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<h2>SL Paper 2</h2><div class="specification">
<p>Let <em>f</em>(<em>x</em>) = ln <em>x</em> − 5<em>x</em> , for <em>x</em> > 0 .</p>
</div>
<div class="question">
<p>Solve<em> f '</em>(<em>x</em>)<em> = f "</em>(<em>x</em>).</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><strong>METHOD 1 (using GDC)</strong></p>
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg </em><img src="data:image/png;base64,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"></p>
<p>0.558257</p>
<p><em>x</em> = 0.558 <em><strong>A1 N2</strong></em></p>
<p><strong>Note:</strong> Do not award <em><strong>A1</strong></em> if additional answers given.</p>
<p> </p>
<p><strong>METHOD 2 (analytical)</strong></p>
<p>attempt to solve their equation <em>f '(x) = f "</em>(<em>x</em>) (do not accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{x} - 5 = - \frac{1}{{{x^2}}}">
<mfrac>
<mn>1</mn>
<mi>x</mi>
</mfrac>
<mo>−</mo>
<mn>5</mn>
<mo>=</mo>
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span>) <em><strong>(M1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="5{x^2} - x - 1 = 0,\,\,\frac{{1 \pm \sqrt {21} }}{{10}},\,\,\frac{1}{x} = \frac{{ - 1 \pm \sqrt {21} }}{2},\,\, - 0.358">
<mn>5</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mi>x</mi>
<mo>−</mo>
<mn>1</mn>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mrow>
<mn>1</mn>
<mo>±</mo>
<msqrt>
<mn>21</mn>
</msqrt>
</mrow>
<mrow>
<mn>10</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mn>1</mn>
<mi>x</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mo>−</mo>
<mn>1</mn>
<mo>±</mo>
<msqrt>
<mn>21</mn>
</msqrt>
</mrow>
<mn>2</mn>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mo>−</mo>
<mn>0.358</mn>
</math></span></p>
<p>0.558257</p>
<p><em>x</em> = 0.558 <em><strong>A1 N2</strong></em></p>
<p><strong>Note:</strong> Do not award <em><strong>A1</strong></em> if additional answers given.</p>
<p><em><strong>[2 marks]</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = - 0.5{x^4} + 3{x^2} + 2x">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mn>0.5</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mi>x</mi>
</math></span>. The following diagram shows part of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_06.09.00.png" alt="M17/5/MATME/SP2/ENG/TZ2/08"></p>
<p> </p>
<p>There are <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-intercepts at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0">
<mi>x</mi>
<mo>=</mo>
<mn>0</mn>
</math></span> and at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = p">
<mi>x</mi>
<mo>=</mo>
<mi>p</mi>
</math></span>. There is a maximum at A where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = a">
<mi>x</mi>
<mo>=</mo>
<mi>a</mi>
</math></span>, and a point of inflexion at B where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = b">
<mi>x</mi>
<mo>=</mo>
<mi>b</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the coordinates of A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the rate of change of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> at A.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of B.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the the rate of change of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> at B.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="R"> <mi>R</mi> </math></span> be the region enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> , the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-axis, the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = b"> <mi>x</mi> <mo>=</mo> <mi>b</mi> </math></span> and the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = a"> <mi>x</mi> <mo>=</mo> <mi>a</mi> </math></span>. The region <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="R"> <mi>R</mi> </math></span> is rotated 360° about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-axis. Find the volume of the solid formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>evidence of valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><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="f(x) = 0,{\text{ }}y = 0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>y</mi> <mo>=</mo> <mn>0</mn> </math></span></p>
<p>2.73205</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = 2.73"> <mi>p</mi> <mo>=</mo> <mn>2.73</mn> </math></span> <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>1.87938, 8.11721</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(1.88,{\text{ }}8.12)"> <mo stretchy="false">(</mo> <mn>1.88</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>8.12</mn> <mo stretchy="false">)</mo> </math></span> <strong><em>A2</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>rate of change is 0 (do not accept decimals) <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p><strong><em>[1 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1 (using GDC)</strong></p>
<p>valid approach <strong><em>M1</em></strong></p>
<p><em>eg</em><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="f’’ = 0"> <msup> <mi>f</mi> <mo>″</mo> </msup> <mo>=</mo> <mn>0</mn> </math></span>, max/min on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’,{\text{ }}x = - 1"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mn>1</mn> </math></span></p>
<p>sketch of either <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’"> <msup> <mi>f</mi> <mo>′</mo> </msup> </math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’’"> <msup> <mi>f</mi> <mo>″</mo> </msup> </math></span>, with max/min or root (respectively) <strong><em>(A1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 1"> <mi>x</mi> <mo>=</mo> <mn>1</mn> </math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p>Substituting <strong>their</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span> value into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><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="f(1)"> <mi>f</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 4.5"> <mi>y</mi> <mo>=</mo> <mn>4.5</mn> </math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p><strong>METHOD 2 (analytical)</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’’ = - 6{x^2} + 6"> <msup> <mi>f</mi> <mo>″</mo> </msup> <mo>=</mo> <mo>−</mo> <mn>6</mn> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mn>6</mn> </math></span> <strong><em>A1</em></strong></p>
<p>setting <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’’ = 0"> <msup> <mi>f</mi> <mo>″</mo> </msup> <mo>=</mo> <mn>0</mn> </math></span> <strong><em>(M1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 1"> <mi>x</mi> <mo>=</mo> <mn>1</mn> </math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p>substituting <strong>their</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span> value into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><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="f(1)"> <mi>f</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 4.5"> <mi>y</mi> <mo>=</mo> <mn>4.5</mn> </math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing rate of change is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’"> <msup> <mi>f</mi> <mo>′</mo> </msup> </math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><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="y’,{\text{ }}f’(1)"> <msup> <mi>y</mi> <mo>′</mo> </msup> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </math></span></p>
<p>rate of change is 6 <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to substitute either limits or the function into formula <strong><em>(M1)</em></strong></p>
<p>involving <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^2}"> <mrow> <msup> <mi>f</mi> <mn>2</mn> </msup> </mrow> </math></span> (accept absence of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi "> <mi>π</mi> </math></span> and/or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{d}}x"> <mrow> <mtext>d</mtext> </mrow> <mi>x</mi> </math></span>)</p>
<p><em>eg</em><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="\pi \int {{{( - 0.5{x^4} + 3{x^2} + 2x)}^2}{\text{d}}x,{\text{ }}\int_1^{1.88} {{f^2}} } "> <mi>π</mi> <mo>∫</mo> <mrow> <mrow> <msup> <mrow> <mo stretchy="false">(</mo> <mo>−</mo> <mn>0.5</mn> <mrow> <msup> <mi>x</mi> <mn>4</mn> </msup> </mrow> <mo>+</mo> <mn>3</mn> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mn>2</mn> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mtext>d</mtext> </mrow> <mi>x</mi> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <msubsup> <mo>∫</mo> <mn>1</mn> <mrow> <mn>1.88</mn> </mrow> </msubsup> <mrow> <mrow> <msup> <mi>f</mi> <mn>2</mn> </msup> </mrow> </mrow> </mrow> </math></span></p>
<p>128.890</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{volume}} = 129"> <mrow> <mtext>volume</mtext> </mrow> <mo>=</mo> <mn>129</mn> </math></span> <strong><em>A2</em></strong> <strong><em>N3</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>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>Contestants in a TV gameshow try to get through three walls by passing through doors without falling into a trap. Contestants choose doors at random.<br>If they avoid a trap they progress to the next wall.<br>If a contestant falls into a trap they exit the game before the next contestant plays.<br>Contestants are not allowed to watch each other attempt the game.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The first wall has four doors with a trap behind one door.</p>
<p style="text-align: left;">Ayako is a contestant.</p>
</div>
<div class="specification">
<p>Natsuko is the second contestant.</p>
</div>
<div class="specification">
<p>The second wall has five doors with a trap behind two of the doors.</p>
<p>The third wall has six doors with a trap behind three of the doors.</p>
<p>The following diagram shows the branches of a probability tree diagram for a contestant in the game.</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>Write down the probability that Ayako avoids the trap in this wall.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that only one of Ayako and Natsuko falls into a trap while attempting to pass through a door <strong>in the first wall</strong>.</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>Copy</strong> the probability tree diagram and write down the relevant probabilities along the branches.</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>A contestant is chosen at random. Find the probability that this contestant fell into a trap while attempting to pass through a door in the second wall.</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>A contestant is chosen at random. Find the probability that this contestant fell into a trap.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>120 contestants attempted this game.</p>
<p>Find the expected number of contestants who fell into a trap while attempting to pass through a door in the third wall.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{4}">
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
</math></span> (0.75, 75%) <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{4} \times \frac{1}{4} + \frac{1}{4} \times \frac{3}{4}">
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
</math></span> <strong>OR </strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2 \times \frac{3}{4} \times \frac{1}{4}">
<mn>2</mn>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
</math></span> <em><strong>(M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their product <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{4} \times \frac{3}{4}">
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
</math></span> seen, and <em><strong>(M1)</strong></em> for adding their two products or multiplying their product by 2.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{3}{8}\,\,\,\,\left( {\frac{6}{{16}},\,\,0.375,\,\,37.5{\text{% }}} \right)">
<mo>=</mo>
<mfrac>
<mn>3</mn>
<mn>8</mn>
</mfrac>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>6</mn>
<mrow>
<mn>16</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>0.375</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>37.5</mn>
<mrow>
<mtext>% </mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (G3)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (a), but only if the sum of their two fractions is 1.</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><img src="data:image/png;base64,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"><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for each correct pair of branches. Follow through from part (a).</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{3}{4} \times \frac{2}{5}">
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>2</mn>
<mn>5</mn>
</mfrac>
</math></span> <em><strong>(M1)</strong></em></p>
<p>Note: Award <em><strong>(M1)</strong></em> for correct probabilities multiplied together.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{3}{{10}}\,\,\,\left( {0.3,\,\,30{\text{% }}} \right)">
<mo>=</mo>
<mfrac>
<mn>3</mn>
<mrow>
<mn>10</mn>
</mrow>
</mfrac>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.3</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>30</mn>
<mrow>
<mtext>% </mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (G2)</strong></em></p>
<p><strong>Note:</strong> Follow through from their tree diagram or part (a).</p>
<p><em><strong>[2 marks]</strong></em></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="1 - \frac{3}{4} \times \frac{2}{5} \times \frac{3}{6}">
<mn>1</mn>
<mo>−</mo>
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>2</mn>
<mn>5</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>6</mn>
</mfrac>
</math></span> <strong>OR </strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{4} + \frac{3}{4} \times \frac{2}{5} + \frac{3}{4} \times \frac{3}{5} \times \frac{3}{6}">
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>2</mn>
<mn>5</mn>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>5</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>6</mn>
</mfrac>
</math></span> <em><strong>(M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{4} \times \frac{3}{5} \times \frac{3}{6}">
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>5</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>6</mn>
</mfrac>
</math></span> and <em><strong>(M1)</strong></em> for subtracting their correct probability from 1, or adding to their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{4} + \frac{3}{4} \times \frac{2}{5}">
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>2</mn>
<mn>5</mn>
</mfrac>
</math></span>.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{93}}{{120}}\,\,\,\,\left( {\frac{{31}}{{40}},\,\,0.775,\,\,77.5{\text{% }}} \right)">
<mo>=</mo>
<mfrac>
<mrow>
<mn>93</mn>
</mrow>
<mrow>
<mn>120</mn>
</mrow>
</mfrac>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>31</mn>
</mrow>
<mrow>
<mn>40</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>0.775</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>77.5</mn>
<mrow>
<mtext>% </mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (G2)</strong></em></p>
<p><strong>Note:</strong> Follow through from their tree diagram.</p>
<p><em><strong>[3 marks]</strong></em></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="\frac{3}{4} \times \frac{3}{5} \times \frac{3}{6} \times 120">
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>5</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>6</mn>
</mfrac>
<mo>×</mo>
<mn>120</mn>
</math></span> <em><strong>(M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{4} \times \frac{3}{5} \times \frac{3}{6}\,\,\,\,\left( {\frac{3}{4} \times \frac{3}{5} \times \frac{3}{6}\,\,{\text{OR}}\,\,\frac{{27}}{{120}}\,\,{\text{OR}}\,\,\frac{9}{{40}}} \right)">
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>5</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>6</mn>
</mfrac>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>5</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>6</mn>
</mfrac>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>OR</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mrow>
<mn>27</mn>
</mrow>
<mrow>
<mn>120</mn>
</mrow>
</mfrac>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>OR</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mn>9</mn>
<mrow>
<mn>40</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> and <em><strong>(M1)</strong></em> for multiplying by 120.</p>
<p>= 27 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (G3)</strong></em></p>
<p><strong>Note:</strong> Follow through from their tree diagram or their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{4} \times \frac{3}{5} \times \frac{3}{6}">
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>5</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>3</mn>
<mn>6</mn>
</mfrac>
</math></span> from their calculation in part (d)(ii).</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.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><strong>All lengths in this question are in centimetres.</strong></p>
<p>A solid metal ornament is in the shape of a right pyramid, with vertex <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>V</mtext></math> and square base <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ABCD</mtext></math>. The centre of the base is <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>X</mtext></math>. Point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>V</mtext></math> has coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>1</mn><mo>,</mo><mo> </mo><mn>5</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>)</mo></math> and 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><mo>-</mo><mn>1</mn><mo>,</mo><mo> </mo><mn>1</mn><mo>,</mo><mo> </mo><mn>6</mn><mo>)</mo></math>.</p>
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"></p>
</div>
<div class="specification">
<p>The volume of the pyramid is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>57</mn><mo>.</mo><mn>2</mn><mo> </mo><msup><mtext>cm</mtext><mn>3</mn></msup></math>, correct to three significant figures.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AV</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>Given that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mtext>V</mtext><mo>^</mo></mover><mtext>B</mtext><mo>=</mo><mn>40</mn><mo>°</mo></math>, find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</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 height of the pyramid, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>VX</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>A second ornament is in the shape of a cuboid with a rectangular base of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>x</mi><mo> </mo><mtext>cm</mtext></math>, width <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo> </mo><mtext>cm</mtext></math> and height <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo> </mo><mtext>cm</mtext></math>. The cuboid has the same volume as the pyramid.</p>
<p>The cuboid has a minimum surface area of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo> </mo><msup><mtext>cm</mtext><mn>2</mn></msup></math>. Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>attempt to use the distance formula to find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AV</mtext></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mfenced><mrow><mo>-</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mn>5</mn><mo>-</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mn>0</mn><mo>-</mo><mn>6</mn></mrow></mfenced><mn>2</mn></msup></msqrt></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>7</mn><mo>.</mo><mn>48331</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>7</mn><mo>.</mo><mn>48</mn><mo> </mo><mfenced><mtext>cm</mtext></mfenced><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><msqrt><mn>56</mn></msqrt><mo> </mo><mo> </mo><mtext>or</mtext><mo> </mo><mo> </mo><mn>2</mn><msqrt><mn>14</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">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>attempt to apply cosine rule OR sine rule to find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mtext>AB</mtext><mo>=</mo></mrow></mfenced><msqrt><mn>7</mn><mo>.</mo><mn>48</mn><msup><mo>…</mo><mn>2</mn></msup><mo>+</mo><mn>7</mn><mo>.</mo><mn>48</mn><msup><mo>…</mo><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>×</mo><mn>7</mn><mo>.</mo><mn>48</mn><mo>…</mo><mo>×</mo><mn>7</mn><mo>.</mo><mn>48</mn><mo>…</mo><mi>cos</mi><mfenced><mrow><mn>40</mn><mo>°</mo></mrow></mfenced></msqrt></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mtext>AB</mtext><mrow><mi>sin</mi><mo> </mo><mn>40</mn><mo>°</mo></mrow></mfrac><mo>=</mo><mfrac><msqrt><mn>56</mn></msqrt><mrow><mi>sin</mi><mo> </mo><mn>70</mn><mo>°</mo></mrow></mfrac></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>5</mn><mo>.</mo><mn>11888</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>5</mn><mo>.</mo><mn>12</mn><mo> </mo><mfenced><mtext>cm</mtext></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext></math> be the midpoint of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[AB]</mtext></math></p>
<p>attempt to apply right-angled trigonometry on triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AVM</mtext></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>2</mn><mo>×</mo><mn>7</mn><mo>.</mo><mn>48</mn><mo>…</mo><mo>×</mo><mi>sin</mi><mfenced><mrow><mn>20</mn><mo>°</mo></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>5</mn><mo>.</mo><mn>11888</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>5</mn><mo>.</mo><mn>12</mn><mo> </mo><mfenced><mtext>cm</mtext></mfenced></math> <em><strong>A1</strong></em></p>
<p> </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>equating volume of pyramid formula to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>57</mn><mo>.</mo><mn>2</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>×</mo><mn>5</mn><mo>.</mo><mn>11</mn><msup><mo>…</mo><mn>2</mn></msup><mo>×</mo><mi>h</mi><mo>=</mo><mn>57</mn><mo>.</mo><mn>2</mn></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>6</mn><mo>.</mo><mn>54886</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>6</mn><mo>.</mo><mn>55</mn><mo> </mo><mfenced><mtext>cm</mtext></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>M</mtext></math> be the midpoint of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[AB]</mtext></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>AV</mtext><mn>2</mn></msup><mo>=</mo><msup><mtext>AM</mtext><mn>2</mn></msup><mo>+</mo><msup><mtext>MX</mtext><mn>2</mn></msup><mo>+</mo><msup><mtext>XV</mtext><mn>2</mn></msup></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mtext>XV</mtext><mo>=</mo><msqrt><mn>7</mn><mo>.</mo><mn>48</mn><msup><mo>…</mo><mn>2</mn></msup><mo>-</mo><msup><mfenced><mfrac><mrow><mn>5</mn><mo>.</mo><mn>11</mn><mo>…</mo></mrow><mn>2</mn></mfrac></mfenced><mn>2</mn></msup><mo>-</mo><msup><mfenced><mfrac><mrow><mn>5</mn><mo>.</mo><mn>11</mn><mo>…</mo></mrow><mn>2</mn></mfrac></mfenced><mn>2</mn></msup></msqrt></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>6</mn><mo>.</mo><mn>54886</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>6</mn><mo>.</mo><mn>55</mn><mo> </mo><mfenced><mtext>cm</mtext></mfenced></math> <em><strong>A1</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><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mi>x</mi><mo>×</mo><mn>2</mn><mi>x</mi><mo>×</mo><mi>y</mi><mo>=</mo><mn>57</mn><mo>.</mo><mn>2</mn></math> <em>(A1)</em></strong></p>
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mn>2</mn><mfenced><mrow><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mi>y</mi><mo>+</mo><mn>2</mn><mi>x</mi><mi>y</mi></mrow></mfenced></math> <em>A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Condone use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>.</p>
<p><br>attempt to substitute <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mrow><mn>57</mn><mo>.</mo><mn>2</mn></mrow><mrow><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mrow></mfrac></math> into their expression for surface area <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>S</mi><mfenced><mi>x</mi></mfenced><mo>=</mo></mrow></mfenced><mo> </mo><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>6</mn><mi>x</mi><mfenced><mfrac><mrow><mn>57</mn><mo>.</mo><mn>2</mn></mrow><mrow><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mrow></mfrac></mfenced></math></p>
<p><br><strong>EITHER</strong></p>
<p>attempt to find minimum turning point on graph of area function <em><strong>(M1)</strong></em></p>
<p><br><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>S</mi></mrow><mrow><mo>d</mo><mi>x</mi></mrow></mfrac><mo>=</mo><mn>8</mn><mi>x</mi><mo>-</mo><mn>171</mn><mo>.</mo><mn>6</mn><msup><mi>x</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo>=</mo><mn>0</mn></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>77849</mn><mo>…</mo></math> <em><strong>(M1)</strong></em></p>
<p><br><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>92</mn><mo>.</mo><mn>6401</mn><mo>…</mo></math></p>
<p>minimum surface area <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>92</mn><mo>.</mo><mn>6</mn><mo> </mo><mfenced><msup><mtext>cm</mtext><mn>2</mn></msup></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[5 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;">
<p>Parts (a), (b) and (c) were completed well by many candidates, but few were able to make any significant progress in part (d).</p>
<p>In part (a), many candidates were able to apply the distance formula and successfully find AV. However, a common error was to work in two-dimensions and to apply Pythagoras' Theorem once, neglecting completely the <em>z</em>-coordinates. Many recognised the need to use either the sine or cosine rule in part (b) to find the length AB. Common errors in this part included: the GDC being set incorrectly in radians; applying right-angled trigonometry on a 40°, 40°, 70° triangle; or using <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mtext>AB</mtext></math> as the length of AX in triangle AVX.</p>
<p>Despite the formula for the volume of a pyramid being in the formula booklet, a common error in part (c) was to omit the factor of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>3</mn></mfrac></math> from the volume formula, or not to recognise that the area of the base of the pyramid was <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>AB</mtext><mn>2</mn></msup></math>.</p>
<p>The most challenging part of this question proved to be the optimization of the surface area of the cuboid in part (d). Although some candidates were able to form an equation involving the volume of the cuboid, an expression for the surface area eluded most. A common error was to gain a surface area which involved eight sides rather than six. It was surprising that few who were able to find both the equation and an expression were able to progress any further. Of those that did, few used their GDC to find the minimum surface area directly, with most preferring the more time consuming analytical approach.</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>
<br><hr><br><div class="specification">
<p>160 students attend a dual language school in which the students are taught only in Spanish or taught only in English.</p>
<p>A survey was conducted in order to analyse the number of students studying Biology or Mathematics. The results are shown in the Venn diagram.</p>
<p> </p>
<p style="padding-left: 240px;">Set <em>S</em> represents those students who are <strong>taught</strong> in Spanish.</p>
<p style="padding-left: 240px;">Set <em>B</em> represents those students who <strong>study</strong> Biology.</p>
<p style="padding-left: 240px;">Set <em>M</em> represents those students who <strong>study</strong> Mathematics.</p>
<p style="padding-left: 210px;"> </p>
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"></p>
</div>
<div class="specification">
<p>A student from the school is chosen at random.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of students in the school that are taught in Spanish.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of students in the school that study Mathematics in English.</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 number of students in the school that study both Biology and Mathematics.</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>Write down <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n\left( {S \cap \left( {M \cup B} \right)} \right)">
<mi>n</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>S</mi>
<mo>∩</mo>
<mrow>
<mo>(</mo>
<mrow>
<mi>M</mi>
<mo>∪</mo>
<mi>B</mi>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</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>Write down <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n\left( {B \cap M \cap S'} \right)">
<mi>n</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>B</mi>
<mo>∩</mo>
<mi>M</mi>
<mo>∩</mo>
<msup>
<mi>S</mi>
<mo>′</mo>
</msup>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this student studies Mathematics.</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 the probability that this student studies neither Biology nor Mathematics.</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>Find the probability that this student is taught in Spanish, given that the student studies Biology.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>10 + 40 + 28 + 17 <em><strong>(M1)</strong></em></p>
<p>= 95 <em><strong> (A1)(G2)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for each correct sum (for example: 10 + 40 + 28 + 17) seen.</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>20 + 12 <em><strong>(M1)</strong></em></p>
<p>= 32 <em><strong> (A1)(G2)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for each correct sum (for example: 10 + 40 + 28 + 17) seen.</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>12 + 40 <em><strong>(M1)</strong></em></p>
<p>= 52 <em><strong> (A1)(G2)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for each correct sum (for example: 10 + 40 + 28 + 17) seen.</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>78 <em><strong>(A1)</strong></em></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>12 <em><strong>(A1)</strong></em></p>
<p> </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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{100}}{{160}}">
<mfrac>
<mrow>
<mn>100</mn>
</mrow>
<mrow>
<mn>160</mn>
</mrow>
</mfrac>
</math></span> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{5}{8}{\text{,}}\,\,0.625{\text{,}}\,\,62.5\,{\text{% }}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>5</mn>
<mn>8</mn>
</mfrac>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>0.625</mn>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>62.5</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>% </mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)(A1) (G2)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Throughout part (c), award <em><strong>(A1)</strong></em> for correct numerator, <em><strong>(A1)</strong></em> for correct denominator. All answers must be probabilities to award <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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{42}}{{160}}">
<mfrac>
<mrow>
<mn>42</mn>
</mrow>
<mrow>
<mn>160</mn>
</mrow>
</mfrac>
</math></span> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{{21}}{{80}}{\text{,}}\,\,0.263\,\,\left( {0.2625} \right){\text{,}}\,\,26.3\,{\text{% }}\,\,\left( {26.25\,{\text{% }}} \right)} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>21</mn>
</mrow>
<mrow>
<mn>80</mn>
</mrow>
</mfrac>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>0.263</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.2625</mn>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>26.3</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>% </mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>26.25</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>% </mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)(A1) (G2)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Throughout part (c), award <em><strong>(A1)</strong></em> for correct numerator, <em><strong>(A1)</strong></em> for correct denominator. All answers must be probabilities to award <em><strong>(A1)</strong></em>.</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{50}}{{70}}">
<mfrac>
<mrow>
<mn>50</mn>
</mrow>
<mrow>
<mn>70</mn>
</mrow>
</mfrac>
</math></span> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{5}{7}{\text{,}}\,\,0.714\,\,\left( {0.714285 \ldots } \right){\text{,}}\,\,71.4\,{\text{% }}\,\,\left( {71.4285 \ldots \,{\text{% }}} \right)} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>5</mn>
<mn>7</mn>
</mfrac>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>0.714</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.714285</mn>
<mo>…</mo>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>71.4</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>% </mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>71.4285</mn>
<mo>…</mo>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>% </mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)(A1) (G2)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Throughout part (c), award <em><strong>(A1)</strong></em> for correct numerator, <em><strong>(A1)</strong></em> for correct denominator. All answers must be probabilities to award <em><strong>(A1)</strong></em>.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.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.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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = 6 - \ln ({x^2} + 2)">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>6</mn>
<mo>−<!-- − --></mo>
<mi>ln</mi>
<mo><!-- --></mo>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \in \mathbb{R}">
<mi>x</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>. The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> passes through the point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(p,{\text{ }}4)">
<mo stretchy="false">(</mo>
<mi>p</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>4</mn>
<mo stretchy="false">)</mo>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p > 0">
<mi>p</mi>
<mo>></mo>
<mn>0</mn>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The following diagram shows part of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span>.</p>
<p><img src="images/Schermafbeelding_2018-02-12_om_13.30.18.png" alt="N17/5/MATME/SP2/ENG/TZ0/05.b"></p>
<p>The region enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span>, the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-axis and the lines <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - p"> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mi>p</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = p"> <mi>x</mi> <mo>=</mo> <mi>p</mi> </math></span> is rotated 360° about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-axis. Find the volume of the solid formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><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="f(p) = 4"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>p</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>4</mn> </math></span>, intersection with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 4,{\text{ }} \pm 2.32"> <mi>y</mi> <mo>=</mo> <mn>4</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mo>±</mo> <mn>2.32</mn> </math></span></p>
<p>2.32143</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = \sqrt {{{\text{e}}^2} - 2} "> <mi>p</mi> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mtext>e</mtext> </mrow> <mn>2</mn> </msup> </mrow> <mo>−</mo> <mn>2</mn> </msqrt> </math></span> (exact), 2.32 <strong><em>A1 N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to substitute <strong>either their</strong> limits <strong>or</strong> the function into volume formula (must involve <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^2}"> <mrow> <msup> <mi>f</mi> <mn>2</mn> </msup> </mrow> </math></span>, accept reversed limits and absence of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi "> <mi>π</mi> </math></span> and/or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{d}}x"> <mrow> <mtext>d</mtext> </mrow> <mi>x</mi> </math></span>, but do not accept any other errors) <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_{ - 2.32}^{2.32} {{f^2},{\text{ }}\pi \int {{{\left( {6 - \ln ({x^2} + 2)} \right)}^2}{\text{d}}x,{\text{ 105.675}}} } "> <msubsup> <mo>∫</mo> <mrow> <mo>−</mo> <mn>2.32</mn> </mrow> <mrow> <mn>2.32</mn> </mrow> </msubsup> <mrow> <mrow> <msup> <mi>f</mi> <mn>2</mn> </msup> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>π</mi> <mo>∫</mo> <mrow> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mn>6</mn> <mo>−</mo> <mi>ln</mi> <mo></mo> <mo stretchy="false">(</mo> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mtext>d</mtext> </mrow> <mi>x</mi> <mo>,</mo> <mrow> <mtext> 105.675</mtext> </mrow> </mrow> </mrow> </math></span></p>
<p>331.989</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{volume}} = 332"> <mrow> <mtext>volume</mtext> </mrow> <mo>=</mo> <mn>332</mn> </math></span> <strong><em>A2 N3</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>On one day 180 flights arrived at a particular airport. The distance travelled and the arrival status for each incoming flight was recorded. The flight was then classified as on time, slightly delayed, or heavily delayed.</p>
<p>The results are shown in the following table.</p>
<p><img src="data:image/png;base64,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"></p>
<p>A <em>χ</em><sup>2</sup> test is carried out at the 10 % significance level to determine whether the arrival status of incoming flights is independent of the distance travelled.</p>
</div>
<div class="specification">
<p>The critical value for this test is 7.779.</p>
</div>
<div class="specification">
<p>A flight is chosen at random from the 180 recorded flights.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the alternative hypothesis.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the expected frequency of flights travelling at most 500 km and arriving slightly delayed.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of degrees of freedom.</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 <em>χ</em><sup>2</sup> statistic.</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 associated <em>p</em>-value.</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>State, with a reason, whether you would reject the null hypothesis.</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 probability that this flight arrived on time.</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>Given that this flight was not heavily delayed, find the probability that it travelled between 500 km and 5000 km.</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>Two flights are chosen at random from those which were slightly delayed.</p>
<p>Find the probability that each of these flights travelled at least 5000 km.</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>The arrival status is dependent on the distance travelled by the incoming flight <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Accept “associated” or “not independent”.</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{60 \times 45}}{{180}}">
<mfrac>
<mrow>
<mn>60</mn>
<mo>×</mo>
<mn>45</mn>
</mrow>
<mrow>
<mn>180</mn>
</mrow>
</mfrac>
</math></span> <strong>OR </strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{60}}{{180}} \times \frac{{45}}{{180}} \times 180">
<mfrac>
<mrow>
<mn>60</mn>
</mrow>
<mrow>
<mn>180</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>45</mn>
</mrow>
<mrow>
<mn>180</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mn>180</mn>
</math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into expected value formula.</p>
<p>= 15 <em><strong> (A1) (G2)</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>4 <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A0)</strong></em> if “2 + 2 = 4” is seen.</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>9.55 (9.54671…) <em><strong>(G2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(G1)</strong></em> for an answer of 9.54.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.0488 (0.0487961…) <em><strong>(G1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Reject the Null Hypothesis <em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from their hypothesis in part (a).</p>
<p>9.55 (9.54671…) > 7.779 <em><strong>(R1)</strong></em><strong>(ft)</strong></p>
<p><strong>OR </strong></p>
<p>0.0488 (0.0487961…) < 0.1 <em><strong>(R1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Do not award <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(R0)</strong></em><strong>(ft)</strong>. Follow through from part (d). Award <em><strong>(R1)</strong></em><strong>(ft)</strong> for a correct comparison, <em><strong>(A1)</strong></em><strong>(ft)</strong> for a consistent conclusion with the answers to parts (a) and (d). Award <em><strong>(R1)</strong></em><strong>(ft)</strong> for <em>χ</em><sup>2</sup><em><sub>calc</sub></em> > <em>χ</em><sup>2</sup><em><sub>crit </sub></em>, provided the calculated value is explicitly seen in part (d)(i).</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{{52}}{{180}}\,\,\left( {0.289,\,\,\frac{{13}}{{45}},\,\,28.9\,{\text{% }}} \right)">
<mfrac>
<mrow>
<mn>52</mn>
</mrow>
<mrow>
<mn>180</mn>
</mrow>
</mfrac>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.289</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mrow>
<mn>13</mn>
</mrow>
<mrow>
<mn>45</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>28.9</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>% </mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)(A1) (G2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct numerator, <em><strong>(A1)</strong></em> for correct denominator.</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{35}}{{97}}\,\,\left( {0.361,\,\,36.1\,{\text{% }}} \right)">
<mfrac>
<mrow>
<mn>35</mn>
</mrow>
<mrow>
<mn>97</mn>
</mrow>
</mfrac>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.361</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>36.1</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>% </mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)(A1) (G2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct numerator, <em><strong>(A1)</strong></em> for correct denominator.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{14}}{{45}} \times \frac{{13}}{{44}}">
<mfrac>
<mrow>
<mn>14</mn>
</mrow>
<mrow>
<mn>45</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>13</mn>
</mrow>
<mrow>
<mn>44</mn>
</mrow>
</mfrac>
</math></span> <em><strong>(A1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for two correct fractions and <em><strong>(M1)</strong></em> for multiplying their two fractions.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{182}}{{1980}}\,\,\left( {0.0919,\,\,\frac{{91}}{{990}},\,0.091919 \ldots ,\,9.19\,{\text{% }}} \right)">
<mo>=</mo>
<mfrac>
<mrow>
<mn>182</mn>
</mrow>
<mrow>
<mn>1980</mn>
</mrow>
</mfrac>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.0919</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mrow>
<mn>91</mn>
</mrow>
<mrow>
<mn>990</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mn>0.091919</mn>
<mo>…</mo>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mn>9.19</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>% </mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1) (G2)</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.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>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {x^2}{{\text{e}}^{3x}}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mn>3</mn>
<mi>x</mi>
</mrow>
</msup>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \in \mathbb{R}">
<mi>x</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>.</p>
</div>
<div class="question">
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> has a horizontal tangent line at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0"> <mi>x</mi> <mo>=</mo> <mn>0</mn> </math></span> and at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = a"> <mi>x</mi> <mo>=</mo> <mi>a</mi> </math></span>. Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a"> <mi>a</mi> </math></span>.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>valid method <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'\left( x \right) = 0"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </math></span>, <img src="data:image/png;base64,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">, <img src="data:image/png;base64,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"></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = - 0.667\left( { = - \frac{2}{3}} \right)"> <mi>a</mi> <mo>=</mo> <mo>−</mo> <mn>0.667</mn> <mrow> <mo>(</mo> <mrow> <mo>=</mo> <mo>−</mo> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </math></span> (accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - 0.667"> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mn>0.667</mn> </math></span>) <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>Sila High School has 110 students. They each take exactly one language class from a choice of English, Spanish or Chinese. The following table shows the number of female and male students in the three different language classes.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
<p>A <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
<mrow>
<msup>
<mi>χ<!-- χ --></mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> test was carried out at the 5 % significance level to analyse the relationship between gender and student choice of language class.</p>
</div>
<div class="specification">
<p>Use your graphic display calculator to write down</p>
</div>
<div class="specification">
<p>The critical value at the 5 % significance level for this test is 5.99.</p>
</div>
<div class="specification">
<p>One student is chosen at random from this school.</p>
</div>
<div class="specification">
<p>Another student is chosen at random from this school.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the null hypothesis, H<sub>0 </sub>, for this test.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the number of degrees of freedom.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the expected frequency of female students who chose to take the Chinese class.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
<mrow>
<msup>
<mi>χ</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> statistic.</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>State whether or not H<sub>0</sub> should be rejected. Justify your statement.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the student does not take the Spanish class.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that neither of the two students take the Spanish class.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that at least one of the two students is female.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>(H<sub>0</sub>:) (choice of) language is independent of gender <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Accept “there is no association between language (choice) and gender”. Accept “language (choice) is not dependent on gender”. Do not accept “not related” or “not correlated” or “not influenced”.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>2 <em><strong>(AG)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>16.4 (16.4181…) <em><strong>(G1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\chi _{{\text{calc}}}^2 = 8.69">
<msubsup>
<mi>χ</mi>
<mrow>
<mrow>
<mtext>calc</mtext>
</mrow>
</mrow>
<mn>2</mn>
</msubsup>
<mo>=</mo>
<mn>8.69</mn>
</math></span> (8.68507…) <em><strong>(G2)</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>(we) reject the null hypothesis <strong><em>(A1)</em>(ft)</strong></p>
<p>8.68507… > 5.99 <strong><em>(R1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from part (c)(ii). Accept “do not accept” in place of “reject.” Do not award <strong><em>(A1)</em>(ft)<em>(R0)</em></strong>.</p>
<p><strong>OR</strong></p>
<p>(we) reject the null hypothesis <em><strong>(A1)</strong></em></p>
<p>0.0130034 < 0.05 <em><strong>(R1)</strong></em></p>
<p><strong>Note:</strong> Accept “do not accept” in place of “reject.” Do not award <strong><em>(A1)</em>(ft)<em>(R0)</em></strong>.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{88}}{{110}}\,\,\,\left( {\frac{4}{5}{\text{,}}\,\,0.8{\text{,}}\,\,80{\text{% }}} \right)">
<mfrac>
<mrow>
<mn>88</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>4</mn>
<mn>5</mn>
</mfrac>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>0.8</mn>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>80</mn>
<mrow>
<mtext>% </mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em></strong><strong><em>(A1)</em></strong><strong><em>(G2)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em></strong> for correct numerator, <strong><em>(A1)</em></strong> for correct denominator.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{88}}{{110}} \times \frac{{87}}{{109}}">
<mfrac>
<mrow>
<mn>88</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>87</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)</em></strong><strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for multiplying two fractions. Award <strong><em>(M1)</em></strong> for multiplying their correct fractions.</p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{{46}}{{110}}} \right)\left( {\frac{{45}}{{109}}} \right) + 2\left( {\frac{{46}}{{110}}} \right)\left( {\frac{{42}}{{109}}} \right) + \left( {\frac{{42}}{{110}}} \right)\left( {\frac{{41}}{{109}}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>46</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>45</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>46</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>42</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>42</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>41</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(M1)</em></strong><strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for correct products; <strong><em>(M1)</em></strong> for adding 4 products.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.639\,\,\,\left( {0.638532 \ldots {\text{,}}\,\,\frac{{348}}{{545}}{\text{,}}\,\,63.9{\text{% }}} \right)">
<mn>0.639</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.638532</mn>
<mo>…</mo>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mrow>
<mn>348</mn>
</mrow>
<mrow>
<mn>545</mn>
</mrow>
</mfrac>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>63.9</mn>
<mrow>
<mtext>% </mtext>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p><strong>Note:</strong> Follow through from their answer to part (e)(i).</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1 - \frac{{67}}{{110}} \times \frac{{66}}{{109}}">
<mn>1</mn>
<mo>−</mo>
<mfrac>
<mrow>
<mn>67</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>66</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)</em></strong><strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for multiplying two correct fractions. Award <strong><em>(M1)</em></strong> for subtracting their product of two fractions from 1.</p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{43}}{{110}} \times \frac{{42}}{{109}} + \frac{{43}}{{110}} \times \frac{{67}}{{109}} + \frac{{67}}{{110}} \times \frac{{43}}{{109}}">
<mfrac>
<mrow>
<mn>43</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>42</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<mn>43</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>67</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<mn>67</mn>
</mrow>
<mrow>
<mn>110</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>43</mn>
</mrow>
<mrow>
<mn>109</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)</em></strong><strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for correct products; <strong><em>(M1)</em></strong> for adding three products.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.631\,\,\,\left( {0.631192 \ldots {\text{,}}\,\,63.1{\text{% ,}}\,\,\frac{{344}}{{545}}} \right)">
<mn>0.631</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.631192</mn>
<mo>…</mo>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>63.1</mn>
<mrow>
<mtext>% ,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mrow>
<mn>344</mn>
</mrow>
<mrow>
<mn>545</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)</strong></em><em><strong>(G2)</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">e.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">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>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>In a company it is found that 25 % of the employees encountered traffic on their way to work. From those who encountered traffic the probability of being late for work is 80 %.</p>
<p>From those who did not encounter traffic, the probability of being late for work is 15 %.</p>
<p>The tree diagram illustrates the information.</p>
<p style="text-align: center;"><img 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wicaB8OieULH8LkqpiATIB1Y5kEv3pKgI2yp8S4PBMYgwDrxmPA4UNuEWD5wi1MXIgJjE1AqRsvWLAArBuPzYuPuibAV8qu2fARJuAWAUrF9MorryAjI0PSjadOnerWeVyICTgjwEbZGRXexwTcIEC6cXl5Oa5fv87+xm7w4iLuEWCj7B4nLsUEhgiQbvzmm2/i1KlT2L17NzQazdAxfsMEJkqANeWJEuTzo4YA6cYUUpP8jSlbNOnGbJCjZvoDNlC+Ug4Yam4onAmwbhzOsxdefWejHF7zxb0NMAHWjQMMnJsDG2X+EjABJwRYN3YChXcFhABrygHBzI2ECwFZN16xYgUSEhJYNw6XiYugfvKVcgRNJg9lYgRINyYXt7lz50oP9OhhHm9MINAE2CgHmji3F3IESDd+++23Qa+7du3CwoULQ66P3KHoIcDyRfTMNY/UgQDpxlVVVVi/fr0UUpP8jtkgO0DijwEnwEY54Mi5wWATUOrG1BfyN6ZUTLwxgVAgwPJFKMwC9yFgBFg3DhhqbshLAmyUvQTHp4UXAdaNw2u+orm3LF9E8+xHwdhJqlDqxseOHWPdOArmPZyHyEY5nGeP+z4mAYpTkZ6eLpU5e/Ysp2IakxYfDBUCLF+EykxwP3xGoLu7W3JtI3/jo0ePSn7HPqucK2ICfibARtnPgLn6wBHgVEyBY80t+Y8Ayxf+Y8s1B5gAZfz4zne+I7VKbm5kpHljAuFGgI1yuM2YR/01Qf/efhQfuQKrR+e5KmyCvrEYS2NiEBOjRmbNH2DSN0K7VI0Y2pe5H41vrUWMuhitJt+06KonrvaTvzEZZFoiTXGPSVemh328MYFwIcBGOVxmypt+mjpRnbsXXRZvTh59jlX/Dl5afRpzGvpgEQY0bYjFOy9tRt2cKvRbBETTy1j1gxMQhhIsSwjeV+uBBx5ATk6OlC/vww8/lB72kX8yb0wgHAgE7z8nHOhwH50QuA/TpzyIEV+c6VMwecQOJ6cFYRfJGWVlZdLDPgo0tHHjRim+RRC6wk0yAfcJCN4ik8BAiyhUQQD2P1WRaBn4VLQUpghkFIq3ynOEio5J+y1CWAyis6Fc5AydoxIZhdWiRTcghLgtdNVrhuuS6xzxmiIKW/5sKyfXKZG9KwydtaIwQ2U7X5Ujypt1YjAI1JuamsSiRYvE66+/Lm7cuBGEHnCTTGB8AiF4feP+DwqXHINAwjKUXmlBoUoFTfVlWJSSQtsv0D61AHpxF4a255CWYEJX5UY88e4D2NR1F0IICMtvsTPuOJY/V40u8yTMzTsBi64aGqSgsOW6vcxlVGtUUBW2YEB0onTZDIcO3cPVxq1IST0KvNSKQWHBYOsy9OSuxpbGP/lI53ZocoyPlE+P9eYxAPGhkCDARjkkpiHAnVA9gdynv4F4TIJq7sOIN13EicpryM7NQppqkq0zsTORsSELmrYP8JHhnncdtH6Mpp81AoVa/GjVPMQjFvHzHkdu9n2o+VkLeoPwLJD1Zu+mks8KHAH2Uw4c69Btia6qDZ2AWY/Wxl/hFvX01gUcyC9DG9Ygy8ueW3t/g+PNQHKWGvFDdUzHstJOSVMZ2hWEN7LeTDExCgsLcfjwYRQUFPBCkyDMBTc5kgBfKY/kEaWfTLhSkw/15CQsP3DBZpSnrMRPO9+CBh9D12+OWC606o/iKK9Zs0aKq1xSUsL+zRE72+ExMDbK4TFPfu0lubptye/ASnJ1+2Up8latwqpV/wD1wH+gx68th07lrDeHzlxEe0/YKEf7NwBWmPt70YP5WLzgywpXty8weMs0ITqxiY8iSwP06AwYvta+A33NWsTErEWN/s6E6vf1yc705ubmZl83w/UxgTEJsFEeE0+YH4xXIyn5r2yD+NwMs9MHa7FISH0M2ap21B3+NYxSmXswdhxC8eaDME4EQewcrNQ+h6SyUuxtvSp5W1iNv8bhuovIKN+GtXPvn0jtfjtX1pspmNFPfvITPPXUU+zf7DfaXLEjATbKjkQi6bNkFLNxL38+4h7Mw4leF8uNE5bgh6dLkfZBLtRxtIQ6Bdt/NR25p06iUDURIJOgWlaE+s71sLy2CHExMYhTV8CyoR71W9MUD/8m0ob/zpX15hdffFHSm+mBIMfT8B9vrtlGIIZcmRkGE2ACYxOg+BlnzpzB6tWrceTIEenBIMkdvDEBXxPgK2VfE+X6IpIAGWAKdnTjxg309/dL8TRYb47IqQ76oPhKOehTwB0IRwLk30zxNK5fvy7F1yCpgzcm4AsCbJR9QZHriFoCFH3ulVdeQUZGBrZv3w56SMgbE5gIAZYvJkKPz416AosXL5biaVBwfYrfXFtby/Gbo/5bMTEAbJQnxo/PZgJgvZm/BL4kwPKFL2lyXUwAkHyaWW/mr4K3BNgoe0uOz2MC4xBgvXkcQHzYKQGWL5xi4Z1MYOIEWG+eOMNorIGNcjTOOo85YASc6c2UzJU3JuCKAMsXrsjwfibgBwJK/+Zdu3Zh4cKFfmiFqwxnAmyUw3n2uO9hS0CpN7/88suYNWtW2I6FO+5bAixf+JYn18YE3CKg1Jtp+XZVVRX7N7tFLvILsVEOgzmmqyoKiMNbZBGQ9eazZ89KA0tPTwfrzZE1x96MhuULb6gF6Byl/lhWVsb54wLEPVjN0Hy//fbbkp8z683BmoXgt8tGOfhzMKoHFLO3vr5eWrJL8RTo9pa36CFAd0a0+ISCHLHeHD3zLo+U5QuZRAi8kkRBt68rVqyQenPu3Dk2yCEwL4HuAunNx44dA8XTYL050PSD3x4b5eDPgdQDujp65pln8OGHH0qGefPmzVJMhRDpHncjwARYbw4w8BBqjuWLIE8G64hBnoAwaZ6/J2EyUT7oZgheKd+DsasO2qVqxMQkI3ffeXsyz7FGa4VZ34SK3GTExFCOuUxoj3Q4P8/UCq2aysh/wcmqTLoxuUGtX79euk09deoULyQYa4qj/Bjpy/Swt6CgAPQQkPIFUgYU3iKPQIgZZSvMXQexbtvHyKzvg7CcRe71PVhX2aFIUT96EqxXz+LQvwH/dPAjCHEXhgv/hGtFTzk57x6uvt+IOmWKZs0KLEkMXFZl1o1Hzx/vcZ8A683uswrbkpQ4NWQ2y2VRrXlUFLZcH+7SQIsoVK0R1brbw/tGvLsten/5gei3KHfeFrrqNQKqItEyoDgweEGUa3aO3Kc8zc/v29vbxZNPPikKCgrEJ5984ufWuPpIJ3Djxg1x4MABsWjRItHQ0BDpw/VgfBYxqDsryot+LnSKf/+RFdhthKZ6jDIjz5A+DepEc/lucdilPXJyjoe7QupK2dr7GxxvnomkWfHDP3IJ30Rm9lUcb++DdXiv4t39+FrGdzBzxEgm4aHZiVApSgFWmDpOobL5bbz2ejUaW/VjXn2POHWCH+g2k243yc2Jbj/pNpSX1U4QKp8upZ6iB8JHjx6VHhA/9dRToAfGvN1ER/WPUNB1x8coyIYcRm7BR7D4uGZldSNMmfJA4N/fQW/7WTSrEjH7oUkOzd9F8/HfoNe5VXYoO/zxr1amIinePkSrHu+UHoYRRrSV/QCrl2fgCW0j9GYPKx2uftx3JFWQbkxuTeTeRG5OdPvJGxPwJQGl3kw//HQBQA8GeQtPAiFklM3o130MJCdilmxIvWZ6E51NV/H8i8uGr6Bj5yGvyQBhMaDz1FsozADayjbjuTc7/XLFTP7GtGyWNlpGS4aZ3Jx4YwL+IqDUm+kBMl0Q0APl8Ng+Q6s2FTGZB9HaIT/oj0GMOhcV7znc1Zr1aK3RYqn8sH6pFjVDd75UzwosL+sCmvORFJcKbetn7iGwGtHVWIHcIUcANZZqa9CqN0G6027dgXnL98CIk8hPegBqbSvoCKB0TrA7GtS0en3BF0JG2T1u45eih4X1ODJjE55PmTK6eKwKKU9uRGnLb9FSlIy2ylPoMPnuarm7uxt0G0n+xnRbSbeXnOF49DTwHv8QcPRvpoVIdIEQNrFTml/Haw0PIv90v+2h/dE5+DfNVrzZdcsGzHwJNZtWY/25r6LUcNdWpvSrOLc+A09UkEPAdCwrPYuWwhRAUw2dpROly6a7AfsWuio34ol3H8CmLqpXQFh+i51xx7H8uWp0mYGEZbtxpaUIKqxBte42DKXLkIB7uNq4FSlPvI+HSrtgofMG/wVJ57YgY8spXPXCtISQUY7HrKQ5QE8v+iciKZg7cejE36Do+VQolOnRkxI7E8u2a1GIZjR1TvxqQtaNyV1J1o3ptpI3JhAMAnQhQBcEZJDpAoEWJoWF3qzagJ0/egpzpbvlSVCl/j3SVBfx3kfXYJWeC9Vjx3vpqCrZiDQVyZyToEp7AQeOboCuoAIn9F7qyKaLOFF5Ddm5WfZ6AcTORMaGLGjaPsBHhnvOp9HUjv2bG5G8uwhb0lSQDGr8AuQdeAPZZ0qwv83Nq3RF7SFklO9H4pIV0Cg6J721foa+7lvQZD2KxPF6a/0T3j30H1i583uY544EEq9GUnLSyAeLju2P85l143EA8eGgEqAHyvRgmS4WwlJvlv5HgR6dAWaQLNkMY/IjWCAZZBltLOJnJSIZH0PXb5Z3evaasAylhk6Upt1Ea2Oj9GPWWKPF8qR8NLusyQpT5/uoM6qxcPZ0m0GWy0r9NqCu6fd2iUM+MP7reGZu/Bp8WCI28VFkJZ8beeVqNkDX8wiylsweOWjHdq1X0frGGUz+H/992CCbL+FIzXnXUMwG9Kbk4+m53vkps27sOAn8OVQJUIYTWqBED5zDT2+2U5Uu0AxjIDagu+8zF15aY5wmHTLhSk0+1JOTsPzABUhiyZSV+GnnW9CMa+y7ULZ8hmJBWgxi4uYjv1m5IGK89oePh5RRRuxcrC15Gh2vHUSr8R5AhnZvJTq2bsPaIcNJGs5mqJfuQ5csc5ivoLEoD8u3voDl6vuG4UzWoB7TJBnDauzCu+92Da3ysxrPY9/rF/HYS0uQMMzDrXeybnzmzBnWjd0ixoVChQA9cKZAV7SFnd4cOx2zF6rHQOnkinWM0spDVv072JLfgZUNfbD8shR5q1Zh1ap/gHrgP9CjLOj0vU1jlnRo0pQVfzbd2elJLneGllFGLOJTNqG+dDqOpNyHmLg8NCW9ivqtaa71Yeuf0LhlDVaXObvJWKK4wr6JC//zCajjbE90K8//Fx7fuRXLRtwGueQkHaAn2eRu9IMf/EDSjQ8dOsQxjsdGxke9JWDW472KXKjJw2DpZmgphEBiBbq+8LbC4fPoYWBY6s2YitRMDVQ9F3GJLtqGNivM/b3owRwvpUj5/PlYvODLijvyLzB4y+ZfMdTUiDexSEh9DNmqyzh/6dORV+jmDlQsTURmzZWR+0ec7+KDh4tNorL4559/Lo4cOSIASCun6DNvTMBfBCyGZlGU8TWRUdggdIP/JQZaioQKEKrCFjHgh0Z/97vfDa001el0fmjBnSqvi5bClNGrcKVVvqrhsQ/2iOqcBUKVUyUuGO4KISxi8PJhkaNSiYzyC2JQakq5Wu+2GBz8LycdUJYRQkgrh1Uio6hZGKRVgHeF4UKVyFFBAClDq4wtumqhAa0w/k/xn4P/KSziruhv2CRUqhxRecEgpFMHL4uGQo1ARqXoHHS5pNBJn2y7QuxK2cUvRxB3Nzc3S/7G5F1x48YN9jcO4lxERdPWP+HUjq04PKcMR/eswtz4LyFhfiq+CxWSk9Su7xgnACes9GbybDjYgKPpf4ZWkirjMPmFPyD9aBtOb5PvqO9H4sqNKLq3A0lxc7D6RO/4V6sJS/DD06VI+yDXdjcdk4Ltv5qO3FMnUahYGhybmAlt0QDykx7Eg6v/Fb3WSZi5qgRtR9NxTZuCOLqzmbwG7854Dp31m5DijsOBw9xx6E4HIPJHWhFFUsWMGTMkqYLd22Qy/Oo/Ajaf10Wr/z/s1tUiz/4c5YuuCsxL7UCxYp+/+kDeRNXV1UNZb1auXMmLnvwF20W9fKXsAEbWjekJNfkbs27sAACen3QAACAASURBVIg/+o+A9WM0/awRKHxe4RF0Cx/9sg1/dBp+wPddCV+92fcsglUjG2U7ebpCqK2txbRp0yS3IXpCzXEqgvW1jNJ2JfdPKGQKWp36v7Ct4N+A76ZifkLg/l0d/Zs3btzI8TQC9LUM3CwHaEDeNMO6sTfU+Bz/EDCi5/wfYLTeg7HjMN5s+CMAFTRLJsPwO+P42qiPOyXrzSRj0N1jSUlJGMXT8DGMAFUX1UaZdGO6AvjJT34i+RsXFxdznIoAffG4GScEElLx/d15QM1qzJq1ET8fWILnX1qGr8KI5vrfYOChaQp3LSfn+3GX7N+ckJAg3U2GVTwNP3LxR9VR+aCPdOM333xTWuG0e/duaDSjFnf7gzXXyQQiggD9/+zduxdtbW3Yt28fy3w+ntWoMsqkG9MqvNWrV+PIkSNYs2YNP1n28ReKq4seAuyh5J+5jhr5giJkUXxjiphF/sY5OTlskP3zneJao4QAuYlSPA26uGG92XeTHvFGWdaNKUIWxTemiFkc39h3XyCuiQmQ/EfeSuSxQd5L3uvNJugbi+3B69XeLVEOkemw6muQGeNBgH1FvyPWKJPuRU+K6RecfsnpF50XgChmnt8yAR8SIP9muvuku1C6G6W7Uk/jN1NQoJdWn8YcCgokDGjKmxe0B5s+RONxVRFnlEk3pl9q+sWmX276BecHeR5/L/gEJuAVAboLpbtRuiulu1PP/Zvvw/QpD0alMZaBR5RRVurGn3zyCevG8izzKxMIMAHP9OY70NesRZwUUN4em1hdjFYpTZsJ+tYaaJeq7SF5M6Edkf/OnttvqRaH5Kh6Q+cOD9qpnGBqhVYdo8i1R+Vt9Q3l3xszHyAAqQ7K5bcfFRTJL8ZW38Bw0/Z39njN6lzs6xjH39xlqKIwOkCRrQoKCqRIVxTxijcmwARCh4AyyuJY/5+2CGzDEdmEGBCXq/NGRGCzGNpFZc4CRQQ2e3Q5LBA51T1iUNwVBl2fPVqcgoFjtDlhGYq+B0210MnB3KRocfY+jIpIJ0eOU0Skk8pDQJUnqi8PCGH5VOh6B8TIscjjsJdRdMvZWwrIHLbbjRs3xIEDB8SiRYukkJphOxDuOBOIAgL0/zpW2NuRhkwOp7lA5DX02UJiyozsYTY11ZeFRbgI+SmXHXp1CNUpbJ9V63LEOhWF4rwthQGVwqSqikTLgD1kqmqTaOinEKHyJhtz+zl2o+wYVnV4LL32Hxb3DDK1EpbyhawbU+YE2kg3phVHvDEBJhC6BEhvpgeC7m1y/jvHwPMARuTtc682wJ4DtPks2nvvANY+tB+/iuwN38fy5Kv23H62HIDIfgypCbd8kA/wLq417cML+WeQvLsAG+a5l+Mo7Iwy6caUmZee8NIDPcqg4P5EuzuBXI4JMIHgEriHa329GCvLnbG7D9es7vdSygGquYjj7X2wUvCnP6Yj89tpWJI105bgVMoBeB+yM7+JBJ/kA7yE2rJ/xyOFS9Gzowqnriqzpbju95dcHwqtI+Rv/Pbbb0uRqigzLwVK4Y0JMIFIJTAJD81OhAq9LgeoWjgbD8UC/S5LOByInY0lWY9gh+4TXO38Jeq+loj8+PuldnC8DwZ9H473pEObOhXk/iHlA+x2qGPoo5wPcKxErikobPk5SjM+w991L8PmV5fh24dWYeY4l8LjHB7qQdDekL9xVVWV5G9MmXjJ35gNctCmgxtmAgEiMFb+O8pwrwxx6m6XbIYedT/BjupmJGc9isRYezs9ddizpw49knRBZtGH+QClhNAFSKopwf62z8btbMgaZdaNx507LsAEIpuAFDUvDWc2v4o3ZDcy8yXUvLQFZUkFKFk710N/ZrsBxinU1gMLZ0+3nS9p1DrU1g7apAuJaiwS0tZh93fPYXPxIXRIiVqtMF+pw0vrDyOpfBvW2jPDjD8JlBD6+6gofwhlr9Whyzy25hKSRrm7u3tINyYndNaNx592LsEEIo9AAubl7XPIf/fP0KW/Ad3pLV7lv0PCN5GZnQKoNMgkmYI2SdZYAjhmw3YrH6C71KfgW8/kIU9Xjm1vdsI8xmkhFSWOkpPu379f0o0pFRNn/hhj5vgQE2ACEUkgJK6USaog3Zjc2kg3PnbsGBvkiPy68aCYABMYj0DQjTK5tVHwEtrOnj0rGWZ2cRtv2vg4E2ACkUogaC5xpBuTaxutkSfdmCO4RepXjMfFBJiAJwQCbpRZN/ZkergsE2AC0UYgYPIF68bR9tXi8TIBJuANgYAYZVk3NplMrBt7M0t8DhNgAlFDwK/yhTKxIuvGUfOd4oEyASYwAQJ+McqcgnwCM8KnMgEmENUEfCpfkG5cW1srpWIif2MKqckLQKL6+8WDZwJMwEMCPjPKzc3Nkr8xeVdQ8kRaCML+xh7OBhdnAkwg6glMWL5g3Tjqv0MMgAkwAR8S8Noos27sw1ngqpgAE2ACdgIeyxesG/N3hwkwASbgPwIeGWVZN7506RLrxv6bE66ZCTCBKCbglnxBunF5eTmuX7/OcSqi+MvCQ2cCTMD/BMY0yqQbv/nmm1IKpt27d0Oj0fi/R9wCE2ACTCCKCTiVL0g3pqXR06ZNw6xZsyR/YzbIUfwt4aEzASYQMAKjrpTPnz+PV155BRkZGZJuPHWqPWVKwLrEDTEBJsAEopfAkFFm3Th6vwQ8cibABEKHgCRfUMD5pKQkqVeUiokDzofOBHFPmAATiC4CklFeuHChJFX8zd/8jbRUmlzfeGMCTIAJMIHAExiVzVpeNk1dKSsr46vmwM8Jt8gEmEAUExhllGUWygd+27dvBz/wk8nwKxNgAkzAfwScusRRcxRyk0JvUghOco2jkJzkKscbE2ACTIAJ+I+AS6NMTVLoTQrBSaE4KSRneno6WG/232RwzUyACTABl/KFMzRKtznWm50R4n1MgAkwgYkRGPNK2bFqcpU7dOgQCgoKsH79ehQWFoKWYvPGBJgAE5gYgTvQ16xFTGYN9FYPajLr8V7F6ziiv+PBSS6Kmq+gUZuJmJgYxMSsRY0v6nTR1Fi7PTLKckWsN8sk+JUJMIHgEbDC1HEYuQUfwTLhTtyB/sSrWF33dTT034UQJ5A39/4J1+pNBV4ZZWqI9WZvcPM5TIAJhDaBBEyZPLTQOShd9dooy70lV7ni4mIppOfJkyfx1FNPgbRn3pgAE2ACEyJgNaKrsQK5apIT6E+NpdoatOpNAKwwte7AvOV7YMRJ5Cc9ALW2FXQEuAdjVx20S9X28zKhrWmF3uxCF7FeQU3mHCTlnwSMe7D8r+OG6zLr0VqjxVKp/RjELNWiplUPszwwUyu0aurXflTkJkvtDfdDLuThq/Dx1t7eLhYtWiQKCgrEjRs3fFw7V8cEmEBkErgtdNVrBDTVQmehEf5FdJY/LlQ5VeKC4a5tyJZ+0VKkEcioFJ2DVMgiBlqKhAprRLXuth3LXdHfsEmoVDmi8oJBSFUN9ojqnAVCldcg+qUdzgja21cViZYBeyH5vKE+3BWGC1UiR6USGeUXxCBVM9AiClUQUOWJ6ssDQlg+FbreAWcNuL1vwlfKjr8BjnpzVVUV+zc7QuLPTIAJjE3AdBEnKq8hOzcLaapJtrKxM5GxIQuatg/wkeGe8/NN7di/uRHJu4uwJU0FycDFL0DegTeQfaYE+9s+c37eqL2kV9djx3vpqCrZaO/DJKjSXsCBoxugK6jACcWDQFX29/D0vAQg9m8x92sJo2rzZIfPjTI1rtSbTSaT5N9M8Zl5YwJMgAm4RSBhGUoNnShNu4nWxkYpvntjjRbLk/LhOjKPFabO91FnVGPh7Ok2gyw3Fq9GUrIBdU2/t0sc8gFXrzfR2dQMY/IjWCD/KEhFYxE/KxHJ+Bi6/iERw1UlXu33i1GWe6LUm8+cOSPpzRSRjjcmwASYwNgETLhSkw/15CQsP3ABt6jwlJX4aedb0IxrELtQtnyGXU+269Fx85HfbBy7SeVR62fo