File "SL-paper1.html"
Path: /IB QUESTIONBANKS/5 Fifth Edition - PAPER/HTML/Math AA/Topic 2/SL-paper1html
File size: 339.34 KB
MIME-type: text/html
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-02ef852527079acf252dc4c9b2922c93db8fde2b6bff7c3c7f657634ae024ff1.css">
<link rel="stylesheet" media="print" href="css/print-6da094505524acaa25ea39a4dd5d6130a436fc43336c0bb89199951b860e98e9.css">
<script src="js/application-9717ccaf4d6f9e8b66ebc0e8784b3061d3f70414d8c920e3eeab2c58fdb8b7c9.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>
<!-- - if current_user.is_language_services? && !current_user.is_publishing? -->
<!-- %li= link_to "Language services", tolk_path -->
</ul>
<ul class="nav pull-right">
<li class="dropdown">
<a class="dropdown-toggle" data-toggle="dropdown" href="#">
Help
<b class="caret"></b>
</a>
<ul class="dropdown-menu">
<li><a href="https://questionbank.ibo.org/video_tour?locale=en">Video tour</a></li>
<li><a href="https://questionbank.ibo.org/instructions?locale=en">Detailed instructions</a></li>
<li><a target="_blank" href="https://ibanswers.ibo.org/">IB Answers</a></li>
</ul>
</li>
<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 class="pull-right screen_only"><a class="btn btn-small btn-info" href="https://questionbank.ibo.org/updates?locale=en">Updates to Questionbank</a></div>
<p class="muted language_chooser">
User interface language:
<a href="https://questionbank.ibo.org/en/users/set_user_locale?new_locale=en">English</a>
|
<a href="https://questionbank.ibo.org/en/users/set_user_locale?new_locale=es">Español</a>
</p>
</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="https://mirror.ibdocs.top/qb.png" alt="Ib qb 46 logo">
</div>
</div>
</div>
<h2>SL Paper 1</h2><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right) = {p^x} + q">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>p</mi>
<mi>x</mi>
</msup>
</mrow>
<mo>+</mo>
<mi>q</mi>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x{\text{, }}p{\text{, }}q \in \mathbb{R}{\text{, }}p > 1">
<mi>x</mi>
<mrow>
<mtext>, </mtext>
</mrow>
<mi>p</mi>
<mrow>
<mtext>, </mtext>
</mrow>
<mi>q</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
<mrow>
<mtext>, </mtext>
</mrow>
<mi>p</mi>
<mo>></mo>
<mn>1</mn>
</math></span>. The point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}\left( {0{\text{, }}a} \right)">
<mrow>
<mtext>A</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>0</mn>
<mrow>
<mtext>, </mtext>
</mrow>
<mi>a</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> lies on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span>.</p>
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {g^{ - 1}}\left( x \right)">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>g</mi>
<mrow>
<mo>−<!-- − --></mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span>. The point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}">
<mrow>
<mtext>B</mtext>
</mrow>
</math></span> lies on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> and is the reflection of point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}">
<mrow>
<mtext>A</mtext>
</mrow>
</math></span> in the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = x">
<mi>y</mi>
<mo>=</mo>
<mi>x</mi>
</math></span>.</p>
</div>
<div class="specification">
<p>The line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_1}">
<mrow>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
</mrow>
</math></span> is tangent to the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}">
<mrow>
<mtext>B</mtext>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the coordinates of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}"> <mrow> <mtext>B</mtext> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'\left( a \right) = \frac{1}{{{\text{ln}}\,p}}"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mrow> <mtext>ln</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>p</mi> </mrow> </mfrac> </math></span>, find the equation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_1}"> <mrow> <msub> <mi>L</mi> <mn>1</mn> </msub> </mrow> </math></span> <strong>in terms of</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q"> <mi>q</mi> </math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_2}"> <mrow> <msub> <mi>L</mi> <mn>2</mn> </msub> </mrow> </math></span> is tangent to the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g"> <mi>g</mi> </math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}"> <mrow> <mtext>A</mtext> </mrow> </math></span> and has equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = \left( {{\text{ln}}\,p} \right)x + q + 1"> <mi>y</mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mrow> <mtext>ln</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>p</mi> </mrow> <mo>)</mo> </mrow> <mi>x</mi> <mo>+</mo> <mi>q</mi> <mo>+</mo> <mn>1</mn> </math></span>.</p>
<p>The line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_2}"> <mrow> <msub> <mi>L</mi> <mn>2</mn> </msub> </mrow> </math></span> passes through the point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( { - 2{\text{, }} - 2} \right)"> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>2</mn> <mrow> <mtext>, </mtext> </mrow> <mo>−</mo> <mn>2</mn> </mrow> <mo>)</mo> </mrow> </math></span>.</p>
<p>The gradient of the normal to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g"> <mi>g</mi> </math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}"> <mrow> <mtext>A</mtext> </mrow> </math></span> is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{{{\text{ln}}\left( {\frac{1}{3}} \right)}}"> <mfrac> <mn>1</mn> <mrow> <mrow> <mtext>ln</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> </math></span>.</p>
<p> </p>
<p>Find the equation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_1}"> <mrow> <msub> <mi>L</mi> <mn>1</mn> </msub> </mrow> </math></span> in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>.</p>
<div class="marks">[7]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the binomial expansion <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>7</mn></msup><mo>=</mo><msup><mi>x</mi><mrow><mn>7</mn></mrow></msup><mo>+</mo><mi>a</mi><msup><mi>x</mi><mn>6</mn></msup><mo>+</mo><mi>b</mi><msup><mi>x</mi><mn>5</mn></msup><mo>+</mo><mn>35</mn><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mo>…</mo><mo>+</mo><mn>1</mn></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mn>0</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mo> </mo><mi>b</mi><mo>∈</mo><msup><mi mathvariant="normal">ℤ</mi><mo>+</mo></msup></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>21</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The third term in the expansion is the mean of the second term and the fourth term in the expansion.</p>
<p>Find the possible values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows part of the graph of a quadratic function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math>.</p>
<p>The graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> has its vertex at <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>3</mn><mo>,</mo><mo> </mo><mn>4</mn><mo>)</mo></math>, and it passes through point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Q</mtext></math> as shown.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The function can be written in the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>a</mi><msup><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mi>h</mi><mo>)</mo></mrow><mn>2</mn></msup><mo>+</mo><mi>k</mi></math>.</p>
