IhpMdXHb1odXqNXo9UOG7ovLfdY6QniStQ1h1q5z3IeauMnreBDON/0wbTW25aYENyw9Y35+3n0mv2H8ZesJ3JEUuzhjWTzFpTU/bcc0c7BpKeNz2JUMd6x4jSIPUehuoxhvF6h5b6AJ7iwlA9xjCed66wxxjiwZ87jNc7edCfgeLC0DeMIYx33zDG4LSbMj2ih8X0SB7CobSfFvCyfAAvSwP5kNPn6T9D7/cYfZieSb9MxoiZuquoO+oxStiVCDE28PHnGBUX8l9KAZUVIIYRHiFfvdOIKKCi9Imn98OKKj2hhnOObtjvpK/YB9NpW8dCytB5qyfTzujI2PgGiDnG2vhVq2NU2vN+C+AT16w6XGYYr7cN40yHXnwIMWRrHxm1Gq44mnf0QgybDGMcPm/1vZetxlA6y/0jmQ/t4jLsvmnVkfNWz5iD9GAYXWdMZ6wydM4Gkln75+l5+2L2nE01Ekuz1H1tIz9OGkyRrimHssZ2rw0jdQL5/E8CVU8ULmYQqItl9RE+GMayfC6mh/eDYSSPZXlYjmEsqg+k8b43jAhPxbzb2+fjG0b4+jC9q6LF0gVf/zxFcNwO4CF+Ph70KJ6K6sfrGRjDQb5Zxq2IYeKO9JD9L+kZq6UzVsvm7Kcmr1l99ymrNa515+bSG854YEDcPcYc4xWr4bDdnr/rwMAZ7xpGwReESdcwLohv86oms7Zm84hVxxcurvi4uWG82Enfh7k5RNdjPO96rTXmNJnP7Mg6a7XkhlWGz7l8V51zeXsBJ1E441bO0UONVfDshv3PjdP2xeRQ26E9dTrEhYNPIfVnJV0TMtdLYwvrgXAoD/7oiuDwVGMSjR9Ch9FhmOnH6xm4DCNxsXSgJw1gIZx3YOCIZyxknhRZY/TEyTCGcPGi3bC4UQSHN7fwwxA9Iie6DmG8w7csH5JReojxwM8SOWMw4qAtanfw51Z9KOJxV93DCPGyeowISEXilsLJ1N3cKnh6Yhgc/gGL+GnTziI4G2rSWIrg+ErJOMZwkEV+iD785s2bduzEi25DhoZz0J6y39xz1D40/JZVhs64G9/A+tApqw2dsRp+gkOnOzDhENIbBE7P0o/XMwsvg7vPWv/wuSi8NoQP4lsuHdH4YX33WfvAll1W29GVzYfXhs61ZUSWs+5eAG/LV8PwDZ11d7WdR/Cg71c+dp+yyvDCfJbpYf3wafufhl+xL0wetH3MP7peZMv1wPHFU9lQtyhHvftloWfKShvRKs4PaWhsxgGeH+8/y9fSj9MzMsQ2qhWcEBmpUzyD78MwNBg90ghhwideMhThAC+r0/S+cZOK0ZMOBgU9lsHRE/ry5fef+dopJoN4wh963hUnet6Zh+fjBnQSwsGDVhvVis4PofF9LQUjXrf+ROmFr8S1LMNIohhH/mVkIBHoTm94QEvIZDz+cKxexXijABTIXZQejaAMTgGCU0RPGnLpAYd3VlXZ0IENGVrZhG0dnrBf2vG89bvP82as3rju7trktA1MXHGGZmDsstUaM871Br/EBffefEXYfcUSwviSZfyy1YbOW21ieiFdG9d9wTJ8yuqsOkfoB8av2qpHhq3GHGIEXmtcb/sxXuzI7uO5r2n2XLQaQ+WJaRsIeCifbo7RfZ1zrZNO/iVORA9tHdUnr9nAxLxVG5ftH3xh2P7r+H5rpewGlPcg+XOcn5935UM5lpUVjYPGqjoUlilw9TJCmMp2sTQw1i+99FKnjoZ8VN+KZIA/N/XIp/XxqW9F+QQPevLi0/vPzNXSY/Tj/Gd0UMQfPGQDpygNZFA+fb7+M/Rluva/fPHppAdoY3oSrvQQywcwbnqSmuK4L4ZxJRMnA+JHT7HMXQc8CpE7dgFHkUVwDLqMHrjhRRzKRfngwufc6VNuxTlxW3k17T81X7LK5hGrbH3Z+lssOuCEnX+PnM+tzeaGsTFt1eYtq+H3F9yaY6xmc7fBwK1OTltlmGFsHM4mEa5XyvA94M07izarHxnNPymMwPGdrGA0cfDGdactv3hVmres2l58YVg9kN3M89jmVWFuNJ2zfgynk/FGVw7mHt0cY6CHdhqV5g0bbM7bYDJrax/ebdUnX7R/ml20bdlhazYm3a5B+6cOuHm9+ZvzrsLHyoqy48+Z8iyCqy5QlrELOsoaPrELeLj44uMBV33kmVuX3jE23MgQgxMng+LDfT7Q0/BjcPAYojLkL4KjhzJ66jz5ACd2wRceyBFewLihB4fLl0Nw5Iu56wgOfUxPSg884JRVWXmKn+juJlxWj/FuEiqiVWYWM4zQS4ExXvBRYyiC08MAB9zwIg7F01jAoyCzrGnNxl4bSQ/aP2ycN+bTVm/cYZWtJ6ya3cr9/Norvc4XMJ2x+vC5fPEFfz9v1bfz/GPjx3jOBrLZhXnEGby9+MIw3C1CMTfZ1kMt48/kupuvXLV5l/VvO+b0+KHGnP1682UbYQ/JrGEZizSt1N566y1nOFRH/HKjQWMYiy4aOvWlrCGVGUb43qlhlEykTxqSX/F6J6SnVGaUoC8zbLSbMgdv6nsRf+SRYSz7g4BHzDBCTx7IJzh6dw9ep6fIMAof2piefD4yjIq712HPMLY1TAFTOVgMYFHALbAkif2X5EX7cGvaKs1ZG0hnbe3mnT3DyOrzyMoZxkrrmvWn79pPZ7P2sfQ1m2TXoST3hTxy5IjbH5IG7F89w5hro2cY/Vqxcs93ZBj9f7ylPF+9etV9WsXnVUzEYoBCOr/HqKFHiKMeYxivd/55wNF7GPpD6RD23e9+206dOe12kqHXsiM5YP93+rr1N6etnrCizHfEN2z1xmc8w5jvgeh8A4Oekltpbu+RSC+qc49fdl++sLLbifPhnrtODI7/Yq395UsM7n/5EoPTe+t++XK7DFXcecYuW8V9+ZKvMvt5cavWzjCe7bjrKJ3F9TDf6TGu3vSM9W893t4WjeH6jNNvXzZvH0kv2W8kX7XRRtNSNtRtNe2FY8fdnxZlTNnJMIblqHfVhaK6BJ56jKIJQ7/HGMJ4V08pBhOcnk4RnHh6jMpTDA969RhjcNqNhtIxOLRl9H6PMUZP3GLtbjE9hD3GMJ3F+IOvHmNIq/eVM4k5pzsyjEsVAqGpmPS+xsbG7LHHHrNPfvKTrgegDCn0DSNxXAr1LAXG0gdXjaEI7htG8YTua1/7mj3/3LOWpvmWYP81PWoDzWmrZO8Ywz8cnPHdc4Zxk2cYvaFyrYkRmXVD6QGGix5swTPbho3nztcL4oXvGcYonDTu8pNAtzDDIpDS9EIc0p0T+p6Lue+iNxTO8dFH3mN0foxON/m0Ab6O5Xq4aYPOAM4bhrHy5IncMLbTh559JytTc1aZuGYfHDtr/zk7aWMJ3503rJlOuUW6ubk59+f6XswxahMJ1RfVLeoN9ZGbZ25deqcxx+DiBZ5vGEXvw33D6MP17BtGxfkhbUKG0Y/XM50UZCwbSgNHjvDy8+kbd+EJHhrGEA7/oqG0ePiGUfT3Mly2YUTJLK2zxL+Umz37wFOv8bd+67dcr5F4nw8rkiy+sDotmpA/bjPcYTzv0JTBwZmdnXU44Lo03nnXbkxft0MHD1vCymia2Ed377efHjrptu0aYOuuoTesvvuc66VVd5+yBzbutr4vPmdV5hJ3475yxsEqQ6etuutNtzBT2/Wmi3Mw5+LSxsPtZcdrVtlx0mq7unE+XnXnG65HWsEfMqDN0zplla0vWXVXMXw130rvfLOA/oz1P/2qVbe/GoWTx8r216z/qVetTv7d3ZUVdyDi+p962Wq73sq3N5Ocu3Fdkh5espge6rvfcrpZjR7/+Kj1j3R5kz/8QAfgg462n7Tq0AX7yMhJe3S4Zc0WZ9k0rNlM7dVXv+o8Bvy64j+zByb1gT+9ovrCeTdFcGjYc5LFDZ+veBFXVN+AcbPCzg1NEQ+MPHxicOigJy9FcNoNckquMIR3GT3n/YBDGNLyTrpF+RQcGcGJ0ROHfMgpfB8P/tBTFjwX5VNlVQTnD2YlryUbRiw3vT/8qvCd4usPbvyTim53gNOBA84p+lOf+pR9/OMft0cffdR9/RDSYhTlOF3EDzhfnJTBOcckBic93EJIR2nzmVo2NWUTzQnb38js//jDEVv9/z1pqx56yh54cJs98NDT9sCD7ZvnjVtt/ae+ZGse2mb/7UNb7YEHwXvaPvDQ0/aBh7fbqoehedIeeGibrXpwe5dWPAgf2pbz/t2ctsNfOA9vtbUPbbO/uTEO/wD0pO3S9+Rr0696aJut/90v2gMF6X/g4afsgYe32ipH35alnY88L+Qf+cnftrYuPFmc3NBttdXQwa+d9gfQxcNPF+rhAw9utVUPb7cHfvcpW/XwE7b6oe225lPwuj0fTk/k9XeBPWXrH9xl/+TzO23beMMd/EXvXvWBeqYyVdmzQ/rk5GR+iFikjqo+4IolmjCkrlFfiFddFo7oqVMhDBzg0AMXjR9KXvJQJoPqbCwN+AEvaxM6O8hPO3zmcLUyHshY1K7gBayM3tcD54n76UtPpMGz9OLj8Ew5hOUsfEJcqzRtshIGclmGkQSZk8DFgK4vN89lt3DoHbJhJcaRCXUsPDddZOjpKZJ5VoOL+OGHKEfPEAdeDK3K4PxTwQM85jpTnLUbkzbROGK/lr5ua8cvWT89lrHLNjB2xfAJHJjA9+5avo3X+BVbtXnI+r58zKqNmQ68zu7YY1dtYOySVZ45ZYN8UtemE73C+vB55yNY9XgLRsjmsZWdp2yA4XaER41dvneetvr4pSicr2rcly97LkThtYmrhsN2feisDbgdvLt5JD3chWpsYjt02u0cPuh8D3MdOPkmrtmGsStW2XXG6uzCs0BOdhjP9dAf08P4Nesfn7YNY5dt9cZhW/elF92QOZbP+sgF91kheqyPXbJBPqMcm7Gfmbxin2odsyRpdv5IX3vttY6jtOoFngVyPFacH1JfqCvg+fH+M/53zIsTp3rsw+HPXdQWgBXxFz85cPt8/WfJiLx+vJ5pN7QrvYfhYnqgLZTJSbrwKGpXpCc9hGnrHfmQM5YH4qCHfwwuHoKHONI9Q/n7Zhg13idcyiV89jDEpQDL/4lPfMIZRsEUMmTBMGqj2pA/eEVzHeAuBe4q6Xe+444ZYEK/mTZsa3rQ/nF23irJTauwCDJ6vvOJn1tUaH/K5+YZ0zlbs2mnWzSouE1d88/8mHtk0aOeXje+GKm7T+Fy2ILP/Zivw5jgAI4PoD4T9EKMbMW5usThNTaRwCglM1F65ujWbRm2Co7iHl89u01x2QUcJ258Kbk9WZxv49glq462/RQdbKEsfCLIqjRzqjl9qIeZth7YTNfXA+48+er+mo07rX/bifZ+jz5O+xm3pj1sjYafJPtEMv845/wu2Q7tf01O2Y7GfrdRLmV5/Pgxe/vWrc58n+oKjSV2UV80b1UEDxdffDzRkw7P3OEFf+4QrndCGr7m53x64dDwY3Dhao5R72EIbdkco7/4EtLyjhzwIB+xCzg6AEf4wlMeaPvIqfcQDi35jBk20aiseC+6hFsEX078knuMy2EqXAn61FNP2Wc/+1n73Oc+Z6Ojo+4fCCVIEeDFFl/ER6Equ979EB4oGJzYRVoYxpdPvGSTrabtazTsyeyg/W2MmVtxZhPWGbcaW8cf0VtUYLEBR+588aXnruNWn+/SXWf1JvTIqnS+mBMuBLlvvfdeji4QgVtJZu3Do2/Z76dHLUmnrJk2bf++Kdd7og5gDAgp99hFfaExFi06QOMbxpAH9PDn5pk7vICRRgjXOyE9IGSNXcChLzNstJueH2NMe3cX954YRhnAMPQryL02jDSAV1991ZJG07J0r305PWp/K7tiA3za5zZf7RlGt9rMn8CSNqq9Oz/GuzWMA/RaR0/ZQHrLTYMMZ1OWJfkcMsM2FjUwTPSIYpeMTs8w9vZjjNWPe2oYYwmGcTKO98IwwhtjTOV/87WTlrZa7vyVrdmBvKfIUQMdVxHOPpnJvyPu9RiXsIP3/TWMbifz4XPu88S+qVv2C8ll+0z2gqVu7nHCLWgw96jelv6UVf96hjHXxHsxlC5y10ECykFDadkClZFC4jWUVty9Dn/sDSMN44033rCpJptANOzx9JD9LL5yLeayusO4gaxnGH+UeowyjO4AL+c/mW+Y+6/SN21v2nILM6x0sskCLh4YRv/qGcZcGz3D6NeK7vOSDaOsOeFKXuK7EosvGEGGT1zw/avvf9/eOPm6ZdmUJSy0NA7Zz4xxyNO8Dbrvdr1NVt1c16xVRy66DVYxEt3NWfOdr5ljXMWXL84x+W0bdJssdDdacAsiw+dtILnuNl/w6fWsTST0HobsdMNhWGzQEMJ4xyC4VeWiHb75nnsLO3hfi9IPsIjB4sveS1E4m0wwlObsaZ35skCOdp7ZqJbNJBbqKd9wAj1Uh27XA07yHIcAX+fgjT9m81ZUDpzMa3vzc2sWpK/NffkCaOSccygnT/yxUR6V7KZ9OJ2xP2kcsTRtWpIldnD/frt0+aL9MPjiqmyOkfrjzzGG9Z53zWnz7MP1Ti+HO9ZbFQ5zjPDx6dW+iFvqHGOMHj7wLuIPnNFUWW8Mvsqn5PJD4LQ5cLh8OXjmLuoxCg699BT7AwNPMvIcu8SrCB6jKYtbtmFEcAyQFH63oXjxz84/PO46RTxxLdAqXogDH5b9qWgomvc33njTJpxT8Jg92ThgP+vOY37LrXay4unf/aP5mczOaXvPJatwhCh3B++Ce1+3cbtVHnvO+nDJ2XOhA2fHGg6Qws2lPnre+vdc7MC6PC5ZncY8eq4Q7jaRHTpt/aOc1Oennz/XRi/bwPAZt0NODF7dc8HWbN6d75kYoa/suWw1du8ZOR/l7864HrngHNhz/gvzgcGs7r1g9WHOpeZ5oYy+HljhX6gHdEa6l23Nph3W98TzhjyxfKBDzrfuK9AjekCGCjsBKZ/Iwoq6W1U/a/9u4oRl401rNBNrZVN24pVXnFuIGiL1iQYX1iXeqT9y14nBiYOeuwhOXZXhK8LBDQUZ1A6EJ2NDnYaP3gVXyHwqiy8hveAYVrUJxfkhaSsNP95/ZtGyLB/AYu0Smblx18H3uUxGZCjKI7IgQ1FZAcfAyziWGbylwu7IMCIEmVypm4z5PcYivihf/6AxHBQHDjB2Dc6aLZtqjNuX0+ftZ5ILNrD3gg2MXrLBxrXbblxs6o3LznDh31dvXLWBxMNLgE/b2k3brfrlr1gtuW4b2nw44xlYne+gR844H0N2r46mg1EZu2g1n7eHiztPbeiUDUxcj9IPsk8jfojjVwvgV2ztliEbGLsYhQ9MTlud76D3XIjCB8ennSuP2ySCHcnxdfTk20A+kyvOuA86PXXzeZsexi66HXakh4HGdRuYvGzIsGbzDqt86Ss2MDEdlYOycq5Tk0X5nHaGkX0txT8vQ8oJua9Ydfd5+0jylj2RPG+tZNwaae7wzUYh1BEZjFhdok7iNMwngTyDo1DP1EVu4kMY79RF0gA/1mbAUYOPyUAc9DIIMRzajQxjDI6xKWszkpM0YvTEKZ9l8CJ6+NMW6fiEOgDGDa3/B+OnA5x3lZXefRyemRK4r4ZxpbqqstzKzGKLL+BRyCgxdtGTdf843/tLu3nzlk3t329ZkjiXnA812WL/plX3XHG9PO2h6IfuHJMMdx2MFv55bLCQu+koZIOFBzY9Y31bTxj7Fjr/RXDaZ504dx8cuBP89xbS6h2H6ArDxAI4G9SyK7bb6zCC0xlKOxkjaSSz5j4JZBPZCL2G0rXg+FThaihN7xe3HPk/Cq44tx+j84P0ZFigh3Puz0N0ecj35vhfaih9It+3MiInemJfSIbqC3nk7+jBDaUL4IOTs1Ybfsud0rghm7XfSk5YmrUsaxtHtjTDubqop0F9W2woTX3jVh0O6yV1lftuh9IYA9KIXXLXKYJDW0ZP/pER4xK74At9UbsD7trdIkNp5AQ3lFP00lM4lEYmcICrrIrkjMXfadySe4x3msBidFLWYoYRPhTAYgU0O33d9h06ZK2kYU8199vPZlfchrLMU7nNE4LT8Wh4+TxZb/EFPSz9XOn3x6p0kR8kvVemNaru6NpbVkvm7Zeyszaa7LNmwp6PmfHhAccjyHCFjdY3jGE9VoMuM4zA6G2pjouH3gnVoxTMD4Grt8dz7JJhjMGIw6gVGT3gvcWXuOZ+rAwjH5q3spZNZOM2mTxr/yjjJLtbnQWCnmHMF5SYk2PxpdsT624m++NmGPMeL4tts85n9UOtGXuk8bz7xljfMXMULgYivHqGsetOs1iHBAPM5RtwnrmLFl+ED23sD0TlAQ/1GBV3r8MfacMoxfOP/62/+KY9e+Qr1kjHrdlI7Z8133K9hG6PsNdjzHvG/n6MGqb+GBtGjoBtjwr88NezkzY5uc8NrbNW01577av2ne982/UeNZzrGcaeYbzXBriQv4zbnQ6lqcQMWV468ao1s6Zxit+/SN6wipvv6jaK3lBaUwY9w4iBrGTz9vcnXrOnkmdt/0RmjVbTjj2fbzHWM4zd5kr7XIk5xtiZL6Qi/j+yPUYZsDDsqvDOnsRvMcMIHt1pbtEo5JjLrJlaljbt3zfeyBdFklv5wUzOP7G9ueqey+4QKL/n4DagFQ6O36Oct8xZJvniSxeeL0Sw+MLmB9Xm2+0zX+CN/x4b1c7kB9Fz9rPrpQgGPL/ZVYeFBRZuxFswF7pNJPBjRIac3g/ZRML5MbKZRATOog2HYbGLTgyODyeuSDXcdtziSr54JNwKfo6cfe30kPtvuk8mlVbbj9GdEnibjrp64NzpekQPzveRndA37bZ+58fYzaMvj7/4ItkWhG7xhakSDH6XR+e5wfncZ9ymFZ04D6/W5ECvy/bBxiV7JDthSXPSsqRlBw5O2fS1WddzZAj4yiuvLBgeqpZT9/hDLppj9OsrhpZ3Xaq3hMwxYnh8OHjCwWDE4OJFu0HOogtayRjDWcocI/R3M5Qu2kQCecgn/MlnqCfBwYkNpaUjQuG6hxX4WdZQGsFRJKtDKHwlbpTC5DD+WMz5FPkxgkcl8pftiWM7M/beY1OIL0w27afYedptAXY13xZs/JoNjF+zwbFLVhs9a9XRs/mWXmyXxRZZbXidd9xoRs7m7jTjl8zFCe784y47d53+Lz/vtssadDzyLclqHGc6diF319l7cQGtS2Psmg2MXctdUPacL4QP7LnkNmrFpUey+SEuQWwZVt8bhw+OXbDVW56xATZ5aMu+MMTv8KxV9px1Lj+4/bitwpRPVszxz2TrsTF0cPk2OHoCzvZsbPYg/nVWwkv04HYuH7tqtbHc17LypRfa27vlZSRZCJ2/4+j5BWWkdAgpG87m9svIh9coS3wtPfl8ONu2VUbOufpSHb9m/2zsFZto4RCeuT06cdPhD7fs+FTqotxMqMNhe1B9lXHy4eBTf3HXwSjw7MP1DP+Yj6DgLCDhDqP3MIR3GT3pkoYMcEjPu5+PIngZPf6gbFSL3YjlE/mQIQZTHHCMo95DOcpWrO/ETi7ZMMo6IwACSlkIfKe3KhaKwQEUw4hfVhE/nEC5lTa7L7OVGXR/mDxrA8McIH8qd07mwHrukfzGLw8fw+rIaec4jPOwYC50Ts/nrE4vA7rRLi1wvvSojFyw9Ru3W//jz1kfjs5t3hVgOHfjvI2DN/HD4HfTdjC26qKx4phcAGdn8IHdZ60/lK/Nqx8eQ4HsHTly/ms2P2PVZ97qpC85CMkbPSl04cd3nnE3QsahXE/8kXRg7XyRP3wp+ROpLICX6wGd19hncfSUrd34jPU/dtR9IbOAfzsvyEDP2NeTj+fchYbOW79zBF9YVuA5P8yh2+N9Hm6LOHCGT1t1+E37R3vesCcmD9sUG41kWeePWg3Xr5fUQdx9cNAmXnVZOBg8YOCEMNVfcFkVB1d0YQg9dT6MFw/azZkzZ25LQ/hqM3oPQ9IuSkO4fj4V54fk02+XPoxn/mDYTDamR+DQoweei3QBnDR8uHRAiKFUz/FODGFIs2zDKAO50qGG0sePH+8MI8I0MMjc6rkeP3HCkjSzybTlTvJzPYgxhpAMU/ncr/vJg7FrsgAAIABJREFUH0OuGn5x9Mg6sC58gO+mGabyKVwyu4CW+Uk39E0YAu5yRw/wje5g2qZ3Q9I5G2CPRAxsY9oNs/1P2TR8d+epjF1xB2zF4BxyX8GBO5mJfiqXf25XDEf2NVtG815e8FmjywdnuqADbuTX3cZ1q9J7r1iNTyP5LNHdvp7mbSC54f4oBt1w3/t00dNDlU8jceiWjtr8808CZ23Npl1WffIlN8XQ0YNkYR9J13O9fJsehYseapxtHcmjw2FPzKEz7ohX0fghe0ryZ+b03N52jumRDzWv2ufSI25aZjJr2MGD+922/dQ5DfVUL+m9cOs9DIGpvoYwvWMs5E6jOD+EHrgfx7MuDaVDuN7Vs9J7GDICBEc9rhDOO/DF8gkOV4w+XJUOcaBdTE/Ay2T0y0a6uZtwyYbxbhIpo5WSZBiLNqqFh1/R6J7vSxP3z/5vU+YV20aJIVZkFZJG0XPXWeiuE9PTe+Wu43q1W0903KlCWRbbj7G7iQTzi/nCkh/Kj5GNdP34zjOnIY6yqTBztTl97r50y6rNr9m/yU7aVNq0RvvoATYioWH6DZD66BuMsJ4DY4ipOi643gnp7cgwCq4QOPQyjIr3Q9oNc3jgxi6MThF/8JcyxyjDFeNPuuTTN4zCA8YdGkbBCYFDG9OT8MCRYVTcvQ5/JA2j81dstayRNowT/fLJ9VljmOnmuGINpWcYnQHgD0J+jDIIfviTbRhvWL05bz+VzFp/86b98s7nbNtIww2pOdeEeUeGczKOPcPYXTzpGcYVNtX6V1msx6h/DU4zO3rkiDWTKXsma9ovpnz6Rq/glpsbcxPzPcNoVRZBCvQgw/gT4eC9jB6jr69qdsvWPX7E/tbn+db+mDWzxCazxJ599pi98+47rqfzfjKMRc0Sg9XrMRZppzj+R6bHyL803enDhw9bI0vdGdD/ML1g1eRPbUMD15aeYaRhc37LWo5P7RlGt4C0nKF0zDCu+YMp+1By0/5j8xXb10icQ/jBg4fc0a09w9jrMTrTqt6db2cVd6ehhiX+7jrw4vJ5/uAHP3QbzjaS3Ch+NDlpfU3mh+asv5nPEbHiWBtnwwh90dENWXBxW2Qt+BTOh+cbHLD9WL6JRBfm+LGwkNywVZt2Wd/W427zA7ehQjutKj596az1O/+96Y4fZCiL20RijM0Rbt+kwuFOsB/jWccrpHXvzo/xbPsgqkBGFiLSWVv9CIYxvokE6Vba24VF+Ts/xssOp7OBBHmXTvG/TPEBPOd034l38JvOd9TpYQg/xoV6qGY3baB9+NYDm3blh2GJbxD6fowL02jLkrJ35vmuXAE9aVfRY7jRRRsPPfTvOW+1xvUCHnmPcd3nm1Zvzlk1nbd/nZ6zPdlhtzkJLmLT01fse9/r+tX67YJn/si5/XocPrP4Qq8ujNe73GD0rlBpLbb4Qm+xjL/mGDWPKf5+CH1ZPsI5Rp+W53COMYRDTz5lC0I476QfW3yRHsDhUqj4Ow2X1WMkURSJEvVvebchGUbx+DHq+FTxJJ5nQs7waE6xY86E/WFyxAYnrtgA22JxvGb7mFEMI/59ivPDQY4FxT+P0+/aNH44ODnjjuhkq6sBjApbann8OUYU/DUbd1jly8es1pjNj1Vt8wJ/YOKKcxEaYPWb7bsi6bCHoVsVZvuwCJxvmDnUnuNTY3DmUKtD+ChejsI52nT1I8PG8aMxeo4qRQdFemCjXFbu3Yqv0/FVwz9RvNgObQPHvDo9Xcn1pHxMXnPvRXrA6dxtmzZ5ydZsGrLql4677dXE2w/dXo+jF21w4nonbR/ufCbxAKCclL4fckoicE92H29gfNq5X+GL6cfreWBy1vr/5LD1fa5lA40rxjZy1cmr9pGJc7YjazpviCydsjdOvuUareqsH7KwgguK6rEP0zPuJxhHvYch9DKOIYx3tvPCjzEGIw7e0BfBiUfOMhxg4BTxAFaWB7Zvw98SPdDexUfv0JJPxcdC0vBpQxzsEvbpvhlGrLb+hcjY3d5kEB44gIYb1QqGn9PBA/ssa7Rsa7bPPrz7dVvNhqe78HPDJ5D7nNVG8EE87cUJlofV4dOF8P4h/PvO5v55w2esHz++Du+cvm/4rK3b+LSt/+IRWzt03qr4E7ZxnEM0O2/j3zd81uAnmB86H8Hhc4VwfPcGd5+x/qJ84FiNfx9+iIF8vOOisnbLLqvsfDMK73e+nqdzP8UIfZ/zYzxntd3k/4zzefTT6R8m38onci6Uo1wPZ6yGnkdO2Tr8GL941JyfYkQO/D3RL+n56euZdNG180eN0CM7egrlEz3pOp9O5yvZLUfB+4cvWt8f7bO+RxPn85n7j+Y+j78wdNr+uHHEppIx92eOEziLMmoLqrc0ZuquGrHgfoh/noyKHy8e8hHUu4/DM+0Gw1MERwZftpAeOj6SkPEN4bwDh08MBj3GvQgODWe448fIcygn79CiB55jcOjQgwxjTA6/N3mnvUSfbtk9Rlllur1lXV/hlYXQY+kJ/aG0eBOSYVYDm7jmJIn9y+R1qzifQ3ZL4cZ/kMUXzjrOD4FXnB/yiR27W9MT8eM7z2zTz/CLnhAuHMlsfryA+CdzrpeYn253zCr43Pnp4++XcK70WbdJKvQd3m0evPM1CTtMO/85L1649fFrVsVJnOMRYnD2esQw4StZAF/zyHD+xUcMLj3Qs3ZnYZPvXIdOPuB7L5r75K8d78Nzv0aGsWfdMQVhPuGJHtyfTOOq06PkrCc3bJBPGZMZw12n8uSLC3QsPMI6etp70U0p+PF6rjMExmGcIx48+fXMRrU4qdfSIj2y9yZlVaTHG7b+8UO2/vMtw1+TaQXKmymTSjZrP9O4Zl/MnrepBqvWTXv2yKHO2TKq0zRkbr2rLfj1WwaFuBgco4khKIJro1ofLj6EMjRFcI3+iobS0MEDw+nz1TN5k8EC109H7/okUO+iJSQOeviX6QkcbEGMvx8Hz5W4lmUYVyLBkIeUFFuVBnb9+nVrtVrWTCftUxPHbD1Dq8hq63u5+FJlo9r2dmZOFjcHh1P5jNX4XI+5NY5kjcjJJ2o4L+ffSkdwJpgb41vp7o43C/hgsHfj4B33z7vbxRfm86pjl53zM649yIFR6Mjgjpqdz78syVj08vLg6YHeXj7H2IXzLfhget3xXMyPkZ3MkYNvuxekofTQA6ME9/3z7Th34sfop8OxrOueOOIMI/PTLp32GTfg9bfm7YNjb9lvjj9v+xuT1kin7MiRI8bXWKrTNHYatN5V9/VOiGHEKMUu4PCQ0YrhyI8xBiMOo1rEHzjGCMOH0YldyAAP8hG7gMv4AuddF8/c4Ryj4MKHv294fbhwZBhD2L16f18aRv4BuOii0wXnk78vZ4ftg+773ovxhvIerkr3DGPPMLqNNYb5kuqi/dv0TWsmE66esijDJ3oYGhpzzzD2DOMdGW/9q/g9Rgwj/3IvnTjuthGbzFr2KymbH5xzq63+P3v3ueeugy7utsf4Xjl451MSxwt7fPfjy5duXWJ1v7zHyKo2UzMDoxdsffOG/W/pOdue8d3+mDWb+9z3wfSC1BPSnz2NRHWesNdj7H35EjWcqiShYbx69aq1Wvttfzphn0xetXVTc1bbc84G20dq+pU4f+4Zxp5h7A6p7/VQWoaR7dsGsmmrtubs5xvXbVfKsRoTxpcyrMS+++67HUOoBqA63zOM+Z/Ej/xQmoJcyQt+mjj1DeM3vvlNO3T4kCVZw55Mj9qG1lX3qdYgK9G4ZGieyQuZA2JnmsGxOJxPvfJNJPIDlkIeA26/RO3HGJu/Y65tzlZtfsb6t54wvoxggwTHp+3nxwKPW3xhgaQZ/4aXbbJqbCIhWi8PjpebY8QHMCZD91xpFhnCPPCOjGs6+zF2DUUH150rfSl3yen49HXxkJtzpXUYlpPTny91zzfyxZl0zvkAdnh7esCliDlGf46QMhrgDBZ3GNbOfDOO5tvRfLhtxTiiNtSP3lnIcptIxPXMBhZu9dxtKNLNX0dWeny4brl9LW+HD2Rv2/rHj1jf5/e5DUWc7F6ZkS96jBwXW09vWjVlL8o5+zvNaduUvug+QsgaTXv22cP29T/vnitD+1mKYRTOUuYYmcMrapuMvDA8RddS5xiZR4xdpLuUOUbat/Lk86H9Q08+ZQt8uGgWm2MUnk97N89LnmNUwoQreYmvvyp96vXXLUsaNp6m9k8ydkhhNXPOnddcZ6/Fzq4v2v1lzjk849pBj7KzY4yHx6p1fe9lG+AfvrOLS5ferTwmuW8baXV24GnzcGeGZHO2atNOq2497gw1ztSd3WdYcW3kq7Ucv8qQdKGc+U42yODk6NBKhjZ84qpVdp+zQVa1Pfn1XG/MWv/u0zYwyc41ou2GrGav2jKS764TgbOKy9nQ9VF/dx2PHsOHEzyr826lvgvjHblY6UXXGGcMcVcOVm7begCOHppdOAaR3XUI12zaaZUnGUrzB9PFUdkMunO7Lzlvg4XwNi4rxMOsjKM3n7797E5bPOPqTQzOanp1+ILRs4zCm/O2/rHD1vcH+2xDxk5H5K2bTjWbdX8enJGNDL4e6tl1+0/Zy7Y/2WtJmtrhQwft6vTVTsNXnSdkKI1hCNuVcDAIGDd/KO63P/x/OYIhpBeODGMRnLlQ0gcvdpHuYosvyAhOmIbygOEuMozgkD48MNJFPKSHEC6ZlVYRXHhLDZdtGKUozZ/cbYg7ApnGURU/RiavJ7PMWo3E/t+JE9aHoWNvRHbfxg/RHRTPoe0Lbxo723W5zWgDGLjuoPiRs/mejBE4PaTq3vPON67uegLn3cHy3XQuuM0X1m3cbpXHnrM+nKBxlIYXtG4/RvaDPOvi63sXyic+uIiwqwv7EirOD50LCf6R7qD523m4HcaHThl7QPp0esbNZv3m3VbdfToKr5JuiR6YrnD5YsUXh/jOnafn9MxGu0NnXI+r4utygR5O53rYw9xwTutk33vOqnsu2trNz1jf40fb/G/PiytHp8uLHXrxycOLNoAvJ/ti+jLomS3F2GexQI9sLzc4RFmdjdLX9lyxdX+8z9Z+NrH6nrOubjjH+Db/2ugF5+eJyxDxfEUjOTi3m/rwv+991Z5oHDB6jlmr4dzO5LCtdsNeh7QBvYch/nshjY/DcB0/RtqQH69neLOIWQQHDxkw0KIJwzIZxB960oilw2LUoUOHOj1Dnz/00JKGHx8+44sZxvnvGHYZx6UavzK8JRvGMiZ3A1Nm+Edh9Zkbf8XPZUdtgzd0YQcdGqr7kkHDqQVhb45RQ+net9Lzrifo/BjvcBOJ7uLLlA00Z63W5FNIf8idL76wKs0xCc61SfXRnTc0746XqA2fsd/D3zFJLEmb9txzz9vbnksPRqGot0bbwNCo0cfaGe0GP8Gii55cEX9oljqURo7YhYz0+DRc512X2nbPXUcaWUYo5fmGsZGm9ovpeRts+BWxZxjd/Ng99mPsrUrndW6lDGN1+KINNqftd9LXLEsb1miO28GpA+4TV+p+zzD+hK5Ky/BhK8Nn4hiac7/geoyJpWliH8tet0r2jlVavgNxzzD2DKP3R/meOXhP5Rtf0BtcMIIp7zG6jS/4TptjFtqnEv7TxiW3dVkjzezwgUM2ff26fbv9LTVtI7yI6/UYc7uBHoqc0EO9rcT7PR9KyxjKAOod4fXMPMORI4etNTlpO9KD9sF02jYk77hduburiD3D2DOM98Mwtjqr0u4TSg2X236M8aH0Tauzuu8MIx8k5ENtFmh+JTtnY1lmjWzc9rWa9sLLJ5zxoy2EF3HMo/WG0t3ddUId3av3e2oYZfiYWH399dfdp334dWEkBeOZ3UGazdSaSct+5Ustq6f50aQV5nU6FbFnGHuG8UfbMOL50N+as3+QXLM/Sl+wZtKwVtJyR7Rqjs5v6D3DmGsDPbxve4wyZAr9Aix7xvA9/vjj9oUvfMEeeeQRe/DBB21+fr5jHJljYfNZFl3+yzN7be3vN9z+d/zL4gbRNYz4jZ23mjvsymsgHcN5w+rD521DIXzO+e5xCJTPs/PcxL1mxgZGLuauMm7Svps+h2XV0lvGFxvr2Y+Rw7A8HzlcPpwrCi4kbFFV8A0vR646X8Zm3A+Rw7CYsHfuSZ28efnFjWfXGbehQUd2D499A9duGS4+4oE/G1ZkF+ihm0/3TTDuOiO462j42IWTJnmtDV+wDbjJeIsb+bfVXT0McCCVrwenYxYxpm3tRg4VO94+uMzLXzsvbts19630wrQ7eU5mbXD3Wec21Ynz9DAwOW2Du8643loUns65lePu2dcLZRho3rLKY3wrjbsOh4EhhydL84axMs0WbYOuR9iFOd/L5rzbxg5d1zM2uriR+7a26/Rg66r9cfoVa6UTljQzO/7ii2512G9fMgiL9RhZ3Ci6MLgxoyt8Lb4ULdDQfqFngSV2ISMwbl92cPVe5K4DHP7Q0jPmmTj/Eo/FDKPwQnqf13Kel9xjJEEEl/C+IEXPwqfHyPwAG0J84hOfcC45wCgUjlZkH8YkTey//8zTtuazTef7hv/bgjubM+cawu4zIcytCrJ56gW3l2IMXsPvzG1McKmAHiMwm5+O15jJN4r10mGDiA3pjNuotrr1hXxDVoZTzbl8xZJG05h2G7iyT2SVXWo8ej27UwJx8kaeGHwy30SCP4UYHMdv5xLEDjYR+oH0uq15ZI9VJ4ryOefcjmp74/AaeWITCT53o8FjBL103KYSWe4Iz24z+EVKDlZunb9f43q+kS16YNejNn2liQ7nbaA5Yw9s3m01t+FvQT7Hr1gFA+2lLT6E6MEdSevxXwB3emRD3276Ppy84epTS+L1qda6ZZXHD9vqL7C7Tu4n68vidnNyG/7iFzu7sDzbhpJjNnCPoqxduUkPrVkbaMzbB5uXbePECWsmTWs0E+fSwtEdfnvCIGCY/Dj/mUVL+TH68XqWYdR7GMqPkTCE8U47lWEsg8t4hzjQs2rOefGyBz6O+JNP7AG3D9czxhMZi+DwEe5yDGAR7rIMIwnj88RJfjhkc+NgWnbjnwiccGhoyH7jN37DxsbGOjR8OtVoNOzT28fsv3n4aVv18A5bu3nXbfeqR4bcYfdrNu++DQb+mi1DtnrTM7ZmyzNR+CrgW56x1Vt2RuFrN48YaazZ+Iyt2Txkq7bstjVbummt2TxqH/j0sK1+8Glbs2m3PUA6bTh4bA67