6zYo9zi8N6C77zO4UKkdynr2MSCPGWX/ZoqnsWvXLinI0csvvyxlNfGsu1yaCTCBaCBg1b+DLfkdWNnQh0OrHrZf9dLDvWb0AFg4JoQ1qNbVTsylLXY6Zi9UAy6vIeWr8bEM95iddHnQr1fKjq2S3kzxmimeBi3fZr3ZkRB/ZgJMgDwrzP296MF8LF7wZYUM8QUGb9n8K5xTikVC6mPIVl3G+UufjryKNXegYmkiMmuujNzvvCIAU5GaqYGq5yIuGZX6tdy3OUiaFe/y7IkcCKhRpo7KevPZs2elflM8DdabJzKFfC4TCA8CFD/HvRXAsnFtR93hX8MoaQT3YOw4hOLNBzEsQsj6Lo3fis/Nn8OasAQvV6XjzOZX8UaH0WaAaaXeaztRgE0oWTtXYeTH4haLhLR12P3dc9hcfAgdkmG2wnylDi+tP4yk8m1Y66fFJQE3yjIG0ps3b94s+Td/+OGHrDfLYPiVCUQYAYouSXfFdHf85z//2b3RJSzBD0+XIu2DXKjjSBdOwfZfTUfuqZMoVA1XEZuYCW3RAPKTHsSDq/8VvdZJmLmqBG1H03FNm4I48i+evAbvzngOnfWbkBLvgckjr42DDTia/mdo1fchJiYOk1/4A9KPtuH0tjT45zoZ8Cgg0TAK378jvbm8vJz1Zt+j5RqZQNAI0F3w3r17kZOTg3Xr1nFcdjdmImSMMvWVflHJS0OexPz8fEnucGMcXIQJMIEQIkBeVvJD/WeffZYzGHkwNyFllOV+k+5UX18vBdanrCd028MbE2ACoU+AdOP9+/dLoRYomiQ93OfNMwIhaZTlIVAMjbfffluaYPrVpQSvvDEBJhB6BOgut7q6euhCauXKlXyX6+U0eaB6e9nCBE4j/2YKpk+/uGSUKX4z/RLzxgTCjgAF1zliD2yjzsU+2TNgvIFQQJzGelTkZkLb6mqJ8Gdo1aYqFkuoPXD9Gq8D4x8n3Zi8qGgjryq6syUvK968IxDSRlkeEvs3yyT4NTwJ3EJX5YvYpnsM9RYBS9d6XNe+iMouaZ2a6yFR9LL/sQNHGvagoPaGy3LWq7/Cz+u6FMeXIGvJbDddvxSnefiWdGOKCkneU0ePHpW8qTjBsocQnRV3O3RRiBSkyHMHDhyQItE1NDSIzz//PER6xt1gAs4JWHTVQqOMPiZHNxuKiOb8PHmvdD5SRGHLdXmX4pWiqeW4OKYo5sO3n3zyiRQF8sknnxQUFZI33xIIiytl5Y+Jo3/zM888A3Kn440JhCaBO+htP4vm5ETMGvKRtS+O6DmL9t4JpjGSoqnVouy1ctQ0trmOGewDOEp/Y1qVS6tz+UGeD8A6VBF2Rlnuv1JvJv9m0ps5uL5Mh19DhoC1D+3H26FaOBsPjfpva8fx9j43l/06G9Ed6N95E2W0xK2tDPmrlyLpiR1olILAOyvv3T4yxpGlG9vzAaqL0WryR0gh7zjLZ436msgHwuVVqTdTMldaOeTeUs5wGSH3M6wJmA3Q9QDJSWo/rAC7H3PzTkCIuzB0nkZ1oQZo24PVz1Wjy1WWDQ9h0l0o3Y2ybuwhuAkUD3ujTGOX42mcO3dOQrFixQrpl51+4XljApFPYBJUKf+IvNLTMLTsQkbbz3GiY2JZ5umuk+4+6S6UvJ/IC4ruTnnzP4GIMMoyJjLOFE+DbrXol531ZpkMvwaNgBRcHejRGYbzuvmtM5OgWrYJOwvhQTD3kZ2hu0y626S7zsDpxs7kBArTWQx1TOpIV0ApJ55in1c59N63xWdWDt18CTW5yVDnHrQHH1IeDOz7iDLKMrpZs2ZJv+zk28x6s0yFX4NCIHY2lmQtGdW09Vofuo3+cF2Lx6ykJI/lElk3prtM2uiuM3D+xvcjcckKaIzNaOqUr/DtmT+gDCZvzywCDTJTpwJkSDetxvpzX0Wp4a5Nxin9Ks6tz8ATFR2KH0Ej2uo+wtSi8xCWT9H2gzRMUc6IVM8z2IFtaD34wnD6KWWZAL6PSKMs86MVgKdOnZJ+8Vlvlqnwa2AJ2AxOct376Bx6qGSPyatZgSWJ9/u4O2b09yZD+7S7ISoheS/JujHdZdLdZqAXf8QmPoosza3hbB5S5g9gXc630XP8N+iVnsfZDDWyH0NqAnyTQ2+wBzWbZIOcjXlDHjI+nhYPqotooyxzoF981ptlGvwaaAKxc1ehZOtlvLa3RYoNbDW2YO9rl7G1ZBXm2v8DrVcbka/+R1SMt6BE2XlaJfjuL9AlB2G3GtGxrxJtj2UjI2H8f22lbkx3laQb011mUDbpjuIRNNsNsLX3Nzjeo8GGTf8NyT296KcHl6bfo6kOyM78JhLgixx6f0JTZSHya+dj94+yQsIgE/vxZy4oM+T7Rllv9j1TrtFdAlOQsvUnKJ1xFClxMYhb9z6SKn6CrSkjbqKdVGZbPh0nJQu1553LrIF+yIvLioELbyBVivWbjNzKX8H8+Hb8eNnMMf+xHXVjupsMflwZu4TRTL7bn0uZR/6Y/Ri+nfr3yEo+J8kakuQjSxe+yKFnrEfZxa+jMOcydpT+AleHuDqZikDu8u1alPCp7Xe/+52gFUkFBQVCp9OFT8e5p0zASwK0+pVWwS5atEhaFRtyq2Etl0W15lFR2PL/ipbCR4Wm+rKwiOv29xfF5eo1QlXYIgak8dP+FAEnqyJHrIAcaBGFKijOo5NvC131GgH7Kktb+QUir6FPWLxk68vTouZK2fGHjvVmRyL8OZIJKP2Ng6Ubj8tXSlZ6F3XVpaium2mP30G58tLRU1eBPXVX7dIF1eS7HHqSvFT+MGo2/wxtQ7r/uL31W4GoNcoyUdabZRL8GokEQko3HhewzdCivhb1SMTshyZJCmv8rEQkt9WjVpdu87qQ6vFlDr0pSHn+VZQnncBrb3UqvDbG7bBfCkS9USaqjnozhSHkeBp++b5xpQEiEJq68XiDlxOmAirJw8JmnmyeGSpgRPwQAL7MoRe/EM+8tAK6gh/jTU8eto43JC+Oh3SQey/G45NT5FQ2M2bMkFYz8Uomn2DlSgJAgPyNOaVaAED7sQk2ymPAJe2N8gVSzNjnn3+ekz6OwYoPBZ8A3d1x8uHgz8NEe8BGeRyCdOVx8uRJ5ObmoqGhAZzmZhxgfDjgBEg3JmN8/fp1KUNP8N3bAo4gohpkTXmc6SS9mdKj37hxQ4qnwXrzOMD4cMAIkG5cUlIixamgi4XQ8DcO2PAjtiG+UvZwauWn2aw3ewiOi/uMgKwbr169GgcOHEB+fn7Al0X7bDBc0SgCIXilfA/Grjpol6oRE5OM3H3npaWpo3o+Yodj4siY4SSSI1ZAAZCiTCmOx6xFjd797A/00I+uSNasWSNdodCVCl2x8MYEAkGAdGO6W6MoiHT3Fow4FYEYZzS3EWJG2Qpz10Gs2/YxMuv7ICxnkXt9D9ZVKiM+OZkuaU28MnGkXEYFTdajSBwa5T1cfb8RdZSpQd68DAqj0WikeBoUK2DatGkcv1nmya9+IUB3aBs3bpS0Y0pSSnEqOEmpX1AHvdIhcxX0nlAHrHqcKH4HaTs3YZlqEhA7E8u2b0VaZQVOuLyapXB+l3Df0X5YhIAY+ruOlsJ/GpnV19yNYz+biqMDluFyTXlDQWE8ZcB6s6fEuLynBJS6Md2d0V0au2h6SjG8yoeUUZYiQzXPRNKs+GGKCd9EZvbVMXKZfYH/nPUkCh2CsFj1/zdKu9MUoRGtMHWcQmXz23jt9Wo0tup9tnKHrljoyoWuYOgpOF3R0JUNb0zAWwJyfGO6C6O7MYpySHdnvEU+gRAyyvasvyp5eaUS/t2hkH7Kvbb3k6Ca+7BD/jOq6zxmPbd8WLqw6vFO6WEYYURb2Q+wenkGntA2+jT7L+vNo2eH93hOwFE3Ju8fuivjLToIhJBRNqNf9/HopZTezANlEG6cie899pXhEIax85DXZICwGNB56i0UZlAC4M147k3fr3VnvdmbSeNzWDfm7wARCCGj7LsJIRmk8e8ykOos0HesCilPbkRpy2/RUpSMtspT6PBDZCjWm303n5FeE+vGkT7Dno0vhIwy5RabA8hZBjwbh6I0SRcd+DspO4Fit+Nb6SGiFoVQ5gVzLDTxz456My3ZZr154lwjoQbWjSNhFn0/hhAyyvbMA45jlDIM3HJwbXMspPgsSRd/qwjxpzjm+FbKNJw08sGiYxkffZb15hdffFHyb6b07ezf7CO4YVgN68ZhOGkB6nIIGWVACtFnT/0yNH6zAbqeR0a6tg0dHP1mTOnCsbjZgN6UfDw919fJKx0bGv4s680LFiyQ/Jtra2tBV0y8RQcBukuiuyXy0mF/4+iYc09HGVJGGbFzsbbkaXS8dhCtlAzSehWteyvRsXUb1g4Zznu42rgZ6qX70EXJFEdsrqULq7EL777bNbQ60Go8j32vX8RjLy1Bwog6/P9BqTf39/dLK7Sam5v93zC3EDQCdFdEd0eUVZ3ultjfOGhTEfINh5ZRRiziUzahvnQ6jqTch5i4PDQlvYr6rWkOLm8uuJJ0cf4bWJs21UmBm7jwP5+AOi4GMepcVJ7/Lzy+c6ttkYqT0oHYRXpzcXGxdMVEkeh8qzdbYWothjpmLQ61tuGINtO+9DwZuRVNDq6AJuhba+xL22kJeia0Na0OZQJBJPLaoLsguhsif2O6O2J/48ibY5+PyJcJ/7iuiRFob2+XklpSMtcbN25MrDJhEQMtRUIFCGQUiQadLd2kxdAsijK+JjLKL4hBqYUBcbk6T6hUOaLygkFKHGkxtIvKnAUCGZWiczAUUklOEEWQTm9qapLm8/XXX/fBfAZpENxswAnQcmPeQoiAnHEYgDhy5IjwPuOwbJRTRGHLdcUIHbIAS9l+nWTylfar7BmFFafz23EJUHZ0ypT+7LPPcqb0cWlxAUcCISZf+PxGIOwqJL2ZkrlSBDD/6M1K18MvYOp8H3XG+Vi84MsjndYlzxSgR2fw2XL0sJsMDzus1I0LCgpw6NAhjlPhIUMuHqGLRyJhYh31Zv/4Nt/Dtb5eKIPmObIzdvfhmuPzVMdCUf5ZqRt/5zvfkXTjxYsXRzkVHr63BPhK2VtyATqP/Jv9d8U1CQ/NToRqjLGoFs7GQ/wtcUmIvGYovjHd1dDdDd3lcJwKl7j4gBsEvuRGGS4SsQTklO6ncf7Sp9gw9+FhCUPyDweSs9Tueb5ELCPnA6M7F3Jxoww05G/M4TSdc+K9nhNgo+w5s8g6IyEV39+dhmWbX8Ubs/ZiS5oKseZLqHlpC8qSCtC5du6woY6skXs1GtKNKcN5W1sb9u3bB5YpvMLIJ41BgG9Mx4ATHYcSMC9vH9qOpuOaNgVxMTGImfzP0KW/Ad3pLUiJ568IfQ9YN46O/4ZQGCUnTg2FWeA+hDQB0o137NghLe55/vnnOQ1TSM9W+HeO5Yvwn0MegZ8IdHd3Y9euXawb+4kvV+ucABtl51x4bxQTIE+K/fv3s24cxd+BYA6dBcNg0ue2Q4oA6cZVVVX4yle+AvY3DqmpiarOsFGOqunmwboi0NjYKPkb03H2N3ZFifcHggDLF4GgzG2ELAFZNyY/Y/Y3DtlpiqqOsVGOqunmwcoEZN2YFoFQnAr2N5bJ8GuwCbB8EewZ4PYDSkDWjWk5NOnGx44dY4Mc0BngxsYjwEZ5PEJhfdwE/Xv7UXzkCnwTU8gEfWMxltICkxg1Mmv+AJO+cTg4fuZ+NL61FjHqYrT6IUP4RKdCqRufPXuW41RMFCif7xcCLF/4BWuIVGrqRHXuXnTv1vikQ1b9O3hp9WnMaehDy6qHEWu9gpqVm1E3pwr9LaswU/qJfxniBz5pzmeVsG7sM5RcUQAIsFEOAOTIauI+TJ/y4Mh4GNOnYHII3nOxbhxZ37yoGY1j1Hv+HCEEpMwhEJTBRPpTFYmWgU9FS2GKQEaheKs8x5YqStpvEcJiEJ0N5SJHJZ+jEhmF1aJFSiN1W+iq1wzXJdc54pUynPzZVk6uU0J5Vxg6a0VhhsrejxxR3qyzp6LyD2vK1nLgwAEpFVNDQ8MEsrf4p39cKxMYi0AIXt9Eze+hfweasAylV1pQqFJBU30ZFkMJliXYp7vtF2ifWgC9uAtD23NISzChq3Ijnnj3AWzqukspwiAsv8XOuONY/lw1usyTMDfvBCy6amiQgsKW6/Yyl1GtUUFV2IIB0YnSZTMcxkSZx7ciJfUo8FIrBoUFg63L0JO7Glsa/+QjnXtkk6wbj+TBn8KPABvl8JuzifdY9QRyn/4G4jEJqrkPI950EScqryE7Nwtpqkm2+mNnImNDFjRtH+Ajwz3v2rR+jKafNQKFWvxo1TzEU7byeY8jN/s+1PysBb2+efo41DfyrPjwww+lz9/61rc4cNAQGX4TTgRYUw6n2fJXX+mq2tAJmPVobfwVblE7ty7gQH4Z2rAGWV62a+39DY43OwbKn45lpZ2SRuJltS5Po4wfZWVlkAPQHz58WPJB5gD0LpHxgRAkwFfKITgpge+SCVdq8qGenITlBy7YjPKUlfhp51vQ4GPo+s2B79IEWiQjfOrUKaxZswbr169HSUkJKDg9b0wgHAiwUQ6HWfJzH8nVbUt+B1Y29MHyy1LkrVqFVav+AeqB/0CPn9v2Z/UajUZKYjpr1ixMmzYNpDeTxMEbEwhlAmyUQ3l2AtI3K8z9vejBfCxe8GWFq9sXGLxlmlAPYhMfRZYG6NEZMHytfQf6mrWIiVmLGv2dCdXvzskkaeTk5EhBhkhvpiSn58+fd+dULsMEgkKAjXJQsAeo0Xg1kpL/ytbY52aYnT5Yk5OntqPu8K9hlMrcg7HjEIo3H4RxIl2NnYOV2ueQVFaKva1XJW8Lq/HXOFx3ERnl27B27v0Tqd2jc6dOnSrpzRR0qLy8HBs3bpS0Z48q4cJMIAAE2CgHAHLQmpCMYjbu5c9H3IN5ONHr4tY9YQl+eLoUaR/kQh1HtvhjOAAADoFJREFUS6hTsP1X05F76iQKVRPp/SSolhWhvnM9LK8tkvL/xakrYNlQj/qtaUHJks1680Tmk88NBAHO0RcIytxGSBIgffnkyZPIzc3FkSNHpAeDJHfwxgSCSYCvlINJn9sOKgGl3nzp0iVJb6YkqbwxgWAS4CvlYNLntkOKgOzfTJ0if2f2bw6p6YmazrBRjpqp5oG6S4C8M1555RVkZGRg+/btvDLQXXBczicEWL7wCUauJJIIUBaSc+fOSUHwyb+5traW/ZsjaYJDfCxslEN8grh7wSFAejNlJ6EkqhQClPybWW8OzlxEW6ssX0TbjPN4vSJAejP5N1+/fp31Zq8I8knuEmCj7C4pLscEAGk1IOvN/FXwJwGWL/xJl+uOOAKsN0fclIbcgNgoh9yUcIdCnQDrzaE+Q+HdP5Yvwnv+uPchQID15hCYhAjqAhvlCJpMHkpwCbB/c3D5R0rrLF9EykzyOIJOwFFvrqqqYv/moM9K+HWAjXL4zRn3OIQJKPVmk8kk+TdTcH3emIC7BFi+cJcUl2MCXhBQ6s27du3CwoULvaiFT4kmAmyUo2m2eaxBI0B6My0+oSBHL7/8MihFFW9MwBkBli+cUeF9TMDHBEhvPnbsmBRPg5Zvs97sY8ARVB0b5QiaTB5KaBOQ9eazZ89KHaV4Gqw3h/acBaN3LF8Egzq3yQQAKUfg22+/Lb2y3sxfCZkAG2WZBL8ygSARYL05SOBDtFmWL0J0Yrhb0UOA9ebomWt3RspG2R1KXIYJ+JkA681+BhxG1bN8EUaTxV2NHgLk38x6c/TMt3KkbJSVNPg9EwgxAqw3h9iEBKA7LF8EADI3wQS8JcB6s7fkwvc8NsrhO3fc8ygh4Epvvn37dpQQiK5hsnwRXfPNo40AAkq9uaCgAHQ1zVvkEGCjHDlzySOJMgJKvfnZZ5+V4mpEGYKIHC4b5YicVh5UtBAgCePMmTPYu3cvcnJysG7dOkydOjVahh+R42RNOSKnlQcVLQRkvfncuXPSkFesWCHF02C9OXy/AWyUw3fuuOcRSeALGBufR0xMjO0vtxFGN8ZJxnnz5s2SQf7www/xzDPPgOQN3sKPAMsX4Tdn3ONoIGBqhXbeenTvbsWZvHnw9Oqpu7sbFOSI4jez3hxeXxhP5zq8Rse9ZQJhScAKU+f7qDMuQdaS2R4bZBoyZTg5deqUFL95/fr1UvzmmzdvhiWNaOs0G+Vom3EebxgQuInOpmYYv5aG/2PO/RPqLwXUZ715QggDfjIb5YAj5waZwDgEvvgTLjZ0QbX6EXz9S+OUdeMw681uQAqhImyUQ2gyuCtMgAhYP/4I7/0xBc8kDeJ/azPtD/0yoW28AvMEEFFewLKyMklrpnyBhYWFUoD9CVQZoqdaYdY3oaK4Hnqrqy7egb5mLWIya8Yo4+Rcsx7vVbyOI/o7Tg76ZhcbZd9w5FqYgI8IfIFPL3WgGV04dq4f8394GmKwB9U5BpStfhUnfGAMIl9vvomO6h+hoMvXhtMKU8dh5BZ8BIuPZttZNWyUnVHhfUwgaARu4fKFTiCjEqcPvoA01SQgfh5WPklLqa/j5uAXPusZ680+Q+nTitgo+xQnV8YEJkjA9Hs01RmgyV6Jb8XL/55fYPAWeU4kYY56Yg/+HHvnqDdTMtfg+Dd/hlZtKmIyD6K1ow7apWqbbKPORcV7+pGyjVmP1hotlsq+3Eu1qGmVy1A9K7C8rAtozkdSXCq0rZ85Dtv5Z6sRXY0VyFXbfcRj1FiqrUGr3kSiEkytOzBv+R4YcRL5SQ9ArW0FHQHuwdil6HNMJrQ1rdCbXWonztuX9wremAATCBkCFl210CBFFLZcH+6T5bKo1qiEKq9B9FuGd/vj3e9+9zvx5JNPimeffVbodDp/NOGizuuipTBFACqRUdggdIM00LvC0LJLZOBxUd75F9t5gz2iOmeBUOVUiQuGu7YyF6pEjkolMsoviEGplL0uTbXQueR1W+iq1wgMlfmL6Cx/XFGvEMLSL1qKNAIZlaJT6o9FDLQUCRXWiGrdbfs47or+hk1CpcoRlRcMQmpO7qOX8yX/FMs2ml+ZABMIGoE76G0/i2aVBpmpcvyKe7h6qgo7elZid8FjmOnn/1hZb165ciXIv7mkpAQB9W9WbcDOHz2FudJdwiSoUv8eaaqLeO+ja7DS1WpHPXa8l46qko02aQeToEp7AQeOboCuoMJ7zd10EScqryE7N8teL4DYmcjYkAVN2wf4yHDP+bfC1I79mxuRvLsIW9JUNp/y+AXIO/AGss+UYH+bm1fpitr9PMWKlvgtE2AC4xC4jkvnLkKV/RhSE2IBup0+shPrV/87Nhz9MTbMSxjnfN8dlvVm8tiYNm1a8OJpxKuRlAz06Awww+6/nfwIFpDWPrTFIn5WIpLxMXT9XvqnJCxDqaETpWk30drYKI23sUaL5Un5aB5qx/GNvMhHjYWzp49c5CP124C6pt/bJQ7Hc11/ZqPsmg0fYQIBJvBl/J8vl2HrtS34a9JL41Kw7Q9J2Kk7iZJlM0f+0wegZ6Q3U+S5GzdugOJpBE9vtg/W+hn6ug1jjNyA7r7P4J2Sa8KVmnyoJydh+YELuEWtTFmJn3a+Bc24xr4LZctnDMcrkeZuPvKb3YlaMno4PnBNH10p72ECTMAbApOgSlmFbUfoz5vz/XMOhQIl/2YKrk++zYcPHwYF16e4GgHdYqdj9kI10O2qVSdXrK6KOuy36t/BlvwOrGzow6FVD9t/AOnhXjN6aNm6Q/mRH9egWleLvLm+eQjLV8oj6fInJsAEXBAgI0zxNNasWRMcvRlTkZqpgarnIi4ZlRqvFeb+XvRgDpJmxbvo/Vi75fPnY/GCLyvuSMjrxeZf4fzsWCSkPoZs1WWcv/TpyCt0cwcqliYis+bKyP3OKxqxl43yCBz8gQkwgfEIaDQaKZ5G4PXmWCSkrcPu757D5uJD6JAMsxXmK3V4af1hJJVvw1rpajUes5Lm2IdxB2bzeL7dsnFtR93hX8Mo6R/3YOw4hOLNBxWhU2Xtmqq24nPz57AmLMHLVek4s/lVvNFhtBlg8xU0vrYTBdiEkrVzFUZ+PLK242yU3ePEpZgAE1AQCJreTJ4NBxtwNP3P0KrvQ0xMHCa/8AekH23D6W1psF0n34/ElRtRdG8HkuLmYPWJ3vGvVhOW4IenS5H2QS7UceSnnILtv5qO3FMnUagaHnhsYia0RQPIT3oQD67+V/RaJ2HmqhK0HU3HNW0K4khPnrwG7854Dp31m5Ay5Gs+XMd47zie8niE+DgTYALjEpD15hkzZgRHbx63h+FTgI1y+MwV95QJhDyB5uZm7NixA0899RSef/55zhfoxYyxfOEFND6FCTAB5wSCpzc770847mWjHI6zxn1mAiFMwJneTFfQvLlHgOUL9zhxKSbABLwkIOvNdHpVVRXIa4M31wTYKLtmw0eYABPwIQG6Wp49e3bgF534cAyBqIqNciAocxtMgAkwATcJsKbsJiguxgSYABMIBAE2yoGgzG0wASbgBgET9I3F9uD1aq+WKLvRSECKWPU1yIzxIMC+olcckEgBg98yASYQPAIUFOil1acxp6EPLUNBgYLXn2C1zFfKwSLP7TIBJuCEwH2YPuVBj+NFOKkobHexUQ7bqeOOM4FIIXAH+pq1iJMCyttjE6uL0WqiyEAm6FtrhnP2jcp/Z8/tt1SLQxW5UFPsiaFzh/k4lRNMrdCqYxS59qi8rb6h/Htj5gOk7lEdlMtvPypyk6WYynTuwHDT9nf2eM3qXOyTAxeNKmPbwUbZBRjezQSYQKAI3I+5eSdg0VVDgxQUtlyHMJRgWYIZV2peQcb6c3iotAsWIWAxvIqHzm1B0hNvoEuZmLTtF2ifWgC9uAtD23NIo8wtii028VFkaZSZQOSsIYCxuw/X5Mj4UuJaIDvzm0gwX0LNptVYf+6rKDXchaC6S7+Kc+sz8ERFhyKZqxFtdR9hatF5CMunaPtBKv5a0Tb9sNA4lu0AdrcewCty2qgRZYY/jOz58H5+xwSYABMILgFTJ/7Xjg6srPrxUP67WNVivHLgDRTqylF8Qj8c/U31BHKf/gbiKWff3Ift0eIU3Y+djSVZSxQG+B6u9fUC63Kwrucs2nvv2DJWd76POlCOxCke5QNUZX8PT1O6rti/xdyvKdN2DSgM8j7kuZHSi42yYt74LRNgAqFCQL6SdQw8D2BE3j53+3s/EpesgKbZboCtfWg/fhXZG76P5clX7bn9bDkAIeVIvIXOpmYYJ5QP8C6uNe3DC/lnkLy7wO0ci2yU3Z1TLscEmEAACdiuZMfKcjdCdnCjZzYJ4yKOt/fBajZA98d0ZH47DUuyZtoSnEo5AO+zSRc+yQd4CbVl/45HCpeiZ0cVTl1VZktx3WE2yq7Z8BEmwASCRmASHpqdCEV8+VE9US2cjYc8sWCShPEIenSf4CrJFF9LxKz4+6V20N0Hg/43ON6TjszUqYCcD3BUq/IOd/IBkj7+c/zLnp3YndyIza/+P7gqa9dyNU5ePRmSk9N5FxNgAkzAHwTkFE3O8t8ZoOsBkpPUo7XjMbtiM/So+wl2VDcjOetRJMba2+mpw549deiRpAsyiz7MBxg7F2tLCpBUU4L9bZ+N2UM6yEZ5XERcgAkwgaAQSEjF93enOeS/u4Sal7agLKnAi/x3dgOMU6itBxbOnm4zgJJGrUNt7aBNupAG624+QHfIxCI+5fuoKH8IZa/VjfQacXI6G2UnUHgXE2ACoUAgAfPy9jnkv/tn6NLfgO70Fq/y3yHhm8jMTgFU5GEx1TZIu2cGHLNhu5UP0F1OU/CtZ/KQpyvHtjc7Fe50o8/nKHGjmfAeJsAEmEDQCPCVctDQc8NMgAkwgdEE2CiPZsJ7mAATYAJBI8BGOWjouWEmwASYwGgCbJRHM+E9TIAJMIGgEfj/AaCFLkGKIoPAAAAAAElFTkSuQmCC"></p>
</div>
<div class="specification">
<p>The company investigates the different means of transport used by their employees in the past year to travel to work. It was found that the three most common means of transport used to travel to work were public transportation (<em>P </em>), car (<em>C </em>) and bicycle (<em>B </em>).</p>
<p>The company finds that 20 employees travelled by car, 28 travelled by bicycle and 19 travelled by public transportation in the last year.</p>
<p>Some of the information is shown in the Venn diagram.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>There are 54 employees in the company.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <em>a</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <em>b</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the tree diagram to find the probability that an employee encountered traffic and was late for work.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the tree diagram to find the probability that an employee was late for work.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the tree diagram to find the probability that an employee encountered traffic given that they were late for work.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>x</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>y</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of employees who, in the last year, did not travel to work by car, bicycle or public transportation.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n\left( {\left( {C \cup B} \right) \cap P'} \right)"> <mi>n</mi> <mrow> <mo>(</mo> <mrow> <mrow> <mo>(</mo> <mrow> <mi>C</mi> <mo>∪</mo> <mi>B</mi> </mrow> <mo>)</mo> </mrow> <mo>∩</mo> <msup> <mi>P</mi> <mo>′</mo> </msup> </mrow> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em>a</em> = 0.2 <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>b</em> = 0.85 <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.25 × 0.8 <em><strong>(M1)</strong></em></p>
<p><strong>Note</strong>: Award <em><strong>(M1)</strong></em> for a correct product.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.2\,\,\,\left( {\,\frac{1}{5},\,\,\,20\% } \right)"> <mo>=</mo> <mn>0.2</mn> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mspace width="thinmathspace"></mspace> <mfrac> <mn>1</mn> <mn>5</mn> </mfrac> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>20</mn> <mi mathvariant="normal">%</mi> </mrow> <mo>)</mo> </mrow> </math></span> <em><strong>(A1)(G2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.25 × 0.8 + 0.75 × 0.15 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for their (0.25 × 0.8) and (0.75 × 0.15), <em><strong>(M1)</strong></em> for adding two products.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.313\,\,\,\left( {0.3125,\,\,\,\frac{5}{{16}},\,\,\,31.3\% } \right)"> <mo>=</mo> <mn>0.313</mn> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mn>0.3125</mn> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mfrac> <mn>5</mn> <mrow> <mn>16</mn> </mrow> </mfrac> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>31.3</mn> <mi mathvariant="normal">%</mi> </mrow> <mo>)</mo> </mrow> </math></span> <em><strong>(A1)</strong></em><strong>(ft)<em>(G3)</em></strong></p>
<p><strong>Note:</strong> Award the final <em><strong>(A1)</strong></em><strong>(ft)</strong> only if answer does not exceed 1. Follow through from part (b)(i).</p>
<p><strong><em>[3 marks]</em></strong></p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.25 \times 0.8}}{{0.25 \times 0.8 + 0.75 \times 0.15}}"> <mfrac> <mrow> <mn>0.25</mn> <mo>×</mo> <mn>0.8</mn> </mrow> <mrow> <mn>0.25</mn> <mo>×</mo> <mn>0.8</mn> <mo>+</mo> <mn>0.75</mn> <mo>×</mo> <mn>0.15</mn> </mrow> </mfrac> </math></span> <strong><em>(A1)</em>(ft)</strong><strong><em>(A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for a correct numerator (their part (b)(i)), <strong><em>(A1)</em>(ft)</strong> for a correct denominator (their part (b)(ii)). Follow through from parts (b)(i) and (b)(ii).</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.64\,\,\,\left( {\frac{{16}}{{25}},\,\,64{\text{% }}} \right)"> <mo>=</mo> <mn>0.64</mn> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>16</mn> </mrow> <mrow> <mn>25</mn> </mrow> </mfrac> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>64</mn> <mrow> <mtext>% </mtext> </mrow> </mrow> <mo>)</mo> </mrow> </math></span> <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p><strong>Note:</strong> Award final <strong><em>(A1)</em>(ft)</strong> only if answer does not exceed 1.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(<em>x</em> =) 3 <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 Mark]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(<em>y</em> =) 10 <em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Following through from part (c)(i) but only if their <em>x</em> is less than or equal to 13.</p>
<p><em><strong>[1 Mark]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>54 − (10 + 3 + 4 + 2 + 6 + 8 + 13) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for subtracting their correct sum from 54. Follow through from their part (c).</p>
<p>= 8 <em><strong>(A1)</strong></em><strong>(ft)<em>(G2)</em></strong></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> only if their sum does not exceed 54. Follow through from their part (c).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>6 + 8 + 13 <em><strong>(M1)</strong></em></p>
<p><strong>Note</strong>: Award (M1) for summing 6, 8 and 13.</p>
<p>27 <em><strong>(A1)(G2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>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 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>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of the function <em>g </em>(<em>x</em>) = 10<em>x</em> + 40 on the same axes.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAdwAAAGWCAYAAADSYDL/AAAgAElEQVR4Aey9C3Rc1ZEuXGq1Wu+3ZFsIIYxDjGOMsTEGA3HAEK5DGJKQBIZwE5JMhtzcrPmZ/H8m80hWhrmTmcmayZ1hSAghAUIgGOMXxvht45dsy0/Zer8ly7LeUqvVarVarVaff311erdastRdm0hgoGstu1un69SpXVW79jn71P52jGEYBkUpaoGoBaIWiFogaoGoBWbVApZZlR4VHrVA1AJRC0QtELVA1AJsgeiAGw2EqAWiFohaIGqBqAXeBwtEB9z3wcjRS0Qt8KdY4Pe/+z199vP30r133x0UMzw0RNd98jr65XP/HTwW/RK1QNQCV7YFrFe2elHtohaIWuBbf/ktysiZQ1975IvU0z9AuZnpRPGJdOeqVVR2vipqoKgFohb4kFggOuB+SBwVVfPjbYEbbriWPD4fOXq7ecBNtFror77/FNXW1n68DRNtfdQCHyILRKeUP0TOiqr68bVAQlISpSQkUF9fPxvB5/PR+j+uo6985SsfX6NEWx61wIfMAtEB90PmsKi6H08LJCWlkDUhgewuOxtg5zvv0CNf+3NKTEz8eBok2uqoBT6EFogOuB9Cp0VV/vhZICkhgRLwhNvWTy0tLVRRW02333570BA9PT3B79EvUQtELXBlWiA64F6ZfolqFbXABAskp6ZSotVKTqedXvr97+hHP/xR8Pe9u3fTjZ/6FJWVVQSPRb9ELRC1wJVngZgo0tSV55SoRlELTGWBm29eTjarld548w1asGABs/T399Ott95KjY2NtGrVbXTkyFGyWqO1kFPZL3osaoEP2gLRJ9wP2gPR60ctILRAQX4e/fzf/z042OK0f/uXfybf2AilpaRRfX0jPf/rZ4XSomxRC0Qt8H5bIDrgvt8Wj14vaoH3YIETJ07Qn3/tEVqzZhz84syZMvrlL5+nf/v5f1J6ShI9/bOf0dP/+M/U0dH2Hq4QPSVqgagFZtsC0Snl2bZwVH7UAu/RAmXnz5OfiJwOBx0/c4J+9MO/I3WHPDw8zFPIa+5eQz/4m/+PVi5fSTUNDfSdb36D+gcHaffOndGp5fdo9+hpUQvMlgVU/50t+VG5UQtELfAeLfCNb36T/vzPH6EDR47Q34UMthD33PPPU1//AP39j39MGJXjLEQW8tO//+IXVFxcTNu2bX+PV42eFrVA1AKzZYHoE+5sWTYqN2qBP9ECu/fupySblVaHYChDZGV1Nd2xciW9/sYb9OCDD1JrWxutXL6c6hoaKDU1lV743e/oH370I6qpq6Pc3Nw/UYvo6VELRC0wUxaIDrgzZcmonKgF3icLPPrYV8nr8dPGzRvJarHwgHv7XcupoqSBMjNTyTfio9WfuYvW3Hcf/exnP3uftIpeJmqBqAUiWSC6fiCShaK/Ry1whVngqe/9gBYuXsCDrVItxuUntRrIGm+lNzdupL7+KBiGsk/0M2qBK8EC0QH3SvBCVIeoBTQscMfqO6bk9gVLqogKCgr435SM0YNRC0Qt8IFYIFo09YGYPXrRqAVm0gJ+GrNYyco1zTMpNyoraoGoBWbSAtEBdyatGZUVtcAHaAEf1hBFKWqBqAWuWAtEB9wr1jVRxaIWEFogsCwo+oQrtFeULWqBD8gC0QH3AzJ89LJRC8yUBXyBXuyzREsyZsqmUTlRC8yGBaID7mxYNSozaoH30QJWstCIzU9Wn+99vGr0UlELRC2gawHxLbHP56PBwWEi8lFCQiolJk5/6uDgIIEfhJ1LUpOTiSxTj+2m3MGg3tjzM9ym2qGycVJmZmbw3Mu++P3UPzAQPKwrGyAC4XZewU4tiridqanqz8s+PYPDNOzzBI+nJqWTNX5qm4BJR/ZkG0bSe3BgkHz+EP+E0VtbdqjvLVZKTZ/eJpNlJ9qSKSHZFrTR5C86vp8sW9f34eLqT5adnj5tf5js+0h6Dw95yeV0UpzbTw6XkxJTk2csZn0jIzTodgfdEDmuBsjnN18kR+oPk20YUXZIXEEhHf+kJiWRNT4+2I7JX0LjCj0yPUxOmax3ZP8MkcfrDV5SR+8Em40SkTunIcB7ejzjOSUzXFz5/dQ3NEiWwIt+Xdk6/plp3+vkQphK8Ye1xzQ2ne3D04+ak64M565b9zJ5PD66555P0/LlK+nokSN08vRp8o+OkiUujh555BFeilBUVETV1dVktVooJSWNnvif3yJrPPHawEsXL9LI6CjdvnIlrVmzhhDsL774ClksZkddtWoV3XHHHVRWdp727Xs3KHvt2gdo8eJFDFtXXl5ONouVLDaib3zj24yuc+DAATp37hzzL/jkJ+nhhx8mz4if1q17lXVGc5Ts1tZWWv/666wzdL9z9Wq+5sljp6m08hwlJFj5nG9/+9vcsZ977r/5b/DOycujJ554gq3z8ssvB620aNESeuCB+2lgYJB++/xzQdnf+e53WUZZbSUVHT7Menv9Pvr2k9+h9Ph0euP3r1GnvZv1tiXG01NP/eAy2fPnz+f24If/+PnP+XfYG23Eb/X19bRz506yWKzk9/voG9/4BiMMbdu2jWqrqoK6/M3f/R2fu2HTBnI4HPx93rx59Pjjj/P3UNn33nsv3XzzzQRbbdmyhX3p8/mD1zx04ACdDdgbujz11FOc6Pft20fNzc0sLyUlib773e/x9+eff55vfuLj4uiWW2+lu1evJmyavm7duqBN7rvvPlq6dCkdP36cjh05EtT723/5l5SdnU2nT59mH0MgfPT97z/Fsl9//XVqb21l/ttuvZXuCpGtfLls2TKOt1OnTlBR0TG29ygRPfboo2zD4mPFVF5pxpXP6qfvfft7lJCcwHY9X1ZGcUS0dPlyuv/++wl94ZVXXmVbQwEVV9W19bT9rc1Bve+9fw33E6U3dEHu/c53zJg9dOQInT19mvvDgvnz6dFHH+X2hMas0rujo4Ntpfqaamd55Rnaun0nDbq99NIf/kDf/+532ffKhhRPlJaUHvTDhg3ryOUyk/SCBdfQF7/4VU7azz33HPnGhskam0hKdv3FC7Rz2/ag7x955GEqKJhPJSWnaM/e/WSLi+dz/vZHP2G9t2zZSr32Xv6ek5MT7CccVxjvRogW3byIHlz7haDvkSMQVw8+uJYWLlzMsbNh4+usB/RRskPjKtT3//FfP2e5fouPrs6fz7Hc1dFB6zdsCOr9mXs+QyuWr+B8VXz2uMkfT/TUk39FCcnJdPjwfqqtbWK9k5KS6HvfM2P2dy+8QA53P/OvuvsOuuv21ZzMX3311WCOWHXbbXTHXXdxzBYdPRDU+xtf/wvKy8uj02fPctxCOPT+3vf+iiwWC6GNrRc72X6rbl9Nq1ev5riC7/1eIuSIxcuW0to199H58+dpz97tQdkP/dmXadGiRdwXAOMJstgs9M3/+U3ONbv37qXykhKC7xcu+BQ99NBD/AC0Zf0G8rjcLBvnP/DAA0F7W/xW5r/zNjMXVleX08GDRSwb/33ta1/j9qi4gr3nzS0I+njTpvVktzuZX+UrDHwvvvACy4XvlQ2RH5CbFEEP6APZaA/8npKYTt//q79ili1bNpHDYcqeMyeLHnvs65xrkJca6+qC8lV+w3Hkt28++R3KTk1Xl7kyPrEfroSczmHj2WefNTo7L0nYjaamJqO4uFjEC6Zdu3YZdrtdxH/x4kVjX9FBES+YDh48aLS3t4v4ofevf/1rY3R0VMT/7rvvimXbnQ7jnXfeEckFU1FREdtResKmTRukrMaOHTuMPXt2ifnXrV9vjHrGRPx1dXVavt+8ebPR63SIZF+8dMkoPiaLK+j74osvGlU1VSLZ8P2xY8dEvGDat+9dcX9A/CHGpVR0uEgcV1VVVUZGWoa4/5w8WSyOq+HhYWPjxo1StY2SkhL+Jz1hwwZ5zB47dtjYrMG/fv06A/pLqOnCBQN2kdKWLVvE9obvDx+W5SvE7MuvvmKUlp4TqdLd3a3Vj5GTEecScjqcxtatW4zRkREJO+t8oU4mG7n+mWf+U2xD+AZxLqGRsTFjy3p5XElkzhSP+Ak3NdnGT7B40pAQployM2W8kJeVlRF2Kiz0mpA9N12OEQudcY6EwFc439zcW8IPvaWyrRTP7ZTIBU96egpZrTK9wZ+bmycVTfPmzeGnLekJBflziWIxCzH9NLiSBXuk58rvLPGUnSCQC/k2i41SU5LUpcJ+WuNMAIikpLSwfOpH1jvMdKLiU5/Z2Zlks8l0gezc3Lnq1IifmdnZZLFGtjUEYQoPG9NLCa8zpDGLqcecOXOkoikpK4lsPrku+fn5Ytnpabnk88tsAqF5eflEYzL+lIQEGk6Sx+zcuXPF+Qr+yc6W+R6vmQrzCyhV+GQGP2ZlZcltmJ4q9j3Fx/NsicU2/Wue0AuzzjaZ7xNtNsrPny+2YWZaNtmSZX0NGmTnyceH0DbM9vcolvJsW/jjKh/v8qZ5b/9xNclstbu1rZW356trqOPXK7N1najcqAWiFvjTLCC7/Qtc49ChI/zu5U+75JV9Nt4p473lR53wTlAVF8xKW6+QwRa+hE8/yoRCJb/fTx914IuPU98cDCn2/CjGLuogVK3HR7F907VJa8Ctra0kl8s1nawJx1H0hAIVKe3fv1/KygVZhw4dEvOfOHGKfCGVguFO7O3tpb1794ZjmfAbChqkAxf4Nm3aMOH8cH/Ahh1tbeFYgr+hevKNN94I/h3pC4oTmpvrI7EFf4fs0IrI4A9TfMFgXl5ePcUvUx964803xTYc9Hi5aGdqSZcfRTHdpUuXLv9hiiPwJQo3pKQTg80tLbR3726paDpz5ozY3lwIQ14SzkBzQSIK1iTkGfLQ66//QcLKPJWV1VqJVEc2/Lj/gLzfv/HG6zQ4MCTSHX0T/pfS1m3bCHEuIfSbM6dOSViZBzHb3GIWHkpOAr+UThw/xf6X8r/9zttSVpYL/0sI48i2bVslrMzDuVBob+RCnbgSKzEDjLIJ98CFrFbZXD7YMaMYGzt9Kf5k3XUeiFDRjDt6OelNb/o11jOaesvMiHc5IyNjYrXRRJ2VlVomIdJ6h6sr2zBGxO3ExunoJBKyjI6QThxCJuw+G6QTs7i+rg2lOqM/cJWp9AQdvlgwy/u9rk10ZNvISlaLLE7MJloIxbcSQvzp6G6Myfsxrh8Tizp3GenGq47eKJXQicO4WA4AkeKmXHm/R3W6DqklZ7Jz5DErkzczXFpPuDqOQhCMjcmNrzOA+slCFqwJEhLK8H0jcudatBO0LAmgU+uKFuYLtoRWx0MalZtQKxkJ3RJkw42ZNMnAizpxiItIB3NTIXmX0NLD7581G/r9FrIE1lUHjRrmC+wttcnoKF7Fy/uOlk3C6DjVTx6Lj3zSEZTjxEtWoUKIPyErq2aVm4RjWzcX6uiiw6vjSzQUsSUl5J+YGJ2HLHl2Qxux97OUNFilImeEL1o0NSNmjAqJWuCDs0BrWxvduWIFldbUUWYYoJEPTsPolaMWiFoAFpDfMnxM7IU7fxRnSJ8APqxmGRz08EL7D6v+Ur0/Dr4EatiIz09+jSdRqf2uJD68C/2oF8DB3h+LmFV5Vufx/EoKxveoi3jARYJ+8803xFXKXa0dJH2Bjrmc4ydO0YCwMq+nq4vOnTknbnJp+Xmx3qhqXbfuj+IpaKBb9feNQzyGUwodSacoB4habRpFU0eOHAl3+Qm/FRXtp6KiwxOOhftj/4ED4psQ2BBIY1KC3tJEimKfyvJKkWivz0cbNmxgJC7JCWaxV7mElXnOnj0nLvZCUQ6K96QE30sLm7xulwmp6B2H+Qt3ner6amptkRXjYZDD6gQp1dfWiu0NmToxC4QrIE5JCXrrFPrpxCz6sTxm+6m8vFSkNmJ226atVFFRIeJHXJ3SKMiCHtJiL5WvpA8f9fW1WrJffvlFklZjwzfSqmboe+SIvLhOZOgZYop9+umnn5bI8nqHqbj4KNlsCeRyuyg3x1xYDCMARgv/sAg7Li6OjV5RX00Ou53GxsYIMG8gOBpVwOCFUZKTk7lDVFaVUdulDnK7h1gGjsPZ7e3tQdkKgxTJvL6hgTq7OoOyY2JiODl1d3czPzoZsD9xjcrKSrrQ3Ewez0hQNkrSUfGo9FayoR/aA17DSjQnK5sssbGcVDs7O5nf7XZSWloGtwdJsaWlmdzDw/x+ITUtja/Z0tISlA098A4ZyRMQjNAf76vT09P53Q46jJINTNz0DFN2aXklXWq9QENDbvJ6fZSdbS5un8resFVNTQ1dutROI6MeyszIZNnT2bCxsZG6ujr5ndWYMTalL/FOKz4+ntveUNdAFy40k5/8lJacQrb4eOrp6qPunq5gO5UNa+sbqb35IrV1d5M11k9ZWabv0W673c78MB7wsqFfVVUV29DrMyg5KZGPh9oEPlI2hAzI7+7tpDHfGC/KnxxXSjZioKqykvVHWwDZh7iaLDs0ZuGf3t5u8nhHaS5idlJcqZhVcXXxYjO53cNsa+g42d7Khoiryupa6u3rojHfCKUlZ5HVNjGuVMxCf5VcBgaHKM4SQ2np6TQ87KNLl8bjSrWzp6+fqirLaMO6N2ntA5+jjIw5FB9vndBOVIQi3kCI2ebmFhoeHuK4xHG0JzRmlU1gq9raOmptvUCGASCWy2MW/lG+Z70vXqIBRz9Z/BbKzDZxzkNjVtlkeGiIqqrLqenCRbKMGpSYksTxNtmGSjb83tfbRS6Hh2LiLTRnivyDl+SJALDw+qiurJIaLzTS6Ogo+x7xNtmGwbhqaaPGpgbuhyMjIwRQC9BUMQtblZaWsr2QR9AeyEGNSEvrhWB/UDZEv6+urqTu7h4KlR2aC3Et6AfZNdXV1OdykIViGKo1IyM9bFwhZjs7u2l01EvZmZmcr3BNlQshE3GPz9raWmptbaf+ATslxCew3pNzodJF5Svkt5gYC6UkJXG/D+0/k2O2ta2TfUQUwzGBa4bGlZINGdAb+R6y09LSgrkmmAtDYha8zc2NNDjo4nYo8KXQuFLtRPwgFzY3X6AlS5bgklcUyd9aM5psoGAlpBZqcHCA4uIuf1GO2S1eGxhSiQajwEmYRUhJSWFDGIbBL+ZxzOcbB/kGL2RPrnTGcRBeikM+/mFA8/v8QdnoBCB8Kn5TvnkujrndnsuKWIK8hKrPwEW46MbL/CzUP7HSCHK9Xm8QtB08obLR4ZU+4PX7vTQ8jEpbU0dcEzaZTKjcVTYB3qyiUHsrffEbeMfGhon8RKqCcjrZPq+P+Vmm2tstRG/zugE7W6089cw+Zv0DulhMeyu9kHCAkgO9veSlBMbInah3TIxZ8RiqN86PiYnj85RSiAPYEAQ/h9oQ8iE1tGYF9lM2x80Jy8QIgfM5BrzBOAi1SWg78d2LaVkI5jWtfr6JCpWNJBpK4GX+kIMqvqE3viMZg2zcjjHyek074Rh0Bc9kwnGcz/+CVXajE3iVDbEHrsdrIZvNxGm2Ws12ezzuAL//8qputM83bhNcP1RvpQ+u4feb1bjQCX1V0VT8MAb8A+94fOObHkzZj1kHM148kwq+lE1CbQu5Pp+FrDZfEIB/st5q6V8c+WkIfSFAylZEsCH0Go9LsPjI7A+wdyhBD+ULfIIC4cHnhPIi9pXeocf52shPaO+IWY2v8pLiV59wOIqwgYdu5jVTEmRM1+/BMWaMmHEYaAB0hUzYT+UZFByZ/vSSP6TPj8tGFbXJA5kmL2LQzKGqkNSMK9OG0DOU/NicxWILXhO/Tae32Xe8E/oPrhm0RYhgHCeyEp7+QwmyQchNqm+q9obyXVHfpRiRwCR99Y9/NIDdKSHgHZeVnZewMs/hosMGsDslBGzS06fPSliZ5+Tpk2K9gTP629++KMZgPXlSLtvpdBqHDx8W63327Fnj0iUZdrUxNmbs2rNPLHvXrj3Gnn1yfuAuS/GlgUt7/nyZWJd9e/YYsI2E2tsvGufPynBmgQELLGVgO0sIMXvurDyugLts7+2ViOb4O3asSMQLJsS3tK8BYzZtTpqYv6KszEBbJQQb7tqzR8LKPMCtlmLe4oR9++SygQO8frMcIxcxK8VSBkZ3mTCuoPfBd98Vxyz8ePbsaZkNx8aMP77yRzGWMjCJjxXJc0rZubNi3wM//9135f2+pqbOuHChQdROh91u/OIXzxr4lFBpxTnjohAD2syF8riSXH+meKJVypNuf3A3hSmP3NwrE4tzkrrv+U9MveD2MjUw1fieBV3hJ2JqDLMpmLL7qFJbSwutWHk71dXVhd0O8cPefoBY4MlcTVV/2Nszpf5+P/UMDFJKgu0jHbPIs8hBmAG64p9Kp3TUezuoMaX83i7wYTsLzv+oD7bwiZrq/LD5R1ffj4Mv/YFXDhMn3HQtdeXzp6Zjb9jp94e98lsg0NBiodxM+SYKAolXJAvyrHo/f0UqOEtKTXprEf4qv/vdS+JKMV1oRx3YOxRn6MDqnTh+IvgOL3wLidv30ksvRWIL/q4H7TioBb8IG6JwQ0K4Y9SBdsSekaj6lBKg0jxD4+/Yw52HghDoLiUtaMdBD53XkP37P7wmrprVhXbUqYREgYdOjOtAO7pd5vvakFf9YU0P3+DJX0J4p6YDk6cKviSywfP663I40uraaoI/pQTZPJMjOAGzWlrQjlu3iityPcM+LZjbN998U6v/HDggh8U9evSofPUIEelAO2JVitSGiL//+K//K/CMyQK5yCsSQp7SiVmJzJni0RpwUfAjJbwUn1zwFO5cvJyfLcKG4tJtuqDDbEE7ojxjcmFGuDZz0YjGCcwfTuCk3zTcaSJ7ydHpJl0p/J9mQYz0+WxUyz+AAjSLLsLr8F5+9WugHkE+CvukpOF2s8AmWFwlvYKczz+pUDDcmboxSCTPKTa/LrSj3N7h2jTVbzFjMVMdnvIYqvW1SNOIOrnTZkuk0dGQqtcIisXGyDs90LR04haV7LNBXLypgUQ4GzpMJ1OrxToYtjC8DpzZ5MrB6RR+L8dtgL6Txw1XtupdRzpYXF7VGu46sKHObYgubJtOTPLN1mg4bSf+ppMzdKAdieK03vkAChAYvBJCtSOWPknJooXrGyi5FgrXsR9E+hNQMi0TDnujClZCgHa0auAY6iRc1ltjMPdasRpA5kvI1tFFZo1xi/nIK84TwACO1cBSRjYRuocVmlwtPK7l5d9U1fnlv0x9RCenQGedh6zQ1RdTX/29H9Wx33u/iv6Z4nW4EI3S8Kvz83nNVMRLWeIoLTVV/K4wLs4aXCsYSTbm/1EIo9YWRuLHWlqsw8TyoUiE8vmE5GSaF1iLF5HfGkOJiRkUFxdZNtYo22w2+TtiSxwlJ5vrEyPpgbZZrXFi2Qj23NyrKCVF9k4sNi6R5szLJUtM5Dt7+MeWkEQpwg2j4Xtsog37RCJgqfspltJSzWVlkfgTbbGUmzdPVICCpmWkZ4hj1mKJFcegitmMwDrrSHrDFlg/KYlZt9NFLz//Iv0/P3hK1DfRTrzDl9rbZjM3Io+kM363kpUSkhJE9gY/ljNJ37NbrfGUnppEublzJKpwf5DGFaIaS0tgcwnFJydRRqq5fjQi/5iFYq0WcVwlJtgoZ06euP9YrPGUkZ4WUQ0wxMZaCDEobafFEkdZWeZ66kgXiI2N5XwlkY24TkqyUV5efiSx/DtkI4cDGyASQTZyijSuIsmbyd+jVcozac2orKgFPgALtHa00aqbbqbypguUmSobMD4ANaOXjFrgY2+ByI9lARPhPRgKeHwjsulTIJigEEFEKIXv6RG/a9OSTcR64BwJdXT0mMUtwjkJ1ltoE9hQWqwCXWE/IPJICIvqO/plRQWQV1JSQqUlZRLRzMPtFNoEhSpi3wcQyKTvWXV8D5nYK1QKj6kjG0aBTYBqJCHI1va9MGbdLg+NABQgBDgmnE4cV0LZsGFXlwwGEteEbGmhEvilhTDgraqtpRMn5Hts68jW9X1XV9es5CvY++iRQ/JiyZH3kFM0fM8xq9HvYUcJIUZ2794rjhWOK+HexrChTl+T6DtTPOIBd3homLZt20I9dll1Y+fFi9TQcEGkJ96f6ODS9tq76ezZsyLZYCotPReEFIx0ksfjosbG5gnIUeHOATap1CaDg8N0/PjRcOIm/AYIuUudnROOTfeHNY7oxF755unt7Z3UYW+fTtxlx/ejElLY8QDPBlxVKRUXF4s7HqBBa6tlWMq4PsO/OV0iVaA3oEClBP84+7tE7IBA1InZ8vJKccz6/F7G3/LQ5ahVUykHiD9Am0oIN3JFRcUSVua5cOECNTQ0iPl1+oOjr4tahFX7UAArGaZCLppKOd2YPXmyWIz9Dt9LsZRR3NnS2kZ9fX1TqXnZsX5nP507J8+FtbX11N5+8TI5Ux3AoHjy5GnyCvs94BcB1SkhDIqoaMenhJqaLlB7p2w8gTxgv1+JJJ5SxuYFf/zjS5SWkUO52em0Zs19XLzy+uuvMxQZGrd27QM8b45lB2rjgszMbFp7/31cwYAOgKcNGHnJksW0fPkKviPevXdvABKOaPmKlXT9ggWcKI8ePRKEFnviiSfYfhiYGxpqCH5KTk2lBx9Yy3ogmQHwG4VdeXlzac2aNdzZcBc1NDTE+9Dietdffz3fVePJR9Hjjz/OX4EzW1VVwVBhwD390pe+xO91UJKO9qBwKDsjgx74sy8w/7Zt22hw0JR9w/ULaeny5XzNjRvf5IINxOkXv/gwv7sBHmhJyRkes/Aq+YEHHuTjZil9CctDwc7XH/86f3/r7bfJ43bxOzy851i9ejUff+21P7AMtHPNmrspLy+P2xO6TGrt2rW8xg2DTehmCaqdsLfb5WQbpmVkmP4hIsjGPsNo5+233xG0VVC2hei+Nfexj9EWDE5mhaSFHn30q+wHLJXp7rYzbmxubibdf/9a1nvjxo0Mk4c3sIsWXU/Ll69k32OpDHyJIts77riLCgoKeGkBEhRkYz/OBx8023Pq1AmOC+y5mbDcQesAACAASURBVJJiYxtC+O7du6mPN5AYl41ksXPndvYlqjJvvGk5LV60kDv5mTOngnrfvfouyi8o4GUY8AWKPmJjDfrCF77A7cEyipYW4F97aeHChbRy5e3s4307dpHb5+H9P2+44Tq66aabqbmlhZ9O1F7NF1sb6c8ffZxhJ9UyKavNRmvvv599b8ZVJfcf4PcqW+3cuZO2v/0W/f6VPxKW+qB2ApXzk4ucLUl+sngsfBx8v/rVb+ihhx9i3yvZsE9KShJ94Qtf4pqqHZvfIpfXhDUtnH893b5yBWHZyuYt6MfopjZyOR10+513UVZmBt8gqnz74INmzCJRmjY0Y+XrXzf75t69e3mgQHzj/RlyBMiMKxQ7WWj1XXdQQWHhZb4HL85pbWuhI4fMm1LkCdXvEVdtbR1s77S0cd+by4oAyemjFStW0qJFi/jmbfv27XxtdMTbV66k+fPn8zVhWxM6kejRrzxGCck2OnHqDGP1ooo8IclGX/7Sl/lcyMDAh762ePEiuvnmm9n3b731VqAPEn1q4U205ObFXIT2+uuvBfuPyoXVFbVUVlnCesfGjrEf8D4fS3kwm4a4WrzYzIW4OdizZxeNjhk0OjJCCxbM53hrbMSTfQnzwj933HE7twfxWlFxnnXBu/DPf/7POF+hn9TXN6P0ivLz8+nuu+/mnIu2IxeC0B7ELGYB9u/fa65CID/nZRyHjxGzk32vciGqy9PTswkxAdq5eydvRAD++fMX0O23r2Q/bN26JShb9XtcE/7Ee1lg7Svf43rl5dj0BHCkyCmPsez9+w9QT495Yzt37nhcYexRtGABrnl7MK5wXJ2veK6ITylkFWC+fvWrZ4z2S5cmwKU5HS7+GxBqCvoPn4DTO3ay2BgeGQleYtg1Ygw7TX73yGjwOODj3nnnHQOQjaEyIFPxK2b8DvhFQMKFwra53aPjeoRecxjwZPsYzkzJhixACbqcTsPpcivRfG3o/evf/sYYHByccJx1GR42nMMh7RkeNgAfB5g8JXvUM8Z6wF6hNoEwQLxt3bplgt44D3oo+eqiOH7w4EG2o5KN3xTfZNn4e9OmTZfJRjvxWyh0IuTt2LGNdYftFQ27TJ2nlL1ugzE4NKRYub3gwzmOYVfwOI4B2g8whlPq7RqPE5wE/s2bN7JtFD8+cRy+GXaNy8ZxwEYWFRVNaCfzTmHvQceQ8corLxvnyyoMwL2BgrIDdgm9Jnx/+PDBibIRs2gnt3XcViOjo5f7PqA3+9M1bCy7Zalx9uRZviZiZNcuE2oweE2Px1Bxgr6hCL/v23fQOFdzzui1241uu50/O7u7jd7eXqPd0cmf+I7f0M8y0jK4/ygZHrebdXagv7mG1WHuj4CkRFsn+D7QRuj+yCOPGL/51a8MWAzQgevXr5tgE2VDZRclHG0A1OnJkyUT+BUfdFFthz9wfANidmTEQL8BKdkqbpVs/H7s2GFj07oNE2W7zPZBVlB2IK7WrVtnOB2O8eNjY+P2Hh63CXThfHVsYlwFfQPZHo9Sha//zuaJ+Qo/qnayLiHtQb5CX8ZxRWizyp2T9X7llVeMsrKyoN74fYIuo2buxHHkzHd27Jgg2zXq4X6jzlHXBD/6ZUVVzQTZ0Ev1NaULPpGv3n77LWN4aOgyftVWJRu+LykpM+oqKoK8+C0o2zlRBmQ/++yzE2IW12T+QN9UsnEcsJ6wCX5XpHgRK0pvvubQkLFu/XrFdkV9ApBcRGgQAsftHh+gwp0IPnRWKXV32ycYLdx5urKhh1RvBDAGc5UAwumB3yA71Nnh+MGHQJOSw+EQ6w2ZOrKB7XrubKlUFaO9V4jpHLiZQTKREvSW2lDH90jh7777rhiPWkc22hbJ9zkZWUavy8RaRvvsvfL+oBOzGCzmZOXwoCyxeSTZ3//+941//Md/DIrSiSskP3fITVJQyDRfdGRXlVfxgD6NqMsO42ZF2o/he52Y7XR0imOWfa+RC4G33tQkwySGbNx4SUknp0C2jn/ge5d0fHC5jHd27ZjwIBCuDfbe2cuF4a4707+Jp5SviMfxqBJRC3xILIAp7euuvY5aL7VRQqKNp7oam5tpxfLlU7YAxSbHjhXxOuBVt9055RISTLGeOX+Gett66NN33EXpuYHt79pa6TMrVlJpXcOMVCljx06Ho4+eeeaXU+oaPRi1QNQC780C4qIpiMe7AWn1aUdHG79zkaqlU2SDCjS8oJdSa2uLlJX3zJQWLEAo2imtzAOfepcnUQiypRs0o7hFR7ZOpSp0xbsbaYEDBhvoLiXoLbchKhBlhUq4fl9fF/tUogt0lkJpQl64GKytr6e5+bnU0dlGP/3pT+naa66hH//9j6dUA+/a/8dnP0uv/eEN2rl9N61adScdOnpggr3hr0e/+lX6l3/6FzpafIyWLb+Jjhwx33UCl2LE5yds1SchjitsXjENFeQXUH+/k3+Fz+F7KaFvSnMEZOrIRoz0SVc+qJgdkaEq6cZsTVmFuNAPNtTJQcg/2LtXSuHicLIM1CPo9M2qmqrJIqb9G3K7umRFtbCJTiVxpJgNVUo3ZkPPne3vWgOuTuUkjNnWJh/oWlvlCbrX3kstLXL+ttaOCckrnFE7O1tp69at4Vgm/IZ2ejyyzoGiCLMoYIKIaf9A8DpcsgpbS7xFXglJRAcPHqTq6vJprz35BxRoIJAlhA3P7XYzYUv4IVtaTerzDWsNitu376aLF2UV07B3a6t8aRWS13RUX19N8+ZdRRlZWfSDH/yAUJyGYpDJBJt+++tfp4JFhfSH135PzzzzDH3xoYfo8a8+TkND40ss/uZH/y8nKBTs/PznP6dnn3ue/uzzn+MiMtjba8NGqpOlT/032hnOl3nz83kzdpwNvsrK0qkFTXEUiRFVuVLSkY0K6O3btklFs95DwphFO3UGgJqmJoLdJQTZKCSU0v79+6m+vkLKrpULdQZFKNAkXGkCXthPuoQMNxWvvPJHcRsRs1J7QyiKvq5E0hpwpXBwaCiq1XRgvsTZImBFLV1Qwjmm1VRNX8kGIgiVoPuEXlwKZGfawxZ6asTvXjmMLcsCCpeUdGA9TahBqTJ60I6AprP4J24cP10bAO3oEy6tmU6GOt7a0kZ4UsxMT+eq4czA9K/6XX2+/dZmOnTsGD3x5W+pQ/T41x+n9s5OWr9pPR/DNPJLL75C33riCa6cxsFP3/MZrkj95XPPmee5UGIcFBH2C9wYbsC99qqrqadvfBZBB0sZNtQjecwColMHfperxYU3IbCHTr4yDDnOKaqSR8fk/Hr2gy+lfceUrOOj2YJ2BBqUTe56XZNwRbf2Se/DCcIuqq8JnKoDkq3Kz6VXEud+P6bafIDgFZNfFyNXiNULBXQ6KidGodbSgTlUnE7Asy66Tgq9WJjvJui5rPf5LaNaCQbYu16LLCFBD6sGVm84bPGG+mYqLCgItnq6m5VX/riOeVbdeVuQF0tbADOI5TSgPVt38+eyW28N8qSnplJ+YSFt27yZ+KYC66qEg0tQyDRfCgoKqadrfB2ouK9NI2+mDvss8mlzdU3pNDsPijqg/rHyGwsM5haNvgPsZR3SwiT2+7Qw7rEsT0q6OV8qV5tvVh+utLWZcIJW0RSm/RCY+BeJ1B20hBeywC/lZX6vl7CmUUJasv1+8ni9nPBmXDYRT50imUoJ72ax+4WE4B+pbMgFzYZsyNWxuU4bWWkkJOEowHqAV8APXraJIL4jtRHreB966CH6i7/4C5a5/KabKK8gn3bs2MV/8/l+P92wYAENOBzUM+nd5Cfmz6c+h4P6+/rosSeeoC3r11PTxYuUn5cXPP/zn/8c7dy5m+oaGujeu+6ic3U1lJ0aeS9VeN4fIa4woA8E3vNqxZWmDXVko+HYeg1rZyXEspEjBL6HPK2Y1cxXEn0VD/fNWKxFjZxnWe8IvlRy8cm+19DdN+wja6JQj1n0PXyD9eiyTEjkHfGTTZg3Q+0z29+l+rMeSObSIACflBfCdXiZXzjYasvG5gUaA6Ku3jqyWXeNoNGRjYFWOthCDx3ZujbX0QOypQk0qIcw4c5UzCJhNrc208JFC1ld/s+GzSUmdjfAQg65XZSdmzvOF/iWlJnK3/oHBsjR2cv2t01KwEpeV08XA2PYhOkIWkSyOTYHUcVPOr7XtaGObBhEOtgyL/qx0Pfg1+nLOrzsSI3/uG9O8nW40yP5MvRc9r2ObOFgi2vMpu8he2LvCW3V5d+vxMEWWorbgLtFIPeoTnh5EyceAZpItRSCz+/nCmhUCkqop6tHqyK3tLRcrHdLfTM99/zz4s3WgbgktQnad+qUfNN3VO92dIy/SwtnG9wBhqJKhePFb9t37mR0mEh86vcTR46SV1iAgkpfQMhJCXrr+L68VlYEhZh96aWXxAUUfR098phlPOqpfe+P9VNPawctXbJ0ggnc7olThXHkp7hp9oF295t9gRMNHtKANjVBGp7IzCM+r5+GvD5x4Rn6ZSSc4ey8XGpra+WnPqACSQkV10BVk9LRo3I40uPHjxA2Z5fSoSNHxDaBPXT0BiSlOGb7eoLIe5F0x83aH/7wB3F+Q+5BDpKSxPdKlspX0noZVEtHiislG3r/x3/8lzh3Qm8pJjpyoU7MKp3ej0/ZXAERjY6MUX1zI1deupxuKig0t1WCgZEU0EhAs+E7psEam1vI63FRSkoaw/WhMTAy+PAPd9DYIgzf0UnbO3vJaq1nyLLMzExeJoJqRyQa0NzAUwBAw4Gn2t3ZTamp6TS/sJDvYpVs8EIHyIBsJH9US48FihaUbFXxBh7AI4JQZdfR30MZaSnU2t7CukAWAs/tdjN8G7bXy87OZv7mxhbq7Ozm+xZMQ+fNncvXxNIFQPEpPZRN2jo6eXlAZlo2zf9EIf8O2RgYoAf41JZSkH2ps5tcLjcBuy+vwNQR9lZbtmVnZJM13tSvu7eXZTc359GcefMoOTGRbeh0uYK6KNkIXOhnS7CxLdW7RpYdsHdaSgpvsYZlSb12OzW3tVJm81y65qqrKDE5eYIvQ9sJGbC5y+WgpISkYJzAtmo6CxW7Sr9L7e3U2trMW4bl5edzkRFs4vQ6yeozfQ974xqQjX+Ozm5qTUhgiEDlN0DkYXM4bOGFuMISks72dn4yRGwgJjOzs9mXsDcINg/GbH8/1bc2k8NupwToXVDA18S5uNGAvZKwJWQgZtHGixcvUYI1iTDg5c7N5msirvDPEzJtxzJcHhpOGeRYV7LHDIPScjMJVfRoM/QGQXZHby/l5eSQz++jwquvof2u/Zxw1B0y+k/PQD+3zxIYinFeSmo6YXs3M2ZRKW7leFG+b6yv5+V6gCQFIfZhB9V/lC+zMnKosrqW4uMTuXK7ubGR7Y3fYVv0TXwHKdnox0i6eLcNW6npb/gMvLgOtoZLDMQm8JxRNYuB7uqrrw4eh/0m9wcUoXk8XrJZbAyhyf2eiNr62jhO0CfwtBzMKQ0t1IVlXo0tNOfaHEpPzmaZXQNd43GFfGWxUEdXF9vc4bCznoCBBKmq5VC98R3tBMxkRkoW5ebNpdxcU/ZkG6LNeBfe2tZKnZ3tlJSUwDkFssHr9rtZF/gSW9pBdkd3K1kTLOR0uAi5DpCfyt6q36elpbGtIAN5FrkQa7wL8/P5NRuOewMVkchXwVzY0katLa0mHK3FFoxZ5AjEVWg7UUXcEchXsCkgcdGe0HwFe0M2CDkZ8afqGlRcwYZKb9U3IQMxMWdOBn9abAmUnpw4rWzAfcLeAz0DfC3AVYJUXOG78r1naIg6urv5N2a6wv4TD7jE1Z4WcrmcFB8fRz5/HgerWhOJCj81iLo9XnK7HFypjCBGggGhI/X39zG+Lfl93DlGR0fJ2T9AY6PDjDkLp4OQFNGpgWmMWSE14GLgA9ar3+8hp9PFmwyg03jcXurpM5d0IEAQCAiQrp4exvB1Op0T7nYx6EAuNoZWAy6u6XTYmR/v1FTHc7s91NXVwXrbrOMDbv8AZHsJslXSge7o6IpUQPrIT3b7ANuk39lDhVTILLgmkg4IRQdKjsvtJJ/HTR6rhZweJ+WRuino4mpKFPhwAMebNy19PV1k8Vl5jeq8efOCsqEL2ogbDiXb4XByG0dGRrm9FPCP3e7gQjdUUqMDIjGigKO318GJf6C/j3xzrmLZ8FN3d2+wAGNctp2we43X6yOnCwnf7BzdvXb2MZ9MfkpOzOcO3t/XQ7GxidTb2x3UDzFm73Wyf9BOJBj40uvxEuLJ7feR3eGkAtOEHAewI/wJnFz4PyYmhnr6gFWLuHPye3lcO9Te+FslDfC4ECPko/6+/pCY9VB/v2lzVINiwAUhjkG9TjulZmJLvGzyeb3sy5OlZxkP3Olysw1xTQ+eRr2IAQfNyy/gMjuX00W33XIbvVz+ClWWV9Ltd9zOMusb68ntctGyBx8gl8NNt929mp7/7W+pFPjSgRn19NRc6m1po1tvuYUTM2arHY5eImOMZbAN7U72T2JictC2A4MD5PX6OWahFwi2RQyiD8Pe6Me52bnUfvEiFeTnMc51l8NF8+aNMC/6cWjfVL7ndrIf/OS09wYHXOQIJTshKcmMK5+P/QZ/wZY5OTnB46YuE2PW7XVxfnB5XTQwgF3ITOc7Op3sYxSOzZkzxxxw/X7qc5i+7xjsoxxPDlEyEXKNvd1JhjHCfYJvnDl3uNkew8OIr/ElTfg+PDwUqF72UyJidsTP+hqxsdTr6KZUnvo3bwhD+4MaAJA37XY7xzrkod/A3ohjl8vL9s7NnRvc+7i7w0F+r4WcAw6+wYB/3G4ny8CEJPyDQRR9Ez5GnvXiBsjuCBbpwQ8qLwPLXuVCzlc+H9vR48WSpmx+iOgI5kIUgpntRF5zOAbI6/MzPwZ99CszF5qxYrNZggOu0+Hg36xWP3k8bo4r/Id4B0HvuXPzTf9w7ugmr9tL3d3dVMgPE4nBvqliReVO5HnErIPclIy4Cgy4sKcqzAUv9EMtuLmTU1CFK+uLFLoKuJUvv/yyGOoL2LEVFVUi8YDgA8YnoMEk1N3ZaZw5UyJhZZ6yc2VivQFf+Zvf/HoCzmy4C50sOS+WDRsCq1dK58+XGRcvyCEV9x18Vyra2LFjh7Fvzz4xPyASAfUmoYb2JrHvIQ+ygfsqIUDNnas4J2FlfV988UXGdpacAFjPsnPnJazMU1x8ckr40mefedZ48sknJ8gBrvJ9n713wjH8cfHiBSMhIcH4zYsvBn/buG4dHzt97jQfAx5wTk6O8U8hcIuVdZXMs2nLFqOmpsbIysoRx2FZ2XnG/w5ecIovT37nSeMf/+lfuB/s2rMniEU9BeuEQ1UVNYxLPOFgmD+Acy4lYCmv37xBys5xFYoXHe7E9s5OA3aRUlHRQXm+6u42AKUqIeRC5NmKigoJu2G3Ozl3ipgNg/vCxUuynIJ8jHZK+z1yJ/5JyO50Gc88859T9p+pzgc+e9MFmezRsTH2/VRyPuhjWlXKV9atwuxogzs5bAGXNyc/YmHJ7Gjw/kjFkyXmEvAkM+OkUUU849eeJBDTXJjGxN3v+0U//OEPKSMji37yk38IXvLGG26gnKuuokMhu1SpH3/2r/9K6159ld49+C5PRT/6hS/T2gcepP/zf34aLPrBzjXf+vrXaf/hI3RNwdX05JNPUoLVSr9/7TWesrx9+UqquTBzG9D/5Kc/Jbezn/7zCoJ37O/pJ4/PE5yRUvb7qH1iqjQhJYkyBRXnH9a240kf7cTsIp74Py708Wmp0KOYqlFT4MJTPpRsmbMx0CpLaFSGqlNm6/OD8GVldSV97SuPcJPaWtroD2+8xrUILrudnnvuOfra174WnIoD00/+4R8oP28uff7PvkB4d/6Dv/17euxRc4s4ZRdsg/bamxvp+//7u1ws9dXHvkpPff8pTlZYHhdvQ1GVHIBFyZ3uMzc7m041yuFTp5Mzk8enAw+ZyWtcCbLUK64rQZfZ0gGD7AfRN2erPWK5Oo/Y69atjzgVpeRVVpbzdkrq70ifOlOt5lZaxyKJDP6O6RzptAimwtdrbO2Edjodsqlw8GF7PilBNqY5JYT2bdkil71nzx6jtFQ2NYvrT95WMJxOmPatqakLxzLht107domnljDNVVVeM+H8cH9s3rzZaGiQ7bwCe58+fTacuAm/YUp5Klp4/fVG0bGiCT9hGu/YNPwTGAN/wDehW5FNxaOOoT9kZGTxNo/qWLhPtBM7BoWjV15+xVi79gHWQSdmoQv6kJR0YrauocHYuPktqWjuD9LXVLAH7CKlXXv2iafw4UdsLSelt956W0sXvI6T0tmzZ7Vk79snf00F+0n7PXIEXvdICbLFuXBkRCsXSnWYCT5V9CgaoPGSXhU1RToBfCg4kJLHq3d3HvpiPtI1fL4YLnaIxIffoTeKQqQEflSSSgh8KDqQEgqPUGwlIdwxwj9SQmUiihakpKM3bDIyIvc9iovMKmOBNnHxNOxB0YyMUBEJfSQEPrcGTJ7XO14couT39A/QwMAgFaqKrsAPKKhyOeV4ulKdIR68eL6VRQrQzmInFBAq3UM/8woLqG/QLAxzueQxC110dNeJK4vXT8NDct+bRWEyiDksfUF/k9LIsDyusNJCJxeCFz6Sko7eKIYyjBipaJoqxqc7GTrrtNOpgbeuE1OonlQFgdPp+kEd1xpwdZTEa7yYGDn82XTQd1Ne02chyzTrF6fi9/tHyaaxgHsqGeGPSWfmsUQjvKTQX8GLnWAkhITB2LES5sACbIsMsIclwp9SUssApPyoGpXqbhkdIatNjtQl1UHxWQNrW9Xf4T6nsokLVdRuF+XkmdXZwfN1HE+6OOREfosVq8dEhMrOSO/N5uVkkaPdwZXXRPIbM5ECE5jksr1WLwGqU0qoKo+zmFXbknN0MIan8v1018CSMr9P3vHBiapeKaHSW0rgVUskJefoQDtCZ60w1+jGOvZGu8Q38BIjzCCPPHqJ6JZblnEBiuT6KN3WeQqdPz+wxkMgPGtOBpFVHmSFhQVc/i4ZCFBgs2zZMoEWJkteXj4lJMjMCD7g5EoJZfRYKyshtG3JErls6JGRkSYRzTw333xTxCSthGG5EnSX0k033SyWHW9LpFwN2fBlVlaWSBXonJ0pf5orLDTXa4YKb2lrpoULF1LiJFQpxJVaZhbKP933OXOyxDZJsNnIaiOadMnpRNPcubm89GdaBl5bO5c8wwM0asTQzTevDMc64Tcs74k0mIeecNNNctlXZVxFS5fIB6Lly1eSIRwBELNZWfL+cOONN0a0oWon7FG4QJ7fbrr5Zq2+uWBBCKKZuug0n4WFC7T8s3Dh9dNIuvwwcqF0IwUsPcOSOClBNtYxSwj21olZicyZ4olWKc+UJaNyohYgYmQroIm98MIL75s9AKyw4qbl1HChaUarsVMTE+lie/uEAq/3rVHRC0Ut8BG0gHieA3PoKOOWzqVjeQ3en0kIi8l13rUN+UbEsnF9yMY5EgIyCmDbpHBmOnrDdkCBkRJkw44SMhfky2WXVVdTvQb8oo7ew0NDWv6B7FmJK5+PIUMVYlAkO+rELGRN5fuW5ma64frLnwrQPvBLyfS9bBYHKGeYy5PaUBpXQItyuQFWI48ryNZpp47s5pYWrT2fZyuu4EMd2b4RjXzFMLdnxEhJnFOAGiacc5X6Hm1k2Rq+R/+R5ivoAajOwUHZjBLrPSSrC9HVW9onZ4JPPOAOD/toy5YNQbizSBdvb79INTUNkdj4d4BvHy46LO7Yjo5uOnnypEg2mE6fPk3OHlnBCgqmgL0sHXCLi4+JbTI4OKyF8Xnu3FkC/J2I4ogOHNgvYgVTe0sz1Tc3i/n37t0tTuh4KhLjaBPRwYMHxUkaa6TLy+UbopeXV/K6aklDOzs7tWTD94DxDKXisydp0Y03hh7i7xj0jxUVXXZ8ugPnzpWSw2Eip03Ho477PF5GPJMOuNXVdXSppV2dPu3ngkWLqLm+mXbvN7cHnJYx5IeGhgbCPynt1ZDd0dZCVTV1UtG0e7c8Zju7u7ViFli9ajelSAr12O109uzZSGz8u9fvp9rackZLkpwACMbTxQeD67UjnVNZWUmIcwmpfCWNq9raWnG+Qh3j6dNnyeeTPVAgnzRdlOVC1APt3rtX0sT3nUc8pYw7jPXr11Fubh6lpaXQ6tWr+V3Ahk1bgi/K7/nMnZSdPZeBuquqKig21qC0jDl09+q7mBcg9XA2bsYWLJjP70pxp1hUVMTVbXFxibRs2VJ+14W72WCQ+v30la98hY1z9lwpNdRV8XfAlq1Zs4Zlnzt3jhoa6hiyDdCGd9xxB29AcODwburvH6LExDi6ZcktVHj9fB4gDx4uolhjjIyYWPrKVx5meeXl5Qy6j5f/KKB44IEHGPqvsrqaKsrOU3xMMiVlJdD9993P/Lu37ab+oX6KS4ynRYXX0+JlSwhYntv37KGx0RHmv/dz9/A0H7BoyysraXCwn5KTM2ntvfdSQmoy1VbWU3ltOQEPd8yIoa9+2Vx/uX/3Xuob6OP9WfMK87k9uOibG98IQM1Z6M5Vt/HCcSTzomNFNDw0QqmpyfTpT3+apwEB+nDy9GkyxkbZLg8/bLbz0JGj1NHWStjQO3NuJq1Zcx+3Z/PmjVzBGBNj0PLlK9gPgMYsPlZMQ0OwYTzdc889LLu0vJJq66spbnSMxuLj6IsPPhT0cWtrC18vIyuH7ltzN8veseMdApSkYYzRpz51I7/Lhu8PHy6ioaF+SkxMpVtvvZXX5p0vKzOTdgBOVF0TPm5sbOaCEvj+/vtNPxw6tJ96ueLRQp/8xLWEd8KIVwzk0Ds+Pp6WLFnCeLDA7T1//jzFxsayLnfccRfbEMni/PkSjk1A/qm4OnXqDF1sv0AxowZd94lPcMyiAvLQoSM0MNBHMXHxtGTRIm5Pa1sbAeDi33/xC35vvGKFacOasgqqPMNyYAAAIABJREFUqKtjvePi4+mBtWZcIYkArxiUk5NFd682bbV//27q6Rsgq89CN9x0A+sOW+GGKibG1FvZsLm1hfbu3k8/+eEP6dnfPEtr1z7I/sHGF01NF2lsbJhti1gG7d69lwYGegh97dprr6Xly5dzYdTW7dv5d/x3b8DHjz76KC2Yfz0tXrKYkpPj6J57P0fpqcmMfYwbGfQTwIaquDpw4AAPFLB3Vk4O3b16NcvcuPFNjlkU7Ny26jYqyC/gm+sD+/czTnVcfCLd85lVnDswi4YZJhDaqmQfOXqEOtt7GcoP2MXK94hZlGdjBQBiFpi/yveAgExOHo8rHMcGLHjHh4raBx80/VBSUkL19bWsI94TKlvhJhMV9KBFCxfR4sWLuPp1+87dNDoyzHG1eOFiWrh4Ia+C2LpjK+fC0ZERuv/+tewHxBs2F4CdgC1+/9r7+fpH0Z7uXpZ9/YLraenSJeyH3fsP0OBAP8XHJ9P8+QUcb5g1OX3uHPPiv1tuuYUx5Ctrq6mmpILGYmMpLSGB7r5/Decr9JOmJvOmB+8+kQsxA7b/8F4a6O/ndqItqONA7jh8+DChz4NUXEHvyspSGh4eJcTs//jsZzmPlVfWUm1tJfNmZaQFc8f+A4eoB/C38Ym0YH4h6w1779u3j3mR8z/5yeu4b7KPjx4lrExBXr7nnnvZVugLldXlFDdqUGxiPG9viQ555Ljp+5iYEcqdW8jjCYRi7GHMDD/Rtddew/43c8phftJ+7LHH+NpX0n9aA+6rr75M99//AGFAU8g9PT0dZFay+Sg7Yy6D6WNaAQ4DhiiCQ/HCGLzjjN9LSUlpE44fO3qUlt58cxBTFTKAUQyMVNwNqcXgmK7EYNx+qZ2WrbqV0m2pjAgF56pScHQohcOJa+JJEZtqK4B0c8qhh4HdsTl5frZZ4IPjVVVVdPJkMX3xoa9Qbm4m3zkq2X6bn6xeS3A7tb7BATpbXEzz5y8I2gSFol0KrN3qo9xUc0MHbMXW29XBuwUhmaempzMWtdlOPH2b2xmqjRFwzdOnz1HOnCzuXMqGanoUVXi4uUFboTf4kZAxeIIXxzEr4XR2cQUweJQNwfvuuwcpKclKq1Z9OugHyAYfzkVRA2MpK9m799Jda1dTdqA9Q0MD5A4sK5osu762kTxeNw8USm/4Af6BbIUzq/TGwIjBVqHOYJAEfmwwrgLthK0AHA/MWhTwhco2wdqxKUZGEAgeGy9s2b6Nli1ZyskF7YEMzGLwDIbFwkAT6nhtfSM5Hb20ZMnSoA3xFOMNwRwOjSs84S5etJiwWQRk4AZnxfLldOTEccpKywjaEH64dAm76NTSqlV3BmWbcWUuQbNaEigz2wSCN31/kmP2qquv5o0eYCvYUPkn1IbnS87QZz/3OSopOU8FALAPAZlXyUbhHUNGefk5ysiaMyGugD+Lvga7qLj667/+a0Lx1ic/eSPde+89vLEERhTY0OG2k9VvY31C4wo3p6jKxQ2O8g/iykseslFC0Cbjvj9M99zzGUpNSud+DFu5XOasAXiCsgeG6FzpSepq66O1D64NysYMA/gwVadiFn0QAwsGzNWr7w5umAA+tB8U2n9UXAHPG75XPu7pAa+HbRLMV34/YctE9DUM8DnAb04GljYwfNs4ZmF/yMAnZPMGHS3NtGzZLUHZuFkzY5YowZbE+QAyoPeWrdtp6dJFdP2CRZSanswynLykDKsc/BzjKmYx41NaWkqrPvNpSk9O5ZxixpU5Vat0wcDVPzBE5eVnGQUNNyaQAZvAP+ADqbiCH3p7OwiD96fvvNPMV1Yrmf1eLYcb32wFetfW11KSNYkfapTvMbjyBjR+L6WkZQVjGce3bNtCDz/0cEi/D+QUix9l90H8b7QHD185GTlcfKZkm2MPYtZCKRhP0s0NINBn9+/dTY8+euUNuCRdzAtgBeAXu91u0SngAwaslLq72w33KJBEIxNkR1q4HyoFvG63DAcYi6vffvttY2xMpgtkS0E1wIcF31Iy9ZbZGzKlC8PBC9CGYyeLpaoYl3ovGaMemU10/QO9pTbUkQ194UspEIOObBhusn8OHz5sLFhw/ZRtcY+MGvbe8GAToc6YLDv0t8nfq2qqjDlZOUZvBDALdZ6912G4XC7157Sf//rP/2z8+O//Xiuu0OelYBO4sE7MAhP93YNy7GUd2bq+Rz+ejZiFTfbs2WHU1cnAXaC3bk6R+B56oH2woazXG+x3h0eW850ut7Fh/XpxrDicTjGvMTZmNF24MG1cf5A/iJ9w+fYn+l/UAlELTGuB37/0Em3dto3efvvtaXlm4wdMZa9cvoKqGhooM9V82pqJ67z0wgt0/NQprryeCXlRGVELfNwtIC6agqFOnToRnJKJZDhssYU9DKWE6TYpYQoE+25KCe8UpYQpFs+QfDE+2olpIwmBD+/WpATZmE6REPTGu0kpAfkIW+9JCbJxDQlBZ+guJdhEx4ZdXXgdICP1mkHCDZ1bWlolrMwzOQbxGgVTdVMRpjJ1YhwxK7U3pguBo3z5FvVTaYJ9RGUxmzkvl1paW7RiFr5R07ZTX33iUZ3+AHv4hmUxiKsgZqVxhZjViStMnev0TZ0c5BnWQ+uaHIcTLTzxL/Aif0qpqsasl5HwI66kNoQvdfumjr11cqGkbTPFozXglpZWTtgvMpwScCo2fpdSa6t8cO6191JLizyht7W2iZMX3sO9vv41qdocvB6PLAkgwCorq7Vkh+7PGe5EvIPRqd7dtn07lZ0/E07khN+gt3QAwDtSacfDRSBb2vl8MbHU1iq/2XrzzTepulpmc8Rsi8aNwuTBubqxmRZPAz4CP6LgS0qwn9Te2CMa+4VKCe2UwJfOycyhpupmrZi127vFOQL6lpfLfANe7BP82qbXpc1kvbEvsoRga52bxIa6GpENcW3I7u6WrZIA/9vb3iQUnUqppUWeZzt6sLG8PHdeaLggVYPsdqdYNm7Knv/l82LZ6A/Yr1pKOnlWKnMm+LQGXB24LDw86UA76sg2QWPlT6H+Wd/+STbgwmGoVpQSP4AKkXLQqVXhg1i+3IQsUgd+UwcmD7zSwSVudIQsVhniDJT2W4irsaU2sUnxEQMbwYfKbawvpdW3m5XGocfVd6ErmR11I1IC3rZOR8YG3xJ7Z+fmUr/TrgWTpwMFaLZPHoRWi1X8FK9kY9P52SAdPGL0S7VRukQXn98SWIkg4QaPDOkOnBavV0+2RiCijToxTvJubBpCKpxhbqW2e3/55J6CW4EfJ6Tk5GQaHBwQchMBWk1KqKSz2YQwbH4/ATFHSugcCSnySEhMxDszmRkhOz5eDkoO2TLJgPWz8HIjaTuTklK02pkCmwgDHu2MidHAsI2PpQQhPvJoXDzFx8tvWrLTM8kvDFssxfAlyZ6IYOeEhPGYxQDW2tJFCxYumNIFHFch/FMyhRyM13gXayVgi8uHXPgGfSgSpWSkBeIvMq+SZbOZ1fbq70ifKSnCfozBwkqUmGxWckeSi99N2fJYge5SSktLE9/gIjaQD6WUmZ6u1X8QW1JK1pQdGuORrmHmwkhc5u/QOS1J7nsd2X6LResmUabxzHBpFU1hKiolJZMSZ3UjgJlpWFRK1ALvpwVOnDpF/+vJJ7Xeo8+Ufrwc6a4V1FDWQKnpqTMllvoHh+iTN1xDp46foflT4EbP2IWigqIWmGELYMpaLe+aYdF/kjj5bTEDmueKB1sUKwwOyKC4MHs2OCDf7oplC4uJYB28bJcWT4APNxaMgCAwLWRLpucgCnw6BSU6eqMASkc2eKVIOdAd/Fg8L6EhDVjPoGxhQZaW7/1+9qWO76WFGdA71PdnT56mcEDv8L2ubKyFlJLfiW0iZdxmXEWWjYrnRL+N2jTqKyBbp506MQu5/X0Tkb3CtZhjdjbiSvUHoWxd3yP/SGNWV7bpe1mRp26+gs46emMtLq4hIR29Ie9KHGyhl3jAhSEBZwYwAQldvNRO1bXlElay+P10+Jgc2hGLvU+flkM7YtG0tPgISFibNm0iQKxJ6IqBdvT7taAdi4uL6WTxMUkTmQcgAiScnWu/eJEAISclbWjHUplsz4iftm3bRhcuyAo/TGjHcUSfSPofO3YseJNTXVVB118//a4tSKJAA5MSwAx67bLiFhRAWayYRlOABOGvwvB+7bJCmzmFBbRz+9bwAkN+1YV21IEjBWDH3v1yyL7ZhHYsKjpMA8JcCN8HUfNCbDXVV9zUbt+9U1zRjpsK6CKlc+WlGtCOg3TsWHFgi8bIV9CBdsQAun79BvHNWXVlNTXVy/oxBvHSEnk/jtyymeOIffrpp5+WiPN4xmjfvh1EMbG80XlmZha/Nzp05AhdAPJTW1sQ6QVVcBeam6m/304+3yhlpuWQxRrD1aIopwe/4ffzXQgG8tKK89TT1U1jY36KjY2h1NQ0rnYrL6+gxuZmutTWRnFWCx9HeX1j8wUacAyQ1+uh7Owc1gMIRKXl5awHntzm5Oby3VNFRRm1t7fRyIiX4uJiWQaCFJCH0BnyYy0WSk9PZ6SgxsZa7kiWGAvrFxcXR0ePH6VLrZcY5QjYpQr9BqXnnZ1tvHH12JhBmZkZfId38mwxXWxqoaaWFsqbM4escXEMRt7cXEvd3T3czvSsHIqLtRDDyjVWU9ulDl6CcU3BNewOJRsbdAN2DfYGTWVvtAdwa93dfTQ6OsxIMtAb1bmwN9rZ3FJPhdeY28mhArKj4yK53X5+pwwbKtmXWlrY3taAvdExAPHW29tPIx4XpaVlMKSdsrfyPWyC94hY+tJysZVcLgdXzs6Zk8uysaSsvrGJdcEB2BuyoSNwt3F/A0hAvOuCT2qqq9neWGOam5NDaA9839JykXp7WmnMH0tKdllZGdUDx7WtjVGOMjIzWTYwaYFKhUpV+D49PYN9jAEH1wiNWSyXgOz+/kEaGXEH44oh7qpL2T+opAYSGMDoyyoqGFnI4/FSfHwivfDy72jFimU05vPzNTDNq2wIvZubL5C9D9CEPkZTg60A2VdVXc2fjoEBmjt3LtsKS2W62jsZ7tRqTaC0tFRuz+mTJ7mNOC8mELN4SiivrKbNGzfRZ+67h+bNmce2UjbEZ3dXB+XnXz0uu+sSOQadZImJ4bhCgjp6/BC3EfyqPyCu3n5rK6WlJNNVVxewb+Aj9O/S8gpqCtiwoKCAZSOu2ts7GE7T6/NSbo7pe0C6wh74p2yofN/a1k5kGOx7IB/hmqfPFpv9oa2ZrrmqANWXHFeXWjpo2DPIxZjYYhAE2bAH+pozYEMlu7OzncbGvGSzJUyIK8V/dX5+IHc0UvOFRurpdtDI6AjNC/gBfbO2vp7QJ5S9ka8QP8gpPt8Yv8cF8pGyt5KdnZXFbVK+7+vrIb8/hrKyMvmagC9tamw08w/6Q4aZO2rrqqiro41iYmxks5kxC3sjFyob4v07+gmONzbWUV+fncbGfJSWls6+h851tbUse9jtZsQm+Bi5sLsTceVhCFfkK9ibIVMDvoRN0Tdxk4Bc2NnZQaO+MUb2gu/RPhWzzr4BmpNnxix839Z2iQYHXbzfLnIKbHWsuDg4PgBlMCszk6+Jwdlu7yCr1ezzCqntXGkp27tzUsy2d7SRZ9RLYz4g7F2erxTKGPJPW1s7VdfV0ZIpMM05aD7A/8RPuERmtV9jSws1NDQFCwbwdIp/6Ejq5X1PTx+hVL2rr8fkjTcvA6czPxoceILEsfraZurtdVB1bT3hXCa/CVkIfkDrqYKtjrYudnpPXw8vEwBuKUjJxvpSYyxQsDNmoeraasYsrW9sHpeNR3u/n+/c+DMwrYF1wyh8ASEgIBNk8Vu4fXjmDX3uRcfr7nUQZCP4FXldWBdpkvrEE3ZtbQtvTo7zfCOBaR3YwWcjj9vLOikZLLvbQW1tbRS6ZIrtB3tjh5gAOZwOqq5uJpfDSZXVjawr/wTfELH9/L7xyiH4r7vXSXZHLzXXjz/psK29pmxLoFwGT0+VlY3kcrmpvr55wkxBUJcQ37e2Qt826ujoosbGeqUiD74Wn+knhvcEaJ7Hx8kLNxWNjY1B2dAZfoTt4HvlB1NmI+Mm19SML5vA714f5HlQ2cfXhOza2mby+r1sw+6OQFxhxarHx3B9zB/QMBizPR1UXVs7Hp8jfoLtmDcQs8NjBtUirgK+RyJsa2iiRYuWMh944U9FSm/YEPB3SEQgbp/Xz3CnMf7xYrrq+npq7eygxmasaxxfLofqVchFVCqbOB1Oamyu5RuNxvrmoO+VDeGj0ImsCxcuUltbH7W19rCfWJExC/k85m5D4FeysdwIBWoA38eNm1pK5PPCJmZfdgdgLyHHlN3Kvr8QwPLFcbYHbBLiS/Z9dSV5Xe7LZJPfyrHhc/mDhXqtbR3U1dtBdrubaiom+d4bqNIO+AfXQf9xuTwTYlbZBLFi2oVbT2ZOgewuag7ZQQsxyP3H6w+uWVeyAWtaj5i1m3jISjZ8Eyq7v3+AYxu4yYhZVekfGxNj5h/YJ9CXcWOI2PO4/ByziBsQKr9DbWhqTZzPGhvbOHdWVtYH/aZ0CdUD58A/Ks5D8xVk4xx8KkJ+Rb4CvC5yofoN0QTf4dPlH+eHbMBuIl/BniDI5H8q1waEI46Q630+bNRQH8SrRtxx/AXiXOnCsru6qA03bSHr5MGL5XCwnxp7mlta2fd+6fsVdZH361MKczU8PGz89re/EcOIXahrMoqL5dCB+/bsE8M1Aqrv4MHDUtWNw4cPiiHkmpqajF//+tdi2LaDB981Ojs7RboAru+dd3aIeMFUVHTMgD5S2rJlk5TV2LNnlwGbS2n9+nViuMu6ujot32/evNmw250iVeD7w8WnRbyApnvxxReNiioZTB5sXXTspEg2mPbt22f09nYavQ67kZaSEhb2FBB5u3btEssuOlwkjtmqqiojJyND3H9OniwWQ9/927/9m/HFLz4s1rvkbJlRUlIi5t+0aYOYF/kEsSKljRs3G8hbEoLvAV0rpS1btojtDd8fPlwkEz02Zrz8yqtGaek5EX9vby/3ZREzQ7oWi3MK+uQ777wjzoXQGX1fQoD//M9/f8bodcqgIE+dKjFqKqskopnnnR3yPCsWOgOM4npyTGP85V9+V3wfkJKVRoUay2sK5xeIlipAgbSUFCosLBTrgs0FMOUgoYyMDLr11tskrMxTWAjZsmUTmHq67jpzylhygcLC/AlLTyKd88kbLt8WbrpzgIgU8pA8HVvwOHbgAbC9ZPlJTk6O2N64AHYtSUiQhSL8U+gbf3oMKjjFF9z1Llu2jObNyZji18sPQbZNY4kFdrxKSEjhXaAWLlzIYPCXSzWPIP7CveOdfB7iWxqztqQEslis5Bcu28vPL6SkhPEZj8nXDv07Py+PsMuPlK7On0MaGBx0w6dukoqm/Pw8SkoZX4oV6UTsTqOefCLxZmRl8SuASHzq9xtvvFGcr+DH+fOF+cpioVuWLaW5c/PUpcJ+2mw2rbjCJi7YEUlCqamJdN1114ptiJ2JpAS/fPrTqyhJGLNXXTWPdJZtPRjYHUuqz/vFp7Us6P1SKnqdqAU+TBb4r//6b54+/9WvfvWBqI0p7VXLl1N1U1NwF52ZUuTIkSP006efpkMHDsyUyKicqAU+thbAFLuYtm3fycU/khPw0h0FHVJqbB5/lxjpHLzoR5KREusReL8T6Rzw7ty5MxJb8He00zciewLAuzsU4UgJslEAIiG8/2isrg++O450DhKpDrYvipuky4KgM3SXEmyi3mtGOgft1JG9e+9OcaxArk7MtrSa7+1hG2xHF44Qs80tcmhH6KHepYaTi988Xg8N46WakNBOqb1REFUvhMbE5fv6usQxC361t6pEdfR57OcrJeyvKrUh7KETV7oxqxNX2FdYp2/q5kKddqI4UkqQK5WN/rBly5tS0SxXJxeiQv1KJK0Bt6OtJfjyPFJjOjpa6dKlzkhswd9bNDYjwPINFNlICRWoPiHCG4oDdDoHig8G3bJBEcUGJSWnpGpzIZbDJcMPxRTNiZLjXKQguQCWVvVrIIFhc3ZfjOzGAkURqA6WEjboVkUZkc7B2tTQgo9I/B0dfeR1jRd3hOOHzjqJriVQFIYN069fPPWmBep6jKVcL09e3Z3d4sHC5/WRPwF7iKqrhf9EYYsqgArPae4xi1iREjCDdfjPnCmTimadUe0rpbLzJTQi3FgE8Qe7SAlVudKlhhj0Q4t9Il0Dg5b0hgiytHJhY6NW3yyrkPsH/VLa72GTxsb2SKYI/g7Z0phFQW5/vyqSDIq4Ir5oDbiqUliieWxsIhmGWUEs4RdnC4aYtGq9V8JgZBGuIYWuwrzFzTIfnGXvH/F60OeTmxyyrUJlzDt52Xs55Q+L7FVogN0SrNxV54f7HBuT+14LcztujFAlKyWrxUc+IR4sdJa+88P1LVYbL3Ho6+miwjxzyVU4vXTwwscM4R0i9ED7uKI33NXHf9NAgSQsS0L9hs5N6PiVIn/T0QV3k9InVlwZNQfSSDHrEyLrqzjGjPGqcnUs3GdsfHy4nyf8hjYC71pKOu/YEbM6uM6xMRqJk4h0+r1NI10JJyhNkzG0ozzPSu08E3xaWi1duoxQWCIhHadCHgJeSghIi0XuLX9sPPmFKElo3y3LlklVCcALy578oLdGTQ7rIJOM5I9BXz6ColApv1Be5CA2yHtgxIAhTaTWUT9ZbfKwXbr0FsrKMtcwR1INIagDvo8BFLtWxfqJCgvNtajTXoOTwLS//kk/2AKDohC0h5O51N6440tPSSHMWElIoxuzOJ+wAA7MV2XNizh1H6qjzmCOYkAd3a3Cm7igPhqFZ8uXL6esLDnOMArmpKRjE8jkmzmhcNhPeqOAQjKd4lShCsyGm+Yl0+zapSNnNng/HkVTiATdSJsNa0dlfuQssHHjRnrxxZdpz55dH1jbmtta6TMrVtK5uhrKTk2fcT1W3L6Sfvy3P6YvfekLMy47KjBqgY+TBcSPCrgjxrsF6Z0x+KS8MLj0HR54tWUHQBQkju3v6yOgIkl119msHjK1+LFJvPDJnG04JH/Cra+pZ8AOiU1Ydsii+EjnsH909NaVLXyUgx54Pywt5GC9hbKVTQCwcNutt0QyiRmzGuuwECfAx5YQABqGPV6yChf7A3gEbZVS/txcsgvf474XG0r1aGltofJKGVwsZM5qTpnFmMV7UwUeEck2yA8KSCYSL9sEOUXoe8iW8kK2ju/xjvr48SMkxQvXkY2pioFBGY6/xGYzySMecGGg9evXi5MXKudKS2WdA44FTjMq1yTU0dVFKFSREpJul7Bi2uF0MtSZVPaJc8cZ4k/CDxseKtovYWWeU2dKqLVTVmiD5Lz/oLwyr76pkZoba8W6vLNjh7jzoRq3tKJULHv33v00oOH7kjMlYtlnz5VTd69s82+8pzxz6oxY9olTJ+jQ0QN0y22R120DEvTQEXnMllWWUE+XidgTSSGfBzda8veV50vOECAzJYREBwjQth6ZLuXl5QzXKZENnn075DMDHW0dVF9VIxXNqw2kg25rSxvfnEmF7z8gz1ddfW104oSsWBJby507fY56+mQrPAbdA3TowH5xfUV1WZm4an/YO0R79+4V93ugRkmrmlFAevr0WfJ4ZAWnGEuksjGeHHx3j9SV7yufGEvZ6zWorq6MnM4hrs6bm5PH+Mi7d+6kusZmam6opbT0DMb4rK+tpvKKSnI6B8hu76WCAD4wnhzLy6uooaGeX9zn5s7hJQRFRxG8A9Tba6f4eFsQ17j42DFqaGmhmppK+mQAGL68vJRqa4DDCdl9lB/AQ8XSDGxo0NzcRP39TrrqqjwOlP379zKcGSDN4uKsjI+MJ55jx4qourqGmi5coE8sMPcwhYzq6nqyWGK4SOTqq6/mIhpUrp4+fYYAzN7d2U4F15iL2FG+393ZS319vYyrmpuby3fV+/fvp7q6KmpsbCYlAzcgp8+eJkf/AFfZAtsW7xpCZQPC7LrrzOIb3IBgAGjv7qIRtyeI37xz53ZqbGyimroayszIZHujPcXHj5Ld7mSMV2DyAvcU18QGBfUNjdRQV0efuN6spEXn7+6+RF7vGA0M9Af9g1L6moY6utDUSDZbfBBTFbYadg/RpYutlJObR4mJ8VRbUU8nSk5SU1MzNTXWU+HV13E8wMdNjcDR7mY4SPgHhHWcNbW1LD/G8DMeKm6wDh8+TEOuAerq7qKUlFReR1pfU0Unz5ym5oZ6qm2op4K8ArLarFRWeZ6aKuuo2w6b91Bh4bUs++iJE1RTUUbVdTUUZ7FSZlaWGVdFh2nM5yPXoIPbgx1E0Gmx4QTiBP7HMeDSwg+VlTXUZ+9lOEXELN7rYQA5e/Y0NdbX0bBnmObOncc+hn+6u/ro+edfoP/9nf9FV///7L0JeFzVkS9earXa2iVrlyVZyEIIIbwbE5Yh4GQYwmNIIBNIwjePx/DPNllIYJKQTCYhGZLw+DMkQMISCEsIYbVZjI33XZZXyZv2tbXvarVaLanV6vu+X92+rZbU6q5DbGMSnw+j7tvn1q1TVafOuefU+dXCbNYXEhrU1tdSQ30DhYeHM33QPnGigoaGeqmjo4NxjVn31ZV09MhxqqmvoP6+fsrO1veBfbrv6KQwLYxSUlO4Pdt3bqGG2gaqb2oibWKcklNSObJ2Z0kJbVr/AV26YhllpqczAEclaB86zHVbrE2Ul7eIZYVkAYBR7e1sI5d7kvGb8Ya8cetmry6rKClJ1zHsr6S0hGqrKhlO9dZbb2WbhQxLDpZSY30D6/OiC3W7Aq4x2tfX18N+Ijtb1z3sykhqAFkDAAa65wQADgf3h8TE+ZwTG7a8e/dOtvHa2moqKLiI+YZdtbS00rjLTTb7IOV6+yCSatTUVHN9Q944PgIawPVFdGtkZJQPu3vn9u0sk8a6GsrKzuH2cL+vPkX4nDqYAAAgAElEQVT9/YPU2d1Li/J0u9q1bx/VVp6iqto6CiPdZjGAQ4a2wUHq7u5mnG7G13a7aeOmTYwvXV9TQ8kpKayHpoYGOnG8gnHlUR/HrGBXhw4dYttCPw6jMB2j2+Wikn37+NTD2OgoeTwa4yCjHyPZCPpwY9NU34RdlZcfI4djhLp7ethHwK7gI8vLT1BjYx0NDdop0+sLd+3aQZ093dTT3UMREfMY1xny3rt7N8uktq6GzOG6j4SOy8uPk90+yHLPzFxI8+aZqaGugQ4c1n1Kbw/aowP57Nu3n6zWOhoYGPDxDT0gMYmhe02b5H4Puzp8uJTjcPr6uiklBVnoovx8YTU1N7f5fCFernAPsLHRVsOnbNy0kX0E9AOMZWM82b13N+s+1FE9Nqyz/D/5bjtNEIDa8/PzGXzd7MVHLiwq0lk2mXzIOBkLsmloZJycDhujoGCWDEMA4lNqqoPrGyg6EPTixUvpwNFDBOQeIygLfwuLi2fN3LIXoDOYuCMh8McoGRkZFIkk9h7PNASY5ctXcqaOhXnZlJShB3whp28g1J+FCxfQyOg4HS9vpauvvIZ5Bv2UlDQfljPaYRQo9OjRcg6YwfNR8DtQh3jP2OPxo5FCBfkFVFGBM5tLp66nZfhoG3Txt6iomFyuk5SUlEh5eVMRsEXFi30yMWSIQQM0kdhg6dKlPsQjyLCgcEpGBv3CggLCKoHFEjFNDsy3t5KhB8iKae/aRctXriSgz6CkZaWQJWZKFiavPUCuiIR02O3T+M4vKOAJEJZU4r2Bd3C84BfOBHwaz0xJzyRzlDdht8dD2jw9QC4vO4+Ammvu7WP5GO3Jz82lMS/gvEGD7ap4MWeXycsvYJtFfaBg+WRoMvlsJSNjAQ0PYzI5wO01aEOvsfF6AEss7IsTz0dScfFi2vj++5QIBKliPUsQns39wbsUjGehgPaYa5xarQjmWDyle7RzXhTbin9CeEP3QFbKyF7ANKIsUVRU5EVl8nh8skJAWFF+HoPWLi4q8gFfZKVj0IxhW5lus0vZIccnpvBkEMTNFgsVG3bCMtH1ivYsLl7ME5ixrq4pvlNSaDEVcQSw/xIZ0Muw0gKMW/9UhYHsCrqHXZWUHOS/CbH63jNsGu03+g83nojtFJjbmGgVGbziuvHZTyZRlhimiYkLnmHoATbh81fevqrrJ4OP4TgdTiosmsr4VJCXRy5sA5hMlOi1gUiLhWkePHiQ+7l/vy82/JGfXaUtWEAjzlHq6u5hRDVDF+jTmKCjGP0YvxUU51N3azulpS0ggzbblZ9PMWwcdgXFA+uY7SpM7yfZ2QspNtZrs16EPdCGLCpOVlB8Yjylpem2iWf7+1mDtiGzsrIhWrlypS8ta1JKEhVZdDs02oI2QN/4jlAZg2+fvL39waCNv9Dbti2baPXqVRQdqSNfsZ+1RM6yWb0/HOcJGXyoUdhOvF+MvolnwqdA9+dkkcJDjjrGtd07d2s2uwzzFrjBbW0dUvJaY319UCxaf0IDNpsYDxT3NTe3aMDulBRg9QI3eGJyUlJda2ysF9N2Op1aba0M1xcPBy8DfX0iPlCpuvqUuC7wpcX4rpqmAa8X2MSS0tPTI8YBBj3QhmwkxW6zaW0tMruaGJvUXnvjNa25XoZHDZuFrUjLk48/oV3xD/+gaQJbgf0p635gQMQKsKLTklI04OpKCrB90VZJgc5ffP55vZ2CG0C7rUOGLQ5yFRUnBVT1KuUHD2sbFPCoT52S26xtYEBrbJHrvrq6Vm6zdjv3ZWlD33j7La2iqkJU3eF0avVC+wbBlpZmse6dzgnWj0q/7+qR2aDd5tBefPF5se8E3z1dMtrw3CdPHhfJ72xX+vuIUlac6hhv5Iq3ffyq/x1Eb0vxnz+M8n76k59Sj91GTz/++Ie5/bTdgyXHT1yziqqP1VNcQtxpo2sQwvLiP33qU1Tb2Ghc+kj+cpjXqJvMUVMrKx8JI2f6oQhqwqvi3/jJCuy1GiulZ1qk5wp9/xWhkDwhT6cUXgt7A1h3lxY4DWnB/o9KfeZDGPEJHvyXSkLxhHZKI+0QNHXGoB3HPUrBKtwuhQ6NfS5MRCQFNgK5SIsKTB5krUJbkmzB4FPVZpGybqWxjGgQmePv8NDQGYN2hGMOc3jILdSnbrPe9JBz8Gtc5qCpsTHqFuoTfVMaAIdnwK6kBcOsymCrYrPomyp2pWKzkKGKL+TD+kJdQnaqvlClnZhsSQvoqtBWGWxBVzr2QN4qdiVt3+mopzTgHjx4VAzbhmAFJF+WlqqqCmlV6unpoLo6ObRjq9UqhnaEgT31zDNiXgAIII20+1DQjnYZtCP2UAG/KC3r1q3j40/S+seOHRMPuIBgU4HJU4F2DPOMK9F+4YUXxJ0PPKs4mONlR+jTN1wvEmHfwADnfRZVJiJE5EonONgvH3G5ySzEVVKBdgQPp04c431GicMD7OqAzSZtJiHJu7TAib700kvS6gSbxUAqKXaXXQxLCHpnEtrx5Vde4VgPCd+o06AAi9vUZKWenh4paVLxy/D5+CcpnYOd9JtHHpZU5TqgK4Z2JFLyhWImTkNFpQFXBZoOL5RS1BG0QwkthRAcIHvbAm2cZjSCeiQyU0nRpqdYli1xfShoRwnDaCO/fSqpk8gsr6+CBAaWEQUpLbAT6eAywSkCpZRhVyYOtJLfIauJN7n2ri4OBJTdgVryc9KkiGSkkrpM4eWJm4a+nJ6VRTUKiTekMlFZgZDSNOqp+Cuz26wEeaiwYMbsRETJ+wP8jwpSH7C0pcXkcdPkpBw2VA15Te7zLR4LkRJ8pbSFej0VvtUo/3W15R6Xl1rlcIpwuCq4miodz8VOVzbIGeLRByTj2+n+KzN4DCp+Qc4hmYBjlFHWSanA5OEOFSxlVSetontVDGNNCwspO18Fj5mEqV99t0g+bNm2jQqKpiImQ96jCB2o6tBdCk5XZYJjtCs/K5fqquTnto37Qv1VsVn4CBU/gUm8S5jOQ4Uu2hQWpoClrJlpYlz2pg3a6PMqLysqW2Aus0mJtgq0o4rP5wm2EKgllA3N+p3nEwqT21kEztwFpaApLLelZWRQTJR+NCQYW9jHwcCYmpwcrJrvN5yTTU2V1cXSFs4OzhfSxtsIjiGoGKaPsRAfwAtC0SW0YWRYzkNycUnBvh+ObIC+pGCfKDNTlrhaQs+/Tmt7K+UgwbRg5MUy3hj0kyCDGQTfOCogaSdkCJnjKNTpLmxXbreI9ne/8x0iTaPfPvGEiI2RkRFyOhyU6j2+FOomFbvCHt5Vq1fT8epami8ImlLpD5B3Z3cn/frBByk7K4d+/JOfBGUdfKOgv0lKa2e7bleSyop1OtvbWd6ivjnuptGxEYo7AzbL2WuGhkR2pdhEro79TeOIUaj74VNwdEvaf1R8ikr/CcXnzN9BG3qU+AjcC2CXHC8GwExaH+V3pQH3o2T0bD0bDgb//M9Fnq1nn83n4AA/DFjijM4mX6f7WWeindiiWPPpa+juu79G//qlO043y8r0zjSWMhj6xYMPUkdbGz399NPK/J2uG7hvjnsoMka+0na6nn026ZwJmz2b/EufhXb+rfvZmbIQLykPj7lo26ZtYvhFzLpUIvMACzYyMjSTv4DfMUNHjltpASKLMfMOdQ/eFl599VUxDqsKbbz5IdhCWtDG3m5ZXkc4o2Mn5Lkrd+3bRbt27fOBaITiCRHqCOOXFOheJWAOYCDS4BboXkob/L765iviQKihXthV6EC/keFhqquoo9S4+WK7gv3BVqQFupfa7JjdQcPOMSLhsjLaCDlKCuwKus9KThf1Z/R5lX4P2tKC4Lot2zdKqzPf4F9SVOwK9BDAhVULSUHeaam/gs2+++7bBH8oKR/GrqS6N/yVtN8jsKm7V+avBgeH6dlnnxXbIfp8d6fs5INhsxL5ne064o3QiIlxqmmooMSMJMocG6Ms79IlOkx4uJ4zceHChT7YNiw/2+12flsEnBkKjM7p1HFfgaCUmZnFR2q6ulo5Gm50fJzy80w+Gh0dSGDv4U3+JUuWMQ3dmbdSR0cbIzRhCRVvae3tnYwShICAhIRkRn+C4LG00NBgZRShvPx8XuaEkYIXfZ/EQ8VAtCLikHbQx74FBl6gwYA2DAmwieDFEmlhxCjUR52auiamjTZiWQfPxKBqyGTRokJGaYGRwxGhowIBCPVBG8/DMjP2P7Baa6BnGbSTEuPJ7XH5looNeU9MTDDqF5bu0DEQHdpYX0sJcXGM9IKlF8OJoJ2Tk6O0ZMkKbif4GB0ep3nzXIw4ZSxDG7Qhw5ycXF52Mmgz3zFxlL1gAS/rgEZvbze3E7wsW6brB9fBO3SP/MkGbaDhgBbaCZQbyMqgferUMQoL01gmaI+/vMHwokWL+JmG7gEdiGA1w64wkLlcsJNxSk/PovR0XQ9NLU1k8phYxkDOwTIaaIC+oXt/m61pqCG73UZms8kHk4e2IJk19JmYmERAf0KSbURMuslDrQ1WyszNYtqGvNFGBL3AvtFOXEd/aGlpYZkYujfaCb5jYhIYac2wq7q6JoYkNRCJICu0E3u7oI/0baAPW4bMzSYTtbY2UXR0AtvbFO1RioqKI6BAGbQBwdfZGc3XptssAns8Pnlj+bGrp4dqaxuJok0+/GXIEEnm0UbIsbhYRzODrMCjkTfb0D0SPEBfaGdObh73QUP3gFKNi0vw2exU34ygmXZltztoaHSU7cvQPSZrho9Iz8yh9NRk7oPgBb+FR0TRwuwF7FMMGRq6BwKW0QehH5sNfdzfrupodHSEdQ8UJMOuQBt9HPxlZmXxttlUv9dleMEF2axTJENpsnojg01myvNuJ+F5w8ND0+wKNDp79Oj0/v5u6u3V+4lhV4ZPWbBggZ+9tc6yKwxOdruT5e3vC2EnON2RFNtP+UUFTGNK3jrfaWlpPpttb++g+vpGipoXRTm5ubN9ocXsQ6qDTKzWVvadJir09e/GxuYp/Xj7pm6zrRQdbWFd4i0X/qq7u5dx6aEff18IvjEBiY6NJQ+5fT4F/sroD/GxsZSTm+PzKdC9MWaw4Z8j/xO/4Y5isLFEkq3PpicC8EZ12GwOxiAF5Jrx/gNn1NPXR06ng3p7p4DjAQ0JEHdgljqc+swTxzxaO1vZeJGRZMzpZNFguQEOHXVhPEaxDSB8f4Cw346jEzSpN8HlQv1exu8dGdbhI+GEOttxbMdJtoE+GnPodGDYAwPgG0Y9NdMH330DGCiip4W3w5mDb9AfGZoC225tbSe3a5hsAzZfyDpo6zLpZd4jTJPMOq53dPSwgWCAnfC+LYI3h8PJ9Af7p3iBkY05HWTvG2Dsal/7Wd56O0ETBbLChGN8fILawZP3OvZqBgZs3E6bbcwgwc7S7R4jh2P6+UDIGW3EX9A0aFutVuYbsjRoI0gH7ewd7Oe2G7qHvuGMoevOzqnjB9Cj0+mk7sFBcjr0o06gBeeADgacVOOZbrch70GWi8H4gN1BfT3AaNZ1bVzHJA6DIvh2OnXaOK/b3ttJFlMkwVEbRwrwDJtNlzd4QiwACn632WwE+EC2Ky9x1NflAv512njTuuzyywl8tg10eB01/IpHr9ut8+Lx5nrl/sBHMQBJ2unTvWFX/nzjsXA8Y2Pgx+7jG7KCvCFDxDvg2TrfY9Q/2M/7ch09feRx6/ap0+4mu93NOOXe5hBsFvLD0R201yhTMuklt0un7XJ7uB9gYEXQtNM7gQYv3d39XjufSmqA/gr5ORzTj9jAptB/0E4ybJN1jyMkiGvo9NP9VP9BvzAK8J8djiEyQQ79U3zr/kS3WffYVP9GnuKIiAjq755J29D91NsS5AoM4NFR4JxPYQcMDQ0zz7rtTtks+IX8u9hf6f0EAzfaZ/gJI0rW4XRyH4Qd9XZ2+/qPYVeg7XJNtRP9AcFeDofLZ1f+dSFLow/CPjD5xItKZ2e3b7XKsCvIz/CF8JOYhCG2os9h55cTyBa0dF8Ivwy7m+oPwKofHx+l1nYrjY6Msyq4b/aibr/35UnXkI39eh85bQ72h7ga5gmnwf4p3Rv9B8/s6mojIgvL3WgPfLjhlwf9sv3An8Cu4MMx2TUK9Gb4Tkx+UUDL8ClGvXPqrxTaatQxqv3hD0+LIfsaGxu1ssNlc5OfAYe3fft2MeQY4ONKSvbOTXvGLyUlpRrgBiUFfD/55JNiGMPS3SVal5A24P02b94sYYPrlB48KIebm5zU1m9YL6a9YcMGbevmreL6H7y7QRufobO5boYMjx49PNfPs66DF0C9SUpLW5t2tKxcUlXTJia05557TqutrhXVB5RmaVlovu+55x7t8d/+VivZvVcMpwj7275dLu/SklJxXztVXaklxieKeSkrOyKGGhwdHdXeffdtraOrS0tMTAzZR08cr9ROnDghkjcqvf/+e+K6JSW7tbVr14rrv/POOg38Swp0D7lIy+bNH4SUhUELui8tOSiCAAUs4YsvvqgdPy6zcUB07ty523hUyL9lZWVi3dvsDg3tlEI71lfWatWNsr4GiNZHH/3t3DKc4WuOHTuiVVfJaEMI7733TkhZfBQV5EFTHg8Nj7goLk4Hmg41a8C6vwqSCGYmmCVKi0p93oMIn0okEOwZWO7ADOmiiy4W8cOzM5OJl/SC0eXfPB5+E5G2k2krIF+pyBxt9JjNlIvIY0HBzBjA7ZKiyjdm8JbISOEBDn0WK5Eh5rzVlad46VUUlSnUz6WXXkpP/uFpWr1qNVksFhHfKjYIGavYd4O1iRPQn2xspvlx3qQPwRQlbKdBwrCreRER1NzS4lvSM36f9he0J0jc91Xa2d7eS07ngG8Zc9pzA3yBXakE5RjtDEBq1iWsjOAEgaTADj3S+h4P1TXU8fYFlvslRYUXVTtUkaGKLkfc49RY1UgXXniBKPIYfANLQboki3zS52JwnXzAlWj+fJ3zEvgblwCW9C668CJC+jtjj/KjbjLiFK5YtoyqGhvFx3E+DM9Lll1Mzz/3Gq1ape/Xfxga5+85L4G/ZwlIJwwsI+SBhMORlFZrEzUIIj4NWsg7Ki04X6cCOVbT0ODb3wj1DLRvz549oar5fsebIt6KJQX19h2QJyEHbQRMSApmlyq0kY/TKo309nho/4H9vr2jUPwYQR6h6hm/I9epVIYIfGlXwN2GLv335YxnBvqL4JZQkcQVNScpPSuVg0KqFCLOYVfIUyotTQ11vN8mqT/mGqNRfQtLUp1XcMR25XLRngP7mW5ubhH1dAeH7oPNSn0EiO7fp9OWMA49IueutBw4cICQV1ZShkdGOJBSUhd1ysvLlfpmXbUs6hi00UbsE0uLki+sq1SiXXZSDr0J3Te1B7cPo00IyNu0ZZPxNeRfVV9o2GxIwme5gtKAi+MERvBJKD7tCGzplhsNAi6kxe5wcNCGtP5Qfzcv5Urqo30qCQbguIQnD/QN/Sa1JA1SeSNAzNogp93W1sbBNhKZIGTQ2tQkHnCNIA8RbSJqaUEydNnxDXdYOLV3ytuJgC9ETEvK8NAgByQFq1t+sIIuv+xy3m7o58j1YLWnfoMeVZxo/9CQeJJITg95TDL5gSME6kgLAu8QiY1SXFRIdfX1QW9FEIvUZkEIkxxpQUCOSt9saKihcSFkF4I19RMUMm5aWpp9gV6h7sBk2DE+FRgVqj4ifhHQKS3IbS0tQ4NI0iCv32HFSRFZgS8c7pe9kGGLquKkPHEFbBZ+RVraFV72pDRPRz2lAVcFhg1HAASgRL42qGD1AoZNBSfV5ZHvDfsYUvogd3ZGaL+EPHwFBlJJ4cTfsqo+ch4F9DMj6tJ3c4gP0L+0MG0hM6aJcYqM1BPBS+ir2JXum4ML8UjZfrp2zbX8aBUbxA3GcRkJ3yp13CY3md2I9w3Ou0ETJoVBQFQ4yF43FCyhS1cLRLS5ktwIXWZ5XZA2mSw4MSQqiAlQwS9Wghf9ENCOIqa9leQ7m0Quz6iSX1aBdkT/0Y9cybi3CH2bjJpfLcQReE8I+F09Jz7KeqiX1aKiYs4aIuF8fmomL7tJ6qJOZqZ+VldSPzo+ls9bSuriqEaWEDIS9GJjY31nFiX0589PFwcT4azZBRcskJDlOsnJ6WSOlAWpwWHk5spluCC3gNIzZUEZYCY/L18URIa6kZZoPuMnbShkgnskJTwigiAXacH50/j4eFH11NT0kPCi27btojXX6hmCMtNlAWd4OOwqPV0GXYr66cmZviNvoZiH7k2RZjJ7ZIMobFYSdMbPDSfKz9fP2WZfkB0y8xIgOtFWacnJK5RWpaTYDMrPl+NX5+fnUaQwQQfkkZwshwvNW3iBOCArcp5JyRcW5OYr9Z90IVwoBJ2VmkVxyfJ+j/P40oJ+GR8v68cIZiv0nt+W0E9ITRXLG7rML9SxFSS0z2ad80FTZ1Pa55/1sZYAljPXrFnDIBbiAesstBhLkFesWEHiKOUPydOB/fvo/3z1q1R9qvJDUjh/23kJ/H1LQPyGi7BsrKFLl6JQT1oXKlBZn1em7QU3kKga+xAMkSjd+1HYVwDfCFeXFgZlEPKhKkMgbcFRS8sZ1Y+iDKV2hXpABBIHCIWw2W1bttCyFSt8b4dnVCawWaHux9wumjSZiVyyPS7l/uPVT2p6JvVa24Ou0mIvXqofVZvFcnaooDZ/ez6j+jnDNiuFSFTVpYpPAe0zJUMEP6rkK2abEvYHVbvyt5kz/Vk84I5qbnrppWfFEYhw5tLIYwhz3/79YseIKMj9++XRvmVHDon3nuw2G5WWlIqdBhJoS/e1YGR7SnaIdXqg7BBZhYMi9ip3bt0upl1T0xByedCf2Natm8UyabI2MY6t//3BPu/YsYOArSopkPUxhaTlpaUHqaNrCvEq2DNAGyhSc5VDFUfo8pUrfT8j0lsakYtBf8+eXb57Q304UXaEYTdD1cPvrjE3AaVnTJhvEW2U2iwc7rZtus1iad4SHR00SrymqkrJrqB7aWlqqqOyk3K88PUbNogHDMhD6q/A784d25X8FSLxJcVkNtPRg+XULQwMhF0hqpkHJMEDTpw6JQ5UY3+1Z5eYdm1ttXgSD7vauXO3WD+AcZQGzEEW27bJI6AFYjttVcIfeOCBByTUXCNOOlp2jCYmJgmQX8AQRVZSOBGrtZn/xccDxzWKZ6E1NbXU3d1JIyNOwh4DAp0gtJqaaq7r8Wg6lufQMO09UkKO7gHq7OmmyGgLJcQnMlRZefkhQpQp6OfmXsBsAtMX2Kx2+xANDAxRWloqv3Fg5ltRcYrrOp2jvGcCwe/as4t6e3poYGCQwsIjKGl+IneUw4cPUmtrBzU3N/hoI8F2Fef8dFFP7xDj5mLpEG+DFRXVXLe/t48yF+j7sMaRk77BLpqc0PiZMCQcR2hubqSmpmbGiAUNTEAOHz1MjuFRamuzUlZWNvMN/NETJ8q5bkdHhw8feN++/dTd2UG9/XYaHrfTgnQ97V4geaPT7du3hwaHhhiXGfKeN28eDwZHjx6m1tY25seQIQYK4FePjbnJ6RxmXiBc0DbqWizz+EwnBpSDB0sZHhBOyaANLFgcczHqZ2UsJJM5jI9LNNQjMniQBgftlJ2t73PqMmmmxsZGCg8Pp4SEBNZDSUkp29PgYCdFR8fxMyHvkydP+PSTlJTM7YHu8c82BN33UU7OQrYJDCB1dbWse5NJp41jRqWlJeRwjtL4qJNh/gB+AT0cP17uo+1vs9Ax6PrbFY5c1NTUU3NzHT3z+LP0jW/+O+NJ7ykppZ7uLm/Ep0bJySl+8oZd1TEUKrChYZtoD6ACu7u7fTjN0+yqv48yM3W7ggO1trWTbXCIJiZdlJqSysemoAfYbEuLlfHF589P4oGzZP9e2vL+B7R65Scoc0Emy8qQIfpOd3cPZXlTle3atYch/Hp6ANs3xvrkCe++PWyDbW0dNH9+ItPobO+mw0cOMAQkIlsXXVhATz35GF155dX8XOgS0bqGXYFvRL8PDQ3S0JBtml2hL6BudHwcxURFs+5LS0sZIhCQg9AxfAegQg8fPETgw79v4hiOtbWdJuyj5Bgd8fUT3Wb1uobu0QdxhHHEMcL6iY6Mo7j42GkyBO309Azug7CpkxUVNGSzMUZ7Xt4itisMkk1NLcyHxzNJkDdoQ4Y22wB1dXVTeFgEJSXP50EJfdDwKYlJyRQ5bx77L/g99M2uzg7KzVvEflMfQBqZttszSUle2qX799HouJMTI7jdGvs39Lvjx49zH0Z/A2SlYVcVVbXU16vDi6JvwtdgYKqoOMn9YWhohNLT03z89fR0U19fP2OXw2bhO+ALDR9uyNBqbaAjZadoyNZPPT16+j/4lGA229KC6OpBmoTNpqaxrPBiZPgIQ4aQ92P/8z80OGyjmOgYSkpKYt1P0a7jiH4DLxv+qq2tnXr7+vjEgWHLhi+EbU2MT1JyShLruKSkhHr7h2npkktZj+fS/8R7uMPDY/SnPz1Da9ZcTwCC5zy3c0SZYWYEoTrsDioqLgoeMODxUDfeWA8coGWXXkoZXnD8uYSE81vNbVbqbO+g5ctXBqfNRyD66fDRo5Sbk0MXXBAc1QR8w1gx073mmmv0fIpztBH8YTA6erScg5Wys7ODgg6AdkdXF508fpKuuuoKnmwE2wcEbfCBIJT8vFxKmD93wM2oy02OIf0N6uprrqXk+fO5480lw6GhISopLeUI6OXLlweVIZwxeMHACL5Tk5LIPA9A54ELOjADwdtttHzp8qDBH6DdPdhJpbsP08qVy30A9oEpE3cmvD3b+uxUVKwDpM9VF8uxOC6BSVFhYT7l5xcG1Q8GaBwjAaYwwPhnovz0Dw/ShQsXUUdHLycHgEzgqBBIiP4ABzhXge6bm5upqamVli9fzLRD6R4OFo5FYleY+PzTP36GDh055Eu4MRcv4BuTiNjYeK4bDIEL+oGzh9O85pprme8rr7ySfvqLB+imG4pfTrMAACAASURBVG6c9Yje/kGqq9GPeiAJRyja4GXfvn20Zs01FB2NAXfu0wSwWUyUbA4HXXHZ5bP0488Mtr8G7f086KI/JIXItQzaGGCAN15UVBCUNuyqu7+fV8EWL11MCzIygiIlGbpvb+2kxcsXUzpyeIfwKXjrz83Lp6LCPE7E4t82/8+gjQkOEoNcfvnlIp+ClxWsVCCYMJTNdnV08ETksssuC2mz6PewK5wgQMKNmbqHLR04coBe+9Nr9PLLL9Hyy5fTpZesoPu+d0/Ifg/asHGpzeJIFSZFt9/+JX9xnROf57bwGeyhM1x22eUhHQBuw0w1LyePxtxjwY0XlU0mnmUvW7IkpOBRHQmiL6Bcio+dH5o2ESUnJ1NRYREhOxH4ClbwO4wQwPF4gw/WMUAHTrmwsCCkw0Vd0EbnBKD9TGceiCfUQURmfGx00MGWaVvMFJWaShdfsoTSBXBweLvEUYJIizkkLxgYcBwEDhQ8BRsowAs6GjpXpjtzVqeb2U7QykrNoeJiB2Vk5AR1uLgXusnLzaOehL6QfEN38+OTyeV0UVTM/KDOxaCdm5tPycn2gLT3btpGn7jySh+PkIVksAVt6B4Dp5GFaKYcZn5n3RcVUUp8fEi+dZtNIDITJaWkhNQPaLvdhRzxOdMpzuSDdZ+WxVlXDFStvLxc6rQG3vtPxZteXh6TEdHOzCTAZEqizmGzFnM0ucf7A+rHn3dAyur6KeL+EMpmQTuHI4NtIWmzv0pNpYsuWhRysAVPhu45Sl3QN2GzOMsUFxMTdLA1aGdk6G/paG+ownaVX0ixsZEiu0KGoNFxfbUwlAyh74ICPeLcX/cYLP/0wp/o2eefJSRn+drXvkKnKispNjaR3nrtT5SYmBLSL4MeJswWi1nkU1LTs2hp0eJQ4vhIfhe/4X4k3H0UD/V4GOFHBYP1o2Dzr30mBkUcUbQo4Ff/tc/8KO5nDGi0MchbhYSvr3793yk7I4N++sBPJdXPap3W9la6YtmZj1JGo+6//36yxMbTL37y47PaRn4Y+uao+5zEyD2dwsCyNQa4UIPc6Xzm6aa1Z9cuzne7ceNGuvaGNXTX7XfRp/7pU9MGVwTY8Vncv7Jvnm7ezyQ9cdAUmMD+lxSCDzMb/JOWXgW0FPDQrYCW0i+Eo2ReTSbxeS/UBy8YvCQF9QBLKS1Dg4Oc31FUH4hAwgAr0ENnVhlsQVvaTix1Se0EvGDZEvdICnhQoc0JF4QdGvtsAW0W0Jb79tCVV39iGou9/bJk27gJPGMJVVqQR1Uqb1gfgm2kUc1oI9IXSgrbrF/Kuvy8POpumBumEO1U0Q8mC+KCvhkjSxgAmqAtlSHkMTws91eqNjs4JKeNyb7KYKtih6p+WQXFytpgpd889hitXrWC/u3uuyk3N4/KTpygta+upZs+d9O0wRb6Yf+j0DdVfISKLxTb32moqDTgbtq0iXOdSp4L7EuVEP5yBSzlrrYuDpyS8IE6DU1N4mg47D/+8Y9/lJKmhoYGsYOBI9qlgNNsbbVSn20qn3AwpoA0tWePPHJ73bp1VFZ2KBjJab8hIETqvJBnFQEQ0oLgB8zqJQWOsamhRlKV67zw8ktUU4ME6KFLR1sHVZycXbe9s5O629tp+crLphGpqpDjfyOn59GjR6fdH+wL9qql8h6zO2jYOUZCjAfGUnY6ZZMF8LBt2xYfq4VFRVTTOrdusaeItkrLrh1ym0VcyMsvvywlTXt27SP3uGxiAXk0N8thDBEE6J9POChTHg/VcDBm0Fq+H199/VWlKP/j5eW+e0N9gAw7OuTtPHogeHQ1BkHszX717rvpklUX0dtr36af/PQXVN/QQA/+6kGOnQnEEyafjz32m0A/BbwGaFmxvCdNtGePPPo94APP0EXxHq7q83FkSgXmS+oswIcbIHY4dygsODIjTS0nJPkhq8l5xgMgQ7MQmk5fMpWf8WX6CtVVoR1VBOQRQhIyzQiTGLsa9S0e7IjJ5pWAowwk7pNVFVRQWMDBaP7tUjgWyLepQDuq0sb+lkoR63NyUodI9BLHXn5jVZPKo4LWNQmPMjERQFIGUtCcT3DRhGeCIik0WhtgIFXgSMPCcUZDVjAZRmSxuKj6ToVtIY/Jo9ROCg/MN96Un33mGfrTn/9MjsFB+v+++W1685X1tGBBGi1bJssmpQCPIBYdVwznzTK1e85SbZkn+hDMRETMU8ImVcG8xXILgo+kxUV6HlpxfeESMejpKyJSZ4eJgpQLvZ5sfq6Pzowdq0DeI1+d40AOBdLS1U0mGREeIX6bo4lxMisMLiZEEwkLBrlApA/s20/X33DzLCrK8hbiReNB4RQ+63nBLoypjUTBSE3/LRx8TPU1BK4N2W3iLYDpxAJ9kxuhxWMms0KSBhX9wP+o9E1tUgvUmDmv4diKtOAIpcrgLwaMhr9yq70I+WMpY7Vjz44d9KW77qBLLrqIDh4tpwcffJCq6uvpJz++n7Kz0wh+X1qE6YSl5Hz1lOZkvrvO0geVrPflx49rdrtddEtPT4/W0dEhqotKLS0t4roDAwNK9fs6erSJiQkxfZWK4MXpdIpuAQ+VlZWiuqjU1dMnljfqn6qsFtNWrQi+pTKEPMC7tNTW1irJsKOtS0paqR54DmSzxcXF2t7SvbNoqdgs+k1jY+MsGnNdQP+Ryht85GRkaAM2Wd9EO1Vs1t+uxicmtMKCAq2i4mRA1tEf8E9aVPqDlKZRD3xL24l6kLm0NNbXi2mDZleP3BdKeTDqNbe0GR9D/oUvVGlnfWMz94nfPf07bfnylVp+foH2ox/+SGtsaZ71LFvPgBLtWQSCXADP0rEHZM6kXQVhM+RP56OUZ05skGnC41EKWphJ4uPw3T3qJnOQc48fhzZIeORISIUlt5k0ERyz5JJLqLKxmVLnJ8z8+Zz43tTeSp9ctZrKa6spOe7M83jtmjX07Xu+SZ//7OfPavuhS9OkiXDs52+54BwxhX+0PggQtMeqyuipJ56i9957j66+5kr69je+TWs+/enT5hvxxqwSHPa3oHOx5Y4NjzISUcAozgCSwKY4nJWkwMAQYCWNQgMPCG6SFtSVRk62trfT66+/Kl7iBN9S2mgfsH2lBYFHUnljDVeF9p7SfUpQg6AtDeKB7hE0Jy0I5FDRvTQCEfy+vXYtB7ZJeIGsZ/K9bdcOzmqSmjAb2ELFZmEjKkGE0L3UrtzOMRoec4mxlCE/REFLCmQI/fiXrPRMaqhp8b/k+4w+L+33uGkmbR+hAB9OnThGW3bKIfuAiS61WeheJV9xRZXcX0GP0iBC8PvOB++I/ZtOW+4Lofv+ILoHvYd+9Qu6+pNX0i233ELRkbEMd7r+7fV0/Q03BB0ggRgWjLa/SvGcl156Sezf0C+lUf6BbNb/2R/lZ/EG14SJGO0DKczQIOOgtf/Ah0PYOOgNYUKxSPyNGYxRFx3RiEaNjY6n1PRkptU70EvA9nW7PT40KNDwj3YEegkKOgYiIaFchM8bB/KhDCPxtXEdfOI6HJ3T6aSFCxfygW84966uqUg9f9qo73LpCDugDf7xTCNCDt8NyDG0p6nJynyj7TigjWf6Dwioi3tGR0aoraOD6usbaf78ZJbJLNomE+GwOQr4aGiwUnx8P6PCGIfJA8kb7QF/QKbypz2XDEF7dHSINC2Cn2Pox5+2gZ5k0K6srKW4uAQfLCFoGPIGv4YMe3sxaOm6B+qMQRvXIBsUoGcZsgKdiooqlhHAIWA//vJGfUOGhu67+7tZ9xLa0DucQFpaGut+Jm1/m0X7BwZsDMnIACImE5WXHOYBF4nSAV6AZ6IdoAP9wGYNNKiZ8jZkiOuNzS0M8we0HNCYqXvDZtFeyKSpwUpDziHKzcin+ckJPCHxt1lDhtBPe3s3mchFfX02BkuYSRvf/W0WkfWx8fGUD3CQADablrOAYszzaHhkhGwDAwwyj+cZfGflp1NjzQnfoDCle72vITgMzzT0E9iu3GSz9dKpslNsD6Bv+I5A/R4yGbDbGR4TnwPRTkxKovkJCbpP6e2lmqoKSk5IoJS0NKY9s9/72xX0axvo431cw6cEs9nqyhNcN3vBArarmf3esCvYSUtbB+HYI/qDQdvfF8YnJnJAnmFX4yM6JCXsB/oJZlewiZrKSl9/gNwhH6NvzrRZ+MLExCSyWCzTfOHJspO0duPbtOm99wkrGPfddx+tWrGKTlZUUaQlUl/1M5mm9c1ZNtvURCZzJMP4BrIrf5sF3x6Pm3084gKC2Sza09DQRNHRSP0Hu9LTKPrblX87UR+TLQT4nWtFPOB6cEjZEknA/h0c7GcUHyzt+M/agR6CTtPT00dtbS00Pj7BvwM9BXUxgxwY6OGox5ycTB5w0QkA2wXHCNpQIjowBhAIGYmEEcxgdGooCg5jYmKCamrqfE4AGLjAXUbJzMzyGTZm0MCwdbt1hUG5MEZ/vg3afT09HDKPoJyTFScp05tnEk4YsH8oUKzhvKpqKmi4f4gavOF2hpH50zacbp+3PcPDI9xeQOXByNBOQLOhjQjyMAZc8A05Ox12Hw4wnm/UNXiBvJ1jY4y1iqAfyPKKK67izoR2BpJhXV0DOZ0IhHGxHAzn5c836BuyAk0k5z5ZdZLbj3baHHZqqKnz8m2mnAW5rOOOjgZqaWkjmpzkZ/vThkNBG3Nzs7yORNc9AkTwbMgW7enr6/E5c/BhyNDQ/eTklO7xe2trO9sPEsJDl+DPsCvYE+wxNbWP2zPTriKjo/mZXT09bLOwq6qaKh0e02KhLbu20ffuuYca6uooMytHd/QTupyHh4eoocHFCFJxcYXkGHNyO9BGIwE2ZAjardYmGh0Z4jc68Afd+7czNjnFZ7OAF+0f7CeHc4xiLDE84EJ2NQ11ZOLgnikZoj1Wax2ZyEInTpyiBd4BwN9mIQPDZtFn+vt7yW630byICJYVZOive8ib4ubRmNPJ/QC/nzxZTldcsYbi4syUn1NEf9z1AtXV4c1Kl7lBo6/PTlrYBM0zR/kGRcjTYo5kmcRGR7MenG69H3jMbrbZyy+/igAEhwm5v40bfROD32BvP5HHzfCrhl3B6bpcLoYpzS8o8A24gMZEOV5RQctNJsrKySH4MP/+kOPFl4ZddbS10OjoOMMTGoMi/JHTaZ9ms9AD+oOmhVNTQx0/1xgw0E6zN/JKR1Aictoc1N7aRCMjOtwt+IbuWzs7ydan+8KsrHR9wCWiivLjfAIDNpuQ0MX6GbAPMGQmBjPYOPTJdtXVwbIYco6xXRky6evsofaebq4LXRrXMbHFBMDhcFFcXAzZbNH06iuv0GNP/Z7iYqLomiv+gT7YvJVWrFhGOJYGHzQ+PsI2cEV8MuvesCucEomMnnrhgf2AZwzkbVG6XbHN+vk2o987HDa2HbQD94FH9An4cPh29B+007BZ6BhnjSNsdg7eTE3Vz8P7yzsvL5/biX4P3XvcsmOGbCRn838hd3m9Fez2Ue3ppx8PGFQSiAYCRI4cKQv0U8Brmzd/IA62aGlr03bv3h2QTqCLJSUlSnw//fST2sTYZCBSs65t37lbHChgs9m1DRvWz6Ix14WSvXu1xvrZwQmB6oPft9+V0/7gg83a5s1bA5EKeO3tt9/VJsbHA/4282JtVa1WevDgzMtzfl/79lrNLgz4QVDTwdLSOWn5/4AAn+eee04cQAGbPXjwiI9ES0uztiAjY87gpe3bt4t1D763bt3uox3qw+7de8U2e6q6UkuMT9T6hMFK6JfSAK5R54T21ltvTGN35/at2mVXXa5pk7P7yJGyY9qJEyem1Q/2Zd26t4L9PO23kpLd2puvyeu/ufZtbXR0dBqNub40Njcr+av16zeI/RV0L/VXkOiLL76olZeXz8XqtOsIUNu6dfO0a8G+QIZ//vNr2r/cdpuWmJio3Xzzzdr2rVsDBoChT27YsGFO+5/5HAQqVdfWz7wc8Dv4fuS3j4plCH9SX1sbkNbMiwg2hL86F4tS0NTQ8AjFWKJEQQsIPMK+ImZzkqIU3KIY2ISZlpQPLN9gyRrg3qJ7wAsWOoRnCjCDx8xOVBRpI9elWRhrj1mjJTKSsjL1LESh+FHhG3vyZhzfE8pERT/gk+H9JAFfHg9V1NQw5i1m0KEKB6uEuX0yfOyxJxhc/803Xw94K/OtL00E/H3mRZV2qtSFLj+xajVVNzbS/AB7zTP5wBEYzwSJ+jHunRlg12RtpU9eeSXV1jbMRn5S7JtiXWKpvbOXbA4b982ZbQr0XaU/wFepBEuq6Id5gz8U9oe6mhpeBpfYLOtH0O+xzPrMs8/Qa395jZzDI3TP9+6hmz/7z4Q3wzmLokxUZAhAEmRmu7BwEa8wzcmD3w8qMocfxyrAuVaUBtxzjfnz/JyXwJmUwC2f/yytueYG+vY93ziTj/mraWO59arVZy9KGQwnxMVxli/x5PGvbuV5AqoSwAAFlLA333yT1q17h9asWUN33nk33XTzjUIoGNUnnq8fSgLiKGUQQn5I7AFICvI9SpMug96WLfLoQ+wtIP2StOzfJ0/QjPYdOCSHPORcl0KZIMk6IqClBbSlWLPoXK++KqcNGcJRS8urr77iC3gLdQ/SLR47dixUNd/vr77+ulJ0I+QiLWVlZRxEIqkPunu8UHaYIR85VEafvvEf5rx11y55Qnm8harYOHL8GgGGczLg/WHM7aJxt5sihW4U7cQbj6Qg+vmVV16aVRU4uUg4PrPArtBWaQlEe657wTP0KS3oD9CjpCCwTsWu3n77bXE0Nt7iVXzhiRMnOChUwjfqIPevf0G//v0TT9DFF19M37r3u5SZnkm1tbW0du1aSkuJ52Ay//rBPr+7/t1gP0/7DfKTyhB6Qf5kaYE/kUa/wxeq+B8pD6ejntKAe/JkhS9aN9TDsYKiAu1IQmdhPBeb6uIC+KBJWVMRhFKhgOuMdsqLGDeKSeq0ZXxjuUoFrQuOsbdXdmwLzIihAFGXg6PkUrF4hG30ktTcchQmRG77R72G4srsRWwC/nZUTAwVFcydxFq4Quh7pEcBDUrFrtxjLpa5iilK65omxjky1NcI7wfkI66omo07PbNe6O9ypCnoEflcpUXJR7CNSymf2XonKyoIwWfSggAmDDLI/fzZz3+WVi1bQdv27KA/PP08HT9cTg/+6le+wCmTOYqDWaW0w8MCQzsGul/F52MyWVpaGohMwGvc1xQ6BQLEzsUi22D1cq7i0CEglwudVVZE+6VeUip1eR8Zu6xyu5Ex7K2lO125GBVshp8gpsyEFQd0hTkLnJeS3BWk6DYhelk46EbMo0nPiAJ1PTOS5AZ9gujgqu+sW0e3fu5zIW6TDxYgZLYI9+6x/a06AYXTFY6iMBWhtCk8IiKgbvLyCqjiZBXR7dNFpGrf/rCR0ykF+KaIpYxoV2nHh2+TwhJCzOFhcixljmcI0Jy5LiEeRNNkvhNvfX984QW697vf5RWRO7/8v+mRRx6lgjn2Zj0eYGPLJ6z+0I5z8WtcRxdWgaREfmhpgV255dWnwZFKn3E26on9OZjBcRvpnk16JsLw5R4dQUrSgjByKR9488vKydczAQicOuime48DSfjJysokS5zM8WITXwrszfLOyqHoSBltDIarV1wpYZnrQIYJyXJUolWrV4tp47ydyuC8YsUqsT7jzCbKypXbCo54SG0lLS2FkpIS+W3hvXfeoV89/FDQNufl5QT93f9HyFul5OTq57cl95jMFgbJlfqvrKwsPoIloQ09BrJZHKnZf2h2JpkFCzIkZH11Vq2anvLQ90OAD4nRiZSZGTr4zbgVfFvMMsxjHEmTFvj9xUuXimUIujk5+vl6yTNwHBHH4+YqOPpSUlJCr7/6Cq3DudlrrqGf/ffP6Z//+bMhJ1K5CnaF5xcqJHKHzzcFTP8xuyVmM46qLZj9wxxX8rJyyRQpHK4mTQS8iHOxnJagKU7yLYyOPReFcJ6n8xLwlwD2wJYtW0H1tdU0PznZ/6dz8rMRNHW8ulYUpXw6GvH+xvfpFw/8gg4pxDucjuf+3dLweAi5ad944w164vHfEc0Lo/9925fpK1/5GmVmyU4a/N3K7hxquNJLeiC+sfn96evX0Esv/JHfDIw6/f3dcqg05Iusa6CRkSHj9qB/EdikEpihApMH2ghw4CMiQbnQf8RBemlgBmamKvCLKtCO2MNR2beoqKgRw82hpaCNZ0gKgltmQiQGuw/7yZCNpEA/UtrgVyVoimlbrXwUaPWVq0IOtji0L+UbNuIPLhGqrSo2i3aOIp+wR6YfDNDSoCnQDhQIszA7m7rap5DjjPZgiVMa3IJ7VGwWeoetSIsKtGNvdz8DqEhpq9gsdK8C7Yigqe7uqaC2Hdu20S1f+AJdfNHFHND59FNP0cnD5fTTBx6g+MR4BvOQ8g0Zws4lBbYNoBRpvwf632CvnDaCpqT9B3xLbVbSto+qjnjAhdE8++wzszpTlCWGfvAfP6bfPPYYXbvmWtqxQ0/86xhwyh3jBFFTQxW5XLJNKAejUsmxeoEYY0CdhRI0gqbKkdBZuOdrtTaIaSNQoLk5MAZtIL4A2acS8NNQJ0/M3t7eRDVVcycSn8nPiVMnZl6a8/uAzSafbHnxdKURudCj1do+57Nn/gBd2vtsMy8H/A7dIyp848ZtdOvNtwas438RfOAeSTFQvyR1UQe6t9llgTOQncdkZnQeCf329naxzcLZ1tY2ziKLJdIht30WJjNQm/BPWqqr5djicLonTsnrA9pROlg4XA7qbJf7FERoi32Kw876lMgES/iHjx6m48cP068efpBWLFtGX//Wt+gTS1fSsRPHGBnq09d/mgP6QA8IfQYKnoQ+7Kqnb0BSlWXH+hFuzGOS0GfrE9GGzR48eFgciQ+Uwr5uId+jbtq0aYuIj7NdSbykjAH3xRdf5D0uYOreeOONZDKbac++HWTy7mbv2LOLnn3qGbp0xTL61Cevo9TMdEpOmM91YUiIGAXWLlLIA7YL+7ag+97779GY00WRZgstXr6YlixZQp3trVRVg+MFmLWbqaiogKHv9u8/RHV1VWQyAWoymj772Vt4jw5weJi5owDKbPHixWwwa9e+SWMAdiei5cuXM23M8MqPHgdZJp+Xn8uQgPv2HWDjRQAFIMrQRhw+37NrH7k5KtpMsbGRtNq7n/nKK6+Qc8zF+6yAoLvyyit5xoboOwQ+4CD9FVdcwfsxgIMD9B4MDXuKN998Mx/MPnLkCGNOQ5bY/wDkIwpoG84CssIZOhRjQoPPaA/4w9s+ZosG7RtuvJGh4nR5T82UDRrI/oGjOxYv3i3aiYJjLmg7eC8oLGR5420Fz3Q5XWSJttA1a66hnMwchpQz5I17Ddqoa1yPjY2mz3/+C0x7/749pKvBzbKGvDBj3bJlC8NMRkdbaMWKFYx/ivb4r2BcdtllLCssXxpvOICVu/0LesQO3mKNgQ90/WmPjTkI+0WFxUUMDgG64A+yhU0CbxX2AvnBhsZcHvrBvd+hE5XVlJuTxc+DrPDymJWTSYVss2O0cdO75LA7WJewNdgs2gOZM8CBm6igMI/37sB3XVUducjNtnLjjTdxe4CX3GRt4PrzY+fT8lVLWVavv/k6jTl1aDrwB3tDPzl8+LA3YnhKhrCrLXt20IP3/4Ie/u0j9C+33uqzCUOGsDfYJgr6g8Ph5M+GXUEWiHA1iiFDyAnXDbuCjrEnjjcZwIP+r3/6DP32ySfp7rvu5FthV8bbE2Rq2JW/zeJ+tMnQvUH76quvptzcXD4eZsAygug0u2pqJZfHTfHx0XT77V/iZ27bsYssZCI3uSkxPpFWrFrBS694KwR8aTC7gkwgG7QRssK4AtqGzUJvxqBqyATt27hxI8NUAjN6yZJLafHipXy/IW8wZvTNsiPHCBCwLoeT4lMS2V9N+UK9bwLOtSA/n2X31DO/p+07d9O+HXvoisuuont/fC9dtnI51TQ0MawnaBs2izdh2BtkCF/4hVtvpsiYGKqqq6Pe9nZye0yUmZnK9XE0acvWjfwMBELl5xeyTSCJBeAvARmKBazcglzKz82jyupTVH7wOI25dX91/fXXcz9BG/V2TveF77z3Pg32DxJ2FhHrA73h7VWPRNYdrSFDw64wWQA+MvSA35g24HndCDAkny985533aGhIf3MGJPCaNdez7v3typA3/AlsC0TuuEO3S658jvxPuAsNbvVXvvz8AoqP1wMM8Hps9pjJ5M3afd8936Pvfe8++uV//zf/u/baa+lH//Wf+pEcsx4tGskb32ZfUA2Mb9mSFXSi8hjl5eRRaqq+Z4aITqMuno56KDk56YyT2TegI84Y1/HXCI4xruEo0KWXLqPa2kreRPfRRt1obzCSZYp2fn4uud1jvPQHJ2rQi4xG2L2+GOCjTUTFxcXU0FBH6emZlJmpb9JHRET47vMXbkbGAsZThbFhomEERWBgN57jH7WHgA/MopOTk32Yomi/UZeF4f0fgpTAS1VVBRUVFVO0F8kKdQPVLywsopGREYqMtNAFFyz0kQIvU0VfbUAwCWgDW3rx4mJKjI7nKjNpGwNYXl4uD04ut4suuCDbR84SGUtkwiAypXuDdkXFcSooKGRMVdzgr0vjO/5CxsDNtdkGCFGyRvGvb+iHaS8upvKj5YyBnJulBzihzahj1DP+5uRkMe2N779Defn5lJaSxOTxOyYmmJwZy0FRUWYqKiyk+vpmyshImrJZPxskP7sy+AbW7IUXXkBmsx4QY7aYfPoJj5yKer30kiVUWwu7SuIzlEY7p3Q5xX92xkIqzCtk5oqLptDRwLdR3/gLOpdevIzqmqoISRQQQGMU/zqGTJBgBANBnbWJiguLpgUJIQK4aGkx2Xu7DRJUVFSoYxVPIAnJlF0FpO21K0ygMIDEx+t2hWh1//pM3OOhnIJccjodNNQ/wvWNh8bHAqPZA6siXSa8LgAAIABJREFUYKCjxHtpw67AU1KSHrDmLxPUM9rJNuvxMG5ydvYU3/71jbrgDZP/ujoryy8pRQ8S86/rTzszK5WcY7mcFIP7A44n+nyhHrU+PDRIjzzyCP3huec4ycmqVavpL6/9hVavXsUTNgwgFgR8zgj6hD/DQNXe3kqFhYU0OU9vfyTs22Lh9wlM5FEi55nowgsXUXNzG0VHI2Api6+DJts35GEhioTh4qUlOZ3yCwvJaq2hwsJin0782+mvp6WLoXsruT1uwhlto0zVmbJZ9M38/HyeQMLPwn+hMG34IO47Rm8jyi8sIGtDHUVagGPv5XumL/RGDEKXSFSislVh8HpW/krxJoFPuXvnbnES4N0792qf/NR1WlpKivZ/f/3rkHic6zfIsUlb2lo04NhKy86dO8W4tMCYZSxlYcL67dvltIEfCgxWadm7t0SrrZJhk4LmG2/JcWaBXQ08ZWn5y2uvhdShQau2vl47eFCGd4x71q4FlrLNuD3oXyRb37t3djL4QDdNOL1YytWVgX6edQ26//Q//qP2/fvum/VboAvARgZOrqSgHmQuLXt3y+0KGLbAUpYmfi8tLZVjKY+Pa+tem46lbLThhz/8ofbk735nfOW/ZYeBpXxs2rVgX96Yg3age4AD/NrawLwEqv/nv7wmx1JubNQOHZJjv7/zzjqxvKF7+KCZBRjIn7v1Vi0lMVG77YtfZkxkp9Op/eXFP2vHj8uwlJGYXQWjW0X3A3abtn79ejGuPHiuFeIdDwzYtd/97rdiGUI3ldWnZopwzu/HFPC85yRyBn4QLymrjv7GciiWTO//wf2cJehnP/sZ3fKF231vCv40gXtKmlmE74qAJtCPjPF/I/OnNv2zsWw1/Wrgb6A7OuqmuDjZmUkV2niiSn1DhsbsOjDHU1dVaKMu6J4J2uAb78fGzHmKw8CfVPieiXccmOLUVaaNWfOMt4OpGn6fPB66sKCA3np3LS27dJnfD4E/qvLt1vRML4GpTb+qovumVit9cvUn6HhtPc2Pi5lOKMA3Fdq4fa52PvvMM7x8+egjj/ieokzb5aLIaSsrPlKzPoA2MHgjY05/32Ta8ClCnHPIxBxmkfkrb7Ah+hr2od944y16+eWXyOX20Jdv+yLdede/Tjs2xLSlfdPjIT4losL3GaKtpHuPh4ZHkLVIpksl2rMs59y5oDTgYmkDe4ZSJ+3fzNdff5P+62f/RWkpKfTbxx+lFStWBxx4/e85//m8BM6mBI7VVNG/3HgT1TfIg8nOJn9zPau1s52uWLKMqhobzypg+7Zd2+iBBx6gfbv2zcXa+etEvJd59PhRevapZwmAKoiD+NpXvkE33XTTefmcIQlgr12a/OEMsRCQ7NRCecCfp19ct+4tX0DM9F9mf0M4OaLqjHL77V+g4+XldOe/3kn/eN0/0Re+cMu0KOY9e9RwaQ8EOHRvPGvmX+DSGjOkmb/N/I491tdfD5wdZmZdfEc7jUCRQL/7X0Pgy7vvvu1/KehnHCGSHrFA+1RoI7gg0HGPuRgCbcy8JQUTM5XjT+9v2iSX4ZhLifa6des4GErC9/NPPEU3fOYzkqpcR+UMqh4oIrdx6EYqb6fdSaNA4pEF+bP8+oVHQ8DDXHaVm5NHFQg+9Cv+wYt+l+f8OBftQDfUNTTQ22/K+w/wjqUyRB9WsVngYuvBOYE41a/h94cfeohWLl/JQV7FRUvpVGUlrX93Q9DBFsFn8CvSsn+/fMJzqKxM3B/w/C075NG+kB/0LyndQ930wh+flVTlOqq+8P333xPTPpsVlQZcHSpNxt74+DBNjE9HeUGg0Fe+9hWqra/lSLhVK1YxJNng8BBHyMko60tcTocOwSe5x+WSp+fDwGVEJkpoo516uHPo2qDt9Eafhq4NaEzZuUrQwqqDEX0qoY02GknSJfVV+EY7Jyfl8HEj3ghECR/A9gV9acEkR1KwVLllxyZaunSxpDrXGRvTo30lN4Bn6bE30FPRPeARPSY3mYUoP6ANvGtpcTgCH09KSkzkFI/+k0K0U0U/DodsEgdeTS4P2cYC8xKoLdDP+ORkoJ9mXQPPSCovLWNjgdsJOls2bqQv3fEluuSii+h4zXF66JcP0dpX36Qf3H/vtADIuZ41MjrCid/n+n3mdSVbGcOWmRwa1eWU2wn4kPJidhMN9Kn1n5ntnvP7pEm0gzTn/WfwB6UBVwUMPDw8ak5cTRwZePiRR2nP/gN82PzSiy6mt15/VXwIGmHtKoM/QjilM111WUOEcqNUoY9tR6nz0oE61PjAtrm0CI/i+chJsWBxQ1jYPPEZUk/EPHIrTERAXyLDusY66u/spYKCYl8bTvcHlf6j8mwkljB5EEYt687Caj4WPJ7AsRIJCQm8bNfQ9NcswcuN0GV2ESkkuoBczELDxYR1ghM1+Jod9INnxuQGKxi/eeQRWrZqBX3r3nsJJwGOVZ6iV154la7/X9dTxDzhwf4PgaM9FT8flGX+0U1yeeMGFSxlYFFLZcjJUMzCJRnVxBLhHEESWhgfQY3wB7AJIywAvcY5OuNIS7DbgO2N8POEBD3kO1DdlOQkuu322+iqq6+ml156iR594jHKy72AFi1aFBAw3aAxqYVTTHSkeI1e09yUnCzDso1LSKBLi4vF+9SQCc6S4TiQpFgskZSWliqpCoh0ioqLpqh5oQMLTOYwHrjS02W0cc52QdoCwn2SEh5uZr6lSQYiIswUF6cf9QhFf2JygtLTMvjsc6i64aSRKTxMTPvSSy+l1PR0CtXKZ5/9I2VkZ9E/33QDzZ+vHwkKxYvHE0bz589t39PuN5loniVCbIeaFkbx8XFB+4FBH5PJl5//I33l29+kaImtmMI5OGjevHkGiaB/w8M1Sk+fjZEMW3hn/buUm5lLS5frZ4hBCP1B4iNQF5Mtqc2mzk+hxcWXkClc9iYKm01KThL3TRzLk9qsZ3KC6wJY5Yc/+hHdd++9NBmu0S9+8jN6+OGHac1111G8n/2Hh4eL99cvLriEUtNTRbqHDDXNI/aFJlMExccnUmxs6OA63SjC+Gii/jn4/w2fL5FhTEwMrV59mbiNYWHhFBMTTRKb1X3UZECbDd6CM/+rUtDUmWQHbyGbNm6i7977XVqQkUEPPfQQXXn11Wfykedpn5cASwC2d3FhIb34ykt09Sc+fjYHdKzVK1ZTfX0txcTFnVWtfu0b36Cs9HSGGTyrD/4IHzY4NES/f+x/6LU31tHwyCjd+93v0Oc+dysDpUhXGT5C9s8/+iOUgGwNyrssd/RoOQ1L8Y6Hh0IGFRjtxgJAe387feofbyCgzNxy6+fp81/6An3pjjuoJsAmPPbl/PeNDDpz/UVdKWYn6r733js0NiJbelGhDR6w9CQtoC3eg3S7lWgDXUclKTajywiX5wb75bqHLEBbsuyLupBHqGAVQ76giQAUHRnHuDr7b9mx/TTq9FB+br6YNqio6F7dZnvF2OJOh5M8Hjc5FYLaoCNJgQyDye/iwnyqa5hKOA/dSPWD5wejPZM/oGr5owvN/H3m99NpV5DDxo2b6F/vuIMuvvBC2rRpF/38Zz8jwKnec889OojIHGv1AJnp7JxCfJvJp/93IL0ByQoY7ZICn9LeKc9rDd1IfYrhr6S48gg8Uwkgff31V8W8gG8pbbbZVjlMp0TOp6uOPxhSUJqjI+N04MAeBsumNCy9xPEuRndnJ0M84uZk75EhVlSTlRGBIiNX+pZSILAxGiP8B7QR0IBwhoeG6MSBKlq2AlBkmfS9e79HX7zjy/Qf//FdWrZkCX3vnnvo2/fcw7/BWIDVam1q4mUxI/QbtEEL/3CWDtdhKEOuYU5aDdi47OxsXuoCf3rQkB5MhT1lFNAGnd7ebhoeG6bIGB31CtcBQ2ZAPgL9CQV14QTy8vIpe8ECxjfF82EcQHhBYApoY38IzwT8IAY5o+24zrSBhQuoQYuJEV4M2kCOSklJYzQZyAoFTh734TkGbXwGHUQrXn/9DSxX/2ca9SFbFNQF5CGgevE5EG2gv2BZ0KBt8G0cC+sfHiS3U5+UQC7+tFvbZ+seMgEtFKP9Bm0sy4FH0MBflonTzknvsTwEeRvXu7payWrtoMsvv9zHdzDag4P9NDI4TKMZo9wegzYC3cA3ZPj+ezvoxhuvJSTcQOLvpUvNviU6w2YRsBMZHU8JXpsdGh2h8vKjVFRYRBnQfVSUT8fGsjvQk4zrXT09VFdTRZGRV/n0w7x4dR8dHUsJCbqO8cyamgpCGr3sbItPD2gn5IACG4feYFeDw4OEzmhz2JlvQ1awcR0yVIc7xX2gDbuKT0whc6SZ4mJiWC+IWoYNor5/P4bdHzh0iNGA8DzQNvoP6F2QV0ivv/YW84T2GAOowR9+8LfZmXaFEwS45k8b/cSQoZEqE7TBe+9gPw0PDVOcV1bBaMNmwUcq7Mdi4XZy3zSZWPf+NtvQZCW7bYDbZ/gU1O219dL29dvpqT/8njxmM9160820b/9+qqipopVLl9PExIRPJ93dU6hbhs1CVh0dHdTaCn912XS7GhvjdmIJHu03+gNsFraYsSCDYvztyqt7IGn57Kqri/UZbbnCl2wDcnK54K9M0/ra6MgI142NTWQELoOGbczGPhm6jY6N9T2zz95Hhw+X03WfjKa48ARuJ/Rg2BXO2RuywjORnAMwqqBjtEeXN16pzLzVYFyHjoG8hr/gw7BZTBphh5bISLZD2A+eCZsFOppB27Arwm7bGDHfvr45PExH9hyivDvkKRHZgM/C/8R7uM6JUaqpqqYh2zD19/fQBYvy+Rzt1q1bqcXaRM3WFspITyeszdfW11NNdS0Lc2hoiHLz8ngPDW/IDSdrqbG9lSwmM6Wlp9Gwa5T27dlJdswCO5ooNn4+zU9MJNvgICXHptA1111Dmz7YQD9/4L8pPAJgChZqbGoiO950BvspL2ch7+nU19cT6Le1WWlsbJIhwDw0Sfu27qB+2yBjtEKx6AhQMo4hWVvbqK2hiYou1QNlGhsbqbKymrD/2GJto0WL8ljB9fWNdPToEepFMoHBXlq0KJ9Vs3PnThoaslFfXz+5TWbKTE9jeEBcb7Zaqa3VShdeqMPttbW1MZSZyzXBb6KANoPx4JmHjxyhntZ2amrvoqLCi5j23r17yWYbpp6eTnKOTdDCHB0mcdOWLcxzS3sL71FA3v39/bRz916a9L7lLvAOAJiYlJYepOYWK7W0tlLxJZcw7ZKSvdTbO0CaBgcMmEQdim3z5q2+uvFxcdyZ4ER2g/bkBLW3d9GCBfoeflNtI50sO07NrU3U0tJOl1xciA05OnjwIDU0NdHYqIuGhu10Qa5u9Nu3b+fEDe3tbbwPg4EOtgFZjY+PU2dnNyUkxBMCcapqaujU8SqytrUw37kLF/I9lZWVVFVVT0PDDrIN9tCiRRdye0rxzMZ6amudoo2lvh07t1GE2ULdfT3cqZGTtqWlhQ4cOkZdVis1trdRWmIi/ft37qH/89WvknN4iPr7bWSz9VJWRi6ZLeFUebKCqo9VUUNLB4VpE5SZuYBcbjft27Gbhh126uruI7M5gve3Ie+DB0vJ2tpCba0tFBUTS8lJSVRbW0+VFadoeNhJXV2dLG9D90ePHKKOjm4GhsnLW6S3p7SUMEB3tLczbGpGWjrLau/eEmqyNpK1uZXmzTNTamoaTz4P7D9A67e+R8svXkm5eQu5rbDZsrKj1NRcT7bBIYbSA3HI22YbIttgH3km9YkSJh7btm6m1qY2arTWUd7CRTQvch7TxiRuwjVJbW2tTAN8w5b37T9A7Y36ysSfX3qRfnD//bR7927GWR4YGGSdAqsZxd9mwTOcLnS/fftOHrCw6gM4PtgyknWUlB6k1pYmam6ZstnSg4dZHpMTHhoY7Pe1Z+v2rdTUbKXWthaKjorm/g34T/gll2uS5R0fN58SEuMZznTHrl3UYm2llrZWKrzwQvYdpyqrqaW5luEXMUBk5+XT4f0l9NWvfJN++YufU+9gD91733/QE7/5DX3yumvpYOlBco6MUFtbC8VAx8nJPFhu3rqV+zz8SnraAoqJiaLm5mbGOx4aGqbO7k7Kzy3guImDhw9TXX0ttVibKZwslJ6RRp5xD+3eu5s0zUR9AwMUpk2yvYEGVv4aGxqotbmZ5iclcT+BzwOW8siIkzq7uhiLGvqprq6msmOV1NHZSq7RMcrKzmZc9x179pBtoJtsNjvHS6AP2mx9VLr9MFk7WtiPR5jD2a7wzKOHysntHqGOzm7KyF5IUfMsBLs6duwwNVtbaXBggONtoGNgJqNvY3DUNI0nz3iz37lzN7W0tVNXazeZzBqlpaUTkmcAFxz7sfAvmLBGR0WxL0R/gK11NLVQ4SVFbD/o3x2dXWQbxGBv53bih61bP6CO+h5q7WgkU3gEjz+wq107d9KEZ4Lx9JnAufQ/KXqV3T6qPf7441pXV5volvr6au3IESFU2uSk9kEIaMfSo6XajTfcoOUvWqT98v/+MiBU2lyM7dw9NwTf5IybAO/35JNPiuHMtm7dqnV1dc2gEvir3W7X1q1bF/jHAFd3796pNTY3B/gl8KW33not8A8Brm7Y8IG2efPWAL8EvvTmm2vF0I6QISDkpEUJ2rGtRSstPSgiDTjS5557Tquurp6zPmDxiouLuW3gu6REzjeg+QCtJymq0I4lJXvFsJGnKqu1xNh4MUyeCrzf6Oio9uabbwZtYnZ2to9XQDuWlQn7PcN6Bqft/2DwDVuRltde+4sY2rGluZmhN3/+s5+zPWQvWqg9/pvfaI2NgaFV1617Syxv6B4wrZICf/T8889rgOuUFB3aUd6PS0vksJ42LxQt+pE2OdNTzubu1KlKrVIIowoo10cflUM7Aiq2unbufjyTmzfekPvCmfeeye+YjcjK5KTW19cndrpO54QGXFBpwWDEig1yA1SOgeKylcu1pUuXah+s/0CbEBiChLbx2J6+Pq30cKnIwHCPCm20D/WlxW5zaGMKMgQ+qbTUVtdq9fW10upi5wKC0LvT4VCiHUr3BrGJsQkl2qWHDwcdFP/t3/5N+8/v/4jJw2aV9COwWR/fqroH7bEJ4/agfzFRSEtK0aT6h12p9M1QGM2fvO4630SSdX+GbLaluUU7Xn4iqCz8f2S+Q/gH2N0HH2zQvvzlL2vxsbHaF2+7TduwYUPI/n8m+/3Ro4d9Exj/9gT6rOpTdP3I7Aq0Q+nenyfQltos6u4tPSjuy6jvULKrAX/WzpnP50yUsupb/7PPPku//v9/TQULF9EvH/4VrVqxWpXE+fp/5xLA/toFixbSnj37Oe3ex1UcepTyKt7KwXLt2S5fufsuys0roJ/85Mdn+9Ef+nlYxgYK2RNPPMHbVF/84m307fu+R/PjEj40zfM3KkoAQZhzBJopUvrYVBdHKaNFR46UceCCpHXImYmkwdIijcoDve7efkJ+xuOHy+nmz99Cn/nUZ+jzt0yHivR/LgDDpQWb/8ivKi1oJxy3pKCeCpwiaGNPRFQ8Hjp2bApKM9Q9SIvWrpDIHbSNoKdQtMEzeJcWyERFhkh0LS3QJfblApV1b71FxYXLfYMteFaJIm9SAHwwgkoC8RHoGmxWKm+A17stHg6cCkRr5jUVmwUPoewqt7CIaupO8mMga7RVWkLR9qcD2ip9E7T97Qpt2bNrF91yy2c5GBPBYMjxffTUKfr+D3/IOZ/9nxfs86lTJ8R9E89ttcpPJyDPrUr/UbFD1J2rPwRqb2V1ZaDLAa+BZ2nfhI/Yf+BAQDqBLoK21BdKbDbQM87GNaUB9+jRgxxwJGEMSm1vlw90TU0yDE48e2Cgh2A4AKn45je+SZX1tVRQWERLliyjr3/967OODGHghxIkBQFVRznRt6Q2sfEC5k1SAFBQXV0vqcp1IEMbQokFxT1BvuTsgup6YvV++aCIAVoqQ0QxSjseeEVQkfRIC3jo6uqQNJHrIKgE9hKoPPPMM3TH3Xoic/wOeasMuFYFJwq7UppUdk9FdQfi3f+ae8xFbrtbDDiEdkJHkgJ5I69ssFKYX0BNXlkg6AltlZZQtP3pgHZFRYX/paCfkRM1LCyM/cGDDzxAq1aton//1rdozSevY5z3V195hZD4PsqsI9GpDHINDQ1KMuztn4pgDso06f1Ypf8YkeGh6OL33u5epcG8ubFZQpbrwK66u2U+Bb5QT04vIw95SG0WFM/VfLhKA64KnCJWC8LDZUg2usiVWEHyN5+mEPb/0EO/IswMR0ZHadWKFZzFZGqmbSKa8FUP+cFI2hyyoq+CbMBFdU2TMwIZis9tRZAYHtFgW861lzaSZwsLYN6khWHePLJzz0QRFBYmw8fF8xkG1DMbqQtwhCcrKujmG6YytrC9Cs8ag7YZGbsVCiJIxUUuaiapbrNiTmguaEeDAhLfdzR0fkj4VDUZGs8M9RdvtsdPHqQ777yL32bLq6rooV89RCdOnaJvf/e709LhhaIV6PewMBmynHGvCk4zJjkq/cdkktsVDugomDhqG00I+VfV5wPZ68wVqT85cxwEoqzU4vj4WD7KEojQzGsI8VdxjICBlJZoi5ksltms4xjCyy+9RFu2b+PjKQAPx14vY9jOm10/0PPgFHEmUlqiomLILDR40Aa0o7RAhtJBEV0uIUEG64jno40Ws5yXhIRkjHWignaq6H5eVDiZTTJeGEETuMHCEh2bSHxWb0b9ta+/SbffdhufwzV+As+R0dHG15B/LQoOQ9e9nO+oeVLoPQbfJY/CkjJsVqXExwfXzUX5l1BvXwcv36Kd+CctsbHBafvTwZla9Im5CgYqrFA88sgjVHzxJbTuzfW0dHExZ+hZ+/rrdMONNwRNCWqxyPnG2VmVdgbyV3O1A2dbVfqPxSK3WeheRf+RkXLaKj4fssO5WmlR4RlTBBXaUh5OR72PbdCUpPEHjhyg73z9W2RzOOhHP/w+3XXX3ZLbztf5G5cA3n4WLlxIH2ze8DcRbNfe2kpXrF5NFdW1PkCIs63CFatW0ZNPPkmfWP3RBC9u2bSJHvv972n/nn100+duprvvuovBUXD2/nw5L4FzRQKy175zhVtFPj6x6hN06MgRevjhR+n3v/89rVi1gt5ZGzyfJjbmMUvGbPlvuQAhrH+OYKK/lXYbbzwzgy3ee+cdysnKouKiFX8TTR1ze2gcqdFM8uW/093wy1aupOMKsQ8f5vnYIgKylFEQWPbATx8gJKi49/4f0LVXXUWVlSd4levaa69lABCj7sfpL/zPTJv9OPEv4RV9UwV6U0Lz41BHPODCAF544YVpBh+sgRAmIPskBUg3O3ZsE0c3tra30z4kXRZuRqSlxNMHH2ymb3ztG/SD//wRrV61mnbt2hVwUEVgxsaN70vY5jpArEKwgKRAhps2yRM6A+WnySoLPIMBb9iwXsIG1zl+8jgdPirTD254+913A8or0AOhe0SASguwY6f224PfBWekkvh9y5Yt1NPWNY3oi3/6E935lbsoKmr6EqJOWx45CTxqqe4xUOzatWcaH8G+HDhwiDo7ZZGtrjEdS5mEaQuhG2mgDYJbgEcdqlx80UV0sqqKkY8QqCYt770v72tVVScZS3nThk30r3d+iS69ZAk/89FHHqFTx07Q9++/nzKzdHQrPP/99zeK95Wh+6NCfwXa6MdSm4Xu9++X2RX68bYduzgoVCJD2B98p7QA7lKqe/gr9B/YgKQgSXxNnSxVI2gDsx5/JQUQoNLk9pDhe+/J7Ury/NNVRwztCLg0OLqwMI0c9hFKz0hnHsrKDnFEKmDtsIYPuC6r1UqAHYNBjo+P+tIkAWuztbWNIeMmJzVOPwaBnzh2jDp7emnYZqeY2BimM9Q7SNV1NVwXtDMy9PRgdTV11NBQT47BMXKMDlFqYhqZIkyE2W5TUzPXHx+foMTEBB4gjhw5RF1dPTQ8PEJXXnkF/eD73yeXa5y+/tWv0/atW2h+QgLlLypkuLWmplZCtDQmAHb7MEOOhZtMHNXX0NDItAHRlpKiYyn/P/a+BLyq6tp/5eZmIPNAmBGRoiIKiEgpWuujPP+UOo9Fn/KsbS21lj5rrW19fT61ffY9a63iQBUVEZB5nuchQAghEDLP8zze3CQ3Nzf3/L/fOjk3J8lN7toKFS37++DenLvO2muvtfY6w177t+C8elYmtkGgVFs0r2MhkxIyl5cXU1zcUMZLxaRLSztHtbXV1NrawmXasI6BzMiCgnyqqKikuroGT+m+s2fPMexZU2M9uVyap09sdQBvs76h56SzyVRbXcvwdYBHhB1wPCurrw6B/wwcUyKth33MvAMC/HidFzwAK1dfhyzBZoqKimbe0HdRUSHLbbYPME+LCgoZgs3h6LY9tv5gjKBFqS2UB4PtcVNWXV1JDkc7P5HAh6ATQ9+gj4wcTAEBFsZqzSsopKbGRrK32mn4MB0b2uxXZt4Yp621ndpcLRQ6KJQhBU+fOkWvvPwyvfDb/6TaumoKCdF9FuPJyAIMYh21tNgpNm4IwfbIhi8qKma5DZ/FhNb9SteJv78fl6HsrW+UZMN4wDsnJ5chUaFDlIo0bG+Ms6WljWJiorvm1CmGv4N+LORPUdFRPfwKOtG0Ti4Ph4B78tRJ2rR+C930LzfRkMFD2D5mHfb22RrMtaZm6nSj9Fo0zxMkHIKvru9ILmlXU1VHaekpVFOj+xWgMSE3+kTwAy1sh9J9Da02+uiDD+nGG28gm62JXK5Oz/q42a/gl3jNa9i+HgU6WlsZqhC/AVc9IzPTIwvPe7ebjh4/Th8uWUp/++sbtGPXDrpj7n300dIldMPUyRQZFUuVlWWEUpnQd5vLTcmnEpgHiq0HBw/Sj7e1cZazMU6MB5jNBXkFlJObQ/V1sH0zwynCELiAlJWVMx/Dr3DxQfAvLy+ltjYUUA+gqKiIPjr0xMKSMsqM5kMsAAAgAElEQVTNyaaGhlqGgR05UodoNftsJ0oxhoeRy+mkc6mp1NhUT+5OJAb6s0+Y9Q3ZDR3Cr7KysqmpyU6NtiYaFhfHUJU4jliI+ON0uj2x8MyZ01RdXU31jU00KDjEE3+xA8HQCXwZcJVGvKqpqeZ4GRGhxxSzXzU3N3nKTeo6qSRbUz3boXcsBH+zz6LP9nYH/4uJie3js+ZYiHlcWVnL88ccU8x+1dHeQZFRkexXoC+rKKPJk7pLRp6vC+YX5dPzFn9AbgGc8RkVFUMxQwbrT5cWC40erePw4lRjvQSg7WERqBPayOD7KCJgDbLQsGEjGGsYFzQkQBjnREfFUWV1JcUMjmHQahwPDAtm8HYmMv2H/huaAM5dq1/Mup5SAPJvLPAjKKAhc3No7HCqrq0nJHwBNB+/LfjZz+jue+6hjVs3049/+jOaccP79Ke//h/Xh0WSjauiigCabjz+o09PRqopqXL48JFUXV1PETFDmDf6DLAEMdYngrK5QSdRUYMZxxQXYUPGHrxNJ8TERPGFB4v/kN1oALTXm4ssg3RhoMvRg0dSTUUFy2216utWON5Nb3AgtkleXgkhSQT9G2306OGeggFICkEDD+gCd8W95Tb0bZyPT7ZPQxNRayv3Y/w2evQYvpEx2x46AG9g88bExHh8ordOjFLDsHEDeLuJ4mK7E8QGDx5BUVH6XXgPv4qII3Ll0ZCwKA/vt999lx6ZP5/Gjh+nF4zo8hXoOSYkjGrdLoqOjKPArg35uIBFRMX0oMWYYHsEkZjBgz0JGsHB4T30DX9D020YQTZbax8dGn5l+APoh8YNperaRp5DYVF6YgnqLcOWuEBAh2b7wC5w1mGDh5Fh+946ZEG65IYc8KmoKN3G6NvsJ0Zt55CIEJYX259QU9iQMSwsmtgN8Qq7qyD85SNGEegAXh8cHMgFCYw+zbwN+xi2h1/BBwze1sDQHrJs37qV3n3/fX6yvfnbN9HTC5+meY8/QuNH63jmmOOYa5irhr4DCEUphvI2LHwafRo6RF/m+QkdY37ihVm0ya9gY4PO4GH1C2TexeXlXAAiIqKvDpEZb8TCmIgwqouIIIejlX3GiIVDhgxjfGMA9Ru8LYGBFBEVRRYuOtA97zEuw/ZOi9NDb/gVCkygRKIBIhETM5hjoaFT2AF6io2No9raeraNkaQKOb3ZBzIhXtXXoyBGrGc8Zr8y84eubDY7hQSGdNuhVyw0xonxYL7jYQBz2uBj5m34Dj5BU1XVQIHWEBo8pLsus1nuwAg9FmI8kDcoQL510NzXBf8uxbwCpuq2bVvEUF/VlZUaIOekLSUlRQPknKQBbkyKNQp+2dnZ/cpdWVut/fb3/6mNGDZM+8HDD2sbN27U3nvvHa3N3i4RRctMz9QaG2tFtBhfSnKyiNaQW4rVC/qkpCQx7127dmg7dsgxWE8nnfYJd2d0Xl4K2xcbf/r8PJ14WrMJoSBh++xs7/i2vTsCNJ0ZSxm6jImK0jKzvUNa4vfsXLnPwgel0Hegg49L20A+25tHZmaqFjEkQquulsHZYV4C31fSoEMJdjWgDocMHqwdOnRIKyyU296bzxYXF2qvvvwyYxoD5/q1//kfrby8VEs4fkRbt3q1RGymSUhIEGMpw/b5uTK/AvPkpCQxDCjHq0wh785O7eOPP9bOnpXFCegdfuUb6VhXW35u4YBQp2bl2ttbeZwdDhn34uJiMa48dKKCpZxbmK/hmiJpkDYxQYa3LuF3Pmm+1lnKKncreMX129/+hpYvW0XzH3+Ea1yi7N6l9vXRwEsv/Ymyss7R8uUrvz6DIiLkNEyfOo2ys7+8LGUodNK1k+iNN9+kWbNuVdYvMsdRxWrJR0tp++bNNOu22+ipBQto9uzZyrwunXBJAxerBoy3piL5pEXZwQyvYozXMRLmqrR4rSZtEt7AoF206B1KzUzl11NTp06jeY88wutvA/Uj4W2cD4mlCQg4B7ylxZ9Br8y712tvQ05vn0q83W4l26vwxns/FZ0D9hB6x/rq4rffogVPP+VteHyM9a2gExU5VG2pwhs68XfLkaZUeUvt882bvkVp5wZGpeqt/LKqCnrppVdo4uSJ9LOf/4K3FWVmZ9OGdev6XGwxF1AaUdqkcoMf20eBN9Zb5RFI5y+Wu80lTgg1ZJfyhtwq9lelVaFXtY90jKBT4a3C94vSKl1wl366RJzhhoQDLKRL28HDB6WkLMPBg/vF9EhukjqC0+GgiddNppOnz3DSB+AiFzy1gCrKvGeMYpwI5pLW1NAgyvg0eKWmplJNvQwqDTcg69atMk71+YnM05QUOWb0mjWrSHrDVVdTwQknPoXoIkA2KRJDJK25xanEe9XKlZSVkUEbN26kcePHEbaK9ddgyxMK+K7IIpe2kooy2n9InqGecvqMOGgA8q7NTeQSXgEwTrG+nS6xX02ZMIE2bdviM0ZgLm7esI7uu+8+uvryK6ggL4f+/s57lH42ld8sGYXhe+s2Jz+L1iyTv53YsGGDOAsWb7igF2nbsm0bYWudpCH4q8TCTVvX0JmUFAlrpsFOCVFzu+nk6dNK49y2Y5uINYigP8QsSYP/YaumtIE3MsklDTcVsP3F2JQuuEaCh2QggMlTeAj1JChJePPF02LKXvJxEi/KK8ASgt34sWPozTfeoDOnT5PT4aRrp0yl5559ts82HX2M8tyzTs4+9CGw6Wc9HcR0oJ+v+hO/XCdg41RAP2PbC5GmANWoYvvOznZOBupnaD0OuwM6ySnc/mKc2NneTn948UV68aVXPAkaxm99P+VTQmWM4qthl0BduUh9xevniNviIgXgq3649D0c0AkoUplfXT99BhViW0g/giDj+8+vvML7Zl/875fp+usn06tvvEkfLV1Ks2ffRtaggecRJ4wNTNJjAGwfoZEQU/z9hQ7OkKE9uvL5hwpvJKIpFdERIt2BKbxbqBIek78ChCX4SiEpgf6nBEkJmFspgpnFQi6XQnDzab3zRyCPLvzaRT6Ijg4EUbmg0rtzcHQTHEe2Nwz0fIGWz6UeQo8ZO5aWLFlCZ06dpqqaGpo6ZQo99+wznn1y+hhlr7ngMCrODkGswqcWHUtXbh/wDpTF0W59KAgvnXhgrmNuC3XY4ebs6m6hBv6GjNH3Pv6QhsfF0i233DwwMWdzKjitT249CZwKTq6Hxp7nD/SXVaa+gVh4/83fH7dm3n/rdXT8+HFUVllJFke30+LJcf/evXTPAw/Q9KnT6WTyWXrnvffoZMJpeuGFPxCyeFWaS+lFrpPcwiCNudnRIcc51zQ/FbGVaF1ut1qcwHKCsOFFuMrcxPyRNvBF3Jc04PKr8JbwNGggsQruv3HeP+RTJQMLGYXSrEwUDJZmHUMGZNtJG4qyq9BDFmlDAeXa2v6z4fLzC7WFC5/WgoNDtAd/8LCGv5HJKWmfp6Bza4csQxD9SwuQ67T157UIuXn8GKeKzuFTUh1qnZ1KvBvrG7URl43SNmzYYBbR63f2Wfihj6Llxskq/o3xqfqsVCf5hYXa6GHDtPpG2RzCOKW8oQvpnMdOhnGXX64lJBzXKquR/f9b7aoJ47XLLr9CW7RokYYs1t5NyhvnQW4VeswH6ThBp+KztkY5b0P23mPv7+/GxkY1WRRiZ6vdrsRbJaZAf1IdQt8qOzDAV2pL6FXFT/qzw4U4filL+XPe1mD/4F9f+19atXot3X7nnfSrpxfSNVMmfU5ul067UBp49bVXaefmnaSSI3ChZLlQfLG2BfS07OxMLll5ofrxxRdvkmbeejO57A5eern7B7fTvDsepdvmzPbsEfXF49LvlzTwddaA+P0ZJhNqQJoLOg+kGLxKkiZm4P0JkE0uCO+uOqfNTS0Diev5rayiiuHMsPA+UBs7diy9+fa7dPDwMX7J/e1/+Q49On8+nTp9ut8ELeiwoKJAvIgC/QF5R9KwhguEL2kDatjZ0/LEjJKCAnK2y14vNdTVUV1dnVQUKikq61dnvZm0tLQwAlfv497+RjLbW3/5Gz3zzC+9/dznGPusgtzw2RaX7BVaW0sLlQmTbCBYWU2VeD4gE9tpaWUghT6D8nIASyMtQkg9+CzsM1DD2uxfX3uNrr7qKko7m0ZDBw/mLUofvbuMbpt724AXW2kiDPpPz8mhY8cw32StpKhI7FdK8QpbsUpK5LZvaxND4iIW7t67n0FEJKNEzJQmb4GfSkxh25fIYwrmG/QoaaBDsqSUvqauhpB0Kmm63LIEKwm/80kjvuC2tbTTzp1bGcrQnHLd1NJCTY4WcrQ4PM6NAReWFjPSi5kW30Hf3NJGrnY9UIG21emk5OQkLlyNv9Hw2dzsIAf4N3dfLJEpW1ldzZitZt5wvGaHkwNJW1dSDdZCQAOor0YbIBJ78XY4uA9DoY42F7XabVSUV0AIYkbDeeBj/DOO4++KiiJ68cWXKD07m8aMGU3f/9f/R3fdcQehUhGcydwnHDL1WEoP3m1tLh4jbgigF6OBNyAiS8vLe2Srgif+4Xczb0BvAm6w93GDFp9GA019dS1V1Pfm7WAZEIzNvEF/7ORJcnY6PEHd2e7Sbdmsn2MsOoG2vLqWsrIyesgNnvAR2N9se9AnJiVwprfRJ6D5QG/Y3zjOti8v5xs/nGc0fAe9zrvbxn/7298oOjaWxo0f32M8Bl/4lcEbn8Bczkg710Nu8IZd4Ictzp72OXcugxqrKnvwAD3k6D0fauvr6VxyMvM2blvgs8y/y57m8eSlZTD6mlk+1l9zC58Dv0HD762tDnK3WshuA9Sg3gbinZOVRcVF5Z4tNpgnPIebu+Zm1zzBHIB8R48d5k+DN/qEL2Nt9o577qApk6bSscRE+vv7i+kPv/k9WQeFs94NevAw/nnG0+7meXA8MaEPb9aJw8k6N/NorKriCx1+Nxp0Atv01jdojp041mcOMm/MNYfTc+OLY4gpQD7qwZvjgz7fPHJ3xYKkpCSy1VR7bA95+publbXeecP/0B9sZTTovKaqjOrqqjy80Tey8405YZalsbGREpOTqdWsE8iNMZr8CluqwJuhXqu75QYv9iv4d695DxufPn2aC78b2xMH8ivceBUWFvaQG+PT50MLeeJylw5Bjwx7gzeP0xTfPDpxOCgvp4CKS0t72Mesb0OH4IF/RxVuzIx+/hGfYizl1o42SjuXzlicNQ11NG7sFSzfmlUrKSczl86lptDwscMpfFA4paamUNq5NLLZ6qi+vpHwNIh29OhRSk5KosyMFHJ1ajRixAjG/t22dTM5HE4qK6ug0NAQxiTGK9t9+3ZQWno6FeTn0rXXXsc8zmWkUEZaJuO1FhcX0je+MZ4zXIH3eyL+KGVlZ1OzrYHGjLmc3B0dtHPXLmpoaKTi4mKGw4uNjeUnpN27t1Nq6jnKzs6iSZP0V8EZ2RmUcjaJggYFM0bp+CuuImugPxe2P3ToCGVkpFNldRmN/8ZVLAsAzOvr65l3QGAw/dvDD9PDjz1K8ceP0H8+/wKtXL2Chg8bQRMnTuSnz6NHD1O7q4MvGKNHX0FBQVbKzc2ivfv2UH5BLuVkp9O11+qyADQcOM3Aqm1tbSPU+kVbv34tZWZmMS7zsGHDGR8YT5Pbd+6kDmcn5efnMVQbIM7wxLt3737KyEihrKw8mjRJ1yG2EdQ31lNbi4MDp2GftWuXU052DmVkplJoaDhBVzV1dbRr53ZyuzUqyM+n4cOGsR7PpZyh+KNHKScng7KzMmjCtdeRxc+Pn0CAHdvcbKPa2ga64grd9lt37KIzZ09RXk4uaUSMjd3U1MSFIpzONiooKGJoz8iISEpLOUvxx45SZuY5ysjMpdHjLqeQoGCC7dPTs6i+voYqqipp/DfGs04A3n7mLPziHPlbLYztm56eTj9+4gn65cJfk6PdTv4BwTQkbjAHnIMHd1NWNvSdQUOGDGUdwmfPnEuh5mY7P42MHjOGrH5+dCIxkU6dPE6paakM7wgsXASRnXt3U2N9FRUXl1NgIOD+4hj/GIUvcrJyKSMzxaND8E5JSaOW1mbKySumsaNHUmBQEAF3+uDBI5STk0nArB037hs8nt27d1JNbR1VVdYQdDN8+AiCrrZu20xZmdnsh1arm4YOHU4ozbdn3346uHsnXTnpahozegzD8Bm8s7IyeS/51VdPYN4ocNHQUE9VNRXU7myjkSNG8TxZt3o1ZefmUnZWOl12mc6jprqc9u07QprWwfMEc6qx0UbPP/9rWvj0L2jVmjU0ddIUWr9xA/3w8ccpKyefGuw1tG7Vai6NN2bMGO5z5crllJmZQxkZmRQbF0OwcVNzI23ftoncLo1vzGNjIxgCs6qqilDMIisjhef+5MlTmAe2YJWVl7EfVlRVeGy/Zt0aSk07R6lpaRQ0KJRtjJvPTZs28D1gfn4uRUfHMFZzU1MLbd68lvLyc3m/8FVXT+DM15Rzqfx3U5ONEFPMukpLS+endWDIAzPa4N3Rgdq7VWTR3DRk6FAO8th6lpmZTWlpKTRq1GjGbwbmdGLCSb6w5Obn01VXXsnximPh6SSuboSEx2FDh7Ff7dm2gzrcbqqrq2cIT2yRwpvF/ft2UGZWDs834BoDq5h99sw5amttobL8QhpzxVgeDy6Sx08cY+zxlpZWLkXppk7au2cX1dbWMD60MR7oG34Fn83OyWYI2yFD4rhP6Bw7AnJzs2nMN8ZScKDus4cPH2GdlJWV0ZVXXsn22b9/P+PkAyseeMeYJy0tTtq4cR1lZ6ayLQO65ib2Xh/cf4DjCPQ98rLRFDJoEI/nyBHInc3LI0bMP3r0GPsweNfX19HYrmuPORYCd3rEiOH8RnD3nj3U7mglw3dYwIvlP+nCsM3Wpi1a9IYYEq4wO5+TJ6T8t2yRw0Yi+WLfPjks4b74A2K5AXv3zjvviRfodxzYo1VWlvYZJhJkFr35JsPT3XjD9donn3zCSQJbtmzrQ9vfgSNH4rXsLDkk3Lp1q/pj1ef4DoZ23NXneH8H1qxZI9YJYAmPHz/eH6s+x9etWydO+ILt44/45v2Df/uB9uRPfsLQjumZ6X369HYAto9XkHvPnj1adbUMIhFQioDTlLYjh46IfTYzM1OLiogSJ4ogqUkKu4pEqBUrVmjbtmzSHnzwQS0qKkp77LHHtF27vM+/M2dStOCwYHHyzIZ1vpPZDJ3FHzmirVkjp1+zZp0Y2hGJZ9CLtGEeSxNzYHvYU9KQIglox2QhBCwSj+BX0tTK48dPiW2PhCnEZWmyUmpquiada4iPr//vG2IdwjaZGbJY2NHaoa1at06i7n84DUl7hNKLS0vFyge9SoYtsIulhgWdFOsY4+tolfPWHXiP2IE72ts1X1ijH3/8iXb95MnasFHDtNf//Gdxdh6CnVQnGGebvU1qTsZqTU46K6a32WQ416zvjg41udvkciNrFhivA7Vtmzezrhvttdq+fYe00lLZRZH9SkEWto8QZ1b3Wfk4VWyfmZutDYkZrNXWy7CU2x0y+2RnZ2pvvPEG6xKYxv/9X//lM9Ma4/zWN2/SduyQ3VzgRl7asjOytQSFGyLVLHKVmKJiHxW/6ujs1I4cOuQ1o9ubnhB7IIu0qWT7QhaVmIJx4p+kIVt6x54dPv3J4NWuwBvn2BUyt40+/hGfl7KU/0GvGrCuABSj//qv/6bUM2fogXkP0O9//5/8KlK8ofsfJOtXuRus5dxw/fX0m9/8muY//sRXeShi2UvKSniPa3puLkWHh4rP80aI1+WHDx6ktxa/TUcPHqM5c+fSUwuepBtumNGnfrC383HsFz9/kiKi4uiVV17pj+TS8Usa+KfUgDhpCtpBTVNz8s1AGkM2HLI4pa2kTC0bTiW7EXIYC/O+5EGigArEG8ZpLNgPxBsX1RtmzKS//30R7TqwjzrIQtdccw098sgjhELm3hpnFJqSnbzRGMcwvrSsDONPn5+oxwn+0ob6lbhpkDT4iApvrHNJdIi+Xe2uAXn/xy+eoXETr6L58x9nUWFL2FTSILOSzwqh5tA3ZEBegrSxzwr17XK6yO12kVUIgIBx9tY3aqi++MIfaNq0afTMs8/SnH+Zy9Cfy5Z+RCPj4sQXWyT7jBg1gZMaJWOFX0mb6txU8VnoQ9VnkTEvaZg3Kn6lOjdVY6HKOFV8FnylvKFv1FKXNvCVXnugbxW/kspwPuiULrgJCUmcyCPpGIWKMYmlLSsjS0rKdUiziuT0BSVFZBEiTSHr7/jxBLEsGKfDIbsQuVpa6OTJ0zRl0iRavGgRJ1hcNX48PTb/Ebrl5ptp2bJlPZwKSQmNdptIFmsAUcppOTbyuXNpnKwiYk7Ek0N604KnJMgubcCZxTmS1uZs6xfXGk9mmzZupjdefc2zFeVsIopXV0pYU0VFiZJOkMwibfArBFJpg/6kNzjQHYNYCaHdwJvxl9vaaPvWzXzTh+SnrIIcev21/6WU1FR66hcLCDWMIcPRk3K/Qn3o4SPDGb9aIj8SfKQNdkxITJaSs8/2vrHo72RVn81MSSWbTTY3oQepD0K+k6dOK80fJC5KW0FeAdfZltKnpMq3DmL+oFC8pEF3hw4dl5AyjeGz0hNQnP5ibEoXXOBfShtQAHXIPukZCiCpgDx0BXrS+n31wHWyFWAJffHr+7vwgut29YC7HDo0jl565RXKyCmiJxcsoLfeeouuvvJK+tMrr3j24UmhHV0dUIeSOZWgHRkqTXjTggAjjP2sSuDMSoIzEwcEkcsLRGJNVRU99Ogj9MZ7/8vbgAwbOQmyyPQC/QlJmb0KtjhOUIGbC1DA9QVvdzCKwRuj7v8Teq6ur6W//e0tmnDN1fTss8/TxInXUWZ+Pq1cvpJumzO3D665xSKf9+j5uonXMwyq7M2CbO6AL+xoUZrHgai83r8yvsAvLgXIQ6vFIoY8hEiQWA1+UQGj1eJWissBCljKRBbSNNm+dNjS2zzuzyQ8L4W2xzRQuVb11+eFOC6LRF09qwQYFVxNsFfC1TSkVomOQu1ZUBkL/yk06xec1IOsFn7KwKb+Tdu2UV5BEV199ZX0k5//lPe/ikQJUNShiGkvIqHD9zpL8KdhUAFpRztZA/sG0R/96Ed02+xZdN/t83owkV5se5wk/EN1UqvQd2pyXF8W1+5GvOu3Achl6/btdM99d9EDd91HRSVF9OnSZZSYmky/+93zFBsd3e+50uIFBgNsWYkbOpTyBK/QVW5CcJ/lzfZGv30/nRQguQth6Jq+Zw90ROVhAvucVehR/AEFPaRNcJ/VzcoaqMSbFG4sEB5UxhncT5GLbmG7v4G3awD/7qbUp4GKX5nPvdDfLyVNXWgNf07+2JO8evkyev/DD1Emgx6+/356/MkFNHL40M/J8et72u9+9wId3L+X9h04wHtQv74j9T4yrOHdNH06nc3MpujI8B5EWNZZsvh9WrtxI1ktgfTYj/+N5t37AA0fqe/r7kF8Hv/45S9/SRPGj6cnn+q//vB57O4Sq0sa+EpoQHjP8JUYy3kRUjV54rx06oXJyJHD6T+ee47SMzPp9ddeo8Sz5+jaq79BDz30EO3cKYdE88KaD+F1X0OdDDayPx4Xw/Hly5bRipVLacmyj7xebJFsIV3HuxjG83llaHd2l+fDeD1rs1OmUVZeAb2zaBGdSTlNzzz9zAW/2GIM1113Hdde/bzj8XYekmZkr6m9nf3VOIY8iZqmr7/PYmkDc1O8lPTVMJ9PKcUXXDj78uXLxFloRUV54kxFKB3oR9LJhIw/1ULh0uy52tpKWrt2vTiJB6+BpbyhQyCySNvZ02eoqKKA5syZQ5s2rKPswkK68cZv0i+ffY6u/saV9Lvnn+dsPOgP/4BOJW1IDEtKTpSS8+tI6eRAZuO5c+fEvCG3NAOxrKKETp3SE212795LzzzzDK1YuoYmjNeRlMydOlHofPNmKiwuNR/u9zueFFWSeFRsDx8BYo60nTx1UpzZigQoh9VJhXl5vP6Ptdnnnv8dTZ8+g9JzMwlIT7fcequna6DASTNbkUwERDVpQ3Yo/l1//fUif1Tx2XPnkunAgQNSUWjrzp3ieQx9qPjs/v3yeAXbA7tc1AKIdq/fSrm5hSJyxExxAXpOfjwltr0Rr6TzXqVIPHh/9tln4nl/9uw5KhAmKeKmRcVnRYo+T0RiaEenU6OEhKNktQZTS4ud94/CEIAXA4RfZWUJRUREUUBAAGcn5+aWUGNjPXV0dlJ0eAxZrH5cQ7a8vIoqK5GBqVFERDg/fQCGr7ISd3WtFBwczJBocCRkddbW1lF5eTlDAWLMwN8sKCjkixzqV8ZGxJIlwMKwkIWFeVRRUcl1LSMjI/kiBMjH8nIURmingAArw/jB2MD6hdyA1BsyZAirE5MuL6+InE47+fn5U1xsLFn8/Tmrr6Agn6qqKslua6aY2FimxwQtLS2l9i5caKNPQyfgHRMZSYBuQ1IP4AQrKys4CAwBbxyvqaG8vByqr2+g6upaAqwaGnjnFxaQo6GDNIubodxCBwH2Moruv/deuubaiZSTm0vPPfMMrV+/ngoKC8litZDFz0JhYWEUFBTENzC6DnuOMy0ng2oqq3jlyuXqZFuiT2z7gr4hE+wIeEjYITMzkyo5G7uNACsH3rjpgS0M+pjIwWxjbPHBBbehoY7MvDEZQYusbovFn20MO8D20HtnZwcFBgbxcdAUF5exn8CekZGDKSDAwolkRflFVN9QQ4ePxtPPF/yUPlq2jMZeMYbKyyuppqaWNI0oLCyU/SojPZ0hEf0tfgy/GB4e3kPf6CckJNQznpycPGpoqCWHo51hLbH+C9mKigpY9o6OTvZZ+H1achqVVhRTe7teSBu+DF3l58M3q6myEpCPQaxD6AoYtnV11dTW5mBbYpuYMU7Qt7Q0MwShYfvysnJqa2kjP4sfwxLiqRVwjfBB+K2fn5tCQ8N4PKtXr6Xtm3fRp59+QjxstyYAACAASURBVCNGjqSX/vQyLXx6IY0cOYJa7S2MUQ6YTuZ9Jo0KSwoYUlXr9KPomCieJxkZ2Camyw0bw/6AcE3LSKfqylLC2KOi9PkN/wBUKuSHLIbP4kLL+Li2ZrIEBNCnH33EBT3MfhIQFESDgoM50GamZ1JxWTG5Olw87+Fv8AnwqatDTCljOEXIjTlSVlZN7e0OhjwcOlRfWklLy/DIbfgVMLfT0lKprLSEYwGgN0NDu3wiI80Tr2Jj4zgRC2vNhQVFbJ/W1nYaNkznDV8uKyth26P+LfwKtkdMKSgpJJdTX2fHvAeOJGBoa2rqWG5Dh4btAUsIiFZANaJhjuB1P+aE2a/gsw02G3V2dpK/n4WioqPYr3T/0XUSEjyIgoKDOebl5uZQRW01OdvaKDp2MFn9/ZlvUVEh+4rT2cH+wz4LbPbSMp4byMeBz/aOhX5+fl1zED6bQdXVkM/piSmwOXjgE+PBej0abFZaipjfhCQY9iv4bHZ2LtsHPgM4SfisHttzuG9sZ4uKiu6ag2VkxFnEQ8ClGryLi/PI1tzG9jeOI14hPsBX2tscFBkVSc0tLZSZmU6gnzRJhwVlJhfJf32zT/oVTHcu5CkhWMCA+AyPjO7KFg72nGmxBpPV4iYH9gZaLIQtK2hhYVFEhFT6YAoJ7s6sA5/eSQI9eXtYk9Wi9wOHAW8K0h/SQ0KCyenSZcFNARr3bbUyPigMG9xVcb1f3l3Fqt1uK++TNVJWg0PCKDrSRUilMngYEnnL2+rWCVdX12UJRMFlJDbp2ZYdfv6cjWiWBd+Nhu+BSA4KMY7on7ghQbvlllvowQcfpL/+9a+0fu162rx1M7379ts0dtw4euLf/53uf+ghniQ9ZOliFUJW6tQ6yeXo7g8/mWkNWYxPP78AsgYEs81BCzl60HfZQR+grnPjXIM3EneCQ0I8PIzfdR1aPMeDg0MoJMRJZAlh3wqwdHLuJujc5KadO3bQurXradE779DcOXN6PAmyzogIgcNiDSSnUy/ywL7SZT9DbshibswfGSid3S9+zOM0ePM5bAadTpdf1wn8kBsOGj9AehQ479TI6gfd6HqHX4UARL9Ln/qJOi3L0i0GXwBZbhC53VRSUkZv/+0tWrF2Lbnb2ykw0EJr1m2gb3/7Vt4zi6Bm+IrRH061BEEsq57x2zUF8btHbs6Q1SeslSwUZhlEfn6DWDRchNHAl/9Bf70S6cDLYgnmYBk7cjilZZyjceOu0uksFvLkuyEj3IrD+iDNskYiiDPfLl3qQ+a+kdlqHo9HbovFMzcRb+AnLuwK6NI9Tob84eGRzId9S/9GIcHBHlOZTMZjtCJmuN36XOyix8egLl2EGD5ksTA2MJPAb7say4rsaksgWf0CPXEzLCRM9w+3u4fucRreKiCJFDfQaODh0Ql4dwlpyBpA/hRiDdHjIcfZCH2bmNmvOjG/uoTiJFX9O3gb88HoC5+42QwOjKCOTr3qDm6G0OCzwY6ueWwIwL/gnEA2mzVQlxv69tiHx9Ed83EK5iZfK7oEg04ckXrCqjFfQQcZLaTbyBx/zfMhLELXeaBHNz376hLxy/+QwlkBPmz1is/EsITAD5XitQKeDBis0gLdwDA9ezZZKrqWnp4uxuyEzO+8844GyEZJSzmTIubdam9XwmtNT8/WqisrJWIwTXz8Ee3NNxdp3/nOd7SIsDBtzpw52qcrVmiFhYV9eGzbtEvbtU+OpZyQkKB1CguzV1dWa4AFlLaE44maBIYPsHQv//FlbdiQIdq+Q/E+2QNm7oMPPtCA7Sxp8FkpLfilpKj5bEryGYkYTJOamd3HrzA/du3Ypt3/4P1aRESUdv+DD2rAFwaW8pDBg8VzE7aRFv+GDuFX0pZbWOyBJfz3f/+h9vrrbwx4amKibzsaDOLjD2nA3ZY2+KwUarC6ulbJZ5MSk5TiVXamfD4AS1ka3+ATiJ3Slpmbr2F+Shp4JyUlaoBTlTTgnHvDlfd2LmI4fEOKR52fnyvGFkd/Bw4d8tbtl37sUpZyr3sePLmjdmk4XhN9hRte4ezeu5df66Hizfhx4+juu++meY/MY0CDdncH4cHRuHO92IeKV3A/+9nPqKKiijZsWOepQOVLbrwywxj5ScMX8UX6OyoCvbt4MS1dupTL3j35xBP04MM/oLhY/ZVbQVkJfXvKVDqXX/iFoR3PpwoWv/02HT1xjJYtW35e2PLcbGvjZaHzwvAiZQKftVoHidG9LtJhDCgWXiQ5W1rIGhT0lZ6bAw7Sy4+XLrhelPJ1O4SL7/GEBNq+aQut27iRYuMi6Vs3fpNmz5lLd95++0UdwPBq9H/++EdatnQpPbVwIf3qV7/6ytwkfBE/wsVlw7p19PGnn9Cxo8fokUfm0f33P0g333xznwCFdWZsC0rLzLyobhSxdvuvs2+jXGGyyxfR16VzL2ngq6AB/WW7UNJ3331XjAcLaK2TJ08IORPt3b9XTIsFetRAlbYTx47x2omEHk9S7y9ZIiFlGowTFwVJA93KlSslpEyDpAAEU0nDHeOyZUu9kiLJABfW995fTDU1VfTh3z+kVreT/vKXP9MVl11GN988kzOe123Y0G9/4I21JUlDoghkl7ZVq1ZSnUmHuNgcPXyYfv7zn9O111xDJRUVtPfoQXrhhRfI5fJjjF8pbzwVwl8kDTKjBqi0HTx4UErK82bnzp0+6ZEc89KLL9H4q8fQ//z5/2j2rbO49uiiRe/Qrbfe2udiC4Y2eys1uxzkEgKw6MkmMpxz2Hz5cu9+5W0w4I05hDZ8+Ehqsdmooqz/vvrzWW+8YUfYU9ogN54WJQ01pVXgAPGWBX4uadChSixcvny50vxRiYWHjx1V4o26wtIG/UnnPXT3l7/8Rcqa+UpjIXJFVPxKLMR5IDQto/vmhmw/laaCOiIEhOHuGZXKIpfFbc4WkAxACBoPVvoavVyNvfIMJNKIaNycxCbTycybb6bK6nq6fOEQmjBpGh0/epS3z/z5j3/kovWDwkLou7Nm08yZM3l7x8iRQ/VkiAskPPJjGuurKSMrjXZu3Ukrli3nvKX77rmHjp48QWNH64XMoQgkUBmJNhLFuAeCX/LCQIW3qjr6o8dF4Xj8EXp38ft09OBBmj13Lv3uVy/So4/Np+BQ3za1WlxkcVvFxQswbJVX7G63bxkMVZohCZEINX7CBC7O8dC8hwySHp9KiEBKjwd6Eg+RDI9UFZGsV65YjzF5+wPwpdKmYhvwRBKctAUr0IKnSgxXQRfEGK2KSFNSvbi7ktSkOvlH0skthUotLjmmKpTvdMqBFfoLRl6VYQkmC+cMe/21z0GEC+zNkl53sV3nQjXViWpkJPqSR11mF7ldFhoUaKVZs27lf+ijpqGJSgryKCkxkZKTk+mPf/4j1VXUUUhYCD9djB8/nq4eP54mTrmWJk6YTLGx0Xp2JLLRobeuAfaYqG7kjOrN3e6mNlcbpWWlUWJ8AgPlH9m/n6rq6xkO8OEf/IBWrFtJkydO9vrquMPtlqqEO7RQz6zWLjG8fkB0JT/kPHOvrPoe9MKY7/L/9n+0fv1GCrYE0n/85tf05jvv0ejhQwkFHcjf0FpfduYjLjf07hILr49TdvXq6CAKDJTJYZbJ+D71+usp6WwS9X/BNShln1YFvHAdShO7K7qznWW9+KYKCtKzdn1TGhQyfYPajfmipHIF3mRR4q0CuYudJl7c3FBAn0+n/HKixFcNb7uPWBf0gNIaLsrITZgwwbM/6oJK9iUxx96x8spqGje2+6nqSxLlgnaLYI9tMdGC5LCGmgauJION53kFeVReXkaZqTlUWJ5P+A3bKrDHNSwmikKCIyg8MogvRcaE6uhsp0abjez1jfz6HU/jo8eNY9D8SROuoisnTqSpU6bQ6NHnH24Qr6GwfxTyXQwNr8s3r9tEH634mE4eO0F333s3zZv3iNe1Wam8eIX7nZkzKTk7k2KNbS/Sky8w3cpVy2nJko9oL8AzVKKxF7nwJgBVly6En3jp7ks7hLmJvfQXi89eCEVgHmBujh079kKwJ9SIHn2B4Us/j+BKF9zP08Glc77+GkAgrK2tpbqqGqquq6Fmu73HoK3BVhoZO5JiR8bRqGEjvD659jjha/gH1mbXrVpDby9ezHjYD9x/P/3oySc9wAFfZMgIXNOnTafc3GwKvUhuLIzx4OIxddIkKiqtokBjr7bx46XPSxr4Z9OAdGMS9rNhn6J0X1tufiHvU5TwB89Dhw6I92RBDuyxk7YjCfHifYfYS/bZZ59p2HcsafHxct7Y17Zv3z4JW6ZJTEjWcovzRfTQ4a5d8n21h/Yd0o7Ey/dAgrfU9tAh9j5L2649e8R7Gtn2SUki1thLjX2b0v3gkDtJyBsC+LJ9q92u7dqxg/dDR0VEaf/6//6fdvz4cZEeIUd5tWwPdmZmtjZ4cJTYx1OTU8V+hXmwbdsWkb5BhL3JvW0/btz4fve4qvgs9oSq0G/ZsUM8j2F7yC5tmMfSPaTY8xwff1zEGnNs06ZNGmwqaZABsVPaoEOMVdKMeCWd95BZOtdqbY3axx9/ojXW10tE4b3G0j3ykFe6z1zU+XkkEr/8x6vW9etXM5Sc5KYEa2ctLS0SUl77a22Vv9B3uZ3i4s8QwNWqow1JhMGrjsbGWnFSCTIQcY6kgay5Wb6uDYhJi1O+mKPC2+5qJZut55PoQGNoamgiElaMg06UZLHZCK+ZJQ26hj0lDTWCkRkOeSQNvB2OVgkp09jt4NtXbsDePffLZ2ni9dfRs88+Q/feey/tObSPnn/uOZoxY4bIt1pbWwnZlpIGFDWkV0iTSpodzUp+pTQ3WYc99X3TTd+indu9Z2g3NMmyiKEHR6uD6hrk9C1Nst0D4A3bq/isCi37rKunTvqzK2xYU1dD7e2y2Am88FbhfECfTqdbHK9Aj3FKIxBkxlglzeJyM/TvheCN/lXwpSXyni8a8Svl5mYHffzpEiKHi6whwfTjJ57gCf7nV18lAO8FBQQw1CDWVw4ePsxJN9SpUURcOD3+qE4LzN+c7GzOG71++nSaPWsWB8QPUYKOiNo7OujWW27h7FikmO/bt89z/J677uL1490799K5tLMUCHi6QKLHHvshr3WgKMCJkyc5J3H8NdfQ3XfeSQ6nk95/+11yIqGEiG648Ubmj1dwy5YvZ5nNfe7evZPOnUvjrD8Esccee4zXq99++2/kcLjI3dFBQ4YPp/nz5zM/c1o71rbnzp3L2xDeevttD+8FXa8NUWwhPj6eM/MAT/fDH/6QXyd+tGwp1WLbRBBRoCWIFi78jz68sc6BoI32yquvghQ4dYypjN+wXWLrzu1kJStB7ocffpgxWwHcDzxYo2EPK9qSJUt4LQzfhw0bxrV48d08nu9+97s0ZcoU3uIBu1kCLeR2ulkO9In1/MTE7uIHCxcuZH9gXOeubSFhYSH05JMLuM/Fi98lu12/mH3rW99iG+N144oVKzz6nj1rNk2+fjKhKED84cN8fYdfGXbYuXs3pXUVRQgOttJTTy1k3thGUVRSwjo3bGzwBh1sBzD9WbNm0YkTJ2n/wf0e+8x76CFeR9q+fTvrUYc9dLPcyLLF8bSUFK6RfP2U6XTbbbdRc1MTffjxh54C2t+88Uaa8c2ZtOST9+mtt96ivJwCmnjdZHp6wY9p/uNPcMEKJKAhKxNZ0D/6ke6zGOfx48d5DKNGjeJKUPjD7G83TJtBs2bfyltQoCujGTo8efIUrd++lhb/ZTEt/M2vCKAYwOvFtqqExET22YjoSI8d3n7rLZ4X4GP4FS7s//v668wa+jZ0mJWVQ1u3bvb4LHwQ55w+fZK27zxIg4L8ec6iiAaa2a9iBg+hx+c/ysfvuOsuKigoovnzH6WJXfPEsA8TENGcubfTxAlXsb+tXLXKYx+Dt9mvoEdjnvzfq6/yXACu+pjRo9mXMb9Xr15NFreF3BY3ffumb9P0GdP7+NVPf/ITfgVvnidmv8J4ausqyOo/yKOTqqoy+uTTzygk2EpNzW106803E7L+YUvEPegPMeXx+fPZDuZ5At5PPvmUZ54Awxkx5VszZzJUa3NTC3348d/ZRzCPUXEJ/oatNlu37/TwNmKhYWPoEH7105/8kPdhoyAEsNghB7bV3YlY2OaipZ+8zzefiD9GvML6P3QLORBYbvqmHn+xjenIkXjDPJ7YbowHvEeaYiF0hRt4yD1m1CiGlsXNLgBbkJ8NbG3DrzKyMmj71u0e3oibkMesQz9/jZ755bNMY44d5nnyJ9i+17UHsaCyspJGjBhB8+b1rI3t6fDL/CJ9WrbZ2rQ333xTyy3M8gnDBwi+9HPpDAnXWG8bEBoMoGF4LbJ+40attLhYw7kDNfyelp2h7di1i19DAhZyoIbXInv27NHyc/NFvM+eTdfee+8drbqy1uerP8i9Y8cOhgNEPwM1vObAq5y1a1eLXkWBN+Q+e/asz9et4A09r/hsBX/6egUEWfHaatOWbSLetkab9umnK7TqWt86AW/IfODAAd+8HZ2si3Xr1ohtn52Rwbzr4VcDtI7OTq2+tlb7+98/0JKSUnzb3t7Ocu/bh6UNm0/b19rs/Kp1164d2n//18vasFHDtOuvv0H748sv9xk3fDY7N1fbsmWL1miz++Rta2zT9u3bo2VnC3zW3q4lJSZqeGUN//Jp+7Z21p/Ur/BqbsWKFWwnn7xtNu348QSe9+b5kHA8QRt3+eU9ZAMv+DjmA14rSnjv27eLl3t82p55w2c/1iqrq33yxqv/5LPn+NWsWW6v7gW/qrdpq9eu7fLZDq9kxkG2fXY2z2VfcgNCsb7RpgHaMTHhuNZoHzgW2jscWnFhqe5XdpsGnx+oAT4V81Ji+9ZWxKtyto8kFrbZ7bzMl5iSrOFaMVCDrRHr33jjdZnP2tpYbiyz+LIP+oZfffbZioFE+NJ+E+9/CQ8NpNtvv52GDRntE3IMUHphkWHU4W6nyOiBs0PxThuZsthegmpDvqAG8XtsWCTZwiJEWXzI9IsIC6GwiDAR7+joMM5qjRuqV1cZ6GYIlTIiIiIoYnCMT1nwqgjZsrGxQ0WJMuAdExPDtL6yFcEbekZFGF/6xnjALyomioIpUCR3eGQ4xcVFU2x0NIOaD6QT8A4PjeTKID7lDrJQdFA0RUGHcUNpkKmghbc+dL+KpIhWO0X78CuAnwOeMzo2gmBTn34VGkiRQyPJz+X0yRvQnwlHDtArL71CGVk5dOedt9OGDRto2pRpXl/rom+MMSYmiiLDQ70Nrcex8MhgLvQRFSWTOyg8lLdmIbPV12vl8OBAio2KoKjoaJHtMTcjoyNFPgt7R0aGsyxm2183+Tqqqa+lsrIyGjNGz/6HnPDx8PAQYmD+Hhro+wf4RUUMJqfL4tM+Om/Mh+EUGR7uUyeDQkM5/vi7nT51gkxr+F50ZDRFRCFeDRxC2fZRUdTQ1OBTbvAODw+l2PBo1klk6MBbj0KtQeSMCKGYqAiKDB04zkKj4ZGhFBGF+eDb9hhXXAx2HISTJBYGh4ZSWHQYRVrDKTx84G1YsE9sTAxFReFflE/7gB+uD2GCmK/3HUyzZs3u60QXwRHxK+WLQNZLIlzSwJeqAZRuXPzuW7Rx61audvXUUwvo9tvv9pRc+7KEK6koo5umTqOz2bkXFZayWR9AyfqPX/2K7rrjDvPhS98vaeCfSgPipClopayggJra5Uk/X0VNYosL1oC+7q2srIgamr7etoQNYUvY9PM2JAtu3riR7rnvPrp5xjSqqqmh9xYtojNnUujHP17wpV9sMS6Xw0ntKFvXlavwecd6Ic+bPWc2JSUkfKEu/mnmZkWFGC72Cyn0SzwZ88qAAD3fYiBx62KN4UoX3K2791N9eb1IP1joV8EP3bt3t4gviJAkhMV7aUOijDR7DvtJkXQgbRinHEu5mYAbLG3gLXYct1sJ8zYhIYkK8rKkojBvFPaWNCTEpKWlSUiZhrGU6+pE9Ejeg16kDcl05eXFInIk6iFxA1A8CAav/ulV+sYVV9AfXnyRbvrWtyg7P5/RtmbN1l9XHT58TMQXRAVFRYSkPGkD0pQ0u7rV4SQXoX6wbDpDfyhoIWmOFocS/jfmprdAesvMW2j9xo19uly+XD4fSktLOQGtD5N+DqxcuVx8swV9oJi9tK1bt0YJSxlJk9J2cP9+LiIvpVfBUj567IQYWxz9b9++VSoGY5xLdWi32zlZS8occxNxRdQ6iI4elV8fRDzPE5Fshno6kwVckAOarAe8n4fHF/8CdDcV6DMVeLLPJ93A6zjdPGUp8wY9xuhrTc6gdbFC5Ji3OM8tN6eO1yqHg6XOTuEeoi68VsDZSZv05gn8ApG5LcRTxvVq99799P3vf5+mTJpEyCJduWkNHT91mp599lkv63tymZUctmv+SPUBLGUCvOMFaB3+yKxWcJR+ZEAWKtZwpRf6ftiI54N+vjy8YZ51dLT3122f40FBvtfizScFBfHeAvOhfr9L57zBQAVLmSwupXGqYIv7+w9S4q0ktzFYwac7QM/aFpD+w0mUZqnVKg/owFJ2OFReWcpFwZYglSCgEMvZAAphVNlgKrLgAiC9uGCSqugEgivUf9ALBqgIr6AZYLBKgwyKF6hMVDz7+Wp4IluyeDF9tmYNBQ8aRAsWLKAPPvxQ8LrYN29z326X3LOED6vMHkHRcoFeJwcQ9m2aR/H5vqNiFRKm8AbhrrvuMjGRX8zhI9L5YOpA9FVuGZ0dfFbaIHd7u5weN88qDyvYiiNtuDdT4a3ysKKKpYztSRei6bdZcr+6EDL0y/NC5UdjOwFQgaRNin4Cfkj7VqFXQciSymvQ1dZWag4fW5kMWqTD90bhMX7z9llZXeszDd58XnqmHN3JfJ7ke3Z6ts/tFQYfbIVQQXoBggzOkTTosLxShsA0ED+73a5t2rBBu/Peu7WYqCjt4X97TNu2ZcsF81lsZwD6mrRBf762yhi8MBdGDxvGW0qMYwN9wq9U9K3iV+CN+emt/fTJp7Xf//73PX5KTc/s8ff5/ANzDdtbJE3ZZ3NzxXOTfVYhFkrkNdMUFpea/xzwe215tdLcLMyV+yxsrzLvBxS014/g62tLUK9TLso/L2Up97oVwR10c3MbRUeGitfEerH4SvyJtVCrVfO5XeYrMZgBhESiDbZm8BO0200lZWX00ZIl9P77Syg0OpIW/mQB/eDRh0XbXgbo5kv9Cev8U2dOpfzUfN7G8aUKM0DnmzdsoNff/isd3Pv51tewpg2AC/OWowG6+8r+1MNnv7KjGFhwxFkkTn3dbdlbC+JFDjgBklukazBY4DajHPXu2Pw31u/OnD6tmOAgT8pBkog0sQnBa/XqT8gpfH0KRBcpb+jw9OnT5qEP+B0JKNJEAZQfBNKWtB05spcOHTgiJedXgdLXeRUlFQSUImk7duykku2zhAXlkeQFxCH44YZ1a+i73/8eI+9UllXQqg3LKfXMGVrwi6c8F1v4NnQubSq2h4+cPXtOyprlqBEmkqEAvcsmh6WEPqR+hYvcyRNyvyoqKCBUlfLW/vX7d1ByQnKP18JIaJQ2HeFKnnh29OhRceIZbC+NV5AX8xjzWdJge6lfYY4B+Sk1NVXCmpqamhhVSkRMRFkKtsf4Tp48KYZ2LCkp4nV6iSzg/eGHH4hjZ05OFpWUyJKmoEOVpFqJvOeLRr5wSgFUW1vNGYh2m43GjhvHMpgzEgETiKeJuooaKijIYSg/PFkADg4Nk9zIvMQmfazr4C6ntLiY8otLCbigqLeKjdkwCDKGjWbwqCqpoIKyIqqtrafAwEDmjT4wYZD5hgZIPsDbQfEF2QVUXF5OjlYXjR0/huJi9T4B/2U0g3dFRRXLGBYWRQjqSPQAb0wYlAVDw99GeTBM0IKCPL7rxriMPs2ZxaBlHnV1/HQFeugI4+zLm2j0aF1XCFqgxeZwjMPo05u+m1uaqLy4nMpLiyknMpJGXXYZ99GfDvNKCngswKTOK8ihcWPH899m3oMHD+a7T/AoLS/nrEnY5XLwDg3toW+cbOgQYy8qyiPg7wZbLTSmy09wHONAw2Z38ILtiwsLqaQkj+vtjh0znCIjY3voG/SGDuE/eUUFZG+0UWBwsKdPs18ZvJ3t7XQiKZ42bt1Mf3jhBYobGkdPzH+S3nvnHbKiCDeedktKGNqSfRYBNyuPGm21FBwYQqPHjmYAB7NfGT7LflVQQEVFRWx7/A1f7q1vQ4e4cBbkFFBldSnv3x09aiwXljf7leGzGC/sAN6AkHQ6HDRy5EjWldlnjXGCB7CbUcu7qKSMAsMiCIAJZt69fRbJYBFhYRxIAc8H+c0+a8xj8ECfKMkIAARvPgt5DdtDbvwDnKI1MNCrz467ahzt3rmT/uW736XCvGIqKsphUINRI0awX/XWocEb8jXaUcPZxX0Yx80+GzU4hqLDI3k8uOErKyuhuJgYhmM1/M2sQ7NfgY/dbsNweJz49Oaz0FVeXhbl5xeyD40eM4Zt358O4T/gXV1dzW/MJlx1Ffdh9tnefgVfsNlsVFFWRsNHjuzXrxBni8pKqLi0mGPJ+MvHk3VQz1ho5o15WVRQRhEhgQxgM3To0H79CnKXVVTzvMdTKPQNucx+hfgL30TLK8pjHw8JCSHULB46uq9fmX0WugXQUV5BEV1ltXKsMfNGxv3YLpAU6K+goISsgXg+9B4LjXF6Ygrgci/CpnDB7SCXy8pOGRDanaEHcGskSJmbzeUgu83BF1AzQD6c0nzB5XPc/lTT1ECdHW1kdzjIjSIG0XqyEIDke2fJ1TtbyW5r5AQhTE6jmXkjwKDhs8Zew/sU7a12cjn1gG/Q9n6IdbmcPD6nE6+VzbydDBCORBY4ndHgIOBRX2/zPCXhNwDPW7qyXvAKDHIgEaK+vpGcLjc1NNRRZ8fl+nGTTgy++MQeWciBaTqxWQAAIABJREFUC310dJznJwM0HTrHONBcTjcBBL69vYP3iQJvlI974+12k7PBQXZ7G/n7u/lGhIk9cusZfs4u4Hz00VBXw+OsaWgggzfOMWxp9IVxNrQ2kN3uJOiy3uEgo6ow5Pbz8+euPHK7XFTVtRfYVl9PzpHDu37v1jcOGDpsxZNcq4P7he6NoAs5DD+EjhPjj9BbS5bSsYP7+cbwhT/8gW6//U4aPXok3yiYb+QMWWxO9NlIyONoaKih0WNGcoCEDxrj7G379o52amy0UXScgwwLGbSQG9t1UC3P3tpKNns926euqYlGje1K63ACeL7bV3jwsH1XwQX4LPzFaGbehtz4rKmpIpfbQvX1tRTY9TyC49AJEmQCA7uneVNdAxdFaG20UaupjCJ4w5d7J2vVdT1lNzQ0UUd7d3KbWRZDvoYGG8Fv0Let0UbUVd5YLwihj3nq5Bto996D9O1v/ws12FBcwEJVVTU0BDfrXYy88W5tspPL0UAWt34DbLa90T/2I1M4Ubu7g5qaAaTvpKraRooxocZ54223Yz5Adhfr3uAHWrOe+bjbTXU1zYQEIbxZMPjB943vxvn4hP0aOV4RtTQ3MD+OB11zE5nRuFgYDbEBJgfuuMOpFzyADOANWvO8t3ERl3qeHy2g7dpFYNCDJ/pCQzxqamghp7OV6slNI7uKdIDW8BPY3hivw+Ume2Md67Cupo4uv/xy5mOm5wNd/9nrmvnm0EVWanDYaWjXvDXrxOCNUzBPLRYXx3KDD34HPfzQau32ezxIOVkXlh71kM1yG3MTPGrqmshq6T7f4H9RfEpXllGm64MP3hMviiORIyXljJS9duTIEa2xsVZEj6QZlfJ8oJUu5qO8FPB3peX5VHhj0X/PoT2iMYIIpbRUEs927JLz3rFrh7ZHgZ7L8wkTUIoLUZpRbvt9CuX5YMek5L7l+eBvSMgZNWqUNnHiRG3Re4u06tp67YMPPmCsa4nSwSMpOVlCyjTH449otbWNInrIHR9/REQLosTEJLHPZmZmMpYyEvgkLSklSSstlSXaYB7s2CEv+4hEpYESA9euXqvd9J2bPGLu2ifnHR9/iMstek728QU+K53HpeXFWkqS3PZ79u0TJ/GwzyYl+pC26+fOTsZSPntWJgsS1NivfOAoG50npaRqxcKSn4hX+/bIy4kCL7ywMNfoasBPW2Oj9vrrb/SbYNf75PTUVC03V1aqFOdu27GtN4uL4u9LSVO9bnvwSgLl+YYP77o97/X7F/7T22PEF2aqzgBPUWh41fZVbbibXbNuHX368cd06tQpuu/ue+nhJx6lGdO6S+DhtVxEVBiFhkZ+VYfpU+6CogKaOX0mpedevNCOxiDgd6NGjaDS0nJl32tq1p+i8Pr+69zwOhdPbF/nhCJ+Eq2p4dfxxlP419mmxti63zUZR/7JP7GeN2jQBbrYQre939l9Sfr+Kl9os7KyaNXKlfTxR0tp2PA4mjfvcfp0xQqvARxrYF/3hjXpAAtd1NCOhg3gdzfc8E1KSkqk2bNvMw6LPlGIgN/Ri6i/ukRf9xsKWAYXWeS8/LM1cZYyFIO6hOYkhYGUhcxgFWhHFdg7ZPwdPHhwoO57/IYsS2kxb4wPtR2lTSUDGnf3q1evlbJmCENzMstAJ+KOceVKOUweMiFVMkQBk2dejxlIFiSEQC/StnbtWjLWCvs7B7rbvXM73XHHPTRzxgzKyMmh9ds20LETJ+nphQu8XmzB66OlyygvQ5YxDZmPHpXDNaoUuQa0486d8gxbPLFL9Y21xGaXg1xCRC2ME09RkgYZli9fKiFlGsxNXzHie7fNpq1d9VBVfBa8ly6VywLe5lyMgQYBfQA+UNo2bdogz/RucSrFwuUrVyrNHxVoR8x5lbm5afsmqUoYGlOqQ+jbXH/bVycq0I7YnaDiV776Pp+/Kz3hqiBN4c2pCqIJkiekTQX9hHliAb0reUDah5QO41RpKpCHnDyg8ESMJBGVFigHDlNhy7SqevEG7Wi8dvrrn/9Ca7evp4iQMHryqafo17/5Nd1y80yRTIA9dABeR9gs4k0QYKgwfdxupZcbCmbnDGUMEZnKF6bJHUVi9xtmzKBf/OLnLKqSz1pRoEE+SBXkNTxxqehc0/zEqrYGyWUGUwWvYhlUkNd0ncjt6Q+cRGFTQZrCfLdeIIeFvlVsLxzeeSFT8gTJZDKkgvOqwp8Z5/r6tLoDPdl0vmjxO8utIDy2J0mbPknlU0RlUoNWLInFQio3RNLxGXS9s8WN4/199s5c74/O23Gsoy9dtoy+f9cdjGnc6nLRJ598whV6Hn94PoWFKOjbFSy+lcMNolPpgiu2Dg9TBdpRwV05q1U5SntTvJdjHaw9+Y2c5Gb4xhtuoIaqOn4SVvFZqyuYXErZp9j+JQtxuLlTeUDQNM2LtrwfcslhxZmBW9GYStCOlkA9HnoXtc9RiT2Nk+Czfn49d6wYv/X+RNZ010aI3j+dl78tKri156VHGRP/F1988UUZKfbRltJll42RLeZbAigCxcix7iJouMOMjJQltvhZLbyXE8XfJc3f359CQ0M9W3UGOgeFy6OjIykubshAZN2/Wf0pKjSELIIn6ICAAAoICOREgW4GA3yzBFB4aAhJgM8tfn4UbA2m2LjYARh2/4S7y7i4ERQW1r3Fq/vXvt8GDUIR6FiZDq1WCgiwss77cup7BHrBntXs7Gxa9OYimv+j+VSQm0v33nEXfbh0Kd1zz1102ajL9BOxVhkYQmGhIX0ZeTliHeRHw4eO4H3JXn7ucQjbpKIjY8Q+a7H4i30WfoWC5VIfh06kPttib6YPFy+hX/xyochXCH4VFkrow1fzJ43Cg8IpRuxXAZzwg1yI/hp+27JtO40dezldc+0kGhI3uD/SHsctVj+KiMD+fdncDA0YRIOHDRb5LC4AKj6LfcZD4uJEOrT6E1n89b2mPQbUzx/BwVaKixsqnj8WaxBFRcpiIUweHhkrnj8WSwDFxMgSKwMC/Fhm+K2vBn1HR4fS0KGydVw//wAKDRkk8m/wxvXkYlwLv5Sl7MszLv1+QTUApJz4wwfptTf/Rmmnz9HcO++khb96mq69+lrPHsILKsDXgDnW+W+aPp3OZmZTdKTsBvfLHvZfX3uNCgoL6c1Fi75sUS71f0kD/zANyN63AFyhC42mrU32Gg30eDUobUhuwDmSBjppMgT4qfCuqaqh7Xt3EqASJa1FUW5pIgz6Bq1UJ8Y4JTKDBtB0p07Jk0RU9I0ENV+2BwzcL37+c7r22mvp+d/+lh55+FFKzUynjz5aQlOundLvxRb6aBf6FWhRDxdJXJIGel9ym/kAj1pqH9Cp6FDFZ1uhbwAGCNfwVfxKVW7wlujw9rvuoJWrVokTw6D3rMwsJfhSFR2q2/7CxCvIgYTQoqISs6v1+x30iEHSpmp70EvfQcPukEfSYJvt27eL5wTLLXwHjcgN4BOp3BJ5zxeN+ILb1tJGmzevp8ZGWXYjILvOnTsrkhMXt/j4Q2LlA8ouKSlJxBtEycnJ4qxMoPuU5BUQ+ckcJyExUcwbRRH2bNshlhtZ3r4yPg1mcPRdu3YZf/r8rKwsp8b6buhMXyegELV0bTsnt4jOnu1re0zIpcuX0fe/9z2aPnUarz0im/DFl16he+9/UPQKqKKqjBITk32J6/kd+jNgOT0H+/mCJ0UVvzp+fH8PZKJ+2PJhZGXGx8cPRNLjN+hPmknsdjrJDbhK4Yo/Mj5V/EqlCDkyiTMzM3uMxdsfw0aPpciwMHrj9Te9/ez1WF19FQGrWdogt/QCUFRSQsnJ8phy4MABcbyCHaW8sfRQUFRCTU11omHW1VXR8YREES2ITp8+JbZ9c0sb7dq1Q4wrj+16Kn4F+E2pfZBZDRxoSXO3uWjv7s0XzRZMs8ziV8q4I1mx4jOKigrjLRizZs3mp5Dly5eTsWg/Z85cDppQDiYeFtGjo2Npzm2zefC4c0MRatBPnDiRpk6dxgFr797dpGkBnGQ1bdo0xjKF4Y4ePcy1T2GU+fPns9xJScmUna1PaGD63j53LsuBQGlMdOB73nrrreRoc9G27RsYsg0JSOgPeLB44sGTj9EeeeQR/goweoCGc7KS20IP3XcPY8IiQKWlAdTezeu7c+fezvTYGtDa6mD6b1x5Dd1w/WS+Y1+zZhX/joSQ22+/ndcEgS198uQpz02XcRx8z5zRCxq4yU2PPvIon7th0yZyMrQlMV7pLbfcwsfN+sY+Ruxlq6qpoYP793LdUiwl33bbHLYRdIj6o0YzxomxV1VV8eHI6EiaO2cuf1+2DFsugLPqpunTp3t0Zd6CNXv2bLYxtq1kZaGABAK9hR566AG2A0DDcUOEG924uGiCnwBzGqkCO7dvp7jBg+nBRx6h3//+9wwFh+1g8BPofObMmxl/t1vfuuRz5+rjQXGGooIchvtkv5qj7+PEdpu6OsBsOmny5Mk0adIUam5qpl179rBPgf+UKVMYGxt+eerUSdKTKtw0a9Ys1qHhs5oWRCFBGt122x2Md3zs2FEqKChiQcaOHcMy4gl+w5Yt5Kf5MdzexIkTuM+CkiI6dvgo6wOyTJ02gyZOuIq3YcDOSMrx8+sgzBPkNujjTOP5AFxb2A0NW2ZaWppYL1ddNd4zT7Zu3cxym8cJG+/cvZuef+5Zeu2NRXT/3Xey7Q3e4BcWFkJ33XUP8zZ8Fn+MGzeO7Yynhw0bNhAyRzE3AYOJ/bIlRWV07MRhj1/B7yG3WYeQ5dFH9bm5e/du3t4FW2L9DLZHg1/pmbQWuuUW3cbY5vW9732Pxo4ZTXffey/T4pyykhLaf3C/xz6Gz2ILVllZRVdMCSdjDi5fjq1wutzTpk1nGzc7nLR1wzruG//NmDGDYUDRJ56qMEb4xEP3z2Mbnzh5iooKstivBg0KpbvvvpPP3bp1K48H83jChHE0dep0nt/QldGunTCJrpsykXW3fPkyzzhvu02fJ9AVbOHvH8DY77ffrscrbOWpqABkqtMTC2EH6LCtrYXlGzduLE2fPoPnD2IHIaXPTXTzzbfweOCz2dn5XGsX677f//4dvH6OG/WcHNyYuDl2cCxscdKu/dvI0epgP7zyyivYZxELEX8xHzDvEZcxfyA3+KM/NCNeYSx4kIJO4As4jrZz526GrHW5XXTV+PEsN64ZGzeu99hywgT48nTGiD58VK8YBf5GTEF/587pcRY5Jg89NE/nvXs3NTXUsSzDhyO267EQW8QgB3R41fgJNH3GdL6eGNvv5s3Tz2cmF8t/UrwrwHwtWvQG16FtM0H8ATrN+GfU78Qn4N2OH4nvAa3WZjfRtrd7usb527ZtYhhDMw+DLz6Nht8Bv7hv354evHHcZm/V2uz2HschK2gB29eDt92u2VramN7MG7VZ33nnHa2tpUXr7PoB53mTBcd27drRk7ejswetp09HJ0P1bdy4vod8LLetWy9mWQ4cOKD1rkNrlsPgrXV2ai1tbdratZ/1y9tcSxLnbduyQwOsnoeHpulyd+nPc7yzU4MOP/tsBevELB9kMXRuPp6amq7t27dLW736M+273/2uNmTwYO1HP/mJlpicqNlsbX36XLdunVZdXe85jr4NO9ptNoO1hnFm5+YzlB36Nlqbvd2jc4/cmqY1NzcztCN80TjOvOGzvcaJ47D9oUMHtDaTb3a0d/M211ZF/zt27Ojrszbd//C7uc/C/HxtRy+owQ6HwyM3xmA09Anbw889PPrzq44OLSUlRRscFdUDBpTHiTF2zTmDN+SKjz/OYzXrEP6Bv81yQ9/1zS267U36Zt6mee/hbW9nyNWEhNPMx3PcoLXbPePBb+998I42efL1Om0XNGEP3vZuG3c4Ohn+9bPVq73zNukbchs+C+jD/nRoyAfeuenZff3KkNvMu2uebNrUFa9MkIqG/sw6RN+wI+yJ40ZrR7xq1H3FkA+/gebjjz/WzpxJ6Za7V/wx6PEJ6FfAGJp5t7a19/Fv8AY9YCBRg9jMA+diPtja2j3HoUNAUm7atIHnfR/6Lt0Y44HPJiYmatmp3byN8TB/kw6hb/B+441FfX0WMaUrHhq8IQvkTklO7TFOgy8+DfmMPhGvLsZGUqEwIARSu7BQOCawOcj76qe8tLKH0gaiR7Ho8srqgUh6/AbjSgtul5aXa5hM5gDYg1mvP3ChkPKGDsFf2upra7XGVu/FvPvw6OxU4n3kSLyWkBDfh01/B4C9a9yA9EeD4+fS0rQnn3xSGzFsmPatb35T++DjD3xiAiNomCfMQPyha+hF0sATtiwslBXRhr/2VzzdW38qfsU+q2L7erlfpWama0NiBotlxxjFc7OzUysW4i5DR42Y940yfGnIEBwc4k21Xo8Bn3vfPjm2L/uV6YLolWnXQcQ1FduXlpdquGGSNNi+ulYWr3AxAgZ0dnamhLWGm8DqShmGNhhijHa7XcQb8wc6lMx7MIQ9pX4FOlwUpfT11fXyWKhpSj4rUsZ5IhK/Ur5YnsgvyXHxaaCupY52b9xNn3z2KZ05cZLuvPdufs148803X3zCfg0lwtrz9GnTvxJYyr3Vj9edTz31FD3wwAO9f7r09yUNfO00IE6awsixNoB1EElDggze4UubCu2F5i0dI8amkpmHtWhV3uKs8HaU/ZPZBnKDFrJLG+jNCQ74jnWeV155iSZdMZX+7y9/oblzbqP84mJ6++136YYbbpCyZlnMvAc6EXSqckvpQafihyq0sKMKPWilmfLQl9viEmMpY5wq+lbxK/CW6htyY30Va9OSBr41NWo+rjJOFbl7z4cB5Xe7qbmpZUAS8491TWpzU9WvVMdplm2g7+Ar5Q27SJMC0Sf4qthSxWcHGtP5/k3pgnv2bJo44xMZaxkZSKqRteMJCTJCIiosLKTERDk95JAaCwWqgTMsbTk5WeJAiolhLOhL+EOHjY2yLS2ohbl9uyxwoW9kWZ49e04iBtOANy4ADqeTVq1cTnPmzKGZM2dSWUUJbdmxgW/Gnn5qIQNMYCLl5haKeUMn2I8rabhwZXACm4SaaPPmzewvEmroW5pZD37SzFPQVlaW0PHj8ixl+JVLkyE8oV4o7whCtpKgYZzSgIR5o+JXmJvmIu++xEFR8YSjx6i5xfeugMLiQiVZcCFva5fBPKESEfQibUgklF4wnG43ZWTJ59rurduVZFGJhUjeUxmnkdwk0Qv4wm8lDf4H9DhpA++KrkRPn+d0qMVCn/zOI4EcIw930W5ZADDkU4FKk4WKLs4WZLXK8UCNTDtDrvP5qcIb6Ccq9JAThcVFjbF65ToBTxUs5crKWnrut8/R5i3raMTQkfTEkz+m5StX0dB+EIg0rV0kNoh0GEjfARe07oBOsihisELv8ibUNzNU4SuXgCmlducCVG5yWV1IShU14XWZeXXIrleeflX9e+KE6+jd+sVUWp5JE8Zf6+Hj7Uug2ypFauTTkRltccv8ClZXiW/IxpU2t6IOddQrGUQiZFDROcaoEjv9/XyjkZn1oBTzeSub+eyBv2PLlKTp8M8XcG5KhOiHRkkqpGBLG4KowyF7apHyNNMZW5HMx87Hd28g+gPx1X1Apkb9KVvtpkXGmYg6Zc5oHouvkMFP5Nu304crPqFj+w/T/Q8+SJ+tXMOvAc18vH1XCQL6lUI2UmuHm9QKDOigLd5k/OLHfGnQ1IMFgOqmv318xRYxaQPOtdUl0x94qsihoz/K570K9q4xvofmzaOt67bShOcHvuCiCEWgS+7nuHA5yE2+gQZ1HwkKkqN0BXKxA6EsfsBpll+4MMQLhkNvHaRkf4smv1tALFSR+/P4iuEzA33qVhHaZiBGF+A3paQp7BMLxmOR4E7DeIUrfboAvZTW4zECOaAzJd5dCE8oAC1uiGBSWdrdpFI9BK9xpfRsH6Hcxvpgb97QVUFBHn20bBl9sngJDR46nH781BP02MOP8b47sU4UCNlXOi3icarYU4UWIqvQK9ECuczPxfu6JapR4e2BdkzPpuho2UVDxa9UZGG/8kclGNkNAOh3H9pNLzz3PJ0WlMfDkgbHIIESsV+a5ZDOTYUYpKI/Zb+CryjqsPc87k89n8c+F4q3aryy4p7lAtiyP11diONKF9wLIcAlnheHBhBUV61ZRe8vfp+Sk5Lox08+Sff/4H6aNnU6SV/lXBwj+eeToqSshKZPnc6AMOHCAiAXk5awFnrtNdcwbOPYsWMvJtEuyXJJA+dVA+LnbtyNACpNmmxRU1VFOUIYNtx1AeVJmm1XU1fHGbJSTSCbVip3Vk4eLV78rhjjFXLXNcvgLptbWhjDWEVuAxHK1zkut5tOnjrpi8zzOwpLb9+9k5G1nn3mOfrG+LH07lvv8vaMwuJieu2112jGtBmeiy3QeDxvFjxcvH8Beo2OdOP9995HT54+IdY37AjkKkmDzy5ZskTsKwj8Ut7oX8VnITfopS1DIbHJZmslp9NBreQQsc/JyxMnoOBGzIxW5quDvKICKiqRwy+eOHWSUakmTZtCBw93o7956+fYscO0apWO4ubt997HTp48KfYrVdsDi1war2B7xCBJw0ICfBaoS5IGGeBXmP+SlpWXI0724nh16pR4cQMoYWVVsiRP6AQF6PEpaUBUK1PARIftL8Yme+/Dadkd/Kpx2LARhKxIQAqiQWHGK6ewsDA9S7WujgOuw2mnYKuV4cWwngJa4PG6XS4KCQujyPBw/rustIjyCvKoo6ODIcsAK4c0cGDg4pUQ+Bv9IZjDsJW1tRQYHExjRo7k13TM29nKUIOBgYEMTYfzCvKLWG4jXd3gjTGgmXnj4gYIscDAYMYEBQwk+odTt7baGPoNvFGmDq0gL49xTzu1DnLFuWjo8OHMD5MX6xNITkB/4AH5ykpKWRaUaBszejTLbfAGRCJ0ZJSUgoPhVaE+LjeNHq3rG+M3dAJafG9pa6Pq0lLKyyuguNg41hVeiZt1CHkN3nk5eZRwIoG2b95OJUVFvG929cpNNO6qsQxRB53gXJRRY97l5QypGBkWSZddeRmFWoOouamJM5ZBCxkM3pAPsjscrRQcEkijR45kXUEnaKCPiopi3m0tLVReWUmFueUUbA1hWEfoCzrBxdLgbegQvEvKyshWXct9Gk9DBm/wx7gBOdfmclNpSQkXuYYOQQMZWd8AZMdaJmSJjaNBgVb+/f+z9yZwclVV/vi3qyu973uWTtM0IcYQsoCRTcQYEBgHcUFBB9Hx7zAojCK4jOO4/MZRR2VUBDFABAyLAmIgkJB9XzvpTm/pfd/SW3V1dXV1dXV1vf/ne1+/6kqnu+tcTDAwOZ9PUtWvzjvv3HPOPfe9d8/9XurtdDqU7Fz6Z9xv1IXf+Y+6UC/6prm5WcUseSmbNnO53Uouea3+wOtTdltbC+Li4pCblwfOAVq6UA/qTdkk4vrSL7RxXn4+sjMzQ+LKvEemHLaTMro629Wute21rUhalIrY+Ch1nDFOPUiWf+rr6xUeMc+nJEJKsj20D3n5nbz83t83gF5Ht9Ins7ZW9U0eny6u2MbmxnpEKXjQCd/Tb9b2lUnjOYIy2po70NbUgsbUdAUR+NprG3H7pz8Ll8sBsCgy4EN2thk/hJn0eHwqX9DueXl5ql3tfe3j89d+JCWlqbjiq+Tm9nawrcnJ8ciZM1/lmtB28mQrrvhw0FjfDKfbCbstCvkFpuyp4ooy2E5Ou7C/0vfMBzxOXGP2+VAbUgZjhXHO3FHAJ3jmwr4+dYPEufeEhBjExyer8+j3uLgElftoN+a9UHtTttV/GFf1jY3oGI8rK6fwuJc3X16oeGO+4XnsO8219ehLMbfyC8asy6FyG9vDLU/Z7ymjo70Njc2N4FsTtpMxqmLW41F5IjQXUo/25kbYouLALYupt2mTCUxoK2YHmAvb29VWi7QN5fKalO32u2HzmVMS6enZpo/b29FYXY+YpDh100/oXlJoXMVZ/X48p1AfwtOeayQecO3qBTpUQomcFa0cYDa6XVWZjo6OID+/QLXP63HD43XB6/WpwJmbm6uOu1xuBcptVqUGVCfgIOvs78foyCjcbpdyEpmZ5BwOZ3AS3hpwmcjdHi/YqTxuF2CYncPn9aHX4VKv+GNizIGOATTo7ldYykyElGkRHW5NB1iy4QsoHeLiGFgDwSc6XrO316VOjYqyBwdcp4vJ1QeX04v05IliKN4o8IaTBQRMulYic3gHFC5tX18PcnLnKBRi6mTJJr+VGJkseV22weN2AjAH3J4eEwOZylA2k67P60UPbxQCNnT29CAny9wv1LShA2Njo/CPt23Nmiew7qlnEB0ThU988jZ8+vZPBwOTOKm0CXVnQmMnULL7etTG0gOuPmA4A0iMhtvtRU9fp8Jlpd6pSelqDtbpcKkYoX+4OYI14Pb2dqvByaxiDCA2dq66K6ctWNHM9rKDkohP3dXVHpRt2dDn88PtcsIT8Ct+xQyo78pf4wMLbWIbHVHYruzMPM+STZtwgCKxkIXJDlHmIOpyuTA0NASn04XxkFXxwCdI0zdmAuC5/f19GBkdUbrSTyReg7LZRvIT95U2ZHscDgdGx8bAa4yx9NduD7aT5yYmJgcHXNqEMj2eGDPGMzOV7eh7SzYHIraT7XG6XGojiF41UI0pXXjcihXiA1tx5fF41Dn0s4c3ndlmm6y+xr7JhM6YZeZUMgJc492HefPmqeP0FfnZ5ynHks3+6/MF4A14lZ8wnhgt2VQsKteMK9rKNeRSsUks8FtvvBXf/873VL5wOHh8RLXVGnC9PlNv9k3a0CJHh/mdenCwo71p3r7xftLfP4SUJPdErnE6FfYw+dUNTiAAt9cHt5e6++BwO5APM6ewHw8PDyIyMhZpaUnK3ryuq38APn8ALsaiJ13lA9ortB9bfZPtpL2YJ9xup9pegknX5fHA5TRv+gP+NDXgcurG4XLDZvPIGqoxAAAgAElEQVSrmPV4zZzCm33LhvS/NUDR3l6PByOjYxgY6GenVWZRubDXqXzDOOKAS9lul0vdsPCc0Ji19ObJLEZl32T89DkGMWZEKjzpeXPmKNk8r7eXm57YlB7Ww4dP5XwfWCxvycYYFC/zD+OKshmzfBZnH2M7eIPL3IRYs9/3djPXmXO11oDrpJ39XnjdfiQ7XeoBjiymTYaVf5KSzBtQphD2H+nbOPNib+P/UsQq4lU+/fQfjJNCGDHihxIPVEKEDiPesRRara2lxSA0oZQK9x822nrbROzUm1jKUqjBvXt3h4UutC7scrqM7Zvk0HQHDx42GoSwhISEI6bqZGI7nv7jH43VN65WmMZf+9rXjIOFB4033thgbNq0dTL7tH+vf229QbxUCdGGx44VSlgVzxtvvKHwUyUnEBP72LFjElal75NPPqmwYyUnUPbBw3K9ibtMeEcJkY8xLqXDhw+egjM703nEik5JSjF6hZCX9A19JCH6/JX16yWsioe4zqXl5WL+119/zeQdGzOu/MAHjOefnx4Dd//+3QZxt6U0Gbd8pvPMuJL7nvCL0nxFeET2ZQmxv/7xj88bJSXFEnalw86d8pxyrPCY0SLMKYRd3Lp1kzgXlp44YbQJ44q2I5ay1IaM2ZqqOpFNiL2sE7MyoWeG6/9O0ZSwkpivNbhwn68r1V3+23jzc6Yuxbvq8hMn8OKzz+P5l57D/LkFuO22z+Czn78d6eOvLVtbO2G3BTB7/CnkTF37XJPDOdmcnAwkJpqva881/c6EPpw3/eDlK1HW0ITURMkimDNx1TMv46c//jGOl1Tgzy9xB6DTqb2zS+2gZU0lnM7x7jhC8IiMjKzgG493R6tObQVzFPvm/AUXqimqU3999/71f2fAfff6MNgyzrvs3bULT/zhDzh66BBW3XAzvvnv96sN3YNM57+86yzAubkrly1DZUND8LXnO7GRtY3NuO6qK9Sc8Tv1ZvedaPfzOr99FhBXKVOlF174syoAkKh34kS5VlUm97uUEosWuE+plLjpslp/JjiBk/g6lZBsZ3+/DDOaAyL3I5USZbMwYCbinWJrazO+8fWvq6UV3//RD9Rm7qVVJ/Dcc89MO9hy383j5bJKSF6fenNeR0IsFKHuUuIepbSNhPgGQkc2YTpZeS4hyi06au5NLOE/cOCQhE3xMK527Zq5CjdUWOnxUrG9ORc7HCAqWaiE6b+znaEFQdNzmrUUOjHLpxa2VUqhe8suyM9DXl4udmzbNuXp9bW1WL/+5Sl/m+ogZQ96ZDHL+NOJq20b39SyoU6FOuFIdXTRyYVHjxZpyd6ybctUpp3yGHXmpvISYvyxGltKlMu6DgkxJ4bGleSct4tHa8Bl9SAbIyHDiFQFKBJe8vil2YIFVT6vKiqQyvb4ArBFy5rK9rHASkqmPWQ2ocyREbOoRSKfxT7TESsXn1m3Djf9401YcekyeGHH3ffcjePHS/HFu+5U1crTncvjqpDDN1HoNRMvf2Phj5RoE/pfSsRR1oHVM8YMqWgMDA4hSgjDR709wpsKKuD369mERTlS8ilwZBm32jiemxfIQlz1HZ0nSBbISYk2NPuE7IzJcXXzR29VcT3V2Vz6Mtgv33CDxTu2MRlSks/mw9iYPGbdIYV4U+l6yjGDld3yzQvYt3V0YaGalPx+n1bu9Hmnz0GTr8k+r9NOj0ueZymXiGoiGtXLVyKZZ4hJ2ALzajoYnKwyZCWglHQhFVklJyU7AmqphpRfLtmSKC72hqEBlUbpk9fXHS8txfe/931cePGFWPPoGtz60VvVDj2/+/UvUVCgBxqgA40tXOZnGURVmQb/CPPFrFqX2nAWRg35TQthID3ClYTCaf5ga3RtAsghEuUp1FSH1aFSYr+UDoqjBNLUCRSpEkG+U29Cbrnlo9i2ZQu4mcCUJA0TVXErBwHl8hzmLClFRMgGcsrjAg+dWGGf18Ei5yCqQ2Z/k52hA79oVa3LJAM+4Y2wVF6QT6Fo6tkkeO5Z/hL5wx/+8IfSa0REBDB79hxVeh/uHJstErGxMUhOTgnHqn6PiDCQmpom4rVFBBAdHYe0NFkhjGGMITExSS2xkVyA5erBpUJhTmA7uVRhlgk6G4abkWAgJycnDJ/5c0REJBLjYuEZHgZf7Xzlnq/glz/9KbJmz8cjv/sN/uM738HK978f0dEm0HlERDSyszNFssmUlZOp7CI5ITLSjqysTLEN6Z+EBFkBj98/gpyc2SIbRkYCY/5RcVxxWVVOVjbi48PrQnsnJCQiOdlcpxjOLpGRkWrJRTg+6/fo6Eikp2dYf874GRUZifiEBJG9uSzomaf/iHvuvQ+xMeFB7xmzjHErbmZSJBIGIiNtyM6WxSxlcb0ll+dIaHLMcl0waxCWL12CCy80lxlaciIiItRaVmnfBMaQmZkliivKtttt4v4QEcHlgWkiG/JhYtasSLHsWXZTNnOWhLi8LSUlWcIKwzAQH8+16jLZQERwGWS4C7A/MOdLZLNf2qLsmD/PXDIaTjZzOPumJGb5pBeh1pjLYzbc9c/U7+eLps6UJc+CHM7N/uJ/foG/vvqqWnv21a/ehxtvvhGZ48AbZ+GS50W+Ay3wbimaskz/i5/9DM0tbXjkd49Yh85/nrfAu8IC4renfAVFJCbpqyjyeYfkj/UsyNGSrTHXpiObk/ksQpDqoiNb2SSM3py/WbduHf7hppuwcsXlCNjseOmvL+HQoUO4887PzTjYUhcpcY/gWmGBA2XqyH5Lvidgu4B0ZJP3yJFD4uIWiX9CVTzTvn+rsqnHsF0+d3rW9daYq54qrm795Mexbt0zILRgKBGNTme/YsqWRZX5iv2cyFeEaD1yNGyxpGWXcylmqQv/SYjFjwf27QPR5iRE30hl0+dTxZXkOmebRzzgciB4+eU/iZNXfWMzSitkFZ+sIN62a4eC9pI0uL2zXQvflYOVtCqTxUQ6G7NzcJbKpg03b950WhMZSMRa/f73voeLLrxQYTnffOstWPfCn/HA1+5TmMannTTFgQ0bNkxxdOpDhA8k/JmUWPUnDXhWkUt9z+uzSnnQN82c3SQFWbVdVFYknhQrK6sYR8aZJGiKP1lde6RIFrM8nZX10upqxohOJf7Ro0fFeMfwBhDw2sT+IaJYY13zFBY4/RB9rlOlzDguq6g4XdA0R17dcHrVfsGChShYuBBvbtx4ylmd7T04UVtzyrGZ/mDMEilNQvS9Tsxu2vSGOF/R97zxkxA3q6+uLlMPNxJ+xp9OXNH30ipyK19Jb0TKy8vFKwJ4J3TwWKGCh5W0s7TyOLgJvYQCPp96Kyjhfbt5xK+UBwe9eP75J5CemYu0lCSsWrVK6friy6+o4qix0RHccMONarF2RWU1ykuLEDErGhkpKbhu1SpV4kQQdIJKkAryC7B0+VK1pGb//u0YGCB2bzSWL1+uQCcYFBzMTEiwAD71qU+p844Vl6Cu5oSCfYuPjsb1N31EAVSUHC9BbQOXf3DOLgvXXHOVesLetnMjhoaGlZwlS5aA+MjsAHv37lXyONH/mc/cob6zdJ/LGkZGRtRcwc0336zmuphE+I+8qemZuGH1asXPgYIVtpxXoFzK550VE5RZmBDA9R++CYnJ8QqrtbjsGEaGx2V/5GaMBkbx/LN/xNq1T6ly+muuuwo//Z+H8N6LL8auHbtAyLvY2FnIypmHa666Ql3z5VdegTE6hsjoSFx95fsV1qxqz/69Sjb5P/jBDys/0IaHCwvVefSP1c49e/YoLFP+kJk9G6tXXad4lC/tAUSOGFi28nLlB77VOHz4sKo4Zzs/9KEPKdnsuHUNDeo8lqbccsutyg8EmG9u7cSsyEikZKRh9XVmnLz5+kYFz8ZKw4svugCXXrpMDVbbd+7GyPAAYmMT8b73vU9BhrIwrK6uLij7wx/6MJJTU1FcXKzwosfGhpGamokbbrhB8WzbsQ0uJ7GugcWLF2LRosUqGe7cuRNDQ4OIjo7H4sWLsHDhQuXf48eLVPxwH94rr7xSzdfTvwSM55xiUlIUVq+6QWFdEwS9ra1NyS4oyMPy5ZcpH+/YsUP5flZ0LBYv4jUXqURWOG5vxsrKlVcoG/JtQkVlLUZHTHzqG6+/HjHx8SqmeF0S4RStPrVt25vo6RuA3W/Dey59j4or4s9u3blT8TLGLRvSx6+9uRHfe/BB/O73j+PGG80+yGtWVpoJilCnN9/8UXWuurkZHFDxecEFF2DFihUq6W18/XX1O+cbP/zhifg5euAQPH4/YuOj8ZEPX4/4xERlQ2uZS2j/4XKenj4u7/IrQJVrr7lWySSQRURkNIzREVx77XXK3hwodu7eieGhEUTHxuIDH3o/slNnqye7/QcP4qUXXkBvfw+2bzOXC+47cAjtrfXw+4k3nh70/SvrXwkWJC1ZvBALF074nnCH8fETccWnqq1btyqdqPfHPvZx1b+5EQHBJgibyHoM9nsSl86pav6QuGL/pg2tHMGYWrx4sdnOP7+g7ErZVi5kPuGyRMomLCxls0Kcg2Rvr0OdF8wdPh92bGNc9auYzc/PVfmQN7CMfRJlX3XVNaqfVFRUoqr8BHwBn6pRYH/g3Dx5eQ4pKyvHzIXDfuzauw2MIxL7H2OWuWP37r3BAlce4z/qXVZRZuaUxHh88OoPmLm9ohLV1ZXK5oS7XLXKzIVbtmxTUJeRY2OYf9HFuOyy5aoPWvZm37z44gvVdbs6W7H34DEMDw0o/1g5pbq6AmUV1WqssNnsuPXWW5SuzFedne3KbumZ2bjuWjOuuOTPory8fHVNxtXe3XsxMDSAOz93p/XzOfOpNeA+/fQTuPnm65GWNje472ZPj7VO1AR2ZzDxzqi+vgFOZz+WLlmiwK/ZYhpDPerHAHF2c/MCeq5/YAD79+/C0qWXIyMjQxVcUAaDncS7bKtQgq8gCErf3NKEy678AJIT45WDiIFLrFJuAhATY0dysrnBQP/gEAoP70d+Xj7mzctHbKypH2VTLvW1sGCHhwlMXoODB/filo9+Cqnpyep3dlTyc6Lf2hjBbM8gDh/erxI59SZOKIlBrJ4GY4DMRBMInn/z6Yx3unNz87DmySewZcPr4N38l++5G9dccYUCDrewSXnN4uJjSErJQEF+XojsTnNPyIBNdQDqT9nk37ZtG1avXq14LT9YNqFeVjvJu3fvboU9e/XVV54qG3b47X6kxJgbDFiyt2x5E9ddex3SrQ0ThobUhg60N6tYLcxbyuamDsTDvex9y4OyCezOt01M6Bb4uiWbAyMHW/p4Qm/63nw9xcHVOs5EQixX3phZ9mZcURaJCYfH+TePc4erxUuWq0GRhTwTceWHzxZAWpwJeM/jSnZ3N5YsXaoGeL7+YXtM3wcQFRWnbM7rcO11YeFBFBTMx5w54/jAI370uLsAn03pSzxd65octJnUr7zyaqUf22PJtvS2Ni/g8cLCY5ibn4t5OXMQHxur2tPX16c2xeBNiwUy7x8ZwfGyCtx0/YfV07m16UKobF7L8j31rqgoU8DxRGyybGiucbTDb/OpgY/n0IZ94wnswx/+UFBvy4b0JfuEJZvXrOCOSHHA4vzFwX5PvclLsmwS6nuVcNl3eM0RP/pd/QrDetmly3Cyu1vZkLKLiwvR09OnBjNLb/Y1xgnlW5sXmP7pB2OWA3xovJGfbSNZmxdYvu/u7sbSpUtDfGzmK1bqxsVNYCkzrjhILb1sKXIysoIFYla/p/xQ2W1q849GXHbZZUHZrMLm0zf7TlRMAlLHt1XkgLj+9fVYvGgpFi5YqG7WLXvTZpRt2ZDHTzp6UVlSouIqNH5UzNrtiImyBXOhaUMzpyxcUBCMTfKaleh2VfBG2zIXOh09OHBoH1Zdt0r5ktemDGI7WytWQn3Pm7yYmDh1kxnaBy3Z1JvFi2wHc+Frr7yGWz5xS7DfM4cT65u/R0XZYGEp85p865gQE4eChQXBmLUwCkL9Y8XV9u3bgw9pytnnyn9ShEhifB4vOm64PR7RKcThlOLMUmBbR4fhEcqmDsQnlVL3yW6xbMp9+eUXjdExIjyHJ/JL9Ha6XMaTf3jcWLp0qTEnJ8e47/6vGYWHZ8ZXpf1oRylJMVIpb//+/Vp4x1JMZ8pWvhfi+pKfekuxq2lraVwRX3rD5vVGU5MMg1U3Zk3fj4rcQ721Yra723C7nSLZVVVVRlpKhtHrcIj4deNKirvMixMbt7tbpgf5Z4rZ1TfeYPz+8SeDbSovPWFs3yrHoyY+sjSudH1P2ZJ+T+V1Ypb8mzdtMmpqqoLtnunLW4kraU6h7dhOWSY0fe9wyWLW5Ro2Xn7lRXF+I4a/wymTTXuxT5yLJH7CPVduEN5JevBui69mXvjzC3ji0ceQX5CPz33uLgVQYd1lv5Pac17Xc9MC3ID+6stXoqSm7h2NpTzZuo8+ugZ/ffUlbNsyNfLUZP7zf5+3wLluAXHRFBvC16F8nSIhvnNvb7deN4c/g3u5SomvbrgfpZRam+WyOUhKYSB5fbaTr3ZCia/Nn3vmOay67jpcc821cDtd2LR9KzZvP4APfPDq4Cut0HOm+k7Z3BNVQtRZumk15VFHtlVKnLOV8vMVEHWXEvWebMPpziWfjmxuExic5JtO6Phxym1ulsMS6sQg+w1fKUuJS8Kk9ra8GBh/BR/uGmyn1N7Ugb6XEvumNEdQ5kyyP/vZT6Pw4GFwv1oSdZHaxJItbaduXPH1KeNcQtSZ/pSSd1jNvUjZtXIh41un/+hATFJuV5e573U45ZmvvBrV7JQttTevraYuwynxd/hda8AtKalQ+1VK9GTHa2+XB5lO8up19KK5WZ7QW7vG51QFirMI5ZlnnxJwmixsp3cc/qy0tBxf+cq9KFi4AE+sXYMv3v1l1NXV4H9//WtwPirg4/yZWSQjuQBlO4Uwk/Zom9aSCRZ+lJbKK3KptzTZcU6Ic7hSqqlpUHM3En7q0N05vmem4ARWelcIlz8xWbS3ywdcncGZe6vq3FRSF6m9vS43Br1exAjR1xhX9JGEqENFRYmEVfF0d/eKcwRPmKk/cE7ylls/gaeefV7Jrq2vxXPPPSfWhXoT0EJC+jFbo2XD7m6zQEqiy6uvv4TS8lIJq+Jp1LhJ1BkUKbyhoUWsB/u8dDAfcPfg0d/+Viyb/UEas6yqfldgKZuT3zIbsSpPB85MBwaSGoh1YWGHxpOcrHUTXNwk+uVXnlfFSjd95HrYjAD++pe/YteePfjinXcFiyR4hl8KdjsuXsd+ZnKWQwfyEjqIfbr+0YHJI69VVDNh2em+zUKEXQ7BZ1OFPdLVmNNdc+rjujbRmUaYFanw6aa+8BRHo+x2aEDqTiFh+kOBgDyudG0CzLxW/3OfuwN/fGqtuvmIChCkVecZIQqj3I1eQPQNK4ClxI3ZpcTN33VkQ4oZbCmgkyiA8RUU1skzf+pAO+rA+bLwT4yNPLOKp/3Khw/x+HDa2Wf3gAYyKYsI5R2PAcwyeCmx+ldKcVGsRJZBRrLenUsZMGZjQW1Yot4JCXEz8nFw49zsM888g7Vr1iAvfwG+et89uP3224MVi1MJ4BNIYqIMgo3nx8bGS1RWlzL1jpnqslMeY8WgPU7Oz+pfXkNC5LNr+DM+MVUsmwiaNo04TE1PBeNFQqygDARkT0SUx6plKdEmOv0hIlK+QYPSIQDx5gWMKx1KSpLHifK9ME6oQ2LizFCkH/jgB9Hf1QUuFaMvuSpBSsnjlb9Sfh3/JLH/CNtJbGQJtKilJyvbuZRNSnFxCVJWxERFISJCjkXOqmMp6ehMmVlZwhxu5UKhvSnbqqKW6v528WkVTfFVVGpSKuzRsgT2djXi7boO5wPXPvMMXnjuORQfO4Z7vvpV3H77p3HJpcvAu9jzdN4Cfw8LENpx5YoVqKmrCy6Z+Hvocbau+a0HH4Q9yo6f/ORnZ+sS5+W+yyzAOgJrmdS51DStUYJrrqSDLZ8CVcGKsLU6RTyUrTMprit78uR8UdFx3HvvvbhoYQFeWLcOd33xTjS1tOBnP/sZ3nvJpeKinLOpN82saxPvkAyFJyhb+OqKftf2vQ60oxA9iHMaBGyh3SV0Nv1zNmWznf6oAHE8RKTbH3TjSmpvKiuR/cUvfQlPPbHWXMevGbNSXZR/zhEo2ndqzNKGYnuzaGpo6LTd0KYLYJ2YpYxzcbClXuIBl1V8OlB2hHYsOi4rymHF2q5du8RVaFzwrLPpsg60I4umnn/+WbUw+7kXXsBHrr8e//gPN2F0ZATrN2ww52bv+lLQofv27NGCdty06XRox+mCjPB+FmLMdDzWcdpww4ZXrT/DfhIpac9+E8UnLDOgihAmbxU43Xn1Da04qgGRqNCPpNCO7e04IqyaZbXniy8+p17/T6dr6HH6nji2UtLpD3w7xBiXEn3PcyTkcnsAt1/tEy3hLyotlUM7jgT0oR0JfiEkbswRjhZcuBB5BQX4wX//AK++Hp7fkqcDR0rf60A7EqJ18o25dd3Jn/SjFNqR/Xj9+hfEm8TzSe5sQztKb54J7dhcK1sRQijXR3//uHgVBlcycBpPQsxTZcfl8KISmWeKR7w9n9c7hq1b3wAht9xul9pKjygzLA5qa25GW3t7EAGFlWpNjY3o7+eG9aNBXsLYVVRWoqm5GUYgoAYtDuSVVSfQ2dmMkRGvmhfh9k6UUVZWDmL+trS2IjYmRs2DsLy+ubkFDgfRayLUFn3Uo765FidKK9DS3Iwhj0eh3/Buq7y8FB0dXAbhVihRlM0gPVZSiJaGZsUfYSMaS7Iqrz906DDWPfsMfvj9/4fa6hp84Z+/iLv++Qt43/tWYnRkFF09fZgz29z2iUsaOjpa1IbO3F6QWxGyPYT3YwfmPyJQces+3iQ01jeiu+ckRke9yMzMVig9hJWrrq1FR3s7mlubMT93vvItZbNidnjYi9CtC6eyN9tTXVOOzq5uGAHqkayuadmbsombfEFenpLNUv/OzhZ4PNzmcGLLON480H70pbVVGZMKqz37+vpVAQrnl/iPNwIlZWXKl5RPlCj6gUtfWtpb4Rroh8c7gpzsbHVNJhyij/H1J2dJqSNlU0faMOA3FEQm57qoa1VlpfqkbMuG9H1jUz36u7sxFohQ2wVSeGlpKSqrq1UcWr6kbNqEVbOsVOX2aPQPfVJRURGUbaH2sEqecTU46ITXO6y20TPbQ4i7CuUfbk6fkZ6ufMxlIZRNf1tbrzGxlpSUBGVbNlR6Nzahr68Ho6N+1R7Kbm5sxInKSvXpHBgAt6Yz23McXV3dyj6REZFITjFtdezYMcVL/wT8fqSkpqq4Kq84gVf+8iJWfYQ7SSUjKirmFBs6+vqCSG1MXN3tLfCMmFXK3BKT/WTPvn1BX/r8fqSlpqKnvw/1NRXo6OoF1LZu8cpH7JvFxceVL4n6RnQrEuOqo6MTg4P9GB0bQ2aGOT/LmGWfpy+JsJSVmRn0fXdXq+rHhA1lXIXakOcwZm32CLS1tOGNNzbg6quuUPCb1jaUhItlvJDXNW5DK65OnuzA2JgP9qg4JMTHnWKT0JhVvm9tw0lHN/zekeBWhFbfpL2NcXvT34yfzs4OjIx4VAESUZVCfUl+oluxTZbvHY4ejI1FICsjHYiIQAXhS+vr1XljfiA1zcwd1TUn0NXVi0BgDNHRUSpmrVxo5RTWU7Cf8HhjYxO6u7tUXFn9nvmkprpayR7x+dT2evRxFfNs+0m4h0xEvtTUFDMXFhaqPs82WP2HfiB2cU9PN0b93N7U3BovtJ2uvgFkzM5W/Zm+b29vg3PIDUQYSEtNU32DMJ2W7624Uvmqsgr9/Sdht0erttD3bF9xSclpuZAx29HRgaEhrnywB7dlDY0rqx8z/7S3tKKqphyX8O3jOUbiJ1xgVFWVcVCoq2sIFgywCpRvsmhMax6T8GutrY3o6RkAl3xYxQV0Oi8YZZsAWucxJl2ny4fq+lYF3aZsFLCrdVoEouY/a5Pl1tYuNDc3w+n0oKqqXDmV/ARvpx7q5aFtvChgzIbK+lq4et1obG4PymayC3gD8Adsip+vK5544gl88rbb8K//8i9IiE/Gt/79m9i8fSu++MUvIi4qDl6PuVtF6JbWvHlwO7xKn9bWiWVKlMd/tIlFTocL1bXV8Hp9qKyuD+rN14G0ibJNYGJunDZxudwK87i1dWI9s+Ilf8gaNqfLiYrKRvj9AVRWVEy8prNk+3ywTaiChoYmOJ1+BdHWWDuxdIssPl9AybaKDliKX11dD7fbqzog22URdaFc6mL5mHZob21VA3RLU5PFCt/4aRwoLLuwzUxe1Luxuj64nETFB3Uebyf5SJ2dXait74TT5Va+t4Qr26kYNO3I41yqVV3dqDBi29vbg7i1fO/q95pxGNoWxizjijFLDGLrmpZstpH6kDiA0z/EDa6tZ5z3jf9i+TGg4sU6aOrdCLfHi/ra6qDvrX7D1oUuX6lViW5cn/4J2SoGx/ua9fbY2edEc3MjAn6b2v2J/iNZfcy04YTPmppa0NXrRnNzF1rH18mz3ypfjtvbaqfP41Wx6veZfrKWZfjHr0FoQl9IHCrZXV3o6elHU93EchJVKT4e49Hj+0bT9vS9z2dTMaue0plOxyElrXMsG15z7TVobGxHS3snqk5MLJmxfMmSS8tnlmyvN4Da2ka4nOaSnNC48vk9sAqYVU5pbIS7z4Xa6on1/ZbvGbOWvS3ZbHdjYyec47JDfRkaV/3jMcIcVF5VCv940XQgIkL1AzOyzf9VXFVXw+MNqPWsjBsSq3kZf5QbKptxZ/Ybt8otVvtNn/tUbrOOUQ7zNh8YmE84WFvEq7NPsg0Wf09fD+rrQ/u9qeMp7YTZjyhH+b6/X90Ato8v2VQx5Tdfo1q2JC/jiLI5eFL/YFyNjw9sK31lkRlXXNtPnSaecq0YoU2s/MMlUszLZ6sC2hJzzu0AACAASURBVNLpLX9K4a+Gh4eNxx//vRhWr