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</div><h2>HL Paper 1</h2><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the function \(f:x \to \sqrt {\frac{\pi }{4} - \arccos x} \).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Find the largest possible domain of <em>f</em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Determine an expression for the inverse function, \({f^{ - 1}}\), and write down its domain.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \(\frac{\pi }{4} - \arccos x \geqslant 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\arccos x \leqslant \frac{\pi }{4}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x \geqslant \frac{{\sqrt 2 }}{2}\,\,\,\,\,\left( {{\text{accept }}x \geqslant \frac{1}{{\sqrt 2 }}} \right)\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">since \( - 1 \leqslant x \leqslant 1\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow \frac{{\sqrt 2 }}{2} \leqslant x \leqslant 1\,\,\,\,\,\left( {{\text{accept }}\frac{1}{{\sqrt 2 }} \leqslant x \leqslant 1} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Penalize the use of \( < \) instead of \( \leqslant \) only once.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) \(y = \sqrt {\frac{\pi }{4} - \arccos x} \Rightarrow x = \cos \left( {\frac{\pi }{4} - {y^2}} \right)\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({f^{ - 1}}:x \to \cos \left( {\frac{\pi }{4} - {x^2}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(0 \leqslant x \leqslant \sqrt {\frac{\pi }{4}} \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[8 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Very few correct solutions were seen to (a). Many candidates realised that \(\arccos x \leqslant \frac{\pi }{4}\) but then concluded incorrectly, not realising that cos is a decreasing function, that \(x \leqslant \cos \left( {\frac{\pi }{4}} \right)\). In (b) candidates often gave an incorrect domain.</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">A function \(f\) is defined by \(f(x) = \frac{{3x - 2}}{{2x - 1}},{\text{ }}x \in \mathbb{R},{\text{ }}x \ne \frac{1}{2}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find an expression for \({f^{ - 1}}(x)\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Given that \(f(x)\) can be written in the form \(f(x) = A + \frac{B}{{2x - 1}}\), find the values of the constants \(A\) and \(B\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Hence, write down \(\int {\frac{{3x - 2}}{{2x - 1}}} {\text{d}}x\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(f:x \to y = \frac{{3x - 2}}{{2x - 1}}\;\;\;{f^{ - 1}}:y \to x\)</p>
<p>\(y = \frac{{3x - 2}}{{2x - 1}} \Rightarrow 3x - 2 = 2xy - y\) <strong><em>M1</em></strong></p>
<p>\( \Rightarrow 3x - 2xy = - y + 2\) <strong><em>M1</em></strong></p>
<p>\(x(3 - 2y) = 2 - y\)</p>
<p>\(x = \frac{{2 - y}}{{3 - 2y}}\) <strong><em>A1</em></strong></p>
<p>\(\left( {{f^{ - 1}}(y) = \frac{{2 - y}}{{3 - 2y}}} \right)\)</p>
<p>\({f^{ - 1}}(x) = \frac{{2 - x}}{{3 - 2x}}\;\;\;\left( {x \ne \frac{3}{2}} \right)\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>\(x\) and \(y\) might be interchanged earlier.</p>
<p> </p>
<p><strong>Note: </strong>First <strong><em>M1 </em></strong>is for interchange of variables second <strong><em>M1 </em></strong>for manipulation</p>
<p> </p>
<p><strong>Note: </strong>Final answer must be a function of \(x\)</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>\(\frac{{3x - 2}}{{2x - 1}} = A + \frac{B}{{2x - 1}} \Rightarrow 3x - 2 = A(2x - 1) + B\)</p>
<p>equating coefficients \(3 = 2A\) and \( - 2 = - A + B\) <strong><em>(M1)</em></strong></p>
<p>\(A = \frac{3}{2}\) and \(B = - \frac{1}{2}\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Could also be done by division or substitution of values.</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 class="p1">\(\int {f(x){\text{d}}x = \frac{3}{2}x - \frac{1}{4}\ln \left| {2x - 1} \right| + c} \) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>accept equivalent e.g. <span class="s2">\(\ln \left| {4x - 2} \right|\)</span></p>
<p class="p3"><em><strong><span class="s2">[1 mark]</span></strong></em></p>
<p class="p3"><em><strong><span class="s2">Total [7 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Well done. Only a few candidates confused inverse with derivative or reciprocal.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Not enough had the method of polynomial division.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Reasonable if they had an answer to (b) (follow through was given) usual mistakes with not allowing for the derivative of the bracket.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Write \(\ln ({x^2} - 1) - 2\ln (x + 1) + \ln ({x^2} + x)\) as a single logarithm, in its simplest form.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\ln ({x^2} - 1) - \ln {(x + 1)^2} + \ln x(x + 1)\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \ln \frac{{x({x^2} - 1)(x + 1)}}{{{{(x + 1)}^2}}}\) <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \ln \frac{{x(x + 1)(x - 1)(x + 1)}}{{{{(x + 1)}^2}}}\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \ln x(x - 1)\,\,\,\,\,\left( { = \ln ({x^2} - x)} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">There were fewer correct solutions to this question than might be expected. A significant number of students managed to combine the terms to form one logarithm, but rather than factorising, then expanded the brackets, which left them unable to gain an answer in its simplest form.</span></p>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the equation \(y{x^2} + (y - 1)x + (y - 1) = 0\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the set of values of <em>y</em> for which this equation has real roots.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Hence determine the range of the function \(f:x \to \frac{{x + 1}}{{{x^2} + x + 1}}\).</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Explain why <em>f</em> has no inverse.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">for the equation to have real roots</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({(y - 1)^2} - 4y(y - 1) \geqslant 0\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow 3{y^2} - 2y - 1 \leqslant 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(by sign diagram, or algebraic method) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( - \frac{1}{3} \leqslant y \leqslant 1\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Award first </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for \( - \frac{1}{3}\) and 1, and second </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for inequalities. These are independent marks.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f:x \to \frac{{x + 1}}{{{x^2} + x + 1}} \Rightarrow x + 1 = y{x^2} + yx + y\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow 0 = y{x^2} + (y - 1)x + (y - 1)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">hence, from (a) range is \( - \frac{1}{3} \leqslant y \leqslant 1\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 36.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">a value for <em>y</em> would lead to 2 values for <em>x</em> from (a) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 36.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Do not award </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>R1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> if (b) has not been tackled.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 36.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 36.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) The best answered part of the question. The critical points were usually found, but the inequalities were often incorrect. Few candidates were convincing regarding the connection between (a) and (b). This had consequences for (c).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) The best answered part of the question. The critical points were usually found, but the inequalities were often incorrect. Few candidates were convincing regarding the connection between (a) and (b). This had consequences for (c).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) The best answered part of the question. The critical points were usually found, but the inequalities were often incorrect. Few candidates were convincing regarding the connection between (a) and (b). This had consequences for (c).</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(f(x) = {x^3} + a{x^2} + bx + c\) , where <em>a </em>, <em>b </em>, \(c \in \mathbb{Z}\) . The diagram shows the graph of <em>y</em> = <em>f</em>(<em>x</em>) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><br><img src="data:image/png;base64,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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Using the information shown in the diagram, find the values of <em>a </em>, <em>b </em>and <em>c </em>.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">If <em>g</em>(<em>x</em>) = 3<em>f</em>(<em>x </em>− 2) ,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) state the coordinates of the points where the graph of <em>g </em>intercepts the <em>x</em>-axis.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Find the <em>y</em>-intercept of the graph of <em>g </em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>f</em>(<em>x</em>) = (<em>x </em>+ 1)(<em>x </em>− 1)(<em>x </em>− 2) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {x^3} - 2{x^2} - x + 2\) <em><strong>A1A1A1</strong></em><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>a </em>= −2 , <em>b </em>= −1 and <em>c </em>= 2</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">from the graph or using <em>f</em>(0) = 2</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>c </em>= 2 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">setting up linear equations using <em>f</em>(1) = 0 and <em>f</em>(–1) = 0 (or <em>f</em>(2) = 0) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">obtain <em>a </em>= −2 , <em>b </em>= −1 <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><span style="font-size: medium; font-family: 'times new roman', times;">(i) (1, 0) <span style="font: 11.0px Helvetica;">, </span>(3, 0) <span style="font: 11.0px Helvetica;">and </span>(4, 0) <em><strong>A1</strong></em><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><span style="font-size: medium; font-family: 'times new roman', times;">(ii) <em>g</em>(0) occurs at 3<em>f</em>(−2) <em><strong>(M1)</strong></em><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-size: medium; font-family: 'times new roman', times;">= −36 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-size: medium; font-family: 'times new roman', times;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was well answered in general. Part b(ii) was often the most problematic, usually because of candidates going to the trouble of finding an explicit and sometimes incorrect expression for </span><em style="font-family: 'times new roman', times; font-size: medium;">f</em><span style="font-family: 'times new roman', times; font-size: medium;">(</span><em style="font-family: 'times new roman', times; font-size: medium;">x </em><span style="font-family: 'times new roman', times; font-size: medium;">− 2)</span><span style="font-family: 'times new roman', times; font-size: medium;">.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was well answered in general. Part b(ii) was often the most problematic, usually because of candidates going to the trouble of finding an explicit and sometimes incorrect expression for <em>f</em>(<em>x </em>− 2).</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The function \(f\) is defined by \(f(x) = \frac{{3x}}{{x - 2}},{\text{ }}x \in \mathbb{R},{\text{ }}x \ne 2\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Sketch the graph of \(y = f(x)\), indicating clearly any asymptotes and points of intersection with the \(x\) and \(y\) axes.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find an expression for \({f^{ - 1}}(x)\).</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 class="p1">Find all values of \(x\) for which \(f(x) = {f^{ - 1}}(x)\).</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 class="p1">Solve the inequality \(\left| {f(x)} \right| < \frac{3}{2}\).</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 class="p1">Solve the inequality \(f\left( {\left| x \right|} \right) < \frac{3}{2}\).</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 class="p1"><img src="images/Schermafbeelding_2015-12-24_om_11.13.35.png" alt></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: </strong><span class="s1">In the diagram, points marked \(A\) and \(B\) </span>refer to part (d) and do not need to be seen in part (a).</p>
<p class="p2"> </p>
<p class="p1">shape of curve <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>This mark can only be awarded if there appear to be both horizontal and vertical asymptotes.</p>
<p class="p2"> </p>
<p class="p4">intersection at \((0,{\text{ }}0)\) <span class="Apple-converted-space"> </span><span class="s2"><strong><em>A1</em></strong></span></p>
<p class="p1">horizontal asymptote at <span class="s3">\(y = 3\) <span class="Apple-converted-space"> </span></span><strong><em>A1</em></strong></p>
<p class="p1">vertical asymptote at \(x = 2\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(y = \frac{{3x}}{{x - 2}}\)</p>
<p class="p1">\(xy - 2y = 3x\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p1">\(xy - 3x = 2y\)</p>
<p class="p1">\(x = \frac{{2y}}{{y - 3}}\)</p>
<p class="p1">\(\left( {{f^{ - 1}}(x)} \right) = \frac{{2x}}{{x - 3}}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Final M1 is for interchanging of \(x\) and \(y\), which may be seen at any stage.</p>
<p class="p3"><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>METHOD 1</strong></p>
<p class="p2"><span class="s1">attempt to solve </span>\(\frac{{2x}}{{x - 3}} = \frac{{3x}}{{x - 2}}\) <span class="Apple-converted-space"> </span><span class="s1"><strong>(<em>M1)</em></strong></span></p>
<p class="p2">\(2x(x - 2) = 3x(x - 3)\)</p>
<p class="p2">\(x\left[ {2(x - 2) - 3(x - 3)} \right] = 0\)</p>
<p class="p2">\(x(5 - x) = 0\)</p>
<p class="p2">\(x = 0\;\;\;\)or\(\;\;\;x = 5\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1A1</em></strong></span></p>
<p class="p1"><strong>METHOD 2</strong></p>
<p class="p2">\(x = \frac{{3x}}{{x - 2}}\;\;\;\)or\(\;\;\;x = \frac{{2x}}{{x - 3}}\) <span class="Apple-converted-space"> </span><span class="s1">(<strong><em>M1)</em></strong></span></p>
<p class="p2">\(x = 0\;\;\;\)or\(\;\;\;x = 5\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1A1</em></strong></span></p>
<p class="p2"><span class="s1"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>at \({\text{A}}:\frac{{3x}}{{x - 2}} = \frac{3}{2}\) AND at \({\text{B}}:\frac{{3x}}{{x - 2}} = - \frac{3}{2}\) <strong><em>M1</em></strong></p>
<p>\(6x = 3x - 6\)</p>
<p>\(x = - 2\) <strong><em>A1</em></strong></p>
<p>\(6x = 6 - 3x\)</p>
<p>\(x = \frac{2}{3}\) <strong><em>A1</em></strong></p>
<p>solution is \( - 2 < x < \frac{2}{3}\) <strong><em>A1</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>\({\left( {\frac{{3x}}{{x - 2}}} \right)^2} < {\left( {\frac{3}{2}} \right)^2}\) <strong><em>M1</em></strong></p>
<p>\(9{x^2} < \frac{9}{4}{(x - 2)^2}\)</p>
<p>\(3{x^2} + 4x - 4 < 0\)</p>
<p>\((3x - 2)(x + 2) < 0\)</p>
<p>\(x = - 2\) (<strong><em>A1)</em></strong></p>
<p>\(x = \frac{2}{3}\) (<strong><em>A1)</em></strong></p>
<p>solution is \( - 2 < x < \frac{2}{3}\) <strong><em>A1</em></strong></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>\( - 2 < x < 2\) <strong><em>A1A1</em></strong></p>
<p> </p>
<p><strong>Note: <em>A1 </em></strong>for correct end points, <strong><em>A1 </em></strong>for correct inequalities.</p>
<p> </p>
<p><strong>Note: </strong>If working is shown, then <strong><em>A </em></strong>marks may only be awarded following correct working.</p>
<p><em><strong>[2 marks]</strong></em></p>
<p><em><strong>Total [17 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="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A function is defined by \(h(x) = 2{{\text{e}}^x} - \frac{1}{{{{\text{e}}^x}}},{\text{ }}x \in \mathbb{R}\) . Find an expression for \({h^{ - 1}}(x)\) .</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 2{{\text{e}}^y} - \frac{1}{{{{\text{e}}^y}}}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> The </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>M1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> is for switching the variables and may be awarded at any stage in the process and is awarded independently. Further marks do not rely on this mark being gained.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x{{\text{e}}^y} = 2{{\text{e}}^{2y}} - 1\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2{{\text{e}}^{2y}} - x{{\text{e}}^y} - 1 = 0\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({{\text{e}}^y} = \frac{{x \pm \sqrt {{x^2} + 8} }}{4}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(y = \ln \left( {\frac{{x \pm \sqrt {{x^2} + 8} }}{4}} \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">therefore \({h^{ - 1}}(x) = \ln \left( {\frac{{x + \sqrt {{x^2} + 8} }}{4}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">since ln is undefined for the second solution <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Accept \(y = \ln \left( {\frac{{x + \sqrt {{x^2} + 8} }}{4}} \right)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"> </strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> The </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>R1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> may be gained by an appropriate comment earlier.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A significant number of candidates did not recognise the need for the quadratic formula in order to find the inverse. Even when they did most candidates who got this far did not recognise the need to limit the solution to the positive only. This question was done well by a very limited number of candidates.</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The polynomial \(P(x) = {x^3} + a{x^2} + bx + 2\) is divisible by (<em>x</em> +1) and by (<em>x</em> − 2) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the value of <em>a</em> and of <em>b</em>, where \(a,{\text{ }}b \in \mathbb{R}\) .</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">As (<em>x</em> +1) is a factor of <em>P</em>(<em>x</em>), then <em>P</em>(−1) = 0 <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px 'Hiragino Kaku Gothic ProN';"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow a - b + 1 = 0\) (or equivalent) <em><strong>A1</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px 'Hiragino Kaku Gothic ProN';"><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;">As (<em>x</em> − 2) is a factor of <em>P</em>(<em>x</em>), then <em>P</em>(2) = 0 <strong><em>(M1)</em></strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow 4a + 2b + 10 = 0\) (or equivalent) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Attempting to solve for <em>a</em> and <em>b</em> <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>a</em> = −2 and <em>b</em> = −1 <strong><em>A1</em></strong> <strong><em>N1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">By inspection third factor must be <em>x</em> −1. <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\((x + 1)(x - 2)(x - 1) = {x^3} - 2{x^2} - x + 2\) <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Equating coefficients <em>a</em> = −2, <em>b </em>= −1 <strong><em>(M1)A1 N1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 3</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Considering \(\frac{{P(x)}}{{{x^2} - x - 2}}\) or equivalent <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{P(x)}}{{{x^2} - x - 2}} = (x + a + 1) + \frac{{(a + b + 3)x + 2(a + 2)}}{{{x^2} - x - 2}}\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Recognising that \((a + b + 3)x + 2(a + 2) = 0\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Attempting to solve for <em>a</em> and <em>b</em> <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>a</em> = −2 and <em>b </em>= −1 <strong><em>A1 N1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates successfully answered this question. The majority used the factor theorem, but a few employed polynomial division or a method based on inspection to determine the third linear factor.</span></p>
</div>
<br><hr><br><div class="specification">
<p>Consider the function \(f\) defined by \(f(x) = {x^2} - {a^2},{\text{ }}x \in \mathbb{R}\) where \(a\) is a positive constant.</p>
</div>
<div class="specification">
<p>The function \(g\) is defined by \(g(x) = x\sqrt {f(x)} \) for \(\left| x \right| > a\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Showing any \(x\) and \(y\) intercepts, any maximum or minimum points and any asymptotes, sketch the following curves on separate axes.</p>
<p>\(y = f(x)\);</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>Showing any \(x\) and \(y\) intercepts, any maximum or minimum points and any asymptotes, sketch the following curves on separate axes.</p>
<p>\(y = \frac{1}{{f(x)}}\);</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Showing any \(x\) and \(y\) intercepts, any maximum or minimum points and any asymptotes, sketch the following curves on separate axes.</p>
<p>\(y = \left| {\frac{1}{{f(x)}}} \right|\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find \(\int {f(x)\cos x{\text{d}}x} \).</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>By finding \(g'(x)\) explain why \(g\) is an increasing function.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2017-08-09_om_08.15.01.png" alt="M17/5/MATHL/HP1/ENG/TZ2/09.a.i/M"></p>
<p><strong><em>A1 </em></strong>for correct shape</p>
<p><strong><em>A1 </em></strong>for correct \(x\) and \(y\) intercepts and minimum point</p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2017-08-09_om_08.17.28.png" alt="M17/5/MATHL/HP1/ENG/TZ2/09.a.ii/M"></p>
<p><strong><em>A1 </em></strong>for correct shape</p>
<p><strong><em>A1 </em></strong>for correct vertical asymptotes</p>
<p><strong><em>A1 </em></strong>for correct implied horizontal asymptote</p>
<p><strong><em>A1 </em></strong>for correct maximum point</p>
<p><strong><em>[??? marks]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2017-08-09_om_08.20.22.png" alt="M17/5/MATHL/HP1/ENG/TZ2/09.a.iii/M"></p>
<p><strong><em>A1 </em></strong>for reflecting negative branch from (ii) in the \(x\)-axis</p>
<p><strong><em>A1 </em></strong>for correctly labelled minimum point</p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p>attempt at integration by parts <strong><em>(M1)</em></strong></p>
<p>\(\int {({x^2} - {a^2})\cos x{\text{d}}x = ({x^2} - {a^2})\sin x - \int {2x\sin x{\text{d}}x} } \) <strong><em>A1A1</em></strong></p>
<p>\( = ({x^2} - {a^2})\sin x - 2\left[ { - x\cos x + \int {\cos x{\text{d}}x} } \right]\) <strong><em>A1</em></strong></p>
<p>\( = ({x^2} - {a^2})\sin x + 2x\cos - 2\sin x + c\) <strong><em>A1</em></strong></p>
<p><strong>OR</strong></p>
<p>\(\int {({x^2} - {a^2})\cos x{\text{d}}x = \int {{x^2}\cos x{\text{d}}x - \int {{a^2}\cos x{\text{d}}x} } } \)</p>
<p>attempt at integration by parts <strong><em>(M1)</em></strong></p>
<p>\(\int {{x^2}\cos x{\text{d}}x = {x^2}\sin x - \int {2x\sin x{\text{d}}x} } \) <strong><em>A1A1</em></strong></p>
<p>\( = {x^2}\sin x - 2\left[ { - x\cos x + \int {\cos x{\text{d}}x} } \right]\) <strong><em>A1</em></strong></p>
<p>\( = {x^2}\sin x + 2x\cos x - 2\sin x\)</p>
<p>\( - \int {{a^2}\cos x{\text{d}}x = - {a^2}\sin x} \)</p>
<p>\(\int {({x^2} - {a^2})\cos x{\text{d}}x = ({x^2} - {a^2})\sin x + 2x\cos x - 2\sin x + c} \) <strong><em>A1</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(g(x) = x{({x^2} - {a^2})^{\frac{1}{2}}}\)</p>
<p>\(g'(x) = {({x^2} - {a^2})^{\frac{1}{2}}} + \frac{1}{2}x{({x^2} - {a^2})^{ - \frac{1}{2}}}(2x)\) <strong><em>M1A1A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Method mark is for differentiating the product. Award <strong><em>A1 </em></strong>for each correct term.</p>
<p> </p>
<p>\(g'(x) = {({x^2} - {a^2})^{\frac{1}{2}}} + {x^2}{({x^2} - {a^2})^{ - \frac{1}{2}}}\)</p>
<p>both parts of the expression are positive hence \(g'(x)\) is positive <strong><em>R1</em></strong></p>
<p>and therefore \(g\) is an increasing function (for \(\left| x \right| > a\)) <strong><em>AG</em></strong></p>
<p><strong><em>[4 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.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The functions \(f\) and \(g\) are defined by \(f(x) = 2x + \frac{\pi }{5},{\text{ }}x \in \mathbb{R}\) and \(g(x) = 3\sin x + 4,{\text{ }}x \in \mathbb{R}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that \(g \circ f(x) = 3\sin \left( {2x + \frac{\pi }{5}} \right) + 4\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the range of \(g \circ f\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Given that \(g \circ f\left( {\frac{{3\pi }}{{20}}} \right) = 7\), find the next value of \(x\), greater than \({\frac{{3\pi }}{{20}}}\), for which \(g \circ f(x) = 7\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The graph of \(y = g \circ f(x)\) can be obtained by applying four transformations to the graph of \(y = \sin x\). State what the four transformations represent geometrically and give the order in which they are applied.</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 class="p1">\(g \circ f(x) = g\left( {f(x)} \right)\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p1">\( = g\left( {2x + \frac{\pi }{5}} \right)\)</p>
<p class="p1">\( = 3\sin \left( {2x + \frac{\pi }{5}} \right) + 4\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>AG</em></strong></span></p>
<p class="p1"><span class="s1"><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>since \( - 1 \le sin \theta \le + 1\), range is \([1,{\text{ }}7]\) <strong><em>(R1)A1</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(3\sin \left( {2x + \frac{\pi }{5}} \right) + 4 = 7 \Rightarrow 2x + \frac{\pi }{5} = \frac{\pi }{2} + 2n\pi \Rightarrow x = \frac{{3\pi }}{{20}} + n\pi \) <strong><em>(M1)</em></strong></p>
<p>so next biggest value is \(\frac{{23\pi }}{{20}}\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Allow use of period.</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 class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Transformations can be in any order but see notes below.</p>
<p class="p2"> </p>
<p class="p3">stretch scale factor \(3\) parallel to <span class="s1"><em>\(y\) </em></span>axis (vertically) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p3">vertical translation of \(4\) up <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"> </p>
<p class="p3"><span class="s2"><strong>Note: <span class="Apple-converted-space"> </span></strong>Vertical translation is </span>\(\frac{4}{3}\) up if it occurs before stretch parallel to <span class="s1"><em>\(y\) </em></span>axis.</p>
<p class="p4"> </p>
<p class="p3">stretch scale factor \(\frac{1}{2}\) parallel to <span class="s1"><em>\(x\) </em></span>axis (horizontally) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p3">horizontal translation of \(\frac{\pi }{{10}}\) to the left <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p4"> </p>
<p class="p3"><span class="s2"><strong>Note: <span class="Apple-converted-space"> </span></strong>Horizontal translation is </span>\(\frac{\pi }{{5}}\) to the left if it occurs before stretch parallel to <span class="s1"><em>\(x\) </em></span>axis.</p>
<p class="p4"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>A1 </em></strong>for magnitude and direction in each case.</p>
<p class="p1">Accept any correct terminology provided that the meaning is clear <em>eg </em>shift for translation.</p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<p class="p1"><strong><em>Total [9 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;">
<p class="p1">Well done.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Generally well done, some used more complicated methods rather than considering the range of sine.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Fine if they realised the period was \(\pi \), not if they thought it was \(2\pi \).</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Typically 3 marks were gained. It was the shift in the axis \(\chi \) of \(\frac{\pi }{{10}}\) that caused the problem.</p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider the functions \(f(x) = \tan x,{\text{ }}0 \le \ x < \frac{\pi }{2}\) and \(g(x) = \frac{{x + 1}}{{x - 1}},{\text{ }}x \in \mathbb{R},{\text{ }}x \ne 1\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find an expression for \(g \circ f(x)\), stating its domain.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Hence show that \(g \circ f(x) = \frac{{\sin x + \cos x}}{{\sin x - \cos x}}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Let \(y = g \circ f(x)\)<span class="s1">, find an exact value for \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) </span>at the point on the graph of \(y = g \circ f(x)\) where \(x = \frac{\pi }{6}\), expressing your answer in the form \(a + b\sqrt 3 ,{\text{ }}a,{\text{ }}b \in \mathbb{Z}\).</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>Show that the area bounded by the graph of \(y = g \circ f(x)\), the \(x\)-axis and the lines \(x = 0\) and \(x = \frac{\pi }{6}\) is \(\ln \left( {1 + \sqrt 3 } \right)\).</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 class="p1">\(g \circ f(x) = \frac{{\tan x + 1}}{{\tan x - 1}}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1">\(x \ne \frac{\pi }{4},{\text{ }}0 \le x < \frac{\pi }{2}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><span class="s1"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\frac{{\tan x + 1}}{{\tan x - 1}} = \frac{{\frac{{\sin x}}{{\cos x}} + 1}}{{\frac{{\sin x}}{{\cos x}} - 1}}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p1">\( = \frac{{\sin x + \cos x}}{{\sin x - \cos x}}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>AG</em></strong></span></p>
<p class="p1"><span class="s1"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{(\sin x - \cos x)(\cos x - \sin x) - (\sin x + \cos x)(\cos x + \sin x)}}{{{{(\sin x - \cos x)}^2}}}\) <strong><em>M1(A1)</em></strong></p>
<p>\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{(2\sin x\cos x - {{\cos }^2}x - {{\sin }^2}x) - (2\sin x\cos x + {{\cos }^2}x + {{\sin }^2}x)}}{{{{\cos }^2}x + {{\sin }^2}x - 2\sin x\cos x}}\)</p>
<p>\( = \frac{{ - 2}}{{1 - \sin 2x}}\)</p>
<p>Substitute \(\frac{\pi }{6}\) into any formula for \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) <strong><em>M1</em></strong></p>
<p>\(\frac{{ - 2}}{{1 - \sin \frac{\pi }{3}}}\)</p>
<p>\( = \frac{{ - 2}}{{1 - \frac{{\sqrt 3 }}{2}}}\) <strong><em>A1</em></strong></p>
<p>\( = \frac{{ - 4}}{{2 - \sqrt 3 }}\)</p>
<p>\( = \frac{{ - 4}}{{2 - \sqrt 3 }}\left( {\frac{{2 + \sqrt 3 }}{{2 + \sqrt 3 }}} \right)\) <strong><em>M1</em></strong></p>
<p>\( = \frac{{ - 8 - 4\sqrt 3 }}{1} = - 8 - 4\sqrt 3 \) <strong><em>A1</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{(\tan x - 1){{\sec }^2}x - (\tan x + 1){{\sec }^2}x}}{{{{(\tan x - 1)}^2}}}\) <strong><em>M1A1</em></strong></p>
<p>\( = \frac{{ - 2{{\sec }^2}x}}{{{{(\tan x - 1)}^2}}}\) <strong><em>A1</em></strong></p>
<p>\( = \frac{{ - 2{{\sec }^2}\frac{\pi }{6}}}{{{{\left( {\tan \frac{\pi }{6} - 1} \right)}^2}}} = \frac{{ - 2\left( {\frac{4}{3}} \right)}}{{{{\left( {\frac{1}{{\sqrt 3 }} - 1} \right)}^2}}} = \frac{{ - 8}}{{{{\left( {1 - \sqrt 3 } \right)}^2}}}\) <strong><em>M1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>M1 </em></strong>for substitution \(\frac{\pi }{6}\).</p>
<p> </p>
<p>\(\frac{{ - 8}}{{{{\left( {1 - \sqrt 3 } \right)}^2}}} = \frac{{ - 8}}{{\left( {4 - 2\sqrt 3 } \right)}}\frac{{\left( {4 + 2\sqrt 3 } \right)}}{{\left( {4 + 2\sqrt 3 } \right)}} = - 8 - 4\sqrt 3 \) <strong><em>M1A1</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>Area \(\left| {\int_0^{\frac{\pi }{6}} {\frac{{\sin x + \cos x}}{{\sin x - \cos x}}{\text{d}}x} } \right|\) <strong><em>M1</em></strong></p>
<p>\( = \left| {\left[ {\ln \left| {\sin x - \cos x} \right|} \right]_0^{\frac{\pi }{6}}} \right|\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Condone absence of limits and absence of modulus signs at this stage.</p>
<p> </p>
<p>\( = \left| {\ln \left| {\sin \frac{\pi }{6} - \cos \frac{\pi }{6}} \right| - \ln \left| {\sin 0 - \cos 0} \right|} \right|\) <strong><em>M1</em></strong></p>
<p>\( = \left| {\ln \left| {\frac{1}{2} - \frac{{\sqrt 3 }}{2}} \right| - 0} \right|\)</p>
<p>\( = \left| {\ln \left( {\frac{{\sqrt 3 - 1}}{2}} \right)} \right|\) <strong><em>A1</em></strong></p>
<p>\( = - \ln \left( {\frac{{\sqrt 3 - 1}}{2}} \right) = \ln \left( {\frac{2}{{\sqrt 3 - 1}}} \right)\) <strong><em>A1</em></strong></p>
<p>\( = \ln \left( {\frac{2}{{\sqrt 3 - 1}} \times \frac{{\sqrt 3 + 1}}{{\sqrt 3 + 1}}} \right)\) <strong><em>M1</em></strong></p>
<p>\( = \ln \left( {\sqrt 3 + 1} \right)\) <strong><em>AG</em></strong></p>
<p><strong><em>[6 marks]</em></strong></p>
<p><strong><em>Total [16 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 \(f(x) = \frac{1}{{{x^2} + 3x + 2}},{\text{ }}x \in \mathbb{R},{\text{ }}x \ne - 2,{\text{ }}x \ne - 1\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Express \({x^2} + 3x + 2\) in the form \({(x + h)^2} + k\).</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>Factorize \({x^2} + 3x + 2\).</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>Sketch the graph of \(f(x)\), indicating on it the equations of the asymptotes, the coordinates of the \(y\)-intercept and the local maximum.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that \(\frac{1}{{x + 1}} - \frac{1}{{x + 2}} = \frac{1}{{{x^2} + 3x + 2}}\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find the value of \(p\) if \(\int_0^1 {f(x){\text{d}}x = \ln (p)} \).</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>Sketch the graph of \(y = f\left( {\left| x \right|} \right)\).</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>Determine the area of the region enclosed between the graph of \(y = f\left( {\left| x \right|} \right)\), the \(x\)-axis and the lines with equations \(x = - 1\) and \(x = 1\).</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>\({x^2} + 3x + 2 = {\left( {x + \frac{3}{2}} \right)^2} - \frac{1}{4}\) <strong><em>A1</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>\({x^2} + 3x + 2 = (x + 2)(x + 1)\) <strong><em>A1</em></strong></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><img src="images/Schermafbeelding_2017-08-08_om_13.58.40.png" alt="M17/5/MATHL/HP1/ENG/TZ1/B11.b/M"></p>
<p><strong><em>A1</em></strong> for the shape</p>
<p><strong><em>A1</em></strong> for the equation \(y = 0\)</p>
<p><strong><em>A1</em></strong> for asymptotes \(x = - 2\) and \(x = - 1\)</p>
<p><strong><em>A1</em></strong> for coordinates \(\left( { - \frac{3}{2},{\text{ }} - 4} \right)\)</p>
<p><strong><em>A1</em></strong> \(y\)-intercept \(\left( {0,{\text{ }}\frac{1}{2}} \right)\)</p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{1}{{x + 1}} - \frac{1}{{x + 2}} = \frac{{(x + 2) - (x + 1)}}{{(x + 1)(x + 2)}}\) <strong><em>M1</em></strong></p>
<p>\( = \frac{1}{{{x^2} + 3x + 2}}\) <strong><em>AG</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\int\limits_0^1 {\frac{1}{{x + 1}} - \frac{1}{{x + 2}}{\text{d}}x} \)</p>
<p>\( = \left[ {\ln (x + 1) - \ln (x + 2)} \right]_0^1\) <strong><em>A1</em></strong></p>
<p>\( = \ln 2 - \ln 3 - \ln 1 + \ln 2\) <strong><em>M1</em></strong></p>
<p>\( = \ln \left( {\frac{4}{3}} \right)\) <strong><em>M1A1</em></strong></p>
<p>\(\therefore p = \frac{4}{3}\)</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><img src="images/Schermafbeelding_2017-08-08_om_14.20.03.png" alt="M17/5/MATHL/HP1/ENG/TZ1/B11.e/M"></p>
<p>symmetry about the \(y\)-axis <strong><em>M1</em></strong></p>
<p>correct shape <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Allow <strong><em>FT </em></strong>from part (b).</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>\(2\int_0^1 {f(x){\text{d}}x} \) <strong><em>(M1)(A1)</em></strong></p>
<p>\( = 2\ln \left( {\frac{4}{3}} \right)\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Do not award <strong><em>FT </em></strong>from part (e).</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Let \(p(x) = 2{x^5} + {x^4} - 26{x^3} - 13{x^2} + 72x + 36,{\text{ }}x \in \mathbb{R}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">For the polynomial equation \(p(x) = 0\), state</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>the sum of the roots;</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>the product of the roots.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">A new polynomial is defined by \(q(x) = p(x + 4)\).</p>
<p class="p1">Find the sum of the roots of the equation \(q(x) = 0\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>\(\left( { - \frac{{{a_{n - 1}}}}{{{a_n}}} = } \right) - \frac{1}{2}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\(\left( {{{( - 1)}^n}\frac{{{a_0}}}{{{a_n}}} = } \right) - \frac{{36}}{2} = ( - 18)\) <span class="Apple-converted-space"> </span><strong><em>A1A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>First <strong><em>A1 </em></strong>is for the negative sign.</p>
<p class="p1"><em><strong>[3 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>if \(\lambda \) satisfies \(p(\lambda ) = 0\) then \(q(\lambda - 4) = 0\)</p>
<p>so the roots of \(q(x)\) are each \(4\) less than the roots of \(p(x)\) <strong><em>(R1)</em></strong></p>
<p>so sum of roots is \( - \frac{1}{2} - 4 \times 5 = - 20.5\) <strong><em>A1</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>\(p(x + 4) = 2{x^5} + 2 \times 5 \times 4{x^4} \ldots + {x^4} \ldots = 2{x^5} + 41{x^4} \ldots \) <strong><em>(M1)</em></strong></p>
<p>so sum of roots is \( - \frac{{41}}{2} = - 20.5\) <strong><em>A1</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<p><strong><em>Tofal [5 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;">
<p class="p1">Both parts fine if they used the formula, some tried to use the quadratic equivalent formula. Surprisingly some even found all the roots.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Some notation problems for weaker candidates. Good candidates used either of the methods shown in the Markscheme.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Let \(y(x) = x{e^{3x}},{\text{ }}x \in \mathbb{R}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Prove by induction that \(\frac{{{{\text{d}}^n}y}}{{{\text{d}}{x^n}}} = n{3^{n - 1}}{{\text{e}}^{3x}} + x{3^n}{{\text{e}}^{3x}}\) for \(n \in {\mathbb{Z}^ + }\).</p>
<div class="marks">[7]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the coordinates of any local maximum and minimum points on the graph of \(y(x)\).</p>
<p class="p1">Justify whether any such point is a maximum or a minimum.</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 class="p1">Find the coordinates of any points of inflexion on the graph of \(y(x)\). Justify whether any such point is a point of inflexion.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Hence sketch the graph of \(y(x)\), indicating clearly the points found in parts (c) and (d) and any intercepts with the axes.</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 class="p1">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 1 \times {{\text{e}}^{3x}} + x \times 3{{\text{e}}^{3x}} = ({{\text{e}}^{3x}} + 3x{{\text{e}}^{3x}})\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p1"><span class="s1"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">let \(P(n)\) be the statement \(\frac{{{{\text{d}}^n}y}}{{{\text{d}}{x^n}}} = n{3^{n - 1}}{{\text{e}}^{3x}} + x{3^n}{{\text{e}}^{3x}}\)</p>
<p class="p1">prove for \(n = 1\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p1"><span class="s1">\(LHS\) of </span>\(P(1)\) is \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) which is \(1 \times {{\text{e}}^{3x}} + x \times 3{{\text{e}}^{3x}}\) and <span class="s1">\(RHS\)</span> is \({3^0}{{\text{e}}^{3x}} + x{3^1}{{\text{e}}^{3x}}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>R1</em></strong></span></p>
<p class="p1"><span class="s1">as </span>\({\text{LHS}} = {\text{RHS, }}P(1)\) is true</p>
<p class="p1">assume \(P(k)\) is true and attempt to prove \(P(k + 1)\) is true <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">assuming \(\frac{{{{\text{d}}^k}y}}{{{\text{d}}{x^k}}} = k{3^{k - 1}}{{\text{e}}^{3x}} + x{3^k}{{\text{e}}^{3x}}\)</p>
<p class="p1">\(\frac{{{{\text{d}}^{k + 1}}y}}{{{\text{d}}{x^{k + 1}}}} = \frac{{\text{d}}}{{{\text{d}}x}}\left( {\frac{{{{\text{d}}^k}y}}{{{\text{d}}{x^k}}}} \right)\) <span class="Apple-converted-space"> </span><span class="s1">(<strong><em>M1)</em></strong></span></p>
<p class="p1">\( = k{3^{k - 1}} \times 3{{\text{e}}^{3x}} + 1 \times {3^k}{{\text{e}}^{3x}} + x{3^k} \times 3{{\text{e}}^{3x}}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1">\( = (k + 1){3^k}{{\text{e}}^{3x}} + x{3^{k + 1}}{{\text{e}}^{3x}}\;\;\;\)<span class="s1">(as required) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Can award the <strong><em>A </em></strong>marks independent of the <strong><em>M </em></strong>marks</p>
<p class="p4"> </p>
<p class="p1">since \(P(1)\) is true and \(P(k)\) is true \( \Rightarrow P(k + 1)\) is true</p>
<p class="p1">then (by <span class="s1">\(PMI\)</span>), \(P(n)\) is true \((\forall n \in {\mathbb{Z}^ + })\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>R1</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: </strong>To gain last <strong><em>R1 </em></strong>at least four of the above marks must have been gained.</p>
<p class="p3"><em><strong>[7 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\({{\text{e}}^{3x}} + x \times 3{{\text{e}}^{3x}} = 0 \Rightarrow 1 + 3x = 0 \Rightarrow x = - \frac{1}{3}\) <strong><em>M1A1</em></strong></p>
<p>point is \(\left( { - \frac{1}{3},{\text{ }} - \frac{1}{{3{\text{e}}}}} \right)\) <strong><em>A1</em></strong></p>
<p><strong>EITHER</strong></p>
<p>\(\frac{{{{\text{d}}^2}y}}{{{\text{d}}{x^2}}} = 2 \times 3{{\text{e}}^{3x}} + x \times {3^2}{{\text{e}}^{3x}}\)</p>
<p>when \(x = - \frac{1}{3},{\text{ }}\frac{{{{\text{d}}^2}y}}{{{\text{d}}{x^2}}} > 0\) therefore the point is a minimum <strong><em>M1A1</em></strong></p>
<p><strong>OR</strong></p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-22_om_17.44.19.png" alt></p>
<p class="p1">nature table shows point is a minimum <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p1"><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{{{\text{d}}^2}y}}{{{\text{d}}{x^2}}} = 2 \times 3{{\text{e}}^{3x}} + x \times {3^2}{{\text{e}}^{3x}}\) <strong><em>A1</em></strong></p>
<p>\(2 \times 3{{\text{e}}^{3x}} + x \times {3^2}{{\text{e}}^{3x}} = 0 \Rightarrow 2 + 3x = 0 \Rightarrow x = - \frac{2}{3}\) <strong><em>M1A1</em></strong></p>
<p>point is \(\left( { - \frac{2}{3},{\text{ }} - \frac{2}{{3{{\text{e}}^2}}}} \right)\) <strong><em>A1</em></strong></p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-22_om_17.52.15.png" alt></p>
<p>since the curvature does change (concave down to concave up) it is a point of inflection <strong><em>R1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Allow \({3^{{\text{rd}}}}\) derivative is not zero at \( - \frac{2}{3}\)</p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="image.html" alt></p>
<p class="p1">(general shape including asymptote and through origin) <strong><em>A1</em></strong></p>
<p class="p1">showing minimum and point of inflection <strong><em>A1</em></strong></p>
<p class="p1"> </p>
<p class="p1"><strong>Note: </strong>Only indication of position of answers to (c) and (d) required, not coordinates.</p>
<p class="p1"><em><strong>[2 marks]</strong></em></p>
<p class="p1"><em><strong>Total [21 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Well done.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">The logic of an induction proof was not known well enough. Many candidates used what they had to prove rather than differentiating what they had assumed. They did not have enough experience in doing Induction proofs.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Good, some forgot to test for min/max, some forgot to give the \(y\) value.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Again quite good, some forgot to check for change in curvature and some forgot the \(y\) value.</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Some accurate sketches, some had all the information from earlier parts but could not apply it. The asymptote was often missed.</p>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="question">
<p class="p1">The quadratic equation \({x^2} - 2kx + (k - 1) = 0\) has roots \(\alpha \) and \(\beta \) such that \({\alpha ^2} + {\beta ^2} = 4\). Without solving the equation, find the possible values of the real number \(k\).</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p class="p1"><span class="Apple-converted-space">\(\alpha + \beta = 2k\) </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(\alpha \beta = k - 1\) </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\({(\alpha + \beta )^2} = 4{k^2} \Rightarrow {\alpha ^2} + {\beta ^2} + 2\underbrace {\alpha \beta }_{k - 1} = 4{k^2}\) </span><strong><em>(M1)</em></strong></p>
<p class="p1">\({\alpha ^2} + {\beta ^2} = 4{k^2} - 2k + 2\)</p>
<p class="p1"><span class="Apple-converted-space">\({\alpha ^2} + {\beta ^2} = 4 \Rightarrow 4{k^2} - 2k - 2 = 0\) </span><strong><em>A1</em></strong></p>
<p class="p1">attempt to solve quadratic <span class="Apple-converted-space"> </span>(<strong><em>M1)</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(k = 1,{\text{ }} - \frac{1}{2}\) </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[6 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>A given polynomial function is defined as \(f(x) = {a_0} + {a_1}x + {a_2}{x^2} + \ldots + {a_n}{x^n}\). The roots of the polynomial equation \(f(x) = 0\) are consecutive terms of a geometric sequence with a common ratio of \(\frac{1}{2}\) and first term 2.</p>
<p>Given that \({a_{n - 1}} = - 63\) and \({a_n} = 16\) find</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">the degree of the polynomial;</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">the value of \({a_0}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">the sum of the roots of the polynomial \( = \frac{{63}}{{16}}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1">\(2\left( {\frac{{1 - {{\left( {\frac{1}{2}} \right)}^n}}}{{1 - \frac{1}{2}}}} \right) = \frac{{63}}{{16}}\) <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>The formula for the sum of a geometric sequence must be equated to a value for the <strong><em>M1 </em></strong>to be awarded.</p>
<p class="p4"> </p>
<p class="p1">\(1 - {\left( {\frac{1}{2}} \right)^n} = \frac{{63}}{{64}} \Rightarrow {\left( {\frac{1}{2}} \right)^n} = \frac{1}{{64}}\)</p>
<p class="p1">\(n = 6\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><span class="s1"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\frac{{{a_0}}}{{{a_n}}} = 2 \times 1 \times \frac{1}{2} \times \frac{1}{4} \times \frac{1}{8} \times \frac{1}{{16}},{\text{ (}}{{\text{a}}_n} = 16)\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">\({a_0} = 16 \times 2 \times 1 \times \frac{1}{2} \times \frac{1}{4} \times \frac{1}{8} \times \frac{1}{{16}}\)</p>
<p class="p1">\({a_0} = {2^{ - 5}}\;\;\;\left( { = \frac{1}{{32}}} \right)\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<p class="p1"><strong><em>Total [6 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the function <em>f</em> , where \(f(x) = \arcsin (\ln x)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Find the domain of <em>f</em> .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Find \({f^{ - 1}}(x)\).</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \( - 1 \leqslant \ln x \leqslant 1\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow \frac{1}{{\text{e}}} \leqslant x \leqslant {\text{e}}\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) \(y = \arcsin (\ln x) \Rightarrow \ln x = \sin y\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\ln y = \sin x \Rightarrow y = {{\text{e}}^{\sin x}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow {f^{ - 1}}(x) = {{\text{e}}^{\sin x}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Very few candidates attempted part (a), and of those that did, few were successful. Part (b) was answered fairly well by most candidates.</span></p>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that \(\frac{1}{{\sqrt n + \sqrt {n + 1} }} = \sqrt {n + 1} - \sqrt n \) where \(n \ge 0,{\text{ }}n \in \mathbb{Z}\).</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 show that \(\sqrt 2 - 1 < \frac{1}{{\sqrt 2 }}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Prove, by mathematical induction, that \(\sum\limits_{r = 1}^{r = n} {\frac{1}{{\sqrt r }} > \sqrt n } \) for \(n \ge 2,{\text{ }}n \in \mathbb{Z}\).</p>
<div class="marks">[9]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{1}{{\sqrt n + \sqrt {n + 1} }} = \frac{1}{{\sqrt n + \sqrt {n + 1} }} \times \frac{{\sqrt {n + 1} - \sqrt n }}{{\sqrt {n + 1} - \sqrt n }}\) <strong><em>M1</em></strong></p>
<p>\( = \frac{{\sqrt {n + 1} - \sqrt n }}{{(n + 1) - n}}\) <strong><em>A1</em></strong></p>
<p>\( = \sqrt {n + 1} - \sqrt n \) <strong><em>AG</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>\(\sqrt 2 - 1 = \frac{1}{{\sqrt 2 + \sqrt 1 }}\) <strong><em>A2</em></strong></p>
<p>\( < \frac{1}{{\sqrt 2 }}\) <strong><em>AG</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>consider the case \(n = 2\): required to prove that \(1 + \frac{1}{{\sqrt 2 }} > \sqrt 2 \) <strong><em>M1</em></strong></p>
<p>from part (b) \(\frac{1}{{\sqrt 2 }} > \sqrt 2 - 1\)</p>
<p>hence \(1 + \frac{1}{{\sqrt 2 }} > \sqrt 2 \) is true for \(n = 2\) <strong><em>A1</em></strong></p>
<p>now assume true for \(n = k:\sum\limits_{r = 1}^{r = k} {\frac{1}{{\sqrt r }} > \sqrt k } \) <strong><em>M1</em></strong></p>