ZvMud7wq4doCOdZs3um23CKNWD7J37pN2+2BLcNR+Hpk27zdVnuy+Xyc7Bu32bqNcf70Jp2eNsf1sPoRdLTb/QG4/G0hL155bBq2Dzyyu81jyOlM6aOHVfD39fBItzxWP7LT+jbttlWPDNsDD22zdQ+29Rgpb8oROdduiefD6WHLDldWSn9hiCzbbW2BnpFh/aZdRnkspGvnlXQf3m4PPKz6MLSgPiDX6k2kv8tWbyZPvpy7bc3mvD6s3bTTHkBfXnlSRg88MmTrNu2yv7l5l/3zP3rGnWWNH+++ffvcp4T4J9JmODedEZXaUdjW8Ptlo5UiOOdO40MY0ukdOtJkX0fFhSEysHNQGE/7hx7+pMNzKIfgdH6K7AW0yBDSkp54kseYjPDkvnLlyv01jFhu/qH4lnkpNwKDhwH85Cc/aePj4+6d+AuXzlurtc+mmpn9vU9vtzUPbrO1nxmzylMv3Xb3b3vZKo8/Z9Unj90GA7/vqRNWYePTL33Fqttecndlm8/nFet/4nmrfOlolB4e/U+96Jy3+bJlIS18jlv/tq/a6k1PW98X9pmTZ9uLOa9tJ2z91hetCv0Xj9j6rS/kcOWjLY+T60vHrPKlY9a/9eWuHB6cPQr7Hzti/Vt92b3nrcet/4uHC+H1L7/kDEqRnpyunnjOKtySzwv7n3rF6bDy2LO5HtlibduJLi463faiVR87atWtLy6UY9tL+bEPTo+366HvacrlZet/6pite3iHrf9D9Hi8y9uTg3Lse+J59/llTE6G4f2PPWtOXp+u/dzf0aMnu4e3fusJ63/iWQMvWl+ePmH9n5u0tb83YZVtx63P5btbDryve+JZqzxx1H3B4+pDmz/8+p86YdUvf8Vqjx919Yo45aPf8XrZatuO2/rHD9r6J07Yv9pz3BrJVL5LT9J0xo4hKL0tQrWjsM1hlNgoN4zXO/S01yJ64uFf1qaBwUc8FYqn5ORdccKB9pVXXnHGvQheRi9+klHv4q/Q3+6tqBe4nPgl9xhhqq4q4VIu8Ojinjx50n77t3/bduzYYbOzs25HYGDf+8vv2r6p/dZKE/vFTz9tqx7aZus/m1i1dfO2u9685Ry83db8EfhA84b7xKvK8C0Gx+l2b77HXxTuDm5neMUcJMO7W1ZtcbdlYROLbMbWbdxhtW0nrK/5rtUczk03d1RtzRufibEzNEPyeurRikfrpjGHyLEH7hhTL76TzuR1tys183udOA+PT9nYnbrWmIvDs1lbvWXEKgwlPTo9w5fve920QgTOfBzfcvNliPtumv0Zm155uPc56xu55D6Dy/WUw8GvtPXA2TecnePrAdiG9G0bbPJp5a78z6v5taic9fGr7tt2huaS3Q+dHjjjh2/kY/mYnHF6ZC/JGBz9V/gCiU8DI/SV1jvuD2rtF6byzWlZZW6XN/js/9m/97JVxpgWQUdeefPeuunKoI8vslr5/GInnTavejM/d4bPO/uym/Y/NM/YU9kBayb5eem0G/k5FrU5htIYjSI4Q1wNxWNtlqEpnR3C2AVfeDDUDS9g3OFw3ccDjlFFTp6xB7pErzlGDZNDOHgaavMcu8SrCB6jKYtbsmH0E17OM5l99NFH7eMf/7ibX6TX+PTTTzslffd737b9+w66HuNHPvO0G165T7DcpD9zft5NRXbbjl1eGN/GYf6Hbek5RMn5kDERv4Cew7AuuntBvHDam0i4T8Vcg15IP5Dcsv7shq3ZuNP6tp1wDWEwyb+GYGKduTfmmtg8ocpO3uwyLt7tzRWcXONXnIzu2+0IvDo57Y41YO7Op+88JzNW4dNINj/w6PXMfNaqT+82zjRR3IKQTVb5WoOzZTr07a86MMb8wbB7tvtWet4tGnQ2kmB+MMkXX9x3xu577m4+gfGnUqQH8j+IntNZN8dIT5Q5zK4cXZ2zoW+FXcZZ3OnI2YWz+QPHGsAzBueMlv6hUy6tKDydtQqf+lFW2kzDS4eFtb7HDtu6L+x3i2zsv5gvRuXpQdNPfep8c+7pAVzkGr9m9ZG2u47HG3lYzHMLbOyEPjnj5iFr6dv2t5vX7MvJEZtsTloz2WcvHnvRLUwUtTkMDoanCO4bxhiO5hjL5ggxfBimGD1xGDYZ3xgOhluGMQaHHv7+PGGIB7xoHjTELTN4S4Ut2TAulaGPh8BklgnlGzduuNVoVqQ5QwLY977bNYy/8HvbbfWDT9kavk31Vhe7zz13HaeL3pcvef14zxy8V86PUXXZbXLLTkP8KXDSYaO9IxTGOpuzn0sv29bkqDWySUsak27OkTNR1J4Idckw6j0MMVgYvaJLPUaMTuwiLRnGIrgMI3BfNp65MYwsvujd50Mc/FmVjsHFU4bRp72Xz/fcMCqzfqgu83d7hvH2P4H7fLRB75PA3G2n+0nge2gY3VGvM9affc02NK/Zb6avOzc2FmVY/HjnnXc6vSoZhZ5hlCZWNlyWYfSN21LFEI2Pr7jvfe87tn/fAZvKUst7jNts3ecSY2/E8GZOh6Ewx1uGsPz9httxpj4Wh+M24o4t3XMlSs8Qj3mrWsePEdeTrhyDDIWSG7Z60+72PoK3jDiH44bNbEs1Y/Wh885tB7cXn17P+GFW2/sxKs4P68yNcaCW2/qsm75w6swtcp4Kx7d68nWe01lbs2U033YsAucwJzf828OekAz/6Ll006m03XXYRccNHROGxl14Pizl4LEL7pAoN4XQTmfQ+XqCP2P13bfroZ7huM92ardszSb8GDk7p61DeLTlQaYac4zoqUCPAw3tx+jRe/nlGFi3HyPye/F6dluF4d7VYEuxbv70zHxi3+PPWt8f7G9vK8Z5NV08N8THR3HPpdyXU3WhnY/OUNrNWeP21JWTDVHQI/UHPTJvnm+3hn5u2GDKVmwMteft3zdesamkZWmW2sFnn7Nb82/bX3tuc6zIssBBm4pd9Ma4i+B0UuiNFfUqGfEV9RjVjqEHh8tPR3B/jtGHCx96+TH6c5CCQyMZQ3qX6B2sf4iuKLxjw6hM302ooXTLGcanbTWr0p9tOL9AfOL8m4rGllh1DpMKYLzjbMzCB47BUThzVWwV5nZDWcgbfBogiysVnHY5sClIg4aAsXtg8y7rYyXVTcDnPoyO3u2+kvsxVtNrVmvvyBLK4uQfu2zs7xjCHB/Ov247eMfgzEtxiiAbscbg7AWIKwqfo8XgG8gHCyvowuWpmwfwWeyo7b1o/SxMNDkVDzm7OM4vMZuxPjZ5TZmf68KcDlloSKfdcbbVlI1q/XzOWy2bdnrs7Gvp/CS98pBM45fdH6HzEQzKAjnZF5JDw3I/S4++jcs54k5PIf8Or1nrY+u2hLKK0Gfzbo5x/efz3XXwgfTrRL3FHOUF6997IT8EzeeBDvFZ5JxxtiBr4e/Z1VPuTznrPmTo46OFBvt3+nqiLt5wPqB9ey/ar48ds8lsn001xm1qX2bnzl7o+PPRY2SltqgdMkSWYYzh+EPpGNw3jDE4cRpKF8HDoXSIpzlGjSRDuNIAzhWD+3FFxm458cs2jFIkFv5u7298488sS5vum9Gf/8xTtvqhbbb60Qm3+swWY/7dv4cD1E9ZjYoUwHh3+xfS02JCPgLnCwS3dx5nT0fgtVH2V7zgvpbgHA8WYdjLT7juC4Y9l61v407nqtK/50oH5vZipGfA1yLsU7jnvA2OdGnFw4Vu/76z1heTgb0PWfQYPuVWjhfQdfAvWp39GNlSuF85AAAgAElEQVT/sRPnPY+ed76CtV2no3DygUFxezK29w3Mj5Vt8xhl4eWc9Y/kunZfG3np0NsEn70Mya9bvRbc6Sz/amaQo0sDPeT6RD8XnNvTetyv0Hub3u392JaJckRGFjgEXxhetPrwqXwhSel7IWXi9FigJ+rLAIt1o/H6wpEF6/8k349xwO2tyVcuXVnQI4tgrr45PXTz4fb+pMc9fM42DLHfIxsDX+7kA53ysUKdGw+DkXz/zTB/5IHRA39Svzz6uu1sHHbHJmStKfcZLb0o/B3PnTtX2BbZy7FsP0b2KeADDFa/Y+2ZNIDDIwbXfoyxPSOBQcO50rH9GAWHljR4V1yYFvsxFsHA1cLMcoxfGe6yDSP/IFrp4p/obu5vfesb1symIoaRSqabCsUK5RWrjZx2lYn38O4bw2Cw8SgbrN4Or4xh+M653U6icFwv9l60ARq825z1knMX6eDyNcjey7Z24w6rPP689THMczLmabmjPjEYbBC7FyNzNSoHu63U2XjXNfjb5aQxYPhwLeqk7eXHGZfht6zfS9vH69973tZv2m39bNrr0em5f+yiW81FDsX5YYXP8NisliNc0Xl7x3HhMA1QGcsbvdMTX6e003GNH3z0sCs3gNALXtt7NTcGe6/Y6s07bP2XjlqNNCJyoiMMNGnF4K5+jJy2XF4vjTYvZ2SH3mr/wUTg7Obu/mjj/PvGrzrDuP7RxAbJo8tXl48783rojNtEGYMWlld/e2WfzxaRpe7nEZ2QPucXYVzJa6CHDv4IGwKfdW5BH957xnYnLbdfaZpO2elzp51jNRvVFrVDGZsiOL01jBLGpQgHo4jhLIIDI50QDm9sBRvV4sQdsxvEQY/hgz6GQ7yMe5iG3tXbLDN2y4EtyzCKsd9tvZtnhtIH9h9y7jqaY3RDaec6wxkaDL3yYQUrep2hdDtOMEK+R+XMl9oE7jo5jR/yPav7DI5KHoHnQ8Tr1k+vI9Pndl0+dYZG2Zx9gDNf2kNpXGPEqzqFqwtb/nMIfH72tWB+6IZXbjqgS+vDaxPXrDZ82jbwyVtETr7t7R86bXU+W4zAkWH1I/gxFumBz/loyHE94KZSG7vkejT5ELM9BFRabsg4Y/0MpdETQ+c2jKF0fYrFi+tuKJ3roQvnnJSBZj4FsGrzTqtuO9GhFQ+FfE+OjG4orbS90E0pjJ517jyi8UO+le7H6LjP9TwZOjzmrG/0TNtd53Z4vTVv6x8/7L6VHmQo3NJ0S45bb866YXTf2AVjWO3rgekFDseqTF61fnqTrZn2VE1O6+a7WzcM31v+yOoazndku9Eets/lu8jvvWiDzjdy3v679Lr9cfOwNdMJy9LUfV7LUJUOS6wtytDEYMRpBKgeVwwPHvQcYzDiFhtKh3OMIR9/KI2NCeG8k36ZjL5t0vPdhMs2jBL6bhIVrRZf9jUz+7vOXUeLL/nmBO67Wzc5T2O7mf/zTlx1PmLMOfo3h11VcX0Yj8Odo7D7p2bxZSEt70ys4xvHZHh+QFK+KUAHl4//3eLLLqs8ecI5+OaLL7l/G43SNcKhc27+z02gR9Kp4xBMbwG/xxgcB296IkXwhhZn4vQYEj5vLNIDxgsHb9cD8tyiJAt/RvQK6ZnmfnsspnT15RYg3PfabDLB3JknB/6abX/Omlt8ud5esMjpKcNBdxgWi1jP5IsvGMuIHpyTOb00t/gSwUGG0fPuzzNGX29gnPNvpWNwt6kDIwi3+HI7fz4oWPv4EVv3B1NuEwn+mH09uLlNhun4g7p5UY+HW6TBUf6qW8wD7tPm7joLF19Y/LtNTvdRwiU3UnG6c76Q/397b/pkx3EkeM6/sSMBqOO9V1XY3qYIqc1metd2bczG5h9Ys/m0X3Zt98uaTbd1t7p1URIvAaQoHhIvibhJAnWggHpXVQEgiYMkABKi1CRxXwWgcJLs1sGWWmqbNfO1n0d6pr+syPeqgAJAdGeapUVkeISHh2ekZxwe7ldVF3Rd47C0sXbfbMsHH/xC/vu/xE3724iK7zZ2IWwQOgi/2OXXGPNwkwWUpx57tnz2jOBmk8ie83DKMmKNjfqsjNHIc+yyfEXwWJluaUsWjN2QLRUWBGNQ8C71GIOaCCdjWANUpWonuEwHjp3zoW0nCr0IsshfujZYTtcGd1NdJ+kDKoTDD0fXuhG+zuskQvaB5rz8bHqvtFo7pdVuyqH33tPpqI0c7VtE6BQJPfL4EaOV8SGCBhwIptgF3EaMwL1gIs6d33zxeICbYLT8Hm44qR8hfreuUjAmwme4dVN3pXWND3UTnZ5nHZWRFMIqOIo396kJXE+2MGKcl6HR4DZU1Vpigo0p4iSnd8KINBV4lrcUjKrbWd0ZvCku4I/x6V+jgre1rYdghCcsSzzYuCwPvz4ts/WWtFtN3eAwP9YmQErBaJxYWnhLgtEk++2Gf/wDeoyMGE2PMZx8CWuLrC9mN1MJtX+HfptLt7hOZ1hjdEcCDUaonQkbhLq2luG1PExdVf2E3UxUK/wxPp3qBRNcTAFZYxxsg5M1I6aPnJNGcF6V2vZT4SRDrrzVo/TtZDqflM23RQUja2PBZ3NazvI15qW27bjUdI1xYTsYMXJWuoq6jpVxITSzGYBKThx+XZju6w+CcrgG7Sh/XWqNsGyB6S7OKhucn4HnA2tn/AAMHmxUMv2+rlaI0GM02IJQ1XXCscUFMHjtBGMUXr8kQ+yM6xrjQj7xvtVbYwEf+VHiV5qptC7DJLqHVhd8RF1HN+BU3auTD9rf6KvsuiucH2+gQ5Xotb9cU2+RdvLF4BaCg/eg+ruuv4T18JuqP9n3g0n5vza2pNmakmarLnvffFM++/Qf0mlrrzVGm0p3W7+zEWPR9w6cuwieHzHm81GWqXQ+3T/biNGn+fjSxF7v3PdWMP7xn5PNl07BGNYWmUpkNx8du38YF/DpWRzlbNYYz8fhHNzXnUAUcjO8Fmdzho0N3JoGn85B8BlcjY3izB7BuOGQoAit9goJU7/CCK2T6REvK+tDNVKLsVo18rqQDhTYq+y+F8Gb1HFM10E9XosjMHSNcVcQvpaehpyF1g8ae4sL62edC7/XrNfys4EOXSNL8sIHhG917FRioJW1tQRPDz7woYc1xkQwrj+iI5+0vOFBCLABpJsvDr+DqzI+Wgj601rYDmxj6g8EhXJXzuIIbM5asxZpaT4EL4Kx/+lZbSe0h3XfUJcKRlSrUPJGr1LXFTvpYJ2UAwNsxoQ1RisLT+k32NY8LbWpOf1x+/qN56yj8r48zMf7143Lqg1H5P9ufiBTrWmZbUzK7r27VZ2HaTJCB+HohYiPIxC9uouHWRwcCCZ7zodMpbnz6fZ8NwSj1dVb5C0uxy0JRtYxYPrt3r///T/J7PTuBSNGOnX+rtWvBD0wFuQj8GqdtTlGjOcK4FfUQOswOmWR8ozAhhqXguVqfHVMXdaPxvLWGpd1lLIKqzDrD0ulfkWGphI6UcrmA5u6GPwtT80FeKweNZZ7QaqckonCL0gF4wcF8CofEXqMVncex9S89D0ypiPCGP4qmzfsKKNDly8LDzlRwiYVghHhktyWF4VoDC9UR1Eyv6ibFwaDH934AI+H63NSm7qsPxg2sZSPETqGdGf8nFThcwSOFSWWLYrKM2LG93URn2oNDBufELQAovgbV6UfIxI/mpER5cHl7H0rn9jdP626nPQbTtB4PCi50xdrydLK8FQGV542Lik+4LxT+O7LWxwVMxWOOfwGX7luh1R/+q5Up67If22clK3NPdJs1tXM30cffaQCzUZbse/VhB6CLQYnjfK2OeLzIFRtxGl18Gx5LI7rEmwrWn4Pt/Ko+xBHiBuc0MpQP7Ty7OEWz6+tLk78FedakmBEKkMIxNtfAobc6v27330eVfBWXT/0/fg42SUeO6PmwGrbP1arzZbmQ6bZatkaBW+sJiflLA/PwHVjQ3F34h8eRbH5jG5sDPOXxioKo4EEj5YfO6d2BAdeOiCVcfTgAm1aX6LgjS/jQdRIEpgvr/mUvkCjwQgD7IyO1EzB28MtjuJ4ZeyYfiyW5sPK2Ck1gIqCt09P44mCN0rFMT7j7lMVjkePBZ1RPn74YvwcxaIMCt4nZAhn9Q7Wiw+MnobHT+iSyKpHtwgK3hX4bLj1fSe6pujvQaN7B1m+M6pAXxk7vuA9Wx4Ee2X8WLBuk+LP2qEK3ihfF/SXobHz0v+TWel7si7DiRL4sMej/e24DKMPmih4W91qUWcUBfRTqhfLlLs2xgEAqx+ehp9TFeGsuq2dfFB9XISiwvP95XTQ1x0/JSvXbpf+lw/I0MQp7Y9f2/Fz2Vx/S1qNujRbDbWFiNEWvtfYd4rAwUAFuoQxOGkYpzY9Qp+Hsjyjg4iSdr4Og5uCN3LD0ihncXBThz37OixuCuD2bKHJIQQm8mm5riUJRirND1nt+VZC25VecCRQ9QODuXg7tsZUBEXYYRSQ7diYC3E0xJFAfKqENRjWv7Ib1RLWF3VNKMWfwVVnLzkSWGtcUtcEvrxOIVtX5UuPvqZHAgenWS+CxoCD6RS+TCp6jpm1NfQMM/xGkx0JLIT7I4GuvOEaZuSMUOJIYATOSAJr0Xo0MgLHTD8nM8JaayePwad+dnB7wIeLSX69s3bo+mv+SKCrpzsfmBZf0mnkikdfE4zyMi3sbEegaYiRNVNph9vnUz4k6jg+3eLoMcKnQG9Gv8E5kqnqXYyA0TvM1QNd/S+9IX3PzOiRP/QUw3ppwDXMu+dIIMsSrfmO8uBSPuya03XImroB7qTB+IpO6fAuzoRnfQkajffmV0aPcjoaOULI3b92QgY3HNYliT9p3tCz5w+2Lskrrbdkul5XIxQoVyNYYt8oAgXhYoIln8er6+Rh9oyQYjRnz/mw21Qa/CbcGHTly9ozdcRoNEFo+ez5dsMlCUarnPB2L3CYHmPeiITu6Kb264KhAzUswOhk51xq/MCMIBBiHKHC+uBkcMCkTpi8UQI+wInzMjzh7Tk63GpEgl3lM2oMQtfaXHndnEGPESdOrxyRwdbNxA6g4eD87rzURjl/e0nUw6ErHzYpbij92IyscPY2Aq85IxIebnGmgEOvn0iMwFrdWchmw5cfQ48R4Zylp3H0PRGM4wV8SNZiGf2p7UW1NZnhwbAB647oe67WDasMFupI+LD9tOgPRn8YlucTXb9FxxMXEjqV1k0IgxMGe4e6AcRpIxVIHh7iygc2ulBjibSzxlLDthO6eRSFt67JIHqIvLPkQIHPh3HePtYYn5kNwrsdDDtYHgSl+owxZ1hKd0Ib9LAmiWM2ZhL4JHJwcPBsRiTYfPH9xQxIAKd8Fb3TDj5mGz0DayfVOZsqt6sCPQL8qvxp47L8beuobspMN2Zl/779OjK0b9e+ZYQRgim/DmnfN/lsum1l8jgo7wWjL0vevIK3wQmBUx7BF5sOW53kMcHoy1vc8hEux7UkwbgcFXocNmLEtUGpx5io/pTqOqW6TrrRE35ijJy9HiNC1+6BdTulf8O7HXCMKg9MX5PVjUvy35q/lFZrQhrthh7LwyGdjcwQRCYYETqxC0FjgrEIboIRuBdMJqzyI0aPx/Azjbb8Hm44bcSYh92p51IwJp2s1GMMH1tpjzHw4d7YY8wEXtgBv0XBiJoPLixwBzJ1Uf6fyb+XHc1pnVbjPIuz1SYcS8EYF633j2BkuswiNlNp98f0caaxOtWOwJkaY3iANUZfxsc526s7jT0VvA+p32idXlPXEhS81X2q2mMs9ivd/eQLNh+PBz2+SDvvn5MvYSqNWox/BxZH7QrDDPa8IHR6jAtgjLjYSUaPUdfrInUkeowcCYyWb96Uvp8ylUaPkfVB3rNXyje1J3zjcITV1cFUmiUJdsbNtYGD25FAXff2FrxdntsRjOie0ieZkmPSjHXQ/9w6Ka8290u7sVNmWrvl1LET8oc//osKSEZjTKVjF6M4m+p2gzOq5CK/XTYC7DViBH9sxGjlCW3E6PFbPXcivM8EI3qKLFS7TmhxjBuwE1ggOBcnGC+pgyQ9wdLt5Ate8vRsa/KhLEkwzoU2qH5gpB09p9KXE8EY/6CXIhhjfLx7I8bugpFNKk4IdQgce9eEd1gwsg6aCsbEpqSuf6Y03IZgVBzoMV5RzQtT8Pbv43YEo8ejaj3smrc+kT+fPiGvNfZJs71LfbmjQmO7zbcrGGPlTbD1Eow2Vbf8JujsmRDBaKNcg9/J8JYEoyf4duJmqHZRa4w6YiwFI0roYcRYCkbUYXSTLRVW2Y/mdkeM/9oEo44iWzfkT9pz8u3mEZltTKmqHDvWN2/eXLD54r9rGzH6NB+3NUaf5uMIRgzqsqZpGywebiPGPNzyEjKitM0XX9biyy0klyQYIZA/AwQS3urNH4Ky2GNsNlpi6jr4lV65bqfUONGQuzmloLYSc+k+X3XshOr4+TSLc8JA9RwxDBrBgSl+TOGjuIwtwsHRYyF/knd4+yl1nbDykS3S/9JbUmH3OoEx9a2gbzZ6PKnjVDiOFqkH/Gpyn13bGJxTL9uPS38BndBGXUpnpDxl//3jr8nQqx/F8ffgA9NPFTiK+7jUUDbHtmNa12m1/qM6hKPHRcME1osPeFAcGg98XfXwazLw4oHCdoBL+bTtlKvb9YuU5562DM67rox9pArWGe0ZHPeuI9uogzZm6RbnZM/gc7Oy4smGGkhWfUeXL5SDtvAuPB/AMYS3SDVCe0xqYydkEH3JtDw008+4sX1Jft+O0JcyOHnidK5Yu10Gn99X2E4sNalNSMzhpfWflG/tPJio89Sl3mzKydOndVSGkPLfNc+m5+jTidtIz4zIxuCUR49x7969itfjpzzP6FBShz17PKRxo27EqNGXz+czQbocQnJJghHpTOUQCpG3epsi5+ef/0am27OiZsee2CIIxv4np4LvZfwvu1vP/qIIzRqhS0/javvupAypX5jOsuRBfSNVRo6Ur+26pLp/6LYNc8aV9SGXT0+17LokKx/eKoOvvKMnV/DVoXnQmeNEys65YOoKIxGcnHHlLY5rBbV6bWVzeaqTZ6WKmgm6bTkYzxhX0I+JEz4ROFPQLz22LRyfjMB78QH3razlIhh02UL5kLST+jlxsuuCIFj0eKM+J/zuyYfLMjIV2rXykVdl8GfvSoVTLTE6J84GK+URmPJhV8KHIj5NnlMjsHqyJYKD942grvGuInBO1Ay+sFdW/qil7wK++HxV7GaOoYB9WoY4l+75oPguqsVvFO7pO9TnyxtvgaNTim9pDwen4uWwAcrkC+AB36ofjMvgy+9o/+4sH+DqCpe1d9efK405qe68LP+1fVJ21Wel1apLq9GSkydP6sjMvk/7vjmVggK3PedDBFs3BXEsjO/fvz9dq/TlqYuyTOmJI/jycNKpn5Dbwy1u02xk1HJcSxaMNnRdjjDVY0zVdTZKf4H7VNXT4qhawRqiGkcYQ8E7vjmjCtymxxiZeoEfZ1YIrWHWrzoW2rFmEvTDVj3ymlQ3HJHqNHqM2WI8a3vh7OtJPSpXQ88xUg/CUzdgCjYF+MAqeowM5epsamjxqjqaOhUcTkXgKBuvfDwYkbAyPuzFB3Ucj3I1tg51HTQoNhsOPSOOfx11hhXO/BqMsJMP+HfxfAj2GNHhUytFG4/ozqkvn8Z34jQMZf6MxylM65mXYT543kuMD/VL6mai2+YLeoi6NBEpX2l/KgMYkXgWBe+rgl6jX2NkjTm4Ighn7+l/Rodu1OA/hzaoU7GFG21haosu5CkZQnC2PZ947+C7pj961HV4L4bfh+gxDq5HwTur38M5ookhCz33nrQTdR70fnkP/6l1SkYbWOjZJfVmQ94//L78/veZ6gzfuQ2Eir55hBl5iuA2lY7BGWiZMLQRXywfApCZarc8Vu6uC8blqNDjKPUYFwo+/vpMwbzQ9R1dNx1Ke4x3fPPlflbX8f0Fwai+q53g9nA22742+qH8Tf2w1JttabbrcuDAPpmfn9fNDpshIrxiF8LIBCNwnu0yQbWYzRdGgpbfyltIuglGS7vT4ZJGjMtNTCkYS8FYtHlS2mPEEs+t6TF6wddLMGL8oorvm6kr8r+3T8pYfbfqO05PT8svfvELHQnaiDH2/SO0SsEY48xtpP0LZsewx4j71LVbZMV3N8nKgqm02mPkXCprJZGpD36nWcQe5ihcBN5LXWcpCt5MpSt+imjqOq15XeDG2oqfdnXQ8wU3VMs0kClshbVW1YXL6e8lR/ZYg+S8cEfbHB/U9zV8cO8CITiCP5zmNVn5aFiS4L35PGlcrRDhKjfy8wDnHVbXub0R4/VUj1HNjqnr1awdQY+RY4HBNzbqOsPOQjc8sCUEXEws9eRLykPw9Bgx4uKhghtaTO41bsiD7bPy0/rbMtPYJc12S9588025du2aCj8b0RHaVQpG48QyhqVgzD6WtDPf46l0KRjDO/m3JhhrjWuyun5Dz/Cvac/L95tHZKbR0NHj7OysnD9/PtUjLAWjE4L2t2DNgR2g5bj/+fe/k9mZxB7j2s2ykhHjD+vBiEMD233cV/TWEQIWX1D6BZaDk0/X5grgI1hq5uQMo061bYd9vAz/6vpV3TTBqvNQ/aKY/UWrP9Ayr7vS1fXvCh0JnMCHsHiDMQJsDTJqnZqTkalAdyif0Ese3IHi9W0qq1txJ21SZ1lqPQcbfx5Hwgd2cbcdV1t+MThWZVY9NipDuDiN8GkEPhkfsPmodh89LVeUPt0txcbkAvi8tlvNlnG6RN+D0ZbxAVUb5YNrw1D9qow05tT6+MpHX5XKK4dkuAHfrXxCD3Wqe9mzHX3A8hGqLUxUXRx+Dx9mp3g7Bn0vp/g74EwhUQHDuVqMT1OJdZ2nWzKMnU5tZ8Yn3r1aAMcQBaNgx4fhqStqLENP77BrraPk7F1qf9G+g2HkU2pdZ3XDwRvwMeDkJJY6JnNw346+dTtk8JW3dcPQp1sc7Qr8W3fQ18Gzy6pyNKIzsSs6EscYSqVxVf7Pxocy1tyt5sum29Ny7KOP5I+//2f5//579v2zIWI7xcgEnk02EOfGHiPOsOzZ4Jaf9UN2vlG/8TCLU64bnHx+U8aJrVuOLnqN0QQjRNqag22V32r4+W9/Lc1GW2anMSKBYNwoq57YJUzDsjvosw2g35fYU8xg5AtwPMKpHqPqCVr5ANM8GDVVG3/oi6F/diqpI8mz7ZTq56nu2egp9csc6jH8p2Rw9LT0PbJV+l/aJ/2jZ6SmenAn1NQYO8kIRdVTJFT8rn5rE/p5Ck/0JhP6szadkOFtJ2Qg0Xe09lmIcVWctGtb0rJZPejVMU2tvPrRAh4aH+ATVsKDDl3QE8zwB31P+IAJNYz/GoxwMGmX6u9tP6nuYg1O/oV8yNpZQScR3cftpwX/3Ni1hKdWXvXslI+Bl1r/9gxu+ZSORC8Q/UCfbnHSh/C/naM/hdMHVLcP3i3sL5Wxc6k9RtUdha7kfQccp3UKmvLB04EvafRe0WNM3rdvJ/WhXwhvK9vhBzqGne2kP+uturm8h064tWPlulEZeGG/8t3SfKieEunb2ueyfmJ56EfY1gzPgQ+BNt7/cflft78vr001ZbrRkKnWLtn95hty88bNVHUGoYiOoZ2g8bLABOaxY8dkz549Oh23NPIR56YsNiMRfh5ueQix14haTx5u9SFUTUbdsjR0BRctGClDxTZi9MqVtxrHgvdMe1bXGP/c9Bh1xHg1jCT4SyZ/8xq+d/n7Tp5LYOTJ4IwMVGcM9wWMQvTO4Go1WU36MwpJ/s42UmAk15iXEdQmUENBJ411H0YbSR7+oowwcW2AHcEK5upTOPjQ0ZtT/T8drTjcgc5Ak7oNwO9MERwVj21h1Gl1+xB9ST6ooakLKW0evnrqonzpB6MyXMAHjojpqBn3qMYHRi8JPVgWV11R7AROXRRGoLTN4IxusWjNGuRIYkU8hemoJuEDRlpRncK1gLW1fkX1GNHZ63v4dam+cjjog6bwbEQGn9TNq8FyISouVTUR52hzeVQlip+Ip93BaccAptV0xLiwv7AOOvDimzLw1IyshgdT9I+MT6oGM3FWbVvCD/hq7WR2o3FcRIyfltWM/hyPFaY4LwV3verqwvMpWIOH/0PUgdmxfPmkLX0/mJDKzw7l+lNGJybu1Ohy2lczWKCDkTWjVvp7xgf4pjY/py7LV8c+loebB2TPrt2yq7lTmFp/8sknqSK4CbQiOcCI8eDBgzoaZGDl89kgy0aEHubjCEXy+jQfv2cjRhOMJpUtdEJ20VEry640my/h5AubLxul76lG6jSI9a7UVp7qjYWz0CE9OBbK4DhoCh9jBsduXbjRCdMOhlBqBy9rBiNkc4cz0ijT1jAyy9nrpGyABx29zB9y2DSwPMHQKTt8TMXR3+ssn9Kkmy8XCuGqrsPJCaZTrv40Tvr2k/pTSNNcPsqtUD1G6ujkEflZy2RqhlJxFduM3K48z7g2UJuNqRFZ9x7Ub3Sif4dx1RyfUj7wsbGg7/hQbeHACfuH2LUMfqUXtiGhGadm6K26PtCRFz6g8F8AT48EqjOurB8YDgTfIEsz/AgifDJnWAPPZM6w2DSx8rRBN0bgJTYj4ZvjI89sFCof2xihyPpDcArGWia+sVnaob/kyqueK32WzZfzC/BbXegxDqw/pHYpLc2HVQTcOH5nsvo9fER9hNNneVcJ771+LrQze9h1Uf7f5i9ldLolu6fqsnf2DTl2/IROj21X2r5rEwQ8I7Dyeox5OOUZCZKX2y7DR8jIEKFK3C4P93GD3064pBHj7VQUK1uq63zxNl/unhGJV6WC5elEWKebT8kudqmuc5fUdRrXdGlH192dBoG9D7UsxLLL1AUZaH0m/6l+Uja135Rmc6e023X15fLZZ591KHjbt27CqtRjNI4sMiwFYykYS8F4OvUqacKIcLms6yxGXYgXVmwAACAASURBVIc1716CEe+Vf1K/KgPT1+XP6pflpeYBabdaqc4jxwkZ+cVGdKVgjAhEm/uzHnDx4kVdaLVspWAsBWMpGO8fwWiCmyWF/va8/EXjlzLW3CutZl3qrabsP/C2fPbpZ+mUuBwxmqTLhcYYFESfe+45+frXvy64dLSrFIylYCwF4/0nGFmfZfOx1vhE/rfWGXm2/oa0my1pNSdlZnavvP/++7qLbIOiXj5f2FRhjdHkhckHC0m3NUZLu9PhotcYjeh82I1A8qJjxDCb7fpvfOMbHYLxX/74B9nNyReMSKzdIl/+3iZZ8aO61Kav6Y3DIbtJq06e0rUOS/MhmwCV8RMyxK6tK5fFrwqWa9AjzNIcfl14ng9e3dggyONo43Drunz5ka1SXX9Equ1P1YABuLRuXWCf151x3UFnYT2Pg7xT54OFnCI4jpFQTSqC45FuFPh8HH/rmqx6dEytvUTrn74q1R1nVM8xBq8A34kDpjPaLjZTqu2MT4waaO8g+p7tKx00GB+qLTQETqozLIw4WD3q2KqFHcmr6gyrtuE94eSLwTvCqQuCZRhwdqQnPGWDrIr71giPSUNLQVWvXP0+L3RVJk6pDqJPt/hI61OpvLxPLXjjzApnVVjqNniV+I4zUkXfcuaq1Kavp7B0cw//4myeTIdNqqzsNTXiEGjAaRgO3LJ2av/X+q5pHRX67IyrO/k+yNe/dqcMqFGTG2n9aT3whg2wiVMd79DD0Rrgu0Fv0qdbfJjvClUktACM90l7avr+cdh1Uv6P5keyrblHZutT0mg15Y29b8qJE8dUxWYxghHBl998MdniBSNxu/KyyMMsz62GSxKMEM62+qVLl3RazNS4133hwgXhxvQQI0aOGFmZc2fPSLs1rYLxf163VVZ8f5P0PT4hgy/sT+59MvhCuPtfOCCDz+2WgR9naQbT8MWDMvDMXqn++I20TAf8hYMy8OM3ZOC5vcXwF/ZJ5ek9Unl+nwxovdAR6qsoTftk5Xc3y8of7ZKVL1se4Pul8sIBqT6/Twaf3S2V598MOnpJWcNBWPnxXhn8yRtqi9Cnp/GfvCWVZ2Zl8PmDad0pjPLPH1D4wPMZbR6+6oX9ws75wPNvxsvDh+fekMFCPhyQgR+/Kf3P7lE7f4M/2RfCtC0Hpf+l/TL47F7lU3hX9k72S+XFg8qHgQgfBl58S4ZeoPw+Wfm9TbLyR01Z+eKBHJ3h3Vd4V/AKXce0bqsHmg4IdWi/iMArz78lg89ML+hHhmvgxf1SUR7E+QRdq56YkC8/Pi5VeP1iZ5+svHhABp7bI4M/3iv0jQH6Z0IHeoWDLx6Uyo/flMoze0TreiH3Pp/fJ5UX9snAs/S3zv5ifY+w/7m92m8H8+WTb6Tv0e2y6qlmYTuVpudmZXABn42XB2Tw6VntV0Z/Z7hfKs/sloGfRL4beML93B4ZeH5Ghl/cK/9t44Q06w219diY3i1vvPGGHDlyREO++7m5ufT7t2fUeT7++GOVEyYbLER2UAabjgjYfHnLxwYQghEZtRzXogUjlVExQ96rV6+q9Q0scFy+fHlRNw54EIxYDLYyc3PnZXZmjyp4//m6rfLl724QVT/Y+r4MpPdRGdh6VPq2HJWB9W9L/4Yj+kxax73lqPS98o5UNhzqTLd8m49K34ZD6lGto1wC7998VPq3vCeDP3tHKpvfl4Et0JDVMbj1qAy+elT+h0dfk74fT0tt6/sySD7Ls/moDG4+Iv2vHJSBTYel39Lz4cZ3ZWDjIenL4U/xbIKGA9K/6ecZbodjcPNRGfjZQenb9F4UPrTpffnSo69KdcO7UTjl+9e/KwMFfFI+bDgkfevfkcqWozK45X2h7UZf/+afS9/W92Rg/btxPm35uQxuivOhf+t7UqP8q+/JlzD4+5PdUt3c2Q7lM7zeGN5VIR9pxysHQ79w9BmdA9Dws30y4N+Ry6f8X/+ODGw5nLYtLbv1qFQ3vy/9T++SL/1wV7Sd9I++9W/LwMZ3pcK73JJ7X/ABHr/yjvQD570l9StPN4f+0w8Nkf5CX4MXfRve1X7ry2ffxvuy6vFR6X9uRoZzfLS6+jcfkYH1B9K6Ld3Cfvjz0wMysCmjz2AabnlPBn72tvRvivcn2ta//m2pMYva/IEMbP5Q/pcdv5CftPdIs7FLcL71wQcfyFtvvZV+9/b9m/xAuLFBw4DLYD4kHwIyBgfGjQK4jSDvqmC0SgmXclk5tNu/+c1vyocffpgW56z07tk9MtNOjEh8b5N8+ampqFGBYdQ6UNAusLeoRiJGT8pIgREJtW03cU6GC5xhDTduBN1BnBdhoCBvpqmJ/cXEH/KG96XS/izzR5IYT8CHBw65UIouNiIxJ7VJlLPj9vPQY+Q0hTq+j6lPQNs2Dv3nDDgkeSvNK7LqsTGpFvLpmioNjxTwgSkdxy7RfcOIxJD6lc7WQnGwRLoa9M37rTEjEqpreUoVw1mPShftW9eDX+nGNVn5yOtSWX9YKokPZs2TGKhQ3qH0PHEh0FDEB4y8RmCkoYw9hL6nq9/nDW04o0cOfbrFa82bMpBMpUe0DvRcs7ZoPvXPjWtTbFYGHVFNh0f4BNrJgYFgC1F5abQmxjl4x+q