File "markSceme-HL-paper1.html"
Path: /IB QUESTIONBANKS/4 Fourth Edition - PAPER/HTML/Mathematics HL/Topic 6/markSceme-HL-paper1html
File size: 2.38 MB
MIME-type: application/octet-stream
Charset: utf-8
<!DOCTYPE html>
<html>
<meta http-equiv="content-type" content="text/html;charset=utf-8">
<head>
<meta charset="utf-8">
<title>IB Questionbank</title>
<link rel="stylesheet" media="all" href="css/application-212ef6a30de2a281f3295db168f85ac1c6eb97815f52f785535f1adfaee1ef4f.css">
<link rel="stylesheet" media="print" href="css/print-6da094505524acaa25ea39a4dd5d6130a436fc43336c0bb89199951b860e98e9.css">
<script src="js/application-13d27c3a5846e837c0ce48b604dc257852658574909702fa21f9891f7bb643ed.js"></script>
<script type="text/javascript" async src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-MML-AM_CHTML-full"></script>
<!--[if lt IE 9]>
<script src='https://cdnjs.cloudflare.com/ajax/libs/html5shiv/3.7.3/html5shiv.min.js'></script>
<![endif]-->
<meta name="csrf-param" content="authenticity_token">
<meta name="csrf-token" content="iHF+M3VlRFlNEehLVICYgYgqiF8jIFlzjGNjIwqOK9cFH3ZNdavBJrv/YQpz8vcspoICfQcFHW8kSsHnJsBwfg==">
<link href="favicon.ico" rel="shortcut icon">
</head>
<body class="teacher questions-show">
<div class="navbar navbar-fixed-top">
<div class="navbar-inner">
<div class="container">
<div class="brand">
<div class="inner"><a href="http://ibo.org/">ibo.org</a></div>
</div>
<ul class="nav">
<li>
<a href="../../index.html">Home</a>
</li>
<li class="active dropdown">
<a class="dropdown-toggle" data-toggle="dropdown" href="#">
Questionbanks
<b class="caret"></b>
</a><ul class="dropdown-menu">
<li>
<a href="../../geography.html" target="_blank">DP Geography</a>
</li>
<li>
<a href="../../physics.html" target="_blank">DP Physics</a>
</li>
<li>
<a href="../../chemistry.html" target="_blank">DP Chemistry</a>
</li>
<li>
<a href="../../biology.html" target="_blank">DP Biology</a>
</li>
<li>
<a href="../../furtherMath.html" target="_blank">DP Further Mathematics HL</a>
</li>
<li>
<a href="../../mathHL.html" target="_blank">DP Mathematics HL</a>
</li>
<li>
<a href="../../mathSL.html" target="_blank">DP Mathematics SL</a>
</li>
<li>
<a href="../../mathStudies.html" target="_blank">DP Mathematical Studies</a>
</li>
</ul></li>
<!-- - if current_user.is_language_services? && !current_user.is_publishing? -->
<!-- %li= link_to "Language services", tolk_path -->
</ul>
<ul class="nav pull-right">
<li>
<a href="https://06082010.xyz">IB Documents (2) Team</a>
</li></ul>
</div>
</div>
</div>
<div class="page-content container">
<div class="row">
<div class="span24">
</div>
</div>
<div class="page-header">
<div class="row">
<div class="span16">
<p class="back-to-list">
</p>
</div>
<div class="span8" style="margin: 0 0 -19px 0;">
<img style="width: 100%;" class="qb_logo" src="images/logo.jpg" alt="Ib qb 46 logo">
</div>
</div>
</div><h2>HL Paper 1</h2><div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">Show that the points (0, 0) and (\(\sqrt {2\pi } \) , \( - \sqrt {2\pi } \) ) on the curve \({{\text{e}}^{\left( {x + y} \right)}} = \cos \left( {xy} \right)\) have a</span> <span style="font-family: times new roman,times; font-size: medium;">common tangent.</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;">attempt at implicit differentiation <em><strong>M1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({{\text{e}}^{\left( {x + y} \right)}}\left( {1 + \frac{{{\text{d}}y}}{{{\text{d}}x}}} \right) = - \sin \left( {xy} \right)\left( {x\frac{{{\text{d}}y}}{{{\text{d}}x}} + y} \right)\) </span><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;">let \(x = 0\), \(y = 0\) <em><strong>M1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({{\text{e}}^0}\left( {1 + \frac{{{\text{d}}y}}{{{\text{d}}x}}} \right) = 0\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = - 1\)</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;">let \(x = \sqrt {2\pi } \) , \(y = - \sqrt {2\pi } \)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({{\text{e}}^0}\left( {1 + \frac{{{\text{d}}y}}{{{\text{d}}x}}} \right) = - \sin \left( {- 2\pi } \right)\left( {x\frac{{{\text{d}}y}}{{{\text{d}}x}} + y} \right) = 0\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">so \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = - 1\) </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;">since both points lie on the line \(y = - x\) this is a common tangent <em><strong>R1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> \(y = - x\) must be seen for the final <em><strong>R1</strong></em>. It is not sufficient to note that the gradients </span><span style="font-family: times new roman,times; font-size: medium;">are equal.</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;">[7 marks]</span></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;">Implicit differentiation was attempted by many candidates, some of whom obtained the correct value for the gradient of the tangent. However, very few noticed the need to go further and prove that both points were on the same line.</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;">Let \(f(x) = \sqrt {\frac{x}{{1 - x}}} ,{\text{ }}0 < x < 1\).</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 Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Show that \(f'(x) = \frac{1}{2}{x^{ - \frac{1}{2}}}{(1 - x)^{ - \frac{3}{2}}}\) and deduce that <em>f </em>is an increasing function.</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 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 the curve \(y = f(x)\) has one point of inflexion, and find its coordinates.</span></p>
<div class="marks">[6]</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;">Use the substitution \(x = {\sin ^2}\theta \) to show that \(\int {f(x){\text{d}}x} = \arcsin \sqrt x - \sqrt {x - {x^2}} + c\) .</span></p>
<p> </p>
<div class="marks">[11]</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: 11.0px Times;"><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: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">derivative of \(\frac{x}{{1 - x}}\) is \(\frac{{(1 - x) - x( - 1)}}{{{{(1 - x)}^2}}}\) <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;">\(f'(x) = \frac{1}{2}{\left( {\frac{x}{{1 - x}}} \right)^{ - \frac{1}{2}}}\frac{1}{{{{(1 - x)}^2}}}\) <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;">\( = \frac{1}{2}{x^{ - \frac{1}{2}}}{(1 - x)^{ - \frac{3}{2}}}\) <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;">\(f'(x) > 0\) (for all \(0 < x < 1\)) so the function is increasing <strong><em>R1</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><em><strong>OR<br></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;">\(f(x) = \frac{{{x^{\frac{1}{2}}}}}{{{{(1 - x)}^{\frac{1}{2}}}}}\)</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;">\(f'(x) = \frac{{{{(1 - x)}^{\frac{1}{2}}}\left( {\frac{1}{2}{x^{ - \frac{1}{2}}}} \right) - \frac{1}{2}{x^{\frac{1}{2}}}{{(1 - x)}^{ - \frac{1}{2}}}( - 1)}}{{1 - x}}\) <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;">\( = \frac{1}{2}{x^{ - \frac{1}{2}}}{(1 - x)^{ - \frac{1}{2}}} + \frac{1}{2}{x^{\frac{1}{2}}}{(1 - x)^{ - \frac{3}{2}}}\) <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;">\( = \frac{1}{2}{x^{ - \frac{1}{2}}}{(1 - x)^{ - \frac{3}{2}}}[1 - x + x]\) <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;">\( = \frac{1}{2}{x^{ - \frac{1}{2}}}{(1 - x)^{ - \frac{3}{2}}}\) <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;">\(f'(x) > 0\) (for all \(0 < x < 1\)) so the function is increasing <strong><em>R1</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>[5 marks]</em></strong></span></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;">\(f'(x) = \frac{1}{2}{x^{ - \frac{1}{2}}}{(1 - x)^{ - \frac{3}{2}}}\)</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow f''(x) = -\frac{1}{4}{x^{ - \frac{3}{2}}}{(1 - x)^{ - \frac{3}{2}}} + \frac{3}{4}{x^{ - \frac{1}{2}}}{(1 - x)^{ - \frac{5}{2}}}\) <strong><em>M1A1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\( = -\frac{1}{4}{x^{ - \frac{3}{2}}}{(1 - x)^{ - \frac{5}{2}}}[1 - 4x]\)</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(f''(x) = 0 \Rightarrow x = \frac{1}{4}\) <strong><em>M1A1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(f''(x)\) changes sign at \(x = \frac{1}{4}\) hence there is a point of inflexion <strong><em>R1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(x = \frac{1}{4} \Rightarrow y = \frac{1}{{\sqrt 3 }}\) <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;">the coordinates are \(\left( {\frac{1}{4},\frac{1}{{\sqrt 3 }}} \right)\)</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;"><strong><em>[6 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;">\(x = {\sin ^2}\theta \Rightarrow \frac{{{\text{d}}x}}{{{\text{d}}\theta }} = 2\sin \theta \cos \theta \) <strong><em>M1A1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {\sqrt {\frac{x}{{1 - x}}} {\text{d}}x = \int {\sqrt {\frac{{{{\sin }^2}\theta }}{{1 - {{\sin }^2}\theta }}} 2\sin \theta \cos \theta {\text{d}}\theta } } \) <strong><em>M1A1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\( = \int {2{{\sin }^2}\theta {\text{d}}\theta } \) <strong><em>A1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\( = \int {1 - \cos 2\theta } {\text{d}}\theta \) <strong><em>M1A1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\( = \theta - \frac{1}{2}\sin 2\theta + c\) <strong><em>A1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(\theta = \arcsin \sqrt x \) <strong><em>A1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{1}{2}\sin 2\theta = \sin \theta \cos \theta = \sqrt x \sqrt {1 - x} = \sqrt {x - {x^2}} \) <strong><em>M1A1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">hence \(\int {\sqrt {\frac{x}{{1 - x}}} {\text{d}}x = \arcsin \sqrt x } - \sqrt {x - {x^2}} + c\) <strong><em>AG</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[11 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;">Part (a) was generally well done, although few candidates made the final deduction asked for. Those that lost other marks in this part were generally due to mistakes in algebraic manipulation. In part (b) whilst many students found the second derivative and set it equal to zero, few then confirmed that it was a point of inflexion. There were several good attempts for part (c), even though there were various points throughout the question that provided stopping points for other candidates.</span></p>
<p> </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;">Part (a) was generally well done, although few candidates made the final deduction asked for. Those that lost other marks in this part were generally due to mistakes in algebraic manipulation. In part (b) whilst many students found the second derivative and set it equal to zero, few then confirmed that it was a point of inflexion. There were several good attempts for part (c), even though there were various points throughout the question that provided stopping points for other candidates.</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;">Part (a) was generally well done, although few candidates made the final deduction asked for. Those that lost other marks in this part were generally due to mistakes in algebraic manipulation. In part (b) whilst many students found the second derivative and set it equal to zero, few then confirmed that it was a point of inflexion. There were several good attempts for part (c), even though there were various points throughout the question that provided stopping points for other candidates.</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: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The first set of axes below shows the graph of \(y = {\text{ }}f(x)\) for \( - 4 \leqslant x \leqslant 4\).</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><br><img src="images/Schermafbeelding_2014-09-11_om_12.03.04.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;"> </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;">Let \(g(x) = \int_{ - 4}^x {f(t){\text{d}}t} \) for \( - 4 \leqslant x \leqslant 4\).</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) State the value of <em>x </em>at which \(g(x)\) is a minimum.</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) On the second set of axes, sketch the graph of \(y = g(x)\).</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: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \(x = 1\) <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;"><strong><em>[1 mark]</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) <strong><em>A1 </em></strong>for point (–4, 0)</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;"><strong>A1</strong> for (0, − 4)</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>A1 </em></strong>for min at \(x = 1\) in approximately the correct place</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>A1</em></strong> for (4, 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;"><strong><em>A1 </em></strong>for shape including continuity at \(x = 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; min-height: 25.0px;"> <img style="font-family: 'times new roman', times; font-size: medium; background-color: #f7f7f7;" src="images/maths_6_markscheme.png" alt></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 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 [6 marks]</em></strong></span></p>
<div><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></div>
</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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The function <em>f</em> is defined by \(f(x) = {{\text{e}}^{{x^2} - 2x - 1.5}}\).</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 \(f'(x)\).</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;">(b) You are given that \(y = \frac{{f(x)}}{{x - 1}}\) has a local minimum at <em>x</em> = <em>a</em>, <em>a</em> > 1. Find the</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;">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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \(\left( {u = {x^2} - 2x - 1.5;\frac{{{\text{d}}u}}{{{\text{d}}x}} = 2x - 2} \right)\)</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;">\(\frac{{{\text{d}}f}}{{{\text{d}}x}} = \frac{{{\text{d}}f}}{{{\text{d}}u}}\frac{{{\text{d}}u}}{{{\text{d}}x}} = {{\text{e}}^u}(2x - 2)\) <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;">\( = 2(x - 1){{\text{e}}^{{x^2} - 2x - 1.5}}\) <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;">(b) \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{(x - 1) \times 2(x - 1){{\text{e}}^{{x^2} - 2x - 1.5}} - 1 \times {{\text{e}}^{{x^2} - 2x - 1.5}}}}{{{{(x - 1)}^2}}}\) <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;">\( = \frac{{2{x^2} - 4x + 1}}{{{{(x - 1)}^2}}}{{\text{e}}^{{x^2} - 2x - 1.5}}\) <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;">minimum occurs when \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\) <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;">\(x = 1 \pm \sqrt {\frac{1}{2}} \,\,\,\,\,\left( {{\text{accept }}x = \frac{{4 \pm \sqrt 8 }}{4}} \right)\) <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;">\(a = 1 + \sqrt {\frac{1}{2}} \,\,\,\,\,\left( {{\text{accept }}a = \frac{{4 + \sqrt 8 }}{4}} \right)\) <strong><em>R1</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: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was successfully answered by most candidates. Most candidates were able to make significant progress with part (b) but were then let down by being unable to simplify the expression or by not understanding the significance of being told that <em>a</em> > 1.</span></p>
</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="specification">
<p>Consider the functions \(f,\,\,g,\) defined for \(x \in \mathbb{R}\), given by \(f\left( x \right) = {{\text{e}}^{ - x}}\,{\text{sin}}\,x\) and \(g\left( x \right) = {{\text{e}}^{ - x}}\,{\text{cos}}\,x\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find \(f'\left( x \right)\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find \(g'\left( x \right)\).</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>Hence, or otherwise, find \(\int\limits_0^\pi {{{\text{e}}^{ - x}}\,{\text{sin}}\,x\,{\text{d}}x} \).</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>attempt at product rule <em><strong>M1</strong></em></p>
<p>\(f'\left( x \right) = - {{\text{e}}^{ - x}}\,{\text{sin}}\,x + {{\text{e}}^{ - x}}\,{\text{cos}}\,x\) <em><strong> A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(g'\left( x \right) = - {{\text{e}}^{ - x}}\,{\text{cos}}\,x - {{\text{e}}^{ - x}}\,{\text{sin}}\,x\) <em><strong> A1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>Attempt to add \(f'\left( x \right)\) and \(g'\left( x \right)\) <em><strong>(M1)</strong></em></p>
<p>\(f'\left( x \right) + g'\left( x \right) = - 2{{\text{e}}^{ - x}}\,{\text{sin}}\,x\) <em><strong>A1</strong></em></p>
<p>\(\int\limits_0^\pi {{{\text{e}}^{ - x}}\,{\text{sin}}\,x\,{\text{d}}x} = \left[ { - \frac{{{{\text{e}}^{ - x}}}}{2}\left( {{\text{sin}}\,x + {\text{cos}}\,x} \right)} \right]_0^\pi \) (or equivalent) <em><strong>A1</strong></em></p>
<p><strong>Note</strong>: Condone absence of limits.</p>
<p>\( = \frac{1}{2}\left( {1 + {{\text{e}}^{ - \pi }}} \right)\) <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>\(I = \int {{{\text{e}}^{ - x}}} \,{\text{sin}}\,x\,{\text{d}}x\)</p>
<p>\( = - {{\text{e}}^{ - x}}\,{\text{cos}}\,x - \int {{{\text{e}}^{ - x}}} \,{\text{cos}}\,x\,{\text{d}}x\) <strong>OR </strong>\( = - {{\text{e}}^{ - x}}\,{\text{sin}}\,x + \int {{{\text{e}}^{ - x}}} \,{\text{cos}}\,x\,{\text{d}}x\) <em><strong>M1A1</strong></em></p>
<p>\( = - {{\text{e}}^{ - x}}\,{\text{sin}}\,x - {{\text{e}}^{ - x}}\,{\text{cos}}\,x - \int {{{\text{e}}^{ - x}}} \,{\text{sin}}\,x\,{\text{d}}x\)</p>
<p>\(I = \frac{1}{2}{{\text{e}}^{ - x}}\left( {{\text{sin}}\,x + {\text{cos}}\,x} \right)\) <em><strong>A1</strong></em></p>
<p>\(\int_0^\pi {{{\text{e}}^{ - x}}\,{\text{sin}}\,x\,{\text{d}}x = \frac{1}{2}\left( {1 + {{\text{e}}^{ - \pi }}} \right)} \) <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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<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 drinking glass is modelled by rotating the graph of \(y = {{\text{e}}^x}\) about the <em>y</em>-axis, for \(1 \leqslant y \leqslant 5\) . Find the volume of the glass.</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;">\(y = {{\text{e}}^x} \Rightarrow x = \ln y\)</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;">volume \( = \pi \int_1^5 {{{(\ln y)}^2}{\text{d}}y} \) <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;">using integration by parts <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;">\(\pi \int_1^5 {{{(\ln y)}^2}{\text{d}}y} = \pi \left[ {y{{(\ln y)}^2}} \right]_1^5 - 2\int_1^5 {\ln y{\text{d}}y} \) <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;">\( = \pi \left[ {y{{(\ln y)}^2} - 2y\ln y + 2y} \right]_1^5\) <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;"><strong>Note:</strong> Award <strong><em>A1</em></strong> marks if \(\pi \) is present in at least one of the above lines.</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;">\( \Rightarrow \pi \int_1^5 {{{(\ln y)}^2}{\text{d}}y} = \pi {\text{ }}5{(\ln 5)^2} - 10\ln 5 + 8\) <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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Only the best candidates were able to make significant progress with this question. Quite a few did not consider rotation about the <em>y</em>-axis. Others wrote the correct expression, but seemed daunted by needing to integrate by parts twice.</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">A curve is defined by \(xy = {y^2} + 4\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that there is no point where the tangent to the curve is horizontal.</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 the coordinates of the points where the tangent to the curve is vertical.</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 class="p1">\(x\frac{{{\text{d}}y}}{{{\text{d}}x}} + y = 2y\frac{{{\text{d}}y}}{{{\text{d}}x}}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p1">a horizontal tangent occurs if \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\) <span class="s1">so </span>\(y = 0\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p2">we can see from the equation of the curve that this solution is not possible <span class="s2">\((0 = 4)\) </span>and so there is not a horizontal tangent <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p2"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{y}{{2y - x}}\) or equivalent with \(\frac{{{\text{d}}x}}{{{\text{d}}y}}\)</p>
<p>the tangent is vertical when \(2y = x\) <strong><em>M1</em></strong></p>
<p>substitute into the equation to give \(2{y^2} = {y^2} + 4\) <strong><em>M1</em></strong></p>
<p>\(y = \pm 2\) <strong><em>A1</em></strong></p>
<p>coordinates are \((4,{\text{ }}2),{\text{ }}( - 4,{\text{ }} - 2)\) <strong><em>A1</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<p><strong><em>Total [8 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 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 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">Using integration by parts find \(\int {x\sin x{\text{d}}x} \).</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>attempt to integrate one factor and differentiate the other, leading to a sum of two terms <strong><em>M1</em></strong></p>
<p>\(\int {x\sin x{\text{d}}x = x( - \cos x) + } \int {\cos x{\text{d}}x} \) <strong><em>(A1)(A1)</em></strong></p>
<p>\( = - x\cos x + \sin x + c\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Only award final <strong><em>A1 </em></strong>if \( + {\text{ }}c\) is seen.</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p class="p1">By using the substitution \(u = {{\text{e}}^x} + 3\), find \(\int {\frac{{{{\text{e}}^x}}}{{{{\text{e}}^{2x}} + 6{{\text{e}}^x} + 13}}{\text{d}}x} \).</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p class="p1">\(\frac{{{\text{d}}u}}{{{\text{d}}x}} = {{\text{e}}^x}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p2"><strong>EITHER</strong></p>
<p class="p1"><span class="s1">integral is </span>\(\int {\frac{{{{\text{e}}^x}}}{{{{({{\text{e}}^x} + 3)}^2} + {2^2}}}{\text{d}}x} \) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p1">\( = \frac{1}{{{u^2} + {2^2}}}{\text{d}}u\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p3"> </p>
<p class="p2"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>M1 </em></strong>only if the integral has completely changed to one in \(u\).</p>
<p class="p3"> </p>
<p class="p2"><strong>Note: <span class="Apple-converted-space"> </span></strong>\({\text{d}}u\) needed for final <strong><em>A1</em></strong></p>
<p class="p3"> </p>
<p class="p2"><strong>OR</strong></p>
<p class="p1">\({{\text{e}}^x} = u - 3\)</p>
<p class="p1">integral is \(\int {\frac{1}{{{{(u - 3)}^2} + 6(u - 3) + 13}}{\text{d}}u} \) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p3"> </p>
<p class="p2"><strong>Note: </strong>Award <strong><em>M1 </em></strong>only if the integral has completely changed to one in \(u\).</p>
<p class="p4"> </p>
<p class="p1">\( = \int {\frac{1}{{{u^2} + {2^2}}}{\text{d}}u} \) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p3"> </p>
<p class="p2"><strong>Note: <span class="Apple-converted-space"> </span></strong>In both solutions the two method marks are independent.</p>
<p class="p3"> </p>
<p class="p2"><strong>THEN</strong></p>
<p class="p1">\( = \frac{1}{2}\arctan \left( {\frac{u}{2}} \right)( + c)\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p1">\( = \frac{1}{2}\arctan \left( {\frac{{{{\text{e}}^x} + 3}}{2}} \right)( + c)\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2"><strong><em>Total [7 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p class="p1">Many good complete answers. Some did not realise it was arctan. Some had poor understanding of the method.</p>
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider the function defined by \(f(x) = {x^3} - 3{x^2} + 4\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Determine the values of \(x\) for which \(f(x)\) is a decreasing function.</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">There is a point of inflexion, \(P\)<span class="s1">, on the curve \(y = f(x)\)</span>.</p>
<p class="p1">Find the coordinates of \(P\)<span class="s1">.</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 class="p1">attempt to differentiate \(f(x) = {x^3} - 3{x^2} + 4\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p1">\(f'(x) = 3{x^2} - 6x\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1">\( = 3x(x - 2)\)</p>
<p class="p2">(Critical values occur at) <span class="s2">\(x = 0,{\text{ }}x = 2\) <span class="Apple-converted-space"> </span></span><span class="s3">(</span><strong><em>A1)</em></strong></p>
<p class="p1"><span class="s1">so </span>\(f\) decreasing on \(x \in ]0,{\text{ }}2[\;\;\;({\text{or }}0 < x < 2)\) <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">\(f''(x) = 6x - 6\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p1"><span class="s1">setting </span>\(f''(x) = 0\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p2">\( \Rightarrow x = 1\)</p>
<p class="p2">coordinate is \((1,{\text{ }}2)\) <span class="Apple-converted-space"> </span><span class="s2"><strong><em>A1</em></strong></span></p>
<p class="p2"><span class="s2"><strong><em>[3 marks]</em></strong></span></p>
<p class="p2"><span class="s2"><strong><em>Total [7 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>Show that \(\sin \left( {\theta + \frac{\pi }{2}} \right) = \cos \theta \).</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">Consider \(f(x) = \sin (ax)\) where \(a\) is a constant. Prove by mathematical induction that \({f^{(n)}}(x) = {a^n}\sin \left( {ax + \frac{{n\pi }}{2}} \right)\) where \(n \in {\mathbb{Z}^ + }\) and \({f^{(n)}}(x)\) represents the \({{\text{n}}^{{\text{th}}}}\) derivative of \(f(x)\).</p>
<div class="marks">[7]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(\sin \left( {\theta + \frac{\pi }{2}} \right) = \sin \theta \cos \frac{\pi }{2} + \cos \theta \sin \frac{\pi }{2}\) <strong><em>M1</em></strong></p>
<p>\( = \cos \theta \) <strong><em>AG</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Accept a transformation/graphical based approach.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">consider \(n = 1,{\text{ }}f'(x) = a\cos (ax)\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1"><span class="s1">since </span>\(\sin \left( {ax + \frac{\pi }{2}} \right) = \cos ax\) then the proposition is true for \(n = 1\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">assume that the proposition is true for \(n = k\) so \({f^{(k)}}(x) = {a^k}\sin \left( {ax + \frac{{k\pi }}{2}} \right)\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">\({f^{(k + 1)}}(x) = \frac{{{\text{d}}\left( {{f^{(k)}}(x)} \right)}}{{{\text{d}}x}}\;\;\;\left( { = a\left( {{a^k}\cos \left( {ax + \frac{{k\pi }}{2}} \right)} \right)} \right)\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">\( = {a^{k + 1}}\sin \left( {ax + \frac{{k\pi }}{2} + \frac{\pi }{2}} \right)\) (using part (a)) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">\( = {a^{k + 1}}\sin \left( {ax + \frac{{(k + 1)\pi }}{2}} \right)\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">given that the proposition is true for \(n = k\) then we have shown that the proposition is true for \(n = k + 1\). Since we have shown that the proposition is true for \(n = 1\) then the proposition is true for all \(n \in {\mathbb{Z}^ + }\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award final <strong><em>R1 </em></strong>only if all prior <em><strong>M</strong></em> and <em><strong>R</strong></em> marks have been awarded.</p>
<p class="p3"><em><strong>[7 marks]</strong></em></p>
<p class="p3"><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" 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;">Find the value of the integral \(\int_0^{\sqrt 2 } {\sqrt {4 - {x^2}} {\text{d}}x} \) .</span></p>
<div class="marks">[7]</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;">Find the value of the integral \(\int_0^{0.5} {\arcsin x {\text{d}}x} \) .</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 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;">Using the substitution \(t = \tan \theta \) , find the value of the integral</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;">\[\int_0^{\frac{\pi }{4}} {\frac{{{\text{d}}\theta }}{{3{{\cos }^2}\theta + {{\sin }^2}\theta }}} {\text{ }}.\]</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: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">let \(x = 2\sin \theta \) <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;">\({\text{d}}x = 2\cos \theta {\text{d}}\theta \) <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;">\(I = \int_0^{\frac{\pi }{4}} {2\cos \theta \times 2\cos \theta {\text{d}}\theta \,\,\,\,\,\left( { = 4\int_0^{\frac{\pi }{4}} {{{\cos }^2}\theta {\text{d}}\theta } } \right)} \) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px 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 expression.</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;">\( = 2\int_0^{\frac{\pi }{4}} {(1 + \cos 2\theta ){\text{d}}\theta } \) </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: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 2\left[ {\theta + \frac{1}{2}\sin 2\theta } \right]_0^{\frac{\pi }{4}}\) <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;">\( = 1 + \frac{\pi }{2}\) <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>[7 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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(I = [x\arcsin x]_0^{0.5} - \int_0^{0.5} {x \times \frac{1}{{\sqrt {1 - {x^2}} }}{\text{d}}x} \) <strong><em>M1A1A1</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;">\( = [x\arcsin x]_0^{0.5} + \left[ {\sqrt {1 - {x^2}} } \right]_0^{0.5}\) <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;">\( = \frac{\pi }{{12}} + \frac{{\sqrt 3 }}{2} - 1\) <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;"><strong><em>[5 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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{d}}t = {\sec ^2}\theta {\text{d}}\theta {\text{ , }}\left[ {0,\frac{\pi }{4}} \right] \to [0,{\text{ 1]}}\) <strong><em>A1(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;">\(I = \int_0^1 {\frac{{\frac{{{\text{d}}t}}{{(1 + {t^2})}}}}{{\frac{3}{{(1 + {t^2})}} + \frac{{{t^2}}}{{(1 + {t^2})}}}}} \) <strong><em>M1(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;">\( = \int_0^1 {\frac{{{\text{d}}t}}{{3 + {t^2}}}} \) <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;">\( = \frac{1}{{\sqrt 3 }}\left[ {\arctan \left( {\frac{x}{{\sqrt 3 }}} \right)} \right]_0^1\) <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;">\( = \frac{\pi }{{6\sqrt 3 }}\) <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>[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;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The graph of the function \(f(x) = \frac{{x + 1}}{{{x^2} + 1}}\) is shown below.</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_2014-09-15_om_08.53.43.png" alt></span></p>
</div>
<div class="specification">
<p><span style="font-family: 'times new roman', times; font-size: medium;">The point (1, 1) is a point of inflexion. There are two other points of inflexion.</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;">Find \(f'(x)\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p 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 find the \(x\)-coordinates of the points where the gradient of the graph of \(f\) is zero.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">Find \(f''(x)\) expressing your answer in the form \(\frac{{p(x)}}{{{{({x^2} + 1)}^3}}}\), where \(p(x)\) is a polynomial of degree 3.</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 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 the \(x\)-coordinates of the other two points of inflexion.</span></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 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 style="background-color: #f7f7f7;">Find the area of the shaded region. Express your answer in the form \(\frac{\pi }{a} - \ln \sqrt b \), where </span>\(a\) <span style="background-color: #f7f7f7;">and </span>\(b\) <span style="background-color: #f7f7f7;">are integers.</span></span></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 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) \(f'(x) = \frac{{\left( {{x^2} + 1} \right) - 2x(x + 1)}}{{{{\left( {{x^2} + 1} \right)}^2}}}{\text{ }}\left( { = \frac{{ - {x^2} - 2x + 1}}{{{{\left( {{x^2} + 1} \right)}^2}}}} \right)\) <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;"><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;">\(\frac{{ - {x^2} - 2x + 1}}{{{{\left( {{x^2} + 1} \right)}^2}}} = 0\)</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;">\(x = - 1 \pm \sqrt 2 \) <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>[1 mark]</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;">\(f''(x) = \frac{{( - 2x - 2){{\left( {{x^2} + 1} \right)}^2} - 2(2x)\left( {{x^2} + 1} \right)\left( { - {x^2} - 2x + 1} \right)}}{{{{\left( {{x^2} + 1} \right)}^4}}}\) <strong><em>A1A1</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>A1 </em></strong>for \(( - 2x - 2){\left( {{x^2} + 1} \right)^2}\) or equivalent.</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 \( - 2(2x)\left( {{x^2} + 1} \right)\left( { - {x^2} - 2x + 1} \right)\) or equivalent.</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;">\( = \frac{{( - 2x - 2)\left( {{x^2} + 1} \right) - 4x\left( { - {x^2} - 2x + 1} \right)}}{{{{\left( {{x^2} + 1} \right)}^3}}}\)</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;">\( = \frac{{2{x^3} + 6{x^2} - 6x - 2}}{{{{\left( {{x^2} + 1} \right)}^3}}}\) <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;">\(\left( { = \frac{{2\left( {{x^3} + 3{x^2} - 3x - 1} \right)}}{{{{\left( {{x^2} + 1} \right)}^3}}}} \right)\)</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;"><strong><em>[3 marks]</em></strong></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;">recognition that \((x - 1)\) is a factor <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;">\((x - 1)\left( {{x^2} + bx + c} \right) = \left( {{x^3} + 3{x^2} - 3x - 1} \right)\) <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;">\( \Rightarrow {x^2} + 4x + 1 = 0\) <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;">\(x = - 2 \pm \sqrt 3 \) <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> Allow long division / synthetic division.</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">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<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;">\(\int_{ - 1}^0 {\frac{{x + 1}}{{{x^2} + 1}}{\text{d}}x} \) <strong><em>M1</em></strong></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;">\(\int {\frac{{x + 1}}{{{x^2} + 1}}{\text{d}}x = \int {\frac{x}{{{x^2} + 1}}{\text{d}}x + \int {\frac{1}{{{x^2} + 1}}{\text{d}}x} } } \) <strong><em>M1</em></strong></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;">\( = \frac{1}{2}\ln \left( {{x^2} + 1} \right) + \arctan (x)\) <strong><em>A1A1</em></strong></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;">\( = \left[ {\frac{1}{2}\ln \left( {{x^2} + 1} \right) + \arctan (x)} \right]_{ - 1}^0 = \frac{1}{2}\ln 1 + \arctan 0 - \frac{1}{2}\ln 2 - \arctan ( - 1)\) <strong><em>M1</em></strong></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;">\( = \frac{\pi }{4} - \ln \sqrt 2 \) <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>[6 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;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p 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 complex number \(z = \cos \theta + {\text{i}}\sin \theta \).</span></p>
</div>
<div class="specification">
<p><span style="font-family: 'times new roman', times; font-size: medium;">The region <em>S</em> is bounded by the curve \(y = \sin x{\cos ^2}x\) and the <em>x</em>-axis between \(x = 0\) and \(x = \frac{\pi }{2}\).</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: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Use De Moivre’s theorem to show that \({z^n} + {z^{ - n}} = 2\cos n\theta ,{\text{ }}n \in {\mathbb{Z}^ + }\).</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: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Expand \({\left( {z + {z^{ - 1}}} \right)^4}\).</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 Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Hence show that \({\cos ^4}\theta = p\cos 4\theta + q\cos 2\theta + r\), where \(p,{\text{ }}q\) and \(r\) are constants to </span><span style="font-family: 'times new roman', times; font-size: medium;">be determined.</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><span style="font-family: 'times new roman', times; font-size: medium;">Show that \({\cos ^6}\theta = \frac{1}{{32}}\cos 6\theta + \frac{3}{{16}}\cos 4\theta + \frac{{15}}{{32}}\cos 2\theta + \frac{5}{{16}}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p 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 find the value of \(\int_0^{\frac{\pi }{2}} {{{\cos }^6}\theta {\text{d}}\theta } \).</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: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em>S</em> is rotated through \(2\pi \) radians about the <em>x</em>-axis. Find the value of the volume generated.</span></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><span style="font-family: 'times new roman', times; font-size: medium;">(i) Write down an expression for the constant term in the expansion of \({\left( {z + {z^{ - 1}}} \right)^{2k}}\), \(k \in {\mathbb{Z}^ + }\).</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 an expression for \(\int_0^{\frac{\pi }{2}} {{{\cos }^{2k}}\theta {\text{d}}\theta } \) in terms of <em>k</em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({z^n} + {z^{ - n}} = \cos n\theta + i\sin n\theta + \cos ( - n\theta ) + i\sin ( - n\theta )\) <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;">\( = \cos n\theta + \cos n\theta + i\sin n\theta - i\sin n\theta \) <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;">\( = 2\cos n\theta \) <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><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;">(b) \({\left( {z + {z^{ - 1}}} \right)^4} = {z^4} + 4{z^3}\left( {\frac{1}{z}} \right) + 6{z^2}\left( {\frac{1}{{{z^2}}}} \right) + 4z\left( {\frac{1}{{{z^3}}}} \right) + \frac{1}{{{z^4}}}\) <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> Accept \({\left( {z + {z^{ - 1}}} \right)^4} = 16{\cos ^4}\theta \).</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;"><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;">\({\left( {z + {z^{ - 1}}} \right)^4} = \left( {{z^4} + \frac{1}{{{z^4}}}} \right) + 4\left( {{z^2} + \frac{1}{{{z^2}}}} \right) + 6\) <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;">\({(2\cos \theta )^4} = 2\cos 4\theta + 8\cos 2\theta + 6\) <strong><em>A1A1</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>A1 </em></strong>for RHS, <strong><em>A1 </em></strong>for LHS, 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'; 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;">\({\cos ^4}\theta = \frac{1}{8}\cos 4\theta + \frac{1}{2}\cos 2\theta + \frac{3}{8}\) <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;">\(\left( {{\text{or }}p = \frac{1}{8},{\text{ }}q = \frac{1}{2},{\text{ }}r = \frac{3}{8}} \right)\)</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;"><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;">\({\cos ^4}\theta = {\left( {\frac{{\cos 2\theta + 1}}{2}} \right)^2}\) <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;">\( = \frac{1}{4}({\cos ^2}2\theta + 2\cos 2\theta + 1)\) <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;">\( = \frac{1}{4}\left( {\frac{{\cos 4\theta + 1}}{2} + 2\cos 2\theta + 1} \right)\) <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;">\({\cos ^4}\theta = \frac{1}{8}\cos 4\theta + \frac{1}{2}\cos 2\theta + \frac{3}{8}\) <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;">\(\left( {{\text{or }}p = \frac{1}{8},{\text{ }}q = \frac{1}{2},{\text{ }}r = \frac{3}{8}} \right)\)</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;"><strong><em>[4 marks]</em></strong></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;">\({\left( {z + {z^{ - 1}}} \right)^6} = {z^6} + 6{z^5}\left( {\frac{1}{z}} \right) + 15{z^4}\left( {\frac{1}{{{z^2}}}} \right) + 20{z^3}\left( {\frac{1}{{{z^3}}}} \right) + 15{z^2}\left( {\frac{1}{{{z^4}}}} \right) + 6z\left( {\frac{1}{{{z^5}}}} \right) + \frac{1}{{{z^6}}}\) <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;">\({\left( {z + {z^{ - 1}}} \right)^6} = \left( {{z^6} + \frac{1}{{{z^6}}}} \right) + 6\left( {{z^4} + \frac{1}{{{z^4}}}} \right) + 15\left( {{z^2} + \frac{1}{{{z^2}}}} \right) + 20\)</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;">\({(2\cos \theta )^6} = 2\cos 6\theta + 12\cos 4\theta + 30\cos 2\theta + 20\) <strong><em>A1A1</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>A1 </em></strong>for RHS, <strong><em>A1 </em></strong>for LHS, 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'; 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;">\({\cos ^6}\theta = \frac{1}{{32}}\cos 6\theta + \frac{3}{{16}}\cos 4\theta + \frac{{15}}{{32}}\cos 2\theta + \frac{5}{{16}}\) <strong><em>AG</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 a purely trigonometric solution as for (c).</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">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;">\(\int_0^{\frac{\pi }{2}} {{{\cos }^6}\theta {\text{d}}\theta = \int_0^{\frac{\pi }{2}} {\left( {\frac{1}{{32}}\cos 6\theta + \frac{3}{{16}}\cos 4\theta + \frac{{15}}{{32}}\cos 2\theta + \frac{5}{{16}}} \right){\text{d}}\theta } } \)</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;">\( = \left[ {\frac{1}{{192}}\sin 6\theta + \frac{3}{{64}}\sin 4\theta + \frac{{15}}{{64}}\sin 2\theta + \frac{5}{{16}}\theta } \right]_0^{\frac{\pi }{2}}\) <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;">\( = \frac{{5\pi }}{{32}}\) <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">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{V}} = \pi \int_0^{\frac{\pi }{2}} {{{\sin }^2}x{{\cos }^4}x{\text{d}}x} \) <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;">\( = \pi \int_0^{\frac{\pi }{2}} {{{\cos }^4}x{\text{d}}x - \pi \int_0^{\frac{\pi }{2}} {{{\cos }^6}x{\text{d}}x} } \) <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;">\(\int_0^{\frac{\pi }{2}} {{{\cos }^4}x{\text{d}}x} = \frac{{3\pi }}{{16}}\) <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;">\({\text{V}} = \frac{{3{\pi ^2}}}{{16}} - \frac{{5{\pi ^2}}}{{32}} = \frac{{{\pi ^2}}}{{32}}\) <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> Follow through from an incorrect <em>r</em> in (c) provided the final answer is positive.</span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">(i) constant term = \(\left( \begin{array}{c}2k\\k\end{array} \right)\) \( = \frac{{(2k)!}}{{k!k!}} = \frac{{(2k)!}}{{{{(k!)}^2}}}{\text{ (accept }}C_k^{2k})\) <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) \({2^{2k}}\int_0^{\frac{\pi }{2}} {{{\cos }^{2k}}\theta {\text{d}}\theta = \frac{{(2k)!\pi }}{{{{(k!)}^2}}}\frac{\pi }{2}} \) <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;"> \(\int_0^{\frac{\pi }{2}} {{{\cos }^{2k}}\theta {\text{d}}\theta = \frac{{(2k)!\pi }}{{{2^{2k + 1}}{{(k!)}^2}}}} \) \(\left( {{\rm{or}}\frac{{\left( \begin{array}{c}2k\\k\end{array} \right)\pi }}{{{2^{2k + 1}}}}} \right)\) <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">g.</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) has appeared several times before, though with it again being a ‘show that’ question, some candidates still need to be more aware of the need to show every step in their working, including the result that \(\sin ( - n\theta ) = - \sin (n\theta )\).</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;">Part b) was usually answered correctly.</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;">Part c) was again often answered correctly, though some candidates often less successfully utilised a trig-only approach rather than taking note of part b).</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;">Part d) was a good source of marks for those who kept with the spirit of using complex numbers for this type of question. Some limited attempts at trig-only solutions were seen, and correct solutions using this approach were extremely rare.</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 well answered, though numerical slips were often common. A small number integrated \(\sin n\theta \) as \(n\cos n\theta \).</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;">A large number of candidates did not realise the help that part e) inevitably provided for part f). Some correctly expressed the volume as \(\pi \int {{{\cos }^4}x{\text{d}}x - \pi \int {{{\cos }^6}x{\text{d}}x} } \) and thus gained the first 2 marks but were able to progress no further. Only a small number of able candidates were able to obtain the correct answer of \(\frac{{{\pi ^2}}}{{32}}\).</span></p>
