File "SL-paper1.html"
Path: /IB QUESTIONBANKS/4 Fourth Edition - PAPER/HTML/Mathematical Studies/Topic 6/SL-paper1html
File size: 430.17 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-746ec5d03ead8d9e8b3bb7d32173f2b4e2e22a05f0c5278e086ab55b3c9c238e.css">
<link rel="stylesheet" media="print" href="css/print-6da094505524acaa25ea39a4dd5d6130a436fc43336c0bb89199951b860e98e9.css">
<script src="js/application-3c91afd8a2942c18d21ed2700e1bdec14ada97f1d3788ae229315e1276d81453.js"></script>
<script type="text/javascript" async src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-MML-AM_CHTML-full"></script>
<!--[if lt IE 9]>
<script src='https://cdnjs.cloudflare.com/ajax/libs/html5shiv/3.7.3/html5shiv.min.js'></script>
<![endif]-->
<meta name="csrf-param" content="authenticity_token">
<meta name="csrf-token" content="iHF+M3VlRFlNEehLVICYgYgqiF8jIFlzjGNjIwqOK9cFH3ZNdavBJrv/YQpz8vcspoICfQcFHW8kSsHnJsBwfg==">
<link href="favicon.ico" rel="shortcut icon">
</head>
<body class="teacher questions-show">
<div class="navbar navbar-fixed-top">
<div class="navbar-inner">
<div class="container">
<div class="brand">
<div class="inner"><a href="http://ibo.org/">ibo.org</a></div>
</div>
<ul class="nav">
<li>
<a href="../../index.html">Home</a>
</li>
<li class="active dropdown">
<a class="dropdown-toggle" data-toggle="dropdown" href="#">
Questionbanks
<b class="caret"></b>
</a><ul class="dropdown-menu">
<li>
<a href="../../geography.html" target="_blank">DP Geography</a>
</li>
<li>
<a href="../../physics.html" target="_blank">DP Physics</a>
</li>
<li>
<a href="../../chemistry.html" target="_blank">DP Chemistry</a>
</li>
<li>
<a href="../../biology.html" target="_blank">DP Biology</a>
</li>
<li>
<a href="../../furtherMath.html" target="_blank">DP Further Mathematics HL</a>
</li>
<li>
<a href="../../mathHL.html" target="_blank">DP Mathematics HL</a>
</li>
<li>
<a href="../../mathSL.html" target="_blank">DP Mathematics SL</a>
</li>
<li>
<a href="../../mathStudies.html" target="_blank">DP Mathematical Studies</a>
</li>
</ul></li>
<!-- - if current_user.is_language_services? && !current_user.is_publishing? -->
<!-- %li= link_to "Language services", tolk_path -->
</ul>
<ul class="nav pull-right">
<li>
<a href="https://06082010.xyz">IB Documents (2) Team</a>
</li></ul>
</div>
</div>
</div>
<div class="page-content container">
<div class="row">
<div class="span24">
</div>
</div>
<div class="page-header">
<div class="row">
<div class="span16">
<p class="back-to-list">
</p>
</div>
<div class="span8" style="margin: 0 0 -19px 0;">
<img style="width: 100%;" class="qb_logo" src="images/logo.jpg" alt="Ib qb 46 logo">
</div>
</div>
</div><h2>SL Paper 1</h2><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A liquid is heated so that after \(20\) seconds of heating its temperature, \(T\) , is \({25^ \circ }{\text{C}}\) and after \(50\) seconds of heating its temperature is \({37^ \circ }{\text{C}}\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The temperature of the liquid at time \(t\) can be modelled by \(T = at + b\) , where \(t\) is the time in seconds after the start of heating.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Using this model one equation that can be formed is \(20a + b = 25\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using the model, write down a second equation in \(a\) and \(b\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using your graphic display calculator or otherwise, find the value of \(a\) and of \(b\) .</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><span>Use the model to predict the temperature of the liquid \(60{\text{ seconds}}\) after the start of heating.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A plumber in Australia charges 90 AUD per hour for work, plus a fixed cost. His total charge is represented by the cost function <em>C</em> = 60 + 90<em>t</em>, where<em> t</em> is in hours.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the fixed cost.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>It takes \(3 \frac{1}{2}\) hours to complete a job for Paula. Find the total cost.</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><span>Steve received a bill for 510 AUD. Calculate the time it took the plumber to complete the job.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The straight line, <em>L</em>, has equation \(2y - 27x - 9 = 0\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the gradient of <em>L</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Sarah wishes to draw the tangent to \(f (x) = x^4\) parallel to <em>L</em>.</span></p>
<p><span>Write down \(f ′(x)\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the <em>x</em> coordinate of the point at which the tangent must be drawn.<br></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c, i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of \(f (x)\) at this point.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c, ii.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the two functions, \(f\) and \(g\), where</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> \(f(x) = \frac{5}{{{x^2} + 1}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> \(g(x) = {(x - 2)^2}\)</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Sketch the graphs of \(y = f(x)\) and \(y = g(x)\) on the axes below. Indicate clearly the points where each graph intersects the <em>y-</em>axis.</span></p>
<div>
<br><span><img src="images/Schermafbeelding_2014-09-03_om_07.24.03.png" alt></span>
</div>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to solve \(f(x) = g(x)\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A quadratic function \(f\) is given by \(f(x) = a{x^2} + bx + c\). The points \((0,{\text{ }}5)\) and \(( - 4,{\text{ }}5)\) lie on the graph of \(y = f(x)\).</p>
</div>
<div class="specification">
<p>The \(y\)-coordinate of the minimum of the graph is 3.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of the axis of symmetry of the graph of \(y = f(x)\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of \(c\).</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 \(a\) and of \(b\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Maria owns a cheese factory. The amount of cheese, in kilograms, Maria sells in one week, \(Q\), is given by</p>
<p style="text-align: center;">\(Q = 882 - 45p\),</p>
<p>where \(p\) is the price of a kilogram of cheese in euros (EUR).</p>
</div>
<div class="specification">
<p>Maria earns \((p - 6.80){\text{ EUR}}\) for each kilogram of cheese sold.</p>
</div>
<div class="specification">
<p>To calculate her weekly profit \(W\), in EUR, Maria multiplies the amount of cheese she sells by the amount she earns per kilogram.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down how many kilograms of cheese Maria sells in one week if the price of a kilogram of cheese is 8 EUR.</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 how much Maria earns in one week, from selling cheese, if the price of a kilogram of cheese is 8 EUR.</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 an expression for \(W\) in terms of \(p\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the price, \(p\), that will give Maria the highest weekly profit.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">In a trial for a new drug, scientists found that the amount of the drug in the bloodstream decreased over time, according to the model</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\[D(t) = 1.2 \times {(0.87)^t},{\text{ }}t \geqslant 0\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">where \(D\) is the amount of the drug in the bloodstream in mg per litre \({\text{(mg}}\,{{\text{l}}^{ - 1}}{\text{)}}\) and \(t\) is the time in hours.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the amount of the drug in the bloodstream at \(t = 0\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the amount of the drug in the bloodstream after 3 hours.</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><span>Use your graphic display calculator to determine the time it takes for the amount of the drug in the bloodstream to decrease to </span><span><span><span>\(0.333{\text{ mg}}{{\text{1}}^{ - 1}}\).</span></span></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The number of bacteria in a colony is modelled by the function </span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">\(N(t) = 800 \times 3^{0.5t}, {\text{ }} t \geqslant 0\), </span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">where \(N\) is the number of bacteria and \(t\) is the time in hours.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of bacteria in the colony at time \(t = 0\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the number of bacteria present at 2 hours and 30 minutes. Give your answer correct to the nearest hundred bacteria.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the time, in hours, for the number of bacteria to reach 5500.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A company sells fruit juices in cylindrical cans, each of which has a volume of \(340\,{\text{c}}{{\text{m}}^3}\). The surface area of a can is \(A\,{\text{c}}{{\text{m}}^2}\) and is given by the formula</p>
<p>\(A = 2\pi {r^2} + \frac{{680}}{r}\) ,</p>
<p>where \(r\) is the radius of the can, in \({\text{cm}}\).</p>
<p>To reduce the cost of a can, its surface area must be minimized.</p>
<p>Find \(\frac{{{\text{d}}A}}{{{\text{d}}r}}\)</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>Calculate the value of \(r\) that minimizes the surface area of a can.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Given the function \(f (x) = 2 \times 3^x\) for −2 \( \leqslant \) <em>x</em> \( \leqslant \) 5,</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>find the range of \(f\).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>find the value of \(x\) given that \(f (x) =162\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A potato is placed in an oven heated to a temperature of 200<span class="s1">°</span>C.</p>
<p class="p1">The temperature of the potato, in <span class="s1">°</span>C, is modelled by the function \(p(t) = 200 - 190{(0.97)^t}\), where \(t\) is the time, in minutes, that the potato has been in the oven.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down the temperature of the potato at the moment it is placed in the oven.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the temperature of the potato half an hour after it has been placed in the oven.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">After the potato has been in the oven for \(k\) minutes, its temperature is 40<span class="s1">°</span>C.</p>
<p class="p1">Find the value of \(k\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Sejah placed a baking tin, that contained cake mix, in a preheated oven in order to bake a cake. The temperature in the centre of the cake mix, \(T\), in degrees Celsius (°C) is given by</p>
<p>\[T(t) = 150 - a \times {(1.1)^{ - t}}\]</p>