/G2Vv2m5w3ZW+HvoXOojqPjVXd5K3X92nHpZKzghFigul9LEzhf0RPUY9xlrgFGw1Syfo5mJo19FncW3D+FmpTs2JGsdoz8tA66Y83Dwq042WWu5mtnjo0KEFgstkg9djzMsXy2NrjHm4CRPLVwS3fIsNlzRiXCzSWD4E47e//e0OwVhuvnR+DNrZ7rERiVKPMbyT2zMisRgvgcG6jtpKrC+0CPVFVNcxYWghCuEMIFiPRp2HwQn3YOumPNR+T1rNpgpGZosxwYicQJDd15svMWG3lDTm/p9++qnuLlm5UjCWgrHclb4Pd6WTkWMpGE2SLXNYCsZSMJaCsRSM/6ZHjDGZWgrGUjCWgrEUjPe1YFzuxU0EZUwwrlpgRCI52I7xgx1npbrLG0fIYKx7oG/FWkd6GN4OxdtaCIYTMCLBJoHdSR61JI2TJ3WQFDY2PJ5gZAI9xtdlcMN7Um1/ogvaHXkoP3om2DhsYrggoy+N75qTyiRWZ+Jw9MUGMVfFRk6sPPp7qZGJhfjRSwtGJOai5TFugG4dC/ox/KqziAVv+MDmgN5ZPdDNOhLOsNQCtaORdwDOIeVDMNDQ0U7duJlX3n8ZK0Ub30sML2T4jSbesxpPcPgNpmHzim4ABeMIC8sPNS6q2awahi4iOFgbG5xAKHkjEhkejEj0/RRnWLNhHY3NPzVIkbSxdU0q9EccTSWOqNJ62Ihp3xQ8FFbGzwm6gGqB3uhI+h7riBWMliSWztPyykM2dMK7qpjhEyvvwr51k9K/ASMSGe0eT5X2jcffNfn0XeER0huRcPix0q56jti3dOkWH4YP6LyyOZNsnrHG+J32e3pcEP1lNl/wK20yxAZJPLPExuZLkR6jlVns5ovhvt1wSZsvNILbbDIi6W/lhhHc+JVut2ZUj/E/PLFFVnxvo6x8cpcqaaOo7W8OsbNQjRkmn25xzCZhXQcDpxhI5TZYCC9KDUsm46eDqSnMTWGcM8mnZpfwSqcWenDxeSGFkUdNie2cU0O1lVfeCWagLI+GF2R45/lg4QdjubhHdTSkNCVGYovgtZ1ngh9ndmVd+TTOjwH/zDtx0ZrRb/GRyfOy4rHtMkxbI3AMvKrLTyzLROGYujqjfMA96rC6J3W07Lwo1AGfRqDReAAuzwcM9iofLmX17LooI7vOqWbBKsyO/exQcDMbocPczA7vdOV9PviQmF+LtgNlfs4A74rzKbi6PSPDaAhE+8sV6X/xTel7qi3DiuNiZ3/ZeSlY9xk/IyPQ0sGHORnh/aPcjTFcXN6iJZDQrzyFt1haoj/uOC8juy6ncOUjvMXCEEJL32VnfzJcq9ZOSOXld3VAYGk+rKkb2aJ3jZvg8+pHnP4U4wNp6tN9EjN0nd+VmqXbifO202qtCXq5Kzvn5aHGYWk1mmqiDB3FAwcOqKxAwJnMMIFo7lOBkWZwwkxWBPepvrzPl7e8c9cEo0luTrJALPqM3BB6qzd+pVuNdjj54gQj1qHzNwZahzEsqk7MF8KxxQhsCAOvaOont+EZ7AHX8tSLY/Oxk8FQ7NiJjI7x02qDsO/hzTKIcjd/+oRO6qqMJzQl5VN8jhbygV+NwGL41JU3eiucatmGg/bTKdzyEWJYdBjDoklZDyOOMV/1p/LaR9HynFiBhuGEznx5+IQh3KHtx9TQamrcN6lPDdFaO8ZOyIDjUQcfcCivbc/aEcoeV+Ox/d/fosrBAwXthAY16Dqalfe0Gh/0hE2EF/oxYyw2AgNP6C+JkV73jqyOgfHEUO0T9fDOtP9k/a4CXduDIVoM0nbwYZT+d0qG4M3oMTWgrP0voUX5lBobPi5DY9Dp+1MwREwb6c/0a1/eaCTs/8FoOGAAfZG2an/aDr6Mdp+Pfqv9CX5H+KDtVOPBC+FqaDcxoFtTg7qB7r7Rs/KdqbdlptnUUSPHgPfu3ZvKjby8+O1vfyu/+tWv9PBIHmZyhjx5Q7UGI0RImoy6XaFI+UWPGK3S5Qz/+Iegx2j2GDkN0fdUU6doTNP8zZC/NoHj8PMd6ZYHOJap1fVBrix5mGLWOArHiDICVz0yjkVhoBWjtFomo2GocVW41R7j+sNqw9DjqaJXqMfQgp9g8nq4xXHwjrOpIvgQ0y8+OAyRRujE0RYfpJrsj8CxgciIEbP60fJMQVGvKOADU3iOTupIJsHvaVW9Rmz4MWJs4n/btZP0hA9YpcbYL9NPo4OpFs6w0OFU1wb4Q3Zwy0eIQWKWTjg+6NMtTvsZTakhXE+D0YxeHXxqFvGR45+8K3QIY3Vcl76X35T+p6eTdl4TdP4sL7quVfojMxhsJ3ocqvt5LfgPVx1Clg9c2cSm5Yj2WWiYE8x7GW5C63+8Kz3C2brSAbe8fWsnZGD9O8KU1tJ8WEOnVmnoxJ/mwcAzzrAwtOtozOIsWZzQkWCWFnCFNjPVRs/xYlp+sHFNHmofllazoQKRI8FMpZlt5uWHTaURbnkXBT4vAtNGhT7d4h73XRWMy1FZHkeHM6x1W2Tl9zbr8SbTk+oMg4Pz+91LIAIL69ILlIV1HRTjpvfWrzRrR+olkB9EstYVnMMnG0XJOpIaBS69BKpg5Ay18sreITxq3xD8rdxpL4Gcle7f8K7W1/m9hPe1GLNjQTByhn3hZqDZY0Tw5eH0FQQyP1H6LTzgNj3GdrOpNhKKFLyRBwg2RnsIRhNyeTlBugnGPOxOPS96xHgnCCgF48KOWArGhCel+1QVRL3cp5aC8U5IpiVMpe9E9bFd6fvBr3QFayaY6bdjXHYUrjkfFrLvY7/S5cmXIJjLky8JHzAvhrWnghFjefLlDkjGUjB+8UaMpWAsBaOfMveaSpeCMVkPsHWA5QgRjKUzLHPUlOjHscaY6ikazIWlM6yg+1g6w1I+3BFnWM6p1wh2K9nR7tAPDv0xOPUKTsHUz3eyRjnYuqFnpW2NkbPSXo8xLztsjdFvoOTz2BpjPt2eGbf5+O2O45a0xkjFEM/ukbkuZKdoqbeVLd2nmitLXGcm7lVL96nq1rV0n4rr2nvnPlVdq+JSuH5ZVYVU2yPpo+a2GA+LeBfElS6uckemcJ17WQbrV+Wh5hFpJ3qMJ06cUKdZ9t17eYFQxMbrP/3TP6lM8TDiVgZVHdQEebY8BuMZmXRPBaMRRYNu90bBu9loqz3G/7hus6z87kZZ9cQu5wA9c6Y+wDoH+mGJfhujqnAHZ+HqUBxdKnVU3wlTZ+I4N1dH8ydUQRolaV++ilNy9APVSfopGSSudRj+U+ocvu+RrWpotX/0TOqAPe5ovtNRfUov9NOOnIP1FL79hAxvOxH0KJWGUL85SEefEx0/bUsEjooKeoyVVz9yfHQ4Rk+p+kUVz2/m3N61E/1JpY86SCe/q2dQ+QYPA38GtS0Jj3Akrzgph75mZzsr24IOZWX7aVn18NZgzNc5ksctbEoTDueVrrij+UFGMdtPCqGnz+KkD41+rDqTluZD2oECuLXDv2vyVcYSPcYn0WOkX51K33fAc1rVXKx8Bx3boAkn90HPET4MunZSV+hr9Lnj2s5arj/Qn/VW/UD4GefDynWjgmFc6PPtszg4hujb7j0ZjJB+NJK+X+ju5Cf6k6jrwAPfRykL/7Wd29EdzvQc+7aflW9NHVR1nVarpRa10GNEkOVlBsIOofeP//iPqTK3zwOc59/85je6M23PpFncBCSCcbmuRY8YTRozYrRRI1L6du5//v3vZHZmd2KPEcG4SVb+sJ46LscpujmFVxuJqAVwmsIcpzs4+RBqRfARjkYlp07UIxr251z51fWrMly/KFV0suoX1dQ7dVr9gZZ5PflSXf+u1BrXBJzAh+pXVO+wVp8Ltu2m+HvmyiY041qhtuNscN4ecXg/NMnJFhzF4+je4whx0oe2HQ/6dxE4tiBXPTaqrgtifBqBT8YH/vj618/4TJ3QhwI0owHV6XR8gg/KSwQP/pBpV0KH5wMfDiclqC+DX5WRxpyeGlI9xlcOhZFyWj6hB5pwGTBxVu0lWnkf6tQNYeXwe7ieVNp+LOh7RvPMq0Iz+aJ8mrom/S+9IX1Pt2QY3VFtZ9ZWeEBf4VRKrXlZ+ZjWP3VF7U6imqWnjIA3PR+uhJNTHMPjpNWuC7La9TX6Ha4GeDeV8dPqv1pHaZF29K3bIYOvvK32OdP6XT5UhoY5IeTeU2e+y9rfhtFDTPqo/+7Qi+Unx+mdDJ61hRGiKrNzkqdBf7kslamr8lDrsDSbDdm9e7cwYnznnXfSkZ6XGQy0mCYzarRBVx5OOnAEoIf5uE3D77pgXK4KPZ4OdZ21W2QFgvGpxgJ9qbAY/K9Dj5EjU6rgnTd6ajpkXxQ9RqZHiUHVDp3LUo8x6Z+JHULOnd9DPcYBNVT7xdRjLO0xemm3hHgpGL94u9KpgncpGNWIRP8z06rErFaAOJFiPzAz0FoKxkIF71IwLkEY+qylus4XTzCW6jqluk4m/DnJUuoxepl1V+KlYCwFY2mPsbTHyEbKfX0k0DZglivMBGNT/uM61hg3yqofNcI5Ytbg9MZmHALkhh6mr+HsKlnn8qFOAUdPychkHI4dwtrEeRnijpSvtrA9yII89hTdlMnW1PDz27wqK7EjiBMnnA85+qp68B+fz2xaXFI/xLF6dHNl8oLgrzkGVxt+20/pgfwoPHGGVSOMtAMjECseG9dzujE4fKjiCGvifGqT0udDUGHoQjcVsL/n2kg+tX+oxg9Yg7yqunQd5eFDA5uRC/lQU3uM0H1DVjzyqgxuOCKVxK6lx6FxzFdhP1MdTSV9wLcX1REs3Oh7iMDrl9UZljr38uWSOO9ycByhxMbIwvK19k3pe/kt6X+m0x6j5YUubCkqL+kbaq8x4MHWJ3DOxFfHzuqoy8r5EHuM9Lda/dKCdtKf9Z7AmMZ59Vvty4a+d029apo9xk54oKVaxzDKaX1vMThqYrpzzSZihA+8Y/o0/TIPV/rw+80G1NSl1F7jgOkxNsJZ6V56jOwuswFjGyhevjBC4xnByeaLh8XiyzWiW/SutFUIMbEGxIgsSrPyf/jD70Xdp7ZbgrqOCsan6hKMi2JgNLvZ1Rtix3gSg5lZusWxtoKJJGwAWpoPdXeV9SDuJtZOMFDKHXDh4Q/jpkPY12MXlmdXz0hzXq2srHrkVamtPyQ4S8dyi5bXsldkhF3a8dMyklhLMdw+VBuF7KxbWVeH5sPRPEJl6nJKmy/PTnp123GpTWGQdyEf2EFd+dio2vqLw9lNPVPMBwTuxDltR6qvpkZzQ10j7Fw2g01HdNx0BzWhw3ZeV8OHsQgfmldldeOSWqkJ1nUO6c8lozN5LxytxLoOlmsK+MTOKepbwaBvhA98yGgpNLJ3nNXDu7afYAEfW9dk4KU3ZeDpWVmtbeZ9Z/VAl/IRDQPd3ecnkcF5v8O0Yfy0lldvfMYnLOWgIwi+iTML+otaBGKXGtrxEsjufEE7+taOy8Ar8DHeTlXM5rtxtHs61T7ndrQc4v1tGMGKatOu+HelFqVYj3a72oMNdqWDHiOGarGuw650TB4gCxCMRdZ1gHP3UvA2mWJy6nbDRQtGaxRb5La9zhb6rdzoLVHut7/9tbSa06qu8x/WblZDtSue3BX0y9T2YtBVQ19KlUi3H0t0ELN01X1Dn2rsjAyiT4XuGPpwuRu1CbVhWABHjwwzVAgd1A9ULy3RlQPX0OgpGRw/Iyuwx/jSPhnEzarT5QKm9umUBmzfYXA2QgdwLYc9vwhcbSGe1Lpi8CHoTPTzYnDoXvXwa1J97eMC/EH/TlWb0HFTXb6MDtVZwz4gtKHDlnsP6MQNjKOHh73G48FOYNIOPiAdAaEzGuFDReHH9V3ygxl46UAwxOr4AD2pviq6d2r3MKPP2jw0eloq47zvOB9xY1sZO6bubK2MD9HXxL0qqig+3eJDqsc4I31P1mVIbRl21kO9oY3HVV9R7UqmfKA/og8a9D35SQyi92pwdBTVJiS6ikHfc0F/SXkf9Hdpr5XXMHkvK9dul76X9odRneOj5R1kBsO7wu5lDM5octvHhXwcQG0LPcfId6P6mOhPJjZGzc5j3+gZ+VYdPca6TE9PC4Zq0WNEbti3b3KDZ2wtosdIPAYnL3qMKIFbuXzIdNxk1O0KRcovWjD6yoyA2w0ZMe6e3RsM1epUOlHXSafRNp0OZt6xf5ea7MrlQbUEE09q/TgHY9qBOaSaTiHP5abqoY6a2hK8GAyYMrVBl6wDT5girnh4iwxueFcqqsrCKOKa+l5maqY2AredlBp6kB1ls3boNNXMjsXyqEVk7AhmZXxcTfFvO6H6ez7d4tChfqWxKF2Ao4rbAh2Nxeq4Lpw60SUFTPkndigNF+3iZvqlSw/Ak3qws+j5oHqOjoZa47oMNy+rDmiwa3lEp19WviNEB5CRNbvADkcaZ2TLFK8Ajn3BIYzlMpqPlWcaqzqr2N5cyAf8Zwd7jG21t1hlmqnLF0neZFeaJYcqI0HHh+CL+6raxOSHiw4keq9WD3H4pKNA2sDoP0cD+LRPYgU8cUNh5X3YvxbXBu/qsohPT+PoGWIlPIc/hdeZSp8IltRjefgO+HnoElbWBiuvU21sRuJDO6F5oHlDvtM+Is1GIzU7ZvYYbWRnssNGgwg64h5ucUKbSlualbfQy6fliN9TwfjHAsFodt18yLqUCUafnsadYEzTEvtw9myC0Z59yPpJrRU6EdMsDsd7uBkCXfnIVqlsPCzV9g3BETt5Rvho1FBo+FgxJsvOXmf58IwJeRPuUbjTY4zB9SNLBGMUnghGTO3H4HToIBjPFcCDYOSDT8vzE0jaY+tMjL7xB8IansE6+MBygFoZyuA4oR9pzWv+FY+8LpX1QTBaeR/CJxOMPt3iKqRUMAYfNJaeholgVGOqkXcR+MA6aKAnLWd5TTA+My0jrBe28QOdtSU1npCo63S8b12rC4JxCB9AGKE1vKbu074uI/CPkVwiGDvyJHWZ2TF+AB5u8VQwFsCZIptgtDI+HHKC0adbXJdKsCrv/EYbTEPWIDkwgD3GRO/VBKMZqs37lTZhZqFNpe05FjLa7LbGuBzC0OO4JcHoEdxOPNt8YY2xh4K3CsYzwXeGdS4fItjwPcFozKcncV6iCcYYXAVjMxOMumjv8fA3VQveiWBshQ9FPwgVqlhQdmbHfFkfTz54/eP6dIs7wRij0wvGKNyPGA2nD9kY0BHjOccnnDWFHXJ1EsaIEcGoH7iNkNwOOjiYYiWC0crqqF1/EPMypBtI4QdhcDbQWKul7R0jRk+f0QGfdpxP6cpwJHSkI8Yb0TyMGGs6YnQbab4eP2L06UlczY5hwdvpMTI6yuhIFLxZA2z7dEbF4UfJyZcgGINzNSsLj4mzjq2CUS2dO/5CQ2Ll2wtGK+9DLxh9usVrrB1yYoz+G2mnF4xRODQmgjEON8Fo1tqvSS/B6GUGQjAvGA3uBaRfYzT4nQzvH8HIbikm+XFgFXvBrZvhOB5D/gi8l2DEKxybMQgEFrIZEXg8NmVjN7W0xxgEIyNGz6Mw6kaQzut6lo0YLQ87t7g2CIIRPh4Ou7mR91VFqCyHYGSTLIIfGtKpdARe2mNMhHepx3gn5W8c95JGjKVgDB84I6Vt7LbGP/iONcbYB4/rAtZaO9ynZj+BUsHbRnPBfaofMaoflpSn3Y4E4j41uDYYYt07mUqbgA4jRmYcV9XzJWvSBrPQpu2M7lljBJ/BfLgcRwLZYFP7AWnbstFrqeAdl10dqX5o2wG4xQcEI+o6M+1Mj7EPPUYdrTHyYEqBviCd4mZw4qT6VEmawdRH8zXdeRvZgfpFsBeXlk3g6DEOd+gxOjzooen0LKhG6NTD4Wf9jCnSykdel+p69O9udtLH1Ie1SVQbpi5K0GvM8Kc0TeJX+oIMqrrPQnhtF2pHJ9VhlKc/jbMmpEYmgj5gmm60NuZlxWNjUkt8V+fhNdU7O1fIhyr6nujNjZ3RtdPhhnsHqocIH3CGBdw2NkI72LBgE0GXFLCkg1GOjnZ+osYVRpo3ZeXDr+vIu8LHaLT7cHIu+J6Zph9kfLL4cD3o1wV/3wvhuramTsPi5XXEqDqrqLnE+ssN6X/5LVXXGdFpKBbbs3rgI6o0qDYhPHxfRV8T4TWCTu0YSxY4j+psJ8/0qRprkLj+dXyiHmC6Zjt+TiroMqo+p6sfvVtUinTz5bD6lTbe+DCbSnfWn+apX0n0GINOKrxIYfq+6W+o66Cn2Mmn8Bz6wvCuyynN/a2b8lD7qEw3Wrr5ktdj9OICmcI0mds2VvJwy4MxCeKxy2RTDHYraUueShsByxFmmy8IRqfHqB8YHxkb/Ru0dwAAIABJREFUIrywqzKsCtphDdHSfKgGNdFjRKm2dTW9Lc9qOh76eSyW69oYGwcBdwjpaPNBrQFrKgojLeShc9MRv/To6zK48YhUZugkAYd2au24l1R9pdqko2f4PT26BoqXwAK4LsSPnlBdP6vbh+jDVbcfF/TLfLrFq81L8qXHR4Mjpo72hXbAB9ONi/FhNT8lFKvZsWWqrPpvnk/E59W96xA7zL4OFL6n2XG9pB9bng9hA4F1R9YYX5XahiMqZDtwJPiwksRISUcsvo4kjtUe1EMYxcXKj+A/Gz6xqxopX2tfkQEs1zSCULJ3ZHkZsQ289Ib0