File "markSceme-SL-paper1.html"
Path: /IB QUESTIONBANKS/4 Fourth Edition - PAPER/HTML/Mathematical Studies/Topic 3/markSceme-SL-paper1html
File size: 1.33 MB
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-size: medium; font-family: times new roman,times;">Consider the following propositions.</span></p>
<p style="margin-left: 30px;"><em><span style="font-size: medium; font-family: times new roman,times;">p </span></em><span style="font-size: medium; font-family: times new roman,times;">:</span><em><span style="font-size: medium; font-family: times new roman,times;"> Students stay up late.</span></em></p>
<p style="margin-left: 30px;"><em><span style="font-size: medium; font-family: times new roman,times;">q </span></em><span style="font-size: medium; font-family: times new roman,times;">:</span><em><span style="font-size: medium; font-family: times new roman,times;"> Students fall asleep in class.</span></em></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write the following compound proposition in symbolic form.</span></p>
<p><em><span>If students do not stay up late then they will not fall asleep in class.</span></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><span>Complete the following truth table.</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>Write down a reason why the statement \(\neg ( p \vee \neg q)\) is not a contradiction.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\neg p \Rightarrow \neg q\) <em><strong>(A1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for any 2 correct symbols seen in a statement, <em><strong>(A1)</strong></em> for all 3 correct symbols in correct order.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span> <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C3)</strong></em></span></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for each correct column. 4<sup>th</sup> column is follow through from 3<sup>rd</sup>, 5<sup>th</sup> column is follow through from 4<sup>th</sup>.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Not all of last column is F <em><strong>(R1)</strong></em><strong>(ft)</strong> <em><strong>(C1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(R1)</strong></em><strong>(ft)</strong> if final column does not lead to a contradiction.</span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider the statement <em>\(p \Rightarrow q\)</em>.</p>
<p class="p1" style="text-align: center;">If I break my arm, then it will hurt.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down in words, the inverse of <em>\(p \Rightarrow q\)</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 class="p1">Complete the following truth table.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-03_om_07.18.13.png" alt></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">State whether the converse and the inverse of an implication are logically equivalent.</p>
<p class="p1">Justify your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">If I do not break my arm, then it will not hurt <span class="Apple-converted-space"> </span><strong><em>(A1)(A1) <span class="Apple-converted-space"> </span>(C2)</em></strong></p>
<p class="p2"><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for “if… then…”</p>
<p class="p1">For Spanish candidates, <strong>only </strong>accept “Si” and “entonces”.</p>
<p class="p1">Award <strong><em>(A1) </em></strong>for “not break my arm” and “not hurt” in correct order.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2015-12-03_om_07.19.15.png" alt></p>
<p class="p1"><strong><em><span class="Apple-converted-space"> </span>(A1)(A1) <span class="Apple-converted-space"> </span>(C2)</em></strong></p>
<p class="p1"><strong>Notes:<span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1) </em></strong>for each correct column.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">logically equivalent <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)</strong></p>
<p class="p1">last two columns of the truth table are identical <span class="Apple-converted-space"> </span><strong><em>(R1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C2)</em></strong></p>
<p class="p2"><strong>Notes: </strong>Do not award <strong><em>(A1)</em>(ft)<em>(R0)</em></strong>.</p>
<p class="p1">Follow through from the last two columns of the table in part (a).</p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">For events <em>A</em> and <em>B</em>, the probabilities are \({\text{P}}(A) = \frac{4}{13}\) and \({\text{P}}(B) = \frac{5}{13}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>If events <em>A</em> and <em>B</em> are mutually exclusive, write down the value of \({\text{P}} (A\cap B)\).</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>If events <em>A</em> and <em>B</em> are independent, find the value of \({\text{P}} (A\cap B)\).</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>If \({\text{P}} (A \cup B) = \frac{7}{13}\), find the value of \({\text{P}} (A \cap B)\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\({\rm{P}}(A \cap B) = 0\) <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span> \({\rm{P}}(A \cap B) = {\rm{P}}(A) \times {\rm{P}}(B)\)</span></span></p>
<p><span>\( = \frac{4}{{13}} \times \frac{5}{{13}}\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for product of two fractions, decimals or percentages.</span></p>
<p><br><span><span>\({\rm{P}}(A \cap B) = \frac{{20}}{{169}} (= 0.118)\) </span></span> <span><em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{7}{{13}} = \frac{4}{{13}} + \frac{5}{{13}} - {\rm{P}}(A \cap B)\) <em><strong>(M1)(M1)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for \(\frac{4}{{13}} + \frac{5}{{13}}\) seen, <em><strong>(M1)</strong></em> for subtraction of \(\frac{7}{{13}}\) shown.</span></p>
<p><strong><span>OR</span></strong></p>
<p><span>Award <em><strong>(M1)</strong></em> for Venn diagram with 2 intersecting circles, </span><span><em><strong>(A1)</strong></em> for correct probabilities in diagram.</span></p>