<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;">
<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 g) proved to be a challenge for the vast majority, though it was pleasing to see some of the highest scoring candidates gain all 3 marks.</span></p>
<div class="question_part_label">g.</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;">The graphs of \(f(x) = - {x^2} + 2\) and \(g(x) = {x^3} - {x^2} - bx + 2,{\text{ }}b > 0\), intersect and create two closed regions. Show that these two regions have equal areas.</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 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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">to find the points of intersection of the two curves</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;">\( - {x^2} + 2 = {x^3} - {x^2} - bx + 2\) <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;">\({x^3} - bx = x({x^2} - b) = 0\)</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;">\( \Rightarrow x = 0;{\text{ }}x = \pm \sqrt b \) <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;">\({A_1} = \int_{ - \sqrt b }^0 {\left[ {({x^3} - {x^2} - bx + 2) - ( - {x^2} + 2)} \right]} {\text{d}}x\left( { = \int_{ - \sqrt b }^0 {({x^3} - bx){\text{d}}x} } \right)\) <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;">\( = \left[ {\frac{{{x^4}}}{4} - \frac{{b{x^2}}}{2}} \right]_{ - \sqrt b }^0\)</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;">\( = - \left( {\frac{{{{( - \sqrt b )}^4}}}{4} - \frac{{b{{( - \sqrt b )}^2}}}{2}} \right) = - \frac{{{b^2}}}{4} + \frac{{{b^2}}}{2} = \frac{{{b^2}}}{4}\) <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;">\({A_2} = \int_0^{\sqrt b } {\left[ {( - {x^2} + 2) - ({x^3} - {x^2} - bx + 2)} \right]{\text{d}}x} \) <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;">\( = \int_0^{\sqrt b } {( - {x^3} + bx){\text{d}}x} \)</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;">\( = \left[ { - \frac{{{x^4}}}{4} + \frac{{b{x^2}}}{2}} \right]_0^{\sqrt b } = \frac{{{b^2}}}{4}\) <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;">therefore \({A_1} = {A_2} = \frac{{{b^2}}}{4}\) <strong><em>AG</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>
<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;">Most candidates knew how to tackle this question. The most common error was in giving +<em>b</em> and –<em>b</em> as the <em>x</em>-coordinates of the point of intersection.</span></p>
</div>
<br><hr><br><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;">Consider the part of the curve \(4{x^2} + {y^2} = 4\) shown in the diagram below.</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="font: normal normal normal 25px/normal Helvetica; text-align: center; margin: 0px;"><img src="data:image/png;base64,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" alt></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;">(a) Find an expression for \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) in terms of <em>x</em> and <em>y</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;">(b) Find the gradient of the tangent at the point \(\left( {\frac{2}{{\sqrt 5 }},\frac{2}{{\sqrt 5 }}} \right)\).</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;">(c) A bowl is formed by rotating this curve through \(2\pi \) radians about the <em>x</em>-axis.</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;">Calculate the volume of this bowl.</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) \(8x + 2y\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\) <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;"><strong>Note:</strong> Award <strong><em>M1A0</em></strong> for \(8x + 2y\frac{{{\text{d}}y}}{{{\text{d}}x}} = 4\) .</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;"> </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;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = - \frac{{4x}}{y}\) <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> </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;">(b) – 4 <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;"> </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;">(c) \(V = \int {\pi {y^2}{\text{d}}x} \) or equivalent <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;">\(V = \pi \int_0^1 {(4 - 4{x^2}){\text{d}}x} \) <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;">\( = \pi \left[ {4x - \frac{4}{3}{x^3}} \right]_0^1\) <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;">\( = \frac{{8\pi }}{3}\) <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> If it is correct except for the omission of \(\pi \) , award 2 marks.</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>
<h2 style="margin-top: 1em">Examiners report</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;">The first part of this question was done well by many, the only concern being the number that did not simplify the result from \( - \frac{{8x}}{{2y}}\). There were many variations on the formula for the volume in part c), the most common error being a multiple of \(2\pi \) rather than \(\pi \). On the whole this question was done well by many.</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 curve C with equation \(y = f(x)\) satisfies the differential equation</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;">\[\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{y}{{\ln y}}(x + 2),{\text{ }}y > 1,\]</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;">and <em>y</em> = e when <em>x</em> = 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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the equation of the tangent to C at the point (2, e).</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;">Find \(f(x)\).</span></p>
<div class="marks">[11]</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: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Determine the largest possible domain of <em>f</em>.</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: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Show that the equation \(f(x) = f'(x)\) has no solution.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{\text{e}}}{{\ln {\text{e}}}}(2 + 2) = 4{\text{e}}\) <strong><em>A1</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;">at (2, e) the tangent line is \(y - {\text{e}} = 4{\text{e}}(x - 2)\) <strong><em>M1</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;">hence \(y = 4{\text{e}}x - 7{\text{e}}\) <strong><em>A1</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>[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: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{y}{{\ln y}}(x + 2) \Rightarrow \frac{{\ln y}}{y}{\text{d}}y = (x + 2){\text{d}}x\) <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;">\(\int {\frac{{\ln y}}{y}{\text{d}}y = \int {(x + 2){\text{d}}x} } \)</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;">using substitution \(u = \ln y;{\text{ d}}u = \frac{1}{y}{\text{d}}y\) <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;">\( \Rightarrow \int {\frac{{\ln y}}{y}{\text{d}}y = \int {u{\text{d}}u = \frac{1}{2}{u^2}} } \) <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;">\( \Rightarrow \frac{{{{(\ln y)}^2}}}{2} = \frac{{{x^2}}}{2} + 2x + c\) <strong><em>A1A1</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;">at (2, e), \(\frac{{{{(\ln {\text{e}})}^2}}}{2} = 6 + c\) <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;">\( \Rightarrow c = - \frac{{11}}{2}\) <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;">\( \Rightarrow \frac{{{{(\ln y)}^2}}}{2} = \frac{{{x^2}}}{2} + 2x - \frac{{11}}{2} \Rightarrow {(\ln y)^2} = {x^2} + 4x - 11\)</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;">\(\ln y = \pm \sqrt {{x^2} + 4x - 11} \Rightarrow y = {{\text{e}}^{ \pm \sqrt {{x^2} + 4x - 11} }}\) <strong><em>M1A1</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;">since y > 1, \(f(x) = {{\text{e}}^{\sqrt {{x^2} + 4x - 11} }}\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px 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>M1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for attempt to make </span><em style="font-family: 'times new roman', times; font-size: medium;">y</em><span style="font-family: 'times new roman', times; font-size: medium;"> the subject.</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;"><em><strong><span style="font-family: 'times new roman', times; font-size: medium;">[11 marks]</span></strong></em></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: 25.0px 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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x^2} + 4x - 11 > 0\) <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;">using the quadratic formula <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;">critical values are \(\frac{{ - 4 \pm \sqrt {60} }}{2}{\text{ }}\left( { = - 2 \pm \sqrt {15} } \right)\) <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;">using a sign diagram or algebraic solution <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;">\(x < - 2 - \sqrt {15} ;{\text{ }}x > - 2 + \sqrt {15} \) <strong><em>A1A1</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>OR</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;">\({x^2} + 4x - 11 > 0\) <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;">by methods of completing the square <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;">\({(x + 2)^2} > 15\) <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;">\( \Rightarrow x + 2 < - \sqrt {15} {\text{ or }}x + 2 > \sqrt {15} \) <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;">\(x < - 2 - \sqrt {15} ;{\text{ }}x > - 2 + \sqrt {15} \) <strong><em>A1A1</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>[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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(x) = f'(x) \Rightarrow f(x) = \frac{{f(x)}}{{\ln f(x)}}(x + 2)\) <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;">\( \Rightarrow \ln \left( {f(x)} \right) = x + 2\,\,\,\,\,\left( { \Rightarrow x + 2 = \sqrt {{x^2} + 4x - 11} } \right)\) <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;">\( \Rightarrow {(x + 2)^2} = {x^2} + 4x - 11 \Rightarrow {x^2} + 4x + 4 = {x^2} + 4x - 11\) <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;">\( \Rightarrow 4 = - 11,{\text{ hence }}f(x) \ne f'(x)\) <strong><em>R1AG</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>[4 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;">
<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;">Nearly always correctly answered.</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;">Most candidates separated the variables and attempted the integrals. Very few candidates made use of the condition <em>y</em> > 1, so losing 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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (c) was often well answered, sometimes with follow through.</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;">Only the best candidates were successful on part (d).</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<address>Find the area enclosed by the curve \(y = \arctan x\) , the x-axis and the line \(x = \sqrt 3 \) .</address>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><strong><span style="font-family: times new roman,times; font-size: medium;">METHOD 1</span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({\text{area}} = \mathop \smallint \limits_0^{\sqrt 3 } \arctan x{\text{d}}x\) </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;">attempting to integrate by parts <em><strong>M1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\( = \left[ {x\arctan x} \right]_0^{\sqrt 3 } - \mathop \smallint \limits_0^{\sqrt 3 } x\frac{1}{{1 + {x^2}}}{\text{d}}x\) </span><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;">\( = \left[ {x\arctan x} \right]_0^{\sqrt 3 } - \left[ {\frac{1}{2}\ln \left( {1 + {x^2}} \right)} \right]_0^{\sqrt 3 }\) </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;"><strong>Note:</strong> Award A1 even if limits are absent.</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;">\( = \frac{\pi }{{\sqrt 3 }} - \frac{1}{2}\ln 4\) </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;">\(\left( { = \frac{{\pi \sqrt 3 }}{3} - \ln 2} \right)\)</span></p>
<p><strong><span style="font-family: times new roman,times; font-size: medium;">METHOD 2</span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({\text{area}} = \frac{{\pi \sqrt 3 }}{3} - \mathop \smallint \limits_0^{\frac{\pi }{3}} \tan y{\text{d}}y\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">M1A1A1</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\ { = \frac{{\pi \sqrt 3 }}{3} + \left[ {\ln \left| {\cos y} \right|} \right]_0^{\frac{\pi }{3}}} \)</span> <em><strong><span style="font-family: times new roman,times; font-size: medium;">M1A1</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\( = \frac{{\pi \sqrt 3 }}{3} + \ln \frac{1}{2}\) \(\left( { = \frac{{\pi \sqrt 3 }}{3} - \ln 2} \right)\) <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>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates were able to write down the correct expression for the required area, although in some cases with incorrect integration limits. However, very few managed to achieve any further marks due to a number of misconceptions, in particular \(\arctan x = \cot x = \frac{{\cos x}}{{\sin x}}\). Candidates who realised they should use integration by parts were in general very successful in answering this question. It was pleasing to see a few alternative correct approaches to this question.</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">A curve has equation \(3x - 2{y^2}{{\text{e}}^{x - 1}} = 2\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">Find an expression for \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) </span>in terms of \(x\) and \(y\).</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 class="p1">Find the equations of the tangents to this curve at the points where the curve intersects <span class="s1">the line \(x = 1\).</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 class="p1">attempt to differentiate implicitly <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\(3 - \left( {4y\frac{{{\text{d}}y}}{{{\text{d}}x}} + 2{y^2}} \right){{\text{e}}^{x - 1}} = 0\) </span><span class="s1"><strong><em>A1A1A1</em></strong></span></p>
<p class="p3"> </p>
<p class="p4"><span class="s1"><strong>Note: </strong>Award <strong><em>A1 </em></strong></span>for correctly differentiating each term.</p>
<p class="p5"> </p>
<p class="p2"><span class="Apple-converted-space">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{3 \bullet {{\text{e}}^{1 - x}} - 2{y^2}}}{{4y}}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p3"> </p>
<p class="p1"><strong>Note: </strong>This final answer may be expressed in a number of different ways.</p>
<p class="p3"> </p>
<p class="p1"><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(3 - 2{y^2} = 2 \Rightarrow {y^2} = \frac{1}{2} \Rightarrow y = \pm \sqrt {\frac{1}{2}} \) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{3 - 2 \bullet \frac{1}{2}}}{{ \pm 4\sqrt {\frac{1}{2}} }} = \pm \frac{{\sqrt 2 }}{2}\) </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p1"><span class="s1">at \(\left( {1,{\text{ }}\sqrt {\frac{1}{2}} } \right)\)</span> the tangent is \(y - \sqrt {\frac{1}{2}} = \frac{{\sqrt 2 }}{2}(x - 1)\) <span class="s1">and <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></span></p>
<p class="p1"><span class="s1">at \(\left( {1,{\text{ }} - \sqrt {\frac{1}{2}} } \right)\)</span> the tangent is \(y + \sqrt {\frac{1}{2}} = - \frac{{\sqrt 2 }}{2}(x - 1)\) <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: </strong>These equations simplify to \(y = \pm \frac{{\sqrt 2 }}{2}x\)<span class="s2">.</span></p>
<p class="p4"> </p>
<p class="p3"><strong>Note: </strong>Award <strong><em>A0M1A1A0 </em></strong>if just the positive value of \(y\) is considered and just one tangent is found.</p>
<p class="p2"> </p>
<p class="p3"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</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;">A curve has equation \(\arctan {x^2} + \arctan {y^2} = \frac{\pi }{4}\).</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 \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) in terms of <em>x </em>and <em>y</em>.</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 the gradient of the curve at the point where \(x = \frac{1}{{\sqrt 2 }}\) and \(y < 0\).</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) <strong>METHOD 1</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;">\(\frac{{2x}}{{1 + {x^4}}} + \frac{{2y}}{{1 + {y^4}}}\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\) <strong><em>M1A1A1</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;"><strong><em> </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;"><strong>Note:</strong> Award </span><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>M1 </em></strong>for implicit differentiation, <strong><em>A1 </em></strong>for LHS and <strong><em>A1 </em></strong>for RHS.</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;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = - \frac{{x\left( {1 + {y^4}} \right)}}{{y\left( {1 + {x^4}} \right)}}\) <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;"><strong>METHOD 2</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;">\({y^2} = \tan \left( {\frac{\pi }{4} - \arctan {x^2}} \right)\)</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;">\( = \frac{{\tan \frac{\pi }{4} - \tan \left( {\arctan {x^2}} \right)}}{{1 + \left( {\tan \frac{\pi }{4}} \right)\left( {\tan \left( {\arctan {x^2}} \right)} \right)}}\) <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;">\( = \frac{{1 - {x^2}}}{{1 + {x^2}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(2y\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{ - 2x\left( {1 + {x^2}} \right) - 2x\left( {1 - {x^2}} \right)}}{{{{\left( {1 + {x^2}} \right)}^2}}}\) <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;">\(2y\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{ - 4x}}{{{{\left( {1 + {x^2}} \right)}^2}}}\)</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;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = - \frac{{2x}}{{y{{\left( {1 + {x^2}} \right)}^2}}}\) <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;">\(\left( { = \frac{{2x\sqrt {1 + {x^2}} }}{{\sqrt {1 - {x^2}} {{\left( {1 + {x^2}} \right)}^2}}}} \right)\)</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;"><strong><em>[4 marks]</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> </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) \({y^2} = \tan \left( {\frac{\pi }{4} - \arctan \frac{1}{2}} \right)\) <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;">\( = \frac{{\tan \frac{\pi }{4} - \tan \left( {\arctan \frac{1}{2}} \right)}}{{1 + \left( {\tan \frac{\pi }{4}} \right)\left( {\tan \left( {\arctan \frac{1}{2}} \right)} \right)}}\) <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;"><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>Note:</strong> The two</span><span style="font-family: 'times new roman', times; font-size: medium;"> <strong><em>M1</em></strong>s may be awarded for working in part (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 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{1 - \frac{1}{2}}}{{1 + \frac{1}{2}}} = \frac{1}{3}\) <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;">\(y = - \frac{1}{{\sqrt 3 }}\) <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;">substitution into \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\)</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;">\( = \frac{{4\sqrt 6 }}{9}\) <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 \(\frac{{8\sqrt 3 }}{{9\sqrt 2 }}\) <em>etc</em>.</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 [9 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: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Let \({x^3}y = a\sin nx\)<em> </em>. Using implicit differentiation, 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;">\[{x^3}\frac{{{{\text{d}}^2}y}}{{{\text{d}}{x^2}}} + 6{x^2}\frac{{{\text{d}}y}}{{{\text{d}}x}} + ({n^2}{x^2} + 6)xy = 0\] .</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: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x^3}y = a\sin nx\)</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;">attempt to differentiate implicitly <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;">\( \Rightarrow 3{x^2}y + {x^3}\frac{{{\text{d}}y}}{{{\text{d}}x}} = an\cos nx\) <em><strong>A2</strong></em></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>Award <strong><em>A1 </em></strong>for two out of three correct, <strong><em>A0 </em></strong>otherwise.</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;">\( \Rightarrow 6xy + 3{x^2}\frac{{{\text{d}}y}}{{{\text{d}}x}} + 3{x^2}\frac{{{\text{d}}y}}{{{\text{d}}x}} + {x^3}\frac{{{{\text{d}}^2}y}}{{{\text{d}}{x^2}}} = -a{n^2}\sin nx\) <strong> <em>A2</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>Award <strong><em>A1 </em></strong>for three or four out of five correct, <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;">\( \Rightarrow 6xy + 6{x^2}\frac{{{\text{d}}y}}{{{\text{d}}x}} + {x^3}\frac{{{{\text{d}}^2}y}}{{{\text{d}}{x^2}}} = -a{n^2}\sin nx\)</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;">\( \Rightarrow {x^3}\frac{{{{\text{d}}^2}y}}{{{\text{d}}{x^2}}} + 6{x^2}\frac{{{\text{d}}y}}{{{\text{d}}x}} + 6xy + {n^2}{x^3}y = 0\) <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;">\( \Rightarrow {x^3}\frac{{{{\text{d}}^2}y}}{{{\text{d}}{x^2}}} + 6{x^2}\frac{{{\text{d}}y}}{{{\text{d}}x}} + ({n^2}{x^2} + 6)xy = 0\) <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;">[6 marks]</span><br></em></strong></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 are comfortable using implicit differentiation found this to be a fairly straightforward question and were able to answer it in just a few lines. Many candidates, however, were unable to differentiate \({x^3}y\) with respect to <em>x </em>and were therefore unable to proceed. Candidates whose first step was to write \(y = \frac{{a\sin nx}}{{{x^3}}}\) were given no credit since the question required the use of implicit differentiation.</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">Let \(y = {{\text{e}}^x}\sin x\).</p>
</div>
<div class="specification">
<p class="p1">Consider the function \(f\)<span class="Apple-converted-space"> </span>defined by \(f(x) = {{\text{e}}^x}\sin x,{\text{ }}0 \leqslant x \leqslant \pi \).</p>
</div>
<div class="specification">
<p class="p1">The curvature at any point \((x,{\text{ }}y)\) on a graph is defined as \(\kappa = \frac{{\left| {\frac{{{{\text{d}}^2}y}}{{{\text{d}}{x^2}}}} \right|}}{{{{\left( {1 + {{\left( {\frac{{{\text{d}}y}}{{{\text{d}}x}}} \right)}^2}} \right)}^{\frac{3}{2}}}}}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find an expression for \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\).</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">Show that \(\frac{{{{\text{d}}^2}y}}{{{\text{d}}{x^2}}} = 2{{\text{e}}^x}\cos x\).</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"><span class="s1">Show that the function \(f\) </span>has a local maximum value when \(x = \frac{{3\pi }}{4}\).</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"><span class="s1">Find the \(x\)</span>-coordinate of the point of inflexion of the graph of <span class="s1">\(f\).</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 class="p1"><span class="s1">Sketch the graph of \(f\)</span>, clearly indicating the position of the local maximum point, the point of inflexion and the axes intercepts.</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 \(f\) <span class="s1">and the </span>\(x\)<span class="s1">-axis.</span></p>
<p class="p2">The curvature at any point \((x,{\text{ }}y)\) on a graph is defined as \(\kappa = \frac{{\left| {\frac{{{{\text{d}}^2}y}}{{{\text{d}}{x^2}}}} \right|}}{{{{\left( {1 + {{\left( {\frac{{{\text{d}}y}}{{{\text{d}}x}}} \right)}^2}} \right)}^{\frac{3}{2}}}}}\).</p>
<div class="marks">[6]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of the curvature of the graph of \(f\) <span class="s1">at the local maximum point.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value \(\kappa \) for \(x = \frac{\pi }{2}\) and comment on its meaning with respect to the shape of the graph.</p>
<div class="marks">[2]</div>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = {{\text{e}}^x}\sin x + {{\text{e}}^x}\cos x{\text{ }}\left( { = {{\text{e}}^x}(\sin x + \cos x)} \right)\) </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p2"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(\frac{{{{\text{d}}^2}y}}{{{\text{d}}{x^2}}} = {{\text{e}}^x}(\sin x + \cos x) + {{\text{e}}^x}(\cos x - \sin x)\) </span><strong><em>M1A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\( = 2{{\text{e}}^x}\cos x\) </span><strong><em>AG</em></strong></p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = {{\text{e}}^{\frac{{3\pi }}{4}}}\left( {\sin \frac{{3\pi }}{4} + \cos \frac{{3\pi }}{4}} \right) = 0\) </span><strong><em>R1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(\frac{{{{\text{d}}^2}y}}{{{\text{d}}{x^2}}} = 2{{\text{e}}^{\frac{{3\pi }}{4}}}\cos \frac{{3\pi }}{4} < 0\) </span><strong><em>R1</em></strong></p>
<p class="p2">hence maximum at \(x = \frac{{3\pi }}{4}\)<span class="s1"> <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></span></p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(\frac{{{{\text{d}}^2}y}}{{{\text{d}}{x^2}}} = 0 \Rightarrow 2{{\text{e}}^x}\cos x = 0\) </span><strong><em>M1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\( \Rightarrow x = \frac{\pi }{2}\) </span><strong><em>A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: </strong>Award <strong><em>M1A0 </em></strong>if extra zeros are seen.</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><img src="images/Schermafbeelding_2017-02-28_om_14.29.02.png" alt="N16/5/MATHL/HP1/ENG/TZ0/11.e/M"></p>
<p class="p1">correct shape and correct domain <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2">max at \(x = \frac{{3\pi }}{4}\), point of inflexion at \(x = \frac{\pi }{2}\)<span class="s1"> <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></span></p>
<p class="p1">zeros at \(x = 0\) and \(x = \pi \) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p3"> </p>
<p class="p1"><strong>Note: </strong>Penalize incorrect domain with first <strong><em>A </em></strong>mark; allow <strong><em>FT </em></strong>from (d) on extra points of inflexion.</p>
<p class="p3"> </p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>EITHER</strong></p>
<p class="p1"><span class="Apple-converted-space">\(\int_0^x {{{\text{e}}^x}\sin x{\text{d}}x = [{{\text{e}}^x}\sin x]_0^\pi - \int_0^\pi {{{\text{e}}^x}\cos x{\text{d}}x} } \) </span><strong><em>M1A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(\int_0^\pi {{{\text{e}}^x}\sin x{\text{d}}x = [{{\text{e}}^x}\sin x]_0^\pi - \left( {[{{\text{e}}^x}\cos x]_0^x + \int_0^\pi {{{\text{e}}^x}\sin x{\text{d}}x} } \right)} \) </span><strong><em>A1</em></strong></p>
<p class="p1"><strong>OR</strong></p>
<p class="p1"><span class="Apple-converted-space">\(\int_0^\pi {{{\text{e}}^x}\sin x{\text{d}}x = [ - {{\text{e}}^x}\cos x]_0^\pi + \int_0^\pi {{{\text{e}}^x}\cos x{\text{d}}x} } \) </span><strong><em>M1A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(\int_0^\pi {{{\text{e}}^x}\sin x{\text{d}}x = [ - {{\text{e}}^x}\cos x]} _0^\pi + \left( {[{{\text{e}}^x}\sin x]_0^\pi - \int_0^\pi {{{\text{e}}^x}\sin x{\text{d}}x} } \right)\) </span><strong><em>A1</em></strong></p>
<p class="p1"><strong>THEN</strong></p>
<p class="p1"><span class="Apple-converted-space">\(\int_0^\pi {{{\text{e}}^x}\sin x{\text{d}}x = \frac{1}{2}\left( {[{{\text{e}}^x}\sin x]_0^x - [{{\text{e}}^x}\cos x]_0^x} \right)} \) </span><strong><em>M1A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(\int_0^\pi {{{\text{e}}^x}\sin x{\text{d}}x = \frac{1}{2}({{\text{e}}^x} + 1)} \) </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[6 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\) </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space"> </span><span class="s1">\(\frac{{{d^2}y}}{{d{x^2}}} = 2{e^{\frac{{3\pi }}{4}}}\cos \frac{{3\pi }}{4} = - \sqrt 2 {e^{\frac{{3\pi }}{4}}}\) <strong><em>(A1)</em></strong><br></span></p>
<p class="p1"><span class="Apple-converted-space">\(\kappa = \frac{{\left| { - \sqrt 2 {{\text{e}}^{\frac{{3\pi }}{4}}}} \right|}}{1} = \sqrt 2 {{\text{e}}^{\frac{{3\pi }}{4}}}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(\kappa = 0\) </span><strong><em>A1</em></strong></p>
<p class="p1">the graph is approximated by a straight line <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p 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 circular lake with centre O, diameter AB and radius 2 km.</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 src="data:image/png;base64,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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;">Jorg needs to get from A to B as quickly as possible. He considers rowing to point P and then walking to point B. He can row at \(3{\text{ km}}\,{{\text{h}}^{ - 1}}\) and walk at \(6{\text{ km}}\,{{\text{h}}^{ - 1}}\). Let \({\rm{P\hat AB}} = \theta \) radians, and <em>t</em> be the time in hours taken by Jorg to travel from A to B.</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;">Show that \(t = \frac{2}{3}(2\cos \theta + \theta )\).</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;">Find the value of \(\theta \) for which \(\frac{{{\text{d}}t}}{{{\text{d}}\theta }} = 0\).</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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">What route should Jorg take to travel from A to B in the least amount of time?</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;">Give reasons for your answer.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">angle APB is a right angle</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;">\( \Rightarrow \cos \theta = \frac{{{\text{AP}}}}{4} \Rightarrow {\text{AP}} = 4\cos \theta \) <strong><em>A1</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;"> Allow correct use of cosine rule.</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;">\({\text{arc PB}} = 2 \times 2\theta = 4\theta \) </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;">\(t = \frac{{{\text{AP}}}}{3} + \frac{{{\text{PB}}}}{6}\) <strong><em>M1</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;"> Allow use of their AP and their PB for 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;">.</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;">\( \Rightarrow t = \frac{{4\cos \theta }}{3} + \frac{{4\theta }}{6} = \frac{{4\cos \theta }}{3} + \frac{{2\theta }}{3} = \frac{2}{3}(2\cos \theta + \theta )\) </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>AG</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><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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}t}}{{{\text{d}}\theta }} = \frac{2}{3}( - 2\sin \theta + 1)\) <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;">\(\frac{2}{3}( - 2\sin \theta + 1) = 0 \Rightarrow \sin \theta = \frac{1}{2} \Rightarrow \theta = \frac{\pi }{6}\) (or 30 degrees) <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>[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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{{\text{d}}^2}t}}{{{\text{d}}{\theta ^2}}} = - \frac{4}{3}\cos \theta < 0\,\,\,\,\left( {{\text{at }}\theta = \frac{\pi }{6}} \right)\) <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;">\( \Rightarrow t\) is maximized at \(\theta = \frac{\pi }{6}\) <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;">time needed to walk along arc AB is \(\frac{{2\pi }}{6}{\text{ (}} \approx {\text{1 hour)}}\)</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;">time needed to row from A to B is \(\frac{4}{3}{\text{ (}} \approx {\text{1.33 hour)}}\)</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;">hence, time is minimized in walking from A to B <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><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<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 fairly easy trigonometry challenged a large number of candidates.</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: small;">Part (b) was very well done.</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;">Satisfactory answers were very rarely seen for (c). Very few candidates realised that a minimum can occur at the beginning or end of an interval.</span></p>
<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: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Using the definition of a derivative as \(f'(x) = \mathop {\lim }\limits_{h \to 0} \left( {\frac{{f(x + h) - f(x)}}{h}} \right)\) , show that the derivative of \(\frac{1}{{2x + 1}}{\text{ is }}\frac{{ - 2}}{{{{(2x + 1)}^2}}}\).</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 Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Prove by induction that the \({n^{{\text{th}}}}\) derivative of \({(2x + 1)^{ - 1}}\) is \({( - 1)^n}\frac{{{2^n}n!}}{{{{(2x + 1)}^{n + 1}}}}\).</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: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">let \(f(x) = \frac{1}{{2x + 1}}\) and using the result \(f'(x) = \mathop {\lim }\limits_{h \to 0} \left( {\frac{{f(x + h) - f(x)}}{h}} \right)\)</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;">\(f'(x) = \mathop {\lim }\limits_{h \to 0} \left( {\frac{{\frac{1}{{2(x + h) + 1}} - \frac{1}{{2x + 1}}}}{h}} \right)\) <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;">\( \Rightarrow f'(x) = \mathop {\lim }\limits_{h \to 0} \left( {\frac{{[2x + 1] - [2(x + h) + 1]}}{{h[2(x + h) + 1][2x + 1]}}} \right)\) <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;">\( \Rightarrow f'(x) = \mathop {\lim }\limits_{h \to 0} \left( {\frac{{ - 2}}{{[2(x + h) + 1][2x + 1]}}} \right)\) <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;">\( \Rightarrow f'(x) = \frac{{ - 2}}{{{{(2x + 1)}^2}}}\) <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;">[4 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;">let \(y = \frac{1}{{2x + 1}}\)</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;">we want to prove that \(\frac{{{{\text{d}}^n}y}}{{{\text{d}}{x^n}}} = {( - 1)^n}\frac{{{2^n}n!}}{{{{(2x + 1)}^{n + 1}}}}\)</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 \(n = 1 \Rightarrow \frac{{{\text{d}}y}}{{{\text{d}}x}} = {( - 1)^1}\frac{{{2^1}1!}}{{{{(2x + 1)}^{1 + 1}}}}\) <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;">\( \Rightarrow \frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{ - 2}}{{{{(2x + 1)}^2}}}\) which is the same result as 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;">hence the result is true for \(n = 1\) <strong><em>R1</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;">assume the result is true for \(n = k{\text{ : }}\frac{{{{\text{d}}^k}y}}{{{\text{d}}{x^k}}} = {( - 1)^k}\frac{{{2^k}k!}}{{{{(2x + 1)}^{k + 1}}}}\) <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;">\(\frac{{{{\text{d}}^{k + 1}}y}}{{{\text{d}}{x^{k + 1}}}} = \frac{{\text{d}}}{{{\text{d}}x}}\left[ {{{( - 1)}^k}\frac{{{2^k}k!}}{{{{(2x + 1)}^{k + 1}}}}} \right]\) <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;">\( \Rightarrow \frac{{{{\text{d}}^{k + 1}}y}}{{{\text{d}}{x^{k + 1}}}} = \frac{{\text{d}}}{{{\text{d}}x}}\left[ {{{( - 1)}^k}{2^k}k!{{(2x + 1)}^{ - k - 1}}} \right]\) <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;">\( \Rightarrow \frac{{{{\text{d}}^{k + 1}}y}}{{{\text{d}}{x^{k + 1}}}} = {( - 1)^k}{2^k}k!( - k - 1){(2x + 1)^{ - k - 2}} \times 2\) <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;">\( \Rightarrow \frac{{{{\text{d}}^{k + 1}}y}}{{{\text{d}}{x^{k + 1}}}} = {( - 1)^{k + 1}}{2^{k + 1}}(k + 1)!{(2x + 1)^{ - k - 2}}\) <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;">\( \Rightarrow \frac{{{{\text{d}}^{k + 1}}y}}{{{\text{d}}{x^{k + 1}}}} = {( - 1)^{k + 1}}\frac{{{2^{k + 1}}(k + 1)!}}{{{{(2x + 1)}^{k + 2}}}}\) <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;">hence if the result is true for \(n = k\) , it is true for \(n = k + 1\)</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 result is true for \(n = 1\) , the result is proved by mathematical induction <strong><em>R1</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>Only award final <strong><em>R1 </em></strong>if all the <strong><em>M </em></strong>marks have been gained.</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;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[9 marks]</span><br></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: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Even though the definition of the derivative was given in the question, solutions to (a) were often disappointing with algebraic errors fairly common, usually due to brackets being omitted or manipulated incorrectly. Solutions to the proof by induction in (b) were often poor. Many candidates fail to understand that they have to assume that the result is true for \(n = k\) and then show that this leads to it being true for \(n = k + 1\). Many candidates just write ‘Let \(n = k\)’ which is of course meaningless. The conclusion is often of the form ‘True for \(n = 1,{\text{ }}n = k{\text{ and }}n = k + 1\) therefore true by induction’. Credit is only given for a conclusion which includes a statement such as ‘True for \(n = k \Rightarrow \) true for \(n = k + 1\)’.</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;">Even though the definition of the derivative was given in the question, solutions to (a) were often disappointing with algebraic errors fairly common, usually due to brackets being omitted or manipulated incorrectly. Solutions to the proof by induction in (b) were often poor. Many candidates fail to understand that they have to assume that the result is true for \(n = k\) and then show that this leads to it being true for \(n = k + 1\). Many candidates just write ‘Let \(n = k\)’ which is of course meaningless. The conclusion is often of the form ‘True for \(n = 1,{\text{ }}n = k{\text{ and }}n = k + 1\) therefore true by induction’. Credit is only given for a conclusion which includes a statement such as ‘True for \(n = k \Rightarrow \) true for \(n = k + 1\)’.</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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Calculate the exact value of \(\int_1^{\text{e}} {{x^2}\ln x{\text{d}}x} \) .</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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Recognition of integration by parts <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;">\(\int {{x^2}\ln x{\text{d}}x = \left[ {\frac{{{x^3}}}{3}\ln x} \right] - \int {\frac{{{x^3}}}{3} \times \frac{1}{x}{\text{d}}x} } \) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0px 0px 0px 30px; font: 28px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \left[ {\frac{{{x^3}}}{3}\ln x} \right] - \int {\frac{{{x^2}}}{3}{\text{d}}x} \)</span></p>