</div>
<div class="specification">
<p>The line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> is tangent to the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Q</mtext></math>.</p>
</div>
<div class="specification">
<p>Now consider another function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>. The derivative of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math> is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>′</mo><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>-</mo><mi>d</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation of the axis of symmetry.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Q</mtext></math> has coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>5</mn><mo>,</mo><mo> </mo><mn>12</mn><mo>)</mo></math>. Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math>.</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>Find the values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math> for which <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math> is an increasing function.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> for which the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math> is concave-up.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the functions <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfrac><mo>+</mo><mn>1</mn></math>, for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mn>4</mn></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>x</mi><mo>-</mo><mn>3</mn></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math>.</p>
<p>The following diagram shows the graphs of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The graphs of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math> intersect at points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>. The coordinates of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> are <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>3</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>)</mo></math>.</p>
</div>
<div class="specification">
<p>In the following diagram, the shaded region is enclosed by the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math>, the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math>, the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis, and the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>k</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>∈</mo><mi mathvariant="normal">ℤ</mi></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The area of the shaded region can be written as <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ln</mi><mo>(</mo><mi>p</mi><mo>)</mo><mo>+</mo><mn>8</mn></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>∈</mo><mi mathvariant="normal">ℤ</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>.</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 value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math> and the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>.</p>
<div class="marks">[10]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows the graph of a function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>, with domain <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 2 \leqslant x \leqslant 4">
<mo>−<!-- − --></mo>
<mn>2</mn>
<mo>⩽<!-- ⩽ --></mo>
<mi>x</mi>
<mo>⩽<!-- ⩽ --></mo>
<mn>4</mn>
</math></span>.</p>
<p><img src="images/Schermafbeelding_2018-02-11_om_09.13.25.png" alt="N17/5/MATME/SP1/ENG/TZ0/03"></p>
<p>The points <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="( - 2,{\text{ }}0)">
<mo stretchy="false">(</mo>
<mo>−<!-- − --></mo>
<mn>2</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0</mn>
<mo stretchy="false">)</mo>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(4,{\text{ }}7)">
<mo stretchy="false">(</mo>
<mn>4</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>7</mn>
<mo stretchy="false">)</mo>
</math></span> lie on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>.</p>
</div>
<div class="question">
<p>On the grid, sketch the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^{ - 1}}"> <mrow> <msup> <mi>f</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></span>.</p>
</div>
<br><hr><br><div class="specification">
<p>Olava’s Pizza Company supplies and delivers large cheese pizzas.</p>
<p>The total cost to the customer, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math>, in Papua New Guinean Kina (<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>PGK</mtext></math>), is modelled by the function</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mfenced><mi>n</mi></mfenced><mo>=</mo><mn>34</mn><mo>.</mo><mn>50</mn><mi>n</mi><mo>+</mo><mn>8</mn><mo>.</mo><mn>50</mn><mo> </mo><mo>,</mo><mo> </mo><mi>n</mi><mo>≥</mo><mn>2</mn><mo> </mo><mo>,</mo><mo> </mo><mi>n</mi><mo>∈</mo><mi mathvariant="normal">ℤ</mi><mo>,</mo></math></p>
<p>where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math>, is the number of large cheese pizzas ordered. This total cost includes a fixed cost for delivery.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State, in the context of the question, what the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>34</mn><mo>.</mo><mn>50</mn></math> represents.</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>State, in the context of the question, what the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>.</mo><mn>50</mn></math> represents.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the minimum number of pizzas that can be ordered.</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>Kaelani has <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>450</mn><mo> </mo><mtext>PGK</mtext></math>.</p>
<p>Find the maximum number of large cheese pizzas that Kaelani can order from Olava’s Pizza Company.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The graph of the quadratic function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = c + bx - {x^2}">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>c</mi>
<mo>+</mo>
<mi>b</mi>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> intersects the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis at the point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}( - 1,{\text{ }}0)">
<mrow>
<mtext>A</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mo>−<!-- − --></mo>
<mn>1</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0</mn>
<mo stretchy="false">)</mo>
</math></span> and has its vertex at the point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}(3,{\text{ }}16)">
<mrow>
<mtext>B</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>3</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>16</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-06_om_09.57.03.png" alt="N16/5/MATSD/SP1/ENG/TZ0/09"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation of the axis of symmetry for this graph.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the range of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x)">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows the probability distribution of a discrete random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A">
<mi>A</mi>
</math></span>, in terms of an angle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\theta ">