PzMjQ+i70i4VRkl901dkcOKMDOB5ErgqeQcYuFh3ZJNN1bim0XDopFN527qqOLDmVG17OoMOLXmCl8BzMgy+pB0cRqiy5t68If1rJ2Rww+EOuOUjrDYuSWUHCt5ZeR9HB1PdDk/Np9+M0p/kX43XSP3Zzy2AV6GpPS+VHSipM+oNdFeaGKp9X9qNlqrp4Ayrl6Fa1hlRBSySKwZHyBXlsfRbEYT5MksSjFQM8RCZ1yO6leff/OZX6ld690xbvB4ju2jZfUbX/Qb5a44ekxq6hqhI5O4hphyokKjOGT56O/PoM7pj6FyNg4ObekK+4VGEwRmdpg6rD2nScSMa4OCvjZ+X/odflcGXD0hl/IIqgwPnBERt/JxOi1ARAffw6ML6VVdN6cMHcAEc1YrRYzLo6jYaCBFqAZ7R7uFsivQ//LrUXoeOzjpCefQtT0ht/GSUD9XRs4k/6GMyhI4bprVQx0hw1cZQ/j4jq7ed1PZ6HjGKZJrOhsIw+qDwoaOdZ2V4nLrPyKpHt8jAy/ulMpbx2OrQEDuLCL4ufMDnsgqeSDvBAZ/0dEoUflZG0Osr6i/j56Xv+Vk1g6e8YufV4cElKQJlWP058y5C/wltOCs6hR6lH5wMiurjYUMrwE8rb4dQP0NVhhlCBx8SvtNHsceo7yp7B/Rb3bQZOy3oMfa/fKCDtlBHyK/vAv1f1H4c/RaHP8PA6d/q29rXc0YqE8DpK4lurnuf8GOIXXX6U9Kv6TMD4xfk2/V3VF0HPcYPP/xQ3njjjUL9588//1x+/etfL9BhRKaYXmMvPUYbTSKjluNasmBkuGt20241NMOSv/vd59JuzcjsdDsZMW4QFLyHdlxI7+EdF4S7suOCOuXBt7Sl+XBQdwBP6ofs0y1emeSDxgn6qRQ39RicHVD8KdMJhnecDR+4g6N/WNlxXlZ9f6tUXj4oAw42NHEhqOBwCoJTKdgS3DGX4rY6NESxGAE3mdXt4XTgoe0fd4Gfl+r2j6U6eS6Kn7/3wKPbwnTc0Wh1VHeeCwKngA9M8/Xnw06kvofzHfVUOc44eU6VfofU57GDT1wQjjwOT5xVwcmOas3RMKQ8Oa14VyAYf3ZQd56Nto73rj+tU1LhnTgcFkfDACdN0GNpPtSRFnxi1Bkprzveo8dUnzMGH9h5Qfpf3C39P2yqbUtGfz5fjf6EYEx+HJ3tvCAVZi6cekH4Tp6TEUeDtnMy9A9+pJzoyvcH3Xiiz2MgFsGYbyc6npPnpf/xMel/+e0F5Y1WXT5C+Bb0R11v3v5xIR8GaScHEvhhuzYQD8db2Xk/pT8we3/9kxflO/V3pd1oqIL3sWPHZP/+/amhWpMbJgcQgAhHezY4oaWh3M2ADEVuD7e4jTaXQyiCY0mC0SpFKiMgb/W2IS9rjHt2v+EUvDfKKj0SmA37h5iicqu6DVPp8+HZ0i1k2qFnOi9E4Uy1a0wRddMhwY+aRVJe197a8zq1YToapglJ3TpNuqJTiX//6GthKt3Gd3BSninLzDWpti4LFq3VcClrSkabCzEcWsXfsEvz+TjCxUmC1WyuRPIwNeSED0ZkY/Bq+7KseHxMKlPFfNBRFMLbplfWjvY11c3kQ64wmkmmh76eME0M01D0PplipnCWK3husU56SqrsQDM1T9pRa1+X4fZlxfvlR8OudCfcvXdV1zkXjmYW8AGBMRyBUR8GewcR7qyDRvLQ9sHxEzrVjME5U96Pus6zszpdrPp2gn/6qk4h+5lGMg12cOXr9DWpTs2F2cQ0U0zPh6ui+FgjnDgdDCPnaFQcnMeeOC3VHWdlNWuxaR42R27q3b9uUgZeOaym0TK4qwtjt0z3tb9m6ZbXlmbU8G+K3+Vrzusa49DUnKvfwfEJw3eFelTSn6qN6/JQ6z1pNprpVPrQoUPpFNjkRiYHsiOByBiD+5A1SBN+Pt3iJpuWK+wqGG1Yag3w4e0QYHjCrvQemdWz0lv0SGAwIsFCcbhNmdRvvliaD3XdhWNTO+eiirDqGJxNBVRADLdTXB5JNl84PaObKLoBlCnV6gJ845qseDhsvtRaN1MFbxbSUyMSTDGnOA9coHjMpgijhUamLOzbMcTmS7Jp4NMtzm40cIxIWJoPEQSrHh0r5AMfqC5LuE0o6Dcc/IAYnVQ4n6t8YjMlg2s82XwJ58k7YemJjm3hvLduWiXKx2yUrNZ1y+tBj3Hje1JBWJpycvJeeD+MoIIeY5xPGD9gRAa9aXkXV18k7LZywsSlp3FOn2A9u0DB24xI9D09m6xzhs03K09/CGu1yeaLr4NNC/oTp0FsV9rxUPufqi6h9hTOGY9omawtbA7Ba0Z0zFSGUTD3dahi/TXpw1Dt+iM5WIZneIq1WHRS8+WTPI1r2p/UqncH/gBH2KkV8qiCN5tE8PGc4A899I3rUml9It9pv98hGP1ZaZMdmRzIBCNp/rI8vfQYLV9R6HEuJh4VjIbcpDHPzPUZ1pLG83JcpbpOphbBB653DwVv3Tkv1XUSDQKOBMbVWFIFb0axxlsflnqM4afSuKZr8/e7ug4yCdmEnLI4od1LlVddBSNIP/vsM/nlL38pH3zwgc7xb7WiGGGlYCwFY5FgKxW8w0i51GMMu9A2YozJEdJswHbu3Dk5cuSIXLlyRdcib1Ve/TsraIh5ZoFzbm5OWBfAmc3s7KzcvHkzlb5W5nbDP/7hD4q/1ZyRP1+3Sfoe2igrnmqG40v5A+2oSqB2UGSAQYf82GOMG09Q9QkUZVFuzuNmOtC6puah1HgC+ow6lUYHLty6fsI09WGOBB6SWvMTdeSUwnXqE1QbWN/SNcRIPWaPkSmnle0ImX5tT9YYI+U5Ejj0+nE1TNBRLsnLlL7/se1SnWLJIKM/jbeZgp7VDZI0zdESFLwTs2PwwMHIj57iajUiwfSMNcHOOqifKTYqHnk+6NQw4fOKh1+TgY3vyVDzkzidTKWxGZnDbzRXVWf0ZCF8aOqi7owXG5G4EqbinKmO8Kna+kwqL+2TVc/OyIiqx3S2U1V3dMf8rK5z2sko4xH9B5eiymsdtaIfmOBI2oRKEFZ6MNnFUlAK174Unpmu67FA1oGtvAtXPTEp/evflaHmp1E49hiH2TnO4U9xwUc2DDHj5vBaXFW62DXfObcArjj1u0MXM/CRJau+9nX5TuuotJv1dI2xm7oOQg8jEV4G5WWLCcZ8ev6ZfAcOHJCZmRkNccSF9R5bn/T5i4Qs6algpCBb5thOe+utt6TdbguuD5vNpuogMUSl0uW8P//N5zKze1Z3pv/LD7fKyCNbZPUzTflq8+KCe03rojw4eVwe3HVuAUzzN+bkgYmTsmbyVBT+YGtOHpg8KQ/uOBmFg/9rjfPywMQJWdO4IA8254Q0o2VN86J8pXleqj8Ylwc2HZI/bV/WPMCBPQjNjQvywPhxWTN1Vta0s7KGg/DBnaflwV1ntIxPt/iaqXPywOiHsqY+l9ZtMA3rc/KV0Y/kwfr5KPzPWCR/YkK+uvNMFL6mNSdf2XFS1hTw4cHWRfnK5Cl5YOK4fNXab6G29bJ8LeH1VxtzKQ+UttYlWdO8JGvgY4QPX6Pu1iX5s8Z5GVo7Kn+66V15sH0hSueDu07LAztPyVdbl+Lw5pw8MP5xIR8fnDonXxn7SNY04nzk/X5F33W8Pz0wfUkeeHmvrP7xjHyteUHW0DZHi/bHHSflK5P0J/jg3jf8al2UNTtPy5/uOKHwNa3LHe14sHFB1tAGaJg6Kw/m+4vyPLyrB6inFW/H//jkDvmTTW8L/bujnyT00E8enDjeQbvPB5z+tKYefw9rmhfkK2N8d6cX4IcH2p+0DQkfWxflf2pekkeaR6VVD9Z1zB4jsgMBaDKEODc70ggveza45bc8yCDiHp6PA2dQh5oQsgs5hk3In//853Lt2rWO5UCEZNH170B8+fJlnSozMkQYNhqN9AY5lQBb7nvPzB7Z1WrIdGNKmvUZaTbr0mo0pdlsL7inWjPSatSl2aDBC+Htxow0Gy1pNOPlG41paQAvwN9qtKXRakpd62hLXXG5ehozMtVsyuxUS5r1hjT0pxHgjSZloQ/8dWk0G1o+Rme92VAaqS8GbzSnpd2oS701G4WHdtaF9kTLg7exqxDeSvjUbPLTW0hDvdFQX9/1etY2n4/yjWZL6s2m6qA2WhkO5UNzWlrNOB/gC/2p2ZyWemtKmo1ZqTcL2tGChw1pRWgM9MyI8rKADy3ed7Mh2t4IDvpTu17cX+qNWWm04EVL21OnnlYnrbxrTGtBD+/f8ymkAQtw307lk/aVttIIT0jrKN8Cxm39eSF+8rfq9LcZaUJrHgflG63A6wI+8y6wgtOqd7bNcMG/6UZb6q6/GyzQBw9Dn9Y2QLe+k7o0WnV938gPZIrNPvNyBDhyh1Eet4fbswk5DyuKW302sKMsce63335bOImD+k9XwUgGDEkySqRgXiiShtQtIuJ2040Z4YMJDYjhJF835gCH9iJarTztKcJvDCUvL5HQ8gKzOizu4eTjGRqBW7l82IuflK3X6x11exzUAbxXHXnaDAfp8KmID+Szd0Gc/B6XPfei0d6VL2v4CHvxgffInS9PWcNDO4rgi+Fjt/LUAQ7jk7Xb6jcY7czTYHmhPwY3HITQAK48DstDeWgogvfiUy8awNurPwEHj9HkQ8p3e5e0jbLWhnw7ePY05uFWF3zoxifLR0g+8tsNj7mhge/6/ffflxs3bhQNFjU9nUqjZHnp0iVduDRCQQZyhqFont+JmyE0U/iDBw8q4WzrF9XDRhB3Efwf/uEfusJZJyVPrDx0/OpXv5JPPvlE6Ynlgc59+/apA/EiOOWxRhyDkwbs008/LYRDHzd1xXBAI3DCGBz8rLF0qwMeFvGBeo2GGH5LA38RjaTT8Yr4ABw+ovhbhAMai8pDA+3nfRo9+ZA2dOsr5KcNRXwEDn2HDx8urAP83EVtAH8Rn41e2tCtneAHB/3TyviQd338+PEojHzg7kYDtFNHEQ3AgZHH1+vjRqNP83H4yPft04hbmyjfDT95u/W3PF7kGALWhCECkYEfU3ra49cyi6RjKhhtURJNcoiE2ZgjR0giZUmzPHciZHGWBrCjVIQfzXem/jE4jWXTqAhOGUbH3gR6Hg/rrPwgPON8HtJ5wRcuXIjSQHlTa/LlfJw8rIP4NB+HPtpZRAPlgRP6chYnnZ9LtzrsBIGVyYe9+Aht4O9Go51kyOPmmXJMadhBLMLBe0Q9LFaeNNppqhmxPL34SBnaQH+PlYcu6Dt69GgUThn4yB0rTxpt6AYnD/2tW58ERzc43w10FtEAD7uVh4+9eE158hTV0as/nT17Vjdyu73rbv3JeFnU5z1dvE9+Zia33nvvPbl48WLKAwShz18oGGMAClrHo1F8aL/4xS86PsZYuVtJMyLzgjGGixfAC4pd4OEFkid2AedjtU6Sz2NtpqMaTfk8vFgvGD3cl7cP2sMtbh3RnvMh9HFTV+yiPHA6QOwCDi/paLELOn1HzucBDv3+Q/B5gEOb78h5ODR4wejhxCmPYDx//rzyOg/n2X+sMTh18KMrumgD7SziI+0wwViEA/pMMObzGB+pgzh3/gJGHXm4PRPajzRflmfglO/Wn3jXfKNFF32F8kUXfITOov4EDeDo9t1Rnjxc5LeLODeC2598Mbjlp2yMT5YPHNRfRCP5eM/cqOnwjbI8yCiT9hX1AcMfC3vqMUIUyBnyQ9ytVBKr2NKMeaVgDByhk3AX8Zl3AbyokwAvBaOoMOCDLeIj/a4UjKLf9r8Wwcg3gTCMzfpM3iw2LBSMhsAEVz40eK+Qclz58vnnvGA0uMfPC+z15+oG9yPGPH6eESp+xEiaXcT5yPgbxUY6vny3Pzx12N/RcPvwVgQjddsNfkb48MFoJrSLuP3hrUweDv1W3sPAwTN8oA2ERfDYiJG83NDIiJGRDnG7DE5I/fCCeOyiXLcRI2VNMHq8hou0boKRtvGeWV8nL8/+Ig383Ibf4PYMLMZHgxPS3/L9xcOhsRuc7yY2lTZarD+BM3bBR+gs+tFSDhy0I3YBp7y9K18PcW7eM3Tas8dDGmXtm/B8tvyE1A+NxGOXz2t58mGsXFFaVDAWZV5quhFLg3h57AaxMGofFHCLwzjWBVhjtDRrGPUSt44Wo2Mx8MUKxlj9pNFBJycn1VKI5TFaqJ9OFuvIlofQ8vi2ebh1ZPLFLnhJHt+RwcVN3XzI27dvlzNnzmhdMTrzHdnTQpx2Wkf1MOjh2dqQx+3hMcEIHNyYodq2bZsuiIMLnPmb+u1ji/GBcgjGPH2Wl7K0M4/f4JSjDs9HgxEC54PesWOHLtrn2woc/NzEue2yZz7mXoKRqXS+nVaeEBpjghF62NQYHR3VXVjiVs7oIAR3Hr+Hwx/a0I0PwGOC0eoDZnWQ5i/oxB7j2NiYblrm4TyDn3aSl9suw09IHdCYL295lzu8JcFoDVhMCONZX/jmN78pzz77rIYoYJJOeUJuRhDsgLNw6mG+DpjjGehhxHvB2QXjJcTww3AYT0c1mjx+dpuffvpp+cu//Et57LHHUhw+D+UZAdBJfLqPWx6f5uO0wTqqT7c4HwlwQkuzcGJiQvn7N3/zN/J3f/d3+iOKtcXqiPEBXNBPO2JlgZNucKvbh7QRXuf5QDkE9re+9S2l76/+6q/0ndsHYLgNP+30eH2cOhC+Ps3HKUs7yWftIPR5bLTm0yxOXn4wf/EXfyHPP/98isPDwc9tafmQvtqtv5LfBKMv6+mM9Sdrz49+9CPtj7zvZ555RunwZcEJH3rxkTbk35Wnh/Ld2gHM+ODrJ85G5cMPPyxf//rXdVDh8VqcsrST53x5y0MdsT5v8HsmGK3zQrgxCmK73TQW+KOPPipbt25V1Yh169bJxo0bNR245WGKyvY6QtTSDWZ1sNVOR7JnH5IOnI/Fp1scXKYiEMNvaahvWJzQypPOefGHHnpIHnnkkZR+4Pl8jGSsXD4EhtDIp9sz7TAaLM2H1AU8XwfptA/VCrQIEDqvvPJK+rMwHOCnfm7K2G1wnuEhuIiTbiFxyvMMDcStnOUDxg0dwH0e0q39aCDwQT/33HNKo+G18tDQjU/k68Yn6ukGh17amKfP2shRMn4u3//+91Xo8PHm2wp9xifoMThx8EIDfdLaZHBCSzM+ejrycHjh4VbX448/ru+YmRh1GU5fD+nQ6NN8HLzQQD6fbvFucOoDDh+g0eonjTj1wr8nn3xSf4DsU5BuuC0/ZYveleWJ8dnwECLYTUYth5Bc8ojRKl9K+MQTT+ixHKT7li1b5NVXX00bQRq4itYYrR7y2d/P0nwI3EZTPt3HYbJnoIcRR+jDZHAZXZaHZ+AI9rVr16b0G9zKUwd0+HQfZwTDR+bTfBz6uKnLp1vcfkzgsTQfko6S61//9V/reqiHWRw+duNDNz4ab2hnNxr50GJ8oDyjRn4w3BzTMrp82ItG6uYDzL8nw0H7wFEEJx/wWBto2wsvvCCbNm3Sj5q4tdvw80z5bnXwnoFbGR8aXb36Czhoi+U3HAijp556Sn8uf/u3fyvohebzkJd30O1dW3+KvSvKg7NbfyAP+H0dRsff//3f60iR74WfzHe/+90F75u8lKWdVs7a6EP4WNTnfT7iy3EtSTB6AhZTueVHmDCK4SVs3rxZhaMxwUI2DLweYx4/uIyBeRjPi4HzsdoLzOOgPIynoxpNPg9w0vlL/+AHP0g7u+UBRvsoX1QHea0O8MUuynKDL3ZR3jqJwcFlN39W+M20H8Fh6T6vfWwxGkijfvLky4KDNGizH0geh/GBUYB9bL5u8jOK2rlzp077mT3kcZDfjwKsvA/hNXXEypKPNpjQ8uUsTjnqgJ92kcbNOi1TPwQPQodlIEzz+7poJ/i5rZzhISQN/EaDL2v5CXlHeT5ZeeCxd0U6eHnXKDIjeL7xjW/I9evXF9Bi/YkyscsEo+eDz0c56w8+3eJGC3mI+xvByLIJs0DWQlmWYK3RX1a+qD8ZPvgAjTzHLssXg91K2pIE41IrMGJZC+HvywfBS2RBm45lcML8iDFWF50BBsUucNjHUATnQ7IXmM9DeRNsRpfPY/AiwWhwPwLw5S1OHUVtIA/0ccOf2EV54L4jG72oKiAQ+ZDplPPz8ymfDRd54WM3PvChQqPhtbKEpEFbt44MjTHBSHmmTHzAjHBYkqBvxC7qjwkMy0sd/OiKLsqaUIrloR15wWh90jZd1q9fr7z83ve+p2vflLGLOPi5iXuY5QFGHXm4PROaYLQyPgRO+Rgf4C+HLliCYs37O9/5jj7n+w3vmfJFF3yETt+ffF5oAEdRnwVOefJw8Ww3itXf/va3dW1xfHxc10PffPNNj17zUjbGJ8sIPuovotHyLWd4RwUjhNIoDm2zzsiUmr+wnaKxjkie+0Uwsl5CG4x2exm0gU52rwQjdfNXZnrK2h0fM5sGMTqtI0Nz/iKND+lOCEZwc5rKRjh8zChQx657IRihD34Zz9g44EezYcOG9GM3WskLH7mJc+cvYLEP3vIT3opgpByKzPARHnIzyjW6PR33QjBSPzRCD30S4ciIFl7yY/QX+f7NCUYabTeN90KDdGMg8ftBMPKiceqDflu+E9KGeykYqZ8/KgKFHX4/OjZeG7