<p>where \(t\) is the time, in minutes, since the baking tin was placed in the oven. The graph of \(T\) is shown in the following diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_18.27.39.png" alt="N17/5/MATSD/SP1/ENG/TZ0/12"></p>
</div>
<div class="specification">
<p>The temperature in the centre of the cake mix was 18 °C when placed in the oven.</p>
</div>
<div class="specification">
<p>The baking tin is removed from the oven 15 minutes after the temperature in the centre of the cake mix has reached 130 °C.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down what the value of 150 represents in the context of the question.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(a\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total time that the baking tin is in the oven.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function \(f\left( x \right) = \frac{{{x^4}}}{4}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <em>f'</em>(<em>x</em>)</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the gradient of the graph of <em>f</em> at \(x = - \frac{1}{2}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <em>x</em>-coordinate of the point at which the <strong>normal</strong> to the graph of <em>f</em> has gradient \({ - \frac{1}{8}}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Shiyun bought a car in 1999. The value of the car \(V\) , in USD, is depreciating according to the exponential model</span><br><span style="font-family: times new roman,times; font-size: medium;">\[V = 25000 \times {1.5^{ - 0.2t}}{\text{, }}t \geqslant 0\]</span><br><span style="font-family: times new roman,times; font-size: medium;">where \(t\) is the time, in years, that Shiyun has owned the car.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of the car when Shiyun bought it.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the value of the car three years after Shiyun bought it. Give your answer correct to <strong>two decimal places</strong>.</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><span>Calculate the time for the car to depreciate to half of its value since Shiyun bought it.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider the quadratic function, \(f(x) = px(q - x)\), where \(p\) and \(q\) are positive integers.</p>
<p class="p2"><span class="s1">The graph of \(y = f(x)\) </span>passes through the point \((6,{\text{ }}0)\)<span class="s1">.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the value of \(q\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The vertex of the function is \((3,{\text{ }}27)\)<span class="s1">.</span></p>
<p class="p2">Find the value of \(p\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The vertex of the function is \((3,{\text{ }}27)\)<span class="s1">.</span></p>
<p class="p1">Write down the range of \(f\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A sketch of the function \(f(x) = 5{x^3} - 3{x^5} + 1\) is shown for \( - 1.5 \leqslant x \leqslant 1.5\) and \( - 6 \leqslant y \leqslant 6\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down \(f'(x)\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the equation of the tangent to the graph of \(y = f(x)\) at \((1{\text{, }}3)\) .</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><span>Write down the coordinates of the second point where this tangent intersects the graph of \(y = f(x)\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A function <em>f</em> (<em>x</em>) = <em>p</em>×2<em><sup>x</sup></em> + <em>q</em> is defined by the mapping diagram below.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of</span></p>
<p><span>(i) <em>p</em> ;</span></p>
<p><span>(ii) <em>q</em> .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of <em>r </em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of <em>s </em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The number of fish, \(N\), in a pond is decreasing according to the model</p>
<p class="p1">\[N(t) = a{b^{ - t}} + 40,\;\;\;t \geqslant 0\]</p>
<p class="p2"><span class="s1">where \(a\) and \(b\) are positive constants, and \(t\) </span>is the time in months since the number of fish in the pond was first counted.</p>
<p class="p2">At the beginning \(840\) <span class="s1">fish were counted.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of \(a\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">After \(4\)<span class="s1"> </span>months \(90\)<span class="s1"> </span>fish were counted.</p>
<p class="p1">Find the value of \(b\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The number of fish in the pond will <strong>not </strong>decrease below \(p\).</p>
<p class="p1">Write down the value of \(p\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The size of a computer screen is the length of its diagonal. Zuzana buys a rectangular computer screen with a size of 68 cm, a height of \(y\) cm and a width of \(x\) cm, as shown in the diagram.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="images/Schermafbeelding_2018-02-12_om_18.05.15.png" alt="N17/5/MATSD/SP1/ENG/TZ0/06"></p>
</div>
<div class="specification">
<p>The ratio between the height and the width of the screen is 3:4.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use this information to write down an equation involving \(x\) and \(y\).</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>Use this ratio to write down \(y\) in terms of \(x\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(x\) and of \(y\)<em>.</em></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Gabriella purchases a new car.</p>
<p class="p1">The car’s value in dollars, \(V\), is modelled by the function</p>
<p class="p1">\[V(t) = 12870 - k{(1.1)^t},{\text{ }}t \geqslant 0\]</p>
<p class="p1">where \(t\) is the number of years since the car was purchased and \(k\) is a constant.</p>
</div>
<div class="specification">
<p class="p1">After two years, the car’s value is <span class="s1">$9143.20</span>.</p>
</div>
<div class="specification">
<p class="p1">This model is defined for \(0 \leqslant t \leqslant n\). At \(n\) years the car’s value will be zero dollars.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down, and simplify, an expression for the car’s value when Gabriella <span class="s1">purchased it.</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 class="p1">Find the value of \(k\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of \(n\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Factorise the expression \({x^2} - 3x - 10\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A function is defined as \(f(x) = 1 + {x^3}\) for \(x \in \mathbb{Z}{\text{, }} {- 3} \leqslant x \leqslant 3\).</span></p>
<p><span>(i) List the elements of the domain of \(f(x)\).</span></p>
<p><span>(ii) Write down the range of \(f(x)\).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the quadratic function \(f\left( x \right) = a{x^2} + bx + 22\).</p>
<p>The equation of the line of symmetry of the graph \(y = f\left( x \right){\text{ is }}x = 1.75\).</p>
</div>
<div class="specification">
<p>The graph intersects the <em>x</em>-axis at the point (−2 , 0).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using only this information, write down an equation in terms of <em>a</em> and <em>b</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using this information, write down a second equation in terms of <em>a</em> and <em>b</em>.</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>Hence find the value of <em>a</em> and of <em>b</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The graph intersects the <em>x</em>-axis at a second point, P.</p>
<p>Find the <em>x</em>-coordinate of P.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The golden ratio, \(r\) , was considered by the Ancient Greeks to be the perfect ratio between the lengths of two adjacent sides of a rectangle. The exact value of \(r\) is \(\frac{{1 + \sqrt 5 }}{2}\).</p>
<p>Write down the value of \(r\)</p>
<p>i) correct to \(5\) significant figures;</p>
<p>ii) correct to \(2\) decimal places.</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>Phidias is designing rectangular windows with adjacent sides of length \(x\) metres and \(y\) metres. The area of each window is \(1\,{{\text{m}}^2}\).</p>
<p>Write down an equation to describe this information.</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>Phidias designs the windows so that the ratio between the longer side, \(y\) , and the shorter side, \(x\) , is the golden ratio, \(r\).</p>
<p>Write down an equation in \(y\) , \(x\) and \(r\) to describe this information.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(x\) .</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The graph of the quadratic function \(f (x) = c + bx − x^2\) intersects the <em>y</em>-axis at point A(0, 5) and has its vertex at point B(2, 9).</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of <em>c</em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of <em>b</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the <em>x</em>-intercepts of the graph of <em>f</em> .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down \(f (x)\) in the form \(f (x) = −(x − p) (x + q)\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A building company has many rectangular construction sites, of varying widths, along a road.</p>
<p class="p1">The area, \(A\), of each site is given by the function</p>
<p class="p1">\[A(x) = x(200 - x)\]</p>
<p class="p1">where \(x\) is the <strong>width </strong>of the site in metres and \(20 \leqslant x \leqslant 180\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Site <span class="s1">S </span>has a width of \(20\)<span class="s1"> m</span>. Write down the area of <span class="s1">S</span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Site <span class="s1">T </span>has the same area as site <span class="s1">S</span>, but a different width. Find the width of <span class="s1">T</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 class="p1">When the width of the construction site is \(b\) metres, the site has a maximum area.</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>Write down the value of \(b\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Write down the maximum area.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The range of \(A(x)\) is \(m \leqslant A(x) \leqslant n\).</p>
<p class="p1">Hence write down the value of \(m\) and of \(n\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p style="text-align: left;"><span style="font-size: medium; font-family: times new roman,times;">A quadratic function, \(f(x) = a{x^2} + bx\), is represented by the mapping diagram below.</span></p>