<mi>θ<!-- θ --></mi>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-11_om_09.10.36.png" alt="M17/5/MATME/SP1/ENG/TZ1/10"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\cos \theta = \frac{3}{4}"> <mi>cos</mi> <mo></mo> <mi>θ</mi> <mo>=</mo> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> </math></span>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\tan \theta > 0"> <mi>tan</mi> <mo></mo> <mi>θ</mi> <mo>></mo> <mn>0</mn> </math></span>, find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\tan \theta "> <mi>tan</mi> <mo></mo> <mi>θ</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = \frac{1}{{\cos x}}"> <mi>y</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>cos</mi> <mo></mo> <mi>x</mi> </mrow> </mfrac> </math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 < x < \frac{\pi }{2}"> <mn>0</mn> <mo><</mo> <mi>x</mi> <mo><</mo> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </math></span>. The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y"> <mi>y</mi> </math></span>between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = \theta "> <mi>x</mi> <mo>=</mo> <mi>θ</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = \frac{\pi }{4}"> <mi>x</mi> <mo>=</mo> <mfrac> <mi>π</mi> <mn>4</mn> </mfrac> </math></span> is rotated 360° about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-axis. Find the volume of the solid formed.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is defined for all <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math>. The line with equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>6</mn><mi>x</mi><mo>-</mo><mn>1</mn></math> is the tangent to the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>4</mn></math>.</p>
</div>
<div class="specification">
<p>The function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math> is defined for all <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mi>x</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>f</mi><mfenced><mrow><mi>g</mi><mfenced><mi>x</mi></mfenced></mrow></mfenced></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>′</mo><mo>(</mo><mn>4</mn><mo>)</mo></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mn>4</mn><mo>)</mo></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mn>4</mn><mo>)</mo></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find the equation of the tangent to the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>4</mn></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is defined by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mrow><mn>2</mn><mi>x</mi><mo>-</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfrac></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi><mo>,</mo><mo> </mo><mi>x</mi><mo>≠</mo><mo>-</mo><mn>1</mn></math>.</p>
</div>
<div class="specification">
<p>The graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math> has a vertical asymptote and a horizontal asymptote.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation of the vertical asymptote.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation of the horizontal asymptote.</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>On the set of axes below, sketch the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>.</p>
<p>On your sketch, clearly indicate the asymptotes and the position of any points of intersection with the axes.</p>
<p><img src="data:image/png;base64,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"></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, solve the inequality <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo><</mo><mfrac><mrow><mn>2</mn><mi>x</mi><mo>-</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo><</mo><mn>2</mn></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>-</mo><mn>2</mn><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math>, for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math>. The following diagram shows part of the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p> </p>
</div>
<div class="specification">
<p>For the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>find the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-coordinates of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-intercepts.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>find the coordinates of the vertex.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> can be written in the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>-</mo><mn>2</mn><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mi>h</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>k</mi></math>.</p>
<p>Write down the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> and the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>a</mi><mi>x</mi></msup></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>,</mo><mo> </mo><mi>a</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mn>0</mn><mo>,</mo><mo> </mo><mi>a</mi><mo>></mo><mn>1</mn></math>.</p>
<p>The graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> contains the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>,</mo><mo> </mo><mn>4</mn></mrow></mfenced></math>.</p>
</div>
<div class="specification">
<p>Consider the arithmetic sequence <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mn>8</mn></msub><mo> </mo><mn>27</mn><mo> </mo><mo>,</mo><mo> </mo><msub><mi>log</mi><mn>8</mn></msub><mo> </mo><mi>p</mi><mo> </mo><mo>,</mo><mo> </mo><msub><mi>log</mi><mn>8</mn></msub><mo> </mo><mi>q</mi><mo> </mo><mo>,</mo><mo> </mo><msub><mi>log</mi><mn>8</mn></msub><mo> </mo><mn>125</mn><mo> </mo><mo>,</mo></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>></mo><mn>1</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>></mo><mn>1</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>8</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mi>x</mi></mfenced></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><msqrt><mn>32</mn></msqrt></mfenced></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>27</mn><mo>,</mo><mo> </mo><mi>p</mi><mo>,</mo><mo> </mo><mi>q</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>125</mn></math> are four consecutive terms in a geometric sequence.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> and the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram shows the graph of the quadratic function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>a</mi><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mi>x</mi><mo>+</mo><mi>c</mi></math> , with vertex <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>−</mo><mn>2</mn><mo>,</mo><mo> </mo><mn>10</mn></mrow></mfenced></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>k</mi></math> has two solutions. One of these solutions is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>2</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the other solution of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>k</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Complete the table below placing a tick (✔) to show whether the unknown parameters <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math> are positive, zero or negative. The row for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math> has been completed as an example.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></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>State the values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> for which <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math> is decreasing.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A quadratic function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> can be written in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = a(x - p)(x - 3)">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>a</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mi>p</mi>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mn>3</mn>