6qmzjh6tEgq3ti0abOChZOcQLix7dvlEG87d++cElavsLjQ+PbXHjBy5uUYH/zgB43HH3/cKCkpMX7/+9+JIeG2bt86peyp2kHYuw0b3pjqpymP7d6939CB1Vv/4itTypnq4BtvvGFs3iy34fN/+pNhCOEua2pqjIMHD0512SmP/eUvfzF6hZBwhEfcvX//lHImHyQ855NPPmmcOHFi8k9T/k1bE/JSSlu3bjV6hRCW1Hvz5k1S0cbevfuNjo4WEX9VVbmRkpMm1uXw4YPiuBodGTFeeukvIj3IVFRUZBQdOy7mJ4yqlL70hX82Pnv7p6Xsxp/+9LzBvCUhQkzSLlJ69dU3xPmKvt+5c6dUtPHsH/5glJQcE/F3OBhX20W8ZNq/f6/Y906Hy1i//hVxLiwpKTYaquQwqv/7v78W27CwsNBgXpHS+pfXS1nfVj7xK2XeQVx22eXi8vZIG1/j8VWtrPTbMPxISUlVr33D3T3wLis+Ll69tgnHy98jbZEK7J2vePg64/XXX8d9X78PD//iEczNn4PH1vwe33rwWwpcnMuT4uLi1es9PgmHo0j7LCQnJanXR+F4+XtU1MQr3HD8vHxcXJzY5mN2IGv8NV5Y2QTAz0hGRpq5yUM4fntkJFLT0tRr43C8tFpCYqJWxWxmWrp6DR5ONp824qJj1WvWcLw2w1Cv7/i6W7osIzE+HolJSeFEq98NIwIpKfHqFa7khNjYic0PwvFT9fjEJDWVEo53cGAQzzy+Fv/2b19HTGz4JTw2W2Rw+iec7IA/AgFwcwpzGiUcP39PSIwX+96IsCMrM0MiFlExsXjk0Udxzz33iGIlMtLctEHSj/nEGc2+nCLLV1xzmpmZJdKDjWM/5ivfcMTcZkREYM6ceaKYtcOOyEhDTYGEk83f7fZZYt+PzQKiIqODUzfh5DOuomLNV8TheLnuPjLajty580Q2HBsbRUJCosgmvPZ73vse9cQuX+QXTuMz87vWsqAzc8m3XwpfZ3B+4Fc//xX+8spLyM3Lw333fw03j29l9vZrdP6K5y1w5ixALOUrl61AWUPTuwpLeSoLLVt2qVoeZG2hNxXP+WPnLXCuWiD8I1yI5q+9vlG9ow85NO1XTrpb2ydNyxTyA+fPpMSnVA6g4YgFDk88sRY33XADVl6+ElHxUXh10xs4cOQQPnfHHcFK41A51JlVs1JiO3kdCZFPWmlHeZTNAhAJ8aaC84pS4h6TOti+lG3N74S7BnWm7lKiTaQ2pA46sl9/801RrFBXym3lvJlw+ZMkBi0bcAtKacU5z2EcSu3t9XgxTOCL4EyjddWpP9lOHXtLN/7m1dg32VYpcQ9UKdHeV7z/avzy5z8XnaITs7SHTlzpxqxOLuQKAh0YUJ04pB467dSJWcqVymac/Pmll0R+JBPl6uRCbs14LpLWgNvZ3nzKpP1MDWKhirXZ/Ex81m86A1F3d8eMAxeXpHz3W9/B/Pnz8dxz67Bk2TLUddThl7/8JS5fsSJY/GJdO/STE/A6nYPFBxaWcqicqb6Tr6joyFQ/TXmMsp0uGSYxC19mAoKffAHuKTs4KE+MlC0dAFgEwb1FpcQlMKHFIDOdx8QYWvAxEy9/6+/pFMtmzLY21pr7DYcTDIwXfggYATgdDlV0JuM2N8WQ2lvKZ12b7bQKVaxj031SNv0jJfZ5tlVKR49OFECFO8ftcWPhe9+DsrIKlFaWh2NX/UF6Y8F9WGkXKXEJDPGxJUQbdnSclLAqHg4uQ0PyvhlaSBTuItyrmtX1UqrUwHTu7GzFyZMy2comTW1SNVSfl8YshbJw71wkrQFXB9qR8486+KGC6dKg/exTYLvyjumll17Ctddcg3/8yEfQOdCFfXv3qrWPn/70p5E8y9wcPijkjH4xK/jCiSQymd8vNzkftCbqlmeWzrkf4YNZUJBMa5NdVzbnXKQ0axZxt9kCGRl+OY6tn/i7GqDRZr2uTA+d/kCJOvwa5jDxhUPL0MOor9PXRs1a8TAS/5afZ8ZSniw5KyMDt33qVjy79unJP03xtzymGH+s8ZBSpAbWNetfdHLhjE8EUygojhUy2u3QwTkPRMgxvSMjY7VkI3y5QbC14jYyD6qz9OIqeKGz/EWaz5UaS5cuFxcq0UDcwEBKOmXcflsgWAbONWe/eugXePUvbyBvYS7u/+rXsOoGrkdMDV6aCYbl+HaBOlw/t3z58uC54b7otJF3dRpwoGpJi3RQ1Bmw2KZFixYhKU5WHER+HRBz8kdECIw9blwT9Fx6IzILETb5YH7Z8qVISZMX/OiA4+sM5GyqDr/O5gVRMXbEwh6ySGPcsNN8MGYZixKyjY6cVVxaa/mZRJe0tCwsWbIEV1xxDa64fBn+8wc/mLE4SyencFAcGZFvXmAY8hhU/V6I5007LFq4CNnZsyUmUTySorBxRnDxj07O0un3OpsXcN3s+y97v7iNOozcyGPZspU6p7xtvO/Ioim+y3/x5Zfxp3XrUF5Whjvv+hI+cfutuOLyK942w52/0HkLnCsW4Bze1StXorimCukam2OcK/q/FT2uv+kjuHH1DXjggQfeyunnzzlvgb+LBaSPFeqOmK9tpXfG5JPysuXh5vAoq+j4cXz/e9/DxRdeiLVr1uITn/kMGlpa8PNf/mzGwVZnQ2e2UafYIpzeoV5lG3T4qfeZtGGoLkzS9Rr7aOroTZ3Plt46sslbWV6N/hDwiFAbTP6uI5vnct9NKVG2Dr+OvT1+P0Z8ftj9sleoZzOutG0YAqQSzpasraivr1Zs9/7rv+K5detmjDMdG55NvXVlE8Wsp2sC8GQmuxAKkvKlpKVLIKCVr3Rkc269rKxMXLxHYA62VULk09ncXiLzTPGIB1wa6OWXXxRXoTGhl5QIMVUDAezat09VOE5umKpme+EFXHvtdbjlIzfB0d+HdX/+M37ysx/jnrvvnnE7PEvWkcJ96OwyUVusY9N9shBCB/P2yJEj4iIr2pAViFIqOnZAXGHLYN+yZYtUtAr2Ro0K0Q1vvCHu2KxsLCqSF9ps27gNfcICrs6uThByT0oHDu9Dd7esYIUJXYp5y+sfOCzH0e7r68Oew/ukaiv7iYv3fJ4gUpDkApVVJeK44qBFSEUpMYnqVMvrxGxjYy2Ki81K/I997OPweHzYtm3btKq9/vpG8YDR2tyuFbPsx8xNEmIRFPOEhNiPjx4tQmdX+FUYlNfnJUb3HoloxcO+I61q7h8cwp5dO4LIcOEuQnhHqWzG1Y4d28T+qSgrQ23TBMrUjLpEBrDlTflKkxllneEfxcAXhDIrLy9D/4ALzv4BzJkzW8HRvb5xAxpq61FTX4uM9Aw1ANZWV6LiRC0cji44nf1qcTPxQw8dOYSqiipU1VbAP+pXC8f5enjvvgNwOvrR0dEM7u3IBeL7Du3D/V+7H9/9znew79AhfPNb38QvfvkLvPeSxXD09qO3twv9/U7MnTtXgTFUVpThWFEx6urqMDQ0jJycbDVAbNu2RXWM7u4eVRTBOVp2gL27d6OmsVZBvy24qECZlYmCcHOcdu/p6VWyObfD5TOHC4+guqYWvT09QezYbTt2oburTcEGjhE7NjNTBRBL0hsbG1BZWaUqpSmDgVhYeBgDAy5VDTlv3jw1D83B6eDB/aitrVHnFBRcpHThsp2u7i509/bBMzQUxMIlaEddQx3q6xqRnJykFoKzPfv374fL5VKY1GlpsxEbSxzXVhym7IZG1NRWY8FFC5TsA4cOoetkBzzDwxga8mLevLnq+MY3N6C+xvRlTHSM8oNlq9HRMbS0NCIjI1P5mHfhhceOorGuEdV11ci/IF/5gQNWQ0MjBgc9IH5s7jg2NDtXZeUJ1Na3wBYxhrS0dAz092Hb7l0Y8jjR1dGF5MREBZhRXV2LoqOHUVlThab6ZmRlZynflZWVoLaqAV3d3eh1dOKCvAuV3ocOHEJpZSlqK6sV0EV6erpaQrB//14MDXsx4HQjJiZaLQML2ru+DrU11QpshaAYvGZ5eQkGBgbQ3d2HeXNmwxYZqSpdS48XKV3G/IGgjwkYz0pIxmEAkchIT1M3Xvv37lV9gbESa49Bcmoy6mvrUXy8EB63B21tLZg71/R9bdUJFBYVK9/0O/rUcTZI+b7rpMIlHhszFPBA/8Ag9u7ajsqaajTU1sCwRSI9LU35eO/+g9i4cQOWL1+hAFuIS8vkR//UNzSipbkR+fmmreiH9vZO8AaAfZr4zYTS27h5Mxpqq1FTX4eM9BwVPxzwGZsej3fKmGWM19Y24KLx/rNv3wG0tTXC6XTD5eoPtufNN99EXU0V6mprEJ+UjMSEBNUnd+/erWKW1cH0mYWlvHv3ToW7ze0GF1xk9gduKtHc2oER76CKrfnzcxEdZcdPf/JzXJifq/wTaY9BWmqK8v3OnTsxNORW1a0xMbFB7O7tW7eidrz/MO7ZN9nvK6vKFRxpZ1cPLsy/QMUVfVxReUL1+1l2u4ofa6Do63Mq3wMRJlbxSABvbtuExrpaVNbVInM8F1bX1qO8rBQOh0PpMn9uvsKGPlB0BBUlZaipqQICkUjPSFMD2949e9TqAUKpAoaKN6sfm/2hFTGJkUhKSFF5qfxIGRwDDpXTCPDC9pSUVeB48RHU1TUpP8yePUflwl27dqC3tw9dXV2YFRmJtPR0dR77SXVlFerrakAgH+60w35SXFSIfqcLJzs7VZywqEzlwsPERSeGc2ewf9NWrMQmdOSob1gBpXA3si07tqBa9eN6+A1bsJ8UFhYrvGiHozeYUyj7YOERlT+IM31RgZmXDx06goaWWrj6XBgIiavXN25EXW21ipVh9zCyc7Kh+sme7XC5htR8v3LkOfSfRtHULPh8XixcsMAEXx9vxOLF49vT2WwgqDYpZ848DA4Nw+V0YsGChQiMY7UW5C9QGx+wcihhfGNjdrLFixepJ4t58/KwceNreHH9aygvKsXn7vgM7ln3DBYuXBQc5HiNgJ9FU8CCBQuCxVM58+YjZnwjZksPBt/y5ZeBoO95eXnIyMpS+nHCfuGiRebyj5DytwsuuEC94qioqFRFRTyflJGRBXtUjCoDtmTz+NIli3HsmA95ebnIyTELc3jOosVLgiXDEzIysGDBYrURwNKlS4N68wZA8bOKNaR8lEVNPp8faSlJyM/PV3rwv8WLFwf1ZjtI7CCUuW/fPixZchkSE2PVccpesGhxUBd1kEUZCxYqrNbE2GgUFEzIXrRowpc8l5SQkIqly5erHUmWLH4/EuPMam/6WNnbst+YTZVU0982eww8bicW8drjtGDhIvMJORAIFt7FJybjsqXLcfDgQSxmEdf4NbOyMhAVExXUmzFCuuCCC0F0p95eBxaHyM7Lz0O2b7bit/TmOYwbJpeL5l+gYpYyMtLSgvbm35Y/58zJwdDQIBwOJxYuXABbFNF5oW66klNTlWzL3vTpkiVL1Q0U25uTY8YVr23FFSMnIc0sSsvKyYLPv0gtI+J5wZiYPRf26FjlT24MbpHl+7lzZ4M3ZqTE+FjQhopsNqSMo2FxY4cFBfmIskWp3wkyT5o9Nxex8YlKb3uIbF6/rKIMKSlpQdn8XcUVTwwEkBhn6pKSkql8eOxYsYqvoN4ZGaZvGa+W/wFlN4rg4fx8M1ny74ULF5oHbTYkJZg5gnoyZpmo+Wn5gTYO7T88n7RgQQG8Xjd6egLB63zq9k+rG/KhsTFcfsmlCk2OvEQLY+EjBxi2lzYiMSYWLVmivlNvqz3su8OjI3A7T43ZAuYu4riHxGxUTIySyd3KTN+P9/tomyp2Uo0Piat5czIAbwGaO9uVje3R5kvFhXPz4U7NVBW1CeO+ZLHPksWL1aCVk5MRzCnBfkzNAwEkxaWpNuTkzFEbvnGgYjGZPcL02/w5OUhKMDeOnxyzFWUVSEpJQtZ4vuLvwbgCgnFFm/BpmzcjjA2rD06XCxctWgquqSai1rx55gYs3MqVBWCWTayYVe1ZkI/OzkZlw5gYM2YzsnIQExWj7G35hg3lmOP1ehAXk4D8fHMDFh5fsmiRGltoE6vfs58sXXqZ1g5Kyphv139SIEliqu7evdNwuVyiU7q7u42mpvBYsKOjo0Z5SYnx2c9/3shISTGufP/Vxu9+9/sZ8Tt7HQ6jSgNXs6aqTqw3cZqJwUq9JER8T5fTKWE1PB6PUVoqx5klti9xWKV0/HiplFX5cvfu3WL+o8eLxFjKJ0+eNBrqGsSyib/r8cjs7eh1Gg0NMrxW+vBPL74oxo7t7u3V0vvEiRpxXFHvqio5Fix97xDiNJefqDLS0lLEuLTEDe7u6Bb5h3jUxYUyXF8KZP/hPymVlspj9tixQoMY4KH0ox/8wLj7//vX0EPB78Ryl/ZjR7dDHCe8APVmf5aQ0+XSkk1scSluMPOxTlzVNdQZ3Sd7JWobw+4Rg/jIUmKuOnlSFlfDbrfx+B+eFPcfjiUcU6RE7OVzkf5uVcrDQ0N45ZVXsGbNGlRXVuPOu+7El778ZSxYuPCUJ72368bDuo6amI+cuPu1jp//fIdagLtZjb9heYe2IKza3PLw6ssvR0lN3bse2pH903pKpGH4OvqSSy5R86+hT9VhjXYOM/DJMvQJ7xxW9W9STfmSy3xD3uz9TQLfASeLi6bYFu5LKIVt49zfVEUfpeXHce+99+Kiiy7C2qfW4Z6vfhVVTXX42v33m69xBcZnsYJ0cp56Uw81kAocws6sE+xsJ4uhJEQ+HSg7ytaBM9MpVpHoG8pD2UwEEqLO1F1KujB5OrLZmaVBTrlTxex07dCJwf6B/rMG7Uj9uKnD2YJ21IkrnZil3jqyyR862PJv1nDcfMuteOzRJ/jnKaQTs+ybOnHFmNXpmzpxpZN/2GCdOKQeOu3kXK6UKFdHtvKlIN/z+pSrY2/duJK28W/lk+YidZ3Dh4+JYdsIv8fNl0kcINetW4fVq1fjpn/4R9hgx4Zdm7FjxxbcQUzjxGRUElJPSISP04EzI06zTQiYwgBbu3atUBMTgk+6/IB8JSXmsgbJBbSgHe12LdhIvl3QqcjVhXbUgV9kRbPUhkyMne2yCk7a+KmnnhIndeqsg2HLjcul5HQ4tbCrqYv0BsftcmFIuCSI+upCO+rAkRIylP+kpFNxziT61DPrThP9/e99F+ueWXta1XBR0XHxzTDjTwfasaKyWgses1VjCd5zzz2nHm5Oa+g0BziHK6XGxmYt2NXSswTtyAH0oYcekqqtDe2oA3MrVuIMMGoNuDpIOaylqKiuD66bXbPmMdx5111or2/Ew4/8GisWXnqK+rbxTa1POTjNH0Q/0UGR4SOOb1j2dMZLylZ7hSonqz3jnevYmOxpWOmhAe1oJmeZHpbmtoDc/bpIVjpoNjrIR8Ass1DCakSYT6LwSNGjqEdAAyJRDrwZRsmpftbwjZ3wlVF+ceAKHypCtJoo6Ao5eEa+ilGSeDXW5U3hHxbVXLvqWvzmV785RScdlKRTThT8EaGBNEVxs2KFd/wKAlSvH8Mm52d868CuRmpCOxqGHK1LYOYgC8cTomRJye+Xr5EPlcmHQ+kby9DzpN/lGVeIBTswNIzHHluDL3zh8/jWv92rSt33HDiAXdv34a4771RYnlMpp5MEmEB1+OmnmFh5UGoZRTVGNpibg6JcOtsok2zNg8hlU22bVh71A6xEFpIOXit5xa/RZtkQ8ImtogbbOKHaSo+APE40vKOspgNjGNBILj47QS+i1IAkdI+cbYys8uQVUrQsuoZOYowK2EFs7Kno/vu/icfWrDnltWMgoBEngYBWTmG1vJQY2yPD8oGIeULLjhrtjIJWp9eCdNXCi1bjibBjjhvaLp4c4rSwXjstX/7nf/4nrr7yShw5WnRKBb71+9/8qVPJxepGt9s95SkHDx82vvrVrxpzsrKMG6//iPHHZ582TmpUlUkr53hxVuZ1dzum1GOqgw5Ht8FqSwm53ayClVfYUhdpJST5dCo4KVtaCcm2dbS1SZqoeJpa2gyHsLqaJ7R0yGVTZ+ouJVY3SttJGzocct+3tTWJdaFcHdmsapYS26dTca4TV4zXuRkZ4nbqxJWKWY24omwd37doyp6p/9xw42rj1w/9KugSytbpmzr9QSdmjbExw+GUxyxl69hQLxc6tPq9bsxKbcj+oJtnpTmCAdCmUSkfDBjDMHp7e437H7jfiLLbjfvuu0+8UiBUxkzf/6YqZb6H536j69auVVuPffKTn8Td992DxQsn1l/+zXcE5wWct8B5C8xoAW5Av3LFSpyoqUFq8tncFWtGNf7uP+7bswe33fUZ1ByvQmJy8t9dn/MKvHMtcOTQIfzrvV+By+nCw7/+NW7+6EfPSGPEz/R8r80iG77jPl5aiq//29dxycUXY+1ja3D33XejpqEBDz/ySHCwHejph06hAJFxpO/OqYNOwQoLYaQVbo3NzarQhug7EmLBglQ228d2SoltFGOq+v3KL1LZ27btwLZtu6TsqohDWsTDGzGrYE5yAQKN6PheKpv6PvXMMzPunRyqnxlXZqFf6PHpvuv4njGiV9xSL44rIlix6CcgnLdqbG09rcBoujbShlydICWiWOlU5OrIZv557bX106pyzbXXYkHuQrz4pxcVD2VLY7a/r08vZiur5TE7OCDOV9T3z39+AewTEnorccU4l5CVr6QrPFjoR6QpCfX3D+Kxxx4VxyH7PPOKhHRjdiqZK6+4Avv37sfn//kL+ORtt+G2227TiuupZPLY1BMiU3Bz89//+u//RmtzF6ory5CXn48v3v1lhfjDwWn9i2aQ81Svz4+uvj54PC7k5y1AzAxXYXGl3+dFRW0tCubNU9B+LAKwc/6SRUOTPhHwo9fVj672boVgw/kRi0c1aJzfagJl1zbWY3ZGFlKIGDReYDDVOXSUs68HJ2qr4fP6FPrNVHzWddjO2vpazM7ICMq2+Cd/Um+3x6uqq4mqpJCrLCWn+KTeTIwJcXHIzJ6r2jgFm3koYG4WUFJZiaVC2ZW1tWA5UXNjPWKiODdmirL05l/8zjaSisuKsWThUsSMoxBN5rPOZzubO7vg93qQl5ev5man5YXp+2NlZVh80UVISJ7YUnGqc5R/BvrR19uLgoIJlDFT89P/pw0Li4rQ3tqK3Nmzg74/nVOtq0FnT49CG8ovWBC0iaXH5E8zrhoxNysLSXyamiGuVMz296Oz4yQWLVwg9n1qQgJS0jNnnt+mvbs6Va3E888+g6SkdNU8S1/+EfqdNmxsrkdiTBwysk0owCntwYMBv/I/8ZGXL10S1DtUXuh3ym5ub0Q07MiZmxu04WQdrHNow5KKSiwlShJv/WewoaW3c2BQ3YRO1e95nSsuX4Hv/fj7am1nYXExli9eFESgm1YPvx89fT1wOd0oyM9V7bR0nHwO/6beFZWVyGO+Sk4N6x8nfd/dqxDBJP3+cNFx1FZW4tCBvBltyL7pHRpEY0ubPK7aW5Eal4CMzMwZ7a3yFW8SW5qwaOFihCKh0QaTif4hznm0LYCs7LlKtmXDyZ+U7fIO4eihQgRGRoP93uKj7NDv5K+tb0RiXEwwZkN/D/3Oc1W/LynDB97/vmBem6xvuL8pk1QwNxfffOAB/Pa3j+LSSy7Fmt//Dp+47bZwp0/7u/iVcmtzMy666GJcs+papCQkzLiZNgsh3B4fDAwgPiYTUSHQclNpQkxXDtCpifGIi0uasXjBkj0yMozU5GSR7L6+fgV3KJHt9QXQ09+F2enpiIkxoROn0pnHqHdPfw+S4xPD6s0iCI/Pjb6eAczOntkmLFAlpFyfswf2yBikJqcqnOKp9CCvLWDq0t7TiVyVRKcvGLBk9/QPIMpuQ2J8osiGlC2xCf0zMDioVKVse0yU0m8q3S0bWr5PSJh5f17L9yxukuhNKMDOvj5kJqYjLiEGthmqOS3Zw6PDyExOnjG+Lb3p+9TEdNij7CAs33RE2T5fAP2DfchMlfme/iH05kwxqwqZ/UBfXw+I4bz6htWYyYam773g04XNbkNqcvqMfY0x6/O50SWIWbad7ezvH1CyiYttt08fh5YNiV3M/kDemQohLdm+gO8UG1rxz0JKK/EWHyvEyOiYWqObnckckRBWNvOVFVeEmZypKt/KV+kcbGNsClZzOt/Thm6PC0PDI0gX5iv2NcZVQlzUjDakLfzegML/Tk9PFfXjvgGz30t8L81Xli+JQz4rOjas3pZN3ty4BTfffMOMMTs5rqQ5pae/HbOzC9RDxXS+mem4KswdL1z0+n1487XX1U3tt//j2/jZj38206kz/zbTBG/ob4RTTElJMcrLT4QenvZ7Q1OTcfxY+bS/T/5h+/bt4oIVTuTv3793sohp/z548KC4gIsT+b/73e/EMIb79+8XQ465XS5j69at0+o5+YfDh49qFVm9seFU2LvJ8kL/3rx5k7F5s1yXTa++YcjKzgxVDKEDM0m4PmmRCH1/+JgMapD6Pvnkk8YJIaQiC3KOaUDC7d27XxVZhNp1uu/UWwdKc//hw8bJk7JCtaqqciMtLUPcf44WHRfH1cjo6GlwitO1kcdPlJwwyiuqZmI55bdNm+Uxy35M2MNwtHvnTqPgwguNV1991RgeHg7Hrn6nf1j4KaVNmzeJIV1ZPFp4+KBUtPH000+L8yyL/LZrQLSWF5UaDS1NIl1c7hFj69ZN4lx44sQJcSEU+1pSQoIhLZo7fvy4WDYbt+Gvm0RtDMd0rKzYuPrqq42ceXOMZ599Phx72N8RlmOcgQlxzpz5Rl2dsDONjYkrBHkJaTWhpe+oV5r+9WSznRUVZYZUPvWWa2IYTGBSGqMNz1I7iU06U8XnZB2HR0YmH5r+b13f68jWiBXajjizTmlV8zmiNw2r4/e6JrNKudc19QqCyY5SfU1Ytc9zdXzPvqDTPBqThAAAIABJREFUl4nRLiUOinVCjO4bb7zR+Pdvf1sq2lzFoGETnTZSiRGNfsyY7e09KdddI6fo+l7HPzo2oS9TUtKMk92ydurG1bCGTaYyNCui//3b3zTi4hKMu//lX8Q3s1PJCj0mfqXMyfnFF1+M3QcOnLJ7zczPz+d/PW+B8xY42xYglvLlV61AXWkdEv8PVymH2vnQkQP45Mc+ifITJ9RuWqG/nf/+97cAC6Auee97UcXKetbWnEPE7SQffPBBBa70yCO/xqpVq86YduIqZcyKxggCYgi+1uZGNLa2ixWVVuVRIKsguR+rlGrr68WLmBkI3I9USqyeGxzk3pXhiRs27DtyIDzjOAdlSysKuVJ+zwH5BufcEFta7Ut19h3YJ6/4VFjX8mpfVp8ODg2J7MLKSZ3q9z2H9qCrSxaHLFIjRq6UTlTLIfUYV9zPV0q1jY1ie6sKZZdPDHxhxqw5zx5OH5/fj0MH9GJWWk3Ka3NvZimx3x8Q6nLFyqswNy8Xv/3NYyLxfKDQ6Q9Hjx4R900WFNU3y2FA2UZWe0tJKxfWVqO1Uyg7EMDRoiKpGsp+Ur0ZV16vbCUIFdDJhbS3TsyGNvBXv/oVPnPHbbjllk/g2LHDZ3Sw5XXkA+7oCKJhw/CwrKO63F50aWDeSpMilXY4XeLyc/J39XWJEZtYja2TdDkg+v0yuEavz4eOpo5Q/874nbLdHs+MPNaP/lGgs1WOMdzW1oaeni7r9LCfHOQYyBLiAOByyfSmPC7bki7D8kdEoqdPmDCIG1zdquJFovdAX5946QHldUsTF6Bwd7u6ZEsmKNvjdIrtDW8AfqusUtBQxhV9JCFuilCvgXPudnvEGMO8fmO9/KaFfZMbukvpjs/cgYd+81PR4MXYZnGllDo6usU25M1wT7vc99yMoK9P3jdZeCalvr4B9Ev7vc2G7pMnpaJVn5fmFB+XsLF6Skj0jTRmKZLLO98Kcc9t3gT+5Cf/L7gHMOXwRn/bti149NFH1b7jluwd27Zhzdo1Yt3EAy6rtkYVguDMlYeWIqz4m6nq0OJ7K5+srpWuOaR8uyrPlDtXX6fpK1QnyzI0MFg14pEQwzrxO1mtM/43/S+lWbOixUCGtlHCQMpikNf3iW+1AOohBiRWfUHaQpNPB4t8zFCYiqILBOw+LZRJhRktkmwxye1tnSH/lMvmoDgVlvJ018rISMOq1TfgoV/8dDqW4HGfzQcd/G+d+OYG9tHxcizloFLCL7p5ViuviHsmVJW3ji7BpYTCdkrZmOl1+lqo3I9//GNBLInQ47NmzcLsuXnYsW2X2u2Ov3FDnptuuglf/8rXxWt0xSMF12ySbFGyU9JTM+HVsGg210kKKSUlBf4R2dMWRap1rELZCQkJWLBggZAbSM2cjZgo2X1LbEy8WpsqFZ6ZmY24GFlCsttsKCjIl4pW8/BJSWka/AUzrzcMkcRlFenp2SFHZv6an58vXhAeOWuWlmz6UtrOpKQ4RGkM5rNnz525YSG/JiQlYbZGjGdynaQQuzoqKs5cwiq8p2Q748Is1QtRHQsWyOOKfVOMiw0gf0FB6KVm/J6RkYHcPHnfXFCwCP/781W4auUKfP6ee7Bs4aJp5SfZU+FLkT31UwiXSDLOJWSPiEJK0sxL3kLl5BcUaM1rZmr0tWy1BEuWr6hTTq7c98z5fuFLU7WOWmY+ZRqVZ4W5kEv0Cgqm93WoraXfqe/iRQvxy//9GS688CLs2LFDvQntdThQXFwsrmvSKppa8p73YveuPciTdkDeSunc8khbfy7x/V9o47lk7/O6nGYBFk1duWwZyhqa3vUb0J/WeMGBb3zjG2hursdfXvrruz8fCexxLrBwnv8973kv6uqERVPnUJ6dO3s2cvPysHXrViQm6kGpym91AIzY/PATZUFAfP3DVylS0nk/r2QL5xN5fSVbqAuLJ7gnLq8hIc7LSt/lUqZOO8kr1YPwazqyWYDS3imfJ9KR/Zb8IzG2AlcwUbUk7Iw/Jlr6VEJnVe+RgNiX1JVFJdL+4/H5MEZQDyG0o3dYbkP2YB3fsz9IY5bt1JHNJK0DG2nJ/tGPfoQDR45iz67piwrPqu/pS2E+ob2Zf85azOr4J6CXU7RsGAiA9QFSu7AvSHl140qSG0J5Vt9wA+Li4rQHW8oQD7hsrNftFVeWNbe2o6JCVpVJ2QcOHRBX/fV0deHAEXl1Izc47+ySDS7cPHvLljchxQ89evSQQskKdch03znxvmePHL/4eHkpWptlFbacw922Y8d0lz7teHFxCSpLZP7hyZs2bxYHPFHJisvKTrvmdAf4ekZajc2EK9603O9XeNEtbbJCNS3ZAA4dOSIusupzdmLfPnm17/GiIjDOJRTgjZnPOyM6UqicyqoScVz5vF5s2bIl9PQZvzfW1oIbxUtp2443payora0ENyiQ0ubNm9SAzqeQH37vh3jwW1/H8DRbO9L3ZcflMcuVDNKY7ervxFFu9yYhrjbYs0eMvdw31GfGlfCBorKiTHzTwpUDzFfSga6mpgos+JIQ0Zu4faJ1UxTuHG4o38jVJgJiAeaWHdsEnPos9Hl1dbXCupbeFIVeJfKHP/zhD0MPTPedhtm4ZSMuvmgBCKs4e/YcxUqHNDc3qX9JScmqsoug+3W1tejr68PgkAdzxueuCCZeXV2leAMBQ81TUGm+A+862YWBgX7ExMSqO4f2znYcLy5Ca2sHmprqkZd3gbreidpaNDU0oKfrJIaHPEjLzgbnL2urK1FxokLJ9niGwTkwBsqhQ4fQ3d2D/oF+2GfFICU5SXWUw4cPo6XF1NuSzTtLVkGO+b1wDw1ibu582CIiVPCXlZUq2X19juBcHGVzIB/od2FszI/09HQVQAcO7FO8tEt2do6a02KHLikpVtB3hOKzjjc3t6K0tFjxs63z5+eqdnKpTFdnJ3oHejE2Oqbawx8sezc2NiE52bQ3g+DY0UMYcLrQ29uNtLR0REdHo7OzR12zqakB5L/gAtOG6gakpxP0gcfjPsWX5Gtr68CsWXblB8ouLDyMAWc/nM7+oGxWFpeXlyi5tGNu3gXgDqHHS4+jubkNA/2s4vQjJ8ecyzVt0qZ8GQiMITU1Td3FHz58EH19vXC7hxEdHaWuyfix7B1qw8rqStTX1So9BofcmDMeg2xPbW2NsiEQiZSUZAx4h1BUWIzBIRcxBzErKkrZiwmBfrDiKjRmK2tr0N/ngNPRi5y585TvueSisvKE4h8Z8SA9PUPFFZdVdXechGvQCZttlromn8COHStUvC0tzYiIiFDXpI8rq+vQ7+iGwzGArCwTH5ntrKioUjZxOgeDtmJybm9vQ38/K1sNZXP2k4MHDyrfsD9YNuSgfOjwYax/bT2uuupqZGdnK9+H2rCrq1vBHDJ+jhw6grb2dvS5exEZMJA23p59+5jkTd+npqYoGZRdfPw4HA6H0sWKWcuGVr+3+g9vhJqaG+FyDWJ4eCTYHitmyR8XE4v4hAQMDPThyJEi9DvcqiLX8gM3ESg8eiQYV5bsiooKtLe3Y9g7Bq/Pg7lzzPlzLqFhW1tb24L25qB6cP8eOBxODA4OIC4uHu973+V4/InHMdjXA25lS/9bfuCqBG4s0dvXB4ejF7m5880+eOgQ6hvqTokr75APh44cRHd3B5xOF1hMw37IXEMbWjax+iBtVVfZiN6+bpzs7sYFeXlK9lS5kDIOFh7GYL8TI75R1R7mFOaO4uJjQZvEJMQjIS5etbvuRD16ersx4HKpHMG5xulyIZcydXR0wOHoR2RkhOqDVv+29LbZIoP9hMvYenr6MDQ0BM7NM6eExlVfvwOzc8zaG/ZBrnyg7LExAxkZE7nQiquxMZ+6JvvJ4SPHUHj4CJYtvxRZObMRMy7b6g+Mf8sPlN3V1aty4cjwsMqdk3PhmGEgLTVV5ZRjRcfh6O3GJZcsUbY+U//RPw/96hf43D99Hk+u+T1u++ynkZGWocYTPvFKSFYBBSA2KhZ3feYuVUCRnT1XPQHao21gYY9FVhFBSkoaUlL64HLZMDvbBFMnT2pq+nglKIIFB7GxsWoAY+dIy8gBi5ZIcTFxQdmhN2+z09Lg5rIGnxcstIoZnyNOSEhD5vgbbEsGB+Lc3Fw43S7MSctBWopZuMCgZGKaTAwq8hDsXhXE8MI2m8L6tNoZFTUx0z937lzVqdPSUlRAUh5lW7z82zAMdRnqlJMzR5XO5+bmBQtL4uJiTuG3dOL1Xb0eJKUlBGXzt1DZvBaJds/NK1BLD0zZsePH7crm/CN0Kp2yO1q6YcwaRWb2RLHahOxA0D+m7Hx0dDgQqndSUgK83uygXOtVSXZmNtxuL3xeG7KyMpQe/I+yGbAkC+/XHhuvZHZ3O1QHtfzG3yd0mbBhTlYOhoeG1QDA61jEuIqNjVd/xo1vrhBvj8bc2dmor69GTEJSMK7YHks23WvZkDGbltQHZ8CGubl55jSB8j0Ly8zWWfHNC5m+70VKWhpoC1KobG7GbbWHvzOuPG4n5s6d2DCA7UxPN9cihspmYYvTSdlZSEowC9smx6xlw5i4OBXLNtgxZ86cYHtCbWi1kTrOnjsbLrcLaSkpiEsZ98/YRD8mhrDFH5eUpNrZ1dV5iu+ZXCwbqoaP/8f+6HK51ablk31v8dnjzP4TH5OM3Ny56GlvR25efjDe7FFRU8pOS0tDZ2eCWp4xOyRmQ0ETLBvOskHpe/Ikb47nKtnMMw//+mF87GMfx7WrbgCxh612st+npGXAbneq8yxdU3nTPr5rGPspiTmPvueN9rysOYhJMBMtZYXaJFR2UkoCfH4PCvLzg3EVmgvj4sz44Tl5c3PRWN+o9KFepNC44t9R45jg1HlwcAguN/XODbYnISnl9Fxotytb0D9JSUlgvJNC9WZ/sGyYkJKErKwccJkXH15oP1JoXFm8PK7ylduj5DEfkuwRp9rEiln2i4svuhAPfPNrmD//giAOOX+3+oMSMP4fZXN8iItJQUZGVvCnUHvHjRewxUZFgf2nvf2tLQsKCg/5wjcOxUeKMeQfwDVXXIP3X3216ttvvrYFFSUVuPbaa9XDVsgp038NhZ2a6TsxSYnZ6Zpi03JuOvyjH/2X0RGySfnJ7l6tDbdraqrEm5C7XA6D0IRSamioE2P1Ekv5ySd/L4bW05HtGR1TsJFSvVtamrQgxcqrZDjXvP6mrZuMrdt3S1UxTpwoF0P2OXr1fE8M1lGvV6QLsWNbWjpEvKOeUePZZ/8ohiOl7A6NDdEJM+h2y+AUCRnKGJdSS1OTOGbp97SkFIN45xIirB59JCHC9dE/UqJs/pOSTswSS/nVV/8qFW2UlBSfFrO33nKL8c1vng75yLzW0CDDGKYChF+UbohO3zNPSGh0bMx4/tnnjbIyGV44dZDCXfL6OjmFvifMrZS6u7vFkJS0ycMPP2w4HC6ReJ2YJQxkZYlc73AK/OEPfzDmzZtnvLFhQ5D1gQceMN532XKjvEq+XwBPFlcpTz9kA9948EH86qGH1KvhZcuWzcT6jviNhR/htqN6RzRkBiXV0yafZjSWh8wg7pz9iVMhXJbBJ5N3K/G15dUrV6Kkpu5dXaXMF1i+QT9iEsUv5k5zeXN7K1YuW4HNO7di2SXnYK5icRAfNcds7+qYpWNYGBjFV2+hr99O89i764BWFpqqeu7NDRvw2suvKKuELjYe6O8XFxXwZGlRE3k5n6XD38O5MAaxkHQG2/7BgeCr0nDiOcgxOUqJ8ysstJIQi7xaNV6j8FWSzmBLva1XwuH0oc7UXUo6sqkDY0tKfO0lHWw5z6+jN+eipMSY1eHv75PHFRPWKG+ehCAFKq6mKR6a3B4VsxqIcWwn/0mJS5qkxGSlM9i2tp8es3xle9999+Fb9z54SjwPD/sxOCiPK86rivum3y+PK5tNvZaVxixtpxNXPayrGRiQmlwrzzKupL6vqK7ADatXIyIyEtzK8cEHvzGjPVXMSnNhQC8Xio1xBhi1BlxWk7KK1yIa4dEnH8d//OhHap7LZpsAaWjrOKmquSzecJ+snpPSybaT0OGvr64VL7HgTcXatWulqqC5Xl7Cz2Bk8ZCUmpub0et0iNht0Tbs2SWvgH7llVdQVHREJJtMu3bJK6CdTqcWLu3Bg4XoGZQNXkyMza3y+Zmn1j0jhursaDuphXfMQh4pmQvkj0nZ0dhaf8qAMNOJbpcLHnjFIFmMK8+gDGqQA+6uHfKYZeFMaI6YSW/+tkujmpTVz+vWPRVOZPD3Pbt2TAmQ88B3v4emlhb8+aWXgrweTx+amuQwhiyYZJxLiDZsaGiQsCqe5557DiyqkpIORnd9dT3qGxulonFMA+uaeMcsqgpHnZ3t+O6D38FVV1yj6jE+8alP4aGHfoVnn3922lMZs1J7s0hyzy75ioBpL3oWftAacEM3ZWYQfeGOO/Dj//qJ2sh8cm/XhXYMlR2unQHhWuAJOVrNnDhN8M18GyJ9xWXXedBWV7cLH8y5pg1ivCazYQE5djh4M0WfS0kLJs8YQQwmitFmukZg1hh8GghmfOqT6s2YtYpdZtLB+k33TZjGSxYENNpIfez+KKu2y1Jv2k/qHVC710/LcsoPNptGoAifsq0LhN6kW8em+4yCHf6AtK/xTWUURqfoP7F2Gx5+/BF85xvfCC69Iq8OXKOu70dH5FCdjEGd/iN2PB+L5OYz3RAph6RkfEdEEB51ZnL0u/DwI48gMztTrVR5+OGHkRATg+pKOa72jFew2c7Zt9RveSTiU+CnPncHll46UXod+kqZxtcLGnkkcHDW6ag27QF6RndO8aN0IPJrBQI7tVQylbJpZoGQFxJTtOnUQ7o21ElesyJnideQ2kcD4zd4p+o33V9M0EzUEjIHxLfcJSSXEPNouhK2gE6kiNUA5OOEEqozkGtooVgJuqODpWzmIyLAn043rr4B1924Gv/13+Fxlk8/m5XzkVMdnvZYdHz4gcg62Y+A5uAvj1mdmz7qo9PviUUu6feL37tIAUdYslkBbY+JwapVqy0T/G2fo7yh1LlJ/Nsup3V2sOxK8KW4pERVThaWlxqfvf32YAXgs88+y7UvRnFxcVAKK9Z0qhV1NkM3K1XlVcrUQ2dz5GAjBF+oi9fjEXCaG3PrVHyy0pvVfFIqPyGvgpXKtPgoW2pDVk7S/1KqqZFXfFKH7pOyTaul17f4HN0Oo6VDLrutTc5rVqo2WJcK+0n7Se3d0tZm5ObkGA6nLFYYV9IKW+qgE1fsD/wnJZ3+IJVp8VFvrgyYjpgXMjIyjN07dyp76MQsVzNI+yZtqJMLp9N3uuNNLW3T/XTaceqh006dCmjK1ZFtKffqK68Y93/7mzPGu24urKo6e7nQ0vutfAarlMvLy/Hyyy+HHazvvvtufOXef8Ufn342CG3FOYd/+qd/etdUKYc1wnmG8xY4hyzAwqMVy1agoaEu2CfPIfXOaVWeeOIJPProbxUSlM50wjndqHeIciw8e+yxNfifn/63err9w9NPmvgH7xD934qawXcReXl5uOWWm6f9d/PNN6hF+0+sfQb7dhzCBz/0Aay4fJn695/f/a669u2f/CTuuO2T6vtAT7+4cIYVtkR6kVb9sViLxU1Smqq6erpzWTH70kt/CS54n47POk7EJWllHtt34kS5dWrYTxYgEHlHRIGAghsT8QLYsWOPeDNvyjxeWioVraomdTbzZjGMju+J3CQhgha8vP4Vhacs4VdxxSpy4Xs3nZhljJBfSmyjtGrW4/aAu3n5fLI9iAnsIo0rzn9XVMihGplE+U9KOjCQRceLtGAmWXgUbv7+y1/+MmbPzsG9//YVdGps+k54P2nM0veSYiLajPpu3LgR1dW1IhOasuW5kPmNcS4hto8oXOFsaMliMRTzvoSoN292lixZjNWrV+PNLW/iH//hY9NWADCfSKuxqa9OXEn0PVM8wckt4o2uWLFyWrmDA14UFhbiipUrkPvLnyBuHBGKJxzctw+/eeQRfPnue7B4xaUqEOs7m+FxeRSiyUw7KtA4gx4mo0a1z2lOTk4Q1WQqZegoVkHW19crBKZQpJnJ/Er24KDi5XfewVqIKZN5+Tdl85/b7UD/wADSMzNnBJtm4NbW1ypMUJ4/UzsJj0aIvJqaBnUXR96Z7qj/f/beBLyt6zgbHoIgCIIkCO6iJFqmZXmLLdv6bNlxZCexnXxJm2ZpmrhumrhO2rpumjTN069f/7/f/zV9kjRN4ySO662J49hW5EXWvu8SRZEUJZEUdxLc9x0kQQIEQBD3f965vCBIUcAcR7JlR/M8EkDcuXPnzMyZc+89c94D2Z2dvTThmODlO9Fko23Qt7b+PC1fvoz1iCYbbfQFp4h8Fm5vLNngb2txUl5uLiOqxJIN/Gevb0rm+8lJrsgE+kxeTh6ZE8MheYGLoEf/YD+NDIwQ0Gxi6T0xOUnTk9M0NjFNOdPTUX2P5IJkNO5ykSMlJer2aPNxhWppE61cuTKm7IGBAWpu7mSkHInvMTgvX7mS8vMslJqmo2hdYJC5jbEBk+ijACN8paXpcb4UL35DXLW2tzKCFZaFRbMhYAwnvRNUWyuLK8g2boThz2iyDRvWn68l9PlYNoHvgZIEZKWxsUlKT7/4Li2GbCRdoBEhR0SiIi22zY9+/BR99CMfoQ/fcz999rOfEfm+traaLBYL6x41p0x4aGBogB8+gO4kyVejY2O0fGKCJic8MX2P6ve66mrOham2tIsugcNDzURAH/ihB+wRTW/0h5GRce6bWRkZlJqWJshX3Sx3tVWHhV1sZ+NvbK2KimOgY9177730uS98gR776lfpzTff5FUcG+7bYLDyJ3yPXAi0L+gtiSs8INx886Xdom+BUu/wDzGWcmAmyK+M4aRV117LG+/eeuutNDAArONeKiktph/9+Ad0/0ceoLa2DmptbqaJiXGaBCZxbj6ZzHH82qa6uopaWloI0HfZ2TmM03ni1EnyTrlpZHiEAwfYpEh+wI4Fr9NZT2vW3MhNdDqdVN9YTx6vhybGJxl7GMVCdQ1NVFF+jvnd7nHGB0ZxVXFxMTt3aGSIUlNSOeBxp1RUVMS8kH/99dez7K6uLmpsdFIoFEeDg3205rrVZIqPp9bWZjpz5izz9/X1MK4zih9Lioq5jUMjA5RoAWRgNvk8Ht5EAHLxz8C2HRwcJNyhB/wz1NvfQ9cVXMcBjAQFXGfw4pXg6tW6LsXFwBgepslJL3lmApS/XMeuPnBgD7W0tDE/7JScnMyY1WXFxRQMmtgfgJ7TsZT7uf2GLkY7y8+WUW/fKPl9fnJPeejaVTp27IEDB1gu+HE+5AMPu7SkhLzTPhoZHKTs3FwueGiobaDyivIwP3Ca4YfyynLq7u4gn2+GJiZcYQzsY8eOUFOTk/k1bZYxiScmJqj45EnGjR1xjfD1ADuHwebsWd2XkTZsamqgtuZ2mvRMkMs1SgUF17HfsNSqrq5+gWyPJ0BFhUcppM3SmMvFcHZIdrB3aWkR4c0EZCenJnNcIGYbWxvIO+WhkZFh1huvfypqa6mqspJ5p/xTBHhJxBVic2xshLGR4xNMlJ2VzU92iDfD3vHx8RxvkN1UV8+4zsOjw7TqGh3aEzqcOaP7fmgIGL4ruT2lZaU0PuiisXEXWZISKTsLEH6TdPz48bBsw4YYyMvOnqNDew7S2tvvoOuuK2DfRdoQWNeGrYqKi2h8zEMjY4NkjtchTjFAYYMCQ28jZofHhuh0aQljYvcP9i0ZszjHiKuys2U0PIS1mKM8+Bu44JFxhXhFwoTvT5SeIr/fR+hT2XkrKTnJyk8xS/XN8vJKGujvo2m/l2Z8HrpmDlsdG400N+t9zbB3IBDg/UpnZ000ONjLsYZrLrbhyrxryGyJp9GhIfIFQvSrl56jm2+6hW666Sb2AzabqK+vY7sY9mbZJ46Rb9pPExOTZKJ4ys7R8bUjbQgMZOTKvv5eqqmpoXH3JE1ikLnmGr2flFfS4lyo56simgn4adzjp3jLLOXmLKPO3k46faqEWlpbWRfDhoir6vNV5AtM04h7gq5blc/5Cm8kKub6ppELTSaNSk4V0diYh4aHB8mWmECZWdkX2NtoJzb8qDl/lqZ9AeoDtOfKfI6rpXIhjAXfI3+PuNykUZAxlgE6c+TIkXBcGbIHhwcJuM5+/xSNjo3TirxraO3aW+nFF1+kNTfdSJ7JqQW5ELKHBvsZQx2Y60vFlTGeIK5OnjpJM/4A3XbbfEEvO/RK+E868Ts9Nc1QXAMDF07QL1U0haKCc+cqROJnZ2e1wwcPMyzYxUsc5kWhSKSw8Pj8D1G+zfhmmZeLFmajS0dxA/R+/vnnNc/0dBSp84eOHz+sDaCIJ4ZsnIFikt17d8yfHOPb8cJC1kciG7qHYe8EuuzfvV87eHC/SG9cf/v2nRrgPSXkbHBqxcWlElbm2bl1t7jgB8V1paVlIujN6Sm/9tJLLzE0IewTi+D7ouJinU1gw6NHj4qLRBB/sLdEDyhQWFqq9QghElF45LA7WBfEeywqKyvV2jo6YusyO8s+37JlsyxONE2rqKjQqqurY6mgH5+d1Xbs2KZ/F/inuKhQ27p5swb4QwlBb8SsxObOlhZtzY03at//t3+TiNb27t0r8j00he8LCwtFMQs40tdee41hKSX9fmRkRO/HAvtBHvu+rU2TWJDz1e692ozfL7IJ4F9RACkhyH7qKUA76gV2sJHVYmXoyaXOh96NQtmwIcfsUoLe49/CRVOxBn/jNc1Sr36wddLLv32d/p9/+BblrdB3uwE/KNrrx8hrYr5NBflIhR+vU6TILfzKrbWd7lp3hwhyDLK5nULoQBVdYENswCBdS4Q7ymivziLt3drcyst2Vxesjvz5ot9VZMMiJsyDCte2sC+xEYOUf2564KLKRhyoOFdBBasLor7Ki2DnuXtpHOKJBP9GB0kJAAAgAElEQVTEMa4Qhyq+xw5XD913r3gDehXZsE3AHyKLNL4V+z1eW1uT5wFzIn2x+Dveek1NTNHNt8peFarELK6Ftx8b7ruPATE2bFj4WnOxLmzDuc1DFh9b8m+F/lBRfZ7yc/P4bdKSshb9qJRTVPOVQl+DTUCx+gPGi4a6Bu6Xt99+O78JeOGFF3j7vf986qlFrZv7cw7yMpZs42RV3xvnXe5P8YB7uRW5Kv+qBa5a4J1ZAFXK69etI2fL1Srld2bB+bP+64Vn6b+fe5HOlpVRUvLF587nz7j6TdUC3/nOd+gXv/gFff7zn6c//9qfUUdTK3UPDND3v//9qPOzqte5EvnDVcoS5bBHK54AJYQKQfBLCXMxUkIxBOYEpQQYNuPuK9Y5aN+5CuFm0URcVCC1CfjeeOONWCqEj8OGuKuXENqnIhtFBagqlNKmTW+IN4tGlSp0l9Jbb70hrkDEPBz2x5TSufMVYtnQ+eRJOYzhCQUoTTw9qcR4xbkzYnvjDUEAaFBLoCotZSc8YUgrPmFvlbhC30RbpbRp06tSVtYZe+5KCTEL/SU0OjpINTUN9K0n/46Lbb793e9GzRlvb90qrsbG05ZKLqxW7JsqufDU6RKlvrlz906J+ZgH/UfS73/4wx/Ss88/T4GAj1D09eXHvkpPP/101MEWMSvF3UYuBP+VSEoDblVVnRjPEihTwtUVbBcV5CjdkEqqi22P6jkUyUhJpY2QKXxrypdn2QonBINydJW2lhalAVeczaWGi+BDO6WvinQbXrySOUIsf22oqVLC9iWLXLaCaxarFfPvUNT6+IWnI6GHfJh6WPj7xf5S0RsbrKug9qB4RY1kr5MhE6sTVPCrDSQjiT6R0I7PPPM07diyjY4dO3TRUxMT5EhTJrMapGtNXR2NjLgveu0LDijgNWIvXZWcFR936aEdUfT15T/5E3r44U/RE994gvLzVlzQpKV+4Om1pQ4s8ZvKUrYlTr9sPwm7qH59lY4HiC+Vjq2a0E0KQaZqPeGDAovV2yhP0irBjgvIJasNWqo2UfOleCkrq8FJXUEh8EsJ0I7SwRw3iZa5eSiZfBXvEAUUnK9qb4vZRIrwy6ImziyNjHjRcwHvd6VQ6B3CXWLD842vbKSvPPpXF10/q83EiZsJnHOT9G5ors9rmsKNi0I7EYIqsaVy0yKFdhQb7ndilD98/E6XUTxZKWPk568SF+Xk5uVTSOGJ68Yb9WU/Ev2xbg/r/KQEUA9plKHoKC87WyqaclesoFSb7C4dBWcq+wWjAM1mlcnGXfRdd9wr1jsraxklJqaJ+e+4Y5144HI4HGQyy/SGAiicsFllmxdgqUVGRoZY7/y8XHHM5uRkkd0uj6uCglViPRxZGXQnyZcpoK9JbxQYQxtvCYS3z+ibKSk2ke6pyRa6Y51KXGWJ7Q0F1qE4UUjo81iyJCXoHW2taaQc9HsspzPoU3/0KXrkK1+kb//t39H23bsv8MUtd9zCSxgN/mifkL1qtV5MGo3POJa3YoVYb5yzeo2siAy8q1blX9AW47pLfd5884eW+nnJ39B/pASbrFy+TMrOxbjSXBiaNVF2vjxOxEpcAsarRVOXwIhXRVy1wHtpAcxt3XXfOmqpbqHUtIsDQryXOr4fr425QAAzfOYzn6Hvfe9778cmXNX5CrOA8J5YXWsUZUgh3hDYWKgvhUpD8ZFKYQZg1aTFE5CNAgdjuU+slkNvqWy073JBO8KGKvMWDQ31F31dtlSbGdpR+EoUvr8ioB2DQUKRjbRASI8r+V67Kr5HjIBfSioxi6KpkDtAQeGrRcBGqkA7SgphjHapQjuqyEZMoShLSpCNfiEh+H5xzOINw1tvvUUvPPccAzhEyqlrUoAjnZgQ9zXkHZWiKcQVAFSkhCJMaX8w8pXUhijCHBNCO0J2SUmJOOerQDtKbfFe8IkHXDh206aNYmd5x6cImwZLCIHd2tpJU1NTEnaa8nqVBlwkGKlsFE1VomhKOE3IawOFeqO4pa2tS9RGMPX2DtLIqGyTa/C3KiT07u4uamqIvVm0oWyLs4WCwgEXNuxVwKVFEoVtJAQ/dvfLKrchD76UbogOvQcVZANuTkVvlcQI34+7ZYUz0AHzt9LEODjYzdWhEntDJuBIpQTkK/yTUovCxuxIuufPy7HIcQMqtcnFYnb16tX07H//N3318ccWxHRbbaM4p/i8XvFqA+AFnK0sI5dL7vvmpjqpuam3t1eut89HXS1d4um4wcFhGhkfEemCmC0rOyvuP8gnI4MukewAkNMOyFe9iIReIibxK+XJSR+98sqv6JprVlJSWho9eM8DZE4yM4Saocudd97JAANIoOdrqykUCFJeXh498MADPG8AiDPj7go4mmvWrOGnw8LCQoYQxBzNLbfcwmX5/b2D1BARSMDFhKzKMxXU1t1OPp+XoRQfeOBjPGcEkG1jCQ0gFgHrBaeePHmC+geHKcVmC8vG3SwPqnOKFxQUEP7haQgYzW63i7Kz8+jjH/84l6pDRnCuIgU6rl+vY07v2LWLPBMTZE1JoYJVq2jdunV8xwbYP4M+/OEP83xMQ0MdNTe38rIqQAwass+cORPuAGazidAe0K5du9g2ZouJVq1aTffOXfPYsWOGaLrtztspOz2T2w3b4unCkeeghz/yMMMkRtobJz344IN8LmTotgpRQcFq9g8ORMo27A1/6TCGo5Senkl33303+yHS3pGysQQLNgRlZ2fSJz/5Kf4eaUPD3vADYPzGxnTZuCZiAm8vIt9g4JqY/z5Xc546na3s18zMFPrUpz7HsuE3JExQpGzo3d/fTSkpDvY9YgJJG34wCL8hXiDDAGqH7I997H9yXCGWjTc1iD/oiJvP0tJi6u8f5FoCI2ZhK9jcoDVrVhPmYisqaqi93ckxCxvef/+DlJpqXdBOxAT6DwjLh4aHR7nPQDZ0xDWBZW6Q0c6m5iY6dfIU/dN3vkPPv/IKffLBB7kPRtoQ82X33XffAtkWi4ny5+IKg9LJkycN0WEbIkbQT0YHRyklx0YP3/cwpWdnUn9vNzVEgOtHxpVhK8yHfuxjeixHxhWgQW/70Ie4HxSdOkaDQ1OUm51O99x5N+Xm53F+iLShIbvk9GkGRkC/z81bQZ/5gz9gfSNlp9jttP6uu1gGbDXYO0iZuZl084c+RGtWr15gb5xs5CX0QbQV+SIyZrlver1cuPiTn/6YaEajlzdu5P4wOjFGmWnpBB9jnjPS3pBt5EK0BXC0hmzs+YoHjMi+GZkLi0uLqbe7l2Nv7dq17Pvuzm7GbDccZPRNbKBQW19PU243x/D999/P/SSyb2Zn5dFta28m33SQSkpPcMzi+uhnyFcXy4WQgdhHHGZn2zlmDWhUo29G5kL4ITK3I97wFBuZC42YRYzAP3giRoEabAUbtLd2Unun3jcjc+GRI8docLCfTBYz5a/Iow33PXCB7w17nzp1inMB+sujjz5qmOyK+RQ/4UJjVLclpSZTlt1BNIc8g85s/IMjQXBEWnIqDzQooDEIxxfz4je9CCbEiQLngjDQGLz4NGQ7stM5qFDGD9mapl9zSdlxOg+KSZCww7Ij9IiUjWSIknWvN7SgIGIpPaBjTlYWYflG6hw+LH5DBW0kPzeGiIH8cX0UuGRlZYXbE8mL7waBB5XbqclplJY6Py8XyW+eq3zEb1yoZDJTniMvvBF9JG+kbMMnIbP5ou00qsZhV+iCGw58GnIWyzaeJIC/jI6ZmJjEQP1Ge1JS7GG7GL6MlI1B0SjkifQlrmPwZ6akUTI2qzYnkcORZ4jm44Y+Bi8+U2x21jsxKVngez2uEq3gzQ1fM1IXQzYKcdAe2AhtXSquLBZbWEZ6ug7kHwrBlhlkNmP7aL2q3NA7PqLyWvfPQtngN3gjbWKHXVNSKGg2c5wYOkbqDX6DMjJyCMksOVpcRfRj6BKyBGlFegGFl0yZFvZNQzbiA7bBP2BiGxSpt9WiF9NBv6zMPLLO9QeyXdiPI/VOZ/B8pCsT5WTNF80hZsLy52Tjb+jtMwX5M2Wu8PBiNoEPoTPsYvQN6M78Fgsj4D311LM0OD5OP/zh9/X+GzSx35fyPa6Pc0GQh9yDVRUse1ZPuUvpwnFlc5ApGKIki40sdr2wzToH2m+005Bts9k49+BvPa4utKElcZb1sCaayG7P4HZCH/wzyJAbqTfsirbBJhlZeTrinWGTiJxvyIDvE5OTKTk5kfuE8ftSsqEvZE9NefnTbr0w56P/GJSRYed8kpyYRJn2ed9HyjaKYhF3KkWVxjXetU8ptCQwSYEFOz4+LjqlpaWFcTslzMA63b9/fxhXM9Y5XV1t2tGjhbHYwsePHy8UbwANPN0XX3xWhHuKCwBPl3Gaw1e7+BcDm/TiHAuPFBUVa20tLQt/jPLXlje3RDm68ND+g/u1g/sPL/wxyl+/ff1NESYtRDjrnGLfg3/r1q2aWxhXwNEuLpXhNCOugKUsxXeF74uL5XF1+LDc9waWchQTLzhUVFQqjitgKWc5HOL+U1pcqmN0L7ji0n9Me2e0t99+e+mDS/wKLGX8kxJ8LyX45nWFGH/zzdfF+N/w/Zkz0fXu6+vRVl27Unvttd8yBrSBAxxLf/j++HEZ9jtkvfTKL7Xq6vpYYvk4NnxnTHQRt6YVFxeJfW/kK78Ep1nTtMrKSq2tUZavIPupp58WxyxjKdfIN5WHLlciiV8pq94B4HVCMBCKur1UpEy8AtDvMvW7tMhji79PB4IU9E8vuEtbzBP5t6rsqYkxfkUTKeNi31Vk4ykQ/LijlhB4cTcIu0gIr4eksifGxghLiSLvdKNdg2WnpYnmc9j3waCSbOhh3LlH0wNbe/kDk5ScKrMhXnPhblpiw+npIAWDlyeu4HvYRWpvFd+3d3fT/evWibGUPdPTZKIESkqK3dfgC5W4QhtBEnurysZ2dcFQQBzjKnp7gn4KTQdi+ufYsRP0yBe/QNv376Z777pXFrOKvh8bHSM81UpsqOeU6ajbFbJD5v6DDfH2UC57kvB2wXiCjJS1+Luq74HulZaWKbKhit6L9bqS/lYacJG80u3pUfcsvZIad1WXqxb4fbDA1WVB766XAbT/06eeotLTp8U35u+uhr/fV1N9sHk3raU0h7tjxy7q7pNViGL5S2TxQ6xGoahGSu3tzbxRsZQf2LtwgoRQPIGlAFJCO7EhtoTw1LJnzz4JK/M0NTWHC3ZinYT27dy5PRZb+Dj27lRZkgHZKPyQEG7MoLuU9hw4wE9REn7YsKlBvrxm27ZtXNAikQ1fonhKSiiqkRLi6sSJ+cKkWOfBN1J7owo2MB4QQzvqMSvDRIcOKnEVWbATq404riob/pQSZKPYU0LY9xl2kdCTTz5Jq2+4if70S18S5RXYUCUXomBSqgv0xX7QUkIuhI+kFFmUFusc6CyVjRzx61//OpbI8HHkk95h2diDk/bt2xU+90r6ojTgqkA7alo8by4vbaxRBSzh9/mCvGG0hBc8PNjOFSvEOge80iVEYdkkG8wh2+OZiKVC+Ljf7xF1aJyA17FTU7KlBOBHG1Wwl71eWeKCbLQTuktpckKW/CEvwZRAHhXZk5PigQt6q7QTFbNSguxAQI1fRTamB6SbF0AX/JOSSlypy1aLK+O1pUR33Zd60ZCEHzlLSn/z139Jw243ffOb34x9imam6Wl5f0AbAwG5f8S8oRD5ApjakOuiEuPQA7lZSipxBZ1NQdkUiH59OdKdVN9Lwac04JoV4PpUsZSxr6iUeK4vJMfK5OQiXFcr1WEhnzQQ1IDDYRLJvCZ0QRtDIbUgC8hNuLC5l/ivhHg5QL4/NKuELw1VpTaEvVVwZpXMYDIpgcZTSKVr6vvyKsD1ilVXxVIWCw4zyoMQflS5UcADgkl6F0JEyFkq9NamV+jo0aP085//NDp4eFyQ4uPlCShIIVLDpBbGislEkA3McCmFFOIQOqtgQF8p+Udqi0vBF/89RcwyrEWUTLgTxfPSCbt9vvw8msJxcRqlp8+XfEfjNYVMlJRsFfObzQmUbLOFl8tEk41jKDdHOyVkMsWTzWbl5UCx+RHscZSbK8MQjYuLp8QkKyVFLOu42DWw3CgublYsG3KWLcum1NT55RsXk43fsawhJydbbMPERCwrkO0nqmlxlJWVTZa5ZR3R9DDHmygUR2QX623ieTYs94pF8fHxvOwoLWIpW7RzQqE4Sk+fX/YWjZc0jaxWC2VmyvBmQ3Emsqfqy8iiyiUit9tDr732En3rm9+iRFGsxHOMJybGTrzx8VjqlsS+j6WHcRzLVWQ5Qj9D2h9wU67SNzGwZGRmiPpmXFwcxcebxP0Bg//y5fn02c9/nh7788fohltvpJtvvDimMfqyNBcmUBylZ2I5kaxvapq+hMywf7RPS5yZkmwWsey4OKLMzMxoIsPHNI04F0r0Rr5KSkqgFStWhs+P9gX2S062kSRm+fYjLqSUC6Nd+1IeUyqaupQXvirrqgWuWuDSWKC7t5vWr1tP9U4npV/FUr40RlWQUnLqFP3hH/0R7dy+nR6YA/tQOP0q6++RBYTvIvRXluXllbysRWIfFLegLF9CeJmMSXQsy5AQ5jjALyVdtr5cIdY5QEHZuvVt8asrFdl4HaaiN+zn8cjmW4DBOqhgk1MlJVRyWl70A7tIoR0nPR6x7+EPli2cU4TvpXEFe6MApXMOvSaW71ViFrJUfK8as2gjzpGQd8pH2IouFJTNEUM22ioh2BD+kRJkS/0DmSqya2qqFqChxdJJJa7Qz1T1Nl5v37dhAz377LP0yFe/QnUN80hjhn4qMYun+H379onxkd9JXF0u30OuVDb43njjLTG/aswaaFiGD66UT/GAO+3x0+nTJxmXNlblHwbOnp4eApxhrEpLBK0HsHVlZ8nl6o050EFeT18fVVVVsexoM7+QDX7wDgyMxJSN9b1Yn4qCIgSE0aEu5izIrqwsZ5vESo6QhQR94uRJUZAZsrvau8gTiJ54IXs64KGiwkJddoz5cMh2j7vI5x0X+Qf8J06cIJ/QJq3NrWLfQ3ZxcSlhTZ7E3j2dfYTEGysG2SY8OI/SlBfrtqPfzBkxi2pS6BSNcHMDHgOnOZbvIRv4wmfLz5LP44vZTrQNbUQf8k1Hn+NEO1GIh/sVrzcgkD3JvoEdfTEGdMhGP8AKAkkihU1QpYp/MW3Isn1cYYv2Snw/MYGb+FGRbFwfMTs5IevHnZ19vLk9/BONDN8DB3hwcJCwcQToK1/5Cn33m39Pn/vM5xfcRKBdPX0DnCckMYuBf3JygiYmRmP6HnEHSNOysjI9rmL0e1y/rq6O+vq6Yj7cQG/kK0C1YrCL5R/EB6Am2zq6RP5BjnW7h+aKN6P3TfgSekvjCnY5d+5cNDe+Z8fEc7g+v5+qqysZjsvlGma8VWi9b9cOamrtoMaGesrJyeG5m5aWJsbhHB11sbNWFRQQtms+feYcVZdXUGtzC3lmfLQsJ5ef4I4fP04e7yT19g7xe3qAN2AZRXFxMWFXDmdjExn75SIhNjU2kmvcRcMjg1SQv4pM8fFcdl9eXs7XnZiY4L0tcbd44MABDsrh4X6yWBJ5PgKBVHS8kJwtDbx85YYbbmAHOBtrqJGXs8RRZ3cv3bTmepbd0NRA5afPUqOziXoGuqhg1XXMj6U1Y2Mu6u8fIpMJc7O5HGz43Ug82LsX8w7YyAH4obPBAHV0dFLBNQVktpj5+udOl1Gts4F6WjrpujWrw7IxNzcw2EvTnmnGGsWBHbv2UEdTCzU2NzEAAOYmsaQBNkTVMWQvm5tnxx1+0fGjYf8YNgRuLnzj84VodHTel3v27GHc15aWFi40gh+QVCB7dnaWOru6aPny5ezjpvoGOlVaSm3NrdTc0kwFq1eTKS6OdFzaLpYPP1x77bV6e44co6b6Gmp2tlJwNsjzqjh++PBh8vn81N8/wHCAgIZsaqqjcyXnuI2NjY18TdiQfd/cSBMT4zTiGqbV1+m2wq4juKkCZq2maQy9h8QFvYk06usfpKSkeIaaxJ1vYXExdbQ4qb6ukef4YEMjZicmxqivr5/jG/NMlRWVVFVeyb6HTMztB0IzdOzoUdJ5B8liSeD2wN7FhUVU7Wyi5sZGnpOGDSEbunumPNTd082yMQcYjquWJhrpd1H+Kn0+q7DoCA0PDdPIyCiRNku5y5bx0rPCo0c5TtoibNiJflJSSvuO7KLbb72DrrnmGvYPcHARb7BlV0cPXbdaj1kU+QwODtHYhIv8oSAtX5bHyRS+BwY2zjP6cW93PxWXnKJgcJbjd+XKlRzLsCEwchHj4I+Mq97ebhofHyO3e5J4H2oi2rNvBznr2qjR2cA+BvgHfH/06GEKBGaos7Odli3LIpsthQcr2HBx30Rc9fR0MVQn+i82FQAd2rOHmp0tVN/YELZ3YDpA+w7so5mZaerp7QvHFQaF4wePUm1zAznrm2j1dQXh3AEfuVwu6u3rJSMfHDtxjJpqG6je2UyhuZgNBP38BOrzTfNNlCkhgbIBfeoP0bTPSz09g/R/v/9/6ct/8iXGM29ubKLauhqanHRTX18nXXf9DdxPMJBhVyAMUtMzfs6FyFeIWfQH9P3Z0AzHG3Lh8aJCgt8bGudtiH6Kmz5UEvf0dtK1qwq43yLWSs+WUUdjK7k9kywDA+bx40doZGSIhofHCVjawBA3cmFjSxPV1zm5xgRzts2t7VRRfo78fj/nwlXX5LPvwzHrbKK+vr5w/0auhn8mxsc5ntBPMFAe2reHmlpbqKWhjQI0QzlZ2ZxTED8mUyINDPTP55TmViopPsVxiNgC3jMIb+P6+3pocnJKH0+wv/kc3rwRs4FAgPOvHldHaWZmhnGomfFK+k8Kf+V2T2vPPvu01tXVpc34/VFPA6Qe4PRKS0u16anovBAEnt3792p9AwOx4QNnZ7W2lg7t6NHDMfWAbOgCXkACarOzIr2ff/55ESQc7AB4P7aJAP5sYMSlbdu27aKyI7Wb8c1qhYXH2Y4z3pmYeqOdb27ZLLI3ePfu3avt3n9QiyXbsCFg8jzT01qkjkspBdmAGiwtLorpS/DiH+D9XCMjIv6Ojg6Gp4sVg9ANcKSAdmypd8aG6pydZVsXFup6w/7RCHoDUg+wffgelWZnOUYQ49A7Fj+uXVRUpLV1dMTkRUzX19ZqDrtDBAWJawPeD/1TYsPJyUkNvo+lM9oPewPWsazivCyu/H7tzc2vx/YN+vEs+kMhx4oop3hntNfffJOhaCW6O1ta9LiK5cu5nLJ9+05tYAnf41pf/4uva/fcc4/mdru5vyA/HD16XGRvtO2VV17RqirLY9oc1xoYGNB2796t+WPEK/wDfuTkFvg+VjtnZzXARu7cuV2kN2IWOqPvx5StaRpy4dNPPbOkDRf3pdnZWa24qEirrq4WyYYNX9/8+mIxV8Tf4qIp3CHhDj4rC1XKsZfB8Gu2UIiSBNWhuAHB3ScqGyVLOKAL5KvA5Ell444Pd+3Y7UKii4reWBeC+U0VvU1JFko2x64mhQ3xOjxNCBt5vraWbCaiG265VXT/h9dKYog3D0AYZtmfEuGQDZtI7K3iezx1lJSfpNWrb6QVubGrzhFTmKfGZhQSUvG9it64topsPA1suPc+qm9ro0xB0RT3zcsJ7ajQ7wEak54uW8nQ3NxOY2PD4d26YvmIY1bYH1T9Ey1mIeuLX/gCr9J6ffNmrpJWyVcnSk7RjatWU96K2DGrqjfiCv1MUkVuyE6yJBO2DYxFeg3OjEg23hYVlxXT/R++X8SvIht6quTCWO26lMfFA+6lvOhVWVctcNUCl84CqFL+8B3rqKGtTXwzd+muflXSUhbAYIXKZYum0eY9+ygJW5Zdpd97CyhFwZkz+gS6xGrY61BlE/Jmhc3T8RTa3j6/p2ksfQDuLiXcuarA+6Gd+hND7CuATwVOEbJxRyolFdl4iu/t7JWKpvPnz8csnDCEQWfoLiXorWJDbHQtJfgS8SIh6Iz5MimpxCDiSiXGsW8vkraEfAHMjgHUQNad0U48YUgo6Pez7yW84IGt0VYpIa6kBNnnz8uLYVTiSjVmAWMYrW/iKRIwlGPuKfrrr36F92GWthNzuyr9RyUOEd8qsusb66Vqs1xp34TtUHshJegczd6RctBvVHJh5LmX+7ush85pUVNTF97oO5ZiLpdbKci6u+VLD0ZcI9SpMFgMdneLkxdX/UVs9B2rnUgCUjgzFBFgoJMSghebS0sIr09rauSyocfgqHxQBL90AEAFosulbwgv0d3pbBPDaQbj4qmzW36zhQKSoRGXRA2CvVUG3M5O+eCMuGptbRfpASYs8ZLaO+gLUCgYILMQVQkx6/XKlhAFNY3q6qrEeiMxoq1SUpE9MjJClVXyGEelNwAtJIS+iZwlpZaWjpgxi72b9+7cTQ3dzfRP3/1HoXeI6mpqlPqPyhKY3t5eJdltLR1Sk/DN1uCgLKfA3mXFZUqykVekpJILpTIvBZ/SgKuCvasK7UhCPGJudLS1QEtYBdWmKmSZ2zxafo7sSYSQEhV0h9pSycTIcdGXkMjbcyEn42gL8ahx9uzszIVCLvLLzOyMaP4WpyfM+Mlint9Q/SIiwz+HyMRz1eEfLuEXxbBSgo2Mj5PN2xvNCZnMFFSILeM8yacKZKgaJCGurgBHaiKyKLyaNZksXK0qaSOeSGdm5NCOs7PRl+oZ10zLTqf9uw9SZcV5evyrXxXdRAEXW6X/AAVOSlivrSZbHlTIbSqwkSTvxpw3AUspIk49ly8XinS4CJPSSORwZIgTY1JSMplN8s4kgfUz2mC12ZQ6nrRwC/LR8bB/qpS4ncIBGmyAgZRSYmKyGDcYXS4tLVsqmpdgWMw2MT/2rdQH9dinwIZmAUyjIclhsxEGDBElYB9XWVET5GWmp1FQmKSxPMicLLeJ1Srnhbg+VeQAACAASURBVE1U+OPj5aD7/CbZzLdzIhOq2A8C7XZ5zLLvhf0BslNS5LJtFlmxj2GE5OQ046vo02IRxiD3Ndk+rrhwqiWVXntjE7/d+sbjj8ecPklKTVbqPxaLPA5hE+QVKanELPoP4GUlhDix22TQlZCHmLVIR6tEQHTKc6FE30vFc7Vo6lJZ8qqc380CuD1WfWT83a74gTkb++F+5K67qM7pvFo0dQV7FXPbn/7DP6Jsewpt3r5dVJ17BTfnqmrvwALSe4Z3IPr9eQom5jGPJ50/e3+2UofUw1zeFUOXYbCFD+FLabHFFWMLRUWwLZo/oLblnuIlrgj24dHRBShOV4RSCkoABIXBPuLi6Mtf/vLScRkK/V7ELPom5p4/6Hl2cXiIB1wkrVdf/Y044JHoULQgIRgdmyhLqxuxHhgV01ICr3RwQWEGUHekdPr0GbFs2BDoNVLCZtHSIh7Y8NixI1LRVFlTRWfLK8X8Bw4dEncOdKS6OnlxCza5lg6K8H3Fefkm8UD9AkSihGDrigpZzEIefA9ISgkh/lQ3CpfGbDAwRQFhRTN0Rb/sFhYdorjlwBF5XKG4TqUw8MgReX9obqqj0lPyzdYPHToQE2bQ8B2KiaT5Cuegr0ljFn5EXwZxIdXu3TwL8IlPfOKCnBecIYaklFYeI2eqxBWKCKU5Be0DrKd0UEQVPhD1JATZu3btENsQ+URaHAZ9VWJWou+l4hFDOwYCGp09q5dxu6c8tCw3l3VAWT9wYvEP7/B1GMN2amxspfFx4J5Oh7dJgkO6u3uYd3ZW4+2qYHgEel/fCLnd47xlU0qKnQZHh6nF2cy8wP7My1vB18Mi/9bWJhoZGSO/f4YysjIp3mTiiuj29g7mx+8ORxrjnJ4uL6ehgX5yjU/wNncAWMA1kRQMvQG/CIJDoaPf7yOvd5pyMpeR2RLP5e6trW3MDzzXrCx9uyoM5BgAAPFH2FIrPZ3nZ4D7CdnQOzs7l7e06+3vp8aGOhrqHqZJL2Rk8XwxqjoN2aOjY+Ft0NBBe3qGaHwcGNCAK9SvWVFxhqtpI+2NTldVVUlDQy62ucORzn7A74COW9xOtvfAEJHfTyhYMrZHi/RlXEI8pdiSOSFUVVbR4GAfTU1NkiEby1YMe0P+spwcorg4tiuSxcBAH9sE8HEgdJi+vl7WRdNmeXsw+AHQdH19PSzbZkvmGIq0CWzocORSQoKJfdPa2kIjw6NkQLlBdmRcGbInfB46f+4cTU15mBexCd8j+SGGDJskJydSYmISLzODbMD7YWPs7Owc9hva0tnZxfwoqklLc/DgVl1VRR0d7Qx1ii0X8TvsDV0AUwn5vN1fcjLHZl1DI425JsjtHuMt+jCHFdlOj2eaMjLS2VZVVUiKneRyjXGVbWRcDQ0NsHyjnWhP2dmztHvndtrw8Y9RdmYW+z5Stss1wu2BcMRsX98ADbtdZI4zccwiQWEpCmyNSm3AayYkJLCt6upqaKCvn5cRGTG72IZG/0EyB0wj9AYUqOH7yLhCfgDoguH7/v4uGh93sx44ZsSsoYshu6GugXp6B2jSM0UzZKbly3LYVoZs8GO/bvgZS8zOni2j/v5B3mzdak0K/15TUxnuP2gPCirR7xvr68k1Nk6Tkx5avlwHnMDSn97ePvYltofDdpO4AeEb4d5+mhx3U5w5nhxpaQztWF0LzHbd90lpiWRNSCL0+3rYcGCEcwpk45rr7/kwHTq0n37x86fp4f/5EGVlZnNcVZ4/S2Nj4+T3+igh0cJ2WWxvw4at3e3krGuioWG0M8Dxg7iK7JvYuB3bnsLH589XcB90uUYZ5hZ+XpwLEcvJyTrEJnwPG3q9PkpLs18QV8B8NrabxPK7nh5UQI9QKDTLv8MPRi6EXSJjtqGhiZBLZ2cDZLencUxExizi3MhLyFcdHW00Nuam6emp8O+RuXDGP0NpDr09nK8GuunWW9dyjFxJ/8mrBGiGsBkxCqeyMub3rV2xQh8I0SgDvcRud3AxRCBgpoysHA5GIJUsW7acHQ/nY19L4xwMSt0DvZSVkUO2uYn0zJR0MuejKs28YG7P4XDQ2EQGeX1ByshwhFceZmXlcFFKyBIiy9xG7Cjcyc/NJdfIOGU4HJRi04sLoGd+fj4FTAEyB+dNkJGRQQ5HFg0PjzIup3kOUUsvFtMLwBDQBuEmYGTERXZHFqXY9QKABFMiY8iijZG8DrudbQdsYmAuG8ciZZtM81V4sAkGUBRw2e3zRVwFBWvCd5yGvfU9QlcQlqlAJ7M5iVXE70u2MyuHktrbKN5sJUfG/P6s+fl5RCh0C4UIe5qCICM3L5faO9spOyMvrDfsDexbEDBgQyYT+4L9MzbG++fa52wCnuXLl4X1NorSoCds0dPTxzjHRkwgfixWG4XmbJgwt3e3w55FYykTc3E4vw9tVtZycjh8BPtZ5+IH6Fy52bnU3t5J8KshG9c2Yhb8ZrOOcgQ/2FIA0o7BSb+ZhN5oJ24AQYYMvBZCssY6c7vDHnE8NXxjCNmGfXA+4g+7+mTnztsQv2OQMGKBL0LEcd3fb2W9YU8QBkBDb/xt2JD9wzc1Zspy6Ddx+nE794fFcYj4cLu9HFO2uT6I60M2PsGPa4GsFhvbAk8tkTFr2BBtjNygHLoODw9ymwy9IWcF4ipkYvmGDXEtyMQAbVwbvLgpQswuJkeGg6y9qPJPotyM+WIbnMurEEwmMtoD/dHO9vZuys7MI2PVAX43+g90NwjtcWRkkNvtppyc+f6Ql7eKgkEf6234yBxnmbNJN+Usywn3TeQ3YEejL4CSTXrBlt1m4/wAuyJfGYTv2C3nxz/5MT388Kfo0L4DdPOHbmZ9OWazs8I+hn7zsudzZ1aKgyYcY+T1eVlvQ0f0E6PYKdLe6WnZNDIyTg6HnX0LXZBDDPtDR4MfvodNsFQqMzM9nNsRs5C9OK6yM3PZfsgb6Esg5EIjp6AvGzGLTyOn6XlbHwuMXGi0w7AVeHAjCNn4blB+vo4dDV0M2WhPZnYmdXbLl+AZ8t6VTynAJHBSt2zborlcLtEpwJh1OhtFvGA6W1bJuKeSE0aGhrTq6loJK/NUVVWK9W5ra9NefPF5EWYnhKvIdo9PaWXllTExnY2GVVXVMp6p8Xe0T+CNAidVSnt3HtSOHj0oZWfZwLOVUE9Pj+ZsaZOwMk9xcTHjzkpOAL6rs1EWV8B0BZYy8F0lBGzcxnqZbMgDtqu0P4CvvPysRA3mgc5DIyMifvACSxm2kZCzsV7r6xmQsHI/KCoqFvGCCf0HWOdSKi0tk7JyDG7dvFnMj7jyx8IMnpPG+aqxRSy7rKxMnK/ge+SJi9HPnnpKW7V8uVZYVMyY0a+99nJU/kg5wGs+X14ZE+PcOKcevu+TxQlyfllZKetknB/tE5jRXV190VjCx2ATYPNL+09jo5PxyMMCYnw5XiiP2RiiLunhq1XKi25rcLeE1yx4jfdBJr/HQz4yUVqy/jT8QW0rfIm73sV3zR+k9rb3dtNH71pPVc4WSk+VL/l4v9kAeLrBoBxD/f3Uvldf3Ujf+c63aePGjfTRj36U31JJMOvfT21crCtwtFNTP9h9c3GbxUVTOBHzF0A0khAGLvyTEmRLSVW2ih5IzCqDrYpsvKoFDJ+UWLYCUoaKDROTk5UGWxXZqv5RkQ3bqdhcuimCIVdFtm9aHt+qNlHRw0wm/fW7EBhARTbsouIfyJZlCL0XqMjGAAR/SklFNjatULGLDxt0KFAs2Y899lXau3s3Pf7Y4/Tyyy+TMY0iuUQs2ZEywKvEr5ivVGRj0wrpjbCKXLRXxfeR9rnc35UG3I0bN1F3n6wKDQUHRmWepBEqlXYoejmlUK147lxFeKPoWLqgCGrfvn2x2MLH0U4UekhobNJDO7e/LWFlHsjGGksJISC3b98uYWUe7ImLAh8pbd36ljiIUeRRW1srFU07d28X2xBPrLX1ctn7DhwSVzdCZ+y7KqVzc0WEEn5Uhh45dEjCyjwoBpImDZ/XS9MhEiNNIa7gIwlBB/heSk1NzdTZLp8/U5ENGx44IF9B8Pbbb/HbKonukxMTSjF78Mhe8YoN3JhJcuF9GzbQqdMl9NTPfkZPPPlN8cCISmIplZw5rdTvdx/aLxVNiCv8kxBy5ltvyeMKfRO5WULIhSpxJZF5qXiUBlyG9xNeWRXmS+FBjjVQg2uUgyogwUgdC0WU9A4F1fhxAYX1qSr+wfKn0dEJoTehhhw1DEJVIP4AYyi/g00gk4LRR4d7KeSTP4mKDQLfKz3LEZmEiFcqOoA3AExHU5Ck4hXMx6qoQDtGFiNJ2qEiG1i6/YOym1tcGwVpgPZ8r8kcj+IymRY3rllD3/s//4cqz5bRw3/0oCgXSWVDA6sC3CX4E6XwcnO5UArtiP6ur2SQ2UWJiw2ilq+U5P8OzErRiACWEsYJ4ClLSWFc4dcQKrjOAYXEaFQZquk9X7kc6zyVGwWVjkSzJuVBUQF9UZwwjPar+B7LbaSJOpQwSwozFRQMmclnUhlwlbqE0VzRp+pNi0go7skwrCg0UaWv0SxutuSvTyOrliX6K+liIrIqDKC4AU00xUvUUOaZ0eRy8brarAAbiRUPL738El2/fA2tv/deOl8Rfd259LUsGhkMyX3JRomo5o5lJNWcr/C2OtalFx7HionL140XXkvxL/E6XENuXh42oJcU2mDdmp3X2hrnRvsMBmfCa7qi8eEYBsWkpJTwusVY/JZ4MyVbU8lkjr1zCJayoAQf6/kkZDLFMz6ysZQi+jlYbqGRsbYwOi+WtcZTqi2JEueWb0TjR9uwzs1YuxaNF8egA5ZOyPQGKLmJcnL0tamxZON4QgLm2+aXb0Q7B+DrOTlYazu3/icKM+YrkUOlsq8vuJayMzLJLJCtr7W08TrUKCqED4VCWHs9v9QjfOAiXyyWeHGMx8Vp3EbJDdqU10u/feUVeuKb36Ika+xNDxCzWP6B9ZwxyYQB1ySOK2zOg+UbshyBq8tjNj01nZZfv4KSrbK+GReXSBmZDlFcQROzGRi8sphNiMfyrUyZDYko3hQvnn9G/snNzacvfuFzlJqaTH/x2NcpNyeb1t55Jy2VwTRNE9edmM0JlJqKZZsyGwJfIDNTxwCIGSuk53yJ7ERzEt3yodXhpXOxZCO3paSkiuyNeMU6cGmejXXtS3n8apXypbTmVVlXLfAeWABzm+vvWk9OZyOlpqkB9r8H6l69pKIFUK/yyCOP0qOPPkLf//73FW5mFC90lf2yW0D84I137ihWkm4UjuIWaTERWokiDuk8HnRQkT02OibWu7d/kAAHKC1YUdEb7ZMWq8AmaKPU3pgiUpGN4qCqimpxgKnMa097PEr+ARjI5fA9ZB45dkwMZacaVyq+h+zhYfn8o4rvUfkeMHkJry4lpCIbNlTxPWSj70tJRXZDQ53ipuX9Yptcbt/DLiIKhejQiUMLYnbDhg107txpqjxzhj7z6U9Tc/v8ftBYKqXS71V9rxLj8Ls0X4EXxanSWFGJK/QD6b68Ip9cQibxgDvt8dOhQ/sIxTbhwSgUoolJD3kmJ2nSFwgnzWAgwPi1zU1N87xzpdow8ITHQ8FpfS4BHRryysrKaHR0dF4G1sN6ArrsyfklQyjHBzYuIAHDekTIxm+G0w3Z5VVnWW/8DcLn5KSPJj3T5PN4wubEud4pN8P8Gbxh/gkPtxFtNQj8VVVVnJAMXYxrop2RwYTfR8dGGffU4GXZfj/rAShCnyeinT4fQ152dHQsaKdhP+hu6IjPgM/H+K6QHfk7+PFbpC742zU0Qv2uvgWy4UvmnfAskIHfTpw8yRtuG7L909PMC3sstklLWxuhWhXnGQQetA9641xu+5zvi4uLeYBeLBs6L9YbvgcsZ6Rs1tmIK/+8j6cDQepsB8To+IL2wPfwO9prXBOfsDUgKBfLht7sn7mYhe7gqawsZ99HytB18fHxyN8HhoaosrJUlz03MCJZQo/JCd3uhq0gA1CdOCdSBusx5yOca9hwaspH5DXRlHt+U3lP0B+29+IYB9we2rpA9lyMRNobx32T0wT/QCdjSSB+N3yD3w3Cd9yUL/ZPJO/ia2J1AsuO6JtGrCBPGAQeQJ92d3bqNpw7ANk4hs/Fsk+ePEaoPl78O+yNfGUUJuD8nr4+hiHEd4MMuUvJRn9YPBhdrJ3ImeXl5Qv0NmTj08hXuK43EKD+5kFG7IrUOz09k7bsO0A3rr2FNty7gY4cOcLtcrl6l5btmeZ+GfY9liT6fNRQV3OB7y9mQ6yTNbCUDV2Mfm+cE2krrHpoaWm5wN7wI/RAfwRBFnRpbm8mr9dtiKDpYCg8lizOKYCoXZwLjZzJudCv1wtBNsafwiL55vZhBd6FL+I53MCMnyorqxgrc8g1SqtXXcsVtFu3bCVncyPV11bTypV5lJycSrV1NVRXV8vYpNjhY/V113FT0LnKyyvY6VqcRnl5yxmjdc+eXeT3BxjmDXMoWAfb3dpJh4/uJmdzGzmdtXTbbbezjJqGamqobyK3e4K6ujro+uvX8BwT8GeLi0uorq6aPJ4pWrXqWp7r3b17J026PdTT00WJSSmUlZlBeKI6cGAXtbY0U01tDd1++x0sG4miuvo8z2+1tXXSddfp0GG1tdVUXFJMzsY6GhoeoOuvv4H5cYeGZA7ZmkaE+W1g/GI5gtPZzMnn2muv5XkHwOMVnSqmmcAMv/qDfphDwxKX4lOnqKm+gZpbGsL4nwcOHaGhwV6GNEOHNODutmx5k5yNLdTsrKWcnGU8L4QblQMH9nH+aG1tZag2zKHhmtgYAPo7na20du1trDc6kWvcRZ5JH42Pj1FBQQH//vbmTeR0tlBjUw2lpqYxtCBsBRB4LTRLLS3NlJ9/Db/SOl9VxYm4odFJjU1OunXtbTy/BB93dfXS6OgwjY2NUkGB7vv9u/ZQVV0dNTvryRSvzwlOTEzQvn17KBCYpc7ONsYjBiRgfUMdnThRRE1NTmpudtLKlSv5mnU1dVTfUM94x/2DPbTm+htZbwDJV1VVc1zFm3XZHo+HDh/azwV2wPYFrjGwfdFxT5w4RE3OFmqor2K4UazthI0aG5tpdLSfBgaG2N4oRjl9+jSVnS1j/wQCftYFyQJvQSYm3Oz7+HgLY2ADAB/taWlpotraGrJYkyknO4tlV52vJK/Xz0uUluevImuihRoaqunkqWK2t2t8nK6bsxXsDcjQnu5ujmHEFWy1Z+8uanY6qb6+nszmEOXm5lFvdzcdO3GEDu0/SDfdfhOtyl/FtqqvrqWi4iJqbKimzq4euvnmm9lWe/fuprExF2ORe70ejhXA7r29ZRvbGzbPz9ftjfYcOYbEHqLm5ka64cYb2J6wIWLI6dTbafSfEyeOUFfPALknXAS8XsP3iNmmplZqamrkmAKGL7dn3z6aCcyybOQC1E309vfSwYNHqKGxmpyNTlq7VsfDhR/w6lwjot7BQbrh+uu5Pdu2baH6+iaOE+ypDR+jD+7cuZ0wx97W1sJYwvo1PbRr1xZqbWuhupoquvGmm7k9VTV11Fhfxzd9yCk33TRvq7q6enI6nYQ5ddRHGLLRH4AlbjVbKSsniweRHTt2UGNjIwGDeOXKfG4PbHXu3BmanvZSc2sb3XjDDZyvTp0qoYqKcqqvbyQKaZS3PI8HocNYOhY/yzE+MxNiXGdgPR8+fJSaGmpoVf519NH7P0Lf+tu/pcqaGrImJlEg4GPZyLOI2YqK81RacoKcza3k8XrpmmuuocDsLB3Yv5dGRscY79mwld6/D7Ee6GtGO5FHSkpO6rKbm6mg4EZKTDRTbV0dFRUVsU2AfbxmjZ4LkWc6u3toeGiI/P4QrViRx7l9x45d5Gysobr6ekqY65uIK8SP1ZJMvb0DlJ2dxbZqqK2iU8Ul1FhfRR2dnXTLLR9iH8NW3d1dNDQ0xDdWmOMGvf3GG+RsbuYYD8zM0IoVK/kG69Dhw+T3TYdjh5mvlP+kuFVu97T2zDPPaAMDPaJTGp0t2rlzFSJeMO3eu1cM8wUIsaNHD4tlFxYe1wDdJqEwtKPfL2HXjh49KpbtHndr27ZtE8kFEyD1oI+UtmyRw97t3btXO3hQbsO33t4uhqR0Op1KMJNbt27VYBsJwffFxTIIyxmvGrQjbF1cVCRRg3kOHz6qDQzIIBIRf/v37xfLLiosEscVoB2zHA5x/wEEqDSupv1+7c03XxfrXVFRoVWUnxfzq8RscXGhpgLt+PbbWzXAE0oI9gCMoZTQj6WwhPC9CjzmK6+8otXWRocjbWnp0D760Y9q99x9t/bKK69J1eZ+KfW9y+XWdu/erQRz2yaEXXW5p7RnfiaHdoRvAO8oIUC6vrlZHrMSmZeKR/yEG59gomtXraKs9BzResJkWxKlpqaIJ/izM7Io1Z6qA5HHuBvR785yxLKxG0W6PV2kN55epqam6frrbhBVNeOJDE/kkmrSeHM8LV++XKw37Jdis1OiVbYcCzvcSKursdMH7AjgcgnlZGdSYoJNZBMdwNwhbic2AlDxPSqDJVWwqGYeGh2llStWiCqPUbmbnpEhkg2bQQ/4X+J76JudmU1JNkmFP/HOJ/ClpHIbb1l+9epv6G//5luULIDqRGFVsjVFFFfm+Hh+spPGFUDkc3KzRXrDhioxi00XZimOCq7Vn3BixS38g7cXEv/A99jxSRJXuC5iFk/NEtl46sROUBLZeCUKf2ZkpEWtaMfmB3/xF39BLa2t9POfPkUrV+TRTTffElOf5KRUcqTru0HFsl9CAqrqM8XV1djtKyU9nSyCFQHBgJ+GR0dozZo1ospje0oqpWXIZMMn2bzpyPymL7Ha+m4dv1ql/G5Z+up1rlrgMlkAr1o/sn491Tmd4uR4mVS5KvY9sEDJ6dP0Z48+QvfctZ6e/+UvKfMDjgP/Hpj4kl1SXDSFK2J+c2xChk6EggKVCkTp5sLQAxVrSDJSUtEDsjGfJyW0M7LoIdp54MM8sZQgG8UJEkJBS0NznYSVeVDgAPlSgt5G4USsc6CzimyV6nfooCIbUHPwqYQgVyVWVGIQOqjEOKrlpfb2BoPknytIkbZTGrPQ4XLFLHRVkQ0bSqEDDdlSG8IeKnGlGrMqcYW+OTg8KnEl8+SvWEGVFecpze6gtXes5fnri50MPVTaqRKzkCuVDXtjP1spQa44FyrGrFSHS8GnNOCWlZXTuMslui4m1LHRtZQwSS8lbGaswo/iIWnHw+ucsrKzUlUIBQB4DS0h8AEjV0qwIeDsJGROIKo4I79RqKmpo9ZWOeYt9JbakCH4+mUY0GgbcGalNkRH7e+V32ydPVvORSISG8KXKgkGm9NLCXGlgl2NNkrtTQEvBRQQgVTiCpWjKokRFbn4JyVsXC4l9PvyskopO+sN/SWE+IP/pQRsX/hUQvAjdJcSsN8H++UxjlyIaa1f/vpX9F9P/Yz+9tvfpm/81RNLDn7t3Z00MCD3T7XCwwfiamhIJhs5orCwVGoSUolZCFXJs2IlLgGj0oCrgtWLlQ8q8H6SuZB33l6lZipdRocQU4F2lIuHDaVJFxvAE6nBtqlBO8oSl9E6KaYq+MErbSf4VaAdwa8CfWfoL/uU+x3yVKAdE+Jjo24ZOgJO0SwcWIxzpJ8mht2U1RBApnApcMTl5X2Tc4SCydneMzJ4WaDXqcEBKvQHzUyALxWT6Z3YUZf+x1/6EtWer6bxkSG6e/06OrBv3wJgW1MwSJom1yUhTiUO1XI+qt9VSLrOHDLV41BFk3fOK4/2OTBw6aVUwOt1mXLjW8hMoZC+pkuijxSnVyLrd+VRGYhwLelgoQP6yxMjZKsMAGaFRAfZKjdb4DUpXCBRBC2q7in1mJXHILRRuWGd1WbEDQBAf1ABY1glBuMTEpT0Vhu00ES1m0RVrHOpETGYqyTphARZ8RtfPy6otJmHiUxK/IvbiKfdrdu307P/9QI9/sQ36Etf+AJjHIDPhA0d5KmWSOHNiWr/sdmUhh8yS4NrhlesLjbLFfH31aKpK8INV5W4aoF3bgGjaKqq0UnpafL9Yt/5Fa+e+X6xwOjoIP3rv/6I3nprE/3g339Af/VXTyjcmr1fWvn+0VPtFuP90653rKlRPKFyE/iOL/YenogCFGkx0Xuo5u90aRSSodgCPv0gE576ZhCwCm993o/2QNHMBz1m4ZdLGbOZmbn07LNP09a336YXnnuOPvbABjpz7tx77n5MIaGAS2Uq6T1X+hIoIB5wEeybNm1cciJ+KT1gTMDkiSgUotOnz4ir0PoHh6mqpkokGkwoypFWzw0MDdCWLdsoJNw7Cigy0iQAG5aUlIj1rqmpkRdyhEJ04sRJsezi4jKGx5SeANnSzoEnLpXq05MnT4p9Dz/WSH0fH6Ide3YxFKiknYhZ2FxKlZXnwq/qYp2DGDl9Ws330pid8nm56Ez6uhX9UlphDShVlbhC9S7+SQm+l1JNTSUdOHRMyh6GOpWcAN+rxCz6sbRqdngUMSuLK/QxINhJC+wQV2fOnI7ZxAc+9jFCMdb6ezfQJz7+cfrud74TMyca+Ura76Ez7CghyN6yZYvYhk0NTeKCxkAwSCpxJdH3UvGIgS8CAY1KS0t4kbLbPcVQdpgMAGRXX18f45wmJelbfnV3d1JDg5NcrgGGhQPcGqizs5U6OrqYd3Y2wFthwfD1DQ3U0dVJnqkpXhyORfYIJC6PHxygwcGB8PZgTe3N1NXWSv19AzQzM0PpmZkUbzJRb28/w39hU2Ofb4YcjjQeIIB13NXVTdPTfkpMNPGWgbhmU1MDw9sNDw/xtnPQD0kIcI/T0x7yzYYoOzOT51BRIQe4QvBOTIyFF6SjE3V2dhFAJEIhfYusoN9PDU1NvLnyyMgor4sEeAECEdWEqGwNBme5qhDzs0iqra3NBN7h4VHdrkTcQVFd7XYDB3g2vEUWQJ3p/AAAIABJREFUlmaBFzaHnQAPCVvVNzRRZ3c7BWeCBPAB43fYcGRkjHXH9nogJJaBgS6G08T2W4Z/UNkHvNq+vl4+Hwv1x0YnqLGpgdramkjT4sKy0R60BbrA5rnZOdhPkJMtfh8aGuYtsgzZWM4xNIQ2DjF8XHJyCne22tp66upqJ59vmqy2ZEq22bgiEfYeGOimkZFxBlCBDSG3tbWNZcOfy5blcnvQxoGBYebHVn+wCzZQQFyNDGF5zQxhUT5AEObtrdsEbYStED+NjXUMSQgIxqysTAYRQEx0drZzO2dmZnm7SSQgxFVnZzd5vT6KiwsxaAL80NbWwW3EdeLi4lgX7g9NLTQyPEwezzSDIMD3RlwNDKAaXf8dDdLjqpMmJiYpPp5YNp7SAd6vx8nwnC+SuT3nz1fRzr2b6aGPPxzeMi5S9vj4JLfHkA17AxoVvsd8H9qDpXDoZ/gHoBjYG7CsTU111NXVxTzgXRizgAnsDffNmro6am9rIbd7kiEQDd8vFbPog9XV9dTb3sqwgwCegC+AfdzQ2MhxGCm7qbmZ+7yfVwQAZlH3vS5b96Vhb9iqurqWYTcDgRkGeOGYCNsQendTZmY2+7i9tZNa29q47X6/PywbNw69vYjB0bC9YSvcZHd397AvAQhkT7WHbYi+Btl2u74tYG9/N7U0NlNvXx+/aQFMJwjV8IgL2Bu5A7EJ2eibg4NYrhcikzmR0h1p3L/b2to4P8AmFksi2woxC7jVgYFBzlkAEcFcNPpmV1cPDQ+PkN/vY4AOXjbYVE/pjlR68KFP0vGjh+jffvTvRCaNbFYb21vvm3rMQgZyZF/fIM3MBCL6fS/19PRy7Hq90xw/aA/0BtQl8kdcvInSHQ5ub0uLk/sr+oOePyJz+wjHt8ORzn0Q7e7s7JjLnWPhXAjZLa1O8nj0G8vFcYX8Ewxq3DfR73FD2dHRTrfdpkPZssGvkP8USmFmwpuEWyxmBjI3J5p470tMZvMmy3OFL1azjSv+zGYrd1AEEjqqzWanEJm5hMxqsbIJ0LFxjDfRjpgUx2+paekXmCnFYqUxsvA5OGiZO8dms1IgYCMym8gypwdk4B8QlUBGkVBY9qLqAfBZLDbGUk61JIWvYbWlkA1g5yhiWlTaazZDFwufwwzx2B/Xps/ah0JhxB0kFJChC3QAReoSWTc0f3y+reBnm2BDa5NpXj+Lhe1tVLbOnztnw0XtxHEUzsCPFJp/yZGGBfPgNdnCss0W/Xhior5/piEb7TF0wcVRJQ1ODHh6uy7UG6DixjH+nNsoGsUWJrOVrEb8GPY22VgfxAgIvgHB5fC3QSl2B/m83gV6x8XHcxus7JuUsF5Wi2Veb0PAnEz4MRTy6XaZOxbZTrYX85rIkmBhRcymeb3AG6mX4XOb2UYWs4lM2izHZtiGc+00w94RcYXjaKMe2rr9YYOwvdkWhp3NZDFbiQKI8Xmbh2MWsuf6iNFc+EiPW10GCtbS09IpCL6IWMF5SUnz+6Zi31VQpE2wJbxB4Nf9b57vDxExO9cgZkcbzdYQxSUmYmgJ88MOiEMUAYbg/zlCn+ZzFhUSpqZnhsvWDbvCVmgK9sMFRf4etmGEbKs10t7GFfV2sl9CoQUxkZiIgin0wch4j+hrEbLhG/QNzhEWCw+q0Ac3xYY9jDgx9NR9YyErLjCnP+cU/iMl3J6wWyF/Lp/O8+t+CctO0O0A2Svy8+ilVzdRU10N/fM//xP96oVf0b/8y78QdiUydMDAbbXYaXZWX56EmyEQ4srqC5DVdmFcQTZ00qMKe2InkNUa4UPkmzCZyG63EpnmYxb9y8idkTELnUI8RlgI/degeV+awv4JJeibz4dtYzBfKZ9SjEhgkr65+U1taGhIdArwQ+tbouOBRgoCVqbbLcPThQ6VVZWRp0f9fv58tRj3FDijL774vDY9JcNSLi8/K5aN9pWWlkXVNfJgVVWt1tcjw67GecCMltLBg/u1/fuPStm148cLxZiqPT09mtPZKJZdVHRcc49Pifjh+1g4s4YgYKq+9NJLWqMQ35Vjtlaud0XFWW3EPWJcLurnkGtcqzh7NipP5MHq6krNNeKK/Omi31WxlOtr6sU4zbDhcYW4Qv9pa2m5qK6LDxQqYFczlvLWrYtFXPRv9AcplnLfwIAGu0ipuLhYKV/BRxKCvV977WWttrZWwq6Nj48oYdbX19cu8D2u9/Qzz2g5Ocu0P/3zP9WAg26Q2zOtFRcXiTHU29paNPR9CY27XNrPFLCUnY2NWkdHh0Q067v/4EEZ77vMdXmrlPlpSb9Lu1JuMGLpgadxvJLCK54PMvFWWTN+Skqef4L5ILYXry5xd27cuX8Q2wgwg/vX3UU1bR2UnvrB9Sfm5rA93Ae9b3LMWixkTtSf0N+NmMV0yE9+/CN67rkX6KuPPUb/+q//Gp5quhzXR42fZ8JDqalJ4Sf9y3GdK03m5R0Nr9jn+ou7AYn5g96h0foki/kDP9iinfDlB3mwRRvx+m0Wr4kXQBxcPMbfr0fwWvn3oW9yzL6Lgy3iAfPz//4f/0nnz9fya+9bbrmF/t9//ufLVuGPgSc1Lfn3arCFnZUG3BdeeEFcKYYCHEn1nNH5sQeolBqaGrgCUcqPvTTx5CohFDO88N//LWFlHrQTd4cSAt8bb7whYWUeFIRIq0lRFLFp0yax7C1vvaUE2bdx46ti+EUUXEB3Kb311hs0KrShXmwjl/3qq6+Kq0+h80lUkUfMY0Zrw4kTJ6IdXnAMcbXnwL4Fv0X749w5OdwldtHxCavqcU3ELIpYJIRN7+F7KcGGKvCYKrJRPAN/SgmyES8SQvzBLlLavn27uCLXNx1UyoWb3nhDqf9gM3oplZScjtrOgtWr6MUXX6TDxw9TXVMdrVy+nH7+i5/S2GhsbGfYT9rve0d76edP/adUbZaLvCIh5HqVuJLIvFQ8SgOuUfAjvbgKoo1RbCOVjQKRy0VG0ZVEvv4QH1kMIDlLgUf6loDrimQ3Fbi6KSGB5NwouLh89kacYBN0KaHaUYVQlCMh6GFWmgZR87tR4CfRRS9Bk3DirhkVrfKV49KQ0q8+Gy42lGijijZkFDJKZKvycMxGFAVGO18WIfMSVGAGzfEh6T0cXyCyYGj+ihf/pvIGB7GCqvxYdMetd9DO7bvp/37ve/T2W9vpzrvuoF/9+jdRb2AQV0ahWiz5VrJSKE6O1iW8B9YvO6sXTsXS4b04rhRnKo1Gx1PBD1UZcC0hJDo1SLjLa1zZYIGOoWJD5hWeoKd++aAI/F2TggmFaoTNrMLP0I7iUSCB4uJmw9eRfJFCe0KPxZW60eSbTDK/swxF6EAVSD2Wjz4hNLqQjcXOMKazQqBEM9jveIz7j/DmCZcClGYo9tjyjrRC1bmUMDir3EBJ5Rp8YphbON5sISx9ktLq1WvoVMkp+u3GN2jzpt/QbWtvoR/84AdLvmrGDasUp5mxqxWAWsTpAQ2Lx82nPBdKbXEp+MTrcHGxyYlxWpmfL9rkPCHBzJs0G+XksZRNwRrMFFnBR4LVwmthsbZOQsZ6VQY/j3GCyUp0TXY+2dPTYnDqh7G+E/IlsuPj4ykz28HbaEmEQy6WDxjLYqKdE4qLo5xsbLgt0zs9PY1yVuZRUuL8so5o8rOzs3j+TNJOszmJHI5U0Z00rpmZCb2zKCEhdhLDulSrJYWSIpYFRdMbG2gvy80iS8SyiYvxw5fZmWmUZJNtXI1NsZOwBExA2JQb67qTsRxEQFiTnGS1iuIKO69seuU39MTffZuSrLFHGMQVlotI4irRFEfpWTmUZrcLtNaX0mBph+QpCgIz0x1kT5PFLN6wLc9bxutKJcpkZ2aTwy7bJB62QK6S5qv09AxKS5PFLJZdpaXZ5TbJzKTM7Bz2v6SdDns6JdkET4tYF25LIkdGhlh2erqDUpKT6ZprrqGvPfY43XLLOnrjjdfo//u379H0hJtuu/32sM2Aw5Caag//HU13PMWvuGZleB1vNF4cw9pjaS5Ejpqa8lB+/spYYt/145e3Svldb87VC161wO+fBbp7u2n9uvXkdDZSqnDw+v2z0tUWX0oLnDl9mv7tRz+kM6dO05NPPkGPf+NxKihYfSkv8YGUFfuRYq7ZmIjGpLW0+AjFPioQbyUlp6LOD0RaH4gklZXlkT9F/a4C7Yg27tu9k7AEQUJVVYCNlBVNoYBDBdoRBQjdnbI9OlE0pQJnhkKyM6flmKrq0I51EvMxz6lTct/3Dw/KYfKmg3To0CFx4Rl8X1Ulg+CD4igKlBbMoUhJpYgQ+xWLC5u8PvKSl8FnJEavqauRF/z4fErQjk1NTUr9XiVmq+vqlGIcMSvdZxm+R1GWlFShHaVxhfx64NARceHZ2OgYnRZAOxrtAgoT2iohI18Fpy/MhevvvZf27txNp06XUGtnN92x9i760he/SKdOnxKNEZC9bds2cc4Hypq0gBRTKxOTHkkT33Ue8YCLtanbtm0WJwEEzqigsg0tBq9r3C1yFPgDAR+NTQCaTkZ45Sa9UUAH7ezpE88UjY4CelG2AT1WbQwPD8qUJiKuPhXKBuqXimyXy0VTXpdYl/5B2cAPgb5JH8MSSoUPDQ2J/RP0BRhKUyI7GB/iTgr/Swi+93jkccX+YajB2NIRf9INyyFtcnJMPFhAtjmooxjF1oQY9nJqwithZZ5BBd97vV6S2hvCBwfl/WFqYpRGFPhV9Ibvx8ZiV+IaRsNG64GAzIbBQJAmJmSy8ap1sL9XHuOhILnHxw21Yn4ib3q97ph8BgPnlChb4t64Zg1t2vgqYaP6Ffn59Ief+DQ9/PDDtGPHDkPEkp+IWUCjSvMyYE6lcYU58wMHdi153ff6R/Er5clJH/32t78mny9IdnsKPfbYY7y+8d//4z8ocQ5678tf/jLl5+fTqZISKist5bY5HI4wL+5oWp1O/v1/rF9PDz74ID8hvPzyy2E73HP33bThgQcYDxNPmiBU1H7iEw/R2rV38BMLsGYtJjNQwehrX/s6zy0eO3aMyisrKTQzQ2tuuIH++I//mAAl+F/PvRDeO/fDH/4w3XfffZyEN27axHr7Z2boYw88wL9jaRKeLCA7EArS1772NV78/dxzv+B2Q3ZOXh63B3r95D/+g3XD95tvvpn+4A/+4IL2fP3rX+d5CjxRFhcXk9lsYnxp4/ffvLqRXCNDBD2SkxLp7//+H7jNP/3pT/kT/xUUFHB78B32BsHmaCOO4c4cgOcG/dmf/RkBs3XXrl1UW18fbifW1YF+/etfh5P/smXL6Ctf+Qr//pOf/jR8o/HQQw/RHXfcwXfa8Bts4qNp+vynv0RrblrNTxrwM/SA7v/0j//I8bBl2zbqbG9neSkpNnriiSf5O5aUTU1MsL0MH+NO+7evvkrmxCT20cc//lFat+4ufgtQfPIkYUdYyDf8cOTQIaqaA4EHHN83v/n3LBvLoTq7u5n3f9x9N/sTsl9//XUCH2L2zjvv5HjDJhnHThwL6/3oI4+wDWE/2BHFeyiyeuIvnyRrspXter66mpBzbl+3jj75yU/S5MQkvfzKS+xHKGBc0/AD7AH61CcfpHXr1vMTS11NFdswZArR1772l5Senso2PHv2LNtvdUEBPfLII3xeZLwZ/cRoD2IQ/cGw4ZkzZ3iDhv/6yS/of//L/6ZvfOMb7Hs8gcGGlEhkt6Ut8AMGRZARV+gn//mzn/FvsPd8e5po37494Zg14q2i4gwdP17EesMu/2uJuMrKyrqgn0D3D61dy/3EaA9flIh/Qx/CkqI33nor7B8jZre9/Ta1d3UxO/rQUv3EiGU8CW3evJm4MNAUovs/cj+tv3c9x9WJkyfDsgHgj7ls9BPjbRzmn598Uo9Z9JPB4eEFcYW3Dq+99hrHCYqVPnzPPXTfhg0XyH78scfYD3iCh49BiMUnnvgm9xP0qUank+PqnvvuowceeIDj6qXXXiJz0MT5B1jAiDcstzl69CjbG3K+8LnPcb5BW8rnZKOtf/PXX+cpBbzVQY5EHN56yy302c9+lrA06dXXfkUBb4BlG/kK9oYuBhk5Ev2kuLjI+JmMnIK4Kp3L7Ya9wfSbja+S2+WiCY+felqb6fTZMvJ6A7Tm5tV09513UlpaZjhmYWvY3CDkTehjxCziOy5eo+9+5x+ZBbnDiNmVK1eG+0lkLjTGHuSCgYEBWr58OT366KPGJa6cTymylds9rT3zzDNaW5szJpSh1+vV6urqGBbM5XLHhAZzj7u1vXt3a11dfRrOjUY4Dvixo8cLGVptxjcbjZ15jh49rAFyTiK7rs6pvfzyy9rQyHhMKMMR95R28OhBraOtTRufiq43INS6urq0vXv3xrQfGgSbAJoOdowFeQnZLpdL27Fjmwad8Hc0grzdu/dqhw8fFsmGLpu3bNFcIyMi2TVVVXO+jw5NODM7qyE+du7cyXBzseA0Dd8XFRXzedHaaNjk5Vde0aqq6oW+r9MKC4s0VywbQm/4fv9ehrKLFVe+qSnN2dahIQ7HXW4N7Y5GLte0VlhYqDlbWmLqjXaWny3XshwOjq+Yvh8fZ99I42pkaEh7e+t2jq+Yst1uraysjP8Bui8aGf6B7xGPsWXDJse1zZu3iH2/ffvbDEUbW7ab+xlgV9GPopGhN/ox+rN3JrovjZgFNCrnwijCkctgi9df/61WXl4u6pvQYf/e3dr4VOy4mkJOKS3itsaKWbTTyFcjLpfAP26tvLxSc9bWat4pHab16P7D2kMPPaQ5HA7t77/1D9rZ8nKWY8j+5S9/KYtZt5tjtqqyJqZNME7Bh2+++XoUS793h8SvlJOSzPSZz3yGli0riFlZhkq/tKRUSk1J5zt5A6T7YrcZqWmpZLOnkD1F3zHkYnz4HbLtDgdZrRYdRSgxehOA2mJLcXCFW6wKRBxPTbWSzW6j7PTYCEWZqclkt9rJlpJCacnRqwSxpAFP+6iWBapLLIJNUJUH/WOh60A2ZEJ/6IS/oxHkZdntfHcvkQ1d0qBHWppIdhLzwvfR24nXZ3jSswH0P91O1uTopfxoH2ydYoMNo0Nvsk3S0ig1OY3S0iwxKyd136eS3W5jeMSoNoTeqcmU4sjgnVZwbjRKTE4mR4qNzFYA86desJnA4nPT062EtwMOe+yKT+iZlJxEQWzokDIPbL9YpvE3fIhKdmlcpaWlUYrNxr6MapM5VK/U9DRKT0vjDQiMay71yf5JTyerDZWtsfsa+mWK3U6ZaXM5ZSmhc7+FZVvtQtl6H0tOTowds3N9DfnHYXdQUozlQYgN9HuOq1gxm2ii5NRU3jAiOVnW7/FEnpGRRWnJseMqGTnFamObxIpZ2BC78pgtZu77It+nJpHZZgsj2D34qYcJoBwVFec5p37+039I9927njZu3Mh5BBt9wDYi2WnplJb2/7d3rcFRXFf6aDQaPRACSchCFopKUbQYGxIMikzAIYRgnHWI1y7WRaVSKf9KxSlvlTcvb7Y2tV7HW1vZ3Uo2/pMtCscOcRzMYhvzMCCQeEpYCJBsMERCKCOhBxZ6jKSZkUaa19Z3eu6oNUgz58aAhdK3CkbTc/r0ud8599Hd537X2PErjuu5/0a/s/rhtfHEPrXfxI+UPzULrQtbCFgIxEUAj1DXVFTQpStXuDONK2z9aCHwKSGARKnK6mr67datVF9XT//0zz+h5583XnN9Sibd8cvGvz2MMQf72SJ5ajYXBIU4G+4uBqKrq0ucYXsXV5N9CZ/O5oLEE3+IKBB9Az87aws/og+a7QXvt2djzOJJxt8/8QQdPHiQTp6uocLC4tvjypCRLHl7lH8yrVoD7qFDh/mFtOSSWNKiswyiquqoRC3LIDkFSVLSAv5QaTZcX18fHTIlICW6BuopXRricnu1uJSRLNFxXZ4drMOlfObMGXI6WxJVL/r7G29sJ59XxjiEDuPSJfmyoLd37BJjiOQ9KV8rjEecdHZ2RusR7w/orak5HU9k0m8nT2pwKbe306FDcr7weg0u5ZFxH2c0SzcvQD3FS468Xi2ObrRNHS5lxJW0dHZ30tHjcv+At1w6cKEN63Ap79lz+7iUEbNOp3xicfSonEsZd5Y69VSJqxIfIa6kuu9ZsID6+j6WqGUZ6EW/IinjISyRrJGI3nEZrQFXh08XLGJ6XMpyLljjmb+GvC1EFJRXFcwwOsUe2XQ94TmBcaabSyhnEhBT5GLDbg2qNFzi5tV1pgvH/Mmct3GWB8SIUzBoZOrGHp/q+zgFaFzIM2kjv3jypK6V6B2RksOnPErMZwn+Br2fhvIErwYnXdARMDL2Jx28VV9A7aURKTq0kYaJ8d/bx1ZDh1IR1I63q+jUE1zKOkUnXqFXhxYXlujEYShJ3uiBiZRhDHZr7LehAx/ZuK3pYa51gU8grNEFiKla2Rw4Fdy00qITwIFQQER5p649jlrK40adJvqE3QGhb2GGDlk7MJQOiszXKh34mWdWj0s5EBhPmOwjAmwKIfBu2wOySU4oBdSFQsAj15I+3cAEEYO/vMhsZn2aXMpa7cEW0EREXkNDUj4o6nTm2laE7FqTLbQ1IX+NrimEPkha0DZDyGqTFh3nc1uW2wIT0JalRcpDDn1oxzo8zQ55WEnNNeRsWHqph4neBf5yaS0u5ZUrVyTM4ouaYkuhLEGGrZIHlykyIiXFnuKgzDmZYvl0u4Pmgnc5KfEuM8hwW7FihcQMlklKSaa56Wlkj6xFjnciZJBVCH5fUbGl0Nw5Ql5am40yUuZQbl6OSPX9999H9y4qFMlCyJGWSrk5uaKJDmboqalpIs5t6AbvNjCRcPsmU5gzvcEHLClYS4xsS0lJTg5R9rwcceKRzZYkjkF7cjL7PlHmtrITWEg5ukHa8Put2+gfnntOdoeBuMqcI8Ib9qSmOsQYwvdY25ooC3ainkY2rPoe7zMnL5fXhseTMf8GWwoK8kUxi/NgtzSu0tIzKW+BLGZhR0qajTLnxM+sV7YvXbaM8vMXqq8JP232VJo/T8Z1jW4qa/49lDlHyAFuS6X5OfMT2gABdK9ZWVkiDIHzqlVfEumFEHjopRzd4FL+wheWi3XfSUErSzkGbcyMkBiWaLlMzGl33Vf1PjbRUpy7rmIxBmMwQoeHf7O1IMmvoryCPrraRLnCzSvuRiyw569/bGzWt023b5yXG83mmEX8/TW0zdh2Jn7OgeSDvXvfFSdb4AW3NHkCgxz4jqUJDkj40EnKAXuUNLEJnddbb70lptUDo4tUN+pXX98Q64Npv4P3VEp9h8dWdXXyRIGTtUfp9Bm5vE7i2fWO69TcLE/Iqjt9mrzCTGL4vkWoG3GFRDJpHEL3ny7J+XTBjyv1PeQQ49IC37tcsk3iwcKDzovGZY/RwPQjTUABhmAAkhZgrVibJOfoxOyFDxro2LFqiVqWAT874yI4g+OqRR6z5+rrxf0VfH/hgiyJEHjv3bmDLl/+SGA10dDQkJhbHAovNzeL+3C310tgMpO+wEHf2d4hS/IEJtu2bRNj2NLSTB0dsqQpYAhmv5lYNKb9KdTR0U4LF97LnJaghUMxd2ag+sKjpJ7e6+Rsbadhj8HxqWTRyFUDAKkDHvXhbrLz2jW61vkxv5orKS3lx9YYnJAxrIpZB6gD+wYGyOHIoJKSIr57QYNRXJt4NARqQwCPxt/R4aTRUS9BN7ZIwzVB/6XKhO4e7oiQbIF6lZWWkt3h4E5V8eBi1gn6ShTohpzf7yffyAgVFBbyNc3LiiCLc2Af6t/R0Urz5qZTaVkZH0fgKd1kt1FJkZEq3wrd7U4aGnKRbzxAxUXG49+p8AZW1zqvUXf3AIE8fuGizzARx3QYQseQ100pSanU6nQSaAVRzLpBzYe7fEN3N3V3d1Jzczp99rN/wz42441zFYbtHU7ecAF8rVjYrrACJvAHCha749Eq/NDW1kbtHe1MalBYWMjHJ2FCxDqAoYFfB/X13eDsprKyMtZnjquo7kCI2lpamJbw+vUu3pIMvo/VrWK2nwfyVhoc7mMyBrPfVFypmEU9nK2t3B6C/jEKFBdzLMfirTDEZhvt7U7q/vgGzZ3TzFjFxpWKWVTI2eLk5S9DbjcVFweosKDgpphV9XQNuZjWMmAfJ2erk7CFHfxmrqc5ZpsjMZsV2SZQtRNzzCpMoKO7u5vr+afmXCorKbmpPcBe5XvEj4qhNIeDioqNWFbHIKswge+72zqp1dlBudnNtPDee6PxNlW7h319fQPk9rqppbmVyhYbO9OYdStMsPFISxPafQfNn5/DfYGKN3O7Vz6+3tVDzvZWGhgc5DwF9BMoU8UsfN/a2kx/vtZN2LO4uKiE8vLzb2r3CkNQQ8L3fTduUHqqncoWL2bdU8UsKDadbR0UshENDAxyvMM/08UV2iD6iO7ObvaL8o+5bUZjdixEHZ1O6mxvp8Feg9dZ9b9mTBSGE/1VO7f3JYsX3+T7STHrdFJraytlZqYREtumiiulG/XB+IB3uK3OdlqCR/np6ZNi1twXGnHVQXYH7g8D0T7F7HtVTzWeQO+qVasY65n0n8aAa2SdejwjlJ4+QX6N2XXsHqnjvgANeAbJTjZyuYapqCjAgwuC1TzgMhChZOodcpF/zEvDnshMnV/sB5jAGy/izcUTmc1Dl9uNwDEGP3wfGfFxBh46GBR8gvd2fDxAIx4fhSIbASg7YnMTkEwAHfa0TOrvd1FZmfEAwOcz7II8BhFV3ENDvOf34ODApHfbBiaQsvFgbNhjp8GBPpbvGRqiz/j9N2FiTgZCZxuCPYPD5MsG3saA63YPcfY3J1RFBjDGwuUmv99LGDg+s8jYB1LVU9mrPjGApCSlMFYjngkCdoUf5HCu+hxy9XI9XC5v9Dh+U75UcqgncAapPzaYBi5qwIXdSUnIeJ2sG4Txyckp3Jnm5+fz7+yvSFwBc0xooBuTGo9nmP2Jx26qwG5az59MAAAR/0lEQVT4CHGIc1FCo16e/aNT8PlC5BsZJ8o1rq3shm5VT8+Ijzwjw5wA19vbH7UbPMwK8+ieukEbwT84d3DYQ3kj2BzBeE+sdMMG/I3BD5tteIaHKegfpX63mxb5eR9wIy6naD8ur4t/840M07hpcwTog83wvaonE+O7+iktlEYDgwPEvTVngKKtwQ/YS3QiO8XtcjHHOHBUEwllKwMX8x/uoKDD1dtPo4sW0dyILnM91SloM+PjyMQHLsORlomNGIY4oQZ6VAF2XS6Dp/i6y0UYoFSZSrdn2EMhCvEk27zBhFlW+TI0FqCh4X5KSkqhG30Dk94/m+XV9YbHPTTiGaZQIMQbrqgBF7JKp/oEGP29bgoHR8njGY/uKsbx6UNbQp8xUdGAz8dtAv5SMQNZ6FO2qE+sjugZ7Od3lT7fOHkivoeswhA2K1vgX7Q3tA+vZzSafmzWjWtxSSHC5Ax2eAi+HyGkNkAW7QfF3Kf4AiEaHBgk33iIJ3ujeJTvcHBMKXuBlyro5zFhGBy0UV6esVnIGAWjfTLklN34HBwZpszMBYw7zqP09KgtsMMemhiaEKdoQ8AWNyeqTzGPPWjn6hrXe3rJjpUpM7FIWSVHR0fDv//DH8IDffG5RpU+8AufP39WfU34ebCyMpyIf1UpAccneFWl5f0Tp8KdfZ0icXAu/+Y3v0nI/6yUgfP2xo0b6mvcz8FhT/jgwT1xZcw/nqqtDbddu2Y+NP3fwWB4z5590/8e80tl5cHwkfcqY45O/3X37j3hYAIOYHX2latXwufONaivCT9379mXkCNVKenu7g6///77Iv+As/WVV14JX266rE6P+wnfv3/2TFwZ849HqqvFvofd4FKWltozZ5lfWiLf1NQUnp81PyEPsNL1/pkzzGGrvsf7RLt/55234olM+u3ChQth/JOWd959Vyoarq09EX777bfF8uAWh/2Scq2zM3z2bK1ElGWknOgQhu9ra0/JdAeD4d+9Cv7vRpE8eIN14krH9+B1rqzcF/aPxOdmV4Zevnw5jLYvKcODg+Ff/devxTHb0NAQbrp8VaKaZd59Sx5XYqW3QNBKmoqZBeGRBLa7ys3JJ2x5N1sLHheiSLNm71YcrncZj5OlWbN3Yz2dHe20ank5NbW1Mcfz3VgHic14ooS7voLIkxDJOXejTG9PD/NiSzOm78Y64i4Xj62Zr1ndhd/iiuAed6b14NaAe4udbKmzELjTCOBdI3MpNzXxBhN3+vrW9SwELARkCGhNALZu/d9oUkQi9aD50qF21KEnA33c8eNyWj3s7ajeOySyGy/isQ+mtIByTN0tJjrH5XJrUTsCQ3SmkoJ3pjo0edgDs76hXqKaZW4ntePOnTvEGCLhArhIy/bt26m5WZYhCr0zhdqx4Zw8ZpH74EZ+Al5+CQrqibsLSUG70Ymr20ntCN1vvPa6xGyWef317eIsWOAhpSWE8t27NagdfT6qO63R1nbs0Ipxnb4Tmds67WfPAWNPcgno0CvV3dPTRb98+X8kalkGepFoJilYPqYTsxKdt0pm4s20QKMutWNS0uSEp3iXwIAhLSHtBwUhQtbk7SgGE4sURjBkadQzRGJ2JwM/qR0GEkI2RRZmhiwNijodakfEiQ4NXzhgJF9J/WkLTSS6JTrHZkp4SSQb7/fYCR4SQ2LHQyWDxJZocktEqU6Mw2Ybkkw02lA822N/C4XkbUfXBB3dSIoLaLQfUB6GYkGPrVzkO/AXikbOkLdjnJA6R051h20r9YpcnjHRMD05JLcbvo9Ncp2uHtyfyFaxsQqduAJ+Oox+09l4O47LPcUUYnJPIWbCYTm1o07ljEFLbgt0g9D69hRAKIsccC4HNCjegKFMsxqYtdxJNnk/agyIGnzUOlgnB4PIKZedkpJKwZBXJouYRUavcGZhUDvqxMnUNmP5XH5eHi+nwLtj/DtaNZlgfvtvt9Ha9Wvp2e9/nx5Zt+6m33X6XLQHnnDpnCRE0I+MajGhN26ydfCD/ES2ucSk2BUR8c6BrF3Y7vFOUYf7PSUl/h7IZrswAIyNyvtC+FJoNl/mNrg9ar6OPzHY+v3yejo0DNcQZdt18ItW9g78MXWPMc2Fv/jQQ7yecZqfJx2eM2cepabK6PdwYna2jH4PslmZGeSbJ6RH5I2x54nviRfk5NDKh1ZOqku8L9jMO/buZFp5G1FBgbyewDDNIbs7w0w+Ly/+hu9mu5Yte4CysmQ0kDgvP7+I7OmycEGKPmyXlnkF2ZOWrsQ7z+Yfo+xcY/lQPDn128Nf/CItuGdiyYk6PtVnWpqd8jLlcYU1h1OVf/23f6fnfvQDys02dGG5x+NPPEHt7cbrAexi88MfP08fXLjASxx2H9hPTz31FJ1raIiuaZ2bIccvzZ5BdjD1Ccc6nZgFFaCYipTpETOYInEqXKY6lp8vpxe9Z+FCWrnywanUTHksPz+PQphxCQpi1sHrPAXC6IOy5PVE29TBsLx8BWXNXyAzhIjmafaF5qWNiS6CdczSAgwzMmSzeKybXfMVObUjEsiwdl1UglgHLO9nRTpvkZCVNHWLgLTUWAgAAWyr9rOf/oze2LljSkBGvV564MFl9OU1X6Htr70WlVm6dCmVlJXQvt37osekf3R0ddGa8nL68PIVys6W8fVKdVtyFgIWArcOAdn0L7KI//DhQ+LkFjyiwRIbUQmFCPuc4hxJgRzkpQW0gVLdSJ7APqeBMdntgs+rZ7d6byex3eedTDSR6BwkFEnLxQ8u0aWP5DSGrFv4nEbL90Q05PWK3z/q6IYsaAmlyRaQ1/KPiRhB4f7aa6/T0dMn6ZlnnqHTNRPUmUr3+fPnmUmqfPlkcvU1a9ZQzfEaut7Tw6pgB86RlBGfj0aZJEEmj5gFG5OkoB0gDqUFdo8K902GThDTSAuYjBobG6XinDAFylNJAdZadqNPEfYR0C1um6EQ1Zyuo64uWYIQdEtpUYGDTlxBt057QH+PcyQFstj3V4oLuN91bJHqldh6K2XEA65/LEjgs5RWGtm+Fy9+KLPVZqNTpw6LwcfaysZGOVfm2fPnxVmZYDVBNqR0O7+aMzVi3QgCTFqkpf58ozgrHIGuo7vrRgd1dcoyoGHvgQP7xe/BQRf54YdC3xPRkYOVzAolwQWDZ2PjeYkoD+Lw5cDgBDNavBOREd6gkbmNiZk5Qx1to6urg/Lycmnr1m205stfpi1btnBcq4nc8ePGIHzvvQYbmLInP6+AWXR6Inyx586dE08UKOCjANnJR7JJ6AcXPyDQo0pKIClAe/bvlYiyDPBuuiLLCscJR6qPiHUjs/XK1ati+QMH9jL7keQE+L7xopzn/NixY+QeGZKo5v5BGrOYILQ7W6m/35h4JbqAa6ifTtXWJhKL/o5MbDMlYvSHKf5wu0epsvKgGEPQykp1o62Ai1w6QF+41CDWDZ3or2ZiET9SHnJ7qfrIEcrJzKR1GzdwXfbs20OeYdCZgXLNwe+h8AMIr9vb23nfxcLCIlq9ejW/58RSHiSUIINscVkplVdU8Ay3+tgxGhvzssyKFeX8HguOq6k5yZsrA8Cnn36ar3m+sZHa/nyVKcqy5mfRo197hJ/t486hqamJZcDJu27dOsKs6PCJKhp1u5n2r2J5ORWXlXBHVlV1GJvOIZ2KvvMdQzc2IsAsGkkL4XCQvvGNb/L7KAQpyOQhi/clmzZt4uscOrSf+l1e5g697777aNmyZTwh2bVrZyTj0UGPP76J6f1QH7yjQ7aqw2GP6r5woYEuXWrmayLJ41vf+hbrhn29vT1c/5KSUqqoqODjIONXG81v2LCROUu7ejuo4eQ58oz7GIsN69czocUEhg5OelL1PHn0OPUN9nEGZ05WDq1fv451YxmFsZm1jSoqyglcxdBdd7Le2EPTbqeN6zewbgwIxnIbvNe10ZYtT7H/ak7XUEd7O2cr5uTMp/XrjVjZtWtXhI4wREuWlNGKFRXU73JRTdVx8oV8hISyilWr+J0m8MZkzciotNGmTV/na57/sJHaLl+lcVuA349u3Lgx4odDTMWJOFS6ced04tQp8o37KDnJT0uXruD6YEA4d66eYxCZ0evWb6CiwkImi//w4iVKSU6mrIxMWrthPaXZ7VRTV0fO1haWLy4rpocrVrOPq6uP0PCwh3153/2fpweWLOYlXCdP1rDvBz0e2rnzdTpRfYq+9NBD9KOf/Ijr/8c336T9e/fSsRMnKDc7jz766APG9vChA/SHP/4fVVZXc/oYfP+Tf/whjQUChHfAoUCA70rxiYL3ZebjoBB85Xe/p40bDf+omEUdMzIzaPOTT/F57723jylUwXdbVFTMcYV2suudHYRVCKA33bTpccYbgxCW9oGuMT19Ln31ka/SvDlz6dKfmgkbCUAWPvr2t7/NuquqqnigwLH8/AJau3YtHzfH1dqHVzPHMiYqWM4CqkG0B8QJSFhwzePHj0b9o2K2pqaGerp6KJicxFvAfT3SB+F9uGGHg1asWE5Lliwh0H4efm8P60Z+BTh1QQeIax44cIBtwn+bN29mHBsaGvhmAhSj6emp3Dbx+/79+6MTwQceeIC3BsRAAQzRJ6GeeBWAa6Kgnijo3+AHkDqAbx2bViAhKz09hR599G+5nQArcGwbMbuY0O/hqUPV4UMEWkckEZaUFNKDD65k7ua6uomNL9Cfgr8aOQBtf25jnvisrEz62tce4frAZy0tmFCFSPWF0F1deZAGPSO88kHZjQks+hrYjAQp1PPzn1/OdmMDBaa6dThI9SkqrqA7O3sePfaY0Rcerqoi95CLk72Ki4uoomIVTzT37t3PfQ8eNDz44BdYN16BnKuvo3A4TP5wONqnYOnPxYvoZ0PMgb5li9EXIh5AtxpOTqJFCxbS6rUPM85Y8mesnAlRaWkp+3nI5aLDR49yP6v6UhaeIf+JB1zYq+5u0dij35Fhmmws01DHEYz4p4o6rs6nYJBsqankAKdoKDRpBoUGgn/T6cCAZX5MpHRDfnTMTynIHElO5sCLtTFsd/C2V4gKrNVSxaxjKruns4XrE6k/MhHVS30cR3YnEk6mq4/5+OhogGVhj7IlilXEyKmOR3WMhSgQltcnnm6/P0gpKckTdsfqRuJCZINn4OIPhhnztMj+tGb/YECAj1HM14zaLfF9MEhR3YniKsKfDf3SuIraMo1uPJUAqX0IE6W0NDKqY49wBhuPK6FD8UAHxsai7QEx8ePnn6eXX36ZTpyqpYryFfTss8/Sq6++SrW1tTzYjY2OUnJKCv3iF7+gF198kQfiVZHJlcGnPdGOIqEw7QcGLF7+pvxjsiVe/Ezrn1hMYn3v9/OeulPphs5Jx/1BInNcxehO5AcMGDzZiLS3SbpxsWCQ7KmpHLex7fsm3ZwVn0xpc4x+LG77hmq/n1LT01k3PG7mt1a6xRiqvhOP3SPL7DDwKCa0aDsx1Qf2cd+GUUuKYcT3Ovahz0pPT9D/xvjtJj+gDaq+MKafVbbE4j3p+NgY+ZOSKcVmih8TVjfFVYzvzbqVbRCZKUVrwJ0pRlt2WAjcKQRwJ//mm28mvNx3v/c9WhzZvcgs3NvfT/d/7nP0q1//mr7z9NP0Hz//Of3LCy/Qu3v30t9985tR0ed/+lP671/+J108e5GWLl8aPW79YSFgITB7EJCt85g99bVqYiGghUB5eTnh319asCVgXkEBZecWsIq1eAz+wgv0cWf3JJV4p3rP/AVUGNn6cdKP1hcLAQuBWYGAOGlqVtTWqoSFwB1GANvbYW33VyJrDleVl/N7MvPG63gMVlN3mp7cvJmyc+Xrb+9wVazLWQhYCHxCBKwB9xMCaJ1uIaAQQJb4M9/9npFdjKVuQ1566YUX+XEy9sVFwfuql156id55511CNjfeCW7bupUpxXDcKhYCFgKzFwHrkfLs9a1VszuMQGZGJh2qOkA73vwjbXr8MSpfvZa+/4PnqLS4eJIlTz75JAVefZW2bNlMGWlZVFpaRIerDkzaKH3SCdYXCwELgVmBgJU0NSvcaFXCQsBCwELAQmCmI2A9Up7pHrLssxCwELAQsBCYFQhYA+6scKNVCQsBCwELAQuBmY6ANeDOdA9Z9lkIWAhYCFgIzAoErAF3VrjRqoSFgIWAhYCFwExH4P8BlHfANzk9MEcAAAAASUVORK5CYII="><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><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>
<div class="question" style="padding-left: 20px;">
<p>correct line, <em>y</em> = 10<em>x</em> + 40, seen on sketch <em><strong>(A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for straight line with positive gradient, award <em><strong>(A1)</strong></em> for <em>x</em>-intercept and <em>y</em>-intercept in approximately the correct positions. Award at most <em><strong>(A0)(A1)</strong></em> if ruler not used. If the straight line is drawn on different axes to part (a), award at most <em><strong>(A0)(A1)</strong></em>.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[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.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>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>Show that the stationary points of the curve are at <em>x</em> = 1 and <em>x</em> = 2.</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 <em>y</em> = 2<em>x</em><sup>3</sup> − 9<em>x</em><sup>2</sup> + 12<em>x</em> + 2 = <em>k</em> has <strong>three</strong> solutions, find the possible values of <em>k</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p><img src="data:image/png;base64,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"><em><strong>(A1)(A1)(A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct window (condone a window which is slightly off) and axes labels. An indication of window is necessary. −1 to 3 on the <em>x</em>-axis and −2 to 12 on the <em>y</em>-axis and a graph in that window.<br><em><strong>(A1)</strong></em> for correct shape (curve having cubic shape and must be smooth).<br><em><strong>(A1)</strong></em> for both stationary points in the 1<sup>st</sup> quadrant with approximate correct position,<br><em><strong>(A1)</strong></em> for intercepts (negative <em>x</em>-intercept and positive <em>y</em> intercept) with approximate correct position.</p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Rick <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A0)</strong></em> if extra names stated.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>6<em>x</em><sup>2</sup> − 18<em>x</em> + 12 <strong><em>(A1)(A1)(A1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em></strong> for each correct term. Award at most <strong><em>(A1)(A1)(A0)</em></strong> if extra terms seen.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>6<em>x</em><sup>2</sup> − 18<em>x</em> + 12 = 0 <strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for equating their derivative to 0. If the derivative is not explicitly equated to 0, but a subsequent solving of their correct equation is seen, award <em><strong>(M1)</strong></em>.</p>