<p style="text-align: center;"><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use the mapping diagram to write down <strong>two</strong> equations in terms of <em>a</em> and<em> b</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of</span><span> <em>a</em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of <em>b</em>.</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><span>Calculate the <em>x</em>-coordinate of the vertex of the graph of <em>f </em>(<em>x</em>).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">An iron bar is heated. Its length, \(L\), in millimetres can be modelled by a linear function, \(L = mT + c\), where \(T\) <span class="s1">is the temperature measured in degrees Celsius (°C)</span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">At <span class="s1">150°</span><span class="s1">C </span>the length of the iron bar is <span class="s1">180 mm</span>.</p>
<p class="p1">Write down an equation that shows this information.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">At <span class="s1">210°</span><span class="s1">C </span>the length of the iron bar is <span class="s1">181.5 mm</span>.</p>
<p class="p1">Write down an equation that shows this second piece of information.</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 class="p1">At <span class="s1">210°</span><span class="s1">C </span>the length of the iron bar is <span class="s1">181.5 mm</span>.</p>
<p class="p1">Hence, find the length of the iron bar at <span class="s1">40°</span><span class="s1">C</span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Consider the quadratic function <em>y</em> = <em>f</em> (<em>x</em>) , where <em>f</em> (<em>x</em>) = 5 − <em>x</em> + <em>ax</em><sup>2</sup>.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>It is given that <em>f</em> (2) = −5 . Find the value of <em>a</em> .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the equation of the axis of symmetry of the graph of <em>y</em> = <em>f</em> (<em>x</em>) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the range of this quadratic function.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The following is the graph of the quadratic function <em>y</em> = <em>f</em> (<em>x</em>).</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the solutions to the equation <em>f</em> (<em>x</em>) = 0.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the equation of the axis of symmetry of the graph of <em>f</em> (<em>x</em>).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The equation <em>f</em> (<em>x</em>) = 12 has two solutions. One of these solutions is <em>x</em> = 6. Use the symmetry of the graph to find the other solution.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The minimum value for <em>y</em> is – 4. Write down the range of <em>f</em> (<em>x</em>).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A quadratic curve with equation <em>y</em> = <em>ax</em> (<em>x</em> − <em>b</em>) is shown in the following diagram.</span></p>
<p style="text-align: center;"><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The <em>x</em>-intercepts are at (0, 0) and (6, 0), and the vertex V is at (<em>h</em>, 8).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of <em>h</em>. </span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the equation of the curve.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Factorise the expression \({x^2} - kx\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Hence solve the equation \({x^2} - kx = 0\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The diagram below shows the graph of the function \(f(x) = {x^2} - kx\) for a particular value of \(k\).<br></span></p>
<p><br><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Write down the value of \(k\) for this function.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The diagram below shows the graph of the function \(f(x) = {x^2} - kx\) for a particular value of \(k\).<br></span></p>
<p><br><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Find the minimum value of the function \(y = f(x)\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the graph of the function \(y = f(x)\) defined below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Write down <strong>all</strong> the labelled points on the curve</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>that are local maximum points;</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>where the function attains its least value;</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>where the function attains its greatest value;</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>where the gradient of the tangent to the curve is positive;</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>where \(f(x) > 0\) and \(f'(x) < 0\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Consider the function \(f(x) = a{x^2} + c\).</p>
<p>Find \(f'(x)\)</p>
<p> </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>Point \({\text{A}}( - 2,\,5)\) lies on the graph of \(y = f(x)\) . The gradient of the tangent to this graph at \({\text{A}}\) is \( - 6\) .</p>
<p>Find the value of \(a\) .</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(c\) .</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram shows part of the graph of a function \(y = f(x)\). The graph passes through point \({\text{A}}(1,{\text{ }}3)\).</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_06.22.37.png" alt="M17/5/MATSD/SP1/ENG/TZ2/13"></p>
</div>
<div class="specification">
<p>The tangent to the graph of \(y = f(x)\) at A has equation \(y = - 2x + 5\). Let \(N\) be the normal to the graph of \(y = f(x)\) at A.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of \(f(1)\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of \(N\). Give your answer in the form \(ax + by + d = 0\) where \(a\), \(b\), \(d \in \mathbb{Z}\).</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>Draw the line \(N\) on the diagram above.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Water has a lower boiling point at higher altitudes. The relationship between the boiling point of water (<em>T</em>) and the height above sea level (<em>h</em>) can be described by the model \(T = -0.0034h +100\) where <em>T</em> is measured in degrees Celsius (</span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">°</span>C) and <em>h</em> is measured in metres from sea level.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the boiling point of water at sea level.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use the model to calculate the boiling point of water at a height of 1.37 km above sea level.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Water boils at the top of Mt. Everest at 70 </span><span><span>°</span>C.</span></p>
<p><span>Use the model to calculate the height above sea level of Mt. Everest.<br></span></p>
<p><span> </span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p>Consider the following graphs of quadratic functions.</p>
<p><img src="images/Schermafbeelding_2017-08-16_om_06.31.16.png" alt="M17/5/MATSD/SP1/ENG/TZ2/15"></p>
<p>The equation of each of the quadratic functions can be written in the form \(y = a{x^2} + bx + c\), where \(a \ne 0\).</p>
<p>Each of the sets of conditions for the constants \(a\), \(b\) and \(c\), in the table below, corresponds to one of the graphs above.</p>
<p>Write down the number of the corresponding graph next to each set of conditions.</p>
<p> <img src="images/Schermafbeelding_2017-08-16_om_06.39.22.png" alt="M17/5/MATSD/SP1/ENG/TZ2/15_02"></p>
</div>
<br><hr><br><div class="specification">
<p>The following function models the growth of a bacteria population in an experiment,</p>
<p style="text-align: center;"><em>P</em>(<em>t</em>) = <em>A</em> × 2<sup><em>t</em></sup>, <em>t</em> ≥ 0</p>
<p>where <em>A</em> is a constant and t is the time, in hours, since the experiment began.</p>
<p>Four hours after the experiment began, the bacteria population is 6400.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>A</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>Interpret what <em>A</em> represents in this context.</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 time since the experiment began for the bacteria population to be equal to 40<em>A</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the function \(f(x) = p{(0.5)^x} + q\) where <em>p</em> and <em>q</em> are constants. The graph of <em>f</em> (<em>x</em>) passes through the points \((0,\,6)\) and \((1,\,4)\) and is shown below.</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down two equations relating <em>p</em> and <em>q</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of <em>p</em> and of <em>q</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the equation of the horizontal asymptote to the graph of <em>f</em> (<em>x</em>).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A population of mosquitoes decreases exponentially. The size of the population, \(P\) , after \(t\) days is modelled by</p>
<p>\(P = 3200 \times {2^{ - t}} + 50\) , where \(t \geqslant 0\) .</p>
<p>Write down the <strong>exact</strong> size of the initial population.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the size of the population after \(4\) days.</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>Calculate the time it will take for the size of the population to decrease to \(60\).</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>The population will stabilize when it reaches a size of \(k\) .</p>
<p>Write down the value of \(k\) .</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The function \(g(x)\) is defined as \(g(x) = 16 + k({c^{ - x}})\) where \(c > 0\) .</span><br><span style="font-size: medium; font-family: times new roman,times;">The graph of the function \(g\) is drawn below on the domain \(x \geqslant 0\) .</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The graph of \(g\) intersects the <em>y</em>-axis at (0, 80) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of \(k\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The graph passes through the point (2, 48) . </span></p>
<p><span>Find the value of \(c\) .</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><span>The graph passes through the point (2, 48) . </span></p>
<p><span>Write down the equation of the horizontal asymptote to the graph of \(y = g(x)\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the function \(f(x) = 1.25 - {a^{ - x}}\) , where a is a positive constant and \(x \geqslant 0\). The diagram shows a sketch of the graph of \(f\) . The graph intersects the \(y\)-axis at point A and the line \(L\) is its horizontal asymptote.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the \(y\)-coordinate of A .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The point \((2{\text{, }}1)\) lies on the graph of \(y = f(x)\) . Calculate the value of \(a\) .</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><span>The point \((2{\text{, }}1)\) lies on the graph of \(y = f(x)\) . Write down the equation of \(L\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the graph of the function \(f\left( x \right) = \frac{3}{x} - 2,\,\,\,x \ne 0\).</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">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation of the horizontal asymptote.</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>Calculate the value of <em>x</em> for which <em>f</em>(<em>x</em>) = 0 .</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A population of \(200\) rabbits was introduced to an island. One week later the number of rabbits was \(210\). The number of rabbits, \(N\) , can be modelled by the function</p>