<p><br><span>\({\rm{P}}(A \cap B) = \frac{2}{{13}}( = 0.154)\)</span><span> </span><span> <em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question proved to be difficult with many candidates unaware of the significance of mutually exclusive events in probability. A significant number gave the answer to (b) as the answer to (a).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question proved to be difficult with many candidates unaware of the significance of mutually exclusive events in probability. A significant number gave the answer to (b) as the answer to (a).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question proved to be difficult with many candidates unaware of the significance of mutually exclusive events in probability.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">This part proved to be difficult for some but most of the candidates who used the formula were able to achieve full marks. Very few candidates used Venn diagrams to answer this question.</span></p>
<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 universal set <em>U</em> is the set of integers from 1 to 20 inclusive.</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;"><em>A</em> and <em>B</em> are subsets of <em>U</em> where:</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;"><em>A</em> is the set of even numbers between 7 and 17.</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;"><em>B</em> is the set of multiples of 3.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>List the elements of the following sets:</span></p>
<p><span><em>A</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>List the elements of the following sets:</span></p>
<p><span><em>B</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>List the elements of the following sets:</span></p>
<p><span>\(A \cup B\) ,</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>List the elements of the following sets:</span></p>
<p><span>\(A \cap B'\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><em>A</em> = 8, 10, 12, 14, 16 <em><strong>(A1)</strong></em> <strong><em>(C1)</em></strong></span></p>
<p><span><strong><em>[1 mark]<br></em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>B</em> = 3, 6, 9, 12, 15, 18 <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(A \cup B\) = 3, 6, 8, 9,10,12,14,15,16,18 <em><strong>(A2)</strong></em><strong>(ft)</strong></span></p>
<p><em><span>Award <strong>(A1)</strong> only if a single element is missing or a single extra</span> <span>element is present, <strong>(A0)</strong> otherwise. <strong>(C2)</strong></span></em></p>
<p><em><span><strong>[2 marks]<br></strong></span></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(B'\) = 1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20 <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>\(A \cap B'\) = 8, 10, 14, 16 <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Parts (a) and (b) were well done although some candidates added 1 as a multiple of 3.</span></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Parts (a) and (b) were well done although some candidates added 1 as a multiple of 3.</span></p>
<p> </p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Part (c) was reasonably well attempted although some candidates found the intersection instead of the union.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"> </span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Part (d) was successfully completed by those candidates who managed to find the complement of B correctly. If they had not shown the set containing the complement of B in the working they could not be awarded the method mark.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Dune Canyon High School organizes its <strong>school year </strong>into three trimesters: fall/autumn (\(F\)), winter (\(W\)) and spring (\(S\)). The school offers a variety of sporting activities during and outside the school year.</p>
<p>The activities offered by the school are summarized in the following Venn diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_10.56.10.png" alt="M17/5/MATSD/SP1/ENG/TZ1/04"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of sporting activities offered by the school during its <strong>school year</strong>.</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>Determine whether rock-climbing is offered by the school in the fall/autumn trimester.</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>Write down the elements of the set \(F \cap W’\);</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down \(n(W \cap S)\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, in terms of \(F\), \(W\) and \(S\), an expression for the set which contains only archery, baseball, kayaking and surfing.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>15 <strong><em>(A1)</em></strong> <strong><em>(C1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>no <strong><em>(A1)</em></strong> <strong><em>(C1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept “it is only offered in Winter and Spring”.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>volleyball, golf, cycling <strong><em>(A1)</em></strong> <strong><em>(C1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Responses must list all three sports for the <strong><em>(A1) </em></strong>to be awarded.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>4 <strong><em>(A1)</em></strong> <strong><em>(C1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\((F \cup W \cup S)’\)\(\,\,\,\)<strong>OR</strong>\(\,\,\,\)\(F’ \cap W' \cap S’\) (or equivalent) <strong><em>(A2)</em></strong> <strong><em>(C2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(p\) and \(q\) represent the propositions</span></p>
<p style="text-align: left; margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\(p\): food may be taken into the cinema</span></p>
<p style="text-align: left; margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\(q\): drinks may be taken into the cinema</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the truth table below for the symbolic statement \(\neg (p \vee q)\) .</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 in words the meaning of the symbolic statement \(\neg (p \vee q)\).</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 in symbolic form the compound statement:</span></p>