<p>6(<em>x </em> − 1)(<em>x</em> − 2) = 0 (or equivalent) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award (M1) for correct factorization. The final <em><strong>(M1)</strong></em> is awarded only if answers are clearly stated.</p>
<p>Award <em><strong>(M0)(M0)</strong></em> for substitution of 1 and of 2 in their derivative.</p>
<p><em>x =</em> 1, <em>x =</em> 2 <em><strong>(AG)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>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">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) = 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="specification">
<p>The function has one local maximum at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = p">
<mi>x</mi>
<mo>=</mo>
<mi>p</mi>
</math></span> and one local minimum at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = q">
<mi>x</mi>
<mo>=</mo>
<mi>q</mi>
</math></span>.</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 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>.</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>Sketch 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> for −3 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> ≤ 3 and −4 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> ≤ 12.</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>Determine the range of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right)">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> for <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="x">
<mi>x</mi>
</math></span> ≤ <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">h.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>−1 <strong><em>(A1)</em></strong></p>
<p><strong>Note:</strong> Accept (0, −1).</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><img 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"> <strong><em>(A1)(A1)(A1)(A1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em></strong> for correct window and axes labels, −3 to 3 should be indicated on the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis and −4 to 12 on the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-axis.<br><strong><em> (A1)</em></strong>) for smooth curve with correct cubic shape;<br><strong><em> (A1)</em></strong> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-intercepts: one close to −3, the second between −1 and 0, and third between 1 and 2; and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-intercept at approximately −1;<br><strong><em> (A1)</em></strong> for local minimum in the 4th quadrant and maximum in the 2nd quadrant, in approximately correct positions.<br>Graph paper does not need to be used. If window not given award at most <em><strong>(A0)(A1)(A0)(A1)</strong></em>.</p>
<p><em><strong>[4 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=" - 1.27 \leqslant {\text{ }}f\left( x \right) \leqslant 1.33\,\,\,\left( { - 1.27083 \ldots \leqslant {\text{ }}f\left( x \right) \leqslant 1.33333 \ldots {\text{,}}\,\, - \frac{{61}}{{48}} \leqslant {\text{ }}f\left( x \right) \leqslant \frac{4}{3}} \right)">
<mo>−</mo>
<mn>1.27</mn>
<mo>⩽</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>⩽</mo>
<mn>1.33</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mn>1.27083</mn>
<mo>…</mo>
<mo>⩽</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>⩽</mo>
<mn>1.33333</mn>
<mo>…</mo>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mo>−</mo>
<mfrac>
<mrow>
<mn>61</mn>
</mrow>
<mrow>
<mn>48</mn>
</mrow>
</mfrac>
<mo>⩽</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>⩽</mo>
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)</strong><strong><em>(A1)</em>(ft)</strong><strong><em>(A1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em></strong> for −1.27 seen, <strong><em>(A1)</em></strong> for 1.33 seen, and <strong><em>(A1)</em></strong> for correct weak inequalities with <strong>their</strong> endpoints in the correct order. For example, award <em><strong>(A0)(A0)(A0)</strong></em> for answers like <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="5 \leqslant {\text{ }}f\left( x \right) \leqslant 2">
<mn>5</mn>
<mo>⩽</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>⩽</mo>
<mn>2</mn>
</math></span>. Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> in place of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right)">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span>. Accept alternative correct notation such as [−1.27, 1.33].</p>
<p>Follow through from their <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> values from part (g) only if their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( p \right)">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>p</mi>
<mo>)</mo>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( q \right)">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>q</mi>
<mo>)</mo>
</mrow>
</math></span> values are between −4 and 12. Award <em><strong>(A0)(A0)(A0)</strong></em> if their values from (g) are given as the endpoints.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">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">h.</div>
</div>
<br><hr><br><div class="specification">
<p>A rocket is travelling in a straight line, with an initial velocity of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="140">
<mn>140</mn>
</math></span> m s<sup>−1</sup>. It accelerates to a new velocity of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="500">
<mn>500</mn>
</math></span> m s<sup>−1</sup> in two stages.</p>
<p>During the first stage its acceleration, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> m s<sup>−2</sup>, after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> seconds is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a\left( t \right) = 240\,{\text{sin}}\left( {2t} \right)">
<mi>a</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>240</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>sin</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mi>t</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant k">
<mn>0</mn>
<mo>⩽<!-- ⩽ --></mo>
<mi>t</mi>
<mo>⩽<!-- ⩽ --></mo>
<mi>k</mi>
</math></span>.</p>
</div>
<div class="specification">
<p>The first stage continues for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> seconds until the velocity of the rocket reaches <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="375">
<mn>375</mn>
</math></span> m s<sup>−1</sup>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for the velocity, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v"> <mi>v</mi> </math></span> m s<sup>−1</sup>, of the rocket during the first stage.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the distance that the rocket travels during the first stage.</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>During the second stage, the rocket accelerates at a constant rate. The distance which the rocket travels during the second stage is the same as the distance it travels during the first stage.</p>
<p>Find the total time taken for the two stages.</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>recognizing that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = \int a "> <mi>v</mi> <mo>=</mo> <mo>∫</mo> <mi>a</mi> </math></span> <em><strong>(M1)</strong></em></p>
<p>correct integration <em><strong>A1</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 120\,{\text{cos}}\left( {2t} \right) + c"> <mo>−</mo> <mn>120</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mi>t</mi> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mi>c</mi> </math></span></p>
<p>attempt to find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c"> <mi>c</mi> </math></span> using their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v\left( t \right)"> <mi>v</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </math></span> <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 120\,{\text{cos}}\left( 0 \right) + c = 140"> <mo>−</mo> <mn>120</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>+</mo> <mi>c</mi> <mo>=</mo> <mn>140</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v\left( t \right) = - 120\,{\text{cos}}\left( {2t} \right) + 260"> <mi>v</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>−</mo> <mn>120</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mi>t</mi> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mn>260</mn> </math></span> <em><strong>A1 N3</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>evidence of valid approach to find time taken in first stage <em><strong>(M1)</strong></em></p>
<p><em>eg</em> graph, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 120\,{\text{cos}}\left( {2t} \right) + 260 = 375"> <mo>−</mo> <mn>120</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mi>t</mi> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mn>260</mn> <mo>=</mo> <mn>375</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 1.42595"> <mi>k</mi> <mo>=</mo> <mn>1.42595</mn> </math></span> <em><strong>A1</strong></em></p>
<p>attempt to substitute <strong>their</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v"> <mi>v</mi> </math></span> and/or <strong>their</strong> limits into distance formula <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^{1.42595} {\left| v \right|} "> <msubsup> <mo>∫</mo> <mn>0</mn> <mrow> <mn>1.42595</mn> </mrow> </msubsup> <mrow> <mrow> <mo>|</mo> <mi>v</mi> <mo>|</mo> </mrow> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int {260 - 120} \,{\text{cos}}\left( {2t} \right)"> <mo>∫</mo> <mrow> <mn>260</mn> <mo>−</mo> <mn>120</mn> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mi>t</mi> </mrow> <mo>)</mo> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^k {\left( {260 - 120\,{\text{cos}}\left( {2t} \right)} \right)} \,{\text{d}}t"> <msubsup> <mo>∫</mo> <mn>0</mn> <mi>k</mi> </msubsup> <mrow> <mrow> <mo>(</mo> <mrow> <mn>260</mn> <mo>−</mo> <mn>120</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mi>t</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="353.608"> <mn>353.608</mn> </math></span></p>
<p>distance is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="354"> <mn>354</mn> </math></span> (m) <em><strong>A1 N3</strong></em></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>recognizing velocity of second stage is linear (seen anywhere) <em><strong>R1</strong></em></p>
<p><em>eg</em> graph, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s = \frac{1}{2}h\left( {a + b} \right)"> <mi>s</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mi>h</mi> <mrow> <mo>(</mo> <mrow> <mi>a</mi> <mo>+</mo> <mi>b</mi> </mrow> <mo>)</mo> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = mt + c"> <mi>v</mi> <mo>=</mo> <mi>m</mi> <mi>t</mi> <mo>+</mo> <mi>c</mi> </math></span></p>
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int {v = 353.608} "> <mo>∫</mo> <mrow> <mi>v</mi> <mo>=</mo> <mn>353.608</mn> </mrow> </math></span></p>
<p>correct equation <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}h\left( {375 + 500} \right) = 353.608"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mi>h</mi> <mrow> <mo>(</mo> <mrow> <mn>375</mn> <mo>+</mo> <mn>500</mn> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>353.608</mn> </math></span></p>
<p>time for stage two <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="=0.808248"> <mo>=</mo> <mn>0.808248</mn> </math></span> (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.809142"> <mn>0.809142</mn> </math></span> from 3 sf) <em><strong>A2</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.23420"> <mn>2.23420</mn> </math></span> (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.23914"> <mn>2.23914</mn> </math></span> from 3 sf)</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.23"> <mn>2.23</mn> </math></span> seconds (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.24"> <mn>2.24</mn> </math></span> from 3 sf) <em><strong>A1 N3</strong></em></p>
<p><em><strong>[6 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A company performs an experiment on the efficiency of a liquid that is used to detect a nut allergy.</p>
<p>A group of 60 people took part in the experiment. In this group 26 are allergic to nuts. One person from the group is chosen at random.</p>
</div>
<div class="specification">
<p>A second person is chosen from the group.</p>
</div>
<div class="specification">
<p>When the liquid is added to a person’s blood sample, it is expected to turn blue if the person is allergic to nuts and to turn red if the person is not allergic to nuts.</p>
<p>The company claims that the probability that the test result is correct is 98% for people who are allergic to nuts and 95% for people who are not allergic to nuts.</p>
<p>It is known that 6 in every 1000 adults are allergic to nuts.</p>
<p>This information can be represented in a tree diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-13_om_14.31.34.png" alt="N17/5/MATSD/SP2/ENG/TZ0/04.c.d.e.f.g"></p>
</div>
<div class="specification">
<p>An adult, who was not part of the original group of 60, is chosen at random and tested using this liquid.</p>
</div>
<div class="specification">
<p>The liquid is used in an office to identify employees who might be allergic to nuts. The liquid turned blue for <strong>38 </strong><strong>employees</strong>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that both people chosen are <strong>not </strong>allergic to nuts.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><strong>Copy </strong>and complete the tree diagram.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this adult is allergic to nuts and the liquid turns blue.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the liquid turns blue.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the tested adult is allergic to nuts given that the liquid turned blue.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the number of employees, from this 38, who are allergic to nuts.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{34}}{{60}} \times \frac{{33}}{{59}}">
<mfrac>
<mrow>
<mn>34</mn>
</mrow>
<mrow>
<mn>60</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>33</mn>
</mrow>
<mrow>
<mn>59</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for their correct product.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.317{\text{ }}\left( {\frac{{187}}{{590}},{\text{ }}0.316949 \ldots ,{\text{ }}31.7\% } \right)">
<mo>=</mo>
<mn>0.317</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>187</mn>
</mrow>
<mrow>
<mn>590</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.316949</mn>
<mo>…</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>31.7</mn>
<mi mathvariant="normal">%</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from part (a).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2018-02-14_om_05.54.09.png" alt="N17/5/MATSD/SP2/ENG/TZ0/04.c/M"> <strong><em>(A1)(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for each correct pair of branches.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.006 \times 0.98">
<mn>0.006</mn>
<mo>×</mo>
<mn>0.98</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for multiplying 0.006 by 0.98.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.00588{\text{ }}\left( {\frac{{147}}{{25000}},{\text{ }}0.588\% } \right)">
<mo>=</mo>
<mn>0.00588</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>147</mn>
</mrow>
<mrow>
<mn>25000</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.588</mn>
<mi mathvariant="normal">%</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.006 \times 0.98 + 0.994 \times 0.05{\text{ }}(0.00588 + 0.994 \times 0.05)">
<mn>0.006</mn>
<mo>×</mo>
<mn>0.98</mn>
<mo>+</mo>
<mn>0.994</mn>
<mo>×</mo>
<mn>0.05</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>0.00588</mn>
<mo>+</mo>
<mn>0.994</mn>
<mo>×</mo>
<mn>0.05</mn>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em>(ft)<em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1)</em>(ft) </strong>for their two correct products, <strong><em>(M1) </em></strong>for adding two products.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.0556{\text{ }}\left( {0.05558,{\text{ }}5.56\% ,{\text{ }}\frac{{2779}}{{50000}}} \right)">
<mo>=</mo>
<mn>0.0556</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.05558</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>5.56</mn>
<mi mathvariant="normal">%</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mfrac>
<mrow>
<mn>2779</mn>
</mrow>
<mrow>
<mn>50000</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from parts (c) and (d).</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.006 \times 0.98}}{{0.05558}}">
<mfrac>
<mrow>
<mn>0.006</mn>
<mo>×</mo>
<mn>0.98</mn>
</mrow>
<mrow>
<mn>0.05558</mn>
</mrow>
</mfrac>
</math></span> <strong><em>(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for their correct numerator, <strong><em>(M1) </em></strong>for their correct denominator.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.106{\text{ }}\left( {0.105793 \ldots ,{\text{ }}10.6\% ,{\text{ }}\frac{{42}}{{397}}} \right)">
<mo>=</mo>
<mn>0.106</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.105793</mn>
<mo>…</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>10.6</mn>
<mi mathvariant="normal">%</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mfrac>
<mrow>
<mn>42</mn>
</mrow>
<mrow>
<mn>397</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from parts (d) and (e).</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.105793 \ldots \times 38">
<mn>0.105793</mn>
<mo>…</mo>
<mo>×</mo>
<mn>38</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for multiplying 38 by their answer to part (f).</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 4.02{\text{ }}(4.02015 \ldots )">
<mo>=</mo>
<mn>4.02</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>4.02015</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Follow through from part (f). Use of 3 sf result from part (f) results in an answer of 4.03 (4.028).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">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>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = x - 8">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mn>8</mn>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right) = {x^4} - 3">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mn>3</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h\left( x \right) = f\left( {g\left( x \right)} \right)">
<mi>h</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</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="h\left( x \right)"> <mi>h</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </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>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{C}}"> <mrow> <mtext>C</mtext> </mrow> </math></span> be a point on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span>. The tangent to the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{C}}"> <mrow> <mtext>C</mtext> </mrow> </math></span> is parallel to the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span>.</p>
<p>Find the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-coordinate of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{C}}"> <mrow> <mtext>C</mtext> </mrow> </math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>attempt to form composite (in any order) <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^4} - 3} \right)"> <mi>f</mi> <mrow> <mo>(</mo> <mrow> <mrow> <msup> <mi>x</mi> <mn>4</mn> </msup> </mrow> <mo>−</mo> <mn>3</mn> </mrow> <mo>)</mo> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\left( {x - 8} \right)^4} - 3"> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mi>x</mi> <mo>−</mo> <mn>8</mn> </mrow> <mo>)</mo> </mrow> <mn>4</mn> </msup> </mrow> <mo>−</mo> <mn>3</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h\left( x \right) = {x^4} - 11"> <mi>h</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <msup> <mi>x</mi> <mn>4</mn> </msup> </mrow> <mo>−</mo> <mn>11</mn> </math></span> <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing that the gradient of the tangent is the derivative <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{h'}"> <mrow> <msup> <mi>h</mi> <mo>′</mo> </msup> </mrow> </math></span></p>
<p>correct derivative (seen anywhere) <em><strong>(A1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h'\left( x \right) = 4{x^3}"> <msup> <mi>h</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>4</mn> <mrow> <msup> <mi>x</mi> <mn>3</mn> </msup> </mrow> </math></span></p>
<p>correct value for gradient of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'\left( x \right) = 1"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>1</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m = 1"> <mi>m</mi> <mo>=</mo> <mn>1</mn> </math></span></p>
<p>setting <strong>their</strong> derivative equal to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1"> <mn>1</mn> </math></span> <em><strong>(M1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="4{x^3} = 1"> <mn>4</mn> <mrow> <msup> <mi>x</mi> <mn>3</mn> </msup> </mrow> <mo>=</mo> <mn>1</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.629960"> <mn>0.629960</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = \sqrt[3]{{\frac{1}{4}}}"> <mi>x</mi> <mo>=</mo> <mroot> <mrow> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> <mn>3</mn> </mroot> </math></span> (exact), <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.630"> <mn>0.630</mn> </math></span> <em><strong>A1 N3</strong></em></p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {{\text{e}}^{2\,{\text{sin}}\left( {\frac{{\pi x}}{2}} \right)}}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mn>2</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>sin</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mi>π<!-- π --></mi>
<mi>x</mi>
</mrow>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</msup>
</mrow>
</math></span>, for <em>x</em> > 0.</p>
<p>The <em>k </em>th maximum point on the graph of <em>f</em> has <em>x</em>-coordinate <em>x<sub>k</sub></em> where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k \in {\mathbb{Z}^ + }">
<mi>k</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<msup>
<mrow>
<mi mathvariant="double-struck">Z</mi>
</mrow>
<mo>+</mo>
</msup>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <em>x<sub>k</sub></em><sub> + 1</sub> = <em>x<sub>k</sub></em> + <em>a</em>, find <em>a</em>.</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>Hence find the value of <em>n</em> such that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sum\limits_{k = 1}^n {{x_k} = 861} "> <munderover> <mo movablelimits="false">∑</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mrow> <mrow> <msub> <mi>x</mi> <mi>k</mi> </msub> </mrow> <mo>=</mo> <mn>861</mn> </mrow> </math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p 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 to find maxima <em><strong>(M1)</strong></em></p>
<p><em>eg</em> one correct value of <em>x<sub>k</sub></em>, sketch of <em>f</em></p>
<p>any two correct consecutive values of <em>x<sub>k</sub></em> <em><strong>(A1)(A1)</strong></em></p>
<p><em>eg x</em><sub>1</sub> = 1, <em>x</em><sub>2</sub> = 5</p>
<p><em>a</em> = 4 <em><strong>A1 N3</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing the sequence <em>x</em><sub>1,<sup> </sup></sub> <em>x</em><sub>2</sub><sub>,<sup> </sup></sub> <em>x</em><sub>3, …,</sub> <em>x</em><sub>n</sub> is arithmetic <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <em>d</em> = 4</p>
<p>correct expression for sum<em> <strong>(A1)</strong><br></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{n}{2}\left( {2\left( 1 \right) + 4\left( {n - 1} \right)} \right)"> <mfrac> <mi>n</mi> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>+</mo> <mn>4</mn> <mrow> <mo>(</mo> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p>valid attempt to solve for <em>n</em> <em><strong>(M1)</strong></em></p>
<p><em>eg</em> graph, 2<em>n</em><sup>2</sup> − <em>n</em> − 861 = 0</p>
<p><em>n</em> = 21 <em><strong>A1 N2</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The population of fish in a lake is modelled by the function</p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( t \right) = \frac{{1000}}{{1 + 24{{\text{e}}^{ - 0.2t}}}}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>1000</mn>
</mrow>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mn>24</mn>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mo>−<!-- − --></mo>
<mn>0.2</mn>
<mi>t</mi>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span>, 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> ≤ 30 , where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> is measured in months.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the population of fish at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> = 10.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the rate at which the population of fish is increasing at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> = 10.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> for which the population of fish is increasing most rapidly.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>(10)</p>
<p>235.402</p>
<p>235 (fish) (must be an integer) <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing rate of change is derivative <em><strong>(M1)</strong></em></p>
<p><em>eg</em> rate = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f'}">
<mrow>
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
</mrow>
</math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f'}">
<mrow>
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
</mrow>
</math></span>(10) , sketch of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f'}">
<mrow>
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
</mrow>
</math></span> , 35 (fish per month)</p>
<p>35.9976</p>
<p>36.0 (fish per month) <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> maximum of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f'}">
<mrow>
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
</mrow>
</math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f''}">
<mrow>
<msup>
<mi>f</mi>
<mo>″</mo>
</msup>
</mrow>
</math></span> = 0</p>
<p>15.890</p>
<p>15.9 (months) <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {x^4} - 54{x^2} + 60x">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mn>54</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>60</mn>
<mi>x</mi>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 1 \leqslant x \leqslant 6">
<mo>−<!-- − --></mo>
<mn>1</mn>
<mo>⩽<!-- ⩽ --></mo>
<mi>x</mi>
<mo>⩽<!-- ⩽ --></mo>
<mn>6</mn>
</math></span>. The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">There are <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-intercepts at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0">
<mi>x</mi>
<mo>=</mo>
<mn>0</mn>
</math></span> and at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = p">
<mi>x</mi>
<mo>=</mo>
<mi>p</mi>
</math></span>. There is a maximum at point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}">
<mrow>
<mtext>A</mtext>
</mrow>
</math></span> where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = a">
<mi>x</mi>
<mo>=</mo>
<mi>a</mi>
</math></span>, and a point of inflexion at point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}">
<mrow>
<mtext>B</mtext>
</mrow>
</math></span> where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = b">
<mi>x</mi>
<mo>=</mo>
<mi>b</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the coordinates of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}"> <mrow> <mtext>A</mtext> </mrow> </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="f"> <mi>f</mi> </math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}"> <mrow> <mtext>A</mtext> </mrow> </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 coordinates of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}"> <mrow> <mtext>B</mtext> </mrow> </math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the rate of change of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}"> <mrow> <mtext>B</mtext> </mrow> </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>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="R"> <mi>R</mi> </math></span> be the region enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span>, the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-axis and the lines <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = p"> <mi>x</mi> <mo>=</mo> <mi>p</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = b"> <mi>x</mi> <mo>=</mo> <mi>b</mi> </math></span>. The region <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="R"> <mi>R</mi> </math></span> is rotated 360º about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-axis. Find the volume of the solid formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>evidence of valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = 0"> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 0"> <mi>y</mi> <mo>=</mo> <mn>0</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1.13843"> <mn>1.13843</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = 1.14"> <mi>p</mi> <mo>=</mo> <mn>1.14</mn> </math></span> <em><strong>A1</strong></em><em><strong> 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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.562134"> <mn>0.562134</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="16.7641"> <mn>16.7641</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {0.562{\text{, }}16.8} \right)"> <mrow> <mo>(</mo> <mrow> <mn>0.562</mn> <mrow> <mtext>, </mtext> </mrow> <mn>16.8</mn> </mrow> <mo>)</mo> </mrow> </math></span> <em><strong>A2</strong></em><em><strong> 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>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> tangent at maximum point is horizontal, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f' = 0"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo>=</mo> <mn>0</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 16.8"> <mi>y</mi> <mo>=</mo> <mn>16.8</mn> </math></span> (must be an equation) <em><strong>A1</strong></em><em><strong> N2</strong></em></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><strong>METHOD 1 (using GDC)</strong></p>
<p>valid approach <em><strong>M1</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'' = 0"> <msup> <mi>f</mi> <mo>″</mo> </msup> <mo>=</mo> <mn>0</mn> </math></span>, max/min on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f'}"> <mrow> <msup> <mi>f</mi> <mo>′</mo> </msup> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - 3"> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mn>3</mn> </math></span></p>
<p>sketch of either <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f'}"> <mrow> <msup> <mi>f</mi> <mo>′</mo> </msup> </mrow> </math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f''}"> <mrow> <msup> <mi>f</mi> <mo>″</mo> </msup> </mrow> </math></span>, with max/min or root (respectively) <em><strong>(A1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 3"> <mi>x</mi> <mo>=</mo> <mn>3</mn> </math></span> <em><strong>A1 N1</strong></em></p>
<p>substituting <strong>their</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span> value into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> <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( 3 \right)"> <mi>f</mi> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = - 225"> <mi>y</mi> <mo>=</mo> <mo>−</mo> <mn>225</mn> </math></span> (exact) (accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {3{\text{, }} - 225} \right)"> <mrow> <mo>(</mo> <mrow> <mn>3</mn> <mrow> <mtext>, </mtext> </mrow> <mo>−</mo> <mn>225</mn> </mrow> <mo>)</mo> </mrow> </math></span>) <em><strong>A1 N1</strong></em></p>
<p> </p>
<p><strong>METHOD 2 (analytical)</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'' = 12{x^2} - 108"> <msup> <mi>f</mi> <mo>″</mo> </msup> <mo>=</mo> <mn>12</mn> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> <mo>−</mo> <mn>108</mn> </math></span> <em><strong>A1</strong></em></p>
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'' = 0"> <msup> <mi>f</mi> <mo>″</mo> </msup> <mo>=</mo> <mn>0</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = \pm 3"> <mi>x</mi> <mo>=</mo> <mo>±</mo> <mn>3</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 3"> <mi>x</mi> <mo>=</mo> <mn>3</mn> </math></span> <em><strong>A1 N1</strong></em></p>
<p>substituting <strong>their</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span> value into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> <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( 3 \right)"> <mi>f</mi> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = - 225"> <mi>y</mi> <mo>=</mo> <mo>−</mo> <mn>225</mn> </math></span> (exact) (accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {3{\text{, }} - 225} \right)"> <mrow> <mo>(</mo> <mrow> <mn>3</mn> <mrow> <mtext>, </mtext> </mrow> <mo>−</mo> <mn>225</mn> </mrow> <mo>)</mo> </mrow> </math></span>) <em><strong>A1 N1</strong></em></p>
<p> </p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing rate of change is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f'}"> <mrow> <msup> <mi>f</mi> <mo>′</mo> </msup> </mrow> </math></span> <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{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="f'\left( 3 \right)"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </math></span></p>
<p>rate of change is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="-156"> <mo>−</mo> <mn>156</mn> </math></span> (exact) <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>attempt to substitute <strong>either their</strong> limits <strong>or</strong> the function into volume formula <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_{1.14}^3 {{f^2}} "> <msubsup> <mo>∫</mo> <mrow> <mn>1.14</mn> </mrow> <mn>3</mn> </msubsup> <mrow> <mrow> <msup> <mi>f</mi> <mn>2</mn> </msup> </mrow> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi \int {{{\left( {{x^4} - 54{x^2} + 60x} \right)}^2}} {\text{d}}x"> <mi>π</mi> <mo>∫</mo> <mrow> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mrow> <msup> <mi>x</mi> <mn>4</mn> </msup> </mrow> <mo>−</mo> <mn>54</mn> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mn>60</mn> <mi>x</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> </mrow> <mrow> <mtext>d</mtext> </mrow> <mi>x</mi> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="25\,752.0"> <mn>25</mn> <mspace width="thinmathspace"></mspace> <mn>752.0</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="80\,902.3"> <mn>80</mn> <mspace width="thinmathspace"></mspace> <mn>902.3</mn> </math></span></p>
<p>volume <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 80\,900"> <mo>=</mo> <mn>80</mn> <mspace width="thinmathspace"></mspace> <mn>900</mn> </math></span> <em><strong>A2 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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = \ln x">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>ln</mi>
<mo><!-- --></mo>
<mi>x</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x) = 3 + \ln \left( {\frac{x}{2}} \right)">
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>3</mn>
<mo>+</mo>
<mi>ln</mi>
<mo><!-- --></mo>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mi>x</mi>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, 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>.</p>
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> can be 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 two transformations:</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="\begin{array}{*{20}{l}} {{\text{a horizontal stretch of scale factor }}q{\text{ followed by}}} \\ {{\text{a translation of }}\left( {\begin{array}{*{20}{c}} h \\ k \end{array}} \right).} \end{array}">
<mtable columnalign="left" rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mrow>
<mtext>a horizontal stretch of scale factor </mtext>
</mrow>
<mi>q</mi>
<mrow>
<mtext> followed by</mtext>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mrow>
<mtext>a translation of </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mi>h</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>k</mi>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mo>.</mo>
</mrow>
</mtd>
</mtr>
</mtable>
</math></span></p>
</div>
<div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h(x) = g(x) \times \cos (0.1x)">
<mi>h</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>
<mo>×<!-- × --></mo>
<mi>cos</mi>
<mo><!-- --></mo>
<mo stretchy="false">(</mo>
<mn>0.1</mn>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 < x < 4">
<mn>0</mn>
<mo><</mo>
<mi>x</mi>
<mo><</mo>
<mn>4</mn>
</math></span>. 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> and the line <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>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-14_om_10.34.27.png" alt="M17/5/MATME/SP2/ENG/TZ1/10.b.c"></p>
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span> intersects the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{h^{ - 1}}">
<mrow>
<msup>
<mi>h</mi>
<mrow>
<mo>−<!-- − --></mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</math></span> at two points. These points have <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> coordinates 0.111 and 3.31 correct to three significant figures.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down 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">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span>;</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>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>
<div class="marks">[1]</div>
<div class="question_part_label">a.iii.</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="\int_{0.111}^{3.31} {\left( {h(x) - x} \right){\text{d}}x} "> <msubsup> <mo>∫</mo> <mrow> <mn>0.111</mn> </mrow> <mrow> <mn>3.31</mn> </mrow> </msubsup> <mrow> <mrow> <mo>(</mo> <mrow> <mi>h</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <mrow> <mtext>d</mtext> </mrow> <mi>x</mi> </mrow> </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>Hence, find the area of the region enclosed by the graphs of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{h^{ - 1}}"> <mrow> <msup> <mi>h</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </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>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d"> <mi>d</mi> </math></span> be the vertical distance from a point on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span> to the line <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>. There is a point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(a,{\text{ }}b)"> <mrow> <mtext>P</mtext> </mrow> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>b</mi> <mo stretchy="false">)</mo> </math></span> on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span> where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d"> <mi>d</mi> </math></span> is a maximum.</p>
<p>Find the coordinates of P, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.111 < a < 3.31"> <mn>0.111</mn> <mo><</mo> <mi>a</mi> <mo><</mo> <mn>3.31</mn> </math></span>.</p>
<div class="marks">[7]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q = 2"> <mi>q</mi> <mo>=</mo> <mn>2</mn> </math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q = 1"> <mi>q</mi> <mo>=</mo> <mn>1</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h = 0"> <mi>h</mi> <mo>=</mo> <mn>0</mn> </math></span>, and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 3 - \ln (2)"> <mi>k</mi> <mo>=</mo> <mn>3</mn> <mo>−</mo> <mi>ln</mi> <mo></mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </math></span>, 2.31 as candidate may have rewritten <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> as equal to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3 + \ln (x) - \ln (2)"> <mn>3</mn> <mo>+</mo> <mi>ln</mi> <mo></mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>ln</mi> <mo></mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </math></span>.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h = 0"> <mi>h</mi> <mo>=</mo> <mn>0</mn> </math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q = 1"> <mi>q</mi> <mo>=</mo> <mn>1</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h = 0"> <mi>h</mi> <mo>=</mo> <mn>0</mn> </math></span>, and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 3 - \ln (2)"> <mi>k</mi> <mo>=</mo> <mn>3</mn> <mo>−</mo> <mi>ln</mi> <mo></mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </math></span>, 2.31 as candidate may have rewritten <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> as equal to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3 + \ln (x) - \ln (2)"> <mn>3</mn> <mo>+</mo> <mi>ln</mi> <mo></mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>ln</mi> <mo></mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </math></span>.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 3"> <mi>k</mi> <mo>=</mo> <mn>3</mn> </math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q = 1"> <mi>q</mi> <mo>=</mo> <mn>1</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h = 0"> <mi>h</mi> <mo>=</mo> <mn>0</mn> </math></span>, and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 3 - \ln (2)"> <mi>k</mi> <mo>=</mo> <mn>3</mn> <mo>−</mo> <mi>ln</mi> <mo></mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </math></span>, 2.31 as candidate may have rewritten <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> as equal to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3 + \ln (x) - \ln (2)"> <mn>3</mn> <mo>+</mo> <mi>ln</mi> <mo></mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>ln</mi> <mo></mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </math></span>.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>2.72409</p>
<p>2.72 <strong><em>A2</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing area 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="h"> <mi>h</mi> </math></span> equals 2.72 <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><img src="images/Schermafbeelding_2017-08-14_om_17.00.04.png" alt="M17/5/MATME/SP2/ENG/TZ1/10.b.ii/M"></p>
<p>recognizing graphs of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{h^{ - 1}}"> <mrow> <msup> <mi>h</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></span> are reflections of each other in <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> <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>area 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="h"> <mi>h</mi> </math></span> equals 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="{h^{ - 1}}"> <mrow> <msup> <mi>h</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2 \times 2.72\int_{0.111}^{3.31} {\left( {x - {h^{ - 1}}(x)} \right){\text{d}}x = 2.72} "> <mn>2</mn> <mo>×</mo> <mn>2.72</mn> <msubsup> <mo>∫</mo> <mrow> <mn>0.111</mn> </mrow> <mrow> <mn>3.31</mn> </mrow> </msubsup> <mrow> <mrow> <mo>(</mo> <mrow> <mi>x</mi> <mo>−</mo> <mrow> <msup> <mi>h</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> <mrow> <mtext>d</mtext> </mrow> <mi>x</mi> <mo>=</mo> <mn>2.72</mn> </mrow> </math></span></p>
<p>5.44819</p>
<p>5.45 <strong><em>A1</em></strong> <strong><em>N3</em></strong></p>
<p><strong><em>[??? marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid attempt to find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d"> <mi>d</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>difference in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y"> <mi>y</mi> </math></span>-coordinates, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d = h(x) - x"> <mi>d</mi> <mo>=</mo> <mi>h</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>x</mi> </math></span></p>
<p>correct expression for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d"> <mi>d</mi> </math></span> <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\ln \frac{1}{2}x + 3} \right)(\cos 0.1x) - x"> <mrow> <mo>(</mo> <mrow> <mi>ln</mi> <mo></mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mi>x</mi> <mo>+</mo> <mn>3</mn> </mrow> <mo>)</mo> </mrow> <mo stretchy="false">(</mo> <mi>cos</mi> <mo></mo> <mn>0.1</mn> <mi>x</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>x</mi> </math></span></p>
<p>valid approach to find when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d"> <mi>d</mi> </math></span> is a maximum <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>max on sketch of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d"> <mi>d</mi> </math></span>, attempt to solve <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d’ = 0"> <msup> <mi>d</mi> <mo>′</mo> </msup> <mo>=</mo> <mn>0</mn> </math></span></p>
<p>0.973679</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0.974"> <mi>x</mi> <mo>=</mo> <mn>0.974</mn> </math></span> <strong><em>A2 N4 </em></strong></p>
<p>substituting <strong>their</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span> value into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h(x)"> <mi>h</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </math></span> <strong><em>(M1)</em></strong></p>
<p>2.26938</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 2.27"> <mi>y</mi> <mo>=</mo> <mn>2.27</mn> </math></span> <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[7 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">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A particle moves in a straight line such that its velocity, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo> </mo><mtext>m s</mtext><msup><mrow></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>, at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> seconds is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfrac><mrow><mfenced><mrow><msup><mi>t</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></mfenced><mi>cos</mi><mo> </mo><mi>t</mi></mrow><mn>4</mn></mfrac><mo>,</mo><mo> </mo><mn>0</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mn>3</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine when the particle changes its direction of motion.</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 times when the particle’s acceleration is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>.</mo><mn>9</mn><mo> </mo><msup><mtext>m s</mtext><mrow><mo>-</mo><mn>2</mn></mrow></msup></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 particle’s acceleration when its speed is at its greatest.</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>recognises the need to find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>0</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>57079</mn><mo>…</mo><mo> </mo><mfenced><mrow><mo>=</mo><mfrac><mi mathvariant="normal">π</mi><mn>2</mn></mfrac></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>57</mn><mo> </mo><mfenced><mrow><mo>=</mo><mfrac><mi mathvariant="normal">π</mi><mn>2</mn></mfrac></mrow></mfenced></math> (s) <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognises that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mi>v</mi><mo>'</mo><mfenced><mi>t</mi></mfenced></math> <em><strong>(M1)</strong></em></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>26277</mn><mo>…</mo><mo>,</mo><mo> </mo><msub><mi>t</mi><mn>2</mn></msub><mo>=</mo><mn>2</mn><mo>.</mo><mn>95736</mn><mo>…</mo></math></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>26</mn><mo>,</mo><mo> </mo><msub><mi>t</mi><mn>2</mn></msub><mo>=</mo><mn>2</mn><mo>.</mo><mn>96</mn></math> (s) <em><strong>A1A1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>M1A1A0</strong></em> if the two correct answers are given with additional values outside <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mn>3</mn></math>.</p>
<p> </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>speed is greatest at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>3</mn></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>.</mo><mn>83778</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>.</mo><mn>84</mn><mo> </mo><mfenced><msup><mtext>m s</mtext><mrow><mo>-</mo><mn>2</mn></mrow></msup></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>In part (a) many did not realize the change of motion occurred when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>0</mn></math>. A common error was finding <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>(</mo><mn>0</mn><mo>)</mo></math> or thinking that it was at the maximum of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math>. </p>
<p>In part (b), most candidates knew to differentiate but some tried to substitute in <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>.</mo><mn>9</mn></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>, while others struggled to differentiate the function by hand rather than using the GDC. Many candidates tried to solve the equation analytically and did not use their technology. Of those who did, many had their calculators in degree mode.</p>
<p>Almost all candidates who attempted part (c) thought the greatest speed was the same as the maximum of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math>.</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>
<br><hr><br><div class="specification">
<p>A scientist conducted a nine-week experiment on two plants, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math>, of the same species. He wanted to determine the effect of using a new plant fertilizer. Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> was given fertilizer regularly, while Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> was not.</p>
<p>The scientist found that the height of Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>,</mo><mo> </mo><msub><mi>h</mi><mi>A</mi></msub><mo> </mo><mtext>cm</mtext></math>, at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> weeks can be modelled by the function <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>h</mi><mi>A</mi></msub><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>sin</mi><mo>(</mo><mn>2</mn><mi>t</mi><mo>+</mo><mn>6</mn><mo>)</mo><mo>+</mo><mn>9</mn><mi>t</mi><mo>+</mo><mn>27</mn></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mn>9</mn></math>.</p>
<p>The scientist found that the height of Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>,</mo><mo> </mo><msub><mi>h</mi><mi>B</mi></msub><mo> </mo><mtext>cm</mtext></math>, at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> weeks can be modelled by the function <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>h</mi><mi>B</mi></msub><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mn>8</mn><mi>t</mi><mo>+</mo><mn>32</mn></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mn>9</mn></math>.</p>
</div>
<div class="specification">
<p>Use the scientist’s models to find the initial height of</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</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>Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> correct to three significant figures.</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 values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>h</mi><mi>A</mi></msub><mfenced><mi>t</mi></mfenced><mo>=</mo><msub><mi>h</mi><mi>B</mi></msub><mfenced><mi>t</mi></mfenced></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>For <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mn>9</mn></math>, find the total amount of time when the rate of growth of Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> was greater than the rate of growth of Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math>.</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><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>32</mn></math> (cm) <em><strong>A1</strong></em></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><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>h</mi><mi>A</mi></msub><mfenced><mn>0</mn></mfenced><mo>=</mo><mi>sin</mi><mfenced><mn>6</mn></mfenced><mo>+</mo><mn>27</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>26</mn><mo>.</mo><mn>7205</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>26</mn><mo>.</mo><mn>7</mn></math> (cm) <em><strong>A1</strong></em></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>attempts to solve <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>h</mi><mi>A</mi></msub><mfenced><mi>t</mi></mfenced><mo>=</mo><msub><mi>h</mi><mi>B</mi></msub><mfenced><mi>t</mi></mfenced></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>4</mn><mo>.</mo><mn>00746</mn><mo>…</mo><mo>,</mo><mn>4</mn><mo>.</mo><mn>70343</mn><mo>…</mo><mo>,</mo><mn>5</mn><mo>.</mo><mn>88332</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>4</mn><mo>.</mo><mn>01</mn><mo>,</mo><mn>4</mn><mo>.</mo><mn>70</mn><mo>,</mo><mn>5</mn><mo>.</mo><mn>88</mn></math> (weeks) <em><strong>A2</strong></em></p>
<p> </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>recognises that <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>h</mi><mi>A</mi></msub><mo>'</mo><mfenced><mi>t</mi></mfenced></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>h</mi><mi>B</mi></msub><mo>'</mo><mfenced><mi>t</mi></mfenced></math> are required <em><strong>(M1)</strong></em></p>
<p>attempts to solve <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>h</mi><mi>A</mi></msub><mo>'</mo><mfenced><mi>t</mi></mfenced><mo>=</mo><msub><mi>h</mi><mi>B</mi></msub><mo>'</mo><mfenced><mi>t</mi></mfenced></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>18879</mn><mo>…</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>23598</mn><mo>…</mo></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>33038</mn><mo>…</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>.</mo><mn>37758</mn><mo>…</mo></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>47197</mn><mo>…</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>.</mo><mn>51917</mn><mo>…</mo></math> <em><strong>(A1)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award full marks for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfrac><mrow><mn>4</mn><mi mathvariant="normal">π</mi></mrow><mn>3</mn></mfrac><mo>-</mo><mn>3</mn><mo>,</mo><mo> </mo><mfrac><mrow><mn>5</mn><mi mathvariant="normal">π</mi></mrow><mn>3</mn></mfrac><mo>-</mo><mn>3</mn><mo>,</mo><mo> </mo><mfenced><mrow><mfrac><mrow><mn>7</mn><mi mathvariant="normal">π</mi></mrow><mn>3</mn></mfrac><mo>-</mo><mn>3</mn><mo>,</mo><mo> </mo><mfrac><mrow><mn>8</mn><mi mathvariant="normal">π</mi></mrow><mn>3</mn></mfrac><mo>-</mo><mn>3</mn><mo> </mo><mfrac><mrow><mn>10</mn><mi mathvariant="normal">π</mi></mrow><mn>3</mn></mfrac><mo>-</mo><mn>3</mn><mo>,</mo><mo> </mo><mfrac><mrow><mn>11</mn><mi mathvariant="normal">π</mi></mrow><mn>3</mn></mfrac><mo>-</mo><mn>3</mn></mrow></mfenced></math>.</p>
<p><em>Award</em> subsequent marks for correct use of these exact values.</p>
<p> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>18879</mn><mo>…</mo><mo><</mo><mi>t</mi><mo><</mo><mn>2</mn><mo>.</mo><mn>23598</mn><mo>…</mo></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>33038</mn><mo>…</mo><mo><</mo><mi>t</mi><mo><</mo><mn>5</mn><mo>.</mo><mn>37758</mn><mo>…</mo></math> OR</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>47197</mn><mo>…</mo><mo><</mo><mi>t</mi><mo><</mo><mn>8</mn><mo>.</mo><mn>51917</mn><mo>…</mo></math> <em><strong>(A1)</strong></em></p>
<p>attempts to calculate the total amount of time <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mfenced><mrow><mn>2</mn><mo>.</mo><mn>2359</mn><mo>…</mo><mo>-</mo><mn>1</mn><mo>.</mo><mn>1887</mn><mo>…</mo></mrow></mfenced><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mn>3</mn><mfenced><mrow><mfenced><mrow><mfrac><mrow><mn>5</mn><mi mathvariant="normal">π</mi></mrow><mn>3</mn></mfrac><mo>-</mo><mn>3</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mfrac><mrow><mn>4</mn><mi mathvariant="normal">π</mi></mrow><mn>3</mn></mfrac><mo>-</mo><mn>3</mn></mrow></mfenced></mrow></mfenced></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>3</mn><mo>.</mo><mn>14</mn><mo> </mo><mfenced><mrow><mo>=</mo><mi mathvariant="normal">π</mi></mrow></mfenced></math> (weeks) <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[6 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Many students did not change their calculators back to radian mode. This meant they had no chance of correctly answering parts (c) and (d), since even if follow through was given, there were not enough intersections on the graphs.</p>
<p>Most managed part (a) and some attempted to equate the functions in part b) but few recognised that 'rate of growth' was the derivatives of the given functions, and of those who did, most were unable to find them.</p>
<p>Almost all the candidates who did solve part (c) gave the answer <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>05</mn><mo>=</mo><mn>3</mn><mo>.</mo><mn>15</mn></math>, when working with more significant figures would have given them 3.14. They lost the last mark.</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>
<br><hr><br><div class="specification">
<p>A manufacturer makes trash cans in the form of a cylinder with a hemispherical top. The trash can has a height of 70 cm. The base radius of both the cylinder and the hemispherical top is 20 cm.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>A designer is asked to produce a new trash can.</p>
<p>The new trash can will also be in the form of a cylinder with a hemispherical top.</p>
<p>This trash can will have a height of <em>H</em> cm and a base radius of <em>r</em> cm.</p>
<p style="text-align: center;"><img 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"></p>
<p>There is a design constraint such that <em>H</em> + 2<em>r</em> = 110 cm.</p>
<p>The designer has to maximize the volume of the trash can.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the height of the cylinder.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total volume of the trash can.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the height of the <strong>cylinder</strong>, <em>h</em> , of the new trash can, in terms of <em>r</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the volume, <em>V</em> cm<sup>3</sup> , of the new trash can is given by</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="V = 110\pi {r^3}"> <mi>V</mi> <mo>=</mo> <mn>110</mn> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>3</mn> </msup> </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>Using your graphic display calculator, find the value of <em>r</em> which maximizes the value of <em>V</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The designer claims that the new trash can has a capacity that is at least 40% greater than the capacity of the original trash can.</p>
<p>State whether the designer’s claim is correct. Justify your answer.</p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p 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>50 (cm) <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi \times 50 \times {20^2} + \frac{1}{2} \times \frac{4}{3} \times \pi \times {20^3}"> <mi>π</mi> <mo>×</mo> <mn>50</mn> <mo>×</mo> <mrow> <msup> <mn>20</mn> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>×</mo> <mfrac> <mn>4</mn> <mn>3</mn> </mfrac> <mo>×</mo> <mi>π</mi> <mo>×</mo> <mrow> <msup> <mn>20</mn> <mn>3</mn> </msup> </mrow> </math></span> <em><strong>(M1)(M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their correctly substituted volume of cylinder, <em><strong>(M1)</strong></em> for correctly substituted volume of sphere formula, <em><strong>(M1)</strong></em> for halving the substituted volume of sphere formula. Award at most <em><strong>(M1)</strong></em><em><strong>(M1)</strong></em><em><strong>(M0)</strong></em> if there is no addition of the volumes.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 79600\,\,\left( {{\text{c}}{{\text{m}}^3}} \right)\,\,\left( {79587.0 \ldots \left( {{\text{c}}{{\text{m}}^3}} \right)\,,\,\,\frac{{76000}}{3}\pi } \right)"> <mo>=</mo> <mn>79600</mn> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mrow> <mtext>c</mtext> </mrow> <mrow> <msup> <mrow> <mtext>m</mtext> </mrow> <mn>3</mn> </msup> </mrow> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mn>79587.0</mn> <mo>…</mo> <mrow> <mo>(</mo> <mrow> <mrow> <mtext>c</mtext> </mrow> <mrow> <msup> <mrow> <mtext>m</mtext> </mrow> <mn>3</mn> </msup> </mrow> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace"></mspace> <mo>,</mo> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mfrac> <mrow> <mn>76000</mn> </mrow> <mn>3</mn> </mfrac> <mi>π</mi> </mrow> <mo>)</mo> </mrow> </math></span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (G3)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (a).</p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>h = H − r</em> (or equivalent) <em><strong>OR</strong></em> <em>H</em> = 110 − 2<em>r</em> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for writing h in terms of <em>H</em> and <em>r</em> or for writing <em>H</em> in terms of <em>r</em>.</p>
<p>(<em>h</em> =) 110 <em>− </em>3<em>r <strong>(A1) (G2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {V = } \right)\,\,\,\,\frac{2}{3}\pi {r^3} + \pi {r^2} \times \left( {110 - 3r} \right)"> <mrow> <mo>(</mo> <mrow> <mi>V</mi> <mo>=</mo> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>3</mn> </msup> </mrow> <mo>+</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>×</mo> <mrow> <mo>(</mo> <mrow> <mn>110</mn> <mo>−</mo> <mn>3</mn> <mi>r</mi> </mrow> <mo>)</mo> </mrow> </math></span> <em><strong>(M1)</strong></em><em><strong>(M1)</strong></em><em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for volume of hemisphere, <em><strong>(M1)</strong></em> for correct substitution of their h into the volume of a cylinder, <em><strong>(M1)</strong></em> for addition of two correctly substituted volumes leading to the given answer. Award at most <em><strong>(M1)</strong></em><em><strong>(M1)</strong></em><em><strong>(M0)</strong></em> for subsequent working that does not lead to the given answer. Award at most <em><strong>(M1)</strong></em><em><strong>(M1)</strong></em><em><strong>(M0)</strong></em> for substituting <em>H</em> = 110 − 2<em>r</em> as their <em>h</em>.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="V = 110\pi {r^2} - \frac{7}{3}\pi {r^3}"> <mi>V</mi> <mo>=</mo> <mn>110</mn> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>−</mo> <mfrac> <mn>7</mn> <mn>3</mn> </mfrac> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>3</mn> </msup> </mrow> </math></span> <em><strong>(AG)</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(r =) 31.4 (cm) (31.4285… (cm)) <em><strong>(G2)</strong></em></p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( \pi \right)\left( {220r - 7{r^2}} \right) = 0"> <mrow> <mo>(</mo> <mi>π</mi> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow> <mn>220</mn> <mi>r</mi> <mo>−</mo> <mn>7</mn> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for setting the correct derivative equal to zero.</p>