<p>\[N(t) = 200 \times {b^t},\,\,t \geqslant 0\,,\]</p>
<p>where \(t\) is the time, in weeks, since the rabbits were introduced to the island.</p>
<p>Find the value of \(b\) .</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the number of rabbits on the island after 10 weeks.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>An ecologist estimates that the island has enough food to support a maximum population of 1000 rabbits.</p>
<p>Calculate the number of weeks it takes for the rabbit population to reach this maximum.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A rumour spreads through a group of teenagers according to the exponential model</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;">\(N = 2 \times {(1.81)^{0.7t}}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">where <em>N</em> is the number of teenagers who have heard the rumour <em>t</em> hours after it is first started.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number of teenagers who started the rumour.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of teenagers who have heard the rumour five hours after it is first started.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Determine the length of time it would take for 150 teenagers to have heard the rumour. <strong>Give your answer correct to the nearest minute.</strong></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Jashanti is saving money to buy a car. The price of the car, in US Dollars (USD), can be modelled by the equation</p>
<p>\[P = 8500{\text{ }}{(0.95)^t}.\]</p>
<p>Jashanti’s savings, in USD, can be modelled by the equation</p>
<p>\[S = 400t + 2000.\]</p>
<p>In both equations \(t\) is the time in months since Jashanti started saving for the car.</p>
</div>
<div class="specification">
<p>Jashanti does not want to wait too long and wants to buy the car two months after she started saving. She decides to ask her parents for the extra money that she needs.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the amount of money Jashanti saves per month.</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>Use your graphic display calculator to find how long it will take for Jashanti to have saved enough money to buy the car.</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>Calculate how much extra money Jashanti needs.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The \(x\)-coordinate of the minimum point of the quadratic function \(f(x) = 2{x^2} + kx + 4\) is \(x =1.25\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Find the value of \(k\) .</span></p>
<p><span>(ii) Calculate the \(y\)-coordinate of this minimum point.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Sketch the graph of \(y = f(x)\) for the domain \( - 1 \leqslant x \leqslant 3\).</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagram shows part of the graph of \(y = 2^{-x} + 3 \), and its horizontal asymptote.</span> <span style="font-family: times new roman,times; font-size: medium;">The graph passes through the points (0, </span><span style="font-family: times new roman,times; font-size: medium;"><em><span style="font-family: times new roman,times; font-size: medium;">a</span></em>) and (</span><span style="font-family: times new roman,times; font-size: medium;"><em><span style="font-family: times new roman,times; font-size: medium;">b</span></em>, 3.5).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of</span></p>
<p><span>(i) <em>a</em> ;</span></p>
<p><span>(ii) <em>b</em> .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the equation of the horizontal asymptote to this graph.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">In an experiment it is found that a culture of bacteria triples in number every four hours. There are \(200\) bacteria at the start of the experiment.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of \(a\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate how many bacteria there will be after one day.</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><span>Find how long it will take for there to be two million bacteria.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The diagram below shows the graph of a quadratic function. The graph passes through the points (6, 0) and (<em>p</em>, 0). The maximum point has coordinates (0.5, 30.25).</span></p>
<p style="text-align: center;"><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the value of <em>p</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Given that the quadratic function has an equation \(y = -x^2 + bx + c\) where \(b,{\text{ }}c \in \mathbb{Z}\), find \(b\) and \(c\).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The number of cells, <em>C</em>, in a culture is given by the equation \(C = p \times 2^{0.5t} + q\), where <em>t</em> is the time in hours measured from 12:00 on Monday and <em>p</em> and <em>q</em> are constants.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The number of cells in the culture at 12:00 on Monday is 47.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The number of cells in the culture at 16:00 on Monday is 53.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use the above information to </span><span>write down two equations in <em>p</em> and <em>q</em> ;</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use the above information to </span><span>calculate the value of <em>p</em> and of <em>q</em> ;</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use the above information to </span><span>find the number of cells in the culture at 22:00 on Monday.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The graph of a quadratic function has \(y\)-intercept 10 and <strong>one </strong>of its \(x\)-intercepts is 1.</p>
<p>The \(x\)-coordinate of the vertex of the graph is 3.</p>
<p>The equation of the quadratic function is in the form \(y = a{x^2} + bx + c\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of \(c\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(a\) and of \(b\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the second \(x\)-intercept of the function.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The amount of electrical charge, <em>C</em>, stored in a mobile phone battery is modelled by \(C(t) = 2.5 - {2^{ - t}}\), where <em>t</em>, in hours, is the time for which the battery is being charged.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><br><img src="images/Schermafbeelding_2014-09-20_om_13.45.23.png" alt><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"> </p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the amount of electrical charge in the battery at \(t = 0\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The line \(L\) is the horizontal asymptote to the graph.</span></p>
<p><span>Write down the equation of \(L\).</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><span>To download a game to the mobile phone, an electrical charge of 2.4 units is needed.</span></p>
<p><span>Find the time taken to reach this charge. Give your answer correct to the nearest minute.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The function \(f\) is of the form \(f(x) = ax + b + \frac{c}{x}\), where \(a\) , \(b\) and \(c\) are positive integers.</p>
<p>Part of the graph of \(y = f(x)\) is shown on the axes below. The graph of the function has its local maximum at \(( - 2,{\text{ }} - 2)\) and its local minimum at \((2,{\text{ }}6)\).</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>Write down the domain of the function.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the line \(y = - 6\) 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 \(f(x) = - 6\).</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 \(k\) for which \(f(x) = k\) has no solution.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">A computer virus spreads according to the exponential model</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\[N = 200 \times {(1.9)^{0.85t}},{\text{ }}t \geqslant 0\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">where \(N\) is the number of computers infected, and \(t\) is the time, in hours, after the initial infection.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the number of computers infected after \(6\) hours.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the time for the number of infected computers to be greater than \({\text{1}}\,{\text{000}}\,{\text{000}}\).</span></p>
<p><span>Give your answer correct to the nearest hour.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Passengers of Flyaway Airlines can purchase tickets for either Business Class or Economy Class.</p>
<p class="p2">On one particular flight there were <span class="s1">154 </span><span class="s2">passengers.</span></p>
<p class="p2">Let \(x\) be the number of Business Class passengers and \(y\) be the number of Economy Class passengers on this flight.</p>
</div>
<div class="specification">
<p class="p1">On this flight, the cost of a ticket for each Business Class passenger was <span class="s1">320 </span>euros and the cost of a ticket for each Economy Class passenger was <span class="s1">85 </span>euros. The total amount that Flyaway Airlines received for these tickets was \({\text{14}}\,{\text{970 euros}}\).</p>
</div>
<div class="specification">
<p class="p1">The airline’s finance officer wrote down the total amount received by the airline for these tickets as \({\text{14}}\,{\text{270 euros}}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Use the above information to write down an equation in \(x\) <span class="s1">and \(y\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Use the information about the cost of tickets to write down a second equation <span class="s1">in \(x\) and \(y\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of \(x\) <span class="s1">and the value of \(y\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the percentage error.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The graph of <em>y </em>= 2<em>x</em><sup>2</sup> \( - \) <em>rx </em>+ <em>q</em> is shown for \( - 5 \leqslant x \leqslant 7\).</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The graph cuts the <em>y</em> axis at (0, 4).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of <em>q</em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The axis of symmetry is <em>x</em> = 2.5.</span></p>
<p><span>Find the value of <em>r</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The axis of symmetry is <em>x</em> = 2.5.</p>