<p><span>“no food and no drinks may be taken into the cinema”.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span> <em><strong>(A1)(A1)</strong></em><strong>(ft) <em>(C2)</em></strong></span></span></p>
<p><span><strong>Note:</strong> <em><strong>(A1)</strong></em> for each correct column.<strong><br></strong></span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>It is not true that food or drinks may be taken into the cinema.</span></p>
<p><span><strong>Note:</strong> <em><strong>(A1)</strong></em> for “it is not true”. <em><strong>(A1)</strong></em> for “food or drinks”.</span></p>
<p><span><strong>OR</strong></span></p>
<p><span>Neither food nor drinks may be taken into the cinema.</span></p>
<p><span><strong>Note:</strong> <em><strong>(A1)</strong></em> for “neither”. <em><strong>(A1)</strong></em> for “nor”.</span></p>
<p><span><strong>OR</strong></span></p>
<p><span>No food and no drinks may be taken into the cinema.</span></p>
<p><span><strong>Note:</strong> <em><strong>(A1)</strong></em> for “no food”, “no drinks”. <em><strong>(A1)</strong></em> for “and”.</span></p>
<p><span><strong>OR</strong></span></p>
<p><span>No food or drink may be brought into the cinema. <em><strong>(A2) (C2)</strong></em></span></p>
<p><span><strong>Note:</strong> <em><strong>(A1)</strong></em> for “no”, <em><strong>(A1)</strong></em> for “food or drink”. Do not penalize for use of plural/singular.</span></p>
<p><span><strong><br>Note:</strong> the following answers are incorrect:</span><br><span>No food and drink may be brought into the cinema. Award <em><strong>(A1) (A0)</strong></em></span><br><span>Food and drink may not be brought into the cinema. Award <em><strong>(A1) (A0)</strong></em></span><br><span>No food or no drink may be brought into the cinema. Award <em><strong>(A1) (A0)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\neg p \wedge \neg q\)</span></p>
<p><span><strong>Note: <em>(A1)</em></strong> for both negations, <em><strong>(A1)</strong></em> for conjunction.</span></p>
<p><span><strong>OR</strong></span></p>
<p><span>\(\neg (p \vee q)\) <em><strong>(A1)(A1) (C2)</strong></em></span></p>
<p><span><strong>Note: <em>(A1)</em></strong> for negation, <em><strong>(A1)</strong></em> for \(p \vee q\) in parentheses.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(a) was generally answered well.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(b) lack of precision in language led to many errors.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(a) was generally answered well.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(b) lack of precision in language led to many errors.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the three propositions <em>p</em>, <em>q </em>and <em>r</em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em> p</em>: <em>The food is well cooked</em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em> q</em>: <em>The drinks are chilled</em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em> r</em>: <em>Dinner is spoilt</em></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write the following compound proposition in words.</span></p>
<p><span>\[(p \wedge q) \Rightarrow \neg r\]</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>Complete the following truth table.</span></p>
<p><br><span><img src="images/Schermafbeelding_2014-09-20_om_07.32.41.png" alt></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><strong>If </strong>the food is well cooked <strong>and </strong>the drinks are chilled <strong>then </strong>dinner is <strong>not spoilt</strong>. <strong><em>(A1)(A1)(A1) (C3)</em></strong></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for “If…then” (then must be seen), <strong><em>(A1) </em></strong>for the two correct propositions connected with “and”, <strong><em>(A1) </em></strong>for “not spoilt”.</span></p>
<p><span> Only award the final <strong><em>(A1) </em></strong>if correct statements are given in the correct order.</span></p>
<p> </p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><br><span><img src="images/Schermafbeelding_2014-09-20_om_07.34.40.png" alt><span> <strong><em>(A1)(A1)(A1)</em>(ft) <em>(C3)</em></strong></span></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for each correct column.</span></p>
<p><span> The final column must follow through from the previous two columns.</span></p>
<p> </p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Consider the following propositions:</p>
<p>\(p:\) The lesson is cancelled</p>
<p>\(q:\) The teacher is absent</p>
<p>\(r:\) The students are in the library.</p>
<p>Write, in words, the compound proposition \(q \Rightarrow (p \wedge r).\)</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>Complete the following truth table.</p>
<p><img src="data:image/png;base64,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" alt></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><strong>Hence</strong>, justify why \(q \Rightarrow \neg r\) is not a tautology.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>if the teacher is absent then the lesson is cancelled and the students are in the library <em><strong>(A1)(A1)(A1) (C3)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for If…then.<br>For Spanish candidates, only accept “Si” and “entonces”.<br>For French candidates, only accept “Si” and “alors”.<br>For all three languages these words are from the subject guide.<br>Award <em><strong>(A1)</strong></em> for “and”,<br>Award <em><strong>(A1)</strong></em> for correct propositions in correct order.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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" alt></p>
<p><em><strong>(A1)(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p>Note: Award <em><strong>(A1)</strong></em> for \(\neg r\) column correct and <em><strong>(A1)</strong></em> for \(q \Rightarrow \neg r\) column correct.<br>Award <strong><em>(A0)(A1)</em>(ft)</strong> for a \(q \Rightarrow \neg r\) column that correctly follows from an incorrect \(\neg r\) column.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>not all of the entries are true (or equivalent) <em><strong>(R1) (C1)</strong></em></p>