<p>(r =) 31.4 (cm) (31.4285… (cm)) <em><strong>(A1)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {V = } \right)\,\,\,\,110\pi {\left( {31.4285 \ldots } \right)^3} - \frac{7}{3}\pi {\left( {31.4285 \ldots } \right)^3}"> <mrow> <mo>(</mo> <mrow> <mi>V</mi> <mo>=</mo> </mrow> <mo>)</mo> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mn>110</mn> <mi>π</mi> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mn>31.4285</mn> <mo>…</mo> </mrow> <mo>)</mo> </mrow> <mn>3</mn> </msup> </mrow> <mo>−</mo> <mfrac> <mn>7</mn> <mn>3</mn> </mfrac> <mi>π</mi> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mn>31.4285</mn> <mo>…</mo> </mrow> <mo>)</mo> </mrow> <mn>3</mn> </msup> </mrow> </math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of their 31.4285… into the given equation.</p>
<p>= 114000 (113781…) <em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note: </strong>Follow through from part (e).</p>
<p>(increase in capacity =) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{113.781 \ldots - 79587.0 \ldots }}{{79587.0 \ldots }} \times 100 = 43.0\,\,\left( {\text{% }} \right)"> <mfrac> <mrow> <mn>113.781</mn> <mo>…</mo> <mo>−</mo> <mn>79587.0</mn> <mo>…</mo> </mrow> <mrow> <mn>79587.0</mn> <mo>…</mo> </mrow> </mfrac> <mo>×</mo> <mn>100</mn> <mo>=</mo> <mn>43.0</mn> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mtext>% </mtext> </mrow> <mo>)</mo> </mrow> </math></span> <em><strong>(R1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Award <em><strong>(R1)</strong></em><strong>(ft)</strong> for finding the correct percentage increase from their two volumes.</p>
<p><strong>OR</strong></p>
<p>1.4 × 79587.0… = 111421.81… <em><strong>(R1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Award <em><strong>(R1)</strong></em><strong>(ft)</strong> for finding the capacity of a trash can 40% larger than the original.</p>
<p>Claim is correct <em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from parts (b), (e) and within part (f). The final <strong><em>(R1)(A1)</em>(ft)</strong> can be awarded for their correct reason and conclusion. Do not award <strong><em>(R0)(A1)</em>(ft)</strong>.</p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>A particle P moves along a straight line. The velocity <em>v</em> m s<sup>−1</sup> of P after <em>t</em> seconds is given by <em>v</em> (<em>t</em>) = 7 cos <em>t</em> − 5<em>t </em><sup>cos <em>t</em></sup>, for 0 ≤ <em>t</em> ≤ 7.</p>
<p>The following diagram shows the graph of <em>v</em>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAb4AAAGUCAYAAABKuke5AAAgAElEQVR4Ae3dD2xV133A8Z+zqItRxgokakPtqCWp3UppsBOgqDbCzaiJtUm2zGhHphppGFZ1gERVEwpoKVrCiJGKhFkVBahqWmFVCMtIlYw9RrGwJ2QcbDIEsdVGSe0SVS6EMgRb1eHpd5NLX4j/vPfuPfeec+/3Spud9949fz7n1T/OuedPwcTExIRwIYAAAgggkBKBB1JST6qJAAIIIICAJ0Dg44uAAAIIIJAqgSwD36i0r31SCgoKpKBgkbx4+ncfIN19S360cr4UfHWfvHHrbqrgqCwCCCCAgJsCWQa+YqlvHZHf/8f35DF5Q45feFf+qPV9YIHUvPiPUjU8Lr8n7rn5DaDUCCCAQMoEsgx8qvKAzF60Qr75mMiv/utdGfegPiGfKvqsLPhOnSyZnUNSKUOmuggggAAC9gjkFq1mf16+/LUnRPrelqva5bv7rnT84LL89ZoyedieOlESBBBAAAEEphTILfBJoXzy05/8MLE/yG86fipDX98sdZ/5xJQZ8AYCCCCAAAI2CTyYW2Eekr989C9EfnVFLv7iZ/KL/66VrfWfkRyjZ25Z8mkEEEAAAQRCFMgxZj0k8xeUikin/OQXn5a//+ZTDHGG2BgkhQACCCBgXiDHwKcFelCqvtcqR1/+mjw2yd137tyR7u5u8yUnBwQQQAABBPIQKAh7y7Ldu3fLjh07pKurS6qrq/MoErcggAACCCBgTiDUwDc0NCTl5eVeaRcvXiwnT56UuXPnmis9KSOAAAIIIJCjwCSDlTmm8OHHdYhzw4YN0tjYeC+B11577d7v/IIAAggggIANAqH1+I4cOSJr166V0dFRKS4u9oY6V65cKYODg1JWVmZDXSkDAggggAACEkrgGxkZkdLSUjl+/LjU19d7e3rqaUfr16+XixcvSk9PjxQWFsKNAAIIIIBA7AKhBL66ujqvIm1tbV6A082sNfCNjY15vb/W1lZpaGiIvbIUAAEEEEAAgcCBr729XVatWiXDw8NSUlLiifqBT/9jsvdhRwABBBBAIC6BQIHP79G1tLTIxo0b79UhM/DppJc1a9Z473V0dNz7DL8ggAACCCAQh0CgWZ3vvvuu1NbWyrp166Ysuz7ba25ulqtXr3pDn1N+kDcQQAABBBCIQCBQj2+q8mX2+Kb6DK8jgAACCCAQh0CgHl8cBSZPBBBAAAEEgggQ+ILocS8CCCCAgHMCBD7nmowCI4AAAggEESDwBdHjXgQQQAAB5wQIfM41GQVGAAEEEAgiQOALose9CCCAAALOCRD4nGsyCowAAgggEESAwBdEj3sRQAABBJwTIPA512QUGAEEEEAgiACBL4ge9yKAAAIIOCdA4HOuySgwAggggEAQAQJfED3uRQABBBBwToDA51yTUWAEEEAAgSACBL4getyLAAIIIOCcAIHPuSajwAgggAACQQQIfEH0uBcBBBBAwDkBAp9zTUaBEUAAAQSCCBD4guhxLwIIIICAcwIEPueajAIjgAACCAQRIPAF0eNeBBBAAAHnBAh8zjUZBUYAAQQQCCJA4Auix70IIIAAAs4JEPicazIKjAACCCAQRIDAF0SPexFAAAEEnBMg8DnXZBQYAQQQQCCIAIEviB73IoAAAgg4J0Dgc67JKDACCCCAQBABAl8QPe5FAAEEEHBOgMDnXJNRYAQQQACBIAIEviB63IsAAggg4JwAgc+5JqPACCCAAAJBBAh8QfS4FwEEEEDAOQECn3NNRoERQAABBIIIEPiC6HEvAggggIBzAgQ+55qMAiOAAAIIBBEg8AXR414EEEAAAecECHzONRkFRgABBBAIIkDgC6LHvQgggAACzgkQ+JxrMgqMAAIIIBBEgMAXRI97EUAAAQScEyDwOddkFBgBBBBAIIgAgS+IHvcigAACCDgnQOBzrskoMAIIIIBAEAECXxA97kUAAQQQcE6AwOdck1FgBBBAAIEgAgS+IHrciwACCCDgnACBz7kmo8AIIIAAAkEECHxB9LgXAQQQQMA5AQKfc01GgRFAAAEEgggQ+ILocS8CCCCAgHMCBD7nmowCI4AAAggEESDwBdHjXgQQQAAB5wQIfM41GQVGAAEEEAgiQOALose9CCCAAALOCRD4nGsyCowAAgggEESAwBdEj3sRQAABBJwTMBb47ty54xwGBUYAAQQQSL6AscC3efNmIfgl/wtEDRFAAAHXBIwFvvHxcSH4ufZ1oLwIIIBA8gWMBb62tjZPj+CX/C8RNUQAAQRcEjAW+AoLC2X//v2eBcHPpa8EZUUAAQSSLWAs8CkbwS/ZXx5qhwACCLgoYDTwKQjBz8WvBWVGAAEEkitQMDExMRF29QoKCuT+ZMfGxqS+vl4WLlzoDYFqQORCAAEEEEAgagHjPT6/QkVFRdLe3i4XL16Uw4cP+y/zEwEEEEAAgUgFHowyNz/4FRcXe9lu3LgxyuzJCwEEEEAAAYlsqDPTuq+vTyorK6W3t1cqKioy3+J3BBBAAAEEjApENtSZWQsNdq2trV7wGxkZyXyL3xFAAAEEEDAqEEuPz6/R7t27paOjQ06ePClz5871X+YnAggggAACxgRiDXy6l6cubtdLF7sz09NYO5MwAggggMCHArEMdfr6GuheffVVZnr6IPxEAAEEEDAuEGuPz6/d0NCQlJeXM9nFB+EnAggggIAxgVh7fH6tysrKvMkuW7ZsEV3ozoUAAggggIApASt6fH7ltm7dKu+//z7P+3wQfiKAAAIIhC5gRY/Pr9W2bdu8533Hjh3zX+InAggggAACoQpY1ePTmvnP+wYHB0WHQLkQQAABBBAIU8CqHp9WTINdS0uLbNiwQa5fvx5mXUkLAQQQQAABsS7waZusW7dO5s+fL3v27KGJEEAAAQQQCFXAuqFOv3a6lVlpaal0dXVJdXW1/zI/EUAAAQQQCCRgZY9Pa1RSUiLHjx+XnTt3MuQZqIm5GQEEEEAgU8DawKeFrKmpYcgzs7X4HQEEEEAgsIC1Q51+zXRBu57fx5CnL8JPBBBAAIEgAlb3+LRiengtQ55Bmph7EUAAAQQyBawPfFpYf8jztddeyyw7vyOAAAIIIJCzgPVDnX6N/FmeLGz3RfiJAAIIIJCPgBM9Pq2YzvLUU9t1Ybue48eFAAIIIIBAPgLOBD6t3OrVq71Znvv27cunrtyDAAIIIICAODPU6beVv5fn8PCw1wv0X+cnAggggAAC2Qg4F/i0Unp8kT7z6+joyKaOfAYBBBBAAIF7Ak4Ndfql1uOLrl69Ku3t7f5L/EQAAQQQQCArAScD39y5c0WDn25izQkOWbUzH0IAAQQQ+FDAycCnZa+vr/cmurC2j+8yAggggEAuAk4+4/Mr6K/t6+3tlYqKCv9lfiKAAAIIIDClgLM9Pq2Rru3TQ2v37t3L2r4pm5g3EEAAAQQyBZwOfFoRPbRWJ7p0dnZm1ovfEUAAAQQQmFTA6aFOv0bd3d2ycuVKuXbtmujEFy4EEEAAAQSmEkhE4NPKrV+/XubMmSPNzc1T1ZXXEUAAAQQQcG/nlqnajIkuU8nwOgIIIIBApoDzz/j8yjDRxZfgJwIIIIDAdAKJCXxaSSa6TNfUvIcAAgggoAKJecbnNycTXXwJfiKAAAIITCaQuMCnlayrq/PW+DHRZbIm5zUEEEAg3QKJDHz+RBdOa0/3l5vaI4AAApMJJDLwaUV3794t/f39HF00WavzGgIIIJBigURNbslsx29961scXZQJwu8IIIAAAp5AYgMfRxfxDUcAAQQQmEwgsYFPK8vRRZM1Oa8hgAAC6RZI7DM+v1n9iS7Dw8PeTE//dX4igAACCKRTIPGBT5uViS7p/HJTawQQQGAygVQEvuvXr8u8efOkq6tLqqurJ3PgNQQQQACBlAgk+hmf34Y60eX48eOyc+dODqz1UfiJAAIIpFQgFYFP27ampkbmz58vhw8fTmlTU20EEEAAARXIIvD9Qd574yfy4lfnS0HBl2Ttvj557657eIWFhfL9739fNm3aJDrhhQsBBBBAwF4B/Tut8zP0UVXY1wyB767ceuPf5IXvvi0rj74jE/93UtaO/6u88IN+uRV2SSJIr6ysTJqammTv3r0R5EYWCCCAAAL5CjzyyCPezls6P6O9vT3fZCa9b/rJLXffkh/VrJPhF0/Iq8898kECN0/Li194TUrPHJF/KHlo8kQLCmRiYmLS9+J+kYkucbcA+SOAAALZCdy5c0f27dsnO3bskMbGRq/jomevBr2m7fHd/eV/ys+6PyOlRQ//KZ/ZT8vKb/5Gftb7jjg44ilMdPlTU/IbAgggYLOAPqLavn276Drs8fFxKS0tlSNHjgSepDhN4Psf+WXvSel+7En57Kc/cZ/N/0r3z/5Tfuli5GOiy31tyX8igAACdgtoL6+trU1aW1tl7dq1smbNGhkaGsq70NMEvlsyNvy2yJeelKKHp/lY3lnHdyMTXeKzJ2cEEEAgHwH9u93Q0CCjo6Py6KOPSnl5uRw4cCCfpOTBvO7K4qaCgoIsPhX/R7TrzIUAAggg4J7AxYsX8yr0NIHvYSkqXSDyk1/K2K27UjI7t16frZNbMpV0osvzzz8v27Zt8za0znyP3xFAAAEE7BLQ4c0NGzbI+fPnvU1J9CCCfK5potlD8mTl8/KxDb7u/k7eGboh1d/4ijw5zd35FCbqezi6KGpx8kMAAQRyF9BOiq7p0+HNqqoqb7gz36CnuU8buh548ivyjS/1SNdAxgLCW1dl+L+ekW9Ufnb6m3OvWyx3+Du67NmzJ5b8yRQBBBBAYGqB7u5ub2Suo6PD22+5ublZioqKpr4hi3emDXzyQIl8ffffSv+//Jucfu8PInd/I6f3/ED6v/Nd+foUa/iyyNOqj+gDU4XURe1BZglZVSkKgwACCDguoL28rVu3ysqVK6Wurk5OnjwZ2iED0wc+eUAefvaf5Oirj0jrs38uBX/2D9JV+s9y9DtLJGNln+O84p3T19LS4m1ppgsmuRBAAAEE4hW4cuWKnDlzRgYHB721fPpoKqxr+p1b8sxFZ3S6MLkls3oa8JYvXy4bN270psxmvsfvCCCAAALJESDwZbRlX1+fVFZWersEhLEtTkbS/IoAAgggYInADEOdlpQyomJUVFSwiXVE1mSDAAIIhCvwB3nv9Cuy7kdvzbidJoHvPnld06eLIsPeDfy+bPhPBBBAAIHQBG7KSPv35YW/uigVWaw4YKhzEnidPqsziXRrnKDTZidJnpcQQAABBMISuPuutK//G1n1o0v3Unxi74C89d1np9yajMB3j+qjv6xfv9574eDBgx99g/9CAAEEELBLwDtC7znZWfZTeevV52T2DKVjqHMKoJdeekkOHTrEkOcUPryMAAIIWCPw28vS0z1Lvvblz88Y9LTMBL4pWk6HOLu6umTVqlUyNjY2xad4GQEEEEAgXoG7cvPKgPy7PCPLn3o0q6IQ+KZhqq6u9mZ57tq1a5pP8RYCCCCAQHwC12Wgq1veq35eKp98KKtiEPhmYPJneeqpv1wIIIAAApYJ/PFduXD8DXms7LPy6SwjWpYfs6yiERZHt8l5+eWXvVN/R0ZGIsyZrBBAAAEEZhK4+/ZF+fdfPSvfXDFHBvb9RN64dXemW3jGN6OQiLcxalNTk7dhKnt5ZiPGZxBAAIEoBW5I/0/PiPzdN+TZh2fuz7GcIcu28ffy1F3Ct2/fnuVdfAwBBBBAwDYBAl8OLaLHFulBiLpbeFlZWQ538lEEEEAAAVsEZu4T2lJSC8qhwa61tVU2bNjAEgcL2oMiIIAAAvkI0OPLQ83f1WX//v2iB9lyIYAAAgi4I0CPL4+20l1ddCPrw4cP53E3tyCAAAIIxClAjy9Pff95X29vr+hxRlwIIIAAAm4I0OPLs538531btmzheV+ehtyGAAIIxCFAjy+guj7vGx8fl7a2Np73BbTkdgQQQCAKAQJfQGV/fV9VVZU0NzcHTI3bEUAAAQRMCzDUGVBYZ3Xqae1nzpwR9vMMiMntCCCAQAQC9PhCQu7r65PKykphsktIoCSDAAIIGBKgxxcSrM7s1MXtGvw4vy8kVJJBAAEEDAg8aCDN1CbZ0NAgN2/elPr6em/4Uw+z5UIAAQQQsEuAoc6Q20Mnu2zevJmZniG7khwCCCAQlgCBLyzJjHT84Kcvsa1ZBgy/IoAAAhYIEPgMNYI+59Mhz4ULFxL8DBmTLAIIIJCPAJNb8lHL4h59vqfLHHRPT93bkwsBBBBAwA4BAp/BdvCDn67xO3DggMGcSBoBBBBAIFsBZnVmK5Xn5/zgp8Oeem3cuDHPlLgNAQQQQCAMAQJfGIozpEHwmwGItxFAAIEIBZjcEiG2P+Glrq5O9FQHDrGNEJ+sEEAAgQ8FCHwRfxX84Mdsz4jhyQ4BBBD4UIDJLRF/FfxhT53tqQvddc0fFwIIIIBAdAIEvuis7+XkBz99QYMfe3veo+EXBBBAwLgAgc848eQZaPDTXV300hmfBL/JnXgVAQQQCFuAZ3xhi+aYng51Hj58WDZt2sSRRjna8fGPCug/ni5fviwDAwNy48YN2bt370c/8OF/NTY2yuc+9zlZtGiR939z586d9HO8iEBSBQh8lrSsHmK7du1a72gjPeWBC4FsBIaGhrx/MOn35/z581JbWysrVqyQ+fPny4IFC2TWrFkfS+bSpUty9epVOXXqlJw4cUI0EK5evVqqq6s/9lleQCCJAgQ+i1pVD7PVZQ7M+LSoUSwsyvXr1+Xo0aPiB7umpiYv2GkPLtfe28jIiHR3d3tpaVVffvllAqCFbU6RwhUg8IXrGTg1Ha7S3V30X+S616c+C+RCQAU0SB06dMgbwtSe3be//e3Qhip1yL2zs1NWrVrl9QA1mJaUlACPQCIFmNxiWbNqoGtra5OqqiopLi72/jVuWREpTsQCGvC2bt0qpaWlXs6Dg4PS0dHh9cxy7eFNVXTdTEEnWV27dk3mzJnj5aX/8OJCIIkCBD4LW1X/CDU3N8vx48dl5cqVsnv3btb7WdhOpot0f8AbHh72vhdlZWXGstZAqt+9rq4ur/enm6uz1tQYNwnHJEDgiwk+m2z1X+D6x66/v1+WL1/uDXVlcx+fcVtAn+Fl9vD8gBfl0KNOdNF89TkiGy24/X2i9B8XIPB93MSqV/SPnQ596v6eOtSlf4j4F7hVTRRaYbRdtX3nzZsn77//vhd4tPcVZcDLrIzmq8Od4+PjBL9MGH53XoDJLQ41YeasTyYfONRwWRTVb1v96L59+6SioiKLu6L5iAZk7fXppZsusLl6NO7kYk6AHp8529BT1j+GJ0+evDf5gN5f6MSRJ6izeNevXy+VlZXebN6enh6rgp6CaKB76aWXhP1lI/96kKEhAQKfIVhTyWZOPtCJB2vWrOHZnylsg+lqL0rbT2fu6ixKnU2pGxfY2pvy95fV4Kc7DXEh4LIAgc/R1tPJB9o7WLJkiffsj5mf7jSkDmvqZCXdOaW3t9ebRRnWsgSTChr8Xn/9dW97PV30zoWAqwIEPldb7sMhqO3bt39k5id/kOxtUH+2pg5rau9OJy3Z9CwvGzldSuEvs2Fj9WzE+IyNAgQ+G1slxzL5Mz+3bdvmrfvTZ0a6BozLHgGdHZk5W1N357F1WHMmNV1mo5OrtA7MMJ5Ji/dtFCDw2dgqeZRJ/4jev/OGPkPSXgZXfAL6DxBdirJnzx5vUfjBgwdjW54QpsKuXbu8bfV0BioXAq4JEPhca7EZyutPftFtrfQZkvYytLfBv8xngAv5bX/yiq691B65zsZN0ukH+g8tfd63Y8cO0RMiuBBwSYB1fC61Vh5l1aCnvQ292Hk/D8A8btHnrDt37vTu1OBgcouxPIoX6i06qUr3DdWJVq4O3YYKQmJOCNDjc6KZ8i+kDn/qHyX/+Z8Ou+msQq7wBXRYU5+v6v6q+vxL3ZMc9FRQj9HS69ixY+GDkiIChgQIfIZgbUo28/mfHlKqswo1ADIBJpxWyhzW1DV5o6OjVq/JC6fWH6Si3y0dSdBDlJnlGaYsaZkUIPCZ1LUsbX3+pz0RXSztr//TzZAJgPk3lA5r+mvy9Lmq7q2ZtjMU9dmlzvLU7cy4EHBBgMDnQiuFXEYNgP76P01aJ2CwBCI3ZH+2pg5r6jCyrslL+rDmdEK6l+fevXsZRp8OifesESDwWdMU0RdEZxtqD0WH5vzDRzUA8gxw6rbQgOcfGaS9Zu0963PUtE/s0F5uS0uLF/ym1uMdBOwQIPDZ0Q6xlkL/aPkBcOHChfeeAeowHssgPmgaXQ+p6yL9U9D1rDrtNbuw1VhUX64XXnhBTpw4IeweFJU4+eQrwHKGfOUSfJ/+kT969Kh3NpxWU4fyqqqqUvlH3rfYtGmT1NbWes+yXNtmLMqvqr98huUNUaqTV64C9PhyFUvB5/1JMP4yCF0HqAvhtceTlokwfg9P6+1vJq3r1Qh60/8PoKamxvtAZ2fn9B/kXQRiFCDwxYhve9b+Moj+/n7vFAE9ksafCKPPAZM4DKqBXRdlE/Dy+3bqd0ZHCPQfS0n8fuSnwl22CRD4bGsRS8ujPR3dZ1InwuhzQF24rNP4tRfo+pZV+gdaA7mubdTAfuPGDS/Q08PL78tIry8/N+6KToBnfNFZJyonDRYXLlzwJjPoNPbFixd7awSffvppZ6b1a+9OJ2LoSfbnz5/3ZiVq8EvbOjwTX0ye9ZlQJc2wBAh8YUmmOB19HjYwMOBtW3Xo0CEvCOp5c7pDjPagbJrqr7uLnD592tu4W2cgNjY2yurVq2XZsmVWldP1r5P+w0hHBNgf1vWWTGb5CXzJbNfYanV/ENSC6K4eS5culaeeeiryI3n8nqnuquL37HR2pgZmXYdH787cV0WHwXVikA4ZcyFgkwCBz6bWSFhZNOjoerfe3l7vD6D2sPTSQKhB8IknnpBHH31UiouLQ+ltaX76DPKdd97xZp/qZBztgfp56j6lixYtSuWyDA8h4v+n/wjSSULa/syGjRif7KYVIPBNy8ObYQr4gfDtt9+Wc+fOyZkzZ7xna34eGhD10t5h5rVgwQKZNWuW99KlS5cy35K33nrLm4ySmZb26LQ394UvfCGWXuZHCpjy/9Ben/4DRCdGcSFgiwCBz5aWSHE5dJLJ+Pi4/Pa3v5Vbt27J/cFNJ8/4lz6T0+3V/Ovxxx+X+fPny6c+9alQe49++vwMJqBtq895teevW+RxIWCDAIHPhlagDAgkWED3NtV/oOjJIFwI2CBA4LOhFSgDAgkW0DWSOsNXN/Rmb9MEN7RDVWMBu0ONRVERcFFAJ7boc1d9DsuFgA0CBD4bWoEyIJBwAV0+otuYcSFggwBDnTa0AmVAIOECLG1IeAM7Vj16fI41GMVFwEUBfbanB9X6azldrANlTo4APb7ktCU1QcBqAX9pA5NcrG6mVBSOHl8qmplKIhC/gK7j00kuP//5z+MvDCVItQCBL9XNT+URiFZAJ7noyQ1cCMQpwFBnnPrkjUDKBPxJLrppeFlZWcpqT3VtEaDHZ0tLUA4EUiCgk1x0T1bduJoLgbgE6PHFJU++CKRUwN/J5fbt26GcypFSRqodQIAeXwA8bkUAgdwFnnnmGe+w4gsXLuR+M3cgEIIAgS8ERJJAAIHsBQoLC72DgH/84x9nfxOfRCBEAYY6Q8QkKQQQyE5gaGhIysvL2bg6Oy4+FbIAPb6QQUkOAQRmFtAZnWxcPbMTnzAjQOAz40qqCCAwg0B9fb0cOXJkhk/xNgLhCzDUGb4pKSKAQBYCY2NjUlxcLKOjo1JUVJTFHXwEgXAE6PGF40gqCCCQo4AGOx3uPH36dI538nEEggkQ+IL5cTcCCAQQYAuzAHjcmrcAQ51503EjAggEFfC3MGO4M6gk9+ciQI8vFy0+iwACoQroFmaNjY3S0dERarokhsB0AgS+6XR4DwEEjAusXr2a2Z3GlckgU4ChzkwNfkcAgcgF/OFOTmyInD61GdLjS23TU3EE7BDwhzs5scGO9khDKQh8aWhl6oiA5QIMd1reQAkrHkOdCWtQqoOAiwL+cCezO11sPffKTI/PvTajxAgkTsAf7mQxe+Ka1soKEfisbBYKhUD6BJYtWybt7e3pqzg1jlyAoc7IyckQAQQmE2DvzslUeM2EAD0+E6qkiQACOQv4e3f29/fnfC83IJCLAIEvFy0+iwACRgX0qKLOzk6jeZA4Agx18h1AAAFrBBjutKYpEl0QenyJbl4qh4BbAv5w5+XLl90qOKV1SoDA51RzUVgEki+wYsUKOXbsWPIrSg1jE2CoMzZ6MkYAgckEhoaGpLy8XK5duya6vo8LgbAF6PGFLUp6CCAQSKCsrEwWL14sV65cCZQONyMwlQCBbyoZXkcAgdgE6urqpKenJ7b8yTjZAgS+ZLcvtUPASYHly5dzOK2TLedGoXnG50Y7UUoEUiVw584dmTVrlnBGX6qaPbLK0uOLjJqMEEAgW4HCwkJpamoSzujLVozP5SJA4MtFi88igEBkArqs4dSpU5HlR0bpEWCoMz1tTU0RcEqAM/qcai6nCkuPz6nmorAIpEdA1/DV1tYKm1anp82jqimBLypp8kEAgZwF2LQ6ZzJuyEKAoc4skPgIAgjEI+Dv4nL79m3RCS9cCIQhQI8vDEXSQAABIwL+Li4XLlwwkj6JplOAwJfOdqfWCDgjwC4uzjSVMwUl8DnTVBQUgXQKsItLOtvdZK15xmdSl7QRQCCwgL+sYXh4WEpKSgKnRwII0OPjO4AAAlYL6LKGxsZGOXfunNXlpHDuCBD43GkrSopAagWWLVsm7e3tqa0/FQ9XgKHOcD1JDQEEDAiMjY1JcXExh9MasE1jkvT40tjq1BkBxwSKioq8w2kHBgYcKznFtVGAwGdjq1AmBBD4mEBDQ4MQ+D7Gwgt5CDDUmQcatyCAQPQCfX19UsPb4HUAAAx/SURBVFlZKRMTE9FnTo6JEqDHl6jmpDIIJFfgi1/8olc53caMC4EgAgS+IHrciwACkQn4yxrefPPNyPIko2QKEPiS2a7UCoFECtTU1LCsIZEtG22leMYXrTe5IYBAAIGRkREpLS1lWUMAQ24VocfHtwABBJwR0C3LFi9eLFeuXHGmzBTUPgECn31tQokQQGAaAU5rmAaHt7ISYKgzKyY+hAACtgiwrMGWlnC3HPT43G07So5AKgVY1pDKZg+10gS+UDlJDAEETAuwrMG0cPLTJ/Alv42pIQKJE2BZQ+KaNNIK8YwvUm4yQwCBMATSuqzhzp07UlhYGAZhqtOgx5fq5qfyCLgpkNZlDWfPnpUlS5a42WgWlZrAZ1FjUBQEEMheII3LGvR0Cj2lgiuYAIEvmB93I4BATALLly+XHTt2xJR7PNl2dHRIeXl5PJknKFcCX4Iak6ogkCYBf1mDPu9Lw6Wn0J8/f178eqehzqbqSOAzJUu6CCBgVMBf1nDu3Dmj+diS+OnTp6WxsVG03lzBBAh8wfy4GwEEYhRYtmxZak5r0IktWl+u4AIsZwhuSAoIIBCTQFqWNegyhlmzZsng4KCUlZXFpJ2cbOnxJactqQkCqRNIy7KG4eFhr231SCau4AIEvuCGpIAAAjEK6PT+np6eGEtgPuve3l5pampi8XpI1AS+kCBJBgEE4hHQ6f1JX9Zw6tQpWbFiRTzACcyVZ3wJbFSqhECaBK5fvy7z5s0THQ7Uoc+kXX79RkdHpaioKGnVi6U+9PhiYSdTBBAISyDpyxr0tHk9dZ6gF9Y3RoTAF54lKSGAQEwCSV7WoM8vdXs2rvAECHzhWZISAgjEJLB06VI5ceKE6LBg0i7dpky3Z+MKT4DAF54lKSGAQEwCSV3WoOsU2aYs/C8VgS98U1JEAIEYBJJ4WsOlS5fYpszAd4nAZwCVJBFAIHoBHQ7UYcEkXZ2dnWxTZqBBWc5gAJUkEUAgegF/2n9StvVimzJz3yF6fOZsSRkBBCIU8Jc1vPnmmxHmai6rCxcueImzN2f4xgS+8E1JEQEEYhJI0rIG7bm+8sorMUkmO1sCX7Lbl9ohkCqB5557zlvWoIe2un4dOXKEZQyGGpHAZwiWZBFAIHoB3d2ktrZWLl++HH3mIebIaeshYk6SFIFvEhReQgABdwV0M+eBgQF3KyAi/f39XgDntHUzzUjgM+NKqgggEJOAf1qDzop09dJlDPX19a4W3/pyE/isbyIKiAACuQg888wz3sf9WZG53GvDZzVgHzp0SJ5++mkbipPIMhD4EtmsVAqB9AoUFhZ6h7bqrEgXLz9gs4zBXOsR+MzZkjICCMQkoM/5dFakixfLGMy3GoHPvDE5IIBAxAKLFi3yNnfWTZ5du1jGYL7FCHzmjckBAQQiFvB3cTl37lzEOQfLjtMYgvllezeBL1spPocAAk4JuLiLiwbqxsZGYRmD2a8agc+sL6kjgEBMAi7u4nL27FlOY4jg+0LgiwCZLBBAIHoB13Zx0dMldBmDBmwuswIEPrO+pI4AAjEK6CLwY8eOxViC7LPW3WYWL14sGrC5zAoQ+Mz6kjoCCMQooIvAtRflwi4up06dkoaGhhi10pM1B9Gmp62pKQKpFCgoKJDe3l6pqKiwtv4cOhtt09Dji9ab3BBAIGKBlpYW6enpiTjX3LLzd2spLS3N7UY+nZcAPb682LgJAQRcERgaGhLduPr27dui25nZeO3evdsr1vbt220sXuLKRI8vcU1KhRBAIFPA70X5varM92z5vaOjg0NnI2wMAl+E2GSFAALRC2gv75VXXrF2uFN7pOfPnxf/VInohdKXI0Od6WtzaoxA6gT6+vqksrLSyuHOAwcOyM2bN4Vhzui+lvT4orMmJwQQiEnA703ZONypm1Lrptpc0QkQ+KKzJicEEIhJQIc7bZzd6Q9zEvii/WIQ+KL1JjcEEIhJQGd27tixw6rF7Lq+kE2po/9CEPiiNydHBBCIQcDG4U4d5ly9enUMGunOksCX7van9gikRsAf7jxx4oQVdWaYM75mIPDFZ0/OCCAQsYDO7Ny7d6/oSQhxXzrM2dTUxNl7MTQEgS8GdLJEAIF4BMrKyrwTEPQkhDgv3ZtThzlra2vjLEZq8ybwpbbpqTgC6RTYuHGj/PCHP4y18rqsgkXr8TUBgS8+e3JGAIEYBGw4mV03zdblFbbuHRpDs0SaJTu3RMpNZgggYIPA+vXrZeHChaK9v6gvfb44b948GRwcFB165YpegB5f9ObkiAACMQvoEgJ9xhbHdebMGe85I0EvDv0P8iTwxWdPzgggEJPAsmXLvGdsuodn1JcG3Dh6mlHX0+b8GOq0uXUoGwIIGBPQM/Bu3Lghzc3NxvK4P+GRkRHRY5JGR0elqKjo/rf574gECHwRQZMNAgjYJeAHoWvXrkW2lk5PYrh48aIcPHjQLoyUlYbAl7IGp7oIIPAngbq6OlmxYkUkQ4+6dm/WrFmiC9crKir+VAh+i1yAZ3yRk5MhAgjYIqA7p+gzNw1Kpq/Ozk5vUou/Z6jp/Eh/agEC39Q2vIMAAgkX8IPQ2bNnjddUA+y2bdtYu2dceuYMCHwzG/EJBBBIqIAuIG9oaDC+k4vOHtXNsauqqhIq6Va1eMbnVntRWgQQCFnAX1Bu8tnb1q1b5fHHH4/kWWLIPIlMjsCXyGalUgggkIuAzrY8deqUdHR05HJbVp/1Z48ODw9LSUlJVvfwIbMCBD6zvqSOAAIOCJjs9WlvT68o1ws6QB5rEQl8sfKTOQII2CJgotdHb8+W1v1oOQh8H/XgvxBAIKUCfq+vq6tLqqurQ1HQzbDnzJlDby8UzfASIfCFZ0lKCCDguIAuOdCenx4bFPTIIJ3JqSe+R7kzjOP8kRWf5QyRUZMRAgjYLqCnNuh17NixQEXVBfFbtmzxztybO3duoLS4OXwBAl/4pqSIAAKOCmgv7/XXX5e1a9eKPp/L9zp8+LB367p16/JNgvsMCjDUaRCXpBFAwE0BnYmpga+trS3nIc+hoSEpLy/noFmLm54en8WNQ9EQQCAegV27dsnVq1dl3759ORVgbGxMNmzY4A1xctBsTnSRfpgeX6TcZIYAAq4I+EsRWlpastpxRZ/rbd682ave/v37c+4puuKShHI+mIRKUAcEEEAgbAHdZUW3MdOZmbNnz/b29JwqDz/o6Vl7YcwInSofXg9HgKHOcBxJBQEEEiig5+Zp8NPJLvrcT9f63X/pM73ly5d7L7e3t9PTux/Iwv+mx2dho1AkBBCwR0CD3+joqOhzv3nz5kljY6PU1NTIrVu3RAOdnrrQ2toquhQi6No/e2qd7JLwjC/Z7UvtEEAgRAHt3WkP8Ne//rWX6tKlS2XJkiVSVFQUYi4kZVqAwGdamPQRQAABBKwS4BmfVc1BYRBAAAEETAsQ+EwLkz4CCCCAgFUCBD6rmoPCIIAAAgiYFiDwmRYmfQQQQAABqwQIfFY1B4VBAAEEEDAtQOAzLUz6CCCAAAJWCRD4rGoOCoMAAgggYFqAwGdamPQRQAABBKwSIPBZ1RwUBgEEEEDAtACBz7Qw6SOAAAIIWCVA4LOqOSgMAggggIBpAQKfaWHSRwABBBCwSoDAZ1VzUBgEEEAAAdMCBD7TwqSPAAIIIGCVAIHPquagMAgggAACpgUIfKaFSR8BBBBAwCoBAp9VzUFhEEAAAQRMCxD4TAuTPgIIIICAVQIEPquag8IggAACCJgWIPCZFiZ9BBBAAAGrBAh8VjUHhUEAAQQQMC1A4DMtTPoIIIAAAlYJEPisag4KgwACCCBgWoDAZ1qY9BFAAAEErBIg8FnVHBQGAQQQQMC0AIHPtDDpI4AAAghYJUDgs6o5KAwCCCCAgGkBAp9pYdJHAAEEELBKgMBnVXNQGAQQQAAB0wIEPtPCpI8AAgggYJUAgc+q5qAwCCCAAAKmBQh8poVJHwEEEEDAKgECn1XNQWEQQAABBEwLEPhMC5M+AggggIBVAgQ+q5qDwiCAAAIImBYg8JkWJn0EEEAAAasECHxWNQeFQQABBBAwLUDgMy1M+ggggAACVgkQ+KxqDgqDAAIIIGBagMBnWpj0EUAAAQSsEiDwWdUcFAYBBBBAwLQAgc+0MOkjgAACCFglQOCzqjkoDAIIIICAaQECn2lh0kcAAQQQsEqAwGdVc1AYBBBAAAHTAkYC38TEhOlykz4CCCCAAAJ5CRgJfHmVhJsQQAABBBCIQIDAFwEyWSCAAAII2CPw/xz5rfC9NTitAAAAAElFTkSuQmCC"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the initial velocity of P.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the maximum speed of P.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of times that the acceleration of P is 0 m s<sup>−2</sup> .</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the acceleration of P when it changes direction.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total distance travelled by P.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color:#999;font-size:90%;font-style:italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>initial velocity when <em>t</em> = 0 <em><strong>(M1)</strong></em></p>
<p>eg <em>v</em>(0)</p>
<p><em>v</em> = 7 (m s<sup>−1</sup>) <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing maximum speed when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| v \right|">
<mrow>
<mo>|</mo>
<mi>v</mi>
<mo>|</mo>
</mrow>
</math></span> is greatest <em><strong>(M1)</strong></em></p>
<p><em>eg</em> minimum, maximum, <em>v'</em> = 0</p>
<p>one correct coordinate for minimum <em><strong>(A1)</strong></em></p>
<p><em>eg</em> 6.37896, −24.6571</p>
<p>24.7 (ms<sup>−1</sup>) <em><strong>A1 N2</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing a = <em>v </em>′ <em><strong>(M1)</strong></em></p>
<p>eg <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = \frac{{{\text{d}}v}}{{{\text{d}}t}}">
<mi>a</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>v</mi>
</mrow>
<mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
</mrow>
</mfrac>
</math></span>, correct derivative of first term</p>
<p>identifying when a = 0 <em><strong>(M1)</strong></em></p>
<p><em>eg</em> turning points of <em>v</em>, <em>t</em>-intercepts of <em>v </em>′</p>
<p>3 <em><strong>A1 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing P changes direction when <em>v </em>= 0 <em><strong>(M1) </strong></em></p>
<p><em>t</em> = 0.863851 <em><strong>(A1) </strong></em></p>
<p>−9.24689</p>
<p><em>a</em> = −9.25 (ms<sup>−2</sup>) <em><strong> A2 N3</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution of limits or function into formula <em><strong>(A1)</strong></em><br><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^7 {\left| {\,v\,} \right|,\,\int_0^{0.8638} {v{\text{d}}t - \int_{0.8638}^7 {v{\text{d}}t} } ,\,\,\int {\left| {\,7\,{\text{cos}}\,x - 5{x^{{\text{cos}}\,x}}\,} \right|} \,dx,\,\,3.32 = 60.6} ">
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mn>7</mn>
</msubsup>
<mrow>
<mrow>
<mo>|</mo>
<mrow>
<mspace width="thinmathspace"></mspace>
<mi>v</mi>
<mspace width="thinmathspace"></mspace>
</mrow>
<mo>|</mo>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mrow>
<mn>0.8638</mn>
</mrow>
</msubsup>
<mrow>
<mi>v</mi>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
<mo>−</mo>
<msubsup>
<mo>∫</mo>
<mrow>
<mn>0.8638</mn>
</mrow>
<mn>7</mn>
</msubsup>
<mrow>
<mi>v</mi>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
</mrow>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mo>∫</mo>
<mrow>
<mrow>
<mo>|</mo>
<mrow>
<mspace width="thinmathspace"></mspace>
<mn>7</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>cos</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>−</mo>
<mn>5</mn>
<mrow>
<msup>
<mi>x</mi>
<mrow>
<mrow>
<mtext>cos</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
</mrow>
</msup>
</mrow>
<mspace width="thinmathspace"></mspace>
</mrow>
<mo>|</mo>
</mrow>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>d</mi>
<mi>x</mi>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>3.32</mn>
<mo>=</mo>
<mn>60.6</mn>
</mrow>
</math></span></p>
<p>63.8874</p>
<p>63.9 (metres) <em><strong>A2 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A particle P moves along a straight line. Its velocity <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_{\text{P}}}{\text{ m}}\,{{\text{s}}^{ - 1}}">
<mrow>
<msub>
<mi>v</mi>
<mrow>
<mtext>P</mtext>
</mrow>
</msub>
</mrow>
<mrow>
<mtext> m</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mrow>
<mtext>s</mtext>
</mrow>
<mrow>
<mo>−<!-- − --></mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</math></span> after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> seconds is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_{\text{P}}} = \sqrt t \sin \left( {\frac{\pi }{2}t} \right)">
<mrow>
<msub>
<mi>v</mi>
<mrow>
<mtext>P</mtext>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<msqrt>
<mi>t</mi>
</msqrt>
<mi>sin</mi>
<mo><!-- --></mo>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mi>π<!-- π --></mi>
<mn>2</mn>
</mfrac>
<mi>t</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 8">
<mn>0</mn>
<mo>⩽<!-- ⩽ --></mo>
<mi>t</mi>
<mo>⩽<!-- ⩽ --></mo>
<mn>8</mn>
</math></span>. The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_{\text{P}}}">
<mrow>
<msub>
<mi>v</mi>
<mrow>
<mtext>P</mtext>
</mrow>
</msub>
</mrow>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-14_om_10.04.21.png" alt="M17/5/MATME/SP2/ENG/TZ1/07"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the first value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> at which P changes direction.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <strong>total </strong>distance travelled by P, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 8">
<mn>0</mn>
<mo>⩽</mo>
<mi>t</mi>
<mo>⩽</mo>
<mn>8</mn>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A second particle Q also moves along a straight line. Its velocity, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_{\text{Q}}}{\text{ m}}\,{{\text{s}}^{ - 1}}">
<mrow>
<msub>
<mi>v</mi>
<mrow>
<mtext>Q</mtext>
</mrow>
</msub>
</mrow>
<mrow>
<mtext> m</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mrow>
<mtext>s</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</math></span> after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> seconds is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_{\text{Q}}} = \sqrt t ">
<mrow>
<msub>
<mi>v</mi>
<mrow>
<mtext>Q</mtext>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<msqrt>
<mi>t</mi>
</msqrt>
</math></span> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 8">
<mn>0</mn>
<mo>⩽</mo>
<mi>t</mi>
<mo>⩽</mo>
<mn>8</mn>
</math></span>. After <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> seconds Q has travelled the same total distance as P.</p>
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 2">
<mi>t</mi>
<mo>=</mo>
<mn>2</mn>
</math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>substitution of limits or function into formula or correct sum <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^8 {\left| v \right|{\text{d}}t,{\text{ }}\int {\left| {{v_Q}} \right|{\text{d}}t,{\text{ }}\int_0^2 {v{\text{d}}t - \int_2^4 {v{\text{d}}t + \int_4^6 {v{\text{d}}t - \int_6^8 {v{\text{d}}t} } } } } } ">
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mn>8</mn>
</msubsup>
<mrow>
<mrow>
<mo>|</mo>
<mi>v</mi>
<mo>|</mo>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>∫</mo>
<mrow>
<mrow>
<mo>|</mo>
<mrow>
<mrow>
<msub>
<mi>v</mi>
<mi>Q</mi>
</msub>
</mrow>
</mrow>
<mo>|</mo>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mn>2</mn>
</msubsup>
<mrow>
<mi>v</mi>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
<mo>−</mo>
<msubsup>
<mo>∫</mo>
<mn>2</mn>
<mn>4</mn>
</msubsup>
<mrow>
<mi>v</mi>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
<mo>+</mo>
<msubsup>
<mo>∫</mo>
<mn>4</mn>
<mn>6</mn>
</msubsup>
<mrow>
<mi>v</mi>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
<mo>−</mo>
<msubsup>
<mo>∫</mo>
<mn>6</mn>
<mn>8</mn>
</msubsup>
<mrow>
<mi>v</mi>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
</mrow>
</mrow>
</mrow>
</mrow>
</mrow>
</mrow>
</math></span></p>
<p>9.64782</p>
<p>distance <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 9.65{\text{ (metres)}}">
<mo>=</mo>
<mn>9.65</mn>
<mrow>
<mtext> (metres)</mtext>
</mrow>
</math></span> <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct approach <strong><em>(A1)</em></strong></p>
<p><em>eg</em><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="s = \int {\sqrt t ,{\text{ }}\int_0^k {\sqrt t } } {\text{d}}t,{\text{ }}\int_0^k {\left| {{v_{\text{Q}}}} \right|{\text{d}}t} ">
<mi>s</mi>
<mo>=</mo>
<mo>∫</mo>
<mrow>
<msqrt>
<mi>t</mi>
</msqrt>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mi>k</mi>
</msubsup>
<mrow>
<msqrt>
<mi>t</mi>
</msqrt>
</mrow>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mi>k</mi>
</msubsup>
<mrow>
<mrow>
<mo>|</mo>
<mrow>
<mrow>
<msub>
<mi>v</mi>
<mrow>
<mtext>Q</mtext>
</mrow>
</msub>
</mrow>
</mrow>
<mo>|</mo>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
</mrow>
</math></span></p>
<p>correct integration <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int {\sqrt t = \frac{2}{3}{t^{\frac{3}{2}}} + c,{\text{ }}\left[ {\frac{2}{3}{x^{\frac{3}{2}}}} \right]_0^k,{\text{ }}\frac{2}{3}{k^{\frac{3}{2}}}} ">
<mo>∫</mo>
<mrow>
<msqrt>
<mi>t</mi>
</msqrt>
<mo>=</mo>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
<mrow>
<msup>
<mi>t</mi>
<mrow>
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
</mrow>
</msup>
</mrow>
<mo>+</mo>
<mi>c</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<msubsup>
<mrow>
<mo>[</mo>
<mrow>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
<mrow>
<msup>
<mi>x</mi>
<mrow>
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
</mrow>
</msup>
</mrow>
</mrow>
<mo>]</mo>
</mrow>
<mn>0</mn>
<mi>k</mi>
</msubsup>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
<mrow>
<msup>
<mi>k</mi>
<mrow>
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
</mrow>
</msup>
</mrow>
</mrow>
</math></span></p>
<p>equating their expression to the distance travelled by their P <strong><em>(M1)</em></strong></p>
<p><em>eg</em><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}{3}{k^{\frac{3}{2}}} = 9.65,{\text{ }}\int_0^k {\sqrt t {\text{d}}t = 9.65} ">
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
<mrow>
<msup>
<mi>k</mi>
<mrow>
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
</mrow>
</msup>
</mrow>
<mo>=</mo>
<mn>9.65</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mi>k</mi>
</msubsup>
<mrow>
<msqrt>
<mi>t</mi>
</msqrt>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
<mo>=</mo>
<mn>9.65</mn>
</mrow>
</math></span></p>
<p>5.93855</p>
<p>5.94 (seconds) <strong><em>A1</em></strong> <strong><em>N3</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>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">null</span> or any scalar multiple <em><strong>A2 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct scalar product and magnitudes <em><strong>(A1)(A1)(A1)</strong></em></p>
<p>scalar product <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 1 \times 4 + 1 \times - 1\,\,\,\left( { = 3} \right)"> <mo>=</mo> <mn>1</mn> <mo>×</mo> <mn>4</mn> <mo>+</mo> <mn>1</mn> <mo>×</mo> <mo>−</mo> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mo>=</mo> <mn>3</mn> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p>magnitudes <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \sqrt {{1^2} + {1^2}} "> <mo>=</mo> <msqrt> <mrow> <msup> <mn>1</mn> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mn>1</mn> <mn>2</mn> </msup> </mrow> </msqrt> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {{4^2} + {{\left( { - 1} \right)}^2}} "> <msqrt> <mrow> <msup> <mn>4</mn> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </math></span> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( { = \sqrt 2 {\text{,}}\,\,\sqrt {17} } \right)"> <mrow> <mo>(</mo> <mrow> <mo>=</mo> <msqrt> <mn>2</mn> </msqrt> <mrow> <mtext>,</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <msqrt> <mn>17</mn> </msqrt> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p>substitution of their values into correct formula <em><strong> (M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4 - 1}}{{\sqrt {{1^2} + {1^2}} \sqrt {{4^2} + {{\left( { - 1} \right)}^2}} }}"> <mfrac> <mrow> <mn>4</mn> <mo>−</mo> <mn>1</mn> </mrow> <mrow> <msqrt> <mrow> <msup> <mn>1</mn> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mn>1</mn> <mn>2</mn> </msup> </mrow> </msqrt> <msqrt> <mrow> <msup> <mn>4</mn> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> </mfrac> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{ - 3}}{{\sqrt 2 \sqrt {17} }}"> <mfrac> <mrow> <mo>−</mo> <mn>3</mn> </mrow> <mrow> <msqrt> <mn>2</mn> </msqrt> <msqrt> <mn>17</mn> </msqrt> </mrow> </mfrac> </math></span>, 2.1112, 120.96° </p>
<p>1.03037 , 59.0362°</p>
<p>angle = 1.03 , 59.0° <em><strong>A1 N4</strong></em></p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">attempt to form composite <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {f \circ f} \right)\left( x \right)"> <mrow> <mo>(</mo> <mrow> <mi>f</mi> <mo>∘</mo> <mi>f</mi> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span> <strong><em><span style="font-family: 'Verdana',sans-serif;">(M1)</span></em></strong></span></p>
<p><em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">eg </span></em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( {f\left( x \right)} \right)"> <mi>f</mi> <mrow> <mo>(</mo> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( {\frac{{16}}{x}} \right)"> <mi>f</mi> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>16</mn> </mrow> <mi>x</mi> </mfrac> </mrow> <mo>)</mo> </mrow> </math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{16}}{{f\left( x \right)}}"> <mfrac> <mrow> <mn>16</mn> </mrow> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </math></span></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">correct working <strong><em><span style="font-family: 'Verdana',sans-serif;">(A1)</span></em></strong></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{16}}{{\frac{{16}}{x}}}"> <mfrac> <mrow> <mn>16</mn> </mrow> <mrow> <mfrac> <mrow> <mn>16</mn> </mrow> <mi>x</mi> </mfrac> </mrow> </mfrac> </math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="16 \times \frac{x}{{16}}"> <mn>16</mn> <mo>×</mo> <mfrac> <mi>x</mi> <mrow> <mn>16</mn> </mrow> </mfrac> </math></span></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {f \circ f} \right)\left( x \right) = x"> <mrow> <mo>(</mo> <mrow> <mi>f</mi> <mo>∘</mo> <mi>f</mi> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>x</mi> </math></span> <strong><em><span style="font-family: 'Verdana',sans-serif;">A1 N2</span></em></strong></span></p>
<p><strong><em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[3 marks]</span></em></strong></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: Verdana, sans-serif;font-size: 10.5pt;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^{ - 1}}\left( x \right) = \frac{{16}}{x}"> <mrow> <msup> <mi>f</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>16</mn> </mrow> <mi>x</mi> </mfrac> </math></span> (accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = \frac{{16}}{x}"> <mi>y</mi> <mo>=</mo> <mfrac> <mrow> <mn>16</mn> </mrow> <mi>x</mi> </mfrac> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{16}}{x}"> <mfrac> <mrow> <mn>16</mn> </mrow> <mi>x</mi> </mfrac> </math></span>) </span><strong style="font-family: Verdana, sans-serif;font-size: 10.5pt;"><em>A1 N1</em></strong></p>
<p style="text-align: left;"><strong>Note:</strong> Award <em><strong>A0</strong></em> in part (ii) if part (i) is incorrect.<br>Award <em><strong>A0</strong></em> in part (ii) if the candidate has found <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^{ - 1}}\left( x \right) = \frac{{16}}{x}"> <mrow> <msup> <mi>f</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>16</mn> </mrow> <mi>x</mi> </mfrac> </math></span> by interchanging <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y"> <mi>y</mi> </math></span>.</p>
<p><strong><em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[1 mark]</span></em></strong></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>recognition of symmetry about <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = x"> <mi>y</mi> <mo>=</mo> <mi>x</mi> </math></span> <em><strong>(M1)</strong></em></p>
<p><em>eg</em> (2, 8) ⇔ (8, 2) <img src="data:image/png;base64,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"></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">evidence of doubling <strong>their</strong> angle <strong><em> (M1)</em></strong><br></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2 \times 1.03"> <mn>2</mn> <mo>×</mo> <mn>1.03</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2 \times 59.0"> <mn>2</mn> <mo>×</mo> <mn>59.0</mn> </math></span></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">2.06075, 118.072°</span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">2.06 (radians) (118 degrees) <em><strong>A1 N2</strong></em></span></p>
<p> </p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><strong>METHOD 2</strong><br></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">finding direction vector for tangent line at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 2"> <mi>x</mi> <mo>=</mo> <mn>2</mn> </math></span> <em><strong>(A1)</strong></em><br></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} { - 1} \\ 4 \end{array}} \right)"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>4</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 1 \\ { - 4} \end{array}} \right)"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">substitution of <strong>their</strong> values into correct formula (must be from vectors) <em><strong>(M1)</strong></em><br></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{ - 4 - 4}}{{\sqrt {{1^2} + {4^2}} \sqrt {{4^2} + {{\left( { - 1} \right)}^2}} }}"> <mfrac> <mrow> <mo>−</mo> <mn>4</mn> <mo>−</mo> <mn>4</mn> </mrow> <mrow> <msqrt> <mrow> <msup> <mn>1</mn> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mn>4</mn> <mn>2</mn> </msup> </mrow> </msqrt> <msqrt> <mrow> <msup> <mn>4</mn> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> </mfrac> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{8}{{\sqrt {17} \sqrt {17} }}"> <mfrac> <mn>8</mn> <mrow> <msqrt> <mn>17</mn> </msqrt> <msqrt> <mn>17</mn> </msqrt> </mrow> </mfrac> </math></span></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">2.06075, 118.072°</span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">2.06 (radians) (118 degrees) <em><strong>A1 N2</strong></em></span></p>
<p> </p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><strong>METHOD 3</strong><br></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">using trigonometry to find an angle with the horizontal <em><strong>(M1)</strong></em><br></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{tan}}\,\theta = - \frac{1}{4}"> <mrow> <mtext>tan</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> <mo>=</mo> <mo>−</mo> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{tan}}\,\theta = - 4"> <mrow> <mtext>tan</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> <mo>=</mo> <mo>−</mo> <mn>4</mn> </math></span></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">finding both angles of rotation <em><strong> (A1)</strong></em><br></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;"><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\theta _1} = 0.244978{\text{, 14}}{\text{.0362}}^\circ "> <mrow> <msub> <mi>θ</mi> <mn>1</mn> </msub> </mrow> <mo>=</mo> <mn>0.244978</mn> <mrow> <mtext>, 14</mtext> </mrow> <msup> <mrow> <mtext>.0362</mtext> </mrow> <mo>∘</mo> </msup> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\theta _1} = 1.81577{\text{, 104}}{\text{.036}}^\circ "> <mrow> <msub> <mi>θ</mi> <mn>1</mn> </msub> </mrow> <mo>=</mo> <mn>1.81577</mn> <mrow> <mtext>, 104</mtext> </mrow> <msup> <mrow> <mtext>.036</mtext> </mrow> <mo>∘</mo> </msup> </math></span></span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">2.06075, 118.072°</span></p>
<p><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">2.06 (radians) (118 degrees) <em><strong>A1 N2</strong></em></span></p>
<p><strong><em><span style="font-size: 10.5pt;font-family: 'Verdana',sans-serif;color: black;">[3 marks]</span></em></strong></p>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f''\left( x \right) = \left( {{\text{cos}}\,2x} \right)\left( {{\text{sin}}\,6x} \right)">
<msup>
<mi>f</mi>
<mo>″</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mtext>cos</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mn>2</mn>
<mi>x</mi>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mtext>sin</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mn>6</mn>
<mi>x</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, for 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> ≤ 1.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f''}">
<mrow>
<msup>
<mi>f</mi>
<mo>″</mo>
</msup>
</mrow>
</math></span> on the grid below:</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-coordinates of the points of inflexion of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find the values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> for which the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> is concave-down.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><img 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"> <em><strong>A1A1A1 N3</strong></em></p>
<p><strong>Note:</strong> Only if the shape is approximately correct with exactly 2 maximums and 1 minimum on the interval 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> ≤ 0, award the following:<br><em><strong>A1</strong></em> for correct domain with both endpoints within circle and oval.<br><em><strong>A1</strong></em> for passing through the other <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-intercepts within the circles.<br><em><strong>A1</strong></em> for passing through the three turning points within circles (ignore <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-intercepts and extrema outside of the domain).</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>evidence of reasoning (may be seen on graph) <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'' = 0">
<msup>
<mi>f</mi>
<mo>″</mo>
</msup>
<mo>=</mo>
<mn>0</mn>
</math></span>, (0.524, 0), (0.785, 0)</p>
<p>0.523598, 0.785398</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0.524\,\,\left( { = \frac{\pi }{6}} \right)">
<mi>x</mi>
<mo>=</mo>
<mn>0.524</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mo>=</mo>
<mfrac>
<mi>π</mi>
<mn>6</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0.785\,\,\left( { = \frac{\pi }{4}} \right)">
<mi>x</mi>
<mo>=</mo>
<mn>0.785</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mo>=</mo>
<mfrac>
<mi>π</mi>
<mn>4</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>A1A1 N3</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>M1A1A0</strong></em> if any solution outside domain (<em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0">
<mi>x</mi>
<mo>=</mo>
<mn>0</mn>
</math></span>) is also included.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.524 < x < 0.785\,\,\,\left( {\frac{\pi }{6} < x < \frac{\pi }{4}} \right)">
<mn>0.524</mn>
<mo><</mo>
<mi>x</mi>
<mo><</mo>
<mn>0.785</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mi>π</mi>
<mn>6</mn>
</mfrac>
<mo><</mo>
<mi>x</mi>
<mo><</mo>
<mfrac>
<mi>π</mi>
<mn>4</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>A2 N2</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>A1</strong></em> if any correct interval outside domain also included, unless additional solutions already penalized in (b).<br>Award<em><strong> A0</strong></em> if any incorrect intervals are also included.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>All lengths in this question are in metres.</strong></p>
<p> </p>
<p>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \sqrt {\frac{{4 - {x^2}}}{8}} ">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msqrt>
<mfrac>
<mrow>
<mn>4</mn>
<mo>−<!-- − --></mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mn>8</mn>
</mfrac>
</msqrt>
</math></span>, for −2 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> ≤ 2. In the following diagram, the shaded region is enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> and the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">A container can be modelled by rotating this region by 360˚ about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis.</p>
</div>
<div class="specification">
<p>Water can flow in and out of the container.</p>
<p>The volume of water in the container is given by the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( t \right)">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</math></span>, for 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> ≤ 4 , where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> is measured in hours and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( t \right)">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</math></span> is measured in m<sup>3</sup>. The rate of change of the volume of water in the container is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g'\left( t \right) = 0.9 - 2.5\,{\text{cos}}\left( {0.4{t^2}} \right)">
<msup>
<mi>g</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0.9</mn>
<mo>−<!-- − --></mo>
<mn>2.5</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>cos</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.4</mn>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
</div>
<div class="specification">
<p>The volume of water in the container is increasing only when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> < <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> < <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
<mi>q</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the volume of the container.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q"> <mi>q</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>During the interval <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span> < <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span> < <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q"> <mi>q</mi> </math></span>, he volume of water in the container increases by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span> m<sup>3</sup>. Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>When <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span> = 0, the volume of water in the container is 2.3 m<sup>3</sup>. It is known that the container is never completely full of water during the 4 hour period.</p>
<p> </p>
<p>Find the minimum volume of empty space in the container during the 4 hour period.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>attempt to substitute correct limits or the function into formula involving <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^2}"> <mrow> <msup> <mi>f</mi> <mn>2</mn> </msup> </mrow> </math></span> <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi \int_{ - 2}^2 {{y^2}\,{\text{d}}y} "> <mi>π</mi> <msubsup> <mo>∫</mo> <mrow> <mo>−</mo> <mn>2</mn> </mrow> <mn>2</mn> </msubsup> <mrow> <mrow> <msup> <mi>y</mi> <mn>2</mn> </msup> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>d</mtext> </mrow> <mi>y</mi> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi {\int {\left( {\sqrt {\frac{{4 - {x^2}}}{8}} } \right)} ^2}{\text{d}}x"> <mi>π</mi> <mrow> <mo>∫</mo> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <msqrt> <mfrac> <mrow> <mn>4</mn> <mo>−</mo> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> </mrow> <mn>8</mn> </mfrac> </msqrt> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mtext>d</mtext> </mrow> <mi>x</mi> </math></span></p>
<p>4.18879</p>
<p>volume = 4.19, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{4}{3}\pi "> <mfrac> <mn>4</mn> <mn>3</mn> </mfrac> <mi>π</mi> </math></span> (exact) (m<sup>3</sup>) <em><strong>A2 N3</strong></em></p>
<p><strong>Note:</strong> If candidates have their GDC incorrectly set in degrees, award <strong><em>M</em></strong> marks where appropriate, but no <em><strong>A</strong></em> marks may be awarded. Answers from degrees are <em>p</em> = 13.1243 and <em>q</em> = 26.9768 in (b)(i) and 12.3130 or 28.3505 in (b)(ii).</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<p> </p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing the volume increases when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{g'}"> <mrow> <msup> <mi>g</mi> <mo>′</mo> </msup> </mrow> </math></span> is positive <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g'\left( t \right)"> <msup> <mi>g</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </math></span> > 0, sketch of graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{g'}"> <mrow> <msup> <mi>g</mi> <mo>′</mo> </msup> </mrow> </math></span> indicating correct interval</p>
<p>1.73387, 3.56393</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span> = 1.73, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span> = 3.56 <em><strong>A1A1 N3</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<p> </p>
<p> </p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach to find change in volume <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( q \right) - g\left( p \right)"> <mi>g</mi> <mrow> <mo>(</mo> <mi>q</mi> <mo>)</mo> </mrow> <mo>−</mo> <mi>g</mi> <mrow> <mo>(</mo> <mi>p</mi> <mo>)</mo> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_p^q {g'\left( t \right){\text{d}}t} "> <msubsup> <mo>∫</mo> <mi>p</mi> <mi>q</mi> </msubsup> <mrow> <msup> <mi>g</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> </mrow> </math></span></p>
<p>3.74541</p>
<p>total amount = 3.75 (m<sup>3</sup>) <em><strong>A2 N3</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>Note:</strong> There may be slight differences in the final answer, depending on which values candidates carry through from previous parts. Accept answers that are consistent with correct working.</p>
<p> </p>
<p>recognizing when the volume of water is a maximum <em><strong>(M1)</strong></em></p>
<p><em>eg</em> maximum when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = q"> <mi>t</mi> <mo>=</mo> <mi>q</mi> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^q {g'\left( t \right){\text{d}}t} "> <msubsup> <mo>∫</mo> <mn>0</mn> <mi>q</mi> </msubsup> <mrow> <msup> <mi>g</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> </mrow> </math></span></p>
<p>valid approach to find maximum volume of water <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.3 + \int_0^q {g'\left( t \right){\text{d}}t} "> <mn>2.3</mn> <mo>+</mo> <msubsup> <mo>∫</mo> <mn>0</mn> <mi>q</mi> </msubsup> <mrow> <msup> <mi>g</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.3 + \int_0^p {g'\left( t \right){\text{d}}t} + 3.74541"> <mn>2.3</mn> <mo>+</mo> <msubsup> <mo>∫</mo> <mn>0</mn> <mi>p</mi> </msubsup> <mrow> <msup> <mi>g</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> </mrow> <mo>+</mo> <mn>3.74541</mn> </math></span>, 3.85745</p>
<p>correct expression for the difference between volume of container and maximum value <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="4.18879 - \left( {2.3 + \int_0^q {g'\left( t \right){\text{d}}t} } \right)"> <mn>4.18879</mn> <mo>−</mo> <mrow> <mo>(</mo> <mrow> <mn>2.3</mn> <mo>+</mo> <msubsup> <mo>∫</mo> <mn>0</mn> <mi>q</mi> </msubsup> <mrow> <msup> <mi>g</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> </mrow> </mrow> <mo>)</mo> </mrow> </math></span>, 4.19 − 3.85745</p>
<p>0.331334</p>
<p>0.331 (m<sup>3</sup>) <em><strong>A2 N3</strong></em></p>
<p> </p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A particle moves along a straight line so that its velocity, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v">
<mi>v</mi>
</math></span> m s<sup>−1</sup>, after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> seconds is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v\left( t \right) = {1.4^t} - 2.7">
<mi>v</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mn>1.4</mn>
<mi>t</mi>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mn>2.7</mn>
</math></span>, for 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> ≤ 5.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find when the particle is at rest.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the acceleration of the particle when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 2">
<mi>t</mi>
<mo>=</mo>
<mn>2</mn>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total distance travelled by the particle.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>valid approach <em><strong> (M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v\left( t \right) = 0">
<mi>v</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0</mn>
</math></span>, sketch of graph</p>
<p>2.95195</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = {\text{lo}}{{\text{g}}_{1.4}}2.7">
<mi>t</mi>
<mo>=</mo>
<mrow>
<mtext>lo</mtext>
</mrow>
<mrow>
<msub>
<mrow>
<mtext>g</mtext>
</mrow>
<mrow>
<mn>1.4</mn>
</mrow>
</msub>
</mrow>
<mn>2.7</mn>
</math></span> (exact), <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 2.95">
<mi>t</mi>
<mo>=</mo>
<mn>2.95</mn>
</math></span> (s) <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong> (M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a\left( t \right) = v'\left( t \right)">
<mi>a</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msup>
<mi>v</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v'\left( 2 \right)">
<msup>
<mi>v</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</math></span></p>
<p>0.659485</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a\left( 2 \right)">
<mi>a</mi>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</math></span> = 1.96 ln 1.4 (exact), <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a\left( 2 \right)">
<mi>a</mi>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</math></span> = 0.659 (m s<sup>−2</sup>) <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct approach <em><strong> (A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^5 {\left| {v\left( t \right)} \right|} \,{\text{d}}t">
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mn>5</mn>
</msubsup>
<mrow>
<mrow>
<mo>|</mo>
<mrow>
<mi>v</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
<mo>|</mo>
</mrow>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^{2.95} {\left( { - v\left( t \right)} \right)} \,{\text{d}}t + \int_{295}^5 {v\left( t \right)} \,{\text{d}}t">
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mrow>
<mn>2.95</mn>
</mrow>
</msubsup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mi>v</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
<mo>+</mo>
<msubsup>
<mo>∫</mo>
<mrow>
<mn>295</mn>
</mrow>
<mn>5</mn>
</msubsup>
<mrow>
<mi>v</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
</math></span></p>
<p>5.3479</p>
<p>distance = 5.35 (m) <em><strong>A2 N3</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = x{{\text{e}}^{ - x}}">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>x</mi>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mo>−<!-- − --></mo>
<mi>x</mi>
</mrow>
</msup>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x) = - 3f(x) + 1">
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mn>3</mn>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>1</mn>
</math></span>.</p>
<p>The graphs of <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> intersect at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = p">
<mi>x</mi>
<mo>=</mo>
<mi>p</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = q">
<mi>x</mi>
<mo>=</mo>
<mi>q</mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p < q">
<mi>p</mi>
<mo><</mo>
<mi>q</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
<mi>q</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the area of the region enclosed by the graphs of <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>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>valid attempt to find the intersection <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 = g">
<mi>f</mi>
<mo>=</mo>
<mi>g</mi>
</math></span>, sketch, one correct answer</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = 0.357402,{\text{ }}q = 2.15329">
<mi>p</mi>
<mo>=</mo>
<mn>0.357402</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>q</mi>
<mo>=</mo>
<mn>2.15329</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = 0.357,{\text{ }}q = 2.15">
<mi>p</mi>
<mo>=</mo>
<mn>0.357</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>q</mi>
<mo>=</mo>
<mn>2.15</mn>
</math></span> <strong><em>A1A1 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 set up an integral involving subtraction (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="\int_p^q {\left[ {f(x) - g(x)} \right]{\text{d}}x,{\text{ }}} \int_p^q {f(x){\text{d}}x - } \int_p^q {g(x){\text{d}}x} ">
<msubsup>
<mo>∫</mo>
<mi>p</mi>
<mi>q</mi>
</msubsup>
<mrow>
<mrow>
<mo>[</mo>
<mrow>
<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>
</mrow>
<mo>]</mo>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
</mrow>
<msubsup>
<mo>∫</mo>
<mi>p</mi>
<mi>q</mi>
</msubsup>
<mrow>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
<mo>−</mo>
</mrow>
<msubsup>
<mo>∫</mo>
<mi>p</mi>
<mi>q</mi>
</msubsup>
<mrow>
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
</mrow>
</math></span></p>
<p>0.537667</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{area}} = 0.538">
<mrow>
<mtext>area</mtext>
</mrow>
<mo>=</mo>
<mn>0.538</mn>
</math></span> <strong><em>A2 N3</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The displacement, in centimetres, of a particle from an origin, O, at time <em>t</em> seconds, is given by <em>s</em>(<em>t</em>) = <em>t </em><sup>2</sup> cos <em>t</em> + 2<em>t</em> sin <em>t</em>, 0 ≤ <em>t</em> ≤ 5.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the maximum distance of the particle from O.</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 acceleration of the particle at the instant it first changes direction.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>use of a graph to find the coordinates of the local minimum <em><strong> (M1)</strong></em></p>
<p><em>s</em> = −16.513... <em><strong>(A1)</strong></em></p>
<p>maximum distance is 16.5 cm (to the left of O) <em><strong>A1</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>attempt to find time when particle changes direction <em>eg</em> considering the first maximum on the graph of <em>s</em> or the first <em>t </em>– intercept on the graph of <em>s'</em>. <em><strong>(M1)</strong></em></p>
<p><em>t</em> = 1.51986... <em><strong>(A1)</strong></em></p>
<p>attempt to find the gradient of <em>s'</em> for <strong>their</strong> value of <em>t</em>, <em>s" </em>(1.51986...) <em><strong>(M1)</strong></em></p>
<p>=–8.92<em> </em>(cm/s<sup>2</sup>) <em><strong>A1</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A 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>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><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><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><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">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">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>In this question distance is in centimetres and time is in seconds.</strong></p>
<p>Particle A is moving along a straight line such that its displacement from a point P, after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> seconds, is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{s_{\text{A}}} = 15 - t - 6{t^3}{{\text{e}}^{ - 0.8t}}">
<mrow>
<msub>
<mi>s</mi>
<mrow>
<mtext>A</mtext>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mn>15</mn>
<mo>−<!-- − --></mo>
<mi>t</mi>
<mo>−<!-- − --></mo>
<mn>6</mn>
<mrow>
<msup>
<mi>t</mi>
<mn>3</mn>
</msup>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mo>−<!-- − --></mo>
<mn>0.8</mn>
<mi>t</mi>
</mrow>
</msup>
</mrow>
</math></span>, 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> ≤ 25. This is shown in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>Another particle, B, moves along the same line, starting at the same time as particle A. The velocity of particle B is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_{\text{B}}} = 8 - 2t">
<mrow>
<msub>
<mi>v</mi>
<mrow>
<mtext>B</mtext>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mn>8</mn>
<mo>−<!-- − --></mo>
<mn>2</mn>
<mi>t</mi>
</math></span>, 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> ≤ 25.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the initial displacement of particle A from point P.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> when particle A first reaches point P.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> when particle A first changes direction.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total distance travelled by particle A in the first 3 seconds.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that particles A and B start at the same point, find the displacement function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{s_{\text{B}}}">
<mrow>
<msub>
<mi>s</mi>
<mrow>
<mtext>B</mtext>
</mrow>
</msub>
</mrow>
</math></span> for particle B.</p>
<div class="marks">[5]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the other value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> when particles A and B meet.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{s_{\text{A}}}\left( 0 \right){\text{,}}\,\,s\left( 0 \right){\text{,}}\,\,t = 0">
<mrow>
<msub>
<mi>s</mi>
<mrow>
<mtext>A</mtext>
</mrow>
</msub>
</mrow>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>s</mi>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>t</mi>
<mo>=</mo>
<mn>0</mn>
</math></span></p>
<p>15 (cm) <em><strong>A1 N2</strong></em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{s_{\text{A}}} = 0{\text{,}}\,\,s = 0{\text{,}}\,\,6.79321{\text{,}}\,\,14.8651">
<mrow>
<msub>
<mi>s</mi>
<mrow>
<mtext>A</mtext>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mn>0</mn>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>s</mi>
<mo>=</mo>
<mn>0</mn>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>6.79321</mn>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>14.8651</mn>
</math></span></p>
<p>2.46941</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> = 2.47 (seconds) <em><strong>A1 N2</strong></em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing when change in direction occurs <em><strong>(M1)</strong></em></p>
<p><em>eg</em> slope of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s">
<mi>s</mi>
</math></span> changes sign, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s' = 0">
<msup>
<mi>s</mi>
<mo>′</mo>
</msup>
<mo>=</mo>
<mn>0</mn>
</math></span>, minimum point, 10.0144, (4.08, −4.66)</p>
<p>4.07702</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> = 4.08 (seconds) <em><strong>A1 N2</strong></em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1 (using displacement)</strong></p>
<p>correct displacement or distance from P at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 3">
<mi>t</mi>
<mo>=</mo>
<mn>3</mn>
</math></span> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p><em>eg</em> −2.69630, 2.69630</p>
<p>valid approach <em><strong> (M1)</strong></em></p>
<p><em>eg</em> 15 + 2.69630, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s\left( 3 \right) - s\left( 0 \right)">
<mi>s</mi>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
<mo>−</mo>
<mi>s</mi>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
</math></span>, −17.6963</p>
<p>17.6963</p>
<p>17.7 (cm) <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><strong>METHOD 2 (using velocity)</strong></p>
<p>attempt to substitute either limits or the velocity function into distance formula involving <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| v \right|">
<mrow>
<mo>|</mo>
<mi>v</mi>
<mo>|</mo>
</mrow>
</math></span> <em><strong> (M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^3 {\left| v \right|{\text{d}}t} ">
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mn>3</mn>
</msubsup>
<mrow>
<mrow>
<mo>|</mo>
<mi>v</mi>
<mo>|</mo>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
</mrow>
</math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int {\left| { - 1 - 18{t^2}{{\text{e}}^{ - 0.8t}} + 4.8{t^3}{{\text{e}}^{ - 0.8t}}} \right|} ">
<mo>∫</mo>
<mrow>
<mrow>
<mo>|</mo>
<mrow>
<mo>−</mo>
<mn>1</mn>
<mo>−</mo>
<mn>18</mn>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mn>0.8</mn>
<mi>t</mi>
</mrow>
</msup>
</mrow>
<mo>+</mo>
<mn>4.8</mn>
<mrow>
<msup>
<mi>t</mi>
<mn>3</mn>
</msup>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mn>0.8</mn>
<mi>t</mi>
</mrow>
</msup>
</mrow>
</mrow>
<mo>|</mo>
</mrow>
</mrow>
</math></span></p>
<p>17.6963</p>
<p>17.7 (cm) <em><strong>A1 N2</strong></em></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognize the need to integrate velocity <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int {v\left( t \right)} ">
<mo>∫</mo>
<mrow>
<mi>v</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="8t - \frac{{2{t^2}}}{2} + c">
<mn>8</mn>
<mi>t</mi>
<mo>−</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mn>2</mn>
</mfrac>
<mo>+</mo>
<mi>c</mi>
</math></span> (accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> instead of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> and missing <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c">
<mi>c</mi>
</math></span>) <em><strong>(A2)</strong></em></p>
<p>substituting initial condition into their integrated expression (must have <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c">
<mi>c</mi>
</math></span>) <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="15 = 8\left( 0 \right) - \frac{{2{{\left( 0 \right)}^2}}}{2} + c">
<mn>15</mn>
<mo>=</mo>
<mn>8</mn>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
<mo>−</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mrow>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mn>2</mn>
</mfrac>
<mo>+</mo>
<mi>c</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c = 15">
<mi>c</mi>
<mo>=</mo>