<p><span>Write down the minimum value of <em>y</em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span><span>The axis of symmetry is <em>x</em> = 2.5.</span>x</span></span></p>
<p><span><span>Write down the range of</span> <span><em>y</em>.</span></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A function \(f\) is given by \(f(x) = 4{x^3} + \frac{3}{{{x^2}}} - 3,{\text{ }}x \ne 0\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the derivative of \(f\).</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 point on the graph of \(f\) at which the gradient of the tangent is equal to 6.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A store sells bread and milk. On Tuesday, 8 loaves of bread and 5 litres of milk were sold for $21.40. On Thursday, 6 loaves of bread and 9 litres of milk were sold for $23.40. </span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">If \(b =\) the price of a loaf of bread and \(m =\) the price of one litre of milk, Tuesday’s sales can be written</span> <span style="font-size: medium; font-family: times new roman,times;">as \(8b + 5m = 21.40\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using simplest terms, write an equation in <em>b</em> and <em>m</em> for Thursday’s sales.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find <em>b</em> and <em>m</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a sketch, in the space provided, to show how the prices can be found graphically.</span></p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAcMAAAD3CAIAAADueKiGAAALlElEQVR4nO3dv2sbacLAcf8nEkwlgSAv17hy9RZZF8IcVxy42cMxZIuFFFscJ6HA8XYHMjGBhcAik7DwcrDIZIsXjixDmnB4Ee9bbCEG9iBshAqzBDGFEcswb+Ef5zgbe7JPohnZnw9TxEYiw8T+5nlmHs2s5ACEWSntb57F3UY9qh1vm3vJUWl7AhCmrJLOJ8N7rdppSduDJCtpRwCClVTS9GCn/dd4Jp/AdVBKSbNZ3GvVmuudr/bjJC1jDwA+oDJKmo332s3TM6TN9c4wSd85OI3OzgCcbj///PMidxbgSuVdccqmo6dfdW83o1pzvX/wrpHp2yVNkmSh+wlwlfJKeiybxL121OgVOWeaJImSAhVUdknz4+VQa9348MoXKilQTRUoaTbea39aZD2pkgLVVIGSzuL7vXhW4IVKClRTCSXNpqNvn46m2fGfX+x2+vF0XuSNSgpUUyklfXb/djOq1aPGnZ1vnl+yBOoCJQWqqQKz+8KUFKgmJQUIpaQAoZQUIJSSAoRSUoBQSgoQSkkBQikpQCglBQilpAChlBQglJIChFJSgFBKChBKSQFCKSlAKCUFCKWkAKGUFCCUkgKEUlKAUEoKEKrcks4nw3ut9iAp9sR7JQWqqcySZpPhZ416pKTAkiuvpOnBztYX3a1VJQWWXVklfT3qf7EzSuLOmpICy66Ukmbp6OF2/yDND4uUNKrVL2yL2k+AQsooaXqws/VwlGa5kgLXwuJL+nr04G/7k3me5wVLesbsHqimBZc0S0eP7g9fnpZTSYHrYMElPYw7a2/P1qNac2MwvjKnSgpUU7kr841JgetASQFCKSlAKHcwAQilpAChlBQglJIChFJSgFBKChBKSQFCKSlAKCUFCKWkAKGUFCCUkgKEUlKAUEoKEEpJAUIpKUAoJQUIpaQAoZQUIJSSAoRSUoBQSgoQqpSSzqcHX2436lGtud4ZJmmxZzQrKVBViy9plv7v0ycH0yzPs+mL3a3VVieeFXunkgLVtPCSZv96/vyn01FoNot7rUYvnhUaliopUE3lnic9SgafrvcP0mKvVlKgmsoraZrEg95279m06GlSJQUqqpSSZrO416rVo1o9ut3bT644TRodv/J0U1Kgakqc3c+no6+7t5tR497+ZH7J65QUqLiS15NmyWCjttaND4u82OweqKayV+Zn4732fyopsNTKLuks7t66YnZ/RkmBalp0SbPJ8LNGu/v4eGn+JO5tbg9+sAoKWGoLH5OmP+xtrR5fO2pt9fdHxRdBKSlQUWXP7t+HkgLVpKQAoZQUIJSSAoRSUoBQSgoQaiWfDreP1yR14lk63u+0o9rqZ8OXWT5Lnu1uN+pRe5AUX6n0MSkpUE0reZ7ns7jbWOsOn+11+vFPL3Zu1X/Xf/FT3O8OXsT9T6LCd2L+2JQUqKaV03vcfbJ9t7c3nuXT4XZt7c9ffXn/wUGaH8adNWNSgMut5PlRMtiMas2NwTg7u3Po7d1RmuWzuNs4/n4lKClQTSt5Nt5rN0+n8IdxZy2q/X5n9Pp0rLq5lxyVvZMnlBSoppU3Bp7HVT2Zzh8lg83qnCTNlRSoqpXjk6Q7ozQ/ue/yG1Vtdf7+3eC/R4UfSf9RKSlQTSvnBp5vTud/Ge3cKvScpYVRUqCarMwHCKWkAKGUFCCUkgKEUlKAUEoKEEpJAUIpKUAoJQUIpaQAoZQUIJSSAoQqo6Rp8l3/TqtWj2rN9c7Xo+m84PuUFKimhZc0e/ntg0ffJbM8z7Ppi92t1ZP78xegpEA1Lbqk2Y8vnk/+PQjNksFGba0bHxZ5r5IC1VT2edLjx5oqKbDMKlDSW/f2J4VOlSopUE3lljSbxX/d6B+kxV6tpEA1lVrS9GBn6+Hll5uiWv3CpqRA1ZRY0tejB/+1N77iIVFKClRfWSWdT54+enJVRi8wuweqqZSSzqfxo914cjqrn40ff/18dvWSUiUFqmnxJZ0lw976hTl7e5AUWJuvpEA1Lbik88nwXuviqc/mxmBc5ENOSgpUU9nrSd+HkgLVpKQAoZQUIJSSAoRSUoBQSgoQSkkBQikpQCglBQilpAChlBQglJIChFJSgFBKChBKSQFCKSlAKCUFCKWkAKGUFCCUkgKEUlKAUEoKEEpJAUKVVdIsTZ7vf9PfvtWLZ0WedZ/nSgpUVTklzZLBHz6986dGPWooKbD0SpzdHyWDTSUFrgElBQilpAChlBQg1BKUNKrVz29KClSNkgKEWoKSnjG7B6pJSQFCKSlAqJJKOou7jbNTn82NwbhITZUUqCZ3MAEIpaQAoZQUIJSSAoRSUoBQSgoQSkkBQikpQCglBQilpAChlBQglJIChFJSgFBKChBKSQFCKSlAKCUFCKWkAKGUFCCUkgKEUlKAUEoKEEpJAUIpKUAoJQUIVUZJs+nocWe9Vo8ad3YPplnh9ykpUE2LL+nrUf+P671n0yzPps/u3/7jzuh1wXcqKVBNiy5plgw2Gr14djwSzWZxr9UeJMXGpUoKVNOCS3qUDDaj8+mcxd3G5l5yVOTNSgpU02JLmo332s1WJ56dfWcWdxvNjcG4yKhUSYFqWmxJ3+7mVSWNanWbzWar4Ha+VEpqs9lsv2U7Xyqz++vm7X9jznN8CnKgLlF2SfOjZLB5vqRZMtioueL0IfkFuJzjU5ADdYnSS2oV1EfnF+Byjk9BDtQlyi9pyMr8V69edf7yl1evXn3U/Vt2fgEu5/gU5EBdogolzfNs+v2DO61aPbrdeTJ6j0+LUoRfAFi8ZbqDCUA1KSlAKCUFCKWkAKGUFCCUkgKEUlKAUEoKEEpJr5MsTZ7vf9PfvnX2eVzOZGnyj52t1ahWj2rt7uP3eYLYTXP22Zlauzscp2XvTiXNJ8N75z/pviQl/a0P0btRsmTwh0/v/KlRjxpKelE2+Z/dB/9I0izP59ODL7cbzfX+gUb8mtf/N/zm++n89ECtdePDsnepcrLJ8LNGPVq2kv72j+rfPEfJYFNJ33L04/N/Tv59SByld8p+fPF8Mj/96jDurL1xG0zyPE8Pdra+6G6tLllJQ24fdfNoRBHZLO61HKUrZeO9toHLBa9H/S92RkncWVuukgY9RO/mUdIislnc+93d4cRBeqcsTeK9zuf3YwfpvCwdPdzuH6T54bKVNOw2+zePkhZxGHfuGGq922HcWYtq9ajWXO8Mk9TP0qn0YGfr4SjN8uUr6fs/+ulmU9IrnQ0ruNTpZd6WwfuJ16MHf9s/OYmspNeckl4lPdjtfD02zirEj9OZLB09uj98eXoglq6kZvfvx4/+pbKX3z74u4wW9+b13pvs7IzHhe2kRZUvadhD9G4eJX23bBI/eBRPT5f4pD88GbywvudSLs29y9KNSa2Cej9K+g7peL/T/tXRBOfMJ8N7rdPHAmXTZ/fbn++N/XfztiUsqZX5Rc3ibkMmfk32cv/u6lvzMjObt2Xp+Mn2yU/R6nZ/ODobwvOGpSyph+gBlbYkJQWoMCUFCKWkAKGUFCCUkgKEUlKAUEoKEEpJAUIpKUAoJQUIpaQAoZQUIJSSAoRSUoBQSgoQSkkBQikpQCglBQilpAChlJSb4Jfp8POTB+FtDadl7w3Xj5JyY8zibsMjV/kolJQbIpvFvZYnM/NxKCk3xGHcWYtu9Ue/lL0jXEdKys3wy2jnVr3ViWdl7wjXkpJyI2TJYKO29ufB0yeddlSrR7V2dzhOy94rrg0l5SY4uXbf2vry++k8T3/Y21qNnDPlw1FSboLDuLMW3d4dpcfX7Y/D+snOyKiUD0NJuQEurn86SgabUe3z/anLT3wYSsr1d3yStBsfnn493ms3W3eHEytL+UCUlGvvKBlsRo1ePDsO53wyvNdq3N0bu4zPB6OkXHs/7W/9x8n6p2w6etxZr7Xvx8ajfEhKyrU3n46GO1urUa0e1ZrrnUGcGI3ygSkpQCglBQj1/0dmnfcCK+RdAAAAAElFTkSuQmCC" alt></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A hotel has a rectangular swimming pool. Its length is \(x\) metres, its width is \(y\) metres and its perimeter is \(44\) metres.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down an equation for \(x\) and \(y\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The area of the swimming pool is \({\text{112}}{{\text{m}}^2}\).</p>
<p class="p1">Write down a second equation for \(x\) and \(y\).</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 class="p1">Use your graphic display calculator to find the value of \(x\) and the value of \(y\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">An Olympic sized swimming pool is \(50\) m long and \(25\) m wide.</p>
<p class="p1">Determine the area of the hotel swimming pool as a percentage of the area of an Olympic sized swimming pool.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Part of the graph of the quadratic function <em>f</em> is given in the diagram below.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">On this graph one of the <em>x</em>-intercepts is the point (5, 0). The <em>x</em>-coordinate of the maximum point is 3.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The function <em>f</em> is given by \( f (x) = -x^2 + bx + c \), where \(b,c \in \mathbb{Z}\)</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of</span></p>
<p><span>(i) <em>b</em> ;</span></p>
<p><span>(ii) <em>c</em> .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The domain of <em>f</em> is 0 </span><span><span><span>≤</span></span> </span><em><span> x </span></em><span><span>≤</span></span><span> 6.</span></p>
<p><span>Find the range of <em>f</em> .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>In an experiment, a number of fruit flies are placed in a container. The population of fruit flies, <em>P</em> , increases and can be modelled by the function</p>
<p>\[P\left( t \right) = 12 \times {3^{0.498t}},\,\,t \geqslant 0,\]</p>
<p>where <em>t</em> is the number of days since the fruit flies were placed in the container.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of fruit flies which were placed in the container.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of fruit flies that are in the container after 6 days.</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>The maximum capacity of the container is 8000 fruit flies.</p>
<p>Find the number of days until the container reaches its maximum capacity.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>On the grid below sketch the graph of the function \(f(x) = 2{(1.6)^x}\) for the domain \(0 \leqslant x \leqslant 3\) .</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the coordinates of the \(y\)-intercept of the graph of \(y = f(x)\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>On the grid draw the graph of the function \(g(x) = 5 - 2x\) for the domain \(0 \leqslant x \leqslant 3\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to solve \(f(x) = g(x)\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The graph of the quadratic function \(f(x) = c + bx - {x^2}\) intersects the \(x\)-axis at the point \({\text{A}}( - 1,{\text{ }}0)\) and has its vertex at the point \({\text{B}}(3,{\text{ }}16)\).</p>
<p class="p1" 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 class="p1">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 class="p1">Find the value of \(b\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down the range of \(f(x)\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The graph of the quadratic function \(f(x) = a{x^2} + bx + c\) intersects the <em>y</em>-axis at point A (0, 5) and has its vertex at point B (4, 13).</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><br><img src="images/Schermafbeelding_2014-09-20_om_14.11.23.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of \(c\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>By using the coordinates of the vertex, B, or otherwise, write down <strong>two </strong>equations in \(a\) and \(b\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of \(a\) and of \(b\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider the functions \(f(x) = x + 1\) and \(g(x) = {3^x} - 2\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>the \(x\)-intercept of the graph of \(y = {\text{ }}f(x)\);</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>the \(y\)-intercept of the graph of \(y = {\text{ }}g(x)\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Solve \(f(x) = g(x)\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down the interval for the values of \(x\) for which \(f(x) > g(x)\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">A quadratic function \(f:x \mapsto a{x^2} + b\), where \(a\) and \(b \in \mathbb{R}\) and \(x \geqslant 0\), is represented by the mapping diagram.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><br><span style="font-family: 'times new roman', times; font-size: medium;"><img src="images/Schermafbeelding_2014-09-03_om_08.19.32.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using the mapping diagram, write down two equations in terms of \(a\) and \(b\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Solve the equations to find the value of</span></p>
<p><span>(i) \(a\);</span></p>
<p><span>(ii) \(b\).</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><span>Find the value of \(c\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the straight lines <em>L</em><sub>1</sub> and <em>L</em><sub>2 </sub>. <em>R</em> is the point of intersection of these lines.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The equation of line <em>L</em><sub>1</sub> is <em>y</em> = <em>ax</em> + 5.</p>