<mo stretchy="false">)</mo>
</math></span>. The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> has axis of symmetry <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 2.5">
<mi>x</mi>
<mo>=</mo>
<mn>2.5</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-intercept at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(0,{\text{ }} - 6)">
<mo stretchy="false">(</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>−<!-- − --></mo>
<mn>6</mn>
<mo stretchy="false">)</mo>
</math></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a"> <mi>a</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = kx - 5"> <mi>y</mi> <mo>=</mo> <mi>k</mi> <mi>x</mi> <mo>−</mo> <mn>5</mn> </math></span> is a tangent to the curve of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span>. Find the values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span>.</p>
<div class="marks">[8]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows part of the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mi>k</mi><mi>x</mi></mfrac></math>, for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mn>0</mn><mo>,</mo><mo> </mo><mi>k</mi><mo>></mo><mn>0</mn></math>.</p>
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>p</mi><mo>,</mo><mo> </mo><mfrac><mi>k</mi><mi>p</mi></mfrac></mrow></mfenced></math> be any point on the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math>. Line <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>1</mn></msub></math> is the tangent to the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>Line <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>1</mn></msub></math> intersects the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis at point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mfenced><mrow><mn>2</mn><mi>p</mi><mo>,</mo><mo> </mo><mn>0</mn></mrow></mfenced></math> and the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-axis at point B.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mfenced><mi>p</mi></mfenced></math> in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the equation of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>1</mn></msub></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mi>x</mi><mo>+</mo><msup><mi>p</mi><mn>2</mn></msup><mi>y</mi><mo>-</mo><mn>2</mn><mi>p</mi><mi>k</mi><mo>=</mo><mn>0</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AOB</mtext></math> in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is translated by <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd></mtr></mtable></mfenced></math> to give the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math>.<br>In the following diagram:</p>
<ul>
<li>point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Q</mtext></math> lies on the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math>
</li>
<li>points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext></math> lie on the vertical asymptote of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math>
</li>
<li>points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F</mtext></math> lie on the horizontal asymptote of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math>
</li>
<li>point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>G</mtext></math> lies on the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis such that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>FG</mtext></math> is parallel to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>DC</mtext></math>.</li>
</ul>
<p>Line <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>2</mn></msub></math> is the tangent to the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Q</mtext></math>, and passes through <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F</mtext></math>.</p>
<p><img src="data:image/png;base64,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"></p>
<p>Given that triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>EDF</mtext></math> and rectangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>CDFG</mtext></math> have equal areas, find the gradient of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>2</mn></msub></math> in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A particle <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math> moves along the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis. The velocity of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> seconds, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mn>4</mn><mo>+</mo><mn>4</mn><mi>t</mi><mo>-</mo><mn>3</mn><msup><mi>t</mi><mn>2</mn></msup></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mn>3</mn></math>. When <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn><mo>,</mo><mo> </mo><mi>P</mi></math> is at the origin <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">O</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math> reaches its maximum velocity.</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>Show that the distance of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math> from <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">O</mi></math> at this time is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>88</mn><mn>27</mn></mfrac></math> metres.</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>Sketch a graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math> against <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>, clearly showing any points of intersection with the axes.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total distance travelled by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p>The following table shows the probability distribution of a discrete random variable <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>1</mn><mo>,</mo><mo> </mo><mn>2</mn><mo>,</mo><mo> </mo><mn>3</mn><mo>,</mo><mo> </mo><mn>4</mn></math>.</p>
<p style="text-align:center;"><img src="data:image/png;base64,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"></p>
<p style="text-align:left;">Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>, justifying your answer.</p>
</div>
<br><hr><br><div class="specification">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>m</mi><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mi>m</mi><mi>x</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math>. The line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>m</mi><mi>x</mi><mo>-</mo><mn>9</mn></math> meets the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> at exactly one point.</p>
</div>
<div class="specification">
<p>The function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> can be expressed in the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>4</mn><mfenced><mrow><mi>x</mi><mo>-</mo><mi>p</mi></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>-</mo><mi>q</mi></mrow></mfenced></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>,</mo><mo> </mo><mi>q</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math>.</p>
</div>
<div class="specification">
<p>The function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> can also be expressed in the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>4</mn><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mi>h</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>k</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>,</mo><mo> </mo><mi>k</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mn>4</mn></math>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> and the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> and the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find the values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> where the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is both negative and increasing.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A function, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math>, has its derivative given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>′</mo><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>12</mn><mi>x</mi><mo>+</mo><mi>p</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math>. The following diagram shows part of the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>′</mo></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>′</mo></math> has an axis of symmetry <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>q</mi></math>.</p>
</div>
<div class="specification">
<p>The vertex of the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>′</mo></math> lies on the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis.</p>
</div>
<div class="specification">
<p>The graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> has a point of inflexion at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>a</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of the discriminant of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>′</mo></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence or otherwise, find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of the gradient of the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>′</mo></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>0</mn></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>″</mo></math>, the second derivative of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math>. Indicate clearly the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-intercept and the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-intercept.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> for which the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is concave-down. Justify your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Jean-Pierre jumps out of an airplane that is flying at constant altitude. Before opening his parachute, he goes through a period of freefall.</p>
<p>Jean-Pierre’s vertical speed during the time of freefall, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math>, in <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>m s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>, is modelled by the following function.</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mi>K</mi><mo>-</mo><mn>60</mn><mfenced><mrow><mn>1</mn><mo>.</mo><msup><mn>2</mn><mrow><mo>-</mo><mi>t</mi></mrow></msup></mrow></mfenced><mo> </mo><mo>,</mo><mo> </mo><mi>t</mi><mo>≥</mo><mn>0</mn></math></p>
<p>where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>, is the number of seconds after he jumps out of the airplane, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi></math> is a constant. A sketch of Jean-Pierre’s vertical speed against time is shown below.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">Jean-Pierre’s initial vertical speed is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo> </mo><msup><mtext>m s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In the context of the model, state what the horizontal asymptote represents.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find Jean-Pierre’s vertical speed after <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> seconds. Give your answer in <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>km</mtext><mo> </mo><msup><mtext>h</mtext><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> .</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = 1 + {{\text{e}}^{ - x}}">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>1</mn>
<mo>+</mo>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mo>−<!-- − --></mo>
<mi>x</mi>
</mrow>
</msup>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x) = 2x + b">
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>2</mn>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \in \mathbb{R}">
<mi>x</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span> is a constant.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(g \circ f)(x)"> <mo stretchy="false">(</mo> <mi>g</mi> <mo>∘</mo> <mi>f</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {\lim }\limits_{x \to + \infty } (g \circ f)(x) = - 3"> <munder> <mrow> <mo form="prefix">lim</mo> </mrow> <mrow> <mi>x</mi> <mo stretchy="false">→</mo> <mo>+</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <mo></mo> <mo stretchy="false">(</mo> <mi>g</mi> <mo>∘</mo> <mi>f</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <mn>3</mn> </math></span>, find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b"> <mi>b</mi> </math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>-</mo><msqrt><mi>x</mi><mo>+</mo><mn>3</mn></msqrt></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≥</mo><mo>-</mo><mn>3</mn></math>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>A function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is defined by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>-</mo><mn>1</mn><mo>-</mo><msqrt><mi>x</mi><mo>+</mo><mn>3</mn></msqrt></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≥</mo><mo>-</mo><mn>3</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe a sequence of transformations that transforms the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><msqrt><mi>x</mi></msqrt></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≥</mo><mn>0</mn></math> to the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>-</mo><msqrt><mi>x</mi><mo>+</mo><mn>3</mn></msqrt></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≥</mo><mo>-</mo><mn>3</mn></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the range of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mi>x</mi></mfenced></math>, stating its domain.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of the point(s) where the graphs of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>f</mi><mfenced><mi>x</mi></mfenced></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mi>x</mi></mfenced></math> intersect.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span> intersects the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis at point A and the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-axis at point B, as shown on the diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_17.18.01.png" alt="M17/5/MATSD/SP1/ENG/TZ2/04"></p>
<p>The length of line segment OB is three times the length of line segment OA, where O is the origin.</p>
</div>
<div class="specification">
<p>Point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{(2, 6)}}">
<mrow>
<mtext>(2, 6)</mtext>
</mrow>