<mn>15</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{s_{\text{B}}}\left( t \right) = 8t - {t^2} + 15">
<mrow>
<msub>
<mi>s</mi>
<mrow>
<mtext>B</mtext>
</mrow>
</msub>
</mrow>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>8</mn>
<mi>t</mi>
<mo>−</mo>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>15</mn>
</math></span> <em><strong>A1 N3</strong></em></p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{s_{\text{A}}} = {s_{\text{B}}}">
<mrow>
<msub>
<mi>s</mi>
<mrow>
<mtext>A</mtext>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mrow>
<msub>
<mi>s</mi>
<mrow>
<mtext>B</mtext>
</mrow>
</msub>
</mrow>
</math></span>, sketch, (9.30404, 2.86710)</p>
<p>9.30404</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 9.30">
<mi>t</mi>
<mo>=</mo>
<mn>9.30</mn>
</math></span> (seconds) <strong><em>A1 N2</em></strong></p>
<p><strong>Note:</strong> If candidates obtain <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{s_{\text{B}}}\left( t \right) = 8t - {t^2}">
<mrow>
<msub>
<mi>s</mi>
<mrow>
<mtext>B</mtext>
</mrow>
</msub>
</mrow>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>8</mn>
<mi>t</mi>
<mo>−</mo>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> in part (e)(i), there are 2 solutions for part (e)(ii), 1.32463 and 7.79009. Award the last <em><strong>A1</strong></em> in part (e)(ii) only if both solutions are given.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A particle moves along a straight line so that its velocity, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo> </mo><msup><mtext>m s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>, after <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> seconds is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><msup><mtext>e</mtext><mrow><mi>sin</mi><mo> </mo><mi>t</mi></mrow></msup><mo>+</mo><mn>4</mn><mo> </mo><mi>sin</mi><mo> </mo><mi>t</mi></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mn>6</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>t</mi></math> when the particle is at rest.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the acceleration of the particle when it changes direction.</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 total distance travelled by the particle.</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>recognizing at rest <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>0</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>3</mn><mo>.</mo><mn>34692</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>3</mn><mo>.</mo><mn>35</mn></math> (seconds) <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>(M1)A0</strong></em> for additional solutions to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>0</mn></math> eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>205</mn></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>6</mn><mo>.</mo><mn>08</mn></math>.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing particle changes direction when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>0</mn></math> OR when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>3</mn><mo>.</mo><mn>34692</mn><mo>…</mo></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>-</mo><mn>4</mn><mo>.</mo><mn>71439</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>-</mo><mn>4</mn><mo>.</mo><mn>71</mn><mo> </mo><mfenced><msup><mtext>ms</mtext><mrow><mo>-</mo><mn>2</mn></mrow></msup></mfenced></math> <em><strong>A2</strong></em></p>
<p> </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>distance travelled <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><msubsup><mo>∫</mo><mn>0</mn><mn>6</mn></msubsup><mfenced open="|" close="|"><mi>v</mi></mfenced><mo>d</mo><mi>t</mi></math> OR</p>
<p style="padding-left:30px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mo>∫</mo><mn>0</mn><mrow><mn>3</mn><mo>.</mo><mn>34</mn><mo>…</mo></mrow></msubsup><mfenced><mrow><msup><mtext>e</mtext><mrow><mi>sin</mi><mfenced><mi>t</mi></mfenced></mrow></msup><mo>+</mo><mn>4</mn><mo> </mo><mi>sin</mi><mfenced><mi>t</mi></mfenced></mrow></mfenced><mo>d</mo><mi>t</mi><mo>-</mo><msubsup><mo>∫</mo><mrow><mn>3</mn><mo>.</mo><mn>34</mn><mo>…</mo></mrow><mn>6</mn></msubsup><mfenced><mrow><msup><mtext>e</mtext><mrow><mi>sin</mi><mfenced><mi>t</mi></mfenced></mrow></msup><mo>+</mo><mn>4</mn><mo> </mo><mi>sin</mi><mfenced><mi>t</mi></mfenced></mrow></mfenced><mo>d</mo><mi>t</mi><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mn>14</mn><mo>.</mo><mn>3104</mn><mo>…</mo><mo>+</mo><mn>6</mn><mo>.</mo><mn>44300</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>20</mn><mo>.</mo><mn>7534</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>20</mn><mo>.</mo><mn>8</mn></math> (metres) <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>The majority of candidates found this question challenging but were often able to gain some of the marks in each part. However, it was not uncommon to see candidates manage either all of this question, or none of it, which unfortunately suggested that not all candidates had covered this content.</p>
<p>In part (a), while many recognized <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>0</mn></math> when the particle is at rest, a common error was to assume that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn></math>. It was pleasing to see the majority of those who had the correct equation, manage to progress to the correct value of <em>t</em>, having recognised the domain and the angle measure. Inevitably, a few candidates ignored the domain and obtained <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>205</mn></math>, or found <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn></math>.</p>
<p>Part (b) was not well done. The most successful approach was to use the GDC to find the gradient of the curve at the value of t obtained in part (a). This was well communicated, concise and generally accurate, although some either rounded incorrectly, or obtained <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>4</mn><mo>.</mo><mn>71</mn></math> rather than <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>-</mo><mn>4</mn><mo>.</mo><mn>71</mn></math>. Of those that did not use the GDC, many were aware that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>v</mi><mo>'</mo><mo>(</mo><mi>t</mi><mo>)</mo></math> and made an attempt to find an expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>'</mo><mo>(</mo><mi>t</mi><mo>)</mo></math>. However, the majority appeared not to recognise when the particle would change direction and went on to substitute an incorrect value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>, not realising that they had obtained the required value earlier.</p>
<p>Those that had been successful in parts (a) and (b), particularly if they had been using their GDC, were generally able to complete part (c). However, it was disappointing that many candidates who understood that an integral was required, did not refer to the formula booklet and omitted the absolute value from the integrand.</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>
<br><hr><br><div class="specification">
<p>A particle moves in a straight line such that its velocity, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo> </mo><msup><mi>ms</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>, at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> seconds is given by</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>4</mn><msup><mi>t</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mi>t</mi><mo>+</mo><mn>9</mn><mo>-</mo><mn>2</mn><mo> </mo><mi>sin</mi><mfenced><mrow><mn>4</mn><mi>t</mi></mrow></mfenced><mo>,</mo><mo> </mo><mn>0</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mn>1</mn></math>.</p>
<p style="text-align: left;">The particle’s acceleration is zero at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>T</mi></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>T</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>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>s</mi><mn>1</mn></msub></math> be the distance travelled by the particle from <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>T</mi></math> and let <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>s</mi><mn>2</mn></msub></math> be the distance travelled by the particle from <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>T</mi></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>1</mn></math>.</p>
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>s</mi><mn>2</mn></msub><mo>></mo><msub><mi>s</mi><mn>1</mn></msub></math>.</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 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>attempts either graphical or symbolic means to find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>v</mi></mrow><mrow><mo>d</mo><mi>t</mi></mrow></mfrac><mo>=</mo><mn>0</mn></math> <strong>(M1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>465</mn><mo> </mo><mfenced><mi mathvariant="normal">s</mi></mfenced></math> <strong>A1</strong></p>
<p> </p>
<p><strong>[2 marks]</strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempts to find the value of either <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>s</mi><mn>1</mn></msub><mo>=</mo><munderover><mo>∫</mo><mn>0</mn><mrow><mn>0</mn><mo>.</mo><mn>46494</mn><mo>…</mo></mrow></munderover><mi>v</mi><mo> </mo><mi mathvariant="normal">d</mi><mi>t</mi></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>s</mi><mn>2</mn></msub><mo>=</mo><munderover><mo>∫</mo><mrow><mn>0</mn><mo>.</mo><mn>46494</mn><mo>…</mo></mrow><mn>1</mn></munderover><mi>v</mi><mo> </mo><mi mathvariant="normal">d</mi><mi>t</mi></math> <strong>(M1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>s</mi><mn>1</mn></msub><mo>=</mo><mn>3</mn><mo>.</mo><mn>02758</mn><mo>…</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>s</mi><mn>2</mn></msub><mo>=</mo><mn>3</mn><mo>.</mo><mn>47892</mn><mo>…</mo></math> <strong>A1</strong><strong>A1</strong></p>
<p> </p>
<p><strong>Note:</strong> Award as above for obtaining, for example, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>s</mi><mn>2</mn></msub><mo>-</mo><msub><mi>s</mi><mn>1</mn></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>45133</mn><mo>…</mo></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>s</mi><mn>2</mn></msub><msub><mi>s</mi><mn>1</mn></msub></mfrac><mo>=</mo><mn>1</mn><mo>.</mo><mn>14907</mn><mo>…</mo></math></p>
<p><strong>Note:</strong> Award a maximum of <strong>M1A1A0FT</strong> for use of an incorrect value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> from part (a).</p>
<p> </p>
<p>so <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>s</mi><mn>2</mn></msub><mo>></mo><msub><mi>s</mi><mn>1</mn></msub></math> <strong>AG</strong></p>
<p> </p>
<p><strong>[3 marks]</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><strong>Note: In this question, distance is in metres and time is in seconds.</strong></p>
<p>A particle P moves in a straight line for five seconds. Its acceleration at time <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 3{t^2} - 14t + 8">
<mi>a</mi>
<mo>=</mo>
<mn>3</mn>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mn>14</mn>
<mi>t</mi>
<mo>+</mo>
<mn>8</mn>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 5">
<mn>0</mn>
<mo>⩽<!-- ⩽ --></mo>
<mi>t</mi>
<mo>⩽<!-- ⩽ --></mo>
<mn>5</mn>
</math></span>.</p>
</div>
<div class="specification">
<p>When <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 0">
<mi>t</mi>
<mo>=</mo>
<mn>0</mn>
</math></span>, the velocity of P is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3{\text{ m}}\,{{\text{s}}^{ - 1}}">
<mn>3</mn>
<mrow>
<mtext> m</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mrow>
<mtext>s</mtext>
</mrow>
<mrow>
<mo>−<!-- − --></mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 0">
<mi>a</mi>
<mo>=</mo>
<mn>0</mn>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence or otherwise, find all possible values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> for which the velocity of P is decreasing.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for the velocity of P at time <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total distance travelled by P when its velocity is increasing.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = \frac{2}{3}{\text{ (exact), }}0.667,{\text{ }}t = 4">
<mi>t</mi>
<mo>=</mo>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
<mrow>
<mtext> (exact), </mtext>
</mrow>
<mn>0.667</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>t</mi>
<mo>=</mo>
<mn>4</mn>
</math></span> <strong> <em>A1A1 N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v">
<mi>v</mi>
</math></span> is decreasing when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> is negative <strong><em>(M1)</em></strong></p>
<p><em>eg</em><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="a < 0,{\text{ }}3{t^2} - 14t + 8 \leqslant 0">
<mi>a</mi>
<mo><</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>3</mn>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>14</mn>
<mi>t</mi>
<mo>+</mo>
<mn>8</mn>
<mo>⩽</mo>
<mn>0</mn>
</math></span>, sketch of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span></p>
<p>correct interval <strong><em>A1 N2</em></strong></p>
<p><em>eg</em><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}{3} < t < 4">
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
<mo><</mo>
<mi>t</mi>
<mo><</mo>
<mn>4</mn>
</math></span></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach (do not accept a definite integral) <strong><em>(M1)</em></strong></p>
<p><em>eg</em><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="v\int a ">
<mi>v</mi>
<mo>∫</mo>
<mi>a</mi>
</math></span></p>
<p>correct integration (accept missing <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c">
<mi>c</mi>
</math></span>) <strong><em>(A1)(A1)(A1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{t^3} - 7{t^2} + 8t + c">
<mrow>
<msup>
<mi>t</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>7</mn>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>8</mn>
<mi>t</mi>
<mo>+</mo>
<mi>c</mi>
</math></span></p>
<p>substituting <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 0,{\text{ }}v = 3">
<mi>t</mi>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>v</mi>
<mo>=</mo>
<mn>3</mn>
</math></span> , (must have <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c">
<mi>c</mi>
</math></span>) <strong><em>(M1)</em></strong></p>
<p><em>eg</em><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="3 = {0^3} - 7({0^2}) + 8(0) + c,{\text{ }}c = 3">
<mn>3</mn>
<mo>=</mo>
<mrow>
<msup>
<mn>0</mn>
<mn>3</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>7</mn>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mn>0</mn>
<mn>2</mn>
</msup>
</mrow>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>8</mn>
<mo stretchy="false">(</mo>
<mn>0</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mi>c</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>c</mi>
<mo>=</mo>
<mn>3</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = {t^3} - 7{t^2} + 8t + 3">
<mi>v</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>t</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>7</mn>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>8</mn>
<mi>t</mi>
<mo>+</mo>
<mn>3</mn>
</math></span> <strong><em>A1 N6</em></strong></p>
<p><strong><em>[6 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v">
<mi>v</mi>
</math></span> increases outside the interval found in part (b) <strong><em>(M1)</em></strong></p>
<p><em>eg</em><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 < t < \frac{2}{3},{\text{ }}4 < t < 5">
<mn>0</mn>
<mo><</mo>
<mi>t</mi>
<mo><</mo>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>4</mn>
<mo><</mo>
<mi>t</mi>
<mo><</mo>
<mn>5</mn>
</math></span>, diagram</p>
<p>one correct substitution into distance formula <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^{\frac{2}{3}} {\left| v \right|,{\text{ }}\int_4^5 {\left| v \right|} ,{\text{ }}\int_{\frac{2}{3}}^4 {\left| v \right|} ,{\text{ }}\int_0^5 {\left| v \right|} } ">
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mrow>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msubsup>
<mrow>
<mrow>
<mo>|</mo>
<mi>v</mi>
<mo>|</mo>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<msubsup>
<mo>∫</mo>
<mn>4</mn>
<mn>5</mn>
</msubsup>
<mrow>
<mrow>
<mo>|</mo>
<mi>v</mi>
<mo>|</mo>
</mrow>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<msubsup>
<mo>∫</mo>
<mrow>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
</mrow>
<mn>4</mn>
</msubsup>
<mrow>
<mrow>
<mo>|</mo>
<mi>v</mi>
<mo>|</mo>
</mrow>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mn>5</mn>
</msubsup>
<mrow>
<mrow>
<mo>|</mo>
<mi>v</mi>
<mo>|</mo>
</mrow>
</mrow>
</mrow>
</math></span></p>
<p>one correct pair <strong><em>(A1)</em></strong></p>
<p><em>eg</em><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>3.13580 and 11.0833, 20.9906 and 35.2097</p>
<p>14.2191 <strong><em>A1 N2</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d = 14.2{\text{ (m)}}">
<mi>d</mi>
<mo>=</mo>
<mn>14.2</mn>
<mrow>
<mtext> (m)</mtext>
</mrow>
</math></span></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider a function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced></math>, for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≥</mo><mn>0</mn></math>. The derivative of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mrow><mn>6</mn><mi>x</mi></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfrac></math>.</p>
</div>
<div class="specification">
<p>The graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is concave-down when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mi>n</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>''</mo><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mrow><mn>24</mn><mo>-</mo><mn>6</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><msup><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced><mn>2</mn></msup></mfrac></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the least value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∫</mo><mfrac><mrow><mn>6</mn><mi>x</mi></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfrac><mtext>d</mtext><mi>x</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> be the region enclosed by the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math>, the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis and the lines <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>1</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>3</mn></math>. The area of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>19</mn><mo>.</mo><mn>6</mn></math>, correct to three significant figures.</p>
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced></math>.</p>
<div class="marks">[7]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><strong>METHOD 1</strong></p>
<p>evidence of choosing the quotient rule<em><strong> (M1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>v</mi><mi>u</mi><mo>'</mo><mo>-</mo><mi>u</mi><mi>v</mi><mo>'</mo></mrow><msup><mi>v</mi><mn>2</mn></msup></mfrac></math></p>
<p>derivative of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mi>x</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math> (must be seen in rule)<em><strong> (A1)</strong></em></p>
<p>derivative of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>x</mi></math> (must be seen in rule)<em><strong> (A1)</strong></em></p>
<p>correct substitution into the quotient rule <em><strong>A1</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>6</mn><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mn>6</mn><mi>x</mi></mrow></mfenced><mfenced><mrow><mn>2</mn><mi>x</mi></mrow></mfenced></mrow><msup><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced><mn>2</mn></msup></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>''</mo><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mrow><mn>24</mn><mo>-</mo><mn>6</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><msup><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced><mn>2</mn></msup></mfrac></math> <em><strong>AG N0</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>evidence of choosing the product rule<em><strong> (M1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>u</mi><mo>'</mo><mo>+</mo><mi>u</mi><mi>v</mi><mo>'</mo></math></p>
<p>derivative of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mi>x</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math> (must be seen in rule)<em><strong> (A1)</strong></em></p>
<p>derivative of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mi>x</mi><msup><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced><mrow><mo>-</mo><mn>2</mn></mrow></msup></math> (must be seen in rule)<em><strong> (A1)</strong></em></p>
<p>correct substitution into the product rule <em><strong>A1</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><msup><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>+</mo><mfenced><mrow><mo>-</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mn>6</mn><mi>x</mi></mrow></mfenced><mfenced><mrow><mn>2</mn><mi>x</mi></mrow></mfenced><msup><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced><mrow><mo>-</mo><mn>2</mn></mrow></msup></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>''</mo><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mrow><mn>24</mn><mo>-</mo><mn>6</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><msup><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced><mn>2</mn></msup></mfrac></math> <em><strong>AG N0</strong></em></p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1 </strong>(2<sup>nd</sup> derivative) <em><strong>(M1)</strong></em></p>
<p>valid approach</p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>''</mo><mo><</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>24</mn><mo>-</mo><mn>6</mn><msup><mi>x</mi><mn>2</mn></msup><mo><</mo><mn>0</mn><mo> </mo><mo>,</mo><mo> </mo><mi>n</mi><mo>=</mo><mo>±</mo><mn>2</mn><mo>,</mo><mo> </mo><mi>x</mi><mo>=</mo><mn>2</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>2</mn></math> (exact) <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><strong>METHOD 2 </strong>(1<sup>st</sup> derivative)</p>
<p>valid attempt to find local maximum on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo></math> <em><strong>(M1)</strong></em></p>
<p>eg sketch with max indicated, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo>,</mo><mo> </mo><mn>1</mn><mo>.</mo><mn>5</mn></mrow></mfenced><mo>,</mo><mo> </mo><mi>x</mi><mo>=</mo><mn>2</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>2</mn></math> (exact) <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>evidence of valid approach using substitution or inspection <em><strong>(M1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∫</mo><mn>3</mn><mfenced><mrow><mn>2</mn><mi>x</mi></mrow></mfenced><mfrac><mn>1</mn><mi>u</mi></mfrac><mtext>d</mtext><mi>x</mi><mo> </mo><mo>,</mo><mo> </mo><mi>u</mi><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo> </mo><mo>,</mo><mo> </mo><mtext>d</mtext><mi>u</mi><mo>=</mo><mn>2</mn><mi>x</mi><mo> </mo><mtext>d</mtext><mi>x</mi><mo> </mo><mo>,</mo><mo> </mo><mo>∫</mo><mn>3</mn><mo>×</mo><mfenced><mfrac><mn>1</mn><mi>u</mi></mfrac></mfenced><mtext>d</mtext><mi>u</mi></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∫</mo><mfrac><mrow><mn>6</mn><mi>x</mi></mrow><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced></mfrac><mtext>d</mtext><mi>x</mi><mo>=</mo><mn>3</mn><mo> </mo><mi>ln</mi><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced><mo>+</mo><mi>c</mi></math> <em><strong>A2 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing that area <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><msubsup><mo>∫</mo><mn>1</mn><mn>3</mn></msubsup><mi>f</mi><mfenced><mi>x</mi></mfenced><mtext>d</mtext><mi>x</mi></math> (seen anywhere) <em><strong>(M1)</strong></em></p>
<p>recognizing that <strong>their</strong> answer to (c) is their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> (accept absence of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>) <em><strong>(M1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>3</mn><mo> </mo><mi>ln</mi><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced><mo>+</mo><mi>c</mi><mo> </mo><mo>,</mo><mo> </mo><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>3</mn><mo> </mo><mi>ln</mi><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced></math></p>
<p>correct value for <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mo>∫</mo><mn>1</mn><mn>3</mn></msubsup><mn>3</mn><mo> </mo><mi>ln</mi><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced><mtext>d</mtext><mi>x</mi></math> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>.</mo><mn>4859</mn></math></p>
<p>correct integration for <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mo>∫</mo><mn>1</mn><mn>3</mn></msubsup><mi>c</mi><mo> </mo><mtext>d</mtext><mi>x</mi></math> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mfenced open="[" close="]"><mrow><mi>c</mi><mi>x</mi></mrow></mfenced><mn>1</mn><mn>3</mn></msubsup><mo> </mo><mo>,</mo><mo> </mo><mn>2</mn><mi>c</mi></math></p>
<p>adding <strong>their</strong> integrated expressions <strong>and</strong> equating to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>19</mn><mo>.</mo><mn>6</mn></math> (do not accept an expression which involves an integral) <em><strong>(M1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>.</mo><mn>4859</mn><mo>+</mo><mn>2</mn><mi>c</mi><mo>=</mo><mn>19</mn><mo>.</mo><mn>6</mn><mo> </mo><mo>,</mo><mo> </mo><mn>2</mn><mi>c</mi><mo>=</mo><mn>7</mn><mo>.</mo><mn>114</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>3</mn><mo>.</mo><mn>55700</mn></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>3</mn><mo> </mo><mi>ln</mi><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced><mo>+</mo><mn>3</mn><mo>.</mo><mn>56</mn></math> <em><strong>A1 N4</strong></em></p>
<p><em><strong>[7 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A particle P starts from a point A and moves along a horizontal straight line. Its velocity <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v{\text{ cm}}\,{{\text{s}}^{ - 1}}">
<mi>v</mi>
<mrow>
<mtext> cm</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mrow>
<mtext>s</mtext>
</mrow>
<mrow>
<mo>−<!-- − --></mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</math></span> after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> seconds is given by</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="v(t) = \left\{ {\begin{array}{*{20}{l}} { - 2t + 2,}&{{\text{for }}0 \leqslant t \leqslant 1} \\ {3\sqrt t + \frac{4}{{{t^2}}} - 7,}&{{\text{for }}1 \leqslant t \leqslant 12} \end{array}} \right.">
<mi>v</mi>
<mo stretchy="false">(</mo>
<mi>t</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mrow>
<mo>{</mo>
<mrow>
<mtable columnalign="left" rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mo>−<!-- − --></mo>
<mn>2</mn>
<mi>t</mi>
<mo>+</mo>
<mn>2</mn>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mrow>
<mtext>for </mtext>
</mrow>
<mn>0</mn>
<mo>⩽<!-- ⩽ --></mo>
<mi>t</mi>
<mo>⩽<!-- ⩽ --></mo>
<mn>1</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>3</mn>
<msqrt>
<mi>t</mi>
</msqrt>
<mo>+</mo>
<mfrac>
<mn>4</mn>
<mrow>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>−<!-- − --></mo>
<mn>7</mn>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mrow>
<mtext>for </mtext>
</mrow>
<mn>1</mn>
<mo>⩽<!-- ⩽ --></mo>
<mi>t</mi>
<mo>⩽<!-- ⩽ --></mo>
<mn>12</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
<mo fence="true" stretchy="true" symmetric="true"></mo>
</mrow>
</math></span></p>
<p>The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v">
<mi>v</mi>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-03_om_16.40.29.png" alt="N16/5/MATME/SP2/ENG/TZ0/09"></p>
</div>
<div class="specification">
<p>P is at rest when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 1">
<mi>t</mi>
<mo>=</mo>
<mn>1</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = p">
<mi>t</mi>
<mo>=</mo>
<mi>p</mi>
</math></span>.</p>
</div>
<div class="specification">
<p>When <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = q">
<mi>t</mi>
<mo>=</mo>
<mi>q</mi>
</math></span>, the acceleration of P is zero.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the initial velocity of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P">
<mi>P</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
<mi>q</mi>
</math></span>.</p>
<p>(ii) Hence, find the <strong>speed </strong>of P when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = q">
<mi>t</mi>
<mo>=</mo>
<mi>q</mi>
</math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) Find the total distance travelled by P between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 1">
<mi>t</mi>
<mo>=</mo>
<mn>1</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = p">
<mi>t</mi>
<mo>=</mo>
<mi>p</mi>
</math></span>.</p>
<p>(ii) Hence or otherwise, find the displacement of P from A when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = p">
<mi>t</mi>
<mo>=</mo>
<mi>p</mi>
</math></span>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>valid attempt to substitute <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 0">
<mi>t</mi>
<mo>=</mo>
<mn>0</mn>
</math></span> into the correct function <strong><em>(M1)</em></strong></p>
<p><em>eg</em><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(0) + 2">
<mo>−</mo>
<mn>2</mn>
<mo stretchy="false">(</mo>
<mn>0</mn>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>2</mn>
</math></span></p>
<p>2 <strong><em>A1 N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = 0">
<mi>v</mi>
<mo>=</mo>
<mn>0</mn>
</math></span> when P is at rest <strong><em>(M1)</em></strong></p>
<p>5.21834</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = 5.22{\text{ }}({\text{seconds}})">
<mi>p</mi>
<mo>=</mo>
<mn>5.22</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mrow>
<mtext>seconds</mtext>
</mrow>
<mo stretchy="false">)</mo>
</math></span> <strong><em>A1 N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) recognizing that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = v'">
<mi>a</mi>
<mo>=</mo>
<msup>
<mi>v</mi>
<mo>′</mo>
</msup>
</math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><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="v' = 0">
<msup>
<mi>v</mi>
<mo>′</mo>
</msup>
<mo>=</mo>
<mn>0</mn>
</math></span>, minimum on graph</p>
<p>1.95343</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q = 1.95">
<mi>q</mi>
<mo>=</mo>
<mn>1.95</mn>
</math></span> <strong><em>A1 N2</em></strong></p>
<p>(ii) valid approach to find <strong>their </strong>minimum <strong><em>(M1)</em></strong></p>
<p><em>eg</em><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="v(q),{\text{ }} - 1.75879">
<mi>v</mi>
<mo stretchy="false">(</mo>
<mi>q</mi>
<mo stretchy="false">)</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>−</mo>
<mn>1.75879</mn>
</math></span>, reference to min on graph</p>
<p>1.75879</p>
<p>speed <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 1.76{\text{ }}(c\,{\text{m}}\,{{\text{s}}^{ - 1}})">
<mo>=</mo>
<mn>1.76</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>c</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>m</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mrow>
<mtext>s</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
<mo stretchy="false">)</mo>
</math></span> <strong><em>A1 N2</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) substitution of <strong>correct</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v(t)">
<mi>v</mi>
<mo stretchy="false">(</mo>
<mi>t</mi>
<mo stretchy="false">)</mo>
</math></span> into distance formula, <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_1^p {\left| {3\sqrt t + \frac{4}{{{t^2}}} - 7} \right|{\text{d}}t,{\text{ }}\left| {\int {3\sqrt t + \frac{4}{{{t^2}}} - 7{\text{d}}t} } \right|} ">
<msubsup>
<mo>∫</mo>
<mn>1</mn>
<mi>p</mi>
</msubsup>
<mrow>
<mrow>
<mo>|</mo>
<mrow>
<mn>3</mn>
<msqrt>
<mi>t</mi>
</msqrt>
<mo>+</mo>
<mfrac>
<mn>4</mn>
<mrow>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>−</mo>
<mn>7</mn>
</mrow>
<mo>|</mo>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>|</mo>
<mrow>
<mo>∫</mo>
<mrow>
<mn>3</mn>
<msqrt>
<mi>t</mi>
</msqrt>
<mo>+</mo>
<mfrac>
<mn>4</mn>
<mrow>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>−</mo>
<mn>7</mn>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
</mrow>
</mrow>
<mo>|</mo>
</mrow>
</mrow>
</math></span></p>
<p>4.45368</p>
<p>distance <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 4.45{\text{ }}({\text{cm}})">
<mo>=</mo>
<mn>4.45</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mrow>
<mtext>cm</mtext>
</mrow>
<mo stretchy="false">)</mo>
</math></span> <strong><em>A1 N2</em></strong></p>
<p>(ii) displacement from <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 1">
<mi>t</mi>
<mo>=</mo>
<mn>1</mn>
</math></span> to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = p">
<mi>t</mi>
<mo>=</mo>
<mi>p</mi>
</math></span> (seen anywhere) <strong><em>(A1)</em></strong></p>
<p><em>eg</em><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=" - 4.45368,{\text{ }}\int_1^p {\left( {3\sqrt t + \frac{4}{{{t^2}}} - 7} \right){\text{d}}t} ">
<mo>−</mo>
<mn>4.45368</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<msubsup>
<mo>∫</mo>
<mn>1</mn>
<mi>p</mi>
</msubsup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>3</mn>
<msqrt>
<mi>t</mi>
</msqrt>
<mo>+</mo>
<mfrac>
<mn>4</mn>
<mrow>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>−</mo>
<mn>7</mn>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
</mrow>
</math></span></p>
<p>displacement from <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 0">
<mi>t</mi>
<mo>=</mo>
<mn>0</mn>
</math></span> to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 1">
<mi>t</mi>
<mo>=</mo>
<mn>1</mn>
</math></span> <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^1 {( - 2t + 2){\text{d}}t,{\text{ }}0.5 \times 1 \times 2,{\text{ 1}}} ">
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mn>1</mn>
</msubsup>
<mrow>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>2</mn>
<mi>t</mi>
<mo>+</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.5</mn>
<mo>×</mo>
<mn>1</mn>
<mo>×</mo>
<mn>2</mn>
<mo>,</mo>
<mrow>
<mtext> 1</mtext>
</mrow>
</mrow>
</math></span></p>
<p>valid approach to find displacement for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant p">
<mn>0</mn>
<mo>⩽</mo>
<mi>t</mi>
<mo>⩽</mo>
<mi>p</mi>
</math></span> <strong><em>M1</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^1 {( - 2t + 2){\text{d}}t + \int_1^p {\left( {3\sqrt t + \frac{4}{{{t^2}}} - 7} \right){\text{d}}t,{\text{ }}\int_0^1 {( - 2t + 2){\text{d}}t - 4.45} } } ">
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mn>1</mn>
</msubsup>
<mrow>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>2</mn>
<mi>t</mi>
<mo>+</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
<mo>+</mo>
<msubsup>
<mo>∫</mo>
<mn>1</mn>
<mi>p</mi>
</msubsup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>3</mn>
<msqrt>
<mi>t</mi>
</msqrt>
<mo>+</mo>
<mfrac>
<mn>4</mn>
<mrow>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>−</mo>
<mn>7</mn>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mn>1</mn>
</msubsup>
<mrow>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>2</mn>
<mi>t</mi>
<mo>+</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
<mo>−</mo>
<mn>4.45</mn>
</mrow>
</mrow>
</mrow>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 3.45368">
<mo>−</mo>
<mn>3.45368</mn>
</math></span></p>
<p>displacement <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = - 3.45{\text{ }}({\text{cm}})">
<mo>=</mo>
<mo>−</mo>
<mn>3.45</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mrow>
<mtext>cm</mtext>
</mrow>
<mo stretchy="false">)</mo>
</math></span> <strong><em>A1 N2</em></strong></p>
<p><strong><em>[6 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = {({x^2} + 3)^7}">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>7</mn>
</msup>
</mrow>
</math></span>. Find the term in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^5}">
<mrow>
<msup>
<mi>x</mi>
<mn>5</mn>
</msup>
</mrow>
</math></span> in the expansion of the derivative, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’(x)">
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span>.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><strong>METHOD 1 </strong></p>
<p>derivative of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x)">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span> <strong><em>A2</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="7{({x^2} + 3)^6}(x2)">
<mn>7</mn>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>6</mn>
</msup>
</mrow>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mn>2</mn>
<mo stretchy="false">)</mo>
</math></span></p>
<p>recognizing need to find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^4}">
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
</math></span> term in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{({x^2} + 3)^6}">
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>6</mn>
</msup>
</mrow>
</math></span> (seen anywhere) <strong><em>R1</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="14x{\text{ (term in }}{x^4})">
<mn>14</mn>
<mi>x</mi>
<mrow>
<mtext> (term in </mtext>
</mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
<mo stretchy="false">)</mo>
</math></span></p>
<p>valid approach to find the terms in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{({x^2} + 3)^6}">
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>6</mn>
</msup>
</mrow>
</math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 6 \\ r \end{array}} \right){({x^2})^{6 - r}}{(3)^r},{\text{ }}{({x^2})^6}{(3)^0} + {({x^2})^5}{(3)^1} + \ldots ">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>6</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>r</mi>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<msup>
<mo stretchy="false">)</mo>
<mrow>
<mn>6</mn>
<mo>−</mo>
<mi>r</mi>
</mrow>
</msup>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mi>r</mi>
</msup>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<msup>
<mo stretchy="false">)</mo>
<mn>6</mn>
</msup>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>0</mn>
</msup>
</mrow>
<mo>+</mo>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<msup>
<mo stretchy="false">)</mo>
<mn>5</mn>
</msup>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>1</mn>
</msup>
</mrow>
<mo>+</mo>
<mo>…</mo>
</math></span>, Pascal’s triangle to 6th row</p>
<p>identifying correct term (may be indicated in expansion) <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{5th term, }}r = 2,{\text{ }}\left( {\begin{array}{*{20}{c}} 6 \\ 4 \end{array}} \right),{\text{ }}{({x^2})^2}{(3)^4}">
<mrow>
<mtext>5th term, </mtext>
</mrow>
<mi>r</mi>
<mo>=</mo>
<mn>2</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>6</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>4</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<msup>
<mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>4</mn>
</msup>
</mrow>
</math></span></p>
<p>correct working (may be seen in expansion) <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 6 \\ 4 \end{array}} \right){({x^2})^2}{(3)^4},{\text{ }}15 \times {3^4},{\text{ }}14x \times 15 \times 81{({x^2})^2}">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>6</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>4</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<msup>
<mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>4</mn>
</msup>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>15</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>3</mn>
<mn>4</mn>
</msup>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>14</mn>
<mi>x</mi>
<mo>×</mo>
<mn>15</mn>
<mo>×</mo>
<mn>81</mn>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<msup>
<mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
</mrow>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="17010{x^5}">
<mn>17010</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>5</mn>
</msup>
</mrow>
</math></span> <strong><em>A1</em></strong> <strong><em>N3</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>recognition of need to find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^6}">
<mrow>
<msup>
<mi>x</mi>
<mn>6</mn>
</msup>
</mrow>
</math></span> in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{({x^2} + 3)^7}">
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>7</mn>
</msup>
</mrow>
</math></span> (seen anywhere) <strong><em>R1 </em></strong></p>
<p>valid approach to find the terms in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{({x^2} + 3)^7}">
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>7</mn>
</msup>
</mrow>
</math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 7 \\ r \end{array}} \right){({x^2})^{7 - r}}{(3)^r},{\text{ }}{({x^2})^7}{(3)^0} + {({x^2})^6}{(3)^1} + \ldots ">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>7</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>r</mi>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<msup>
<mo stretchy="false">)</mo>
<mrow>
<mn>7</mn>
<mo>−</mo>
<mi>r</mi>
</mrow>
</msup>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mi>r</mi>
</msup>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<msup>
<mo stretchy="false">)</mo>
<mn>7</mn>
</msup>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>0</mn>
</msup>
</mrow>
<mo>+</mo>
<mrow>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<msup>
<mo stretchy="false">)</mo>
<mn>6</mn>
</msup>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>1</mn>
</msup>
</mrow>
<mo>+</mo>
<mo>…</mo>
</math></span>, Pascal’s triangle to 7th row</p>
<p>identifying correct term (may be indicated in expansion) <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span>6th term, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = 3,{\text{ }}\left( {\begin{array}{*{20}{c}} 7 \\ 3 \end{array}} \right),{\text{ (}}{{\text{x}}^2}{)^3}{(3)^4}">
<mi>r</mi>
<mo>=</mo>
<mn>3</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>7</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>3</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mrow>
<mtext> (</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>x</mtext>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<msup>
<mo stretchy="false">)</mo>
<mn>3</mn>
</msup>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>4</mn>
</msup>
</mrow>
</math></span></p>
<p>correct working (may be seen in expansion) <strong><em>(A1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 7 \\ 4 \end{array}} \right){{\text{(}}{{\text{x}}^2})^3}{(3)^4},{\text{ }}35 \times {3^4}">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>7</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>4</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mrow>
<mtext>(</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>x</mtext>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<msup>
<mo stretchy="false">)</mo>
<mn>3</mn>
</msup>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>3</mn>
<msup>
<mo stretchy="false">)</mo>
<mn>4</mn>
</msup>
</mrow>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>35</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>3</mn>
<mn>4</mn>
</msup>
</mrow>
</math></span></p>
<p>correct term <strong><em>(A1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2835{x^6}">
<mn>2835</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>6</mn>
</msup>
</mrow>
</math></span></p>
<p>differentiating their term in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^6}">
<mrow>
<msup>
<mi>x</mi>
<mn>6</mn>
</msup>
</mrow>
</math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(2835{x^6})',{\text{ (6)(2835}}{{\text{x}}^5})">
<mo stretchy="false">(</mo>
<mn>2835</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>6</mn>
</msup>
</mrow>
<msup>
<mo stretchy="false">)</mo>
<mo>′</mo>
</msup>
<mo>,</mo>
<mrow>
<mtext> (6)(2835</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>x</mtext>
</mrow>
<mn>5</mn>
</msup>
</mrow>
<mo stretchy="false">)</mo>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="17010{x^5}">
<mn>17010</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>5</mn>
</msup>
</mrow>
</math></span> <strong><em>A1</em></strong> <strong><em>N3</em></strong></p>
<p><strong><em>[7 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>Consider the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> defined by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>90</mn><msup><mtext>e</mtext><mrow><mo>-</mo><mn>0</mn><mo>.</mo><mn>5</mn><mi>x</mi></mrow></msup></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>∈</mo><msup><mi mathvariant="normal">ℝ</mi><mo>+</mo></msup></math>.</p>
<p>The graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>x</mi></math> intersect at point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math>.</p>
</div>
<div class="specification">
<p>The line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> has a gradient of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math> and is a tangent to the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> at the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Q</mtext></math>.</p>
</div>
<div class="specification">
<p>The shaded region <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> is enclosed by the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and the lines <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>x</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math>.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-coordinate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</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 exact coordinates of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Q</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>Show that the equation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo> </mo><mi>ln</mi><mo> </mo><mn>45</mn><mo>+</mo><mn>2</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 the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-coordinate of the point where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> intersects the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>x</mi></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>Hence, find the area of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> is tangent to the graphs of both <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and the inverse function <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>.</p>
<p style="text-align:center;"><img src="data:image/png;base64,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"></p>
<p>Find the shaded area enclosed by the graphs of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> and the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math>.</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 find the point of intersection of the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>x</mi></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>56619</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>5</mn><mo>.</mo><mn>57</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>-</mo><mn>45</mn><msup><mtext>e</mtext><mrow><mo>-</mo><mn>0</mn><mo>.</mo><mn>5</mn><mi>x</mi></mrow></msup></math> <em><strong>A1</strong></em></p>
<p>attempt to set the gradient of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>45</mn><msup><mtext>e</mtext><mrow><mo>-</mo><mn>0</mn><mo>.</mo><mn>5</mn><mi>x</mi></mrow></msup><mo>=</mo><mo>-1</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Q</mtext></math> has coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo> </mo><mi>ln</mi><mo> </mo><mn>45</mn><mo>,</mo><mo> </mo><mn>2</mn></mrow></mfenced></math> (accept (<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo> </mo><mi>ln</mi><mo> </mo><mfrac><mn>1</mn><mn>45</mn></mfrac><mo>,</mo><mo> </mo><mn>2</mn></math>) <em><strong>A1</strong></em><em><strong>A1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>A1</strong></em> for each value, even if the answer is not given as a coordinate pair.</p>
<p style="padding-left:30px;"> Do not accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>ln</mi><mo> </mo><mfrac><mn>1</mn><mn>45</mn></mfrac></mrow><mrow><mo>-</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></mfrac></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>ln</mi><mo> </mo><mn>45</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>5</mn></mrow></mfrac></math> as a final value for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>. Do not accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>0</mn></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>00</mn></math> as a final value for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>.</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>attempt to substitute coordinates of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Q</mtext></math> (in any order) into an appropriate equation <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><mo>-</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn><mo> </mo><mi>ln</mi><mo> </mo><mn>45</mn></mrow></mfenced></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>=</mo><mo>-</mo><mn>2</mn><mo> </mo><mi>ln</mi><mo> </mo><mn>45</mn><mo>+</mo><mi>c</mi></math> <em><strong>A1</strong></em></p>
<p>equation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo> </mo><mi>ln</mi><mo> </mo><mn>45</mn><mo>+</mo><mn>2</mn></math> <em><strong>AG</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>ln</mi><mo> </mo><mn>45</mn><mo>+</mo><mn>1</mn><mfenced><mrow><mo>=</mo><mn>4</mn><mo>.</mo><mn>81</mn></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>appropriate method to find the sum of two areas using integrals of the difference of two functions <em><strong>(M1)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Allow absence of incorrect limits.</p>
<p> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mo>∫</mo><mrow><mn>4</mn><mo>.</mo><mn>806</mn><mo>…</mo></mrow><mrow><mn>5</mn><mo>.</mo><mn>566</mn><mo>…</mo></mrow></msubsup><mfenced><mrow><mi>x</mi><mo>-</mo><mfenced><mrow><mo>-</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo> </mo><mi>ln</mi><mo> </mo><mn>45</mn><mo>+</mo><mn>2</mn></mrow></mfenced></mrow></mfenced><mo>d</mo><mi>x</mi><mo>+</mo><msubsup><mo>∫</mo><mrow><mn>5</mn><mo>.</mo><mn>566</mn><mo>…</mo></mrow><mrow><mn>7</mn><mo>.</mo><mn>613</mn><mo>…</mo></mrow></msubsup><mfenced><mrow><mn>90</mn><msup><mtext>e</mtext><mrow><mo>-</mo><mn>0</mn><mo>.</mo><mn>5</mn><mi>x</mi></mrow></msup><mo>-</mo><mfenced><mrow><mo>-</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo> </mo><mi>ln</mi><mo> </mo><mn>45</mn><mo>+</mo><mn>2</mn></mrow></mfenced></mrow></mfenced><mo>d</mo><mi>x</mi></math> <em><strong>(A1)(A1)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>A1</strong></em> for one correct integral expression including correct limits and integrand.<br> Award <em><strong>A1</strong></em> for a second correct integral expression including correct limits and integrand.</p>
<p> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1</mn><mo>.</mo><mn>52196</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1</mn><mo>.</mo><mn>52</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>by symmetry <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>52</mn><mo>…</mo></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>3</mn><mo>.</mo><mn>04</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Accept any answer that rounds to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>0</mn></math> (but do not accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math>).</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.</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>A particle moves in a straight line. The velocity, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo> </mo><msup><mtext>ms</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>, of the particle at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> seconds is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>t</mi><mo> </mo><mi>sin</mi><mo> </mo><mi>t</mi><mo>-</mo><mn>3</mn></math>, for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mn>10</mn></math>.</p>
<p>The following diagram shows the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAATIAAAF4CAYAAADXBXXPAAAgAElEQVR4Ae2dvW7cSLqG9z4ONl8Yys8aihcDKz1YwErPBla4k1jZTmRlZzMr2Q2tYCYdAzPxGJjcwtyAdm5AvgIevJRLza7mTxVZv6yngEY3ySLrq6c+vvyqWGT/oSNBAAIQqJzAHyq3H/MhAAEIdAgZTgABCFRPACGrvgmpAAQggJDhAxCAQPUEsgnZ+fnL7o9//K/+c3//uQf56dMv/fLt7fvqwVIBCEAgHYFsQqYqSrAkZka4Hh8fu4uLV93Nzbt0BCgJAhConkBWIVMkJiG7vn77DFIipsiMBAEIQMCVQFYhk5FnZy+6y8vXvb0PDw9HouZaCfJBAAJtE8guZOpKarxM6erqTScxI0EAAhDwIZBdyBSNScg0Tvbx448+tpMXAhCAQE8gu5BpfGw44E+7QAACEPAlUISQcZfSt9nIDwEIDAlkF7KhMfyGAAQgsIYAQraGGvtAAAJFEUDIimoOjIEABNYQyC5kP//8U/fly5c1trMPBCAAgZ5AViH77bff+juW33zzF8QMh4QABFYTyCZkErEXL/7UC5m+JWYkCEAAAmsIZBEyI2ISL80hM8vffvv3NXVgHwhAoHECyYXs99//00dipjspIVP64Yfve1FDzBr3SKoPgRUEkguZBveNiMleI2T6LTHTNokdCQIQgIArgeRCZhs2FDJ7G8sQgAAEXAggZC6UyAMBCBRNACErunkwDgIQcCGAkLlQIg8EIFA0AYSs6ObBOAhAwIUAQuZCiTwQgEDRBBCyopsH4yAAARcCCJkLJfJAAAJFE0DIim4ejIMABFwIIGQulMgDAQgUTQAhK7p5MA4CEHAhgJC5UCIPBCBQNAGErOjmwTgIQMCFAELmQok8EIBA0QQQsqKbB+MgAAEXAtGE7Pb2fXd+/rJ/35h+TyVe4zNFhvUQgIArgeBC9vDw0F1cvOpFbE7AjIEImSHBNwQgsJZAUCF7fHzsBUxCpt8uCSFzoUQeCEBgjkBQIbu6etOdnb1wFjEZhpDNNQ/bIAABFwLBhExdSomSxOzy8nX/W6J2d/dh1g6EbBYPGyEAAQcCwYRMgiVRurl591ysEbRPn355Xqc89ud5Iz8gAAEIrCAQTMgkYBKo4djY/f3nft319dtJ07QPCQIQgMAWAsGETHcobSGTYepeImRbmoh9IQCBJQLBhMxEX/aYmIRsbhoGEdlSE7EdAhBYIhBMyFSQIi9NgtXAv1nWVIy5hJDN0WEbBCDgQiCokKlA3bWUOOmjwf7hmNmYQQjZGBXWQQACPgSCC5lP4cqLkPkSIz8EIGATQMhsIixDAALVEUDIqmsyDIYABGwCCJlNhGUIQKA6AghZdU2GwRCAgE0AIbOJsAwBCFRHACGrrskwGAIQsAkgZDYRliEAgeoIIGTVNRkGQwACNgGEzCbCMgQgUB0BhKy6JsNgCEDAJoCQ2URYhgAEqiOAkFXXZBgMAQjYBBAymwjLEIBAdQQQsuqaDINzE/jy5Uv373//q/vnP/+v++GH73ObQ/ld1yFkuAEEPAj89ttv3YsXf+q+/fbvvZD99a//0+kjcSPlI4CQ5WNPyZURMCJmR2EStW+++UtltdmXuQjZvtqT2kQioIjrz3/+775LOVaEorLvvvvH2CbWJSCAkCWATBH1E5BISaym0u+//6d/27GiNlJ6AghZeuaUWBkBI1L6nksa/J8Tu7l92baNAEK2jR97N0BAY2D6LCV1P3Uj4Ndff13KyvbABBCywEA53L4ISJz0BzlL0ZiptaIyF9Ez+fkOQwAhC8ORo+yUgG930bUbulNc2aqFkGVDT8E1ENCdyp9//snL1L/97X/7OWZeO5F5EwGEbBM+dt4zAY11Sch8k4RvzX6+5ZD/QAAhO7DgFwSOCGisa+3cMA36MxXjCGfUBYQsKl4OXjOBLWIkAWTQP13rI2TpWFNSRQS2dg/N40wVVblqUxGyqpsP42MR2NKtNDZpnIzupaER9xshi8uXo1dKYEu30lRZ3cu1Y2zmGHy7EUDI3DiRqyECiqJC3HVU95S3YqRxHIQsDWdKqYhAyNn5iuxcnwqoCFFxpkYTsk+ffukf7bi//zxbaT3+QYJASQQURflOgp2yX5Nj7feXTeVl/XoCUYTs8fGxOz9/iZCtbxf2zETAPFup7xBJr8SWmJHiEogiZFdXb7qLi1cIWdy24+gRCCgSC/kqHnUr1b0kxSUQXMju7j5019dvu9vb9whZ3Lbj6BEIaNqFoqiQiWkYIWmOHyuokD08PPSRmIpCyMaBs7ZsAjFEJ4Y4lk0xvXVBhUzdSYmZEkKWvjEpcRuBWN1ADfYzTratbZb2DiZk6k7qTqVJU0Kmu5T2x+zDNwRyEoglOLEEMier0soOImS6S2mL03BZkdpUUj4SBEogELMLGKPLWgKzUmwIImRjlZmKyOy8CJlNhOVcBGKKTUyRzMWrpHIRspJaA1uyEVD3L+ZFNVa3NRuwwgpGyAprEMzJQyD0/DG7FqGe37SPy/ITgWhC5go45lXQ1QbyQUBvqdAzljETz13Go4uQxWPLkSsioNn8sf+PUmWEeoazIrRJTEXIkmCmkNIJqGcQ6vnKqboq4osd9U2Vvff1CNneW5j6LRJQJJbivWEqJ+RznIsVaygDQtZQY1PVcQJ6tlLTI2In82aN2OW0eHyErMVWp85HBFK+MyzmXLWjSjW2gJA11uBU95RASnFJKZqnNd3vGoRsv21LzRwIpO7uabCfPyRxaBjPLAiZJzCy74tA6gH41OXtq7Wma4OQTbNhSwMEckRITAIP71gIWXimHLEiAjnGrFKOyVXUFJtMRcg24WPn2gnkEJUc4ll7Oy3Zj5AtEWL7bgmkHug3IHN0Z03Ze/1GyPbastRrkUCugfdc5S4CqTgDQlZx42H6NgK5IqNckeA2WmXvjZCV3T5YF5FAzrEqjc3pZY6kMAQQsjAcOUqFBPSguLp5ORKv9AlLHSELy5OjVUQg53wudWv1IYUhgJCF4chRKiOgSCzFq3umsMR+tfZUuXtdj5DttWWp1ywBvbpHY2S5Eu/wD0seIQvLk6NVQiDFO/qXUKR4K+2SDXvZjpDtpSWphxeBFO/oXzIo582GJdtq246Q1dZi2BuEgKKh3NMf+NPeIE3ZHwQhC8eSI1VCQAKmv2bLnXJNyM1d7xjlI2QxqHLMogmUcseQR5XCuQlCFo4lR6qEQCmRUCmRYSXNNmsmQjaLh417JJDz0SSbJ3cubSLrlhGyddzYq2ICJd0tLOHuacVN+Ww6QvaMgh+tEMj5aJLNmDuXNpF1ywjZOm7sVSmB0mbUlzJeV2lzPpuNkD2j4EcLBH744ftO3blSEncuw7QEQhaGI0ephIAiIH1KSdy5DNMSCFkYjhylEgIlvgeMO5fbnSeokH38+GN3cfGqU8Poc3PzbtHCkgZeF40lQ/UEcvxr0hI07lwuEVreHkzIHh4eusvL193j42Nf6u3t+17Mrq/fzlqBkM3iYWNgAiX6m+a16bVCpPUEggmZhMuImDFHwnZ29sIsjn6X6FijhrKyegK5X6Y4BbC0cbspO0teH0zIxip5dfWmj9LGtpl1CJkhwXdsArpjmfNlilP1K+XZzyn7algfVcjOz192GjebSwjZHB22hSRQauRT2ty2kMxTHSuakEnA1LVcSgjZEiG2hyJQ4h1LUzfOA0Ni3Xc0IdPdS3vMTCaqwezPOtPZCwJ+BEq8Y2lqULJtxsaSv6MIme5U6i6mS+JK5EKJPCEIlOxrJUeLIdjHPkZwIdPcsfv7z852l+xczpUgY/EEdMdSUU+pqdTxu1J52XYFFTJNwbBFTGNld3cf7HKflxGyZxT8iEig9DuDmkemN2GQ1hEIJmTqTkqU7I/mkY2NlRlzETJDgu+YBEqPeHh4fFvrBxOytWYgZGvJsZ8PgZLeCjtmNw+Pj1FxX4eQubMiZ8UESnor7BRGXdS/fPkytZn1MwQQshk4bNoPgRoi/xrEtlSPQMhKbRnsCkZAM+dL+B/LpQqV3v1dsj/ndoQsJ33KTkKgloH00m9IJGmslYUgZCvBsVs9BCQQ3333j+INLvWh9uLBdV2HkNXQSti4iUAt/1RUS+S4qTEi7YyQRQLLYcshUMsbWHXHsoabEuW07MEShOzAgl87JaCBfs3TqiExBWNdKyFk67ixVyUEaotyaokeS2t+hKy0FsGeoARqG3eSkGnQn+RHACHz40XuygjoYewSX289hZEpGFNk5tcjZPN82Fo5gdqEgbdgrHM4hGwdN/aqhEBtLyysrStcihsgZKW0BHZEIaCXKUocakm8BWNdSyFk67ixVyUEapyXVaPNud0BIcvdApQfjUCtf7PGWzD8XQIh82fGHpUQqHW8qbZxvRLcASEroRWwIQqBWh4WtyuvB9xlO8mdAELmzoqclRGo5WFxG2utAmzXI+UyQpaSNmUlJVDr4z61domTNq5VGEJmAWFxPwRqelh8SF1CpgF/kjsBhMydFTkrI1DzNIaabc/hJghZDuqUGZ1A7VFNrdFk9IadKAAhmwDD6roJ1P7a6FrH93J5DUKWizzlRiVQ28PiNgz+UckmMr+MkM3zYWulBGoXgtqFOLXbIGSpiVNeEgK1d81qe49akkadKQQhm4HDpnoJ6K6fXnNda2IumV/LIWR+vMhdAQG9Cqf26Qu8zsfP0RAyP17kroDAXqKZ2sU4pasgZClpU1YSAnt5XbReCqlXEZGWCSBky4zIURmBvdzxq/2GRUq3QchS0qasJAQkAD///FOSsmIWUuvbO2IymTo2QjZFZmJ9TeMWNdkq3KHsTfWG1VD2Trha/04yRZehUmx7Q9mp4zw+PnaXl6+dD4mQOaN6yliTM9Rkq+iGsjfUcZZcI3Y5oR+zim3vEi9t10VmSZwlYhcXr7qbm3cuh+zzIGTOqJ4yluAMribXZKvqFMLelNMWQtg715ah777GtneuLmabxFl2qNs8lj5+/LHfrjz6nJ+/HMt2sg4hO0Eyv6IEZ5i38LC1JltldQh7Q5/8B5qnv0LYe3rUw5rQohzb3oPl87+WxOz29n13dvZi/iDWVoTMArK0WIozLNmp7TXZGspedVumrvYuzHzypOAbsoyQx/LhNJZ3KGb2ExhXV286fXzSs5CpknxggA/gA6l9wL7DrGhMUZlPehYyn51C5hW0mlJN9tZkq3wghL0p516FsHfJ90PWJ4W9S/XRdkVgGvTXyyM1FDBM9/efez/Qt09CyHxoBTrZPItcnb0Ux3WtQAh7U86GD2HvEpuQryNKYe9SfYYiNvbUwprxMZWJkC2Rt7aX4AyWSZOLNdmqSoSwN8QxJoFaG1KUFfIphRT2WohOFk0kNiZiyqyxMU27uLv70H9ODjCxAiGbADO1ugRnmLLNXl+TrbJ9q706ORSRpUpb7XWxM+RzoynsXaqT6jMlYtpX88c05YIxsiWSbN8tgZRTL1JB3GOdYrALHpGZRwuk/rr7oBBxLpVwlZizj231EFA37Lvv/lGPwQ6Wpo4yHUwqMktwIdPzUWYOiO48SMw+ffplsvII2SQaNngSkIgtPf7iecgisnOOLDdDUCEzjxc8PDw8l6yBu7nHDGikZ1T82Egg5FSFjaYE3V3niGb5k6YJBBWy6+u3J6I1Jm5Dc2oQMgmzIk3Zqo9+qwtdQ1I0LJt95+XkqJuY6sJnOPvanGrqhQaijY369h2Y9mXrK9A659Qr0sD5WNJwj3pKsr0mXx6ri1kXVMgETmCGSc4oYII7lrSt9KQ6mZNK9ZATTDlJSXWRMCgaFmNjf0n2DW0xXMV6aVx1uN/wdwpfMiJm/Flc5Q8xxUxCZs9+H9Z7+FsXLtPmYz6q7bLX+IMEzz5nh8er5XdQIRMgMz5mAAhYzUKmhjdOa+pknNk4g1lf2re5KpcuZCZqtH3Hh2eqQXHZKD8fJglGTCFbM5fMtP3QTv2Wreo5maSLneqz9uJhjpP7O6iQCZLtjMZJbTEwFU9xFTVlhfqW09rOHOrYoY4jx5TD1iC6iiDGogcfFopYFLnETobn0J/lC/LzWGnN3dgxIdMQic43W7RscYtVj5jHDSpkY2NkgiZ4wxsAwwrVKGSqp89L34b1TfFbrI0wmBOv1OjR+IfxHfmDbPe1d83JvrYt1PamOyb7ze+1x1vab41IjwmZxFd8bdEdy7tkU2nbgwqZccqhaMlBzUk1VvnahMyMO+m71CTepg1KFzL5x7BrI7sVoenjwzjl++1lozn5Y4uYfGzNpFhj39BHp3xhLO9wvxp+BxUyVVgnkcAo6QqwFHbXJmSqm31FK6mhJQxD+6actxSb5S/2hc7YrAuja/K9s+d6XDufEVp96yPbx6Ice78ty3rQ2vc8GRMnE5HZ0a7E2G6DLfbm2De4kOkqKjACr6vqcCxhrIK+DTR2jFTrdIIt1SeVLWPliL14Tn1KdNaxE04nmurgI2R6JUyKuVby7WEUJubiOlw31jZb1/meJ2NcJbxjXHWe6gJYcwouZL4wfBvI9/ih8uukkpDVlkx0Y1+FS6mHsU8nmUmKKOUXPjan8iOd9LZoacws9kXCd47cmJCJry1aRtxKvkAbv5j7Rsjm6Hzdpka2RUwOYK9zOFTyLEYofEQhtZHDiMZE9D4RgsaQ9HqYFMlM2DXRovxA9sf2Bd+us8RWomUn+bKGe4w/KJ8tzPY+NSwjZAutJIfV1X7sU8NVrAYhkxjoZDKMfe8Ir7mrt9Dss5sNU9krUYgtYjLG9WbG2PCCES1TKfm07Jb9itz2kBAyj1bUlX/uXUoehyJrQAJrJowGLD7JoVqo4xaQCNkEPQmW3qagkN5ECuq+6KNlvYIYUZuAl3i1a7SS2KygxYV8wWJQwwo5GEJmNYT+pkoDq/pIyNRtsf+uSstyLN0p05WSlJeA7/hRXmvXlb5mLtm6kurcCyH72m5yFImXIi6JmUvS7X7lT/U/ii42tZgn1dSLnGxT3tDIWc+1ZTcvZIquFHnpZHAVsCFs7S8x0zFIeQioq99CaqWea9qyaSEzEZW6Jnb30Qem9pUQqhtKSkugpUgFIZv2rWaFTAP1Ep9Q3UKdUC10caZdKc+W1FMv8tTyqVRF/vIz0imBJoXMiNiaruQpwsMac5fzsIZfsQm0NC2hhZsaa/2lOSGLJWJqAHUxdcOALuZad/Tfr4WpF4ZKS3U1dXb9bkrIjNDEnDJhpm+4NgD5thFoKUppKfr09YqmhCzVVAmVo3lmpPgENACe4q0X8WuyXAKTYqcZNSNkCsslMCmSGfjfcic0hZ21lyG+Ld3Jk18pAiWdEmhCyDRmlfqOohyOqOzU4UKuae3EVn1TXYxDtlOKY+1eyNTtyDHHi7Gy+O4rxnrmtaXUUgTq0667FzJFRrlm3esOZugpHj6Nu/e8LQ5+I2TjXr1rIVPXTmKSa6xK5dMVGHe8EGsVjbV2oZA/qYtJOiawWyEzXcqcjS4BVbeW1/0cO12opZamXhhmLdbZ1H3ue7dCpqt1qMeP5gAubZMNJdixZGeN29XNyhVt5+IlX+Im0in94EKm1/6a1+jq27zb/LTopzUx+vyKwhQJleDk5kmCEmyZaoMa14tnDN8pnUWL44IubRJUyCRawz+NMO9hnxOzGM5Y2iC7xjVaG8txcb4teXSxUjertSQhy3XzqmTWQYVs7E8jFJXN/cFBaCFTQ5c2wM6gf/hTQExbm3ohiq0K+JIHBRWyscIkZHP/MhNSyNTdUJcy5wD/GAPTDWrlUZoxBqHXtdrFQsjGPSmqkOlvviRk+ouqqRRSyBRyl3qVll06+UhhCKhb2WJ33VwUw1Dcz1GiCpm6mnY0JuGyPyFwKtrRcUuNevSYlMbuSGEItDyfKuTFP0xr5D+Kk5BpAN8WH3vZHtDXn4K6/INxqEZRxFP6IChzysI5fCi/CWdRuiPpgsjcxGPeTkJ2vMvykrqScwP8wyOEcEiNG5Qy3WJYN/u35gCVLra2zSUum8nOJdqWwiYmxZ5SjiJkErG5cbGhGSGETA1bw/gT3cthy6//3fqAt/ydtxAf+09wIVM31BYxjZOpqzmWtgqZnLqmsSe6l2Ne4LdOUy9aflqi1Tu2c14STMgkXmYCrMRp+Lm4eDVpw1YhK23y62RFv26ge7lEaHm7uuc1RODLNVmXAyE75RZMyE4P7bZmi5Dp9ntN0ZiI0L1084u5XK13reRDYkA6EKhWyDSfRiKmrmVtSeJd6jSRGliq3Vu+a9f6GOGYj1YrZAqva70qaaoIbzAYc0e3dVuieLcSys4lEa+tJxKbaJVCVuqjSK6NpS5xac+DutqeOx8n8VMLtC7mth9WKWQaMK/5rpV5zETfJD8CjA898ULIjv2mOiHTFXkPY0y82ufYEV2XNKTApOKuj+hrHB92bWfffNUJmcbF9nDrvfW5UL6OavIrEmd8sevHhxEy4xVdV5WQmekWe+iSKbLU5FiSHwFdyDiBu35opcW3f0x5SzVCZgb49/RoRq3TR6acKcV6iT9TV7q+V7KHnkkon6lGyDRlQZ89JY31MN7j3qLmJon7HvvNyVjhcdtWIWSKwmp4u8Ux2uUl1YtpGMucTA51KeH1REMsap1Hadoz5HfxQmZe2bKnLuWwAXUHdg9jfsM6xfqtMaG9ReVrWSFkx+SKFjKd4LoC77n7pROTQdtjp5xaUneKcaEnOuYCP8WqtfVFC5lC572Hz0zDcD/lEP1jVkyKPfAoUsgUiclpFY3tvdvFNIyDMy79kj8w9eJAiWGJA4vihEwnthxWkdjeRcw0Q+tvczAclr6JQI4J6RxB2J+YFCNkEjDN2paztjYOwmz14xN0bIkxoVMqCNmBSRFCJvEyg/otTnbkbtzBIad+cZfulAwXwAOTIoTsYE6bv9SFpts03/ZMAD3lw13cAxOE7MAi6y8GsufxawpOa0MO80SeHlPa89SkpfoPtyNkQxoZf3OizsNnPOiUD93tAxOE7MAi6y85paIy0jgBHhY/5YKQHZggZAcW2X9pnKyVKSc+sBlDHKfFndwDF4TswCL7L3Wf9vpM6Ra4RKvT9LhJ9MQGIZv2keRbuDM3jpzpKeNctJYo/okNQjbtI8m3EHmMI2eawTgXreUmyBMbhGzaR7Js2eN717aCpMs9TRAhe2KDkE37SJYteliecbJj9LwS/JjHcIk3gjzRQMiGXlHAb17rc9oIDGifMjFr6HY/kUDIjEcU8q2H5xWBkJ4IwGPeExCyJz4I2byfZNnK5M8DdnWzNQ5EGicAnycuCNm4f2Rdy7jHAT8Rx4HF2C9m9z9RQcjGvCPzOsbJDg2AqB9YjP2i6/1EJaqQ3d6+787OXozxf17HQO4ziucfOOcziv75U0UdpGkCnENdF03IPn36pZ91jJBNO+DcFsbJnugwc33OSw6MlnPtO0c0ITs/f9ldXLwiIlvpP3Spuo6Hot2ch/98iBSRXV+/7e7uPnRXV28QMjdfPMnFOFnX/7EGdyxPXONkBbP7IwiZBExCpoSQnfic8wrGyXgDqquzSMhafxokaNfy4eGh706aBhgTMo152B+Tn+9jAq2Pk/HnGsf+MLXEFBXHiEwRli0+9rIiscvL193j4+Mz7zEhe9749YeOQxon0Po4GV2mcb+w1yJkjkJmgxtb/vjxx1mxu7l5N7Zbv8/oBlZ2rY+T6SLHG3OXT4TW/USEgnYtbeREZDYRv+WWx8m4Y+nuK8zuR8jcvSVTzlbHyTg53R0OVgiZu7dkytnqOJnGffjPRjenI3qNLGQuzcBg/zylVsc/dMdS7+onuRFo/TyKOkbm0gStN8ASo1bHyfjn9SXPON7e+o0RhOzYH4pcanGcjAucnyu2PlUFIfPzlyy5WxsnazUK3eJcCNkWegH25cq7DFHjZBKzVhJvPfVv6dYudjYhIjKbSIHLilDUvWwlMVPdv6VbZ4aQ+ftMlj0kZBK0FlLr0cWaNkbI1lALuA9dSzeYOrnVxWwh6Y5lK6Idqj01VaWl4QebGxGZTaTQ5ZbGybi4+Tth67P7ETJ/n8myRyuzt3VCKiIj+RFAyPx4Bc/N1dcdaQuvNFYXSbP6SX4E9JaQls8lIjI/f8mau4UXDer5Sg1ck/wJIGT+zILt0TJ8X4gtDOi2PrHT1yeG+XUutfr+NiKyoScU/ruFcbIWH8cK5XYtXwQQslBelOg4ex4na0GoY7oJQhaT7sKx6VouALI273mcrPU7b1ZTey+2PJGYiMzbXfLusOdxMg3y8zLF9f7V8ux+hGy932TZc8/dr5YjihDOhJCFoLjyGHQt/cHt9RGevdbLv4XX7bHnaH2JCBHZEqECt+91rhUXtW3O1vIYI0K2zXey7L3H93XxaNJ2V0LItjNcfQSuwv7o9vg4Sqt/suLf+tN77NEvpmt7vIWI7JhHNUsaT9IVeC9pz9NKUrZRq4EBQpbSywKWtbepCnsT5oBN7XUoCVmLjykhZF5uUk7mvY0ptRpJhPaoVmf3I2ShPSnh8fZy9dXbYBWRkbYTQMi2M1x1BK7Eq7D1O+1lAinvIFvvA/aeEjLd1W4tEZFV3OJ7udO313lxOVyr1dn9CFkObwtUprpkehtG7anV7lCMdkPIYlB1OCZdSwdIM1n28FqfvYz1zTRTsk17idJ9gRGR+RIrLH/t86/2dvc1t3u0OrsfIcvteRvLr/1B4VYjiI3NPrk7QjaJJu4Gupbb+Nb+WErtEeW21gu/917GTX3JRIvIHh8fu5ubd/1fVEms7u8/j9qGkI1i8VqpOVi13nJnRr9XUztlbvGciiJkHz/+2J2dveguL193d3cfZuG3CH0WyIqNNT+uRPuvaPCFXVpkGlzIPn36pY/Crq7eLOB+2twidCcwHplq7U4w0O/RyB5Z93An26O6fdbgQnZ+/rK7uHjlbAdC5oxqNmONf6NWcyQ52xiZN7Y4Ly+okKkbKWG6vn7bSRh6tEIAAAbuSURBVND0W6I2NT6m9kbIwnh9jYPme3nEKkwLhjsKQraRpQRMY2NmXOzh4aEXNImaBv+VJFz2Z2Ox7N51naZhyIFrSooi1S0mhSVQ40VtKwGniEwCZYuPvSzxUvRldytvb9/3+xpxsw3WcUjbCZhpGLW8i2rP/wa1vTW3HaHFx5SchMwVqwb4bSFTt1JihZC5UlyfTxGZIrMaUo0RZA1cZSNCtrGlTPSlLqVJ5i7m1DgZEZkhtf27plnyvPFie3tPHaHFi0TQiExgFZFp/piSxsX0W13TqYSQTZHxX19Td42JsP7t67pHi48pBRcyRWMSLwmUPprdP5cQsjk6/ts0h6j0Wf5mPM+/duzhQgAhc6EUOA9CFhaoumy6a1VyYiJs3NZp8UIRPCLzbSKEzJfYfP4aZvkzEXa+DUNsbe28QshCeE1hxyj9ERXdXS29+1tYk3qbg5B5I9u2Q2vAt9Fy21vdS31KTWrzWua7lcpwya7WbqYQkS15RIXbS+5eMj6WxqFae0wJIUvjV8lLKbV7yfhYGldAyNJwfi6FruUziqA/Su1eMj4WtJknD6b210WjlUREttOWLrF7aaYFMD4W3+lae0wJIYvvU9lKKG1yrO5UahCaFJ8AQhaf8VEJdC2PcARdUPeipMmxpXZ3g0Iv5GC6aKgb30oiIttxS6t7qXd+lZIUIequJSk+gdYeU0LI4vtU1hLUlSvh1T56oJ3oO50rIGTpWPcl4dxxgevVPnqldO5Uih25OaQq39xYSVVe7nKIyHK3QOTyTSSk75xJYioxI6Uj0FKQgJCl86tsJUlEcs8p0kmVW0yzNUCmghGyhOBbgp0Q61FRuoOlgfZciWkXeci39LwlEVkeH0teas45ZZoCoqkXpLQEWnpMCSFL61vZSlPXMtegP3/7lqfZEbKE3OlapoGda9A/d7c2Dd0yS1EknHtsNBUZIrJUpAsoR46deqY/3cp8Dd/SY0oIWT4/S16ymemf8qFtupXJm/m5QITsGUX8H3Qt4zMelqBxk1TdDbqVQ/Lpf+uJjlzjoqlrS0SWmnjm8vToiqKkFFEZ3cq8jd3SY0oIWV5fy1J6iqjMPCLDJNgsTdwXipAlZE/XMiHsr0WliMrUrZFgkvIR0EWkpLefxCRBRBaTbsHHjh2VaQJuCW/dKLgJkpjWSqCAkCVxp/IKiRmVmWOXV+v2LELIErV5K6AT4fQqRne0YswrK+EhdS8QO86srmUL45REZDt24qWqmTEURVChko6pi1MLJ08oZjGPoyGEkO0b09Ytx0bIttDbwb56R1jIPwRRhBcjytsB6ixVQMgSYadrmQj0TDFy9hBvpyAam4GcaZO6+S3cdCEiy+RgJRUbqosZShBLYlO7La08poSQ1e6pgezX40Rbnos0+6d4YiBQlZs4DEK2spnv7j505+cv+wFfdRuvrt7MHomu5SyepBvl9Bov8xUj5c/54sakkCorTG0aYtig9GoHjcju7z/3AnZz866v9+PjY3dx8WpWzBCyslxEA/W+YhZrGkdZZOq0Rncs1eXfewoqZLe373shk6CZJFG7vHxtFk++EbITJNlX6AqubqbLbfs1wpe9gg0ZgJCtaGw7ItMhJGISuKmEkE2RybvejHlJqMbmhKk7iYjlbSOX0hEyF0ojeT5+/LEfI1O38uHh4fn3SNZ+FUI2RSb/eiNWis7UPTEDxyZi07fveFr+WrVlgdqnhXMsaNfSuIgG+DU2po8EbZgE1f4Mt/O7PAI6GRShGSHTJNqxKK08y7FIBBCyr35wff32RHxsMdLdSiV1JYe/lY+u5VeQfEEgAwGEzBO6BOvs7MXRXorO7HXDDC1AHtaX3xBITUBTY/R/DXtOQbuWitxs0dKYmcTK7mIaqAiZIcE3BOIQ0Pimyx3oOKWnOWpQITOiJUEzSV3NuUmxCJkhxTcE4hBAyFZwtWf2D0Vt7HAI2RgV1kEgHIEWHhwPGpGtQY+QraHGPhBwJ2DuNrvvUV9OhKy+NsNiCHgRQMi8cK3LTES2jht7QcCVgIRs7w+OE5G5egP5IFApgRYeU0LIKnVOzIaAKwGEzJXUhnx0LTfAY1cIOBBAyBwgbc2CkG0lyP4QmCfQwoPjdC3nfYCtENgFgb0HDAjZLtyUSkBgngBCNs9n89a9A94MiANAIACBvf/jOBFZACfhEBAoncDen7dEyEr3QOyDQAACCFkAiHOHoGs5R4dtEAhDQEKmt/zuNRGR7bVlqRcEBgT2/rwlQjZobH5CYK8EELLILUvXMjJgDg+Brnv+45i9wsgeke0VLPWCAATSEUDI0rGmJAhAIBIBhCwSWA4LAQikI4CQpWNNSRCAQCQCCFkksBwWAhBIR+D/AVOfLP2hH/iaAAAAAElFTkSuQmCC"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the smallest value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> for which the particle is at rest.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total distance travelled by the particle.</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 acceleration of the particle when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>7</mn></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>recognising <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>0</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>6</mn><mo>.</mo><mn>74416</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>6</mn><mo>.</mo><mn>74</mn></math> (sec) <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Do not award <em><strong>A1</strong></em> if additional values are given.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mo>∫</mo><mn>0</mn><mn>10</mn></msubsup><mfenced open="|" close="|"><mrow><mi>v</mi><mfenced><mi>t</mi></mfenced></mrow></mfenced><mo>d</mo><mi>t</mi></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msubsup><mo>∫</mo><mn>0</mn><mrow><mn>6</mn><mo>.</mo><mn>74416</mn><mo>…</mo></mrow></msubsup><mi>v</mi><mfenced><mi>t</mi></mfenced><mo> </mo><mo>d</mo><mi>t</mi><mo>+</mo><msubsup><mo>∫</mo><mrow><mn>6</mn><mo>.</mo><mn>74416</mn><mo>…</mo></mrow><mrow><mn>9</mn><mo>.</mo><mn>08837</mn><mo>…</mo></mrow></msubsup><mi>v</mi><mfenced><mi>t</mi></mfenced><mo> </mo><mo>d</mo><mi>t</mi><mo>-</mo><msubsup><mo>∫</mo><mrow><mn>9</mn><mo>.</mo><mn>08837</mn><mo>…</mo></mrow><mn>10</mn></msubsup><mi>v</mi><mfenced><mi>t</mi></mfenced><mo> </mo><mo>d</mo><mi>t</mi></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>37</mn><mo>.</mo><mn>0968</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>37</mn><mo>.</mo><mn>1</mn><mo> </mo><mfenced><mtext>m</mtext></mfenced></math> <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>recognizing acceleration at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>7</mn></math> is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>'</mo><mfenced><mn>7</mn></mfenced></math> <em><strong>(M1)</strong></em></p>