<p><strong>Note: </strong>Accept “One entry is false”.</p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Question 4: Logic.<br>All candidates recognized that to fill in a truth table the answer is either true or false. However, given that there are truth tables in the formula booklet it was surprising that some candidates made mistakes when negating a given column of the truth table. Most candidates recognized that in a tautology the column is always true with a small minority confusing tautology and contradiction. Candidates were able to write a compound proposition in words.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 4: Logic.<br>All candidates recognized that to fill in a truth table the answer is either true or false. However, given that there are truth tables in the formula booklet it was surprising that some candidates made mistakes when negating a given column of the truth table. Most candidates recognized that in a tautology the column is always true with a small minority confusing tautology and contradiction. Candidates were able to write a compound proposition in words.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 4: Logic.<br>All candidates recognized that to fill in a truth table the answer is either true or false. However, given that there are truth tables in the formula booklet it was surprising that some candidates made mistakes when negating a given column of the truth table. Most candidates recognized that in a tautology the column is always true with a small minority confusing tautology and contradiction. Candidates were able to write a compound proposition in words.</p>
<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;">You may choose from three courses on a lunchtime menu at a restaurant.</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;"><em>s</em>: you choose a salad,</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;"><em>m</em>: you choose a meat dish (main course),</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;"><em>d</em>: you choose a dessert.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">You choose a <strong>two</strong> course meal which <strong>must</strong> include a main course and either a salad or a dessert, but not both.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write the sentence above using logic symbols.</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 in words \(s \Rightarrow \neg d\) .</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>Complete the following truth table.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(m \wedge (s \underline{\vee} d)\) <em><strong>(A2)</strong></em></span></p>
<p><span><em><strong>(A1)</strong> for</em> \(m \wedge \)</span></p>
<p><span><em><strong>(A1)</strong> for</em> \((s\underline{ \vee } d)\)</span></p>
<p><em><strong>(</strong><span><strong>A1)(A0)</strong> if brackets are missing</span></em>.</p>
<p><strong><span>OR</span></strong></p>
<p><span>\((m \wedge s) \underline{\vee} (m \wedge d)\) <em><strong>(A2)</strong></em></span></p>
<p><em><span><strong>(A1)</strong> for both brackets correct, <strong>(A1)</strong> for disjunctive “or” <strong>(A1)(A0)</strong> if brackets are missing. <strong>(C2)</strong></span></em></p>
<p><em><span><strong>[2 marks]</strong></span></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>If you choose a salad then you do not choose a dessert. <em><strong>(A2)</strong></em></span></p>
<p><em><span><strong>(A1)</strong> for “if …then…”</span> <span><strong>(A1)</strong> for salad and no dessert in the correct order.</span></em></p>
<p><strong><span>OR</span></strong></p>
<p><span>If you choose a salad you do not choose a dessert. <em><strong>(A2)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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" alt></p>
<p><em><span><strong>(A1)</strong> for each correct column <strong>(A1)(A1)(ft)</strong> </span></em><em><span><strong>(C2)</strong></span></em></p>
<p><em><span><strong>[2 marks]</strong></span></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">(a) This caused problems for many candidates. They seem to expect to include the implication symbol somewhere.</span></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">(b) Most candidates managed to write this correctly.</span></p>
<p> </p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">(c) Not all candidates could complete the truth table correctly. Many managed the first column but then made mistakes in the last column.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;"> A group of 33 people was asked about the passports they have. 21 have Australian passports, 15 have British passports and 3 have neither</span>.</p>
</div>
<div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A group of 33 people was asked about the passports they have. 21 have Australian passports, 15 have British passports and 3 have neither.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number that have both Australian and British passports.</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>In the Venn diagram below, set <em>A</em> represents the people in the group with Australian passports and set <em>B</em> those with British passports.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Write down the value of</span></p>
<p><span>(i) <em>q</em> ;</span></p>
<p><span>(ii) <em>p</em> and 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><span>In the Venn diagram below, set <em>A</em> represents the people in the group with Australian passports and set <em>B</em> those with British passports.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Find \(n(A \cup B')\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(21 + 15 + 3 - 33\) or equivalent <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct use of all four numbers.</span></p>
<p> </p>
<p><span>\( = 6\) <em><strong>(A1) (C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) <em>q</em> = 6 <em><strong>(A1)</strong></em><strong>(</strong><strong>ft)</strong></span></p>