</math></span> lies on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span> in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = mx + c">
<mi>y</mi>
<mo>=</mo>
<mi>m</mi>
<mi>x</mi>
<mo>+</mo>
<mi>c</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-coordinate of point A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the functions <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {x^4} - 2">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mn>2</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right) = {x^3} - 4{x^2} + 2x + 6">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mn>4</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mi>x</mi>
<mo>+</mo>
<mn>6</mn>
</math></span></p>
<p>The functions intersect at points P and Q. Part of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> and part of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = g\left( x \right)">
<mi>y</mi>
<mo>=</mo>
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> are shown on the diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the range of <em>f</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the <em>x</em>-coordinate of P and the <em>x</em>-coordinate of Q.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the values of <em>x</em> for which <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) > g\left( x \right)"> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>></mo> <mi>g</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right) = {x^2} + bx + 11">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>b</mi>
<mi>x</mi>
<mo>+</mo>
<mn>11</mn>
</math></span>. The point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( { - 1{\text{, }}8} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mo>−<!-- − --></mo>
<mn>1</mn>
<mrow>
<mtext>, </mtext>
</mrow>
<mn>8</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> lies on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b"> <mi>b</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {x^2}"> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> </math></span> is transformed to obtain the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g"> <mi>g</mi> </math></span>.</p>
<p>Describe this transformation.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mrow><mi>ln</mi><mo> </mo><mi>x</mi></mrow><msup><mi>x</mi><mn>4</mn></msup></mfrac></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mn>0</mn></math>.</p>
</div>
<div class="specification">
<p>Consider the function defined by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mfrac><mrow><mi>ln</mi><mo> </mo><mi>x</mi></mrow><msup><mi>x</mi><mn>4</mn></msup></mfrac></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mn>0</mn></math> and its graph <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>f</mi><mfenced><mi>x</mi></mfenced></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>d</mo><mi>y</mi></mrow><mrow><mo>d</mo><mi>x</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn><mo>-</mo><mn>4</mn><mo> </mo><mi>ln</mi><mo> </mo><mi>x</mi></mrow><msup><mi>x</mi><mn>5</mn></msup></mfrac></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> has a horizontal tangent at point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math>. Find the coordinates of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>''</mo><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mrow><mn>20</mn><mo> </mo><mi>ln</mi><mo> </mo><mi>x</mi><mo>-</mo><mn>9</mn></mrow><msup><mi>x</mi><mn>6</mn></msup></mfrac></math>, show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math> is a local maximum point.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Solve <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>></mo><mn>0</mn></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mn>0</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math>, showing clearly the value of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-intercept and the approximate position of point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo></math> for different values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>.</p>
<p>Both <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math> are one-to-one functions.</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mn>0</mn><mo>)</mo></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>f</mi><mo>∘</mo><mi>g</mi><mo>)</mo><mo>(</mo><mn>0</mn><mo>)</mo></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> such that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>0</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is defined by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>4</mn></mrow><mrow><mn>3</mn><mo>-</mo><mi>x</mi></mrow></mfrac></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi><mo>,</mo><mo> </mo><mi>x</mi><mo>≠</mo><mn>3</mn></math>.</p>
</div>
<div class="specification">
<p>Write down the equation of</p>
</div>
<div class="specification">
<p>Find the coordinates where the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> crosses</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the vertical asymptote of the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the horizontal asymptote of the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-axis.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> on the axes below.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the series <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ln</mi><mo> </mo><mi>x</mi><mo>+</mo><mi>p</mi><mo> </mo><mi>ln</mi><mo> </mo><mi>x</mi><mo>+</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mi>ln</mi><mo> </mo><mi>x</mi><mo>+</mo><mo>…</mo></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi><mo>,</mo><mo> </mo><mi>x</mi><mo>></mo><mn>1</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi><mo>,</mo><mo> </mo><mi>p</mi><mo>≠</mo><mn>0</mn></math>.</p>
</div>
<div class="specification">
<p>Consider the case where the series is geometric.</p>
</div>
<div class="specification">
<p>Now consider the case where the series is arithmetic with common difference <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mo>±</mo><mfrac><mn>1</mn><msqrt><mn>3</mn></msqrt></mfrac></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>></mo><mn>0</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mo>∞</mo></msub><mo>=</mo><mn>3</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></math>, find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math> in the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo> </mo><mi>ln</mi><mo> </mo><mi>x</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>∈</mo><mi mathvariant="normal">ℚ</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The sum of the first <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> terms of the series is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo> </mo><mi>ln</mi><mo> </mo><mi>x</mi></math>.</p>
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">b.iii.</div>
</div>
<br><hr><br><div class="question">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>5</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>-</mo><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>+</mo><mi>k</mi></math>.</p>
<p>Find the values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math> so that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>0</mn></math> has no real roots.</p>
</div>
<br><hr><br><div class="specification">