</div>
<div class="specification">
<p>The equation of line <em>L</em><sub>2</sub> is <em>y</em> = −2<em>x</em> + 3.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>a</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>Find the coordinates of <em>R</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Line <em>L</em><sub>3</sub> is parallel to line <em>L</em><sub>2</sub> and passes through the point (2, 3).</p>
<p>Find the equation of line <em>L</em><sub>3</sub>. Give your answer in the form <em>y</em> = <em>mx</em> + <em>c</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The graph of a quadratic function \(y = f (x)\) is given below.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the equation of the axis of symmetry.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the coordinates of the minimum point.</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><span>Write down the range of \(f (x)\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A small manufacturing company makes and sells \(x\) machines each month. The monthly cost \(C\) , in dollars, of making \(x\) machines is given by</span><br><span style="font-family: times new roman,times; font-size: medium;">\[C(x) = 2600 + 0.4{x^2}{\text{.}}\]</span><span style="font-family: times new roman,times; font-size: medium;">The monthly income \(I\) , in dollars, obtained by selling \(x\) machines is given by</span><br><span style="font-family: times new roman,times; font-size: medium;">\[I(x) = 150x - 0.6{x^2}{\text{.}}\]</span><span style="font-family: times new roman,times; font-size: medium;">\(P(x)\) is the monthly profit obtained by selling \(x\) machines.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \(P(x)\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number of machines that should be made and sold each month to maximize \(P(x)\) .</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><span><span>Use your answer to part (b) to find the selling price of</span> <span><strong>each machine</strong> in order to maximize \(P(x)\) .</span></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Consider the function \(f(x) = {x^3} - 3{x^2} + 2x + 2\) . Part of the graph of \(f\) is shown below.</p>
<p><img src="data:image/png;base64,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" alt></p>
<p>Find \(f'(x)\) .</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>There are two points at which the gradient of the graph of \(f\) is \(11\). Find the \(x\)-coordinates of these points.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the functions \(f\left( x \right) = {x^4} - 2\) and \(g\left( x \right) = {x^3} - 4{x^2} + 2x + 6\)</p>
<p>The functions intersect at points P and Q. Part of the graph of \(y = f\left( x \right)\) and part of the graph of \(y = g\left( x \right)\) 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 \(f\left( x \right) > g\left( x \right)\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A factory produces shirts. The cost, <em>C</em>, in Fijian dollars (FJD), of producing<em> x</em> shirts can be modelled by</p>
<p style="text-align: center;"><em>C</em>(<em>x</em>) = (<em>x</em> − 75)<sup>2</sup> + 100.</p>
</div>
<div class="specification">
<p>The cost of production should not exceed 500 FJD. To do this the factory needs to produce at least 55 shirts and at most <em>s</em> shirts.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the cost of producing 70 shirts.</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 <em>s</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of shirts produced when the cost of production is lowest.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The graph of the quadratic function \(f(x) = 3 + 4x - {x^2}\) intersects the \(y\)-axis at point A and has its vertex at point B .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAuoAAAGYCAIAAACbB1CmAAAfRElEQVR4nO3df4ykZ2HY8fxz2r+xFEuNGu3p1kYm4lcwO0FIOFKVtNiJu+OqoQTUBNfjYiIFN4gdozghcsyoMW0w0k6RsP+At62pSpk4IbWlcWXchjeViThNDTXSa9pDYVK7OneOHweD8V12+scLy/p2b3d25n3nfZ/3+Xw0f9i+vd3H9t3td573+fFTMwCAoPxU1QMAADgZ+QIABOYV+bKxftrLy8vLy8vLq4avq+ZLXjClJxMAwEnIFwAgMPIFAAiMfAEAAiNfAIDAyBcAIDDyBQAIjHwBAAIjXwCAwMgXACAw8gUACIx8AQACI18AgMDIFwAgMPIFAAiMfAEAAiNfAIDAyBcAIDDyBQAIjHwBAAIjX2iO3e99+9uXdn/0N5e+++3vXa50OACURb7QAN/92mfvv/PtN26s3/zA09+azWaz2fmn7v17G2/+SPrdv614aACUQL7QELvnH7v7uuv/wUPPXp7NZrNL55/u/+abP/j4eRMwAA0kX2iKy88+9MvXv+G+9Puz2Ww2273wF717Pv/87jE/CYAQyRcaY/ynd/z8xh2PvjCbzWYXn334/oefvbj/hyeTyWAwqGZoABRKvtAYLz51700b73jkG7u7P3j20/c8/JUfvPKHP/zhD59aWxuPx9WMDoDiyBca4+LZj9288caPnb3wV5/4gz859/IrnhtlWfa617/+ll/5le1ut6rxAVAU+UJjvPSNR27feM1vbP/uv378+Zeu+LFOp7Ozs/M7H/jAVrs9Go0qGR8ARZEvNMalFx797Y0z7/j4ly9csWA3TdOtdjvLsu1uN//r6XRazRgBKIJ8oTF++M3P3vMvHj136ZX/dDqdbrZaWZbl+TKbzba7XWt4AYImX2iGyxef/Y8f/bfPXDywU3owGOTVspcv4/F4s9WaTCarHyUAhZAvBG33B8/92Uf+8N899eRDv//RJ5+/dGW8TCaTU2treans5ctsNtvp93f6/VUPFoCCyBeC9tK5R+549Zm///6H/vsLB9plNpv1er0kSfK/3p8ve0+UVjfS5nvpxef+x9krff3Fw/6/ACxJvtBkvV5vb5Xu/nyZzWbD4XA4HFY0rkZ66cXn/mrYf+/m+umNM7e8/1/+8YMf++MH7u3c8sbrb/xHv5c8/fyl4z8DwLzkC7G4Il8oxQuP3rl+euONHzv7o1rZvXT+Lz/+a2/YOPPOf/PMd6odGtAk8oVYyJdVuDJfZrPZpfOPffCG9dOvu/cp/QIURb4QC/myCofky+ULT3zohvXTN3zwiQsVDgxoFvlCLOTLKhzIl92Lzzz8GzdurN9yf3reIl6gKPKFWMiXVcjz5cxN//ifde68o3PnHe+65Y0bG2du+8PHvn7wSB6AhckXYiFfViHPl9d+6PH/+9Ls0ovPnf3i4w9t33Lm9Mabbv/4F//G5iOgKPKFWMiXVTh07ctT9/3C+umNN937xHkBAxRDvhAL+bIKh+TLbPbS0w+8/vTG+s0Pnr1Y2cCAZpEvxEK+rMJh+bI7eaL7mtMb6+/+9HM/qG5kQKPIF2IhX1bhkJ1HX3/8vttevf7aX33gLy9YvQsURL4QC/lSsu99I/38v7/vnTesn95Y37jx7e+6847One+++cb1069+22/e9+mnD72UCmAx8oVYyBeAxpAvxEK+ADSGfCEW8gWgMeQLsZAvKzYej7Msm0wmVQ8EaCD5Qizkyyrdc88911577am1tb/7sz/74IMPVj0coGnkC7GQLyuTJMlPX3vtqbW1/PWqa64ZjUZVDwpoFPlCLORL2bIsy7JsMBi87aab9tolf3U6nTRNPUsCiiJfiIV8Kdx4PB4Oh71eb6vdzhtlu9tNkuRgvrzvfe/b6fe3u938I/MPS9N0Op1W/S8BBEm+EAv5UpTRaLTT72+2Wlvt9k6/n6bpeDze/wFPPvnkq665Zq9d/s7P/EyWZfs/IJ+k6fV6m61Wp9MZDAZXfAaAo8kXYiFfljQej/Nq6XQ6w+Hw6MdASZKsnz59am3tuuuvf/LJJ4/4yCzLkiTZarfzT2s+BpiHfCEW8mVhaZrmz30Gg0F5i1fySZ1Ta2s7/b4lMsDR5AuxkC8LSNM0nxdJ03Q1X3EymQwGg81Wa7vbveKRE8Ae+UIs5MuJ5OFSVUNMp9M8Ynq9npkY4CD5Qizky5zG43H+qKjyw1r2IiZJEmtigP3kC7GQL8eaTqdJkmy2WsPhsOqx/MRkMsn3KFWeU0B9yBdiIV+ONhqNttrtXq9Xz3mOLMvqPDxgxeQLsZAvV7M36VLz6Y1QxgmsgHwhFvLlUOPxOKxZjXwaZqffD2XAQBnkC7GQLwcNh8NTa2u1Wukyj+l02uv1Op2Os3ohWvKFWMiX/abT6U6/v9Vuh1sAw+Fws9Va2YE0QK3IF2IhX/ZMp9P8esXQn79kWZZvq656IMCqyRdiIV9y4/F4s9Xa6ferHkgxJpNJp9MJaO0OUAj5Qizky2w2G41GzXvgsrcURsFAPOQLsZAvaZo2eNfxTr9vMS/EQ74Qi8jzJW+XZn93z0+Fafa/I5CTL8Qi5nyJ5/t6DJUGzOQL8Yg2X3b6/ai+oysYiIF8IRZx5kts7ZJTMNB48oVYRJgvcbZLTsFAs8kXYhFbvuSH0sb8/VvBQIPJF2IRVb74zp3z3wGaSr4Qi3jyxffs/fLzYJxoBw0jX4hFJPmSZdmptbUsy6oeSI0oGGge+UIsYsiX/D6jht0JUIher9f4//sQFflCLBqfL9PpdKvdHg6HVQ+kjvJLthtzUSUgX4hFs/PFt+djTafTzVZL3kEzyBdi0ex8yZd3VD2KussfrjX10kqIinwhFg3Ol8FgsNVuW5o6D9uyoBnkC7Foar6MRiPfj09kMBjYiAShky/EopH54mnIYnq9Xq/Xq3oUwOLkC7FoXr7ky3WTJKl6IOHJ/9MNBoOqBwIsSL4Qi+bly06/37B/o1XKJ66c7weBki/EomH5kt/IaAHHMvJlvJPJpOqBACcmX4hFk/JlPB67GaAQNpxDoOQLsWhMvuSn61q3UQiLYCBQ8oVYNCZfLHkplkUwECL5QiyakS/5cg1LXorlvyoER74Qiwbky2QyccpLSZwEA2GRL8SiAfmy3e065aUk7uuGsMgXYhF6vjjqvmxZltlHDaGQL8Qi6HzJd0q72KhsSZKE+4sEoiJfiEXQ+WJz72rYRw2hkC/EItx8yR8bVT2KWJjogiDIF2IRaL74brp6ehHqT74Qi0DzxbOMSvjPDjUnX4hFiPliGqAqdiFBzckXYhFcvnhsVC27kKDO5AuxCC5fHFJXLQfZQZ3JF2IRVr4Mh8OtdtshddXKHyH5vwA1JF+IRUD5Mp1O3YFcE+5CgnqSL8QioHzxLbM+pCTUk3whFqHkiwcWdeNBHtSQfCEWoeSL5aI15BgYqBv5QiyCyBcHvdRTvondMTBQH/KFWNQ/XyaTiWUWteUYGKgV+UIs6p8vvV5vp9+vehQcLl/DOxqNqh4IMJvJF+JR83yxYrf+0jTdarerHgUwm8kX4lHzfLFiNwjW8EJNyBdiUed8ybfmVj0KjucqR6gJ+UIsapsvDkYLy06/b4kSVE6+EIva5ostLWGxQQzqQL4Qi3rmy2QycaBIcAaDQQ1/LUFU5AuxqGe+bHe7SZJUPQpOxiZqqJx8IRY1zBebpcNlEzVUS74Qixrmi124QbPXHSokX4hF3fLF2/fQmTyDCskXYlG3fNlqt9M0rXoULGW72zV/BpWQL8SiVvkyHA7dLN0ATrGDqsgXYlGffHFOXZM4xQ4qIV+IRX3yxakhTeLkHqiEfCEWNckXUy/NYwIGVk++EIua5EuSJL1er+pRUCRJCqsnX4hFHfLFg4am8kAQVky+EIs65IunDE1lAgZWTL4Qi8rzxdRLs5mAgVWSL8Si8nwx9dJsJmBgleQLsag2X0y9xMAEDKyMfCEW1eaLqZcYmICBlZEvxKLCfDH1Eg8TMLAa8oVYVJgvpl7iYQIGVkO+EIuq8sXUS2xMwMAKyBdiUVW+mHqJjQkYWAH5QiwqyRdTL3EyAQNlky/EopJ8MfUSJxMwUDb5QixWny+mXmJmAgZKJV+IxerzxdRLzEzAQKnkC7FYcb6YesEEDJRHvhCLFefLYDAw9RK5fAJmPB5XPRBoIPlCLFaZL75vkUuSRMVCGeQLsVhlvnhqQM4zRCiJfCEWK8sXazbZzwpuKIN8IRYry5fhcGjqhT0mYKAM8oVYrCxfttrt0Wi0gi9EKHb6/cFgUPUooFHkC7FYTb6kabrVbpf9VQhLlmWbrdZ0Oq16INAc8oVYrCZfttrtNE3L/ioEZ7vbNQEDBZIvxGIF+ZJlmakXDuXXBhRLvhCLFeSLd9gcwcwcFEi+EIuy82U8HlvfwBGsi4ICyRdiUXa+7PT7SZKU9/lpgK1224FAUAj5QixKzRdnezAPxzFDUeQLsSg1X1zQyDzyE5llLixPvhCL8vLFLQHMzx0CUAj5QizKy5c0TT0RYE75c0ZLvGFJ8oVYlJcvNsRyIr1ezwZ7WJJ8IRYl5ctoNLIblhPJ7xCoehQQNvlCLErKl+1udzgcFv5pabZOp2PGDpYhX4hFGfkymUwcVccC0jTtdDpVjwICJl+IRRn5YhcJC7NbDZYhX4hF4fniDA+WMRgMer1e1aOAUMkXYlF4vgyHQ/ulWZiTmmEZ8oVYFJ4vW+32aDQq8BMSm51+3w5qWIx8IRbF5ov90izPDmpYmHwhFsXmi/3SFMIOaliMfCEWBeaL/dIUxQ5qWIx8IRYF5ov90hTIDmpYgHwhFkXlS75fejweL/+pYDabJUmihuGk5AuxKCpf3C9NsdxBDQuQL8SiqHxxvzSFcwc1nJR8IRaF5IudrpTBPnw4KflCLArJF+eMURKnIMKJyBdisXy+TKdTp7xTkuFw6AokmJ98IRbL54tvMJRHHMOJyBdisXy+mN6nVB5NwvzkC7FYMl+yLLO4klL5NQbzky/EYsl8sbWVFbAtH+YkX4jFMvmSHyxmXQJlGw6HDkWEecgXYrFMvgwGA4t2WQELeGFO8oVYLJMvFu2yMjv9fpIkVY8C6k6+EIuF88WCSlbJrzeYh3whFgvni+2srJjZPjiWfCEWi+WLtQisngMS4VjyhVgsli++kbB6ohmOJV+IxWL5YhqfSnhkCUeTL8RigXyxiJKq+LUHR5MvxGKBfLGFlQqZ+YMjyBdicdJ8mU6nm62W9QdUZTAY7PT7VY8Cakq+EIuT5kuapo5vp0L5VRXT6bTqgUAdyRdicdJ86XQ6Ls+jWr1ebzgcVj0KqCP5QixOlC+TyWSz1fLGl2qladrpdKoeBdSRfCEWJ8qXJEksO6AONlut8Xhc9SigduQLsThRvmy1275nUAdJktj+BgfJF2Ixf76MRiNHblAT4/F4s9WqehRQO/KFWMyfL9ZLUitWkcNB8oVYzJkvrpuhbly8BQfJF2IxZ774VkHdSGo4SL4QiznzxUQ9NeSBJlxBvhCLefIlP+5lNeOB+VlODleQL8Rinnxx3Au15QAY2E++EIt58sVxL9SWA2BgP/lCLI7NF/Pz1JkDYGA/+UIsjs2XnX5/MBisbDxwUlvt9mg0qnoUUAvyhVgcnS/2plJ/dvXDHvlCLI7OlzRN578RCSoxmUxOra25CB1m8oV4HJ0v292u416ov16v5xcqzOQL8TgiX7ypJRRpmnY6napHAdWTL8TiiHwZDoeOeyEI0+l0s9WySAvkC7E4Il86nY4NHYTCFjmYyRficbV8cZwGYXFAEczkC/G4Wr64KIDguEAA5AuxuFq+uCiA4LhAAOQLsTg0X7IsMw9PcDzxBPlCLA7Nl51+37tYQuQCASInX4jFofliDyqBGgwG1mwRM/lCLA7my2g0cgIYgZpMJp4fETP5QiwO5stOvz8cDqsaDyyp0+m4QIBoyRdicUW+uGKa0LmAmpjJF2JxRb64YprQuauLmMkXYnFFvri5lwbwy5hoyRdisT9f8idH3rYSujRNPT8iTvKFWOzPF3/o0wyWcBEt+UIzfOsr/+Xs+d2jPmJ/vtiyQWP0ej0b6IiQfKEJdp9/9K7rfv2hr33/iI/ZyxcLHmmSNE0dX0SE5AsN8P3nPvWeV69vvPWPnj6iX/byxXZTmmQ6nTo8mgjJF8I3/fKDv3Tjja/f2HjN7z4xuXy1j9rLl06n47IYmsQBjERIvhC6yxeeuu+m7c/9t0/++sb6z7/ns+eutgAmzxdHrdM8rr8gQvKFwO3+9Z++990Pnv3O7jc/+54zpzduffhrLx8eMHm+DIdDF93RPJ4fERv5QtB2X/7aw+13fPq5l3dnu//n8d9+y8b6zQ88/a1DPzTPF0+OaCTPj4iNfCFo3/rSH73jrkf/enc2m812v//0R9+6fvp1209MDsy/ZFl2++23r58+febMGXuOaB7Pj4iNfCFgu+cfu/u6G2959x133tG5847One+++cb10xtn7vpP3/zh/g8bjUbXXnvtqbW1/HXrrbdWNWAoj+dHREW+EK6Xzj3y3vZD//Pln/yTH37zs3e9ev3n/uEr/uHs1ltv3WuXU2trr7rmGmfW0Tw7/X6SJFWPAlZEvhCs6Zcf/KXfumKiZff8Y3dfd3rjLR/90vd/8gBpf7vkr8FgsPLhQrlGo9FWu131KGBF5AuBevn5x7q/8M8fff7KZS4vPnXvTRvrmz9eEDObHTb7YvUujbTZao3H46pHAasgXwjQ7vmzn7n/n75pY+Ntdz34mS9+4wd7ofK9bzz18PbbX7uxfnrjje/4vYefyn8oy7K9dvnpa6+97bbbKhw7lMfzI+IhX4jCV7/61VNra69/wxs+/+d/bucRTeX5EfGQL0RhOBxutdt7N05DU3l+RCTkC1HodDpJksgXGs/zIyIhX2i+/J6jvSsbocE8PyIS8oXmy+85ki9EwvMjYiBfaL78niP5QiQ8PyIG8oWGy58