<p> </p>
<p><span>(ii) <em>p</em> =15, <em>r</em> = 9 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their answer to part (a).</span></p>
<p> </p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>15 + 6 + 3 <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their figures seen in a correct calculation:</span></p>
<p><span>15 + 6 + 3 or 21 + 3 or 33 − 9</span></p>
<p><span> </span></p>
<p><span>= 24 <em> <strong>(A1)</strong></em><strong>(</strong><strong>ft)</strong><em><strong> (C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from parts (a) and (b) or from values shown on Venn diagram.</span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Much good work was seen in parts (a) and (b). However, there was much confusion in candidates’ responses to part (c) as many could not determine the required answer where a union was involved with a complement. The result was that either candidates simply ignored \(n[(A \cup B)']\) and evaluated \(n(A) = 21\) or ignored \(n[(A \cap B)]\) and evaluated \(n(B') = 18\). Irrespective of ability, the modal mark for this question was four with very few candidates achieving more than this mark.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Much good work was seen in parts (a) and (b). However, there was much confusion in candidates’ responses to part (c) as many could not determine the required answer where a union was involved with a complement. The result was that either candidates simply ignored \(n[(A \cup B)']\) and evaluated \(n(A) = 21\) or ignored \(n[(A \cap B)]\) and evaluated \(n(B') = 18\). Irrespective of ability, the modal mark for this question was four with very few candidates achieving more than this mark.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Much good work was seen in parts (a) and (b). However, there was much confusion in candidates’ responses to part (c) as many could not determine the required answer where a union was involved with a complement. The result was that either candidates simply ignored \(n[(A \cup B)']\) and evaluated \(n(A) = 21\) or ignored \(n[(A \cap B)]\) and evaluated \(n(B') = 18\). Irrespective of ability, the modal mark for this question was four with very few candidates achieving more than this mark.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Police in a town are investigating the theft of mobile phones one evening from three cafés, “Alan’s Diner”, “Sarah’s Snackbar” and “Pete’s Eats”.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">They interviewed two suspects, Matthew and Anna, about that evening.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Matthew said:</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">“I visited Pete’s Eats and visited Alan’s Diner and I did not visit Sarah’s Snackbar.”</span></p>
<p style="text-align: left;"><span style="font-family: times new roman,times; font-size: medium;">Let \(p\) , \(q\) and \(r\) be the statements:</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;">\(p\) : I visited Alan’s Diner</span><br><span style="font-family: times new roman,times; font-size: medium;">\(q\) : I visited Sarah’s Snackbar</span><br><span style="font-family: times new roman,times; font-size: medium;">\(r\) : I visited Pete’s Eats</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down Matthew’s statement in symbolic logic form.</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>What Anna said was lost by the police, but in symbolic form it was</span></p>
<p><span>\[(q \vee r) \Rightarrow \neg p\]</span></p>
<p><span>Write down, in words, what Anna said.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(r \wedge p \wedge \neg q\) <em><strong>(A1)(A1)(A1) (C3)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for two conjunctions, <em><strong>(A1)</strong></em> for negation seen on \(q\), <em><strong>(A1)</strong></em> for correct compound statement.</span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>If I visited (either) Sarah’s Snackbar <strong>or</strong> Pete’s Eats (then) I did not visit Alan’s Diner. <em><strong>(A1)(A1)(A1) (C3)</strong></em></span> </p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for If\( \ldots \) (then), <em><strong>(A1)</strong></em> for Sarah’s Snackbar <strong>or</strong> Pete’s Eats, <em><strong>(A1)</strong></em> for did not visit Alan’s Diner.</span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The logic question was clearly difficult for many students. Part a was very poorly done with the majority of students not recognising that two conjunctions were required. Although candidates performed better on part b, many omitted the 'if, (then)'. One of the most common</span> <span style="font-family: times new roman,times; font-size: medium;">errors in part b was to translate the disjunction as 'and' rather than 'or'.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The logic question was clearly difficult for many students. Part a was very poorly done with the majority of students not recognising that two conjunctions were required. Although candidates performed better on part b, many omitted the 'if, (then)'. One of the most common</span> <span style="font-family: times new roman,times; font-size: medium;">errors in part b was to translate the disjunction as 'and' rather than 'or'.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the following propositions.</p>
<p style="padding-left: 210px;"><em>p</em> : the baby cries<br><em>q</em> : the baby is happy<br><em>r</em> : the baby wants to play</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, in words, \(\left( {q \wedge r} \right) \Rightarrow \neg p\).</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>Complete the following truth table.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State whether \(\left( {q \wedge r} \right) \Rightarrow \neg p\) is a tautology, contradiction or neither.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>if the baby is happy and wants to play then the baby does not cry <em><strong>(A1)(A1)(A1) (C3)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for “If… then…”; <em><strong>(A1)</strong></em> for “the baby is happy and wants to play”, <em><strong>(A1)</strong></em> for “the baby does not cry”. Crying must be negated.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"> <em><strong>(A1)(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for each correct column.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Neither <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C1)</strong></em></p>