<p style="margin: 0px 0px 0px 30px; font: 28px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \left[ {\frac{{{x^3}}}{3}\ln x - \frac{{{x^3}}}{9}} \right]\) <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;">\( \Rightarrow \int_1^{\text{e}} {{x^2}\ln x{\text{d}}x} = \left( {\frac{{{{\text{e}}^3}}}{3} - \frac{{{{\text{e}}^3}}}{9}} \right) - \left( {0 - \frac{1}{9}} \right)\,\,\,\,\,\left( { = \frac{{2{{\text{e}}^3} + 1}}{9}} \right)\) <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>[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: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates recognised that a method of integration by parts was appropriate for this question. However, although a good number of correct answers were seen, a number of candidates made algebraic errors in the process. A number of students were also unable to correctly substitute the limits.</span></p>
</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="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="specification">
<p>A window is made in the shape of a rectangle with a semicircle of radius \(r\) metres on top, as shown in the diagram. The perimeter of the window is a constant P metres.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-08_om_17.46.34.png" alt="M17/5/MATHL/HP1/ENG/TZ2/10"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of the window in terms of P and \(r\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the width of the window in terms of P when the area is a maximum, justifying that this is a maximum.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that in this case the height of the rectangle is equal to the radius of the semicircle.</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>the width of the rectangle is \(2r\) and let the height of the rectangle be \(h\)</p>
<p>\(P = 2r + 2h + \pi r\) <strong><em>(A1)</em></strong></p>
<p>\(A = 2rh + \frac{{\pi {r^2}}}{2}\) <strong><em>(A1)</em></strong></p>
<p>\(h = \frac{{{\text{P}} - 2r - \pi r}}{2}\)</p>
<p>\(A = 2r\left( {\frac{{{\text{P}} - 2r - \pi r}}{2}} \right) + \frac{{\pi {r^2}}}{2}\,\,\,\left( { = \operatorname{P} r - 2{r^2} - \frac{{\pi {r^2}}}{2}} \right)\) <strong><em>M1A1</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{{\text{d}}A}}{{{\text{d}}r}} = {\text{P}} - 4r - \pi r\) <strong><em>A1</em></strong></p>
<p>\(\frac{{{\text{d}}A}}{{{\text{d}}r}} = 0\) <strong><em>M1</em></strong></p>
<p>\( \Rightarrow r = \frac{{\text{P}}}{{4 + \pi }}\) <strong><em>(A1)</em></strong></p>
<p>hence the width is \(\frac{{2{\text{P}}}}{{4 + \pi }}\) <strong><em>A1</em></strong></p>
<p>\(\frac{{{{\text{d}}^2}A}}{{{\text{d}}{r^2}}} = - 4 - \pi < 0\) <strong><em>R1</em></strong></p>
<p>hence maximum <strong><em>AG</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p>\(h = \frac{{{\text{P}} - 2r - \pi r}}{2}\)</p>
<p>\(h = \frac{{{\text{P}} - \frac{{2{\text{P}}}}{{4 + \pi }} - \frac{{{\text{P}}\pi }}{{4 + \pi }}}}{2}\) <strong><em>M1</em></strong></p>
<p>\(h = \frac{{4{\text{P}} + \pi {\text{P}} - 2{\text{P}} - \pi {\text{P}}}}{{2(4 + \pi )}}\) <strong><em>A1</em></strong></p>
<p>\(h = \frac{{\text{P}}}{{(4 + \pi )}} = r\) <strong><em>AG</em></strong></p>
<p><strong>OR</strong></p>
<p>\(h = \frac{{{\text{P}} - 2r - \pi r}}{2}\)</p>
<p>\(P = r(4 + \pi )\) <strong><em>M1</em></strong></p>
<p>\(h = \frac{{r(4 + \pi ) - 2r - \pi r}}{2}\) <strong><em>A1</em></strong></p>
<p>\(h = \frac{{4r + \pi r - 2r - \pi r}}{2} = r\) <strong><em>AG</em></strong></p>
<p><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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p class="p1">A tranquilizer is injected into a muscle from which it enters the bloodstream.</p>
<p class="p1">The concentration \(C\) in \({\text{mg}}{{\text{l}}^{ - 1}}\), of tranquilizer in the bloodstream can be modelled by the function \(C(t) = \frac{{2t}}{{3 + {t^2}}},{\text{ }}t \ge 0\) where \(t\) is the number of minutes after the injection.</p>
<p class="p1">Find the maximum concentration of tranquilizer in the bloodstream.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>use of the quotient rule or the product rule <strong><em>M1</em></strong></p>
<p>\(C'(t) = \frac{{(3 + {t^2}) \times 2 - 2t \times 2t}}{{{{\left( {3 + {t^2}} \right)}^2}}}\;\;\;\left( { = \frac{{6 - 2{t^2}}}{{{{\left( {3 + {t^2}} \right)}^2}}}} \right)\;\;\;{\text{or}}\;\;\;\frac{2}{{3 + {t^2}}} - \frac{{4{t^2}}}{{{{\left( {3 + {t^2}} \right)}^2}}}\) <strong><em>A1A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>A1 </em></strong>for a correct numerator and <strong><em>A1 </em></strong>for a correct denominator in the quotient rule, and <strong><em>A1 </em></strong>for each correct term in the product rule.</p>
<p> </p>
<p>attempting to solve \(C'(t) = 0\;\;\;{\text{for }}t\) <strong><em>(M1)</em></strong></p>
<p>\(t = \pm \sqrt 3 \;\;\;{\text{(minutes)}}\) <strong><em>A1</em></strong></p>
<p>\(C\left( {\sqrt 3 } \right) = \frac{{\sqrt 3 }}{3}\;\;\;\left( {{\text{mg}}{{\text{l}}^{ - 1}}} \right)\;\;\;{\text{or equivalent.}}\) <strong><em>A1</em></strong></p>
<p><strong><em>[6 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p class="p1">This question was generally well done. A significant number of candidates did not calculate the maximum value of \(C\).</p>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that \(\cot \alpha = \tan \left( {\frac{\pi }{2} - \alpha } \right)\) for \(0 < \alpha < \frac{\pi }{2}\).</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">Hence find \(\int_{\tan \alpha }^{\cot \alpha } {\frac{1}{{1 + {x^2}}}{\text{d}}x,{\text{ }}0 < \alpha < \frac{\pi }{2}} \).</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 class="p1"><strong>EITHER</strong></p>
<p class="p1">use of a diagram and trig ratios</p>
<p class="p1"><em>eg</em>,</p>
<p class="p1"><img src="images/Schermafbeelding_2017-01-27_om_10.18.06.png" alt="M16/5/MATHL/HP1/ENG/TZ2/03/M"></p>
<p class="p1">\(\tan \alpha = \frac{O}{A} \Rightarrow \cot \alpha = \frac{A}{O}\)</p>
<p class="p1">from diagram, \(\tan \left( {\frac{\pi }{2} - \alpha } \right) = \frac{A}{O}\) <strong><em>R1</em></strong></p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">use of \(\tan \left( {\frac{\pi }{2} - \alpha } \right) = \frac{{\sin \left( {\frac{\pi }{2} - \alpha } \right)}}{{\cos \left( {\frac{\pi }{2} - \alpha } \right)}} = \frac{{\cos \alpha }}{{\sin \alpha }}\) <strong><em>R1</em></strong></p>
<p class="p1"><strong>THEN</strong></p>
<p class="p2">\(\cot \alpha = \tan \left( {\frac{\pi }{2} - \alpha } \right)\) <strong><em>AG</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>\(\int_{\tan \alpha }^{\cot \alpha } {\frac{1}{{1 + {x^2}}}{\text{d}}x} = [\arctan x]_{\tan \alpha }^{\cot \alpha }\) <strong><em>(A1)</em></strong></p>
<p class="p1"> </p>
<p class="p1"><strong>Note: </strong>Limits (or absence of such) may be ignored at this stage.</p>
<p class="p1"> </p>
<p class="p1">\( = \arctan (\cot \alpha ) - \arctan (\tan \alpha )\) <strong><em>(M1)</em></strong></p>
<p class="p1">\( = \frac{\pi }{2} - \alpha - \alpha \) <strong><em>(A1)</em></strong></p>
<p class="p1">\( = \frac{\pi }{2} - 2\alpha \) <strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">This was generally well done.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">This was generally well done. Some weaker candidates tried to solve part (b) through use of a substitution, though the standard result \(\arctan x\) was well known. A small number used \(\arctan x + c\) and went on to obtain an incorrect final answer.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Given that \(\int_{ - 2}^2 {f\left( x \right){\text{d}}x = 10} \) and \(\int_0^2 {f\left( x \right){\text{d}}x = 12} \), find</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>\(\int_{ - 2}^0 {\left( {f\left( x \right){\text{ + 2}}} \right){\text{d}}x} \).</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>\(\int_{ - 2}^0 {f\left( {x{\text{ + 2}}} \right){\text{d}}x} \).</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>\(\int_{ - 2}^0 {f\left( x \right){\text{d}}x = 10} - 12 = - 2\) <em><strong>(M1)(A1)</strong></em></p>
<p>\(\int_{ - 2}^0 {2{\text{d}}x = \left[ {2x} \right]} _{ - 2}^0 = 4\) <em><strong>A1</strong></em></p>
<p>\(\int_{ - 2}^0 {\left( {f\left( x \right){\text{ + 2}}} \right){\text{d}}x} = 2\) <em><strong> A1</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\int_{ - 2}^0 {f\left( {x{\text{ + 2}}} \right){\text{d}}x} = \int_0^2 {f\left( x \right){\text{d}}x} \) <em><strong>(M1)</strong></em></p>
<p>= 12 <em><strong>A</strong><strong>1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p class="p1"><span class="s1">By using the substitution \(t = \tan x\)</span>, find \(\int {\frac{{{\text{d}}x}}{{1 + {{\sin }^2}x}}} \)<span class="s1">.</span></p>
<p class="p2">Express your answer in the form \(m\arctan (n\tan x) + c\), where \(m\), \(n\) are constants to be determined.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p class="p1"><strong>EITHER</strong></p>
<p class="p2">\(x = \arctan t\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p2">\(\frac{{{\text{d}}x}}{{{\text{d}}t}} = \frac{1}{{1 + {t^2}}}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p3"><strong>OR</strong></p>
<p class="p2">\(t = \tan x\)</p>
<p class="p2">\(\frac{{{\text{d}}t}}{{{\text{d}}x}} = {\sec ^2}x\) <span class="Apple-converted-space"> </span><span class="s2"><strong><em>(M1)</em></strong></span></p>
<p class="p2">\( = 1 + {\tan ^2}x\) <span class="Apple-converted-space"> </span><span class="s2"><strong><em>A1</em></strong></span></p>
<p class="p2">\( = 1 + {t^2}\)</p>
<p class="p3"><strong>THEN</strong></p>
<p class="p2">\(\sin x = \frac{t}{{\sqrt {1 + {t^2}} }}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p4"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>This <strong><em>A1 </em></strong>is independent of the first two marks</p>
<p class="p5"> </p>
<p class="p2">\(\int {\frac{{{\text{d}}x}}{{1 + {{\sin }^2}x}} = \int {\frac{{\frac{{{\text{d}}t}}{{1 + {t^2}}}}}{{1 + {{\left( {\frac{t}{{\sqrt {1 + {t^2}} }}} \right)}^2}}}} } \) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p4"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>M1 </em></strong>for attempting to obtain integral in terms of \(t\) <span class="s3">and \({\text{d}}t\)</span></p>
<p class="p6"> </p>
<p class="p2">\( = \int {\frac{{{\text{d}}t}}{{(1 + {t^2}) + {t^2}}} = \int {\frac{{{\text{d}}t}}{{1 + 2{t^2}}}} } \) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2">\( = \frac{1}{2}\int {\frac{{{\text{d}}t}}{{\frac{1}{2} + {t^2}}} = \frac{1}{2} \times \frac{1}{{\frac{1}{{\sqrt 2 }}}}\arctan \left( {\frac{t}{{\frac{1}{{\sqrt 2 }}}}} \right)} \) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2">\( = \frac{{\sqrt 2 }}{2}\arctan \left( {\sqrt 2 \tan x} \right)( + c)\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong><em>[8 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p 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;">Find the equation of the normal to the curve \(5x{y^2} - 2{x^2} = 18\) at the point (1, 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;">\(5{y^2} + 10xy\frac{{{\text{d}}y}}{{{\text{d}}x}} - 4x = 0\) <strong><em>A1A1A1</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>Note:</strong> Award <strong><em>A1A1</em></strong> for correct differentiation of \(5x{y^2}\).</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;"><strong><em>A1</em></strong> for correct differentiation of \( - 2{x^2}\) and 18.</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;"> </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;">At the point (1, 2), \(20 + 20\frac{{{\text{d}}y}}{{{\text{d}}x}} - 4 = 0\)</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;">\( \Rightarrow \frac{{{\text{d}}y}}{{{\text{d}}x}} = - \frac{4}{5}\)<span style="font: 19.0px Helvetica;"> </span><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;">Gradient of normal \( = \frac{5}{4}\)<span style="font: 19.0px Helvetica;"> </span><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;">Equation of normal \(y - 2 = \frac{5}{4}(x - 1)\)<span style="font: 19.0px Helvetica;"> </span><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;">\(y = \frac{5}{4}x - \frac{5}{4} + \frac{8}{4}\)</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;">\(y = \frac{5}{4}x + \frac{3}{4}\,\,\,\,\,(4y = 5x + 3)\)<span style="font: 19.0px Helvetica;"> </span><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>[7 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;">It was pleasing to see that a significant number of candidates understood that implicit differentiation was required and that they were able to make a reasonable attempt at this. A small number of candidates tried to make the equation explicit. This method will work, but most candidates who attempted this made either arithmetic or algebraic errors, which stopped them from gaining the correct answer.</span></p>
</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 function \(f(x) = \frac{{\ln x}}{x},{\text{ }}x > 0\).</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;">The sketch below shows the graph of \(y = {\text{ }}f(x)\) and its tangent at a point A.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><br><img src="images/Schermafbeelding_2014-09-11_om_14.26.30.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;">Show that \(f'(x) = \frac{{1 - \ln x}}{{{x^2}}}\).</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: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the coordinates of B, at which the curve reaches its maximum value.</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: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the coordinates of C, the point of inflexion on the curve.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p 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 \(y = {\text{ }}f(x)\) crosses the \(x\)-axis at the point A.</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 the equation of the tangent to the graph of \(f\) at the point A.</span></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 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 \(y = {\text{ }}f(x)\) crosses the \(x\)-axis at the point A.</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 the area enclosed by the curve \(y = f(x)\), the tangent at A, and the line \(x = {\text{e}}\).</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: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(x) = \frac{{x \times \frac{1}{x} - \ln x}}{{{x^2}}}\) <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;">\( = \frac{{1 - \ln x}}{{{x^2}}}\) <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><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;">\(\frac{{1 - \ln x}}{{{x^2}}} = 0\) has solution \(x = {\text{e}}\) <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;">\(y = \frac{1}{{\text{e}}}\) <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;">hence maximum at the point \(\left( {{\text{e, }}\frac{1}{{\text{e}}}} \right)\)</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;"><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;">\(f''(x) = \frac{{{x^2}\left( { - \frac{1}{x}} \right) - 2x(1 - \ln x)}}{{{x^4}}}\) <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;">\( = \frac{{2\ln x - 3}}{{{x^3}}}\)</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> The <strong><em>M1A1 </em></strong>should be awarded if the correct working appears in part (b).</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;">point of inflexion where \(f''(x) = 0\) <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;">so \(x = {{\text{e}}^{\frac{3}{2}}},{\text{ }}y = \frac{3}{2}{{\text{e}}^{\frac{{ - 3}}{2}}}\) <strong><em>A1A1</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;">C has coordinates \(\left( {{{\text{e}}^{\frac{3}{2}}},{\text{ }}\frac{3}{2}{{\text{e}}^{\frac{{ - 3}}{2}}}} \right)\)</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;"><strong><em>[5 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;">\(f(1) = 0\) <strong><em>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;">\(f'(1) = 1\) <strong><em>(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;">\(y = x + c\) <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;">through (1, 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;">equation is \(y = x - 1\) <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;"><strong><em>[4 marks]</em></strong></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;"><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;">area \( = \int_1^{\text{e}} {x - 1 - \frac{{\ln x}}{x}{\text{d}}x} \) <strong><em>M1A1A1</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>for integration of difference between line and curve, <strong><em>A1 </em></strong>for correct limits, <strong><em>A1 </em></strong>for correct expressions in either order.</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;">\(\int {\frac{{\ln x}}{x}{\text{d}}x = \frac{{{{(\ln x)}^2}}}{2}} ( + c)\) <strong><em>(M1)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;">\(\int {(x - 1){\text{d}}x = \frac{{{x^2}}}{2} - x( + c)} \) <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;">\( = \left[ {\frac{1}{2}{x^2} - x - \frac{1}{2}{{(\ln x)}^2}} \right]_1^{\text{e}}\)</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;">\( = \left( {\frac{1}{2}{{\text{e}}^2} - {\text{e}} - \frac{1}{2}} \right) - \left( {\frac{1}{2} - 1} \right)\)</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;">\( = \frac{1}{2}{{\text{e}}^2} - {\text{e}}\) <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>METHOD 2</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;">area = area of triangle \( - \int_1^e {\frac{{\ln x}}{x}{\text{d}}x} \) <strong><em>M1A1</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: <em>A1</em></strong> is for correct integral with limits and is dependent on 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'; 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;">\(\int {\frac{{\ln x}}{x}{\text{d}}x = \frac{{{{(\ln x)}^2}}}{2}( + c)} \) <strong><em>(M1)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;">area of triangle \( = \frac{1}{2}(e - 1)(e - 1)\) <strong><em>M1A1</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;">\(\frac{1}{2}(e - 1)(e - 1) - \left( {\frac{1}{2}} \right) = \frac{1}{2}{{\text{e}}^2} - {\text{e}}\) <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>[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;">
[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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The region enclosed between the curves \(y = \sqrt x {{\text{e}}^x}\) and \(y = {\text{e}}\sqrt x \) is rotated through \(2\pi \) about the <em>x</em>-axis. Find the volume of the solid obtained.</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;">\(\sqrt x {{\text{e}}^x} = {\text{e}}\sqrt x \Rightarrow x = 0{\text{ or 1}}\) <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;">attempt to find \(\int {{y^2}{\text{d}}x} \) <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;">\({V_1} = \pi \int_0^1 {{{\text{e}}^2}x{\text{d}}x} \)</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;">\( = \pi \left[ {\frac{1}{2}{{\text{e}}^2}{x^2}} \right]_0^1\)</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;">\( = \frac{{\pi {{\text{e}}^2}}}{2}\) <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;">\({V_2} = \pi \int_0^1 {x{{\text{e}}^{2x}}{\text{d}}x} \)</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;">\( = \pi \left( {\left[ {\frac{1}{2}x{{\text{e}}^{2x}}} \right]_0^1 - \int_0^1 {\frac{1}{2}{{\text{e}}^{2x}}{\text{d}}x} } \right)\) <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;"><strong>Note:</strong> Award <strong><em>M1</em></strong> for attempt to integrate by parts.</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;">\( = \frac{{\pi {{\text{e}}^2}}}{2} - \pi \left[ {\frac{1}{4}{{\text{e}}^{2x}}} \right]_0^1\)</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;">finding difference of volumes <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;">volume\( = {V_1} - {V_2}\)</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;">\( = \pi \left[ {\frac{1}{4}{{\text{e}}^{2x}}} \right]_0^1\)</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;">\( = \frac{1}{4}\pi ({{\text{e}}^2} - 1)\) <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>[7 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: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">While only a minority of candidates achieved full marks in this question, many candidates made good attempts. Quite a few candidates obtained the limits correctly and many realized a square was needed in the integral, though a number of them subtracted then squared rather than squaring and then subtracting. There was evidence that quite a few knew about integration by parts. One common mistake was to have \(2\pi \), rather than \(\pi \) in the integral.</span></p>
</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;">The curve <em>C</em> is given by \(y = \frac{{x\cos x}}{{x + \cos x}}\), for \(x \geqslant 0\).</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: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Show that \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{{{\cos }^2}x - {x^2}\sin x}}{{{{(x + \cos x)}^2}}},{\text{ }}x \geqslant 0\).</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;">Find the equation of the tangent to <em>C</em> at the point \(\left( {\frac{\pi }{2},0} \right)\).</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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{(x + \cos x)(\cos x - x\sin x) - x\cos x(1 - \sin x)}}{{{{(x + \cos x)}^2}}}\) <strong><em>M1A1A1</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 </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 differentiation of a quotient and a product condoning sign errors in the quotient formula and the trig differentiations, </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 derivative of “</span><em style="font-family: 'times new roman', times; font-size: medium;">u</em><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 correct derivative of “</span><em style="font-family: 'times new roman', times; font-size: medium;">v</em><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;"> </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;">\( = \frac{{x\cos x + {{\cos }^2}x - {x^2}\sin x - x\cos x\sin x - x\cos x + x\cos x\sin x}}{{{{(x + \cos x)}^2}}}\) </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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{{{\cos }^2}x - {x^2}\sin x}}{{{{(x + \cos x)}^2}}}\) <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>[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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the derivative has value –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;">the equation of the tangent line is \((y - 0) = ( - 1)\left( {x - \frac{\pi }{2}} \right)\left( {y = \frac{\pi }{2} - x} \right)\) <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;"><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: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">The majority of candidates earned significant marks on this question. The product rule and the quotient rule were usually correctly applied, but a few candidates made an error in differentiating the denominator, obtaining \( - \sin x\) rather than \(1 - \sin x\). A disappointing number of candidates failed to calculate the correct gradient at the specified point.</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;">The majority of candidates earned significant marks on this question. The product rule and the quotient rule were usually correctly applied, but a few candidates made an error in differentiating the denominator, obtaining \( - \sin x\) rather than \(1 - \sin x\). A disappointing number of candidates failed to calculate the correct gradient at the specified point.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find \(\int {(1 + {{\tan }^2}x){\text{d}}x} \).</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">Find \(\int {{{\sin }^2}x{\text{d}}x} \).</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>\(\int {(1 + {{\tan }^2}x){\text{d}}x} = \int {{{\sec }^2}x{\text{d}}x = \tan x( + c)} \) <strong><em>M1A1</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>\(\int {{{\sin }^2}x{\text{d}}x} = \int {\frac{{1 - \cos 2x}}{2}{\text{d}}x} \) <strong><em>M1A1</em></strong></p>
<p>\( = \frac{x}{2} - \frac{{\sin 2x}}{4}( + c)\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Allow integration by parts followed by trig identity.</p>
<p>Award <strong><em>M1 </em></strong>for parts, <strong><em>A1 </em></strong>for trig identity, <strong><em>A1 </em></strong>final answer.</p>
<p><strong><em>[3 marks]</em></strong></p>
<p><strong><em>Total [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">Some correct answers but too many candidates had a poor approach and did not use the trig identity.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Same as (a).</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p class="p1">By using the substitution \(u = 1 + \sqrt x \), find \(\int {\frac{{\sqrt x }}{{1 + \sqrt x }}{\text{d}}x} \).</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>\(\frac{{{\text{d}}u}}{{{\text{d}}x}} = \frac{1}{{2\sqrt x }}\) <strong><em>A1</em></strong></p>
<p>\({\text{d}}x = 2(u - 1){\text{d}}u\)</p>
<p> </p>
<p><strong>Note: </strong>Award the <strong><em>A1 </em></strong>for any correct relationship between \({\text{d}}x\) and \({\text{d}}u\).</p>
<p>\(\int {\frac{{\sqrt x }}{{1 + \sqrt x }}{\text{d}}x} = 2\int {\frac{{{{(u - 1)}^2}}}{u}{\text{d}}u} \) (<strong><em>M1)A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award the <strong><em>M1 </em></strong>for an attempt at substitution resulting in an integral only involving \(u\) .</p>
<p>\( = 2\int {u - 2 + \frac{1}{u}{\text{d}}u} \) <strong><em>(A1)</em></strong></p>
<p>\( = {u^2} - 4u + 2\ln u( + C)\) <strong><em>A1</em></strong></p>
<p>\( = x - 2\sqrt x - 3 + 2\ln \left( {1 + \sqrt x } \right)( + C)\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award the <strong><em>A1 </em></strong>for a correct expression in \(x\), but not necessarily fully expanded/simplified.</p>
<p><strong><em>[6 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p class="p1">Many candidates worked through this question successfully. A significant minority either made algebraic mistakes with the substitution or tried to work with an integral involving both \(x\) and \(u\).</p>
</div>
<br><hr><br><div class="specification">
<p>Let \(y = {\text{si}}{{\text{n}}^2}\theta ,\,\,0 \leqslant \theta \leqslant \pi \).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find \(\frac{{{\text{d}}y}}{{{\text{d}}\theta }}\)</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 find the values of <em>θ</em> for which \(\frac{{{\text{d}}y}}{{{\text{d}}\theta }} = 2y\).</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>attempt at chain rule or product rule <em><strong>(M1)</strong></em></p>
<p>\(\frac{{{\text{d}}y}}{{{\text{d}}\theta }} = 2\,{\text{sin}}\,\theta \,{\text{cos}}\,\theta \) <em><strong> A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(2\,{\text{sin}}\,\theta \,{\text{cos}}\,\theta = 2{\text{si}}{{\text{n}}^2}\theta \)</p>
<p>sin <em>θ </em>= 0 <strong><em>(A1)</em></strong></p>
<p><em>θ </em>= 0, \(\pi \) <em><strong>A1</strong></em></p>
<p>obtaining cos <em>θ </em>= sin <em>θ<strong> (M1)</strong></em></p>
<p>tan <em>θ</em> = 1 <em><strong>(M1)</strong></em></p>
<p>\(\theta = \frac{\pi }{4}\) <strong><em>A1</em></strong></p>
<p><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;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A particle moves along a straight line. Its displacement, \(s\) metres, at time \(t\) seconds is given by \(s = t + \cos 2t,{\text{ }}t \geqslant 0\). The first two times when the particle is at rest are denoted by \({t_1}\) and \({t_2}\), where \({t_1} < {t_2}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find \({t_1}\) and \({t_2}\).</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the displacement of the particle when \(t = {t_1}\)</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>\(s = t + \cos 2t\)</p>
<p>\(\frac{{{\text{d}}s}}{{{\text{d}}t}} = 1 - 2\sin 2t\) <strong><em>M1A1</em></strong></p>
<p>\( = 0\) <strong><em>M1</em></strong></p>
<p>\( \Rightarrow \sin 2t = \frac{1}{2}\)</p>
<p>\({t_1} = \frac{\pi }{{12}}(s),{\text{ }}{t_2} = \frac{{5\pi }}{{12}}(s)\) <strong><em>A1A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>A0A0 </em></strong>if answers are given in degrees.</p>
<p> </p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(s = \frac{\pi }{{12}} + \cos \frac{\pi }{6}\,\,\,\left( {s = \frac{\pi }{{12}} + \frac{{\sqrt 3 }}{2}(m)} \right)\) <strong><em>A1A1</em></strong></p>
<p><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" style="padding-left: 20px; padding-right: 20px;">
<p>Using the substitution \(x = \tan \theta \) show that \(\int\limits_0^1 {\frac{1}{{{{\left( {{x^2} + 1} \right)}^2}}}{\text{d}}x = } \int\limits_0^{\frac{\pi }{4}} {{{\cos }^2}\theta {\text{d}}\theta } \).</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find the value of \(\int\limits_0^1 {\frac{1}{{{{\left( {{x^2} + 1} \right)}^2}}}{\text{d}}x} \).</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>let \(x = \tan \theta \)</p>
<p>\( \Rightarrow \frac{{{\text{d}}x}}{{{\text{d}}\theta }} = {\sec ^2}\theta \) <strong><em>(A1)</em></strong></p>
<p>\(\int {\frac{1}{{{{({x^2} + 1)}^2}}}{\text{d}}x = \int {\frac{{{{\sec }^2}\theta }}{{{{({{\tan }^2}\theta + 1)}^2}}}{\text{d}}\theta } } \) <strong><em>M1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> The method mark is for an attempt to substitute for both \(x\) and \({\text{d}}x\).</p>
<p> </p>
<p>\( = \int {\frac{1}{{{{\sec }^2}\theta }}{\text{d}}\theta } \) (or equivalent) <strong><em>A1</em></strong></p>
<p>when \(x = 0,{\text{ }}\theta = 0\) and when \(x = 1,{\text{ }}\theta = \frac{\pi }{4}\) <strong><em>M1</em></strong></p>
<p>\(\int\limits_0^{\frac{\pi }{4}} {{{\cos }^2}\theta {\text{d}}\theta } \) <strong><em>AG</em></strong></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>\(\left( {\int\limits_0^1 {\frac{1}{{{{\left( {{x^2} + 1} \right)}^2}}}{\text{d}}x} = \int\limits_0^{\frac{\pi }{4}} {{{\cos }^2}\theta {\text{d}}\theta } } \right) = \frac{1}{2}\int\limits_0^{\frac{\pi }{4}} {\left( {1 + \cos 2\theta } \right){\text{d}}\theta } \) <strong><em>M1</em></strong></p>
<p>\( = \frac{1}{2}\left[ {\theta + \frac{{\sin 2\theta }}{2}} \right]_0^{\frac{\pi }{4}}\) <strong><em>A1</em></strong></p>
<p>\( = \frac{\pi }{8} + \frac{1}{4}\) <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="question">
<p class="p1">Use the substitution \(u = \ln x\) to find the value of \(\int_{\text{e}}^{{{\text{e}}^2}} {\frac{{{\text{d}}x}}{{x\ln x}}} \).</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><strong>METHOD 1</strong></p>
<p>\(\int_{\text{e}}^{{{\text{e}}^2}} {\frac{{{\text{d}}x}}{{x\ln x}}} = \left[ {\ln (\ln x)} \right]_{\text{e}}^{{{\text{e}}^2}}\) <strong><em>(M1)A1</em></strong></p>
<p>\( = \ln (\ln {{\text{e}}^2}) - \ln (\ln {\text{e}})\;\;\;( = \ln 2 - \ln 1)\) <strong><em>(A1)</em></strong></p>
<p>\( = \ln 2\) <strong><em>A1</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>\(u = \ln x,{\text{ }}\frac{{{\text{d}}u}}{{{\text{d}}x}} = \frac{1}{x}\) <strong><em>M1</em></strong></p>
<p>\( = \int_1^2 {\frac{{{\text{d}}u}}{u}} \) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Condone absent or incorrect limits here.</p>
<p> </p>
<p>\( = [\ln u]_1^2\) or equivalent in \(x( = \ln 2 - \ln 1)\) <strong><em>(A1)</em></strong></p>
<p>\( = \ln 2\) <strong><em>A1</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question" 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;">Use the identity \(\cos 2\theta = 2{\cos ^2}\theta - 1\) to prove that \(\cos \frac{1}{2}x = \sqrt {\frac{{1 + \cos x}}{2}} ,{\text{ }}0 \leqslant x \leqslant \pi \).</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 Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find a similar expression for \(\sin \frac{1}{2}x,{\text{ }}0 \leqslant x \leqslant \pi \).</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;">Hence find the value of \(\int_0^{\frac{\pi }{2}} {\left( {\sqrt {1 + \cos x} + \sqrt {1 - \cos x} } \right){\text{d}}x} \).</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;">\(\cos x = 2{\cos ^2}\frac{1}{2}x - 1\)</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;">\(\cos \frac{1}{2}x = \pm \sqrt {\frac{{1 + \cos x}}{2}} \) <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;">positive as \(0 \leqslant x \leqslant \pi \) <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;">\(\cos \frac{1}{2}x = \sqrt {\frac{{1 + \cos x}}{2}} \) <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><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;">\(\cos 2\theta = 1 - 2{\sin ^2}\theta \) <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;">\(\sin \frac{1}{2}x = \sqrt {\frac{{1 - \cos x}}{2}} \) <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;"><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: 21.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(\sqrt 2 \int_0^{\frac{\pi }{2}} {\cos \frac{1}{2}x + \sin \frac{1}{2}x{\text{d}}x} \) <strong><em>A1</em></strong></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;">\( = \sqrt 2 \left[ {2\sin \frac{1}{2}x - 2\cos \frac{1}{2}x} \right]_0^{\frac{\pi }{2}}\) <strong><em>A1</em></strong></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;">\( = \sqrt 2 (0) - \sqrt 2 (0 - 2)\) <strong><em>A1</em></strong></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;">\( = 2\sqrt 2 \) <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>[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;">
[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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Paint is poured into a tray where it forms a circular pool with a uniform thickness of 0.5 cm. If the paint is poured at a constant rate of \(4{\text{ c}}{{\text{m}}^3}{{\text{s}}^{ - 1}}\), find the rate of increase of the radius of the circle when the radius is 20 cm.</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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(V = 0.5\pi {r^2}\) <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;"><strong>EITHER</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;">\(\frac{{dV}}{{dr}} = \pi r\) <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;">\(\frac{{dV}}{{dt}} = 4\) <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;">applying chain rule <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;">for example \(\frac{{dr}}{{dt}} = \frac{{dV}}{{dt}} \times \frac{{dr}}{{dV}}\)</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>OR</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;">\(\frac{{dV}}{{dt}} = \pi r\frac{{dr}}{{dt}}\) <strong><em>M1A1</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;">\(\frac{{dV}}{{dt}} = 4\) <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;"><strong>THEN</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;">\(\frac{{dr}}{{dt}} = 4 \times \frac{1}{{\pi r}}\) <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;">when \(r = 20,{\text{ }}\frac{{dr}}{{dt}} = \frac{4}{{20\pi }}{\text{ or }}\frac{1}{{5\pi }}{\text{ (cm}}\,{{\text{s}}^{ - 1}})\) <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><span style="font-family: 'times new roman', times; font-size: medium;"> Allow </span><em style="font-family: 'times new roman', times; font-size: medium;">h</em><span style="font-family: 'times new roman', times; font-size: medium;"> instead of 0.5 up until the 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;">.</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>[6 marks]</em></strong></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;">There was a large variety of methods used in this question, with most candidates choosing</span><span style="font-family: 'times new roman', times; font-size: medium;"> to implicitly differentiate the expression for volume in terms of <em>r</em>.</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider two functions \(f\) and \(g\) and their derivatives \(f'\) and \(g'\). The following table shows the values for the two functions and their derivatives at \(x = 1\), \(2\) and \(3\).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-07_om_15.01.17.png" alt></p>
<p class="p1">Given that \(p(x) = f(x)g(x)\) and \(h(x) = g \circ f(x)\), find</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">\(p'(3)\);</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">\(h'(2)\).</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 class="p1">\(p'(3) = f'(3)g(3) + g'(3)f(3)\) <span class="Apple-converted-space"> </span><span class="s1">(<strong><em>M1)</em></strong></span></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>M1 </em></strong>if the derivative is in terms of \(x\) or \(3\).</p>
<p class="p3"> </p>
<p class="p1">\( = 2 \times 4 + 3 \times 1\)</p>
<p class="p1">\( = 11\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></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">\(h'(x) = g'\left( {f(x)} \right)f'(x)\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)(A1)</em></strong></span></p>
<p class="p1">\(h'(2) = g'(1)f'(2)\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">\( = 4 \times 4\)</p>
<p class="p1">\( = 16\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[4 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;">
<p class="p1">This was a problem question for many candidates. Some quite strong candidates, on the evidence of their performance on other questions, did not realise that ‘composite functions’ and ‘functions of a function’ were the same thing, and therefore that the chain rule applied.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">This was a problem question for many candidates. Some quite strong candidates, on the evidence of their performance on other questions, did not realise that ‘composite functions’ and ‘functions of a function’ were the same thing, and therefore that the chain rule applied.</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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The region bounded by the curve \(y = \frac{{\ln (x)}}{x}\) and the lines <em>x</em> = 1, <em>x</em> = <em>e</em>, <em>y</em> = 0 is rotated through \(2\pi \) radians about the <em>x</em>-axis.</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;">Find the volume of the solid generated.</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: 37.0px 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: 37.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(V = \pi \int_1^{\text{e}} {{{\left( {\frac{{\ln x}}{x}} \right)}^2}{\text{d}}x} \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Integrating by parts:</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(u = {(\ln x)^2},{\text{ }}\frac{{{\text{d}}v}}{{{\text{d}}x}} = \frac{1}{{{x^2}}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}u}}{{{\text{d}}x}} = \frac{{2\ln x}}{x},{\text{ }}v = - \frac{1}{x}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow V = \pi \left( { - \frac{{{{(\ln x)}^2}}}{x} + 2\int {\frac{{\ln x}}{{{x^2}}}{\text{d}}x} } \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(u = \ln x,{\text{ }}\frac{{{\text{d}}v}}{{{\text{d}}x}} = \frac{1}{{{x^2}}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}u}}{{{\text{d}}x}} = \frac{1}{x},{\text{ }}v = - \frac{1}{x}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\therefore \int {\frac{{\ln x}}{{{x^2}}}{\text{d}}x = - \frac{{\ln x}}{x} + \int {\frac{1}{{{x^2}}}{\text{d}}x = - \frac{{\ln x}}{x} - \frac{1}{x}} } \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\therefore V = \pi \left[ { - \frac{{{{(\ln x)}^2}}}{x} + 2\left( { - \frac{{\ln x}}{x} - \frac{1}{x}} \right)} \right]_1^{\text{e}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 2\pi - \frac{{5\pi }}{e}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px 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: 37.0px 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: 37.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(V = \pi \int_1^{\text{e}} {{{\left( {\frac{{\ln x}}{x}} \right)}^2}{\text{d}}x} \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(\ln x = u \Rightarrow x = {{\text{e}}^u},{\text{ }}\frac{{{\text{d}}x}}{x} = {\text{d}}u\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {{{\left( {\frac{{\ln x}}{x}} \right)}^2}{\text{d}}x = \int {\frac{{{u^2}}}{{{{\text{e}}^u}}}{\text{d}}u = \int {{{\text{e}}^{ - u}}} {u^2}{\text{d}}u = - {{\text{e}}^{ - u}}{u^2} + 2\int {{{\text{e}}^{ - u}}u{\text{d}}u} } } \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = - {{\text{e}}^{ - u}}{u^2} + 2\left( { - {{\text{e}}^{ - u}}u + \int {{{\text{e}}^{ - u}}{\text{d}}u} } \right) = - {{\text{e}}^{ - u}}{u^2} - 2{{\text{e}}^{ - u}}u - 2{{\text{e}}^{ - u}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = - {{\text{e}}^{ - u}}({u^2} + 2u + 2)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">When <em>x</em> = e, <em>u</em> = 1. When <em>x</em> = 1, <em>u</em> = 0 .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\therefore {\text{ Volume}} = \pi \left[ { - {{\text{e}}^{ - u}}({u^2} + 2u + 2)} \right]_0^1\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \pi ( - 5{{\text{e}}^{ - 1}} + 2){\text{ }}\left( { = 2\pi - \frac{{5\pi }}{{\text{e}}}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px 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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Only the best candidates were able to make significant progress with this question. It was disappointing to see that many candidates could not state that the formula for the required volume was \(\pi \int_1^e {{{\left( {\frac{{\ln x}}{x}} \right)}^2}{\text{d}}x} \) . Of those who could, very few either attempted integration by parts or used an appropriate substitution.</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider the curve \(y = \frac{1}{{1 - x}},{\text{ }}x \in \mathbb{R},{\text{ }}x \ne 1\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\).</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">Determine the equation of the normal to the curve at the point \(x = 3\) in the form \(ax + by + c = 0\) where \(a,{\text{ }}b,{\text{ }}c \in \mathbb{Z}\).</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 class="p1">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = {(1 - x)^{ - 2}}\;\;\;\left( { = \frac{1}{{{{(1 - x)}^2}}}} \right)\) <span class="Apple-converted-space"> </span><strong><em>(M1)A1</em></strong></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>gradient of Tangent \( = \frac{1}{4}\) <strong><em>(A1)</em></strong></p>