czX58ZWPVw4HSuf+IGMgXGi5/cjSTL8TE/Uc0nnyh4fInRzP5Qkx2+v3hcFj1KKBE8oUm23tyNJMvxMTzIxpPvtBke0+OZvKFyHh+RLPJF5ps78nRTL4QGc+PaDb5QmNNJpNTa2t7fytfiIrnRzSbfKGxhsNhr9fb+1v5Qmw8P6LB5AuNtd3tpmm697fyhdh4fkSDyReaaTqdnlpbm06ne/9EvhCbNE09P6Kp5AvNlKbp/idHM/lCfA5GPDSGfKGZer3e/idHM/lClA7+RoBmkC800KFvOuULETo4DQnNIF9ooDRND5aKfCFCnh/RVPKFBjp0w4V8IU6eH9FI8oUGOvS4C/lCnK44AAmaQb7QNFc7bFS+EKf9F5dCY8gXmuZqR3XJF6K1//IvaAb5QtNstlrj8fjgP5cvRGv/1evQDPKFRhmPx1vt9qE/JF+IludHNI98oVGSJEmS5NAfki/EbKvdzrKs6lFAYeQLjbLVbh/65GgmX4jbEWUPIZIvNMd4PD5ihly+ELMjnqtCiOQLzXH0+kT5QuSOmJuE4MgXmuPo3aHyhcjt9PuDwaDqUUAx5AsNcezeCvlC5K52oiOESL7QEMferCtf4ND7NCBE8oWGOPZeOvkCvV7v0DOpITjyhSaYTqen1tam0+kRHyNf4NhJSgiFfKEJRqPRsWkiX2Ce0IcgyBea4GrXNO4nX2A2m213u0c/ZoUgyBeaYJ4FifIFZq5vpCnkC8HLsmye40TlC8xc30hTyBeCN+dlLvIFcp1Ox/WNhE6+ELw5j0KXL5BzfSMNIF8I2/wz4fIFcq5vpAHkC2Gbfx2ifIE9rm8kdPKFsG13u0dc07iffIE985w1AHUmXwjYic7gki+wx/WNhE6+ELATnYAuX2A/x+8SNPlCwE40AS5fYL9jbzmFOpMvBGyew3b3yBfYz/WNBE2+EKosy0708F6+wH6O3yVo8oVQnfToLfkCV+h0OnNu3IO6kS+E6qQHV8gXuMJgMHD8LoGSLwRpgXlv+QJXcPwu4ZIvBGn+w3b3yBc46ETr36E+5AtBWmDPp3yBgxy/S6DkC+E50WG7e+QLHDQajfy+IETyhfAs9geufIGDFnszAJWTL4Rnselu+QKH2u52Hb9LcOQL4TnplumcfIFDLbAQHionXwjMwls95QscyvG7hEi+EJjBYLDYO0X5Alez2IwmVEi+EJiFjzmXL3A1SZIMBoOqRwEnIF8ISb5LYrGfK1/gakaj0YkuQIXKyRdCkqZpr9db7OfKFziC43cJi3whJMucECpf4AgLnGQNFZIvhGSZN4jyBY6wzNQmrJ58IRhL3o4rX+AItk8TFvlCMJIkSZJk4Z8uX+BonU4ny7KqRwFzkS8EY+Et0zn5Akdb8h0CrJJ8IQzLbJnOyRc4WpZltk8TCvlCGJZfVyhf4Fi2TxMK+UIYltkynZMvcCzbpwmFfCEMy78plC9wLNunCYV8IQBLbpnOyRc4lu3ThEK+EIDBYLD8hgj5AvOwfZogyBcCsOSW6Zx8gXnYPk0Q5At1t/yW6Zx8gXnYPk0Q5At1V9RaQvkCc7J9mvqTL9Td8lumc/IF5mT7NPUnX6i7ot4IyheYk+3T1J98odYK2TKdky8wJ9unqT/5Qq0Nh8Odfr+QTyVfYH5b7bbt09SZfKHWtrvd5bdM5+QLzC9JksFgUPUo4KrkC/WVb5meTqeFfDb5AvMbjUa2T1Nn8oX6Go1GBQaHfIETKfDNAxROvlBfO/1+gdPX8gVOxPZp6ky+UF9b7fZ4PC7qs8kXOJECF85D4eQLNVX41k35AidS4LEFUDj5Qk0V/s5PvsBJFTsDCgWSL9RU4c/d5QucVFFXdkDh5As1VfilcfIFTqrY3X9QIPlCHWVZVviZE/IFTio/e6nqUcAh5At1lCRJkiTFfk75AgvodDpFnXx9hSRJip1hJSryhToq409M+QILGAwGhb+X2PvMp9bWkiRxOB4LkC/UTknz1fIFFlDGk9w9k8lku9vdbLWcj8dJyRdqJ03TMjpDvsBiCl9Hf4Usy7ba7U6n445r5idfqJ2S9mrKF1jMam4PGA6Hm61Wr9ezIIZ5yBcWtN3tlvTabLU6nU7hn7bT6Wy2WuUN28urqa+tdnur3V7BF/qdD3zgbTfddGptzWEzHEu+sKCsHPk7sJI+cz47DZzIaDQ6tbZW9ld55plnHnjggVNrazs7Oxbzciz5Qr2Ud0tc5uERLKrs2wPSNM0nRz05Yk7yhXop7ym7fIGFlXd7QJZlnU5nq93OrNvlJOQL9VLeHgf5Agsr4/aAyWTS6/U2Wy0rXViAfKFGsjJPmJAvsLAyTmPabLWcWcfC5As1Ut75njP5Assp7/YAWIB8oUZK/fNRvsAySn13ASclX6iLfHa6vJlk+QLLKPXZ7o9c+u63v3f5x3994YX/91K5X46QyRfqooy1gfvJF1jSqbW1klbW777whY/+1q/94pmNzff/5+d3L1989jN3/+LPbVz3oScuXD7+JxMl+UJdJEkyGAzK+/zyBZZU8u0BLz//6N03rL/roSc/9wf3fOovvvx0+qVzF3dL+2oETr5QF2Uf/CBfYEnlnSqZ2z33yDvXr7/xln+VmnThOPKFWphMJputVqlfQr7Aksbj8Va7XeIXuPzsQ798/evufeo7JX4NGkK+UAtpmvZ6vVK/hHyB5W22WuXdHrB74Qu//+aNjbc+ePYlD404hnyhFso7knyPfIHllfhbdffC2U987FOfvPuG9dsfOffSK3YhwQHyhVoo9S1dTr7A8kqYKL188dzZL527cOHpT37kz8798Nwj71x/y92Pff1/f+4T/yG7WOgXolHkC9Ur/YH6bDaTL1CEEpapvfjUvTdtrL/2V+//r+d3Z7O//foj/+QNG2duu/8Lf3Op0C9Dw8gXqlf2doacfIFCFL5JcPfi+CtfGf94j/TupRf/11fHdkxzDPlC9Uo+TOJH5AsUouwjmmAe8oXqbbZaJR3luZ98gUKUfUA2zEO+ULEsy1aw8GUmX6AgZV9PBvOQL1RsZdfYyhcoSqmXw8M85AsV2+52V/PnoHyBoqzsXQdcjXyhYiubhZYvUJQsyzqdTtWjIGryhSqNRqOV/SEoX6BAlr9QLflClZIkWdkUtHyBAm13uys47wCuRr5QpVUuAJQvUKDBYLCC0ybhauQLlcm3X67sy8kXKNBq7vqAq5EvVGbFh1/JFyjWag6chEPJFyqz4qPH5QsUazXXfcCh5AuV6XQ6xV78djT5AsVazWWrcCj5QjUmk8kqF77M5AsUbTweb7ZaVY+CSMkXqpGm6YpjQr5A4TZbrfF4XPUoiJF8oRo7/f5wOFzlV5QvULjV/0aGnHyhGlvt9orftMkXKFyapr1er+pRECP5QgUmk8nqH5nLFyhcJb+XYSZfqEQl79jkC5Rh9TOpMJMvVKKS5+XyBcpg+QuVkC9UoJK3a/IFymD5C5WQL1Sgkvdqk8nECaFQuMlksrKLV2GPfAEAAiNfAIDAyBcAIDDyBQAIjHwBAAIjXwCAwMgXACAw8gUACIx8AQACI18AgMDIFwAgMPIFAAiMfAEAAiNfAIDAyBcAIDDyBQAIjHwBAAIjXwCAwMgXACAw8gUACIx8AQACI18AgMDIFwAgMPIFAAiMfAEAAnNUvmysn/by8vLy8vLyquHrqvkCAFB/8gUACIx8AQACI18AgMD8f1H4hXJrKrU2AAAAAElFTkSuQmCC" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the coordinates of B .</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><span>Another point, C , which lies on the graph of \(y = f(x)\) has the same \(y\)-coordinate as A .</span><br><span>(i) Plot and label C on the graph above.</span><br><span>(ii) Find the \(x\)-coordinate of C .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Consider the numbers \(2\), \(\sqrt 3 \), \( - \frac{2}{3}\) and the sets \(\mathbb{N}\), \(\mathbb{Z}\), \(\mathbb{Q}\) and \(\mathbb{R}\).</span></p>
<p><span>Complete the table below by placing a tick in the appropriate box if the number is an element of the set, and a cross if it is not.<img src="data:image/png;base64,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" alt></span></p>
<p> </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><span>A function \(f\) is given by \(f(x) = 2{x^2} - 3x{\text{, }}x \in \{ - 2{\text{, }}2{\text{, }}3\} \).</span></p>
<p><span>Write down the range of function \(f\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p><span>The following curves are sketches of the graphs of the functions given below, but in a different order. Using your graphic display calculator, match the equations to the curves, writing your answers in the table below.</span></p>
<p><span>(the diagrams are not to scale)</span></p>
<p><img src="data:image/png;base64,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" alt></p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAeAAAAElCAIAAACzk6bFAAAgAElEQVR4nO3d72sb17ov8Pk35pUMemVjw9n4TcgL4xcXYRIQpmDY1CCM01KHnENDCHOvsGLveyjsgEDGIVAIDBIOhXDCVCLBtIQMQ0rp3k4l72ySHmmGu0vSI8v0iovvMAQdkbvOui80+jH6OSNpbOnJ98O8iS1plp1nvlpes9aSwDkPBmZw4MCBA8dEHZxzgXNey2g+MSaqMTBdUDxAQKOMEdBACooHCEBAA00oHiAAAQ00oXiAAAQ00ITiAQIQ0EATigcIQECTxgqp8B+uJF5aF92Q84fiGTPL0NJybGUjZVTcPJyd5p4qic9n1wc9vnqa++7bxGcL4aTBPDaJneaePNq7trSaLHh96rRAQI8XM7WdhZ7zGefOu5IQ0ITZ8XTJrq7Zz/aU73KnpvHkmeekG6ysbS8FAzPBwMDArbWtkArPuXk8M5KrtfZ7DuiKkVy/mMvqHCGg/VA9Sd9cCCzFtHLLF00jvbO6rZm+npkVHu6/8PcUU2Jqi8cNZhnp2MpccGU7pRn1d1/T0JKxlbng7I5m+pFXtUB0F9Cc1zPdxeNNLTY7REDzen8IAX1BJqoxXtTqpi2gzyE9mZW75/t7wJSY2uIZjJ0+312ZW7j2sGB15JL1ci/8rwhoMhDQfugR0D6f1Co8/Hx2ZgEBzTmf4uIZhL3LbF3qHXzMyikZtxnqCQL6AiCg/dAZ0JX6yGD7wFnHGJxpaOnU9ierycKH05cPt8PBwMzCta9/Pq22vH79j9nayONzw+LV05dffz7bHO9e2NbM+u2XRUdktzw3EI4lNcPuhTHLeJFJbl8JJ40Pp7mD7SuBmeDsZ/denk5p6U9t8QxgF4yrOKvVUnhh+/lJ7c17K33COLcMNfHZQmPk+rk9SNK8rVf41S6AQDh20KiARkCbp7lvYitzwcClz/d/6l0fbQHNLONZY8R84do91ahXpR3Qcq5Qf8DKTsZo7WaYxvN7dnmvbD/MNc6JgL5QE9UYLzoC2nq5t/WwfkXVRqibVcVO0tftHkTjHuPclf+eSD0pWPXvtvSLzULyX1a304bFOD/LJT4JBj7Zy51xbhd645GN6Hc+d2vBrv56pq/cy1nMvkgCM8GV23vJ7wyL2T01vwY0fTe1xdOf/Qbv4u+k5v3qhY1//fZvv59qX11ZuZezfte2l+ykZifaTtjO0OZtvcbbtllIbi0ELl1Pv2PNU4f/RyL51DB73Ghp5QxoU4vN2i9VG6JpvsfUaq/RG7DepK5dCs5upQq1H/Esl9iw3wnsBtcLHgF9sSaqMV50m8vR0uVhRnK1tapq10b9AYO/2xKa7PSne9fC9kXiDOjOrzAjueq4ouy3Cnuah/NE3v+knSxTWzz92bMpOgK6o+TCSYPZb9KOB7N3ma3GvLS2nkTHoITjTbq9HtoLtXtT7cezk/T15pS7sra91Hzv7xziaKlbZiRX26+dxk+EgL5QE9UYLzp60Oxd5n8+GkdAV4zkes9e7YCArl1gji6P4+9lBPQU6N+Dbv8v7hLQdfUBjZlgn4B2vOBIAV1Xn/UcmOkX0M1SbAwJOg/7uQjoCzVRjfGizxg05yMFtLPr0WZAQNcuGOffpPZflzuayRDQ06DeU+5eA+2F1z2ga2PQK9upJy8Lz/v2oB0vOGJA18agl65sy09zf1f796Cbdf7eSK73HnBHQF+oiWqMFwNmcYzag+71yq4C2lnNrdcGAnoqWC/3VuaCzaHhVi4C2nqTurZ0Zef5Ket8fK+Arn1llICuTTEK72onrPEt9z3o2ZuZk2q3UyCgL9RENcYL/wK6PijhmF9xljs4NNjAgGZW7t6VLqPh9UsdAT0d6v+PzdtozW8NCui2BwwM6HLzjuJIAd32l9+AgGYn6euzdqvsgndM3qievPjpH803GAT0BZmoxngx6AZ3LTdrCw3sLQ4a62Lf1y6/5kVV6zE1OhH2jezWIbml9puE7D+0J39vzACx52lwXp/1can1nnhzvYN9osZVZD+4W09tCkxt8bjRmFXZPlHy28RnrfnbXkv1VK31oNlpLmM//h+FJy/+wey/sa7Yc4RMI71zxTGborUe6i9ux3cHe752bcaFPQNkVzthvHqaS+9duxSc3dFO3jzVfmW1nkG9z8FOf7rX7OM3ztta8I02OO9yU4SAHq/O+RtdY7pxgV36PPHMMP89Ff4klkxrxu+OWyLhpHFWn/3Wuq0Bq89TDsy0L/ZN71yxL7APjpY0Y7dlSmnL5d2cjm2f6D/qey9M614HU1g8HlmGlm7Zi8PejuOJZs8gdt5eay2A9M6V+gxoszaJ055oXwvoP+6la9OcW2crl5318O//t7W6OseIzda6XYppZW4VMvak/nuqUT5J31xonUbNTnPpRGOmc0tJd3y3OXG7tUlk12choIEmFI93rtf+wXlBQANNKB7vENATBwENNKF4PHOMGsNEQEADTSgebxyjxlN514EkBDTQhOIBAhDQQBOKBwhAQANNKB4gwBHQXTYlwYEDBw4cF3pw9KCBGBQPEBDEEAeQhOIBAhDQQBOKBwhAQI8Ls/KpiCgIwnxEfk1165YpMlXFA9AdAnpMrKycUEusWlL/tCxG1en8HD9Kpql4AHpAQI9bSYmEZB35fNGmsngAnLwHNDv9ef/2bnMv7drKfWZq93ebn9A+5sZNDSuvRO/IeZIbH06Z6SsegA4eA9p6k9q6Wd+PtTWgeW2f2dXG7u9jbdx0+JCNBwVBEITlRHZ8vwQYzpQVD0A3XgKavctsbfTd6ap6qn212usTFkZo3PSolo7uR8RFSe3xWSpDYpauKcoDaflTWcdWkK5MYfEAtHMf0BUjueHio2XOcomNcX1I0nReY78pkWWXAc10+aqkDhwQYXpq89atiCgIwhoC2qXpLB4AB9cBbWqxWVc7eTMjudr9M+GHb9wUYaVn0dAdl7M4XAY055zzii6vIaDdm8biAWjjMqArRnK9/ZPH2GnuyaO9a+H2z9wztdhs789LHapxk4/pckgQBEEQI4lnutubhAho/0xR8QD04jKgy9r2kvNjGRsfSdmRxayQCs+N5TMc3V5jlq4qD6TQl0qxWmuBlU0sizfq/3Q0zlSjotBHvwRkpWzmcTwSqt0DZJauSMuiMMKsZwS0fxDQQIC7gDa12Gzn5+bWPsG6s7Nc1raXguMY5XB1jZmqZCeuGJLz9mcEF5XNsd+pc5zoF/M4kzoqjfgTIqD9g4AGAtwHdOen4ExGQNeaUlQ2xWZAc85M7VGmSw96ZNZrOTIvXF6NZt4O8+M1U76r1h+hDQLaGwQ0EDD9PWi7LXk5JIqN3ijTlVS224STkYY4Wl5hPEGJHrR/ENBAAKmAFuw11tViRval+1w7lS6HhPGMnyCg/YOABgKGvknI+wf0ud4k5Jzzsiot1gKaFQ/3hxt/cOXsOPPowa1F0W2w9oOA9g8CGghwGdDM1HYW2qbZ8epJ+uZCYK599QorpMJLY1mr4jmgxah69lY9+GHUm3c9MSv7WNHPdHnN7q2z99b74U+GgPYPAhoIGHqhSlnbXmp8ZFZrf/mCFqpUdHlNECN/fpA59mMfDFOVQols6VhRfrHsUY41Wf89rzwd5XQIaP8goIEAP5Z6/7FjvseojXOhFtBd5z6Pg6lK4nwk8aPdN6/dk4zcPyr5NdLdcfaWG5nYztQFBDQQ4HWzpPVdrc9WSMzK3bugzZKYqR2ksM8n1CGggQDv241eW4+lC9360Re43Siz9B9U1wus4WOAgAYChtmwP3dwd6995gYztbvX93863w37z7Lx1ZD8qpg9zGR9uy8I0wkBDQRM80desbfK5rynzYng4zFRlQwwnGkOaIDeUDxAAAIaaELxAAEIaKAJxQMEIKCBJhQPEICABppQPEAAAhpoQvEAAQhooAnFAwQgoIEmFA8QgIAGmlA8QAACGmhC8QABCGigCcUDBCCggSYUDxCAgAaaUDxAAAIaaELxAAEIaKAJxQMEIKCBJhQPEICABppQPECAI6CDgRkcOHDgwDFRB0cPGohB8QABQQxxAEkoHiAAAT0uzNIVaVkUBHFZUnQLHzJ+waaqeAC6Q0CPCcunogd5i7GisimKITmPhL5Y01Q8AD0goMeuostrQkQpXXQ7PnLTWTwADgjosftQUr4QJdW86HZ85KazeAAcENBjV1alq5JavuhmfOyms3gAHLwHNDv9ef/2rlbmnDMjuRr4ZC93Vv9exUiuB1fu5SzGeVlL3H2YOx1lKHYarzFWzETvPCv5MgJt6s8SEVEQBEGMJJ7p6KP3M43FA9DGY0Bbb1JbN/eeGxbnfEBAc24VMtvrnyffWCM3bmpYRwnpIO9hCkdFl79w192uFjP3949KjHNW+jERmRfEqGriTmRP01c8AB28BDR7l9naaIljF9iJtrN+Pf1uuCCZsmvMep2KP8pbjHNm6a/czbRzHdDmK/W4+ZtnuhwSFjGQ0seUFQ9AN+4DumIkN64kXnruDlsv98K3MyfVURo3BazXcmReaAjJuqs3Jfc9aAemyyHxhlIc5rf6kZim4gHowXVAm1psdj1lVLyfomIk1xe2tSFGTN1eY5auKg+k0Jf1wGJWNrHcPb+YqUZFoY81We/5M7JSNvM4HgklsnY3WZGWxdGGGoYL6GpR+eqOWsQARx8IaCDAZUBXjOR6MJw0WiOBneaePNq7Fo5p5cYXniqJz/9pR3MEFjO1nYXZti96a1w/pirZidtcHsKKyqY47hEAx4l+MY8zqaPR7wV6DmhWyirxSDBy/6iE7nM/CGggwGVAl7XtJWcvuGIk14OBmWBgyQ5oVkiF54KBmWBHFjMjudp42FCNG6hj/R4ztUcZP0YAakMZl1ejmbdDpfMoXXjnczHE0RcCGghwF9CmFpud6RimYKa2s+BI3rK2vdQZ0D2e7qFxg7G8HBKby0OYrqSy3YbLRxriaHmFgQ9zaYghDmbpqiyFBEHAcpg+ENBAgPuAnltNFpy5O3EBXb81Vy1mZF+6z7VTjXMGxZA3Ce2fFzPtekNAAwFUetC8rEqLtYBmxcP9Iccf3Dg7zjx6cGtxTL3XYQO6tuOH27kiHyMENBBAK6DFqHr2Vj34wZ+FfJxzZmUfK/pZMxzZe+v9KCcbOqDLqhTaVPx7H5p6CGggYOibhNxjQPt7k9DuUYqRPz/IHPuxF7OpSqFEtnSsKL9Y9ijHmqz/nleejnY6lwHNTDUqipG4ki0xzrmpK9HQpoJ5dn0goIEAlwHNTG1noW2aHa+epG8uBOaaq1fYu8zWpaBj8TfntVkcszeHWKviPaB9m9hgqpI4H0n8aPfNa/ckz3GuGys9iy7XZ/lF4o9VfegF9B8JBDQQMPRClbK2vdT4TMOFbc00tdhs41MOW/vL/i9U4ZxzZmoHqTwmNYANAQ0EnMtS75WNoZYgur/GmKX/oGJ3N2iBgAYCvG6WtL6rnXgZ+TzLJTZ82yzpLBtfDcmvitnDTNa3+4IwnRDQQID37UavrcfSBVf9aL+3G2Vvlc157IwMXSGggYBhNuzPHdzdGzwlo6zt3L738qPbsB8mBIoHCMBHXgFNKB4gAAENNKF4gAAENNCE4gECENBAE4oHCEBAA00oHiAAAQ00oXiAAAQ00ITiAQIQ0EATigcIQEADTSgeIAABDTSheIAABDTQhOIBAhDQQBOKBwhAQANNKB4gAAENNKF4gAAENNCE4gECENBAE4oHCEBAA00oHiAAAQ00oXiAAEdABwMzOHDgwIFjog6OHjQQg+IBAoIY4gCSUDxAAAIaaELxAAEI6Klg6kp0WRAEISQpeeuiWzMVUDxAAAJ6CjD9m6j82uLVonJDFNZkvXLRLZoCKB4gAAE9VVheDs1HlN8uuh1TAMUDBHgPaHb68/7tXa3MOWdGcjXwyV7urP69ipFcD67cy1ms/uBCKvyHK4mXFufcfLG3803utDpE46DuNyWyLKnli27GFEDxAAEeA9p6k9q6uffcqA2DegtoziwjHQv/S6pgem0c2ExVCkZVkw1+5EcPxQMEeAlo9i6ztdESx8Ngp893w7czJ6760RN8jTErm1g+7+HgalH56o5aRDy7McHFA+CW+4CuGMmNel94FMzK3VvdSp+4iJnJvcaso/iyKJxrQDMr+7Ukv8YUDpcmt3gAXHMd0KYWm11PGePII1ZIhf9bTBs8kDqp19hZNr62vLx4jgHNrPyjeKqWzqae/V+I6YEmtXgAPHAZ0BUjuR4MJ43Wbi87zT15tHct3Ihadpp7qiQ+/6cdzR4krZ7mvvs28dnituYcdS5r20sL7V/s17hJwqzsfiSuZeW18wpoZuVTEVGoE0NyHqMcA01k8QB44zKgOyO1YiTXg4GZYGDJDmhWSIXngoGZ4Kwd0MxIrgZmgoGZjiyuGMn1xsPcNK4vZumaIkuhTaU+OnuWjV8Vm/90PNhUo82s62JQ5lpH8ch+1nqvjz2gWSmb+SYe+TSePeOccyuvSCFBWMScjeEgoIEAdwFtarHZzpxlpraz0Ahozms57khet08c0LjeWgO3EZfVonJDFP2Y7XCWjX8Zz55xXhl3QJdVadH+OUKybr5SUn8poZ88AgQ0EOA+oOdWkwVnYkxCQNd0LrEra6nvxz7dgRUz0cSRxbkPAV1j5uVNUVgMRZ9irsaIENBAwLT3oOuvqMuhltEApj9NZbtOBxxhiIO9VaJfZ+0p3gMD+jclEux3nmA8+6Hb80xVEjHKPAYIaCCAUkDXc429zewfjrsHWi0qf040Q39gQP9nWf9bto+//2b9V9efJC+HRFFS3S7mgR4Q0EDA0DcJ+agBPbabhLUTNTqe1WJGzhQ9LCh3/frD3lf0gFnHh48ffOnPAPrHBQENBLgMaGZqOwtt0+x49SR9cyEw11y9wt5lti4FWxZ/s5P09dkZx+JvzmuzOBZcrFXxGNCCKKlnRe1AO4fxW3/GoK1sStE/6HLIfuUPloWN64aEgAYChl6oUta2lxofmbWwrZmmFpttfIjWUkz73dR2Fhofq9XaX/ZjoUptZCDy1QPl1bks4hhvQJdVKRLP/nqsHOYtxlleDgVD8i9m/lA5Hmlh/ccMAQ0EXMxS7yvtnfEBjXPxqnk5JPaY++yHsQf0ohi5f1SqNl9cjCSOMNFueAhoIMDrZknru5qbXTR6s17u+bJZUlmTH+ctBBrYENBAgPftRq+tx9KFofrR/m03aurqDzrSGVogoIGAYTbszx3c3XMxgtzO1Ha3vv55jBv2W0fx5U/l/K/ZzGG2NO5pGzDlENBAwBR/5BUrKpvifCT+PfrO0GmiKhlgOFMc0AB9oHiAAAQ00ITiAQIQ0EATigcIQEADTSgeIAABDTSheIAABDTQhOIBAhDQQBOKBwhAQANNKB4gAAENNKF4gAAENNCE4gECENBAE4oHCEBAA00oHiAAAQ00oXiAAAQ00ITiAQIQ0EATigcIQEADTSgeIAABDTSheIAABDTQhOIBAhwBHQzM4MCBAweOiTo4etBADIoHCAhiiANIQvEAAQhooAnFAwQgoIEmFA8QgIAGmlA8QAACGmhC8QAB3gOanf68f3tXK3POmZFcDXyylzsbdBZmavd3D16esiEbNwU+ZONBQRBvKL/9qkZDQjCe/XDRTfq4TVPxAPTgMaCtN6mtm3vPDYtz7iGgOeemkd5ZvfawYHkI6Sm7xthbZXPx8vJmIuvmFwL+mrLiAejGS0Czd5mtDXdx3FX1VPtqdSt94jqiJ+4aY6VsSloWBEEQhGUplS05f5SKLq8JEaXkz7ktXVOUB9Lyp7Je8eUMtExc8QB45z6gK0Zy40ripTXS6c5yiY3r6XcuI3rCrrGzbPyq4DC/qbxlbQ8Qo6rp4a8EpstXJdUc/LDU5q1bEVEQhDUEtBsTVjwAw3Ad0KYWm11PGaNGAzOSq7M7mrsIm6hrjOny1cj9o1KV85audEjW7R+FWdmvow/u3xLX5Pyvx8cllyHtMqA553YPHQHtzkQVD8BwXAZ0xUiuB8NJozV12GnuyaO9a+GYVrYfUF85vrCtmZxzXta2l4KBmWCgJdlNLTa7FNPKnho3ASq68jjrGEAvq9Jivb/8mxIJiptKkZVV6fLl0J1MserydRHQPpmk4gEYksuALmvbS/XYrWkkcjNt2enz3ZU5x8NY4eHON44bg6yQCjsf46JxfTFL1xRZCm0qRfs8Z9n4VbH5T8eDTTUqCn24j7+yKi2KbrO1d+sR0P5AQAMB7gLa1GKzMx2pykxtZyHQ2h3u6Gibf828aOssl7XtpaC7UQ4X11hr4DaSq1pUbogex4I9M1VJHENWIqB9goAGAtwH9NxqsuAMvM6Abpt4x8wXhy/aU3K8AV1TLSo3REdylbXU99160ONSLSpfhuJHw9wyNVWpXx9eDMn5Hg1HQHuAgAYCxtuDrk3Fu2Q/khUe7r/o6Bv6EdCc6XJIWJTU+mCL/jTVfTLyeIY4WFH5YjOV9zKnu0/L0YP2AwIaCBh3QNtfXE8Z762ckuky68O/gK73PdnbzP6hj91n67UsxdWS29uA/SGgfYKABgKGvknIewS0PR5yJfEks/9vRpeU7PpSAxo3mKlKYi2gq8WM7H4ShWesqCa+Hlc6cwS0bxDQQIDLgGamtrPQNs2OV0/SNxcCcx2rV2oTPDrHrGuvVEiFl1yuVfEY0IIoqWdF7UDzrffMiuqdO3K+ZZZKSd1X9FFOh4D2CQIaCBh6oUpjjnPrxGcbM5KrszczJ126mX4tVGF5OSSKka8eKK9GW+vY5xRFNRrqGLNuDnwP+aoIaH8goIGA81/q/cfuPeu+jRusFtDd5z6PRVmVFrvNufB5Ml9D29yP5gpG6A4BDQR43SxpfVdzv9lR+/Ot3D3fNksqa/LjsUyrABoQ0ECA9+1Gr63H0gXv/Whftxs1dfUHHekMLRDQQMAwG/bnDu7uudtMo/EcU7t7ff+nMW/Ybx3Flz+V879mM4fZ8U2rABoQ0EDAFH/kFSsqm+J8JP49+s7QaaIqGWA4UxzQAH2geIAABDTQhOIBAhDQQBOKBwhAQANNKB4gAAENNKF4gAAENNCE4gECENBAE4oHCEBAA00oHiAAAQ00oXiAAAQ00ITiAQIQ0EATigcIQEADTSgeIAABDTSheIAABDTQhOIBAhDQQBOKBwhAQANNKB4gAAENNKF4gABHQAcDMzhw4MCBY6IOjh40EIPiAQKCGOIAklA8QAACGmhC8QABCGigCcUDBCCggSYUDxCAgPaPlY0vC8L8pqIX1T8tC8vxrHXRTfqITHnxAHCOgPZZtajcEC+HIokjZPM5m/7iARgioNnpz/u3d7Vy3weVtcTdh7lTNqbGTQZm6d/HI/OCIAhiJP5MtzP3/+mP/nkj4rAV/+F/28/R5ZDwhVL64EuLLF1VHsvS1ZCcH/FXTc+EFQ/AMDwGtPUmtXVz77kxuD9oFTLb658n34zSc5yoa4wVDxP7P5YY56x0lIiIwqKk9n+X4pwzK5tYdvXI1ifl5at3VHNQ5LK8vPmlFJkXBBEB3WmiigdgOF4Cmr3LbG3s5c7cvjY70XbWr6ffDZ0dk3SN/Z+s+rr5ZsPyckgUJdXs/yTrKBG9/+DW5ZD8qnj8uuTyF+EyoGuP1eUQArqbSSoegCG5D+iKkdy4knjprUdsvdwL386cVEds3MRheTm0uKm87R2LH0rKF4J4QylWTDUqXl6NZvo8uOPFEdAjm9ziAXDNdUCbWmx2PWVUPL5+xUiuL2xrA3qagxrXF7N0TZGl0KZStFPqLBu/Kjb/6XiwqUZFoY81WR/8M7JiJnrnmdsesVcI6HFAQAMBLgO6YiTXg+GkUY8BZiRXG3t5zO5oJuOcmdrOQmAmGJhbTRYaDzS1nQX7AcM3rrfWwG1ka7Wo3BDFqMuM84aVsko8EowkjvzKZwT0WCCggQCXAV3WtpfaO8LsRNsJBx3hWzEO4qmC81FGcjWwFBsw62NA4wapFpUboqPzW9ZS33frQY/GVKVm93u+7xCHJ2VVWuzXrQ/Jeo8zIaB7QUADAe4C2tRiszOdIxXMSK4GWsc9yi/Sf20fzejxXE+NG4jpcqhlsgTTn6ayXW9mjmOIw9JVWVoWBMGvTjp60GOAgAYC3Ad068BFHSukwn9o3jk0/5p50dFTPr+ArucUe5vZPxx/99mhostrgtf5cy4hoMcBAQ0EjNSD5rx6kr5ZH2KuGAdyl7HmcwlobqqSWMupajEjZ4pDzhtxj+lyyN0dRe8vjYAeAwQ0EDBiQLd0rq3cw7TRJSbOL6AFUVLPitqB5nPvmfPaUEmw+0SR0V8bAT0GCGggYISbhC3fCq4k1PSDh10n4ZlabNbvm4T1lSORrx4or3zZ9cJUJXE+EleypSrnzNIVKfSl4lM/HQE9DghoIMBlQDNT21lomWbn+F5tyl2f787eHG6tiueA9qlLyzlnRTUasu8jipH4Y023LjwS2+Z++DPeMrUQ0EDAOBaqsEIqvNRjSfc5LFSpKWvy4/zFhyZMCgQ0EOD/Uu+VDe/rD9sbN4ipqz9MQJcWJggCGgjwulnS+q524joIz3KJDR83S7KO4sufyvlfs5nDbMn3aRswXRDQQID37UavrcfShUnYbpQVlU1xPhL/Hn1n6ISABgKG2bA/d3B3b+CG/Tu3770ktmE/TBMUDxCAj7wCmlA8QAACGmhC8QABCGigCcUDBCCggSYUDxCAgAaaUDxAAAIaaELxAAEIaKAJxQMEIKCBJhQPEICABppQPEAAAhpoQvEAAQhooAnFAwQgoIEmFA8QgIAGmlA8QAACGmhC8QABCGigCcUDBCCggSYUDxCAgAaaUDxAAAIaaELxAAGOgA4GZnDgwIEDx0QdHD1oIAbFAwQEMcQBJKF4gAAENNCE4gECENCEMUtXpGVREMRlSdEt5vPpzLy8KQqCIG7KedPnc3SDeMoAAAb/SURBVA2G4gECENB0sXwqepC3GCsqm6IYkvN+JjSzsgcJtchYUY2GREm98IRG8QABCOiPQUWX14SIUjqPc30oKTd8fjNwBcUDBHgPaHb68/7tXa08+LVZIRX+w5XES4szU7u/e/Dy1ONVi2tsTD6UlC/OpVfLLF2JSgd534dTBkPxAAEeA9p6k9q6uffcsNy8djOgOeemkd5Zvfaw4OXSxTU2JmVVuiqpLt5TR/MhGw8KgiCIy/EjVxXiJxQPEOAloNm7zNbGXu5s2HNVT7WvVrfSJ64jesKuMVN/loiIgiAIghCSZNX/226cc85KRykpJNSCTzrIlqqeX6GYid55VjqfTi0rHSUiohhVzQvuRE9Y8QAMw31AV4zkRr07PLSzXGLjevqdy2t3kq6xalG5IS5HFd3knHMrr0ghcVMp+p1C1lF82X5PsIk3lKKXjLaOEuc85lBSIghogHFwHdCmFptdTxmVEc/HjOTq7I7m7uqdoGvMVCXnRAimyyFhTdZH/YX0VdHlzUjix1rnt96V9jIfw3qdij/KW4xzZumvzqXLXy2pfwphFgfAOLgM6IqRXA+Gk0b9AmdGcrWxVNwOXGZqOwuBmWBgbjVZYLx6mvvu28Rni9ua41o1tdjsUszNPcaJusZYXg6JrffZmC6HlhNZXyOP6Uoq6/iTxVQlUXB7u896LUfmm13vkKz72NiKLq8JgiAI85H49+cz+NPfBBUPwLBcBnRZ215aaItadqLthIOO7nDFOIinCiZvSfCOZxVS4bn2Lw5qXF/M0jVFlkLNAYezbPxqj/EHZqpR55BBm16d4mpRuSE2VnxYr+XNL7stx6iWsoeP45sh+y6ZqSvRZcF1pA5kqpK46Ljdx0rZzDfxyKfx7Bnn9tiLICz6dEuQlbKZx/FIqPbOVF8IMwEDGp0Q0ECAu4A2tdhsR9TaKdw67lF+kf6rOeBZZW17KehulMPFNdYauI1srRaVGz7cp6qvlFuOSPFvut2sa2tM6Vh5fOT9nl5vzFSjoqMjXFalxWYH2XylpP7i481AU5XsH08Myb+Yx5nU0TndehwCAhoIcB/QtYELJ8dEOs7Nv2ZelJ3P8juga2rd29bOb1lLfT/+O3jsrbI5b8/iUPI97pcyK5+KiOLl0J2Mp7t5rs5e7yk71N45FkPRp77ftOT1kZPLq9HM24lNZ46ABhJG6kFzXj1J31yw07ZiHMiO2D2/gK7dsmv+Xc/0p6kuQcZHGOLg3Hotb0pKscpKPyYi84IwH5Ff98josiot9hjz/U2JBPudPxjPfuj6mtWiIm32OmPHPUx3hmtM7Xfo9w3SUSGggYARA7qlc23lHqYNNvhZ/gV0PaHY28z+4bj7kmVVWmwOJdtDvb1CqqLLaz1GZv+zrP8t28fff7P+q/MFmZU/kPrMZe64h+nOcI1pfzucTAhoIGCEm4Qt3wquJNT0g4dtk/B6B/RYbxLWztXoQlaLGXnMYwttbwDtZ+xgvco8/vqWOLYIYyU1kVB7D/cy6/jw8YMvz2t5yNlx5tGDW4uTsCNSHwhoIMBlQDNT21lomWbn+F5twkbHd9lJ+vrsTHDlXq510hUrpMJLLteqeAxoQZTUs6J2oPkwEmuqkuhcwczycuhytwg+y6ae6h/ycihYi29mWe9HODMrPbvjWGlSLakppbXnbmVTiv6hOS/7g2X5N/jArOxjRT/T5TV7DIe9t95P4lg0AhoIGMdClS6Z25gT3TpRmnP/FqrU/saPfPVAeeXPLhBn2fhVQQhF1Vr6m3l5MxhJteQmM9U7ofhfSsdPlbxpj3KEZN38RRmhSaz0LLrcMWZu95TLqhSJZ389Vg7zFuOs9pbwi5k/VI6HXo7fm6lKoUS2dKwov1jNdTq/55WnxxMw67kTAhoIOP+l3n/sMhtkUOMGqwW0r2uvWSmrxHvvxcFMNSqKkUR95hnT5ZAw31gHOIzmtDZnPttjC2VVWhQj9+sz+WoD380GjJmpSmLLj2O/I94f6zzCcUJAAwFeN0ta39Xcb3bU/nwrd8+3zZLKmvx4Ena5hAmBgAYCvG83em09li5470f7ut2oqas/TMLyYpgcCGggYJgN+3MHd/fcbabReI6p3b2+/9OYN+y3juLLn8r5X7OZwyE24QTaENBAwBR/5BUrKpvipGzNA5NmoioZYDhTHNAAfaB4gAAENNCE4gECENBAE4oHCEBAA00oHiAAAQ00oXiAAAQ00ITiAQIQ0EATigcIQEADTSgeIAABDTSheIAABDTQhOIBAhDQQBOKBwhAQANNKB4gAAENNKF4gAAENNCE4gECENBAE4oHCEBAA00oHiAAAQ00oXiAAAQ00ITiAQIcAR0MzODAgQMHjok6eKMHDQAAkwYBDQAwof4/yeLZ4MXOMDwAAAAASUVORK5CYII=" alt></p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;"><em>y</em> = <em>f</em> (<em>x</em>) is a quadratic function. The graph of <em>f</em> (<em>x</em>) intersects the <em>y</em>-axis at the point A(0, 6) and the <em>x</em>-axis at the point B(1, 0). The vertex of the graph is at the point C(2, –2).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the equation of the axis of symmetry.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Sketch the graph of <em>y</em> = <em>f</em> (<em>x</em>) on the axes below for 0 ≤ <em>x </em>≤ 4 . Mark clearly on the sketch the points A , B , and C.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The graph of <em>y</em> = <em>f</em> (<em>x</em>) intersects the <em>x</em>-axis for a second time at point D.</span></p>
<p><span>Write down the <em>x</em>-coordinate of point D.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The function \(f(x) = 5 - 3({2^{ - x}})\) is defined for \(x \geqslant 0\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>On the axes below sketch the graph of <em>f</em> (<em>x</em>) and show the behaviour of the curve as <em>x</em> increases.</span></p>
<p><span> </span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the coordinates of any intercepts with the axes.</span></p>
<p><span><img alt="onbekend.png"></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><span>Draw the line<em> y</em> = 5 on your sketch.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>Write down the number of solutions to the equation</span> <span><em>f</em> (<em>x</em>) = 5 .</span></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Consider the curve \(y = 1 + \frac{1}{{2x}},\,\,x \ne 0.\)</p>
<p>For this curve, write down</p>
<p>i) the value of the \(x\)-intercept;</p>
<p>ii) the equation of the vertical asymptote.</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>Sketch the curve for \( - 2 \leqslant x \leqslant 4\) on the axes below.</p>
<p><img src="data:image/png;base64,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" alt></p>
<p> </p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The axis of symmetry of the graph of a quadratic function has the equation <em>x</em> \( = - \frac{1}{2}\)</p>
<p class="p1">.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the axis of symmetry on the following axes.</p>
<p><img src="images/Schermafbeelding_2015-12-03_om_13.39.20.png" alt></p>
<p>The graph of the quadratic function intersects the <em>x</em>-axis at the point N(2, 0) . There is a second point, M, at which the graph of the quadratic function intersects the <em>x</em>-axis.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Draw the axis of symmetry on the following axes.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-03_om_12.01.55.png" alt></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The graph of the quadratic function intersects the \(x\)-axis at the point \({\text{N}}(2, 0)\). There is a second point, \({\text{M}}\), at which the graph of the quadratic function intersects the \(x\)-axis.</p>
<p class="p1">Clearly mark and label point \({\text{M}}\) on the axes.</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 class="p1">(i) <span class="Apple-converted-space"> </span>Find the value of \(b\) and the value of \(c\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Draw the graph of the function on the axes.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br>