<p><strong>Note:</strong> Follow through from the last column in their part (b).</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Consider the statements</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;"><em>p</em> : The numbers <em>x</em> and <em>y</em> are both even.</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;"><em>q</em> : The sum of <em>x</em> and <em>y</em> is an even number.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down, in words, the statement <em>p </em>\(\Rightarrow\) <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>Write down, in words, the inverse of the statement <em>p </em>\(\Rightarrow\) <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>State whether the inverse of the statement<em> p</em> \( \Rightarrow \) <em>q</em> is always true. Justify your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>If (both) the numbers <em>x</em> and <em>y</em> are even (then) the sum of <em>x</em> and <em>y</em> is an even number. <em><strong>(A1)(A1) </strong></em><em><strong>(C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for If…(then), <em><strong>(A1)</strong></em> for the correct statements in the correct order.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>If (both) the numbers <em>x</em> and <em>y</em> are not even (then) the sum of <em>x</em> and <em>y</em> is not an even number. <em><strong>(A1)(A1) </strong></em><em><strong>(C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for If…(then), <em><strong>(A1)</strong></em> for the correct not <em>p</em>, and not <em>q</em> in the correct order. Accept the word odd for the phrase “not even”.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>The inverse of a statement is not (necessarily) true, because two odd (not even) numbers, always have an even sum. <em><strong>(A1)(R1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(A1)(R1)</strong></em> if a specific counter example given instead of a reason stated in general terms, <em>e.g.</em> the inverse is not true because, 5 and 7 have an even sum. Do not award <em><strong>(A1)(R0)</strong></em>. Follow through from their statement in part (b).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Although a few candidates did not seem to understand the meaning of the \(\Rightarrow\) symbol, many scored a minimum of two marks on the first two parts of the question. Indeed, many correct statements were seen in part (a). Many candidates however confused converse with inverse in part (b) resulting in the incorrect statement "<em>if the sum of x and y are both even then the numbers x and y are both even</em>" appearing on many scripts earning <em><strong>(M1)(A0)</strong></em>. Despite this incorrect compound statement, many candidates recovered with correct reasoning in part (c) from their correct (or incorrect) statement in part (b). Candidate's responses to part (c) of the question should have been given in the context of the question set and those that simply inferred their answer from truth tables only, earned no marks.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Although a few candidates did not seem to understand the meaning of the \(\Rightarrow\) symbol, many scored a minimum of two marks on the first two parts of the question. Indeed, many correct statements were seen in part (a). Many candidates however confused converse with inverse in part (b) resulting in the incorrect statement "<em>if the sum of x and y are both even then the numbers x and y are both even</em>" appearing on many scripts earning <em><strong>(M1)(A0)</strong></em>. Despite this incorrect compound statement, many candidates recovered with correct reasoning in part (c) from their correct (or incorrect) statement in part (b). Candidate's responses to part (c) of the question should have been given in the context of the question set and those that simply inferred their answer from truth tables only, earned no marks.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Although a few candidates did not seem to understand the meaning of the \(\Rightarrow\) symbol, many scored a minimum of two marks on the first two parts of the question. Indeed, many correct statements were seen in part (a). Many candidates however confused converse with inverse in part (b) resulting in the incorrect statement "<em>if the sum of x and y are both even then the numbers x and y are both even</em>" appearing on many scripts earning <em><strong>(M1)(A0)</strong></em>. Despite this incorrect compound statement, many candidates recovered with correct reasoning in part (c) from their correct (or incorrect) statement in part (b). Candidate's responses to part (c) of the question should have been given in the context of the question set and those that simply inferred their answer from truth tables only, earned no marks.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the truth table.</span></p>
<p><img src="data:image/png;base64,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" alt></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>Consider the propositions <em>p</em> and <em>q</em>:</span></p>
<p><em><span>p: x is a number less than 10.</span></em></p>
<p><span><em><span><span>q: x2 is a number greater than 100.</span></span></em></span></p>