<p>gradient of Normal \( = - 4\) <strong>(<em>M1)</em></strong></p>
<p>\(y + \frac{1}{2} = - 4(x - 3)\) or attempt to find \(c\) in \(y = mx + c\) <strong><em>M1</em></strong></p>
<p>\(8x + 2y - 23 = 0\) <strong><em>A1</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<p><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="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="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;">If \(f(x) = x - 3{x^{\frac{2}{3}}},{\text{ }}x > 0\) ,</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;">(a) find the <em>x</em>-coordinate of the point P where \(f'(x) = 0\) ;</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;">(b) determine whether P is a maximum or minimum point.</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: 37.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \(f'(x) = 1 - \frac{2}{{{x^{\frac{1}{3}}}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow 1 - \frac{2}{{{x^{\frac{1}{3}}}}} = 0 \Rightarrow {x^{\frac{1}{3}}} = 2 \Rightarrow x = 8\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px 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: 37.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) \(f''(x) = \frac{2}{{3{x^{\frac{4}{3}}}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f''(8) > 0 \Rightarrow {\text{ at }}x = 8,{\text{ }}f(x){\text{ has a minimum.}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px 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;">Most candidates were able to correctly differentiate the function and find the point where \(f'(x) = 0\) . They were less successful in determining the nature of the point.</span></p>
</div>
<br><hr><br><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;">The normal to the curve \(x{{\text{e}}^{ - y}} + {{\text{e}}^y} = 1 + x\), at the point (<em>c</em>, \(\ln c\)), has a <em>y</em>-intercept \({c^2} + 1\).</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;">Determine 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: 26.0px 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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">differentiating implicitly:</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;">\(1 \times {{\text{e}}^{ - y}} - x{{\text{e}}^{ - y}}\frac{{{\text{d}}y}}{{{\text{d}}x}} + {{\text{e}}^y}\frac{{{\text{d}}y}}{{{\text{d}}x}} = 1\) <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;">at the point (<em>c</em>, \(\ln c\))</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;">\(\frac{1}{c} - c \times \frac{1}{c}\frac{{{\text{d}}y}}{{{\text{d}}x}} + c\frac{{{\text{d}}y}}{{{\text{d}}x}} = 1\) <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;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{1}{c}\,\,\,\,\,(c \ne 1)\) <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>OR</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;">reasonable attempt to make expression explicit <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;">\(x{{\text{e}}^{ - y}} + {{\text{e}}^y} = 1 + x\)</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;">\(x + {{\text{e}}^{2y}} = {{\text{e}}^y}(1 + x)\)</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;">\({{\text{e}}^{2y}} - {{\text{e}}^y}(1 + x) + x = 0\)</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;">\(({{\text{e}}^y} - 1)({{\text{e}}^y} - x) = 0\) <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;">\({{\text{e}}^y} = 1,{\text{ }}{{\text{e}}^y} = x\)</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;">\(y = 0,{\text{ }}y = \ln x\) <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>Note:</strong> Do not penalize if <em>y</em> = 0 not stated.</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;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{1}{x}\)</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;">gradient of tangent \( = \frac{1}{c}\) <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>Note:</strong> If candidate starts with \(y = \ln x\) with no justification, award <strong><em>(M0)(A0)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;"> </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>THEN</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;">the equation of the normal is</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;">\(y - \ln c = - c(x - c)\) <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;">\(x = 0,{\text{ }}y = {c^2} + 1\)</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;">\({c^2} + 1 - \ln c = {c^2}\) <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;">\(\ln c = 1\)</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;">\(c = {\text{e}}\) <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>[7 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 was the first question to cause the majority of candidates a problem and only the better candidates gained full marks. Weaker candidates made errors in the implicit differentiation and those who were able to do this often were unable to simplify the expression they gained for the gradient of the normal in terms of c; a significant number of candidates did not know how to simplify the logarithms appropriately.</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 curve <em>C</em> is given implicitly by the equation \(\frac{{{x^2}}}{y} - 2x = \ln y\) for \(y > 0\).</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;">Express \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) in terms of <em>x</em> and <em>y</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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the value of \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) at the point on <em>C</em> where <em>y</em> = 1 and \(x > 0\).</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: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">attempt at implicit differentiation <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;"><strong>EITHER</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;">\(\frac{{2x}}{y} - \frac{{{x^2}}}{{{y^2}}}\frac{{{\text{d}}y}}{{{\text{d}}x}} - 2 = \frac{1}{y}\frac{{{\text{d}}y}}{{{\text{d}}x}}\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px 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 each side.</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;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{\frac{{2x}}{y} - 2}}{{\frac{1}{y} + \frac{{{x^2}}}{{{y^2}}}}}{\text{ }}\left( { = \frac{{2xy - 2{y^2}}}{{{x^2} + y}}} \right)\) </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: 31.0px 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: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">after multiplication by <em>y</em></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;">\(2x - 2y - 2x\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{{\text{d}}y}}{{{\text{d}}x}}\ln y + y\frac{1}{y}\frac{{{\text{d}}y}}{{{\text{d}}x}}\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px 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 each side.</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;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{2(x - y)}}{{1 + 2x + \ln y}}\) </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: 31.0px 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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">for \(y = 1,{\text{ }}{x^2} - 2x = 0\)</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;">\(x = (0{\text{ or) 2}}\) <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;">for \(x = 2\), \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{2}{5}\) <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>
<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;">Most candidates were familiar with the concept of implicit differentiation and the majority found the correct derivative function. In part (b), a significant number of candidates didn’t realise that the value of <em>x</em> was required.</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-size: medium; font-family: 'times new roman', times;">Most candidates were familiar with the concept of implicit differentiation and the majority found the correct derivative function. In part (b), a significant number of candidates didn’t realise that the value of <em>x</em> was required.</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;">The diagram shows the graph of the function defined by \(y = x{(\ln x)^2}{\text{ for }}x > 0\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><br><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAk0AAAEiCAIAAABr0nEdAAASI0lEQVR4nO3dT2hk92HA8bk5hzYJbRO8DbXU6OSQhbjpIeTgWUEwbg4mFDwIDEuIY+xRCIQcFnbkmBx6GRnW0IPmtOwSbQ8pqKP7IJZCGGhYw5QebL9TEr+sKWYoQvCMMWJ6+O0+v5W0a2n+vvebzwdBsEy0z1ppvvP7915tNPrs/t7rtVqtVvv2T/b+cDwajUYfH1z7/pW3/+toBADVVnvwv4cH1y7VLl07OByNRqNP7x/8+srVvfsLvC4AmIaHnRv9ae/qWu1h244/uP36zfeOF3ZVADAdeeeO7r19pbb29r3PRqPjP+y9/i8HhzIHQOWd7tzx0b3O9QcLdQBQbXnnwm6U1/c++N2N6/upygEQhROdu3L1J7/eSz/N/3Wapgu5LACYirxzo8/uvb1We+H6wedjuX6/v9VqLeSyAGAq8s4dHx786oVHz8xtNBprK6tJkizgugBgGh507vj+wY0bB/cLy3L9fn9tZXVtZdWQDoDqqr195fu/vHn7V9d+897RI5tPNhqNv/+7Z57+2tcN6QCortq1S5euXNv74NHIhcHc3/zVX3/pqafW63VDOgAqqnbmZzcajY1Go1ar1Wq1/W7XkA6Aijqjc2Ew1+/3Q+eyLDOkA6CizujcVqu10WiMRqPQudFoFIZ0w+Fw3lcHAJM5o3PD4TAkLe/caDQybwlAFZ29Pvfg3xU6BwBVpHMAxEznAIiZzgEQM50DIGY6B0DMdA6AmOkcADHTOQBipnMAxEznAIiZzgEQM50DIGY6B0DMdA6AmOkcADHTOQBipnMAxEznAIiZzgEQM50DIGY6B0DMdA6AmOkcADHTOQBipnMAxEznAIiZzgEQM50DIGY6B0DMdA6AmOkcADHTOQBipnMAxEznAIiZzgEQM50DIGY6B0DMdA6AmOkcADHTOQBipnMAxEznAIiZzgEQM50DIGY6B0DMdA6AmOkcADHTOQBipnMAxEznAIiZzgEQM50DIGY6B0DMdA6AmOkcADHTOQBipnMAxEznAIiZzgEQM50DIGY6B0DMdA6AmOkcADHTOQBipnMAxEznAIiZzgEQM50DIGY6B0DMdA6AmOkcADHTOQBipnMAxEznAIiZzgEQM50DIGY6B0DMdA6AmOkcADHTOQBipnMAxEznAIiZzgEQM50DIGY6B0DMdA6AmOkcADHTOQBipnMAxEznAIiZzgEQM50DIGY6B0DMqti548O7b11e+ed33v2/RV8JAGVXwc4d/3H/je+traxe3rp7uOhrAaDkqte54+TWj1788Wsvfmvt2bfuHh4v+nIAKLXKde7ju1s/+NGt//6w+4vLK99rdv8odAA8QdU6d3j3ze/8Yv/Pn44O77757OraS7cSoQPg8arVuU+SW688XJb7+O7W82srr9xOPln0VQFQXpXq3NHv33nxxw/Ddnz07r/+0G4UAJ6oQp0LxwlW10582I0CwONVp3PH799+6Qdv3v248KlPkluvrK08/+gnAeBzVenc4fu33rj8nRvvfvbopz/qvrayuvbiW/uJyUsAzlCJzh29e+OfHk5U/nz/o4etC5F78PHca90PF3qRAJRRJToHAGPSOQBipnMAxKx6nUvTdLvd3mq1BoPBoq8FgLKrWOeyLFuv1/PDc8PhcNFXBECpVaBzSZLsd7vb7fZms3nykPjK6trK6lartd1u73e7SZJkWbbo6wWgRMrbucFgsN1u5zHbbDa32+1//+1v//G5f8g/eWd3987u7lartdFo5J/caDQ6O53BYKB5AJSuc1mW7Xe7oVvr9frpYiVJstVqnbk+lyRJr9fbbrfzuc3tdrvX65neBFha5epcr9cLidpqtfr9/iRfKkmSO7u7+Thvu93u9/tGeADLpiydS9M0LL9ttVpJkkz3K+fBCwPENE2n+PUBKLNSdK7X64UI9Xq92f0pSZJ0djphvLjZbE44XgSgEhbcuSzLwmaTrVZrPqtoWZb1er18eLff7ZrMBIjYIjuXZVmYq9zvdmf3pzxO2M8SVu86Ox17VQCitLDOpWkaBlWLnT8cDoednY7aAcRqMZ1L03S9Xl+v16e75WRsw+Hwzu5uvtWzJFcFwOQW0LksyzYajfV6vWz7HsPRvbx2Zbs8AMYw787la3KlHTMVa2cmE6Dq5t25sPWj/Hv6syy7s7tr3Q6g6ubauf1uN9yUcopfc6aKu1ScQACoovl1bjAYhHWvaX3BuRkOh+GQXzhvt+jLAeAC5tS58Ny4jUajukOi/LzdRqPhEa8AVTGnzoVClHbvyfn1+/1w7M/xA4BKmEfnwu0rK7Qs94VsyASoipl3LoIZyzNlWRa2qFi0AyizmXcuxCDWKb40TS3aAZTZbDuXJEmY3Jvki5RfcdHONCZAqcy2c5vN5nq9HtmM5ZnCXVSctAMomxl2rt/vL+qZO4syHA5NYwKUygw7t9FoxLf95DwGg4FpTICSmFXnwmCu/PexnBHTmAAlMavOhcHceP/faBSnMWPdcQpQcjPp3JIP5k4YDAbhUPl2u20aE2DOZtI5g7kT8qf8rNfrvV5v0ZcDsESm37kwmPNqflqSJOEZs5vNpoeVA8zH9Du31WotyZm58fR6vTCNeWd313cJYNam3Lk0TSO7ZfMs5A+0c8wOYNam3LlwN0u7Lc4jP2ZnfwrA7Eyzc+HRBNvt9sRXtSzsTwGYtWl2LuxAMRF3UfanAMzONDu32Ww6TjC2/Nmt7p8CMEVT65wdKJNz/xSAqZta58I6k/0Uk+v3+2Fg19npGNgBTGhqndtoNDabzWlcEqMsy8LBg/V63XonwCSm07nw3HA7BqcrSRLP9wGY0HQ6F47NmWSbOgcPACY0nc45NjdTaZo6eAAwnil0Luy09BSeWSs+uHXR1wJQGVPonJ2Wc+PgAcBFTaFzdlrOmSceAJzfpJ0bDod2Ws6fgwcA5zRp53q93trKqs0RCzEYDMLAbrvdNrADONOkndtqtdzTcoEcPAB4skk7F25PNdVL4sKcKAd4nIk6NxgMPIinJLIsc/AA4LSJOhdmzKwMlUfxRLmDBwCjCTu32Ww6UVBCDh4A5MbvXJZlHjhXWk6UAwTjd87iXPk5eAAwfucszlVClmXhaRLr9bp7kAJLaPzObbVaFueqwsEDYGmN3zmLc9Xi4AGwnMbsXHiAuHmwynHwAFg2Y3Yu3NbSDFhFOXgALI8xO9fZ6azX6zO5IuYiP3jgiQdA3Mbs3GazudVqzeaSmJ/iwQOjcyBKY3bOXoZoeOIBELdxOhc2oZjsikmSJPn+FE8TBGIyTudsQonVfrdrfwoQmXE6F6a5ZnZJLFLxxpiG7EAExuncVqtlE0rc8v0p7p8CVN04nVuv1z1DPHrF/Sn2HAHVdeHOhcfxeOFbEsX9Ke6fAlTRhTsXNlt6yVsq+f1TOjsd+1OAarlw5/r9/trKqq3ny2Y4HG63247ZAZVz4c6Fe97P8pIor+LzfbzXASph/OfysLTy5/s4ZgeUn84xjuJtoD2eCSgznWN8g8HANCZQcjrHRIqPKTeNCcxBlmUXemOtc0yBaUxgPtI03Wg01uv187+r1jmmxjQmMFP9fn+9Xr/o06F1jmkqTmM6VA5MS5ZlnZ3OeM8O0zmmz6FyYIrSNA03IBzv3bPOMSv5oXL3xgTGFu47OMnav84xW/mzW7fbbY/4Ac4vy7IwMzTGXGWRzjFz+cR6eMSPRTvgCyVJEt4i39ndnfBL6RxzkqZp/qRyZw+Axyk+/HIqSx46x1z1+/387IFFO+CEcDwurHRMa+5H55i3cPYgf6CdRTsgCKeSpn67CZ1jMYbDoUU7IMhPDmy1WlN/76tzLFKSJG4YBksuH8bN6LitzrF4+Q3DNhoNi3awPIqPbp7dEobOURb5op3bY0L0ipsqZz2Xo3OUyInbY9qiAlHKp3CmuKnyCXSO0rFFBWKV3/x2o9G40DMHJqFzlFRxi8p+t7voywEmla9NzPmZzDpHqeXL1O6iAtVV3G8y/9V3naMC8ruo2JAJ1VJchljUU7p0jsoobshUOyi/4p2PFrjQrnNUSfGeYWoHpVWcqFz476nOUT2OH0BpDYfDst3kSOeoqnzeX+2gDPInTa6trJbqRJDOUW1qB2WQLyhst9tl+zXUOWKgdrAo5X+opM4RD7WDearK8VadIzZqB7NWvF3Rok7FnZ/OESe1g1kobqcs1WaTJ9A5YqZ2MC3F36Y536ByQjpH/Iq/n6VdKofSqvr7RZ1jWagdXFTVCxfoHMuleOewzWazzJvEYIHiKFygcyyjULvilugKLTbATCVJEk3hAp1jqeVHXCu0eQxmJD8tEE3hAp2D0WAwiPLXG86p3+/npwXu7O5G9iugc/BAcbrGRhWWxDJMaegcPGI4HN7Z3Q0bVSzdEavihqzof851Ds6QZVmv18vf58Y3k8PSStO0OG+xDFuOdQ6epLh0t91uDwaDRV8RjClfhAvr0MszM69z8MXCWaJ8kqfX60U8yUNkhsNhfoomLMIt2+SEzsF5ZVmWL9ov2ztiqqi4tWqZ74qgc3BhxZcPwzvKpri6HN6QpWm66ItaJJ2DMZ1+NTG8Y7EGg4F3YKfpHEwqDO/y1bslXP9gsYorcN5ynaZzMB1h9W6z2Szu2PZumtk58SMXVuD8yJ2mczBl4aR5vr2ts9NxGoHpGgwG2+12Pj/pfOeT6RzMSlgsCfOZ4bD5km8HYEInfqK8hTonnYPZCpNLJ959L3fwPvuo+/Pw3Xjk49mfvrP3n8nR8aIvr3SKeQv3KzA/eSE6B3MS9mfmqynLHrzj92+/9K21V7sfhX88Sg5u/PTyyurlN7p/VrrRaCRv06NzMG/D4VDwRqMP91997vPOjR6Wb+WV28knC7ysxcqyTN6mTudgYc4M3tKsuJzq3Ojju1vPL2fnwk9CPrktb9Olc7B4w+GwuIa3Xq8vwcvcic4dJt23frhk85ZJktzZ3c3f6NhaMiM6ByVyetpqs9nc73ZjnNX8cP/V505tRXnr7mHklcuHbkvwV1wWOgcllabp6Tf7/X4/lpNSj47njj96t3vjtWdX15594/b7h4u9sqkL4/XOTie/ZUn+txn1kL0sdA7KLp/VzEcA+UpelV8lT6/PHR/efevyyuraS7eS6g/qTrctrLr1ej1DtznTOaiSNE17vV7+tMww6xWaV7VxXoSdC3872+12sW1brdZ+t+uGkwukc1BVSZLsd7vF5m00Gp2dTjVGDEe/f+fFwvm50acfvftvb774rbWV7zW7f6xK5obD4WAwuLO7W/xbCNuItK08dA5iEJpXnNsMI4lSDvUecz+UldXLr974j7vJ0aKv7wnSNB0MBuHtRfFbvdlshvW2CrzDWD46B7EJK0MnBhl59vr9vnHGOQ2Hw/AGorPTOfHNDGHr9Xq+meWncxC5JEl6vd6Zr9Rhek35RqNRlmVJkoSx2na7feJ7tV6vh3cJwlZFOgfLpTjzVtwukb+ad3Y6efzmMOEZ7nM9tx32YYgWRmnhm3AiaaerVrJZ3+WVJEl4jvFFf1R0DpZdXr4w5isuOxVf98O+wf1uN7z6B5P/6cXHhE6YurxhYQgbrjb8R5353xX+0JC0/W53MBgYq5VZlmXhTcl6vX6h2ukccIY0TfNahFTkQXrcR8jJiY8wNVr8CLOC4eNnm5vFr/Czzc0zv8jjPs5M1+MiHcapYRtkkiRVPnq41JIkuWjtvrhzADPy5b/4y2KTvvrlryz6iqiGr375K8/87TfWVla/+czKF9ZO54BF+sbTl0LkvvH0pUVfC5XxpaeeevprX//mMythIuHJxznMWwILNhwO7fXgnLIs2+92w5T1Vqt1niVVnQOgGi5auEDnAKiAwWDwxML9ae/qWq1Wu/STvfR4dHz/dzeufrtWu/L2vSOdA6Aavmh++/jo3o0rtZdv3rt749pv3jt6cJ9UnQMgGn/au7pWu/SzvfTT/FM6B0A0Pvng5su1q3v3C5/SOQCi8ckHN1+uXbp+cPj5w510DoBIHKf716/98uql7147+Dj/pM4BEIWj/7l5rXPv6H8Prn3/hZvvfZbu/+r2e8c6B0DlHb9384VLtSvX9z44HI2ODw+uX6p9++qN390/Ho10DoC46RwAMdM5AGKmcwDETOcAiJnOARAznQMgZjoHQMx0DoCY6RwAMdM5AGKmcwDETOcAiJnOARAznQMgZv8PU077oIlLsqUAAAAASUVORK5CYII=" alt></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>
<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;">The function has a local maximum at the point A and a local minimum at the point B.</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 the coordinates of the points A and B.</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 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;">Given that the graph of the function has exactly one point of inflexion, find its coordinates.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(x) = {(\ln x)^2} + \frac{{2x\ln x}}{x}\left( { = {{(\ln x)}^2} + 2\ln x = \ln x(\ln x + 2)} \right)\) <strong> <em>M1A1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(x) = 0{\text{ }}( \Rightarrow x = 1,{\text{ }}x = {e^{ - 2}})\) <em><strong>M1</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><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 an attempt to solve \(f'(x) = 0\).</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;">\(A({e^{ - 2}},\,4{e^{ - 2}})\) </span><strong style="font-family: 'times new roman', times; font-size: medium;">and </strong><em style="font-family: 'times new roman', times; font-size: medium;">B</em><span style="font-family: 'times new roman', times; font-size: medium;">(1, 0) </span><em style="font-family: 'times new roman', times; font-size: medium;"><strong>A1A1</strong></em></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;">The 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;">is independent of prior working.</span></p>
<p><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[5 marks]</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;">\(f''(x) = \frac{2}{x}(\ln x + 1)\) <strong><em>A1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(f''(x) = 0{\text{ }}\left( { \Rightarrow x = {e^{ - 1}}} \right)\) <strong><em>(M1)</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">inflexion point \(({e^{ - 1}},{\text{ }}{e^{ - 1}})\) <strong><em>A1</em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: <em>M1 </em></strong>for attempt to solve \(f''(x) = 0\).</span></p>
<p> </p>
<p><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: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This was answered very well. Candidates are very familiar with this type of question. Some lost a couple of marks by failing to find their final <em>y</em> coordinates, though only the weakest struggled with differentiation and so made little progress.</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;">This was answered very well. Candidates are very familiar with this type of question. Some lost a couple of marks by failing to find their final <em>y</em> coordinates, though only the weakest struggled with differentiation and so made little progress.</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: 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_1.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 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 function <em>f</em> is defined by \(f(x) = {{\text{e}}^x}\sin x\) .</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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Show that \(f''(x) = 2{{\text{e}}^x}\sin \left( {x + \frac{\pi }{2}} \right)\) .</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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Obtain a similar expression for \({f^{(4)}}(x)\) .</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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Suggest an expression for \({f^{(2n)}}(x)\), \(n \in {\mathbb{Z}^ + }\), and prove your conjecture using mathematical induction.</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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(x) = {{\text{e}}^x}\sin x + {{\text{e}}^x}\cos x\) <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;">\(f''(x) = {{\text{e}}^x}\sin x + {{\text{e}}^x}\cos x + {{\text{e}}^x}\cos x - {{\text{e}}^x}\sin x\) <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;">\( = 2{{\text{e}}^x}\cos x\) <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;">\( = 2{{\text{e}}^x}\sin \left( {x + \frac{\pi }{2}} \right)\) <strong><em>AG</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>
<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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'''(x) = 2{{\text{e}}^x}\sin \left( {x + \frac{\pi }{2}} \right) + 2{{\text{e}}^x}\cos \left( {x + \frac{\pi }{2}} \right)\) <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;">\({f^{(4)}}(x) = 2{{\text{e}}^x}\sin \left( {x + \frac{\pi }{2}} \right) + 2{{\text{e}}^x}\cos \left( {x + \frac{\pi }{2}} \right) + 2{{\text{e}}^x}\cos \left( {x + \frac{\pi }{2}} \right) - 2{{\text{e}}^x}\sin \left( {x + \frac{\pi }{2}} \right)\) <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;">\( = 4{{\text{e}}^x}\cos \left( {x + \frac{\pi }{2}} \right)\) <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;">\( = 4{{\text{e}}^x}\sin (x + \pi )\) <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;"><strong><em>[4 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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the conjecture is that</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;">\({f^{(2n)}}(x) = {2^n}{{\text{e}}^x}\sin \left( {x + \frac{{n\pi }}{2}} \right)\) <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;">for <em>n</em> = 1, this formula gives</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;">\(f''(x) = 2{{\text{e}}^x}\sin \left( {x + \frac{\pi }{2}} \right)\) which is correct <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;">let the result be true for <em>n</em> = <em>k</em> , \(\left( {i.e.{\text{ }}{f^{(2k)}}(x) = {2^k}{{\text{e}}^x}\sin \left( {x + \frac{{k\pi }}{2}} \right)} \right)\) <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;">consider \({f^{(2k + 1)}}(x) = {2^k}{{\text{e}}^x}\sin \left( {x + \frac{{k\pi }}{2}} \right) + {2^k}{{\text{e}}^x}\cos \left( {x + \frac{{k\pi }}{2}} \right)\) <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;">\({f^{\left( {2(k + 1)} \right)}}(x) = {2^k}{{\text{e}}^x}\sin \left( {x + \frac{{k\pi }}{2}} \right) + {2^k}{{\text{e}}^x}\cos \left( {x + \frac{{k\pi }}{2}} \right) + {2^k}{{\text{e}}^x}\cos \left( {x + \frac{{k\pi }}{2}} \right) - {2^k}{{\text{e}}^x}\sin \left( {x + \frac{{k\pi }}{2}} \right)\) <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;">\( = {2^{k + 1}}{{\text{e}}^x}\cos \left( {x + \frac{{k\pi }}{2}} \right)\) <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;">\( = {2^{k + 1}}{{\text{e}}^x}\sin \left( {x + \frac{{(k + 1)\pi }}{2}} \right)\) <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;">therefore true for \(n = k \Rightarrow \) true for \(n = k + 1\) and since true for \(n = 1\)</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;">the result is proved by induction. <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;"> Award the final </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;"> only if the two </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>M</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> marks have been awarded.</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>[8 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<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 \(f(x) = x{{\text{e}}^{2x}}\) .</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;">It can be shown that \({f^{(n)}}(x) = ({2^n}x + n{2^{n - 1}}){{\text{e}}^{2x}}\) for all \(n \in {\mathbb{Z}^ + }\), where \({f^{(n)}}(x)\) represents the \({n^{{\text{th}}}}\) derivative of \(f(x)\) .</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;">(a) By considering \({f^{(n)}}(x){\text{ for }}n = 1{\text{ and }}n = 2\) , show that there is one minimum point P on the graph of <em>f</em> , and find the coordinates of P.</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) Show that <em>f</em> has a point of inflexion Q at <em>x</em> = −1.</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;">(c) Determine the intervals on the domain of <em>f</em> where <em>f</em> is</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;">(i) concave up;</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;">(ii) concave down.</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;">(d) Sketch <em>f</em> , clearly showing any intercepts, asymptotes and the points P and Q.</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;">(e) Use mathematical induction to prove that \({f^{(n)}}(x) = ({2^n}x + n{2^{n - 1}}){{\text{e}}^{2x}}{\text{ for all }}n \in {\mathbb{Z}^ + },{\text{ where }}{f^{(n)}}{\text{ represents the }}{n^{{\text{th}}}}{\text{ derivative of }}f(x)\) .</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: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \(f'(x) = (1 + 2x){{\text{e}}^{2x}}\) <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;">\(f'(x) = 0\) <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;">\( \Rightarrow (1 + 2x){{\text{e}}^{2x}} = 0 \Rightarrow x = - \frac{1}{2}\) <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;">\(f''(x) = ({2^2}x + 2 \times {2^{2 - 1}}){{\text{e}}^{2x}} = (4x + 4){{\text{e}}^{2x}}\) <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;">\(f''\left( { - \frac{1}{2}} \right) = \frac{2}{{\text{e}}}\) <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;">\(\frac{2}{{\text{e}}} > 0 \Rightarrow {\text{at }}x = - \frac{1}{2},{\text{ }}f(x){\text{ has a minimum.}}\) <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;">\({\text{P}}\left( { - \frac{1}{2}, - \frac{1}{{2{\text{e}}}}} \right)\) <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;"><strong><em>[7 marks]</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;">(b) \(f''(x) = 0 \Rightarrow 4x + 4 = 0 \Rightarrow x = - 1\) <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;">\({\text{Using the }}{{\text{2}}^{{\text{nd}}}}{\text{ derivative }}f''\left( { - \frac{1}{2}} \right) = \frac{2}{{\text{e}}}{\text{ and }}f''( - 2) = - \frac{4}{{{{\text{e}}^4}}},\) <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;">the sign change indicates a point of inflexion. <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;"><strong><em>[5 marks]</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;">(c) (i) <em>f</em>(<em>x</em>) is concave up for \(x > - 1\) . <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> </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;">(ii) <em>f</em>(<em>x</em>) is concave down for \(x < - 1\) . <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>
<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;">(d)<br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px 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>A1A1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica; min-height: 29.0px;"> </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 P and Q, with Q above P,</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>A1</em></strong> for asymptote at <em>y</em> = 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;"><strong><em>A1</em></strong> for (0, 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;"><strong><em>A1</em></strong> for shape.</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>[4 marks]</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;">(e) Show true for <em>n</em> = 1 <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;">\(f'(x) = {{\text{e}}^{2x}} + 2x{{\text{e}}^{2x}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0px 0px 0px 30px; font: 24px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {{\text{e}}^{2x}}(1 + 2x) = (2x + {2^0}){{\text{e}}^{2x}}\)</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;">Assume true for \(n = k{\text{ , }}i.e.{\text{ }}{f^{(k)}}x = ({2^k}x + k \times {2^{k - 1}}){{\text{e}}^{2x}}{\text{, }}k \geqslant 1\) <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;">Consider \(n = k + 1{\text{ , }}i.e.{\text{ an attempt to find }}\frac{{\text{d}}}{{{\text{d}}x}}\left( {{f^k}(x)} \right)\) . <em><strong>M1</strong></em></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;">\({F^{(k + 1)}}(x) = {2^k}{{\text{e}}^{2x}} + 2{{\text{e}}^{2x}}({2^k}x + k \times {2^{k - 1}})\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0px 0px 0px 30px; font: 24px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \left( {{2^k} + 2({2^k}x + k \times {2^{k - 1}})} \right){{\text{e}}^{2x}}\)</span></p>
<p style="margin: 0px 0px 0px 30px; font: 24px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = (2 \times {2^k}x + {2^k} + k \times 2 \times {2^{k - 1}}){{\text{e}}^{2x}}\)</span></p>
<p style="margin: 0px 0px 0px 30px; font: 24px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = ({2^{k + 1}}x + {2^k} + k \times {2^k}){{\text{e}}^{2x}}\) <strong><em>A1<br></em></strong>\( = \left( {{2^{k + 1}}x + \left( {k + 1} \right){2^k}} \right){{\text{e}}^{2x}}\) <em><strong>A1</strong></em><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;"><em>P</em>(<em>n</em>) is true for \(k \Rightarrow P(n)\) is true for <em>k</em> + 1, and since true for <em>n</em> = 1, result proved by mathematical induction \(\forall n \in {\mathbb{Z}^ + }\)</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> Only award <strong><em>R1</em></strong> if a reasonable attempt is made to prove the \({(k + 1)^{{\text{th}}}}\) step.</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>[9 marks]</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>Total [27 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;">This was the most accessible question in section B for these candidates. A majority of candidates produced partially correct answers to part (a), but a significant number struggled with demonstrating that the point is a minimum, despite the hint being given in the question. Part (b) started quite successfully but many students were unable to prove it is a point of inflexion or, more commonly, did not attempt to justify it. Correct answers were often seen for part (c). Part (d) was dependent on the successful completion of the first three parts. If candidates made errors in earlier parts, this often became obvious when they came to sketch the curve. However, few candidates realised that this part was a good way of checking that the above answers were at least consistent. The quality of curve sketching was rather weak overall, with candidates not marking points appropriately and not making features such as asymptotes clear. It is not possible to tell to what extent this was an effect of candidates not having a calculator, but it should be noted that asking students to sketch curves without a calculator will continue to appear on non-calculator papers. In part (e) the basic idea of proof by induction had clearly been taught with a significant majority of students understanding this. However, many candidates did not understand that they had to differentiate again to find the result for (<em>k</em> + 1) .</span></p>
</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="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="question">
<p>Find \(\int {\arcsin x\,{\text{d}}x} \)</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>attempt at integration by parts with \(u = \arcsin x\) and \(v' = 1\) <strong><em>M1</em></strong></p>
<p>\(\int {\arcsin x\,{\text{d}}x} = x\arcsin x - \int {\frac{x}{{\sqrt {1 - {x^2}} }}{\text{d}}x} {\text{ }}\) <strong><em>A1A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>A1 </em></strong>for \(x\arcsin x\) and <strong><em>A1 </em></strong>for \( - \int {\frac{x}{{\sqrt {1 - {x^2}} }}{\text{d}}x} \).</p>
<p> </p>
<p>solving \(\int {\frac{x}{{\sqrt {1 - {x^2}} }}{\text{d}}x} \) by substitution with \(u = 1 - {x^2}\) or inspection <strong><em>(M1)</em></strong></p>
<p>\(\int {\arcsin x{\text{d}}x} = x\arcsin x + \sqrt {1 - {x^2}} + c\) <strong><em>A1</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p 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;">Show that \(\int_0^{\frac{\pi }{6}} {x\sin 2x{\text{d}}x = \frac{{\sqrt 3 }}{8} - \frac{\pi }{{24}}} \).</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;">Using integration by parts <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;">\(u = x{\text{, }}\frac{{{\text{d}}u}}{{{\text{d}}x}} = 1,{\text{ }}\frac{{{\text{d}}v}}{{{\text{d}}x}} = \sin 2x{\text{ and }}v = - \frac{1}{2}\cos 2x\) <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;">\(\left[ {x\left( { - \frac{1}{2}\cos 2x} \right)} \right]_0^{\frac{\pi }{6}} - \int_0^{\frac{\pi }{6}} {\left( { - \frac{1}{2}\cos 2x} \right){\text{d}}x} \) <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;">\( = \left[ {x\left( { - \frac{1}{2}\cos 2x} \right)} \right]_0^{\frac{\pi }{6}} + \left[ {\frac{1}{4}\sin 2x} \right]_0^{\frac{\pi }{6}}\) <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;"> Award the </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> above if the limits are not included.</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;">\(\left[ {x\left( { - \frac{1}{2}\cos 2x} \right)} \right]_0^{\frac{\pi }{6}} = - \frac{\pi }{{24}}\) </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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\left[ {\frac{1}{4}\sin 2x} \right]_0^{\frac{\pi }{6}} = \frac{{\sqrt 3 }}{8}\) <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;">\(\int_0^{\frac{\pi }{6}} {x\sin 2x{\text{d}}x = \frac{{\sqrt 3 }}{8} - \frac{\pi }{{24}}} \) <strong><em>AG</em></strong> <strong><em>N0</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;"> Allow </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>FT</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> on the last two </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 if the expressions are the negative of the correct ones.</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>[6 marks]</em></strong></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 reasonably well done, with few candidates making the inappropriate choice of <em>u</em> and \(\frac{{{\text{d}}v}}{{{\text{d}}x}}\). The main source of a loss of marks was in finding <em>v</em> by integration. A few candidates used the double angle formula for sine, with poor results.</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 class="p1">The function \(f\) is defined as \(f(x) = a{x^2} + bx + c\) where \(a,{\text{ }}b,{\text{ }}c \in \mathbb{R}\).</p>
<p class="p1">Hayley conjectures that \(\frac{{f({x_2}) - f({x_1})}}{{{x_2} - {x_1}}} = \frac{{f'({x_2}) + f'({x_1})}}{2},{\text{ }}x1 \ne x2\).</p>
<p class="p1">Show that Hayley’s conjecture is correct.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p class="p1">\(\frac{{f({x_2}) - f({x_1})}}{{{x_2} - {x_1}}} = \frac{{ax_2^2 + b{x_2} + c - (ax_1^2 + b{x_1} + c)}}{{{x_2} - {x_1}}}\) <strong><em>(M1)</em></strong></p>
<p class="p1">\( = \frac{{a(x_2^2 - x_1^2) + b({x_2} - {x_1})}}{{{x_2} - {x_1}}}\) <strong><em>A1</em></strong></p>
<p class="p1">\( = \frac{{a({x_2} - {x_1})({x_2} + {x_1}) + b({x_2} - {x_1})}}{{{x_2} - {x_1}}}\) <strong><em>(A1)</em></strong></p>
<p class="p1">\( = a({x_2} + {x_1}) + b\,\,\,\,\,({x_1} \ne {x_2})\) <strong><em>A1</em></strong></p>
<p class="p1">\(\frac{{f'({x_2}) + f'({x_1})}}{2} = \frac{{(2a{x_2} + b) + (2a{x_1} + b)}}{2}\) <strong><em>M1</em></strong></p>
<p class="p1">\( = \frac{{2a({x_2} + {x_1}) + 2b}}{2}\)</p>
<p class="p1">\( = a({x_2} + {x_1}) + b\) <strong><em>A1</em></strong></p>
<p class="p1">so Hayley’s conjecture is correct <strong><em>AG</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">
<p class="p1">This was generally answered very well. A small minority attempted to ‘prove’ the result by substituting specific values into the identity and thus gained little or no credit. Some started by assuming the result to be correct, then manipulated both sides until they derived an obvious identity. Reluctantly, they gained credit for this, though such an approach should be discouraged.</p>
</div>
<br><hr><br><div class="question">
<p class="p1">Find the \(x\)-coordinates of all the points on the curve \(y = 2{x^4} + 6{x^3} + \frac{7}{2}{x^2} - 5x + \frac{3}{2}\) <span class="s1">at which</span></p>
<p class="p2">the tangent to the curve is parallel to the tangent at \(( - 1,{\text{ }}6)\).</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p class="p1"><span class="Apple-converted-space">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 8{x^3} + 18{x^2} + 7x - 5\) </span><strong><em>A1</em></strong></p>
<p class="p1">when \(x = - 1,{\text{ }}\frac{{{\text{d}}y}}{{{\text{d}}x}} = - 2\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\(8{x^3} + 18{x^2} + 7x - 5 = - 2\) </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p2">\(8{x^3} + 18{x^2} + 7x - 3 = 0\)</p>
<p class="p1"><span class="s2">\((x + 1)\) </span>is a factor <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p3"><span class="Apple-converted-space">\(8{x^3} + 18{x^2} + 7x - 3 = (x + 1)(8{x^2} + 10x - 3)\) </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span><em>M1 </em></strong>is for attempting to find the quadratic factor.</p>
<p class="p3">\((x + 1)(4x - 1)(2x + 3) = 0\)</p>
<p class="p3"><span class="Apple-converted-space">\((x = - 1),{\text{ }}x = 0.25,{\text{ }}x = - 1.5\) </span><span class="s1"><strong><em>(M1)A1</em></strong></span></p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span><em>M1 </em></strong>is for an attempt to solve their quadratic factor.</p>
<p class="p1"><strong><em>[7 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p class="p1">The first half of the question was accessible to all the candidates. Some though saw the word ‘tangent’ and lost time calculating the equation of this. It was a pity that so many failed to spot that \(x + 1\) was a factor of the cubic and so did not make much progress with the final part of this question.</p>
</div>
<br><hr><br><div class="question">
<p>Consider the curve \(y = \frac{1}{{1 - x}} + \frac{4}{{x - 4}}\).</p>
<p>Find the <em>x</em>-coordinates of the points on the curve where the gradient is zero.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>valid attempt to find \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) <em><strong>M1</strong></em></p>
<p>\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{1}{{{{\left( {1 - x} \right)}^2}}} - \frac{4}{{{{\left( {x - 4} \right)}^2}}}\) <em><strong>A1A1</strong></em></p>
<p>attempt to solve \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\) <em><strong>M1</strong></em></p>
<p>\(x = 2,\,\,x = - 2\) <em><strong>A1A1</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;">Use the substitution \(x = a\sec \theta \) to show that \(\int_{a\sqrt 2 }^{2a} {\frac{{{\text{d}}x}}{{{x^3}\sqrt {{x^2} - {a^2}} }} = \frac{1}{{24{a^3}}}\left( {3\sqrt 3 + \pi - 6} \right)} \).</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: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = a\sec \theta \)</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;">\(\frac{{{\text{d}}x}}{{{\text{d}}\theta }} = a\sec \theta \tan \theta \) <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;">new limits:</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;">\(x = a\sqrt 2 \Rightarrow \theta = \frac{\pi }{4}\) and \(x = 2a \Rightarrow \theta = \frac{\pi }{3}\) <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;">\(\int_{\frac{\pi }{4}}^{\frac{\pi }{3}} {\frac{{a\sec \theta \tan \theta }}{{{a^3}{{\sec }^3}\theta \sqrt {{a^2}{{\sec }^2}\theta - {a^2}} }}{\text{d}}\theta } \) <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;">\( = \int_{\frac{\pi }{4}}^{\frac{\pi }{3}} {\frac{{{{\cos }^2}\theta }}{{{a^3}}}{\text{d}}\theta } \) <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;">using \({\cos ^2}\theta = \frac{1}{2}(\cos 2\theta + 1)\) <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;">\(\frac{1}{{2{a^3}}}\left[ {\frac{1}{2}\sin 2\theta + \theta } \right]_{\frac{\pi }{4}}^{\frac{\pi }{3}}\) or equivalent <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;">\( = \frac{1}{{4{a^3}}}\left( {\frac{{\sqrt 3 }}{2} + \frac{{2\pi }}{3} - 1 - \frac{\pi }{2}} \right)\) or equivalent <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;">\( = \frac{1}{{24{a^3}}}\left( {3\sqrt 3 + \pi - 6} \right)\) <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><em>[7 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 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;">Calculate \(\int_{\frac{\pi }{4}}^{\frac{\pi }{3}} {\frac{{{{\sec }^2}x}}{{\sqrt[3]{{\tan x}}}}{\text{d}}x} \) .</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: 35.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find \(\int {{{\tan }^3}x{\text{d}}x} \) .</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: 27.0px Times; color: #3f3f3f;"><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: 27.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">let \(u = \tan x;{\text{ d}}u = {\sec ^2}x{\text{d}}x\) <strong><em>(M1)</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;">consideration of change of limits <strong><em>(M1)</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;">\(\int_{\frac{\pi }{4}}^{\frac{\pi }{3}} {\frac{{{{\sec }^2}x}}{{\sqrt[3]{{\tan x}}}}{\text{d}}x} = \int_{\frac{\pi }{4}}^{\frac{\pi }{3}} {\frac{1}{{{u^{\frac{1}{3}}}}}{\text{d}}u} \) <strong><em>(A1)</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> Do not penalize lack of limits.</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;">\( = \left[ {\frac{{3{u^{\frac{2}{3}}}}}{2}} \right]_1^{\sqrt 3 }\) <strong><em>A1</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;">\( = \frac{{3 \times {{\sqrt 3 }^{\frac{2}{3}}}}}{2} - \frac{3}{2} = \left( {\frac{{3\sqrt[3]{3} - 3}}{2}} \right)\) <strong><em>A1A1 N0</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>OR</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;">\(\int_{\frac{\pi }{4}}^{\frac{\pi }{3}} {\frac{{{{\sec }^2}x}}{{\sqrt[3]{{\tan x}}}}{\text{d}}x} = \left[ {\frac{{3{{(\tan x)}^{\frac{2}{3}}}}}{2}} \right]_{\frac{\pi }{4}}^{\frac{\pi }{3}}\) <strong><em>M2A2</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;">\( = \frac{{3 \times {{\sqrt 3 }^{\frac{2}{3}}}}}{2} - \frac{3}{2} = \left( {\frac{{3\sqrt[3]{3} - 3}}{2}} \right)\) <strong><em>A1A1 N0</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><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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {{{\tan }^3}x{\text{d}}x} = \int {\tan x({{\sec }^2}x - 1){\text{d}}x} \) <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;">\( = \int {(\tan x \times {{\sec }^2}x - \tan x){\text{d}}x} \)</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;">\( = \frac{1}{2}{\tan ^2}x - \ln \left| {\sec x} \right| + C\) <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>Note:</strong> Do not penalize the absence of absolute value or <em>C</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;"> </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">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: 27.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Quite a variety of methods were successfully employed to solve 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: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates did not attempt part (b).</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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the value of \(\int_0^1 {t\ln (t + 1){\text{d}}t} \).</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;">attempt at integration by substitution <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;">using \(u = t + 1{\text{, d}}u = {\text{d}}t\), the integral becomes</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;">\(\int_1^2 {(u - 1)\ln u{\text{d}}u} \) <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;">then using integration by parts <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;">\(\int_1^2 {(u - 1)\ln u{\text{d}}u} = \left[ {\left( {\frac{{{u^2}}}{2} - u} \right)\ln u} \right]_1^2 - \int_1^2 {\left( {\frac{{{u^2}}}{2} - u} \right) \times \frac{1}{u}{\text{d}}u} \) <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;">\( = - \left[ {\frac{{{u^2}}}{4} - u} \right]_1^2\) <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;">\( = \frac{1}{4}\,\,\,\,\,\)(accept 0.25) <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>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;">attempt to integrate by parts <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;">correct choice of variables to integrate and differentiate <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;">\(\int_0^1 {t\ln (t + 1){\text{d}}t} = \left[ {\frac{{{t^2}}}{2}\ln (t + 1)} \right]_0^1 - \int_0^1 {\frac{{{t^2}}}{2} \times \frac{1}{{t + 1}}{\text{d}}t} \) <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;">\( = \left[ {\frac{{{t^2}}}{2}\ln (t + 1)} \right]_0^1 - \frac{1}{2}\int_0^1 {t - 1 + \frac{1}{{t + 1}}{\text{d}}t} \) <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;">\( = \left[ {\frac{{{t^2}}}{2}\ln (t + 1)} \right]_0^1 - \frac{1}{2}\left[ {\frac{{{t^2}}}{2} - t + \ln (t + 1)} \right]_0^1\) <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;">\( = \frac{1}{4}\,\,\,\,\,\)(accept 0.25) <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>[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;">Again very few candidates gained full marks on this question. The most common approach was to begin by integrating by parts, which was done correctly, but very few candidates then knew how to integrate \(\frac{{{t^2}}}{{t + 1}}\). Those who began with a substitution often made more progress. Again a number of candidates were let down by their inability to simplify appropriately.</span></p>