<p>The functions <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> are defined such that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{{x + 3}}{4}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mi>x</mi>
<mo>+</mo>
<mn>3</mn>
</mrow>
<mn>4</mn>
</mfrac>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right) = 8x + 5">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>8</mn>
<mi>x</mi>
<mo>+</mo>
<mn>5</mn>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {g \circ f} \right)\left( x \right) = 2x + 11">
<mrow>
<mo>(</mo>
<mrow>
<mi>g</mi>
<mo>∘</mo>
<mi>f</mi>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>2</mn>
<mi>x</mi>
<mo>+</mo>
<mn>11</mn>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\left( {g \circ f} \right)^{ - 1}}\left( a \right) = 4">
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mi>g</mi>
<mo>∘</mo>
<mi>f</mi>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
<mrow>
<mo>(</mo>
<mi>a</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>4</mn>
</math></span>, find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>a</mi><mo> </mo><msub><mi>log</mi><mn>3</mn></msub><mfenced><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced></math>, for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mn>4</mn></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>></mo><mn>0</mn></math>.</p>
<p>Point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mfenced><mrow><mn>13</mn><mo>,</mo><mo> </mo><mn>7</mn></mrow></mfenced></math> lies on the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-intercept of the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>5</mn><mo>,</mo><mo> </mo><mn>0</mn></mrow></mfenced></math>.</p>
<p>On the following grid, sketch the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math>.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the graph of the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>x</mi><mo>+</mo><mfrac><mn>12</mn><msup><mi>x</mi><mn>2</mn></msup></mfrac><mo>,</mo><mo> </mo><mi>x</mi><mo>≠</mo><mn>0</mn></math>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the zero of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the coordinates of the local minimum point.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Consider the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>3</mn><mo>-</mo><mi>x</mi></math>.</p>
<p>Solve <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>g</mi><mfenced><mi>x</mi></mfenced></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The points <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}">
<mrow>
<mtext>A</mtext>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}">
<mrow>
<mtext>B</mtext>
</mrow>
</math></span> have position vectors <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} { - 2} \\ 4 \\ { - 4} \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mo>−<!-- − --></mo>
<mn>2</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>4</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>−<!-- − --></mo>
<mn>4</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 6 \\ 8 \\ 0 \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mn>6</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>8</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span> respectively.</p>
<p>Point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{C}}">
<mrow>
<mtext>C</mtext>
</mrow>
</math></span> has position vector <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} { - 1} \\ k \\ 0 \end{array}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mo>−<!-- − --></mo>
<mn>1</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>k</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
</math></span>. Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{O}}">
<mrow>
<mtext>O</mtext>
</mrow>
</math></span> be the origin.</p>
</div>
<div class="specification">
<p>Find, in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span>,</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{OA}}} \bullet \overrightarrow {{\text{OC}}} "> <mover> <mrow> <mtext>OA</mtext> </mrow> <mo>→</mo> </mover> <mo>∙</mo> <mover> <mrow> <mtext>OC</mtext> </mrow> <mo>→</mo> </mover> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overrightarrow {{\text{OB}}} \bullet \overrightarrow {{\text{OC}}} "> <mover> <mrow> <mtext>OB</mtext> </mrow> <mo>→</mo> </mover> <mo>∙</mo> <mover> <mrow> <mtext>OC</mtext> </mrow> <mo>→</mo> </mover> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}\widehat {\text{O}}{\text{C}} = {\text{B}}\widehat {\text{O}}{\text{C}}"> <mrow> <mtext>A</mtext> </mrow> <mrow> <mover> <mtext>O</mtext> <mo>^</mo> </mover> </mrow> <mrow> <mtext>C</mtext> </mrow> <mo>=</mo> <mrow> <mtext>B</mtext> </mrow> <mrow> <mover> <mtext>O</mtext> <mo>^</mo> </mover> </mrow> <mrow> <mtext>C</mtext> </mrow> </math></span>, show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 7"> <mi>k</mi> <mo>=</mo> <mn>7</mn> </math></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>Calculate the area of triangle <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AOC}}"> <mrow> <mtext>AOC</mtext> </mrow> </math></span>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>f</mi><mfenced><mi>x</mi></mfenced></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mn>6</mn></math> is shown in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mn>2</mn></mfenced></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>f</mi><mo>∘</mo><mi>f</mi></mrow></mfenced><mfenced><mn>2</mn></mfenced></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>+</mo><mn>1</mn></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mn>6</mn></math>. On the axes above, sketch the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math>.</p>
<p> </p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo> </mo><mn>20</mn><mo>)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext><mo>(</mo><mn>4</mn><mo>,</mo><mo> </mo><mn>6</mn><mo>)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext><mo>(</mo><mo>-</mo><mn>14</mn><mo>,</mo><mo> </mo><mn>12</mn><mo>)</mo></math>. The line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> passes through the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and is perpendicular to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>[BC]</mtext></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> passes through the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>k</mi><mo>,</mo><mo> </mo><mn>2</mn><mo>)</mo></math>.</p>
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>The functions <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math> are defined for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math> by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>x</mi><mo>-</mo><mn>2</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>a</mi><mi>x</mi><mo>+</mo><mi>b</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mo> </mo><mi>b</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math>.</p>
<p>Given that <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>f</mi><mo>∘</mo><mi>g</mi></mrow></mfenced><mfenced><mn>2</mn></mfenced><mo>=</mo><mo>-</mo><mn>3</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>g</mi><mo>∘</mo><mi>f</mi></mrow></mfenced><mfenced><mn>1</mn></mfenced><mo>=</mo><mn>5</mn></math>, find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> and the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</p>
</div>
<br><hr><br><div class="specification">