<p><span><span>Write in words the compound proposition \(\neg p \vee q\).</span></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>Using part (a), determine whether \(\neg p \vee q\) is true or false, for the case where \(x\) is a number less than 10 and \(x^2\) is a number greater than 100.</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>Write down a value of \(x\) for which \(\neg p \vee q\) is false.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAfAAAACjCAIAAAD6o9tcAAAPnUlEQVR4nO3dv2vjeB7G8e+/odptunRTuXKTZps0U6hwkyLdFAIXC9NdITAcLCwcCIZU16g8WAJiYZgmIMLBsBjBFkMwalIsQkUIRnyukB3rh52Z2Zvv54d5XlV2Ljv43lEey7K9dgQAACfBSd8AAAD4MbaD7gAAwKzhoMvcoZwixGSG4IIQXwMMukeIyQzBBSG+Bhh0jxCTGYILQnwNMOgeISYzBBeE+Bpg0D1CTGYILgjxNcCge4SYzBBcEOJrgEH3CDGZIbggxNcAg+4RYjJDcEGIrwEG3SPEZIbgghBfAwy6R4jJDMEFIb4GGHSPEJPZqQSv83jqnHPuPEo/3sZh4JwL5smqkr5hrzESv9M2+7O4XYaBc+4sXH4qm5dvuYunP8X5X6N/93mdXk/m6boZ/nmZ30TTwLmz8F838Sxws6QYfg8TDLpHiMnshIJvyvTKufNp+D4tqmadzgMXRJnmRbcTv6myReAm0+nbKF3V9FceXzh3mRRPL99Q58vpdJnXvVVu1uk86H5bq1ol82B7l9D+VcEsWQntOQbdJ8RkdkLBH7Po3LmL3XniQxpOXJiWwrfqNXbityfps0XWnmq3953TOK/339J8Sefn/V1+zKI30/iu7v1VTZ0vpy7Y/fn2bjjKHhn+bxxkatA3eTxxzjkXROndf+LwzDkXhB9WtdTd4VeojnlUtXscehHf/jsKJI/O76U1+EMaTl79D+RNwvSh929s8ngS7OejyqLATeJ8I3Djv5VQ/JdLKK+4SstOuWaVzIJgf+XkqUgu+2foRERNkcyC63T93P5TnS+n+3/s/VVufy7/mEXnLlhkldgimRp0ou3vxptZuEiL+mmdXgei94evUx9zrH38OIvSVd18Sednskfn9zIYnIjqPL4YDHpTJLP9xLSXCC4OXdVVRGn8TR5PeoPeFMmsOxr1XTwNDl3O+iuPL7a7X9/F08n4QsomjyfdCyxVFklfGbM26FUWBW5/l1im4fjsRg3tMYee1+l14M7m6ZeGaHvuo/th/oC14K3xoD8VyeX+rvTo4uiiNP5w0JsqWwT705S/8vjCjU+9229dp/PgPMoeiuTSjS6pj67VyF9AJ3ODvsnjyf5UpT1z6V/80kR5zKH6Lp52nqBvVsnswFmJZsaCb40H/TGLztsFacpPy/BM83XFF0rjDwe9c1WkKe+WYbC/mD72VCSX7s10evjCY7s/Z/P0S9OUd/+M43+EwejSDTNbg/5UJJedlwTtj3vZm3WM7pgD7dH5cuC2z/YIH53fy1TwF6NBbx+Gbs2iJCu0HuFdSuMPBv3leTjnnAumUZIVrz7yaR8eHXipYvu/fk62z+Qtb4s/s+hc8AWLLVOD3j6bsX3s2S6O3gvopDzmUP/xY3ukSh+d38tU8KM2eTyxdldKRuI3RTLz9Ji+t05iTA16lUVB+9T/c3n3SxichclnpVdbiEh5zKH948dN+WkZRVF4Jn50fi9TwY8ZPAw1w0L8/pMTP9TwuVYhhga9XZydaZRkheY1J9UxD9k+fgym0U2+/m8yeyN+dH4vY8EPqu/iaaD8FYoHGYjfPkvk43n+Zp0tZsPXR0owNOh1Hk9tnbkojvkVTZHMTL1gsWU3eKt3gdfU64tIffxe2x95h9k/0ZTedDuDjhdd8GmqbBGYuu9smQ1+ChBfAyuD3j4FqvcVigdpjfk1eNQP3w/xNTAx6N139+p9G9GYypiva98GvX1Rl63HQ2Qy+OlAfA1MDLpViMkMwQUhvgYYdI8QkxmCC0J8DTDoHiEmMwQXhPgaYNA9QkxmCC4I8TXAoHuEmMwQXBDia4BB9wgxmSG4IMTX4MCgAwCAUcNB579XOVWIyQzBBSG+Bhh0jxCTGYILQnwNMOgeISYzBBeE+Bpg0D1CTGYILgjxNcCge4SYzBBcEOJrgEH3CDGZIbggxNcAg+4RYjJDcEGIrwEG3SPEZIbgghBfAwy6R4jJDMEFIb4Gdga9TMOj741S+klGemOOGcw7Zin4yUF8DcwM+iaPz8IPq7qh7ee97j66qF6l0Vudn0+vNuaYxbxjhoITDT63eMjcRwAai0/U/yg0w+cxXYYG/defd7PSWxyiprhZqPxcOrUxxyzmHTMUfOflM+M781EXt3F4hkH3rs7j+SJbv5zF7O9H61UazTHoTAaLo5aJmGNW8o5ZDL5bkv75YLO6+XCPQfesvs/yqv1yMOhEVOXZPQadhZXFMRFzzEreMYvBh4Nuc0fIZvy98aDbhEH3yETMMSt5xywG7w16U94to6XBR/pkM/4eBl2QlcUxEXPMSt4xi8FHz4yafC6ObMbfw6ALsrI4JmKOWck7ZjF47wy9Lm5jnKFLwKALsrI4JmKOWck7ZjE4rqGrgEGX87xOrwMXzJJVI31TXmch5piZvGMWgx9+lYtBFuPvYdBlDK446s6vPeaYqbxj9oLvX4d+buXdW8cYjN9RZVHgnHNBlFXSt+X/YW3QTUFMZsaCj98pau0etMtY/L1NmV71fwxXaWn1x4BB9wgxmSG4IMTXAIPuEWIyQ3BBiK8BBt0jxGSG4IIQXwMMukeIyQzBBSG+Bhh0jxCTGYILQnwNMOgeISYzBBeE+Bpg0D1CTGYILgjxNcCge4SYzBBcEOJrgEH3CDGZIbggxNfgwKADAIBRw0Hnv1c5VYjJDMEFIb4GGHSPEJMZggtCfA0w6B4hJjMEF4T4GmDQPUJMZgguCPE1wKB7hJjMEFwQ4muAQfcIMZkhuCDE1wCD7hFiMkNwQYivAQbdI8RkhuCCEF8DDLpHiMkMwQUhvgYYdI8QkxmCC0J8DewMepmGR9/sOo3zWvr2HaA35tjRvMEsWTXSt+4bWQpOhz4kusPc50Ubi09EX/kJKF2V15kZ9E0en4UfVnVD2x/DJEwfiIjqVRq9jbJH4dt3iNqYRzwVyWX/OH4us/cXdpbFWnAiaqpsEQzmoy5u4/DMTvaWwfitxyw679+FNnXxWxz+hEH3aJP/+vNutXuDTtQUN4vd16qojXnEpkyvjJ6YtKwFJ9qfJPazN6ubD/cYdBZ1Hk/Hj4maIv1g8BfBzKB3DQZdLRMxOzDoAoaDXuXZvcn+FuMT0WjQm+rj78buSzsw6B6ZiNnRH/T6cxK+S0tLh7a14ESDQW/Ku2W0tHmHajE+EQ0GvSk/La9+MXa1qwOD7pGJmB3toHddYdB9Gz0vZ/URksX4RLQfdLvPR3dg0D0yEbOjf4befEnnOEP3rneGXhe3Mc7QmXXP0Ju6+C3GGTozDLofuIYuANfQpeEaujQMuh8YdAGHX+VikMX4RHTsVS5GWRz053V6HVh4w4uFmF3t69DPdb6o/1tYC06d16Ebzt4yGL+1ex16sMgq5YvyddYGffAUku47Ve0xuwbvFNUd9hhLwenQ+xRtZm8Zi09Ep/YTILI36KYgJjMEF4T4GmDQPUJMZgguCPE1wKB7hJjMEFwQ4muAQfcIMZkhuCDE1wCD7hFiMkNwQYivAQbdI8RkhuCCEF8DDLpHiMkMwQUhvgYYdI8QkxmCC0J8DTDoHiEmMwQXhPgaHBh0AAAwajjo/PcqpwoxmSG4IMTXAIPuEWIyQ3BBiK8BBt0jxGSG4IIQXwMMukeIyQzBBSG+Bhh0jxCTGYILQnwNMOgeISYzBBeE+Bpg0D1CTGYILgjxNcCge4SYzBBcEOJrgEH3CDGZIbggxNcAg+4RYjJDcEGIr4GhQX9Iw8EHuu7MkkLlp3Urjjky+JDonmmc19K375tYCk6HPqK4y9rHFRuLT0RU5/H0+A/AzGHfZWjQiYiaIpn1D/WmvF1cLHUe+spjdm3y+Cz8sKob2u7MJEwfiIjqVRq9jbJH4dv3bQwFJyLa5PHF+6x8pv22tyPS1EUaaT2qjzEWn4iozuP5Ilu/HPT7u9F6lUZzDLp/ZRraOXfRHrNjk//68261e4NO1BQ3i93XyhkKTkS0+SP72G3ePStsqo+/35s4yneMxSciqu+zvGq/HAw6EVV5do9B9w2D7t9g0A0xGpwODLo9duMTHRp0m0wPerVKrueKd0d7zCMw6Pww6MIw6DKGz92p3h3tMY/AoPPDoAvDoMvonaE/r9N3OEP/4TDo/DDowjDoMnAN3T8MOj8MujAMugwMun8YdH4YdGEYdBHt69CDKKukb8m3UB7ziOd1eh24YJasVL5b6zU2gxNRU2WLwDnnzq285H/MbHwiIqqyKHDOzrYcY2jQB+8UNXAuozjmEYP3Llo7XbEXnOjAW6DDtJS+TX+DzfhEtCnTq15/d5WWpo77DkODbg9iMkNwQYivAQbdI8RkhuCCEF8DDLpHiMkMwQUhvgYYdI8QkxmCC0J8DTDoHiEmMwQXhPgaYNA9QkxmCC4I8TXAoHuEmMwQXBDia4BB9wgxmSG4IMTXAIPuEWIyQ3BBiK8BBt0jxGSG4IIQX4MDgw4AAEYNB53/XuVUISYzBBeE+Bpg0D1CTGYILgjxNcCge4SYzBBcEOJrgEH3CDGZIbggxNcAg+4RYjJDcEGIrwEG3SPEZIbgghBfAwy6R4jJDMEFIb4GGHSPEJMZggtCfA0w6B4hJjMEF4T4Ghga9NFn6b6YJYXKD6hXHHOkTMPDcYNZslJZ9wBLwU8O4mtgaNCJiJoimfU/jL4pbxcXS50fTq885shTkVw6N43zevcnz2X2/iLWWfcAY8E3eXzkFMW5/lFugbH4RER1Hk+P/wC6vwhmGBv09kTSyqGuPebQpkyvjB7HLWPBN3l88T4rn2m/7W38pi7SSOtpyjHG4hMR1Xk8X2TrhvY/gO221Ks0mlv8RcCge6Q95hAGndfmj+zj4/bL3qATUVN9/P3exFG+Yyw+EVF9n+VV++Vg0ImoyrN7e78Ipge9WiXX8/RB+jYdpT3mUH/Q689J+C4tLY2KteB7o0G3x258okODbpPJQe9eaAwx6D9MO+hdVxh0Hhh0YRh0Gb0z9Od1+g5n6D9O/wy9+ZLOcYbOBIMuDIMuA9fQPcI1dDEYdGEYdBkYdI8w6GIw6MIw6CLa16EHUVZJ35JvoTzmSPs69PMoe5S+JX+TteB7GHRhGHR2g3eKGjj0FcccGTzbbPO4thS8p6myReAc7k3FVFkUOGfnZPEYQ4NuD2Iysxl89N+0CNNS+jb9DTbj0wm8uKsLg+4RYjJDcEGIrwEG3SPEZIbgghBfAwy6R4jJDMEFIb4GGHSPEJMZggtCfA0w6B4hJjMEF4T4GmDQPUJMZgguCPE1wKB7hJjMEFwQ4muAQfcIMZkhuCDE1wCD7hFiMkNwQYivwYFBBwAAo3qDDgAA1mHQAQBOBAYdAOBE/A92mmIfffG37AAAAABJRU5ErkJggg==" alt><span> </span></span></p>