</div>
<br><hr><br><div class="specification">
<p>Let \(y = {\text{arccos}}\left( {\frac{x}{2}} \right)\)</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>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>Find \(\int_0^1 {{\text{arccos}}\left( {\frac{x}{2}} \right){\text{d}}x} \).</p>
<div class="marks">[7]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(y = {\text{arccos}}\left( {\frac{x}{2}} \right) \Rightarrow \frac{{{\text{d}}y}}{{{\text{d}}x}} = - \frac{1}{{2\sqrt {1 - {{\left( {\frac{x}{2}} \right)}^2}} }}\left( { = - \frac{1}{{\sqrt {4 - {x^2}} }}} \right)\) <em><strong> M1A1</strong></em></p>
<p><strong>Note:</strong> <strong><em>M1</em></strong> is for use of the chain rule.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt at integration by parts <em><strong>M1</strong></em></p>
<p>\(u = {\text{arccos}}\left( {\frac{x}{2}} \right) \Rightarrow \frac{{{\text{d}}u}}{{{\text{d}}x}} = - \frac{1}{{\sqrt {4 - {x^2}} }}\)</p>
<p>\(\frac{{{\text{d}}v}}{{{\text{d}}x}} = 1 \Rightarrow v = x\) <em><strong>(A1)</strong></em></p>
<p>\(\int_0^1 {{\text{arccos}}\left( {\frac{x}{2}} \right){\text{d}}x} = \left[ {x\,\,{\text{arccos}}\left( {\frac{x}{2}} \right)} \right]_0^1 + \int_0^1 {\frac{1}{{\sqrt {4 - {x^2}} }}} dx\) <em><strong>A1</strong></em></p>
<p>using integration by substitution or inspection <em><strong>(M1)</strong></em></p>
<p>\(\left[ {x\,\,{\text{arccos}}\left( {\frac{x}{2}} \right)} \right]_0^1 + \left[ { - {{\left( {4 - {x^2}} \right)}^{\frac{1}{2}}}} \right]_0^1\) <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>A1</strong> </em>for \({ - {{\left( {4 - {x^2}} \right)}^{\frac{1}{2}}}}\) or equivalent.</p>
<p><strong>Note:</strong> Condone lack of limits to this point.</p>
<p>attempt to substitute limits into their integral <em><strong>M1</strong></em></p>
<p>\( = \frac{\pi }{3} - \sqrt 3 + 2\) <em><strong>A1</strong></em></p>
<p><em><strong>[7 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>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="question">
<p>A particle moves in a straight line such that at time \(t\) seconds \((t \geqslant 0)\), its velocity \(v\), in \({\text{m}}{{\text{s}}^{ - 1}}\), is given by \(v = 10t{{\text{e}}^{ - 2t}}\). Find the exact distance travelled by the particle in the first half-second.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>\(s = \int\limits_0^{\frac{1}{2}} {10t{{\text{e}}^{ - 2t}}{\text{d}}t} \)</p>
<p>attempt at integration by parts <strong><em>M1</em></strong></p>
<p>\( = \left[ { - 5t{{\text{e}}^{ - 2t}}} \right]_0^{\frac{1}{2}} - \int\limits_0^{\frac{1}{2}} { - 5{{\text{e}}^{ - 2t}}{\text{d}}t} \) <strong><em>A1</em></strong></p>
<p>\( = \left[ { - 5t{{\text{e}}^{ - 2t}} - \frac{5}{2}{{\text{e}}^{ - 2t}}} \right]_0^{\frac{1}{2}}\) <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Condone absence of limits (or incorrect limits) and missing factor of 10 up to this point.</p>
<p> </p>
<p>\(s = \int\limits_0^{\frac{1}{2}} {10t{{\text{e}}^{ - 2t}}{\text{d}}t} \) <strong><em>(M1)</em></strong></p>
<p>\( = - 5{{\text{e}}^{ - 1}} + \frac{5}{2}{\text{ }}\left( { = \frac{{ - 5}}{{\text{e}}} + \frac{5}{2}} \right){\text{ }}\left( { = \frac{{5{\text{e}} - 10}}{{2{\text{e}}}}} \right)\) <strong><em>A1</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p 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) Show that \(\frac{3}{{x + 1}} + \frac{2}{{x + 3}} = \frac{{5x + 11}}{{{x^2} + 4x + 3}}\).</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) Hence find the value of <em>k</em> such that \(\int_0^2 {\frac{{5x + 11}}{{{x^2} + 4x + 3}}{\text{d}}x = \ln k} \) .</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) \(\frac{3}{{x + 1}} + \frac{2}{{x + 3}} = \frac{{3(x + 3) + 2(x + 1)}}{{(x + 1)(x + 3)}}\) <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;">\( = \frac{{3x + 9 + 2x + 2}}{{{x^2} + 4x + 3}}\) <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;">\( = \frac{{5x + 11}}{{{x^2} + 4x + 3}}\) <strong><em>AG</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) \(\int_0^2 {\frac{{5x + 11}}{{{x^2} + 4x + 3}}{\text{d}}x} = \int_0^2 {\left( {\frac{3}{{x + 1}} + \frac{2}{{x + 3}}} \right){\text{d}}x} \) <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;">\( = \left[ {3\ln (x + 1) + 2\ln (x + 3)} \right]_0^2\) <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;">\( = 3\ln 3 + 2\ln 5 - 3\ln 1 - 2\ln 3\,\,\,\,\,( = 3\ln 3 + 2\ln 5 - 2\ln 3)\) <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;">\( = \ln 3 + 2\ln 5\)</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;">\( = \ln 75\,\,\,\,\,(k = 75)\) <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>[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 students did not ‘Show’ enough in a) in order to be convincing. The need for the steps of the simplification to be shown was not clear. Too many did not link a) to b) and seemed to not be aware of the Command Term ‘hence’ and its implication for marking ( no marks will be awarded to alternative methods). The simplifications of the log expressions were done poorly by many and the fact that \({3^3} = 9\) was noted by too many. There were very few elegant solutions to this question.</span></p>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the substitution \(u = {x^{\frac{1}{2}}}\) to find \(\int {\frac{{{\text{d}}x}}{{{x^{\frac{3}{2}}} + {x^{\frac{1}{2}}}}}} \).</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find the value of \(\frac{1}{2}\int\limits_1^9 {\frac{{{\text{d}}x}}{{{x^{\frac{3}{2}}} + {x^{\frac{1}{2}}}}}} \), expressing your answer in the form arctan \(q\), where \(q \in \mathbb{Q}\).</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>\(\frac{{{\text{d}}u}}{{{\text{d}}x}} = \frac{1}{2}{x^{ - \frac{1}{2}}}\) (accept \({\text{d}}u = \frac{1}{2}{x^{ - \frac{1}{2}}}{\text{d}}x\) or equivalent) <em><strong>A1</strong></em></p>
<p>substitution, leading to an integrand in terms of \(u\) <em><strong>M1</strong></em></p>
<p>\(\int {\frac{{2u{\text{d}}u}}{{{u^3} + u}}} \) or equivalent <em><strong>A1</strong></em></p>
<p>= 2 arctan \(\left( {\sqrt x } \right)\left( { + c} \right)\) <em><strong>A1</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p> </p>
<p>\(\frac{1}{2}\int\limits_1^9 {\frac{{{\text{d}}x}}{{{x^{\frac{3}{2}}} + {x^{\frac{1}{2}}}}}} \) = arctan 3 − arctan 1 <em><strong>A1</strong></em></p>
<p>tan(arctan 3 − arctan 1) = \(\frac{{3 - 1}}{{1 + 3 \times 1}}\) <em><strong>(M1)</strong></em></p>
<p>tan(arctan 3 − arctan 1) = \(\frac{1}{2}\)</p>
<p>arctan 3 − arctan 1 = arctan \(\frac{1}{2}\) <em><strong>A1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p 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 all values of <em>x</em> for \(0.1 \leqslant x \leqslant 1\) such that \(\sin (\pi {x^{ - 1}}) = 0\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p 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;">Find \(\int_{\frac{1}{{n + 1}}}^{\frac{1}{n}} {\pi {x^{ - 2}}\sin (\pi {x^{ - 1}}){\text{d}}x} \), showing that it takes different integer values when <em>n</em> is even and when <em>n</em> is odd.</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;">Evaluate \(\int_{0.1}^1 {\left| {\pi {x^{ - 2}}\sin (\pi {x^{ - 1}})} \right|{\text{d}}x} \).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p 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;">\(\sin (\pi {x^{ - 1}}) = 0{\text{ }}\frac{\pi }{x} = \pi ,{\text{ }}2\pi ( \ldots )\) <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;">\(x = 1,\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5},\frac{1}{6},\frac{1}{7},\frac{1}{8},\frac{1}{9},\frac{1}{{10}}\) <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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\left[ {\cos (\pi {x^{ - 1}})} \right]_{\frac{1}{{n + 1}}}^{\frac{1}{n}}\) <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;">\( = \cos (\pi n) - \cos \left( {\pi (n + 1)} \right)\) <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;">= 2 when <em>n</em> is even and = –2 when <em>n</em> is odd <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;"><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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int_{0.1}^1 {\left| {\pi {x^{ - 2}}\sin (\pi {x^{ - 1}})} \right|{\text{d}}x} = 2 + 2 + \ldots + 2 = 18\) <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;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">There were a pleasing number of candidates who answered part (a) correctly. Fewer were successful with part (b). It was expected by this stage of the paper that candidates would be able to just write down the value of the integral rather than use substitution to evaluate it.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">There were a pleasing number of candidates who answered part (a) correctly. Fewer were successful with part (b). It was expected by this stage of the paper that candidates would be able to just write down the value of the integral rather than use substitution to evaluate it.</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;">There were disappointingly few correct answers to part (c) with candidates not realising that it was necessary to combine the previous two parts in order to write down the answer.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p>The folium of Descartes is a curve defined by the equation \({x^3} + {y^3} - 3xy = 0\), shown in the following diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-07_om_18.23.15.png" alt="N17/5/MATHL/HP1/ENG/TZ0/07"></p>
<p>Determine the exact coordinates of the point P on the curve where the tangent line is parallel to the \(y\)-axis.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>\({x^3} + {y^3} - 3xy = 0\)</p>
<p>\(3{x^2} + 3{y^2}\frac{{{\text{d}}y}}{{{\text{d}}x}} - 3x\frac{{{\text{d}}y}}{{{\text{d}}x}} - 3y = 0\) <strong><em>M1A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Differentiation wrt \(y\) is also acceptable.</p>
<p> </p>
<p>\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{3y - 3{x^2}}}{{3{y^2} - 3x}}{\text{ }}\left( { = \frac{{y - {x^2}}}{{{y^2} - x}}} \right)\) <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>All following marks may be awarded if the denominator is correct, but the numerator incorrect.</p>
<p> </p>
<p>\({y^2} - x = 0\) <strong><em>M1</em></strong></p>
<p><strong>EITHER</strong></p>
<p>\(x = {y^2}\)</p>
<p>\({y^6} + {y^3} - 3{y^3} = 0\) <strong><em>M1A1</em></strong></p>
<p>\({y^6} - 2{y^3} = 0\)</p>
<p>\({y^3}({y^3} - 2) = 0\)</p>
<p>\((y \ne 0)\therefore y = \sqrt[3]{2}\) <strong><em>A1</em></strong></p>
<p>\(x = {\left( {\sqrt[3]{2}} \right)^2}{\text{ }}\left( { = \sqrt[3]{4}} \right)\) <strong><em>A1</em></strong></p>
<p><strong>OR</strong></p>
<p>\({x^3} + xy - 3xy = 0\) <strong><em>M1</em></strong></p>
<p>\(x({x^2} - 2y) = 0\)</p>
<p>\(x \ne 0 \Rightarrow y = \frac{{{x^2}}}{2}\) <strong><em>A1</em></strong></p>
<p>\({y^2} = \frac{{{x^4}}}{4}\)</p>
<p>\(x = \frac{{{x^4}}}{4}\)</p>
<p>\(x({x^3} - 4) = 0\)</p>
<p>\((x \ne 0)\therefore x = \sqrt[3]{4}\) <strong><em>A1</em></strong></p>
<p>\(y = \frac{{{{\left( {\sqrt[3]{4}} \right)}^2}}}{2} = \sqrt[3]{2}\) <strong><em>A1</em></strong></p>
<p><strong><em>[8 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p 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 body is moving in a straight line. When it is \(s\) metres from a fixed point O on the line its velocity, \(v\), is given by \(v = - \frac{1}{{{s^2}}},{\text{ }}s > 0\).</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;">Find the acceleration of the body when it is 50 cm from O.</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;">\(\frac{{{\text{d}}v}}{{{\text{d}}s}} = 2{s^{ - 3}}\) <strong><em>M1A1</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 \(2{s^{ - 3}}\) and <strong><em>A1 </em></strong>for the whole expression.</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;">\(a = v\frac{{{\text{d}}v}}{{{\text{d}}s}}\) <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;">\(a = - \frac{1}{{{s^2}}} \times \frac{2}{{{s^3}}}\left( { = - \frac{2}{{{s^5}}}} \right)\) <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;">when \(s = \frac{1}{2},{\text{ }}a = - \frac{2}{{{{(0.5)}^5}}}{\text{ }}( = - 64){\text{ (m}}{{\text{s}}^{ - 2}})\) <strong><em>M1A1</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>M1</em></strong> is for the substitution of 0.5 into their equation for acceleration.</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>M1A0 </em></strong>if \(s = 50\) is substituted into the 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 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="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;">Consider the curve \(y = x{{\text{e}}^x}\) and the line \(y = kx,{\text{ }}k \in \mathbb{R}\).</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) Let <em>k</em> = 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;">(i) Show that the curve and the line intersect once.</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) Find the angle between the tangent to the curve and the line at the point of intersection.</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) Let <em>k</em> =1. Show that the line is a tangent to the curve.</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;">(c) (i) Find the values of <em>k</em> for which the curve \(y = x{{\text{e}}^x}\) and the line \(y = kx\) meet in two distinct points.</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) Write down the coordinates of the points of intersection.</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;">(iii) Write down an integral representing the area of the region <em>A</em> enclosed by the curve and the line.</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;">(iv) <strong>Hence</strong>, given that \(0 < k < 1\), show that \(A < 1\).</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) (i) \(x{{\text{e}}^x} = 0 \Rightarrow x = 0\) <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;">so, they intersect only once at (0, 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;"> </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) \(y' = {{\text{e}}^x} + x{{\text{e}}^x} = (1 + x){{\text{e}}^x}\) <strong><em>M1A1</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;">\(y'(0) = 1\) <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;">\(\theta = \arctan 1 = \frac{\pi }{4}{\text{ }}(\theta = 45^\circ )\) <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>[5 marks]</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> </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;">(b) when \(k = 1,{\text{ }}y = x\)</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;">\(x{{\text{e}}^x} = x \Rightarrow x({{\text{e}}^x} - 1) = 0\) <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;">\( \Rightarrow x = 0\) <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;">\(y'(0) = 1\) which equals the gradient of the line \(y = x\) <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;">so, the line is tangent to the curve at origin <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>Note:</strong> Award full credit to candidates who note that the equation \(x({{\text{e}}^x} - 1) = 0\) has a double root <em>x</em> = 0 so <em>y</em> = <em>x</em> is a tangent.</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>[3 marks]</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> </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;">(c) (i) \(x{{\text{e}}^x} = kx \Rightarrow x({{\text{e}}^x} - k) = 0\) <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;">\( \Rightarrow x = 0{\text{ or }}x = \ln k\) <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;">\(k > 0{\text{ and }}k \ne 1\) <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> </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;">(ii) (0, 0) and \((\ln k,{\text{ }}k\ln k)\) <strong><em>A1A1</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> </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;">(iii) \(A = \left| {\int_0^{\ln k} {kx - x{{\text{e}}^x}{\text{d}}x} } \right|\) <strong><em>M1A1</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>Note:</strong> Do not penalize the omission of absolute value.</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;">(iv) attempt at integration by parts to find \(\int {x{{\text{e}}^x}{\text{d}}x} \) <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;">\(\int {x{{\text{e}}^x}{\text{d}}x} = x{{\text{e}}^x} - \int {{{\text{e}}^x}{\text{d}}x = {{\text{e}}^x}(x - 1)} \) <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;">as \(0 < k < 1 \Rightarrow \ln k < 0\) <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;">\(A = \int_{\ln k}^0 {kx - x{{\text{e}}^x}{\text{d}}x = \left[ {\frac{k}{2}{x^2} - (x - 1){{\text{e}}^x}} \right]_{\ln k}^0} \) <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;">\( = 1 - \left( {\frac{k}{2}{{(\ln k)}^2} - (\ln k - 1)k} \right)\) <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;">\( = 1 - \frac{k}{2}\left( {{{(\ln k)}^2} - 2\ln k + 2} \right)\)</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;">\( = 1 - \frac{k}{2}\left( {{{(\ln k - 1)}^2} + 1} \right)\) <strong><em>M1A1</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;">since \(\frac{k}{2}\left( {{{(\ln k - 1)}^2} + 1} \right) > 0\) <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;">\(A < 1\) <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>[15 marks]</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>Total [23 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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates solved (a) and (b) correctly but in (c), many failed to realise that the equation \(x{{\text{e}}^x} = kx\) has two roots under certain conditions and that the point of the question was to identify those conditions. Most candidates made a reasonable attempt to write down the appropriate integral in (c)(iii) with the modulus signs and limits often omitted but no correct solution has yet been seen to (c)(iv).</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following graph shows the relation \(x = 3\cos 2y + 4,{\text{ }}0 \leqslant y \leqslant \pi \).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2017-01-27_om_09.08.34.png" alt="M16/5/MATHL/HP1/ENG/TZ2/11"></p>
<p class="p1"><span class="s1">The curve is rotated 360° </span>about the \(y\)-axis to form a volume of revolution.</p>
</div>
<div class="specification">
<p class="p1">A container with this shape is made with a solid base of diameter 14 cm . The container is filled with water at a rate of \({\text{2 c}}{{\text{m}}^{\text{3}}}\,{\text{mi}}{{\text{n}}^{ - 1}}\)<span class="s1">. At time \(t\) minutes, the water depth is \(h{\text{ cm, }}0 \leqslant h \leqslant \pi \) and the volume of water in the container is \(V{\text{ c}}{{\text{m}}^{\text{3}}}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the value of the volume generated.</p>
<div class="marks">[8]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Given that \(\frac{{{\text{d}}V}}{{{\text{d}}h}} = \pi {(3\cos 2h + 4)^2}\), find an expression for \(\frac{{{\text{d}}h}}{{{\text{d}}t}}\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Find the value of \(\frac{{{\text{d}}h}}{{{\text{d}}t}}\) <span class="s1">when \(h = \frac{\pi }{4}\).</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 class="p1">(i) <span class="Apple-converted-space"> </span>Find \(\frac{{{{\text{d}}^2}h}}{{{\text{d}}{t^2}}}\).</p>
<p class="p2">(ii) <span class="Apple-converted-space"> </span>Find the values of \(h\) <span class="s1">for which \(\frac{{{{\text{d}}^2}h}}{{{\text{d}}{t^2}}} = 0\).</span></p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>By making specific reference to the shape of the container, interpret \(\frac{{{\text{d}}h}}{{{\text{d}}t}}\) <span class="s2">at the values of \(h\) found in part (c)(ii).</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 class="p1">use of \(\pi \int_a^b {{x^2}{\text{d}}y} \) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Condone any or missing limits.</p>
<p class="p1"><span class="Apple-converted-space">\(V = \pi \int_0^\pi {{{(3\cos 2y + 4)}^2}{\text{d}}y} \) </span><strong><em>(A1)</em></strong></p>
<p class="p3"><span class="Apple-converted-space">\( = \pi \int_0^\pi {(9{{\cos }^2}2y + 24\cos 2y + 16){\text{d}}y} \) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\(9{\cos ^2}2y = \frac{9}{2}(1 + \cos 4y)\) </span><strong><em>(M1)</em></strong></p>
<p class="p4"><span class="Apple-converted-space">\( = \pi \left[ {\frac{{9y}}{2} + \frac{9}{8}\sin 4y + 12\sin 2y + 16y} \right]_0^\pi \) </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p5"><span class="Apple-converted-space">\( = \pi \left( {\frac{{9\pi }}{2} + 16\pi } \right)\) </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p5"><span class="Apple-converted-space">\( = \frac{{41{\pi ^2}}}{2}{\text{ (c}}{{\text{m}}^3})\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>If the coefficient “\(\pi \)” is absent, or <em>eg</em><span class="s2">, “\(2\pi \)</span>” is used, only <strong><em>M </em></strong>marks are available.</p>
<p class="p1"><strong><em>[8 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>attempting to use \(\frac{{{\text{d}}h}}{{{\text{d}}t}} = \frac{{{\text{d}}V}}{{{\text{d}}t}} \times \frac{{{\text{d}}h}}{{{\text{d}}V}}\) with \(\frac{{{\text{d}}V}}{{{\text{d}}t}} = 2\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\(\frac{{{\text{d}}h}}{{{\text{d}}t}} = \frac{2}{{\pi {{(3\cos 2h + 4)}^2}}}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>substituting \(h = \frac{\pi }{4}\) into \(\frac{{{\text{d}}h}}{{{\text{d}}t}}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p2"><span class="Apple-converted-space">\(\frac{{{\text{d}}h}}{{{\text{d}}t}} = \frac{1}{{8\pi }}{\text{ (cm}}\,{\text{mi}}{{\text{n}}^{ - 1}})\) </span><strong><em>A1</em></strong></p>
<p class="p2"><strong>Note: <span class="Apple-converted-space"> </span></strong>Do not allow FT marks for (b)(ii).</p>
<p class="p2"><strong><em>[4 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"> \(\frac{{{{\text{d}}^2}h}}{{{\text{d}}{t^2}}} = \frac{{\text{d}}}{{{\text{d}}t}}\left( {\frac{{{\text{d}}h}}{{{\text{d}}t}}} \right) = \frac{{{\text{d}}h}}{{{\text{d}}t}} \times \frac{{\text{d}}}{{{\text{d}}h}}\left( {\frac{{{\text{d}}h}}{{{\text{d}}t}}} \right)\)</span> <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\( = \frac{2}{{\pi {{(3\cos 2h + 4)}^2}}} \times \frac{{24\sin 2h}}{{\pi {{(3\cos 2h + 4)}^3}}}\) </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p1"><strong>Note</strong>: <span class="Apple-converted-space"> </span>Award <strong><em>M1 </em></strong>for attempting to find \(\frac{{\text{d}}}{{{\text{d}}h}}\left( {\frac{{{\text{d}}h}}{{{\text{d}}t}}} \right)\).</p>
<p class="p1"><span class="Apple-converted-space">\( = \frac{{48\sin 2h}}{{{\pi ^2}{{(3\cos 2h + 4)}^5}}}\) </span><strong><em>A1</em></strong></p>
<p class="p2">(ii) <span class="Apple-converted-space"> \(\sin 2h = 0 \Rightarrow h = 0,{\text{ }}\frac{\pi }{2},{\text{ }}\pi \)</span> <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong>Note</strong>: <span class="Apple-converted-space"> </span>Award <strong><em>A1 </em></strong><span class="s2">for \(\sin 2h = 0 \Rightarrow h = 0,{\text{ }}\frac{\pi }{2},{\text{ }}\pi \) </span>from an incorrect \(\frac{{{{\text{d}}^2}h}}{{{\text{d}}{t^2}}}\).</p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span><strong>METHOD 1</strong></p>
<p class="p1"><span class="s2">\(\frac{{{\text{d}}h}}{{{\text{d}}t}}\) </span>is a minimum at \(h = 0,{\text{ }}\pi \) and the container is widest at these values <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1"><span class="s2">\(\frac{{{\text{d}}h}}{{{\text{d}}t}}\) is a maximum at \(h = \frac{\pi }{2}\) </span>and the container is narrowest at this value <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1"><strong><em>[7 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Part (a) was often answered well, though for some reason a minority tended to use the incorrect \(\pi \int {{{(3\cos 2y)}^2}{\text{d}}y} \) and gained few marks thereafter. Incorrect limits were sometimes seen, which led to only method marks being available. A pleasing number were able to deal with the integration of \({\cos ^2}2y\) through the use of the correct identity.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Part (b) was well answered and did not pose too many problems.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Correct answers to part (c) were rarely seen. Only the very best candidates appreciated the correct use of the chain rule when trying to determine an expression for \(\frac{{{{\text{d}}^2}h}}{{{\text{d}}{t^2}}}\).</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: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The curve <em>C</em> has equation \(y = \frac{1}{8}(9 + 8{x^2} - {x^4})\) .</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;">Find the coordinates of the points on <em>C</em> at which \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\) .</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: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The tangent to <em>C</em> at the point P(1, 2) cuts the <em>x</em>-axis at the point T. Determine the coordinates of T.</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: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The normal to <em>C</em> at the point P cuts the <em>y</em>-axis at the point N. Find the area of triangle PTN.</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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 2x - \frac{1}{2}{x^3}\) <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;">\(x\left( {2 - \frac{1}{2}{x^2}} \right) = 0\)</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;">\(x = 0,{\text{ }} \pm 2\)</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;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\) at \(\left( {0,\frac{9}{8}} \right),{\text{ }}\left( { - 2,\frac{{25}}{8}} \right),{\text{ }}\left( {2,\frac{{25}}{8}} \right)\) <strong><em>A1A1A1</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> Award <strong><em>A2</em></strong> for all three <em>x</em>-values correct with errors/omissions in <em>y</em>-values.</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>[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: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">at <em>x</em> =1, gradient of tangent \( = \frac{3}{2}\) <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>Note:</strong> In the following, allow <strong><em>FT</em></strong> on incorrect gradient.</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;">equation of tangent is \(y - 2 = \frac{3}{2}(x - 1)\,\,\,\,\,\left( {y = \frac{3}{2}x + \frac{1}{2}} \right)\) <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;">meets <em>x</em>-axis when y = 0 , \( - 2 = \frac{3}{2}(x - 1)\) <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;">\(x = - \frac{1}{3}\)</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;">coordinates of T are \(\left( { - \frac{1}{3},0} \right)\) <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>[4 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;">gradient of normal \( = - \frac{2}{3}\) <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;">equation of normal is \(y - 2 = - \frac{2}{3}(x - 1)\,\,\,\,\,\left( {y = - \frac{2}{3}x + \frac{8}{3}} \right)\) <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;">at <em>x</em> = 0 , \(y = \frac{8}{3}\) <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>Note:</strong> In the following, allow FT on incorrect coordinates of T and N.</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 Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">lengths of \({\text{PN}} = \sqrt {\frac{{13}}{9}} \) , \({\text{PT}} = \sqrt {\frac{{52}}{9}} \) <strong><em>A1A1</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;">area of triangle \({\text{PTN}} = \frac{1}{2} \times \sqrt {\frac{{13}}{9}} \times \sqrt {\frac{{52}}{9}} \) <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;">\( = \frac{{13}}{9}\) (or equivalent <em>e.g.</em> \(\frac{{\sqrt {676} }}{{18}}\)) <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>[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: 18.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The whole of this question seemed to prove accessible to a high proportion of candidates.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) was well answered by most, although a number of candidates gave only the <em>x</em>-values of the points or omitted the value at 0.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) was successfully solved by the majority of candidates, who also found the correct equation of the normal in (c).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The last section proved more difficult for many candidates, the most common error being to use the wrong perpendicular sides. There were a number of different approaches here all of which were potentially correct but errors abounded. </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: 18.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The whole of this question seemed to prove accessible to a high proportion of candidates.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) was well answered by most, although a number of candidates gave only the <em>x</em>-values of the points or omitted the value at 0.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) was successfully solved by the majority of candidates, who also found the correct equation of the normal in (c).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The last section proved more difficult for many candidates, the most common error being to use the wrong perpendicular sides. There were a number of different approaches here all of which were potentially correct but errors abounded. </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: 18.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The whole of this question seemed to prove accessible to a high proportion of candidates.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) was well answered by most, although a number of candidates gave only the <em>x</em>-values of the points or omitted the value at 0.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) was successfully solved by the majority of candidates, who also found the correct equation of the normal in (c).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The last section proved more difficult for many candidates, the most common error being to use the wrong perpendicular sides. There were a number of different approaches here all of which were potentially correct but errors abounded. </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: 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="question">
<p class="p1">A curve is given by the equation \(y = \sin (\pi \cos x)\).</p>
<p class="p2">Find the coordinates of all the points on the curve for which \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0,{\text{ }}0 \leqslant x \leqslant \pi \).</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p class="p1"><span class="Apple-converted-space">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = - \cos (\pi \cos x) \times \pi \sin x\) </span><strong><em>M1A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award follow through marks below if their answer is a multiple of the correct answer.</p>
<p class="p2"> </p>
<p class="p1">considering either \(\sin x = 0\) or \(\cos (\pi \cos x) = 0\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p3"><span class="Apple-converted-space">\(x = 0,{\text{ }}\pi \) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p4"><span class="Apple-converted-space">\(\pi \cos x = \frac{\pi }{2},{\text{ }} - \frac{\pi }{2}{\text{ }}\left( { \Rightarrow \cos x = \frac{1}{2}, - \frac{1}{2}} \right)\) </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p2"> </p>
<p class="p5"><span class="s1"><strong>Note: <span class="Apple-converted-space"> </span></strong></span>Condone absence of \( - \frac{\pi }{2}\).</p>
<p class="p5">\( \Rightarrow x = \frac{\pi }{3},{\text{ }}\frac{{2\pi }}{3}\)</p>
<p class="p5"><span class="Apple-converted-space">\((0,{\text{ }}0),{\text{ }}\left( {\frac{\pi }{3},{\text{ 1}}} \right),{\text{ (}}\pi {\text{, 0)}}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p4"><span class="Apple-converted-space">\(\left( {\frac{{2\pi }}{3},{\text{ }} - 1} \right)\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong><em>[7 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p class="p1">This was not a straight-forward differentiation and it was pleasing to see how many candidates managed to do it correctly. Having done this they found two of the solutions, often three of the solutions, successfully. The final solution was found by only a few candidates. Again candidates lost marks unnecessarily by not close reading the question and realising that they needed both coordinates of the points, not just the \(x\)-coordinates.</p>
</div>
<br><hr><br><div class="specification">
<p>It is given that \({\text{lo}}{{\text{g}}_2}\,y + {\text{lo}}{{\text{g}}_4}\,x + {\text{lo}}{{\text{g}}_4}\,2x = 0\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that \({\text{lo}}{{\text{g}}_{{r^2}}}x = \frac{1}{2}{\text{lo}}{{\text{g}}_r}\,x\) where \(r,\,x \in {\mathbb{R}^ + }\).</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>Express \(y\) in terms of \(x\). Give your answer in the form \(y = p{x^q}\), where <em>p</em> , <em>q</em> are constants.</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>The region <em>R</em>, is bounded by the graph of the function found in part (b), the <em>x</em>-axis, and the lines \(x = 1\) and \(x = \alpha \) where \(\alpha > 1\). The area of <em>R</em> is \(\sqrt 2 \).</p>
<p>Find the value of \(\alpha \).</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><strong>METHOD 1</strong></p>
<p>\({\text{lo}}{{\text{g}}_{{r^2}}}x = \frac{{{\text{lo}}{{\text{g}}_r}\,x}}{{{\text{lo}}{{\text{g}}_r}\,{r^2}}}\left( { = \frac{{{\text{lo}}{{\text{g}}_r}\,x}}{{{\text{2}}\,{\text{lo}}{{\text{g}}_r}\,r}}} \right)\) <em><strong> M1A1</strong></em></p>
<p>\( = \frac{{{\text{lo}}{{\text{g}}_r}\,x}}{2}\) <em><strong>AG</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>\({\text{lo}}{{\text{g}}_{{r^2}}}x = \frac{1}{{{\text{lo}}{{\text{g}}_x}\,{r^2}}}\) <em><strong>M1</strong></em></p>
<p>\( = \frac{1}{{2\,{\text{lo}}{{\text{g}}_x}\,r}}\) <em><strong>A1</strong></em></p>
<p>\( = \frac{{{\text{lo}}{{\text{g}}_r}\,x}}{2}\) <em><strong>AG</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>\({\text{lo}}{{\text{g}}_2}\,y + {\text{lo}}{{\text{g}}_4}\,x + {\text{lo}}{{\text{g}}_4}\,2x = 0\)</p>
<p>\({\text{lo}}{{\text{g}}_2}\,y + {\text{lo}}{{\text{g}}_4}\,2{x^2} = 0\) <em><strong>M1</strong></em></p>
<p>\({\text{lo}}{{\text{g}}_2}\,y + \frac{1}{2}{\text{lo}}{{\text{g}}_2}\,2{x^2} = 0\) <em><strong>M1</strong></em></p>
<p>\({\text{lo}}{{\text{g}}_2}\,y = - \frac{1}{2}{\text{lo}}{{\text{g}}_2}\,2{x^2}\)</p>
<p>\({\text{lo}}{{\text{g}}_2}\,y = {\text{lo}}{{\text{g}}_2}\left( {\frac{1}{{\sqrt {2x} }}} \right)\) <em><strong>M1A1</strong></em></p>
<p>\(y = \frac{1}{{\sqrt 2 }}{x^{ - 1}}\) <em><strong>A1</strong></em></p>
<p><strong>Note</strong>: For the final <em><strong>A</strong></em> mark, \(y\) must be expressed in the form \(p{x^q}\).</p>
<p><em><strong>[5 marks]</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>\({\text{lo}}{{\text{g}}_2}\,y + {\text{lo}}{{\text{g}}_4}\,x + {\text{lo}}{{\text{g}}_4}\,2x = 0\)</p>
<p>\({\text{lo}}{{\text{g}}_2}\,y + \frac{1}{2}{\text{lo}}{{\text{g}}_2}\,x + \frac{1}{2}{\text{lo}}{{\text{g}}_2}\,2x = 0\) <strong><em>M1</em></strong></p>
<p>\({\text{lo}}{{\text{g}}_2}\,y + {\text{lo}}{{\text{g}}_2}\,{x^{\frac{1}{2}}} + {\text{lo}}{{\text{g}}_2}\,{\left( {2x} \right)^{\frac{1}{2}}} = 0\) <em><strong>M1</strong></em></p>
<p>\({\text{lo}}{{\text{g}}_2}\,\left( {\sqrt 2 xy} \right) = 0\) <em><strong>M1</strong></em></p>
<p>\(\sqrt 2 xy = 1\) <strong><em>A1</em></strong></p>
<p>\(y = \frac{1}{{\sqrt 2 }}{x^{ - 1}}\) <em><strong>A1</strong></em></p>
<p><strong>Note</strong>: For the final <em><strong>A</strong></em> mark, \(y\) must be expressed in the form \(p{x^q}\).</p>
<p><em><strong>[5 marks]</strong></em></p>
<p> </p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the area of <em>R</em> is \(\int\limits_1^\alpha {\frac{1}{{\sqrt 2 }}} {x^{ - 1}}{\text{d}}x\) <em><strong>M1</strong></em></p>
<p>\( = \left[ {\frac{1}{{\sqrt 2 }}{\text{ln}}\,x} \right]_1^\alpha \) <em><strong>A1</strong></em></p>
<p>\( = \frac{1}{{\sqrt 2 }}{\text{ln}}\,\alpha \) <em><strong>A1</strong></em></p>
<p>\(\frac{1}{{\sqrt 2 }}{\text{ln}}\,\alpha = \sqrt 2 \) <em><strong>M1</strong></em></p>