<p>Consider the functions <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msqrt><mn>3</mn></msqrt><mi>sin</mi><mo> </mo><mi>x</mi><mo>+</mo><mi>cos</mi><mo> </mo><mi>x</mi></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mi>π</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>2</mn><mi>x</mi></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>f</mi><mo>∘</mo><mi>g</mi><mo>)</mo><mo>(</mo><mi>x</mi><mo>)</mo></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Solve the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>f</mi><mo>∘</mo><mi>g</mi><mo>)</mo><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>2</mn><mo> </mo><mi>cos</mi><mo> </mo><mn>2</mn><mi>x</mi></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mi>π</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = {x^2} - x">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mi>x</mi>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \in \mathbb{R}">
<mi>x</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>. The following diagram shows part of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-11_om_09.25.10.png" alt="N17/5/MATME/SP1/ENG/TZ0/08"></p>
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> crosses the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis at the origin and at the point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(1,{\text{ }}0)">
<mrow>
<mtext>P</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
</div>
<div class="specification">
<p>The line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
<mi>L</mi>
</math></span> intersects the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> at another point Q, as shown in the following diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-11_om_09.27.48.png" alt="N17/5/MATME/SP1/ENG/TZ0/08.c.d"></p>
</div>
<div class="question">
<p>Find the area of the region enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> and the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L"> <mi>L</mi> </math></span>.</p>
</div>
<br><hr><br><div class="specification">
<p>The function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> is of the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = ax + b + \frac{c}{x}">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>a</mi>
<mi>x</mi>
<mo>+</mo>
<mi>b</mi>
<mo>+</mo>
<mfrac>
<mi>c</mi>
<mi>x</mi>
</mfrac>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c">
<mi>c</mi>
</math></span> are positive integers.</p>
<p>Part of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f(x)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span> is shown on the axes below. The graph of the function has its local maximum at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="( - 2,{\text{ }} - 2)">
<mo stretchy="false">(</mo>
<mo>−<!-- − --></mo>
<mn>2</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>−<!-- − --></mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
</math></span> and its local minimum at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(2,{\text{ }}6)">
<mo stretchy="false">(</mo>
<mn>2</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>6</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_11.28.21.png" alt="M17/5/MATSD/SP1/ENG/TZ1/12"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = - 6"> <mi>y</mi> <mo>=</mo> <mo>−</mo> <mn>6</mn> </math></span> on the axes.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of solutions to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = - 6"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <mn>6</mn> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the range of values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span> for which <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = k"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>k</mi> </math></span> has no solution.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p>Consider the vectors <em><strong>a</strong></em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 3 \\ {2p} \end{array}} \right)"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>2</mn> <mi>p</mi> </mrow> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span> and <em><strong>b</strong></em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} {p + 1} \\ 8 \end{array}} \right)"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mi>p</mi> <mo>+</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>8</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span>.</p>
<p>Find the possible values of <em>p</em> for which <strong><em>a</em></strong> and <strong><em>b</em></strong> are parallel.</p>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = {x^2} - 4x + 5">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mn>4</mn>
<mi>x</mi>
<mo>+</mo>
<mn>5</mn>
</math></span>.</p>
</div>
<div class="specification">
<p>The function can also be expressed in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = {(x - h)^2} + k">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mrow>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mi>h</mi>
<msup>
<mo stretchy="false">)</mo>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>k</mi>
</math></span>.</p>
</div>
<div class="question">
<p>(i) Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span>.</p>
<p>(ii) Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span>.</p>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>, with derivative <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'\left( x \right) = 2{x^2} + 5kx + 3{k^2} + 2">
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>2</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>5</mn>
<mi>k</mi>
<mi>x</mi>
<mo>+</mo>
<mn>3</mn>
<mrow>
<msup>
<mi>k</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>2</mn>
</math></span> where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x{\text{, }}k \in \mathbb{R}">
<mi>x</mi>
<mrow>
<mtext>, </mtext>
</mrow>
<mi>k</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the discriminant of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'\left( x \right)"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span> is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{k^2} - 16"> <mrow> <msup> <mi>k</mi> <mn>2</mn> </msup> </mrow> <mo>−</mo> <mn>16</mn> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> is an increasing function, find all possible values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> defined by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>ln</mi><mo>(</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>16</mn><mo>)</mo></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mn>4</mn></math>.</p>
<p>The following diagram shows part of the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> which crosses the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis at point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>, with coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mo> </mo><mn>0</mn><mo>)</mo></math>. The line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> is the tangent to the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> at the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the exact value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that the gradient of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>3</mn></mfrac></math>, find the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-coordinate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br>