<p>\(\frac{1}{{\sqrt 1 }} + \ldots + \frac{{\sqrt 1 }}{{\sqrt k }} > \sqrt k \)</p>
<p>attempt to prove true for \(n = k + 1:\frac{1}{{\sqrt 1 }} + \ldots + \frac{{\sqrt 1 }}{{\sqrt k }} + \frac{1}{{\sqrt {k + 1} }} > \sqrt {k + 1} \) (<strong><em>M1)</em></strong></p>
<p>from assumption, we have that \(\frac{1}{{\sqrt 1 }} + \ldots + \frac{{\sqrt 1 }}{{\sqrt k }} + \frac{1}{{\sqrt {k + 1} }} > \sqrt k + \frac{1}{{\sqrt {k + 1} }}\) <strong><em>M1</em></strong></p>
<p>so attempt to show that \(\sqrt k + \frac{1}{{\sqrt {k + 1} }} > \sqrt {k + 1} \) <strong>(<em>M1)</em></strong></p>
<p><strong>EITHER</strong></p>
<p>\(\frac{1}{{\sqrt {k + 1} }} > \sqrt {k + 1} - \sqrt k \) <strong><em>A1</em></strong></p>
<p>\(\frac{1}{{\sqrt {k + 1} }} > \frac{1}{{\sqrt k + \sqrt {k + 1} }}\), (from part a), which is true <strong><em>A1</em></strong></p>
<p><strong>OR</strong></p>
<p>\(\sqrt k + \frac{1}{{\sqrt {k + 1} }} = \frac{{\sqrt {k + 1} \sqrt k + 1}}{{\sqrt {k + 1} }}\) <strong><em>A1</em></strong></p>
<p>\( > \frac{{\sqrt k \sqrt k + 1}}{{\sqrt {k + 1} }} = \sqrt {k + 1} \) <strong><em>A1</em></strong></p>
<p><strong>THEN</strong></p>
<p>so true for \(n = 2\) and \(n = k\) true \( \Rightarrow n = k + 1\) true. Hence true for all \(n \ge 2\) <strong><em>R1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>R1 </em></strong>only if all previous <strong><em>M </em></strong>marks have been awarded.</p>
<p><em><strong>[9 marks]</strong></em></p>
<p><em><strong>Total [13 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(g(x) = {\log _5}\left| {2{{\log }_3}x} \right|\) . Find the product of the zeros of <em>g</em> .</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(g(x) = 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\log _5}\left| {2{{\log }_3}x} \right| = 0\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\left| {2{{\log }_3}x} \right| = 1\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\log _3}x = \pm \frac{1}{2}\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = {3^{ \pm \frac{1}{2}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so the product of the zeros of <em>g</em> is \({3^{\frac{1}{2}}} \times {3^{ - \frac{1}{2}}} = 1\) <strong><em>A1</em></strong> <strong><em>N0</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">There were many candidates showing difficulties in manipulating logarithms and the absolute value to solve the equation.</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">The functions \(f\) and \(g\) are defined by \(f(x) = a{x^2} + bx + c,{\text{ }}x \in \mathbb{R}\) and \(g(x) = p\sin x + qx + r,{\text{ }}x \in \mathbb{R}\) where \(a,{\text{ }}b,{\text{ }}c,{\text{ }}p,{\text{ }}q,{\text{ }}r\) are real constants.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Given that \(f\) is an even function, show that \(b = 0\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Given that \(g\) is an odd function, find the value of \(r\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The function \(h\) is both odd and even, with domain \(\mathbb{R}\).</p>
<p class="p1">Find \(h(x)\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>EITHER</strong></p>
<p class="p2">\(f( - x) = f(x)\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p2">\( \Rightarrow a{x^2} - bx + c = a{x^2} + bx + c \Rightarrow 2bx = 0,{\text{ }}(\forall x \in \mathbb{R})\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">\(y\)-axis is eqn of symmetry <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p2">so \(\frac{{ - b}}{{2a}} = 0\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong>THEN</strong></p>
<p class="p2">\( \Rightarrow b = 0\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>AG</em></strong></span></p>
<p class="p2"><span class="s1"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(g( - x) = - g(x) \Rightarrow p\sin ( - x) - qx + r = - p\sin x - qx - r\)</p>
<p>\( \Rightarrow - p\sin x - qx + r = - p\sin x - qx - r\) <strong><em>M1</em></strong></p>
<p> </p>
<p><strong>Note: <em>M1 </em></strong>is for knowing properties of sin.</p>
<p> </p>
<p>\( \Rightarrow 2r = 0 \Rightarrow r = 0\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>In (a) and (b) allow substitution of a particular value of \(x\)</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>\(h( - x) = h(x) = - h(x) \Rightarrow 2h(x) = 0 \Rightarrow h(x) = 0,{\text{ }}(\forall x)\) <strong><em>M1A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Accept geometrical explanations.</p>
<p><em><strong>[2 marks]</strong></em></p>
<p><em><strong>Total [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 class="p1">Sometimes backwards working but many correct approaches.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Some candidates did not know what odd and even functions were. Correct solutions from those who applied the definition.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Some realised: just apply the definitions. Some did very strange things involving \(f\) and \(g\).</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the polynomial \(q(x) = 3{x^3} - 11{x^2} + kx + 8\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that \(q(x)\) has a factor \((x - 4)\), find the value of \(k\).</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 or otherwise, factorize \(q(x)\) as a product of linear factors.</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>\(q(4) = 0\) <strong><em>(M1)</em></strong></p>
<p>\(192 - 176 + 4k + 8 = 0{\text{ }}(24 + 4k = 0)\) <strong><em>A1</em></strong></p>
<p>\(k = - 6\) <strong><em>A1</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>\(3{x^3} - 11{x^2} - 6x + 8 = (x - 4)(3{x^2} + px - 2)\)</p>
<p>equate coefficients of \({x^2}\): <strong><em>(M1)</em></strong></p>
<p>\( - 12 + p = - 11\)</p>
<p>\(p = 1\)</p>
<p>\((x - 4)(3{x^2} + x - 2)\) <strong><em>(A1)</em></strong></p>
<p>\((x - 4)(3x - 2)(x + 1)\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Allow part (b) marks if any of this work is seen in part (a).</p>
<p> </p>
<p><strong>Note:</strong> Allow equivalent methods (<em>eg</em>, synthetic division) for the <strong><em>M </em></strong>marks in each part.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the polynomial \(P\left( z \right) = {z^5} - 10{z^2} + 15z - 6,{\text{ }}z \in \mathbb{C}\).</p>
</div>
<div class="specification">
<p>The polynomial can be written in the form \(P(z) = {(z - 1)^3}({z^2} + bz + c)\).</p>
</div>
<div class="specification">
<p>Consider the function \(q\left( x \right) = {x^5} - 10{x^2} + 15x - 6,{\text{ }}x \in \mathbb{R}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the sum and the product of the roots of \(P(z) = 0\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that \((z - 1)\) is a factor of \(P(z)\).</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 \(b\) and the value of \(c\).</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>Hence find the complex roots of \(P(z) = 0\).</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 graph of \(y = q(x)\) is concave up for \(x > 1\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of \(y = q(x)\) showing clearly any intercepts with the axes.</p>
<div class="marks">[3]</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>\({\text{sum}} = 0\) <strong><em>A1</em></strong></p>
<p>\({\text{product}} = 6\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(P(1) = 1 - 10 + 15 - 6 = 0\) <strong><em>M1A1</em></strong></p>
<p>\( \Rightarrow (z - 1)\) is a factor of \(P(z)\) <strong><em>AG</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept use of division to show remainder is zero.</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><strong>METHOD 1</strong></p>
<p>\({(z - 1)^3}\left( {{z^2} + bz + c} \right) = {z^5} - 10{z^2} + 15z - 6\) <strong><em>(M1)</em></strong></p>
<p>by inspection \(c = 6\) <strong><em>A1</em></strong></p>
<p>\(({z^3} - 3{z^2} + 3z - 1)({z^2} + bz + 6) = {z^5} - 10{z^2} + 15z - 6\) <strong><em>(M1)(A1)</em></strong></p>
<p>\(b = 3\) <strong><em>A1</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>\(\alpha \), \(\beta \) are two roots of the quadratic</p>
<p>\(b = - (\alpha + \beta ),{\text{ }}c = \alpha \beta \) <strong><em>(A1)</em></strong></p>
<p>from part (a) \(1 + 1 + 1 + \alpha + \beta = 0\) <strong><em>(M1)</em></strong></p>
<p>\( \Rightarrow b = 3\) <strong><em>A1</em></strong></p>
<p>\(1 \times 1 \times 1 \times \alpha \beta = 6\) <strong><em>(M1)</em></strong></p>
<p>\( \Rightarrow c = 6\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>FT </em></strong>if \(b = - 7\) following through from their sum \( = 10\).</p>
<p> </p>
<p><strong>METHOD 3</strong></p>
<p>\(({z^5} - 10{z^2} + 15z - 6) \div (z - 1) = {z^4} + {z^3} + {z^2} - 9z + 6\) <strong><em>(M1)A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> This may have been seen in part (b).</p>
<p> </p>
<p>\({z^4} + {z^3} + {z^2} - 9z + 6 \div (z - 1) = {z^3} + 2{z^2} + 3z - 6\) <strong><em>(M1)</em></strong></p>
<p>\({z^3} + 2{z^2} + 3z - 6 \div (z - 1) = {z^2} + 3z + 6\) <strong><em>A1A1</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\({z^2} + 3z + 6 = 0\) <strong><em>M1</em></strong></p>
<p>\(z = \frac{{ - 3 \pm \sqrt {9 - 4 \bullet 6} }}{2}\) <strong><em>M1</em></strong></p>
<p>\( = \frac{{ - 3 \pm \sqrt { - 15} }}{2}\)</p>
<p>\(z = - \frac{3}{2} \pm \frac{{{\text{i}}\sqrt {15} }}{2}\) <strong><em>A1</em></strong></p>
<p>(or \(z = 1\))</p>
<p> </p>
<p><strong>Notes:</strong> Award the second <strong><em>M1 </em></strong>for an attempt to use the quadratic formula or to complete the square.</p>
<p>Do not award <strong><em>FT </em></strong>from (c).</p>
<p> </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>\(\frac{{{{\text{d}}^2}y}}{{{\text{d}}{x^2}}} = 20{x^3} - 20\) <strong><em>M1A1</em></strong></p>
<p>for \(x > 1,{\text{ }}20{x^3} - 20 > 0 \Rightarrow \) concave up <strong><em>R1AG</em></strong></p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2017-08-08_om_16.48.38.png" alt="M17/5/MATHL/HP1/ENG/TZ1/B12.e.ii/M"></p>
<p>\(x\)-intercept at \((1,{\text{ }}0)\) <strong><em>A1</em></strong></p>
<p>\(y\)-intercept at \((0,{\text{ }} - 6)\) <strong><em>A1</em></strong></p>
<p>stationary point of inflexion at \((1,{\text{ }}0)\) with correct curvature either side <strong><em>A1</em></strong></p>
<p><strong><em>[3 marks]</em></strong></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="question">
<p class="p1">The function \(f\) is defined as \(f(x) = \frac{{3x + 2}}{{x + 1}},{\text{ }}x \in \mathbb{R},{\text{ }}x \ne - 1\).</p>
<p class="p1">Sketch the graph of \(y = f(x)\), clearly indicating and stating the equations of any asymptotes and the coordinates of any axes intercepts.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p class="p1"><strong><img src="images/Schermafbeelding_2017-01-27_om_10.01.12.png" alt="M16/5/MATHL/HP1/ENG/TZ2/02/M"> </strong><strong><em>A1A1A1A1A1</em></strong></p>
<p class="p1"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>A1 </em></strong>for correct shape, <strong><em>A1 </em></strong>for \(x = - 1\) clearly stated and asymptote shown, <strong><em>A1 </em></strong>for \(y = 3\) clearly stated and asymptote shown, <strong><em>A1 </em></strong><span class="s1">for \(\left( { - \frac{2}{3},{\text{ }}0} \right)\) </span>and <strong><em>A1 </em></strong><span class="s1">for \((0,{\text{ }}2)\).</span></p>
<p class="p1"><strong><em>[5 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p class="p1">Another standard question. On this occasion, specific coordinates were asked for, so some otherwise good candidates missed out on a couple of marks which they would have gained through greater care.</p>
</div>
<br><hr><br><div class="specification">
<p class="p1">The cubic equation \({x^3} + p{x^2} + qx + c = 0\)<span class="s1">, has roots \(\alpha ,{\text{ }}\beta ,{\text{ }}\gamma \)</span>. By expanding \((x - \alpha )(x - \beta )(x - \gamma )\) show that</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) \(p = - (\alpha + \beta + \gamma )\);</p>
<p>(ii) \(q = \alpha \beta + \beta \gamma + \gamma \alpha \);</p>
<p>(iii) \(c = - \alpha \beta \gamma \).</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>It is now given that \(p = - 6\) and \(q = 18\) for parts (b) and (c) below.</p>
<p>(i) In the case that the three roots \(\alpha ,{\text{ }}\beta ,{\text{ }}\gamma \) form an arithmetic sequence, show that one of the roots is \(2\).</p>
<p>(ii) Hence determine the value of \(c\).</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">In another case the three roots \(\alpha ,{\text{ }}\beta ,{\text{ }}\gamma \) <span class="s1">form a geometric sequence. Determine the value of \(c\).</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>(i)-(iii) given the three roots \(\alpha ,{\text{ }}\beta ,{\text{ }}\gamma \), we have</p>
<p>\({x^3} + p{x^2} + qx + c = (x - \alpha )(x - \beta )(x - \gamma )\) <strong><em>M1</em></strong></p>
<p>\( = \left( {{x^2} - (\alpha + \beta )x + \alpha \beta } \right)(x - \gamma )\) <strong><em>A1</em></strong></p>
<p>\( = {x^3} - (\alpha + \beta + \gamma ){x^2} + (\alpha \beta + \beta \gamma + \gamma \alpha )x - \alpha \beta \gamma \) <strong><em>A1</em></strong></p>
<p>comparing coefficients:</p>
<p>\(p = - (\alpha + \beta + \gamma )\) <strong><em>AG</em></strong></p>
<p>\(q = (\alpha \beta + \beta \gamma + \gamma \alpha )\) <strong><em>AG</em></strong></p>
<p>\(c = - \alpha \beta \gamma \) <strong><em>AG</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><strong>METHOD 1</strong></p>
<p>(i) Given \( - \alpha - \beta - \gamma = - 6\)</p>
<p>And \(\alpha \beta + \beta \gamma + \gamma \alpha = 18\)</p>
<p>Let the three roots be \(\alpha ,{\text{ }}\beta ,{\text{ }}\gamma \)</p>
<p>So \(\beta - \alpha = \gamma - \beta \) <strong><em>M1</em></strong></p>
<p>or \(2\beta = \alpha + \gamma \)</p>
<p>Attempt to solve simultaneous equations: <strong><em>M1</em></strong></p>
<p>\(\beta + 2\beta = 6\) <strong><em>A1</em></strong></p>
<p>\(\beta = 2\) <strong><em>AG</em></strong></p>
<p>(ii) \(\alpha + \gamma = 4\)</p>
<p>\(2\alpha + 2\gamma + \alpha \gamma = 18\)</p>
<p>\( \Rightarrow {\gamma ^2} - 4\gamma + 10 = 0\)</p>
<p>\( \Rightarrow \gamma = \frac{{4 \pm {\text{i}}\sqrt {24} }}{2}\) <strong><em>(A1)</em></strong></p>
<p>Therefore \(c = - \alpha \beta \gamma = - \left( {\frac{{4 + {\text{i}}\sqrt {24} }}{2}} \right)\left( {\frac{{4 - {\text{i}}\sqrt {24} }}{2}} \right)2 = - 20\) <strong><em>A1</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>(i) let the three roots be \(\alpha ,{\text{ }}\alpha - d,{\text{ }}\alpha + d\) <strong><em>M1</em></strong></p>
<p>adding roots <strong><em>M1</em></strong></p>
<p>to give \(3\alpha = 6\) <strong><em>A1</em></strong></p>
<p>\(\alpha = 2\) <strong><em>AG</em></strong></p>
<p>(ii) \(\alpha \) is a root, so \({2^3} - 6 \times {2^2} + 18 \times 2 + c = 0\) <strong><em>M1</em></strong></p>
<p>\(8 - 24 + 36 + c = 0\)</p>
<p>\(c = - 20\) <strong><em>A1</em></strong></p>
<p><strong>METHOD 3</strong></p>
<p>(i) let the three roots be \(\alpha ,{\text{ }}\alpha - d,{\text{ }}\alpha + d\) <strong><em>M1</em></strong></p>
<p>adding roots <strong><em>M1</em></strong></p>
<p>to give \(3\alpha = 6\) <strong><em>A1</em></strong></p>
<p>\(\alpha = 2\) <strong><em>AG</em></strong></p>
<p>(ii) \(q = 18 = 2(2 - d) + (2 - d)(2 + d) + 2(2 + d)\) <strong><em>M1</em></strong></p>
<p>\({d^2} = - 6 \Rightarrow d = \sqrt 6 {\text{i}}\)</p>
<p>\( \Rightarrow c = - 20\) <strong><em>A1</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>Given \( - \alpha - \beta - \gamma = - 6\)</p>
<p>And \(\alpha \beta + \beta \gamma + \gamma \alpha = 18\)</p>
<p>Let the three roots be \(\alpha ,{\text{ }}\beta ,{\text{ }}\gamma \).</p>
<p>So \(\frac{\beta }{\alpha } = \frac{\gamma }{\beta }\) <strong><em>M1</em></strong></p>
<p>or \({\beta ^2} = \alpha \gamma \)</p>
<p>Attempt to solve simultaneous equations: <strong><em>M1</em></strong></p>
<p>\(\alpha \beta + \gamma \beta + {\beta ^2} = 18\)</p>
<p>\(\beta (\alpha + \beta + \gamma ) = 18\)</p>
<p>\(6\beta = 18\)</p>
<p>\(\beta = 3\) <strong><em>A1</em></strong></p>
<p>\(\alpha + \gamma = 3,{\text{ }}\alpha = \frac{9}{\gamma }\)</p>
<p>\( \Rightarrow {\gamma ^2} - 3\gamma + 9 = 0\)</p>
<p>\( \Rightarrow \gamma = \frac{{3 \pm {\text{i}}\sqrt {27} }}{2}\) (<strong><em>A1)(A1)</em></strong></p>
<p>Therefore \(c = - \alpha \beta \gamma = - \left( {\frac{{3 + {\text{i}}\sqrt {27} }}{2}} \right)\left( {\frac{{3 - {\text{i}}\sqrt {27} }}{2}} \right)3 = - 27\) <strong><em>A1</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>let the three roots be \(a,{\text{ }}ar,{\text{ }}a{r^2}\) <strong><em>M1</em></strong></p>
<p>attempt at substitution of \(a,{\text{ }}ar,{\text{ }}a{r^2}\) and \(p\) and \(q\) into equations from (a) <strong><em>M1</em></strong></p>
<p>\(6 = a + ar + a{r^2}\left( { = a(1 + r + {r^2})} \right)\) <strong><em>A1</em></strong></p>
<p>\(18 = {a^2}r + {a^2}{r^3} + {a^2}{r^2}\left( { = {a^2}r(1 + r + {r^2})} \right)\) <strong><em>A1</em></strong></p>
<p>therefore \(3 = ar\) <strong><em>A1</em></strong></p>
<p>therefore \(c = - {a^3}{r^3} = - {3^3} = - 27\) <strong><em>A1</em></strong></p>
<p><strong><em>[6 marks]</em></strong></p>
<p><strong><em>Total [14 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the following functions:</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> \(h(x) = \arctan (x),{\text{ }}x \in \mathbb{R}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> \(g(x) = \frac{1}{x}\), \(x\in \mathbb{R}\)</span><span style="font-family: 'times new roman', times; font-size: medium; background-color: #f7f7f7;">, \({\text{ }}x \ne 0\)</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Sketch the graph of \(y = h(x)\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find an expression for the composite function \(h \circ g(x)\) and state its domain.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Given that \(f(x) = h(x) + h \circ g(x)\),</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(i) find \(f'(x)\) in simplified form;</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) show that \(f(x) = \frac{\pi }{2}\) for \(x > 0\).</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Nigel states that \(f\) is an odd function and Tom argues that \(f\) is an even function.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(i) State who is correct and justify your answer.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Hence find the value of \(f(x)\) for \(x < 0\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><img src="images/maths_14a_markscheme.png" alt> <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> <strong><em>A1</em></strong> for correct shape, <strong><em>A1 </em></strong>for asymptotic behaviour at \(y = \pm \frac{\pi }{2}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(h \circ g(x) = \arctan \left( {\frac{1}{x}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">domain of \(h \circ g\) is equal to the domain of \(g:x \in \circ ,{\text{ }}x \ne 0\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \(f(x) = \arctan (x) + \arctan \left( {\frac{1}{x}} \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(x) = \frac{1}{{1 + {x^2}}} + \frac{1}{{1 + \frac{1}{{{x^2}}}}} \times - \frac{1}{{{x^2}}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(x) = \frac{1}{{1 + {x^2}}} + \frac{{ - \frac{1}{{{x^2}}}}}{{\frac{{{x^2} + 1}}{{{x^2}}}}}\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{{1 + {x^2}}} - \frac{1}{{1 + {x^2}}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 0\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) <strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>f </em>is a constant <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">when \(x > 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(1) = \frac{\pi }{4} + \frac{\pi }{4}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{\pi }{2}\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><img src="images/maths_14c_markscheme.png" alt></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">from diagram</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(\theta = \arctan \frac{1}{x}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(\alpha = \arctan x\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(\theta + \alpha = \frac{\pi }{2}\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">hence \(f(x) = \frac{\pi }{2}\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 3</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(\tan \left( {f(x)} \right) = \tan \left( {\arctan (x) + \arctan \left( {\frac{1}{x}} \right)} \right)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{x + \frac{1}{x}}}{{1 - x\left( {\frac{1}{x}} \right)}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">denominator = 0, so \(f(x) = \frac{\pi }{2}{\text{ (for }}x > 0)\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Nigel is correct. <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\arctan (x)\) is an odd function and \(\frac{1}{x}\) is an odd function</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">composition of two odd functions is an odd function and sum of two odd functions is an odd function <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f( - x) = \arctan ( - x) + \arctan \left( { - \frac{1}{x}} \right) = - \arctan (x) - \arctan \left( {\frac{1}{x}} \right) = - f(x)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">therefore <em>f </em>is an odd function. <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \(f(x) = - \frac{\pi }{2}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The function \(f\) is defined by \(f(x) = 2{x^3} + 5,{\text{ }} - 2 \leqslant x \leqslant 2\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the range of \(f\).</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 an expression for \({f^{ - 1}}(x)\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the domain and range of \({f^{ - 1}}\).</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>\( - 11 \leqslant f(x) \leqslant 21\) <strong><em>A1A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> <strong><em>A1 </em></strong>for correct end points, <strong><em>A1 </em></strong>for correct inequalities.</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>\({f^{ - 1}}(x) = \sqrt[3]{{\frac{{x - 5}}{2}}}\) <strong><em>(M1)A1</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\( - 11 \leqslant x \leqslant 21,{\text{ }} - 2 \leqslant {f^{ - 1}}(x) \leqslant 2\) <strong><em>A1A1</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider the function defined by \(f(x) = x\sqrt {1 - {x^2}} \) <span class="s1">on the domain \( - 1 \le x \le 1\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that \(f\) is an odd function.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find \(f'(x)\).</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 \(x\)-coordinates of any local maximum or minimum points.</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 class="p1">Find the range of \(f\).</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 class="p1">Sketch the graph of \(y = f(x)\) indicating clearly the coordinates of the \(x\)-intercepts and any local maximum or minimum points.</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 class="p1">Find the area of the region enclosed by the graph of \(y = f(x)\) and the \(x\)-axis for \(x \ge 0\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that \(\int_{ - 1}^1 {\left| {x\sqrt {1 - {x^2}} } \right|{\text{d}}x > \left| {\int_{ - 1}^1 {x\sqrt {1 - {x^2}} {\text{d}}x} } \right|} \).</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>\(f( - x) = ( - x)\sqrt {1 - {{( - x)}^2}} \) <strong><em>M1</em></strong></p>
<p>\( = - x\sqrt {1 - {x^2}} \)</p>
<p>\( = - f(x)\) <strong><em>R1</em></strong></p>
<p>hence \(f\) is odd <strong><em>AG</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>\(f'(x) = x \bullet \frac{1}{2}{(1 - {x^2})^{ - \frac{1}{2}}} \bullet - 2x + {(1 - {x^2})^{\frac{1}{2}}}\) <strong><em>M1A1A1</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(f'(x) = \sqrt {1 - {x^2}} - \frac{{{x^2}}}{{\sqrt {1 - {x^2}} }}\;\;\;\left( { = \frac{{1 - 2{x^2}}}{{\sqrt {1 - {x^2}} }}} \right)\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>This may be seen in part (b).</p>
<p> </p>
<p><strong>Note: </strong>Do not allow FT from part (b).</p>
<p> </p>
<p>\(f'(x) = 0 \Rightarrow 1 - 2{x^2} = 0\) <strong><em>M1</em></strong></p>
<p>\(x = \pm \frac{1}{{\sqrt 2 }}\) <strong><em>A1</em></strong></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>\(y\)-coordinates of the Max Min Points are \(y = \pm \frac{1}{2}\) <strong><em>M1A1</em></strong></p>
<p>so range of \(f(x)\) is \(\left[ { - \frac{1}{2},{\text{ }}\frac{1}{2}} \right]\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Allow FT from (c) if values of \(x\), within the domain, are used.</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 class="p1"><img src="images/Schermafbeelding_2016-01-28_om_19.00.15.png" alt></p>
<p class="p1">Shape: The graph of an odd function, on the given domain, s-shaped,</p>
<p class="p1">where the max(min) is the right(left) of \(0.5{\text{ }}( - 0.5)\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2">\(x\)-intercepts <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2">turning points <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\({\text{area}} = \int_0^1 {x\sqrt {1 - {x^2}} {\text{d}}x} \) <strong><em>(M1)</em></strong></p>
<p>attempt at “backwards chain rule” or substitution <strong><em>M1</em></strong></p>
<p>\( = - \frac{1}{2}\int_0^1 {( - 2x)\sqrt {1 - {x^2}} {\text{d}}x} \)</p>
<p> </p>
<p><strong>Note: </strong>Condone absence of limits for first two marks.</p>
<p> </p>
<p>\( = \left[ {\frac{2}{3}{{(1 - {x^2})}^{\frac{3}{2}}} \bullet - \frac{1}{2}} \right]_0^1\) <strong><em>A1</em></strong></p>
<p>\( = \left[ { - \frac{1}{3}{{(1 - {x^2})}^{\frac{3}{2}}}} \right]_0^1\)</p>
<p>\( = 0 - \left( { - \frac{1}{3}} \right) = \frac{1}{3}\) <strong><em>A1</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\int_{ - 1}^1 {\left| {x\sqrt {1 - {x^2}} } \right|{\text{d}}x > 0} \) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">\(\left| {\int_{ - 1}^1 {x\sqrt {1 - {x^2}} {\text{d}}x} } \right| = 0\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">so \(\int_{ - 1}^1 {\left| {x\sqrt {1 - {x^2}} } \right|{\text{d}}x > \left| {\int_{ - 1}^1 {x\sqrt {1 - {x^2}} {\text{d}}x} } \right|} \) <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<p class="p1"><strong><em>Total [20 marks]</em></strong></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The function <em>f</em> is defined by</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[f(x) = \left\{ {\begin{array}{*{20}{c}}<br> {2x - 1,}&{x \leqslant 2} \\ <br> {a{x^2} + bx - 5,}&{2 < x < 3} <br>\end{array}} \right.\]<br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">where a , \(b \in \mathbb{R}\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Given that <em>f</em> and its derivative, \(f'\) , are continuous for all values in the domain of <em>f</em> , find the values of <em>a</em> and <em>b</em> .</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Show that <em>f</em> is a one-to-one function.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Obtain expressions for the inverse function \({f^{ - 1}}\) and state their domains.</span></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="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>f</em> continuous \( \Rightarrow \mathop {\lim }\limits_{x \to {2^ - }} f(x) = \mathop {\lim }\limits_{x \to {2^ \div }} f(x)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(4a + 2b = 8\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(x) = \left\{ {\begin{array}{*{20}{c}}<br> {2,}&{x < 2} \\ <br> {2ax + b,}&{2 < x < 3} <br>\end{array}} \right.\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'{\text{ continuous}} \Rightarrow \mathop {\lim }\limits_{x \to {2^ - }} f'(x) = \mathop {\lim }\limits_{x \to {2^ \div }} f'(x)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(4a + b = 2\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">solve simultaneously <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">to obtain <em>a</em> = –1 and <em>b</em> = 6 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">for \(x \leqslant 2,{\text{ }}f'(x) = 2 > 0\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">for \(2 < x < 3,{\text{ }}f'(x) = - 2x + 6 > 0\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">since \(f'(x) > 0\) for all values in the domain of <em>f</em> , <em>f</em> is increasing <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">therefore one-to-one <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 2y - 1 \Rightarrow y = \frac{{x + 1}}{2}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = - {y^2} + 6y - 5 \Rightarrow {y^2} - 6y + x + 5 = 0\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(y = 3 \pm \sqrt {4 - x} \)<br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">therefore</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({f^{ - 1}}(x) = \left\{ {\begin{array}{*{20}{c}}<br> {\frac{{x + 1}}{2},}&{x \leqslant 3} \\ <br> {3 - \sqrt {4 - x} ,}&{3 < x < 4} <br>\end{array}} \right.\) <strong><em>A1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1</em></strong> for the first line and <strong><em>A1A1</em></strong> for the second line.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The function <em>f </em>is defined by</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\[f(x) = \left\{ \begin{array}{r}1 - 2x,\\{\textstyle{3 \over 4}}{(x - 2)^2} - 3,\end{array} \right.\begin{array}{*{20}{c}}{x \le 2}\\{x > 2}\end{array}\]</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Determine whether or not \(f\)is continuous.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The graph of the function \(g\) is obtained by applying the following transformations to the graph of \(f\):</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">a reflection in the \(y\)–axis followed by a translation by the vector \(\left( \begin{array}{l}2\\0\end{array} \right)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find \(g(x)\).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(1 - 2(2) = - 3\) and \(\frac{3}{4}{(2 - 2)^2} - 3 = - 3\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">both answers are the same, hence <em>f</em> is continuous (at \(x = 2\)) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> <strong><em>R1</em></strong> may be awarded for justification using a graph or referring to limits. Do not award <strong><em>A0R1</em></strong>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">reflection in the <em>y</em>-axis</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(f( - x) = \left\{ \begin{array}{r}1 + 2x,\\{\textstyle{3 \over 4}}{(x + 2)^2} - 3,\end{array} \right.\begin{array}{*{20}{c}}{x \ge - 2}\\{x < - 2}\end{array}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>M1 </em></strong>for evidence of reflecting a graph in <em>y</em>-axis.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">translation \(\left( \begin{array}{l}2\\0\end{array} \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(g(x) = \left\{ \begin{array}{r}2x - 3,\\{\textstyle{3 \over 4}}{x^2} - 3,\end{array} \right.\begin{array}{*{20}{c}}{x \ge 0}\\{x < 0}\end{array}\) <strong><em>(M1)A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for attempting to substitute \((x - 2)\) for <span style="font: 20.0px 'Times New Roman';"><em>x</em></span>, or </span><span style="font-family: 'times new roman', times; font-size: medium;">translating a graph along positive <em>x</em>-axis.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> Award <strong><em>A1 </em></strong>for the correct domains (this mark can be awarded independent of the <strong><em>M1</em></strong>).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> Award <strong><em>A1 </em></strong>for the correct expressions.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of \(y = \frac{{1 - 3x}}{{x - 2}}\), showing clearly any asymptotes and stating the coordinates of any points of intersection with the axes.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-07_om_17.42.06.png" alt="N17/5/MATHL/HP1/ENG/TZ0/06.a"></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 or otherwise, solve the inequality \(\left| {\frac{{1 - 3x}}{{x - 2}}} \right| < 2\).</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><img src="images/Schermafbeelding_2018-02-07_om_17.44.18.png" alt="N17/5/MATHL/HP1/ENG/TZ0/06.a/M"></p>
<p>correct vertical asymptote <strong><em>A1</em></strong></p>
<p>shape including correct horizontal asymptote <strong><em>A1</em></strong></p>
<p>\(\left( {\frac{1}{3},{\text{ }}0} \right)\) <strong><em>A1</em></strong></p>
<p>\(\left( {0,{\text{ }} - \frac{1}{2}} \right)\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept \(x = \frac{1}{3}\) and \(y = - \frac{1}{2}\) marked on the axes.</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p><img src="images/Schermafbeelding_2018-02-07_om_18.03.17.png" alt="N17/5/MATHL/HP1/ENG/TZ0/06.b/M"></p>
<p>\(\frac{{1 - 3x}}{{x - 2}} = 2\) <strong><em>(M1)</em></strong></p>
<p>\( \Rightarrow x = 1\) <strong><em>A1</em></strong></p>
<p>\( - \left( {\frac{{1 - 3x}}{{x - 2}}} \right) = 2\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award this <strong><em>M1 </em></strong>for the line above or a correct sketch identifying a second critical value.</p>
<p> </p>
<p>\( \Rightarrow x = - 3\) <strong><em>A1</em></strong></p>
<p>solution is \( - 3 < x < 1\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>\(\left| {1 - 3x} \right| < 2\left| {x - 2} \right|,{\text{ }}x \ne 2\)</p>
<p>\(1 - 6x + 9{x^2} < 4({x^2} - 4x + 4)\) <strong><em>(M1)A1</em></strong></p>
<p>\(1 - 6x + 9{x^2} < 4{x^2} - 16x + 16\)</p>
<p>\(5{x^2} + 10x - 15 < 0\)</p>
<p>\({x^2} + 2x - 3 < 0\) <strong><em>A1</em></strong></p>
<p>\((x + 3)(x - 1) < 0\) <strong><em>(M1)</em></strong></p>
<p>solution is \( - 3 < x < 1\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>METHOD 3</strong></p>
<p>\( - 2 < \frac{{1 - 3x}}{{x - 2}} < 2\)</p>
<p>consider \(\frac{{1 - 3x}}{{x - 2}} < 2\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Also allow consideration of “>” or “=” for the awarding of the <strong><em>M </em></strong>mark.</p>
<p> </p>
<p>recognition of critical value at \(x = 1\) <strong><em>A1</em></strong></p>
<p>consider \( - 2 < \frac{{1 - 3x}}{{x - 2}}\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Also allow consideration of “>” or “=” for the awarding of the <strong><em>M </em></strong>mark.</p>
<p> </p>
<p>recognition of critical value at \(x = - 3\) <strong><em>A1</em></strong></p>
<p>solution is \( - 3 < x < 1\) <strong><em>A1</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
<p><strong><em> </em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The function \(f\) is given by \(f(x) = x{{\text{e}}^{ - x}}{\text{ }}(x \geqslant 0)\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Find an expression for \(f'(x)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Hence determine the coordinates of the point A, where \(f'(x) = 0\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a(i)(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find an expression for \(f''(x)\) and hence show the point A is a maximum.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">Find the coordinates of B, the point of inflexion.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The graph of the function \(g\) is obtained from the graph of \(f\) by stretching it in the <em>x</em>-direction by a scale factor 2.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> (i) Write down an expression for \(g(x)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> (ii) State the coordinates of the maximum C of \(g\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> (iii) Determine the <em>x</em>-coordinates of D and E, the two points where \(f(x) = g(x)\).</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">Sketch the graphs of \(y = f(x)\) and \(y = g(x)\) on the same axes, showing clearly the points A, B, C, D and E.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find an exact value for the area of the region bounded by the curve \(y = g(x)\), the <em>x</em>-axis and the line \(x = 1\).</span></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="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \(f'(x) = {{\text{e}}^{ - x}} - x{{\text{e}}^{ - x}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \(f'(x) = 0 \Rightarrow x = 1\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">coordinates \(\left( {1,{\text{ }}{{\text{e}}^{ - 1}}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">a(i)(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f''(x) = - {{\text{e}}^{ - x}} - {{\text{e}}^{ - x}} + x{{\text{e}}^{ - x}}{\text{ }}\left( { = - {{\text{e}}^{ - x}}(2 - x)} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">substituting \(x = 1\) into \(f''(x)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f''(1){\text{ }}\left( { = - {{\text{e}}^{ - 1}}} \right) < 0\) hence maximum <strong><em>R1AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(f''(x) = 0{\text{ (}} \Rightarrow x = 2)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">coordinates \(\left( {2,{\text{ 2}}{{\text{e}}^{ - 2}}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \(g(x) = \frac{x}{2}{{\text{e}}^{ - \frac{x}{2}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) coordinates of maximum \(\left( {2,{\text{ }}{{\text{e}}^{ - 1}}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) equating \(f(x) = g(x)\) and attempting to solve \(x{{\text{e}}^{ - x}} = \frac{x}{2}{{\text{e}}^{ - \frac{x}{2}}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> \( \Rightarrow x\left( {2{{\text{e}}^{\frac{x}{2}}} - {{\text{e}}^x}} \right) = 0\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> \( \Rightarrow x = 0\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong> or</strong> \(2{{\text{e}}^{\frac{x}{2}}} = {{\text{e}}^x}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> \( \Rightarrow {{\text{e}}^{\frac{x}{2}}} = 2\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> \( \Rightarrow x = 2\ln 2\) \((\ln 4)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award first (<strong><em>A1) </em></strong>only if factorisation seen or if two correct</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">solutions are seen.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><img src="images/maths_10e_markscheme.png" alt> <strong><em>A4</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1 </em></strong>for shape of \(f\), including domain extending beyond \(x = 2\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> Ignore any graph shown for \(x < 0\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> Award <strong><em>A1 </em></strong>for A and B correctly identified.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> Award <strong><em>A1 </em></strong>for shape of \(g\), including domain extending beyond \(x = 2\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> Ignore any graph shown for \(x < 0\). Allow follow through from \(f\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> Award <strong><em>A1 </em></strong>for C, D and E correctly identified (D and E are </span><span style="font-family: 'times new roman', times; font-size: medium;">interchangeable).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(A = \int_0^1 {\frac{x}{2}{{\text{e}}^{ - \frac{x}{2}}}{\text{d}}x} \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \left[ { - x{{\text{e}}^{ - \frac{x}{2}}}} \right]_0^1 - \int_0^1 { - {{\text{e}}^{ - \frac{x}{2}}}{\text{d}}x} \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Condone absence of limits or incorrect limits.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( = - {{\text{e}}^{ - \frac{1}{2}}} - \left[ {2{{\text{e}}^{ - \frac{x}{2}}}} \right]_0^1\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( = - {{\text{e}}^{ - \frac{1}{2}}} - \left( {2{{\text{e}}^{ - \frac{1}{2}}} - 2} \right) = 2 - 3{{\text{e}}^{ - \frac{1}{2}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part a) proved to be an easy start for the vast majority of candidates.</span></p>
<div class="question_part_label">a(i)(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Full marks for part b) were again likewise seen, though a small number shied away from considering the sign of their second derivative, despite the question asking them to do so.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part c) again proved to be an easily earned 2 marks.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Full marks for part b) were again likewise seen, though a small number shied away from considering the sign of their second derivative, despite the question asking them to do so.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part c) again proved to be an easily earned 2 marks.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates lost their way in part d). A variety of possibilities for \(g(x)\) were suggested, commonly \(2x{{\text{e}}^{ - 2x}}\), \(\frac{{x{{\text{e}}^{ - 1}}}}{2}\) or similar variations. Despite section ii) being worth only one mark, (and ‘state’ being present in the question), many laborious attempts at further differentiation were seen. Part diii was usually answered well by those who gave the correct function for \(g(x)\).</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part e) was also answered well by those who had earned full marks up to that point.</span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">While the integration by parts technique was clearly understood, it was somewhat surprising how many careless slips were seen in this part of the question. Only a minority gained full marks for part f).</span></p>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A rational function is defined by \(f(x) = a + \frac{b}{{x - c}}\) where the parameters \(a,{\text{ }}b,{\text{ }}c \in \mathbb{Z}\) and \(x \in \mathbb{R}\backslash \{ c\} \). The following diagram represents the graph of \(y = f(x)\).</p>
<p class="p2" style="text-align: center;"><img src="images/Schermafbeelding_2017-02-28_om_09.42.27.png" alt="N16/5/MATHL/HP1/ENG/TZ0/03"></p>
<p class="p1">Using the information on the graph,</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">state the value of \(a\) <span class="s1">and the value of </span>\(c\);</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">find the value of \(b\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(a = 1\) </span><strong><em>A1</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\(c = 3\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">use the coordinates of \((1,{\text{ }}0)\) <span class="s1">on the graph <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></span></p>
<p class="p2"><span class="Apple-converted-space">\(f(1) = 0 \Rightarrow 1 + \frac{b}{{1 - 3}} = 0 \Rightarrow b = 2\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p3"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The equation \(5{x^3} + 48{x^2} + 100x + 2 = a\) has roots \({r_1}\), \({r_2}\) and \({r_3}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Given that \({r_1} + {r_2} + {r_3} + {r_1}{r_2}{r_3} = 0\), find the value of <em>a</em>.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({r_1} + {r_2} + {r_3} = \frac{{ - 48}}{5}\) <strong><em>(M1)(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({r_1}{r_2}{r_3} = \frac{{a - 2}}{5}\) <strong><em>(M1)(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{ - 48}}{5} + \frac{{a - 2}}{5} = 0\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(a = 50\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>M1A0M1A0M1A1 </em></strong>if answer of 50 is found using \(\frac{{48}}{5}\) and \(\frac{{2 - a}}{5}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the equation \(9{x^3} - 45{x^2} + 74x - 40 = 0\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Write down the numerical value of the sum and of the product of the roots of this equation.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The roots of this equation are three consecutive terms of an arithmetic sequence.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Taking the roots to be \(\alpha {\text{ , }}\alpha \pm \beta \) , solve the equation.</span></p>
<div class="marks">[6]</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="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{sum}} = \frac{{45}}{9},{\text{ product}} = \frac{{40}}{9}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">it follows that \(3\alpha = \frac{{45}}{9}\) and \(\alpha ({\alpha ^2} - {\beta ^2}) = \frac{{40}}{9}\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">solving, \(\alpha = \frac{5}{3}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{5}{3}\left( {\frac{{25}}{9} - {\beta ^2}} \right) = \frac{{40}}{9}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\beta = ( \pm )\frac{1}{3}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the other two roots are 2, \(\frac{4}{3}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>Let <em>f</em>(<em>x</em>) = <em>x</em><sup>4</sup> + <em>px</em><sup>3</sup> + <em>qx</em> + 5 where <em>p</em>, <em>q</em> are constants.</p>
<p>The remainder when <em>f</em>(<em>x</em>) is divided by (<em>x</em> + 1) is 7, and the remainder when <em>f</em>(<em>x</em>) is divided by (<em>x</em> − 2) is 1. Find the value of <em>p</em> and the value of <em>q</em>.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>attempt to substitute <em>x</em> = −1 or <em>x</em> = 2 or to divide polynomials <em><strong>(M1)</strong></em></p>
<p>1 − <em>p</em> − <em>q</em> + 5 = 7, 16 + 8<em>p</em> + 2<em>q</em> + 5 = 1 or equivalent <em><strong>A1A1</strong></em></p>
<p>attempt to solve their two equations <em><strong>M1</strong></em></p>
<p><em>p</em> = −3, <em>q</em> = 2 <em><strong> A1</strong></em></p>
<p><em><strong>[5 marks]</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The cubic polynomial \(3{x^3} + p{x^2} + qx - 2\) has a factor \((x + 2)\) and leaves a remainder 4 when divided by \((x + 1)\). Find the value of <em>p </em>and the value of <em>q</em>.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(f( - 2) = 0{\text{ }}( \Rightarrow - 24 + 4p - 2q - 2 = 0)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(f( - 1) = 4{\text{ }}( \Rightarrow - 3 + p - q - 2 = 4)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> In each case award the <strong><em>M </em></strong>marks if correct substitution attempted and right-hand side correct.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">attempt to solve simultaneously \((2p - q = 13,{\text{ }}p - q = 9)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(p = 4\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(q = - 5\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates scored full marks on what was thought to be an easy first question. However, a number of candidates wrote down two correct equations but proceeded to make algebraic errors and thus found incorrect values for <em>p</em> and <em>q</em>. A small number also attempted to answer this question using long division, but fully correct answers using this technique were rarely seen.</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">The quadratic equation \(2{x^2} - 8x + 1 = 0\) has roots \(\alpha \) and \(\beta \).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Without solving the equation, find the value of</p>
<p>(i) \(\alpha + \beta \);</p>
<p>(ii) \(\alpha \beta \).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Another quadratic equation \({x^2} + px + q = 0,{\text{ }}p,{\text{ }}q \in \mathbb{Z}\) has roots \(\frac{2}{\alpha }\) and \(\frac{2}{\beta }\).</p>
<p class="p1">Find the value of \(p\) and the value of \(q\).</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>using the formulae for the sum and product of roots:</p>
<p>(i) \(\alpha + \beta = 4\) <strong><em>A1</em></strong></p>
<p>(ii) \(\alpha \beta = \frac{1}{2}\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>A0A0 </em></strong>if the above results are obtained by solving the original equation (except for the purpose of checking).</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>required quadratic is of the form \({x^2} - \left( {\frac{2}{\alpha } + \frac{2}{\beta }} \right)x + \left( {\frac{2}{\alpha }} \right)\left( {\frac{2}{\beta }} \right)\) <strong><em>(M1)</em></strong></p>
<p>\(q = \frac{4}{{\alpha \beta }}\)</p>
<p>\(q = 8\) <strong><em>A1</em></strong></p>
<p>\(p = - \left( {\frac{2}{\alpha } + \frac{2}{\beta }} \right)\)</p>
<p>\( = - \frac{{2(\alpha + \beta )}}{{\alpha \beta }}\) <strong><em>M1</em></strong></p>
<p>\( = - \frac{{2 \times 4}}{{\frac{1}{2}}}\)</p>
<p>\(p = - 16\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Accept the use of exact roots</p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p> </p>
<p>replacing \(x\) with \(\frac{2}{x}\) <strong><em>M1</em></strong></p>
<p>\(2{\left( {\frac{2}{x}} \right)^2} - 8\left( {\frac{2}{x}} \right) + 1 = 0\)</p>
<p>\(\frac{8}{{{x^2}}} - \frac{{16}}{x} + 1 = 0\) <strong><em>(A1)</em></strong></p>
<p>\({x^2} - 16x + 8 = 0\)</p>
<p>\(p = - 16\) and \(q = 8\) <strong><em>A1A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>A1A0 </em></strong>for \({x^2} - 16x + 8 = 0\) <em>ie</em>, if \(p = - 16\) and \(q = 8\) are not explicitly stated.</p>
<p><em><strong>[4 marks]</strong></em></p>