/vpWA0Gjm7ylqjp81/MPdKMEKP3aiYcaSMHwXv21/kuRuCMcYH6oYevinOSjPw4LJ0T+e9EoxGD98E6jrQybuHRn/x/G9OMHoGFMVhDPf9IhiZuthZad8m2nCvBKOnAxpMwdunWxw6ewlGE172bqwsIWl8lIyE8j8Hg0MDghk8sYtyCG9TTI7liQkEn486lnsq7fET9wretNtfxkd4GeMTeYHd7oixFx/4brrx8V4LRngDfdCZ5yE8Iq0UjL5nJXHrVPejYPQvmngpGENHX4xgRHjHThBZF+klEErBGDjFd9ONj6VgtB61tHBJa4x8/EwrGAnYNOJ2Q/6ovDyG2ih486KLcLILxyihG5yRSgxOHZTn5qPjzueDFjaI8un2TBlUYVicB5+lW0h51lBYN4rByQf93dpAWXAYznxodRDmYTxDIzuoqHPE4KSZ/l2MB8ChDz4UwckDjXk4z9wsmQAnzPPByqClwFQ6BicPNNhyQKwd5IHGfHnLS93oUlp9lm4h6fSFIj6CF0MEnMSyMvmQ8vCyqA7aQJ58Of9cxCfLQ/lufGATi6m05c+H8KFbX4B2oyFflmfg8Llbn4U+4OSN8QKdUPpkkdywPl9UHjrgQww3MN4VcskPVJYmBhfmXrJgZBrETSOX4zZB60++kGa31cEzDORFW1o+BFYEpzwdBDjxfFmeYTAvOF+35SWdXTX+0DEcVp6PLQYHDy/S6jC8PuTl086i8tQBHDy+nMWBsw5KHkvzIXiNj7E6SIN+o4HnfD6e7WP1uC0ODSYw8mXJQxofNFMsK5MPeU+9+Egd+XL2bHyEFkvzITTQRvL5dIsDZ22MNUZL8yFwaCziM3kNTl7ufHnS4CPvMgYnP/i78YHvhh91vrzVRfsob8/5kLqpo6g/kZ92cOfL8ky94I/VAYwbwc0SlOX3eKw830TsXQEnPzQCz+cBzuyBG8G4XMJxyYJxOStHThu+/FTa0k2W88xL5o5dwHm53eD2MZM3f5EGc+kAxGN5+CH4NUafx5fnZXmYr4uXTCcqgvPiaQe0xC7SrXMUweFlNz4AA0eMBtKgnzzE7ba6eIYPtIGQZ3/xDI3wuogPlFvMGmMRjdQHH/mY8vUbLcZH6opdlLOPuQjOD/BWzY6BHx7G+ATMbvpbEZ8MRzc+8K57rTFSvujiXZlQjOWBhl7fFXCrg/x2WRv9GqOHk8/wx/jk8cBL3nm+vOWxsBfc8vUKlyQYeyG7FTgN4c4LxhiuXi/IPoZYWepYbsHo6wE/naxbRyc/eXjJRRdt4C76oCkPnE4Su4DDSzpa7IJO68jE8xdpecHo8wCHtqKODBwaFiMYu62NwaMigQE91IFgLLooSzuL+AidtKGIj+C9HcFIeeqnDuritsueCRkJQWvsAk75bnzgXTNiLLroK0X4KQMfobOID9AAjqI+C9z6E/h4tos4N4LxTttjtDqXKywFY8JJXiCdZCkjRv8SfPluHZk6ijoZ+OiE3EUfNOWBF3Vk4KVgLO0xWt+kr5SC0bix+PC+EYwIHv5MRUIFOJ2APLELeDlizKYu8Aqe5C/SELrwmXg+D8+LHTEWCW/KM5W+H0aMZo8xxif6GneeT/Zs/dWeDYc9E5YjxlJdx/pFR2idpNdUmnzW0ToQJA/AS8EYpka3O2IsBWPoVAjuUjCWU+mYvOlIMyG2XCEjB6Z+hN6IBM/5OmwK6tdsfB7KmOD06RanPCNG8sTwk8aUg6m00eTzESfdNl+IG25C4AgUyiOgfVmfjzpoQxEc+rjB5ctZnHTgNl23dAuBw0u/JGAwQuplNNiND9BPHvLabTh4pu20gbp49jCeSbfReQxufGTtycMNDyH0F9EInPazxlhUnrK0If+erA5rQxEfwQt9bL4Qt9vK8wx+q4NnD8vDDUZouAhtR9iX93ngc7f+xLtmjTFf3uqDD734SBuK+ACfjJeG04fGR6P3f1pfAAAHAUlEQVTR00GcG/r4WZPXw62d1E87i+CUAV5Eo9GDsCK+HNeSptJUSqeHQGP47YYwBaaiYmL2GItwostkHSmWB30sPpYYjDTUO0w4xvJACzgI83BLw2ct+nd5OM9W3j7qWB7o60YDZdG/i5W1OoDTUWJ5oAEdwW51oJdm6jQxHNAIH2Iwo6GITwaHxm58QB+0m/4dNEBjLxqK4PQT3Ibae4vlgw/daDT3qZSlj+Zx0B+5SY/VQxuoI1/OP/fiE/i78YHvBrUij9PH4QPlY/STD7rhUzc+AKctHq+Pg78b3DyOxmigfspaf4vxkbrgQxEMOHLJC8jbFY5LFoxIdQQjjVyOm0aBhzUnzI6xe+WZbnWQxsvjtrR8iLCgI+TT7ZkXmO8ABrM6TaCQbrRZnBeD/h1TrDzM8lDehJbh9mEvGqGPPNTly1mcdNpYBKcsHwt0WJl8SHnPhzzcaLQ2Wmj5ePZ8snQLoQ1egydfljykwUdGElbG0oFxG40e7uPgpo4YfvLRPnAUwUnngwSPx+vjCG70GC0tj8vqMLiF5DP80NDte7H+YmUttLoon+ej4SdkBmOK8lbWh9afDJ+HEQc3ebjzMJ4pV9RODyeP0eXx0BcQ3PRJG1B5OGWggXfh0y1udMOHoj5PXuTSPRWMVvlyh36NMT/ctrpgEsyx53wIg8iTT7dnY74950P+OrzgfLo9w3ybSluaD4FTng7g032cOnq1If+i8+WB+z+kh0ODrTH6dB+3DubTfBz6i2jk3djUpug9QQO8Bk8sD2lej9HXbXETWPacD2k/deTT7dn6Qqx+y0MdRXwkj19jtDI+pK9162/wsIiPhof+Aq32nA97vSveNVP+fDl7Bnc3/LSfNhTxAf5Rvls7KN+tDn6AXl3HaLOQ8rwL6ip6X9RfRKPhsfB2R4uUX9KIcTkqzOOwxnjBSFrsgoEwKHZRhpdDntgF3AvGfB7gJtiIc+cvXpoXjB7uy5tg9HCLU0dRG8hDG7ipK3ZRHjidJHYBN8EYg0On78j5PMDzgtHnAQ5t1pF59hfP0MBIqIgPlP8i7EojlIr4SJsQjKbgHWsnfOQG5uH2DMwLFOOTwQltRGkwHwKnfBEfycu7RvAUXfQVyhddvCvoLOIDNICjqM8Cpzx5uHi2izh3qcdoHFlCaMwrBWNgGh2MuxSM3QUCHzQ/uqILYcAHW8RH+l0pGEsF76L+c09GjHRKOiy3CUa/K21wgxFyITCK/mzA+RD4YIouPpaiv6fVWSSUjF6sT/OXN9qoy+gjj32MlpanBfq5i+CGoxecfLGL9Bs3bhTyCby9+AB93fhkOKjL00mc29rQDQ4fGVX68r49i+ET76qovI2EiuCkF71ro4MFfzYeyJvHwzM0Gg0ebvFe8CI+Wf2E9q4Mp4cRx8EUfARX7CIdHEXlSbc+GysPvBufgIO/qH7gbEBBJ3FuuyzOu4rx0fIRWh1WxsPuRPyeCEaYyG0vlMZ6wQiMNBbXTdDxvBimFOWx8kVwmGt58nH/bHmK8CwWXvQyDa+FsXy9YMa/orJG463CKRejwadZHd3SLE83OmKwovqL8sbSu9Vt+C2PhR6PpRHGLg+3uOWz53xocB/6PD7d4ga353x4p+HUV1SHpefDIhrJV3QZjiL4cqffE8FII/l4T548qc7XmdL4qTRTpI8++kjY5jeGGNMszDPC8uXT88+9yhuefD6fbvEYboPly1ve5YIbvny4GPyUKaIvjy//bOWsHg/3aRa3/OQzge1hHh7DdatwcBWVtXq6wYHlbytnuA3u0/Mwy0MYu5YLHsPtaekF70VfrLynvVd5nzeGy9IWg8fy3snwnglGGIAOF/ps2GrD2xn2GPfs2aPP+AYBXl4lB0oOlBy42xy4p4KRafLhw4dVfxHlbgSj3RgIZYRRXiUHSg6UHLjbHLingpFRI97O2u22nnox4cjpksuXL/ecCt1tZpX1lRwoOfBvgwP3RDB61qIPx1TaRooIR3QFSS9ab/Dly3jJgZIDJQeWmwP3VDAi+LjxCWGCkdEjZ1RtoX65G1ziKzlQcqDkQC8O3FPBCHEIRg6QswnDaJHNlyLdsV6NKeElB0oOlBxYDg7cU8FoI0ZGh2y2YETCH8ECXl4lB0oOlBy42xz4QghGBODVq1d11Hjp0iUdRZrQvNsMKesrOVByoOTAPRWMnv0cSzITTz69jJccKDlQcuBuc+ALIxgZIZrFlrvNhLK+kgMlB0oOeA58YQQjRJXTZ/9qynjJgZID94oDXyjBeK+YUNZbcqDkQMkBz4FSMHpulPGSAyUHSg58ESx4l2+h5EDJgZIDXzQOlCPGL9obKekpOVBy4J5zoBSM9/wVlASUHCg58EXjQCkYv2hvpKSn5EDJgXvOgf8fkR46SEnWSrYAAAAASUVORK5CYII="></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>At an amusement park, a Ferris wheel with diameter 111 metres rotates at a constant speed. The bottom of the wheel is <em>k</em> metres above the ground. A seat starts at the bottom of the wheel.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>The wheel completes one revolution in 16 minutes.</p>
</div>
<div class="specification">
<p>After <em>t</em> minutes, the height of the seat above ground is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h\left( t \right) = 61.5 + a\,{\text{cos}}\left( {\frac{\pi }{8}t} \right)">
<mi>h</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>61.5</mn>
<mo>+</mo>
<mi>a</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>cos</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mi>π<!-- π --></mi>
<mn>8</mn>
</mfrac>
<mi>t</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, for 0 ≤ <em>t</em> ≤ 32.</p>
</div>
<div class="question">
<p>Find when the seat is 30 m above the ground for the third time.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>valid approach <em><strong>(M1)</strong></em><br><em>eg</em> sketch of <em>h</em> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 30,\,\,h = 30,\,\,61.5 - 55.5\,{\text{cos}}\left( {\frac{\pi }{8}t} \right) = 30,\,\,t = 2.46307,\,\,t = 13.5369"> <mi>y</mi> <mo>=</mo> <mn>30</mn> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mi>h</mi> <mo>=</mo> <mn>30</mn> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>61.5</mn> <mo>−</mo> <mn>55.5</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mfrac> <mi>π</mi> <mn>8</mn> </mfrac> <mi>t</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>30</mn> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mi>t</mi> <mo>=</mo> <mn>2.46307</mn> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mi>t</mi> <mo>=</mo> <mn>13.5369</mn> </math></span></p>
<p>18.4630</p>
<p><em>t</em> = 18.5 (minutes) <em><strong>A1 N3</strong></em></p>
<p><strong><em>[3 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>A new concert hall was built with <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn></math> seats in the first row. Each subsequent row of the hall has two more seats than the previous row. The hall has a total of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math> rows.</p>
</div>
<div class="specification">
<p>Find:</p>
</div>
<div class="specification">
<p>The concert hall opened in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2019</mn></math>. The average number of visitors per concert during that year was <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>584</mn></math>. In <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2020</mn></math>, the average number of visitors per concert increased by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>2</mn><mo>%</mo></math>.</p>
</div>
<div class="specification">
<p>The concert organizers use this data to model future numbers of visitors. It is assumed that the average number of visitors per concert will continue to increase each year by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>2</mn><mo>%</mo></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the number of seats in the last row.</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>the total number of seats in the concert hall.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the average number of visitors per concert in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2020</mn></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>Determine the first year in which this model predicts the average number of visitors per concert will exceed the total seating capacity of the concert hall.</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>It is assumed that the concert hall will host <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math> concerts each year.</p>
<p>Use the average number of visitors per concert per year to predict the <strong>total</strong> number of people expected to attend the concert hall from when it opens until the end of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2025</mn></math>.</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>recognition of arithmetic sequence with common difference <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> <em><strong>(M1)</strong></em> </p>