<p>acceleration <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>5</mn><mo>.</mo><mn>93430</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>5</mn><mo>.</mo><mn>93</mn><mo> </mo><mfenced><msup><mtext>ms</mtext><mrow><mo>-</mo><mn>2</mn></mrow></msup></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[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>Hyungmin designs a concrete bird bath. The bird bath is supported by a pedestal. This is shown in the diagram.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">The interior of the bird bath is in the shape of a cone with radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>, height <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> and a constant slant height of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn><mo> </mo><mtext>cm</mtext></math>.</p>
</div>
<div class="specification">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> be the volume of the bird bath.</p>
</div>
<div class="specification">
<p>Hyungmin wants the bird bath to have maximum volume.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an equation in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> that shows this information.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mfrac><mrow><mn>2500</mn><mtext>π</mtext><mi>h</mi></mrow><mn>3</mn></mfrac><mo>-</mo><mfrac><mrow><mtext>π</mtext><msup><mi>h</mi><mn>3</mn></msup></mrow><mn>3</mn></mfrac></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mtext>d</mtext><mi>V</mi></mrow><mrow><mtext>d</mtext><mi>h</mi></mrow></mfrac></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using your answer to <strong>part (c)</strong>, find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> for which <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> is a maximum.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the maximum volume of the bird bath.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>To prevent leaks, a sealant is applied to the interior surface of the bird bath.</p>
<p>Find the surface area to be covered by the sealant, given that the bird bath has maximum volume.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>h</mi><mn>2</mn></msup><mo>+</mo><msup><mi>r</mi><mn>2</mn></msup><mo>=</mo><msup><mn>50</mn><mn>2</mn></msup></math> (or equivalent)<strong> </strong> <strong><em>(A1)</em></strong></p>
<p><em><strong><br></strong></em><strong>Note:</strong> Accept equivalent expressions such as <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><msqrt><mn>2500</mn><mo>-</mo><msup><mi>h</mi><mn>2</mn></msup></msqrt></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><msqrt><mn>2500</mn><mo>-</mo><msup><mi>r</mi><mn>2</mn></msup></msqrt></math>. Award <em><strong>(A0)</strong></em> for a final answer of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>±</mo><msqrt><mn>2500</mn><mo>-</mo><msup><mi>h</mi><mn>2</mn></msup></msqrt></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>±</mo><msqrt><mn>2500</mn><mo>-</mo><msup><mi>r</mi><mn>2</mn></msup></msqrt></math>, or any further incorrect working.</p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>×</mo><mi mathvariant="normal">π</mi><mo>×</mo><mfenced><mrow><mn>2500</mn><mo>-</mo><msup><mi>h</mi><mn>2</mn></msup></mrow></mfenced><mo>×</mo><mi>h</mi></math> <strong>OR</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>×</mo><mi mathvariant="normal">π</mi><mo>×</mo><msup><mfenced><msqrt><mn>2500</mn><mo>-</mo><msup><mi>h</mi><mn>2</mn></msup></msqrt></mfenced><mn>2</mn></msup><mo>×</mo><mi>h</mi></math><strong> </strong> <strong><em>(M1)</em></strong></p>
<p><em><strong><br></strong></em><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in the volume of cone formula.</p>
<p><br><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mfrac><mrow><mn>2500</mn><mtext>π</mtext><mi>h</mi></mrow><mn>3</mn></mfrac><mo>-</mo><mfrac><mrow><mtext>π</mtext><msup><mi>h</mi><mn>3</mn></msup></mrow><mn>3</mn></mfrac></math> </strong> <strong><em>(AG)</em></strong></p>
<p><em><strong><br></strong></em><strong>Note:</strong> The final line must be seen, with no incorrect working, for the <em><strong>(M1)</strong></em> to be awarded.</p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mrow><mtext>d</mtext><mi>V</mi></mrow><mrow><mtext>d</mtext><mi>h</mi></mrow></mfrac><mo>=</mo></mrow></mfenced><mo> </mo><mfrac><mrow><mn>2500</mn><mi mathvariant="normal">π</mi></mrow><mn>3</mn></mfrac><mo>-</mo><mtext>π</mtext><msup><mi>h</mi><mn>2</mn></msup></math><strong> </strong> <strong><em>(A1)(A1)</em></strong></p>
<p><em><strong><br></strong></em><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2500</mn><mi mathvariant="normal">π</mi></mrow><mn>3</mn></mfrac></math>, <em><strong>(A1) </strong></em>for <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mtext>π</mtext><msup><mi>h</mi><mn>2</mn></msup></math>. Award at most <em><strong>(A1)(A0)</strong></em> if extra terms are seen. Award <em><strong>(A0)</strong></em> for the term <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mrow><mn>3</mn><mtext>π</mtext><msup><mi>h</mi><mn>2</mn></msup></mrow><mn>3</mn></mfrac></math>.</p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>=</mo><mfrac><mrow><mn>2500</mn><mi mathvariant="normal">π</mi></mrow><mn>3</mn></mfrac><mo>-</mo><mtext>π</mtext><msup><mi>h</mi><mn>2</mn></msup></math><strong> </strong> <strong><em>(M1)</em></strong></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for equating <strong>their</strong> derivative to zero. Follow through from part (c).</p>
<p><br><strong>OR</strong></p>
<p>sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mtext>d</mtext><mi>V</mi></mrow><mrow><mtext>d</mtext><mi>h</mi></mrow></mfrac></math><strong> </strong> <strong><em>(M1)</em></strong></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for a labelled sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mtext>d</mtext><mi>V</mi></mrow><mrow><mtext>d</mtext><mi>h</mi></mrow></mfrac></math> with the curve/axes correctly labelled <em>or</em> the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-intercept explicitly indicated.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>h</mi><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mn>28</mn><mo>.</mo><mn>9</mn><mo> </mo><mfenced><mtext>cm</mtext></mfenced><mo> </mo><mo> </mo><mfenced><mrow><msqrt><mfrac><mn>2500</mn><mn>3</mn></mfrac></msqrt><mo>,</mo><mo> </mo><mfrac><mn>50</mn><msqrt><mn>3</mn></msqrt></mfrac><mo>,</mo><mo> </mo><mfrac><mrow><mn>50</mn><msqrt><mn>3</mn></msqrt></mrow><mn>3</mn></mfrac><mo>,</mo><mo> </mo><mn>28</mn><mo>.</mo><mn>8675</mn><mo>…</mo></mrow></mfenced></math> <strong><em>(A1)</em>(ft)</strong></p>
<p><br><strong>Note:</strong> An unsupported <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>28</mn><mo>.</mo><mn>9</mn><mo> </mo><mtext>cm</mtext></math> is awarded no marks. Graphing the <strong>function</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mfenced><mi>h</mi></mfenced></math> is not an acceptable method and <em><strong>(M0)(A0)</strong></em> should be awarded. Follow through from part (c). Given the restraints of the question, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>≥</mo><mn>50</mn></math> is not possible.</p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>V</mi><mo>=</mo></mrow></mfenced><mo> </mo><mfrac><mrow><mn>2500</mn><mo>×</mo><mi mathvariant="normal">π</mi><mo>×</mo><mn>28</mn><mo>.</mo><mn>8675</mn><mo>…</mo></mrow><mn>3</mn></mfrac><mo>-</mo><mfrac><mrow><mi mathvariant="normal">π</mi><msup><mfenced><mrow><mn>28</mn><mo>.</mo><mn>8675</mn><mo>…</mo></mrow></mfenced><mn>3</mn></msup></mrow><mn>3</mn></mfrac></math><strong> </strong> <strong><em>(M1)</em></strong></p>
<p><strong>OR</strong></p>
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>3</mn></mfrac><mi mathvariant="normal">π</mi><msup><mfenced><mrow><mn>40</mn><mo>.</mo><mn>828</mn><mo>…</mo></mrow></mfenced><mn>2</mn></msup><mo>×</mo><mn>28</mn><mo>.</mo><mn>8675</mn><mo>…</mo></math> </strong> <strong><em>(M1)</em></strong></p>
<p><strong><br>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting their <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>28</mn><mo>.</mo><mn>8675</mn><mo>…</mo></math> in the volume formula.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>V</mi><mo>=</mo></mrow></mfenced><mo> </mo><mo> </mo><mn>50400</mn><mo> </mo><mfenced><msup><mtext>cm</mtext><mn>3</mn></msup></mfenced><mo> </mo><mo> </mo><mfenced><mrow><mn>50383</mn><mo>.</mo><mn>3</mn><mo>…</mo></mrow></mfenced></math> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><br><strong>Note:</strong> Follow through from part (d).</p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>S</mi><mo>=</mo></mrow></mfenced><mo> </mo><mi mathvariant="normal">π</mi><mo>×</mo><msqrt><mn>2500</mn><mo>-</mo><msup><mfenced><mrow><mn>28</mn><mo>.</mo><mn>8675</mn><mo>…</mo></mrow></mfenced><mn>2</mn></msup></msqrt><mo>×</mo><mn>50</mn></math><strong> </strong> <strong><em>(A1)</em>(ft)</strong><strong><em>(M1)</em></strong></p>
<p><strong><br>Note:</strong> Award <em><strong>(A1)</strong></em> for their correct radius seen <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>40</mn><mo>.</mo><mn>8248</mn><mo>…</mo><mo>,</mo><mo> </mo><msqrt><mn>2500</mn><mo>-</mo><msup><mfenced><mrow><mn>28</mn><mo>.</mo><mn>8675</mn><mo>…</mo></mrow></mfenced><mn>2</mn></msup></msqrt></mrow></mfenced></math>. <br>Award <em><strong>(M1)</strong></em> for correctly substituted curved surface area formula for a cone.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>S</mi><mo>=</mo></mrow></mfenced><mo> </mo><mn>6410</mn><mo> </mo><mfenced><msup><mtext>cm</mtext><mn>2</mn></msup></mfenced><mo> </mo><mo> </mo><mfenced><mrow><mn>6412</mn><mo>.</mo><mn>74</mn><mo>…</mo></mrow></mfenced></math> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><br><strong>Note:</strong> Follow through from parts (a) and (d).</p>
<p><em><strong><br>[3 marks]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><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><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="\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><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="0.30055 = 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 <em>g</em>(<em>x</em>) = −(<em>x</em> − 1)<sup>2</sup> + 5.</p>
</div>
<div class="specification">
<p>Let <em>f</em>(<em>x</em>) = x<sup>2</sup>. The following diagram shows part of the graph of <em>f</em>.</p>
<p><img src="data:image/png;base64,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"></p>
<p>The graph of <em>g</em> intersects the graph of <em>f</em> at <em>x</em> = −1 and <em>x</em> = 2.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the coordinates of the vertex of the graph of <em>g</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the grid above, sketch the graph of g for −2 ≤ <em>x</em> ≤ 4.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of the region enclosed by the graphs of <em>f</em> and <em>g</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>(1,5) (exact) <em><strong> A1 N1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img 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"> <em><strong> A1A1A1 N3</strong></em></p>
<p><strong>Note:</strong> The shape must be a concave-down parabola.<br>Only if the shape is correct, award the following for points in circles:<br><em><strong>A1</strong></em> for vertex,<br><em><strong>A1 </strong></em>for correct intersection points,<br><em><strong>A1 </strong></em>for correct endpoints.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>integrating and subtracting functions (in any order) <em><strong>(M1)</strong></em><br><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int {f - g} ">
<mo>∫</mo>
<mrow>
<mi>f</mi>
<mo>−</mo>
<mi>g</mi>
</mrow>
</math></span></p>
<p>correct substitution of limits or functions (accept missing d<em>x</em>, but do not accept any errors, including extra bits) <em><strong>(A1)</strong></em><br>eg <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_{ - 1}^2 {g - f,\,\,\int { - {{\left( {x - 1} \right)}^2}} } + 5 - {x^2}">
<msubsup>
<mo>∫</mo>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
<mn>2</mn>
</msubsup>
<mrow>
<mi>g</mi>
<mo>−</mo>
<mi>f</mi>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mo>∫</mo>
<mrow>
<mo>−</mo>
<mrow>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mrow>
<mo>+</mo>
<mn>5</mn>
<mo>−</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span></p>
<p>area = 9 (exact) <em><strong>A1 N2</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \,\,{\text{sin}}\,\left( {{e^x}} \right)">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>sin</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mi>e</mi>
<mi>x</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> for 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> ≤ 1.5. The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <em>x</em>-intercept of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The region enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>, the<em> y</em>-axis and the <em>x</em>-axis is rotated 360° about the <em>x</em>-axis.</p>
<p>Find the volume of the solid formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>valid approach <em><strong>(M1)</strong></em><br><em>eg </em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = 0,\,\,\,\,{e^x} = 180">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mi>e</mi>
<mi>x</mi>
</msup>
</mrow>
<mo>=</mo>
<mn>180</mn>
</math></span> or 0…</p>
<p>1.14472</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = {\text{ln}}\,\pi ">
<mi>x</mi>
<mo>=</mo>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>π</mi>
</math></span> (exact), 1.14 <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to substitute either their <strong>limits</strong> or the function into formula involving <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^2}">
<mrow>
<msup>
<mi>f</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span>. <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\int_0^{1.14} {{f^2},\,\,\pi \int {\left( {{\text{sin}}\,\left( {{e^x}} \right)} \right)} } ^2}dx,\,\,0.795135">
<mrow>
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mrow>
<mn>1.14</mn>
</mrow>
</msubsup>
<msup>
<mrow>
<mrow>
<msup>
<mi>f</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>π</mi>
<mo>∫</mo>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<mtext>sin</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mi>e</mi>
<mi>x</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mi>d</mi>
<mi>x</mi>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>0.795135</mn>
</math></span></p>
<p>2.49799</p>
<p>volume = 2.50 <em><strong> A2 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>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>A group of 66 people went on holiday to Hawaii. During their stay, three trips were arranged: a boat trip (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="B">
<mi>B</mi>
</math></span>), a coach trip (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
<mi>C</mi>
</math></span>) and a helicopter trip (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="H">
<mi>H</mi>
</math></span>).</p>
<p>From this group of people:</p>
<table style="width: 691.333px;">
<tbody>
<tr>
<td style="width: 182px; text-align: right;">3 </td>
<td style="width: 526.333px;">went on all three trips;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">16 </td>
<td style="width: 526.333px;">went on the coach trip <strong>only</strong>;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">13 </td>
<td style="width: 526.333px;">went on the boat trip <strong>only</strong>;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">5 </td>
<td style="width: 526.333px;">went on the helicopter trip <strong>only</strong>;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;"><em>x </em></td>
<td style="width: 526.333px;">went on the coach trip and the helicopter trip <strong>but not</strong> the boat trip;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">2<em>x </em>
</td>
<td style="width: 526.333px;">went on the boat trip and the helicopter trip <strong>but not</strong> the coach trip;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">4<em>x </em>
</td>
<td style="width: 526.333px;">went on the boat trip and the coach trip <strong>but not</strong> the helicopter trip;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">8 </td>
<td style="width: 526.333px;">did not go on any of the trips.</td>
</tr>
</tbody>
</table>
</div>
<div class="specification">
<p>One person in the group is selected at random.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a Venn diagram to represent the given information, using sets labelled <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="B">
<mi>B</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
<mi>C</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="H">
<mi>H</mi>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 3">
<mi>x</mi>
<mo>=</mo>
<mn>3</mn>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n(B \cap C)">
<mi>n</mi>
<mo stretchy="false">(</mo>
<mi>B</mi>
<mo>∩</mo>
<mi>C</mi>
<mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this person</p>
<p>(i) went on at most one trip;</p>
<p>(ii) went on the coach trip, given that this person also went on both the helicopter trip and the boat trip.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><img src="images/Schermafbeelding_2017-03-07_om_10.03.03.png" alt="N16/5/MATSD/SP2/ENG/TZ0/02.a/M"> <strong><em>(A5)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for rectangle and three labelled intersecting circles (U need not be seen),</p>
<p><strong><em>(A1) </em></strong>for 3 in the correct region,</p>
<p><strong><em>(A1) </em></strong>for 8 in the correct region,</p>
<p><strong><em>(A1) </em></strong>for 5, 13 and 16 in the correct regions,</p>
<p><strong><em>(A1) </em></strong>for <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="2x">
<mn>2</mn>
<mi>x</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="4x">
<mn>4</mn>
<mi>x</mi>
</math></span> in the correct regions.</p>
<p> </p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="8 + 13 + 16 + 3 + 5 + x + 2x + 4x = 66">
<mn>8</mn>
<mo>+</mo>
<mn>13</mn>
<mo>+</mo>
<mn>16</mn>
<mo>+</mo>
<mn>3</mn>
<mo>+</mo>
<mn>5</mn>
<mo>+</mo>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
<mi>x</mi>
<mo>+</mo>
<mn>4</mn>
<mi>x</mi>
<mo>=</mo>
<mn>66</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for <strong>either </strong>a completely correct equation <strong>or </strong>adding all the terms from <strong>their </strong>diagram in part (a) and equating to 66.</p>
<p>Award <strong><em>(M0)(A0) </em></strong>if their equation has no <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="7x = 66 - 45">
<mn>7</mn>
<mi>x</mi>
<mo>=</mo>
<mn>66</mn>
<mo>−</mo>
<mn>45</mn>
</math></span><strong> OR</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="7x + 45 = 66">
<mn>7</mn>
<mi>x</mi>
<mo>+</mo>
<mn>45</mn>
<mo>=</mo>
<mn>66</mn>
</math></span> <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for adding their like terms correctly, <strong>but only </strong>when the solution to their equation is equal to 3 and is consistent with their original equation.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 3">
<mi>x</mi>
<mo>=</mo>
<mn>3</mn>
</math></span> <strong><em>(AG)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>The conclusion <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 3">
<mi>x</mi>
<mo>=</mo>
<mn>3</mn>
</math></span> must be seen for the <strong><em>(A1) </em></strong>to be awarded.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>15 <strong><em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from part (a). The answer must be an integer.</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>(i) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{42}}{{66}}{\text{ }}\left( {\frac{7}{{11}},{\text{ }}0.636,{\text{ }}63.6\% } \right)">
<mfrac>
<mrow>
<mn>42</mn>
</mrow>
<mrow>
<mn>66</mn>
</mrow>
</mfrac>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>7</mn>
<mrow>
<mn>11</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.636</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>63.6</mn>
<mi mathvariant="normal">%</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)<em>(A1)(G2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1)</em>(ft) </strong>for numerator, <strong><em>(A1) </em></strong>for denominator. Follow through from their Venn diagram.</p>
<p> </p>
<p>(ii) <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{9}{\text{ }}\left( {\frac{1}{3},{\text{ }}0.333,{\text{ }}33.3\% } \right)">
<mfrac>
<mn>3</mn>
<mn>9</mn>
</mfrac>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0.333</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>33.3</mn>
<mi mathvariant="normal">%</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for numerator, <strong><em>(A1)</em>(ft) </strong>for denominator. Follow through from their Venn diagram.</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the curves <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo> </mo><mi>sin</mi><mo> </mo><mi>x</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>-</mo><msqrt><mn>1</mn><mo>+</mo><mn>4</mn><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></msqrt></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi mathvariant="normal">π</mi><mo>≤</mo><mi>x</mi><mo>≤</mo><mn>0</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-coordinates of the points of intersection of the two curves.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math>, of the region enclosed by the two curves.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p 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>attempts to solve <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo> </mo><mi>sin</mi><mo> </mo><mi>x</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>-</mo><msqrt><mn>1</mn><mo>+</mo><mn>4</mn><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></msqrt></math> <strong>(M1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mn>2</mn><mo>.</mo><mn>76</mn><mo>,</mo><mo> </mo><mo>-</mo><mn>1</mn><mo>.</mo><mn>54</mn></math> <strong>A1</strong><strong>A1</strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong>A1A0</strong> if additional solutions outside the domain are given.</p>
<p> </p>
<p><strong>[3</strong><strong> marks]</strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><munderover><mo>∫</mo><mrow><mo>-</mo><mn>2</mn><mo>.</mo><mn>762</mn><mo>…</mo></mrow><mrow><mo>-</mo><mn>1</mn><mo>.</mo><mn>537</mn><mo>…</mo></mrow></munderover><mfenced><mrow><mo>-</mo><mn>1</mn><mo>-</mo><msqrt><mn>1</mn><mo>+</mo><mn>4</mn><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></msqrt><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo> </mo><mi>sin</mi><mo> </mo><mi>x</mi></mrow></mfenced><mo> </mo><mi mathvariant="normal">d</mi><mi>x</mi></math> (or equivalent) <strong>(M1)(A1)</strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong>M1</strong> for attempting to form an integrand involving “top curve” − “bottom curve”.</p>
<p> </p>
<p>so <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>47</mn></math> <strong>A2</strong></p>
<p> </p>
<p><strong>[4</strong><strong> marks]</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) = 4 - 2{{\text{e}}^x}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>4</mn>
<mo>−<!-- − --></mo>
<mn>2</mn>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mi>x</mi>
</msup>
</mrow>
</math></span>. The following diagram shows part of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-intercept of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The region enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>, the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis and the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-axis is rotated 360º about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis. Find the volume of the solid formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = 0">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0</mn>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="4 - 2{{\text{e}}^x} = 0">
<mn>4</mn>
<mo>−</mo>
<mn>2</mn>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mi>x</mi>
</msup>
</mrow>
<mo>=</mo>
<mn>0</mn>
</math></span></p>
<p>0.693147</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> = ln 2 (exact), 0.693 <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to substitute either their correct limits or the function into formula <em><strong>(M1)</strong></em></p>
<p>involving <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^2}">
<mrow>
<msup>
<mi>f</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^{0.693} {{f^2}} ">
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mrow>
<mn>0.693</mn>
</mrow>
</msubsup>
<mrow>
<mrow>
<msup>
<mi>f</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi {\int {\left( {4 - 2{{\text{e}}^x}} \right)} ^2}{\text{d}}x">
<mi>π</mi>
<mrow>
<mo>∫</mo>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>4</mn>
<mo>−</mo>
<mn>2</mn>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mi>x</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^{{\text{ln}}\,2} {{{\left( {4 - 2{{\text{e}}^x}} \right)}^2}} ">
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mrow>
<mrow>
<mtext>ln</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mn>2</mn>
</mrow>
</msubsup>
<mrow>
<mrow>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>4</mn>
<mo>−</mo>
<mn>2</mn>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mi>x</mi>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</math></span></p>
<p>3.42545</p>
<p>volume = 3.43 <em><strong>A2 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∫</mo><mfenced><mrow><mn>6</mn><mi>x</mi><mo>+</mo><mn>7</mn></mrow></mfenced><mo>d</mo><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>Given <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>6</mn><mi>x</mi><mo>+</mo><mn>7</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mn>2</mn></mrow></mfenced><mo>=</mo><mn>7</mn><mo>.</mo><mn>32</mn></math>, find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced></math>.</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>correct integration <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>7</mn><mi>x</mi><mo>+</mo><mi>c</mi></math> <em><strong>A1A1A1</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"><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup></math>, <em><strong>A1</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mi>x</mi></math> and <em><strong>A1</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo><mi>c</mi></math></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>recognition that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>∫</mo><mi>f</mi><mo>'</mo><mfenced><mi>x</mi></mfenced><mo>d</mo><mi>x</mi></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mn>7</mn><mfenced><mrow><mn>1</mn><mo>.</mo><mn>2</mn></mrow></mfenced><mo>+</mo><mi>c</mi><mo>=</mo><mn>7</mn><mo>.</mo><mn>32</mn></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mo>-</mo><mn>5</mn><mo>.</mo><mn>4</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>7</mn><mi>x</mi><mo>-</mo><mn>5</mn><mo>.</mo><mn>4</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Violeta plans to grow flowers in a rectangular plot. She places a fence to mark out the perimeter of the plot and uses 200 metres of fence. The length of the plot is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> metres.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_17.40.47.png" alt="M17/5/MATSD/SP2/ENG/TZ2/05"></p>
</div>
<div class="specification">
<p>Violeta places the fence so that the area of the plot is maximized.</p>
</div>
<div class="specification">
<p>By selling her flowers, Violeta earns 2 Bulgarian Levs (BGN) per square metre of the plot.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the width of the plot, in metres, is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="100 - x"> <mn>100</mn> <mo>−</mo> <mi>x</mi> </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 the area of the plot in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </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>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span> that maximizes the area of the plot.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that Violeta earns 5000 BGN from selling the flowers grown on the plot.</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 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{{200 - 2x}}{2}"> <mfrac> <mrow> <mn>200</mn> <mo>−</mo> <mn>2</mn> <mi>x</mi> </mrow> <mn>2</mn> </mfrac> </math></span> (or equivalent) <strong><em>(M1)</em></strong></p>
<p><strong>OR</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2x + 2y = 200"> <mn>2</mn> <mi>x</mi> <mo>+</mo> <mn>2</mn> <mi>y</mi> <mo>=</mo> <mn>200</mn> </math></span> (or equivalent) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for a correct expression leading to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="100 - x"> <mn>100</mn> <mo>−</mo> <mi>x</mi> </math></span> (the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="100 - x"> <mn>100</mn> <mo>−</mo> <mi>x</mi> </math></span> does not need to be seen). The 200 must be seen for the <strong><em>(M1) </em></strong>to be awarded. Do not accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="100 - x"> <mn>100</mn> <mo>−</mo> <mi>x</mi> </math></span> substituted in the perimeter of the rectangle formula.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="100 - x"> <mn>100</mn> <mo>−</mo> <mi>x</mi> </math></span> <strong><em>(AG)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="({\text{area}} = ){\text{ }}x(100 - x)"> <mo stretchy="false">(</mo> <mrow> <mtext>area</mtext> </mrow> <mo>=</mo> <mo stretchy="false">)</mo> <mrow> <mtext> </mtext> </mrow> <mi>x</mi> <mo stretchy="false">(</mo> <mn>100</mn> <mo>−</mo> <mi>x</mi> <mo stretchy="false">)</mo> </math></span><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><strong>OR</strong><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,"> <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=" - {x^2} + 100x"> <mo>−</mo> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mn>100</mn> <mi>x</mi> </math></span> (or equivalent) <strong><em>(A1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = \frac{{ - 100}}{{ - 2}}"> <mi>x</mi> <mo>=</mo> <mfrac> <mrow> <mo>−</mo> <mn>100</mn> </mrow> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </mfrac> </math></span><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><strong>OR</strong><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,"> <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=" - 2x + 100 = 0"> <mo>−</mo> <mn>2</mn> <mi>x</mi> <mo>+</mo> <mn>100</mn> <mo>=</mo> <mn>0</mn> </math></span><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><strong>OR</strong><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math>graphical method <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for use of axis of symmetry formula or first derivative equated to zero or a sketch graph.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 50"> <mi>x</mi> <mo>=</mo> <mn>50</mn> </math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (b), provided <em>x </em>is positive and less than 100.</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="50(100 - 50) \times 2"> <mn>50</mn> <mo stretchy="false">(</mo> <mn>100</mn> <mo>−</mo> <mn>50</mn> <mo stretchy="false">)</mo> <mo>×</mo> <mn>2</mn> </math></span> <strong><em>(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for substituting their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span> into their formula for area (accept “<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="50 \times 50"> <mn>50</mn> <mo>×</mo> <mn>50</mn> </math></span>” for the substituted formula), and <strong><em>(M1) </em></strong>for multiplying by 2. Award at most <strong><em>(M0)(M1) </em></strong>if their calculation does not lead to 5000 (BGN), although the 5000 (BGN) does not need to be seen explicitly.</p>
<p>Substitution of 50 into area formula may be seen in part (c).</p>
<p> </p>
<p>5000 (BGN) <strong><em>(AG)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>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">
<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>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<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>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>The function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is defined by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mrow><mn>4</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfrac></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi><mo>,</mo><mo> </mo><mi>x</mi><mo>≠</mo><mo>-</mo><mn>4</mn></math>.</p>
</div>
<div class="specification">
<p>For the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></p>
</div>
<div class="specification">
<p>The graphs of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> intersect at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>p</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>q</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo><</mo><mi>q</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>write down the equation of the vertical asymptote.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>find the equation of the horizontal asymptote.</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 <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mi>x</mi></mfenced></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using an algebraic approach, show that the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> is obtained by a reflection of the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-axis followed by a reflection in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> and the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</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>Hence, find the area enclosed by the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>.</p>
<div class="marks">[3]</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><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mn>4</mn></math></strong><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>attempt to substitute into <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mi>a</mi><mi>c</mi></mfrac></math> OR table with large values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> OR sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> showing asymptotic behaviour<strong> <em>(M1)</em></strong></p>
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>4</mn></math></strong><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"><mi>y</mi><mo>=</mo><mfrac><mrow><mn>4</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfrac></math></p>
<p>attempt to interchange <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><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mi>y</mi><mo>+</mo><mn>4</mn><mi>y</mi><mo>=</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>1</mn></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mi>y</mi><mo>+</mo><mn>4</mn><mi>x</mi><mo>=</mo><mn>4</mn><mi>y</mi><mo>+</mo><mn>1</mn></math><strong> <em>(A1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mi>y</mi><mo>-</mo><mn>4</mn><mi>x</mi><mo>=</mo><mn>1</mn><mo>-</mo><mn>4</mn><mi>y</mi></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mi>y</mi><mo>-</mo><mn>4</mn><mi>y</mi><mo>=</mo><mn>1</mn><mo>-</mo><mn>4</mn><mi>x</mi></math><strong> <em>(A1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mrow><mn>1</mn><mo>-</mo><mn>4</mn><mi>x</mi></mrow><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfrac></math> (accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mrow><mn>1</mn><mo>-</mo><mn>4</mn><mi>x</mi></mrow><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfrac></math>)<strong> <em>A1</em></strong></p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>reflection in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-axis given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mrow><mo>-</mo><mi>x</mi></mrow></mfenced></math><strong> <em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mrow><mo>-</mo><mi>x</mi></mrow></mfenced><mo>=</mo><mfrac><mrow><mo>-</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mo>-</mo><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfrac></math><strong> <em>(A1)</em></strong></p>
<p>reflection of their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mrow><mo>-</mo><mi>x</mi></mrow></mfenced></math> in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>f</mi><mfenced><mrow><mo>-</mo><mi>x</mi></mrow></mfenced></math> accept "now <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>f</mi><mfenced><mi>x</mi></mfenced></math>" <strong><em>M1</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mi>f</mi><mfenced><mrow><mo>-</mo><mi>x</mi></mrow></mfenced><mo>=</mo></mrow></mfenced><mo> </mo><mo>-</mo><mfrac><mrow><mo>-</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mo>-</mo><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mo>-</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfrac></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>4</mn><mi>x</mi><mo>-</mo><mn>1</mn></mrow><mrow><mo>-</mo><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfrac></math><strong> <em>A1</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>1</mn><mo>-</mo><mn>4</mn><mi>x</mi></mrow><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfrac><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mi>x</mi></mfenced></mrow></mfenced></math><strong> <em>AG</em></strong></p>
<p> </p>
<p><strong>Note:</strong> If the candidate attempts to show the result using a particular coordinate on the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> rather than a general coordinate on the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math>, where appropriate, award marks as follows:<br><strong><em>M0A0</em> for eg</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>→</mo><mo>(</mo><mo>−</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math><br><strong><em>M0A0</em> for</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>−</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>→</mo><mo>(</mo><mo>−</mo><mn>2</mn><mo>,</mo><mo>−</mo><mn>3</mn><mo>)</mo></math></p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to solve <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mi>x</mi></mfenced></math> using graph or algebraically<strong> <em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mo>-</mo><mn>1</mn></math> AND <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mn>1</mn></math><strong> <em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>(M1)A0</strong> </em>if only one correct value seen.</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>attempt to set up an integral to find area between <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math><strong> <em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><munderover><mo>∫</mo><mrow><mo>-</mo><mn>1</mn></mrow><mn>1</mn></munderover><mfenced><mrow><mfrac><mrow><mn>4</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfrac><mo>-</mo><mfrac><mrow><mn>1</mn><mo>-</mo><mn>4</mn><mi>x</mi></mrow><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfrac></mrow></mfenced><mo>d</mo><mi>x</mi></math><strong> <em>(A1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>675231</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>675</mn></math><strong> <em>A1</em></strong></p>
<p> </p>
<p><em><strong>[3 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;">
<p>Candidates mostly found the first part of this question accessible, with many knowing how to find the equation of both asymptotes. Common errors included transposing the asymptotes, or finding where an asymptote occurred but not giving it as an equation.</p>
<p>Candidates knew how to start part (b)(i), with most attempting to find the inverse function by firstly 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>. However, many struggled with the algebra required to change the subject, and were not awarded all the marks. A common error in this part was for candidates to attempt to find an expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mo>(</mo><mi>x</mi><mo>)</mo></math>, rather than one for <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo></math>. Few candidates were able to answer part (b)(ii). Many appeared not to know that a reflection in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-axis is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mo>-</mo><mi>x</mi><mo>)</mo></math>, or that a reflection in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>. Many of those that did, multiplied both the numerator and denominator by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math> when taking the negative of their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mo>-</mo><mi>x</mi><mo>)</mo></math> , i.e. <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfenced><mfrac><mrow><mo>-</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mo>-</mo><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfrac></mfenced></math> was often simplified as <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>4</mn><mi>x</mi><mo>-</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfrac></math>. However, the majority of candidates either did not attempt this question part or attempted to describe a graphical approach often involving a specific point, rather than an algebraic approach.</p>
<p>Those that attempted part (c), and had the correct expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo></math>, were usually able to gain all the marks. However, those that had an incorrect expression, or had found <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mo>(</mo><mi>x</mi><mo>)</mo></math>, often proceeded to find an area, even when there was not an area enclosed by their two curves.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.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>Haruka has an eco-friendly bag in the shape of a cuboid with width 12 cm, length 36 cm and height of 9 cm. The bag is made from five rectangular pieces of cloth and is open at the top.</p>
<p> </p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>Nanako decides to make her own eco-friendly bag in the shape of a cuboid such that the surface area is minimized.</p>
<p>The width of Nanako’s bag is <em>x </em>cm, its length is three times its width and its height is <em>y </em>cm.</p>
<p> </p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">The volume of Nanako’s bag is 3888 cm<sup>3</sup>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the area of cloth, in cm<sup>2</sup>, needed to make Haruka’s bag.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the volume, in cm<sup>3</sup>, of the bag.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use this value to write down, and simplify, the equation in<em> x</em> and <em>y</em> for the volume of Nanako’s bag.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down and simplify an expression in <em>x</em> and <em>y</em> for the area of cloth, <em>A</em>, used to make Nanako’s bag.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your answers to parts (c) and (d) to show that</p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = 3{x^2} + \frac{{10368}}{x}">
<mi>A</mi>
<mo>=</mo>
<mn>3</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mfrac>
<mrow>
<mn>10368</mn>
</mrow>
<mi>x</mi>
</mfrac>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{d}}A}}{{{\text{d}}x}}">
<mfrac>
<mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>A</mi>
</mrow>
<mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
</mrow>
</mfrac>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your answer to part (f) to show that the width of Nanako’s bag is 12 cm.</p>
<div class="marks">[3]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>36 × 12 + 2(9 ×12) + 2(9 × 36) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into surface area of cuboid formula.</p>
<p> </p>
<p>= 1300 (cm<sup>2</sup>) (1296 (cm<sup>2</sup>)) <em><strong>(A1)(G2)</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>36 × 9 ×12 <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into volume of cuboid formula.</p>
<p> </p>
<p>= 3890 (cm<sup>3</sup>) (3888 (cm<sup>3</sup>)) <em><strong>(A1)(G2)</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>3<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> × <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> × <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> = 3888 <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into volume of cuboid formula and equated to 3888.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span><sup>2</sup><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> = 1296 <em><strong>(A1)(G2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct fully simplified volume of cuboid.</p>
<p>Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = \frac{{1296}}{{{x^2}}}">
<mi>y</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>1296</mn>
</mrow>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span>.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(<em>A</em> =) 3<em>x</em><sup>2</sup> + 2(<em>xy</em>) + 2(3<em>xy</em>) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into surface area of cuboid formula.</p>
<p> </p>
<p>(<em>A</em> =) 3<em>x</em><sup>2</sup> + 8<em>xy <strong>(A1)(G2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct simplified surface area of cuboid formula.</p>
<p> </p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = 3{x^2} + 8x\left( {\frac{{1296}}{{{x^2}}}} \right)">
<mi>A</mi>
<mo>=</mo>
<mn>3</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>8</mn>
<mi>x</mi>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>1296</mn>
</mrow>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(M1)</strong></em></p>
<p><strong>Note: </strong>Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for correct rearrangement of their part (c) seen (rearrangement may be seen in part(c)), award <em><strong>(M1)</strong></em> for substitution of their part (c) into their part (d) but only if this leads to the given answer, which must be shown.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = 3{x^2} + \frac{{10368}}{x}">
<mi>A</mi>
<mo>=</mo>
<mn>3</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mfrac>
<mrow>
<mn>10368</mn>
</mrow>
<mi>x</mi>
</mfrac>
</math></span> <em><strong>(AG)</strong></em> </p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{{{\text{d}}A}}{{{\text{d}}x}}} \right) = 6x - \frac{{10368}}{{{x^2}}}">
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>A</mi>
</mrow>
<mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>6</mn>
<mi>x</mi>
<mo>−</mo>
<mfrac>
<mrow>
<mn>10368</mn>
</mrow>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> <em><strong>(A1)</strong></em><em><strong>(A1)</strong></em><em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6x">
<mn>6</mn>
<mi>x</mi>
</math></span>, <em><strong>(A1)</strong></em> for −10368, <em><strong>(A1)</strong></em> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^{ - 2}}">
<mrow>
<msup>
<mi>x</mi>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
</msup>
</mrow>
</math></span>. Award a maximum of <em><strong>(A1)</strong></em><em><strong>(A1)</strong></em><em><strong>(A0)</strong></em> if any extra terms seen.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6x - \frac{{10368}}{{{x^2}}} = 0">
<mn>6</mn>
<mi>x</mi>
<mo>−</mo>
<mfrac>
<mrow>
<mn>10368</mn>
</mrow>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0</mn>
</math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for equating their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{{{\text{d}}A}}{{{\text{d}}x}}}">
<mrow>
<mfrac>
<mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>A</mi>
</mrow>
<mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
</mrow>
</mfrac>
</mrow>
</math></span> to zero.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6{x^3} = 10368">
<mn>6</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>=</mo>
<mn>10368</mn>
</math></span> <strong>OR</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6{x^3} - 10368 = 0">
<mn>6</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>10368</mn>
<mo>=</mo>
<mn>0</mn>
</math></span> <strong>OR </strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^3} - 1728 = 0">
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>1728</mn>
<mo>=</mo>
<mn>0</mn>
</math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly rearranging their equation so that fractions are removed.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = \sqrt[3]{{1728}}">
<mi>x</mi>
<mo>=</mo>
<mroot>
<mrow>
<mn>1728</mn>
</mrow>
<mn>3</mn>
</mroot>
</math></span> <em><strong>(A1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 12">
<mi>x</mi>
<mo>=</mo>
<mn>12</mn>
</math></span> (cm) <em><strong>(AG)</strong></em></p>
<p><strong>Note:</strong> The <em><strong>(AG)</strong></em> line must be seen for the final <em><strong>(A1)</strong></em> to be awarded. Substituting <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 12">
<mi>x</mi>
<mo>=</mo>
<mn>12</mn>
</math></span> invalidates the method, award a maximum of <em><strong>(M1)(M0)(A0)</strong></em>.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="question">
<p>The derivative of a function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math> is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>'</mo><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn><msup><mtext>e</mtext><mi>x</mi></msup></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math>. The graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math> passes through the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>4</mn><mo>)</mo></math> . Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><strong>METHOD 1</strong></p>
<p>recognises that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>∫</mo><mfenced><mrow><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn><msup><mtext>e</mtext><mi>x</mi></msup></mrow></mfenced><mo>d</mo><mi>x</mi></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>5</mn><msup><mtext>e</mtext><mi>x</mi></msup><mfenced><mrow><mo>+</mo><mi>C</mi></mrow></mfenced></math> <em><strong>(A1)</strong></em><em><strong>(A1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A1</strong> </em>for each integrated term.</p>
<p> </p>
<p>substitutes <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>0</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>4</mn></math> into their integrated function (must involve <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo><mi>C</mi></math>) <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>=</mo><mn>0</mn><mo>+</mo><mn>5</mn><mo>+</mo><mi>C</mi><mo>⇒</mo><mi>C</mi><mo>=</mo><mo>-</mo><mn>1</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>5</mn><msup><mtext>e</mtext><mi>x</mi></msup><mo>-</mo><mn>1</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>attempts to write both sides in the form of a definite integral <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><munderover><mo>∫</mo><mn>0</mn><mi>x</mi></munderover><mi>g</mi><mo>'</mo><mfenced><mi>t</mi></mfenced><mo>d</mo><mi>t</mi><mo>=</mo><munderover><mo>∫</mo><mn>0</mn><mi>x</mi></munderover><mfenced><mrow><mn>3</mn><msup><mi>t</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn><msup><mtext>e</mtext><mi>t</mi></msup></mrow></mfenced><mo>d</mo><mi>t</mi></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>-</mo><mn>4</mn><mo>=</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>5</mn><msup><mtext>e</mtext><mi>x</mi></msup><mo>-</mo><mn>5</mn><msup><mtext>e</mtext><mn>0</mn></msup></math> <em><strong>(A1)</strong></em><em><strong>(A1)</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>g</mi><mfenced><mi>x</mi></mfenced><mo>-</mo><mn>4</mn></math> and <em><strong>A1</strong> </em>for <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>5</mn><msup><mtext>e</mtext><mi>x</mi></msup><mo>-</mo><mn>5</mn><msup><mtext>e</mtext><mn>0</mn></msup></math>.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>5</mn><msup><mtext>e</mtext><mi>x</mi></msup><mo>-</mo><mn>1</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[5 marks]</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p>While many students were successful in solving this question, some did not consider the constant of integration or struggled to integrate the exponential term. A few students lost the final mark for stopping at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mo>-</mo><mn>1</mn></math> and not giving the formula for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>.</p>
</div>
<br><hr><br><div class="question">
<p><strong>Note:</strong> <strong>In this question, distance is in metres and time is in seconds.</strong></p>
<p> </p>
<p>A particle moves along a horizontal line starting at a fixed point A. The velocity <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v">
<mi>v</mi>
</math></span> of the particle, at time <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span>, is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v(t) = \frac{{2{t^2} - 4t}}{{{t^2} - 2t + 2}}">
<mi>v</mi>
<mo stretchy="false">(</mo>
<mi>t</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>4</mn>
<mi>t</mi>
</mrow>
<mrow>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>2</mn>
<mi>t</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</mfrac>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 5">
<mn>0</mn>
<mo>⩽</mo>
<mi>t</mi>
<mo>⩽</mo>
<mn>5</mn>
</math></span>. The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v">
<mi>v</mi>
</math></span></p>
<p><img src="images/Schermafbeelding_2017-08-15_om_08.18.11.png" alt="M17/5/MATME/SP2/ENG/TZ2/07"></p>
<p>There are <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span>-intercepts at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(0,{\text{ }}0)">
<mo stretchy="false">(</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0</mn>
<mo stretchy="false">)</mo>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(2,{\text{ }}0)">
<mo stretchy="false">(</mo>
<mn>2</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<p>Find the maximum distance of the particle from A during the time <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 5">
<mn>0</mn>
<mo>⩽</mo>
<mi>t</mi>
<mo>⩽</mo>
<mn>5</mn>
</math></span> and justify your answer.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><strong>METHOD 1 (displacement)</strong></p>
<p>recognizing <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s = \int {v{\text{d}}t} ">
<mi>s</mi>
<mo>=</mo>
<mo>∫</mo>
<mrow>
<mi>v</mi>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
</mrow>
</math></span> <strong><em>(M1)</em></strong></p>
<p>consideration of displacement at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 2">
<mi>t</mi>
<mo>=</mo>
<mn>2</mn>
</math></span> <strong>and</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 5">
<mi>t</mi>
<mo>=</mo>
<mn>5</mn>
</math></span> (seen anywhere) <strong><em>M1</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^2 v ">
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mn>2</mn>
</msubsup>
<mi>v</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^5 v ">
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mn>5</mn>
</msubsup>
<mi>v</mi>
</math></span></p>
<p> </p>
<p><strong>Note:</strong> Must have both for any further marks.</p>
<p> </p>
<p>correct displacement at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 2">
<mi>t</mi>
<mo>=</mo>
<mn>2</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 5">
<mi>t</mi>
<mo>=</mo>
<mn>5</mn>
</math></span> (seen anywhere) <strong><em>A1A1</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 2.28318">
<mo>−</mo>
<mn>2.28318</mn>
</math></span> (accept 2.28318), 1.55513</p>
<p>valid reasoning comparing correct displacements <strong><em>R1</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| { - 2.28} \right| > \left| {1.56} \right|">
<mrow>
<mo>|</mo>
<mrow>
<mo>−</mo>
<mn>2.28</mn>
</mrow>
<mo>|</mo>
</mrow>
<mo>></mo>
<mrow>
<mo>|</mo>
<mrow>
<mn>1.56</mn>
</mrow>
<mo>|</mo>
</mrow>
</math></span>, more left than right</p>
<p>2.28 (m) <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Do not award the final <strong><em>A1 </em></strong>without the <strong><em>R1</em></strong><em>.</em></p>
<p> </p>
<p><strong>METHOD 2 (distance travelled)</strong></p>
<p>recognizing distance <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \int {\left| v \right|{\text{d}}t} ">
<mo>=</mo>
<mo>∫</mo>
<mrow>
<mrow>
<mo>|</mo>
<mi>v</mi>
<mo>|</mo>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>t</mi>
</mrow>
</math></span> <strong><em>(M1)</em></strong></p>
<p>consideration of distance travelled from <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 0">
<mi>t</mi>
<mo>=</mo>
<mn>0</mn>
</math></span> to 2 <strong>and</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 2">
<mi>t</mi>
<mo>=</mo>
<mn>2</mn>
</math></span> to 5 (seen anywhere) <strong><em>M1</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^2 v ">
<msubsup>
<mo>∫</mo>
<mn>0</mn>
<mn>2</mn>
</msubsup>
<mi>v</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_2^5 v ">
<msubsup>
<mo>∫</mo>
<mn>2</mn>
<mn>5</mn>
</msubsup>
<mi>v</mi>
</math></span></p>
<p> </p>
<p><strong>Note:</strong> Must have both for any further marks</p>
<p> </p>
<p>correct distances travelled (seen anywhere) <strong><em>A1A1</em></strong></p>
<p>2.28318, (accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 2.28318">
<mo>−</mo>
<mn>2.28318</mn>
</math></span>), 3.83832</p>
<p>valid reasoning comparing correct distance values <strong><em>R1</em></strong></p>
<p><em>eg</em><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="3.84 - 2.28 < 2.28,{\text{ }}3.84 < 2 \times 2.28">
<mn>3.84</mn>
<mo>−</mo>
<mn>2.28</mn>
<mo><</mo>
<mn>2.28</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>3.84</mn>
<mo><</mo>
<mn>2</mn>
<mo>×</mo>
<mn>2.28</mn>
</math></span></p>
<p>2.28 (m) <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Do not award the final <strong><em>A1 </em></strong>without the <strong><em>R1</em></strong>.</p>
<p> </p>
<p><strong><em>[6 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br>