<p><em><strong>Total [6 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Most candidates obtained full marks.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Many candidates obtained full marks, but some responses were inefficiently expressed. A very small minority attempted to use the exact roots, usually unsuccessfully.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the following functions:</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\[f(x) = \frac{{2{x^2} + 3}}{{75}},{\text{ }}x \geqslant 0\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\[g(x) = \frac{{\left| {3x - 4} \right|}}{{10}},{\text{ }}x \in \mathbb{R}{\text{ }}.\]</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">State the range of <em>f </em>and of <em>g </em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Find an expression for the composite function \(f \circ g(x)\) in the form \(\frac{{a{x^2} + bx + c}}{{3750}}\), where \(a,{\text{ }}b{\text{ and }}c \in \mathbb{Z}\) .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Find an expression for the inverse function \({f^{ - 1}}(x)\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) State the domain and range of \({f^{ - 1}}\)<span style="font: 7.0px Helvetica;"> </span>.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="line-height: normal; font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;">The domains of <em>f</em> and <em>g</em> are now restricted to {0, 1, 2, 3, 4} .</span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">By considering the values of <em>f </em>and <em>g </em>on this new domain, determine which of <em>f </em>and <em>g </em>could be used to find a probability distribution for a discrete random variable <em>X </em>, stating your reasons clearly.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Using this probability distribution, calculate the mean of <em>X </em>.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(x) \geqslant \frac{1}{{25}}\) <strong> <em>A1 </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(g(x) \in \mathbb{R},{\text{ }}g(x) \geqslant 0\) <strong> <em>A1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[2 marks]</span><br></em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f \circ g(x) = \frac{{2{{\left( {\frac{{3x - 4}}{{10}}} \right)}^2} + 3}}{{75}}\) <strong> <em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{\frac{{2(9{x^2} - 24x + 16)}}{{100}} + 3}}{{75}}\) <strong> <em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{9{x^2} - 24x + 166}}{{3750}}\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[4 marks]</span><br></em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">(i) <strong>METHOD 1</strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(y = \frac{{2{x^2} + 3}}{{75}}\)</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\({x^2} = \frac{{75y - 3}}{2}\) <strong> <em>M1</em></strong></span></p>
<p>\(x = \sqrt {\frac{{75y - 3}}{2}} \) <strong> <em>(A1)</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow {f^{ - 1}}(x) = \sqrt {\frac{{75x - 3}}{2}} \) <strong> <em>A1</em></strong></span><span style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 14px; line-height: 20px;"> </span><span style="font-family: 'times new roman', times; font-size: medium;"><strong> </strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Accept ± in line 3 for the <strong><em>(A1) </em></strong>but not in line 4 for the <strong><em>A1</em></strong>.</span><span style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 14px; line-height: 20px;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Award the <strong><em>A1 </em></strong>only if written in the form \({f^{ - 1}}(x) = \) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"> </p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(y = \frac{{2{x^2} + 3}}{{75}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = \frac{{2{y^2} + 3}}{{75}}\) <strong><em>M1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(y = \sqrt {\frac{{75x - 3}}{2}} \) <strong><em>(A1)</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow {f^{ - 1}}(x) = \sqrt {\frac{{75x - 3}}{2}} \) <strong><em>A1</em></strong></span> <span style="font-family: 'times new roman', times; font-size: medium;"><strong> </strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Accept ± in line 3 for the <strong><em>(A1) </em></strong>but not in line 4 for the <strong><em>A1</em></strong>.</span><span style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 14px; line-height: 20px;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Award the <strong><em>A1 </em></strong>only if written in the form \({f^{ - 1}}(x) = \) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"> </p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">(ii) domain: \(x \geqslant \frac{1}{{25}}\) ; range: \({f^{ - 1}}(x) \geqslant 0\) <strong><em>A1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<p> </p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">probabilities from \(f(x)\) :</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><img src="data:image/png;base64,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" alt> <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>A1 </em></strong>for one error, <strong><em>A0 </em></strong>otherwise.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">probabilities from \(g(x)\) :</span></p>
<p><img src="data:image/png;base64,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" alt><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> A2<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>A1 </em></strong>for one error, <strong><em>A0 </em></strong>otherwise. </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">only in the case of \(f(x)\) does \(\sum {P(X = x) = 1} \) , hence only \(f(x)\) can be used as a probability mass function <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[6 marks]</span><br></em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(E(x) = \sum {x \cdot {\text{P}}(X = x)} \) <strong> <em>M1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{5}{{75}} + \frac{{22}}{{75}} + \frac{{63}}{{75}} + \frac{{140}}{{75}} = \frac{{230}}{{75}}\left( { = \frac{{46}}{{15}}} \right)\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[2 marks]</span><br></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;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In (a), the ranges were often given incorrectly, particularly the range of <em>g </em>where the modulus signs appeared to cause difficulty. In (b), it was disappointing to see so many candidates making algebraic errors in attempting to determine the expression for \(f \circ g(x)\). Many candidates were unable to solve (d) correctly with arithmetic errors and incorrect reasoning often seen. Since the solution to (e) depended upon a correct choice of function in (d), few correct solutions were seen with some candidates even attempting to use integration, inappropriately, to find the mean of <em>X</em>.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In (a), the ranges were often given incorrectly, particularly the range of <em>g </em>where the modulus signs appeared to cause difficulty. In (b), it was disappointing to see so many candidates making algebraic errors in attempting to determine the expression for \(f \circ g(x)\). Many candidates were unable to solve (d) correctly with arithmetic errors and incorrect reasoning often seen. Since the solution to (e) depended upon a correct choice of function in (d), few correct solutions were seen with some candidates even attempting to use integration, inappropriately, to find the mean of <em>X</em>.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In (a), the ranges were often given incorrectly, particularly the range of <em>g </em>where the modulus signs appeared to cause difficulty. In (b), it was disappointing to see so many candidates making algebraic errors in attempting to determine the expression for \(f \circ g(x)\). Many candidates were unable to solve (d) correctly with arithmetic errors and incorrect reasoning often seen. Since the solution to (e) depended upon a correct choice of function in (d), few correct solutions were seen with some candidates even attempting to use integration, inappropriately, to find the mean of <em>X</em>.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In (a), the ranges were often given incorrectly, particularly the range of <em>g </em>where the modulus signs appeared to cause difficulty. In (b), it was disappointing to see so many candidates making algebraic errors in attempting to determine the expression for \(f \circ g(x)\). Many candidates were unable to solve (d) correctly with arithmetic errors and incorrect reasoning often seen. Since the solution to (e) depended upon a correct choice of function in (d), few correct solutions were seen with some candidates even attempting to use integration, inappropriately, to find the mean of <em>X</em>.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In (a), the ranges were often given incorrectly, particularly the range of <em>g </em>where the modulus signs appeared to cause difficulty. In (b), it was disappointing to see so many candidates making algebraic errors in attempting to determine the expression for \(f \circ g(x)\). Many candidates were unable to solve (d) correctly with arithmetic errors and incorrect reasoning often seen. Since the solution to (e) depended upon a correct choice of function in (d), few correct solutions were seen with some candidates even attempting to use integration, inappropriately, to find the mean of <em>X</em>.</span></p>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the graphs of \(y = \left| x \right|\) and \(y = - \left| x \right| + b\), where \(b \in {\mathbb{Z}^ + }\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graphs on the same set of axes.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that the graphs enclose a region of area 18 square units, find the value of <em>b</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2017-08-08_om_11.15.31.png" alt="M17/5/MATHL/HP1/ENG/TZ1/A6.a/M"></p>
<p>graphs sketched correctly (condone missing <em>b</em>) <strong><em>A1A1</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{{b^2}}}{2} = 18\) <strong><em>(M1)A1</em></strong></p>
<p>\(b = 6\) <strong><em>A1</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><span style="font-family: times new roman,times; font-size: medium;">Consider the functions given below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\[f(x) = 2x + 3\]\[g(x) = \frac{1}{x},x \ne 0\]<br></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(i) Find \(\left( {g \circ f} \right)\left( x \right)\) and write down the domain of the function.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Find \(\left( {f \circ g} \right)\left( x \right)\) and write down the domain of the function.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the coordinates of the point where the graph of \(y = f(x)\) and the graph of \(y = \left( {{g^{ - 1}} \circ f \circ g} \right)(x)\) intersect.</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 style="font-family: times new roman,times;"><span style="font-size: medium;">(i) </span><span style="font-size: medium;">\(\left( {g \circ f} \right)\left( x \right) = \frac{1}{{2x + 3}}\), \(x \ne - \frac{3}{2}\) </span><span style="font-size: medium;">(or equivalent) <em><strong>A1</strong></em></span></span></p>
<p><span style="font-family: times new roman,times;"><span style="font-size: medium;"><em><strong> </strong></em></span></span></p>
<p><span style="font-family: times new roman,times;"><span style="font-size: medium;">(ii) </span>\(\left( {f \circ g} \right)\left( x \right) = \frac{2}{x} + 3\), \(x \ne 0\)<span style="font-size: medium;"> (or equivalent) <em><strong>A1</strong></em></span></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><span style="font-family: times new roman,times; font-size: medium;">EITHER</span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(f(x) = \left( {{g^{ - 1}} \circ f \circ g} \right)(x) \Rightarrow \left( {f \circ g} \right)\left( x \right)\) <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\frac{1}{{2x + 3}} = \frac{2}{x} + 3\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1</span></strong></em></p>
<p><strong><span style="font-family: times new roman,times; font-size: medium;">OR</span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\left( {{g^{ - 1}} \circ f \circ g} \right)(x) = \frac{1}{{\frac{2}{x} + 3}}\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(2x + 3 = \frac{1}{{\frac{2}{x} + 3}}\) <em><strong>M1</strong></em></span></p>
<p><strong><span style="font-family: times new roman,times; font-size: medium;">THEN</span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(6{x^2} + 12x + 6 = 0\) (or equivalent) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(x = - 1\), \(y = 1\) (coordinates are (−1, 1) ) <em><strong>A1</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[4 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Part (a) was in general well answered and part (b) well attempted. Some candidates had difficulties with the order of composition and in using correct notation to represent the domains of the functions.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Part (a) was in general well answered and part (b) well attempted. Some candidates had difficulties with the order of composition and in using correct notation to represent the domains of the functions.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function \({f_n}(x) = (\cos 2x)(\cos 4x) \ldots (\cos {2^n}x),{\text{ }}n \in {\mathbb{Z}^ + }\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine whether \({f_n}\) is an odd or even function, justifying your answer.</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>By using mathematical induction, prove that</p>
<p style="text-align: center;">\({f_n}(x) = \frac{{\sin {2^{n + 1}}x}}{{{2^n}\sin 2x}},{\text{ }}x \ne \frac{{m\pi }}{2}\) where \(m \in \mathbb{Z}\).</p>
<div class="marks">[8]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence or otherwise, find an expression for the derivative of \({f_n}(x)\) with respect to \(x\).</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>Show that, for \(n > 1\), the equation of the tangent to the curve \(y = {f_n}(x)\) at \(x = \frac{\pi }{4}\) is \(4x - 2y - \pi = 0\).</p>
<div class="marks">[8]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>even function <strong><em>A1</em></strong></p>
<p>since \(\cos kx = \cos ( - kx)\) <strong>and</strong> \({f_n}(x)\) is a product of even functions <strong><em>R1</em></strong></p>
<p><strong>OR</strong></p>
<p>even function <strong><em>A1</em></strong></p>
<p>since \((\cos 2x)(\cos 4x) \ldots = \left( {\cos ( - 2x)} \right)\left( {\cos ( - 4x)} \right) \ldots \) <strong><em>R1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Do not award <strong><em>A0R1</em></strong>.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>consider the case \(n = 1\)</p>
<p>\(\frac{{\sin 4x}}{{2\sin 2x}} = \frac{{2\sin 2x\cos 2x}}{{2\sin 2x}} = \cos 2x\) <strong><em>M1</em></strong></p>
<p>hence true for \(n = 1\) <strong><em>R1</em></strong></p>
<p>assume true for \(n = k\), <em>ie</em>, \((\cos 2x)(\cos 4x) \ldots (\cos {2^k}x) = \frac{{\sin {2^{k + 1}}x}}{{{2^k}\sin 2x}}\) <strong><em>M1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Do not award <strong><em>M1 </em></strong>for “let \(n = k\)” or “assume \(n = k\)” or equivalent.</p>
<p> </p>
<p>consider \(n = k + 1\):</p>
<p>\({f_{k + 1}}(x) = {f_k}(x)(\cos {2^{k + 1}}x)\) <strong><em>(M1)</em></strong></p>
<p>\( = \frac{{\sin {2^{k + 1}}x}}{{{2^k}\sin 2x}}\cos {2^{k + 1}}x\) <strong><em>A1</em></strong></p>
<p>\( = \frac{{2\sin {2^{k + 1}}x\cos {2^{k + 1}}x}}{{{2^{k + 1}}\sin 2x}}\) <strong><em>A1</em></strong></p>
<p>\( = \frac{{\sin {2^{k + 2}}x}}{{{2^{k + 1}}\sin 2x}}\) <strong><em>A1</em></strong></p>
<p>so \(n = 1\) true and \(n = k\) true \( \Rightarrow n = k + 1\) true. Hence true for all \(n \in {\mathbb{Z}^ + }\) <strong><em>R1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> To obtain the final <strong><em>R1</em></strong>, all the previous <strong><em>M </em></strong>marks must have been awarded.</p>
<p> </p>
<p><strong><em>[8 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to use \(f’ = \frac{{vu' - uv'}}{{{v^2}}}\) (or correct product rule) <strong><em>M1</em></strong></p>
<p>\({f’_n}(x) = \frac{{({2^n}\sin 2x)({2^{n + 1}}\cos {2^{n + 1}}x) - (\sin {2^{n + 1}}x)({2^{n + 1}}\cos 2x)}}{{{{({2^n}\sin 2x)}^2}}}\) <strong><em>A1A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>A1 </em></strong>for correct numerator and <strong><em>A1 </em></strong>for correct denominator.</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>\({f’_n}\left( {\frac{\pi }{4}} \right) = \frac{{\left( {{2^n}\sin \frac{\pi }{2}} \right)\left( {{2^{n + 1}}\cos {2^{n + 1}}\frac{\pi }{4}} \right) - \left( {\sin {2^{n + 1}}\frac{\pi }{4}} \right)\left( {{2^{n + 1}}\cos \frac{\pi }{2}} \right)}}{{{{\left( {{2^n}\sin \frac{\pi }{2}} \right)}^2}}}\) <strong><em>(M1)(A1)</em></strong></p>
<p>\({f’_n}\left( {\frac{\pi }{4}} \right) = \frac{{({2^n})\left( {{2^{n + 1}}\cos {2^{n + 1}}\frac{\pi }{4}} \right)}}{{{{({2^n})}^2}}}\) <strong><em>(A1)</em></strong></p>
<p>\( = 2\cos {2^{n + 1}}\frac{\pi }{4}{\text{ }}( = 2\cos {2^{n - 1}}\pi )\) <strong><em>A1</em></strong></p>
<p>\({f’_n}\left( {\frac{\pi }{4}} \right) = 2\) <strong><em>A1</em></strong></p>
<p>\({f_n}\left( {\frac{\pi }{4}} \right) = 0\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> This <strong><em>A </em></strong>mark is independent from the previous marks.</p>
<p> </p>
<p>\(y = 2\left( {x - \frac{\pi }{4}} \right)\) <strong><em>M1A1</em></strong></p>
<p>\(4x - 2y - \pi = 0\) <strong><em>AG</em></strong></p>
<p><strong><em>[8 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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A function <em>f</em> is defined by \(f(x) = \frac{{2x - 3}}{{x - 1}},{\text{ }}x \ne 1\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Find an expression for \({f^{ - 1}}(x)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Solve the equation \(\left| {{f^{ - 1}}(x)} \right| = 1 + {f^{ - 1}}(x)\).</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) <strong>Note:</strong> Interchange of variables may take place at any stage.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">for the inverse, solve for <em>x</em> in</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(y = \frac{{2x - 3}}{{x - 1}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(y(x - 1) = 2x - 3\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(yx - 2x = y - 3\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x(y - 2) = y - 3\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = \frac{{y - 3}}{{y - 2}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow {f^{ - 1}}(x) = \frac{{x - 3}}{{x - 2}}\,\,\,\,\,(x \ne 2)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Do not award final <strong><em>A1</em></strong> unless written in the form </span><span style="font-family: 'times new roman', times; font-size: medium;">\({f^{ - 1}}(x) = \ldots \)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) \( \pm {f^{ - 1}}(x) = 1 + {f^{ - 1}}(x)\) leads to</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2\frac{{x - 3}}{{x - 2}} = - 1\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = \frac{8}{3}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates gained the correct answer to part (a), although a significant minority left the answer in the form \(y = \ldots {\text{ or }}x = \ldots \) rather than \({f^{ - 1}}(x) = \ldots \). Only the better candidates were able to make significant progress in part (b).</span></p>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">The quadratic function \(f(x) = p + qx - {x^2}\) has a maximum value of 5 when <em>x </em>= 3.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the value of <em>p</em> and the value of <em>q</em> .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The graph of <em>f</em>(<em>x</em>) is translated 3 units in the positive direction parallel to the <em>x</em>-axis. Determine the equation of the new graph.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(x) = q - 2x = 0\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(3) = q - 6 = 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>q</em> = 6 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>f</em>(3) = <em>p</em> + 18 − 9 = 5 <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>p</em> = −4 <strong><em>A1</em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(x) = - {(x - 3)^2} + 5\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = - {x^2} + 6x - 4\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>q</em> = 6, <em>p</em> = −4 <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em><strong>[4 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(g(x) = - 4 + 6(x - 3) - {(x - 3)^2}{\text{ }}( = - 31 + 12x - {x^2})\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Accept any alternative form which is correct.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Award <strong><em>M1A0</em></strong> for a substitution of (<em>x</em> + 3) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">In general candidates handled this question well although a number equated the derivative to the function value rather than zero. Most recognised the shift in the second part although a number shifted only the squared value and not both <em>x</em> values.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">In general candidates handled this question well although a number equated the derivative to the function value rather than zero. Most recognised the shift in the second part although a number shifted only the squared value and not both <em>x</em> values.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Consider a function <em>f </em>, defined by \(f(x) = \frac{x}{{2 - x}}{\text{ for }}0 \leqslant x \leqslant 1\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find an expression for \((f \circ f)(x)\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman',times; font-size: medium;">Let \({F_n}(x) = \frac{x}{{{2^n} - ({2^n} - 1)x}}\), where \(0 \leqslant x \leqslant 1\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman',times; font-size: medium;">Use mathematical induction to show that for any \(n \in {\mathbb{Z}^ + }\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman',times; font-size: medium;">\[\underbrace {(f \circ f \circ ... \circ f)}_{n{\text{ times}}}(x) = {F_n}(x)\] .</span></p>
<div class="marks">[8]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Show that \({F_{ - n}}(x)\) is an expression for the inverse of \({F_n}\) .</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) State \({F_n}(0){\text{ and }}{F_n}(1)\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Show that \({F_n}(x) < x\) , given 0 < <em>x </em>< 1, \(n \in {\mathbb{Z}^ + }\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) For \(n \in {\mathbb{Z}^ + }\) , let \({A_n}\) be the area of the region enclosed by the graph of \(F_n^{ - 1}\) , the <em>x</em>-axis and the line <em>x </em>= 1. Find the area \({B_n}\) of the region enclosed by \({F_n}\) and \(F_n^{ - 1}\) in terms of \({A_n}\) .<span style="font: 7.0px Helvetica;"><br></span></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="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\((f \circ f)(x) = f\left( {\frac{x}{{2 - x}}} \right) = \frac{{\frac{x}{{2 - x}}}}{{2 - \frac{x}{{2 - x}}}}\) <em><strong>M1A1</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\((f \circ f)(x) = \frac{x}{{4 - 3x}}\) <em><strong> A1</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><em><strong><span style="font-family: 'times new roman', times; font-size: medium;">[3 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(P(n):\underbrace {(f \circ f \circ ... \circ f)}_{n{\text{ times}}}(x) = {F_n}(x)\)</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(P(1):{\text{ }}f(x) = {F_1}(x)\)</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(LHS = f(x) = \frac{x}{{2 - x}}{\text{ and }}RHS = {F_1}(x) = \frac{x}{{{2^1} - ({2^1} - 1)x}} = \frac{x}{{2 - x}}\) <em><strong>A1A1</strong></em></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(\therefore P(1){\text{ true}}\)</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">assume that <em>P</em>(<em>k</em>) is true, <em>i.e.</em>, \(\underbrace {(f \circ f \circ ... \circ f)}_{{\text{k times}}}(x) = {F_k}(x)\) <em><strong>M1</strong></em></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">consider \(P(k + 1)\)</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(\underbrace {(f \circ f \circ ... \circ f)}_{{\text{k}} + 1{\text{ times}}}(x) = \left( {f \circ \underbrace {f \circ f \circ ... \circ f}_{{\text{k times}}}} \right)(x) = f\left( {{F_k}(x)} \right)\) <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\( = f\left( {\frac{x}{{{2^k} - ({2^k} - 1)x}}} \right) = \frac{{\frac{x}{{{2^k} - ({2^k} - 1)x}}}}{{2 - \frac{x}{{{2^k} - ({2^k} - 1)x}}}}\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{x}{{2\left( {{2^k} - ({2^k} - 1)x} \right) - x}} = \frac{x}{{{2^{k + 1}} - ({2^{k + 1}} - 2)x - x}}\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR </strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(\underbrace {(f \circ f \circ ... \circ f)}_{{\text{k}} + 1{\text{ times}}}(x) = \left( {f \circ \underbrace {f \circ f \circ ... \circ f}_{{\text{k times}}}} \right)(x) = {F_k}(f(x))\) <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\( = {F_k}\left( {\frac{x}{{2 - x}}} \right) = \frac{{\frac{x}{{2 - x}}}}{{{2^k} - ({2^k} - 1)\frac{x}{{2 - x}}}}\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{x}{{{2^{k + 1}} - {2^k}x - {2^k}x + x}}\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><strong>THEN</strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{x}{{{2^{k + 1}} - ({2^{k + 1}} - 1)x}} = {F_{k + 1}}(x)\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><em>P</em>(<em>k</em>) true implies <em>P</em>(<em>k</em> + 1) true, <em>P</em>(1) true so <em>P</em>(<em>n</em>) true for all \(n \in {\mathbb{Z}^ + }\) <em><strong>R1</strong></em></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><em><strong>[8 marks]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = \frac{y}{{{2^n} - ({2^n} - 1)y}} \Rightarrow {2^n}x - ({2^n} - 1)xy = y\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow {2^n}x = \left( {({2^n} - 1)x + 1} \right)y \Rightarrow y = \frac{{{2^n}x}}{{({2^n} - 1)x + 1}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(F_n^{ - 1}(x) = \frac{{{2^n}x}}{{({2^n} - 1)x + 1}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(F_n^{ - 1}(x) = \frac{x}{{\frac{{{2^n} - 1}}{{{2^n}}}x + \frac{1}{{{2^n}}}}}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(F_n^{ - 1}(x) = \frac{x}{{(1 - {2^{ - n}})x + {2^{ - n}}}}\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(F_n^{ - 1}(x) = \frac{x}{{{2^{ - n}} - ({2^{ - n}} - 1)x}}\) <strong> <em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">attempt \({F_{ - n}}\left( {{F_n}(x)} \right)\) <em><strong> M1</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {F_{ - n}}\left( {\frac{x}{{{2^n} - ({2^n} - 1)x}}} \right) = \frac{{\frac{x}{{{2^n} - ({2^n} - 1)x}}}}{{{2^{ - n}} - ({2^{ - n}} - 1)\frac{x}{{{2^n} - ({2^n} - 1)x}}}}\) <em><strong>A1A1</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{x}{{{2^{ - n}}({2^n} - ({2^n} - 1)x) - ({2^{ - n}} - 1)x}}\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note: </strong><span style="font-family: 'times new roman', times; font-size: medium;">Award </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1 </em></strong><span style="font-family: 'times new roman', times; font-size: medium;">marks for numerators and denominators</span><span style="font-family: 'times new roman', times; font-size: medium;">.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{x}{1} = x\) <strong><em>A1AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 3</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">attempt \({F_n}\left( {{F_{ - n}}(x)} \right)\) <strong> M1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {F_n}\left( {\frac{x}{{{2^{ - n}} - ({2^{ - n}} - 1)x}}} \right) = \frac{{\frac{x}{{{2^{ - n}} - ({2^{ - n}} - 1)x}}}}{{{2^n} - ({2^n} - 1)\frac{x}{{{2^{ - n}} - ({2^{ - n}} - 1)x}}}}\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{x}{{{2^n}({2^{ - n}} - ({2^{ - n}} - 1)x) - ({2^n} - 1)x}}\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note: </strong><span style="font-family: 'times new roman', times; font-size: medium;">Award </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1 </em></strong><span style="font-family: 'times new roman', times; font-size: medium;">marks for numerators and denominators.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{x}{1} = x\) <strong><em>A1AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \({F_n}(0) = 0,{\text{ }}{F_n}(1) = 1\) <em><strong>A1</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em><strong> </strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) <strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({2^n} - ({2^n} - 1)x - 1 = ({2^n} - 1)(1 - x)\) <em><strong>(M1)</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( > 0{\text{ if }}0 < x < 1{\text{ and }}n \in {\mathbb{Z}^ + }\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so \({2^n} - ({2^n} - 1)x > 1{\text{ and }}{F_n}(x) = \frac{x}{{{2^n} - ({2^n} - 1)x}} < \frac{x}{1}( < x)\) <em><strong>R1</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({F_n}(x) = \frac{x}{{{2^n} - ({2^n} - 1)x}} < x{\text{ for }}0 < x < 1{\text{ and }}n \in {\mathbb{Z}^ + }\) <em><strong>AG</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{x}{{{2^n} - ({2^n} - 1)x}} < x \Leftrightarrow {2^n} - ({2^n} - 1)x > 1\) <em><strong>(M1)</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Leftrightarrow ({2^n} - 1)x < {2^n} - 1\) <em><strong>A1</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Leftrightarrow x < \frac{{{2^n} - 1}}{{{2^n} - 1}} = 1\) true in the interval \(\left] {0,{\text{ }}1} \right[\) <em><strong>R1</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em><strong> </strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) \({B_n} = 2\left( {{A_n} - \frac{1}{2}} \right){\text{ }}( = 2{A_n} - 1)\) <em><strong>(M1)A1</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em><strong>[6 marks]</strong></em></span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<div><span style="font-family: 'times new roman', times; font-size: medium;">Part a) proved to be an easy 3 marks for most candidates. </span></div>
<div> </div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part b) was often answered well, and candidates were well prepared in this session for this type of question. Candidates still need to take care when showing explicitly that P(1) is true, and some are still writing ‘Let </span><em style="font-family: 'times new roman', times; font-size: medium;">n</em><span style="font-family: 'times new roman', times; font-size: medium;"> = </span><em style="font-family: 'times new roman', times; font-size: medium;">k</em><em style="font-family: 'times new roman', times; font-size: medium;">’ </em><span style="font-family: 'times new roman', times; font-size: medium;">which gains no marks. The inductive step was often well argued, and given in clear detail, though the final inductive reasoning step was incorrect, or appeared rushed, even from the better candidates. ‘True for </span><em style="font-family: 'times new roman', times; font-size: medium;">n</em><span style="font-family: 'times new roman', times; font-size: medium;"> =1, </span><em style="font-family: 'times new roman', times; font-size: medium;">n</em><span style="font-family: 'times new roman', times; font-size: medium;"> = </span><em style="font-family: 'times new roman', times; font-size: medium;">k</em><span style="font-family: 'times new roman', times; font-size: medium;"> and </span><em style="font-family: 'times new roman', times; font-size: medium;">n</em><span style="font-family: 'times new roman', times; font-size: medium;"> = </span><em style="font-family: 'times new roman', times; font-size: medium;">k</em><span style="font-family: 'times new roman', times; font-size: medium;"> + 1’ is still disappointingly seen, as were some even more unconvincing variations.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">Part c) was again very well answered by the majority. A few weaker candidates attempted to find an inverse for the individual case n = 1 , but gained no credit for this.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">Part d) was not at all well understood, with virtually no candidates able to tie together the hints given by connecting the different parts of the question. Rash, and often thoughtless attempts were made at each part, though by this stage some seemed to be struggling through lack of time. The inequality part of the question tended to be ‘fudged’, with arguments seen by examiners being largely unconvincing and lacking clarity. A tiny number of candidates provided the correct answer to the final part, though a surprising number persisted with what should have been recognised as fruitless working – usually in the form of long-winded integration attempts.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">State the set of values of \(a\) for which the function \(x \mapsto {\log _a}x\) exists, for all \(x \in {\mathbb{R}^ + }\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">Given that \({\log _x}y = 4{\log _y}x\)</span>, find all the possible expressions of \(y\) as a function of \(x\).</p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(a > 0\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1">\(a \ne 0\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><span class="s1"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>\({\log _x}y = \frac{{\ln y}}{{\ln x}}\) and \({\log _y}x = \frac{{\ln x}}{{\ln y}}\) <strong><em>M1A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Use of any base is permissible here, not just “e”.</p>
<p> </p>
<p>\({\left( {\frac{{\ln y}}{{\ln x}}} \right)^2} = 4\) <strong><em>A1</em></strong></p>
<p>\(\ln y = \pm 2\ln x\) <strong><em>A1</em></strong></p>
<p>\(y = {x^2}\;\;\;\)or\(\;\;\;\frac{1}{{{x^2}}}\) <strong><em>A1A1</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>\({\log _y}x = \frac{{{{\log }_x}x}}{{{{\log }_x}y}} = \frac{1}{{{{\log }_x}y}}\) <strong><em>M1A1</em></strong></p>
<p>\({({\log _x}y)^2} = 4\) <strong><em>A1</em></strong></p>
<p>\({\log _x}y = \pm 2\) <strong><em>A1</em></strong></p>
<p>\(y = {x^2}\;\;\;\)or\(\;\;\;y = \frac{1}{{{x^2}}}\) <strong><em>A1A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>The final two <strong><em>A </em></strong>marks are independent of the one coming before.</p>
<p><em><strong>[6 marks]</strong></em></p>
<p><em><strong>Total [8 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">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">When the function \(q(x) = {x^3} + k{x^2} - 7x + 3\) is divided by (<em>x</em> + 1) the remainder is seven times the remainder that is found when the function is divided by (<em>x</em> + 2) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the value of <em>k</em> .</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(q( - 1) = k + 9\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(q( - 2) = 4k + 9\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(k + 9 = 7(4k + 9)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(k = - 2\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Notes:</strong> The first <strong><em>M1</em></strong> is for one substitution and the consequent equations.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Accept expressions for \(q( - 1)\) and \(q( - 2)\) that are not simplified.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks] </em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates were able to access this question although the number who used either synthetic division or long division was surprising as this often lead to difficulty and errors. The most common error was in applying the factor of 7 to the wrong side of the equation. It was also disappointing the number of students who made simple algebraic errors late in the question.</span></p>
</div>
<br><hr><br><div class="question">
<p>Solve \({\left( {{\text{ln}}\,x} \right)^2} - \left( {{\text{ln}}\,2} \right)\left( {{\text{ln}}\,x} \right) < 2{\left( {{\text{ln}}\,2} \right)^2}\).</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>\({\left( {{\text{ln}}\,x} \right)^2} - \left( {{\text{ln}}\,2} \right)\left( {{\text{ln}}\,x} \right) - 2{\left( {{\text{ln}}\,2} \right)^2}\left( { = 0} \right)\)</p>
<p><strong>EITHER</strong></p>
<p>\({\text{ln}}\,x = \frac{{{\text{ln}}\,2 \pm \sqrt {{{\left( {{\text{ln}}\,2} \right)}^2} + 8{{\left( {{\text{ln}}\,2} \right)}^2}} }}{2}\) <em><strong>M1</strong></em></p>
<p>\( = \frac{{{\text{ln}}\,2 \pm 3\,{\text{ln}}\,2}}{2}\) <em><strong>A1</strong></em></p>
<p><strong>OR</strong></p>
<p>\(\left( {{\text{ln}}\,x - 2\,{\text{ln}}\,2} \right)\left( {{\text{ln}}\,x + 2\,{\text{ln}}\,2} \right)\left( { = 0} \right)\) <em><strong> M1A1</strong></em></p>
<p><strong>THEN</strong></p>
<p>\({\text{ln}}\,x = 2\,{\text{ln}}\,2\) or \( - {\text{ln}}\,2\) <em><strong>A1</strong></em></p>
<p>\( \Rightarrow x = 4\) or \(x = \frac{1}{2}\) <em><strong> (M1)A1</strong></em> </p>
<p><strong>Note:</strong> <em><strong>(M1)</strong></em> is for an appropriate use of a log law in either case, dependent on the previous <em><strong>M1</strong></em> being awarded, <strong>A1</strong> for both correct answers.</p>
<p>solution is \(\frac{1}{2} < x < 4\) <em><strong>A1</strong></em></p>
<p><em><strong>[6 marks]</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The roots of a quadratic equation \(2{x^2} + 4x - 1 = 0\) are \(\alpha \) and \(\beta \).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Without solving the equation,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(a) find the value of \({\alpha ^2} + {\beta ^2}\);</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(b) find a quadratic equation with roots \({\alpha ^2}\) and \({\beta ^2}\).</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) using the formulae for the sum and product of roots:</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\alpha + \beta = - 2\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\alpha \beta = - \frac{1}{2}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\alpha ^2} + {\beta ^2} = {(\alpha + \beta )^2} - 2\alpha \beta \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {( - 2)^2} - 2\left( { - \frac{1}{2}} \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 5\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>M0 </em></strong>for attempt to solve quadratic equation.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) \((x - {\alpha ^2})(x - {\beta ^2}) = {x^2} - ({\alpha ^2} + {\beta ^2})x + {\alpha ^2}{\beta ^2}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x^2} - 5x + {\left( { - \frac{1}{2}} \right)^2} = 0\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x^2} - 5x + \frac{1}{4} = 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Final answer must be an equation. Accept alternative correct forms.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [6 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">When the polynomial \(3{x^3} + ax + b\) is divided by \((x - 2)\), the remainder is 2, and when divided by \((x + 1)\), it is 5. Find the value of <em>a </em>and the value of <em>b</em>.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(P(2) = 24 + 2a + b = 2,{\text{ }}P( - 1) = - 3 - a + b = 5\) <em><strong>M1A1A1</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\((2a + b = - 22,{\text{ }} - a + b = 8)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>M1 </em></strong>for substitution of 2 or −1 and equating to remainder, <strong><em>A1 </em></strong>for each correct equation.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">attempt to solve simultaneously <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(a = - 10,{\text{ }}b = - 2\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Sketch on the same axes the curve \(y = \left| {\frac{7}{{x - 4}}} \right|\) and the line \(y = x + 2\), clearly indicating any axes intercepts and any asymptotes.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the exact solutions to the equation \(x + 2 = \left| {\frac{7}{{x - 4}}} \right|\).</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 class="p1"><img src="images/Schermafbeelding_2017-01-31_om_09.19.46.png" alt="M16/5/MATHL/HP1/ENG/TZ1/07.a/M"></p>
<p class="p1"><strong><em>A1 </em></strong>for vertical asymptote and for the \(y\)-intercept \(\frac{7}{4}\)</p>
<p class="p1"><strong><em>A1 </em></strong><span class="s1">for general shape of \(y = \left| {\frac{7}{{x - 4}}} \right|\) </span>including the \(x\)-axis as asymptote</p>
<p class="p1"><strong><em>A1 </em></strong>for straight line with \(y\)-intercept 2 and \(x\)<span class="s1">-intercept of \( - 2\) <span class="Apple-converted-space"> </span></span><strong><em>A1A1A1</em></strong></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>METHOD 1</strong></p>
<p class="p1">for \(x > 4\)</p>
<p class="p1">\((x + 2)(x - 4) = 7\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2">\({x^2} - 2x - 8 = 7 \Rightarrow {x^2} - 2x - 15 = 0\)</p>
<p class="p2">\((x - 5)(x + 3) = 0\)</p>
<p class="p1">\(({\text{as }}x > 4{\text{ then}}){\text{ }}x = 5\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>A0 </em></strong>if \(x = - 3\) is also given as a solution.</p>
<p class="p1">for \(x < 4\)</p>
<p class="p1">\((x + 2)(x - 4) = - 7\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p2">\( \Rightarrow {x^2} - 2x - 1 = 0\)</p>
<p class="p2">\(x = \frac{{2 \pm \sqrt {4 + 4} }}{2} = 1 \pm \sqrt 2 \) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)A1</em></strong></span></p>
<p class="p3"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Second <strong><em>M1 </em></strong>is dependent on first <strong><em>M1</em></strong>.</p>
<p class="p3"> </p>
<p class="p1"><strong><em>[5 marks]</em></strong></p>
<p class="p3"> </p>
<p class="p1"><strong>METHOD 2</strong></p>
<p class="p4">\({(x + 2)^2} = \frac{{49}}{{{{(x - 4)}^2}}}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p5">\({x^4} - 4{x^3} - 12{x^2} + 32x + 15 = 0\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p6">\((x + 3)(x - 5)({x^2} - 2x - 1) = 0\)</p>
<p class="p6">\(x = 5\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p3"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>A0 </em></strong>if \(x = - 3\) <span class="s2">is also given as a solution.</span></p>
<p class="p7"> </p>
<p class="p2">\(x = \frac{{2 \pm \sqrt {4 + 4} }}{2} = 1 \pm \sqrt 2 \) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)A1</em></strong></span></p>
<p class="p1"><strong><em>[5 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;">
<p class="p1">Though generally well done, some candidates lost marks unnecessarily by not heeding the instruction to clearly indicate the axes intercepts and asymptotes.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Though this was generally well done, quite a few of the candidates failed to use the graph drawn in part (a) to discount one of the solutions obtained in part (b).</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The diagram below shows a sketch of the graph of \(y = f(x)\).</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><br><span style="font-family: 'times new roman', times; font-size: medium;"><img src="images/Schermafbeelding_2014-09-16_om_05.50.26.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Sketch the graph of \(y = {f^{ - 1}}(x)\) on the same axes.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">State the range of \({f^{ - 1}}\).</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Given that \(f(x) = \ln (ax + b),{\text{ }}x > 1\), find the value of \(a\) and the value of \(b\).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) </span><br><span style="font-family: 'times new roman', times; font-size: medium;"><img src="images/Schermafbeelding_2014-09-16_om_05.54.52.png" alt></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">shape with <em>y</em>-axis intercept (0, 4) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Accept curve with an asymptote at \(x = 1\) suggested.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">correct asymptote \(y = 1\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">range is \({f^{ - 1}}(x) > 1{\text{ (or }}\left] {1,{\text{ }}\infty } \right[)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Also accept \(\left] {1,{\text{ 10}}} \right]\) or \(\left] {1,{\text{ 10}}} \right[\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Do not allow follow through from incorrect asymptote in (a).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\((4,{\text{ }}0) \Rightarrow \ln (4a + b) = 0\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow 4a + b = 1\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">asymptote at \(x = 1 \Rightarrow a + b = 0\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow a = \frac{1}{3},{\text{ }}b = - \frac{1}{3}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">A number of candidates were able to answer a) and b) correctly but found part c) more challenging. Correct sketches for the inverse were seen, but with a few missing a horizontal asymptote. The range in part b) was usually seen correctly. In part c), only a small number of very good candidates were able to gain full marks. A large number used the point \((4,{\text{ 0)}}\) to form the equation \(4a + b = 1\) but were unable (or did not recognise the need) to use the asymptote to form a second equation.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">A number of candidates were able to answer a) and b) correctly but found part c) more challenging. Correct sketches for the inverse were seen, but with a few missing a horizontal asymptote. The range in part b) was usually seen correctly. In part c), only a small number of very good candidates were able to gain full marks. A large number used the point \((4,{\text{ 0)}}\) to form the equation \(4a + b = 1\) but were unable (or did not recognise the need) to use the asymptote to form a second equation.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">A number of candidates were able to answer a) and b) correctly but found part c) more challenging. Correct sketches for the inverse were seen, but with a few missing a horizontal asymptote. The range in part b) was usually seen correctly. In part c), only a small number of very good candidates were able to gain full marks. A large number used the point \((4,{\text{ 0)}}\) to form the equation \(4a + b = 1\) but were unable (or did not recognise the need) to use the asymptote to form a second equation.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the set of values of <em>x</em> for which \(\left| {x - 1} \right| > \left| {2x - 1} \right|\).</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\left| {x - 1} \right| > \left| {2x - 1} \right| \Rightarrow {(x - 1)^2} > {(2x - 1)^2}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x^2} - 2x + 1 > 4{x^2} - 4x + 1\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(3{x^2} - 2x < 0\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(0 < x < \frac{2}{3}\) <strong><em>A1A1 N2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1A0</em></strong> for incorrect inequality signs.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\left| {x - 1} \right| > \left| {2x - 1} \right|\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x - 1 = 2x - 1\) \(x - 1 = 1 - 2x\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( - x = 0\) \(3x = 2\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 0\) \(x = \frac{2}{3}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>M1</em></strong> for any attempt to find a critical value. If graphical methods are used, award <strong><em>M1</em></strong> for correct graphs, <strong><em>A1</em></strong> for correct values of <em>x</em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(0 < x < \frac{2}{3}\) </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1A1 N2</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1A0</em></strong> for incorrect inequality signs.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This question turned out to be more difficult than expected. Candidates who squared both sides or drew a graph generally gave better solutions than those who relied on performing algebraic operations on terms involving modulus signs.</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(f(x) = \frac{4}{{x + 2}},{\text{ }}x \ne - 2{\text{ and }}g(x) = x - 1\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">If \(h = g \circ f\) , find</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) <em>h</em>(<em>x</em>) ;</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) \({h^{ - 1}}(x)\) , where \({h^{ - 1}}\) is the inverse of <em>h</em>.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \(h(x) = g\left( {\frac{4}{{x + 2}}} \right)\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{4}{{x + 2}} - 1\,\,\,\,\,\left( { = \frac{{2 - x}}{{2 + x}}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) <strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = \frac{4}{{y + 2}} - 1\,\,\,\,\,\)(interchanging <em>x</em> and <em>y</em>) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Attempting to solve for <em>y</em> <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\((y + 2)(x + 1) = 4\,\,\,\,\,\left( {y + 2 = \frac{4}{{x + 1}}} \right)\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({h^{ - 1}}(x) = \frac{4}{{x + 1}} - 2\,\,\,\,\,(x \ne - 1)\) <strong><em>A1</em></strong> <strong><em>N1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = \frac{{2 - y}}{{2 + y}}\,\,\,\,\,\)(interchanging <em>x</em> and <em>y</em>) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Attempting to solve for <em>y</em> <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(xy + y = 2 - 2x\,\,\,\,\,\left( {y(x + 1) = 2(1 - x)} \right)\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({h^{ - 1}}(x) = \frac{{2(1 - x)}}{{x + 1}}\,\,\,\,\,(x \ne - 1)\) <strong><em>A1</em></strong> <strong><em>N1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> In either </span><strong style="font-family: 'times new roman', times; font-size: medium;">METHOD 1</strong><span style="font-family: 'times new roman', times; font-size: medium;"> or </span><strong style="font-family: 'times new roman', times; font-size: medium;">METHOD 2</strong><span style="font-family: 'times new roman', times; font-size: medium;"> rearranging first and interchanging afterwards is equally acceptable.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was generally well done, with very few candidates calculating \(f \circ g\) rather than \(g \circ f\).</span></p>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The function <em>f</em> is given by \(f(x) = \frac{{{3^x} + 1}}{{{3^x} - {3^{ - x}}}}\), for <em>x</em> > 0.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Show that \(f(x) > 1\) for all <em>x</em> > 0.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Solve the equation \(f(x) = 4\).</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="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(x) - 1 = \frac{{1 + {3^{ - x}}}}{{{3^x} - {3^{ - x}}}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">> 0 as both numerator and denominator are positive <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({3^x} + 1 > {3^x} > {3^x} - {3^{ - x}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Accept a convincing valid argument the numerator is greater than the denominator.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">numerator and denominator are positive </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>R1</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">hence \(f(x) > 1\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">one line equation to solve, for example, \(4({3^x} - {3^{ - x}}) = {3^x} + 1\), or equivalent <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\left( {3{y^2} - y - 4 = 0} \right)\)<br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">attempt to solve a three-term equation <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">obtain \(y = \frac{4}{3}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = {\log _3}\left( {\frac{4}{3}} \right)\) or equivalent <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"> </strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Award </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A0</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> if an extra solution for </span><em style="font-family: 'times new roman', times; font-size: medium;">x</em><span style="font-family: 'times new roman', times; font-size: medium;"> is given.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><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;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) This is a question where carefully organised reasoning is crucial. It is important to state that both the numerator and the denominator are positive for \(x > 0\). Candidates were more successful with part (b) than with part (a).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) This is a question where carefully organised reasoning is crucial. It is important to state that both the numerator and the denominator are positive for \(x > 0\). Candidates were more successful with part (b) than with part (a).</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Express each of the complex numbers \({z_1} = \sqrt 3 + {\text{i, }}{z_2} = - \sqrt 3 + {\text{i}}\) and \({z_3} = - 2{\text{i}}\) in modulus-argument form.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Hence show that the points in the complex plane representing \({z_1}\), \({z_2}\) and \({z_3}\) form the vertices of an equilateral triangle.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) Show that \({\text{z}}_1^{3n} + z_2^{3n} = 2z_3^{3n}\) where \(n \in \mathbb{N}\).</span></p>