<p>use of arithmetic sequence formula <em><strong>(M1)</strong></em> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn><mo>+</mo><mn>2</mn><mfenced><mrow><mn>20</mn><mo>-</mo><mn>1</mn></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>52</mn></math> <strong><em>A1</em></strong></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>use of arithmetic series formula <em><strong>(M1)</strong></em> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>14</mn><mo>+</mo><mn>52</mn></mrow><mn>2</mn></mfrac><mo>×</mo><mn>20</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>660</mn></math> <strong><em>A1</em></strong></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>584</mn><mo>+</mo><mfenced><mrow><mn>584</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>012</mn></mrow></mfenced></math> <strong>OR </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>584</mn><mo>×</mo><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>012</mn></mrow></mfenced><mn>1</mn></msup></math> <em><strong>(M1)</strong></em> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>591</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>591</mn><mo>.</mo><mn>008</mn></mrow></mfenced></math> <strong><em>A1</em></strong></p>
<p><br><strong>Note:</strong> Award <em><strong>M0A0</strong></em> if incorrect <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> used in part (b), and <em><strong>FT</strong></em> with their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> in parts (c) and (d).<br><br></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>recognition of geometric sequence <em><strong>(M1)</strong></em> </p>
<p>equating their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math>th geometric sequence term to their <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>660</mn></math> <em><strong>(M1)</strong></em> </p>
<p><br><strong>Note:</strong> Accept inequality.<br><br><strong><br>METHOD 1<br></strong></p>
<p><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>600</mn><mo>=</mo><mn>584</mn><mo>×</mo><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>012</mn></mrow></mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></msup></math> <strong><em>A1</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn><mo>=</mo></mrow></mfenced><mo> </mo><mn>10</mn><mo>.</mo><mn>3</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>10</mn><mo>.</mo><mn>2559</mn><mo>…</mo></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>11</mn><mo>.</mo><mn>3</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>11</mn><mo>.</mo><mn>2559</mn><mo>…</mo></mrow></mfenced></math> <strong><em>A1</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2030</mn></math> <strong><em>A1</em></strong></p>
<p><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>600</mn><mo>=</mo><mn>584</mn><mo>×</mo><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>012</mn></mrow></mfenced><mi>x</mi></msup></math> <strong><em>A1</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>10</mn><mo>.</mo><mn>3</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>10</mn><mo>.</mo><mn>2559</mn><mo>…</mo></mrow></mfenced></math> <strong><em>A1</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2030</mn></math> <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>11<sup>th</sup> term <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>658</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>657</mn><mo>.</mo><mn>987</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(M1)A1</strong></em> </p>
<p>12<sup>th</sup> term <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>666</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>666</mn><mo>.</mo><mn>883</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(M1)A1</strong></em> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2030</mn></math> <strong><em>A1</em></strong></p>
<p><br><strong>Note:</strong> The last mark can be awarded if both their 11<sup>th</sup> and 12<sup>th</sup> correct terms are seen.<br><br></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><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math> seen <em><strong>(A1)</strong></em> </p>
<p><br><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>584</mn><mfenced><mfrac><mrow><mn>1</mn><mo>.</mo><msup><mn>012</mn><mn>7</mn></msup><mo>-</mo><mn>1</mn></mrow><mrow><mn>1</mn><mo>.</mo><mn>012</mn><mo>-</mo><mn>1</mn></mrow></mfrac></mfenced></math> <em><strong>(M1)</strong></em> </p>
<p>multiplying their sum by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math> <em><strong>(M1)</strong></em> </p>
<p><br><strong>OR</strong></p>
<p>sum of the number of visitors for their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> and their seven years <em><strong>(M1)</strong></em> </p>
<p>multiplying their sum by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math> <em><strong>(M1)</strong></em> </p>
<p><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>29</mn><mo> </mo><mn>200</mn><mfenced><mfrac><mrow><mn>1</mn><mo>.</mo><msup><mn>012</mn><mn>7</mn></msup><mo>-</mo><mn>1</mn></mrow><mrow><mn>1</mn><mo>.</mo><mn>012</mn><mo>-</mo><mn>1</mn></mrow></mfrac></mfenced></math> <em><strong>(M1)</strong></em><em><strong>(M1)</strong></em> </p>
<p><br><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>212000</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>211907</mn><mo>.</mo><mn>3</mn><mo>…</mo></mrow></mfenced></math> <strong><em>A1</em></strong></p>
<p><br><strong>Note:</strong> Follow though from their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> from part (b).<br><br></p>
<p><em><strong>[4 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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows the graph of a function <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>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 6 \leqslant x \leqslant - 2">
<mo>−<!-- − --></mo>
<mn>6</mn>
<mo>⩽<!-- ⩽ --></mo>
<mi>x</mi>
<mo>⩽<!-- ⩽ --></mo>
<mo>−<!-- − --></mo>
<mn>2</mn>
</math></span>.</p>
<p>The points <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="( - 6,{\text{ }}6)">
<mo stretchy="false">(</mo>
<mo>−<!-- − --></mo>
<mn>6</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>6</mn>
<mo stretchy="false">)</mo>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="( - 2,{\text{ }}6)">
<mo stretchy="false">(</mo>
<mo>−<!-- − --></mo>
<mn>2</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>6</mn>
<mo stretchy="false">)</mo>
</math></span> lie on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>. There is a minimum point at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="( - 4,{\text{ }}0)">
<mo stretchy="false">(</mo>
<mo>−<!-- − --></mo>
<mn>4</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<p><img 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"></p>
</div>
<div class="question">
<p>Write down the range of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </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>correct interval <strong><em>A2</em></strong> <strong><em>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="0 \leqslant y \leqslant 6,{\text{ }}[0,{\text{ }}6]"> <mn>0</mn> <mo>⩽</mo> <mi>y</mi> <mo>⩽</mo> <mn>6</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>6</mn> <mo stretchy="false">]</mo> </math></span>, from 0 to 6</p>
<p><strong><em>[2 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>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 src="data:image/png;base64,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"></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>
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<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>
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<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
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<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
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<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
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<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
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<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
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<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
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<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
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