<p>\(\alpha = {{\text{e}}^2}\) <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Only follow through from part (b) if \(y\) is in the form \(y = p{x^q}\)</p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</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: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Given that \(y = \frac{1}{{1 - x}}\), use mathematical induction to prove that \(\frac{{{{\text{d}}^n}y}}{{{\text{d}}{x^n}}} = \frac{{n!}}{{{{(1 - x)}^{n + 1}}}},{\text{ }}n \in {\mathbb{Z}^ + }\).</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;">proposition is true for <em>n</em> = 1 since \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{1}{{{{(1 - x)}^2}}}\) <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;">\( = \frac{{1!}}{{{{(1 - x)}^2}}}\) <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;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Must see the 1! for the </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;">.</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;">assume 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;"> = </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;">, \(k \in {\mathbb{Z}^ + }\), </span><em style="font-family: 'times new roman', times; font-size: medium;">i.e.</em><span style="font-family: 'times new roman', times; font-size: medium;"> \(\frac{{{{\text{d}}^k}y}}{{{\text{d}}{x^k}}} = \frac{{k!}}{{{{(1 - x)}^{k + 1}}}}\) </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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">consider \(\frac{{{{\text{d}}^{k + 1}}y}}{{{\text{d}}{x^{k + 1}}}} = \frac{{{\text{d}}\left( {\frac{{{{\text{d}}^k}y}}{{{\text{d}}{x^k}}}} \right)}}{{{\text{d}}x}}\) <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;">\( = (k + 1)k!{(1 - x)^{ - (k + 1) - 1}}\) <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;">\( = \frac{{(k + 1)!}}{{{{(1 - x)}^{k + 2}}}}\) <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;">hence, \({{\text{P}}_{k + 1}}\) is true whenever \({{\text{P}}_{k}}\) is true, and \({{\text{P}}_1}\) is true, and therefore the proposition is true for all positive integers <strong><em>R1</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;"> The final </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;"> is only available if at least 4 of the previous marks have been awarded.</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>[7 marks]</em></strong></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;">Most candidates were awarded good marks for this question. A disappointing minority thought that the \((k + 1)\)th derivative was the \((k)\)th derivative multiplied by the first derivative. Providing an acceptable final statement remains a perennial issue. </span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-size: medium; font-family: 'times new roman', times;">A curve is defined by the equation \(8y\ln x - 2{x^2} + 4{y^2} = 7\). Find the equation of the tangent to the curve at the point where <em>x</em> = 1 and \(y > 0\).</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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(8y \times \frac{1}{x} + 8\frac{{{\text{d}}y}}{{{\text{d}}x}}\ln x - 4x + 8y\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\) <strong><em>M1A1A1</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>M1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for attempt at implicit differentiation. <em><strong>A1</strong></em> for differentiating \(8y\ln x\), </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 differentiating the rest.</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;">when \(x = 1,{\text{ }}8y \times 0 - 2 \times 1 + 4{y^2} = 7\) </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;">\({y^2} = \frac{9}{4} \Rightarrow y = \frac{3}{2}{\text{ (as }}y > 0)\) <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;">at \(\left( {1,\frac{3}{2}} \right)\frac{{{\text{d}}y}}{{{\text{d}}x}} = - \frac{2}{3}\) <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;">\(y - \frac{3}{2} = - \frac{2}{3}(x - 1)\) or \(y = - \frac{2}{3}x + \frac{{13}}{6}\) <strong>A1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><em><span style="font-family: 'times new roman',times; font-size: medium;"><strong>[7 marks]</strong></span></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;">The implicit differentiation was generally well done. Some candidates did not realise that they needed </span><span style="font-family: times new roman,times; font-size: medium;">to substitute into the original equation to find \(y\). Others wasted a lot of time rearranging the derivative </span><span style="font-family: times new roman,times; font-size: medium;">to make \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) </span><span style="font-family: times new roman,times; font-size: medium;">the subject, rather than simply putting in the particular values for \(x\) and \(y\).</span></p>
</div>
<br><hr><br><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;">Consider the curve with equation \({x^2} + xy + {y^2} = 3\).</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) Find in terms of <em>k</em>, the gradient of the curve at the point (−1, <em>k</em>).</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) Given that the tangent to the curve is parallel to the <em>x</em>-axis at this point, 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: 36.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Attempting implicit differentiation <strong><em>M1</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;">\(2x + y + x\frac{{{\text{d}}y}}{{{\text{d}}x}} + 2y\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\) <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;"><strong>EITHER</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;">Substituting \(x = - 1,{\text{ }}y = k\,\,\,\,\,\)<em>e.g.</em> \( - 2 + k - \frac{{{\text{d}}y}}{{{\text{d}}x}} + 2k\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\) <strong><em>M1</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;">Attempting to make \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) the subject <strong><em>M1</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>OR</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;">Attempting to make \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) the subject <em>e.g.</em> \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{ - (2x + y)}}{{x + 2y}}\) <strong><em>M1</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;">Substituting \(x = - 1,{\text{ }}y = k{\text{ into }}\frac{{{\text{d}}y}}{{{\text{d}}x}}\) <strong><em>M1</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>THEN</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;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{2 - k}}{{2k - 1}}\) <strong><em>A1</em></strong> <strong><em>N1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 36.0px 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: 36.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Solving \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0{\text{ for }}k{\text{ gives }}k = 2\) <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;"><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;">Part (a) was generally well answered, almost all candidates realising that implicit differentiation was involved. A few failed to differentiate the right hand side of the relationship. A surprising number of candidates made an error in part (b), even when they had scored full marks on the first part.</span></p>
</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 the curve defined by the equation \({x^2} + \sin y - xy = 0\) .</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: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the gradient of the tangent to the curve at the point \((\pi ,{\text{ }}\pi )\) .</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: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Hence, show that \(\tan \theta = \frac{1}{{1 + 2\pi }}\), where \(\theta \) is the acute angle between the tangent to the curve at \((\pi ,{\text{ }}\pi )\) and the line <em>y </em>= <em>x </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;">attempt to differentiate implicitly <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;">\(2x + \cos y\frac{{{\text{d}}y}}{{{\text{d}}x}} - y - x\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\) <strong><em>A1A1</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 Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: <em>A1 </em></strong>for differentiating \({x^2}\) and sin <em>y </em>; <strong><em>A1 </em></strong>for differentiating <em>xy</em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"> </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;">substitute <em>x </em>and <em>y </em>by \(\pi \) <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;">\(2\pi - \frac{{{\text{d}}y}}{{{\text{d}}x}} - \pi - \pi \frac{{{\text{d}}y}}{{{\text{d}}x}} = 0 \Rightarrow \frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{\pi }{{1 + \pi }}\) <strong><em>M1A1</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 Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: <em>M1 </em></strong>for attempt to make d<em>y</em>/d<em>x </em>the subject. This could be seen earlier.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"> </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">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(\theta = \frac{\pi }{4} - \arctan \frac{\pi }{{1 + \pi }}\) (or seen the other way) <strong><em>M1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(\tan \theta = \tan \left( {\frac{\pi }{4} - \arctan \frac{\pi }{{1 + \pi }}} \right) = \frac{{1 - \frac{\pi }{{1 + \pi }}}}{{1 + \frac{\pi }{{1 + \pi }}}}\) <strong><em>M1A1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(\tan \theta = \frac{1}{{1 + 2\pi }}\) <strong><em>AG</em></strong></span></p>
<p><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: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part a) proved an easy 6 marks for most candidates, while the majority failed to make any headway with part b), with some attempting to find the equation of their line in the form <em>y</em> = <em>mx</em> + <em>c</em> . Only the best candidates were able to see their way through to the given answer.</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; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Part a) proved an easy 6 marks for most candidates, while the majority failed to make any headway with part b), with some attempting to find the equation of their line in the form <em>y</em> = <em>mx</em> + <em>c</em> . Only the best candidates were able to see their way through to the given answer.</span></p>
<div class="question_part_label">b.</div>
</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">In triangle \({\text{ABC, BC}} = \sqrt 3 {\text{ cm}}\), \({\rm{A\hat BC}} = \theta \) and \({\rm{B\hat CA}} = \frac{\pi }{3}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that length \({\text{AB}} = \frac{3}{{\sqrt 3 \cos \theta + \sin \theta }}\).</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 \(AB\) has a minimum value, determine the value of \(\theta \) <span class="s1">for which this occurs.</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>any attempt to use sine rule <strong><em>M1</em></strong></p>
<p>\(\frac{{{\text{AB}}}}{{\sin \frac{\pi }{3}}} = \frac{{\sqrt 3 }}{{\sin \left( {\frac{{2\pi }}{3} - \theta } \right)}}\) <strong><em>A1</em></strong></p>
<p>\( = \frac{{\sqrt 3 }}{{\sin \frac{{2\pi }}{3}\cos \theta - \cos \frac{{2\pi }}{3}\sin \theta }}\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Condone use of degrees.</p>
<p> </p>
<p>\( = \frac{{\sqrt 3 }}{{\frac{{\sqrt 3 }}{2}\cos \theta + \frac{1}{2}\sin \theta }}\) <strong><em>A1</em></strong></p>
<p>\(\frac{{{\text{AB}}}}{{\frac{{\sqrt 3 }}{2}}} = \frac{{\sqrt 3 }}{{\frac{{\sqrt 3 }}{2}\cos \theta + \frac{1}{2}\sin \theta }}\)</p>
<p>\(\therefore {\text{AB}} = \frac{3}{{\sqrt 3 \cos \theta + \sin \theta }}\) <strong><em>AG</em></strong></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>\(({\text{AB}})' = \frac{{ - 3\left( { - \sqrt 3 \sin \theta + \cos \theta } \right)}}{{{{\left( {\sqrt 3 \cos \theta + \sin \theta } \right)}^2}}}\) <strong><em>M1A1</em></strong></p>
<p>setting \(({\text{AB}})' = 0\) <strong><em>M1</em></strong></p>
<p>\(\tan \theta = \frac{1}{{\sqrt 3 }}\)</p>
<p>\(\theta = \frac{\pi }{6}\) <strong><em>A1</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>\({\text{AB}} = \frac{{\sqrt 3 \sin \frac{\pi }{3}}}{{\sin \left( {\frac{{2\pi }}{3} - \theta } \right)}}\)</p>
<p>\(AB\) minimum when \(\sin \left( {\frac{{2\pi }}{3} - \theta } \right)\) is maximum <strong><em>M1</em></strong></p>
<p>\(\sin \left( {\frac{{2\pi }}{3} - \theta } \right) = 1\) <strong>(<em>A1)</em></strong></p>
<p>\(\frac{{2\pi }}{3} - \theta = \frac{\pi }{2}\) <strong><em>M1</em></strong></p>
<p>\(\theta = \frac{\pi }{6}\) <strong><em>A1</em></strong></p>
<p><strong>METHOD 3</strong></p>
<p>shortest distance from \(B\) to \(AC\) is perpendicular to \(AC\) <strong><em>R1</em></strong></p>
<p>\(\theta = \frac{\pi }{2} - \frac{\pi }{3} = \frac{\pi }{6}\) <strong><em>M1A2</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<p><strong><em>Total [8 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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the functions <em>f</em> and <em>g</em> defined by \(f(x) = {2^{\frac{1}{x}}}\) and \(g(x) = 4 - {2^{\frac{1}{x}}}\) , \(x \ne 0\) .</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;">(a) Find the coordinates of <em>P</em>, the point of intersection of the graphs of <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;">(b) Find the equation of the tangent to the graph of <em>f</em> at the point P.</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) \({2^{\frac{1}{x}}} = 4 - {2^{\frac{1}{x}}}\)</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;">attempt to solve the equation <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>x = </em>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;">so P is (1, 2) , as \(f(1) = 2\) <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> </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) \(f'(x) = - \frac{1}{{{x^2}}}{2^{\frac{1}{x}}}\ln 2\) <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;">attempt to substitute <em>x</em>-value found in part (a) into their \(f'(x)\) <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;">\(f'(1) = - 2\ln 2\)</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;">\(y - 2 = - 2\ln 2(x - 1)\,\,\,\,\,{\text{(or equivalent)}}\) <strong><em>M1A1</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>[7 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 answered part (a) correctly although some candidates showed difficulty solving the equation using valid methods. Part (b) was less successful with many candidates failing to apply chain rule to obtain the derivative of the exponential function.</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 curve <em>C </em>has equation \(2{x^2} + {y^2} = 18\). Determine the coordinates of the four points on <em>C </em>at which the normal passes through the point (1, 0) .</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span style="font-size: medium; font-family: 'times new roman', times;">\(4x + 2y\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0 \Rightarrow \frac{{{\text{d}}y}}{{{\text{d}}x}} = -\frac{{2x}}{y}\) <strong><em>M1A1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times;"> </span><strong style="font-family: 'times new roman', times; font-size: medium;">Note: </strong><span style="font-family: 'times new roman', times; font-size: medium;">Allow follow through on incorrect \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) from this point.</span></p>
<p><span style="font-family: 'times new roman', times;"> </span></p>
<p><span style="font-size: medium; font-family: 'times new roman', times;">gradient of normal at (<em>a</em>, <em>b</em>) is \(\frac{b}{{2a}}\)</span></p>
<p><span style="font-family: 'times new roman', times;"> </span><strong style="font-family: 'times new roman', times; font-size: medium;">Note: </strong><span style="font-family: 'times new roman', times; font-size: medium;">No further A marks are available if a general point is not used</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p><span style="font-size: medium; font-family: 'times new roman', times;">equation of normal at (<em style="font-style: italic;">a</em>, <em style="font-style: italic;">b</em>) is \(y - b = \frac{b}{{2a}}(x - a)\left( { \Rightarrow y = \frac{b}{{2a}}x + \frac{b}{2}} \right)\) <strong><em>M1A1</em></strong></span></p>
<p><span style="font-size: medium; font-family: 'times new roman', times;">substituting (1, 0) <strong><em>M1</em></strong> </span></p>
<p><span style="font-size: medium; font-family: 'times new roman', times;">\(b = 0\) or \(a = -1\) <strong><em>A1A1</em></strong></span></p>
<p><span style="font-size: medium; font-family: 'times new roman', times;">four points are \((3,{\text{ }}0),{\text{ }}( - 3,{\text{ 0}}),{\text{ }}( - 1,{\text{ }}4),{\text{ }}( - 1,{\text{ }} - 4)\) <strong><em>A1A1</em></strong> </span></p>
<p><span style="font-family: 'times new roman', times;"> </span><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 any two points correct.</span></p>
<p><em><strong><span style="font-family: 'times new roman', times; font-size: medium;">[9 marks]</span></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;">Many students were able to obtain the first marks in this question by implicit differentiation but few were able to complete the question successfully. There were a number of students obtaining the correct final answers, but could not be given the marks due to incorrect working. Most common was students giving the equation of the normal as \(y - 0 = \frac{y}{{2x}}(x - 1)\), instead of taking a general point e.g. (<em>a</em>, <em>b</em>)</span></p>
<p> </p>
</div>
<br><hr><br><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;">Find the area between the curves \(y = 2 + x - {x^2}{\text{ and }}y = 2 - 3x + {x^2}\) .</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: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2 + x - {x^2} = 2 - 3x + {x^2}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px 'Hiragino Kaku Gothic ProN';"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow 2{x^2} - 4x = 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px 'Hiragino Kaku Gothic ProN';"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow 2x(x - 2) = 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px 'Hiragino Kaku Gothic ProN';"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow x = 0,{\text{ }}x = 2\) <em><strong>A1A1</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px 'Hiragino Kaku Gothic ProN';"><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 graphical solution.</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;">Award <strong><em>M1</em></strong> for correct graph and <strong><em>A1A1</em></strong> for correctly labelled roots.</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;">\(\therefore {\text{A}} = \int_0^2 {\left( {(2 + x - {x^2}) - (2 - 3x + {x^2})} \right){\text{d}}x} \) </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: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \int_0^2 {(4x - 2{x^2}){\text{d}}x\,\,\,\,\,{\text{or equivalent}}} \) <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;">\( = \left[ {2{x^2} - \frac{{2{x^3}}}{3}} \right]_0^2\) <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;">\( = \frac{8}{3}\left( { = 2\frac{2}{3}} \right)\) <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>[7 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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This was the question that gained the most correct responses. A few candidates struggled to find the limits of the integration or found a negative area.</span></p>
</div>
<br><hr><br><div class="question">
<p class="p1">Show that \(\int_1^2 {{x^3}\ln x{\text{d}}x = 4\ln 2 - \frac{{15}}{{16}}} \).</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p class="p1">any attempt at integration by parts <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">\(u = \ln x \Rightarrow \frac{{{\text{d}}u}}{{{\text{d}}x}} = \frac{1}{x}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p1">\(\frac{{{\text{d}}v}}{{{\text{d}}x}} = {x^3} \Rightarrow v = \frac{{{x^4}}}{4}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p1">\( = \left[ {\frac{{{x^4}}}{4}\ln x} \right]_1^2 - \int_1^2 {\frac{{{x^3}}}{4}{\text{d}}x} \) <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>Condone absence of limits at this stage.</p>
<p class="p4"> </p>
<p class="p1">\( = \left[ {\frac{{{x^4}}}{4}\ln x} \right]_1^2 - \left[ {\frac{{{x^4}}}{{16}}} \right]_1^2\) <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>Condone absence of limits at this stage.</p>
<p class="p4"> </p>
<p class="p1">\( = 4\ln 2 - \left( {1 - \frac{1}{{16}}} \right)\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1">\( = 4\ln 2 - \frac{{15}}{{16}}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>AG</em></strong></span></p>
<p class="p3"><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="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;">Find the exact value of \(\int_1^2 {\left( {{{(x - 2)}^2} + \frac{1}{x} + \sin \pi x} \right){\text{dx}}} \).</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: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\left[ {\frac{1}{3}{{(x - 2)}^3} + \ln x - \frac{1}{\pi }\cos \pi x} \right]_{(1)}^{(2)}\) <strong><em>A1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px 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 \(\frac{1}{3}{x^3} - 2{x^2} + 4x\) in place of \(\frac{1}{3}{(x - 2)^3}\).</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="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \left( {0 + \ln 2 - \frac{1}{\pi }\cos 2\pi } \right) - \left( { - \frac{1}{3} + \ln 1 - \frac{1}{\pi }\cos \pi } \right)\) </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: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{3} + \ln 2 - \frac{2}{\pi }\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px 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 any two terms correct, </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 the third correct.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px 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: 32.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[6 marks]</em></strong></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;">Generally well done, although quite a number of candidates were either unable to integrate the sine term or incorrectly evaluated the resulting cosine at the limits.</span></p>
</div>
<br><hr><br><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;">André wants to get from point A located in the sea to point Y located on a straight stretch of beach. P is the point on the beach nearest to A such that AP = 2 km and PY = 2 km. He does this by swimming in a straight line to a point Q located on the beach and then running to Y.</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="font: normal normal normal 19px/normal Helvetica; text-align: center; margin: 0px;"><img src="data:image/png;base64,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" alt></p>
<p style="font: normal normal normal 19px/normal Helvetica; text-align: center; margin: 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;">When André swims he covers 1 km in \(5\sqrt 5 \) minutes. When he runs he covers 1 km in 5 minutes.</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;">(a) If PQ = <em>x</em> km, \(0 \leqslant x \leqslant 2\) , find an expression for the time <em>T</em> minutes taken by André to reach point Y.</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;">(b) Show that \(\frac{{{\text{d}}T}}{{{\text{d}}x}} = \frac{{5\sqrt 5 x}}{{\sqrt {{x^2} + 4} }} - 5\).</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;">(c) (i) Solve \(\frac{{{\text{d}}T}}{{{\text{d}}x}} = 0\).</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) Use the value of <em>x</em> found in <strong>part (c) (i)</strong> to determine the time, <em>T</em> minutes, taken for André to reach point Y.</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) Show that \(\frac{{{{\text{d}}^2}T}}{{{\text{d}}{x^2}}} = \frac{{20\sqrt 5 }}{{{{({x^2} + 4)}^{\frac{3}{2}}}}}\) and <strong>hence</strong> show that the time found in <strong>part (c) (ii)</strong> is a minimum.</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) \({\text{AQ}} = \sqrt {{x^2} + 4} {\text{ (km)}}\) <span style="text-decoration: underline;"><strong><em>(A1)</em></strong></span></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;">\({\text{QY}} = (2 - x){\text{ (km)}}\) <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;">\(T = 5\sqrt 5 {\text{AQ}} + 5{\text{QY}}\) <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;">\({\text{ = 5}}\sqrt 5 \sqrt {({x^2} + 4)} + 5(2 - x){\text{ (mins)}}\) <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>
<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) Attempting to use the chain rule on \({\text{5}}\sqrt 5 \sqrt {({x^2} + 4)} \) <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;">\(\frac{{\text{d}}}{{{\text{d}}x}}\left( {{\text{5}}\sqrt 5 \sqrt {({x^2} + 4)} } \right) = 5\sqrt 5 \times \frac{1}{2}{({x^2} + 4)^{ - \frac{1}{2}}} \times 2x\) <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;">\(\left( { = \frac{{5\sqrt 5 x}}{{\sqrt {{x^2} + 4} }}} \right)\)</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;">\(\frac{{\text{d}}}{{{\text{d}}x}}\left( {5(2 - x)} \right) = - 5\) <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;">\(\frac{{{\text{d}}T}}{{{\text{d}}x}} = \frac{{5\sqrt 5 x}}{{\sqrt {{x^2} + 4} }} - 5\) <strong><em>AG</em></strong> <strong><em>N0</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;">(c) (i) \(\sqrt 5 x = \sqrt {{x^2} + 4} \) <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;">Squaring both sides and rearranging to obtain \(5{x^2} = {x^2} + 4\) <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;"><em>x</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: 21.0px 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 the 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;"> for stating a negative solution in final answer.</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;"> </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) \(T = 5\sqrt 5 \sqrt {1 + 4} + 5(2 - 1)\) </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: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">= 30 (mins) <strong><em>A1</em></strong> <strong><em>N1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 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;"> Allow </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>FT</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> on incorrect </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;"> value.</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;"> </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) </span><strong style="font-family: 'times new roman', times; font-size: medium;">METHOD 1</strong></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 use the quotient rule <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;">\(u = x{\text{ , }}v = \sqrt {{x^2} + 4} {\text{, }}\frac{{{\text{d}}u}}{{{\text{d}}x}} = 1{\text{ and }}\frac{{{\text{d}}v}}{{{\text{d}}x}} = x{({x^2} + 4)^{ - 1/2}}\) <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;">\(\frac{{{{\text{d}}^2}T}}{{{\text{d}}{x^2}}} = 5\sqrt 5 \left[ {\frac{{\sqrt {{x^2} + 4} - \frac{1}{2}{{({x^2} + 4)}^{ - 1/2}} \times 2{x^2}}}{{({x^2} + 4)}}} \right]\) <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;">Attempt to simplify <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;">\( = \frac{{5\sqrt 5 }}{{{{({x^2} + 4)}^{3/2}}}}[{x^2} + 4 - {x^2}]\,\,\,\,\,\)or equivalent <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;">\( = \frac{{20\sqrt 5 }}{{{{({x^2} + 4)}^{3/2}}}}\) <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;">When \(x = 1{\text{ , }}\frac{{20\sqrt 5 }}{{{{({x^2} + 4)}^{3/2}}}} > 0\) and hence <em>T</em> = 30 is a minimum <strong><em>R1</em></strong> <strong><em>N0</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 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;"> Allow </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>FT</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> on incorrect </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;"> value, \(0 \leqslant x \leqslant 2\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 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: 21.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">METHOD 2</strong></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 use the product rule <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;">\(u = x{\text{ , }}v = \sqrt {{x^2} + 4} {\text{, }}\frac{{{\text{d}}u}}{{{\text{d}}x}} = 1{\text{ and }}\frac{{{\text{d}}v}}{{{\text{d}}x}} = x{({x^2} + 4)^{ - 1/2}}\) <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;">\(\frac{{{{\text{d}}^2}T}}{{{\text{d}}{x^2}}} = 5\sqrt 5 {({x^2} + 4)^{ - 1/2}} - \frac{{5\sqrt 5 x}}{2}{({x^2} + 4)^{ - 3/2}} \times 2x\) <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;">\(\left( { = \frac{{5\sqrt 5 }}{{{{({x^2} + 4)}^{1/2}}}} - \frac{{5\sqrt 5 {x^2}}}{{{{({x^2} + 4)}^{3/2}}}}} \right)\)</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;">Attempt to simplify <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;">\( = \frac{{5\sqrt 5 ({x^2} + 4) - 5\sqrt 5 {x^2}}}{{{{({x^2} + 4)}^{3/2}}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( { = \frac{{5\sqrt 5 ({x^2} + 4 - {x^2})}}{{{{({x^2} + 4)}^{3/2}}}}} \right)\) <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;">\( = \frac{{20\sqrt 5 }}{{{{({x^2} + 4)}^{3/2}}}}\) <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;">When \(x = 1{\text{ , }}\frac{{20\sqrt 5 }}{{{{({x^2} + 4)}^{3/2}}}} > 0\) and hence <em>T</em> = 30 is a minimum <strong><em>R1</em></strong> <strong><em>N0</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 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;"> Allow </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>FT</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> on incorrect </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;"> value, \(0 \leqslant x \leqslant 2\).</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;"> </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>[11 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>Total [18 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;">Most candidates scored well on this question. The question tested their competence at algebraic manipulation and differentiation. A few candidates failed to extract from the context the correct relationship between velocity, distance and time.</span></p>
</div>
<br><hr><br><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) Given that \(\alpha > 1\), use the substitution \(u = \frac{1}{x}\) to show that</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;">\[\int_1^\alpha {\frac{1}{{1 + {x^2}}}{\text{d}}x = \int_{\frac{1}{\alpha }}^1 {\frac{1}{{1 + {u^2}}}{\text{d}}x} } .\]</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>Hence</strong> show that \(\arctan \alpha + \arctan \frac{1}{\alpha } = \frac{\pi }{2}\).</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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \(u = \frac{1}{x} \Rightarrow {\text{d}}u = - \frac{1}{{{x^2}}}{\text{d}}x\) <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;">\( \Rightarrow {\text{d}}x = - \frac{{{\text{d}}u}}{{{u^2}}}\) <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;">\(\int_1^\alpha {\frac{1}{{1 + {x^2}}}{\text{d}}x = - \int_1^{\frac{1}{\alpha }} {\frac{1}{{1 + {{\left( {\frac{1}{u}} \right)}^2}}}\frac{{{\text{d}}u}}{{{u^2}}}} } \) <strong><em>A1M1A1</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>Note:</strong> Award <strong><em>A1</em></strong> for correct integrand and <strong><em>M1A1</em></strong> for correct limits.</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;">\( = \int_{\frac{1}{\alpha }}^1 {\frac{1}{{1 + {u^2}}}{\text{d}}u\,\,\,\,\,} \)(upon interchanging the two limits) <strong><em>AG</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) \(\arctan x_1^\alpha = \arctan u_{\frac{1}{\alpha }}^1\) <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;">\(\arctan \alpha - \frac{\pi }{4} = \frac{\pi }{4} - \arctan \frac{1}{\alpha }\) <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;">\(\arctan \alpha + \arctan \frac{1}{\alpha } = \frac{\pi }{2}\) <strong><em>AG</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>[7 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 was successfully answered by few candidates. Both parts of the question prescribed the approach which was required – “use the substitution” and “hence”. Many candidates ignored these. The majority of the candidates failed to use substitution properly to change the integration variables and in many cases the limits were fudged. The logic of part (b) was missing in many cases.</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="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;">A particle P moves in a straight line with displacement relative to origin given by</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;">\[s = 2\sin (\pi t) + \sin (2\pi t),{\text{ }}t \geqslant 0,\]</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;">where <em>t</em> is the time in seconds and the displacement is measured in centimetres.</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;">(i) Write down the period of the function <em>s</em>.</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;">(ii) Find expressions for the velocity, <em>v</em>, and the acceleration, <em>a</em>, of P.</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;">(iii) Determine all the solutions of the equation <em>v</em> = 0 for \(0 \leqslant t \leqslant 4\).</span></p>
<div class="marks">[10]</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;">Consider the 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;">\[f(x) = A\sin (ax) + B\sin (bx),{\text{ }}A,{\text{ }}a,{\text{ }}B,{\text{ }}b,{\text{ }}x \in \mathbb{R}.\]</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;">Use mathematical induction to prove that the\({(2n)^{{\text{th}}}}\) derivative of <em>f</em> is given by \(({f^{(2n)}}(x) = {( - 1)^n}\left( {A{a^{2n}}\sin (ax) + B{b^{2n}}\sin (bx)} \right)\), for all \(n \in {\mathbb{Z}^ + }\).</span></p>
<div class="marks">[8]</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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) the period is 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><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;">(ii) \(v = \frac{{{\text{d}}s}}{{{\text{d}}t}} = 2\pi \cos (\pi t) + 2\pi \cos (2\pi t)\) <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;">\(a = \frac{{{\text{d}}v}}{{{\text{d}}t}} = - 2{\pi ^2}\sin (\pi t) - 4{\pi ^2}\sin (2\pi t)\) <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;"><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;">(iii) \(v = 0\)</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;">\(2\pi \left( {\cos (\pi t) + \cos (2\pi t)} \right) = 0\)</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>EITHER</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;">\(\cos (\pi t) + 2{\cos ^2}(\pi t) - 1 = 0\) <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;">\(\left( {2\cos (\pi t) - 1} \right)\left( {\cos (\pi t) + 1} \right) = 0\) <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;">\(\cos (\pi t) = \frac{1}{2}{\text{ or }}\cos (\pi t) = - 1\) <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;">\(t = \frac{1}{3},{\text{ }}t = 1\) <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;">\(t = \frac{5}{3},{\text{ }}t = \frac{7}{3},{\text{ }}t = \frac{{11}}{3},{\text{ }}t = 3\) <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>OR</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;">\(2\cos \left( {\frac{{\pi t}}{2}} \right)\cos \left( {\frac{{3\pi t}}{2}} \right) = 0\) <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;">\(\cos \left( {\frac{{\pi t}}{2}} \right) = 0{\text{ or }}\cos \left( {\frac{{3\pi t}}{2}} \right) = 0\) <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;">\(t = \frac{1}{3},{\text{ 1}}\) <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;">\(t = \frac{5}{3},{\text{ }}\frac{7}{3},{\text{ }}3,{\text{ }}\frac{{11}}{3}\) <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>[10 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;">\(P(n):{f^{(2n)}}(x) = {( - 1)^n}\left( {A{a^{2n}}\sin (ax) + B{b^{2n}}\sin (bx)} \right)\)</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;">\(P(1):f''(x) = {\left( {Aa\cos (ax) + Bb\cos (bx)} \right)^\prime }\) <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;">\( = - A{a^2}\sin (ax) - B{b^2}\sin (bx)\)</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;">\( = - 1\left( {A{a^2}\sin (ax) + B{b^2}\sin (bx)} \right)\) <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;">\(\therefore P(1)\) true</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;">assume that</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;">\(P(k):{f^{(2k)}}(x) = {( - 1)^k}\left( {A{a^{2k}}\sin (ax) + B{b^{2k}}\sin (bx)} \right)\) is true <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;">consider \(P(k + 1)\)</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;">\({f^{(2k + 1)}}(x) = {( - 1)^k}\left( {A{a^{2k + 1}}\cos (ax) + B{b^{2k + 1}}\cos (bx)} \right)\) <strong><em>M1A1</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;">\({f^{(2k + 2)}}(x) = {( - 1)^k}\left( { - A{a^{2k + 2}}\sin (ax) - B{b^{2k + 2}}\sin (bx)} \right)\) <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;">\( = {( - 1)^{k + 1}}\left( {A{a^{2k + 2}}\sin (ax) + B{b^{2k + 2}}\sin (bx)} \right)\) <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;">\(P(k)\) true implies \(P(k + 1)\) true, \(P(1)\) true so \(P(n)\) true \(\forall n \in {\mathbb{Z}^ + }\) <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;"><strong>Note:</strong> Award the final <strong><em>R1</em></strong> only if the previous three <strong><em>M</em></strong> marks have been awarded.</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 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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">In (a), only a few candidates gave the correct period but the expressions for velocity and acceleration were correctly obtained by most candidates. In (a)(iii), many candidates manipulated the equation <em>v</em> = 0 correctly to give the two possible values for \(\cos (\pi t)\) but then failed to find all the possible values of <em>t</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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Solutions to (b) were disappointing in general with few candidates giving a correct solution.</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 Times;"><span style="font-family: 'times new roman', times; font-size: medium;">The graph below shows the two curves \(y = \frac{1}{x}\) and \(y = \frac{k}{x}\), where \(k > 1\).</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 Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the area of region <em>A </em>in terms of <em>k </em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p 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 area of region <em>B </em>in terms of <em>k </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: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the ratio of the area of region <em>A </em>to the area of region <em>B </em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(\int_{\frac{1}{6}}^1 {\frac{k}{x} - \frac{1}{x}{\text{d}}x = (k - 1} )[\ln x]_{\frac{1}{6}}^1\) <strong><em>M1 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>Note: </strong>Award <strong><em>M1 </em></strong>for \(\int {\frac{k}{x} - \frac{1}{x}{\text{d}}x{\text{ or }}\int {\frac{1}{x} - \frac{k}{x}{\text{d}}x} } \) and <strong><em>A1 </em></strong>for \((k - 1)\ln x\) seen in part (a) or later in part (b).</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;">\( = (1 - k)\ln \frac{1}{6}\) <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;">[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; font-size: medium;">\(\int_1^{\sqrt 6 } {\frac{k}{x} - \frac{1}{x}{\text{d}}x = (k - 1} )[\ln x]_1^{\sqrt 6 }\) <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>Note: </strong>Award <strong><em>A1 </em></strong>for correct change of limits.</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;">\( = (k - 1)\ln \sqrt 6 \) <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.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">\((1 - k)\ln \frac{1}{6} = (k - 1)\ln 6\) <strong><em>A1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\((k - 1)\ln \sqrt 6 = \frac{1}{2}(k - 1)\ln 6\) <strong><em>A1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium; line-height: normal;"><em><strong>Note: </strong></em></strong><span style="font-family: 'times new roman', times; font-size: medium; line-height: normal;">This simplification could have occurred earlier, and marks should still be awarded.</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;">ratio is 2 (or 2:1) <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;"><strong><em>[3 marks] </em></strong></span></p>
<p> </p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<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;">Generally well answered by most candidates. Basic algebra sometimes let students down in the simplification of the ratio in part (c). It was not uncommon to see \(\frac{{\log A}}{{\log B}}\) simplified to \(\frac{A}{B}\).</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: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Generally well answered by most candidates. Basic algebra sometimes let students down in the simplification of the ratio in part (c). It was not uncommon to see \(\frac{{\log A}}{{\log B}}\) simplified to \(\frac{A}{B}\).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Generally well answered by most candidates. Basic algebra sometimes let students down in the simplification of the ratio in part (c). It was not uncommon to see \(\frac{{\log A}}{{\log B}}\) simplified to \(\frac{A}{B}\).</span></p>
<div class="question_part_label">c.</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;">A normal to the graph of \(y = \arctan (x - 1)\) , for \(x > 0\), has equation \(y = - 2x + c\) , where \(x \in \mathbb{R}\) .</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 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: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{\text{d}}}{{{\text{d}}x}}\left( {\arctan (x - 1)} \right) = \frac{1}{{1 + {{(x - 1)}^2}}}\) (or equivalent) <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;">\({m_N} = - 2{\text{ and so }}{m_T} = \frac{1}{2}\) <strong><em>(R1)</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;">Attempting to solve \(\frac{1}{{1 + {{(x - 1)}^2}}} = \frac{1}{2}\) (or equivalent) for <em>x</em> <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;">\(x = 2{\text{ (as }}x > 0)\) <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;">Substituting \(x = 2\) and \(y = \frac{\pi }{4}\) to find <em>c</em> <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;">\(c = 4 + \frac{\pi }{4}\) <strong><em>A1</em></strong> <strong><em>N1</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>[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: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">There was a disappointing response to this question from a fair number of candidates. The differentiation was generally correctly performed, but it was then often equated to \( - 2x + c\) rather than the correct numerical value. A few candidates either didn’t simplify arctan(1) to \(\frac{\pi }{4}\), or stated it to be 45 or \(\frac{\pi }{2}\).</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 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 src="data:image/png;base64,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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 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;">At 12:00 a boat is 20 km due south of a freighter. The boat is travelling due east at \(20{\text{ km}}\,{{\text{h}}^{ - 1}}\), and the freighter is travelling due south at \(40{\text{ km}}\,{{\text{h}}^{ - 1}}\).</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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Determine the time at which the two ships are closest to one another, and justify your answer.</span></p>