<div class="marks">[9]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) State the solutions of the equation \({z^7} = 1\) for \(z \in \mathbb{C}\), giving them in modulus-argument form.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) If <em>w</em> is the solution to \({z^7} = 1\) with least positive argument, determine the argument of 1 + <em>w</em>. Express your answer in terms of \(\pi \).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) Show that \({z^2} - 2z\cos \left( {\frac{{2\pi }}{7}} \right) + 1\) is a factor of the polynomial \({z^7} - 1\). State the two other quadratic factors with real coefficients.</span></p>
<div class="marks">[9]</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="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \({z_1} = 2{\text{cis}}\left( {\frac{\pi }{6}} \right),{\text{ }}{z_2} = 2{\text{cis}}\left( {\frac{{5\pi }}{6}} \right),{\text{ }}{z_3} = 2{\text{cis}}\left( { - \frac{\pi }{2}} \right){\text{ or }}2{\text{cis}}\left( {\frac{{3\pi }}{2}} \right)\) <strong><em>A1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Accept modulus and argument given separately, or the use of exponential (Euler) form.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"> </strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Accept arguments given in rational degrees, except where exponential form is used.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) the points lie on a circle of radius 2 centre the origin </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">differences are all \(\frac{{2\pi }}{3}(\bmod 2\pi )\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow \) points equally spaced \( \Rightarrow \) triangle is equilateral <strong><em>R1AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Accept an approach based on a clearly marked diagram.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) \({\text{z}}_1^{3n} + z_2^{3n} = {2^{3n}}{\text{cis}}\left( {\frac{{n\pi }}{2}} \right) + {2^{3n}}{\text{cis}}\left( {\frac{{5n\pi }}{2}} \right)\) </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>M1</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 2 \times {2^{3n}}{\text{cis}}\left( {\frac{{n\pi }}{2}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2z_3^{3n} = 2 \times {2^{3n}}{\text{cis}}\left( {\frac{{9n\pi }}{2}} \right) = 2 \times {2^{3n}}{\text{cis}}\left( {\frac{{n\pi }}{2}} \right)\) <strong><em>A1AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[9 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) attempt to obtain <strong>seven</strong> solutions in modulus argument form <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(z = {\text{cis}}\left( {\frac{{2k\pi }}{7}} \right),{\text{ }}k = 0,{\text{ }}1 \ldots 6\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) <em>w</em> has argument \(\frac{{2\pi }}{7}\) and 1 + <em>w</em> has argument \(\phi \),</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">then \(\tan (\phi ) = \frac{{\sin \left( {\frac{{2\pi }}{7}} \right)}}{{1 + \cos \left( {\frac{{2\pi }}{7}} \right)}}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{2\sin \left( {\frac{\pi }{7}} \right)\cos \left( {\frac{\pi }{7}} \right)}}{{2{{\cos }^2}\left( {\frac{\pi }{7}} \right)}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \tan \left( {\frac{\pi }{7}} \right) \Rightarrow \phi = \frac{\pi }{7}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Accept alternative approaches.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) since roots occur in conjugate pairs, </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>(R1)</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({z^7} - 1\) has a quadratic factor \(\left( {z - {\text{cis}}\left( {\frac{{2\pi }}{7}} \right)} \right) \times \left( {z - {\text{cis}}\left( { - \frac{{2\pi }}{7}} \right)} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {z^2} - 2z\cos \left( {\frac{{2\pi }}{7}} \right) + 1\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">other quadratic factors are \({z^2} - 2z\cos \left( {\frac{{4\pi }}{7}} \right) + 1\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">and \({z^2} - 2z\cos \left( {\frac{{6\pi }}{7}} \right) + 1\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[9 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) A disappointingly large number of candidates were unable to give the correct arguments for the three complex numbers. Such errors undermined their efforts to tackle parts (ii) and (iii).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates were successful in part (i), but failed to capitalise on that – in particular, few used the fact that roots of \({z^7} - 1 = 0\) come in complex conjugate pairs.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Given the complex numbers \({z_1} = 1 + 3{\text{i}}\) and \({z_2} = - 1 - {\text{i}}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Write down the exact values of \(\left| {{z_1}} \right|\) and \(\arg ({z_2})\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the minimum value of \(\left| {{z_1} + \alpha{z_2}} \right|\), where \(\alpha \in \mathbb{R}\).</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\left| {{z_1}} \right| = \sqrt {10} ;{\text{ }}\arg ({z_2}) = - \frac{{3\pi }}{4}{\text{ }}\left( {{\text{accept }}\frac{{5\pi }}{4}} \right)\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\left| {{z_1} + \alpha{z_2}} \right| = \sqrt {{{(1 - \alpha )}^2} + {{(3 - \alpha )}^2}} \) or the squared modulus <strong><em>(M1)(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">attempt to minimise \(2{\alpha ^2} - 8\alpha + 10\) or their quadratic or its half or its square root <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">obtain \(\alpha = 2\) at minimum <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">state \(\sqrt 2 \) as final answer <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Disappointingly, few candidates obtained the correct argument for the second complex number, mechanically using arctan(1) but not thinking about the position of the number in the complex plane.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates obtained the correct quadratic or its square root, but few knew how to set about minimising it.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">The same remainder is found when \(2{x^3} + k{x^2} + 6x + 32\) and \({x^4} - 6{x^2} - {k^2}x + 9\) are divided by \(x + 1\) . Find the possible values of <em>k </em>.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">let \(f(x) = 2{x^3} + k{x^2} + 6x + 32\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">let \(g(x) = {x^4} - 6{x^2} - {k^2}x + 9\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f( - 1) = - 2 + k - 6 + 32( = 24 + k)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(g( - 1) = 1 - 6 + {k^2} + 9( = 4 + {k^2})\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow 24 + k = 4 + {k^2}\) <strong> <em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow {k^2} - k - 20 = 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow (k - 5)(k + 4) = 0\) <strong> <em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow k = 5,\, - 4\) <strong> <em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]<br></em></strong></span></p>
<p> </p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Candidates who used the remainder theorem usually went on to find the two possible values of <em>k</em>. Some candidates, however, attempted to find the remainders using long division. While this is a valid method, the algebra involved proved to be too difficult for most of these candidates. </span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">When \(3{x^5} - ax + b\) is divided by <em>x</em> −1 and <em>x</em> +1 the remainders are equal. Given that a , \(b \in \mathbb{R}\) , find</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) the value of <em>a</em> ;</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) the set of values of <em>b</em> .</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \(f(1) = 3 - a + b\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f( - 1) = - 3 + a + b\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(3 - a + b = - 3 + a + b\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2a = 6\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(a = 3\) <strong><em>A1 N4</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) <em>b</em> is any real number <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates answered part (a) successfully. For part (b), some candidates did not consider that the entire set of real numbers was asked for.</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Express the quadratic \(3{x^2} - 6x + 5\) in the form \(a{(x + b)^2} + c\), where <em>a</em>, <em>b</em>, <em>c </em>\( \in \mathbb{Z}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Describe a sequence of transformations that transforms the graph of \(y = {x^2}\) to the graph of \(y = 3{x^2} - 6x + 5\).</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) attempt at completing the square <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(3{x^2} - 6x + 5 = 3({x^2} - 2x) + 5 = 3{(x - 1)^2} - 1 + 5\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 3{(x - 1)^2} + 2\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\((a = 3,{\text{ }}b = - 1,{\text{ }}c = 2)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) definition of suitable basic transformations:</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({{\text{T}}_1} = \) stretch in <em>y</em> direction scale factor 3 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({{\text{T}}_2} = \) translation \(\left( {\begin{array}{*{20}{c}}<br> 1 \\ <br> 0 <br>\end{array}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({{\text{T}}_3} = \) translation \(\left( {\begin{array}{*{20}{c}}<br> 0 \\ <br> 2 <br>\end{array}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">There were fewer correct solutions to this question than might be expected with a significant minority of candidates unable to complete the square successfully and a number of candidates unable to describe the transformations. A minority of candidates knew the correct terminology for the transformations and this potentially highlights the need for teachers to teach students appropriate terminology.</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">The function \(f\) is defined by \(f(x) = \frac{1}{x},{\text{ }}x \ne 0\).</p>
<p class="p1">The graph of the function \(y = g(x)\) is obtained by applying the following transformations to</p>
<p class="p1">the graph of \(y = f(x)\) :</p>
<p class="p1"> \({\text{a translation by the vector }}\left( {\begin{array}{*{20}{c}}{ - 3} \\ 0 \end{array}} \right);\) \({\text{a translation by the vector }}\left( {\begin{array}{*{20}{c}} 0 \\ 1 \end{array}} \right);\)</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find an expression for \(g(x)\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">State the equations of the asymptotes of the graph of \(g\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(g(x) = \frac{1}{{x + 3}} + 1\) <span class="Apple-converted-space"> </span><strong><em>A1A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>A1 </em></strong>for \(x + 3\) in the denominator and <strong><em>A1 </em></strong>for the “\( + 1\)”.</p>
<p class="p1"><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(x = - 3\) <strong><em>A1</em></strong></p>
<p>\(y = 1\) <strong><em>A1</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<p><strong><em>Total [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;">
<p class="p1">This question was generally well done. A few candidates made a sign error for the horizontal translation. A few candidates expressed the required equations for the asymptotes as ‘inequalities’, which received no marks.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">This question was generally well done. A few candidates made a sign error for the horizontal translation. A few candidates expressed the required equations for the asymptotes as ‘inequalities’, which received no marks.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Factorize \({z^3} + 1\) into a linear and quadratic factor.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(\gamma = \frac{{1 + {\text{i}}\sqrt 3 }}{2}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Show that \(\gamma \) is one of the cube roots of −1.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Show that \({\gamma ^2} = \gamma - 1\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) Hence find the value of \({(1 - \gamma )^6}\).</span></p>
<div class="marks">[9]</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="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">using the factor theorem <em>z</em> +1 is a factor <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({z^3} + 1 = (z + 1)({z^2} - z + 1)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) <strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({z^3} = - 1 \Rightarrow {z^3} + 1 = (z + 1)({z^2} - z + 1) = 0\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">solving \({z^2} - z + 1 = 0\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(z = \frac{{1 \pm \sqrt {1 - 4} }}{2} = \frac{{1 \pm {\text{i}}\sqrt 3 }}{2}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">therefore one cube root of −1 is \(\gamma \) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\gamma ^2} = \left( {{{\frac{{1 + i\sqrt 3 }}{2}}^2}} \right) = \frac{{ - 1 + i\sqrt 3 }}{2}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\gamma ^2} = \frac{{ - 1 + i\sqrt 3 }}{2} \times \frac{{1 + i\sqrt 3 }}{2} = \frac{{ - 1 - 3}}{4}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">= −1 AG</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 3</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\gamma = \frac{{1 + i\sqrt 3 }}{2} = {e^{i\frac{\pi }{3}}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\gamma ^3} = {e^{i\pi }} = - 1\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) <strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">as \(\gamma \) is a root of \({z^2} - z + 1 = 0\) then \({\gamma ^2} - \gamma + 1 = 0\) <strong><em>M1R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\therefore {\gamma ^2} = \gamma - 1\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Award </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>M1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for the use of \({z^2} - z + 1 = 0\) in any way.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Award <strong><em>R1</em></strong> for a correct reasoned approach.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\gamma ^2} = \frac{{ - 1 + i\sqrt 3 }}{2}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\gamma - 1 = \frac{{1 + i\sqrt 3 }}{2} - 1 = \frac{{ - 1 + i\sqrt 3 }}{2}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) <strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({(1 - \gamma )^6} = {( - {\gamma ^2})^6}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {(\gamma )^{12}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {({\gamma ^3})^4}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {( - 1)^4}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 1\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({(1 - \gamma )^6}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 1 - 6\gamma + 15{\gamma ^2} - 20{\gamma ^3} + 15{\gamma ^4} - 6{\gamma ^5} + {\gamma ^6}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Award </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>M1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for attempt at binomial expansion.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">use of any previous result </span><em style="font-family: 'times new roman', times; font-size: medium;">e.g.</em><span style="font-family: 'times new roman', times; font-size: medium;"> \( = 1 - 6\gamma + 15{\gamma ^2} + 20 - 15\gamma + 6{\gamma ^2} + 1\) </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>M1</em></strong></p>
<p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; font: 19px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">= 1 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> As the question uses the word ‘hence’, other methods that do not use previous results are awarded no marks.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[9 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">In part a) the factorisation was, on the whole, well done.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (b) was done well by most although using a substitution method rather than the result above. This used much m retime than was necessary but was successful. A number of candidates did not use the previous results in part (iii) and so seemed to not understand the use of the ‘hence’.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following diagram shows the graph of \(y = \frac{{{{(\ln x)}^2}}}{x},{\text{ }}x > 0\).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2017-01-31_om_06.37.32.png" alt="M16/5/MATHL/HP1/ENG/TZ1/13"></p>
</div>
<div class="specification">
<p class="p1">The region \(R\) is enclosed by the curve, the \(x\)-axis and the line \(x = e\).</p>
</div>
<div class="specification">
<p class="p1">Let \({I_n} = \int_1^{\text{e}} {\frac{{{{(\ln x)}^n}}}{{{x^2}}}{\text{d}}x,{\text{ }}n \in \mathbb{N}} \).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Given that the curve passes through the point \((a,{\text{ }}0)\)<span class="s1">, state the value of \(a\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Use the substitution \(u = \ln x\) to find the area of the region \(R\).</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Find the value of \({I_0}\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Prove that \({I_n} = \frac{1}{{\text{e}}} + n{I_{n - 1}},{\text{ }}n \in {\mathbb{Z}^ + }\).</p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>Hence find the value of \({I_1}\).</p>
<div class="marks">[7]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the volume of the solid formed when the region \(R\) <span class="s1">is rotated through \(2\pi \) </span>about the \(x\)-axis.</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 class="p1"><span class="Apple-converted-space">\(a = 1\) </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(\frac{{{\text{d}}u}}{{{\text{d}}x}} = \frac{1}{x}\) </span><strong><em>(A1)</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\(\int {\frac{{{{(\ln x)}^2}}}{x}{\text{d}}x = \int {{u^2}{\text{d}}u} } \) </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p2">area \( = \left[ {\frac{1}{3}{u^3}} \right]_0^1\) or \(\left[ {\frac{1}{3}{{(\ln x)}^3}} \right]_1^{\text{e}}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p3"><span class="Apple-converted-space">\( = \frac{1}{3}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> \({I_0} = \left[ { - \frac{1}{x}} \right]_1^{\text{e}}\)</span> <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\( = 1 - \frac{1}{{\text{e}}}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>use of integration by parts <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p3"><span class="Apple-converted-space">\({I_n} = \left[ { - \frac{1}{x}{{(\ln x)}^n}} \right]_1^{\text{e}} + \int_1^{\text{e}} {\frac{{n{{(\ln x)}^{n - 1}}}}{{{x^2}}}{\text{d}}x} \) </span><span class="s1"><strong><em>A1A1</em></strong></span></p>
<p class="p2"><span class="Apple-converted-space">\( = - \frac{1}{{\text{e}}} + n{I_{n - 1}}\) </span><span class="s1"><strong><em>AG</em></strong></span></p>
<p class="p4"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>If the substitution \(u = \ln x\) is used <strong><em>A1A1 </em></strong>can be awarded for \({I_n} = [ - {{\text{e}}^{ - u}}{u^n}]_0^1 + \int_0^1 n {{\text{e}}^{ - u}}{u^{n - 1}}{\text{d}}u\).</p>
<p class="p4"> </p>
<p class="p1">(iii) <span class="Apple-converted-space"> \({I_1} = - \frac{1}{{\text{e}}} + 1 \times {I_0}\)</span> <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\( = 1 - \frac{2}{{\text{e}}}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong><em>[7 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(d) <span class="Apple-converted-space"> </span>volume \( = \pi \int_1^{\text{e}} {\frac{{{{(\ln x)}^4}}}{{{x^2}}}{\text{d}}x{\text{ }}( = \pi {I_4})} \) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1"><strong>EITHER</strong></p>
<p class="p2"><span class="Apple-converted-space">\({I_4} = - \frac{1}{{\text{e}}} + 4{I_3}\) </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p3"><span class="Apple-converted-space">\( = - \frac{1}{{\text{e}}} + 4\left( { - \frac{1}{{\text{e}}} + 3{I_2}} \right)\) </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p3">\( = - \frac{5}{{\text{e}}} + 12{I_2} = - \frac{5}{{\text{e}}} + 12\left( { - \frac{1}{{\text{e}}} + 2{I_1}} \right)\)</p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">using parts \(\int_1^{\text{e}} {\frac{{{{(\ln x)}^4}}}{{{x^2}}}{\text{d}}x = - \frac{1}{{\text{e}}} + 4\int_1^{\text{e}} {\frac{{{{(\ln x)}^3}}}{{{x^2}}}{\text{d}}x} } \) <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\( = - \frac{1}{{\text{e}}} + 4\left( { - \frac{1}{{\text{e}}} + 3\int_1^{\text{e}} {\frac{{{{(\ln x)}^2}}}{{{x^2}}}{\text{d}}x} } \right)\) </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p1"><strong>THEN</strong></p>
<p class="p3"><span class="Apple-converted-space">\( = - \frac{{17}}{{\text{e}}} + 24\left( {1 - \frac{2}{{\text{e}}}} \right) = 24 - \frac{{65}}{{\text{e}}}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p3">volume \( = \pi \left( {24 - \frac{{65}}{{\text{e}}}} \right)\)</p>
<p class="p1"><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">(a) and (b) were well done. Most candidates could integrate by substitution, though many did not change the limits during the substitution and, though they changed back to \(x\) at the end of their solution, under a different markscheme they might have lost marks for this in the intermediate stages.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(a) and (b) were well done. Most candidates could integrate by substitution, though many did not change the limits during the substitution and, though they changed back to \(x\) at the end of their solution, under a different markscheme they might have lost marks for this in the intermediate stages.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(c)(i) This part was well done by the candidates.</p>
<p class="p1">(c)(ii) This proved to be the part that was done by fewest candidates. Those who spotted that they should use integration by parts obtained the answer fairly easily.</p>
<p class="p1">(c)(iii) Many candidates displayed good exam technique in this question and obtained full marks without being able to do part (ii).</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">The same good exam technique was on show here as many students who failed to prove the expression in (c)(ii) were able to use it to obtain full marks in this question. A few candidates failed to remember correctly the formula for a volume of revolution.</p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">Given that \(A{x^3} + B{x^2} + x + 6\) is exactly divisible by \((x +1)(x − 2)\), find the value of <em>A</em> and the value of <em>B</em> .</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">using the factor theorem or long division <em><strong>(M1)</strong></em></span><br><span style="font-family: times new roman,times; font-size: medium;">\( - A + B - 1 + 6 = 0 \Rightarrow A - B = 5\) <em><strong>(A1)</strong></em></span><br><span style="font-family: times new roman,times; font-size: medium;">\(8A + 4B + 2 + 6 = 0 \Rightarrow 2A + B = - 2\) <em><strong>(A1)</strong></em></span><br><span style="font-family: times new roman,times; font-size: medium;">\(3A = 3 \Rightarrow A = 1\) <em><strong>(A1)</strong></em></span><br><span style="font-family: times new roman,times; font-size: medium;">\(B = - 4\) <em><strong>(A1) (N3)</strong></em></span></p>
<p><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Award </span><em style="font-family: 'times new roman', times; font-size: medium;"><strong>M1A0A0A1A1</strong></em><span style="font-family: 'times new roman', times; font-size: medium;"> for using \((x - 3)\) as the third factor, without justification that the leading coefficient is 1.</span></p>
<p><em style="font-family: 'times new roman', times; font-size: medium;"><strong> </strong></em></p>
<p><em style="font-family: 'times new roman', times; font-size: medium;"><strong>[5 marks]</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates attempted this question and it was the best done question on the paper with many fully correct answers. It was good to see a range of approaches used (mainly factor theorem or long division). A number of candidates assumed \((x - 3)\) was the missing factor without justification.</span></p>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The function <em>f</em> is defined, for \( - \frac{\pi }{2} \leqslant x \leqslant \frac{\pi }{2}\) , by \(f(x) = 2\cos x + x\sin x\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Determine whether <em>f</em> is even, odd or neither even nor odd.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Show that \(f''(0) = 0\) .</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">John states that, because \(f''(0) = 0\) , the graph of <em>f</em> has a point of inflexion at the point (0, 2) . Explain briefly whether John’s statement is correct or not.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f( - x) = 2\cos ( - x) + ( - x)\sin ( - x)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 2\cos x + x\sin x\,\,\,\,\,\left( { = f(x)} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">therefore <em>f</em> is even <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 36.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(x) = - 2\sin x + \sin x + x\cos x\,\,\,\,\,( = - \sin x + x\cos x)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 36.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f''(x) = - \cos x + \cos x - x\sin x\,\,\,\,\,( = - x\sin x)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 36.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so \(f''(0) = 0\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 36.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">John’s statement is incorrect because</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">either; there is a stationary point at (0, 2) and since <em>f</em> is an even function and therefore symmetrical about the <em>y</em>-axis it must be a maximum or a minimum</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">or; \(f''(x)\) is even and therefore has the same sign either side of (0, 2) <strong><em>R2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Sketch the graph of \(y = \left| {\cos \left( {\frac{x}{4}} \right)} \right|\) for \(0 \leqslant x \leqslant 8\pi \).</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Solve \(\left| {\cos \left( {\frac{x}{4}} \right)} \right| = \frac{1}{2}\) for \(0 \leqslant x \leqslant 8\pi \).</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="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><img src="images/maths_5a_markscheme.png" alt> <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1 </em></strong>for correct shape and <strong><em>A1 </em></strong>for correct domain and range.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\left| {\cos \left( {\frac{x}{4}} \right)} \right| = \frac{1}{2}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = \frac{{4\pi }}{3}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">attempting to find any other solutions <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>(M1) </em></strong>if at least one of the other solutions is correct (in radians or degrees) or clear use of symmetry is seen.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 8\pi - \frac{{4\pi }}{3} = \frac{{20 \pi }}{3}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 4\pi - \frac{{4\pi }}{3} = \frac{{8\pi }}{3}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 4\pi + \frac{{4\pi }}{3} = \frac{{16\pi }}{3}\) <strong><em>A</em>1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1 </em></strong>for all other three solutions correct and no extra solutions.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> If working in degrees, then max <strong><em>A0M1A0</em></strong>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">The functions <em>f</em> and <em>g</em> are defined as:</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\[f(x) = {{\text{e}}^{{x^2}}},{\text{ }}x \geqslant 0\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\[g(x) = \frac{1}{{x + 3}},{\text{ }}x \ne - 3.\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Find \(h(x){\text{ where }}h(x) = g \circ f(x)\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) State the domain of \({h^{ - 1}}(x)\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) Find \({h^{ - 1}}(x)\) .</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \(h(x) = g \circ f(x) = \frac{1}{{{{\text{e}}^{{x^2}}} + 3}},{\text{ }}(x \geqslant 0)\) <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) \(0 < x \leqslant \frac{1}{4}\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Award </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for limits and </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for correct inequality signs.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) \(y = \frac{1}{{{{\text{e}}^{{x^2}}} + 3}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(y{{\text{e}}^{{x^2}}} + 3y = 1\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({{\text{e}}^{{x^2}}} = \frac{{1 - 3y}}{y}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x^2} = \ln \frac{{1 - 3y}}{y}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = \pm \sqrt {\ln \frac{{1 - 3y}}{y}} \)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow {h^{ - 1}}(x) = \sqrt {\ln \frac{{1 - 3x}}{x}} {\text{ }}\left( { = \sqrt {\ln \left( {\frac{1}{x} - 3} \right)} } \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[8 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was correctly done by the vast majority of candidates. In contrast, only the very best students gave the correct answer to part (b). Part (c) was correctly started by a majority of candidates, but many did not realise that they needed to use logarithms and were careless about the use of notation</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">When \(f(x) = {x^4} + 3{x^3} + p{x^2} - 2x + q\) is divided by (<em>x</em> − 2) the remainder is 15, and (<em>x</em> + 3) is a factor of <em>f</em>(<em>x</em>) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the values of <em>p</em> and <em>q</em> .</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(2) = 16 + 24 + 4p - 4 + q = 15\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow 4p + q = - 21\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f( - 3) = 81 - 81 + 9p + 6 + q = 0\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow 9p + q = - 6\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow p = 3{\text{ and }}q = - 33\) <strong><em>A1A1</em></strong> <strong><em>N0</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates made a meaningful attempt at this question. Weaker candidates often made arithmetic errors and a few candidates tried using long division, which also often resulted in arithmetic errors. Overall there were many fully correct solutions.</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Solve the following equations:</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \({\log _2}(x - 2) = {\log _4}({x^2} - 6x + 12)\);</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(b) \({x^{\ln x}} = {{\text{e}}^{{{(\ln x)}^3}}}\).</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \({\log _2}(x - 2) = {\log _4}({x^2} - 6x + 12)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\log _2}(x - 2) = \frac{{{{\log }_2}({x^2} - 6x + 12)}}{{{{\log }_2}4}}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2{\log _2}(x - 2) = {\log _2}({x^2} - 6x + 12)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{{\log }_4}(x - 2)}}{{{{\log }_4}2}} = {\log _4}({x^2} - 6x + 12)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2{\log _4}(x - 2) = {\log _4}({x^2} - 6x + 12)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>THEN</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({(x - 2)^2} = {x^2} - 6x + 12\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x^2} - 4x + 4 = {x^2} - 6x + 12\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 4\) <strong><em>A1 N1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) \({x^{\ln x}} = {{\text{e}}^{{{(\ln x)}^3}}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">taking ln of both sides or writing \(x = {{\text{e}}^{\ln x}}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({(\ln x)^2} = {(\ln x)^3}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({(\ln x)^2}(\ln x - 1) = 0\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 1,{\text{ }}x = {\text{e}}\) <strong><em>A1A1 N2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award second (<strong><em>A1) </em></strong>only if factorisation seen or if two correct</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">solutions are seen.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [8 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part a) was answered well, and a very large proportion of candidates displayed familiarity and confidence with this type of change-of base equation.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In part b), good candidates were able to solve this proficiently. A number obtained only one solution, either through observation or mistakenly cancelling a \(\ln x\) term. An incorrect solution \(x = {{\text{e}}^3}\) was somewhat prevalent amongst the weaker candidates.</span></p>
</div>
<br><hr><br><div class="specification">
<p>The function \(f\) is defined by \(f\left( x \right) = \frac{{ax + b}}{{cx + d}}\), for \(x \in \mathbb{R},\,\,x \ne - \frac{d}{c}\).</p>
</div>
<div class="specification">
<p>The function \(g\) is defined by \(g\left( x \right) = \frac{{2x - 3}}{{x - 2}},\,\,x \in \mathbb{R},\,\,x \ne 2\)</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the inverse function \({f^{ - 1}}\), stating its domain.</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>Express \(g\left( x \right)\) in the form \(A + \frac{B}{{x - 2}}\) where A, B are constants.</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>Sketch the graph of \(y = g\left( x \right)\). State the equations of any asymptotes and the coordinates of any intercepts with the axes.</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>The function \(h\) is defined by \(h\left( x \right) = \sqrt x \), for \(x\) ≥ 0.</p>
<p>State the domain and range of \(h \circ g\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>attempt to make \(x\) the subject of \(y = \frac{{ax + b}}{{cx + d}}\) <em><strong>M1</strong></em></p>
<p>\(y\left( {cx + d} \right) = ax + b\) <em><strong>A1</strong></em></p>
<p>\(x = \frac{{dy - b}}{{a - cy}}\) <em><strong>A1</strong></em></p>
<p>\({f^{ - 1}}\left( x \right) = \frac{{dx - b}}{{a - cx}}\) <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Do not allow \(y = \) in place of \({f^{ - 1}}\left( x \right)\).</p>
<p>\(x \ne \frac{a}{c},\,\,\,\left( {x \in \mathbb{R}} \right)\) <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> The final <em><strong>A</strong></em> mark is independent.</p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(g\left( x \right) = 2 + \frac{1}{{x - 2}}\) <em><strong> A1A1</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><img 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"></p>
<p>hyperbola shape, with single curves in second and fourth quadrants and third quadrant blank, including vertical asymptote \(x = 2\) <em><strong>A1</strong></em></p>
<p>horizontal asymptote \(y = 2\) <em><strong>A1</strong></em></p>
<p>intercepts \(\left( {\frac{3}{2},\,0} \right),\,\left( {0,\,\frac{3}{2}} \right)\) <em><strong>A1</strong></em></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>the domain of \(h \circ g\) is \(x \leqslant \frac{3}{2},\,\,x > 2\) <em><strong>A1A1</strong></em></p>
<p>the range of \(h \circ g\) is \(y \geqslant 0,\,\,y \ne \sqrt 2 \) <em><strong>A1A1</strong></em></p>
<p><em><strong>[4 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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The function <em>f</em> is defined by \(f(x) = \frac{1}{{4{x^2} - 4x + 5}}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Express \(4{x^2} - 4x + 5\) in the form \(a{(x - h)^2} + k\) where <em>a</em>, <em>h</em>, \(k \in \mathbb{Q}\).</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The graph of \(y = {x^2}\) is transformed onto the graph of \(y = 4{x^2} - 4x + 5\). Describe a sequence of transformations that does this, making the order of transformations clear.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Sketch the graph of \(y = f(x)\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the range of <em>f</em>.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">By using a suitable substitution show that \(\int {f(x){\text{d}}x = \frac{1}{4}\int {\frac{1}{{{u^2} + 1}}{\text{d}}u} } \).</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Prove that \(\int_1^{3.5} {\frac{1}{{4{x^2} - 4x + 5}}{\text{d}}x = \frac{\pi }{{16}}} \).</span></p>
<div class="marks">[7]</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="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(4{(x - 0.5)^2} + 4\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note: </strong><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for two correct parameters, </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A2</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for all three correct.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">translation \(\left( {\begin{array}{*{20}{c}}<br> {0.5} \\ <br> 0 <br>\end{array}} \right)\) (allow “0.5 to the right”) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">stretch parallel to <em>y</em>-axis, scale factor 4 (allow vertical stretch or similar) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">translation \(\left( {\begin{array}{*{20}{c}}<br> 0 \\ <br> 4 <br>\end{array}} \right)\) (allow “4 up”) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> All transformations must state magnitude and direction.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> First two transformations can be in either order.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">It could be a stretch followed by a single translation of </span><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\left( {\begin{array}{*{20}{c}}<br> {0.5} \\ <br> 4 <br>\end{array}} \right)\)</span>. If the vertical translation is before the stretch it is \(\left( {\begin{array}{*{20}{c}}<br> 0 \\ <br> 1 <br>\end{array}} \right)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><img 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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">general shape (including asymptote and single maximum in first quadrant), <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">intercept \(\left( {0,\frac{1}{5}} \right)\) or maximum \(\left( {\frac{1}{2},\frac{1}{4}} \right)\) shown <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(0 < f(x) \leqslant \frac{1}{4}\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note: </strong><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for \( \leqslant \frac{1}{4}\), </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for \(0 < \).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">let \(u = x - \frac{1}{2}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}u}}{{{\text{d}}x}} = 1\,\,\,\,\,{\text{(or d}}u = {\text{d}}x)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {\frac{1}{{4{x^2} - 4x + 5}}{\text{d}}x = \int {\frac{1}{{4{{\left( {x - \frac{1}{2}} \right)}^2} + 4}}{\text{d}}x} } \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {\frac{1}{{4{u^2} + 4}}{\text{d}}u = \frac{1}{4}\int {\frac{1}{{{u^2} + 1}}{\text{d}}u} } \) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> If following through an incorrect answer to part (a), do not award final </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> mark.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int_1^{3.5} {\frac{1}{{4{x^2} - 4x + 5}}{\text{d}}x = \frac{1}{4}\int_{0.5}^3 {\frac{1}{{{u^2} + 1}}{\text{d}}u} } \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note: </strong><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for correct change of limits. Award also if they do not change limits but go back to </span><em style="font-family: 'times new roman', times; font-size: medium;">x</em><span style="font-family: 'times new roman', times; font-size: medium;"> values when substituting the limit (even if there is an error in the integral).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{1}{4}\left[ {\arctan (u)} \right]_{0.5}^3\) </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>(M1)</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{1}{4}\left( {\arctan (3) - \arctan \left( {\frac{1}{2}} \right)} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">let the integral = <em>I</em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\tan 4I = \tan \left( {\arctan (3) - \arctan \left( {\frac{1}{2}} \right)} \right)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{3 - 0.5}}{{1 + 3 \times 0.5}} = \frac{{2.5}}{{2.5}} = 1\) <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(4I = \frac{\pi }{4} \Rightarrow I = \frac{\pi }{{16}}\) <strong><em>A1AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question covered many syllabus areas, completing the square, transformations of graphs, range, integration by substitution and compound angle formulae. There were many good solutions to parts (a) – (e).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question covered many syllabus areas, completing the square, transformations of graphs, range, integration by substitution and compound angle formulae. There were many good solutions to parts (a) – (e) but the following points caused some difficulties.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(b) Exam technique would have helped those candidates who could not get part (a) correct as any solution of the form given in the question could have led to full marks in part (b). Several candidates obtained expressions which were not of this form in (a) and so were unable to receive any marks in (b) Many missed the fact that if a vertical translation is performed before the vertical stretch it has a different magnitude to if it is done afterwards. Though on this occasion the markscheme was fairly flexible in the words it allowed to be used by candidates to describe the transformations it would be less risky to use the correct expressions.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question covered many syllabus areas, completing the square, transformations of graphs, range, integration by substitution and compound angle formulae. There were many good solutions to parts (a) – (e) but the following points caused some difficulties.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(c) Generally the sketches were poor. The general rule for all sketch questions should be that any asymptotes or intercepts should be clearly labelled. Sketches do not need to be done on graph paper, but a ruler should be used, particularly when asymptotes are involved.<br></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question covered many syllabus areas, completing the square, transformations of graphs, range, integration by substitution and compound angle formulae. There were many good solutions to parts (a) – (e).</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question covered many syllabus areas, completing the square, transformations of graphs, range, integration by substitution and compound angle formulae. There were many good solutions to parts (a) – (e) but the following points caused some difficulties.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(e) and (f) were well done up to the final part of (f), in which candidates did not realise they needed to use the compound angle formula.<br></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question covered many syllabus areas, completing the square, transformations of graphs, range, integration by substitution and compound angle formulae. There were many good solutions to parts (a) – (e) but the following points caused some difficulties.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(e) and (f) were well done up to the final part of (f), in which candidates did not realise they needed to use the compound angle formula.<br></span></p>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The function <em>f</em> is defined by \(f(x) = \frac{{2x - 1}}{{x + 2}}\), with domain \(D = \{ x: - 1 \leqslant x \leqslant 8\} \).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Express \(f(x)\) in the form \(A + \frac{B}{{x + 2}}\), where \(A\) and \(B \in \mathbb{Z}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Hence show that \(f'(x) > 0\) on <em>D</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">State the range of <em>f</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Find an expression for \({f^{ - 1}}(x)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Sketch the graph of \(y = f(x)\), showing the points of intersection with both axes.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) On the same diagram, sketch the graph of \(y = f'(x)\).</span></p>
<div class="marks">[8]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) On a different diagram, sketch the graph of \(y = f(|x|)\) where \(x \in D\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Find all solutions of the equation \(f(|x|) = - \frac{1}{4}\).</span></p>
