File "markSceme-HL-paper1.html"
Path: /IB QUESTIONBANKS/5 Fifth Edition - PAPER/HTML/Math AA/Prior learning/markSceme-HL-paper1html
File size: 48.67 KB
MIME-type: text/html
Charset: utf-8
<!DOCTYPE html>
<html>
<meta http-equiv="content-type" content="text/html;charset=utf-8">
<head>
<meta charset="utf-8">
<title>IB Questionbank</title>
<link rel="stylesheet" media="all" href="css/application-02ef852527079acf252dc4c9b2922c93db8fde2b6bff7c3c7f657634ae024ff1.css">
<link rel="stylesheet" media="print" href="css/print-6da094505524acaa25ea39a4dd5d6130a436fc43336c0bb89199951b860e98e9.css">
<script src="js/application-9717ccaf4d6f9e8b66ebc0e8784b3061d3f70414d8c920e3eeab2c58fdb8b7c9.js"></script>
<script type="text/javascript" async src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-MML-AM_CHTML-full"></script>
<!--[if lt IE 9]>
<script src='https://cdnjs.cloudflare.com/ajax/libs/html5shiv/3.7.3/html5shiv.min.js'></script>
<![endif]-->
<meta name="csrf-param" content="authenticity_token">
<meta name="csrf-token" content="iHF+M3VlRFlNEehLVICYgYgqiF8jIFlzjGNjIwqOK9cFH3ZNdavBJrv/YQpz8vcspoICfQcFHW8kSsHnJsBwfg==">
<link href="favicon.ico" rel="shortcut icon">
</head>
<body class="teacher questions-show">
<div class="navbar navbar-fixed-top">
<div class="navbar-inner">
<div class="container">
<div class="brand">
<div class="inner"><a href="http://ibo.org/">ibo.org</a></div>
</div>
<ul class="nav">
<li>
<a href="../../../../../../../index.html">Home</a>
</li>
<!-- - if current_user.is_language_services? && !current_user.is_publishing? -->
<!-- %li= link_to "Language services", tolk_path -->
</ul>
<ul class="nav pull-right">
<li class="dropdown">
<a class="dropdown-toggle" data-toggle="dropdown" href="#">
Help
<b class="caret"></b>
</a>
<ul class="dropdown-menu">
<li><a href="https://questionbank.ibo.org/video_tour?locale=en">Video tour</a></li>
<li><a href="https://questionbank.ibo.org/instructions?locale=en">Detailed instructions</a></li>
<li><a target="_blank" href="https://ibanswers.ibo.org/">IB Answers</a></li>
</ul>
</li>
<li>
<a href="https://06082010.xyz">IB Documents (2) Team</a>
</li></ul>
</div>
</div>
</div>
<div class="page-content container">
<div class="row">
<div class="span24">
<div class="pull-right screen_only"><a class="btn btn-small btn-info" href="https://questionbank.ibo.org/updates?locale=en">Updates to Questionbank</a></div>
<p class="muted language_chooser">
User interface language:
<a href="https://questionbank.ibo.org/en/users/set_user_locale?new_locale=en">English</a>
|
<a href="https://questionbank.ibo.org/en/users/set_user_locale?new_locale=es">Español</a>
</p>
</div>
</div>
<div class="page-header">
<div class="row">
<div class="span16">
<p class="back-to-list">
</p>
</div>
<div class="span8" style="margin: 0 0 -19px 0;">
<img style="width: 100%;" class="qb_logo" src="https://mirror.ibdocs.top/qb.png" alt="Ib qb 46 logo">
</div>
</div>
</div>
<h2>HL Paper 1</h2><div class="specification">
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f'\left( x \right)">
<mi>y</mi>
<mo>=</mo>
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span>, 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> ≤ 5 is shown in the following diagram. The curve intercepts the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis at (1, 0) and (4, 0) and has a local minimum at (3, −1).</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The shaded area enclosed by the curve <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f'\left( x \right)">
<mi>y</mi>
<mo>=</mo>
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span>, the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis and the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-axis is 0.5. Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( 0 \right) = 3">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>3</mn>
</math></span>,</p>
</div>
<div class="specification">
<p>The area enclosed by the curve <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f'\left( x \right)">
<mi>y</mi>
<mo>=</mo>
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> and the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 1">
<mi>x</mi>
<mo>=</mo>
<mn>1</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 4">
<mi>x</mi>
<mo>=</mo>
<mn>4</mn>
</math></span> is 2.5 .</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-coordinate of the point of inflexion on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right)"> <mi>y</mi> <mo>=</mo> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( 1 \right)"> <mi>f</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( 4 \right)"> <mi>f</mi> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </math></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>Sketch the curve <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right)"> <mi>y</mi> <mo>=</mo> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span>, 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span> ≤ 5 indicating clearly the coordinates of the maximum and minimum points and any intercepts with the coordinate axes.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>3 <em><strong>A1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to use definite integral of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'\left( x \right)"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span> <em><strong> (M1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^1 {f'\left( x \right){\text{d}}x} = 0.5"> <msubsup> <mo>∫</mo> <mn>0</mn> <mn>1</mn> </msubsup> <mrow> <msup> <mi>f</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mrow> <mtext>d</mtext> </mrow> <mi>x</mi> </mrow> <mo>=</mo> <mn>0.5</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( 1 \right) - f\left( 0 \right) = 0.5"> <mi>f</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>−</mo> <mi>f</mi> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <mn>0.5</mn> </math></span> <em><strong> (A1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( 1 \right) = 0.5 + 3"> <mi>f</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mn>0.5</mn> <mo>+</mo> <mn>3</mn> </math></span></p>
<p>= 3.5 <em><strong> A1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_1^4 {f'\left( x \right){\text{d}}x} = - 2.5"> <msubsup> <mo>∫</mo> <mn>1</mn> <mn>4</mn> </msubsup> <mrow> <msup> <mi>f</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mrow> <mtext>d</mtext> </mrow> <mi>x</mi> </mrow> <mo>=</mo> <mo>−</mo> <mn>2.5</mn> </math></span> <em><strong> (A1)</strong></em></p>
<p><strong>Note:</strong> <em><strong>(A1)</strong></em> is for −2.5.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( 4 \right) - f\left( 1 \right) = - 2.5"> <mi>f</mi> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> <mo>−</mo> <mi>f</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mo>−</mo> <mn>2.5</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( 4 \right) = 3.5 - 2.5"> <mi>f</mi> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> <mo>=</mo> <mn>3.5</mn> <mo>−</mo> <mn>2.5</mn> </math></span></p>
<p>= 1 <em><strong> A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"> <em><strong> A1A1A1</strong></em></p>
<p><em><strong>A1</strong></em> for correct shape over approximately the correct domain<br><em><strong>A1</strong></em> for maximum and minimum (coordinates or horizontal lines from 3.5 and 1 are required),<br><em><strong>A1</strong></em> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y"> <mi>y</mi> </math></span>-intercept at 3</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br>