<div class="marks">[8]</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;">If the visibility at sea is 9 km, determine whether or not the captains of the two ships can ever see each other’s ship.</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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><img src="data:image/png;base64,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" alt> <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;"> </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;">\({s^2} = {(20t)^2} + {(20 - 40t)^2}\) <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;">\({s^2} = 2000{t^2} - 1600t + 400\) <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;">to minimize <em>s</em> it is enough to minimize \({s^2}\)</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;">\(f'(t) = 4000t - 1600\) <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;">setting \(f'(t)\) equal to 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;">\(4000t - 1600 = 0 \Rightarrow t = \frac{2}{5}\) or 24 minutes <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;">\(f''(t) = 4000 > 0\) <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;">\( \Rightarrow \) at \(t = \frac{2}{5},{\text{ }}f(t)\) is minimized</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;">hence, the ships are closest at 12:24 <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>Note:</strong> accept solution based on <em>s</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;"> </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 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;">\(f\left( {\frac{2}{5}} \right) = \sqrt {80} \) <strong><em>M1A1</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;">since \(\sqrt {80} < 9\), the captains can see one another <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;"><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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This was, disappointingly, a poorly answered question. Some tried to talk their way through the question without introducing the time variable. Even those who did use the distance as a function of time often did not check for a minimum.</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;">This was, disappointingly, a poorly answered question. Some tried to talk their way through the question without introducing the time variable. Even those who did use the distance as a function of time often did not check for a minimum.</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: 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 src="data:image/png;base64,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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="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;">A curve has equation \({x^3}{y^2} + {x^3} - {y^3} + 9y = 0\). Find the coordinates of the three points on the curve where \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\).</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;">\(3{x^2}{y^2} + 2{x^3}y\frac{{{\text{d}}y}}{{{\text{d}}x}} + 3{x^2} - 3{y^2}\frac{{{\text{d}}y}}{{{\text{d}}x}} + 9\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\) <strong><em>M1M1A1</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> First <strong><em>M1 </em></strong>for attempt at implicit differentiation, second <strong><em>M1 </em></strong>for use of product rule.</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;">\(\left( {\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{3{x^2}{y^2} + 3{x^2}}}{{3{y^2} - 2{x^3}y - 9}}} \right)\)</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;">\( \Rightarrow 3{x^2} + 3{x^2}{y^2} = 0\) <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;">\( \Rightarrow 3{x^2}\left( {1 + {y^2}} \right) = 0\)</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;">\(x = 0\) <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> Do not award <strong><em>A1 </em></strong>if extra solutions given <em>eg</em> \(y = \pm 1\).</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;">substituting \(x = 0\) into original equation <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;">\({y^3} - 9y = 0\)</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;">\(y(y + 3)(y - 3) = 0\)</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;">\(y = 0,{\text{ }}y = \pm 3\)</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;">coordinates \((0, 0), (0, 3), (0, - 3)\) <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>[7 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;">The majority of candidates were able to apply implicit differentiation and the product rule correctly to obtain \(3{x^2}\left( {1 + {y^2}} \right) = 0\). The better then recognised that \(x = 0\) was the only possible solution. Such candidates usually went on to obtain full marks. A number decided that \(y = \pm 1\) though then made no further progress. The solution set \(x = 0\) and \(y = \pm i\) was also occasionally seen. A small minority found the correct <em>x</em> and <em>y</em> values for the three co-ordinates but then surprisingly expressed them as \({\text{(0, 0), (3, 0)}}\) and \((- 3, 0)\).</span></p>
</div>
<br><hr><br><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;">A packaging company makes boxes for chocolates. An example of a box is shown below. This box is closed and the top and bottom of the box are identical regular hexagons of side <em>x</em> cm.</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="font: normal normal normal 19px/normal Helvetica; text-align: center; margin: 0px;"><img src="data:image/png;base64,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" alt></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;">(a) Show that the area of each hexagon is \(\frac{{3\sqrt 3 {x^2}}}{2}{\text{c}}{{\text{m}}^2}\) .</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;">(b) Given that the volume of the box is \({\text{90 c}}{{\text{m}}^2}\) , show that when \(x = \sqrt[3]{{20}}\) the total surface area of the box is a minimum, justifying that this value gives a minimum.</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: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Area of hexagon \( = 6 \times \frac{1}{2} \times x \times x \times \sin 60^\circ \) <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;">\( = \frac{{3\sqrt 3 {x^2}}}{2}\) <strong><em>AG</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;">(b) Let the height of the box be <em>h</em></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;">Volume \( = \frac{{3\sqrt 3 h{x^2}}}{2} = 90\) <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;">Hence \(h = \frac{{60}}{{\sqrt 3 {x^2}}}\) <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;">Surface area, \(A = 3\sqrt 3 {x^2} + 6hx\) <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;">\( = 3\sqrt 3 {x^2} + \frac{{360}}{{\sqrt 3 }}{x^{ - 1}}\) <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;">\(\frac{{{\text{d}}A}}{{{\text{d}}x}} = 6\sqrt 3 x - \frac{{360}}{{\sqrt 3 }}{x^{ - 2}}\) <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;">\(\left( {\frac{{{\text{d}}A}}{{{\text{d}}x}} = 0} \right)\)</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;">\(6\sqrt 3 {x^3} = \frac{{360}}{{\sqrt 3 }}\) <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;">\({x^3} = 20\)</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;">\(x = \sqrt[3]{{20}}\) <strong><em>AG</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;">\(\frac{{{{\text{d}}^2}A}}{{{\text{d}}{x^2}}} = 6\sqrt 3 + \frac{{720{x^{ - 3}}}}{{\sqrt 3 }}\)</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;">which is positive when \(x = \sqrt[3]{{20}}\), and hence gives a minimum value. <strong><em>R1</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>
<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;">There were a number of wholly correct answers seen and the best candidates tackled the question well. However, many candidates did not seem to understand what was expected in such a problem. It was disappointing that a significant number of candidates were unable to find the area of the hexagon.</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 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 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 src="data:image/png;base64,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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 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="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>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbMAAAF8CAIAAADKMcKxAAAgAElEQVR4nOydd1wU1/f311hRpEhTioCw9F6lK6CAoFIsWBALVsQSSzS2aCwRa4wlGnuJ5WuLEY0dY1cUa1Q0oijS2/Z+nz/O4/1NwJCIuEPwvP/wNcwOMxdZPnvuqRyCIAiC/BUO2wtAEARpcKAyIgiCVAeVEUEQpDqojAiCINVBZUQQBKkOKiOCIEh1UBkRBEGqg8qIIAhSHVRGBEGQ6qAyIgiCVAeVEUEQpDqojAiCINVBZUQQBKkOKiOCIEh1UBkRBEGq88HKKJVKlUolIUSpVKpUKjipUCgIIRUVFfRYIpEolUq4sg6PkMvlzEdIpdI63AdBEKRufKzNyNTH8vLyr776atu2bTweD86AwH0QcrmcfhdVYQRBEHXywcqoVCpFIpFIJALNksvlcCCTybKyspo2bern57d69eqCggI4+aH3l8lkVA3B6lQoFGgzIgiiTj7WZlSpVHK5XCaTyeXyX375RUNDo02bNh06dDh69OjH3BatRQRBWKQufkY4kEgk9Bh8i9nZ2V5eXl988QWHw0lPT6/bgkBq+Xw+3FwqlYpEorrdCkEQpG58sDJSr6JUKqXKCPYdj8dzdHTkcDgGBgZLly4ldfIzisVi5pdKpZJ6LREEQdTDByujUCjk8/lgJJJ3bkeQyLt37+rq6nI4HAsLi61btyoUijr4GYH8/PyLFy/m5ubW7dsRBEE+hg9WxqVLl65YseL48eNgysHmF15atWqVnp5ey5YtW7dufezYsWrW37+kqqrq8ePHEydOtLGxSU1Nffr0KWEYqgiCIGrgg5XxwoUL7dq1s7CweP36NSGEz+fD+YKCgr59++ro6NRhNy2RSOBAoVA8ffrU09OzSZMmurq6Tk5OmzZtgq06WKkCgYA+sW7KiyAI8o98sDIWFBR4enpyOJxZs2aRdwEZoVB4586dPn36ODg4cDic5s2bR0RElJWV1XIfhUIhl8vBGISkSKVS+eLFi507d5qampqYmDRt2rRp06Y//PADeV+mN6byIAjy6ahL1s7u3bs5HI67u3tGRgbsqV++fDllyhQul2tmZtaiRQsul9utW7fCwsJabgKaKJPJaOi5oKAgJSVFT0+Pw+E0adKEw+E0bdq0R48eV65cATuRWqByuRxMSMzsQRDkU1CX2DSPx4uMjGzTpk1kZOSpU6du3bq1Y8cOS0tLPT09TU1NDofTsmVLX1/f+/fv/+PdZDIZrSzct29fixYtvvjiC01NzejoaEtLy2bNmnE4HCcnp8mTJ0PpISFEIpFQiURlRBDkU1DHTO9Tp04ZGRlpaWn5+/tHRkbq6ek1bdp04MCBs2bNMjMzg/B0ZmZm7ZGTqqoqOHjz5s3s2bN79uypra3N4XDatWuXmZk5f/58fX39jh07Ghoauri4ZGRkQKSbbqJxN40gyCfig5WRbn5Xrlzp4OBgaGioo6Ojq6trY2Ozf//+iooKDw8PAwMDb2/vf7QZhUIhISQrK+u7776zsrLS0tLS0tJq1qzZ8uXLCSFFRUVJSUmtWrVq3bq1vr5+XFxcRkYGjbrI5XLMAEcQ5BPxwcpId7IvXrzo16+fubl5y5YtXVxcfvzxx8ePH1dWVhoYGGhqajo5OZ05c+Yf71ZZWTls2DAXF5e2bdtyOBwOh9OqVauioiIwD69evdqlSxcjIyNjY+N27dr169fv999/J4SoVCoMTCMI8umoy25aIpFQ5+Cvv/567dq1nJwcQohKpSorK/Px8dHR0dHT0xs/fnxxcfHf3QQSIZ8/f+7i4qKpqQkOymbNmnXu3PnVq1eEELlcLhaLCwoKQkNDW7VqZWhoaGVltWnTJkKIUqkE6QSrE0EQpH6pz861fD7/5cuXtra2TZo00dbWTktLy8/PZ7Ypo8CZioqKjRs3tmzZElyTgL29fU5ODi2eUalU586dMzY21tfXNzMzCwgIWLNmDQiiVCrFDHAEQT4F9aaMECYWCoWdO3du2bIll8udO3dufn7+e2URLq6srHRzczMxMQFN1NTU5HK58fHxAoEArEIaojl58qS1tbWJiUn79u3d3NymTp16+/bt+lo5giBINepNGaVSqVgsLioq6tevn66urpGR0aRJkwQCQbXLQBYVCsXLly+XLVsGmeGwlZ49e3ZsbGx0dDStclGpVLBtr6ys3LVrl7+/f8uWLS0sLMLCwubNm/f48eP6WjyCIAiTep4Dk5eXFxYWpq+v36dPn82bN0PVMxOQRblcPnny5NatW5uamoLBOHr06JcvX65cuXLQoEFgZsK/tHUFIeTAgQMBAQEcDsfY2Dg9Pb2wsBDzGREE+RTUmzKKxWKVSlVSUjJ69GgtLS0zMzMo7KsGVcZbt265u7traGgYGhp6e3u/efPmwYMHUVFR3bp1q6iogBaN1b5XIpFs3rw5JCRkzJgxEPOpcy8fBEGQWqg3ZYSuEDk5OX5+fs2aNevateuvv/5aXl5e7TK6mxYKhRMnTnRwcIiKioKQy82bN52cnExNTR8+fKhSqaiDUiAQQM9wQkhxcfGLFy/gWbQPBYIgSP1Sn7tp8B4mJCSYmZlBVTV5XwMxGoERi8V3794FX2RVVdWzZ89GjBgRHR399u1beiWp0bAHTE76bz2uH0EQBKg3ZQT9Ki0tjYqKMjQ0dHV1PXPmDIxz+TtxBOORECIQCOBMbGzshAkTSkpKmBfTMA7NXqTWIpbBIAjyKahnZczOzrazs9PU1Ozfvz/tAVELzInVcrn8q6++mjlzZmVlJflrGx4EQRB1Um/KKJPJxGLxhQsXNDQ0dHV1x44du3v37lqup13ImBblvHnzevbsCdEVCq14QRAEUQ/1nLWzZs0aU1NTAwODCRMm1D7FBfbRzHkyEokkLS2tZ8+eb968odfQHTeCIIja+GBlfK/fkBCiUqnevHnz7bffamtrf/HFF+vXr6+Z5l3tPswvBQLBq1evYmJiEhMT4RtVKpVEIoFkoA9dJIIgyMdQD8oIwROhUMjj8ZKTk5s0aWJoaLhmzZqioqJa7lPtJiKRKC8vLyoqqmvXriUlJTQeDek7aDYiCKJOPlYZQbZAyJ4+fers7Kyrq9uhQ4cvv/zy39yNJioSQvh8/uDBg7t06VJVVSWRSJhPwSa1CIKok7pMO2B+CeERqVT6xx9/dO/e3crKSkNDQ1NTc9euXbVnYtNcRWoP8ni8fv36xcfHE0LorGrURARB1M/HRmBghp9YLE5MTNTQ0GjRokW7du1iY2Oh3UMt4lhNYeVy+YsXL/z9/WNiYgijlwQWuiAIon7+Vhlh5OnLly9BwkQiES1khoxrhUIB+Ya3b98eNWqUsbGxmZmZlpaWnZ3d999/Dy/9o8WnVCrhSoVC8eLFi969ew8aNIh5nqA4IgiidmqzGR8+fNijR48VK1bQdEIejwf52zSyvH379u7duzs4OHTo0EFDQ6N169bjxo2DIpaaLSGYUPciVc+ysrJhw4aZmppCtTW4L6FU5qN+RARBkA/kb5URDMP+/ftraWmNGTMmIyPj1q1bcLKiouLSpUsnT54cMGBA06ZN9fX1ORxO27Zt27ZtO3LkyGfPnhFCZDJZ7YpG3YtyuRzEsaioaNCgQT179oTzdKYCqVE6jSAI8kn5Bz/jmTNngoKCNDQ0YLrpjBkzevToERcXZ2Fhoa2t3apVKw6HY2pqampqamVlNWXKlIKCAkJIWVkZGIy1iyPVO7BJHz9+3KVLl++//568q6iBV5VKJSojgiDq5G+VUalUgjbt2bNHW1u7Xbt20GJWT09PS0uradOmHA5HQ0NDS0urTZs2+vr6CxcuhOuh6pn8i+aJEomEKXmZmZmOjo4TJ04UiUTUt6hQKDDTG0EQNVObzSiXy2H7vHfvXi8vryZNmtja2jZt2rR58+agkjo6Os2aNbOzszty5AjMbFEqlXReII/Hq/3ZzIJohUKxfft2Lpc7cuRI2FzD7ECQRXQ1IgiiTv5WGaFEr6SkBMTrl19+iYuL69mzp4GBAYfD0dXVDQkJ6dy5c0RExN69e8FalEgkIGoSiQQiy/+oaDQ1B+YIxsTEpKenw0uQDATHOF0aQRB1UpvNSAufwfoDsVu1atXBgwenT5++adMmPp9Pte9D2+EwO4yBcXr06NFly5alp6fLZDJ6N6ybRhBE/dRzr51/D0iqXC6HxElCyPLly7/66qv+/fuDaAqFQjgP7W/ZWieCIJ8hrCkjtIpgRmB27NgRFBQ0f/58+JKm7GCmN4IgaoZNZaQ53lALeOHCBVtb23379hFGQg/zMgRBEPXAmjIShlUIyY+XLl3q0qXLgQMHoIsteWdXop8RQRA1w6YyUu8h5AatW7cuJCRk/fr1dAQCjcPgtAMEQdQJyzYj0884duxYU1PTxYsX0zM1a6sRBEHUAJvKyPQhyuXyWbNmmZmZffPNN/QMHKDBiCCImmEzAgMHkL1YUlJy6NCh0NBQUEZmFzI6ZhpBEEQ9sKaM4ExkNtTZsWOHr6/v7NmzoYUEeCFxAgyCIOqHzd00NQYVCsXly5cjIyMDAwPnzZtH3k3doldieBpBEHXCftaOVCpVKBSPHz/u2rWru7v7rFmz4FVmvg52IUMQRJ2wXB1ICCkrK4ODRYsWubm5paWl1bwGlRFBEHXCsjIy+zD+73//CwkJGTFiBD2pVCrBrsTdNIIg6oTl2DS085FKpVVVVSdOnPDx8UlLS2NmL6K1iCCI+mEzNk3e2YwghQcOHLCyslq2bBlhpHZjT28EQdQPa8rI7BlBCJFKpQsWLLCxsdmzZw8hRCQSwXYbgtTYhQxBEHXCmjIyO9dKJJK7d++mpKQYGBisWLGi2mW4oUYQRM2wmbVDCBGJRDBdmhDy448/BgQEjBw5srS0lM/nQ+wFZRFBEPXDpjIyIy1Pnz4dOnRofHx8cnJyRUUF9PGm+d5YCYMgiDphTRklEgmoHoRiKioqhg4dGhYWNnnyZHqNTCZDZUQQRP2w35+Rx+MpFIqSkpKkpKTQ0NC0tDS6j6aNGjE8jSCIOmG5bho21CqV6tq1a126dHF0dExLS6PmJAUbkSEIok5YU0Y6mRpSGquqqtLS0rS1tWFCFjUSwdWInWsRBFEn7OczEkLevn17+vTpUaNGeXt7f//994ThYcTYNIIg6ofNumlaBlNQUHDx4sWlS5euX7/+5s2bBCepIgjCKmwqo0qlog5EHo935cqVmJiYTZs2gbXIbOuNERgEQdQJa8pYVlYmk8lo3bRQKMzMzHR3d9+yZQu9RiwWVxsiiCAIogbYrw6EEuni4uL58+eHhoaeP3+eMDozKhQK6nNEEARRDyzPDiTvgtRFRUVTp051c3M7cuSIVCrl8/n0GtxKIwiiZliOwIACymSyoqKi3377zd/ff82aNTRHh8ZhUBwRBFEnLHeUABQKBY/Hu3XrVkJCwrZt2+h56l7EUDWCIOqETWWEXEVo611VVTVz5kxnZ2fwM9LdNGHMPEAQBFEP7E/IIoRIpdLnz58nJSUZGxuvXr2aECKXy5llMJjvjSCIOmHZZpTJZDKZTKFQ8Pn89PT0AQMGrF69WqFQiMVizNRBEIQt2JyQJZfLqTFYWVk5d+7c3r17w7QDZosd3EojCKJmGkQEhhDy4MGDnj17duzY8cSJE/QkM60HQRBEbbA5O5BpM+bn56empsbFxZ06dUokEoEagrWIyoggiJph2WaUSqUSiaSiouLYsWMuLi4mJib379+XSqWgmKCMzFlaCIIgaoA1ZRQKhdBUAr68fPlyaGiov78/j8ej14AyQloPgiCI2mA5awf+lUgkx48f9/Ly8vb2hpA01ErDPlosFrO1SARBPk/Y7OlNDUaBQJCZmRkREeHu7s60GQE6DQZBEEQ9sOxnrKiogIPDhw/7+/tPnToVCgHlcjn04GF1dQiCfKawpozMPXJ5efnGjRvDwsKWL19OzUNqVKI+IgiiZti0GcVisVKplMvlhYWFz58/nzVrVlhYWFFRUc3BgVgdiCCIOmG/owQhRCQS8Xi8b7/91svLKzs7G7bYtAwGa2AQBFEzrCkjM9IilUoPHz4cEBDQv3//Z8+eQUgazEmFQoG7aQRB1AzLEZjy8nK5XK5UKrdt22Zubh4TE1NaWgovUU3ELmQIgqgZNpWRGoMVFRWHDh2KiIiIj49/9eqVRCJRKpXMEA12rkUQRJ2wPyGrqqpKIBBcvXo1MTFxxYoVcJL2ZKRjqREEQdQGy7Fp8i7Scvv27bi4uLlz59a8DP2MCIKoGTaVEQqixWJxeXn5iRMnRo4cuWjRIqFQqFKpqG9RpVKhzYggiJphszqQvHMgPnv2bPPmzSNGjBgyZEhZWRl0+YbdtEqlkkqlaDYiCKJOWI5NC4VCQsi1a9dOnDgxYsSIAQMGlJSUUGsRrkFZRBBEzbCpjFVVVSqVSiwW3759+8mTJ7179+7du3dhYSEoIxVEhUKBHSUQBFEnbHYho826KyoqMjIy/P39XV1d3759C/to2FNDbBrzGREEUSesKSPIX1VVFY/Hy8/Pnz59+vTp07/++uvi4mK4gNqMaDAiCKJm2K+bFolEly5dSktLGzZs2MCBA6kyAmAzojgiCCtU27FB3gj8PdJaDJqbDFcy5zvBvlAqlcL+Dy6QSCSQcNKQB5mwqYx8Ph8OXr16NXv27KCgID8/vzdv3tAhMPA7wK00grALiBrlvQW7CoWC1qqBgIpEotqr1xpybRvLu2lCSFVV1atXry5cuDB58uTU1NT8/Hz4PJHL5difEUEaAiCIzDMgajKZDOw+pVIJZ6RSqVgsZuYgy+XysrIyHo9XWVnJbCfYwP+uWc70hqwdQsiFCxfi4+NnzpxJO0rQHTRupRGELd6rX9X218wDqn2QdlLTtIRxoQqFooHPd2LZz0j/d65duxYeHt6vXz86/wAjMAjCOkxpo+ki0B+LuRcGvQNDB5xg1OgpLy+HOclQ3ka/hTk6tAHCmjLSWanl5eUKheL58+ejRo3q2rVraWkpaCIWBSII6zDTiqu11ofEO7gAHItwXiwW06Leqqqq33777cKFC7/++uvevXu3bNmyd+/eAwcO3LhxQ6VSoTK+B4lEIhKJ6CfS+vXru3TpEhkZSW1Gmu3YkP/7EKRxQ/WOiqBSqaysrITwaWFh4atXrwghlZWVDx484PF4T548yc3NraysvHPnzqFDh5YvXz5nzpyrV69u3LgxLS3Nzs7O2Ni4ffv2Y8eOxd10bahUKolE8uTJk5SUlL59+y5durRaBgB5n/cXQRB1Ak5DsVhcUVHx6NGjkydPHjx48OXLl2fOnDly5EhBQcHhw4eTk5MXLly4ePHi6dOnz507Ny0tbdy4cX379g0ICJgzZ07fvn39/Pw4HI6GhoampuaIESNIww7CsKmMVARfvHiRlJQ0Z86chQsXsrgeBGnIgIMPjmFvC9sp6ncSi8XU90eThan60NZW8Cr1CdJvF4lENGGutLS0qKiIx+Pl5OQUFBTcunXryJEjW7ZsOXTo0MqVKxcvXpyYmLhjx47t27dHREQMHTp08ODBAQEBffv2DQwMtLS0DAwMjIiIGDhw4LBhwzw8PNzc3Ozs7AICAuzs7L744gsrK6tVq1bRWGvDhGWbkbz7JSUkJCxYsODo0aNsLwdBGiIghbTZCnM+UrUdFUQ/3psqCN+Sl5dHv1SpVAUFBTk5OaWlpVVVVa9fv961a9f//ve/Z8+e5eTkZGZmvn79evr06SkpKfv27Vu1alVsbGz//v27desWFRXl5OTk6elpbm7eq1cvMzMzGxubHj16+Pj4uLm5xcXFRUdHd+/ePT4+Pi4u7quvvho9evSXX345fvz41NTU7du3l5eXE8z0fi/gpiWElJSUVFVVpaSkDB069P79+2ytB0EaMszoB9PzTvutQLCYGbcE8xBUEgbSwRnQx/Pnz/P5/IKCgqNHjx45ciQvLy83N/frr7/u16/fkSNH7t69e/Xq1eDg4C1btoSGhg4cOLB79+6enp5eXl7u7u5aWlpcLjcyMnLMmDGhoaHOzs6urq7jx49PS0tbuHDhokWLDh8+fPbs2aysrPz8/LKyMubKeTwelXLmSw0NNjO9aQfGvLy8NWvW+Pn53bhxg631IEhDhpk2+N5UX8ikYX4JuTLwpVAoLCoqkkql9+7d279//9y5c8eMGdO/f/+goKD58+cfOHDgzJkzqampoaGhvXv33rRp05AhQzw9PW1tbc3NzSMjI729vV1cXLy9vfX19f38/CIiItLT0xMTE7t163bu3Lk7d+48fPjwxYsXPB5PJBIVFRUxMxmhNwLNRZFKpTwer+FnnrC/myaEPHv2bOXKlZ07d163bh3ba0GQhohSqQQ/I7ONgEwmg10zM6WGx+MVFxfDNW/evCkoKHj58uXdu3fXrFmzc+fOhQsXzps3LyYmJjY21t/f39fXt3v37r6+vvb29mlpaXFxcREREUOGDDE1Ne3evbupqammpmZERMSECRMmTpy4YMGCefPmDR48+PTp0w8ePKiqqvrjjz/IuzJfuoZ/E1cB/ybNP2mAsKaMNN1JqVSWlJRMnDgxOTn5vXNgEAQhf+3UQKEJ1Xw+v6KioqioqLCwUCaT8fn8169fp6am9u/fPy0tbd++fRMnThw7dqyzs7O/v3+zZs04HI6tre2gQYPs7Oy8vLxiYmJiYmISEhI8PT0jIiKioqJmzpx5+PDh3bt3FxYWPnv2TCAQCAQC2iGQFgXC02nRNFVthUIhEolEIhH8pUulUqh5+69UcLCftUMIkcvlX375ZXJy8tq1a9ldD4I0WJiRFoFAAE5D0B0ej5eZmXnw4ME9e/YcO3bsjz/+ePz48e7duwMDA+3t7R0cHJKSkvz9/blcbs+ePa2srLy8vMaMGRMWFgZb4+nTp3/zzTcnT568c+fOo0ePHjx4cOfOHZFIBI+gG2GQRYFAQFvm0H9h8w4HzNYSNVcOX4rF4oacskNYVEaaJa9UKvPy8qZMmdK+ffvVq1eztR4EaeDQfbRQKMzNzX3z5o1MJnv9+vWTJ082btwITfzi4uKCg4PDwsKMjIy0tbU9PDyGDx8eFBTk7u7u6Ohoa2vbs2fPKVOmREREJCUlrVixYv/+/aWlpSB5lZWVoFYgZPAv3fDCXys1UQmjC1lVVRX5a4yIduWpeRKOIbzekPOUWbYZ4eOovLw8PT19yJAhmM+INDKosjDLhGm0hEaWaUSi5gEN4MKtioqKHjx4sHLlyj179hw5ciQxMTEkJMTV1dXb2zswMNDDw4PL5Zqbm+vo6FhbW/fr12/BggWzZs1KSUn55ptvTp069ezZsydPnuTk5OTn5zfkpBnWYU0ZaXNGpVL5559/rl69eubMmTt37mRrPQjySanmVgObgJlnQ5MQy8rKIN1PLpfTRs7379+/cOHC2bNn09LShg8fnpaWNn36dAcHh8DAwKCgoMjIyJiYGC8vLzMzM29v7+HDhyckJICpcfbs2Tdv3vB4PGbcRiwWM6tvG3IkhC3YtBmpryEjIwNSBHA3jTQyaBCWzn0D6AVCoVAgENDW2dViLK9evZJIJLt27dq6dWufPn369+8PfsOoqKi+fft27NixW7duERERERERwcHBnTt37tev308//ZSTk1NWVkYdgoBEIvm7spMG7vJjBTbnTdPfx+HDhxMSEoKCgtLT09laD4KoB9qXAdxzhOG8A0MSMv62bNly+/btrl27jho1qnPnzn5+fs2bN4+Kiho0aFCPHj0sLCy0tLQsLCw6deo0cODA5cuX7969+9KlS5WVlXArSO0GmCYhJDk28A5gDQE2bUbqoL13794PP/wwaNCgVatWsbgeBKl3mBoE/VOoVQhbWiqLT58+PX369DfffHP06NEZM2Z0795dT08vICAgODh4yJAh8+bN8/X15XK5XC531qxZly5dys7Orqys/P3338ERKRAIYA9OGFMEmOYqqTGguIH3AWMXNpURJkUQQi5fvjxq1ChjY+Pp06ezuB4EqXeg9T+kZL+3dO/u3bsvX77cv39/YGBgYGBgaGhokyZNoCTZ39/f1tbWzc0tMjIyNTV1165dt2/fvnTpUmFhIXlnYNYSRWEOLiaMbJBq16A+vhfWlJG6PAQCQUZGxtSpU11cXDCfEWmsMBsdvnz5sqCg4N69ezt37uzTp09AQICNjU2bNm0iIyOnTJliZ2fH5XL19PRiYmL27Nlz+/bt7Ozse/fuVUsSpKonFourqqrAFIUxLMyuPACd+ceccoWCWAssZ+2AW6S0tHTHjh0DBgyAD0MEaTTQpJyKiory8vI3b96cPHly4cKFQ4YMcXJyiomJCQ4ONjAwsLGx8fX17dWr17Bhw8aMGTN27NhRo0adPHmSMILaSqUSLE2xWAzCV7MkhvlQgBmGpq16mFEgHM/5XliuDiSEyOXy3NzcyZMnh4SE7N69m631IEg1mNV4sCMGRyE9QxhqRd7pFDSlpy4/uLK0tHT9+vWTJk3q0qVL//79Bw4cGB0dPXnyZB8fn65du44fPz4iImLEiBEZGRn5+fkwOAW+F806tmDTZoR3j1gszs3NjYyMjI6OvnjxIovrQRAKjFRmBk/+bvtJ07arqqrgAvDoKRSKgoKCVatWLVq0aM6cOZCG3alTp969eycnJ8fFxS1evHjkyJELFix49OhRXl4eNOyi7WOBajETRG2w32snNzf3+PHjUK60fft2tpeDIH8BpuJBA23YhMKAeWZXbSYSiWTDhg0//fTTnDlz/P39+/TpExwc7O3tbWJi0q1bt6SkpKVLly5fvnzt2rVv374tLi4uKSlhjpdiAo/AZENWYLNzLSGEz+fz+fyLFy+uXLlywoQJ48ePZ2s9CMKEOTf5766ho+WFQiGPx7t27dq+ffvWr1/v4ODA5XI9PT0DAwMjIyP9/PyCgoLCw8OXLl2amZkJ/WaY+W0UTswAACAASURBVIaEEIlEUq0WBaIo7xVfRA2wpozMbIP9+/f36NGja9euGzZsYGs9CMJEKpUyt9LQU6uiokIul/N4PGaY+NmzZytWrBg7dmxCQoKrq6uxsbGFhUVoaGhoaKi9vX1UVNSsWbPOnz+fl5dXbT6BXC6n3RwoNGoMhiQGkdmC/d20RCI5cuSIg4ODo6PjuXPn2F4OgvwfzHErAGxveTze9evXV6xYMXTo0JCQEGtra0NDQ39/f39/fzMzs969e3/77beHDx8+d+7cn3/+Sbt4KRSKmg0jCCHQxxCOq4kg6OPfxaCRTwebysjn82lKwfbt24ODgzdv3sziehCECcSj4VgoFFZVVUkkkqdPn65Zs6Zbt252dnYuLi6urq6enp7h4eGBgYFWVlZ+fn4rVqzg8XhCoZAW6hFCVCoVeCfpnWlDQybv7ewAluOn+RGRv4U1ZWT2gCsvL//hhx/atm37008/sbUeBKkGtdT+/PPPdevWDRo0KCwsLDExMTQ01MvLKzw8PCIiwsHBoXPnztOnT9+8efP169dLS0uZI1AIo1CPMJK94STU7cHGmdkTGwIvGHthF/azdgghN27cmD59emho6J49e1hcD1I78NcrkUj+bp5nAwG2n7BIZodUPp/P7GNC3q0foh8gTFDFTJNvKisrL168OGrUqPDwcC6Xa2Vl5e/v7+LiEh8fP23atNTU1Dlz5pw7d66oqIiVnxT5dLCf6a1QKH777bfevXvPnTsXZwc2WKD3QVVVFdWXhun/goXVDFkwm1GLRCLq+yspKYGDasHiixcvLlmypG/fvtHR0TY2Nj4+Pl26dPHx8enRo8fgwYP37t1bXFxcUVEBed1I44NNm7GkpATahKxcuTI+Pt7R0fHQoUMsrgepBWhPIBaLmTZjA6R2M1Yul4OFSL8khEBWNkx9ysrK+vHHH5OTkzt37mxtba2jo+Po6Kitre3k5DR16tTVq1cXFxe/fv2a7pHhcQ1/RijyobBpM9IJ4lu3br19+3Z4eHhGRgZb60EaB8xUG6arjs/nU1sSrF1o7Arz9k6cOLFmzZpvv/3W3d2dw+HY2dnp6up26tRJS0srOjo6LS1t8+bNb9++hVtB4nfNOVBIY4L92YFCoTAnJ+fw4cM+Pj4HDx5kdz1I7aj+SkM2HmE0c7WTSqWS7qOhd+Hx48eHDx/u5ORkZWWlpaXVvHlzfX19W1vboKCgJUuWLFmy5Pbt2/Tbaf0fRaVSicVi7ITS+GBNGQsKCujB27dv8/Ly4uPjd+zYwdZ6kNoBK6nhJx4zd8rMLjXUvoNkmry8vPXr18fGxnK5XCcnJ11d3TZt2hgZGfn5+Y0ePfrw4cOZmZmEED6fD5mGYGOSdxtwaCSB41MaMWzajDTD68WLF/v373dwcPj+++9ZXA9SCw1cECnM/tVwIJPJSkpKSktL79+/n5GRMW3atLlz50Ihs5aWlq2traGhoaur68iRI7/88svz58+D3jF1kIaqqz2IJtyo8wdE1APL+Yzw/rt37154ePiXX3554MABttaD/HuYDVDZXkt16JJo1k5ZWdkff/yxdOnS0NBQZ2dnLpc7atQoIyMjfX19JyenwMDAXr16rVu3Dkr4mbeqNk8ZMq7poKuaEow0JlhTRnjjQi7F1atXv/3225iYGOzPiPwdzAkqQqGwZgCEqVBw/OLFizVr1syYMWPmzJmmpqZt2rTR1NS0trYODAyMi4v76quvtm3bhv0QkffC5m6a5k88efJk1KhRMTEx0MQYQSjMKEq1HT18uNIG1+ADhS8vX748Y8aMLl26uLm5+fj4cLlcBwcHU1NTLpfbq1evefPmHTx48OXLl4QQ7IeIvBc2lRE+qFUqVXZ2dmxsbEhIyJkzZ1hcD9IwkUqlAoEAaunoXGZCSLWeN7DnvXLlSmpqKoigp6enhYWFvb29v79/cnLyxIkTt27d+ueff8L1NV2E2A8RobDchQzencePH4+NjXV0dNy/fz9b60EaJhATZ56BhmDU5adQKF6/fn3jxo05c+YkJCR4enpaW1sbGBjY2dl5eXlFRkauWbPm/v37YrG4vLy8oqKCOgqrtT7EfogIE5arAyEnLjMzs1evXlwud+/evWytB2mY0N20WCxmtuqCYr7nz58vWLDA19c3MjLSwcFBV1dXS0vL3Nzc2dl56NChe/bsefHiBflraSC9Lcw7xX6IyHthczcNsT+lUllSUtK9e3c3N7ezZ8+yuB6kwcKMt5SVlV29enXVqlVff/11dHS0i4tLmzZtHBwczMzMHBwc4uLixo8fv3XrViiIpj5E2CnD3GdmMAf7ISLvhU1lpJ/kEomkV69e/v7+zHoDBCGM+VOEEJVK9fjx41WrViUkJFhYWHTs2LFTp04+Pj7Nmzc3MTFJSEi4devW/fv3qWkpkUgqKytpX69qd2aO/at2HhNxENaUkZlD+/r166FDhwYGBt65c4et9SANFolEkpube/To0UmTJvn5+VlYWFhYWFhbWxsbGxsbG/fp02fatGmXL19+9OgRefeOkkgkMG4F7kA/g8FspHYijDTAfohITVjOZ4QP53v37nl5eTk6OsKbG2k0MHuC0TprOmJFLpeLxWI4CZ+UpaWl5F12jkwme/Xq1Z49e65cuTJz5kw3N7eYmJiuXbvq6OgYGRk5OjrGxcVt2rSJ1izjFhipR1hTRvq3wefz9+7dGxAQYGtri3NgGg01i6whygGhj5rXV1ZWUsuuuLj42LFjmzdvDgsLGzRo0KxZs2JiYjp06ODk5ATNtBcsWPD69ev8/HzaVJE5SgVBPh6WbUZCSGFh4Zw5c5KSkkJDQ0+dOsXWepD6pdrmVPkO8u7jUCAQgESqVCra3Z0Q8vTp08OHDyckJAwaNIjL5Xbu3NnFxUVPT8/BwWHOnDknT56kCYmEETBBgxGpX9iMwBQWFkKy99q1a4cMGWJhYbFr1y4W14N8IkC8wIRk5mYzAx0ymYzP5//666+9evXq27evvr6+vb29j4+PpaVlZGTkkiVL7t69C1cKBAI+n19ZWQlZjcwHoT4i9QXL/RkVCkVpaemECRNmzpw5bNiw58+fs7sepN4Bs45pP0JvcKlUCnalQCB48eLF2LFjv/7664SEhA4dOtja2rZt29bW1jY2Nvb69euvXr2Cb4S+4rU86L37dASpA6wp4+vXr+Ggqqrqhx9++P7777/++uucnBy21oPUOxDzrZkBQ/VLqVReunRpwoQJNjY2XC5XS0urRYsWzZs3b9++fXJy8rlz52AYBtxHJBJRryIUR0OxICisOn8u5HOATZsRNlCEkDNnzvj5+dnZ2T158oTF9SD1C4xUZnbrgiDJ27dv79y5c/DgwUmTJgUGBnK53I4dO+rp6TVp0sTDw2PatGmHDx8GTaxmbNbOB12MILXDmjIyt0WPHz/28fGxtbXFTO/GRLXaZD6fX1BQsH379qFDh7q5uTk4ODg6Otra2nK5XAsLi5CQkFmzZj169AjUkxlrBsOQ3kehUMCbBxyXhBCVSoWWI1K/cAhjWDjdrdA3HHzJnIBaj8+G97dQKHz9+rW3t3evXr1yc3Pr8f5IvUNjwcyeN4QQiUQC3kN4z4hEIkjBoe+oR48ebdq0qUePHr169XJ0dLSxsTE1NbWwsDAwMBg4cOD27dslEolMJqtm9GH9MsIWHIlEUlPvQArpeebHdX09WCAQ0NRfhUIRGxvr7e19/fr1+ro/Ur/Qhgs11YpZe1dWVkbNN7lcLhQKnz17duTIkbFjx9rY2LRv397GxqZdu3YWFhZBQUGzZ8/evXt3Xl4eIUQmk1Xrc9PAJ3AhjRsOvImpUxzGD1BlZL416/2dqlAo4Lk3b94MCQmJiIigUUikoUF7/TPFCxo9SKVSKMWrZkhu3bo1NTU1KCgoICDA19e3VatWLi4uTk5OgwYN2r17N9OnTHN6aj5RDT8agtTk//sZaWfjau/FatN76/HBUAcGFBYWdu/e3cPDo7i4uB4fgdQjdCAULfir+ZYAaSstLT179uyUKVPs7OysrKzatWvXsWNHZ2dnExOT5OTk27dv01+9RCKBrUPNx1ETVQ0/GoLUhEP+aieqVKqsrKyioiIaIaGdPmtO7/1IeDwemCG3bt2KjIwcNWoUHXaONDTobx/eCUz7DgpaCCEikejq1auTJk2ys7PT0NBo3bq1hYWFsbGxmZlZaGjosmXL3ptv+N4KFlRGhF045J2bHN6FWVlZffr0GTFiBBUpKpH1q4x0TptMJnvy5El0dPTgwYOZhiTSoKBhumpOFRjfTAh59OhRamqqpaVl8+bNtbS0uFyutbW1s7PzhAkTrly5IhAIoCiQECKTySoqKsCx+HePU73jU/5MCPK3cMi7LTP40bdu3aqpqdmiRYtbt27BeRpwrHebEW4ok8lWrFjh7e09d+7c+r0/Uo9QFWN2SwRZvHPnzu7du0eMGOHg4GBiYmJubu7n5zd+/Pg9e/bk5ORANx2xWAwfvcx3EdxTJBLV+1sLQT4SDn13gvzt3r3bysrK0NDwxIkTsPehaWX1OyKD2Tl57dq10dHRkydPph2lkIYJ87fG4/FycnLAn2hpaenm5mZra2tvbz9s2LCbN2+WlJRUa37DnG0PTRJhphWCNEA40BiKvHvLnj9/3tLSUldX9/Tp04Sxh2KOh2Z+wqtUqjp3fwLlzc/P37t3r729fY8ePYqKij7qp0E+kJr9E5leDjgpFArp3BVCiFwuf/bs2atXr7777rvExEQTExMTE5P27dtzudz+/fvv2bMHf4lII+D/dtMggnv27NHR0dHT0zt//rxMJoO/ByhCIDUyb2GqRt0eDI2nqqqqiouLp02blpiYGBcXR51WyKfm7/on0guY5+FALpfn5+dnZ2dPmTKlR48eBgYGtra2pqamNjY2ERER6enptD8YRtKQ/zocwtjgyOXytWvXamtre3l53bt3D66gFiLYhuAtgm+hOb11VjSVSvXq1avJkyc7OzsHBwdTgwX51NTSPxE6NQDwKhxcv3592rRp4eHhGhoaHTt2hE/QhQsXnjt3jgadJRIJhk2QRgAHak7hC5lMtnjxYi0trYSEBMJI/4b90a1bt+bNmzdr1qy8vDzqbIK/GXAhfShwWz6fn5mZGRkZGRERgdWBrMDsn8i0HMHT8uLFi//973+nTp2Ki4szMjIyNjbmcDgdO3ZMSUm5ePEivZJZTIURFeS/zv/ZjIQQoVD45Zdfcjic/v37E0IUCgX4mAghhYWFCQkJenp6HA4HXJBAna085h/PunXr4uPj/fz8cBemfmr2T4RSFpBIPp9/4MCBbt26ubm5aWlpaWlp2djY9O7d+8SJE1AISNvHgqWJGYhI44ADs9PgC6lUOmnSJA6HM3z4cGYDepFIlJ6ezuFw9PT0goKCoL8s2Im0wu9jmD59enBwsJWVFe6m1cl7+yfSePGDBw+WLl2anJwcFRXl6elpY2Ojp6cXHR29b98+mnb6d78vtBmR/zqcapUGc+bMadOmzYwZMwghUqm0srLyxo0bsbGx+vr67du379GjBy13pdJZ5wZQb9++hT+tjIyMKVOmdOvWDbryIerhvf0TpVLp3bt3V61aNWDAAB8fH1NTUx0dHUNDw9jY2J07d9JWOsy9M3y4QjiO2S4MQf67/P/YNH03L1iwQEdHZ+7cuRCVTk9PNzY21tbW7tixY+/evWG3S9N06Py/OjyYBrXfvn07bdq04cOHx8XFffSPg3wA7+2fOHbs2Pj4eDc3N+gmC20gvvrqK6lUCr8y5g4DDmp2HqllJgGC/CfgSCQSeFvLZLLnz58HBQXp6eldv349Ly9v6tSpHTp0gLkcX375Zd0MOrg5TYeE1n7k3R8Y5APNnj17586dISEhYELm5ubS8hvyzrSpt5/480MsFsOHGS3sEwgETIFTKpV//vnnkiVLPDw8OnXqFBwc7O/vb2RkZG5uPnny5OzsbDZXjyBs8P8714I58OLFCycnJw6Hk5qaOmTIEDMzMz09PS6Xu379evKu5dSHPgD+Aqv1ZKZm5suXL7/55htfX98ZM2b4+/snJibOnDkzOjp69uzZe/bsWbNmzaxZs7Zs2VJfP+3nSUVFBT1mbnXho04uly9cuDA8PNzd3b1t27ampqatW7c2MDAYNGjQ6dOnQVKxWAX53Pi/LmSEkOzsbFNTUw6H06ZNGw6H06pVq0GDBj158oTWydQZaqFkZWVt2rRpw4YNgwcP9vf3d3NzMzExadWqlY6OTqtWrXR1ddu2bct5h76+PofD0dbWvnXr1kf+nJ8zYHFDsAWqmGh7m5ycnNWrV7u4uJiZmWlraxsYGNjZ2UVFRa1YseLZs2csrxtB2IMDfyqwySovLx84cCBoU8uWLa2srGAnBSZDnRMyqKqWlZUNHDiwRYsWIHmtWrXicDhNmzbl1EBDQ6NZs2Y6OjpBQUHp6em0NA35UEAWq6qqaN8QQsiTJ08yMzP37t07bty4/v37GxkZGRkZdejQoXv37hs3bszKyqLjLiCogrk4yOcGB2SLetCnTJmiqampqanJ4XBMTEw2btz46NEjeLVu9bBMezMvL69Xr14cDqddu3Z6enre3t4mJibt2rWzsbHp0KFDWFjYhAkTRo8ePXny5MTExKSkpAsXLhBC+Hx+nUuzEXCAgD7C8a1btzZu3NirV6+UlBQTExNdXV0TExNfX9+ePXv+/vvv9JclFoup86RumfwI8t+FQ97ZdHK5/OrVq97e3sbGxuPHj+/du7eurq6Ojs6sWbOys7M/3tMkl8slEsmZM2e+//77DRs2lJSUPH36NDs7++DBg/v27QsPD1+0aBFcSf1i9C8Tx8J9DBDIKigoyMrKys/PHzhwYLdu3WDavYGBQWBgYEhIyKFDh8RiMWwgAPhIw/955POEQ9510CGErFy50szM7Ntvv4Xahj59+piamrZq1crX1/fy5cvkIxSKmdVBC9FAkW/cuPHdd99FRETMnDmTeQ0c8Hg83Ep/JCUlJTKZLCMjY/Xq1RMmTNDS0jI0NLSysjIyMoqOjj506FBubi6tmCZ/bRSiVCpxN418hnDIu/CLXC6fPHmyubn5hQsXICXtwoULo0ePDgoKMjIysrGx2b17dx0eABlz9BGEYQlCjs6DBw/Gjh2bmpo6bdq0srIymjTHLK35+DKbzxaBQFBQUHDr1q2VK1empaW1atVKS0vL3Nw8NjZ2+fLlf/zxh1AoZPaOZY55wa7ayGcLhzBmvPTp08fKyqqiokKlUoEYCYXCvXv3Dh061MLCon379mvWrKmvB8vlcrFYLJPJCgsLBw0aNG7cuLVr12JV2b+BKVjgo4BhzfQCaKNNCJFKpQcOHBgwYICbm1uHDh0MDAy0tLT8/Pzi4uJwvjOC1AKHHhUVFTk4OBgZGdGMburvKy4uXrRoUUJCwvHjx+t9BeXl5atWrYqKilq6dGm937zxQbuv12wjBuepb6Sqqmrv3r1RUVEmJiadOnUyNDS0t7fncrmrV68uKCjA+c4IUgscuVwOkceHDx+6ubkFBgaCW4oaFEKhEOyR8vLyerTpoEdLVVVVXl7evn379PT0Bg8ejP7+fw94ACGCDL+XiooK6qm4du3ajBkz7O3ttbW1mzZtamlp6eLisnPnzjt37sAFON8ZQWrh/2LTZWVlmzdvPnLkCH0NUj0+pnH3v+TUqVMuLi7Dhg37pE9pNDCbfdGCIvo7un79+tq1a5OSksLCwgwNDU1MTLhc7ujRo+E3S6szq4FTTBGEyf/tpukfBt1h0X2ZUqkUCoUCgaAed1tSqZRu6BYuXNi9e/chQ4ZgffS/AXrb0F8TTOYjhDx48GDXrl2jR4/u2rWrubm5lZWVubn50KFDf/vtt8rKSihaJ+8aKda8JyojglA4NAeY9torKSkhfy1coQ3HPoUfSqVSpaWlJSUlTZ8+vd5v3vig4sXj8ehY2nv37gmFwjlz5tjb28NsFh0dHahGB2cI0+p/b9o8RqIRhMn/2YzUYAStrNb4nhAil8uZmcD1hUgkmj9/flRU1Lx58+r95o2PmglMDx8+3LBhw6RJk5KSkuzt7du1a9emTZuJEyfevn2beZlUKqUhNaxpQZDa4TC74IjFYjr6CvSRWigCgaB+wyO0+xmfz9+7d6+zs/OcOXPq8f6NGNpVTC6X//bbb4MGDTIxMbGysrK1tdXS0goMDJw2bRqYk2AqUh2EEakEs3MQ5J/g/PMlnwbat/HSpUt9+/YNCAiYOHEi5jNWAwLQcFzN/1tUVHTmzJnU1FR9fX0bG5vWrVu7u7v7+/tnZGTk5+ejxxBBPgbWlJG8m8WqVCqPHDni5eW1cOFCFhfT0KisrGR6dSGdW6FQlJaWyuXyFy9eJCUldezY0cPDA7yKAQEBZ8+effPmDWEMosC+ighSN9i0GcHtVVlZuX37dm9v782bN2M+IxMej1dSUgKmIjUY7969O3DgQC6X27Fjxw4dOrRp00ZTUzM8PPyPP/4g7xKt6Pb5U6dbIUhjhTVlpBvnt2/fQgvxY8eOsbWYBgg192QyGTWuHzx40K1bN3Nzc1NT07Zt22pqakZGRm7cuJHO6Ya8AihUx9ZtCFJnWFNGKJoWiUSvXr1KSEhISkpavXo1RgaY0CkUhJCSkpLvv//e19fX0NCwefPm7dq1c3d3nzVrVl5eHiFEoVCAnUg34OCgxP9PBKkbbPoZIUqQnZ09bNiw+Pj4tWvXsriYhgbVuJKSkkOHDvXt29fc3NzCwgKaZvbv3//69euEELFYzHQm8vl8ZtM2jMMgSN1gTRnplOp9+/b169fP1dV15cqV6BejSCQSlUp18uTJAQMGeHp62tjYWFpaenl5DR069NChQ2/evOHz+VQ9IdWU+b8nk8lo6j6CIB8Ky35GiURy+fLlyZMn29nZrVixAnd/FIFAsHXrVk9PT1NTU2dn5zZt2hgaGk6dOjU/P595mUQigdxvZuYpc5ItgiB1gM3dNDRJzczM3LZt21dfffX777+zuJhPTS21d3SogEqlAkPv5s2bsbGxAQEBZmZmbdq0MTU1TUpKOnPmjFpXjCCfMWwqIyFEKpUePXp00qRJ27Zta/RbaWjZoHyHQqFQKBQ09xASbp48ebJ06dIhQ4YEBQXZ2NhoampaWlouWLCgtLSUYFUfgqgLNnfTIA0PHz7s1q3byJEj79+/34hdY7U4CsBUFAqFxcXFO3fu9PPzs7a2trGxMTU17dmz54kTJ6BJLY58QBC1wabNSAe6xsfHOzk5HTx4kMXFfGqYysgctAJnSktLDx06lJqaOmLECAsLCxhsm5qa+ujRI7iA2XYMQZBPDcu7aUJITk7OuHHjfH19z549y/ZaPiG0lEUikUA/c/Kus9HDhw937drVt2/f9u3b6+vrczic0NDQRYsW5eTkEELEYjFkehPG/AkEQT4prCmjSCSSy+Uw5HrevHnu7u6//PJLI+5cCxZitZbaIpFo3bp1vXv39vX1NTIy+uKLLzw8PEaPHn3hwgX4FlouKRKJcDeNIGqDNWWke8M///zzu+++43K5hw4dasTKSAhRKpVU6RQKRVZW1k8//WRiYtKmTRsTE5OWLVsGBwdfunQJXqX5noQQlUqFXYgQRJ2wpoxyuRwCtTdv3hw3bpyLi8vNmzfZWox6oNNrlUpldnb2hAkT2rdvDzUtBgYG3bt3h+0zrXdmDvODfTeWQiOIemDfz7h69WpHR0c3N7fffvut0fTageGLcAz9HZjB5enTp3fp0gVmnLZu3drZ2Xn27NlPnz6FV4VCYeO2nRGk4cOmMsLf/88//xwaGmpvb3/y5EkWF1NfMFMOawp9Zmbm7NmzQ0NDXV1dW7dubWhoOGHChBs3bsCrpaWlWLiCIA0B1pSR5nXv378/NDTUzs7uxo0bjcNmBPOQWdQsEonu3bu3ePHirl27enl5cblcTU1NJyenuXPnFhcXw2VSqZT+n0BeN4IgbMFmFzJCiEwmO3bsWNeuXdu3b5+VldUIlJHWLEulUjroJjc3t3v37q6urp6enmZmZjo6Oj4+PocPH4YwlFgsZo5qaQT/CQjyX4fN3bRIJCovL3/w4EFiYmKTJk0aR10wHa9Ixe7hw4eLFi2CCVZubm5OTk7Tp0+nyZsikYg5ORplEUEaAmwqo1gsVigUL168GD58uIGBweXLlxtHP0G6jxYKhWfOnBk/fry7u7uLi0uLFi26d+9+4MABGoqBakiIO9PBjUqlEmPQCMIubPZnhIOsrKwBAwb4+/vn5uY2grppkHtCiFQq3bFjR+fOnfX09Ozs7HR0dMLDw69du0YY2lcz3kLLYxAEYRE2bUahUAhTVQcMGBAeHl5QUMDiYuqX169f79q1a9iwYT4+Ph07dtTV1e3Xr9/Zs2dh/h9hNByDrTSkdtNtNfbUQRB2YbkGpry8vLKyMjk5OTExEabf/YcAlyLkLdIZAyqV6ty5cykpKY6OjmFhYdbW1t7e3nPmzJFIJDKZrJqRiE0iEKRhwpoyCgQChUIhk8nu37/fq1evZcuW/UeHI4MygsZVVFScOHGie/fuGhoaUVFR5ubmHTp0yMjIgPI+uVzOlEJmiQuCIA0K9idk/fTTT76+vn379iXvS41uyBQXF1N3IaQi7tu3z8nJycfHx8zMjMPh+Pr6UkMYSiGZ3w7Na9W/bARB/hGWqwPPnj175MgROzu7iIgIkUj0H+qbwBQ1sAQfP34cERFhZWVlY2PTvHnzSZMmFRUVEUKEQmHNXTMYjKiMCNIwYU0ZIeZQUVFx5cqVyMhIU1PTV69e/Yf8btAzUSKRgJ178eLFYcOGmZiYmJqawigr8ELCMIOajgJURgRpyLDZawcOrl+/bmhoGBAQcPjwYbYWUzd4PB64Do8fPz558mQvL6+2bdt+8cUXI0aMoOlHVDqrUa2n5F+2vAAAIABJREFUN4IgDQo2d9MlJSUlJSWjR492cnJKSUl59OjRf3FI1tGjR6OiokaMGBEREaGlpeXm5gbn37x5AwfUC4kgyH8FludNV1ZWpqWlOTk59e3bNzc3l63F1AGYW3Dw4MGYmBgfHx93d3cOhxMQEPDs2TPI0yTv7GIsaEGQ/xws5zM+evQoPT3dw8Pjq6++evToUcOMTfP5fGZqDnnnN8zMzHRxcTE3NzcwMNDQ0BgyZMizZ8/YXCiCIPUEy7HpBw8eTJ061c/PLyQk5P79++wu5r1QsYa6FIlEAlXPO3fuDA4O7tSpk4mJiZaW1rx581hcJIIg9QvL/RlPnDgRGBhoZWUVFhZWWVnZMDOfy8vLaYmLRCLh8Xh8Pt/Hx8fAwEBfX9/ExGTx4sVgLTbM9SMI8qGwbDNeu3Zt4MCB1tbWkydPJox2tg0K5twClUp14cKF0aNHQy63u7v7li1bmNNa2FsmgiD1BpvKCAWCW7dutbW1TUhIKCkpaYCZ3jR+IhaLZTLZiRMnunTpYmFh0bJlS3t7+wkTJkDGIqTpNEw/KYIgHwqbygiN/tesWWNkZOTl5ZWXl9cAJ0PR1twPHjzYtGlTjx49mjZt2rFjR3Nz8+zs7Ldv31KDsQEuHkGQusHyblqpVK5evdrT07Nfv34NuTmjQCBIS0vT1dW1srKyt7f38PCYN28endZC7UrsHoYgjQM2e+0QQp4+fXrx4sWUlJRRo0Y9ePCArcXUTk5OzrJlyywtLXV0dKysrEJCQo4ePUoYnccIwxeJIEgjgDVlhE2oQCA4e/ZsZGRkcnLy27dvWawjpo+GTbFCoVCpVGKxuKCg4PTp025ubrq6ug4ODra2tlu2bGFrkQiCqAeWpx3k5+enpKQYGxuPGjVKLpfT8VLqp5oy0pUsXLgwJCREW1uby+UGBgaeP3+e/NVaRBCk8cGmn7GysvLu3btTpkyJjIxMTEx89eoVi4uhQOaNUqksKSlZuHChp6cnRKKdnZ0fPXrEvAZBkMYKy51rMzIyxo8fHxoaGhAQ8PDhQxYzpelYK/jy+fPny5cvb9eunaen5+DBgz09PaEH7X+08TiCIB8Ey3XT6enpEydODAkJsbe3v337Not+RtggQ1yosrJyxowZlpaWdnZ2bm5u4eHhRUVFfD4floeFLgjS6GF53vT06dMnTZoUHBwMysjiYsi7ChyFQrF06VJ7e3stLS0HBwdjY+MzZ85A6iXoJp2biiBIY4U1ZYQcwN27d4eHh7dq1crJySknJ4eOqGeFiooKQsjVq1ddXV2NjIy4XG5AQMCOHTuY7dGY8wIRBGmssGkzyuXyV69ezZ0718PDw9ra+sKFCywuBgzG3NzcmTNnWltbd+jQwdzc/Oeff6YvyWQyOAABRRCkEcNy1s6xY8e+++47Dw8PV1fX69evq3MB4C6Ewhtqq86ZM8fHx6d9+/Z6enp79uxR53oQBGk4sBmBUSgUf/zxx4wZM0xNTSMiIp4+faqG3TS4CJl2H+zrCwoKFi9e7OHh0aJFC1NT0x9//FGhULCYX4kgCIuwqYwikUgsFo8ePdrAwGD8+PE1JzJ/CuRyuVKpFIlEdI+sUqkKCgqmTp0aEhJiYmKip6c3fvx4OsUFQZDPEDanqoJRlpiYaGVlNXHiRLU9GuIn0EQHRpuuW7euX79+vr6+HA4nODg4KytLqVSiwYggny1sKiMh5O7du9HR0T4+PtHR0YWFhWqoLQFTEbbtYrGYx+Nt27YtJCQkKCioVatWgYGBx48fpy1z2I2VIwjCFixPOzh48GCPHj3Cw8O9vb3VM14KPIy08Hnfvn0+Pj6GhobNmjXT09O7ePEieed5VCqV2HIRQT5P2LQZlUrlzz//3Ldv37CwsMDAwMLCQnUuQCQS5ebmxsbGmpqampubOzg4LFiwgMfjSaVSUG3cTSPIZwub+YwymeyXX34ZMmSIt7d3eHh4WVmZeubA8Hg8SE4cN26cgYGBkZGRubl5eHh4Tk4Oc23YNgJBPltYrpu+dOlSSEhIaGho//79Sb32sKEFfDDWihCiVCrFYjH9csmSJVZWVnp6es7Ozh4eHgUFBbSpuEqlghB2fS0GQZD/FmxWBwoEghs3biQnJ5ubmycmJtb7I2BelVwuB5WkWqlUKg8dOuTn56ehoeHl5WVtbb1hwwaRSEQvUCgUUqkUx10hyGcLy3NgCgoK1q9fb2hoOGbMGIFAUL+xYNqdGzQOtuoqlerp06ejR4/u2LFju3btDA0NFy9eXC3SAt+CbSMQ5LOFNWUUi8UlJSUPHz5MT0+3sLBYtGhR/SoR7IXp9lwikcA+msfjjRgxAhpGODs79+nTBxLO6XcplUr0MCLIZw6bNuPLly+3bdsWFhbm6+v7448/KpXKehwfCGJHMxMh0CyRSJYuXWphYdGpUyd3d3cnJ6fffvsNroGUb3QvIghCGsLswF69egUHBw8fPryysrIe7w+FLrQFN2yo7927Fx8f369fP3t7e0tLy23bthFCRCIRrYdhyqJSqURXI4J8nrBpMwqFwpMnT/r6+vbp02fatGnkE/Q9hFgKHJw6dWry5Mnm5uZTp06Nj48fN26cSqVixqPpJlqlUoEJia5GBPk8YVMZJRJJRkaGpaVlu3btnJyc6DiB+gIKXaCgRSKRTJgwQVdXV0tLy8rKKjQ09Pfff4fLYN9N3Ysgi7inRpDPGTaVUSqV5uTkBAQEREdHjxs37lM8oqCgAA6ys7NDQ0NtbGyMjIyMjIxOnTpF3okmYST0IAiCEHbzGR88eHD06NG0tLQOHTokJSVVVVXVo6UmEAjASygQCKqqqoYMGeLi4uLn52dsbLxhwwYadZHJZNg2AkGQarBpMz579iwzMzMpKalDhw6DBg0i9TqWj2Z3KxSKPXv2mJubOzs729nZjR8/Hi6AaDWoJ9qMCIIwYbM68O3bt0uXLvX39+dwOMOGDRMIBPWuUOXl5ffv3+/cubODg4Ojo6Ofnx+Mu4JgNHmXDY5TpBEEYcKmzXj37t1vvvmmZ8+eNjY2/fr1q9/eNnK5vLy8nBAyatSopk2bGhsbW1lZ7dixgxAikUhAgiUSST1mUCII0mhg02Y8c+bMsWPHUlJSunbtGhgYSAgpKyurr/uDMXjz5k1nZ2d9ff2mTZvGx8eD+FZzLGK3MQRBqsGmzVhWVnbmzJlly5YFBwenpKQQRrD441EoFMXFxT179nRxcbGzs/P39z9x4gR5N5mLvJNOeCiWAyIIwoQ1ZZTJZE+ePFm2bFlsbGxsbGxYWFj9DqUSCAQpKSlcLtfS0pLL5f7www/knRpSTeTz+bS5N4IgCIVNmxGUMTw8vE+fPv369avzfVQqFRTPgMxJpdLKysrMzMyQkBBLS0sdHZ3IyMj6TQlCEKRxw5oySqXSt2/fLlu2bNGiRY6Ojps2bYI+23W4FUSWmZ3Edu3a5eLiYmtra2xs7O/vf/PmTbgzxlsQBPk3sGkz5ufnb9iwYe/eva6urosWLarzfeRyOTgKwU359u3bhISETp06BQcHW1lZLVmyBHO5EQT5INhUxoKCgh9//HH27NlWVlYRERHkXXPZOlBaWkoIEYvFxcXFZ8+eDQsLs7Ky0tbWjo+Pf/LkCaRzV1RU4IYaQZB/A5udawkhP//888CBA7W1tefOnUvqqowgfGA2rlixYtGiRYmJiaampiYmJidOnKCdxBQKhXomcCEI8l+HTZtRIBAcOXKkd+/e3t7emZmZdUvZod/F4/EuX77s7+/v5eXVq1cve3v7zZs30/po2sIWQRDkH2FTGbOystLT0wMCArp167Zt27a6da6lPsTs7OwZM2Y4OTl17NjRw8PDx8fnzZs38Cpt0Yh5iwiC/BvYjE0XFhaOHTs2ODjY1tZ2/vz5pK6da0FSf/jhh3HjxoWEhMTHx0OwG3QQXJD0ofW0fARBGjNs2oyvX7/euXPn4MGDW7dunZKSUnsEGWSOOg2r7Y4vX77cv39/a2vrrl27Ojo6jho1SiKRyGSyaiEXtBkRBPk3sKmMFy5c+O6774KCgrhc7sKFC0mt1YFUE2mZM3MaQXh4uIuLi7e3t4WFhaWlZVZWlkwmo9k8ADTr/lQ/DIIgjQiW66Zzc3NHjhzp5OSUmppa+8VU42jHsIqKCjg4efJkcHBwx44duVyul5fX3r17CSEKhaKaDsJol3r+GRAEaYywpoxyuVwqlV6/fn3AgAGdOnUaM2YMqbVzbc3ZLFDQkpWVpaur26VLFwcHhzZt2gwePLikpKTmfejQq0/woyAI0thguQZmwoQJPXr04HK5U6dOJbUqI0wBhD21RCIBE/L+/fsJCQm2trZ9+vQxNTX19/eH/XjNSAsqI4Ig/x42lTEnJyc5OXn27Nk9evRIT0//N421ZTKZSqWirsZ58+YZGhqamZnp6+tbWFhkZGSQv2nQrXpH/f4ICII0SlhTRoFAcPXq1eHDh3/99dfJyclXrlwRCoX/JquGNljMzMzs0qWLhoaGkZGRnZ1dv379SktLwerEzhEIgnwMLGftrF+/fvjw4f7+/g8fPvzHwDEzUyc3N3fKlCnW1taWlpba2tpBQUFXrlyBvTYmLSII8pGwOe2gpKTkp59+SkxMtLOzKywsJP+UbwgpinCwZMmSFi1a6Ovrjxo1ysLCYsaMGYShiVgLiCDIx8CmzVhcXHzu3LmAgAAbG5vTp0+Td61n/w5aIXPr1q2YmJiRI0e2a9cuNDTU1dX19evXAoEALqjf3uAIgnyGsKaMfD7/8uXL58+f7927d3Bw8Nq1a//NdymVSolEMmfOHE9PT3d391atWjk7O69fv54wCqhxgAGCIB8Jmzbj2bNnV65c2bdv38jIyF9//VWlUtFCl79DJBIVFhYOHTrU0dGRw+G0bNly5MiRtJWOUqmEsDXuphEE+RhY3k1v3bq1W7duHTp0OHToEDMd573IZDKFQnH//v0xY8a0b9/e0dHR1dX11q1b8KpKpQJr8d8oLIIgSC2wpow8Hi8/P3/79u1BQUEWFhYbN26sPTYNm2WhULhkyZLg4GBra2sbG5t58+YRQsrLywkhNftHIAiC1A02bcYbN26kpKQ4Ozv37t373LlztdeoQDvuCxcu+Pj46OrqOjk5WVpaZmdnk792AgezEWtdEAT5GFhTRqVSWVxcPGHCBAcHB09Pz9OnT//jHKu8vLx58+aZmZmZm5tramouW7YMjEQ6VRU24xKJBI1HBEE+BjZtRkLIunXrfH19fX199+zZQwhRKpVQ+EwTG6GZGPgNT5w4ERoaampqam9vz+Vy7969y+LKEQRpxLCZ6c3n8+fPnx8UFBQWFnbkyBFm7YpAIKhmQgqFwu+++05TU1NbW9vV1XXFihU48QpBkE8Eyzbj/PnzIyIievbseevWLbAWmSXPYEIqFAo+n3/x4sWUlBQjIyMul+vs7Hzz5k1S1+kICIIgtcNmRwmVSjVt2jQ/P7/w8PCysjI4T0ekKhQKmnzD5/PHjh1rbm5uYGBgb28/dOhQsCjrNm4QQRCkdlhTRui3OGnSJD8/v+DgYJqKCK9KpVIaX5ZKpb///runp6eOjk5UVNTAgQPPnj1Lam3miCAI8jGw3J9x0KBBXl5ebm5uf/y/9r48rKlr6ztalRlCSBjDEGYCoqCCFBERUC6zgKjMiEyKCiKIts6iFq1K1UodXq22et/W+rYOvc5DbW8Hbb0OxQGrFwsyCwECJCQ53x/ryXq2J4H6tlfg/Ty/P3gOJ+fss4e11157TbuyEpgjGb6C+SMuXbrk6OgoEAiKiooqKipkMllXV9er5HNkwIABgz+BQeOMjY2Nn332mb+/P5/P53K5ly9fprkiSiQSPIH622+/FQgE+vr6fn5+n332Gdzs7e3tP2aGAQMGDP4cBlNm/OWXX7Kzsx0dHdls9pUrV1CrKJfL0U7d3d393//937a2tmPGjHFzc/vb3/72+PFjhiEyYMDgtWIwOWNDQ8OaNWtSUlImTpx448YNkt+hwlEsFvv5+VlaWs6YMcPOzq6kpAQYKB4cyIABAwb/cQwaZ2xpaamoqJg5c6afn9/bb7/9yy+/UBQFCkR4AMTGa9euubu7W1tbu7q6BgcHY/4IjH4ZpOozYMDg/2cM5qmqH374YX5+voeHR1xcXHV1NXhuwznRIBg2NDRER0ebmZmlpaWZmJjAmdS9vb2kCXuw6s+AAYP/jzFonLGqqurw4cObNm2yt7efNWuWWCxGfod6xosXLxobG9va2hYXF3t5eVVUVFBEWDRGDTJgwIDBfxaDqWe8dOnStm3bxo8f7+Xl9dtvvzU1NXV1dQGz6+3tFYlEa9ascXd39/Pz8/LyysrKunv3LkTIMJ6MDBgweK0YTM64d+/euLi4gIAADw+PJ0+ekD9JpdLLly8HBAQ4Ozv7+Pg4ODhs2bKFUmZpxJBqJtsYAwYMXgcGkzN+8cUXnp6eEyZMCAsLu337NqV084bc3evXr7e2tuZwOC4uLsHBwWTcCyaSYDgjAwYMXgcGjTPeu3evsrLS09PT3t5+w4YNdXV1oGeUSqVwMWPGDIFA4ObmNnr06KlTp7a2tsIxBmh1YRLtMGDA4DVhML122tvbPTw8jI2N7e3tnz17RiltzVKp9OHDh/r6+iwWy9zcPCoq6sSJE4NVTwYMGLyBGDTO2NraKpFIMjMznZycPD0979y5Q1GUXC4HmTE+Pp7NZjs4OIwfPz45ObmysnKw6smAAYM3EIPGGbu7u8+dOycUCm1sbPz9/W/duoXJFisrK2fNmjVlyhQLCwuhUJiRkcFEvDBgwGAgMWicsba29saNGwEBAZaWlqampv/+978ppcy4Z8+elJSUSZMmsdlsZ2fn48ePD1YlGTBg8GZi0DhjfX392bNnw8LCXF1dAwMDQWDs7e2Vy+Vr1qzhcDiGhoZjxoyJiopiAl0YMGAwwBg0ziiVSt95551JkyZ5enoePnwYboJTTmRkJJ/P9/LyGjt27Pvvv08xubsZMGAwsBg0ztjV1XXgwIHi4mJHR8f9+/cD75NIJFVVVebm5qGhodHR0S4uLv/85z8Hq4YMGDB4YzGYnt47duwICQnR0tLasmVLb28vbKhv3rw5bdq08ePHm5mZBQQEgM2a8ehmwIDBQKJPzkiLTe7q6oIAFTLxl4wAeV8ul6vyMkjQjQZoiURSV1eXl5dnamo6a9YsKLmurm7mzJlmZmYODg4WFhZwnyJy6oCzN1xAURKJBDOSQR0wIQX5Fj4GWSDRS5xMCknLT0E2AfIA0foEjrLBFzHPBV7L5XL4EFkUmTgD8gZh3aDOpAe7VCpVDfhRKBTkWJDVlkgkkGiD7GesDzQWn4djyMiBI4vCz0GudVp7oXzUDlMvgywWxwtjOslrKEEmk+EFOWpwB1qklszgYSgNyQD7E6MGKGLEoSi4hp2KVCqFrwPdImnJ5XI8UQO6rrOzkzyuEsuBz8G/OGQ9PT20LHk0+oHKYyGQEwByTcnlcsXLoDUf71DKSQE6evJbSJBknaGvenp6cAhaW1tpyVm6urqwKNrg4v2+EgCSc5+kWCgHs/QrFAq1+aeh4VgNLARukkehvG70yRmBF2CKBwTZI7TekUgkSNYSiQTGA9pPjplUKoV/v/nmm4qKCisrK3d39+rq6sePH+/cudPExMTf33/ChAmBgYGXLl3q6upCfkf7KG2S0C6w2uRMQBLp7OyEpkFluru7aW0BulFr/JFKpUA6ODNhBuIXgWRpITrkKiJXgqQh2rSn1Qf5PlklsVgM7FVtziFM6UYRXIYi+CnZk9hv3d3dePwOLgawjOHDWCxFTFGSprFRcIfkkjgE4IcAXAxvkssGdKDaGYhznoyjV7se01qntijawME1dgL18nJF1hCv4S2yS7FYZG3kFyUSCfJfiIVV21LVdymCEtQC6JCkPSAP+Bzcb2pqgp86OjpIcoIAM1xOyNT6MEY9PT04eWE5IQmMXDhJckIegnwN2nvx4sX169dXV1e3t7e3t7dDf0IJwHlwIKBR/Tf8P47+dtN4tGl3dzdQeUdHB9AfsBuoK65OJGn2RY5QJkVRNTU1e/fuDQ8Pt7S0zMnJaWxsPHLkiK2tra2tLZ/P19HR8fX1rampQekPP4eTDa/JkEEQmsgvqlYDiqItsOSMpZRTAvkCkj6WgO+qciW408/EVgXmpiR7j+SbJP2pLUGhUAAxIffB6QE0R7JIVeEXuRv+SspBH3744ffff08KaJRSKsGHycMq4AJXNawzKaogRyBFfnI96yf6E8UonEhYJvIjrAZOdaBb/BB8nbYzIKc0peSPNOkGqIVcG7B8Mu8yjUvS6A25gEQiobEMnFa0cYGbKB4qlNG0ZMk0Zko7kF2hUJw6dSovL+/+/fswQLQtlOqmQXXBoxVI+1f1YZqwUl9fD5JjYWEhi8WaMmXKhg0brl69Ch2OjYLrFy9ewH2ZTEaeRD8A6JMzki1UnfyqcjuOAVI/zlUYeBgD8hisgwcPzpgxw9HRsaCgoK2tbdKkSfr6+gKBgMVijRkzpqioiLbdwEFCvgwkQpvn5HTFydnb2wvV6OjowOlB7kdkyuOtYdigCXAHqVzt7gynDVQPBRkgYolEAg+QAhQwL9wh0uqPs1q14fC3o6MDTuumXp7M0ATkOCRIHkST32msgVJuA5E6FQpFUFCQjY3N4sWLHz16RCm387j7I9+lXSAjxouenh7oVew3UiNBEYyS3PUDm6CxAPyXVDjQ9vsUsZ3HXSoMDa3hpPSkllPQ9qfkCo3PYCHwoipjUpU0KYLAyK009TJI2sPSyPJpEwGWc+S5SJMZGRksFmvevHk0JkgTiuWESopGTjKl6gOvSSrCHhCJRKp6IXzs2LFjhoaGmpqaLBaLxWKx2Wx3d/fc3NyTJ0/i7oSGAXZQ6ZMzkj1C4/rkGJBCHL5Lu1Zl9kCap0+fDg8Pnzp16po1a65cuRIREcFisd56661Ro0b5+PgcOHAAHoaQaorodKQkkjhoS2X/SW2hCRKJBLobKZ56eVaoXQCBjFTLR7qn0SgprJFVJWUK/Kmnp4fcwtBEPHyF/Dopj5AkS1EUbFIo5cSAxqI0hNyZrBu5ncTroKAgFos1atSojz76iNZqUoQkmQXWBNcYUvIim0yT3UgJvR9XVhSfQVKDJ5FdwrtypbaOelk2VF315crNOwlyoyCTycg9O7mg0saIHH3ocPycQqHo7u7u7u7GSpLMXXXdUm0srXwaz1IrsgFw25eXl8disbhcbnV1tVwu7+zslCt3x1g+WWEsAboIdbg0CqdREfUyiapqvUFgRJiamsKFnZ1dWFhYRUXF/fv3a2pqgJ8iA0GV9wDgD2zTJH8EuR34AgoUqE+kKKqzsxOpv7u7m1SlA9m1tLTAna6urrt37547d66iosLFxWXr1q2ffvqpUCiE3tHW1p4yZcq9e/fImsjl8vb2dlLYpl6mGNCLwTVtDcTZ29bWBloPGvPq6uqSSqWdnZ24aFMvC4xogKKIIcev49YbK4MPwzoJGctVBR8a5MqwcUqdCAatJpXQJKFArWACkCI8Dgf1Muun8VYYL5rQATrH+vp6GxsbHR0dFotVVlYGpcGTOCLYjTQhUW1DsC3ILoFfUEoxHx9TnecKQs9ANoG2F1ModbI4jWnCNfJ9cicOsjBYXfA+2tD6Od+8t7cXuTMoTykl4xOLxaRBg+wrSqkppiiqs7MTuQYJ4MK4SAMpYj/jBKT1LWm7QBEPPhQfHz9q1CgNDQ0QzdD6RCm3YnJCMdLd3U3TA5D1J/uf3IG1t7fTFMdyQiMPI97a2vrDDz8sWbLE29sb+ePw4cM5HA5c6+rqhoeH//jjj1BOU1OTqjHgtaJPzoiWXzS0qQ1eRoU9vkUzhPX29gJJYcdRFNXY2Hjs2DGRSHThwgV7e/s5c+bY2NhoamoOGzaMxWJZWlq+9957FMEBRSJRa2trbW0tTICOjg6xWNzb21tfX6942bYrV6q3KYrCExTa29vFYnFnZ+edO3fu3Llz8+bN3t7eZ8+e/f777xRF1dbWymSy9vb2np6en3/+ubW19enTp48fP4btwG+//dbQ0PDw4cOnT5/CJ9ra2qAaTU1NUMLDhw9FIlFzc/OLFy9QmgDy/emnn6iX5VBSlQZUTinZN8lYab2tUCiQDyoUitraWoowmCoUiubm5vr6eii2o6NDoVCgoh36imSOyCLb29vJBUwkEj1//pwiSBlaB4sWl8s9f/48RVENDQ1oZCTLhMTs0DO9vb0NDQ1QQ5z/IpHohx9+aGhoaG1tlUqlVVVVkLEY9PRtbW2NjY3A+lFnB7zyxYsX9fX1DQ0N7e3t2EstLS3IBEUikVgshjsNDQ24YZcTWuOOjg7oQ7lc3tzcDNcvXrzo6Oiora19/vx5Z2dnXV3d06dPkRN1dXW1trY2NDRQFNXc3Ewp+V13dze8KJVK29raqqqq6uvrKysrJRJJR0cHyDjY/5RygaSIbT6u1lANZEDAyKBDyO1nX3sjSgWwEuOvIpEIuhTWM19fX9i9/vLLLzSRHMe0u7ubts8DsYO2ZQE5WtVnA4ttaWlBkZxSGt8pZcZ+SkmBH3/8cWhoqI2NjYaGBrBFfX19PT094I/p6en9CBOvD31yRmhGd3f3b7/9dvv27SNHjlRUVNy9e/eDDz7Yvn17eXl5eXl5aWnpsmXLSkpKSktLP/7446+//vrzzz8vKyvbvXv3+fPnT5w4sWrVqpycnPT09PPnz+/Zs+fOnTtHjhy5fv16SUmJl5dXSkpKdnY2nPSip6cHfWFnZ2dra5ubm7t///7r169XV1dv3br16NGjCQkJM2bMyMrKWrJkSWpqalJSUlJSUlBQ0DvvvLNo0aJ33nln3759+/btw3+vX7/+zjvvrF279u9///v777+/aNGinJycuLi4hIS5ELRVAAAgAElEQVSEqVOnbtmyJTg42MPDY9GiRbGxsYcOHfrwww+PHDkyefLkgoKCyMhIPz+//Pz8goICd3f30NDQ6dOnp6SkVFRUbNq0KSwszN/ff8OGDZmZmXPmzNm2bVtoaOiCBQtyc3MXLly4bNmy3bt3Hzt2bPPmzTt37vTz8/vss8/+53/+55NPPtm3b9/OnTvLy8t37dr1wQcflJWVrV27dvbs2QUFBcXFxbm5ucuWLdu+ffuqVatiY2OTk5PLyso2b9787rvvlpWVLV26NCMjY9OmTd988822bduSk5M/++yz/fv3/9d//dfChQtLS0vj4uJiYmK++OKL8vJyaLivr29iYuKmTZvmzZtXXFycmpq6c+fOhQsXrl69esGCBUuXLp01a1ZwcHBqaur27ds/+eSTrVu35ubmBgcHr1q1auvWrTt27Pjoo48uXLhw5MgRDw8PFos1YsSI9PT0lStXrly58quvvrpw4cKpU6dKS0vnz5+fn58/d+5cLy+vadOmpaenT5s2bd68eV5eXnFxcfn5+TExMVlZWStWrAgODrazs8vMzCwpKVm3bl1cXFxmZua1a9d27dr1zjvvZGRkzJ49Oy8vb9myZampqXFxcdnZ2fn5+enp6eHh4VOmTAkODk5ISCgqKtq0aVNeXl5UVFRSUlJOTk5JSUlSUtLs2bNDQ0MzMjIiIyMXLFiwevXqnJycoqKizZs35+XllZWV5eTkZGRkrF69esWKFUlJSVlZWeXl5TExMcHBwe7u7v7+/jk5OXPnzo2Li8vJydm0adO+ffuSkpISExOjoqKOHj2ampo6V4n4+PjQ0NC4uLjU1NSIiAg3N7fY2NgxY8akp6fPmzcvMzMT6GrLli1fffXVtm3b8vLyUlNTExMTZ86cGRsbO2vWrFWrVp05c2br1q0LFixYs2bN2rVr161bV1paWlJSsnTp0sWLFy9atKiwsHDVqlVlZWUffPBBfn7+6tWry8rKtmzZsmXLlrKystWrV+fn5584ceLAgQNlZWUrV65csWLF8uXLi4qKFi9efPbs2QMHDnz55Zfr1q3bsGHD559//u6778IzbDbb0NBw2bJlO3bsOH78+JkzZ7744osjR46sW7fuk08+uXTp0nvvvVdYWLh///7Tp0/fvXv35MmT77333tKlS0tKSjZu3Lh9+/YdO3acOHFi7969paWla9asef/99w8cOPDpp58ePXr0+PHjp0+fvnTp0vvvv5+SkrJ9+/YzZ85s3LgxNzc3Pz//8OHDW7du/fvf/3769OnTp08/efLkX//613fffffRRx+dOHFiw4YNAoEA0g+yWCwNDQ0NDQ0ul3vv3j3gv2pXgoHmjICOjo4TJ07Ex8cLBAJbW1sfHx8LCwtzc3NTU1NjY2NjY2MejwcX2traI0eOhCZpaWkZGhoaGBhoaGhoa2tbWVlpaWmZmZnZ2dlZWVmNHTuWw+HweLzhw4fzeDzQLY4YMQKFatDLcjgcTU1NGxsbT09PMzMziKQmwWaz2Ww2l8s1NjY2MTExMjKCpcbQ0NDExMTa2trY2JjL5ZqZmZmamsLDpqamZmZm8C5UXldXV0dHh8Ph8Pl8LpdraGjI4/HYbLampqaWlhZ81NTU1MTExMDAQF9fn8vlGhkZ6ejo6OnpaWtr8/l8Pp+vqalpbGzs7OxsYmICb8Ezurq6JiYmfD7f1NTU1tbW3t6ex+NxOBwbGxs+n6+np6evr8/hcEaOHMnn89lsNnQLi8Xi8/nGxsaGhoawYBgaGnK5XA6HY2BgYGVlBTXn8/kWFhZYQx0dHR6PJxAIHBwcrK2tTUxMYAiggfAMfGv48OE6Ojr6+voGBgYwSYyMjLhcLgylubm5np6epaUlm83W0tKChhsaGgJnBF0Hl8u1t7c3MzMzMTFhs9lGRkZsNhu70czMTE9PT0tLy9zc3MDAQFNT08LCAijE3NwcSjAyMjIwMNDT0+Nyuaampjwez97e3tTUFPoEqsHlcnV1ddlsNo/H4/F4RkZGFhYWQEIwlDo6OjBzrKysYIj19PQ4HI62traTk5OJiQmHwxEIBIaGhs7OzmQbYRTYbDYMKIvF4vF4rq6uQAOmpqZaWlpcLldbW1tTU9PIyMjMzAzaCFXicDhAcjAi0APW1tbW1tZCodDT01MgEGhoaIwaNcrU1JTP5/N4PKBMIyMjc3NzS0tLS0tLnhLGxsZmZmZ8Pt/GxsbW1tbJycnDw8PBwUFXV9fQ0NDV1VUoFMInbG1t3d3dR48eLRAILC0tHR0dPT094VcOh2NiYqKnp2dmZubk5MTlck1MTCwsLKysrKytrS0sLExMTICEYPc6bNgw6Bwej+fs7GxlZWVubm5ra2ttbQ1DaWJi4uDgIBQKPTw84DE+n+/h4REQEBAQEODj4xMVFRUSEgLHHbu6unK5XCcnJ3Nzc4FAwOVyLS0tfXx8fH197ezsLC0tXV1d2Wy2k5OTq6sruCrb29t7e3vb2dmZmJhMmzaNz+d7enrOnz9/yZIl48aNe+utt2BzPWzYMB6Pd+HCBRSoB4QrUlQ/nBE3ff/+978PHDiQlpY2ZcqUiRMnenp6+vr6hoSEREdHR0VFBQcHe3t7wzlWvr6+Xl5eEyZM8PX1DQwMDAgI8PX19fb2joyM9Pf3Dw0NjYyMDAkJSUxMDA4O5vP5o0ePtrCwMDIyggvYUA8fPpzFYo0bNy4kJGTx4sUzZszw8fFJTEwMCAgIDAycPn16REREbGzsnDlzkpOTU1NTo6OjY2NjZ86cGRMTEx0dHR0dPXPmzISEhOjo6OnTpwcGBgYFBfn5+bm7uzs7O7u5uSUnJ8+ePTsxMXHevHk5OTmZmZnZ2dmLFy/Ozc1NTEyERkEhINokJyenp6enpKTExMSEh4dHRkaGhoYGBASEhoYmJCQsX7580aJFU6dODQ4OzsjIyMrKCg4OjoiIiIiImD59+vTp02fMmDFz5swZM2bMmzfP1dUVmu/u7h4WFlZUVBQcHOzl5eXp6Tljxoy4uLi0tLScnJzY2NiCgoKioqLly5evWbNm48aNpaWly5cvz8rKmj17dnR0dEhISEhISGRkZERExLRp04KDg8PDwydMmDBu3Dhvb++QkJCkpKTs7OyMjIyEhISCgoLFixcvXbp0xYoVxcXF8+fPz83NLSgoyMvLmz9/PvQANDAxMTEhIWHWrFne3t4+Pj5Tp05NS0tbtWpVbm5uTEwMrOQGBgZJSUmFhYXZ2dmTJk1ycXEZP348iIRJSUlhYWGRkZFz584tLCycNWtWQkJCYmLi0qVLN2zYMHfu3LCwsOzs7IMHD+7evXvz5s3r16/fuHFjSUnJ3/72N3Nzcz8/v6ysrC1btmzevDk7OzsmJiY1NbW4uHj8+PFJSUlr1qwpLS1duXLl+vXrd+/efeTIkc2bNy9atGj27Nnx8fGpqakLFix49913t27dmpeXl5GRsWLFinnz5sXGxkZHR48dO/btt99ev379qlWrQDZPTEwEIdTHx8fDwyM6OrqoqCgzM9PPzy80NBTaEhgYOG3atPj4+EWLFi1btgyEvoSEhJSUlIyMjOzsbOjhtLQ0kBMzMjIWLVqUlZUVGho6efLkyMjIlJSU9PT0+Pj42NjYmJiYWbNmpaWlZWdnz58/H3o+Ozs7MzMzIyMD+j8pKQk2RomJiVAsEOfs2bODgoJgRMLCwiIiIkJDQyF8Nj4+PjExMSQkJCoqKiYmJjAwMDw8HITcKVOm4JQJDw+PiIgICwsLCQkRCoXGxsbDhg1zdHR0cnKaNm2am5ubo6OjUCh0d3eHrIA2NjZCoXDMmDGurq6WlpYgYVhaWo4dOzYgIADIb+bMmdHR0W5ubhMmTBgzZgyPx7O1teXxeA4ODqNHjxYKhZaWlnw+39nZWSgU2trajhw50t3d3czMjMfjjR8/3sXFxcjIyNDQMCgoKCoqKi0tbevWraNHj9bX1wfBSEtLC+Sk9PR0UIkOpPmF6t/TG7W8pOFJLBaTMi0oyNrb20UiEWgDQd0GniVtbW21tbVgAgMPNfSJkUqljY2NsbGxU6ZMycvLQ3lTT09vxowZjx49QoUduCiKRKKOjg4wldBMZmSdVU1mFEX19vaCtghUP31ZrqGGoCpVtYqCvRVEetCX47daWlpAbwKqQ9Cdg1WBrGpDQwP41tbU1GA4yosXLxobG6FweBiUp6quG2KxuLm5GUuGxuI1mAgaGxtJDSD8RPaYaq2wddhdoI9DjV57e/ujR4/AehgZGQnqNoqimpubOzs7a2tr0QAF+lz4VdXUi4+h4RirBApKdEXC0ezt7X38+DFp1Eapob29HSgNzQtoiMBnuru7Ozs779+/X1VVpXasxWLxrVu3gCqam5tv377d2NhIUVRbW1tdXd3z589fvHiB0opYLAZ/XkodUG9YU1Pz5MkTdACA/lfr50Drf+gWkhKwyXK5vKmpqaWlpa2tTSwWw4xAxT3arNra2jA46sWLF01NTY2NjSKRCLtIIpGkpaUZGxvr6+tfuXIF3oLOaW5uBlV1TU1NfX39ixcvGhoanjx58uuvv/7666+VlZVVVVXPnj1rampqb2/v6uoCdeqjR4+ePXtWVVX1zTff3Lhx4+rVqzdu3Kiqqrp9+/bJkye//PLLmzdv3r1799q1a5cuXfr+++9v3Ljx9OnTurq62traurq6e/futba2isXitra26urqcePGwSYDBEYHB4fZs2ffvHkT6bCfDvyP4w9206Q9nubzRZrMKIJD0UxpNFUulgDmgsWLF8MGFg42sLa2njNnDo40qT6nmeqAeZH1USj9BGVKn/C+yBFrCCZsYNOkgYiiKGB/QIVypaMizecOzFOkZ5xIJCJNsarGU5lMBpwLaB1+Iq0iFEEBsCqAFYs2KGrdieRKJ/y+7IkUMUzggUFGMqBqn1S0gzGxqanJxcVFQ0Nj7ty52FLSVkv6uFFKmw90Y1NTE1iEVGuCkUgkFakdNaA9NHRCgWr3VhKJBCqGbhVo8YBlT9W/BFdKLJCsD61PYMSRJLADoRDaKKitIVjDwBlA7UiBcRlK7urqImul+jCpfQOjDT4MrJZGPMXFxaNGjWKxWKWlpdAtINao1pN62YVQoRKhSL3svYhWPmwFTbzA0vCL0LTW1tbMzExHR0dbW1s3N7dhw4aZm5vHxsYePHgQ/GfVxhG+bvTJGUlTKQCoU0Y4o5J0oNYnjiLc2eFf9KLo6ur6xz/+ERsba2NjA2oI0HD99NNPGBVARlm+isFeQXjzUkpmAe/S3HT+HMhWkOyJLLkveZZmte/nYbygtVqhDMsjmTg+QAvzIh0b0WlRruLhrAqY5LS+EolETk5Ow4YNS05Opvr2DaSBVg2YtH1xBLFYjMWSXkTYZJp5FPsK2ZNqQ/qpG/YGRVHocANiL4YSwcqBFEtbO1VBMimyga9IvVhtWj37EfBh3ql+iNa3ZAmLFy9msVjGxsY7duxAd31KKd4itWCfUy9PKwURnEPWFr+IGy/8F0RgcuLL5XIMXX327Nnbb789YsQIa2vr4cOH6+npLVmy5Pr1642NjSgikA55A4Y/zrWDtvn+6YyUp3qJIBMkQXL8pFLp+fPn7927d/jw4aCgoO3btx88eDAiIiIwMFDVq7OmpoZSYUZk9fr6iVZDuOhVQkZAToRGSJXxof23lxwq8BgnvcbwMZKysUXgOImVoQjXSBB5aPtKskBanfuaObhbpPqYXXIi+AxlHBxEqTK/AzhyPnz4kM/ns1ismJgY6mWXeyBx6D0QE2TKpAyk0wksq2pti+jjRqlEW6kKyzKlwkSVxcuJUGVyze7u7gYZFvutr1WNeoVoTlkfgDKhmdAJMmVEAO5vUK7Eb8mUMSSk1w7ZIuwikkpJ/oXl0EQT2r945+TJk/r6+mw2G5V3tGBnBeGZSNaTtkgDtUDTSA9w8hl8BeYL0DbpJXb58uXx48draGhwOBw3N7dNmzaBGxw5lcgA0L8u3Lw6+vNnpEk0UmVEOgrqsPjTlimyR7CvVcu/e/fusWPHkpKSnJ2db968KRaLS0tLP/30U7lcDpqstrY2yAKi+i6SvlwZRipTCR0jeZ9cXWgKVlWuzoOfIvyBUebqpx+xmTQeTfsXWapc6dKMu2y1bUSBiOxetV+H0VHdeqsFssX+VxSF0kleJBIFBASwWKzRo0e3tbW1tbUpXg5NoxVCzv+uri5cEqCS8CtNuMA29irdPBWEMzPNaY7k4KoetX/YfLLauOsnd45kYA8oNHC3hC/Smqw2XOevBLSR0VB/CDkRZUAumWrHNy0tjcfj3b9/H1kPbbIr1G3bFQRUl3+KoH+4Tyq7epVhCPAM/Hv37l1/f38ul+vi4rJ58+Z79+7Br+BNiepRWnaMV+yQv44/zihBm7Sq+yCFcpeHciL+RBO5AfB6W1vbwoULJ0yYMGLEiGXLltFEAJqf8/9Klsb6qP5ELp40isGZqZYsyMJxdGHS4kYMxGoa/0XSRCkMR5emtIXJr7rSYDlSZWYapE7yui/KVitRqt3X40pDEU658HpHR8e9e/e8vb1dXFyamprkyrANiogyxOUHv0iys75oGtultrZqZUbVVQSBgyhThtWTaTVI0D5EcjqMceh/zejr114iqppSzhdyDSaJkCwQlQ9ql3BK2Vdkn2BvkPMOBWdoPj6vUOawWLt2rZ2d3fXr12GUSR9ykmxQCsb5Qut8GRGMTxG7OnIuY0fB6qhQ5lLo6enZs2fPiBEjDAwMduzYISUyd5CWCVkfRo4BwGvPXKt21YI7+fn54OVXWlqqmu6MwWABt71yIhJGKpWeOnXqyy+/hEVr4CmVwX8KN2/ejIqKKi8vxzsDk6yBTBXR2tpaXFwcFha2cOFCDOiSExZXWFblRLQoLWqIIqQN+Fd1Gf4rZ46+ds6oli3K5fKffvpp7NixOjo6AoHg66+/hp9I2xaDQQHNp6eXSN5Dk0qoV9DKMRiCaG1tPXz48PXr16k+lACvCSAMotsfmKfBQwNiQ+GxftLT0gR5ULmQizQ6JJA67j+HgT7tAPcUTU1N0dHRPB7PwMDg4MGDA297YqAWuDjRRHiZTIa+OK+idWUwNCFXBrCD59OAxduJxWJSs0G9TGBo4JURmdNQ4kOmif5tanM1KpS57vGtv+LuM9CcES1rX375ZUxMjJmZGZfLXbNmDf46wPVhoBYQ6o/EijdxIqFpYtCqyOAvA6fbXxSvXv1bNPWrVCpFSwulcjADbY9PJngFSKVSsNaSm+6enp7Kysrnz5//xUy3g8YZy8rKgoODraysBAIBqjwYzjjoQDMaskXYmCDlyZSZCqmBjWNl8J+CSCQi1zzZyyEJrxXocoBAcxPEVsBNVdVhQ0PDwYMHHz58+Pz586qqqu3btxcXFx8+fPi3336jCMPO77//XlZW5uPjExAQsGTJEoho+nMYtN30zz//nJiY6OrqamFhceLEiQGuBoO+QFo5SbUOWuRRU87g/ygwW61M6cc6AB+lqcvAeRsEQClxEg4syTKlkzk44Uul0rNnz7q6uiYmJgYGBvr7+9vZ2QkEAnd39+Dg4H379gFxvnjxorCw0NraGhK1CASCf/3rX3+6woNmgbl161Z8fLylpaWBgcHx48cVynTHr7s+DP4QuKOB/YhEIrl48SLcIRX2KHow+D8H0utwYAYRZUMIiyB910imCYkp8V90V7py5Qrkx8rMzJwwYYKZmZmVlRVkXZo5c2ZNTU1dXd1HH33k6Og4bNiwt956i8PhvPXWW+vXr//TFR40r51bt27l5uay2WwWi7V27VpqYM1kDPoB6q2BRV6/ft3X1/f48eOwN/nrVj8GgwgMKSE1egNj/yTD5CiKIkPCyZhrtX7jVVVVQqFQV1dXV1dXIBBERkYmJyfPmTPHzc1NS0trypQpQUFBkBvQxsaGxWL5+PgsXboUwq7/HF47ZwRxXTVA5cKFCzNnzoSMgWVlZShOv+76MOgfUuVRn7DTuXz58uTJkyHlpbe3N5gL0TjIbKuHMtA9ELXG4CgDVgsZcRrf0PQMkRPnLjx79uzjjz/Oy8u7cOHC/fv38cSO7du3jxgxAnJkaGpq6urq2tvbFxUVlZSUHDlyhKYoUBCxc3/49YHWM4IGQSwWl5WVnTt3bvLkyQ4ODgcPHqSZrhgMIlBNfvbsWWNjY3t7ewMDA0gM9cEHH5AOjwN5MjqD/y1g0ypTpvAiJX1SYdLP+TaDCLWRQsjBUcCsqKjAhMoaGhp2dnZr166trq6mKEoikYDvJBmj9eoVGCDOiNFREOja0dFx+PDhs2fPQj7Ud999VzVdEoPBAkyh+vr6sLAwPT09TU3NESNGQEbhqKgotbkPGAw1IO9DNxeRSHTnzp3i4uLz588/ffqUIvKZDk3miCBz7ZAh87dv3y4tLYWsjnC25dy5c+vr6yGUXq1gqFDiDz86EHpGuTJFCnqESKXSixcvLlmyxM3Njc1mL1myhKKozs7OAU5OyUAVmJtAJpPl5eVxOBwNDY3y8vJJkyZpaGhMnDgRNzKMgD/E8eLFC7gAL+tff/01PDx8zJgxqamp06ZN27BhA+RI7T+N1mCBxr8g6BsSUAIFPn78eM6cOXB4CYvFcnZ29vb2fu+991CcJN2AAHIiwesfVmAgOKNawfjBgwdr165dvXq1qalpYmLiEBybNxMk0TQ3NwcEBGzcuJGiqMWLF3M4HFtb2ydPnlBKvccAH47O4NUB7ANcqSmKqqio8PDwGDdunEAgcHR0hONiYmJiKisrqaEalStTlyqUUtLehQsXJk+ePHLkSF1dXWNjYwcHh/3798MDciJRJuaUkvedtU8tBnQ3Tf579+7dDz/8cPny5fb29seOHYMUkIOSvJeBKjBnIiTH7OnpKSws1NbWFggEd+7coYgDowe3ngz6AcqM58+fh7PJPDw8AgMDjx8/fvDgwcmTJxsbGx86dOgvxoq8JtBSCkFONplMBmfWd3Z2LlmyhM/nw3Exzs7ORUVFDx48oIhQwr+IQeCMoHCsra09fPhweHi4np7eDz/8wFg5hw5EIhEMB1ii4Xrt2rVsNtvFxQU8IQbMD47BX0Rvb+8//vEPHo83cuTI4uJiuCkWi3/++ecxY8YkJCSAznGoAU7H7utXmUyWmZmJp43a2tpWV1cD60T5F88rJ1PPDSE9I6VuQ61QKPbv379z587CwkIbG5tz584plHkAB6A+DPoB7MLIw9Th5vHjx/l8vrW19cOHD+EnZrCGPmA0ZTLZnDlzJk2adOfOHfIAlqlTpzo4OFy6dGnIyv5isbi9vR25pEKhePDgQUFBwYEDB7Kzs+FAZktLy5SUFHITA8wRzlB7/Pjx06dPa2trm5ubOzo6Xj2DxgDJjHKVvNkVFRXz588fPXq0mZnZ559/Tv0vszEzeN1AdwK4OHr0qK2tLZ/Pf/DggVrbNC7FipePgmAwWMARkUgkzc3NLS0tyDLg17lz5/r5+Z06dWqQK9oHZDLZqVOn0tPTy8vLv/766wcPHpSVlQmFwrS0NB8fHw6HAwLj8OHDIyIiHjx4UFNT09jYePHixe+++279+vUZGRlwrG5WVtbmzZvnzp1bWVmJ6/ofYqB302ibvnLlyrZt2zw9PXk8HsTAqEabMxh4wHGJlFLPjd6L27Ztg/QftbW1YPLDdCl4hgyjEhlSIJcu8lhBvJ+Tk2NkZDR//vxBqNwfQSqVXr161c7OzsXFZfny5aNHjw4PD7e3txcKhdra2np6eiYmJkKhUEtLS0dHh8vl2tjYTJ06tbi4eMqUKWlpad7e3nw+f/ny5YcOHUpOTg4LCysoKPj999+rq6tfURE5EHHTJL8DRUB7e/u+ffvy8/MtLCwsLCzAa4diYiqGBjD3J3l9/vz50aNHOzg4wGkzkK5R7bu0024ZDAoUL587gl5WMGoSiaSyslIoFJqbm6enpw9NH4OamhpfX197e/tFixZBoLSOjg6Hw+Hz+T4+Punp6bt27QoPD+dwOBwOZ9y4cX5+fv7+/i4uLs7OzuBhFhkZmZiYmJubu3fvXsgcTr0ykxkgf0ZkjsAZOzo6vvvuu8LCQj6fb29vn5+f39fJLQwGHhDQCuYXPPbg0aNHXl5eQqEQYssAMuVhp+RZIoNSZwaqIOcdHiADd3p6ej799FMDA4MxY8acPXt2COoZga0fP37cyMiIw+Ho6uqyWCw9Pb2QkJBDhw7duHED2MX58+f9/PwEAsHw4cPt7Ozs7e1dXFwcHBwmTpx4+vTpo0ePVlZWgu83ZMtWEIfS9I+BkBlJ5oi76cbGxmXLlvn5+cXFxX3xxRdqjwxmMOjo6OiAsbt165adnZ2+vv7evXvr6uqAcElP2v7PrmIw8MDtGig90DdQIpE0NjZmZ2fb29s7OTmBv/cQhEQi+f3336dPn25iYuLj4+Pn57dy5cqmpiY8eU0kEvX09Ny7d+/zzz+fPXt2fHx8XFxcTEzMwYMHq6urwW6jUChUI3xeRUYeUNs0efPixYsRERF+fn5ZWVmYfpIRGwcdnZ2doJMiHQlkMtk///lPJycnoVAICnuQMtra2kARqXg5b/4QjzZ7E9C/e8quXbucnJwsLS2Li4tra2uH5ryDfeTNmzdPnjz5/fffQ4gBRMJQL6fmAh037F3gwGfMSE8RrpE9PT3ga/EqGDjOSOv9CxcuxMbGuru7T5w48dy5c8jgB6A+DF4RdXV1HR0doLEG2/SIESPCw8M3btxYXFz8ySefnDlzZt26ddu3b9+1a9f+/fuvXbvG+OoPEZBOfOT9zs7OH3/8MSAgwNraeuLEiW1tbUMzLQgwPkzBhfZAfABy4olEIlyGe3p6yIBISunrDkWRcuKrNHmA9IzkCCkUit7e3osXLy5YsODtt98eO3Ys5vRmNPeDDiC+zs7Ob7/9NiwszMvLy9fXt6CgwN0lIOgAAAQUSURBVNrams1ma2trc7lca2troVDo4+NjYmLi5OTk4ODA5XINDQ3Dw8O/+uorhjkOBciVx3+jUAKy/9WrV8eNG2dlZeXu7l5SUkIN4UAmiJVGiQr8ZzH3AkWoCyGrEOxaWltb4VfS5ELqW19R5zOgWchIr8YdO3akpqYmJCQ4OTldu3YNHhia8ZtvFJB0qqurExIS9PX1DQwMtLW1Md7AxsbGwcHBw8PD2tpaIBC4urpaWVlZWFiYm5vb2tomJia2tLQM2cn2RgFDpymKev78+apVq1asWOHg4ODv7+/t7Z2SknLlyhV4ksx0JRKJYG17wwdxEGRGwI8//piamioUCu3t7X/99VeKyWo1ZCASiWBWfPPNN0FBQXp6enZ2dn5+fkFBQVFRUSUlJRs2bNizZ8/u3bsPHTp08eLFPXv2ZGVlBQUFBQQEFBYWMjLjUAAe60xRVHV1dXp6uqOjo6GhoZ6enrGxsZ+fH6jtRCIRbi3JZF+0E8bfQAxQrh3SDRgsZR9//PG0adNYLJa1tTVYYN7wNWpIAYX3c+fOrVy5sry8vK6urqWlhXR3IBXHUqkU3BhB6cPI/kMEYrFYLBZfunTJwMBAQ0MDpH4LC4uAgADwvlK8fHAuji8T+jkQu2nQC5CH8rS3t0dERISHh1tZWU2aNAmSZFCMnnEIAI8/R8V2Z2en6qIFJkJ0J4BUSZRyeRuansNvFGBc4G9LS0tsbKympiaLxTIyMjIwMDA3N9+xY8e333778OHD9vb2uro6dFMFniiVSt/wQRw0ztja2nr8+HFbW1sHB4czZ868yXL7kAJuwWjHZYCGG62EqC+G+UO67JDHdzAYLHR3d5OjcPnyZWtra09Pz6VLl2ZkZAQEBLDZbE9Pz6ioqHnz5i1YsKC8vPz06dPwMIzmG64VGbTd9IMHD7Zu3eru7r506VI8lO4NH4whAggYoCgKXWrJvRXMN/IvRVFwKDBIkQxbHFIA12iKotauXXvp0iUY0Pr6+ujo6AkTJri7u7u5uXl4eLi7u7u4uPz8888UkeLwTR7KQbPAtLa2trS0YG64rq6u/1TKSQZ/ETBYvb29pD4eAqIppcYD17n29nbIi4c3ydOEGQwWUBbBsYAkxHK5HLTAtbW1V69eXbFiRW5u7ooVK5KTk+Pi4m7cuEER7n5D0wN8YDBoXjsw68jwHYVCwciMgw5QfaByA4LcKSJCifSbxYhPmH7wJKMYGTqAfTFqgZFXwhihMrG1tRX1jKgYYfSMDBgwYMDgJTCckQEDBgzoYDgjAwYMGNDBcEYGDBgwoIPhjAwYMGBAB8MZGTBgwIAOhjMyYMCAAR0MZ2TAgAEDOhjOyIABAwZ0MJyRAQMGDOhgOCMDBgwY0MFwRgYMGDCg4/8BJ5NhRIk2MLwAAAAASUVORK5CYII=" 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="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;">(a) Let \(a > 0\) . Draw the graph of \(y = \left| {x - \frac{a}{2}} \right|\) for \( - a \leqslant x \leqslant a\) on the grid below.</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 src="data:image/png;base64,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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: 0px; font: 29px Helvetica; text-align: justify;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Find <em>k</em> such that \(\int_{ - a}^0 {\left| {x - \frac{a}{2}} \right|{\text{d}}x = k\int_0^a {\left| {x - \frac{a}{2}} \right|{\text{d}}x} } \) .</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span style="font-size: medium; font-family: times new roman,times;">(a)</span></p>
<p style="font: 29px Helvetica; margin: 0px; text-align: justify;"><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>A1A1</em></strong></span></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>A1</em></strong> for the correct <em>x</em>-intercept,</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>A1</em></strong> for completely correct graph.</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;">(b) <strong>METHOD 1</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;">the area under the graph of \(y = \left| {x - \frac{a}{2}} \right|\) for \( - a \leqslant x \leqslant a\) , can be divided into ten congruent triangles; <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;">the area of eight of these triangles is given by \(\int_{ - a}^0 {\left| {x - \frac{a}{2}} \right|{\text{d}}x} \) and the areas of the other two by \(\int_0^a {\left| {x - \frac{a}{2}} \right|{\text{d}}x} \) <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;">so, \(\int_{ - a}^0 {\left| {x - \frac{a}{2}} \right|{\text{d}}x} = 4\int_0^a {\left| {x - \frac{a}{2}} \right|{\text{d}}x} \Rightarrow k = 4\) <strong><em>A1 N0</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>METHOD 2</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 area of trapezium to calculate <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;">\(\int_{ - a}^0 {\left| {x - \frac{a}{2}} \right|{\text{d}}x} = a \times \frac{1}{2}\left( {\frac{{3a}}{2} + \frac{a}{2}} \right) = {a^2}\) <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;">and area of two triangles to obtain <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;">\(\int_0^a {\left| {x - \frac{a}{2}} \right|{\text{d}}x} = 2 \times \frac{1}{2}{\left( {\frac{a}{2}} \right)^2} = \frac{{{a^2}}}{4}\) <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;">so, <em>k</em> = 4 <strong><em>A1 N0</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>METHOD 3</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 integration to find the area under the curve</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;">\(\int_{ - a}^0 {\left| {x - \frac{a}{2}} \right|{\text{d}}x} = \int_{ - a}^0 { - x + \frac{a}{2}{\text{d}}x} \) <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;">\( = \left[ { - \frac{{{x^2}}}{2} + \frac{a}{2}x} \right]_{ - a}^0 = \frac{{{a^2}}}{2} + \frac{{{a^2}}}{2} = {a^2}\) <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;">and</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;">\(\int_0^a {\left| {x - \frac{a}{2}} \right|{\text{d}}x} = \int_0^{\frac{a}{2}} { - x + \frac{a}{2}{\text{d}}x + \int_{\frac{a}{2}}^a {x - \frac{a}{2}{\text{d}}x} } \) <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;">\( = \left[ { - \frac{{{x^2}}}{2} + \frac{a}{2}x} \right]_0^{\frac{a}{2}} + \left[ {\frac{{{x^2}}}{2} - \frac{a}{2}x} \right]_{\frac{a}{2}}^a = \frac{{{a^2}}}{8} + \frac{{{a^2}}}{4} + \frac{{{a^2}}}{2} - \frac{{{a^2}}}{2} - \frac{{{a^2}}}{8} + \frac{{{a^2}}}{4} = \frac{{{a^2}}}{4}\) <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;">so, <em>k</em> = 4 <strong><em>A1 N0</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>
<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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates attempted this question but very often produced sketches lacking labels on axes and intercepts or ignored the domain of the function. For part (b) many candidates attempted to use integration to find the areas but seldom considered the absolute value. A small number of candidates used geometrical methods to determine the areas, showing good understanding of the problem.</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;">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 src="data:image/png;base64,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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="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 src="data:image/png;base64,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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="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 tangent to the graph of \(y = \ln x\) passes through the origin.</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) Sketch the graphs of \(y = \ln x\) and the tangent on the same set of axes, and hence find the equation of the tangent.</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) Use your sketch to explain why \(\ln x \leqslant \frac{x}{{\text{e}}}\) for \(x > 0\) .</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;">(c) Show that \({x^{\text{e}}} \leqslant {{\text{e}}^x}\) for \(x > 0\) .</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;">(d) Determine which is larger, \({\pi ^{\text{e}}}\) or \({{\text{e}}^\pi }\) .</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)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><img src="data:image/png;base64,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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>A3</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;"><strong>Note:</strong> Award <strong><em>A1</em></strong> for each graph</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>A1</em></strong> for the point of tangency.</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;">point on curve and line is \((a,{\text{ }}\ln a)\) <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;">\(y = \ln (x)\)</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;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{1}{x} \Rightarrow \frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{1}{a}\,\,\,\,\,{\text{(when }}x = a)\) <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;"><strong>EITHER</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;">gradient of line, <em>m</em>, through (0, 0) and \((a,{\text{ }}\ln a)\) is \(\frac{{\ln a}}{a}\) <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;">\( \Rightarrow \frac{{\ln a}}{a} = \frac{1}{a} \Rightarrow \ln a = 1 \Rightarrow a = {\text{e}} \Rightarrow m = \frac{1}{{\text{e}}}\) <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;"><strong>OR</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;">\(y - \ln a = \frac{1}{a}(x - a)\) <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;">passes through 0 if</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;">\(\ln a - 1 = 0\) <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;">\(a = e \Rightarrow m = \frac{1}{{\text{e}}}\) <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>THEN</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;">\(\therefore y = \frac{1}{{\text{e}}}x\) <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>[11 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><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) the graph of \(\ln x\) never goes above the graph of \(y = \frac{1}{{\text{e}}}x\) , hence \(\ln x \leqslant \frac{x}{{\text{e}}}\) <strong><em>R1</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>[1 mark]</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;">(c) \(\ln x \leqslant \frac{x}{{\text{e}}} \Rightarrow {\text{e}}\ln x \leqslant x \Rightarrow \ln {x^{\text{e}}} \leqslant x\) <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;">exponentiate both sides of \(\ln {x^{\text{e}}} \leqslant x \Rightarrow {x^{\text{e}}} \leqslant {{\text{e}}^x}\) <strong><em>R1AG</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>
<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;">(d) equality holds when \(x = {\text{e}}\) <strong><em>R1</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;">letting \(x = \pi \Rightarrow {\pi ^{\text{e}}} < {{\text{e}}^\pi }\) <strong><em>A1 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>[2 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><em>Total [17 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: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This was the least accessible question in the entire paper, with very few candidates achieving high marks. Sketches were generally done poorly, and candidates failed to label the point of intersection. A ‘dummy’ variable was seldom used in part (a), hence in most cases it was not possible to get more than 3 marks. There was a lot of good guesswork as to the coordinates of the point of intersection, but no reasoning showed. Many candidates started with the conclusion in part (c). In part (d) most candidates did not distinguish between the inequality and strict inequality.</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;">The diagram below shows a sketch of the gradient function \(f'(x)\) of the curve \(f(x)\) .</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;"> </span></p>
<p style="font: normal normal normal 27px/normal Helvetica; text-align: center; margin: 0px;"><img src="data:image/png;base64,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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;">On the graph below, sketch the curve \(y = f(x)\) given that \(f(0) = 0\) . Clearly indicate on the graph any maximum, minimum or inflexion points.</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 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: 0px; font: 29px Helvetica; text-align: justify;"><img src="data:image/png;base64,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" alt><span style="font-family: 'times new roman', times; font-size: medium;"> <strong><em>A5</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>A1</em></strong> for origin</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>A1</em></strong> for shape</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>A1</em></strong> for maximum</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>A1</em></strong> for each point of inflexion.</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>[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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A reasonable number of candidates answered this correctly, although some omitted the \({2^{{\text{nd}}}}\) point of inflection.</span></p>
</div>
<br><hr><br><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;">Consider \(f(x) = \frac{{{x^2} - 5x + 4}}{{{x^2} + 5x + 4}}\).</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;">(a) Find the equations of all asymptotes of the graph of <em>f</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) Find the coordinates of the points where the graph of <em>f</em> meets the <em>x</em> and <em>y</em> axes.</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;">(c) Find the coordinates of</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;">(i) the maximum point and justify your answer;</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;">(ii) the minimum point and justify your answer.</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;">(d) Sketch the graph of <em>f</em>, clearly showing all the features found above.</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;">(e) <strong>Hence</strong>, write down the number of points of inflexion of the graph of <em>f</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) \({x^2} + 5x + 4 = 0 \Rightarrow x = - 1{\text{ or }}x = - 4\) <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;">so vertical asymptotes are <em>x</em> = – 1 and <em>x</em> = – 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;">as \(x \to \infty \) then \(y \to 1\) so horizontal asymptote is <em>y</em> = 1 <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;"><strong><em>[4 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;">(b) \({x^2} - 5x + 4 = 0 \Rightarrow x = 1{\text{ or }}x = 4\) <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;">\(x = 0 \Rightarrow y = 1\) <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;">so intercepts are (1, 0), (4, 0) and (0,1)</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;">(c) (i) \(f'(x) = \frac{{({x^2} + 5x + 4)(2x - 5) - ({x^2} - 5x + 4)(2x + 5)}}{{{{({x^2} + 5x + 4)}^2}}}\) <strong><em>M1A1A1</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;">\( = \frac{{10{x^2} - 40}}{{{{({x^2} + 5x + 4)}^2}}}\,\,\,\,\,\left( { = \frac{{10(x - 2)(x + 2)}}{{{{({x^2} + 5x + 4)}^2}}}} \right)\) <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;">\(f'(x) = 0 \Rightarrow x = \pm 2\) <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;">so the points under consideration are (–2, –9) and \(\left( {2, - \frac{1}{9}} \right)\) <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;">looking at the sign either side of the points (or attempt to find \(f''(x)\)) <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;"><em>e.g.</em> if \(x = - {2^ - }\) then \((x - 2)(x + 2) > 0\) and if \(x = - {2^ + }\) then \((x - 2)(x + 2) < 0\),</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;">therefore (–2, –9) is a maximum <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) <em>e.g.</em> if \(x = {2^ - }\) then \((x - 2)(x + 2) < 0\) and if \(x = {2^ + }\) then \((x - 2)(x + 2) > 0\),</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;">therefore \(\left( {2, - \frac{1}{9}} \right)\) is a minimum <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> Candidates may find the minimum first.</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>[10 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)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px 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 src="data:image/png;base64,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" alt> <strong><em>A3</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 each branch consistent with and including the features found in previous parts.</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>[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;">(e) one <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>Total [20 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: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This was the most successfully answered question in part B, in particular parts (a), (b) and (c). In part (a) the horizontal asymptote was often missing (or <em>x</em> = 4, <em>x</em> = 1 given). Part (b) was well done. Use of the quotient rule was well done in part (c) and many simplified correctly. There was knowledge of max/min and how to justify their answer, usually with a sign diagram but also with the second derivative. A common misconception was that, as \( - 9 < - \frac{1}{9}\), the minimum is at (–2, –9). In part (d) many candidates were unable to sketch the graph consistent with the main features that they had determined before. Very few candidates answered part (e) correctly.</span></p>
</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 <em>f</em> be a function defined by \(f(x) = x - \arctan x\) , \(x \in \mathbb{R}\) .</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 \(f(1)\) and \(f\left( { - \sqrt 3 } \right)\).</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;">(b) Show that \(f( - x) = - f(x)\) , for \(x \in \mathbb{R}\) .</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;">(c) Show that \(x - \frac{\pi }{2} < f(x) + \frac{\pi }{2}\) , for \(x \in \mathbb{R}\) .</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;">(d) Find expressions for \(f'(x)\) and \(f''(x)\) . Hence describe the behaviour of the graph of <em>f</em> at the origin and justify your answer.</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;">(e) Sketch a graph of <em>f</em> , showing clearly the asymptotes.</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;">(f) Justify that the inverse of <em>f</em> is defined for all \(x \in \mathbb{R}\) and sketch its graph.</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) \(f(1) = 1 - \arctan 1 = 1 - \frac{\pi }{4}\) <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;">\(f( - \sqrt 3 ) = - \sqrt 3 - \arctan ( - \sqrt 3 ) = - \sqrt 3 + \frac{\pi }{3}\) <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><em>[2 marks]</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) \(f( - x) = - x - \arctan ( - x)\) <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;">\( = - x + \arctan x\) <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;">\( = - (x - \arctan x)\)</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;">\( = - f(x)\) <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>[2 marks]</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;">(c) as \( - \frac{\pi }{2} < \arctan x < \frac{\pi }{2}\), for any \(x \in \mathbb{R}\) <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;">\( \Rightarrow - \frac{\pi }{2} < - \arctan x < \frac{\pi }{2}\), for any \(x \in \mathbb{R}\)</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;">then by adding <em>x</em> (or equivalent) <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;">we have \(x - \frac{\pi }{2} < x - \arctan x < x + \frac{\pi }{2}\) <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>[2 marks]</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;">(d) \(f'(x) = 1 - \frac{1}{{1 + {x^2}}}{\text{ or }}\frac{{{x^2}}}{{1 + {x^2}}}\) <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;">\(f''(x) = \frac{{2x(1 + {x^2}) - 2{x^3}}}{{{{(1 + {x^2})}^2}}}{\text{or }}\frac{{2x}}{{{{(1 + {x^2})}^2}}}\) <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;">\(f'(0) = f''(0) = 0\) <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;"><strong>EITHER</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 \(f'(x) \geqslant 0\) for all values of \(x \in \mathbb{R}\)</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;">(\((0,{\text{ 0)}}\)is not an extreme of the graph of <em>f</em> (or equivalent )) <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;"><strong>OR</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 \(f''(x) > 0\)for positive values of <em>x</em> and \(f''(x) < 0\) for negative values of <em>x</em> <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;"><strong>THEN</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;">(0, 0) is a point of inflexion of the graph of <em>f</em> (with zero gradient) <strong><em>A1 N2</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>
<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;">(e)</span></p>
<p style="font: 24px Helvetica; margin: 0px; text-align: justify;"><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: 24.0px 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: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>A1</em></strong> for correct shape (concavities) \(x < 0\) .</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;"><strong><em>A1</em></strong> for correct shape (concavities) \(x > 0\) .</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;"> </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>
<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;">(f) (see sketch 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;">as <em>f</em> is increasing (and therefore one-to-one) and its range is \(\mathbb{R}\) , </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;">\({f^{ - 1}}\) is defined for all \(x \in \mathbb{R}\) <em><strong>R1</strong></em></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;">use the result that the graph of \(y = {f^{ - 1}}(x)\) is the reflection</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;">in the line <em>y</em> = <em>x</em> of the graph of \(y = f(x)\) to draw the graph of \({f^{ - 1}}\) <strong><em>(M1)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>[3 marks]</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>Total [20 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;">Parts of this question were answered quite well by many candidates. A few candidates had difficulties with domain of arctan in part (a) and in justifying their reasoning in parts (b) and (c). In part (d) although most candidates were successful in finding the expressions of the derivatives and their values at <em>x</em> = 0, many were unable to use the results to find the nature of the curve at the origin. Very few candidates were successful in answering parts (e) and (f).</span></p>
</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 src="data:image/png;base64,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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 src="data:image/png;base64,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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="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 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;">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 src="data:image/png;base64,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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 src="data:image/png;base64,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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">
<p><span style="font-family: 'times new roman', times; font-size: medium;"> <!--[if gte mso 9]><xml>
<o:DocumentProperties>
<o:Revision>0</o:Revision>
<o:TotalTime>0</o:TotalTime>
<o:Pages>1</o:Pages>
<o:Words>14</o:Words>
<o:Characters>83</o:Characters>
<o:Company>Bontegraphics</o:Company>
<o:Lines>1</o:Lines>
<o:Paragraphs>1</o:Paragraphs>
<o:CharactersWithSpaces>96</o:CharactersWithSpaces>
<o:Version>14.0</o:Version>
</o:DocumentProperties>
<o:OfficeDocumentSettings>
<o:AllowPNG/>
</o:OfficeDocumentSettings>
</xml><![endif]--> <!--[if gte mso 9]><xml>
<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:TrackMoves/>
<w:TrackFormatting/>
<w:HyphenationZone>21</w:HyphenationZone>
<w:PunctuationKerning/>
<w:ValidateAgainstSchemas/>
<w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid>
<w:IgnoreMixedContent>false</w:IgnoreMixedContent>
<w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText>
<w:DoNotPromoteQF/>
<w:LidThemeOther>NL</w:LidThemeOther>
<w:LidThemeAsian>JA</w:LidThemeAsian>
<w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:DontGrowAutofit/>
<w:SplitPgBreakAndParaMark/>
<w:EnableOpenTypeKerning/>
<w:DontFlipMirrorIndents/>
<w:OverrideTableStyleHps/>
<w:UseFELayout/>
</w:Compatibility>
<m:mathPr>
<m:mathFont m:val="Cambria Math"/>
<m:brkBin m:val="before"/>
<m:brkBinSub m:val="--"/>
<m:smallFrac m:val="off"/>
<m:dispDef/>
<m:lMargin m:val="0"/>
<m:rMargin m:val="0"/>
<m:defJc m:val="centerGroup"/>
<m:wrapIndent m:val="1440"/>
<m:intLim m:val="subSup"/>
<m:naryLim m:val="undOvr"/>
</m:mathPr></w:WordDocument>
</xml><![endif]--><!--[if gte mso 9]><xml>
<w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true"
DefSemiHidden="true" DefQFormat="false" DefPriority="99"
LatentStyleCount="276">
<w:LsdException Locked="false" Priority="0" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Normal"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="heading 1"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 2"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 3"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 4"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 5"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 6"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 7"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 8"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 9"/>
<w:LsdException Locked="false" Priority="39" Name="toc 1"/>
<w:LsdException Locked="false" Priority="39" Name="toc 2"/>
<w:LsdException Locked="false" Priority="39" Name="toc 3"/>
<w:LsdException Locked="false" Priority="39" Name="toc 4"/>
<w:LsdException Locked="false" Priority="39" Name="toc 5"/>
<w:LsdException Locked="false" Priority="39" Name="toc 6"/>
<w:LsdException Locked="false" Priority="39" Name="toc 7"/>
<w:LsdException Locked="false" Priority="39" Name="toc 8"/>
<w:LsdException Locked="false" Priority="39" Name="toc 9"/>
<w:LsdException Locked="false" Priority="35" QFormat="true" Name="caption"/>
<w:LsdException Locked="false" Priority="10" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Title"/>
<w:LsdException Locked="false" Priority="1" Name="Default Paragraph Font"/>
<w:LsdException Locked="false" Priority="11" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtitle"/>
<w:LsdException Locked="false" Priority="22" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Strong"/>
<w:LsdException Locked="false" Priority="20" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Emphasis"/>
<w:LsdException Locked="false" Priority="59" SemiHidden="false"
UnhideWhenUsed="false" Name="Table Grid"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Placeholder Text"/>
<w:LsdException Locked="false" Priority="1" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="No Spacing"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
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"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
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"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
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"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 5"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 5"/>
<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"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 6"/>
<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-->The graphs of \(y = \left| {x + 1} \right|\) and \(y = \left| {x - 3} \right|\) are shown below.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
<p><!--[if gte mso 9]><xml>
<o:DocumentProperties>
<o:Revision>0</o:Revision>
<o:TotalTime>0</o:TotalTime>
<o:Pages>1</o:Pages>
<o:Words>11</o:Words>
<o:Characters>62</o:Characters>
<o:Company>Bontegraphics</o:Company>
<o:Lines>1</o:Lines>
<o:Paragraphs>1</o:Paragraphs>
<o:CharactersWithSpaces>72</o:CharactersWithSpaces>
<o:Version>14.0</o:Version>
</o:DocumentProperties>
<o:OfficeDocumentSettings>
<o:AllowPNG/>
</o:OfficeDocumentSettings>
</xml><![endif]--> <!--[if gte mso 9]><xml>
<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:TrackMoves/>
<w:TrackFormatting/>
<w:HyphenationZone>21</w:HyphenationZone>
<w:PunctuationKerning/>
<w:ValidateAgainstSchemas/>
<w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid>
<w:IgnoreMixedContent>false</w:IgnoreMixedContent>
<w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText>
<w:DoNotPromoteQF/>
<w:LidThemeOther>NL</w:LidThemeOther>
<w:LidThemeAsian>JA</w:LidThemeAsian>
<w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:DontGrowAutofit/>
<w:SplitPgBreakAndParaMark/>
<w:EnableOpenTypeKerning/>
<w:DontFlipMirrorIndents/>
<w:OverrideTableStyleHps/>
<w:UseFELayout/>
</w:Compatibility>
<m:mathPr>
<m:mathFont m:val="Cambria Math"/>
<m:brkBin m:val="before"/>
<m:brkBinSub m:val="--"/>
<m:smallFrac m:val="off"/>
<m:dispDef/>
<m:lMargin m:val="0"/>
<m:rMargin m:val="0"/>
<m:defJc m:val="centerGroup"/>
<m:wrapIndent m:val="1440"/>
<m:intLim m:val="subSup"/>
<m:naryLim m:val="undOvr"/>
</m:mathPr></w:WordDocument>
</xml><![endif]--><!--[if gte mso 9]><xml>
<w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true"
DefSemiHidden="true" DefQFormat="false" DefPriority="99"
LatentStyleCount="276">
<w:LsdException Locked="false" Priority="0" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Normal"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="heading 1"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 2"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 3"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 4"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 5"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 6"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 7"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 8"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 9"/>
<w:LsdException Locked="false" Priority="39" Name="toc 1"/>
<w:LsdException Locked="false" Priority="39" Name="toc 2"/>
<w:LsdException Locked="false" Priority="39" Name="toc 3"/>
<w:LsdException Locked="false" Priority="39" Name="toc 4"/>
<w:LsdException Locked="false" Priority="39" Name="toc 5"/>
<w:LsdException Locked="false" Priority="39" Name="toc 6"/>
<w:LsdException Locked="false" Priority="39" Name="toc 7"/>
<w:LsdException Locked="false" Priority="39" Name="toc 8"/>
<w:LsdException Locked="false" Priority="39" Name="toc 9"/>
<w:LsdException Locked="false" Priority="35" QFormat="true" Name="caption"/>
<w:LsdException Locked="false" Priority="10" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Title"/>
<w:LsdException Locked="false" Priority="1" Name="Default Paragraph Font"/>
<w:LsdException Locked="false" Priority="11" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtitle"/>
<w:LsdException Locked="false" Priority="22" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Strong"/>
<w:LsdException Locked="false" Priority="20" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Emphasis"/>
<w:LsdException Locked="false" Priority="59" SemiHidden="false"
UnhideWhenUsed="false" Name="Table Grid"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Placeholder Text"/>
<w:LsdException Locked="false" Priority="1" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="No Spacing"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
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"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
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"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
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"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 5"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 5"/>
<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"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 6"/>
<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 src="data:image/png;base64,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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>