<div class="marks">[7]</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="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">by division or otherwise</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(x) = 2 - \frac{5}{{x + 2}}\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(x) = \frac{5}{{{{(x + 2)}^2}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">> 0 as \({(x + 2)^2} > 0\) (on <em>D</em>) <strong><em>R1AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Do not penalise candidates who use the original form of the function to compute its derivative.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 36.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(S = \left[ { - 3,\frac{3}{2}} \right]\) <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 36.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Award </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1A0</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for the correct endpoints and an open interval.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 36.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 36.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) <strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">rearrange \(y = f(x)\) to make <em>x</em> the subject <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">obtain one-line equation, <em>e.g.</em> \(2x - 1 = xy + 2y\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = \frac{{2y + 1}}{{2 - y}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong> </strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">interchange <em>x</em> and <em>y</em> <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">obtain one-line equation, <em>e.g.</em> \(2y - 1 = xy + 2x\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(y = \frac{{2x + 1}}{{2 - x}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong> </strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>THEN</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({f^{ - 1}}(x) = \frac{{2x + 1}}{{2 - x}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Accept \(\frac{5}{{2 - x}} - 2\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii), (iii) <br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><img 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" alt><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> A1A1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[8 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"> </strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Award </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for correct shape of \(y = f(x)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Award <strong><em>A1</em></strong> for <em>x</em> intercept \(\frac{1}{2}\) seen. Award <strong><em>A1</em></strong> for <em>y</em> intercept \( - \frac{1}{2}\) seen.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Award <strong><em>A1</em></strong> for the graph of \(y = {f^{ - 1}}(x)\) being the reflection of \(y = f(x)\) in the line \(y = x\). Candidates are not required to indicate the full domain, but \(y = f(x)\) should not be shown approaching \(x = - 2\). Candidates, in answering (iii), can <strong>FT</strong> on their sketch in (ii).</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><img src="data:image/png;base64,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" alt><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> A1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> <strong><em>A1</em></strong> for correct sketch \(x > 0\), <strong><em>A1</em></strong> for symmetry, <strong><em>A1</em></strong> for correct domain (from –1 to +8).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Candidates can <strong>FT</strong> on their sketch in (d)(ii).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) attempt to solve \(f(x) = - \frac{1}{4}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">obtain \(x = \frac{2}{9}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">use of symmetry or valid algebraic approach <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">obtain \(x = - \frac{2}{9}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Generally well done.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In their answers to Part (b), most candidates found the derivative, but many assumed it was obviously positive.</span></p>
<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;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (d)(i) Generally well done, but some candidates failed to label their final expression as \({f^{ - 1}}(x)\). Part (d)(ii) Marks were lost by candidates who failed to mark the intercepts with values.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Marks were also lost in this part and in part (e)(i) for graphs that went beyond the explicitly stated domain.</span></p>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The function \(f\) is defined as \(f(x) = {{\text{e}}^{3x + 1}},{\text{ }}x \in \mathbb{R}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Find \({f^{ - 1}}(x)\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>State the domain of \({f^{ - 1}}\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The function \(g\) is defined as \(g(x) = \ln x,{\text{ }}x \in {\mathbb{R}^ + }\).</p>
<p class="p1">The graph of \(y = g(x)\) and the graph of \(y = {f^{ - 1}}(x)\) intersect at the point \(P\).</p>
<p class="p1">Find the coordinates of \(P\).</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The graph of \(y = g(x)\) intersects the \(x\)-axis at the point \(Q\).</p>
<p class="p1">Show that the equation of the tangent \(T\) to the graph of \(y = g(x)\) at the point \(Q\) is \(y = x - 1\).</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 class="p1">A region \(R\) is bounded by the graphs of \(y = g(x)\), the tangent \(T\) and the line \(x = {\text{e}}\).</p>
<p class="p1">Find the area of the region \(R\).</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">A region \(R\) is bounded by the graphs of \(y = g(x)\), the tangent \(T\) and the line \(x = {\text{e}}\).</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>Show that \(g(x) \le x - 1,{\text{ }}x \in {\mathbb{R}^ + }\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>By replacing \(x\) with \(\frac{1}{x}\) in part (e)(i), show that \(\frac{{x - 1}}{x} \le g(x),{\text{ }}x \in {\mathbb{R}^ + }\).</p>
<div class="marks">[6]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>\(x = {{\text{e}}^{3y + 1}}\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>The <strong><em>M1 </em></strong>is for switching variables and can be awarded at any stage.</p>
<p class="p1">Further marks do not rely on this mark being awarded.</p>
<p class="p2"> </p>
<p class="p1">taking the natural logarithm of both sides and attempting to transpose <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">\(\left( {{f^{ - 1}}(x)} \right) = \frac{1}{3}(\ln x - 1)\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\(x \in {\mathbb{R}^ + }\) or equivalent, for example \(x > 0\). <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\ln x = \frac{1}{3}(\ln x - 1) \Rightarrow \ln x - \frac{1}{3}\ln x = - \frac{1}{3}\) (or equivalent) <strong><em>M1A1</em></strong></p>
<p>\(\ln x = - \frac{1}{2}\) (or equivalent) <strong><em>A1</em></strong></p>
<p>\(x = {{\text{e}}^{ - \frac{1}{2}}}\) <strong><em>A1</em></strong></p>
<p>coordinates of \(P\) are \(\left( {{{\text{e}}^{ - \frac{1}{2}}},{\text{ }} - \frac{1}{2}} \right)\) <strong><em>A1</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">coordinates of \(Q\) are (\(1,{\rm{ }}0\)) seen anywhere <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{1}{x}\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">at \({\text{Q, }}\frac{{{\text{d}}y}}{{{\text{d}}x}} = 1\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">\(y = x - 1\) <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">let the required area be \(A\)</p>
<p class="p1">\(A = \int_1^e {x - 1{\text{d}}x - \int_1^e {\ln x{\text{d}}x} } \) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>The <strong><em>M1 </em></strong>is for a difference of integrals. Condone absence of limits here.</p>
<p class="p2"> </p>
<p class="p1">attempting to use integration by parts to find \(\int {\ln x{\text{d}}x} \) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1">\( = \left[ {\frac{{{x^2}}}{2} - x} \right]_1^{\text{e}} - [x\ln x - x]_1^{\text{e}}\) <span class="Apple-converted-space"> </span><strong><em>A1A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>A1 </em></strong>for \(\frac{{{x^2}}}{2} - x\) and <strong><em>A1 </em></strong>for \(x\ln x - x\).</p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>The second <strong><em>M1 </em></strong>and second <strong><em>A1 </em></strong>are independent of the first <strong><em>M1 </em></strong>and the first <strong><em>A1</em></strong>.</p>
<p class="p2"> </p>
<p class="p1">\( = \frac{{{{\text{e}}^2}}}{2} - {\text{e}} - \frac{1}{2}\left( { = \frac{{{{\text{e}}^2} - 2{\text{e}} - 1}}{2}} \right)\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) <strong>METHOD 1</strong></p>
<p>consider for example \(h(x) = x - 1 - \ln x\)</p>
<p>\(h(1) = 0\;\;\;{\text{and}}\;\;\;h'(x) = 1 - \frac{1}{x}\) <strong><em>(A1)</em></strong></p>
<p>as \(h'(x) \ge 0\;\;\;{\text{for}}\;\;\;x \ge 1,\;\;\;{\text{then}}\;\;\;h(x) \ge 0\;\;\;{\text{for}}\;\;\;x \ge 1\) <strong><em>R1</em></strong></p>
<p>as \(h'(x) \le 0\;\;\;{\text{for}}\;\;\;0 < x \le 1,\;\;\;{\text{then}}\;\;\;h(x) \ge 0\;\;\;{\text{for}}\;\;\;0 < x \le 1\) <strong><em>R1</em></strong></p>
<p>so \(g(x) \le x - 1,{\text{ }}x \in {\mathbb{R}^ + }\) <strong><em>AG</em></strong></p>
<p class="p1"><strong>METHOD 2</strong></p>
<p>\(g''(x) = - \frac{1}{{{x^2}}}\) <strong><em>A1</em></strong></p>
<p>\(g''(x) < 0\;\;\;\)(concave down) for\(\;\;\;x \in {\mathbb{R}^ + }\) <strong><em>R1</em></strong></p>
<p class="p1">the graph of \(y = g(x)\) is below its tangent \((y = x - 1\;\;\;{\text{at}}\;\;\;x = 1)\) <strong><em>R1</em></strong></p>
<p class="p1">so \(g(x) \le x - 1,{\text{ }}x \in {\mathbb{R}^ + }\) <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>The reasoning may be supported by drawn graphical arguments.</p>
<p class="p2"> </p>
<p class="p1"><strong>METHOD 3</strong></p>
<p class="p1"><img src="data:image/png;base64,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" alt></p>
<p class="p1">clear correct graphs of \(y = x - 1\;\;\;{\text{and}}\;\;\;\ln x\;\;\;{\text{for}}\;\;\;x > 0\) <span class="Apple-converted-space"> </span><strong><em>A1A1</em></strong></p>
<p class="p1">statement to the effect that the graph of \(\ln x\) is below the graph of its tangent at \(x = 1\) <span class="Apple-converted-space"> </span><strong><em>R1AG</em></strong></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>replacing \(x\) by \(\frac{1}{x}\) to obtain \(\ln \left( {\frac{1}{x}} \right) \le \frac{1}{x} - 1\left( { = \frac{{1 - x}}{x}} \right)\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">\( - \ln x \le \frac{1}{x} - 1\left( { = \frac{{1 - x}}{x}} \right)\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1">\(\ln x \ge 1 - \frac{1}{x}\left( { = \frac{{x - 1}}{x}} \right)\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">so \(\frac{{x - 1}}{x} \le g(x),{\text{ }}x \in {\mathbb{R}^ + }\) <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p1"><strong><em>[6 marks]</em></strong></p>
<p class="p1"><strong><em>Total [23 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;">
<p class="p1">Generally very well done, even by candidates who had shown considerable weaknesses elsewhere on the paper.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Generally very well done, even by candidates who had shown considerable weaknesses elsewhere on the paper.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Generally very well done, even by candidates who had shown considerable weaknesses elsewhere on the paper.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">A productive question for many candidates, but some didn’t realise that a difference of areas/integrals was required.</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) Many candidates adopted a graphical approach, but sometimes with unconvincing reasoning.</p>
<p class="p1">(ii) Poorly answered. Many candidates applied the suggested substitution only to one side of the inequality, and then had to fudge the answer.</p>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The random variable <em>X</em> has probability density function <em>f</em> where</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[f(x) = \left\{ {\begin{array}{*{20}{c}}<br> {kx(x + 1)(2 - x),}&{0 \leqslant x \leqslant 2} \\ <br> {0,}&{{\text{otherwise }}{\text{.}}} <br>\end{array}} \right.\]</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Sketch the graph of the function. You are not required to find the coordinates of the maximum.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the value of <em>k</em> .</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em><img 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" alt> A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong> </strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1</em></strong> for intercepts of 0 and 2 and a concave down curve in the given domain .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A0</em></strong> if the cubic graph is extended outside the domain [0, 2] .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em><strong>[1 mark]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int_0^2 {kx(x + 1)(2 - x){\text{d}}x = 1} \) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> The correct limits and =1 must be seen but may be seen later.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(k\int_0^2 {( - {x^3} + {x^2} + 2x){\text{d}}x = 1} \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(k\left[ { - \frac{1}{4}{x^4} + \frac{1}{3}{x^3} + {x^2}} \right]_0^2 = 1\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(k\left( { - 4 + \frac{8}{3} + 4} \right) = 1\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(k = \frac{3}{8}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates completed this question well. A number extended the graph beyond the given domain.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates completed this question well. A number extended the graph beyond the given domain.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let \(f\left( x \right) = \frac{{2 - 3{x^5}}}{{2{x^3}}},\,\,x \in \mathbb{R},\,\,x \ne 0\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The graph of \(y = f\left( x \right)\) has a local maximum at A. Find the coordinates of A.</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 there is exactly one point of inflexion, B, on the graph of \(y = f\left( x \right)\).</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The coordinates of B can be expressed in the form B\(\left( {{2^a},\,b \times {2^{ - 3a}}} \right)\) where <em>a</em>, <em>b</em>\( \in \mathbb{Q}\). Find the value of <em>a</em> and the value of <em>b</em>.</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>Sketch the graph of \(y = f\left( x \right)\) showing clearly the position of the points A and B.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>attempt to differentiate <em><strong> (M1)</strong></em></p>
<p>\(f'\left( x \right) = - 3{x^{ - 4}} - 3x\) <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>M1</strong> </em>for using quotient or product rule award <em><strong>A1</strong> </em>if correct derivative seen even in unsimplified form, for example \(f'\left( x \right) = \frac{{ - 15{x^4} \times 2{x^3} - 6{x^2}\left( {2 - 3{x^5}} \right)}}{{{{\left( {2{x^3}} \right)}^2}}}\).</p>
<p>\( - \frac{3}{{{x^4}}} - 3x = 0\) <em><strong>M1</strong></em></p>
<p>\( \Rightarrow {x^5} = - 1 \Rightarrow x = - 1\) <em><strong>A1</strong></em></p>
<p>\({\text{A}}\left( { - 1,\, - \frac{5}{2}} \right)\) <em><strong>A1</strong></em></p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(f''\left( x \right) = 0\) <em><strong>M1</strong></em></p>
<p>\(f''\left( x \right) = 12{x^{ - 5}} - 3\left( { = 0} \right)\) <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>A1</strong></em> for correct derivative seen even if not simplified.</p>
<p>\( \Rightarrow x = \sqrt[5]{4}\left( { = {2^{\frac{2}{5}}}} \right)\) <em><strong>A1</strong></em></p>
<p>hence (at most) one point of inflexion <em><strong>R1</strong></em></p>
<p><strong>Note:</strong> This mark is independent of the two <em><strong>A1</strong> </em>marks above. If they have shown or stated their equation has only one solution this mark can be awarded.</p>
<p>\(f''\left( x \right)\) changes sign at \(x = \sqrt[5]{4}\left( { = {2^{\frac{2}{5}}}} \right)\) <em><strong>R1</strong></em></p>
<p>so exactly one point of inflexion</p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(x = \sqrt[5]{4} = {2^{\frac{2}{5}}}\left( { \Rightarrow a = \frac{2}{5}} \right)\) <em><strong>A1</strong></em></p>
<p>\(f\left( {{2^{\frac{2}{5}}}} \right) = \frac{{2 - 3 \times {2^2}}}{{2 \times {2^{\frac{6}{5}}}}} = - 5 \times {2^{ - \frac{6}{5}}}\left( { \Rightarrow b = - 5} \right)\) <em><strong>(M1)A1</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>M1</strong> </em>for the substitution of their value for \(x\) into \(f\left( x \right)\).</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><img src="data:image/png;base64,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"><em><strong>A1A1A1A1</strong></em></p>
<p><em><strong>A1</strong></em> for shape for <em>x</em> < 0<br><em><strong>A1 </strong></em>for shape for <em>x</em> > 0<br><em><strong>A1 </strong></em>for maximum at A<br><em><strong>A1 </strong></em>for POI at B.</p>
<p><strong>Note:</strong> Only award last two <em><strong>A1</strong></em>s if A and B are placed in the correct quadrants, allowing for follow through.</p>
<p><em><strong>[4 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="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Shown below are the graphs of \(y = f(x)\) and \(y = g(x)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="font: normal normal normal 27px/normal Helvetica; text-align: center; margin: 0px;"><img 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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">If \((f \circ g)(x) = 3\), find all possible values of <em>x</em>.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(g(x) = 0{\text{ or 3}}\) <strong><em>(M1)(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>x</em> = –1 or 4 or 1 or 2 <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Notes:</strong> Award <strong><em>A1A1</em></strong> for all four correct values,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>A1A0</em></strong> for two or three correct values,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>A0A0</em></strong> for less than two correct values.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Award <strong><em>M1</em></strong> and corresponding <strong><em>A</em></strong> marks for correct attempt to find expressions for <em>f</em> and <em>g</em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A small number of candidates gave correct and well explained answers. Many candidates answered the question without showing any kind of work and in many cases it was clear that candidates were guessing and clearly did not know about composition of functions. A number of candidates attempted to find expressions for both functions but made little progress and wasted time.</span></p>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The function <em>f</em> is defined on the domain \(x \geqslant 0\) by \(f(x) = {{\text{e}}^x} - {x^{\text{e}}}\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Find an expression for \(f'(x)\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Given that the equation \(f'(x) = 0\) has two roots, state their values.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Sketch the graph of <em>f</em> , showing clearly the coordinates of the maximum and minimum.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Hence show that \({{\text{e}}^\pi } > {\pi ^{\text{e}}}\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \(f'(x) = {{\text{e}}^x} - {\text{e}}{x^{{\text{e}} - 1}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) by inspection the two roots are 1, e <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 36.0px Helvetica;"><img 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" alt><span style="font-family: 'times new roman', times; font-size: medium;"> <strong><em>A3</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 36.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1</em></strong> for maximum, <strong><em>A1</em></strong> for minimum and <strong><em>A1</em></strong> for general shape.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 36.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 36.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">from the graph: \({{\text{e}}^x} > {x^{\text{e}}}\) for all \(x > 0\) except <em>x</em> = e <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">putting \(x = \pi \) , conclude that \({{\text{e}}^\pi } > {\pi ^{\text{e}}}\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">The function <em>f </em>is defined on the domain \(\left[ {0,\,\frac{{3\pi }}{2}} \right]\) by \(f(x) = {e^{ - x}}\cos x\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">State the two zeros of <em>f </em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Sketch the graph of <em>f </em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">The region bounded by the graph, the <em>x</em>-axis and the <em>y</em>-axis is denoted by <em>A </em>and the region bounded by the graph and the <em>x</em>-axis is denoted by <em>B </em>. Show that the ratio of the area of <em>A </em>to the area of <em>B </em>is</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\[\frac{{{e^\pi }\left( {{e^{\frac{\pi }{2}}} + 1} \right)}}{{{e^\pi } + 1}}.\]</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\({e^{ - x}}\cos x = 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow x = \frac{\pi }{2},{\text{ }}\frac{{3\pi }}{2}\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[1 mark]</span><br></em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em><img src="data:image/png;base64,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" alt> A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em><strong> </strong></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><strong>Note: </strong></strong>Accept any form of concavity for \(x \in \left[ {0,\frac{\pi }{2}} \right]\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Do not penalize unmarked zeros if given in part (a).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em><strong> </strong></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Zeros written on diagram can be used to allow the mark in part (a) to be awarded retrospectively.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">attempt at integration by parts <strong><em>M1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER<br></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(I = \int {{{\text{e}}^{ - x}}\cos x{\text{d}}x = - {{\text{e}}^{ - x}}\cos x{\text{d}}x - \int {{{\text{e}}^{ - x}}\sin x{\text{d}}x} } \) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow I = - {{\text{e}}^{ - x}}\cos x{\text{d}}x - \left[ { - {{\text{e}}^{ - x}}\sin x + \int {{{\text{e}}^{ - x}}\cos x{\text{d}}x} } \right]\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow I = \frac{{{{\text{e}}^{ - x}}}}{2}(\sin x - \cos x) + C\) <strong> <em>A1</em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Do not penalize absence of <em>C</em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong> </strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR<br></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(I = \int {{{\text{e}}^{ - x}}\cos x{\text{d}}x = {{\text{e}}^{ - x}}\sin x + \int {{{\text{e}}^{ - x}}\sin x{\text{d}}x} } \) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(I = {{\text{e}}^{ - x}}\sin x - {{\text{e}}^{ - x}}\cos x - \int {{{\text{e}}^{ - x}}\cos x{\text{d}}x} \) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow I = \frac{{{{\text{e}}^{ - x}}}}{2}(\sin x - \cos x) + C\) <strong> <em>A1</em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Do not penalize absence of <em>C</em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>THEN<br></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int_0^{\frac{\pi }{2}} {{{\text{e}}^{ - x}}\cos x{\text{d}}x = \left[ {\frac{{{{\text{e}}^{ - x}}}}{2}(\sin x - \cos x)} \right]} _0^{\frac{\pi }{2}} = \frac{{{{\text{e}}^{ - \frac{\pi }{2}}}}}{2} + \frac{1}{2}\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int_{\frac{\pi }{2}}^{\frac{{3\pi }}{2}} {{{\text{e}}^{ - x}}\cos x{\text{d}}x = \left[ {\frac{{{{\text{e}}^{ - x}}}}{2}(\sin x - \cos x)} \right]_{\frac{\pi }{2}}^{\frac{{3\pi }}{2}} = - \frac{{{{\text{e}}^{ - \frac{{3\pi }}{2}}}}}{2} - \frac{{{{\text{e}}^{ - \frac{\pi }{2}}}}}{2}} \) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">ratio of <em>A</em>:<em>B </em>is \(\frac{{\frac{{{{\text{e}}^{ - \frac{\pi }{2}}}}}{2} + \frac{1}{2}}}{{\frac{{{{\text{e}}^{ - \frac{{3\pi }}{2}}}}}{2} + \frac{{{{\text{e}}^{ - \frac{\pi }{2}}}}}{2}}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{{{\text{e}}^{\frac{{3\pi }}{2}}}\left( {{{\text{e}}^{ - \frac{\pi }{2}}} + 1} \right)}}{{{{\text{e}}^{\frac{{3\pi }}{2}}}\left( {{{\text{e}}^{ - \frac{{3\pi }}{2}}} + {{\text{e}}^{ - \frac{\pi }{2}}}} \right)}}\) <strong> <em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{{{\text{e}}^\pi }\left( {{{\text{e}}^{\frac{\pi }{2}}} + 1} \right)}}{{{{\text{e}}^\pi } + 1}}\) <strong> <em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks] </em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates stated the two zeros </span><span style="font-family: 'times new roman', times; font-size: medium;">of </span><em style="font-family: 'times new roman', times; font-size: medium;">f</em><span style="font-family: 'times new roman', times; font-size: medium;"> correctly but the graph of </span><em style="font-family: 'times new roman', times; font-size: medium;">f</em><span style="font-family: 'times new roman', times; font-size: medium;"> was often incorrectly drawn. In (c), many candidates failed to realise that integration by parts had to be used twice here and even those who did that often made algebraic errors, usually due to the frequent changes of sign.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates stated the two zeros of <em>f</em> correctly but the graph of <em>f</em> was often incorrectly drawn. In (c), many candidates failed to realise that integration by parts had to be used twice here and even those who did that often made algebraic errors, usually due to the frequent changes of sign.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates stated the two zeros of <em>f</em> correctly but the graph </span><span style="font-family: 'times new roman', times; font-size: medium;">of </span><em style="font-family: 'times new roman', times; font-size: medium;">f</em><span style="font-family: 'times new roman', times; font-size: medium;"> was often incorrectly drawn. In (c), many candidates failed to realise that integration by parts had to be used twice here and even those who did that often made algebraic errors, usually due to the frequent changes of sign.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagram below shows the graph of the function \(y = f(x)\) , defined for all \(x \in \mathbb{R}\),</span><br><span style="font-family: times new roman,times; font-size: medium;">where \(b > a > 0\) .</span></p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" alt><br><span style="font-family: times new roman,times; font-size: medium;">Consider the function \(g(x) = \frac{1}{{f(x - a) - b}}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the largest possible domain of the function \(g\) .</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 style="text-align: justify;"><span style="font-family: times new roman,times; font-size: medium;">On the axes below, sketch the graph of \(y = g(x)\) . On the graph, indicate any asymptotes and local maxima or minima, and write down their equations and coordinates</span>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" alt></p>
<div class="marks">[6]</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 style="font-family: times new roman,times; font-size: medium;">\(f(x - a) \ne b\) <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(x \ne 0\) and \(x \ne 2a\) (or equivalent) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">vertical asymptotes \(x = 0\), \(x = 2a\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">horizontal asymptote \(y = 0\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Equations must be seen to award these marks.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">maximum \(\left( {a, - \frac{1}{b}} \right)\)</span><strong><span style="font-family: times new roman,times; font-size: medium;"> </span><em><span style="font-family: times new roman,times; font-size: medium;">A1A1</span></em></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Award <em><strong>A1</strong></em> for correct <em>x</em>-coordinate and <em><strong>A1</strong></em> for correct <em>y</em>-coordinate.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">one branch correct shape <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">other 2 branches correct shape <em><strong>A1</strong></em></span></p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAkkAAAJ6CAIAAACzDEFgAAAgAElEQVR4nOzdf0wT5/8A8KPQtORom6Pl0pKDkgNsqKlAKthQUsVUtLGGiamwRggqqWxEDIpBN6LGycLciH7CPpjOSaZh06AbkYWPLqgjavxMg+5jdCG6MP0SMUwN/iBAKm3u+8ezdbW0FZBeW+79+sOU6/X6Fq593/Pc+3kejAEATIPT6WQYxuFwhDoQAMDbYaEOAIAw5XK5PH9cuXIlj8fDMGx4eJhhmIcPH0okkra2thBFB8KI0+lEZ8vdu3e9ThtmyokE2AG5DYDpqqmpwTCsu7vb6XROTExkZmbu3bs31EGBcOFyuSiKWrt2rd1uD3UsAHIbAH6gTkhPP/zwA4ZhHR0d6EeTyfTzzz+zHRYIVyMjI2q1Gsdxo9Houb2np6e3tzdUUXEW5DYApsvpdGIY1tLSwjBMb2/vunXrQh0RCC/t7e0ZGRn19fUMw7hcrsePH1dUVGRkZKxcudLhcLhcLuifZA3kNgCmy+l0RkdH22y2p0+f6nS6J0+ehDoiEF7sdntGRkZtbS368aeffiJJMioqymazhTYwDoLcBsAMSKXSkpKSpUuXNjU1hToWEHZ6enqysrJQu41hmCtXrixYsEAoFFZXV6MtUzu6QZBAbgNgBiiKio6OLioqmpiYCHUsIOy8ePFi5cqVe/bsQT/u2rVLqVQKBIL9+/eHNjAOgtwGwNu5L7cNBkNpaSl6PDIywkCFN3iTw+F4+fIlerxr1660tDSCII4cORLaqDgIchsA0/W///1PrVa7f6yrqxsYGAhhPCDMWSwWtVotlUphVAD7ILcBEIjL5RoYGBgYGDh37hxN0zdv3nQ/lZmZaTabmb+bbjBoF3gpKipSKpV8Pv/UqVOhjoVzILcB8BZ5eXkYhi1btgzNSIL09fVhGIZh2C+//OK1v8vlgqm5gMvlstlsarWaIIjOzs5Qh8M5kNsAeIuLFy8eO3bM/ePo6CjDMLW1tSi31dTUMAzz+vVr5s0qOLQFcFlzc3NSUpJQKIQ+SfZBbgNgNnJzc1FuS0xMDHUsIMS8KvvdfdHr168nSVIkEjU0NIQiLk6D3AbAjI2MjGAeYEYlwDCM3W7/9ttvPfNcRUVFUlISSZKocQ/YBLkNgJlxuVyoQzIqKkqv1ycmJpaXl4c6KBB6VqtVpVL9+OOPzN8tufr6eoVCIRAINm3aFOroOAdyGwD/mM6Mfw8fPuTxeMuWLSMIoqSkpKGhAcfxFy9esBMhCEMok507dy4rKys3N/fRo0doe0VFBUEQOI5XVlaGNEAugtwGwF9ev349nSmRjh49imFYW1ubQqHYvn37rVu3MAxzT7MEOOv+/ftardZoNLpHPdbX19M0rVKp3HNuAdZAbgNgZtasWcPn80dGRuRyOZoVV6vV8vl892wUgJsePnxoMBgWLlzoHgS5f/9+jUaTmpq6c+fO0MbGQZDbAJiBJ0+eREVFobI3kiTR9finn37qXvsGJsPlIPRHv3HjhkKhSElJcdcWlZaWqtXq+Ph4dG4ANkFuA2AGrl27xufz0WOpVIq6Ip8+fYph2ObNm0MaGgixW7duJSQk0DQ9ODiIthQWFiYlJYnF4p6entDGxkGQ2wCYGfc3V2JiotVqRY/7+/thZQAuQ1VIJ0+eXLt2bV9fH9q4du1amqYFAsGFCxdCGx4HQW4DwC+n0xmgbDI9Pd29CiUAU61du1atVsfGxn7//fehjoVzILcBMEs0TcN6yiAAs9lM0zRBEMePHw91LJwDuQ2AQCYmJvwVQKpUqt27d7McD4ggK1askEqlfD7/7NmzoY6FcyC3AeCDexD3w4cPb9y44XOf9PR0qB8B/oyOjq5evVoqlYpEIpgrmX2Q2wDw5jmF//379w8ePOhzN4qi0PptAPhUXFysVqsVCkV3d3eoY+EcyG0A+DA2Nvbw4UOn03nkyJEtW7b43IeiqIqKCpYDA5FibGwsOzs7LS1NIpHAGAD2QW4DwIfPPvuMz+dXVVV1dHQkJiaOj49P3Sc9Pb2qqor92ED4czqdw8PDy5YtUygUOI53dHSEOiLOgdwGgA+NjY08Ho8giKamJoqiBgYG0NwTntOOpKWlQZ0k8OfBgwdGo5EgCLFY3NbWFupwOAdyGwA+tLe3R0dH83i8TZs2yeVynzmMpumSkhL2YwMRYWBgIDU1VaFQEATR2dkZ6nA4B3IbAD5cu3ZNJBJhGLZhw4aMjAylUjk6Ouq1j0ajgXYbYN4c448eOJ3OO3fu5OXlodzW3t4e0gC5CHIbAD68ePFCrVZjGGa1Wmmapmm6v7+febNPkqIoyG3A7f79+8ePHx8ZGXH/mJOTo1Ao1Go11JKwD3IbAL5t3boVw7D4+PiUlBSxWOxecNItNTW1rKwsJLGBMPTTTz8RBLFnzx70471799asWaNUKmUyGVqMG7AJchsAvo2NjeE4jmFYbGwsn893OBxeO2RkZMDYbcD83Zr/+uuvVSrVoUOH0MY7d+4YDAapVCqXy7/55puQBshFkNsA8EuhUPB4PB6Pp9Vqpz6rVCqhTxK4tba2Lliw4PDhw+jH+/fvFxYWEgRBkuT58+dDGxsHQW4DwC+z2YxhmEgkysrKmvosSZJ1dXXsRwXCDWq3tbe3FxcXHzhwAG188uRJfn6+VCqVSCSwDgD7ILcB8Bc0QNuzWsRms2EYxuPx3nvvvan7q9Xq7du3o8ee03ShI3huAVzQ1dVlsVjcZSODg4MGgwGtAwBjt9kHuQ0Av2w2W3x8fHR0tHtKSc/l3JKTk202W4AF3gI8Beaftra2tLS0r776Cv346NEjo9EolUphfFtIQG4D4A2eCengwYMCgSAqKsrndMnJyckWiwU9Hh8f98pkU2tPwHyFWurPnj2rqalxdz+OjY0ZjUY05xasA8A+yG0A+PXxxx/z+XwMw9wFAp5UKpXRaGQ/KhARhoaGdDpdUlISSZKwzh/7ILcB4FdNTQ3KbS0tLVOfTUxMtFqt7EcFIsKjR49Wr15NUZRcLt+3b1+ow+EcyG0A+NXU1ITjeHR0dGNj49RnU1NTYf024M/o6OiGDRtIkpRIJNXV1aEOh3MgtwHg17Fjx4RCIY/HW7BgwdT7Z2q1euPGjegxVEUCL4ODgyUlJQsWLCAIAsaKsA9yGwB+nT9/HvVJCoXCiYkJz+EBDMOkpqbC9Tjwp7+/v6ioSKPRSCSSzz//PNThcA7kNgD8evHihVarxTAMw7Dnz597PUuSJMptqEISKv6Bp+Hh4crKSrVaLRKJduzYEepwOAdyGwCBoKlJMMzHJyUtLc09dtsfr6Ye4I6RkZGSkpKkpCSxWAx1kuyD3AZAIAaDwZ3bPJfpYhgmPT29trY2wGunLvkGuMPhcFRXV+fk5IhEoo8++ijU4XAO5DYAAsnIyEC5bWJiwuup1NRUNHY7cG8kNN04yOl0OhwOi8Wi0WhIklyzZk2oI+IcyG0A+DUyMmIymVBue/DggdezarW6pqYmFHGByFBUVLRkyRKCIEwmU6hj4RzIbQD4NT4+rtFoMAyTSqVoi1efJNR2gwA2bdqk1WrlcnlpaWmoY+EcyG0A+OV0OgmCwDBs6tqkw8PDNE3DutvAJ9QRXV1dXVBQQJIkrPPHPshtAASSlpaG+iTv37/v9ZRGo/nwww9DEhWICK2trYsWLRKLxT7XtgVBBbkNgEDy8/NRbvvtt9+8nlKpVBUVFSGJCkQEu92u1+sJgsjNzQ11LJwDuQ2AQNxjAM6dO+dV8ZiXl2cwGGDINvDnxIkTWVlZJElCLQn7ILcBEIjNZhOLxRiGuZdOdmc4pVIJfZKA+Xs2UfeJ4X7Q0tKyaNEiiqJMJtOrV6+cTicMCGEN5DYAArFYLHw+n8fjXb161b0R1ZVotVoYAwAQz+a7+3FLS4vJZKIoymAwjIyMhCg0joLcBkAgFosFzZXc3t7u9ZRKpYLcBtyqq6vd67AjXV1dFouFoqjCwsJQRcVZkNsACKSoqAjdb7t06ZLXU7m5uUVFRSGJCoQhjUajUCiuXbvmbrd99913RqORJMnKysrQxsZBkNsACMRqtaLc9v333zNvdj1lZ2fD2qSAYRin0zkxMbF8+fK0tDS73Y42ulyuEydOFBcXp6SkLF++fHx8nIHFIlgEuQ2AQEpKSlBu6+3t9XpKpVK99957IYkKhBuHw7F///5Vq1Z59l0fPXp01apVNE272/dQS8IayG0ABLJixYqoqCgMwy5fvuz1lEajgfsowG316tVZWVn9/f3uLXa73WAwpKSkmEwmyGosg9wGQCA7d+4UCAQYhrW0tHhuHxsb02q1kNuAW35+PkmSP/30k3uL3W7PysqSSCRo7DZ0SLIJchsAgezfv18oFGIYdvDgQa+n0tLSvOriADeh8W0Gg4Gm6StXrri32+12tVqdlpam0+lCFx1HQW4DIJD6+nq0DsB3333n9ZTRaDQajSGJCoShPXv2GI3GO3fuoB9dLtehQ4d0Oh1JkpDb2Ae5DYBAtm7dimpJpi6xvXbtWphLCXhCN9XcfY/79+9Xq9UikQjWAWAf5DYAAqmoqEC5zWq1ej2l0+mgTxIE0NjYSNO0QqGAdhv7ILcBEMi6detQbtuyZYvn9pGRkfz8fJTboEaA4/zVQHZ3d9M0TZJkdXU1yyEByG0A+OV0Omtra1Fu27lzJ/NmGlOpVGjstsPhgApvMNWRI0c0Go1cLl++fHmoY+EcyG0ABFJXV4fqJKdOHZmVlfX++++HJCoQ/pxOZ1NTk1qtJkkSxoqwD3IbAH9Bs/t72bFjBxq7/emnn3o9pdVqrVbr5OQk+hF6JjnLq4TE5XKhc6m9vT0nJycxMVGj0TidTvep4mV0dNTlckHTf25BbgPgH1Pzk81mQ32SbW1tXk9lZ2dDLQnw5HA4PE+h06dPFxQU5ObmpqamPnjwgIELIBZBbgOAYf6+9J5656y4uJjH42EY1t3d7fUS9/ptcMUNRkZGrFbrokWL0JzIyPnz55cuXZqTk6PVatEWOFVYA7kNAIZhGH/9RWjsNo/HQ+sAMAzz8uVL9CAvL6+4uBg9hu8sLkN//by8PBzH7927595+4cKFgoKC5OTk/Px8ny+EZlzwQG4DXOd1s8RLfX19VFQUn8/v6enxemrlypUwdhu4bdq0SSqV3rhxw73l0qVLBQUFFEWpVKqp+3ven2MpRC6B3AZAIHV1dTweLyYmZmqfpF6vhzVugFtdXZ1CofCcT/Lu3bsLFizwl9tAUEFuA/Ocy+V6l+vi+vp6Pp+PYdjp06fdB0QPFi9eDGuTAoZhUA3ktm3bVCoV6pNEnQF//PGHyWSiKAqtA+D1EgZabMEEuQ2AQLZt2xYdHY1h2NmzZ5k3v4xyc3OnTsQFOGvbtm00TXveb7t06ZJer09OTl6/fr17o/vWLCS2oILcBuYztPjI0NDQrI9QV1eH2m2dnZ1eT2VlZZWVlb1TfGAeOXjwoF6vv337tntLV1eXXq+naZqmaa+d0ZkJggdyGwCBWK1WVCd57do1r6cyMjKmTlYCOMvlcl2/ft1zLH9/f7/JZIqPj09MTAxtbBwEuQ2AQAoKCjAMi4mJOX/+vNdThYWFcL8N+ISaZbdu3dLr9RRFFRQUhDoizoHcBkAgJpMpKipKKBRObbfl5eWVlJSEJCoQtjzvov32229FRUU0TaempoYwJG6C3AaAX6Ojo7m5uSi3PXv2zOvZ5cuXGwyGkAQGIsIvv/xSXFycmpqamZkZ6lg4B3IbiAyjo6NMKKb/SEtL4/F4BEF4zqWEmEwm6JMEPqE+yf7+/vfff5+m6aysrFBHxDmQ20BkCEnB9MjICE3TGIaJxeKpARiNRshtIICXL1+WlJRkZGTI5XIY0MYyyG0gYrDfaOvp6ZFIJFFRUSRJoi2e303QJwnc0InhdDq9sldtbW1iYiJJkr29vSEKjaMgtwHgV1dXl1gsxjDMPY+7J4vFAmvcAIZhXr9+/fTpU59PlZWVpaWlKRSKb7/9loE5tVkEuQ0Av1paWnAcxzCspaVl6rMrVqwwGo3sRwXCk8/+xtra2oULF9I03dXVxX5IXAa5Dcwrc3tdXF9fHxsbGxUVhXKb18GLioqg3QZQSkP/vnjxwuvZpqam7OxsiqKOHj3KwP02FkFuA/PNHKa3vXv38vl8Pp//xRdfTH22sLDw448/nqv3ApHorSfbxo0blUolSZLHjh1jJySAQG4D88ecXxSfPHkyKioqOjp6//79U99izZo1UEvCcSMjI15bvE7CkpKSxYsXJycnHz58mMW4AOQ2ELGmZjKHw+Fz+0y5L8bb2tpkMll0dLTPHLZmzRrok+Q498k2OTl5+/ZtdAZ6qqmp0Wq1ycnJdrudgT5JFkFuA5EtqIVn7733nlgszsnJ2b59+9S3KywsXLVqVfDeHYQ/z/Ohv7+/q6vrwYMHnhs//vhjiqKkUumXX34ZigC5C3IbiFRoppLpXAjP7mJ5dHRUpVJhGCYSiaYuus0wjMlkstlsszgymE/cZ9e2bdtycnIeP37s+WxTU5NcLo+Pj29ra2Og3cYiyG0AeEPX3QMDAziOew7c9rJ69erNmzezGxoIO+5FbbZs2VJYWOj+Edm/f79GoyFJEi6DWAa5DQDf7t+/n5SUxOPx/E32bzaboU8SIKOjo2VlZR9++KHXdrvdrtFoaJqe+hQIKshtAPh26dIlDMMwDFu7dq3PHYqKiuBiHCDPnj3bsWNHXV2d1/b29vbFixeTJImG+UOfJGsgtwHgg8vl6uvrk0qlfD4/Ly/P5z4Wi6WiooLlwEAYQp3YHR0dVVVV7o0ojdnt9oyMDJqmYbgIyyC3AeDbmTNnCILg8/n++iRhjRvg5c8//2TeLJ788ssvNRoNQRA0TYcuLi6C3AaAb3a7XSwWR0dH+2ucrVu3rqCggOWoQBiaOv0/Mjk5abPZ8vPzSZJUKpWsx8VpkNsA8O3QoUNCoVAgEGzbts3nDhaLxV+TDnDc6OgoKpg8evTosmXL5HI56pOE+22sgdwGgA9Op7O1tRXVkkwtEEAsFktNTQ3LgYEwhFbZ9umLL77Q6XQ0TUPZEcsgtwHg24EDB/h8fnR09K5du3zuYLFYVCoVy1GBsDU2NjZ1Y0lJSWpqKkmShYWFDLTbWAS5DQDfGhoaYmJihEKhz8XbGIYpKip6//33WY4KhI/Xr1+jspEA7TabzaZWq8ViMSwZwTLIbYDr0NeT5wU12lJZWYnjOJ/P/+6773y+cN26dVD8Bp49exbgWZvNhsa3mUwm1kICDOQ2ABiGcblcUzuL1q5dy+PxoqKient7fb6qtLRUrVYHPzoQwdDapMnJyUajcXJyEvokWQO5DXCO0+n0HIE0Pj7uc7fCwkKCIHg8ns+JkhmGMZlMUEvCcW9dhsJutxcUFFAUBbUkLIPcBliCrliDuiTN9E3n8rmhoUGhUHguTOplzZo1jY2Ncx0amFe6u7tzc3MTExNRLQlgDeQ2wJ4w6ZB5axgoAW/ZskWn00kkkkOHDvncbcOGDVqtdu7jA/NIW1tbSkoKjuMwvo1lkNtAJGGz2afVaoVCoVAo7Ovr87lDe3s73G8Dbu6T0/Ms7ejoSEtLE4vF7733Xoji4ijIbSAyzPkFL5onyWu1LU/5+fl8Pl8gEFy+fNnnDnv27NFoNHMbFYhQ165d279///37971O1DNnziQnJ0skkoaGBgbabSyC3AYig8PhYPPtJiYmcnNz0RiAc+fO+dynvLw8KyuLzahA2Orp6VmxYsXu3bu9tl+/fj01NTU2Nra5uTkkgXEW5DYQSVjrkxweHqZpGtVJXrx40ec+Vqt16dKl7MQDwlx/f39dXd0nn3zitb2jo0Or1SoUisOHD4ckMM6C3AaAN6fT+ejRo8TERB6PJxAIzp4963O3devW5eTksBwbCE9Xr141GAxT14U4f/58bm5ufHw8mt0G+iRZA7kNAB8ePXokkUjQ2G1/49ssFgssXAKQU6dOLV++vLq6mnkzge3duzc7O1sul6P7bYA1kNsA8GF4eJiiKLQOQIDcBmMAANLU1ORzgPbGjRu1Wi1FUatWrQpJYJwFuQ0AH0ZHRw0GQ1pamkAgCJDbYAwAQC5fvlxaWjp1Gdu9e/caDAaZTIbKjqBPkjWQ2wDw5nQ6h4eHJRKJVColSfLOnTs+d9u2bRvcbwNuY2NjaP42zwTW0NCwdu1adC4NDg5CbmMN5DYAfHjw4IFYLMYwjCCIBw8e+NzHYrFs376d3bhAhOnp6SkuLhYKhQRB3L17N9ThcAjkNgC8jY+P37x5Uy6Xi8VigUDgb3zbhg0bSkpKWI4NRJZr164VFRVJJBKKom7cuIE2ulwufzN0g7kCuQ0AH27cuEEQBIZhFEX98ccfPvcpLS3V6/UsBwYiS29v78qVK0UiEUEQFy5cCHU4HAK5DQAfzp8/L5VKMQwjSdLflChQSwLe6r///W9BQYFQKExISDh69KjnU2GyJsZ8BbkNAB86OjpEIpFQKMzOzva3j8VimTpWFwBP165dW7NmDUEQFEWdPn061OFwCOQ2AHzo6OiQSqUxMTEmk8nfPhUVFUuWLGEzKhBxhoaGiouLlUolQRCdnZ2hDodDILcB4ENzc7NAIBAKhbW1tf722blzp06nYzMqEHFGRka2bduWnp5OkqS/hQBBMEBuA8Cb0+ns7OyUSCR8Pn/btm3+drNarVVVVWwGBiLRli1bUlNTcRyHabfYBLkNAB+uXbum1+sxDMvKyvJ3z99isSxatIjlwEDEsdlsCoWCIAiLxRLqWDgEchvgNH/zROzYsSMlJUWpVK5fv97fa6FOEkxHfX09TdMkSa5bty7UsXAI5DbAUYErsEtLS2NjY/l8/q5du/zts2XLFlibFLzVv/71r4yMDIIgps42CYIHchvgNJ8Zbnx83Gg0CoXCuLi4APdIqqqqoN0G3urMmTM6nY4gCJjFhk2Q2wCnTU5OTt04ODiYl5fH5/PFYvGePXv8vba8vBy+rcBUXh3dPT09+fn5BEFMXQEHBA/kNgC8XblyRaPRREdH4zh+4sQJf7tZLBbIbQA5e/asyWTq6+vzSmxOp/PChQvr168Xi8W5ubmjo6OhipBrILcB4O2HH35IS0vj8/kEQVy8eNHfblarFeokAXL48GGtVvvtt99Ofaq9vR1Nu6XRaPr7+9mPjZsgtwHg7fz58zRNCwQCmqYPHDjgbzer1VpUVMRmYCBsNTc363S68+fPM1P6JH/66af8/Hw+n7948WJ/826DOQe5DYC/oLoSh8NhsVg0Gg1BEAaDIcBcEuvXry8uLmYxQBC+jhw5YjKZfDbLfvzxR6vVSlHUihUrfvvtN/Zj4ybIbQC84cWLF0uXLsVxXCwWJyUlXb9+3d+eFovFbDazGRsIW/v371epVK9fv576VF9fn8ViUSgUWVlZ165dYz82boLcBsAbxsbG6urqkpOTcRwnSfLJkyf+xnevXbsW1m8DyKFDhwwGw/3795kpfZKDg4OrV68mSZKiqEuXLoUoQM6B3AbAP1wu17179/R6PUVRiYmJUqk0wM6lpaUqlYq12EA4O3DggE6nm1p55HQ6f/vtN5PJhOM4QRA7duwIcBCXy4Xyos+hKWBGILcB8IanT5+azWb0TZSQkBBgz5KSkqVLl7IVFwh3RUVFXV1dzJQJAQYHBw0Gg0KhUCgU7e3tIYqOcyC3AfAX9JX07Nkzi8VCEERsbKxWqw2w/4EDBwwGA1vRgXD3+PFjn9uHh4c3bNhA0zRBEJ7LAfrr6wZzAnIbAG94/vx5QUGBSCSKjo7OyckJsGdlZSX0SYK3unPnzurVq9VqNU3TGzZsYCCrsQJyGwBvcDgcZrOZIAgcx1GpiL9ZlTdv3hy4YQfA69evBwcHbTabVqtVKBQajSbUEXEF5DYA/uFyuZ4/f97U1JSZmRkbGxt4+JrFYoF1t8FbPXnyZMeOHQUFBSRJLly4cGhoiHnbMhRzi5vNRMhtALzB5XIVFRXhOB4dHV1XV8f4/2qA3AamA+U2vV4vEolIkhwcHHyXo6FaSpiX8q0gtwHgrampiSAIoVBoNBoD7LZ58+akpCTWogIRamRkpL6+Xq1W4zielpb2ww8/sPbWqHXodDrZbCaGCchtAPwDNdGuXLkik8kEAkHgpUc3bdpUUFDAVmgg3Plr309MTOzZs8doNKampubm5p45c4Zht0+SmyC3AeDt2LFjBEHw+fzA7baSkpKmpibWogLhzDNXeeUth8NRVVW1YMECtVptsVjQGDgQbJDbAPgL+kqanJwsKyvDcTw2Nra+vp7xfz1us9lqampYDRGEJafT6XA4nj17NrU1hrY0NTXl5OTQNL18+XK73Y6e4maJB2sgtwHwD5fL1d/fbzKZYmNjY2Njd+/eHeALaNOmTWq1ms3wQNjKzMyUyWQOh4PxlbR6e3sLCgpoms7IyDh69GgoAuQcyG0AeNu+fTuqJfnkk08Y/7dGampqAk/KBThiYGCgoqLCZDKNj4/73KG7u3vJkiUkSep0ur1797IbHUdBbgPAW319PUmSAoHg4MGDAXbbtGkTjN0GDMMMDAxUVlZu2rTJX2n+6dOndTodGt/W0NAAvZEsgNwGuMs97bqnly9fFhcXy2QykUjU09MT4OWVlZUkSQYzQBAZhoaGtFptZWXlgwcPmDf7JFGjv6OjQ6/Xy+Xy+Pj4zZs3o6cgwwUV5DbAaSMjI2g9SfdIoL6+PpqmhUIhjuOoi8lfn2RJSQmsTQoYhnn16pVKpQpQVXv8+HGj0ahQKNLS0lBHNwg2yG0AMBMTE+7HfX19BEEIBAKCIAK/aufOnVarNcihgciQn5/vc5Iap9Ppcrm+//77rKwsuVxO03Rrayv74XEQ5DbAXT47hf79739LpVIcx+VyeeCXl5eXV1VVBSc0EGFevnzZ39/v79mOjo7i4mK5XC6Xyw8fPkJS7jwAACAASURBVIw2Qp9kUEFuA+ANra2tCoUCwzCKogLvabFYYG1SMB3d3d1Go1EsFguFwrKyslCHwwmQ2wD4C7qv9umnn6KB22+tgbRYLFAnCdx8Fkmik+rEiRM5OTkymWz16tVXrlxhYM6t4IPcBrgO3RFx/7hnzx6SJGNjY1esWBH4hRaLRSgUBjk6MB80NzfrdDqZTEZRFMy5xQ7IbQD8BRVMWiyWuLg4Pp9fUVEReH/IbWCaOjo6zGYz6pNEE7mBYIPcBrgOdSW5m25r164VCoUCgWDbtm2BX1heXi6VSoMeH4hk7j5Jk8kUHx+fkpLinhAAakmCCnIbAG9YtmyZWCyOjo7+7rvvAu9ZXl6u1+uZN4cQADBVd3e32WyWyWRyudw9VzIIKshtAPzjwYMHer1eKBTy+fyLFy8G3rm2tnbVqlXsBAYiFOroPnr06KpVq4RCIUmS7jEAIKggtwHwj97e3sTERJTbAgxXQqxW61vHdwPAMEx3d3dJSQlaFNA9dhv6JIMKchsA/7Db7ampqXw+Pyoqqq+vL/DO1dXV7twGJd0ggEuXLhUWFsbHx6empgaegBsS3lyB3AYA43Q6UXLq6ekhCCImJobP5791nS1UUclKgCBSufsk9Xo9SZIURX355Zfu7V5evHiBHsCl0ruD3Aa4zvN7pKWlBcdxsVgcFRVVXV0d+IXl5eWwDgCYDrvdbrVaSZJMTExsbm4OdTicALkNgH86gk6cOCESiSwWi9VqLS0tDfyq0tJSsVgc/OhABPDsS5zar3jo0KGSkhKJRCKRSAL3B0Cf5FyB3AY4ynNpG7eDBw+KxeKkpKSsrKyOjo7AR7BYLFBLwkGvX7/22WfoXiZp6lN2u/29997DcZwgCBi7zQ7IbYC7XC6Xw+Hw3FJeXp6cnFxYWEhR1Keffhr45eXl5W+dTxlwwdOnT7/77rv29vauri6vwY4o1X399dcmk0kmk5Ek+dZrJjAnILcB8I+SkhKhUEjTtNlsfuu8f/X19TRNsxMYCB9//vkn82b77OeffyYIgqIos9l89+7dqS9pa2tbtWoVRVEKheLYsWPsxcphkNsA+Mfnn38eHR1NkqREIrl69WrgnSsrKw0GAzuBgXA2MDCQnJycmJiICh2n3jO7fPmyyWSSy+UymayhoQFtRLtBSWSQQG4D4B+5ubkCgYAkyZSUlN9++y3wzuvXr4c+ScAwzK1btzIyMtLT0/3tcPr0aYPBIBKJRCJRS0sLm7FxFuQ2AP7S1dWlVCppmkbzkjx48CDAzqOjoyUlJQqFgq3oQPjq6elRKBQqlQr9OLUp1tbWtmTJEqlUStP08ePHWQ+QiyC3Aa5D67eNjY2ZzWaapuPj4/V6fWZm5vPnzwO/sKKiAsYAAIZh2tvbSZLMzc2d+hTKc6dOnSoqKkpMTExJSent7WU9QC6C3AYAwzDMnTt3CgoKSJIUCAQKhWLDhg1vfcn69ev5fD4LsYEwd/fu3eXLl69cudLfDj09PQaDgSAIuVx+5swZGMTGAshtADBOp/PWrVvbt2+XSqV8Pp+m6f3797/1VTabbdGiRePj4yxECMLc6Ojo4OCgv2d7enr0er1UKiUIwmazsRkYZ0FuAxyFuiLR44mJiTt37jQ3N2dkZOA4LhQKN23axPzdoeQ1Bs6ttLQUvqdAYOgUam9vLyoq0mq1EonEfdkErbeggtwGOM19U62hoQF1SBIEodVq29ra0PYAX0Aw5xaYpvb2dqPRmJqaSlFUe3t7qMPhBMhtADAMw+zevXvRokUURfH5/ISEhLcucMMwjNVqXbBgAQuxgciFpnY7f/682WzWarU4jn/88cehDooTILcBTkA9kAEaYefOnaNpGsdxgUAgFAp//fXXtx6ztLRUKpXOaZhgfjp37hyqkxSJRGazmYEh28EHuQ0AhmGYHTt2kCQZHx+PYZhYLB4YGHjr7ZDS0lIej8dOeF5cLhfUsESQU6dOmc1miqLi4+Pd85KAoILcBjjE38Wyw+EwmUwKhUKpVFIUJRQK79+//9ajWSwWtVo91zHOAFz7R4q7d++azWaCIMRi8d69e0MdDidAbgMRDzWwZlp1hhLDy5cvGYaZmJiwWCxoOpL09PTa2tqxsbG3HtBiseA4Pv0IwXyFziV/f2WXy/Xdd99lZWXFx8eLRCJUJwnXJcEGuQ3ME7POH06n8/Hjx4sXL1YqlejbZzqV/ZOTk6WlpUKhMHBIkNW4YGRk5JdffkHXST41NzebzWa0xg2su80OyG0g4jmdzpGRkdm9ED3o7+9XqVQ0TfN4PJIkp1nJZjab31onCZfnXLB3716j0djZ2elvB5vNhta4kUqlTU1NbMbGWZDbAGD27NlD0zRJknw+H8fx/v5+ZhoNwfLycqVSiR6jxU2mQitVBj5U4B4tEP5aW1szMjICLKj91VdfFRYWJiYmEgTR2NjIwEVP8EFuA4Cx2Wzx8fFowq3Y2NinT59O51WVlZWoliTAjZa5jBKEq7Kysry8PPd4f08oh33zzTcGgyE1NVUmkx09epT1ALkIchsATFlZGUVRCQkJPB6Pz+dPs4dz9+7dBEGgx2iI7iw4HI5ZvxaECaPRSJKkz9yGnDlzBq1xQ5Lk4cOHmXc4YcA0QW4DQeFyuUZGRsK848Xlck1OTjqdTp1OFx8fX1ZWZjAYSJJ0OBxvbXJNTk7abDaaptkJFYSzzZs3q1Sqs2fPTn0KfQQuXLiAJpMUiURwv40dkNsAR3leOBsMBqlUGhcXl5OTU1NT8+rVq+kcoaSkJHCdJOAOp9Ppb05thmGuXLlSVlamUCj4fH5ZWRmbgXEW5DbAdcPDw0ajEU21xefz161bh7ZPp5YkJycn+AGCCIbabWfPns3JyZFIJOnp6a2trQzUkgQf5DYQXlwuV4Dr33c8ss905XQ6165dK5PJxGIxjuN2u32aB9ywYYNOp5vTGH3EFiDFQq1KpDh79mxxcTFJkikpKbt37w51OJwAuQ2EEXQxy/Jt9p6eHrFYLJVKY2JitFqtu0jyrVfWVqs1tPfb4No/UnR2dm7cuJEkSRzHoU+SHZDbAFf4aw52dXUtX76coigej5eXlzc2NsZMr0m0fv16Pp8/x1G+yel0ohFyPgV4CoQJdP3x73//u6SkhKZpmUxmNBpDHRQnQG4DXPfgwYPExMSoqCixWLxv37637u+eWglNQTmLd3xr4gzcFQkijt1uLygokEgkBEHAGjfsgNwGuO6///0vqiJJSko6ePDg9F9os9ni4uJm+nZvHTznb4oTELmam5uXLFmiUChomg4wfQmYQ5DbANdduXKFIAgcxzUazePHjycnJwPv725RVVdXu8duzxQ0y7jD5XK1tLSUlJTIZDKJRFJXV+feHtrA5jfIbYC70JfL0aNH4+Pjo6KicnJyZlSluX79es91t1FSZKevyb2sD3RthYPW1tatW7f+/vvvjJ9y3G3btun1eplMptPpAkypDOYQ5DbAaU+fPlWr1Xw+n8fjzXTCCKvV+tZ1AAAXbN++XSqVBijur6qq0mq1YrFYrVZfuXKFzdg4C3IbmP/8DWtjGObs2bNKpTIqKoogiOvXr8/osLW1tZ5jt9nsYoLurLBSU1OTmZm5a9euqbNso9OsoaFBpVLhOJ6amtrX18dALUnwQW4DYWp0dJSFd9m1axdN0wRBaLVahmHQAIBpKi0tnen9NtThGXjN0mkuIw61lOGjtrZ25cqVp06d8rfDvn37zGYzQRCJiYk9PT1sxsZZkNsApzU0NBAEkZaWVlVVNT4+PqOraavVOos6ybeafgzspH/wVh9++GFWVpbPIls0EUFtba3RaJRKpVqtFuU2WAcg2CC3gXA0zbbLO3I4HDabjcfjRUdHHzhwYKZzfe3bt4/H483ifd/9/8XO7wdMk9lsTklJaWlp8bdDaWkpWmsiMzOzu7ubzdg4C3IbmG+m842PZvS4ffs2SZI8Hk8kEp07d25Guc3lcm3duvXd5yVxRwuJKuK4F0y3WCzJycl79uzxt+eOHTvS0tIIgjAYDKjdBvfbgg1yG5hXprM8jftrpbOzUywWYximVCqnuR6pp5KSEgybm08QfNNFtFevXrW1tV28eNHfDkePHlWr1TiOZ2VlQZ0kOyC3gfljpk2f2tra6OhoDMOWLVvmHrI9/YOUlpa++/pt6O0GBwff8TiAfV7lPAHa/R988IFWq8Vx3GAwjI+Po43QUg8qyG2AE9zdR54bKyoqMAzj8Xg2m20Wx7Rarf76JB0Oh/sdA7TJpvnt5r67hhKwz1cNDw9P/4CATRMTE5WVlahPMjMzE/2lQLBBbgMc9erVK5qmMQwTCoVtbW2zOEJFRYVCoZjduzudTnT9Poe9kdCxGZ6ePn1aUlKyYMECdL/t//7v/9B2+HsFFeQ2wBUjIyOezZqTJ08SBBEVFcXj8U6cODGLA1osFp/tths3bhgMBr1ev3r16tmHO4XnfGAB2mfwjRlWnE7nH3/8sWLFCj6fL5PJUlNT+/v7Qx0UJ0BuAxxVWFgYHR0dHR0tlUrRVBEzZbVafd5vczgcH3zwAYZh586de+cwQVibTifww4cPTSYTQRAEQchkstbWVhYCA5DbABfdu3dPoVCgqba6urpmd5ANGzb4qyXJyMgQi8WTk5NTB6J5tatQfSbcJ4tETqdzcnJycnKytbX1o48+8ncjbXJy8oMPPlAqlYmJiVarFe63sQNyG+AWNB9Ed3d3XFycUChUqVSzPlRNTc2SJUvcP6Kk9fr1a4fDgWGYzWZrbW2tr6+/e/cuwzAjIyOzmIri9evX0McY5kZHRzdu3FhdXT0wMOBvn5KSkoSEBIqiCgsL//zzTzbD4yzIbYCLKisr+Xw+n8+vrKyc9UE++OADkiSnbj9x4gSGYQqFIjs7WyAQ8Pn827dvBz6Uy+WaOpUlGmAOwtzw8HBBQUF+fv6vv/469Vl0abJ//340balOp7t16xbrMXIR5DbARampqRiGxcbGtre3z/ogGzZs8DlX8vr16wUCwbVr1xiG2bdvH4ZhaPUcfy2wwC2zwBMrg5B78uRJVlaWTqfzmduQI0eOqNVqmUym0WhgHQB2QG4D3PL69evh4WGNRoNhGJ/PRxlodhoaGrzmSkZfWAqFori4GG1pa2vDMOz48ePvEjMIT6iTeXh4WK1Wp6WlnT9/3t8+bW1tarUazcrd0dHBdqCcBLkNcM7ly5dVKpVCoZDL5bOrkEQqKytxHPfa2Nvbi2GYe8DcRx99hGHY5cuXGbhUn6cGBwf1en1ubu7Dhw/97dPQ0KDT6UiSpGkapUA4GYINchvglqdPn5aWlkZHRxME8e9///tdDmW1WsVi8dSNUVFR7tVnNBqN5/qlYJ5B3cWoYDJA1/HOnTsNBoNEIomNjT158iSLAXIX5DbALT09PQaDgc/nEwSBKhhnzWt8G7oSj4mJQcucMgxz8eJFsVg8NDT0Lu8CIhrqk6yurlar1VKptLCw8NixY6EOihMgtwGuQJfVTU1NMpmMIIiCgoJ3XNtz586dXusAPHz4EMfx/Pz8q1evtrW1ZWRknD179p2CBvPCjh07NBpNfHz8ypUr3ePboEQoqCC3AQ5xuVwFBQUCgSAzMzPAiiTTtGvXrqlr3Dgcjm+++QYNbnv8+PE7vgWYH2pra7VabXx8fHx8fG9vb6jD4QTIbYBDuru7ExISxGKx0Wh896mKKyoqfI4BYGY7UjswqD6IXNXV1QRB4DhOkqS7aBb+oEEFuQ1wAvoe0el0OI7jON7S0vLux0T329xLzwAwFTrxPvroI51OJ5fLVSrV7BadADMFuQ1wxfDwcHJyMo/Ho2navRborO95HDlyBMMwDMPy8vKmTikyt9AicHB7JnJt3brVZDKlpKSkpqa+y3QBYPogt03LnPcvAfZ1d3fjOB4TE6PX69/9aEKhEPvbmTNnZnEEmCtyPgn8p7Tb7R9++CFN0wqFAvVJTv8rxel0wvfPLEBumwHoeopou3btio2NxXF8z549sz6Iu/GEeXjHcXJgfgjQsP76668LCgoSExPlcnlzc/NMj/yOBb3cBLnt7dwpDTqFIteLFy+0Wm10dDRN02iWkNlxnwPl5eUosYlEoj/++GMWx0HFLHBSzQM9PT2XLl0KsMP333+v1+spiiJJ0mKxTP/IcHrMGnu5DXpguNCx4F7nJdSB/AOF1NXVRRCEUCi02WxzdWSdTodh2PQHgIfVrwXMCafTOTo6umDBAoIgAqz2cOvWrQ8//JCiKIVC8fHHH7tfy1aYXMRSbgv2zfYIguoCQh0Ft4yNjZWUlEgkktTU1DmcJWTDhg1ofNuMLq7hrz/PPHr0CNVA+mu+u1yuJ0+e2Gw2mqZpmj58+DDLEXIT9EmyzeFwhDqEIHI4HOHWi+Jyudra2qRSKZ/Pr66udm989yNv2rRp6tjt6Uf17gGA0EKXKS9fviwoKEhOTr5x44a/PUdGRqxWa3Z2dnx8PFrwCAQb5DYw/xUWFsbExJAk2d3dPYeHrampmXVuA/MA6mQeGhqyWCw5OTk9PT0Bdt6+fbtGoxGLxWazma0AOQ0+mWCeGxgYSE9PxzAsNzd3buvNUDkJrI7NcY8ePTIYDPn5+QMDAwF2q62tzcvLk0gk7iEo0HYPKshtYJ5rbW3l8XgEQdjt9rk9ckVFRUxMzNweE0ScwcFBrVar1WrdEwL49OWXX1ZVVVEUtWTJElgaggWQ24IOrs7mxEybR+heSF9fX2ZmJp/Ppygq8GX1LFitVuiT5DiXy/X48WODwbBw4cLffvstwJ52u3316tVyuTwtLe1dVsQF0wSfzGCBesi5hS4RZnqhUFdXJxAISJLcvHnznA+9X7duHeQ2cO3aNbVanZeXd+HChQC7DQwMFBUVyeVyiqJ++eUXBq56gww+mcE1v6siwxa6qhgaGlq1ahWGYSqVas4bbYz/dpvT6YTLGi5AtSSjo6PHjh2rqakJML4NMZvNaJDl3NY0AZ8gt4GIMaOE4XQ6d+3aJRaLo6OjrVZrMOJxj2+bc5AaI850egXKy8sTExOFQuH+/ftZCInjILeB+ampqSkxMZEgCK1W++jRo2C8RUVFRfD6JKHDav757LPPZDIZn8/fuXNnqGOZ/yC3gXlofHx86dKlYrE4ISFh9+7dQXqXsrKyYOQ2mPd9vjp58mRWVlZcXNwcTvwG/IHcBuYPd72JzWbTarWJiYlKpfLOnTtBejs0L8nUBhZarXR0dBTaXsDTuXPnFi5cSJJkeXl5qGOZ/yC3gfnmzp076enpfD7faDRevHgxeG8UYM4tqCECU/X19eXl5dE0vWLFCrilGmyQ28B8Y7PZcBxPSEhobGwM6hsF9X4bmH/Gx8eNRiNN0wRBvHr1KtThzHPwyQTzgfsq+OjRozKZTCaTFRYW/v777+94tMBmOlcyXKqDdevWkSQpEom6urpCHcs8B7kNRDz3bbZnz54dPnw4OjpaJpO1trbOyWEDmH5uc7lc0EsJGIbZunWrUqnk8/kGgyHUscxzkNvA/FFYWFhTU2MwGCiKepfjoDLFtzazzGYz9EmCGTl+/HhSUpJYLKZpOtSxzHPwyQQRDzWwfv/9d5lMplAoVqxYcerUqbk6bACo3TbnU3mB+QRdIbm7Fq5evarVauPj4/l8foD13sC7g9wGIp7D4bh48eKyZctkMhlBEKwNHrLZbNBuAzOCFjLFcZzP53/11VcM3IUNGvhkgoh3/PjxpUuX4jiO4/iiRYtGRkbYed+ysjJY4wYE5h6G735QVlZGkqRQKKyoqAhdXPMf5DYQwZxO58TERH5+vlAolMlk2dnZ9+/fZ+3d0dqkrL0diFyelUQVFRWpqakKhSI9PZ2BdlvQwCcTRLavv/6aoig+n5+RkTHnq48GBn2SYBY6OzszMjKUSiVFUaz1MXAQfDJBpHI6nV1dXQqFQiwWx8XFabXa4eFhNgOA3AZm4cqVKzk5OXFxcSRJnjlzhoGmW3DAJxNEGHfJ2e3bt2tqatasWSMSiXJycn766SeWI5np2G0wz3jVQE7/VRUVFXw+XyaTwYIAwQOfTBCRHj9+nJ+fLxaLNRpNenp6W1sb+zFUV1djGDYxMcH+W4MwNP309umnn1IUJRKJMjMzgxoSl0FuAxGptraWJEmCIBQKRVFRUUhi2Lx5M7TbwP3797/88ssZzcrd3d29YMECHMeFQuHPP/8ctNA4DT6ZIDK4XC7UBTQ2Nnb48GGaptFIbY1G8+OPP4YkJH9r3ABOaWpqwnF8+fLl0z8TfvrpJ7VaHRsbSxCEyWRiYCnaIIDcBiJMa2vrJ598IhaLSZJUKBQ1NTWhigS120ZHR0MVAAgHra2tCQkJM5pD68WLF1988QVFUVKpNC4ujs2BK9wBuQ1Ekm3btlEUlZWVlZ+fv3DhwqqqqpcvX4YqmMrKSmi3cRnqSDh9+rRCoRAIBDOaDntoaEir1UokEqFQuGfPnqDFyF2Q20AEcLlcY2NjTU1NFEWhrshly5bV1ta+ePEihFGh9dtmOp+kZ3EdiHQul+vAgQNZWVkWi2Wal1noBLh9+7ZGo0GTb8XHx4fwEm2+gtwGwh2arKilpUWtVuM4ThCEVqvV6/VPnz4NbWCoTxIGJ3FcU1MTqmma0atev35ttVoVCkVCQgKO4x0dHQwMdJtTkNtABLh27ZpKpSIIIjo6Wi6X5+TkzHrd0TmEaklmsTAbrOU2n0xOTnZ1daGJj2fkwoULy5YtQ+W+RqMxGLFxGeQ2EI48x8PevXtXp9NJJBKdTieXy5OTk7u7u0MdIMP8fb8NPZ7mFfdMx/mC8IEWmJ3Dv93k5OSuXbsoiiIIQiAQHDx4cK6ODBjIbSCcOZ3OFy9ebNy4kSAI1BtZUFDQ3t4e6rj+UlVVNbvxbdBuA0hfX5/ZbFYoFDiOx8TEXLlyhfFYMQC8C8htIHw1NDRkZ2eLxeLY2FiRSGQ0Gvv6+kId1D/QvCShjgKwam7b3C6Xq7OzU6fTCQQCHo8HPZNzCD6ZMwYdSsHj/t26XK6+vr7s7GyRSIRhmEAg0Gq14TaSDN1vQ1GFpAoATkU2zflv233ATz/9NDMzkyCI2NjYzz//PEhvxzWQ22YDypmCx/27/c9//qPVank8nlAoLCgoCLfExvy9DkBIToYw/G2AWbt+/XpOTo5CoZBKpVKp1D0LF3ROvgvIbTMAt0nY4XA4Dh06hO6xy2Sy1tbWmzdvhjooH9D4thAGAJf280ZPT4/ZbE5MTCQIgiRJVAYM19DvAnIbCD3PrsjR0VGLxZKRkaFQKAwGQ7DninyX9OBZJwnALHieftevX1+5cmVGRgaO4zRNDw4Oeu4D1zEzBZ9MEC5QD0xtbW1SUhJN02q1OqiVI+++5HFNTQ3kNjCHLl68WFhYuGjRIh6Ph+P48ePHoek2a/DJBOHC6XTW19fL5XKCIPLy8np7e1l403e5HN6xY8fsxm4D4NPLly937NiRlpYWHx8vEol4PN6KFSsePXrEQLtt5iC3gXcyi48ceonntIoOh+Ozzz5rbGxMTU2Niori8XinT58Oxlu/i6lvB3Mlgzn35MmTxsbG5cuXp6Sk4DgeGxtLkmRPTw8TtBPe67Dz5nyG3AZmb3x8/N0P8urVK5vNJhaL4+Li+Hy+QqFQKBTT7I1krZDM5xuhPknoNQJz7sGDBzabTa1WC4VCoVAYExNz/fp19FSQzjd02Pl0MkNuA7M3u0+Cy+VC14b37t3buXOnXq9HE0XiOJ6fn//w4cPh4WH3ngGOgybgZ+cyc2hoaOpGGLsNgufJkyf79+9XqVRoeW6Kov74449gvJG7VgX1rkO7jUOm+ceeB5c8Mzqt37F8q6amRiaTCQQCPp+P4zhJkg0NDY8fP57d0d4xNne6DczrT4xy20zXuJmOaa6D4/5vzpvvI+D5p3Q4HCdOnJDJZEKhUCAQyOVy903oefBtE2yQ2wKZf+30AGb335z+qzz3PHny5NKlS9EFaVxcnFarvXjx4izePQAWuitnPZ8kANP04sWLuro6tVpNEASPx4uJienq6gp1UJEBPplzYx6MQZldvd+M/suTk5NnzpzZsmVLZmamVCqNj49PSUlpbGy8ceOG525zdTEx/dhmNx4gqOPbAgfveb5NTEwwnLkC46CXL18eP35cp9PFx8cTBEEQRE9PD/y53wpy29vNrmkSQeYwbPehvI75559/9vb2lpWVLVq0CC0xKhQKq6qq6urq2AksGNCcW0EaAxDaJcXB9LHTu9PW1paTk5OQkID68I8fPx7Ut5sHILeBOeY5yQjDMBMTE6dPnzabzTRNo6VqZDJZdnZ2Y2Pjs2fPAhxnpkWY7DeaUW5j+U1B2ArqGTgxMfHVV1+p1erY2Njo6Ggej/fZZ5+53zHMrwJDAj6ZYC65x649efKkr6+vu7u7srLSYDAolUqJRJKSklJcXHzp0qW3tnUioo8XchtAs8T19fWNjY0F43T1HAw6OTl569atoqIiuVwuFAqjoqJWrlzZ2dmJOqWBF/hkzhMhLHvxeuu+vj673V5RUWE2mxcsWJCVlcXj8RISEnJycm7dusV+eMETwnUAQPhoaWlJSkrq7Oxk5+1u3bplNBppmiZJksfjYRiWlpb2n//8Z+rtAI6fmZDbItLY2NjUE5e1U9npdHpeTiKjo6MDAwM7d+5ct26dRqPJzMyUyWQ8Hi87Ozs3N/fMmTNo6qD5BOZK5jh0/tvtdoIgduzYwc6bulyunp6eqqoqmqZFIhGau4TP52s0mqtXr05z9AgXwCcTzIb7wzM5Ofn9998fP348Ly9Pq9WKRKL4+HgcxymKqqioOH78+L179+brjItobdJQRwFC7NSpU1KpNDU1lc03dTgcPT09RqNRrVaTJMnn8wUCwcKFCwsKCnJzczdt2nTmzJmXL19yOcnBJ3PGZto8Cp9Bck6nigwRrAAAIABJREFU89WrVz63o3/99WagH90jxjo6Ovr6+g4fPtzU1KTT6YqKivR6vVgs1uv1OI6npaWVlZW5pwiatfBfmNFz/TavaJ1O5//93/+Fwx89eML/DxRs6DfQ0NBAEIRWq2X/zz08PGy32wsKCuLi4jAMIwgCwzAMw/h8PprKxLOckmt/L8htszGL+TtC8tY+Xzv1CD6P6dXxODo6evv27dOnT+/YsaOsrEylUiUnJ6MhpTKZTKvVpqenNzU1Wa1Wr8Fq7xJqmDf4PvjgAzRXMgdv5nO5QeCloqJCKpUuXrx4eHgYfWrY/OW8ePGit7e3qqoqJSUF1SELBILY2FihUIgac1ar9euvv/aqXuYCyG0zEIzZlWZqOkN63/HI7gd37tz56quv9u7dm5eXl5GRkZaWRlGURCIRi8UZGRkSiUSlUpWWltrt9r6+voGBgVm/9VtDCk+oT/L58+dMeLTLQUicPXu2qKjIZDLdvHkTjUpk/7x1OBx9fX1NTU16vV4ul8fHx0ulUnQfjiAIPp+fnZ3d0tIS5h+ouQW5bbq8vrxev349/a+zmfYG+Dvy1K7CwBUl6H2nbvF84PnsyMhIV1dXc3NzS0vLxo0bVSoVTdNLliyhaVooFCoUCpIkVSqVVqtta2vr6el59+U9I1qAObfmfaoL8yY1m8bHx//zn/8EdR3daXI4HP/73/8aGxtVKlVcXBzKamglATRfl06nu337NsOB85OB3OaTy+Xy/Nt7NWg8yyimeTRmepdyXu8bQF9fn8Ph+O23354/fz46Ojq1T8yrT8/dwci8+d8ZGBj49ddfr169eubMmX379uXl5QmFQoIgkpOTSZIkSZKiqJycnLy8vF27drW2tp47d25wcDBU32vh9oFEYwDQaRBusQGWjY2NhTqEv0xMTNy8ebOlpWX16tUZGRkKhSI2Nhb1UqIHJpPp888/f/nypdfXwjw7hyG3+RBgsb5Z//lfvnw5o3efWsuLTsSJiYnx8fEAN3jQU2NjY7dv3+7v7//jjz/u3bs3Ojp6586dQ4cONTY27tq1q7S0tLCw0GQyZWVlZWZmpqamKhQKuVyemJhIkmRycvLy5ctLSko++uijy5cvP336NHy6MgJPZcKy8vJyzzm3wue3BADDMGNjY7/88ktbW1tFRYVGo1EqlYmJiSKRiM/nYxgWGxtrs9l6e3vn63kLue0v7qQ1Ojo69VmfnW9e1YMzehcv7s5D9zph/macevDgQeAj3759+9tvv21sbCwrK9u4caNOp9Pr9WazWavVpqWlLViwQKVS6fX6hIQEqVSakJBAEARFUUuXLi0uLq6pqTl27Fhvb28Ydjai/2A49Py4oTpJh8MBHXQgzI2OjnZ0dGzevFmj0cTFxYnFYrFYHBMTIxQK1Wr1l19+OTg46N7Z816GzxsfEQFy2z+m9j36bMBNHbbs3tPzJYG7It17uqfq8dmvOPWwaLfHjx/39/d3dHScOHHi4MGDR44c2bJli8ViWbNmDeqFkMlkqampaWlpEokkMTFRLBaLRCLULMvMzES1+/X19c3NzT09Pffu3Xvw4EHEFfuFfF4u1CcJ0/CDCDIxMdHb27tv3z6NRiMWiwmCkEgkaH4TlUpls9n27duH7slFOshtb3B3QL948eLRo0cDAwN2u72np6e9vf3s2bPff/99R0fHjz/+ePPmzevXrw8MDAwPD6P5OO7duzcwMNDf33/p0qXbt2//+uuvv/76a1dXF9p/9+7dfX19nZ2dX3311TfffNPe3r5p06Z9+/bV1dVt27atvb29ubn5X//6V1tbm91uP3To0L/+9a+TJ0/u27dvz549Bw8e3Lp1a319vd1ur66u1mq1Vqs1JSVFrVYnJyenpKSoVCqKogiCEAqFCxcu1Gq1Uqk0MTExPT3daDR+9NFH+/fvP3jw4Ndff3379u0HDx6EYZtsmnzmj1DlNpfLVVtbi2pJ5muvDpjHBgcH29vbt27dajAY0AxeaNhAdHQ0hmE4jm/YsKGtre33338PdaSzFDG5zfN7zV9xYODtU4sGEYfD0dXVZbfbLRbL9u3brVar2WzW6/UGg2Hz5s1qtbqwsDAhIYEkybS0tKSkJJVKpdFoFi1apNVqtVrtokWLUF/2qlWr0tLSlEqlQqHQarU0TSclJaFyjJiYmLq6ugULFuA4ThAEKjgUi8WLFi0iCCInJ2fJkiVisZgkSYVCodFo0CpN7i1paWnoCksqlZIkidaIiYuLo2naYrGgHVB/o8ViaWpq+uKLLzo7OyOxJfHWmKeeBiH8b6J1t0P17gDMiaGhoR9++KGxsbGmpkatVovF4qSkJFRaiWEYj8crLCxsampCS35PLbRmpvGpdH8Ds/lpjaRPplcfFOqp8/xlPX/+fGBgYGBg4PLly729vd98882hQ4dOnjxpt9ubmppaWlrWrFmzbdu26urq0tLSTZs2oflpkpOThUJhcnIyjuM8Hk8ikaC8kp2dje67ZmZmKpVKNFIEJSeJRCIUCkUikUgkIggiNjZWIBDgOC6RSNAMb6mpqSRJoj3Rzhs2bFCr1aiHUKlU0jStUqlQkT1FUei6CQ0dW7dunVwuz8rK0mq1BoPBYDBYLJbMzEy9Xl9eXr5hw4ajR4/abLaDBw9eunTp0aNH165dGxwcnJycnMO7PtM5FPrlz/nIdH8H9HkfNLS2bdvmzm2ReCUBgCeHw3Hq1KlPP/3UYrHodLrk5GSlUikSidCSOlFRURRFVVdX79y588SJE21tbd99993Zs2d7enp+/PHHc+fOXbly5erVq7/++uvdu3efPXsWYMpmdj4sEZPbPL/ynj9/fv36dbvd3t7efvz48dra2oqKipycHIqi5HI5SZLx8fEKhQLH8ejoaJSEBAKBUCiMjo6OjY1FCQxlIxzHU1JS0KJimZmZWq02MzPTaDQaDAaTyZSfn28ymSwWS11d3Zo1a9auXdva2lpbW7tp06b6+vo1a9ZUV1fX1taivze6fXX27NmLFy9eu3bt9u3bt27dGh4efvTo0fDwsMPhGBoaevz4McMwQ0ND7nq/iYkJl8vlcDhGRkbcJ0T41BOHs5BXLaM+SRgDACKUe+kcr+23bt3q7e29fPnywYMHN2zYkJeXp1QqU1JSBAKBWCxGC8hhGBYVFRUdHY3WSkXjxAUCgUwmEwqFOI6jqYtWr15dVlZWXV29a9euo0ePDg8Ps3abfAa5LcAaClMbmz6brgGO6e+1IyMjt2/fHhoaevDgQWNjY0dHR0NDAyrwo2k6JycnLi6Ox+MJhcKYmBg0UBE9iImJQW0s1J2IHlAUpdVqUVdhTk7OokWLSkpK2tvbf/75587OztbW1i+++KKhoaGzs/Pbb79tbm6ur6/v6OhAtYtTmzIBGjczakLNrvbPXyHlO37JhnDSucBdFqhA1N9pxr6hoaGamprgrbsdVpxO5zyYjdBnd9k8+H8Fm8Ph+O9//9va2moymZYsWaLX65VKZUJCArpRolAoaJqWSqUEQaA7MnFxceimCRo2jjo20TczRVE2m62jo2N4eNi9srxnQvEq0fSKxOfEFF4P3N6S23zWBAbY3+l0Pn78eGrnIfN3mca9e/d6e3tv3749MTGBDvv8+fPBwcGffvqpo6Ojqqrq888/b2hoqK6uXrlyJSqXwHGcpmmNRsPn89EwLIFAwOPxBAJBSkqKWCxOTExE98Y++OCDffv2HT58uL29vaen57PPPisvL29padmzZ09DQ8PevXtPnz597dq19vb2GzduhNVIqbASksqIiCvHGBsb86yT5IJwmHPu3XmeaSEvtY04w8PDN2/evHnzZk9Pz4EDB/bt21dfX79v375NmzZZLJa1a9cajUaj0Zifn2+1WjMyMlCRNrrRg+N4VFQUGl2HJnRWKpXr168/cOBAc3PzZ5991tzc3NzcfOTIkZaWlo6Oju7u7p07d9bV1ZWWlpaUlOzZs6e7u/v69etozK5nVD6vL6fbbuvt7e3t7b148WJvb+/Vq1dHRkbQfBbt7e3nzp07fPiwzWZbuXKlQqFYuHDh4sWLrVarxWIpKioqLCzMy8tbt26dQqFITEwkCIIkSZlMRlGUUqnMzMxE5RIikQj1FopEIh6P5/n/R92J6enpJEnSNJ2dnV1eXt7Y2Hj69Ok7d+6Mjo4GqLOfUU3g8PCwv6fYuTaf6S2lYHzX+OumCKrppAfUAxlWd922bt3Kndw2Dzpdp/6loPM/qJ49e3b58uWmpiaLxWI0GtE9vMTExKysrIyMjPT0dKVSiaZK4fP5KO2h7k10L0kgEMjlcoqiUAsnNjYWVSTEx8ejQgdUjoAqFex2O3pTdzp4S25DJ/QPP/yAZhSMiYlB7dCkpCSFQoEeq1SqBQsWuLMRqshA7VDUN8jn86VSqWefISrNQKU4PB4P1W6gZiw6GqqwWLp06d69e0+ePPnDDz/09/d7ji4EXubBV0/EQffbIndMBQBsGh8f7+npuXLlyt27dwcHBzs7Oz/55BOz2VxUVKTVai0WS2FhISo7JwgCzYeJHrirxNPS0latWqXRaFAVHuoRRaUVNpvN/Uaoc3Ja7baLFy/GxsbiOC4UCuPj42UyGXozuVyOsqhKpZJIJKmpqcXFxTt27Fi8eDGaUXfhwoVpaWkGg8FqtZaUlFRWVu7cubOmpqahoWHXrl379+/fsWPHkSNHOjs7L1y40NPTg0owhoaG0Nzq0xSJNzwCLIyC/jtOp/OPP/6YaW9JJP4qIhcaAwCd22GCIw3oeQY1nd3rJ7x48WJgYODChQuHDx/et29fbm5uVlYWqthEbTiKolBHoMFgyMjIQON3v/nmm6m9btPtk+zs7EQDIGpra61W6/vvv282m8vKyr788svOzs5Xr165bwyCkIB2G/vQ/Ta4nggfUBgyzwwPD3d0dNhstiVLlqhUKlSxgjLckiVLcBwnSTIhIUGr1Rb9P3v3H9NEtj6Ofyg2lAxtM22dUDK2ZFpsKKlAKnsbS7piKkrE8FEDuEQ2LBjEJZcNqwb1EjWsGoQ3EcOqAfYSMFwxVZeIYZUgLhHDgkFYooQrBHWJEBYNyBIglTb9/nG+23D5WaalP/B5/WFgOkwfQPr0nDnneeLiiouLi4qKqqurX758afGgPQBWC6fIV3tzyM404Kg7z8vcJlzqS4xG4zKPfubpbcVVTg65zlyof5vtVbDB2nHaehBYeOISIyMjo6OjXV1dBoOhrKzsypUrx48f3759+4EDB5RKpUwm27p1K9r9JRKJsrKyZmZmPC+32cPO/5dL1Zl0js88dS3Dxl+Hw39r1r7bjr0scE8Lf9FocZPBYHBJPMBisczOzg4ODr569er169cGgyEvL8+6hPLzym2WpdciMijq7xImk+mvv/5ydRRux5ZyPrassVzVGwg0J+lWSzfBWlv4PyQpKcklkYDlLZLbFu0c5pxoFm6kW/RN8cKHFu0muvBr5x1Z+J0i6Kb0iu/H51X/suVL5n3t+/fvV/VEnmKZcjuuZctP0vY5xs9nDwCz/4Hu9tu338Iicz09PQcOHHBVPOuSo25g//+5bfmuLgs/XtS8zdrzji/MPXNTy4qp1Gw2L7yvtmhKWyrJzXvBXVWQS32nCy+78IRlWJePL/MqgP6c3Dy9Wf/m3TzOuVDMy6zgX/F7QeskPehbthOD93CrPdnj1NfXFxUVuTqK9cD6/yQkJEShUOTm5r569cqe/zyLjNuWqpePzG1Vt2Ih9qWqQS91wqJfsmidleWfd3kMyoAtf/LcNxo2fvn6e0uLFBcXoy5QaEjq/nO8y1j+d2QymY4fP/75rJP8448/srOzy8vLbf+Sz2HnX1FR0ap+JmBFd+7cwXEcFe7Iysr6888/LYxeSTCLxYLKXJ09ezY3N/f06dMFBQVnzpw5f/782bNnL168eP78+by8vHPnzl26dKmgoODKlSuoREp+fv6lS5dyc3MvX76cn59fWFhYVFR04cIF9EF+fv7FixeLioqKi4svX76MDp4/f76wsBCt1MzPzy8oKCgsLCwsLCwtLb1+/To659KlS8XFxVeuXEFPh5qZFRUVlZSUlJSUVFVVXb9+vaKiory8vKSk5MaNG+Xl5WVlZSUlJaWlpWVlZejjS5cuoU+rq6trampQyWqDwVBaWooqWFdXV9+6daumpsZgMNy6dau0tLSiosJgMNy5c8dgMKAPULe20tLSW7duGQyGxsZG9NDt27fRZdGnNTU1t2/fNhgM1dXV6AOkuroanTz3snO/5N69ewaD4e7du7dv325sbKytrbWegL4KBWB1586d27dv19bW1tbWoodu3759+/btO3fu3L9///79+w8fPqyvr3/y5El9fX1DQ0N/f39zc/OjR4/q6+ubmpoePHjQ1tb28OHDZ8+ePX78GJ3Z0dHx4sWLrq6upqamJ0+ePHv27OXLl8+ePRsfHx8aGmptbR0eHh4cHDQajU+fPm1vb29ra3v27Flzc3Nra+uLFy/Q0Ke3t3dkZOTVq1cFBQVeXl58Ph/DsH379nV0dHR0dLx9+7atrQ3VCG9ra+vt7UUVbTo6Op49e9ba2trZ2dnR0YG2Nj558qSrq6u1tbW/v7+vr6+rqwuVnO7q6nrx4kVvb+/z5897e3t7e3tfvXrV29vb3d3d29vb39+P4nn79i1qBPHixYu+vr7BwcGhoaHBwcGenp7BwUEUJDoyPDyMeu+9ffu2r69vbGxsfHx8bGxsdHR0eHh4aGjo9evXg4ODTU1NAwMD6Mjo6Oj09PSHDx/QD+ft27cJCQkYhr148WJ4eHhsbGxsbGxqaspoNE5MTExNTU1OTk5NTaHjo6OjU1NTJpNpZmYGVdIxm83v37+fnZ1Fcw+omvbcv8zJycnZ2VmTyTQ6Omp9CL2NnTuBseL071KzKUtZ9PxHjx5ZizNkZWUtev6KB5d/aPkJkmW+i3mTKMtPPi31LIuWCVw+SHTO48eP7969u9TT2Tg5tOgJtkyhLXXOvA8Y/DqWD2CZgyv+8M0LSpwvDPvdu3fl5eU6nQ7VANm3b19NTc2ibyIX/vatn2IWi0Wn04WHh0dERISEhISHh6MllUFBQUqlMigoCLUrQ0fkcrlEIpFIJHK5XCaT0TRN03RgYCBN00FBQehT63GKogICAuRyOUVRqLxKQEAA2poQGBiIam4FBAQEBASg7pqo1RlJkqhLGRIQEODv7y+VSgmCQNX9BQIBKvaPyq6gHQ84jguFQhzHBQIBKnFCEAQ6AW0z53K5qCGAQCBAX0uSJKrjEhAQgPoASCQSkiTRLnXUngb1uPH19UVd+1D1LxzH2Ww2KmiJuj94e3t7e3vzeDwvLy8vLy/UD8LLy8taKhv729yP1xSXy0UfoDCWYT1h7plzy75hGGZ9GzXva1GNtLmfYn9/jys+L3Ah1BNj7hHr7wv9r0YdndB/ZlQGcO7JbDYb1RXy9vZG/TRQnSTrH51AIEB/NajGHjqCaukKBAL0h8zlciUSCaq0GxAQgD4QiURisTgwMFAgEKDeT0qlEr3CWHtCKZVKhUIREhKiVCpVKlVISIhOp9NoNBqNJiIiQq1Wb926VavVog+ioqJ0Ol10dPTWrVvROeHh4ehITEyMRqNBTT927doVExOza9cu9OmePXv0ej06Jy4uLiYmZu/evXq9fv/+/fHx8fHx8QcOHEA1BSMjI7dt2xb/N+sJ1g8WPrQqBw4cOHDgQGJiYkJCgvXIwYMH4+Pjk5KSDh06FB8fn5CQkJiYmJKScujQocTExEOHDn399ddpaWmpqalJfzt8+HBaWlpKSkp6enp6evrRo0dTU1MzMzP/+c9/Hj16FD10/PjxY8eOpaenp6SkoIcyMzMzMzNzc3NPnTp18uTJK1eunDp1Kicn58SJE7m5uZcuXUIjn8LCwsuXLxcXF5eWll65cuXatWtFRUXXrl1DIxY0/Lh69SoaWty8eRMdqaioqKmpuXnzJhqEGAwGNAKZ6+TJk1KpFP2vI0nyxIkTTU1Ny79FsH7s8esk5y4aRAX7XWip985L1exnMNBe2AZwnkWX7c1trTA5OTk5OblwYSGa/v3rr7+mp6ets77W90omk+nPP/8cGhp6//799PT09PT00NDQn3/++ebNm5GRkT/++GNwcDA+Pp7FYgmFQgzDdDpdZ2fn0NDQyMjI4ODgf//7376+vt7e3paWFjRQ6+joaGlp6ejo+P3339vb2xsbGzs6OlDN0rq6uocPH9bV1dXU1DQ3Nzc2NjY2NjY1NbW0tJSWltbV1bW0tDQ3N9fX1//6668Gg6G2thadXFdXV1dXhz795Zdf0Ni6tLS0pqbml19+QcerqqpqamqqqqoMBkN5eXlFRUXV3/7973+Xl5eXl5ejcXzpAj/++GNVVVVJScmPP/5YVFSk0WgwDDt79iyan0ATEj/++GNxcTGaSCgtLUVTFMj//d//FRQU5OfnX7hwIT8//8cff0Qf//DDD2jOIz8/Py8vDx1BH6AiPnl5eTk5ORcuXMjLyzt79iz6F020ZGVlnbUPmrNZXlhY2NzclpaWlpmZefbs2VOnTlkvgq5z/Phx9G9WVlZWVhb64OzZs6jmw7fffpudnZ2cnPz999+j19CsrKyUlJS4uLhvv/0WHfnqq6/i4+OzsrK+/fZbVJZ2//79Wq32q6++QulBq9VGR0frdLq5R/bv3x8VFbV79269Xh8VFaXX67VarUaj2bJlC8pzSqUyIiJCq9WGhYVZU1p0dPSXX36JHkUpU6VSqdVq1Ox3y5Yt1vaKFEUpFArUVAT9i2rho3e6qEAUjuPoCI/HQ0fQB6iX1oYNGzh/Q5+it8jofTP6waIahBs2bFiLNzTrhl6vt+XF0ONzG3ArZ86ckUgkcXFx8wp1u8S8SYw12t/2OayT7OrqksvlGIax2ez8/HzLGvwwPfe25fPnz1311EuVrUD/J8fGxqy/JqPRiN6qzszMGI3G8fHxmZmZjx8/fvjwYWpqanp6emJiYnp6emxsbHBw8P3796Ojox8+fBgZGXn9+vXbt2/fvHmDtpGhOwJozh/dDuju7m5ra+vo6Ojs7Hz27FlPT097ezt684puf6A6+w0NDehN6uPHj9EH6HbJkydPHjx4UFtbe+/evfv379fX19+9e9d65+XIkSNisRilNG9v7wMHDpSXl799+7asrAzVX3727JnFYrl58+bBgwfnld2C3AbWyszMjDNXEyz6artGa3ZMJtP4+Pjntk7y9evXsJkPOEFra2tGRkZwcDCGYSRJpqSkVFVVjY6OWk/48OFDY2MjQRD79u0rLy8PCQkhSbKjo2P+/TbwmVtqyhQsD/UmdXUUAKwraAkJhmEURdXU1CxzZkpKCprdXbQ9GfxlAgcbGxtraWlBpS9R0dL1Co3bPHcyjbGBgYEjR47s378/Jyfn8uXL+/fvd3VEYP04ffr00aNH6+vrVywUXFlZiWHYtWvXFn0UchtwpNOnT6vV6ry8vMjISLRilsFFPGUc+fncb5urtLSUy+WiIoqoMkt0dLSrgwKfo+vXr2MYlpOTs+ijkNuAA3z69MloNMbGxqrVanSLKzc3F8OwH374wbJ+N6pnZGRgGOZZ350t0S5zTl1dHYZheXl56NPy8nIMw6wtjwFwJrVazeFw/Pz8LIu9IYbcBphYuN0SNaF++vQp+jQnJwfDsIGBAcZXdn9HjhzBPLDHDdoSvswJS/0KjEajTCYTCoXWdqyHDx/29vb2rOwOPF13d3d/f39sbGxFRcXOnTsxDLt+/fqZM2fmnQa5bZ0wm81rPZVnNBpR/Y6hoSHURc/6jN3d3d7e3rm5udaT1Wr19u3b1zQel5hb1xTNyLk2Hiewlu2ora3FMKyiogId7+vrE4lEMTExLo0OfHZUKhVBEGi2oKKiAsOwvXv3Lrw5t/7/MoFDvH//XiwW4zjO4XDQ3lI2m71hw4bjx49bLBa9Xo9hmHWH+G+//YZh2NxUty59bj1uTp06hWEYqu83OTmJNh5Z5ycBcA5UO8L66VI9vyC3rQdOm8dbqnwcKsuEjjx48ADV6Lp165ZzonKmuT+B7777zrXjtkWL9a3d012+fBnDsDt37rS1te3bt4+iKAzDDh06tHbPCJzAg+4CrArkNuAAarUaDdROnjwZExOj1WoxDNPpdK6Oa22h3Obalwantcr7+PEjur+ICAQClUq1zCo14FkWljD2dJDbgAP8/vvvaKwWExNjNBqTk5NxHO/o6HB1XGsrLS3NVeM2Z74MoTYFarUa1cLG/i57iGHYhQsXnB8PcDiP7kW1FMhtwDFQwTpXR+FUaO+2S556tZ1l7HkKo9GIVqOhmn6oM4aPjw+GYRKJZHx8fKmK7G7+/2HFrcHAo0FuA4Ch9bqWZF5OOnv2LBqUYxjG4/HEYrFQKLSWrlcoFGq1uq6u7s2bN9avddpMqT3cOTZgP8htADCE6pKg7RDr0osXL6qrq0UikfU2m6+vr1Ao5HK5qKMb6lyIYRiO45GRkRqNZs+ePQMDA+Pj4/P6qboVNwwJOBzkNgAYQuM2T8ltS72gz1tEgE7r6+u7d+/e+fPnlUrlvC616E6bl5cXh8Px9/cPDAxEPcxQlzIul4saoel0uqKiooaGBjSuXaYbtefyiOHpZwtyGwAMobUk6+l17dOnT319fY2NjXq9XiqVyuXyzZs3Wyck58JxnKbp/fv3j42NGQyGxMTEsLAw6w5IFotFEIRYLFapVMXFxdZWR+tvzcKKvYKBq0BuA4AhNG5zdRQ2mVtOZa65L8fDw8PNzc379u0LCQkRCoV8Pt/f318oFPr6+qKJRy8vL7SWhMvlBgYGJiYmos6Q6PofPnxobW09f/58ZmZmQkJCQEAAm80mCIIkycTExLKysp6envX66t/b27tuBqPrhmf8ZQLghtD9Ng/tcTP3tfj9+/fPnz9p0jbEAAAgAElEQVTPzMwMCwsjCILNZvN4PC6XKxAIaJqmaXrr1q0ajSYgIEAmkykUip07d547d275YqGPHj1KTEyUyWQEQRAEQVGUSqWKjY2trKx8/fr1uklyRqMxMzMzIiLiyZMnkN7cCuQ2ABhaB71J//rrr7q6Oq1Wa92+xuFw0GJIpVIplUr1ev21a9c+fvw4NjbW2tpaW1v722+/2Z7Oh4aG9Hq9n58fjuMoyYWFhcXGxlZVVaH05umzlCMjI9HR0Xq9vra21tWxgP/h2X+ZALgQ2t/mudukpqamjh8/vmvXLrFY7OPjg+O4WCymafrkyZMGg+H58+f9/f32P8vw8LDBYAgJCUHDQZFIJJPJsrKyHj9+jFooeO5wx2QyTU5O7tmzJzo6urm52dXhgP8BuQ2A1bG+FqMaVJ710myN9v79+zqdDt1OEwqFgYGBCQkJBoNhjVr2jIyMnDt3TqfTiUQiLpcrlUojIyNTU1PLy8vfvn27Fs/oNNXV1Tk5OQzaOYE1BbkNAIbQnKRHdAmft1r9119/1ev1OI77+fkJhUK9Xm+tnrWmBgYGoqOj0fwkj8fj8XgEQeTn53d3d6PY1s19OOBykNsAWDWTyTQ1NeVZc5LWEduDBw+io6P5fD5JkhEREffv33dmaZW3b98mJCSgDeBcLhcNGffs2dPX1+fpFV48awS/7kFuA2AV5r5+nT592v3XSaKAzWbzxMREU1NTamoqGjORJHn48OHBwUHnvyJPTk6WlJQEBAT4+PjQNH3w4MHIyEiVSpWamjo8POyEZj3gcwC5DQCGUK9OV0exHOsU3/T0dG1t7ZYtWzgcDofDIQgiJibGuqV67Z56mTnGoqIiFou1YcMGmqZPnTr1r3/9SywWJycnL9VqEoBVceu/TADc2bFjxzyiVrLRaPzpp58OHDjA4XDYbHZgYGBxcfGHDx/W6OlMJtO+fft6enrQp8uMwBISEthsNpvN1mg09fX158+fJ0kyMzNzTZMu+ExAbgOAIdSbdHR01NWBLMI6Ffnu3buMjAyBQODl5YXjeFBQ0IMHDywLUs7s7KwDpwHj4+O5XG5LS8vyp01MTGRlZQkEAj6fL5fLExISTp8+rVQqjxw54il3MYHbgtz2Wfv06ROsTGMsOzvbze+3TU9PJyUlbdq0CZW/2r17d2dnp/VR67Th2bNnCYIwGAyOet6CggIMwzZt2mTL0sesrCwOh7Nx40aapnNzc3/++We1Wn3q1Cn0n9PTN3cDV4Hc9vmC2/V2QuM2N/wxopDGxsaOHDni7+/PYrEEAsGOHTuGhobmnfnx40e0atHf31+hUDhqMvDJkyfe3t44jtuyo7m3tzc8PFwoFIpEotDQ0Pr6+kuXLtE0nZ2dvUab7cDnAHLb584NX5o9hXveb0PjpHfv3sXFxREEgbZmHzly5N27d/POHBwcRAUkcRyXSCQO3EPd39/P5XJZLNajR48WxrZQXl4eTdP+/v58Pl+lUmVmZiYlJQmFwtTUVHf78QJPAbkNAIbcrZ7k3A3a6enpGzduZLPZJEl+88038zIEmuhLTk5Ge7c3b968f/9+xwYjl8sxDEPjthXnFbu7u2maViqVFEWJxeKIiAitVpucnCyVSv/zn/+MjIzA5CRYLTf6ywTAs6A5SbfqTWo2m/v6+i5duiSRSNBa/5MnTy565tOnTwUCAYvFUigU0dHRhw4dQss3HDKOf/fuHeon8OTJE+vBe/fukSR57ty5hU8xOzsbHx8fEBAQHx9P07RMJtu+fXtYWJhEIpFKpQ68EQg+H5DbAGAIjdvcatJsenr6P//5j16vJwhi06ZNcXFxC5e6oOFdaWmpUqnUarVpaWkGg8Gx5RCHhoZ4PB6Hw2lvb0dH3r9/r9Fo0DBxZGTEeqZ1NGYwGIRCYXNz8x9//JGVlYUmSymK2rBhA0EQVVVVDgwPfA4gtwHA0IkTJzAMc/lmLOswaGZm5v79+4mJiSRJorUhPT09cwdJ1knLoaEhjUZDkuSpU6d++ukno9FoXXOPzl9xcSM6bXZ29vnz5/X19fX19YWFhU1NTda9ByRJ4jhuvd+WkJAgEAjEYvHXX3+96AU/fvwYGhp65swZ9GlPT098fLxEIkGtAyiKys3NRUNk91nZi0qv9fb2Qm9SNwS5DQCG0FoSN5mTnJ6ebmxs1Ol0LBYLx/E9e/a8f/9+0TOnpqY0Gg2O49u3b+/u7p6ZmUHHra/OK75Md3R06HQ6rVYrkUjmtuRmsVjbt29HI8VDhw7hOH7v3r2xsbHExMSAgACKohITEwcHB5e6bHZ2dmhoqPVTk8lUX18fFRXl7++PepweOnTI3VJId3f3nj17pFJpV1eXu8X2mYPcBgBDOTk5bjInOTk5+e9//zs5ORnDMAzDrPeoFh3i1NXV+fn5sdns6upq68Hp6eno6GilUllXV7fi0338+JGmafRcaOecWCzWarXff/99fn4+OmdwcPD777/v7e2trq7esGEDhmH79+9fuAlhrubmZh6P19jYOPfg0NBQSkqKUqn8xz/+QZKku7UAbW9vV6vVWq325cuXro4F/A/IbQAwhPq3uTy3DQ4OXr9+PSIigsvl+vr6cjicpdaPWCwWs9mMxnZffPHF3PteZWVlCoVCKBRiGLZr164Vayg3NDTk5ORkZmYWFhYaDIa2trZF67P09/dv27aNw+HIZLK2trblv5HR0dGAgICoqKiF3+CxY8ekUqlMJtu2bVtTUxP6RtxhchINYSMiIjo6OlwdC/gfkNsAYAjVJXFtdSiTyTQ6OpqbmysUCgUCAbovtcz54+PjoaGhHA6nsLDQGnl7eztJkhRFxcXFKRQKDMNSUlIcMte6fft2Pp8vlUrLyspWPHlmZoYgCK1Wu/ChiYmJnJwciqIkEglBEPX19W5SDmZmZiYzM7OoqMhNpqaBFeQ2ABhCuc2147ahoaGioiLUZZSm6czMzOXPHxgY0Gq1GzduLCoqsl5BqVTyeLyIiIhff/2VpmkOh7N582b7R0X5+fkEQZAkmZyc/PHjx+VP/vTp08DAAI/HU6vVi57w119/ZWZmonamJEkWFxfbGR5Y3yC3AcAQut+2dgX1VzQ5OYkSG5fLlUqlISEhqIH1MmZmZoKCguRyeUNDAzpSWVlJkqRAIMjNzZ2eng4MDPT29haLxU+fPkVjI+vk5Pj4+MTEhI05r7q6miAIgUCg0+lsHGP19PQQBBEdHb3U+RMTE0VFRTqdLiAgQCaTlZeXWyyW2dlZd5icBO4GchsADKE9AC6ZHJuYmKivrz9z5oxOp0PLCBUKxY0bN1b8QrPZHBgYiOO4tcLWrl27SJIMDQ0dHx/v6Ojg8/lsNpvFYhUWFs772sHBwcDAwJqamhWfZXJyUq1WEwQREhKiUCiuXbtm3Vqw6G08dPD58+f+/v4ZGRnLv10YGxvLzc319/dH6zCh5iRYFOQ2ABi6cOGCq+Yku7u7Y2Njk5KSOBwOTdMEQXz//ffooeVrUw0ODtI0LRaLUQOa6elpiqIIgkhLS0PNS1ksFkVRHA5HpVItrHSVnJzM4XDQao5llJeXC4VCmqYvXLiAbuDV1NScOnVq9+7dcXFxS+0I7OjowHHclgnM1tZWrVZL07RKpSovL//zzz+XPx98hiC3AcAQqrm1sAbxWjObza9fvy4tLc3OzqZp2tfX9+DBg3MXPS5jdnaWpmkej2ctRLJ9+3YWi6VWq7lcLo7jAoGgrKwsJyfHx8enrKzMZDKh1m5o3q+2tpbH4+l0Omskiz7LgQMHSJLUarWDg4M7d+5ks9kymczX15fNZvP5fJlMtuhm58uXL3O53IyMDFu+kYqKCoVCIRAIAgMD0caAeSsnzWazm6ylBC4BuQ0AhnJzczEMc2D5/BWZzebp6elHjx7FxMSIxWKRSESS5NatW23vjzozM6NQKEiS7O/vR0caGxspiuJyuSKRKDk5GXUu7e7uDg4ODggIiImJ6e3ttX7506dP0Uhx+Wosjx8/PnPmTGtrq8ViuXjxIo/H8/Ly8vX1zcjIuHXrFkEQarV64VzuiRMnaJo+e/asLd9Ib2+vWq329fX19fVNS0uz8dsHnw/IbQAwhNaSOLnmVkdHR0REBIfD2bJlC0EQfn5+Fy5csP3LTSaTXq/HMGzufqzi4uLExMSKioq5M5DXrl2Lj4//+eef5w598vPzMQyjKGpwcHD5yc/p6Wn0QWdnJ0EQGIYlJiaiT3k8np+f37xlL3/99RdFUXK5/JdffrHxe0G7AsRi8aZNm+Ym4LnfrI2XAusP5DYAVmHuTNfp06cxDLMOgNYUesaBgYH6+vrc3Nzg4GA0/Dp+/LiNs5FWR48exXH8ypUrK565MGEUFRURBEEQxKtXr2x8uitXrqCiXGhHeW5uLo7jQqHw+fPn1uKTFoulrq5OIpHIZLIVl3pajY2N7du3jyRJsVh86NChmZkZSGbACnIbAAyhdZLDw8POebrZ2dnS0lK5XM7lcgMDA4VC4Z49e1Z1BfTSX1lZSRBEfHw8gxiuX7+enp5+/fp1axXKFZ08eRLltrKyMoPBQFGUSCSaV1iyra1NpVIJBIKUlBTrgM8WDx48CAkJkUql4eHh1l0NAFggtwGwWtaFkeh+21IliR3uzp07er1+48aNYWFhQqFw06ZNDx8+ZHCdvr4+dMeLwShnbGzs//7v/6zrGJe/Apq07Ovr8/PzwzAMDfjEYnFiYuK8ClXp6ek0TcfFxZWUlNgShvV537x5k5KSgvqaxsTEOLZTD/BokNsAYAjltjVdJ4lexMfHxzs7O69cuYJexCUSCU3TqKEMg911ZrM5IiLC39//xYsXaxDyIpqammQyWXh4uFwu/+KLL6yNb9BsZH9/P0VRUqn04MGD1h+mjTX1JyYmHj9+rNFo0G7umJiYZ8+eWZx4p62/v//EiRMVFRVosto5TwpsAbkNAIZQza21rktiNpufP39uMBiuX7++b98+qVTK5XIvXbo07xzbr2axWAwGg0wmO3LkyLzjS+2ttp/RaHz37l1fX9/r16/nPXTw4EGRSBQbG/v48WPryau6+MOHDzUaDUEQPB4vOzvbmTmmvr4+KChIr9c77RmBjSC3AcAQGret3d5t6+CjpaVl8+bNUVFRUVFRGzZsQMsU7bx4RkaGWCxOT0+39p1xyUKMn3/+WS6X63S6ly9frnZRjNUff/yRmJioVqs3b96sVqsZX4eB8vJyjUaj1+vdpHYzsILcBgATRqMR5TZHjdvmLhqcq7+/X6/XK5XKXbt20TRNkqS1R5o9Wltbt27diuN4Xl6e/VdbLetOcKlUGhwcnJmZ2dfXZ88FT548KRKJpFIpSZKoMKZlNcNZxmpra3fu3JmYmDg6Ogpzkm4FchsADOXl5WEYZvu+6RXNGzmZzea8vLx9+/ZJJJLo6OiQkBA+nx8dHe2ocUlra2tmZmZPT49DrrZaT548oWlaLpfv2rVrYGAA5TbG6WF4eFihUEil0tDQULVabW1hutaD0dbW1vj4eIe82wCOBbkNAIbQuG3F4oerMve1eGho6KuvvqIoiqIorVZLUZRarW5sbFyL12snT0j++OOPKpVKrVbHx8fbvqFteRUVFZs2bZJKpUqlUq/XL7qbey1YJ6Vhd51bgdwGAEPnz5/HMMzh686tk5ODg4MlJSXHjh3bsWMHakNz+fJlxz6X85nN5kePHmm12uDg4PPnz9tZ1WXuOG9qaurs2bPBwcE0TavVahu3E4D1CnIbAAyhAlRrV3Przp07aNYO9QtVq9VOru+1RoqKir7//nuDwbAWF9+/fz/qbBAVFTU0NLR8YTCwjkFuA4AhVHFjLfa3mUymmZmZixcvKhSK4OBgkiQ5HE5paSl61EPXLFjDnpmZcexE7lzd3d0JCQlhYWH+/v7Hjh1bo2cB7g9yGwAMFRYWYhg2Pj6+Fhd//Pjxzp071Wq1QCDAcTwqKsr2MlefuWPHjkVFRYWEhGg0mszMzHndw8FnAnIbAAwVFBRgGGb/VrOFxsbGysvLURUSDocjl8uhmpTtent79Xo9RVHJyclZWVl27i4AHgpyGwAMofttDs9tZrO5vr4+Pj5eJpOhzmrWFe3AFmazuaioSKVSoTcHhYWFro4IuADkNgAYunjxosPvt5nN5snJSYPBoFKpUBeb0NDQtSt9sl4ZjcaUlBSZTCYWi2maHhgYgDnJzw3kNgAYQnOSjt3VZDQam5ubv/zySw6HIxQKxWJxQUGB5e+a+mBF1l9He3t7WFjYli1bKIr64YcfXBsVcD7IbQAwdOnSJYfX3Hr+/Pnhw4dxHPf19RWJRHK5fI3WqnwOUGPugIAAhUJRX1/v6nCAU0FuA4AhdL/NgTW3LBZLWVmZSqVis9kCgSAyMpJZhzaAPH78WKFQEATB4XB0Ot34+LhjB9kmk2l0dLS7u9tp5SuB7SC3AcBQSUmJY3uTfvr0KTc3l8fjoXYtmZmZjrry52l6elqv15MkuWnTJh6PV1FRYXF0ZaxTp05RFPXjjz868JrAISC3AcDQ5cuXHdu/rbGxMTg4mMvl0jQdFBR08+ZNR135s9XU1ETTNEEQfD5/x44dDm9/U1hYuGPHDrStHsZtbgVyGwCrgF6/UO2rq1evYhj29u1b+y9osVhevXp17do1kUhEkqRCodixYwe8VjrEsWPHtFptYGAgRVHR0dGohrKjRm9lZWUxMTGNjY0OuRpwIMhtADB09uxZDMMcVW++s7MzOTmZzWbL5XI/P7+KigqoK+8QtbW1//jHP7RarVKp3Lhxo7VfnUN+vGfPnlUqlTAn6YYgtwGwauhl8cyZM/bXSkaDs6mpqYaGhrS0NC6XKxKJdDod9HF2lMnJyZycHJlMplKppFLpzp07JyYmHHXxw4cPUxSl0+ksMCfpZiC3AcDQsWPHMAx7/fq1/Zdqa2vbt28fjuNcLlehULx8+dL+azJjNpvRa/Ts7KyrYnC4N2/eaDSagIAAuVweEBBQWVlpcVAqGhgYePHiRWdnp/2XAo4FuQ0AhlBvUof0ncnOztZoNBs2bCAIIjk52f4L2mn9bRVPTk6mKIqmaYqiYmJiXB0OWHOQ2wBg6Ny5c/bfbzObzR8/fjx8+LC/vz9FUQKB4MWLF46KkHFIrg1gLdy4cYMkSYIgZDKZRqNZizJm62mkuw5AbgOAIVRP8tWrV3Zep7W1VaVS4TguFosVCoVjN4MDxGg0ajQakiQlEsnWrVsrKirWZQoHVpDbAGDo1KlT9vcBGBgY+OabbzQaDYfD2bBhg3UVH3C4nJycjRs3UhRFUZRarUbFRMB6BbkNAIZQzS0797cNDAzExMQQBIG2bPf09DgqPIBYx2dFRUVSqZSiKD6fLxQKYWv8+ga5DQCGUG7r7+9nfAWz2fzo0aOoqChUGTknJwfu2ayd7u5upVIpkUgoikLTvx8+fDCZTDA5uS5BbgOAIbR3284yTjU1NWKxGN1s+/PPPx0VG1hUenq6XC5HPUt1Oh3UE1nHILcBwFBeXp4999vQiCE9PZ3FYuE4vnXrVseGBxYaGBhQq9UEQdA0/fXXX0ND83UMchsADKE5SXvGbW/evImIiMAwDMfx4uJiB8YGlpKWliYWi3fv3h0REREfH2/PpdAuQJPJZP3AMSECR4DcBgBDqMeNPUv2KysrKYri8XiBgYHW+iZw+2eNoB8sauoWFham0+nUanV3d7c91xweHn769Onc6wM3AbkNAIaKioowDGO21dpsNtfV1cXHx7PZbA6Hs2fPHoeHBxY1ODgok8mEQmFQUJBMJsvJybHnanv37lWr1Y6qlw0cCHIbAAyhmlt9fX3Mvry4uDgsLIzFYhEEUVVV5djYwDKioqIIglAqlREREWKx2J7MlJKSEhMT88cff1hgTtLNQG4DgCE0JzkwMGD7l6BpK7PZPDo6mp6ejoojS6XStra2NQsTzPfdd98JhUKaptVqtUKhePToEeNLnThxQq/Xw3pLNwS5DQCGCgsLGdeTrKysFIvFPj4+fD7fzhUNYLXu3bun0WiCgoJ27NihVquPHj3K+FLZ2dmpqalNTU0ODA84BOQ2ABgqLS3FMKyjo2NVX4XW1CUnJ/v5+QmFQh6P9+uvv65JfGAJeXl5W7ZskUqlcXFxNE1HR0d//PjRwmhSMT8/Pyoq6pdffoEJSXcDuQ0AhtBaEgYL7cbGxlJTU9lstkgkEolEfX19UI7EmS5fvkxRFEmS586dU6lUKpUKvUFhsNDx0qVLoaGhMCfphiC3AcDQ5cuXV1tzC716tra2fvHFFzwejyTJ1NTUNQsQLK62tlapVNI0fezYMaVSqdfru7q6mF1qeHjYunkf9gC4FchtADCEam4xqEty4cIFiqI4HA5BEAaDYS1iA8vo6+tTq9U4jqenp3/zzTdKpbKoqMjVQQEHg9wGAENoneRqK/e/efPm0KFDbDabJEmZTDYzMwO3apxsdHQ0KiqKz+dHRkbW1NSEhoai5Tww8FpPILcBwNDVq1cZ9CatqalBgwYej5eeno4Owquqkz18+HD79u3BwcEtLS0hISFqtfrhw4euDgo4EuQ2ABgqKCjAMKyzs3NVX6XX68ViMUEQBEHcuXNnjWIDy8vKypLL5cnJyf/9738zMjJoms7Pz3d1UMCRILcBwNCVK1dWu5ZkZGQkMTERbWvj8Xhob5xHz0lOTk5aPHDc2dzcrNfr/f39r127dvr06cDAwNjYWFitup5AbgOACbPZfOnSpdXu3a6trdVqtT4+Pmw2OyMjY+7V1iBGsJz8/HyaptPS0urr61UqlVgsfv78uauDAg4DuQ0AhtDe7ZcvX1r+3pG9DDQ4q62tFYvFbDabxWL9/vvvzogSLCE7O1uj0eTk5Ny5c6empiYrKwtKHq8nkNsAYKiiogLVJZmdnUWNRlf8kiNHjhAEwWaz+Xy+EyIEi0K/qQcPHshkMqVSeePGDYlEwmKxDhw44OrQgMNAbgOAIXS/zdq+a0Wtra0KhYLFYvH5/JiYmDWNba2tg0nUFy9ehIeHUxRVXV0dGRmJYZh12SpYByC3AcCEyWRC+9tsmcgymUwmk6m4uFitVm/YsAHDMDvbhgH7vXnzJjY2liCIvLy88vJyDodDkmR7e/uK08sWD1/+85mA3AYAQyi32bi/raenJy0tLSAgAMMwLy8vqEDocrOzszt27ODxeAcPHnz16pVcLvf29r569arFtlGp0Whc+xgBc5DbAGDo2rVrtu9v6+3tVSqVOI5v2LCBoijrcRgBOJ/JZLJ2Y9i4caNKpTIajRwOh81ml5aWrvjltgzsgMtBbgOAIbQHwMY+AE+ePFGr1T4+PgRBHDx4cK1js9PcpTFLDWLQzrblL+LgsBzt/PnzYrE4KChoZmZGoVB4e3sXFhau9iKjo6NrERuwE+Q2ABhCvUlt7Lt97tw5qVTq7e2N4/i7d+/WOjaHWGZqztpA3J6LuNxPP/0klUp9fX1v3LgRExPj7e196NAhi80xm0ym1NTU5ubmNQ4TMAG5DQCGiouLbcxtRqMxMTFx48aNbDZbr9c7ITY7oWk369ydPdz5vlRnZ+eWLVt4PF5mZubZs2eFQmFcXJztX/7p06fk5GRYFuSeILcBwBDau73MOkmz2YxGADMzM+Hh4Ww229vbu7y83IkxrhXbR2PunNuMRmN2drZMJktJSSkvLw8MDNy1a9eqrpCSkrJjxw7UttudR6ifIchtADBUVlZm4x6AhoaGwMBAHo+nUCjQ6yBwE83NzRKJJDAwsLa21t/fPzQ0dFW3Cd+9e5eTkwM9BNwQ5DYAGELjtr6+vqVOsL5KlpSUSKVSDMNSUlKcFR2wyZ9//imXyzkcTnFxsVQqFYvFq5qGLS4ubm5u/uuvvyyesHbmswK5DQCGzp8/b+M6yfj4eD6fz2az79+/74TAgO3GxsYOHDgQGhqam5sbEhISFBTU3Nxs4+zi9PT0gQMHzpw5s9ZBAgYgtwHAEFon+fz586VeCq3Ht23b5uXlRVHUzMyMEwMEKzOZTHv37g0KCoqLi9u1a1dQUJAtW9wQo9EYExMDY3H3BLkNAIZQXRI0bltmIuu3334Ti8UYhnnECsnPUFVVlVAoJAiCoiiVSvXzzz/b/rUwD+m2ILcBwBDqA9DV1WVZ+jVubGwsKirK19fXy8uroKDAuQGCFaCBdW1tLUmSQqFQIBDQNF1VVeXquIADQG4DgCG0TvLZs2eWpXPbixcv9u/f7+/vj+P40NCQcwMENnn06FFAQABBEARBiEQi2K+2PkBuA4Ch8vLyFfcAlJaWbt68mcPhxMfHOy0wsCpDQ0MajYYgCA6Ho1Qqs7KyXB0RcADIbQAwYTabi4qKMAx78eKFZYlxm9FoTEhI4HA43t7eMBpwW4ODg5GRkQRBcLnc7du3r4/N9QByGwAM3bp1y5rbFvXq1SudTicUCr28vB4/fuzM2ICNTCbThw8f4uPjeTwel8tFy0lsrH8N3BnkNgAYqqqqwjBsmU5sHR0dSqWSw+FwOBxnBgZshEbbRqPx4cOHfn5+OI6TJEnT9DK/U1gY6SkgtwHAEFpL8vz584UPoQV4N2/epGmaxWLB6n83d/XqVa1WGxISIpPJhELhsWPHXB0RsBfkNgAYun79OoZhbW1ty5wQFBTEYrFQ5xTnvOWHgQUDFy9eVKlUAoFAIpFwOJyjR4+6OiJgL8htADAxPT1tMBgW7bttzS4XLlzAcRzDMFh65+Y6OztjY2OFQiFJkhiGZWRkuDoiYC/IbQAwdPHiRev+toX6+vo0Gg0qI3n58mUnxwZWZXx8PCUlJSAggM/nYxh28uRJV0cE7AW5DQCGUB+Ape63vXz5MiAgwNfXlyCIpfIfcB/19fXh4eFcLlcsFsNmxHUAchsATJjNZnS/7enTpwsfslgsd+7c4fP5Pj4+Go3GFQGC1Xnz5k14eAiMwM8AACAASURBVLi/v79QKBSJRJOTkxZoN+rJILcBwMTk5OS1a9cwDGtubl70hG+//VYul+M4np+f7+TYAANDQ0NqtRrHcaVSqVAo3LldOLAF5DYAGKqurl6mf1t8fLxEIvH19bW9ZwpwIaPRePjwYYFAQJJkSkrK7OysqyMCdoHcBgBDqC5Ja2ur5X9X3pvNZrPZvH//foFA4OvrW19f77oYgU3Q3GNmZiZJkgRBqNXqd+/eWWBO0pNBbgOAIbQHoKOjY9EtZfHx8QRBsNnsgYEB58cGGDh+/DhJkn5+fgqFoqOjw9XhALtAbgOACbPZjHIb6t+2UGJiIp/P9/f3d3JggLHKysqgoCAOhyMQCNBwHMZtngtyGwAMVVZWYhi2aBHkDx8+5OTkyGQyPp/v/MDAaqEc9vTp06CgIB6P98UXX9gybjOZTM+ePRsfH1/7AMGqQW4DgCG0lmTRurqDg4PJyclhYWFSqdTpcQGG3rx5ExERweFwpFJpS0vLiufX1dVFRUU9fPjQCbGB1YLcBgATZrMZrSV58ODBwodGR0ejoqL4fD5FUS4JD6yKde4xKSkJx3E2m52Xl2dZaU6yoqIiISFhqUlp4FqQ2wBgCN1vW3ROcmRkJC4ujqIokUjk/MAAYyUlJRRFeXl5HT58eMWTe3t74+Li7t6964TAwGpBbgOAIZTb2tvbFz40NDT0zTffKBQKmqadHxhgLDMzE8MwDMPQuG15Q0NDxcXFS23eB64FuQ0Ahm7cuIFh2KNHjxY+9Pr16+joaJFIRNP04OCg82MDzLS1tbHZbAzDbty4YbFhneTY2JhT4gKrBrkNAIbQ/bZF5yQnJyc1Gg1JkhKJBBqqeZC2tjYej4dhWGVlpatjAXaB3AYAQyUlJRiGNTU1Lfroli1bhEIhrJP0LE1NTRwOB8Ow48ePuzoWYBfIbQAwdPPmzUXHbWazeWRkhKZpf3//wMBAl8QGmGlsbBQKhTiOnzhxwgJ7tz0Z5DYAGCorK1t0D4DFYpmdnUWVCcPDw50fGGDs2bNnJEny+XxoT+rpILcBwFBNTQ2qJ7nwoaGhoc2bN1MUpVAonB8YYKylpUUsFuM4npOT4+pYgF0gtwHAEFpL8uTJk4UP9fb2KhQKkiS3bdvm/MAAY93d3Twez8fH55///KcF5iQ9GeQ2ABhC+9sW5jaz2Tw+Pq7VagUCgU6nc0lsgJn+/n6SJH19fRfdu20ymSDbeQrIbQAwYTKZUG5D9SQ/ffo099HBwUGapgmC0Ov1LgoQMNHb2ysWi9lsdlZW1qInQD9uTwG5DQCGUG5raGiwLHjJ6+/vVyqVPj4+KLfBm31P0dvbq9Fo+Hz+xYsXLf/7i4NfomeB3AYAQ7dv316qLklXVxdN01wud+/evc4PDDD26NEjkiS9vb1tWUsyOTnZ2to6OzvrhMDAakFuA4AhNG5btJxgb2+vWq3mcDhJSUnODwwwNjIysnv3bg6HY0s9yX/96196vf7NmzdrHxdYNchtADC0TB+A0dFRrVZLkuSBAwecHxhgrKioKCwszNfXF+3dXl5sbOzBgwd7enqcEBhYLchtADC01DpJi8Xy7t07hULBZrNhf5tnefLkiV6vZ7PZqamplpXusaWkpBw6dKitrW3FM4HzQW4DgKFl+m4PDQ19+eWXbDabIAiLxQLlkj1FY2OjXq/HcTw7O3vFk2NjY7VaLfR5cE+Q2wBgaO46yXkmJyeVSqW/vz9BENPT086PDTBTWVlJURSXy7VlwJ2cnBwfHz8wMIDeu8CiErcCuQ0AhlBuW7QPwPT09D/+8Q+SJHEcHxgYcH5sgJnu7u7NmzfzeDypVPrp06flB9y7d+/WarUvX750WnjAdpDbAGAI5baFewDMZvPExERYWBhBED4+Pos25gbu6cOHDwqFwtfXl6KoFbdpZ2RkyGSyrq4u58QGVgVyGwAMoXqSi85JdnV1RURE+Pr6ikQimJP0IDMzM2Kx2NfXVyaTrXhyTEzMtm3brl+/7oTAwGpBbgOAITRue/jw4cKHOjo6vvzySx6PR5Kk8wMD9ti0aROLxbKlqWxHR8fk5OTaRwSYgNwGABNms3mpOUmLxdLT0xMWFkZRlEgkcn5swB4qlQoNuHt7e10dC2AOchsADC2zTvL169eoD4BKpXJ+YMAearWaIAiCIAYHB2HXmueC3AYAQyi31dfXL3xocnISbQGG3OZxaJrm8Xg4jv/3v/9FR+Y1eQAeAXIbAAyh3Hb//v15x81m89TUVHR0NJ/Px3HcJbEBxnJycgQCAY7jc9+1wN41jwO5DQCGlsptFotlamoqJiaGy+V6e3uPjY05PzbAWFpaWkBAwLwWbjA56XEgtwHA0DJzku/fv9+9ezeO4xiGDQ0NOT82wBhN00KhEMfx5ORkV8cCmIPcBgBDKLc9ePBg4UNv377V6XRoTtJpy8RhbGG/qakplUolEolwHI+JiYEfqeeC3AYAQ8vcbxseHtZqtVwu18fHp7u722khwWuxnWZmZkpKSkJDQ9lstlwuh3ppngtyGwAMLTMnOTIygvZu4zgOdUk8SHt7O03TYWFhOI5v3ry5r6/P1REBhiC3AcAQym337t1b+NDY2Fh8fDxBEF5eXpDbPIXZbJ6ZmVGpVP7+/mw2W6lUOnPMDRwLchsADC0/bktMTGSz2Xw+3/mBAXvk5uZu3bqVzWYLhcKbN2+6OhzAEOQ2ABhaJrf19vbu3r0b+m57ouLiYo1Gw2KxOBxOXV3diudD41n3BLkNAIZQbrt79+7Ch/r7+yMiIthsti3l5IFbaWpq2rZtm7e3N47jhw8fnp2dNZlMiy7SmZychKbbbgtyGwAMLZPbUD1JHMfDw8OdHxiwx507d2Qymbe3N4vF0mg0y3Rxq6io+O6776BkiXuC3AYAEyaTaZk5yfb29s2bN7PZbI1G4/zYgD0MBgNFUTiOb9iwQS6Xv3nzZtHTPn78+NVXXxUVFTk3OmAryG0AMIR6k96+fXvecbPZ3NDQIJfLfXx84uPjXRIbYKyqqkomkwkEAjabLRAI0Lh87pwkmqI0Go379+9PSEhwXaRgOZDbAGCosrJyqTnJoqIigiD4fD6M2zyL2WxubGwMDQ3FcZzFYvn4+Pzzn/+0LLEpXqPRxMXFOT1GYBPIbQAwhOYka2trFz5UUlKyadMmDMP0er3zAwP2aGlpUSgUQqHQz89PLper1eqF1a5NJpPRaFSr1YmJiS4JEqwIchsADC3TB+Du3bsEQWAYlpqa6vzAgD2am5spiqJpGsMwLpdbWVm56C03s9kcERFx8OBBpwcIbAK5DQCGlqlLcuvWLTab7e3tDbnN4xiNxtDQUJIkMQxjs9k5OTnzTkAb2sxms06n27ZtmytiBCuD3AYAQ8uskywoKOBwOBiGze0BBjyFUqkUi8UYhvF4vJiYmEXPMRqNSqUS9ua7LchtADC0zP229PR0FovF5XIvXrzo/MCAnRISEthsNoZhMpns6NGjC08wm82zs7NZWVmhoaEzMzPOjxCsCHIbAExY97ctWpYpKyvLz8+PxWItOqoDbi4tLU2lUvn5+QmFQjTyXlhY6+XLl1qtNjs7++PHj66IEawAchsADC1zv+3YsWMsFsvLy8u60gQ6q3kE9Gs6evQo2r6N4/hSd0wnJiaGhobg1+q2ILcBwNAyNbcuXbqE4zibzX727Nnc4/BS6BFOnjxJkiSbzSYI4tChQzAy80SQ2wBgaJn7bSkpKRwOh8PhoMbNaDuU0wMEq4bmHq9du0YQhJ+fH4/HU6lUv/32m6vjAqsGuQ0Ahm7evLnU/ravv/4ax3Fvb++enh50BEZsHuTy5cskSeI4rtfrw8PDz5496+qIwKpBbgOAoaX2ABiNxsjISBzHfX19581JAjeHhteXLl3y9/cnSVIkEp04ceLOnTuujgusGuQ2ABiqra1dNLeNjIxER0dzOBw2m93e3u6S2IA9SkpKaJqmaVosFsfExDQ2Nro6IrBqkNsAYAiN2xb2ARgdHdXr9WjvdkNDg0tiA/YwGAz+/v4URfn7++fl5aGbpsCzQG4DgKGlctvAwAAqJI/jOOxv8yzotmhtbS2XyyUIQiQShYeHt7S0uDousGqQ2wBgqK6uDsOwhTdj+vr65HL5hg0bpFLpyMiIS2ID9qivr0frJOVyOUVRxcXFro4IrBrkNgAYWmp/W21trUqlwnGcIIjh4WELLJL0NHfv3qUoSigUymQykUiUlZUFv0GPA7kNACbMZvPt27cXnZOsrq7m8/kYhkkkksnJSZeEBxgzmUz37t2TSCRyuTw8PJyiKI1GA8tJPA7kNgAYunPnzqJzkvX19RRFYRimUqlcEhiwU3t7O1okGRcXR9O0VquFbQAeB3IbAAyhPQCLzklyuVwWixUQEABF4j3R06dPAwMDaZqOj48PCAhQKBTXr1+fd47ZbLY2cnNFjGAFkNsAYAjdbzMYDOhT62vcjRs3uFwuh8NRKBQfPnywwMuf50C/qZGREbTSVSKRREZG5ufnz5t5hl+o+4PcBgBDKLctnK0qLS2VSqUoty3sjQLc3/v3748fP65UKjUaDUVRW7ZsWXROcmxsrLu72/nhAVtAbgOAoaXWkpw7d04gELDZ7MjISJcEBhhDA7LXr18HBwfrdDq9Xh8YGBgREVFWVmY9B71fGRgY0Ol0J0+edFmsYFmQ2wBgaF5us85TZWZm+vj4cDicpKQky4K2lkvdpEFHzGYzzHe53Lt37xQKBYfDEYlEEolEpVIVFRXNO6e3tzcjIyM+Pt4lEYIVQW4DgCG0TnJhj5vMzEyCIDAMy8nJcUlgwH56vf6rr76KjY1Vq9V+fn4lJSVzHzWZTM3Nzd9//z2U43JbkNsAYOju3buLjtv27t1LEASbzT569Oi8L0HnzM7OLnVNGLS5Flr9ODU1FRgYKBaLjx07tmPHDh6Ph36Vc4fgjx49ioiIuHXrluuCBcuB3AYAQ/PWSSImkykhIYHL5bLZ7MLCQnQQMpbHUalUQqFQrVanpKSIxeKkpCT0jsS69L+1tVWtVi+cqwRuAnIbAAzNWyeJXvJaWlpSUlLQnCS88HkutVotFos1Gk18fDxBENHR0fM6p7e0tCiVynlzlcB9QG4DgCG0lmTeuG1oaCg8PBwVk7xx44ZlwVoS4BESEhKEQmFcXNyRI0dwHA8ODn769OncE54+fUrT9MJVssBNQG4DgKFFc9vIyMjWrVtFIhFBEPDC57mys7PFYnF4ePi5c+coivruu+9QbrNOL09MTMBCEncGuQ0Ahurr6+fmNjQ++/XXX7VaLUVRHA4HTVd++vTJlVECRrKysmialsvlnZ2dSqUyOjr648ePi54J43L3BLkNAIYW3bvd1NSEShHyeLxHjx6hg7CWxOPk5eVJpdLg4OCxsTGxWExRVGtrq/VR+IW6P8htADB0//79hXOSVVVVwcHBIpGIpuknT564KjZgp4qKCqlUGhQU1NrayuPxFApFQ0ODBbKa54DcBgBDaO/2vNz27bffkiSJ4ziHw2lpaXFVbMBONTU1mzZtioiIGBgY2LRpE0EQ5eXlrg4KrALkNgAYQj1u5uW2lJQUlUrF5XJJknz9+rUF7sd4poaGBrVaHRkZOTw8HBERQZIkanMD4zZPAbkNAIYWHbclJyfL5XIejycWiwcHB10VG7CTwWBAXUkHBgaysrLEYjGM2zwL5DYAGEL32+bV3EpJSZFIJD4+PgqF4tWrVy4NEDBXXV0tFosDAwP7+/uTkpJomobyWp4FchsADKE5yXnrJJOSkoKCggiC0Gg0ExMTa/G8y5SjBI7S0NCgUChomq6vr09LS/P39z9//rwF5iQ9B+Q2ABhaeL9tcnLyH//4h1AoJEnym2++WYsnhd1yztHa2rpx40aFQmEwGL788kuxWJyYmOjqoMAqQG4DgCHUB2BubhscHExKSsJxnM/np6enO/wZrYMGGD2stdbWVoVCERgYePny5djYWIqi7t+/7+qgwCpAbgOACbPZPK8uicVieffuXVpamkgkwnH81KlTLgwP2KmjoyMsLEytVt++fbujo0MkEs2bk7Q2BADuCXIbAAwtXCf5/v37f/3rX1FRUTweLz8/34WxATv19fWhciQFBQVDQ0MURVk7zc6bFoYM554gtwHA0MI5yWfPnoWFhXG5XJFIVFBQ4MLYgJ1GR0cVCkVAQMDp06enp6cFAsEXX3wxL42NjY2t0XIhYD/IbQAwhNaS3L1713qkt7c3JibGx8fH19fX+jYfeKLx8fHo6Ojg4GDUcVskEikUioGBATQnaTabOzo6kpKSYAuj24LcBgBDC9dJdnZ2Jicni8ViFouVlZXlwtjAqqAB2dzuo0ajUavVqlQqtCZIoVBoNJq5RdRaW1u1Wm1LSwvMSbonyG0AMIT6bs/Nbb29vWq1GsdxDMNyc3NdGBuwX0ZGhr+/f3h4+MjIiEQi2bZtW21trfXR5ubm2NhY1H4WuCHIbQAwhNZJzp2T/PDhg1arxTDM29u7rq7OhbGB1Vo4/CooKNi5c2dRUZHFYtHr9RKJpKmpyfpoWVlZWlpaV1eXU6MENoPcBgBDjY2N1nEbWjv35s2bjRs3YhjGZrN/+eUXVwcI7PLDDz+oVKrY2FiLxaJQKORy+e+//275+3fd0tKiVqthxZDbgtwGAEMot80tM/jhwweVSuXl5UUQRGdnpwtjA/bLz88PDAykKGpyclKn023fvn16etr6aENDQ2JiImzodluQ2wBgqKGhAeU2637e27dv83g8NG6DOUlPl5aWFhgYKJFIOjs7jxw5gtZJWteb3Lt3T6VS1dfXQ40Y9wS5DQCGHj58OG8tSUVFBUEQLBaLxWI1Nja6MDZgv5ycnIiICLVaPTQ0lJmZKZVKq6qqrI/W1NSIxeKSkhIXRgiWAbkNAIZQjxtrbjObzXfv3uXxeN7e3t7e3u3t7a4ND9gpIyMjMDAQ7W/Lzs4mSRKVS0arTh48eKBUKqH6jNuC3AYAQwvvt1VWVuI47u3t7ePj093d7cLYgP0KCgp27Nih1+stFsuxY8dIkpy7Z7Grq8tgMPT09LguQLAcyG0AMLSwVnJubq6fnx+bzWaxWHC/zdMVFxerVCo0Vjt+/DhJkj/88IP10Y8fP/7111+uiw6sAHIbAAw9ePBgXm7Ly8vDcdzLy4vP54+MjLgwNmC/uro6tVodEhIyPT2dk5OD43hMTAx6aO76EVhL4p4gtwHA0KNHjxbmNg6H4+PjQxBER0eHC2MD9mtpaYmMjNy5c2dTU1NKSgpFUXK5fGxszNVxAZtAbgOAofb29nm5rbi42M/Pj8Vi4TgOuc3T/fbbbxEREXq9/pdffsnLy5PL5bt37567xQ24M8htADCE9rfNzW05OTk8Ho/NZrPZ7Ll1dYEn6ujo2Lp1a2RkZGNj49WrVwmC0Gq1rg4K2ApyGwAMLZyTTE1NZbPZ3t7efD6/urrahbEB+338+DEuLk4kEsXGxp45c4bL5VIU5eqggK0gtwHA0MJ6khkZGRiGcTgcNpsNe7fXgePHjyuVyi1btiQlJREE8f/+3/9zdUTAVpDbAGAIjdtu3rxpPbJr1y7UBMDf339uMzDgcdDqx7i4uEuXLmVmZh44cCAgIAD1cgMeAXIbAAy1tLTMm5NMSUnZsGEDi8VSKBQuDAw4SnJycmxs7Pfff79//34OhwP32zwI5DYAGHr8+DGGYT/99JP1SGRkJKpLEhoa6sLAgKMcOnTo3LlzdXV1R48e9fX11el0ro4I2ApyGwAMoTnJuTW3tm/fzmazMQwLDg52YWDAfmhO8vLly2q1+vjx45mZmSKRiCTJ169fuzo0YBPIbQAw1NTUNHdO0mg06vV6NCepVCpdGxtwiGvXrimVyq+++io3N5cgiM2bN/f19bk6KGATyG0AMNTc3IxyG3qPPzY2tm3bNhzHMQwTCASujg44wP3791UqlUajMRgMOI5LpdKZmRlXBwVsArkNAIbm7gGwWCzd3d3+/v4cDgfDMJIkXRsbsBN6v3L//n2apjUazfnz51E79ampKVeHBmwCuQ0Ahrq7uzEMq6mpQZ/29vaKxWKU21QqlWtjAw7R3t6u1Wq/+uqr8vJyNputVqtdHRGwFeQ2ABiaNyc5Pj4eEBDAZrN9fHzCw8NdHR1wgK6urqCgoMTExJMnT+I4rlKpent70UM//fRTTEyM0WiEPgDuCXIbAAw9ffp07h6A2dnZvXv3onWSkNvWh6dPn27bti06OrqiosLX15ckyYaGBtR3u6ioKDY29sOHD66OESwOchsADKFxW1VVlfVIYmIimpOMjY11YWDAUdrb23U63Zdffpmfn8/j8TZu3GgtE5qfn//ll1++efPGpQGCJUFuA4Ah1AegsrLSeiQzMxPDMC8vr7i4OBcGBhxlYGBgx44dOp0uNTWVz+fjOH716lX00NWrV/V6/cTEBMxJuifIbQAwYTabrffbrAeLiorQHoCEhAQXxgbshzJWT0+PTqeLjY3dt28fym3WKegrV65oNJrR0VGXhgmWBLkNAIb6+vrm5bbS0lI0JwlFddeH7u7umJiY+Ph4vV7P4XDEYnF9fT16CG3r7u7uRrffgLuB3AYAQ21tbajmlnVW6sSJE6jBzddff235+70/8ETodzc8PBwcHBwREbFt2zbUv21kZASdcPfuXb1eD93V3RbkNgAYevbs2bxx286dO3k8HoZhKLcBj2YymcbHxyMjI6VSaWBgoK+vL47jT58+RY+eOXOmtLR0dnbWtUGCpUBuA4Chjo6OeblNq9Vu2rSJw+HAnOS6ce3atfT09JSUFA6H4+fnBy1nPQXkNgAYevHixbx1kiEhITwez8vL67vvvnNhYMB+aE7SbDbv2LEjNjY2NTWVy+XK5fJXr165OjRgE8htADCE5iTn5rY9e/ag/m0pKSkuDAw40MGDB+Vy+bZt2wiCoGn6xYsXro4I2ARyGwAMtbe3Yxhm3cxr+XvvNovFSkpKcmFgwH7W1Y9RUVGbN2+Wy+U4jvv5+Q0MDLg2MGAjyG0AMNTa2ophWGlpqXU9JOpx4+3tDWtJ1g2JRCIWi0UiEdrfBuM2TwG5DQAmzGYz2gNw/fp168G9e/ei+20wbls3Tp48mZSUFBIS4uPjg+P4+Pi4qyMCNoHcBgBDaJ3k3DnJ48ePEwSBYZhWq3VhYMCBkpOTc3JyIiIiMAzz8/N7//69qyMCNoHcBgBD/f39GIaVlJRY/r49c/r0aZqmvby8/P39XR0dcIxDhw6h/W3+/v4kSfb397s6ImATyG0AMITGbTdu3LAeOX36tFQq9fHxoSjKhYEBBzpw4IBUKqUoiiTJlJSUyclJV0cEbAK5DQCGUN/t4uJi65q6xsbGjRs3slisiIgI18YGHCU3N3fLli0EQXA4nM2bN7s6HGAryG0AMDR3ThJ5/vw5TdPe3t4BAQEuDAw40NWrV5VKJUmSPj4+ycnJrg4H2ApyGwAMze27jYZura2tKpUKwzC437Zu/PTTT0KhEMdxNps9tw8tcHOQ2wBgCM1JlpaWWo+0tLRotVoMw4RCoQsDAw5UXV0tFotZLBaHw/nPf/7j6nCArSC3AcAQ2rudn59vPfL8+XOtVovak8J7/PXhyf/X3v3HNHH/fwA/ik1LDmuOQkPNAcvxo7FNpaRUmnUhc6kooaQRU4aNGjdMgzNimBLAEF2MGvzRqHFo/NXAYpCgrhHDwgI4A8SpwR9ETQXCrwYMk6WUNUqwbe7zx/u7+17K7w5twdfjD7O+2zteXZs+7973fr+vtVUoFIaGhuI4brFYUKPX6x0ZGTEajXa7PbDlgZlAtgHgJ3Texs6wlpaWpKQkgUDA5/N/++23ANYGFktvb+/atWs5HA5FUegmAB8+fKBp2mQybdq0yeFwwL1JgxNkGwB+QmNJ2H2ST548SUhIWLVqVUhISFtbWwBrA4tlYGDAaDSuWrVKJpOxYywrK0uhUExOTgawNjALyDYA/ITucVNZWUn/O5ZkbGyMoiiSJH3WKwFL15MnT0iSDA0N5fF43d3dTPvmzZuFQmFXVxfcXT04QbYB4CebzeZz3kbTdFJSElp2C8YdLA8dHR0xMTEcDkcikbx+/ZppV6vVSUlJNpstgLWBWUC2AeAPr9fb19fHXisZHb/r9XoejxcSEgJjSZaH9vZ2iqJ4PJ5IJBoeHqb/PUdPT0/PyMiApZODFmQbAH4aGhqaet5mMBiio6MxDLNarV6vFzqslrqamhq0jlpERAS7Xa/XKxSKQFUF5gTZBoCfUJ/k2bNn0UN0OG8ymQiC4HA4165do1m3uARLlNls1mq1XC5XKpWy2/V6fVRU1OjoKHzEwQmyDQA/vX37FsOwo0ePshu1Wi0aJ8nMhQJL2qlTp9BYEq1Wy243Go0kST5+/DhQhYHZQbYB4Keuri4Mw06dOkWzzs/Wr18fFhYWGhp65cqVgFYH/DG1D3nLli0URYWFhaWmpqIW9FnfvXu3qakJbgsQtCDbAPBTd3e3z7okNE3rdDoul8vlcpm+SrDksLsZVSqVWCzm8/k+520gyEG2AeAPr9fb29uLYZjZbGa3GwwGLpfLvg4Hlhz22dvevXsFAgGPx0tOTp7zxSB4QLYB4KdXr15NzTaNRiMSiVauXOnTDpaoc+fOCYVCHo+XmJgY6FrAAkC2AeCn4eFhDMNOnjzJ7sJCaw+KxWI0ThIsdffv3ycIAsfxhISEQNcCFgCyDYDZzDJHDY2T9LneptFowsLC4D4Ay0ZHRwdBEFwulyRJGnoglw7INgD89ObNGwzDzp07hx56vd6xsTE0z1ckElmt1sCWB/wwNbr6+voSEhK4XK5IJApIScA/kG0A+Only5eoT5L+974n9fX16BhfIBD8+uuvgS4QLNj79+99WkZGRgwGA5/PF4vFASkJ+AeyDQB/pBmG7wAAD4ZJREFUeL3egYEBZn4b8vvvv1MUhWEYQRCjo6MBLA8slq6uLrlcHhYWBmNJlhbINgD8hPokT5w4wbQ0NzcnJCSEhoaGhYXBUkzLQ3t7O47joaGhBEHATO0lBLINAD/19/czcwBQn+StW7fEYjE6bwt0dWBxXL9+PTw8XCAQ4DhOwwKhSwdkGwB+stvtGIYdOXKEaamsrBQKhVwuNz4+PoCFgUVkNpvFYjGO45GRkZ2dnYEuB8wXZBsAfhoZGcEw7Pjx4+ih1+s1m80cDic0NDQ3NzewtYHFUltbm5CQQBAEj8dDa4SiUzc0ohJuYxS0INsA8BNac4s9v62kpCQqKorD4ZhMpgAWBhZRdXV1TEwMSZI4jp8+fTrQ5YD5gmwDwB/MOEl2n+S+ffvQuAPmZA4sUczZWG1tLUmS0dHRPB6PvY7amzdvioqK4KQtaEG2ATAjj8fjdrtnehb1SR46dAg99Hq9O3bsEAqFISEhPjfjBktXQ0ODVCpNSUkJCwsrKChg2rdt2yaVSl0uF8RbcIJsA8BP6B43x44dY1q0Wu2KFStEIhGa0A2Wgfr6eqlUGhcXx+FwoqKimHGSBoMhJiamv78/oNWBGUG2ATCbWY7KbTabz323t23bxufzcRyH87Zlo6amRq1Wy2QygiDEYvHff/+N2rdt23bhwoXA1gZmAdkGgJ8cDgeGYWVlZUyLwWBAa27duHEjgIWBRdTQ0JCUlCSVSgUCgVgs7u3tpWna4/Go1WqDwRDo6sCMINsA8AczloS53kbTdHZ2NofDwTDs9u3bAawNLKKHDx9KJJLU1FQcxwUCwePHj1F7dna2Tqej4c4AwQqyDQA/oXvclJaWMi1KpVIgEGAY1tDQQMOv3rJw9+5dnU4nk8lEIhFJknfu3EHtJSUldXV1ga0NzAKyDQA/OZ1ODMPKy8uZFolEwufzMQyrr68PYGFgEVkslrVr12ZkZEgkEqlU+uDBg0BXBOYFsg0AP6E1t9h9kl999RWHwyEI4t69ewEsDCyiBw8elJWV/fTTT8nJyVKptL29PdAVgXmBbAPAT2NjYxiGFRcX0/+uw3Tu3DmKog4dOjQ5ORno6oA/mJW0mBa3222329vb24uLiwsLC589e/bx/i5YRJBtAPgJzd0uLCwMdCHgo5t6z1IQ5CDbAPAHOtC+cuUKM3AOABA8INsAAGA2cM+2pQiyDQAAwHID2QYAAGC5gWwDAACw3EC2AQCAPz58+EDD1bhgBdkGAAALNnUmHAgqkG0AALAA6ETN7XY7HA4a4i1YQbYBAMDcfPoedTrdzz//HKhiwJwg2wAAYG5ut5v+9yxtbGxMIpEcPnyYhvO2YAXZBgAAc2MyzOPxTE5OrlmzpqSkJLAlgVlAtgEAwILJ5XJYSjSYQbYBAMDCOByO5OTkiooKGvokgxVkGwAALExvb29iYqLFYoFgC1qQbQDMAQ2QY//r3x6m7sTj8fyX3YJAGR4epijqxx9/DHQhYEaQbQDMzePxMEfo/h2qe73exsZGNCOqvLz8zp07nZ2d7GcXpU7wafT19cXGxup0ukAXAmYE2QbAbLxer91uLykpSU9PV6lUv/zyix87cbvdWVlZGIbhOJ6QkBASEsLj8Tgcztdff93e3s78oUUtHHwsHo+nr69v5cqVKpWKhg8uWEG2AfB/XYLDw8OHDx9WKBRpaWk5OTlo9hJN0waDITw8XCwWEwSBYdj169fRQoJsg4ODZ8+eHRkZ8VljEP1HY2OjUCjEMIzP52MYxuVy5XI5RVE4jovF4o6Ojk/2TsGiaGtrwzAsJiZmzld++PABfQfQF8Plcr1//767u7uurs5isTDtYNFBtoHPHfrpOXjwII7jYWFhBEEQBCESiSIjIymKysrKio6OJggiMTExPz8/NTW1tLSUvbnb7TYajRkZGWq1OiIiIj09PSsrC92MGx3Rv3///ssvv0R7rqmp2blz5+bNm8fHx7u7u/fv34/jOIfDaW5uDsh7B/5pb28vLi622Wzz38Tj8TQ3N2u1WqlUmp2drVKpUlNT8/Lyuru7P16dnzPINgBomqb37NkjEolEItGGDRvMZvPVq1eLi4vFYnFISAhBEFqtFl0qs9vtIyMjPtvq9XoMw+Ry+c6dO9VqdXJy8t69e9FTXq83Pz+fy+WSJNnb28s0MtteunSJw+EYjcZP8i7B4puzT9Lr9d68eVMikZw6dcpkMmVkZBiNxqKiojNnzqSkpGg0mp6enk9T6mcFsg0AmqZpp9NZV1dntVqZlrq6OoIgOByOXC4fHBycZdv+/v5NmzaRJFlUVPT8+fNHjx4NDw+jp2w2G5/P53A4ZWVl025rNpsxDEtPT1/E9wKCit1uF4lEYrFYo9F0dnY6HA7mhC8nJycqKur8+fMwUHbRQbaBz91MPyt5eXmol7K8vHw++xkfH3/x4kVDQ4PVar106RJq7OjoIAgCx/FpL6o5HA61Wo3j+L59+/yuHwS5ixcv8ng8lUpVWVk5NjbGfmrLli0ikQjNAQeLC7INgOnFxcUplUqCIJigmklJSYlOp5NIJARBhIeHC4VClUqFwqyxsTE8PJwkycnJSZ+tXr9+bTKZhEJhTEwMXHRZxlpaWtRq9bQ3DZBKpVFRUdXV1TQMKllskG0ATHPJxOFw4Dgul8uzsrLq6up8nmVPd6NpesuWLejkTCaT4TgeHx9vMBicTidN0z09PQRBREZGsmez0TT96tWrzMzM+Ph4mUxWX1//cd4WmJ7PVEV02IE+U/YdR10ul81ms9vt/f39Q0ND9Ayn+D57Y3bCtLjdbuZSK1tra2tERIRcLn/48KHP3tC/aCv2Nw26LucPsg0A35+nR48eXbp0iSAILpf7/fffs0+52D80Xq8X/daMjY2VlZWZTKbm5ua2trbOzk673c68rKWlJSIiAsdxtVptMpkKCgpyc3Ojo6Pj4uJMJhMzvw18YgMDA0VFRQqFQqlUHjx48OzZs8zVVpfLVVlZqVQqSZKMjY1FYxpRAk2bNE6nc2hoaGJiYnR0dHx8fGJiwufoZ1qXL19et26dRqOZmJjweer8+fPffPMNn89HI3X7+/vZkQnmA7INAHp0dLS/v5+m6e7u7sLCQoqi4uLiFAoFn88/cuQI+5U2m62xsfGPP/5gRovMx8mTJ1UqlVQqRZ2WaEBmVFTU2bNnF/eNgPnweDx1dXUCgUAoFFIUpdFoJBLJ9u3bSZK8ceNGU1MTSrW1a9ei5IuJiVEoFFKpdOquXC6XxWL54YcfMjIy9Hr91q1bMzMzc3JyTCbT1PG07AIGBwcNBoPFYjl9+jS7nabp+vr69PR0giCioqKEQiGfz//uu+9omr5+/frsY5oAG2QbAHRubq5EIsnJyZHJZKtXr05ISKAoKjExUSqVJicnW63WxsbG4uLizMzMNWvWZGVl6XS6M2fOLOhPTExM2O328+fPnzx5sqSk5NSpU2hSAQKH5P8dcxo9HzabTSKRqNXq/Pz8mzdvVlVVmc1mrVaLpiGSJKlUKrdv337z5s2enp4HDx4cPXoUjffx+aROnDgRERFBkqTBYJDJZCqVasOGDQaD4dtvv71///5MH6vX6y0pKZFIJBcvXvR5amhoSCwWl5aWxsfHr1+/3mg0oiI7OjpCQ0M1Gs3bt2+Zd8ruwAQ+INsAoCsrK9etW4cujCmVSrPZ3NHRUVVVpVKpVq9ezePxhEJhSkpKQkJCdHR0bm5uQ0ODy+UKdNXg//nx+z45OelyudgdzrW1tRRF8fl8vV5vs9l8hv+8e/du6k56e3vT09M1Gk1paWlra+uxY8esVmtTU1NDQ0NfX99MRVosFoIgZDIZWpqE7eHDhyKRaPfu3Q8ePEAtbrfb6XT29fWFhoZiGHbw4EGm/oW+5c8KZBsAtNPpzMnJ2bRpU3l5OXuxiefPn5eXl6tUKp1OJxaLCwsL79+///79e/a2cHl/yZnpI9u5c6dQKExLS1vQTUedTuc///zj862YVmNjY35+/qVLlzQaDUEQGRkZ0+4NfdN8inz58iWfz1+xYgUzFRKybXaQbQDQNE27XK6Ojo6ph/9ut7urq+vRo0c+Ax1BUPnv/XJtbW2xsbGJiYlqtTovL28+mzDx43A4amtrKyoqKioqdu7cWVRUxF5Q9N27d1evXi0oKKAoauXKlTiOo97FO3fuTFu/wWBISUlhf99GRkb0ej1FUSRJRkZGsscfwT2SZgLZBsBHB4PcgtDk5CR7sauWlhaSJGUymUKh2LBhw3w+L4/HY7FYcnNzpVKpSCSSy+USiUSpVO7Zs+fWrVvMyy5fvszlchUKRXR0tFwuJ0kSjZs9fvw48xpmtgBN00+fPqUoymg0Wq3We/fu1dTUSKXS1NTUI0eOWK1WkUikVCrRyEmalWrwBfMB2QbAJzrshcm5QeX+/ftXrlxhHr5+/VokEgkEgrS0NKVSiRpn/2Jcu3YNx3GSJNPS0jIyMgwGg8lk0ul0Fy5cYHdRomXVxGJxXFycSqVKSko6duxYTEyMUCh8+fIl+lY4nc5r167V1dXZbLbBwcGCggK0FADaavv27TqdDg3lLS8vFwgESUlJbW1t7GLQs4AB2QYA+LygU5xdu3ap1WpmpP6tW7fQXYeUSmVVVRX79cygRJfLNTY25nK50B6cTmd2dvbGjRsrKiqePXuGzrp6enrYsxtpmr537x6XyxWLxRRFqdXqpqYmmqbr6+sTExOzs7Orq6t3796dkpKiUCg2btz4+PFjj8czMjJy5MiRzMxMvV6/Y8eO6urqrq4utLfx8fFdu3aRJLlq1SqKonJycrKysuRy+e7du9HIW+gkQCDbAJgbXM9Yfi5fvqxWqw0Gg1ar1ev1OTk5crn8iy++QPcz2r9//8mTJ/fu3VtcXLxnz57du3fn5uYWFBQ0NDSwlwadOu3aB/rmlJSUyOXyzMxM9r1t29vbZTIZQRDx8fEpKSn5+fm3b99mhkciXq/X7Xb7DBsZGxuzWCy7du2KjY2Vy+V5eXl6vT45Obm1tXUR/r8sF5BtAMwNdRxBp+Iyc+DAgU2bNplMJoVCsXXr1vPnz5vN5u3bt8fFxZEkKZVK0SW0tWvXKpXKnJycioqKp0+fsicmzpPT6Xz58uXUDdva2rRabWZm5oEDB/7888+FHkJZLBaTyVReXv7XX38t6GZynwPINgDAZ8rhcFy4cKGqqurFixcWiwXNYBseHm5tbS0uLs7Pzy8tLTWZTI8ePRoYGJhlnRG/eb1em83W2dmJ+jP92NzpdMJUy2lBtoHPGlyZANOamJjwmdkNlpb/AeKppi+a18uvAAAAAElFTkSuQmCC" alt></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[6 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">A significant number of candidates did not answer this question. Among the candidates who attempted it there were many who had difficulties in connecting vertical asymptotes and the domain of the function and dealing with transformations of graphs. In a few cases candidates managed to answer (a) but provided an answer to (b) which was inconsistent with the domain found.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">A significant number of candidates did not answer this question. Among the candidates who attempted it there were many who had difficulties in connecting vertical asymptotes and the domain of the function and dealing with transformations of graphs. In a few cases candidates managed to answer (a) but provided an answer to (b) which was inconsistent with the domain found.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Given that \(f(x) = 1 + \sin x,{\text{ }}0 \leqslant x \leqslant \frac{{3\pi }}{2}\),</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">sketch the graph of \(f\);</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="font: normal normal normal 31px/normal Helvetica; text-align: center; margin: 0px;"><img src="data:image/png;base64,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" alt></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">show that \({\left( {f(x)} \right)^2} = \frac{3}{2} + 2\sin x - \frac{1}{2}\cos 2x\);</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">find the volume of the solid formed when the graph of <em>f</em> is rotated through \(2\pi \) radians about the <em>x</em>-axis.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><img 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" alt><span style="font-family: 'times new roman', times;"><span style="font-size: medium;"> <strong><em>A1</em></strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times;"><span style="font-size: medium;"><strong><em>[1 mark]</em></strong></span></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({(1 + \sin x)^2} = 1 + 2\sin x + {\sin ^2}x\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 1 + 2\sin x + \frac{1}{2}(1 - \cos 2x)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{3}{2} + 2\sin x - \frac{1}{2}\cos 2x\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(V = \pi \int_0^{\frac{{3\pi }}{2}} {{{(1 + \sin x)}^2}{\text{d}}x} \) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \pi \int_0^{\frac{{3\pi }}{2}} {\left( {\frac{3}{2} + 2\sin x - \frac{1}{2}\cos 2x} \right){\text{d}}x} \)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \pi \left[ {\frac{3}{2}x - 2\cos x - \frac{{\sin 2x}}{4}} \right]_0^{\frac{{3\pi }}{2}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{9{\pi ^2}}}{4} + 2\pi \) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Parts (a) and (b) were almost invariably correctly answered by candidates. In (c), most errors involved the integration of \(\cos (2x)\) and the insertion of the limits.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Parts (a) and (b) were almost invariably correctly answered by candidates. In (c), most errors involved the integration of \(\cos (2x)\) and the insertion of the limits.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Parts (a) and (b) were almost invariably correctly answered by candidates. In (c), most errors involved the integration of \(\cos (2x)\) and the insertion of the limits.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graphs of \(y = \frac{x}{2} + 1\) and \(y = \left| {x - 2} \right|\) on the following axes.</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>Solve the equation \(\frac{x}{2} + 1 = \left| {x - 2} \right|\).</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><img 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"></p>
<p>straight line graph with correct axis intercepts <em><strong>A1</strong></em></p>
<p>modulus graph: V shape in upper half plane <em><strong>A1</strong></em></p>
<p>modulus graph having correct vertex and <em>y</em>-intercept <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><strong>METHOD</strong> <strong>1</strong></p>
<p>attempt to solve \(\frac{x}{2} + 1 = x - 2\) <em><strong>(M1)</strong></em></p>
<p>\(x = 6\) <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Accept \(x = 6\) using the graph.</p>
<p>attempt to solve (algebraically) \(\frac{x}{2} + 1 = 2 - x\) <em><strong>M1</strong></em></p>
<p>\(x = \frac{2}{3}\) <em><strong> A1</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<p> </p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>\({\left( {\frac{x}{2} + 1} \right)^2} = {\left( {x - 2} \right)^2}\) <em><strong>M1</strong></em></p>
<p>\(\frac{{{x^2}}}{4} + x + 1 = {x^2} - 4x + 4\)</p>
<p>\(0 = \frac{{3{x^2}}}{4} - 5x + 3\)</p>
<p>\(3{x^2} - 20x + 12 = 0\)</p>
<p>attempt to factorise (or equivalent) <em><strong>M1</strong></em></p>
<p>\(\left( {3x - 2} \right)\left( {x - 6} \right) = 0\)</p>
<p>\(x = \frac{2}{3}\) <em><strong> A1</strong></em></p>
<p>\(x = 6\) <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="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A function is defined as \(f(x) = k\sqrt x \), with \(k > 0\) and \(x \geqslant 0\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Sketch the graph of \(y = f(x)\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Show that <em>f</em> is a one-to-one function.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) Find the inverse function, \({f^{ - 1}}(x)\) and state its domain.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(d) If the graphs of \(y = f(x)\) and \(y = {f^{ - 1}}(x)\) intersect at the point (4, 4) find the value of <em>k</em> .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(e) Consider the graphs of \(y = f(x)\) and \(y = {f^{ - 1}}(x)\) using the value of <em>k</em> found in part (d).</span></p>
<p style="margin: 0px 0px 0px 30px; font: 27px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Find the area enclosed by the two graphs.</span></p>
<p style="margin: 0px 0px 0px 30px; font: 27px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) The line <em>x</em> = <em>c</em> cuts the graphs of \(y = f(x)\) and \(y = {f^{ - 1}}(x)\) at the points P and Q respectively. Given that the tangent to \(y = f(x)\) at point P is parallel to the tangent to \(y = {f^{ - 1}}(x)\) at point Q find the value of <em>c</em> .</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a)</span></p>
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" alt><span class="Apple-style-span" style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 14px; line-height: 20px; display: inline; float: none;"><span class="Apple-style-span" style="font-family: 'times new roman', times; font-size: medium; display: inline; float: none; line-height: normal;"> <strong><em>A1</em></strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1</em></strong> for correct concavity, passing through (0, 0) and increasing.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Scales need not be there.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[1 mark]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) a statement involving the application of the Horizontal Line Test or equivalent <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[1 mark]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) \(y = k\sqrt x \)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">for either \(x = k\sqrt y \) or \(x = \frac{{{y^2}}}{{{k^2}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({f^{ - 1}}(x) = \frac{{{x^2}}}{{{k^2}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{dom}}\left( {{f^{ - 1}}(x)} \right) = \left[ {0,\infty } \right[\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(d) \(\frac{{{x^2}}}{{{k^2}}} = k\sqrt x \,\,\,\,\,\)or equivalent method <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(k = \sqrt x \)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(k = 2\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(e) (i) \(A = \int_a^b {({y_1} - {y_2}){\text{d}}x} \) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(A = \int_0^4 {\left( {2{x^{\frac{1}{2}}} - \frac{1}{4}{x^2}} \right){\text{d}}x} \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \left[ {\frac{4}{3}{x^{\frac{3}{2}}} - \frac{1}{{12}}{x^3}} \right]_0^4\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{16}}{3}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) attempt to find either \(f'(x)\) or \(({f^{ - 1}})'(x)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(x) = \frac{1}{{\sqrt x }},{\text{ }}\left( {({f^{ - 1}})'(x) = \frac{x}{2}} \right)\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{1}{{\sqrt c }} = \frac{c}{2}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(c = {2^{\frac{2}{3}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[9 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [16 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Many students could not sketch the function. There was confusion between the vertical and horizontal line test for one-to-one functions. A significant number of students gave long and inaccurate explanations for a one-to-one function. Finding the inverse was done very well by most students although the notation used was generally poor. The domain of the inverse was ignored by many or done incorrectly even if the sketch was correct. Many did not make the connections between the parts of the question. An example of this was the number of students who spent time finding the point of intersection in part e) even though it was given in d).</span></p>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">The graph of a polynomial function <em>f </em>of degree 4 is shown below.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><img src="data:image/png;base64,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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Given that \({(x + {\text{i}}y)^2} = - 5 + 12{\text{i}},{\text{ }}x,{\text{ }}y \in \mathbb{R}\) . Show that</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \({x^2} - {y^2} = - 5\) ;</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \(xy = 6\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Hence find the two square roots of \( - 5 + 12{\text{i}}\) .</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">A.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">For any complex number <em>z </em>, show that \({(z^*)^2} = ({z^2})^*\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">A.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Hence write down the two square roots of \( - 5 - 12{\text{i}}\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Explain why, of the four roots of the equation \(f(x) = 0\) , two are real and two are complex.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">The curve passes through the point \(( - 1,\, - 18)\) . Find \(f(x)\) in the form</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(x) = (x - a)(x - b)({x^2} + cx + d),{\text{ where }}a,{\text{ }}b,{\text{ }}c,{\text{ }}d \in \mathbb{Z}\)<em> </em>.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">B.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the two complex roots of the equation \(f(x) = 0\) in Cartesian form.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Draw the four roots on the complex plane (the Argand diagram).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Express each of the four roots of the equation in the form \(r{{\text{e}}^{{\text{i}}\theta }}\) .</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">B.e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \({(x + {\text{i}}y)^2} = - 5 + 12{\text{i}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x^2} + 2{\text{i}}xy + {{\text{i}}^2}{y^2} = - 5 + 12{\text{i}}\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) equating real and imaginary parts <strong><em>M1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x^2} - {y^2} = - 5\) <strong> <em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(xy = 6\) <strong> <em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[2 marks]</span><br></em></strong></p>
<div class="question_part_label">A.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">substituting <strong><em>M1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>EITHER<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x^2} - \frac{{36}}{{{x^2}}} = - 5\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x^4} + 5{x^2} - 36 = 0\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x^2} = 4,\, - 9\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = \pm 2\) and \(y = \pm 3\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>OR<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{36}}{{{y^2}}} - {y^2} = - 5\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\({y^4} - 5{y^2} - 36 = 0\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\({y^2} = 9,\, - 4\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\({y^2} = \pm 3\)<strong> and</strong> \(x = \pm 2\) <strong> <em>(A1)</em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Accept solution by inspection if completely correct.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>THEN<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">the square roots are \((2 + 3{\text{i}})\) and \(( - 2 - 3{\text{i}})\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[5 marks]</span><br></em></strong></p>
<div class="question_part_label">A.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER<br></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">consider \(z = x + {\text{i}}y\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(z^* = x - {\text{i}}y\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\({(z^*)^2} = {x^2} - {y^2} - 2{\text{i}}xy\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(({z^2}) = {x^2} - {y^2} + 2{\text{i}}xy\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(({z^2})^* = {x^2} - {y^2} - 2{\text{i}}xy\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\({(z^*)^2} = ({z^2})^*\) <strong> <em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR<br></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(z^* = r{{\text{e}}^{ - {\text{i}}\theta }}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\({(z^*)^2} = {r^2}{{\text{e}}^{ - 2{\text{i}}\theta }}\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\({z^2} = {r^2}{{\text{e}}^{2{\text{i}}\theta }}\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(({z^2})^* = {r^2}{{\text{e}}^{ - 2{\text{i}}\theta }}\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\({(z^*)^2} = ({z^2})^*\) <strong> <em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[3 marks]</span><br></em></strong></p>
<div class="question_part_label">A.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">\((2 - 3{\text{i}})\) and \(( - 2 + 3{\text{i}})\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[2 marks]</span><br></em></strong></p>
<div class="question_part_label">A.d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">the graph crosses the <em>x</em>-axis twice, indicating two real roots <strong><em>R1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">since the quartic equation has four roots and only two are real, the other two roots must be complex <em><strong>R1</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">B.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(x) = (x + 4)(x - 2)({x^2} + cx + d)\) <strong> <em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(0) = - 32 \Rightarrow d = 4\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Since the curve passes through \(( - 1,\, - 18)\)<span style="font: 11.5px Times;">,<br></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( - 18 = 3 \times ( - 3)(5 - c)\) <strong> <em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(c = 3\) <strong><em>A1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Hence \(f(x) = (x + 4)(x - 2)({x^2} + 3x + 4)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[5 marks]</span><br></em></strong></p>
<div class="question_part_label">B.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = \frac{{ - 3 \pm \sqrt {9 - 16} }}{2}\) <strong> <em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow x = - \frac{3}{2} \pm {\text{i}}\frac{{\sqrt 7 }}{2}\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[2 marks]</span><br></em></strong></p>
<div class="question_part_label">B.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em><img 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" alt> A1A1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong> </strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Accept points or vectors on complex plane.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Award <strong><em>A1 </em></strong>for two real roots and <strong><em>A1 </em></strong>for two complex roots.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[2 marks]</span><br></em></strong></p>
<div class="question_part_label">B.d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">real roots are \(4{{\text{e}}^{{\text{i}}\pi }}\) and \(2{{\text{e}}^{{\text{i}}0}}\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">considering \( - \frac{3}{2} \pm {\text{i}}\frac{{\sqrt 7 }}{2}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(r = \sqrt {\frac{9}{4} + \frac{7}{4}} = 2\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">finding \(\theta \) using \(\arctan \left( {\frac{{\sqrt 7 }}{3}} \right)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\theta = \arctan \left( {\frac{{\sqrt 7 }}{3}} \right) + \pi {\text{ or }}\theta = \arctan \left( { - \frac{{\sqrt 7 }}{3}} \right) + \pi \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow z = 2{{\text{e}}^{{\text{i}}\left( {\arctan \left( {\frac{{\sqrt 7 }}{3}} \right) + \pi } \right)}}{\text{ or}} \Rightarrow z = 2{{\text{e}}^{{\text{i}}\left( {\arctan \left( {\frac{{ - \sqrt 7 }}{3}} \right) + \pi } \right)}}\) <strong><em>A1</em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium;"> </strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Accept arguments in the range \( - \pi {\text{ to }}\pi {\text{ or }}0{\text{ to }}2\pi \) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Accept answers in degrees.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[6 marks]</span><br></em></strong></p>
<div class="question_part_label">B.e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Since (a) was a ‘show that’ question, it was essential for candidates to give a convincing explanation of how the quoted results were obtained. Many candidates just wrote</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">\[{(x + {\text{i}}y)^2} = {x^2} - {y^2} + 2{\text{i}}xy = - 5 + 12{\text{i}}\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">\[{\text{Therefore }}{x^2} - {y^2} = - 5{\text{ and }}xy = 6\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This was not given full credit since it simply repeated what was given in the question. Candidates were expected to make it clear that they were equating real and imaginary parts. In (b), candidates who attempted to use de Moivre’s Theorem to find the square roots were given no credit since the question stated ‘hence’.</span></p>
<div class="question_part_label">A.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Since (a) was a ‘show that’ question, it was essential for candidates to give a convincing explanation of how the quoted results were obtained. Many candidates just wrote</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">\[{(x + {\text{i}}y)^2} = {x^2} - {y^2} + 2{\text{i}}xy = - 5 + 12{\text{i}}\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">\[{\text{Therefore }}{x^2} - {y^2} = - 5{\text{ and }}xy = 6\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This was not given full credit since it simply repeated what was given in the question. Candidates were expected to make it clear that they were equating real and imaginary parts. In (b), candidates who attempted to use de Moivre’s Theorem to find the square roots were given no credit since the question stated ‘hence’.</span></p>
<div class="question_part_label">A.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Since (a) was a ‘show that’ question, it was essential for candidates to give a convincing explanation of how the quoted results were obtained. Many candidates just wrote</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">\[{(x + {\text{i}}y)^2} = {x^2} - {y^2} + 2{\text{i}}xy = - 5 + 12{\text{i}}\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">\[{\text{Therefore }}{x^2} - {y^2} = - 5{\text{ and }}xy = 6\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This was not given full credit since it simply repeated what was given in the question. Candidates were expected to make it clear that they were equating real and imaginary parts. In (b), candidates who attempted to use de Moivre’s Theorem to find the square roots were given no credit since the question stated ‘hence’.</span></p>
<div class="question_part_label">A.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Since (a) was a ‘show that’ question, it was essential for candidates to give a convincing explanation of how the quoted results were obtained. Many candidates just wrote</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">\[{(x + {\text{i}}y)^2} = {x^2} - {y^2} + 2{\text{i}}xy = - 5 + 12{\text{i}}\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">\[{\text{Therefore }}{x^2} - {y^2} = - 5{\text{ and }}xy = 6\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This was not given full credit since it simply repeated what was given in the question. Candidates were expected to make it clear that they were equating real and imaginary parts. In (b), candidates who attempted to use de Moivre’s Theorem to find the square roots were given no credit since the question stated ‘hence’.</span></p>
<div class="question_part_label">A.d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In (a), the explanations were often unconvincing. Candidates were expected to make it clear that the two intersections with the <em>x</em>-axis gave two real roots and, since the polynomial was a quartic and therefore had four zeros, the other two roots must be complex. Candidates who made vague statements such as ‘the graph shows two real roots’ were not given full credit. In (b), most candidates stated the values of <em>a </em>and <em>b </em>correctly but algebraic errors often led to incorrect values for the other parameters. Candidates who failed to solve (b) correctly were unable to solve (c), (d) and (e) correctly although follow through was used where possible.</span></p>
<div class="question_part_label">B.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">In (a), the explanations were often unconvincing. Candidates were expected to make it clear that the two intersections with the <em>x</em>-axis gave two real roots and, since the polynomial was a quartic and therefore had four zeros, the other two roots must be complex. Candidates who made vague statements such as ‘the graph shows two real roots’ were not given full credit. In (b), most candidates stated the values of <em>a </em>and <em>b </em>correctly but algebraic errors often led to incorrect values for the other parameters. Candidates who failed to solve (b) correctly were unable to solve (c), (d) and (e) correctly although follow through was used where possible.</span></p>
<div class="question_part_label">B.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">In (a), the explanations were often unconvincing. Candidates were expected to make it clear that the two intersections with the <em>x</em>-axis gave two real roots and, since the polynomial was a quartic and therefore had four zeros, the other two roots must be complex. Candidates who made vague statements such as ‘the graph shows two real roots’ were not given full credit. In (b), most candidates stated the values of <em>a </em>and <em>b </em>correctly but algebraic errors often led to incorrect values for the other parameters. Candidates who failed to solve (b) correctly were unable to solve (c), (d) and (e) correctly although follow through was used where possible.</span></p>
<div class="question_part_label">B.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">In (a), the explanations were often unconvincing. Candidates were expected to make it clear that the two intersections with the <em>x</em>-axis gave two real roots and, since the polynomial was a quartic and therefore had four zeros, the other two roots must be complex. Candidates who made vague statements such as ‘the graph shows two real roots’ were not given full credit. In (b), most candidates stated the values of <em>a </em>and <em>b </em>correctly but algebraic errors often led to incorrect values for the other parameters. Candidates who failed to solve (b) correctly were unable to solve (c), (d) and (e) correctly although follow through was used where possible.</span></p>
<div class="question_part_label">B.d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">In (a), the explanations were often unconvincing. Candidates were expected to make it clear that the two intersections with the <em>x</em>-axis gave two real roots and, since the polynomial was a quartic and therefore had four zeros, the other two roots must be complex. Candidates who made vague statements such as ‘the graph shows two real roots’ were not given full credit. In (b), most candidates stated the values of <em>a </em>and <em>b </em>correctly but algebraic errors often led to incorrect values for the other parameters. Candidates who failed to solve (b) correctly were unable to solve (c), (d) and (e) correctly although follow through was used where possible.</span></p>
<div class="question_part_label">B.e.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The graph of \(y = \frac{{a + x}}{{b + cx}}\) is drawn below.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="font: normal normal normal 32px/normal Helvetica; text-align: center; margin: 0px;"><img 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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Find the value of <em>a</em>, the value of <em>b</em> and the value of <em>c</em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Using the values of <em>a</em>, <em>b</em> and <em>c</em> found in part (a), sketch the graph of \(y = \left| {\frac{{b + cx}}{{a + x}}} \right|\) on the axes below, showing clearly all intercepts and asymptotes.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="font: normal normal normal 26px/normal Helvetica; text-align: center; margin: 0px;"><img src="data:image/png;base64,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" alt></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) an attempt to use either asymptotes or intercepts <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(a = - 2,{\text{ }}b = 1,{\text{ }}c = \frac{1}{2}\) <strong><em>A1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) </span><img src="data:image/png;base64,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" alt><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;"> <strong><em>A4</em></strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1</em></strong> for both asymptotes,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>A1</em></strong> for both intercepts,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>A1</em></strong>, <strong><em>A1</em></strong> for the shape of each branch, ignoring shape at \((x = - 2)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[8 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">It was pleasing to see a lot of good work with part (a), though some candidates lost marks due to problems with the algebra which led to one or more incorrect values. Regarding part (b), most candidates did not succeed in finding the new intercepts and asymptotes and were unable to apply the absolute value function. A significant number of candidates misread part (b) and took it as the modulus of the graph in part (a).</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">The graph below shows \(y = f(x)\) , where \(f(x) = x + \ln x\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) On the graph below, sketch the curve \(y = {f^{ - 1}}(x)\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"> <br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><img 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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Find the coordinates of the point of intersection of the graph of \(y = f(x)\) and the graph of \(y = {f^{ - 1}}(x)\) .</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span style="font-family: 'times new roman', times;"><span style="font-size: medium;">(a)</span></span></p>
<p><span style="font-family: 'times new roman', times;"><span style="font-size: medium;"><img 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" alt> <em><strong>A1A1</strong></em></span><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em><br></em></strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>A1 </em></strong>for correct asymptote with correct behaviour and <strong><em>A1 </em></strong>for shape.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><em><strong>[2 marks]</strong></em><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) intersect on \(y = x\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x + \ln x = x \Rightarrow \ln x = 0\) <strong> <em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">intersect at (1, 1) <strong><em>A1 A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [6 marks]<br></em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most students were able to sketch the correct graph, but then many failed to recognise that they could use their solution to determine the solution of part (b). Those who did were generally successful and those who embarked on attempts to find the inverse function did not realise that this was leading them nowhere.<br></span></p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the function \(f(x) = \frac{{\ln x}}{x}\)</span><span style="font-family: times new roman,times; font-size: medium;"> , \(0 < x < {{\text{e}}^2}\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(i) Solve the equation \(f'(x) = 0\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Hence show the graph of \(f\) has a local maximum.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(iii) Write down the range of the function \(f\) .</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><span style="font-family: times new roman,times; font-size: medium;">Show that there is a point of inflexion on the graph and determine its coordinates.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Sketch the graph of \(y = f(x)\) , indicating clearly the asymptote, <em>x</em>-intercept and </span><span style="font-family: times new roman,times; font-size: medium;">the local maximum.</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><span style="font-family: times new roman,times; font-size: medium;">Now consider the functions \(g(x) = \frac{{\ln \left| x \right|}}{x}\)</span><span style="font-family: times new roman,times; font-size: medium;"> and \(h(x) = \frac{{\ln \left| x \right|}}{{\left| x \right|}}\)</span><span style="font-family: times new roman,times; font-size: medium;"> , where \(0 < x < {{\text{e}}^2}\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(i) Sketch the graph of \(y = g(x)\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Write down the range of \(g\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(iii) Find the values of \(x\) such that \(h(x) > g(x)\) .</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><span style="font-family: times new roman,times; font-size: medium;">(i) \(f'(x) = \frac{{x\frac{1}{x} - \ln x}}{{{x^2}}}\) </span><strong><em><span style="font-family: times new roman,times; font-size: medium;"> M1A1</span></em></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\( = \frac{{1 - \ln x}}{{{x^2}}}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">so \(f'(x) = 0\) when \(\ln x = 1\), <em>i.e.</em> \(x = {\text{e}}\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \(f'(x) > 0\) when \(x < {\text{e}}\) and \(f'(x) < 0\) when \(x > {\text{e}}\) </span><em style="font-family: 'times new roman', times; font-size: medium;"><strong>R1</strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;">hence local maximum <em><strong>AG</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Accept argument using correct second derivative.</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">(iii) \(y \leqslant \frac{1}{{\text{e}}}\) </span><em style="font-family: 'times new roman', times; font-size: medium;"><strong>A1</strong></em></p>
<p><em style="font-family: 'times new roman', times; font-size: medium;"><strong>[5 marks]</strong></em></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">\(f''(x) = \frac{{{x^2}\frac{{ - 1}}{x} - \left( {1 - \ln x} \right)2x}}{{{x^4}}}\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">M1</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\( = \frac{{ - x - 2x + 2x\ln x}}{{{x^4}}}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\( = \frac{{ - 3 + 2\ln x}}{{{x^3}}}\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> May be seen in part (a).</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(f''(x) = 0\) </span><em style="font-family: 'times new roman', times; font-size: medium;"><strong>(M1)</strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({ - 3 + 2\ln x = 0}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(x = {{\text{e}}^{\frac{3}{2}}}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">since \(f''(x) < 0\) when \(x < {{\text{e}}^{\frac{3}{2}}}\)</span><span style="font-family: times new roman,times; font-size: medium;"> and \(f''(x) > 0\) when </span><span style="font-family: times new roman,times; font-size: medium;">\(x > {{\text{e}}^{\frac{3}{2}}}\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;"> R1</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;">then point of inflexion \(\left( {{{\text{e}}^{\frac{3}{2}}},\frac{3}{{2{{\text{e}}^{\frac{3}{2}}}}}} \right)\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1</span></strong></em></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[5 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align: justify;"><span style="font-family: times new roman,times;"><img 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" alt></span><em><strong><span style="font-family: times new roman,times; font-size: medium;"> A1A1A1</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Award <em><strong>A1</strong></em> for the maximum and intercept, <em><strong>A1</strong></em> for a vertical asymptote </span><span style="font-family: times new roman,times; font-size: medium;">and <em><strong>A1</strong></em> for shape (including turning concave up).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[3 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align: justify;"><span style="font-family: times new roman,times; font-size: medium;">(i)</span><br><img src="data:image/png;base64,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" alt><em><strong><span style="font-family: times new roman,times; font-size: medium;"> A1A1</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Award <em><strong>A1</strong></em> for each correct branch.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) all real values <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p style="text-align: justify;"><span style="font-family: times new roman,times; font-size: medium;">(iii)</span><br><img src="data:image/png;base64,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" alt><em><strong><span style="font-family: times new roman,times; font-size: medium;"> (M1)(A1)</span></strong></em></p>
<p style="text-align: justify;"><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Award <em><strong>(M1)(A1)</strong></em> for sketching the graph of <em>h</em>, ignoring any graph of <em>g</em>.</span></p>
<p style="text-align: justify;"><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p style="text-align: justify;"><span style="font-family: times new roman,times; font-size: medium;">\( - {{\text{e}}^2} < x < - 1\) (accept \(x < - 1\) ) <em><strong>A1</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[6 marks]</span></strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates attempted parts (a), (b) and (c) and scored well, although many did not gain the reasoning marks for the justification of the existence of local maximum and inflexion point. The graph sketching was poorly done. A wide selection of range shapes were seen, in some cases showing little understanding of the relation between the derivatives of the function and its graph and difficulties with transformation of graphs. In some cases candidates sketched graphs consistent with their previous calculations but failed to label them properly.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates attempted parts (a), (b) and (c) and scored well, although many did not gain the reasoning marks for the justification of the existence of local maximum and inflexion point. The graph sketching was poorly done. A wide selection of range shapes were seen, in some cases showing little understanding of the relation between the derivatives of the function and its graph and difficulties with transformation of graphs. In some cases candidates sketched graphs consistent with their previous calculations but failed to label them properly.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates attempted parts (a), (b) and (c) and scored well, although many did not gain the reasoning marks for the justification of the existence of local maximum and inflexion point. The graph sketching was poorly done. A wide selection of range shapes were seen, in some cases showing little understanding of the relation between the derivatives of the function and its graph and difficulties with transformation of graphs. In some cases candidates sketched graphs consistent with their previous calculations but failed to label them properly.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates attempted parts (a), (b) and (c) and scored well, although many did not gain the reasoning marks for the justification of the existence of local maximum and inflexion point. The graph sketching was poorly done. A wide selection of range shapes were seen, in some cases showing little understanding of the relation between the derivatives of the function and its graph and difficulties with transformation of graphs. In some cases candidates sketched graphs consistent with their previous calculations but failed to label them properly.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The diagram shows the graph of <em>y</em> = <em>f</em>(<em>x</em>) . The graph has a horizontal asymptote at <em>y</em> = 2 .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><img src="data:image/png;base64,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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Sketch the graph of \(y = \frac{1}{{f(x)}}\).</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Sketch the graph of \(y = x{\text{ }}f(x)\) .</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="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em><img 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" alt> A3<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1</em></strong> for each correct branch with position of asymptotes clearly indicated.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">If <em>x</em> = 2 is not indicated, only penalise once.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><img 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YkzxNenE1yB00knABRcAYCfGscxjayaW19AcAWOb1aLDMMQ65iiKN5VKgDgQ8WuW7fWKZBgn05wBc4iViFpcM3zvO/75WMAgHNKJw2e/RB+ni0IH1RVtTqtxmvKfAaCK3A6XdelwXUcR/UKAHCn5dqtRVEMwxAf4LriLwiuwGHdqjb6vk9rGquEAwB3mqZpdXTru8t1fIIrcHyzrj5pi2uWZSobAGBmtZ/w11pza1mWy2fxdIIrcDqCKwDwgPQSIl5IdF136/Fy7BMJrsDphIXXVrsKq2AA4ORuXQysdhJOm1v5U4IrcDpd18WKp6qqdxcHANiptMNwOkdGbG5tmmb5yPeU9egEV+DIZvPXhx/Sfj6xvgEAuGWapjzPl5MJ33rwi4t3BoIrcDppV+G6rtUuAMCGaZrSi4dIv61XElyB02maZnWMqwQLAHwtLgnGcVyObs3zPF27lb8muAKnc71e01qn7/t3lwgA2J0QX6dpSm95L0e38hqCK3Bwy3bUYRiKoogtrm6XAgC3LOdkCpMJm43pxQRX4HTS4FpV1TRN6h4AYGkcx7Isl82t1+v13UU7HcEVOJ20w08Iru8uEQCwF+mFQboSQTqzY7oIPK8huAJHttqUmo5xrapK3QMALI3juLoEjtkx3kJwBU6nrutY/VyvVy2uAMDMrU7CXdelD3MV8TKCK3AKab2S1kOzm6aqHwA4ldXOWeM4VlW17CRshNEbCa7A6aTB1ZTCAHBOGxF0uf7N5b8rEYivrye4AqeT3kPVVRgA+EqyaN/3WZYtOwm3bXvrKbyA4Aoc2WqNko5x1ecHAE4uvRJI18xL1XXtguG9BFfgdJqmiXdSm6ZRDwEAX19ffd8vJ2S6WP9mHwRX4BRuLYcTu/2IrwBwQvECoOu65eI3oXPWrafwSoIrcGSrVUvbtsa4AgBR3/erqTXP87AAgauFtxNcgdNJg+vyNioAcCp936+Oa017ZvF2gitwfOEuabxXOgxDrJCaplk+EgA4jNWVWtOf01kbU7pl7YrgCpxOOsZ1FlwBgFNJrwrSVXBm6w5IsG8nuAKnk95YFVwB4CSWTa+3OgnneT4Mw/tKygrBFTisW12DVmcV/nIzFQAOarWKT1Nr2tZaFMUytbpIeDvBFTidpmliLWXSBQA4iTR8juO42taaZVmYRvhLWN0ZwRU4l3Ecq6oSXAHgtIZhSJtYU9pad0twBY5v1lU4BtfL5VLX9fIxAMCRzGr5W6m167qNp7tUeC/BFTiXW8EVADi8aZpuLdlqhbydE1yBI1vWOtM0xTGul8ulLMu3FAwA+COrszMG1+t1tbm16zpJdecEV+D4Zl2F0+Vwqqp6Y8EAgGfZTp7TNHVdtzob0ziOd26ENxJcgXMRXAHgDFYXw5s1t6ZzCLNzgitwLuM4lmV5a0ALAPDplq2mbdsuG1ovl8v1en1LCXmA4AqcS9/3eZ7HSstyOABwGLPIGv47juPqbExVVa3OhfG64vITgitwcLMaqOu62E0oy7JbE98DAAcwjuPqNMLpWCFh9SMIrsBhrdZDwzDEFld9hADgkOLKq+n4oCjP83RCpvQpX3LsXgmuwFnE/kKxDktbXNVSAHAMsU5fHdqa57mBQp9IcAWObDWOxlmF8zzXVRgAPtFs0uDlL8dxXC7ZmmWZzlYfSnAFTqeqqhhcTYIPAJ9lNbIuHxOr+zS1amv9XIIrcC5pTZbn+TAM7y4RAPAEaYjtum45rjVtazVE6OMIrsCRLfsOzZbD0VUYAI5kmqau69KJGJfTCPOJBFfgXGbT4guuAPChVoe2tm27HNo662OlufUTCa7AuUzTlAbXMMZVBQYAH+rb1GpCpmMQXIHDmsXR+N90Sbc4OZPsCgCfa5qm6/W6TK2Xy6Usy7Bqq7r+owmuwPHNJsdPx72YnAkAPtGsco9r3S1T67Kul2A/keAKnEsaXLMsE1wB4LMse1Q1TbOaWq17dySCK3Au0zSlwTX0HQIAPkuMr6vjWi+XS1EUUuuRCK7AwS27A6WTM2lxBYDPNVssQFvrgQmuwOmkY1y1uALA51p2Es6ybHVcK59OcAVOZzW4mqcBAD5L3/dpnR7Ude2u9CEJrsCRpXE0/pyOhJFXAeAT9X2frm8XVFV1azE8Pp3gCpxOendWfQYAH2FWZS/Xv8myzLjWAxNcgdNJW1zfXRYA4BvLu8yzVdlDam3b9i3F4zVctAHHN6vwYnDNsmz1AQDAHtyqoJummS2BU5aloa3HJrgCpxMruaIo3l0WAOBn+r6fpdZbnYTdmD4SwRU4rFvVVexclOf5i4sEANxpdZqlaZqWczI1TRMfLKweleAKnMs0TfE2reAKAPuXZtGqqmaptSxLYfUMBFfgdGJVV9f1V3IH993lAgC2dF036yR8uVzMJHwSgitwLuM4zoIrAPARZjMJh07C7y4ULyK4AseXtqamXYVNzgQAe5bW4NfrdTkn02qHKb2oDklwBc4lbXEVXAHgIwzDsOwk3HVd+OutpCrBHongCpzLMAyCKwDs0Oo0wl9fX+M4FkUxS61mWDwbwRU4rNX7rGlwLcvy9aUCAFLTNM0G9cweUNf1ZWEYhtcWkzcTXIFzuRVc9SYCgJ1IK+W2bZepddlnSj1+eIIrcHxpZdb3vRZXANihZfhMp1RM52Qax3H7iRyP4AqcSxpcq6p6d3EA4Ow2YudyGuHL5XK9Xl9ZPHZCcAXOJQ2u1nEFgP2YJdjlqq3L1Kqt9TwEV+BcBFcA2LOQRVdTa1VVMamKrGcjuALnks7xILgCwN5M07ScRjjLsrIshdUzE1yBc0mDa9M04ZcqQgB4pY2at+u6ZVtrlmVt276yhOyN4Aoc2bJevF6vy+AKALxLWlmnq9alqXW5/g1nI7gC5zLrKqytFQBe49s6dxzHoihmkfVyueR53vf9awrJbgmuwLm0bRvn1tfiCgBvFwLtOI5lWS6bW4uicJeZL8EVOJu0xTWOllEjAsB7pRV0mlpnba2q7NMSXIGDm9Vw6RjXruveVSoAIFqdkCnPczU1keAKnIvgCgC7Mo7j6vo3TdOkd5+1tZ6c4Aoc1moNl1aNgisAvNgyizZNs2xuXV1rXXY9M8EVOJeqqlaDq7oQAF4mVLvTNN05tBUEV+Bc0hkLtbgCwBsZ2sr9BFfgXNIW1zirMADw12adm4ZhmK3aqnZmg+AKnEva4lrXtR7CAPBKsZPw6qqt1+v13QVkpwRX4PjSdLoaXMVXAHiZaZrSDlDbEzJBILgC55IGV52RAODFpmlaLn5zuVyqqhrH8d2lY78EV+DIlk2paWXZtq22VgB4pXRB9XRCptk0wipoZgRX4FxmwfXdxQGAE+m6LsuyWWrNsmwYhncXjb0TXIFzqes6VpnX69UYVwB4urRijT/PphEO1XGWZRa/4R6CK3AulsMBgL8zuxcc/zuO43JCpizL1MXcSXAFzkVwBYDXa5pmObQ1dn2K9ITiFsEVOKxltTdNU9pJyWJxAPAXYhUcfrher8uhrVZT50cEV+Bc0uDaNM27iwMAB9f3/eo0wrNwK8SyTXAFTmSapjzPjasBgCfayJzDMMSaNx3aOlv85p5NcXKCK3Ai0zSVZWmMKwD83mrITH/Z9/1yQqbLfeuoS7DMCK7AkS2nfIjB1fz7APB3brW1mmCCxwiuwImkkzMJrgDwR4ZhSLs4mRaR3xNcgRMZxzENrukAG12SAOBOq/P2x5/HcVxNrXVdf7sduEVwBQ4urRSnaYqDbfI8H8fxjQUDgAPYGJWTqqpKTOU3BFfgRNLgWhTFu4sDAB/jnth5q4fwbP05CZYHCK7AiaRdhYuiiC2ualAA+KlZ7dn3fbpYepTn+Z1bgA2CK3B8sV5MZzjM89zkTADwe9M0jeO4nEM41LbDMCwf/5Zy8tEEV+CwlvViGlzNyA8Az7Jsa82yzAT+PJHgCpzILLi2bfvuEgHA3s2mOVw+4FYP4XT2fvglwRU4kXSCfsvhAMCPrNaVqz2Ei6LQ1spzCa7AiaQtrmVZWg4HADbcuqsbfj9N02pba1mW2lp5OsEVOJGu67IsizeD43QRmlsBYMOyopymqW3bO2djWt0C/IjgChxcWlOmwdXYGwD4qVir9n1vXCuvJLgCJ5LeG56NcQUANqQ3glcXv1mdQ1hDK88iuAIn0rbtaldhAGBpNXaO47gc2vrt6ugSLL8kuAIn0nVdvEOcdmdSmwLw0WJFtvzh6Tuq63rZSbiu62+LBL8huAInkra4Xi4XXYUB4EdWh7ZWVSWd8tcEV+DIZvVoOjnT5XKxxBwApHXlav6Mv0xXlYsMveE1BFfgRK7XaxpcVbQAcKdxHKuq+unQVngWwRU4kbSrcJZlIbjGVdTfXToA2Itltdh13erQVhUoryG4Akc2q037vk9nFR7H8V0FA4CPEGvS6/U6S61N03zbzRieRXAFTmSapjg4R3AFgJlb4XM2ScTlcinLUjXKKwmuwFlM0zRNU9ri6t4wANwSa8nZnPyX/y4pN3sw/BHBFTiX2OKaZZlbxQDwtRk7+75fziTctu0riwdfgitwbMuaOA2ubg8DQLQ6YHU5k3BZlqbl5/UEV+BcYmen2WrpQiwAp3JPxTdbRi7c9rX+DW8huALnks6F+O6yAMC+pGl2ObT1crlcr9c3Fo8zE1yBc4l1sKXnAOCWYRiWQ1uLotBJmHcRXIFzicG1LMt3lwUAdmF2J3eapqIoZqnVpIa8l+AKHNZqg2q8f5zn+cbDAOCcpmmq63rZSXgYBnND8EaCK3Ai0zSla9C9uzgA8FLfps2QWi8LTdNIqryX4AqciOAKAFHIomkibZpGamWfBFfgRMZxTGeYSP+kSgbgDDbqu2EYlj2El8ueqzF5C8EVOLJZ5dp1XayJTc4EwMnNxqyWZblMrX3fv7GEEAmuwPHFrlBt26Ydn95dLgDYhWEYVlNr27bvLhr8j+AKnEhscc2yzBLqAJxQbGVNf7g/teonzLsIrsCJpMHVXWQATivNn6vTCOshzN4IrsCJ9H0fq+S6rr/cOQbg3NKaMd7bXZ0GwhRNvJfgChzWsk5Nq+eqqjYeCQCHt0ytYfLC2aRNbywhRIIrcCJmFQbg5NIgmuf5LLXmeS6psk+CK3AKoRpOg2va4goAZ3O9XpedhIdhCH8VX9kbwRU4kTS4hjGuAHAGGwubR+bbZ88EV+BE0rvL1nEF4NhutZoOw5BlWZZlaVtrvJ+rrZV9ElyBE2maRnAF4DxWU+hy1dY4IZOpg9ktwRU4vljvpi2uOkQBcCqhNlyu2lpV1TiO7y4dfENwBU5kGVzdSwbg8GJltxzaWpblrdSqimRXBFfgRNKuwm3bvrs4APA6XdfN1r8pikJbK59CcAVOJO0fJbgCcHix1XQcx1lqzbLsVucjba3skOAKHNay3k2Da9d1bykVALzYOI5FUcw6Cdd1LaDyQQRX4ETSrsJpcFVzA3AAsTpL67XV1LoxtBX2SXAFTiRtce37/t3FAYAn2Lj92rbtrIfw5XLJ81wlyMcRXIETqapKcAXgJIZhWKbWy9pK5noesX+CK3Bks5o4XXJdcAXgqKZpmqYp3q7NsixWf1VVial8IsEVOJE0uIaxPSpvAA6pbds0r8ZOwsMwvLto8AjBFTiRtKuwSSkA+Gize6/pzExd1y17CC+Htq5O5gT7JLgCJ5IG1/SWswobgMPo+351Qqau6yRVPpfgChzWslZOK3ItrgAcwKyyG8cxHRcTtW37rhLCUwiuwImkdbmbzQB8qI2G03ThtzgtU9u2t2o9tSGfQnAFDi6tkgVXAD7XtzVX0zTLttbr9fqa4sGfElyBE9FVGICjul6vy2mE67q+NYcTfBbBFTiRtEZXkQNwAKH+appmmVqLori1+E1a66kB+QiCK3AiaaUefqO2BmDnNqqq8KdhGJbTCF8ul67r7twO7J/gChzWsoZOg6uuwgAcQ1EU36ZW+HSCK3AiadU+W4QdAHYu3JCd/bs6tLUsy+XdW0bQ4vsAACAASURBVC2ufDTBFTi+WLvHnlRZlqm/Adi5b6uqtm1Xh7bOehWp8jgAwRU4i2maYu2eZdnsT+8qFQA8puu6ZQ/hPM/jhExqN45EcAXOIg2ueZ6/uzgAsG41cKY9hL/+240o0p+IAxNcgbMQXAH4INuTCV+v12Vb6+q8g6IsxyC4AmcxjmMMrkVRvLs4AHCvWfhcnZBpNumgvMrBCK7AWaTBddbiqnYHYJ9mNdQ0TatDW+u6flcJ4TUEV+AshmFI1wl4d3EA4D/S8au3HlDX9XJca6zU3IflwARX4CzS4HprIBAA7NM4jk3TrE4j/O6iwSsIrsBhzW48p32rBFcAdmvZcDqOY1mWy9RalqVWVk5CcAXOou/7NLjOJrEAgBdbZs70N+nPVVWttrVuzzz89ALDGwmuwMHFmrtt21jZF0Uxa3FVwQOwT2n9Fce1LiuyQHXGUQmuwFmkXYWrqpqt5A4A+xGrp9U5hJf9hlRnHJ7gCpxFulZ70zTvLg4AbAXOaZrSmivtNDQMwysLCXsguAJnkXa1st4dAO9y58DU2NYaFyEPqdUcDZyT4Aoc1mxBvK7rYt2vxRWAPRuGIc/z2bjWsiy321p1GObABFfgLNq2vRVc1fQAvN6t2md18Ztbba2qME5CcAXOIg2u1+v13cUB4KQ2VsGZpmmapqIovp2NCc5GcAXOou/72O1KcAVgh6Zpqut6OSGTES4guAJnsd3iqqsVAG+3nEY4y7K6rleXbIVTEVyBs5iNcZVUAXivWU2U9gyKyrJcTa1qMc5GcAWOLK3X0xka9bkCYFf6vl8ObS2KIqbWUKPJq5yW4AqcRdd16RjX2RWASwEA3mUYhmVqzbKs67p3Fw32QnAFziIdONS27buLA8DprN4tXU2teZ6rqiAluAKHNWtEnU3OpIkVgLdbHdea57nZ72FGcAXOous667gCsB9pxZT2EJ5VUu60wpfgCpxH2uJa17XrAADeIk6yUFXVampVQ8GS4AqcRTrGte/7LzMzAfASaS0Tf26axmxMcD/BFTiLtEfWMAzvLg4AJzVNU13Xy07Cy9mY3FeFSHAFDi7W+m3bxouD1cXcAeC5Zskz/Leu68uCHsKwTXAFziJ2Fc7zfLXXFgD8tbSHcGx0bZpGZQTbBFfgsJbL4cTg+q4iAXBmy3Gtl8ulLMv0MRIsrBJcgbNILxf6vndlAMALxOpmdcnWsizvnHZBtcXJCa7AWaTBdTYBhqsBAH5vozZZTa1d131bAamhIBBcgVOYpmkjuALAc80CZ1EUs9SaTrggncK3BFfgFKZpipMzxYXyXCgA8NfSCihNrRZmgx8RXIGzGIYhXjE0TfPu4gBwfHEJ8dmqrVIr/JTgChzWbM2btMW1rus3FgyAY4sV0CyvxqGt7y0efCLBFTiFcRzTWTGu12v6V32GAfiN1dGqy3Gty9SqAoI7Ca7AKYzjGC8g8jzv+/7dJQLgsKZpqut62dwa+vssw6r4Ct8SXIGzWE7OBAC/tJo503nsV6cR/tHWgC/BFTi8eBGwMauwCwUAfi/UJn3fzyJrlmVlWS7vmap94H6CK3AWaXC1jisAf2GapmUP4dlU9vIqPEBwBQ5rNqtw7LilqzAAvzerZb7+W9fEGqeqqm+fDnxLcAXOQnAF4ClWM+c0TW3bXv67ZGue5xtPAe4nuAKnECZ4jJcRgisATzSOY6xloqIoVqubWYiVaeEegitwCmlwXW1xdd0AwLZl3+BomVqzLJutGf7AXoBIcAXOIl5VFEUxDMO7iwPAEUzTFCf/S1OrCZnguQRX4CzSrsJ937+7OAB8vHEcl0u2LlMr8HuCK3Bk6R3utMV1HMc3lgqAj7McmDqOY1mWl4Xt1KrpFR4juAJnEW+Kl2WZBlfXEACsWlYQ8TfTNFVVdX9qVdfALwmuwFnEFtemaVxAAPCw1TmEV3sIq27gWQRX4CziRUbbtu8uCwAfYxY+h2H4UVsr8BSCK3BYs0uNeJ2hxRWAxwzDkOf5alurmgX+lOAKnEUMrpbDAWDDch6m8MM4jsu21izL6rreWOIVeArBFTiLOPdjlmWzWYVdZACwbXVc63YP4VC5qGLgKQRX4BSmaSqKIgbX0OLqYgKAW2Z1RNu2y9Ra17U7ofAagitwCtM0xVFJyxZXANjQdV2WZbPUanE1eCXBFTiydMG9GFzzPF8GVxccAKe1PUK167rlhEwxtao+4DUEV+AUpmmKN8uLonCdAcCGWE2strVWVbXac0flAn9HcAXOIt4vF1wBuCWtIIZhiPMjREVRbHfbUcXAXxBcgSNLrx7iLfOqqlxVALCdNsdxjNPRp6m17/vXFhP4+hJcgZMYhiEG19mCe4EoC0BqdfGbtm2Xj1SDwAsIrsApjOOYjk16d3EA2JFZ8pymaZlasyxLU6uwCi8muAJnkXb0endZAHizW8lzmqaqqpZtrdfr9cUlBFKCK3BYs4uSePGR5/n2IwE4m1ARTNO0HNd6uVyaptl41vY2gacQXIGz0OIKcBL358nZI1fbWtMp/WK+/elOgV8SXIFTmKYpDlIyxhWApdXUWtf16pKtwIsJrsApxOAarkLeXRwAXuRW++rs5+V6rZfLpSzLYRheWlzgBsEVOIV0VuHlUCX9uwDOY3bOH4Yhz/M0r4bl02ZtrcuZh19UXODr60twBU5iO7gCcE5t28ZVvm+NawX2QHAFTiENrroKA5zKbGqlYBiG1QmEZ9XE8rkCLbyF4AqcwjAMgivAqWys1Np13WpkvVwubduKprBDgitwZPHiIw2uZhUGOK1pmpqmWY2sWZb1fZ8+8o3lBGYEV+AU0uBalmX6J5cmAB/tntN4XH91dc2by3dTMQFvJ7gCpzAMQ5x+Q1dhgAPbWPNmtYdwlmVN02wkVSEW9kBwBU4hXe1AcAU4m3EcV9ta8zy/Xq+rT5FXYVcEV+AUYnDNsuzWNQoAH+1WW2va6SZtaC3LMu0eDOyZ4AqcQt/3scV1GVzdVgc4qlttrXrfwGcRXIEji4m067p4u12LK8BJ3FqsdWN6ebcyYZ8EV+AU0hbXpmneXRwAnmwZOG+l1qIo0mVvNrYA7IfgCpzCty2urlcAPtHq2Xuapr7vV3sIF0UxDMM9GwF2RXAFTqHve12FAY4t5s9pmmIvm1RZlm3bvreQwGMEV+AUrtdrvHBx1QLw0bYbSKdpWm1rrapKyyp8LsEVOLJ4jdI0za3g6joG4DCGYajrejW1xh7CacPs+0oK/IzgCpxCeh3Tdd27iwPAI2ZRcxZBx3EsimI1tVqvFT6d4AqcwrfB1X13gI+2ul5rlmVlWS5nY0o5/8NHEFyBU0i7Cq+uggDAp1hGzWmaVnsI13WdPlhGhc8luAKnkAZXXYUBDiNk0aZp4tTxsa11llpnTwE+i+AKHFy4QEn7j2lxBfhQq5kzXak7ptamaR7YFLBbgitwCul0HduDnQB4l1vdejdC5jRNZVkuZ2O6NY0T8KEEV+AUbgVXiyIAfJb0dN33/XIa4bIszSEMxyO4AqeQXtm4oAE4gGEYfppa3aOEzyW4AqeQdiTTVRjgI2x09+26Ls/zWWrN83x2hpdU4TAEV+AUZpMzuZQB2LPtEarX63WZWoui6LrO6R2OSnAFTiENrrNeZK5yAD7I9XqdzSEcb0rGxzixw/EIrsBhpRcu6cL0LmgA9m/1XN227WpqXU4jvL0d4OMIrsAppMH13WUB4F5p7LyVWpum+XbWPfEVPp0LOOAUtLgC7MrqqXjj/Lw6rvVyudR1HZ7l3A7HJrgCBxcuZdIlE9LJmazjCvBe95x+q6pabWtt23b5dOdzOCTBFTiFuBxOlmXpBB4A7FPMn+nseqmu6249BTgewRU4vmma0uC6vNYBYCdm4TNdhTvlFiScjeAKHN80TWlX4aZp3l0iAL6+NsdrDMMQTt3LTsJO43BCgitwfOM4xik9sixr2/bdJQJgRZxmKZ1RL5Vl2fV6/enETsABCK7A8c26CqfB1eRMAK+3PaNS13W3UuswDA9sHDgAwRU4vllwNTIKYJ+mabper7dS62yxVgEVTkVwBY5vHMcYXPM8NzkTwGuk2fLb/r3TNDVNs5pai6KYpVbgbARX4LDi9VA6xjXP81lPMyvXA7zYalfhjdT67dOBwxNcgeMbhmEjuALwXtM0tW27mlrruhZTgS/BFTiDuKaC/mYAb7QaQcdxXB3XmmVZWZb3bwc4NsEVOL50jGtZlvoGA+xEen6epdZlW+v2f4FjE1yBIwuXNX3fx/Xri6JwrQPwMrdOudM0DcOwmlrzPE+nf3fSBr4EV+AMuq6LwXV2PRS4KgJ4jXi+7fs+zj4wa2ttmua9hQR2SHAFji+9PCrL0uRMAO+Vzpk3a2u1YhmwSnAFjs/kTAAvtrrgTfx5deWbLMuu1+s9m4J3cTS+keAKHN84jjG4anEF+Avxgn51CqW0h/Ct1DrrISwhsHMO0RcTXIHjm6apqqrY4iq4ArzA8rL+er3eGtca21qFAWCV4AocXzpxpa7CAG+xulhrOC23bfvu0gF7J7gCx5cuh5Pnedri6tY+wBOtnlSnaVrtHnzn8A0nanbFesLvIrgCx5fOKpxl2epFkooH4GHLAa7xh1uLtYbU6tzLYTiY/5rgChxfOqvwrMUVgL+znVrD2Xgj9H4JA+yeQ/RlBFfgsFaXuTfGFeAFpmm6NRXT5XKpqsqpmA81myiblxFcgeNLx7i6WgJ4io0L92EYqqqKJ95UnufX63V5HhYD+ETDMHRd9+5SnIXgChxf13Xx+smQKoCHbZ8/p2nabmgty7Lv+5eVFv7UNE3DMBh/9DKCK3B8aYurrsIAv3RrVtVpmuq6Xm1o1eGFY3Dv+40EV+DIQgUzjmO8kMqybHX+DwB+6dZKraF7sEVEgN8QXIHjG8cx9lvL89zYKoDfWL3917btalur7sEcj4mv30JwBY4v7Sqc57k6BuC5rtframptmubO7sHOzHwEkfWNBFfg+JqmWe0qDMBj0hPprdRa1/XyfOsMDDxGcAWOryiKdKjVu4sDcBx1Xa+Oa01T62pYlWD5aA7g1xNcgeNrmiZeS2VZ9u7iAHyGZfKcXazfSq3LqZgAfklwBY4sXDlN0xQvp4qieHehAD7At0u2lmW52kO4bdsHNgiwTXAFTkFXYYDfuGcC4SzLTCAM/BHBFTiyZYur4ArwsNDQuhpZZ4uNaV8FnktwBY5vGAbBFeBHlst+TNMU18SeyfN8GIblEwGeRXAFji8NrmVZvrs4AJ9nI7VWVXUrrAqxwLMIrsCRhWumcRwFV4DHTNM0juOtQa1N08zSqbAK/AXBFTi+tm3TloF3FwfgA8Qbf9fr9Vb34HRQK8CfElyB4+u6TosrwIbVlVrHcVydiunb+QI0ugJPJ7gCx9f3vRZXgFUbw1NvDWqd3QEUU4EXEFyBIwuXU+nkTIIrwD3SQRb3t7UC/BHBFTi+tMX1er2+uzgAuzNb/OZWai2K4tazAP6U4Aocn+AKsGq5WGvf93Vdr6bWLMv6vv92OwB/QXAFji9OzpRlmeAKcEvXdbeWvZmlVkkVeDHBFTi+dFZhwRVgqeu66/V6azamLMvato0PllqB1xNcgcOKl1bpYK2mad5bKoC9aZpmtaE1quv61nNXQ6xkCzyd4Aocn+AK8LW2WOvGiNY0tQqicL/l0PHZz9/+klWCK3B8aXDVVRgg2OgbHHsIW0IM7hSSp/z5dwRX4Piu16vgCpzZ7GJ6mqbr9brdPTjP87Is06GtwJ1uNbou/8v9BFfg+NLg2nXdu4sD8E7jOFZV9W1D6zAM6bNcbcMtD3879BP+EcEVOL6maeIFmdYD4JzClfE4jmVZbqfWn07FBETjOBZFked56LMwu12+/Ab5Tt1PcAWOT3AF+LqjrTXPcydJeEDIn8MwxHHjoSt+uBM0DMO3HYYl2G8JrsDxpXNm6ioMnFa6qPX9qVVvRrhTOhnkrCNDnudVVTVNM+uEz/0EV+Cw4jVWbGHIskyFAZzTdnNrXdd936ePF1PhR6Zp+nZxqcvlUhTF9Xo1BfEDBNdT21g0fHl7daOHw4+WpdqYZu2n/mhTHE96rXbg4LpxGDvCOZLfH88PbOGN/frijsZx7Lqubdu2bdOeh8sr4NUqeGMaYSu1fjof305sd2pIVVU1jmN84sYZ5rkf7q3L8u2L+e0S3vrlxqnpMYIrP/bYMfd38RW+lc5EcuDgChzYOI5pY06e5+Fsds9KG13XVVW1mlrzPL9er+kFNPCYaZq2x5Af44bRG1f3EVyB4xNcgQ8VLwrTSeaCpmm+fWKY4HQZWcNviqIw7B+e5dYA1w1VVc266H+9KgreakH9th31zq39BcGVr69Hj9Hth33iPaSH/eYN5O+kF3zxuk3DAvBx+r6PU5Wm4XN5yZvqum75rDT3rp4PVV574FP4LNM0DcNQFMVPg+vlv0NeV7f89KKu/rLv+6ZpqqqKryJMKBVGv/+oGDEAP73wgivfuL+L7/bR6RTMG6UtFWdrcfXVgwO4FUHT9tJZBZ3esFtNrVbj+Ag+lE/Rdd3GN+5baT588Yf+7SpZIcG2bXvPlf84jsMwtG1b1/XTp1AWXE/qnpmTbj3lsS3PHpAex3fu9OHMfA8Vw7GlXYUP3OJ6/2H87RwMsHPfziC4/adn7f1l+r5fvSaedfQNTRyrzbOR7sEf6s7mgR/9wBPNvncPhNjZgPOXdRheDkO4paqqZRBNZ4+7Xq9VVaXvQ1VVT3whgis3PWUxt1sPq+t6469/8V390Yn74fvQKoN9+tzg+vAlyFP6///+AsgFE7uyeqdm+z7OPTd3XnCcD8MQrgVnV8Npw2m4AM3zfLuhdeO6848KzwNe+Sk8ds5/2en9U+qRh7sKzxRFkV6Bv+BdTa+RlieZZfHCddSsYH3fz7YTXa/XZ70QwZX/NzukyrJc/v5Wi3/6mL7v+74fhqHv+67rVo/UEFy3C3DnA571lX5liubFPje4fpCdX1JwGN9WBIc8AqdpWm1Eja0Z4zjeumoM8jxfDlQ75Ht1YA9/Xq//oPeZgf/aA5Mz3bLamf/3VhtmfjQT8uVymV3DT9N0vV63h9M/q/yfF1yn/3b+/tH90Vvn6ztvrP50s6sbufXLr8VL297yxmY3vvbfvgPpf6/XaxpTy7Ksqqosy+1She5M8W5NlmWrI3C6rgu//1Gz551/3ThI7rf9Mu/f+PIDvVW82Q8PHI1POYC3f/PAzYWHWzPu+YYu36vVTW3MKnzP4fGbU8c9b/XvK6eHvyxf9324T7nYvec7tX2Q3Plxb+xr+6R3ZwFuPeyBp9/5pbj1Dnxb3dy5l9UH31OnbPz1N+/VPQX+zTf3Tj89T965kXtOEcuNxxbX5RXkOI5h6uCNC83tBW9++ll/++Bvj677t3b/9+vhknxbpDuLd+dvfnq6vv+res+fbm35N9XQ76uwX275/rPQt+fSjVPQ9r6ivu+f0u56uVzKshyGYRzHZ31St17I9j2vVTGL9n2/kXtDInji2ISPCa4PfE53nvv+Ytc/dc8JdPVPf3qyCDE1/DfeQ8qybLULcSzM6lG7rC/D3GU/Ks/sh9UHPPDOPFAJ3b+13z/49x/xnZezGw/+0dXqPft9vfSkvPGwb8v89Arjzgf86BRx/6njN1t44L+/8ZRj9dM9kJR+9PuHT5t3/umPPHYifTgP33M+fCDMfGscx9XgWpblRkNHlmUh2T78uTwlz/w0qv1mX3t+4q3D4F01y9N38dOTyWPfi11dftzaV9u2345xTR+QNvnM5Hm+7L343OM2XSB6o5DLc0td1xvnn1D4cAp6rLRLHxNcUz/9tJ77+Ie39vt66wH3xPXVgoWkmud5+E16NyVk12mawsPS9quu624duGnFOf2b7XC7GNu/v+evX7ffgcfy6v0n5Z/eorv/r499pt9u/M7tvLieeNZm0wP4zgnudnL9/aPzxrcPfuCy5oHrj1/G7Cdee31bkvtjxlN290qHiet3+v059pfX0D/602PubMZJLzRvjdbZLvCdX5ztjWxs8/ff8Z9+NL8PVH/xlHs28qP37YFtbm/5/g/i4Yuxex5/51N+7+EDb/XV/agZs23btm23b0Jtr331gFjU0EqcdpYMU7hN0xSu3rebVZfKsgyx9lZb18M+MrgGoW/MdhR5YgSd3S245wLll1+z9Omrw6BvPTgcZ6t/De9JeN/CGNQwY3WYujr+NX5zsiy7Xq/L+QmzLCvLsizLcHA3TXO9Xq/X68ZBnGVZGIoTdh3uLa02un7Q9dazrnf/oiS78qOvxi8vFpcPm/47NuzbO39PfzN3koFvPeCJb/j9/uKi5Cnb3N7IrfftiUH3zq29+KD66ztWD6eaJ97muGcjf3eg3nNobbdszCrcjcvc5x48t+7+PHHjr3TnV/6BTf3S/e/zb/b77Tf9724B3HNd/aMNrj7r4TfnVvHSrJE+ZqMNc/UL23Xdt420dV3PDoMnHmPjODZNUxTFrQbSaZrueVEhFPzdN/fDgmt8I4ZhqKqqqqq6rq/Xa9u2XdfN5gQKv0yPqmEYrtdrXddlWV6v16Zpwurb4zi2/8TthC20bRsiWVVVYUdxL6HfeRQjWVmWIQper9dQgFiYsLW4zTYR9xv+GwoQthzm6Wqapuu6ECOHYQiLI3VdF15FeDnhpRVFURRFeHPCn9q2DX8Nv6mq6tbybsu+Chu9Fx4z22C8K5MWviiKMKQ2vrSmacK7FLv7D//E1B0/iPCbxw6t+N94dki3PHPr6Rtbnv1meQjN9vXAS4ivPb4V6S5mu1vuZbXA4R2Ofw1bCO9//CzSjd/a/k/fqNl7El/U8rPYeLv6vk+PwPDNSnc6O5xmLyT4+m9Vsf2mpY9MP9nZuzR7Ldvvz2zj0zSlJ6IpuSGV/hw//W/fpVsvJP1NmNlltsHVl5C+A9++omUZ0s/91sd9q8y33KqJV7f87Rv1lZwcZr+fveehSkq/ibOXcGtH6Rc5/DeeAOPW4r/LWmnjuJr9KW4hVD3xqx03G/5dfinuOW7jn1a/RFNyPgnvVfp9WX4ot3ax/BTSHcXj9tY3YnlQzTYVnpXuLjw+vF3xl7Ov9uoBfOuNWorPjfu9tdLGah1dVdXXfw/75SE3+yEWOP30H3gV6Ycefo4j3Gafwuxgju/t1+ZBNY5jPFD7f0L/r7i1+BGk1wnLz/3WLsLFVfrEr6Tii9eH8Qty672avSFhI/FaLh6Z6YXl7EsdXml8IfFlLvdy68Md/3uiSMuc/ne1+rv17UtPa/G/sTzhCja9nI7/vXXxHN6E8K6G6+20pg4fR7xgTi/Rw5XhbBfLHcX3Nh7q4VOITw9X5l//8lu88oxX/vFzj48PP4Sr6/D4MMIubbpcCjuq67qqqrSF885L6J9e3D7X9jpbofPwX5fww4JrMN0X+tO3cvWNDgdKnudh7vioKIr4m/v3srrxsOuwqXQvlxuBcNmwuV2GBw76Txczeci38eMLP6SPzP4rz/NZMI7CBkOqD+egeJ8inIzCU2L4j9uJu043Fc9cG7uIJ8Tw4OqfuJJBuLcSNpLnedxsMHsJ8emh5EVRxBsZYTWt8KaFR6bvW3x6+G94WNxRfMqsDOEdiK8xbjN97elewpbDA8Ivw9ND8WaFjzdcwtuV/jXUW+GMH8oweznhswilSt+i2bcjFKBOxO3Eoys8Ma4qkX6F0//OXuDsE5+9uvD7pmniWxd+jv+dHZzhXDT76NOPJv0Qw6sIe4kvKj0+w6ZmxY5vdbr32ccRDsu4wViY9MsSRrmETkFxa7N3Jn40s7co3l+L/8YvS/yUw2VB2Gz4ZXwh4YsZv6Sz217xiI0/hOMnXo7Er2T5725m/ETS80Z4J8OLmn1YcXex2PHrFv6b1gXxT3H7l+Q8ny/EXYQzQ/qJx2KEd2NVeO7yTJi+e7NvUPqi4p/CE+N+43syO/LTCjQ8ZnbWmn3Z0y9gELYWP6+45fAxzUobP470bSn/ez6MR2P4TVqw9FQcvhqzajrd3a1zS9ha/BKln3t8brE4r4ZXGvdYrJ3M47tRJqfK+yvK1TNVeuSkb1G8nZ1+9HnS8SqePYp/V+Sz7c+OmfiK0mMjVnnpS46X7+mZKj0+V78Rq38Nlwfpx10kZ57wgHAGyxYDC5cXCelbF9+x9K+zp6ff8SypLNLfx2Mmft/jYZa+oviwKLyWy40rvdlZPf1vegzPTsvxh/T8U/6r3/Pb18Cz1zv7Dsb3PH0Dl6WdvY23juH0RaXvdv7fy+lb78y3v59tNpzlikWH/NUX8pj632S8078Rc/c/N5TwxcF1dsNivDHS/rJYwufvfGRwHW7Mrcce/Oh7CB/qMMf5rauTp+/lr3fBfvzdx/2aA+lDD9cPLTacR2iqDXdI7w8y8atd/Vv7KvpRJ45fPis8cRnsL5fLRkPrw/u65WOCa/rKZx3/fsrJfduz3p9vt+ODAIC/o56F/fhRWM3/9dcIHRNmk8I8PRDeE8HCgpfL0o5rE+v8UQk/Jrimfhlcud8r67yn7+vTK+y/KP8r29aW+/r0T+SzLHtV/X6Dl//Wu+HnWa+5X+5le+9/tOWZv9hF+u/vdzR7z2P/wOULee6NyNUt/9FHk+5x+zGXO0bZzEq+fJf+ogJKv4OX/x4GT/cXH8eywH/3HZ99Kf76TPLEHS0Poad/+9Idbf/mWXv5i3MIq1Y/1vLfvDZvCVkbgfN6va4eD+ML57z8yOA6juNyjGusHtLKO+0f/9yz+bLPffxvOrbh/g2u/vLF546/3sXvX0iejGsqkwGl6QCSLLmAy/879iYdtZWOACmTMahxa8VieGE6hCM+IPwQB2XNhm+l47iahXR812yMUxyMlxZ+ufc4Uiv8NUz6tdxFOoNXHFUY9hWmQIg7DdsPvwzPipMWxMFg9b95CJYvZPZDLChXIwAAIABJREFU/GsYOTOOYxipmA4yDPsKY5/Styvdy48Gd/2FWJGkYzJDmZumibNBzKZbi7O7zd6o+r+De+PHmr5dy3cjvmPp5BBx+3FUc9xIeGPD/Bl936djO+PhGg7pYRiaf9OQdF1X13Wc6KL9r3hghE0NwxD3Hj/W+KLi8RMG84Snh12ET7z+72DyuKn4WtK3q0kGn9f/pqYLs2XEn0MXrDB5SXpoxfLHD+L6T3ijwiPDDBxh4Gv8FMJjwrrTbdumc/zESUdufdzp594k43jD7tJZPcKu638DuZt/05CkH0GTzE0S9xU3FQuffnDh5Yftx0M0vuTw3DhNS7rHdL9xVHksQPqVj3tJZx9MD8twEKazp6SFT9+f2bcjPebTOZDC09N5wtKJZ+J8MOn3MU7B0iYzI4aDJ86REw+PcFTH46pt27Is4wE2mxUmnqCWH3e663TqoGmawn7DqSP9bsaSx+/IavvMrA7Nsiy+aeEdi4WMb1d4Y9MPN51dJh4P1X8nRIxflvgBhQ8i/eBmZ+z46YQ38Prf2SiX34743PTgiY8MhUzPlvW/mjE9ZuKxFOriuPE8z9PzZ7qjsLV4ioivOpzH4qtIP47lcTt7l5rkDBz/m34R4kuO35r4c3pwxlNT+hal1Wv6bpT/5kpo/juNUJucDNPvZnpOmH0K4bWH64Fwoo7nq/DgMLNRPHdVVZV+HeLnFd/AsPEymXahSqZ7iFc1s9eSvhVhX/EjDh9ZeEvT8qfvUhwkHEqYDiBPR1/HauX6b6qRLJngJh0AnP93SP/y+v9Z1xhhMHN4sW/JVstsuZzoaxiG1ZfcvLA1+GOC67JXd/vfmXLjIR5PAbP+1nEOsfRZXTJzb/gG1v/mHI4n9NnZuUkumGL9N2sWjxc38cTU/1dazi4JBtckWsQTfXrRk9Yc6QsP5en+BYBYGc9OyvW/mSpmSSz9Mof+63kyC0Ka9Da+qNm/2TvSM1T97xI5XteGF5X2kg9PrP7NHBNPc6HOjrMFpPV6fM+//k0aOTtUZlPtpbMILmcyHJOZG9OZ6GYH4T23lG65+0i/a/vL6f5WC/zwLlZ//lq8q0/ZRfx9+opSITP8skr4zdODPM+v1+v43yk6X9BXJ33nn7679BD65aYeO/x+edCuVrR/9KG8pV/W3238BUfvAT6IO/f4lCItN3LPdB5ZllVV9e2W7/y4H3ghy3PIs04py73MqryvxWE8u+rrf77o5Su/F3+9r7/Y+Grd/RfFWL0Uuecdu3PuovQonf57Cyyd3jn+HK8845245t9KH3defqxeh4QWiJC9w824B96rF8tvzG3edd3XS87PHxNcn2j7rDqtTaz/m3393ad4a+Pbe0xf4K2nD8kyDMFsSvE0e4esG27U/ejFhjupXbJk0Wx69HDrLk6Rf/+WOYB4AKzOBHBPPfEXyrL8iKplb7xpPN2HBu87dzEMw509Tep/85T+aPsspW+Xt457jOM460v/7Rc2dJEIrVbPanJ4ru2D/9bdtGxt4eiNTT38Ffuw4PqaU8kv9/L2892LC/B3qfIF9z43dv2u7fzoKU9/f/7iZvmdO031ff/L7sGx/oiN+fFPebLewAMptyiK9J7u27/vz/X0dpJv//T7Pd46aJ97MB/sg/44f3EBtHzus/Zy62i8cztt225cHc5+822L6yv5mrzRe9/8B9pRnrijB7bwlLI1dy9pEzpHpGvJfpbp3/q3G683z/Nli/cT6/rgw4JrcM+Lv+cr9HGdNFb90Q2bT/xeRQ93TfnN7l55dD3Xt0X9u7pnueUw3vJHM+9l/yYNCkNupmkKzfix9X4YhrIsw+PDkM44QCD2pQ8d6dPVCzfked69ZNaElx1FP93RRo+V7V/u8NJq9td7HvN0T6na3/Le7ufDfa6N1/WsC/TVDz3cs9sYj7P8TVmWD7yobx/wy0/27w6GP7qF8RpvOaU/5W746gY3btA81++PwGfVcUsbX8/wy6Zp4tXIj8rwWHmeuIvZb26Nuk9fe5j4YDuV/PK1fGRw/an7T9bPrYOXm/2LIy8Mgl9uf+dn8LdfY/2oGD+6TP/lI3/z9PsPgN+88L+rmWaDnzdkyUzxs6GnS+M4xvbb7daJaZpCD/ZZY+yyQsrzfHVk9bPejY/woyvIbx/8yy/jc5+y/dzd3lDgxe/Yt8f5j66eNxpawzxDbdsuz0h5nm8U7IGK4P6n/Ojl//LW8D69+C75n27q1pYfbiu6/+kbD74zMH/71/v3e+cxHH8OFwzpFzPcTgr5bZqmO1/UxmPebhiGMDHVxkVRKrQifLvZx17jxwTX+78VP7qn+Pu9f/3u2/J7Yc7DO8ej79Offm939eX/qaec3e68dPj2YU+8lbOUNop+m1fDTF33l2ccx7jxjfFgs/Jcr9cw0+BGYeq6/rt+8k95zMbD7r8g+Oke7/fwS3jsUuCJBXjKU/70O3VgB3jVy6aMjbNNURRx4pNlsi2K4i+K9O3vf7+j13yOvwlOvqF79sr3dntf4zg2yaIDj10V7OFQWb2JfKs7dLiVttE9JE6nurrK68M+Jrim9nCz6qdPfLit79tthjaijw6uHNU9OTncefm2oTW0rz4WFNMW1zuDa/rc7bKF2YZ/9JKBk7jnhuDGPbuiKMJ0o+HB6T246P6uwn/EmQ3ut4fvy/0NFatrOoS79uEx98xIEsa+/rKzdPSRwfUv3Hmb7TU30X+68dgV4SndcuC5bh2Wfd/POp/cEtZRfPjuT9/3sZlittrYT5++Kgxi8Y3jy4mX76RHyPaCN7PxCOG5y2vEtwfXGV8BuMduvykhU9y6oRZS6Oy6bmP4ayosEfzL4gmuf+vp3U6eux14lvt7f43jGKZBuieyFkXx7RDWb3VdFzf40xbXKPaW2ejO96O54IGTWJ4HQjeQjXNgWZarg8TiMNf0kbf2AnCn0CK62q0jPdvc6uDZ931d1/fE11+2sQmuB6T2Yp/GcbzzttwlmYvv9/tNlwivquqe3ryrj9luHrmstZBs8D2Fc9o+k2yf+tLbcIHFpYEHpF01t8csXP4tpvDtqabrujDc99ag/d+PyRdcj0PVxU6sxr/r9Xr/oqlZll2v12cNQU/7+pZl+Zsw3Pd9OB3H1zJ7UXmex27DD8x+BBzJstdVeh9tKaz0uLHBvu+XF5QmuQDudOu+/K2TUrgjH8ck3r+XrutC97owj0lZlk+Zz/LUwfUYV5DHeBUcWJhIfRlNb/3mzlVS74+C6cR3D3QVXm5/OQfybJr4O+eCv6fwwKcLX/Nbc6fHlajbtv12fo2+72cnzzB75+teDHAsIWSuptbVaUHeO+zx1MH1E7nMZedmzYxpaLxzHqanX4SlZXjK3ABBXdcbLySuu7i6O19kOJ5bY7fCahkbJ8C0IeLbhTdm8zNlWba6ljvAhtk5Kp3F49Zqf0/pO3bG5XB+4873a+dn/2+Lt/PyczyrU/5+O0n6LLJ2XXdrva/HDunwrDS4pkvXPLa19L+rM8UvX9cfrfUK7MH2sPll1Ezd2dCaPmA5P1MMrvvkggR2ZfUWW9d1WZY93Hjwm4u0HzldcAWeZeNiaxiG7QbJy38bYJ8y8uGWtK/yPZ2Q7zdNU1jUZ/uVFkURM7k1q+AkQpeTjch6z2QnS8tOfQ+s8gVwp11dqwiuwG+lzQJhtZvtIDcLdWHc/98VL21x/X0/5NWVLeq6/rYj9K3VaIFjSGdl2z4T/mbl5+V6FWm3DmcY4O3+bkJKwRX4sdVT0mxEa7Ad5zbWBHui0AHm98F1u0NgaGSezdK0fMmhyVe7K3yo1S/s7JfbayGmU6bf8/VfPmY5SGGjvzHAw551ubI86ZmcCXibYRi2B3ymKS6sGTMMw2sGf6bB9U9z8jiOXddtL4ZWFEUsgwtN+HSrs46vDh8Iy2g9ZfK51eD6+80CJ/G5lx+CK/Bjs1PerWUelvI8v16v4zh+OxnJE6XtwC9o4A0ziG4MfA29o/+6GMCLrfY6ieq6vqe1dmPj8edlJ2TBFTgDwRV4RBzH1XVdnufLtoVlWguh8fX3+Z7VVXjDcsLh0AS90VM67S4428jn3gqFY9voNbc6qHVjjdbt/26XYXmj8LnTzgHsk+AKPGgYhu0Fb8JF250DWf8utsUFyi6Ptrg+3E6y0fxy+dcC88rGZ+Av9H1/q9dJnudPGRORnhCqqpoNp9eJAzgDwRV4RN/3y4bWWWoNY1lnT3y4neFhaXB9S3vvxhtlnmH4aNM0Xa/XW9/xZ6XWmTAeIc/zeJp1GgFe471nG8EV+Nlsb9sXajG17mdpwWmaYnB9zXRQM13XbQx5TZey+Hp3lQDnsf1du6cnfwiQt77a6Uxsf2EYhtnQVmcP4NgEV+B/vu0QGyLr9jxMeZ6XZXlPv7W/vsZKtx+L97LgOnt1fd9vdKv+o2YZ4Pdunak2xkpkWVZV1U7KCXAYgiuwbjl18PaI1tDCsM8AFkvY9/0rA/Ps97ORabMr3Z+u7gj8hW+/fWHqtVvdKDb6m/zR99rpAjgJwRX4vodw27bbfYOLori12MPbTdMUy/mC5XA2pCvlLBNslmWmBoU9C71ONnr+hxW/ls/6u/L80ZYBdkhwBb6xMYgrqOv6ViB873VV2Pu7gutGD8ONC98waM31KOzN6oI3s/t36b2nF3+LnTSAwxNcgf+3nI9ku3twWZbL5oXldt5rGIZY4J0UbDknc2yAzbJsda1IvYjh6e5fjGp7irUsy+q6Xh0osbH0KwA/IrgCK/q+3xjEdfnXIy5twNztNVkaXF8wxjX4NmeO41iW5eqQ190OFYZTiV/epmk2FmQuy3I2u+/Gpv6ohH+9I4A9EFyB+bXOOI4bI1rD1COr8wb/aI3WlwXIrutiyf96EOlPX9TqdE1ZlhVFoaEG/tQ9X7FhGG7No55lWehyMrvN9K5vq7MEcHiC65Gpxk5uY3mbjWOj7/uN2TKv1+tHTCCUvsDr9fqy4Hp/qaKmaVZvE+R5fs+qQsDMt3Xf9jrV8edbfSIu/4az6hkxs9HT5Naf3KED7ie4wimsXjQsrxLatr11oXbn6qy3tvxGaYvre2cVjmbvTyzh8j1PH7+rdxU+yE+j7DiOGwMlyrLcyZnkLb5d8bvrurZtq6qq67qu66Zpll2pnc2ABwiuwNfX19c0TW3b3rpQ++hRl/F15Xm+28vNW5NgVVXlCg/+zvL7dWtEa/jlrUmYCOq6Xu1CUtf1xrOc5YB7CK7A1zRNG8s8VFX1iRdqsZUyLueT5/nbL482ZjG99RF89F0D2K3VPquzEa2zBNs0zT3nkLefZ15m9kq31077iGEmwJ4JrsdnOQ1Sy09/Y/aRy+VSluVHj0HaW3Cdmb23G9k1XvPt7SXA55p9Abcnpbter9uz+J78uzmO/9fe3Z03qmztAnUKpEAKpEAKpEAKpEAKpEAKpEAKpEAKfS7qbL5a/AnbsgRojIv1uN2yFy2QVC+zataw03v5K1qssfWkffgTCDwkuMKHGsdxGIadQmvY8OYGtb6pOdO0ZPQMVodowzBszRnWqwn+yP6Uk/DWcZLWwSexGuD3n8OgKIq3HDBwD4IrfITZXe1QZd25O746PfiiY7UpuJ5hzPSwr0ncFWZ2gpIk2elxctGzA39t/zWyev9ueullWdZ13Q3u3/21cRy3brrNzBoNqLgCxwmud+Yz4GPtnPphGHaaMH19faVp2rbt1S+e1e1wXhZcf/ns9X2/1dE0TdNldgWOi3t077zWwobVV38nfKW+72dPYJ7nZVnGN+DCN0/bJA84OcEVru3IvnnTH9u23dnjYVrEdbmx2v4BT0H9VFOFY8vj35nFHcbToQR0cDtKYHV5/9ask7BQwovou/q+77quLMu6rvu+H4Zh9XNn1nDOtBHgIMEVLuz4x/wPFnHdxtSc6Vpby+yvQD7Y6vlC/154up3rf6vWmiSJeQ2/tHzau66bNb661rsxcBKCK9xf3/c7i7huP3crnip8uaHSzlTGsizj8vjl/mnwGqs5aiu1hpfVw9/Ad/V9P1sEe9GN1oA3ElzhVmYDrLCidWd6cJZlt68txF2FTz5OWt1Ycme/oqqqjvweIBjHcbbIP76Ft9P8jN8bxzH+MAqLU6a/eu+xAZcguMIdrH7qh7VGW5F1J8jdYwwx/SumJyHLsnMWlh8+4W3bbi3GK8ty2ibnHicOfuBIc9qt7aaSJAndg7d+Ic8yW1ecpun0nuwJBx4SXOGGQqF1p+9IURSrm4Leb97pOI5TufKKU4WDUCbaOqGzTidALLzqu6777syF2W/guK1nbNlt4eGTDzARXOFudvowhRVcN66yLsW7C55/qnBseUamOc9LcSZfnW8Mn2ynFdPqolZ+7MhW1XGjpvht2YkA9gmucBPTesituXB5nt9+OWswG/1MT8iZb+0fiZ1hY4lpzDcrwG7dkoB7e/ja6bpu613xQ94SzyA+TfGt1XilK8A+wRXOazYgW47PZgO1rblwaZpuVRU+4Q73NGa9x/Bop89wURRhwdj+uf6Ek86NHbyAw4qJqqpmG7FIrW/X9/1W0RVgh+AKJ/KbRNE0zer4LM/z1eWsnyOuuN4jsy03RZxkWda2bfzge/yTYdVqlTWsCd9a0Rru5c1eJvyd1e2Fpu21w+lwEwE4QnCFy9hqmxlmXi0794RC6zuO9Fym4Hq5bQN3pg3v7JFzp4gOW7ZeHWG5xFYns9BAeNld3OvlxWabEk3rOJwIYIfgCtcza3Sxunwrz3MlhWCaWHvdCWmrg7mdOcNfjxb0Gh1yP+M41nW9NRkh3Mur63r/4vfSeI1ZcL1uy3fglQRXuIbZMtdgq+x23YT2F6Z0d7+xUdiqd6u41DTN6iS9txwqfMt3L9StvnTxu+KH7AF2WvEzPNub+rSbbAOnIrjC2W0Np9q2XS242d1hZqrAhOZMl35yVoNovLx5FmLbtr30vxeCncs4vAR2Zh9sdafz0nij2eZeSZJ8eC8G4AjBFa5kGmltzYi7X1Hx96YR7Y37f2xt+PH19VVVlW0SuaWwQVSWZVuTDkJkjRdNmCd8EoIr8AOCK5zIwWHTbHXQfmo1FJsGtfeuRQ/DsNWuqSzLeFB44yeBG9iZuxt/J1RZtyLr19dXXdey0DmN4xjfaEuSRHAFjhBc4RS2hmiz77dtm+f5aq01LqwRm56uNE1v8BTtDOu7ros3mVje11j+8+PLTKDlvQ5egWF+wU5kDU2Y/vpoP9nWu9D+H6fvzPZxDadMcAUeElzhdLZGb3Vdr47Vsizzkb9jetLSNH33sbxCVVU7MydvEN35BFsRqGmanciaJElVVdr8vN7Wbm3LP/5bzBP+soMXcIzgCtcQKgzLEVtRFEZp+6YnLUmSDxkbbd3jCPZ7q8KLHbz2wvzS/ULrkXXsLvXf+PGzN/3gtIVbfCqnT7HVWq5TBgSCK5zI1kf11trF2X4nPt0n8ehnGiFlWfbeo3qlsiy3+qwmSTJ7sCuHU1mml9k8gll8TdO0bVu38N5uHMf9j6TVLdzu3X0AeCLBFU5n9hFeluVq/IhbZbIjbs707mN5guO3Krqu2+pes1OoN4LkXbaWRG7duQsebtC68x1+Jl4VH3aTzvM8z/Msy9I0zfM8NHPuuq7ruml5Qtu2y+bnaZo6L8BBgiucwuon9ziOqyO2ZQNGH/xbxnGcktsH9msZx3GrXVPYKSSMKV0/vN7DnWnCBq0PmzB9d9m2q/3Hlk9dnudbJyhJkjRNsyzLsqyu67Isl4/M89wdNOA4wRXOKAzaVrsHJ0kSf9KrKjw0PXVFUbz7WN5ja9ffrwPljp0mxvB7qxfYMAxd121dtMEPIitPFO6r7txWOCJM8B7+Z7W9uXceYCK4wrmED+ll08Ugz3Of4kfEjUDikPbeo3qj6YpaDjSzLFu2tHGZ8XQHL6phGLbWR0wv5J0+6i7d19jvAPddofVg2LLLGQS2CK7wag83vttKrbNWTBwRmjMFeZ6/+3DeaWebnDBkfPcBcnm/r89PLWe3sk14GzQR4O326+G/tGzX5EQD/wRXeKPlB/NyW/Yg9Mxc/ggPxRXXezRn+o1hGJathqc0W1VVPPfSxcbvPbyK4gjaNM1WHAoLJl2T57FzF+wnUfW/v2GaA+KMAzHBFf7Qtz50+76PQ8X08Z/n+Wwpl8/y4+KK68cWFWeNiKfLbDnETNM0jq/qWvyF5eUUOtPuJJnVu04uyzfa6lj+G2maLjfrApgIrvAGy1pr27bHh2sc1/f99GR+YFfhWJxCV1sNT8PQoijCVhbvPWA+Qdd1W4XWMDc4y7KHG7RKsG8RboGF942dAuy0U06e5yGapmk6+yLLMh92wEOCK7zUcoA1DENIrbMPfkHrKeLgGqafGeMGwzDsbI8ZxpQPAwMsbW01PPu667r9Bj+h/v/wf8HLrJbKpzMY8ufX11ee51VVdV0X7n/FfYPbtq3rOnyzaZruf777/wU+k+AK7xE+ifu+39qpdTli06ziuOnJ6bpuFlw/0FZ4GIahaZqt2PD1v4bDNh3hiJ13pPiv+r5v27Yoip3IGrqFuW9yCeM4hu2LQkAN/333QQH3JLjC23Rdt+yUEwZtoRXTFpH1OMH1oa3rcFIUxVQSWa56dTVyUGi/tL82MqyPWN4ucZmdx89e+1u3z6Y/rj7AeQdigiu8wTAMdV2v9nddtmKK+RR/aPYUTYuHBdcd4YLcya5ZllnyyrfM0kjXdVv73MSX2ZEXqbfB8/v9OXKWgSXBFZ4mHqit3jAOX2+tLcyybL/Qyg/EU2E1/4gtx4Vt2+7szRiS/8E2OQadt/SwDrb1/aIo9rf9DIVWc4P5590D2Ca4whMc/6Cd7XkzSdNUResvxMFVs6uH+r6fGg6vzufcWvVqrPmZ9s97uEm3MxE9zDGpqso9O7Z4bwEmgiv8idXlOlutmPI8X5YafFo/RbzPkOA6s3qNjeO43+s1XLHxfRbX6r0dPL+zN739KmuapkVRNE2zdRHOvnaNASC4witMXUmWBYeyLPfHZEZsv2GN6xHLa2xra81JlmXLn3KtEm587FRZwyY3Xde5fgD4FsEV/tA0DlstYYWdWo3e/lQ8VXhrT8gPdOQaC9OGp/i6vIBDx6ZhGB4Wzbioh2tZl73QdjYH/vpvh2oA+BbBFf7cVmqNC4Di63PFtwym59xU4S07F1vbtnF8XS292rbx9h6+HXVdt1+iD9PLXSoA/JjgCs83DfKGYSjLcpla0zTdmrYqrz5XHFw1gFk6eL3t72WSpmnbtiGTfLdGx0WN4xhOZbx0P36vm75O07Su69XI+t3uxAB8MsEVnmB1UN513eqsuaIo7PrwMtNU4SRJzFH8jXEcV+/CxPF19gyLH5e2c/qGYXhYYg3KsvxNZHUJ3ZiTC3yX4ArfcHxCb2iquTq4N1nulR5WXA2evmW1x1hseYNA77G32Hlid97H9t/ixnEMkXV2S271dkae523bCqIAPIvgCs8UhmVh98LlSC7LstVaq8Hcc8XPZ1mW0/Ov4voUfd8XRbG/X87WvsSmhl7ROI5d13Vdt98uOA6xVVXN7tA5xQD8kuAKTzYMw2qtdbb1Ja9RVdV0CqxxfaKH/WO/vr7irZ5U3i4n5NXQnWv/PkUs3J5zfgF4OsEVfmg2g276eiu1Wtf6FlsVVwPr3wv3aPYjTZZlO/cLnIU/svrudHylwzAMTdPsL2kOwgOSJEnTtCzL1d1Z9w8PAA4SXOFpwrrW5VBvqz3JPwO4vxdXBZcVb8//74VVrzsJZ78tllPwFlsF8L7v67re6SAdS9M0y7KyLI/clXOiAfglwRWeJi7uTVb3DjWG+1NbBXBF7x/b38zmSMPhPM+rqgqnYOuX/Ok/gR1TifVIo+BwM6IoCqcMgFcSXOE5VlPr1matvExd19Nsxq3gavz9FG3bLkuvsz+GCaVeF6/x8MIex7Ft27Is8zw/soo1SZIsy6YbEADwSoIrfMNW3WnqtBkP/iztO4OpOVOWZftlQ35g+Uw2TXNkYWRRFMvGs/yd2ZkKraH353jH5ysUzN1xAOCNBFd44GHaWU6SzLJMA+H3mk7WVAlPkkRMeo3lPp9bwlaf4afCKVu+3GZfuOnw71GL5q2+cUFoB/1wV5sgzPFeXe8AAC8muMK37fcQ3tqslRdYDtPjBDUMg9jzMgfja5IkR7YpOt4R92PtPCHTXz3sAh1H1qqqDu4g5VwA8AKCK/xEGKit9t5U1nu9nXFzXFlanhoD7h/bKY3Gj2ma5kh2reu6aZrpjo/iauzHU9ynxw/DsNN4KY6yYWObuq5nc0ZWj8EJAuCVBFf4odlcuyRJttr/GN69UXya3n0sH2F11evBXrWrc+wlpVX7T8v4P1NzsofCquO2bU0YAeCcjORg09bQMOzXOhv2pWmq1npCcWRSx/s7+8/qMAxd11VV9TDBpmkaSq9b87o/8/QdT+8hr642OV8Vpmq3bbv69uUUAHAegit8Qxix1XW9OvhbfTDvFTd8fvex3NDDEDX7Y9/3TdOsdgaaTVjNsqyuazeDdiyf3rAd6+rdgWXdtSzLruvUVwG4CsEVvmcYhuWIsKqq+DHKFOcx9QdK0/Tdx8L/F/LVLKmu1gPTNA3V109bn7xaYt36J4fnZ2cV60xoIPebJ/DeTz4A5yS4woqtUeOy08ys1mo89y5bNwum4Jpl2euP6qM8nM46+2bbtrO8uhVfw76vIbt6if2LnoS+77uuO9grONxi67pu6znUuhmAMxNc+XQHF4+N41hV1WpqNbY7m/iMTDUoFdcTmha+HmwgVJblTiT+VufbV75sd1bL//iQ+r6v63q/xBqe1dA3riiKX1ZZAeC9BFfYM43zuq5bVoeWHVA5lXEcp7Om4npaXdcd2TVnOo/Hbzbt/PHIb3iNbx3YMAxt2x5pcxXWCTdNs7MX69v/7QBwnOAKK2aprgH4AAAcrElEQVTjub7vZ8PEsPNk/GBDwBMax3E6cYLryTVNUxTFat+mpaIotjYa/XdgyuvrX62//z+GSR+re0cvhbXBTzlyADgJwRU2hbHmMAyzweJqD+HZT3EGwzBMwTXP8+UDnKx32ZrxGyYP53l+cNFmlmVVVR2vu77Mwzrqw2XA09dt2zZNM63W3n9C8jwviuKETwgA/JLgCv+xrMwsd0Sc9RDmtDRnOqGDwSlEtYNtctM0zfO8qqqH2+f8aWz7cXOjrYeFKvTOGuDp+9MzIJcCcFeCKx/t4fTCZUOmsiwP/jjvMp2LuFo+BVdn6vWOPOerjzneMnc6y3met217ZKLsu/ozbX0z7hVclmWWZQ//4VmWZVkWdmTd+f2ueQBuQHDlEx0cRu+n1uO/ineJC+bLqcKG9a+3fM6PPPld181S3P4esGmahgpknudlWTZNMwzDOI5nONFbCTZ0CQ6rfI+0WU7TNDQK/tZa1jM8AwDwM4Ir/Mc0sKvrejZSzPP84URETiUOrrNutJzW1mmqqirs7LKf6JbCys+wlc7b2zKN/9P3fVjKG6ZDH/93pWn63e1YAeAGBFfu78gkvZm+72fdTeM2wlxFfB7zPFdivbpwJ+IH2XW6Bqqqatu267r4JtTPuhAfbIA0xdRhGMIc4DzPDzZPnr0FhU5UO53hjhwPnMTbe30DlyO48tFWk8w4jss9JzRkuqJ4992iKN59OPzQckTbtu2ya9oU8I6EwDzPm6bp+/4HbX63HhA2pG3/p2mauq7DBOCDXaZW5Xle1/XDhbtiABelWwRwkOAK/xGWts7Gvsv9b3y4XkLXddNJXK5P/uc8nt7DE9S27Y8LsOGlXZZlKIdO62DHcQx/DCtIQ700dEvKI0VRlGVZVVUIqGVZHlmb+i2h69LOCgUXMFfkugV+RnCF/zOO43Jpa5qmP5ibxxnEqWY1uHJFqxNx67ququoHU3BjoTHS7JtHFtY+N68uq8FwVy5y4DjBlU+0NaeuaZrZsHVZa3342ziPtm2nU1kURThTztdFHTlxoUy6nDRxWmHlavk/bduGwu8Lnk8AuBbBlTv7VoeVpmlmg900TZumecWB8jfiimuWZcsplxLCyf3sBA3DkOf5O3LoA6F4m6ZpaLM0axB18B/rouXSLMYGfkxw5f6OfC62bbtTa33YdJRzipszZVn2rR0vOZud8e7y9dg0zcEk+YO/Oi5k1GDqaXxwH+mdP+58E64iTPIPK8zjb77xkICTE1y5p4cffvED6rpedmOy+c11rW7GO00V5kJ+fMrGcXxB0XV63wh11DRNp9ZNWZYVRRFaK9n/GZb6vg8dzsxsAg4SXPksq5WZZWmlLEtjzRuIT+7UnGlr+xOx9upmZ3AYhtCxqWma0Lcp1D9Dwpxm7Sb/Mwui0xfhYUVR1HXdNE34bXVdd13X933XddP+N1NMDUttf3PwO9+Ea9maHNH3vcgKfIvgyqdYDgHD7d5ZZA0jVKn1HuIZ4GVZigGfLITM8N+w4WoIomHD1aIowoTeNE3DBjlhU5xp6enTt5rc+SUuVABYElz5CMtB5zAMy9RaFMWyh7BB5HV1XTcF17quncrP4VwDwM0IrtzB1iB1Z9ubeL/HaVpg13V/fqy8UDxV2C2JT/DXE25dM/BEWws3AFYJrnycZSumIM/zne1SfKxeURxc3ZX4QD972XqxA8AJCa7cysMRZ1VVq6nVAshbElw/x/4a1B+8un9/08pbCnyXVw2wQ3DlDo7MD1xd1Bo0TfP0ziucQRxcp/aVzjVPvAZcTvB7XjvAEYIrH6Gu63hRazw9eLn0ceKj9KLifVyn4FpVlRP64fYvgG9dHi/uCezS5TbsQwb8mODKVR3cjbPv+zzPt6YHf3evRa4lDq6ra5gB+GvSKfAUgis3sfq5GO+GMlMUhY/S26vrejrjU8VVwy3+PbX6CgC8gODKrcTDza7rVguty0Wt3FVccbWPK8AZPKV9GvCBBFduaBzHtm1XI2ue56YHf46qquKZ4cZGAO8SvwP3fd91nfdk4FsEVy5v+cm3tVNrlmVbqxx9fN5SHFyLooj/yhkHeIHVztuhyf+yOaJ3ZmCH4Mol7Uw0irPKJEmS1aayJizd2ziOccX13YcDwL9///6VZVkUhQlQwLcIrtzHOI5xMx6tmD7WdK6HYZhVXF0GPOQigb82m/3kRQccIbhyScvGsMMwhKlHy1pr13XvO1LeKV7qnOf58gGrc9gAADgbwZVr2N/CZBzH1dSaZVld11u/ijtZPa1xcM2y7PVHBcAOn8jAcYIrp7bzkRZH2eW61iRJdJH9QLMKatd18fWw9UgAAE5OcOWSZvu1rqbWNx4eZzC7o9E0zbuPCACAHxJcuZJllaxpmmVqrarqLYfHeYRLJQ6uy30XAAC4CsGVSwqxZJla0zSN88lyZawJoh+l7/vpdsa02tnFAABwOYIrZ7eVLh6mVj5TfMFM2+GowwOciluHwHcJrpzUVvfg8N+maZIkmc0Qtojxwy2vmXj9c1j2bKgEAHBFgivn8rCN8GoP4a+vr+W2N3yycRzHcSzLchZclw97/bEBAPBdgitnMYsQWwsRdWPioGEYsiybrhMXCXAqbpwBfIvgypW0bRtHEYGEpfiWR1EUqzPJjReBd/H+A/AzgitnN33Gt207W9f69fVVFMXOalg+XNu2y67CAGfjMwvgIcGVE4k/uWef4l3XrabWYRhefphcRjyxXHAFALguwZXTWd54ni1WDPI87/t+/wf5TNOVEPfxWgZXFwwAwFUIrrzNVvulma7r8jxfpla1VmKrV1HcVVjFFTiDnblFAOwQXDmvcRy7rluttS5Tq49/luq6Xm3i5WoBXmyrcz4ABwmuvMHq5/eyANs0TZqmB7sxwdL+VGGAtwgbTb/7KAAuRnDlnXY+ufu+X02tZgjz0Ooa13g7HAAArkVw5VxC5Oj7fnVdq6VB7JtdFfEa17Ztdx4J8Nd8hAH8huDKSx35qF5NrUmSzHoIw0NxxTUEV4NFAIArElx5p+W61q3Uap4nO7biaFEUWxVXAAAuRHDlRKRWnisOrl3XvftwAP7902EY4EcEV07keGr1Mc9D4zjGeykJrsB7+eQC+A3BlbMoyzJJkllwjVOrj3yOiK+TneDqcgIAuBDBlXeadnBd1lq/7F/Cr6m4AgDcg+DKX9mvaMV/G7d+nRRF8ffHyM3FN0RWg6u6KwDAJQiuvNosKjRNs5whXBSFRMHvrQZXlxYAwOUIrrzTamrN83wYhukxYgbHza6W2VThrWvJNQYAcHKCK2/T9/0stSZJUlVVnFqXZAyOS9N0urr2rysAAM5McOU9+r6PQ0VQ17Xd7XiiZXCdriiXFgDAhQiuvMgsJyxTq25MPJ2KKwDAPQiu/K3VulZYeRjPE56ta4WniINr3/eqrAAAFyW48lLjOBZFsezGZIYwTzG7cqabI0mS7D9y9TsAAJyE4MpfiWNA+Hocx+WWrVmWCQz8kekyS9N0+qbrDQDgcgRX/tyUE9q2fVhrhWcZx3E1uAIAcDmCKy9S1/UstaZpaoYwz7U1Vfjry3sdAMCFGczxJ2abjnRdt0ytbdu+9Ri5j9VbHuM4rq5xdX8EAOByBFeeaTUSLLdsTZKkLMsjPws/No5jnuc7U4VdcgAAVyG48rfGcSzLclZutWUrLzAMw3THxBpXAIBLE1z5Q+M4/qwhk1IYPzZdPMMwTFOFBVcAgEsTXHmmWeBcLm3N83wYhncdHh9lGIbpwsuy7N2HAwDAzwmuHPKDGukwDNMKwyk8zBoyqazyd7amCrvqAAAuR3DlV7a6uY7jWBTFrNxa1/XOT8HvxZdWXPDP8/yNRwUAwC8JrjzfOI7LXVuXbYThT8XBdbUfmBsoAABXIbjyNFMMaNt2aoozxQZLW/lTyxQaB1f3TQAALk1w5VdWl7ZmWRan1jRNZ0tb938DPEXf99Mq61nF1VUHAHAtgivfMA33l+P+8J2+75epteu61V8CfyreQ1jFFQDg0gRXfmWWQmcNmZIk2am1bv0SeIo4uFZV9e7DAQDg5wRXnmMcx6qqZktbm6ZZfeTrD49PEC6t+AKbmoQJrgAAlya48hM7CSFuhyOj8l7LqcI7090BADgtwZVD9of7yzbCeZ5rI8x7dV2Xpmm4ILMs6/v+3UcEAMAPCa781rKNcJZly9SqwMWLNU0z3U9JkmTWJAwAgAsRXPmGZfhcthFOkkStlRdbvS0ST183BQAA4NIEV/bszxDuum6WWr++vuq6Pvjj8Bemiy2uuIbLMr4OXZMAABciuPJtYcS/nCEcdm1d9m2Ct4iDa1VVrkkAgOsSXDlqNu6vquproW1b8YC3WF54bdvGzZlMFQYAuC7BlXX7+XO5+U2SJLbK5CTC1dt13dZUYbdXAACuRXDlP5YD+uV3lrXWJEnipa3wFrNrNd6lSUthAIBLE1xZsVOPWtZav76+mqZ55eHBEVVVzSqugXIrAMDlCK48Ng304yQwmc0Qlgo4ifhyLcvy4RpXly4AwGkJruyJh/KzGcIhEqi1cjbTRVsURXx7RS4FALguwZUVyyF+vLPIVq0VTiW+1RIHVwkWAOByBFceGMdxOUM4TdOdWqtgwFvMLryyLHeWYbtKAQAuRHBlUxjZ13Udp9bwtR6tnF9ccZ2aM8mrAABXJLiyYhrcH+8hLA9wNnHFtSzLdx8OAAA/J7h+tDhtLpNn3/fWtXIJq/dNBFcAgNsQXD/UVoF0+n7f92mazlJrnucHfw+83eoaV1csAMAVCa6sGMdxWWvNsizeCVMA4ORW17j+c+kCAFyQ4MrcMAxZlu2nVjibZRzd7yoMAMCFCK78Z8Q/DEOe57PUmqZp3/dvPEI4brqetyqus4cBAHB+guvnmg3cx3EcxzEuUk2ptW3bg78ETmIcx6ZpwjWcJImmYgAAlya48n/6vp+l1iRJVtuxyqucX9u2pgoDANyD4PrR4vy52ka4LEsZlUtYziCYdiFOkmRn1gAAAOcnuH6K/fw5TRKOmwkXRSG1clHjOE5rXJMkWW6H49oGALgQwfXjrC5tjdvYTG2E44ZMRvlcRbhWZwu2rXEFALg0wfWjhSF+vBRwasjUdd27jw5+bhzHoiiWFdd/7sIAAFyQ4Hp/+8P01dSqkw2XM7vOh2GYguts+gAAAJcjuH6iaYjf932WZbPgalIlNxDvSKw5EwDA1QmuH2RWkuq6btlGOM/zYRi2fgSuYtYlezmJwLUNAHAhguuHmrWumShMcWmrswlma1wBALgcwfXmVstKszbCYQsc0ym5k3iNq2ZjAABXJ7jezVZSjb9erbUqSXFpyys/vjszu7zNEwYAuBbB9bOM41jX9SyyqrVyS/ENGvdlAAAuTXC9v7i4VNd1mBg8ayOsAMX9LCuurnMAgIsSXD9I27bL1JokiS0uubrVRBpPLljOKRBiAQAuRHC9iWkUvvwi6LpuuWXrMrUuR/PG91xIfLlOFVeT4QEArk5wvbkwju/7Pq61hq/TNFVr5a6GYcjzfOoq7FIHALg0wfVulgXSeEPLOLsqrnJjgisAwJ0IrjcXD9/j1GpbS25mdttlGIbpfs0suLpBAwBwOYLrfSyH48MwFEUxS61pmobUOtvc9aXHCn8gvozj4KoDGQDA1QmuNzQN35epNUmSYRge/iBc3TAMaZoeuewBADg/wfW2uq5bbn4TdrOE+1nedoknyau4AgBcmuB6Ew83v0mSpCzLhz8ItzFVXL++vuKKq2seAOByBNe7CYPyZRvhqqrefWjw5+JQGq9xDd8XWQEALkpwvaG6rpcNmY78oGE9dxJvh+PaBgC4NMH1JqZxedd1Dze/MYjn9uLmTF9fX655AIBLE1xvZTZYD9q2ffdxwd9a5tK2beN7NzuPBADg/ATXS9oafMdtVIO6rvd/BG4jvsjbto27arv+AQAuTXC9mHj8Pfu6aZpZas3zfOfH4cb6vl+tuAIAcEWC630sd22dLW0NZFc+RPxamP2VVwEAwLUIrncwjuOyk/Dqrq3wCUIuVXEFALgNwfXCpqpR0zSzcmuWZX3fP/xBuJPZ5Pnp5RBvB+XiBwC4IsH1kqbBd1jaOkutaZouU6vxOh9lK7gCAHBFguu1jeM4S61JkkydhOFjxcE1y7Ll377lqAAA+BnB9XricmtZlrPUWpblclBumM69La/wYRh22msDAHAtgutJxel0+c2g67pZuTXP82EYVh8MHyUOrkVR/POKAAC4MsH1GpZj7r7v0zSdLW1d3f8GPkp4scT7uMYVV/EVAOCKBNeratt2tv9NKCsB/7aDKwAAVyS4ntpWdWg5SThJkrZtj/wsfIKu69zTAQC4DcH1GuIU2nXdNEl4iq9VVUmqMImDq4orAMDVCa4ntZVC27adLW39+vqKOwmLr3yg5WWv4goAcCeC69nNRuSz/W+2ejLJsXy4eBG44AoAcHWC65VUVbVMrbOlrcC//wbXsizjv3I3BwDgcgTXk1qOreu6/lpomsYoHJaaptkKrgAAXI7gegpb4XP6ftM0szbCIbV+9xfCvU1Xfnyjp67r9x4VAAC/JLiey1bgXC5tLYpiHMfl40VW+Pff4FpVVfimVwcAwEUJricVd1daLm3Nsqzv+9XHA//+uyBcxRUA4OoE1/fbz5zL1JokybKNMBCLXzizSfXu8gAAXI7gempt2y6XtmojDDPLLBoH12mqMAAAFyW4nlqWZbPUWlXVbIyufARL8RrXsCD8nxcLAMBlCa6nEI+npxH2siFTnufDMHz3F8LnmK782RpXrwgAgEsTXE+qKIrl0taDqRWI7/vEs+slWACAKxJc3285kl7dtXXWRvjffzsPv+JA4ayWL4E8z6fXjmZmAABXJ7iezjiOcWoNX8/mOkqqsBS/LuLgurzpAwDAtQiub7aMo2maLpe2vu8A4ZLi4DpNFXbHBwDgogTXc1nuf5OmqYao8F1xcDVhAQDg6gTX95uG0V3XfS1YngcHxbd44q2k6rp+96EBAPArgutZjOO43LU1y7J3Hxdcw6yOGk+5b5pm62EAAFyC4Ppmq9tOaioDv9H3fTzlPg6uAABckeD6IrM6z+yPXdelabpc3br/S4At8avJGlcAgKsTXN+vbdtZoTVJkjRNh2GYHmOoDQ/FL5OyLM1cAAC4DcH1dVbD52zX1im4aicDv1FV1fTKCveAdOcGALguwfU9pjH06tLWoijefYBwJVMcnb6ImzOpuAIAXJ3g+lLLas8ytc4mCe/8LLAlnsjQtu27DwcAgF8RXN9mHMemaZapdTbIllfhW8Zx7Ps+nnivqzAAwNUJrq8zm80427EjfF2W5fLxO98BloZhiO8HzVaMex0BAFyO4Poe4zjmeT4rt+Z5/u7jgguL7w3Ft4SmWQwiKwDARQmur7DcxLWu6+Uk4a7r3nWEcCeziqs1rgAAVye4vsFskrBlePB78e2hOLjaXAoA4AYE11dbLbdOS1tNZYQfm3aZil9i8V0hry8AgIsSXF+t7/t4h8mvr68sy1b3vwF+puu6eBL+bB9X8RUA4HIE11eYBsp935dlOSu3ankKzxXPxl8GVwAALkdwfanlxq3KrfB7s9s9wzBM8xqyLBNcAQCuTnB9qWVwrapq+TBFV/iNYRiyLFv26/bKAgC4KMH1dfq+nwbTy1qQITU8S9d1OxVXrzUAgMsRXJ9vGhbPxsfLZsKr5VbgB+KXW9wCzQ7JAAA3ILj+uTCebtt2uXer8TT80mr5tOu6uDmTFxoAwNUJrq8wDEOe57Nya1mW2jLBX2jbNr5D1Lbtu48IAIBfEVz/xKwKtNwCJ0kSnU7hj8TT8qfgamkrAMB1Ca5/bjlJOKxuNYyGJ4pfULP15E3TrD4MAICrEFyfbDYsbtt2ahIzyfPc6BmeYvZSCn9crbgCAHBdguufmAbTRVHMUqtWMfDX4sn5uqABANyA4PqHVjsJx7MWgWeZ7hbNeqGlaWo9OQDA1QmuPxRGyVtbtv77969pmizLZuXWuq5nvwH4gZ2XT9M0sxtGoeLqFQcAcF2C69PEw+K+75eptSgKQ2f4jdVX0Oyby/n5pgoDAFyd4PpbqyPp5a6t9r+B1+i6brXiCgDAdQmuzxcXfKYB9KyvqdIrPFH8ghrHMW7OFObnzx7whkMEAOAXBNefWx3+Lqs9Ib4aK8Nfi9ecd13Xtq2NcAAA7kFw/aFlEB3HcRzH5dLWrXKrKAuv4bUGAHB1guszLZe2fn19lWW503wY+L2Dryz3jAAALkpwfYIwDq7rejY9+OvrK8uyrVGy0TN818NXjZcbAMAtCa5Pk6Zp3I1JO1MAAICnEFx/Lq7hrE4SDu1MVx8P/CkvNwCAOxFcf2scx77vl6nVJGE4AxvhAADcgOD6E7OhcFVVy/1vTBIGAAB4CsH1V1ZT69fXV1VVajsAAABPIbj+yjiOoSdTLE1T+98AAAA8i+D6K8vVrUmSVFX17uMCAAC4D8H126Yiat/3WZYtezK99/AAAABuRnDds9OPdBzH1S1wyrJcfTwAAAA/I7j+xDiOXdctU2uapk3TLB/8loMEAAC4B8H1J4ZhWC23Zlk2DMO7jw4AAOBWBNfHQsk0Lpw2TSO1AgAAvIbg+g0hu/Z9v7oFzjRJeLka9g3HCgAAcBeC655l5tyaJFzX9VuOEAAA4PYE18fi+FrX9TK1bm3cqtYKAADwe4LrN3Rdt5wkPO1/M5FXAQAAnkhw/b+cufxi9piqqmapNc/zvu+3fmr/+wAAABwhuG6aBc62bWfl1iRJ2rZ91+EBAAB8CMH1P7aqo6udhMuy3KmmKrQCAAA8heC6YpY5h2EoimI5SdiurQAAAC8guP6f1f1Xx3Esy3LZSbjruuUPqrICAAA8neC6lzaHYYgbMiVJYtdWAACAFxNc96zWWk0SBgAAeCXB9f9Mc4PDH/u+n0qsW5OE4x8EAADgLwiu67quy7JsmVrTNFVuBQAAeCXBdd1qav36+rJxKwAAwIsJrv9fPN23bdvV1JokSVxuNUMYAADgBQTXlfyZZVm8unX6erm6FQAAgL8muK5ommZZbs2yTIkVAADg9QTXuZBO8zyfTRKWWgEAAN5CcF3X932apkmSJEmSZVlVVe8+IgAAgA8luP5njeusRVNVVU3THNz/RkkWAADgLwiuAAAAnJrgCgAAwKkJrgAAAJya4AoAAMCpCa4AAACcmuAKAADAqQmuAAAAnJrgCgAAwKkJrgAAAJya4AoAAMCpCa4AAACcmuAKAADAqQmuAAAAnJrgCgAAwKkJrgAAAJya4AoAAMCpCa4AAACcmuAKAADAqQmuAAAAnJrgCgAAwKkJrgAAAJya4AoAAMCpCa4AAACcmuAKAADAqQmuAAAAnJrgCgAAwKkJrgAAAJya4AoAAMCpCa4AAACcmuAKAADAqQmuAAAAnJrgCgAAwKkJrgAAAJya4AoAAMCpCa4AAACcmuAKAADAqQmuAAAAnJrgCgAAwKkJrgAAAJya4AoAAMCpCa4AAACcmuAKAADAqQmuAAAAnJrgCgAAwKkJrgAAAJya4AoAAMCpCa4AAACcmuAKAADAqQmuAAAAnJrgCgAAwKkJrgAAAJya4AoAAMCpCa4AAACcmuAKAADAqQmuAAAAnJrgCgAAwKkJrgAAAJya4AoAAMCpCa4AAACcmuAKAADAqQmuAAAAnJrgCgAAwKkJrgAAAJya4AoAAMCpCa4AAACcmuAKAADAqQmuAAAAnJrgCgAAwKkJrgAAAJya4AoAAMCpCa4AAACcmuAKAADAqf0/pgGmKqFwZPMAAAAASUVORK5CYII=" alt> <strong><em>A3</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Award </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for behaviour at \(x = 0\)</span><span style="font-family: 'times new roman', times; font-size: medium;">, </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for intercept at \(x = 2\)</span><span style="font-family: 'times new roman', times; font-size: medium;"> , </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for behaviour for large \({\left| x \right|}\)</span><span style="font-family: 'times new roman', times; font-size: medium;"> .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates were able to find the reciprocal but many struggled with the second part. Sketches were quite poor in detail.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates were able to find the reciprocal but many struggled with the second part. Sketches were quite poor in detail.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Sketch the graphs of \(y = \sin x\) and \(y = \sin 2x\) , on the same set of axes, for \(0 \leqslant x \leqslant \frac{\pi }{2}\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Find the x-coordinates of the points of intersection of the graphs in the domain \(0 \leqslant x \leqslant \frac{\pi }{2}\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) Find the area enclosed by the graphs.</span></p>
<div class="marks">[9]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the value of \(\int_0^1 {\sqrt {\frac{x}{{4 - x}}} }{{\text{d}}x} \) using the substitution \(x = 4{\sin ^2}\theta \) .</span></p>
<div class="marks">[8]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The increasing function <em>f</em> satisfies \(f(0) = 0\) and \(f(a) = b\) , where \(a > 0\) and \(b > 0\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) By reference to a sketch, show that \(\int_0^a {f(x){\text{d}}x = ab - \int_0^b {{f^{ - 1}}(x){\text{d}}x} } \) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) <strong>Hence</strong> find the value of \(\int_0^2 {\arcsin \left( {\frac{x}{4}} \right){\text{d}}x} \) .</span></p>
<div class="marks">[8]</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="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><img 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" alt><span class="Apple-style-span" style="font-family: 'times new roman', times; font-size: medium; display: inline; float: none;"> <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica; min-height: 24.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1</em></strong> for correct \(\sin x\) , <strong><em>A1</em></strong> for correct \(\sin 2x\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1A0</em></strong> for two correct shapes with \(\frac{\pi }{2}\) and/or 1 missing.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong> </strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Condone graph outside the domain.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica; min-height: 24.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \(\sin 2x = \sin x\) , \(0 \leqslant x \leqslant \frac{\pi }{2}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2\sin x\cos x - \sin x = 0\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\sin x(2\cos x - 1) = 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 0,\frac{\pi }{3}\) <strong><em>A1A1</em></strong> <strong><em>N1N1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) area \( = \int_0^{\frac{\pi }{3}} {(\sin 2x - \sin x){\text{d}}x} \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>M1</em></strong> for an integral that contains limits, not necessarily correct, with \(\sin x\) and \(\sin 2x\) subtracted in either order.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica; min-height: 24.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \left[ { - \frac{1}{2}\cos 2x + \cos x} \right]_0^{\frac{\pi }{3}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \left( { - \frac{1}{2}\cos \frac{{2\pi }}{3} + \cos \frac{\pi }{3}} \right) - \left( { - \frac{1}{2}\cos 0 + \cos 0} \right)\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{3}{4} - \frac{1}{2}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{4}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[9 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int_0^1 {\sqrt {\frac{x}{{4 - x}}} } {\text{d}}x = \int_0^{\frac{\pi }{6}} {\sqrt {\frac{{4{{\sin }^2}\theta }}{{4 - 4{{\sin }^2}\theta }}} \times 8\sin \theta \cos \theta {\text{d}}\theta } \) <strong><em>M1A1A1</em></strong></span><span style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>M1</em></strong> for substitution and reasonable attempt at finding expression for d<em>x</em> in terms of \({\text{d}}\theta \) , first <strong><em>A1</em></strong> for correct limits, second <strong><em>A1</em></strong> for correct substitution for d<em>x</em> .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica; min-height: 24.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int_0^{\frac{\pi }{6}} {8{{\sin }^2}\theta {\text{d}}\theta } \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int_0^{\frac{\pi }{6}} {4 - 4\cos 2\theta {\text{d}}\theta } \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = [4\theta - 2\sin 2\theta ]_0^{\frac{\pi }{6}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \left( {\frac{{2\pi }}{3} - 2\sin \frac{\pi }{3}} \right) - 0\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{2\pi }}{3} - \sqrt 3 \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[8 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span class="Apple-style-span" style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 14px; line-height: 20px; display: inline; float: none;"><span class="Apple-style-span" style="font-family: 'times new roman', times; font-size: medium; display: inline; float: none; line-height: normal;"><img 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" alt> <strong><em>M1</em></strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">from the diagram above</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the shaded area \( = \int_0^a {f(x){\text{d}}x = ab - \int_0^b {{f^{ - 1}}(y){\text{d}}y} } \) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({ = ab - \int_0^b {{f^{ - 1}}(x){\text{d}}x} }\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \(f(x) = \arcsin \frac{x}{4} \Rightarrow {f^{ - 1}}(x) = 4\sin x\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int_0^2 {\arcsin \left( {\frac{x}{4}} \right){\text{d}}x = \frac{\pi }{3} - \int_0^{\frac{\pi }{6}} {4\sin x{\text{d}}x} } \) <strong><em>M1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1</em></strong> for the limit \(\frac{\pi }{6}\) seen anywhere, <strong><em>A1</em></strong> for all else correct.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{\pi }{3} - [ - 4\cos x]_0^{\frac{\pi }{6}}\) </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{\pi }{3} - 4 + 2\sqrt 3 \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award no marks for methods using integration by parts.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[8 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A significant number of candidates did not seem to have the time required to attempt this question satisfactorily.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was done quite well by most but a number found sketching the functions difficult, the most common error being poor labelling of the axes.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (ii) was done well by most the most common error being to divide the equation by \(\sin x\) and so omit the <em>x</em> = 0 value. Many recognised the value from the graph and corrected this in their final solution.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The final part was done well by many candidates.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates found (b) challenging. Few were able to substitute the <em>dx</em> expression correctly and many did not even seem to recognise the need for this term. Those that did tended to be able to find the integral correctly. Most saw the need for the double angle expression although many did not change the limits successfully.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Few candidates attempted part c). Those who did get this far managed the sketch well and were able to explain the relationship required. Among those who gave a response to this many were able to get the result although a number made errors in giving the inverse function. On the whole those who got this far did it well.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A significant number of candidates did not seem to have the time required to attempt this question satisfactorily.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was done quite well by most but a number found sketching the functions difficult, the most common error being poor labelling of the axes.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (ii) was done well by most the most common error being to divide the equation by \(\sin x\) and so omit the <em>x</em> = 0 value. Many recognised the value from the graph and corrected this in their final solution.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The final part was done well by many candidates.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates found (b) challenging. Few were able to substitute the <em>dx</em> expression correctly and many did not even seem to recognise the need for this term. Those that did tended to be able to find the integral correctly. Most saw the need for the double angle expression although many did not change the limits successfully.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Few candidates attempted part c). Those who did get this far managed the sketch well and were able to explain the relationship required. Among those who gave a response to this many were able to get the result although a number made errors in giving the inverse function. On the whole those who got this far did it well.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A significant number of candidates did not seem to have the time required to attempt this question satisfactorily.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was done quite well by most but a number found sketching the functions difficult, the most common error being poor labelling of the axes.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (ii) was done well by most the most common error being to divide the equation by \(\sin x\) and so omit the <em>x</em> = 0 value. Many recognised the value from the graph and corrected this in their final solution.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The final part was done well by many candidates.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates found (b) challenging. Few were able to substitute the <em>dx</em> expression correctly and many did not even seem to recognise the need for this term. Those that did tended to be able to find the integral correctly. Most saw the need for the double angle expression although many did not change the limits successfully.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Few candidates attempted part c). Those who did get this far managed the sketch well and were able to explain the relationship required. Among those who gave a response to this many were able to get the result although a number made errors in giving the inverse function. On the whole those who got this far did it well.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The diagram below shows a solid with volume <em>V</em> , obtained from a cube with edge \(a > 1\) when a smaller cube with edge \(\frac{1}{a}\) is removed.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="font: normal normal normal 29px/normal Helvetica; text-align: center; margin: 0px;"><img 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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(x = a - \frac{1}{a}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Find <em>V</em> in terms of <em>x</em> .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Hence or otherwise, show that the only value of <em>a</em> for which <em>V</em> = 4<em>x</em> is \(a = \frac{{1 + \sqrt 5 }}{2}\) .</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) <strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(V = {a^3} - \frac{1}{{{a^3}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x^3} = {\left( {a - \frac{1}{a}} \right)^3}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {a^3} - 3a + \frac{3}{a} - \frac{1}{{{a^3}}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {a^3} - \frac{1}{{{a^3}}} - 3\left( {a - \frac{1}{a}} \right)\,\,\,\,\,\)(or equivalent) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow {a^3} - \frac{1}{{{a^3}}} = {x^3} + 3x\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(V = {x^3} + 3x\) <strong><em>A1 N0</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(V = {a^3} - \frac{1}{{{a^3}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">attempt to use difference of cubes formula, \({x^3} - {y^3} = (x - y)({x^2} + xy + {y^2})\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(V = \left( {a - \frac{1}{a}} \right)\left( {{a^2} + 1 + {{\left( {\frac{1}{a}} \right)}^2}} \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \left( {a - \frac{1}{a}} \right)\left( {{{\left( {a - \frac{1}{a}} \right)}^2} + 3} \right)\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = x({x^2} + 3){\text{ or }}{x^3} + 3x\) <strong><em>A1 N0</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 3</strong></span></p>
<p style="font: normal normal normal 24px/normal Helvetica; text-align: center; margin: 0px;"><img 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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">diagram showing that the solid can be decomposed <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">into three congruent \(x \times a \times \frac{1}{a}\) cuboids with volume <em>x</em> <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">and a cube with edge <em>x</em> with volume \({x^3}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so, \(V = {x^3} + 3x\) <strong><em>A1 N0</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Do not accept any method where candidate substitutes the given value of <em>a</em> into \(x = a - \frac{1}{a}\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(V = 4x \Leftrightarrow {x^3} + 3x = 4x \Leftrightarrow {x^3} - x = 0\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Leftrightarrow x(x - 1)(x + 1) = 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow x = 1\) as \(x > 0\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so, \(a - \frac{1}{a} = 1 \Rightarrow {a^2} - a - 1 = 0 \Rightarrow a = \frac{{1 \pm \sqrt 5 }}{2}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">as \(a > 1\) , \(a = \frac{{1 + \sqrt 5 }}{2}\) <strong><em>AG N0</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({a^3} - \frac{1}{{{a^3}}} = 4\left( {a - \frac{1}{a}} \right) \Rightarrow {a^6} - 4{a^4} + 4{a^2} - 1 = 0 \Leftrightarrow ({a^2} - 1)({a^4} - 3{a^2} + 1) = 0\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">as \(a > 1 \Rightarrow {a^2} > 1\), \({a^2} = \frac{{3 + \sqrt 5 }}{2} \Leftrightarrow {a^2} = \sqrt {{{\left( {\frac{{1 + \sqrt 5 }}{2}} \right)}^2}} \) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow a = \frac{{1 + \sqrt 5 }}{2}\) <strong><em>AG N0</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[8 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A fair amount of candidates had difficulties with this question. In part (a) many candidates were able to write down an expression for the volume in terms of <em>a</em>, but thereafter were largely unsuccessful. There is evidence that many candidates have lack of algebraic skills to manipulate the expression and obtain the volume in terms of <em>x</em>. In part (b) some candidates started with what they were trying to show to be true.</span></p>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">The graph of \(y = f(x)\) is shown below, where A is a local maximum point and D is a local minimum point.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><img 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gCV8CNeghE7tnLC23F4jOFnZdb7W+ztNDxiR3ApZ5WEryiKHYcXuOdZEHN0aHzrqJC/qtS2wdushvC1Wo1P14+yWbEjSYtjDuH53hIhx73nb84JRuxY9IW3VT9IpTBd98N86oqafEozYseiLLytOiJzgTCf8KIm4Yg6cplKFIV3qo7IXFDMfYsfpFKClW0nG7FjURMeqi+OuYXn63MihU7IRuxYRIQ3TdOOwGOuviDmFp5vMhFpfY5sxI6FLnyz2eRrPzxhDqovDj+zVsHW5+icBj9KOMKbplmr1fhxbrz3EGnEGE38CC9SJRyau2Jtli28rut8QMVH7xVFoTmVWj4+73JhNslTjtixpQnfbDbfXl7ygBxPlSP7jYeFT+H5+lxA/2tWV/+ulP6iYtwGcTXG2K2hfJEpfqd3ralP5TFI39OTjn51ljlUDH9XcTDDR/DDYoUf8vwom61Wq8JMBVcL/+PY8fvnrK7+p2+LT9elmCzFZCl5XFb11tWLgtpxeXLPUF/tx5+eXRv9W7urq8qXx3vbGeWDt4b0jOvzTDwmS2v7+W80o8cYY91GJZ9cT182pgkzkkr0oZLelPstH3o8KGldt4/bUgvJ9fT5O6PHGLOM2ll6W5ZisrTt1VjLePeaf13J46/vvgjPH8EPwQtvmma9Xj9/cz7kOYbu4eJfeL5taeT/sWeor/altf18WdU7jDFmGZpSzMRjctqlA7RaSjb+qKR9vPuLGzW/I0sxWdr0JrzV1c72peQLtWVx8Q6VVl+Qj1rxkeOP7uwmEqMrDpZefijFtoqaY8jxUSs+cxO+11Ker++daVzL7vVZ/rfvjJ79PTwsN6b5+lErPpL3XqlGzzKuXuztZJX3luOfpn4EPwQjPJf87eWlHYfj43Z4Hh38C8/3zw2e08L1i43co1ZXO9t3Ef5Gze+s54d7fksvP/QovNW4SK7ZV7D08kNp51i96f9rRz2OO/44wtiTJwwlMyz8GCa9xYdKenP00w1/goE2/6CXH8vxgtq5+/qmfQSfzCm8aZq6rler1fM3507Jj7LZt5eXmJ9HkEBC0yNVYnj/7HaDWu8rv/6dPthTDftpYygZb8IP/zQM+t9vT7Ksj+kheSTCpVyKV+FH/HTSUY83nldavelXkJ7Z8YuR72TKR/DJdOG52/V6vaIoby8v+RTINpzP6yqKous6JudRJhDh+VEt9+kSHfU4HhsrwDC3hvLMea/f41V4q6MW1gem1h8q6U2HHuPfgjE2IeVmSHirpRZeuV3kQyW96TZV4WHIpIee+UbN78gbjp8WQ8kMTASmfASfDAjfbDb5YZpDVjsf+Vzu9OSkoij1eh3D9RUiqMXngdR6Q8lIsYHbdxJdrfjA/clehecyjAh/f83RX4ThxrvHHfkHGXi4KXerlTZGBwJdrfjg7lXbjgm5K0MNHh1cTPkIPhkrPLe6oijValXXdXTgq05QwvNlrf6omHvitYdfmPCOAfCtVtwaYwuPQbh/CcM9/PvKoduqobvw/CV3ocop34ar8AOhvgkfwT+RyKUHSyAo4QdKX1mNi+SaLD2+0H/w8NKuVnzg7sNsc3jHjPdWK23EnHGyCbbwCbx7TqfHOfzI2w0yPD8f+xzHl3CrFbcG4xoQHgRAgPmkfCZsmmZ/jcolSs+Y1VJff6MNLCn7n8NPi9JPnADzHQHul3UV3npf+ew/B3+exs3h+y/oqIX7Fbtxn2BylH6Zc3ggMAEKz7NT+6E7q6UWkrK0tp//8n80nkJidfXvSof/cdEY7gjHRektvfzQ0wo26//ExA8vGp1+psrAb82kEPdBKjXuJDmXdXjLePf66dZwZz4pSm8ZVy/2Hr1Qpy2iW+8rh9vr6ctG97arK8cD6/BTPoJ/IDwVgt0xMlgVo2doSqmfbcYTzpR+Atwwo+vwzoiXHf/jvdzafuHKcLnvO7pS2Jd4pp0ykNk2fhGbz0TcDsmckGnndqmBt+inIcj9xtg/efZlk+7+dxuVfLKflag0Bsbu0VyHBytHsMLzGhJznP8xkmk3gRs1n59lZDspTW3uBo8wmGk3mY56PFu+/Ypk2oHoE6zwPqpiWN3GZWbDkUs/7nkt5fPPPN/6fAQ+PhH99OQkuN1+nUb5cOsul348vZaS/3zKKp2DaR8hECA8FQLfBO4I3c3K1N1yPUP7Xan4e89bx6ZsNVtA0Z5pu+UsQ/v6rDQ0XJ+EELvlQHQIXPiB0F20CXRvb3TRdX1qhTgIT4VFlHn511/8IvlPP4/4SZ7VavVf/jn5Dz/9adgNWThc+MmFISE8FQIXvt1u/3Rriwe0B7fQRQj7JEI6Za0mn93yI3Y3NsMDDzzEe/zsk0+GhW+32zxtHg+BH7IU4/sag3rwE7vtR+gf0PXxyydP7Bb+ezYbenuW8zg9OUn+/OeyFPvJ5o+Hco0wpKeCvIAh/X2RwtPTAK8cIH/96195C/O5HIXdX1OPcoHwVAhceHZXK+FhMhnZgrZjynKJCR9zTQ7UQ3gqLEJ4Dk9ii+bJAuMLbwqIrutTV0khPBUWJ7xpmq6VIUNH1KNvPcA3I8Tk+PNKq2cXyd0qahCeCosTnt3tPI3ayHmkAh8xutelvc2H5dq716/snYsQngoLFZ5Xg13c9efArcYuNXg/P1B1C8JTYdFCRu0sKlLhunFYevnhYC0NCE+FRQsftXx1UuG6cYxWHIHwVFi08Dx0FxHHCIfrHFjvK4X8cXrbWXEEwlNhCXPs6Iyioza/CINOo/zqTGt31MJ6sqzf9s8FgfBUWILwEYmTiXSa/Vzw4rl3xbM66nE8Zh99CeGpsBwH8rncvFUxAiOaa4QRAcJTYTnChz55HiibD0aA8FRY2ih3sKDtsqk4D8YBI0B4KixNeK5cKKn1kVopiCYQngpLE55XjBx35MNCCfG3ZlWA8FRYZuA6rLDZQSpFfjVuChCeCssUnqfWL3l9LvR44UoA4amw5KXp5a/PoXv3AoSnwpKFr9frsvtZbgsB3btHIDwVlp98tswuF927RyA8FZYv/NJ6XXTv3oHwVFi+8HxVfAlJOOjevQPhqRDKfpIlLIyje58JCE+FUIRfdOobvz66d+9AeCqEtWOUb5JfUCfPRxDRKbMTfSA8FcISnm9fW0Qnj8z5OYDwVAixJgTPtA28k+eXxca4mYDwVAhR+EV08rysDfa9zwqEp0K4VZ8CD9cfZbOhl9ZZRSA8FcIVPtj5Nj/Nbml5uyIB4akQel1H3sn7XzBvt9vLyecREghPhdCFN02Tp8T5HIfzQ5ERq5sPCE+F0IVnd1lxfprBB/Ohf5DVBcJTISKe8P55vmI4zWYTg3mfQHgqRET4uZfoTNPkkXkM5v0A4akQEeHZXfRu1hg7T7PBJhmfQHgqREd4xthRNjtT4I0n5CPNxj8QngqREp4vrXmM2PNQH3LmAwHCUyFSwrO73NijbHay89z2qU8DHoHwVIia8MyDzHzeDtsDBMJTIYLCszvnD1IpXdebzeZBKsVH73/5y1/4PP/05AS2BwiEp0I0hWeM1ev13URClmJ/v/UTWYrZj91EAtnygQPhqRBZ4RljpmlWFOXv4nHb9l8+eYKOfRFAeCpEWXgOX3vjD1StWhAQngrRF54xVq1WK4oC2xcHhKfCSggPFg2EpwKEBwzC0wHCAwbh6bA6wnf0q7PMoWIs4a0MJZs++6PeWcJbRQQIT4XlCv+hkt50Lqr3H3v5C+X/NKM39nVWSy0k19Pn74weY8wyamfpbVmKydLafv6bSS+cimW8e/10XYrJUmz9XvKOrhT244cXDSrOQ3gqLL2HtzpqYV3azCgf+n82tErx6boUk8cK1mspz9f3zrSuxRhj3etS+mVF7zDWM67PM/GYbP/TzHzUXr88uzYsxizj6sXempws6/0rWV3tbD/+vNLy8WuyOkB4KoQwpDeUjEN4xhhjPUN9tS+NUbejHsd3jtUbxhhjVkc9P9M+3v3bD3r5sSw9KGld3826NZRncrygduwG3Kj5nfW8SqGXh/BUiIbwjNslS7bYNj/o5ceDHjoZtXRubtR8Mqu8d1yID0YeX+g/+L541IHwVIiM8Nyu2EiP+qGS3pTT42J1AXXCXf2Pxadbo9dxb6qAQHgqREZ4dqsVt6TYsNu3WmkjtlXUbt2uZLWU7IbfaXb/fXnc7lBpOccKHfU4PvbdRQLCUyEywvd7+GG7Jghvva8cPindz+fdcfo8/Lj/cekZmlJKbw/PKSb+3IgEhKdCZIQfM4e/1Uobo+N8xlinUX75Um35n7vbWHr54VDDIDwQjGgIPyFK7zqH7xlq8bj8vf/Q/AAd9Tj+aGDIgDk8EIwIrcPvvVJdUmhGo/TDtlvG1cvin/zG7ayWWni0X7gy7n9wEKUHwhGZTLs/6eOSZwbW4e/GAgMP/q/84skX3sf53evS3tp9G36vGQOvxDo8EI5VyKUfzLSbTEc9DibfHpl2QERWQXjGWKdRPty6y6UfT6+l5D8fSJ6Zj55xfZ7ZQC49EI4VEZ5N3y1nGdrXZyWlEUAkD7vlgKisjvBggUB4KkB4wCA8HSA8YBCeDhAeMAhPBwgPGISnA4QHDMLTAcIDBuHpAOEBg/B0gPCAQXg6QHjAIDwdIDxgEJ4OEB4wCE8HCA8YhKcDhAcMwtMBwgMG4ekA4QGD8HSA8IBBeDpAeMAgPB0gPGAQng4QHjAITwcIDxiEpwOEBwzC0wHCAwbh6QDhAYPwdIDwgEF4OkB4wCA8HSA8YBCeDhAeMAhPBwgPGISnA4QHDMLTAcIDBuHpAOEBg/B0gPCAQXg6QHjAIDwdIDxgEJ4OEB4wCE8HCA8YhKcDhAcMwtMBwgMG4ekA4QGD8HSA8IBBeDpAeMAgPB0gPGAQng4QHjAITwcIDxiEpwOEBwzC0wHCAwbh6QDhAYPwdIDwgEF4OkB4wCA8HSA8YBCeDhAeMAhPBwgPGISnA4QHDMLTAcIDBuHpAOEBg/B0gPCAQXg6QHjAIDwdIDxgEJ4OEB4wCE8HCA8YhKcDhAcMwtMBwgMG4ekA4QGD8HTQdb3dbofdChAy/w/9G2F6gsvmHgAAAABJRU5ErkJggg==" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">On the axes below, sketch the graph of \(y = \frac{1}{{f(x)}}\) , clearly showing the coordinates of the images of the points A, B and D, labelling them \({{\text{A}'}}\), \({{\text{B}'}}\), and \({{\text{D}'}}\) respectively, and the equations of any vertical asymptotes.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><img src="data:image/png;base64,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" alt></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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">On the axes below, sketch the graph of the derivative \(y = f'(x)\) , clearly showing the coordinates of the images of the points A and D, labelling them </span><span style="font-family: 'times new roman', times; font-size: medium;">\({{\text{A}}}''\)</span><span style="font-family: 'times new roman', times; font-size: medium;"> and </span><span style="font-family: 'times new roman', times; font-size: medium;">\({{\text{D}}}''\)</span><span style="font-family: 'times new roman', times; font-size: medium;"> respectively.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><img src="data:image/png;base64,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" alt></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em><img 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" alt> A1A1A1 </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong> </strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>A1 </em></strong>for correct shape.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Award <strong><em>A1 </em></strong>for two correct asymptotes, and \(x = 1\) and \(x = 3\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Award <strong><em>A1 </em></strong>for correct coordinates, \({\text{A}'}\left( { - 1,\frac{1}{4}} \right),{\text{ B}'}\left( {0,\frac{1}{3}} \right){\text{ and D}'}\left( {2, -\frac{1}{3}} \right)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[3 marks]</span><br></em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times;"><img 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alt><span style="font-size: medium;"> <em><strong>A1A1A1</strong></em></span></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note: </strong>Award <em><strong>A1</strong></em> for correct general shape including the horizontal asymptote.</span><br><span style="font-family: times new roman,times; font-size: medium;"> Award <em><strong>A1</strong></em> for recognition of 1 maximum point and 1 minimum point.</span><br><span style="font-family: times new roman,times; font-size: medium;"> Award <em><strong>A1</strong></em> for correct coordinates, \({\text{A}}''( - 1,0)\) and \({\text{D}}''(2,0)\) .</span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;"> </span></strong></em></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[3 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Solutions to this question were generally disappointing. In (a), the shape of the graph was often incorrect and many candidates failed to give the equations of the asymptotes and the coordinates of the image points. In (b), many candidates produced incorrect graphs although the coordinates of the image points were often given correctly.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Solutions to this question were generally disappointing. In (a), the shape of the graph was often incorrect and many candidates failed to give the equations of the asymptotes and the coordinates of the image points. In (b), many candidates produced incorrect graphs although the coordinates of the image points were often given correctly.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
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UnhideWhenUsed="false" Name="Medium List 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2"/>
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UnhideWhenUsed="false" Name="Medium Grid 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List"/>
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UnhideWhenUsed="false" Name="Colorful Grid"/>
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UnhideWhenUsed="false" Name="Light Shading Accent 1"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 1"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 1"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 1"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 1"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Revision"/>
<w:LsdException Locked="false" Priority="34" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="List Paragraph"/>
<w:LsdException Locked="false" Priority="29" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Quote"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 1"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 1"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 1"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 1"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 1"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 1"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 1"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 2"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 2"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 2"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 2"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 2"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 2"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 2"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 2"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 2"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 2"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 2"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 3"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 3"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 3"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 3"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 3"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 3"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 3"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 3"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 3"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 3"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 3"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 3"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 3"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 4"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 4"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 4"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 4"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 4"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 4"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 4"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 4"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 4"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 4"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 4"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 4"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 4"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 4"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 5"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 5"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 5"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 5"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 5"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 5"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 5"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
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<w:LsdException Locked="false" Priority="68" SemiHidden="false"
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<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 5"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 5"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 5"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 5"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 5"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 6"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 6"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 6"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 6"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 6"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 6"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 6"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
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<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 6"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 6"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 6"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 6"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 6"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Emphasis"/>
<w:LsdException Locked="false" Priority="21" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Emphasis"/>
<w:LsdException Locked="false" Priority="31" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Reference"/>
<w:LsdException Locked="false" Priority="32" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Reference"/>
<w:LsdException Locked="false" Priority="33" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" QFormat="true" Name="TOC Heading"/>
</w:LatentStyles>
</xml><![endif]--> <!--[if gte mso 10]>
<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:Standaardtabel;
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-parent:"";
mso-padding-alt:0cm 5.4pt 0cm 5.4pt;
mso-para-margin:0cm;
mso-para-margin-bottom:.0001pt;
mso-pagination:widow-orphan;
font-size:12.0pt;
font-family:Cambria;
mso-ascii-font-family:Cambria;
mso-ascii-theme-font:minor-latin;
mso-hansi-font-family:Cambria;
mso-hansi-theme-font:minor-latin;
mso-ansi-language:NL;}
</style>
<![endif]--> <!--StartFragment--><span style="font-size: 12.0pt; font-family: 'TimesNewRomanPSMT','serif'; mso-fareast-font-family: 'ＭＳ 明朝'; mso-fareast-theme-font: minor-fareast; mso-bidi-font-family: TimesNewRomanPSMT; mso-ansi-language: EN-US; mso-fareast-language: NL; mso-bidi-language: AR-SA;">Let <em>f </em>(<em>x</em>) = \(\left| {\,x + 1\,} \right| - \left| {\,x - 3\,} \right|\).</span><!--EndFragment--></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">Draw the graph of <em>y </em>= <em>f </em>(<em>x</em>) on the blank grid below.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><br><img src="data:image/png;base64,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" alt></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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Hence state the value of</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) <span lang="NL">\(f'( - 3)\);</span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) <span lang="NL">\(f'(2.7)\);</span><!--EndFragment--></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) \(\int_{ - 3}^{ - 2} {f(x)dx} \).</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 style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times;"><img 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" alt> <strong><em>M1A1A1A1</em></strong></span></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times;"><strong><em> </em></strong></span></span></p>
<p style="font: normal normal normal 11px/normal Times; display: inline !important; margin: 0px;"><span style="font-size: medium; font-family: 'times new roman', times;"><strong><strong>Note:</strong></strong> Award<strong> <em><strong><em>M1 </em></strong></em></strong>for any of the three sections completely correct, <strong><em>A1 </em></strong>for each correct segment of the graph.</span></p>
<p style="font: normal normal normal 11px/normal Times; display: inline !important; margin: 0px;"><span style="font-size: medium; font-family: 'times new roman', times;"> </span></p>
<p style="font: normal normal normal 11px/normal Times; display: inline !important; margin: 0px;"><span style="font-size: medium; font-family: 'times new roman', times;"> </span></p>
<p style="font: normal normal normal 11px/normal Times; display: inline !important; margin: 0px;"><span style="font-size: medium; font-family: 'times new roman', times;"><em><strong>[4 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) 0 <strong><em>A1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) 2 <strong><em>A1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) finding area of rectangle <strong><em>(M1)<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( - 4\) <strong><em> A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>M1A0 </em></strong>for the answer 4.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><em><strong>[4 marks]</strong></em> </span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates were able to produce a good graph, and many were able to interpret that to get correct answers to part (b). The most common error was to give 4 as the answer to (b) (iii). Some candidates did not recognise that the “hence” in the question meant that they had to use their graph to obtain their answers to part (b). </span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates were able to produce a good graph, and many were able to interpret that to get correct answers to part (b). The most common error was to give 4 as the answer to (b) (iii). Some candidates did not recognise that the “hence” in the question meant that they had to use their graph to obtain their answers to part (b). </span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br>