<p><span><em><strong>(A1)</strong></em> for third column and <em><strong>(A1)</strong></em><strong>(ft)</strong> for fourth column <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(x\) is greater than or equal to (not less than) 10 or \(x^2\) is greater than 100. <em><strong>(A1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for “greater than or equal to (not less than) 10”, <em><strong>(A1)</strong></em> for “or </span><span><span>\(x^2\)</span> is greater than 100”.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>True <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from their answer to part (a).</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Any value of \(x\) such that \( - 10 \leqslant x < 10\). <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from their answer to part (a).</span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This was provocative in the G2 and the comments indicate that candidates found the wording confusing. Candidates were able to write in words the compound proposition \(\neg p \vee q\) and following from their truth table the candidates could state if this was true or false.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This was provocative in the G2 and the comments indicate that candidates found the wording confusing. Candidates were able to write in words the compound proposition \(\neg p \vee q\) and following from their truth table the candidates could state if this was true or false. In part (c) many candidates either stated the correct answer “true” or stated an answer consistent with their truth table and received follow-through marks. Candidates had difficulty writing down a value of \(x\) for which \(\neg p \vee q\) is false.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This was provocative in the G2 and the comments indicate that candidates found the wording confusing. Candidates were able to write in words the compound proposition \(\neg p \vee q\) and following from their truth table the candidates could state if this was true or false. In part (c) many candidates either stated the correct answer “true” or stated an answer consistent with their truth table and received follow-through marks. Candidates had difficulty writing down a value of \(x\) for which \(\neg p \vee q\]) is false.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This was provocative in the G2 and the comments indicate that candidates found the wording confusing. Candidates were able to write in words the compound proposition \(\neg p \vee q\) and following from their truth table the candidates could state if this was true or false.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1"> \(p:x\) is a multiple of \(12\)</p>
<p class="p1"> \(q:x\) is a multiple of \(6\)<span class="s1">.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down in words \(\neg p\).</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 class="p1">Write down in symbolic form the compound statement</p>
<p class="p2"><span class="s1">\(r:\) If \(x\) </span>is a multiple of \(12\)<span class="s1">, then \(x\) </span>is a multiple of \(6\)<span class="s1">.</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">Consider the compound statement</p>
<p class="p2"><span class="s1">\(s:\) If \(x\) </span>is a multiple of \(6\)<span class="s1">, then \(x\) </span>is a multiple of \(12\)<span class="s1">.</span></p>
<p class="p1">Identify whether \(s:\) is the inverse, the converse or the contrapositive of \(r\).</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 class="p1">Consider the compound statement</p>
<p class="p2"><span class="s1">\(s:\) If \(x\) </span>is a multiple of \(6\)<span class="s1">, then \(x\) </span>is a multiple of \(12\)<span class="s1">.</span></p>
<p class="p1">Determine the validity of \(s\). Justify your decision.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(x\) is not a multiple of \(12\)<span class="s1"> <span class="Apple-converted-space"> </span></span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C1)</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(p \Rightarrow q\) <span class="Apple-converted-space"> </span><strong><em>(A1)(A1)(C2)</em></strong></p>
<p class="p1"><strong>Note:<span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1) </em></strong>for \( \Rightarrow \), <strong><em>(A1) </em></strong>for \(p\) and \(q\) in the correct order.</p>
<p class="p1">Accept \(q \Leftarrow p\).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Converse <strong><em>(A1) (C1) </em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">not valid <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1">for example \(18\)<span class="s1"> </span>is a multiple of \(6\)<span class="s1"> </span>and not a multiple of \(12\)<span class="s1"> <span class="Apple-converted-space"> </span></span><strong><em>(R1) <span class="Apple-converted-space"> </span>(C2)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes:<span class="Apple-converted-space"> </span></strong>Do not award <strong><em>(A1)(R0)</em></strong>. Any multiple of <span class="s1">6 </span>that is not a multiple of \(12\)<span class="s1"> </span>can be accepted as a counterexample.</p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Consider the statement<em> p</em>:</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">“If a quadrilateral is a square then the four sides of the quadrilateral are equal”.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the inverse of statement <em>p</em> in words.</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 converse of statement <em>p</em> in words.</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>Determine whether the converse of statement <em>p</em> is always true. Give an example to justify your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>If a quadrilateral is not a square (then) the four sides of the quadrilateral are not equal. <em><strong>(A1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for “if…(then)”, <em><strong>(A1)</strong></em> for the correct phrases in the correct order.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>If the four sides of the quadrilateral are equal (then) the quadrilateral is a square. <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for “if…(then)”, <em><strong>(A1)</strong></em><strong>(ft)</strong> for the correct phrases in the correct order.</span></p>
<p><span> </span></p>
<p><span><strong>Note:</strong> Follow through in (b) if the inverse and converse in (a) and (b) are correct and reversed.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>The converse is not always true, for example a rhombus (diamond) is a quadrilateral with four equal sides, but it is not a square. <em><strong>(A1)(R1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Do not award <em><strong>(A1)(R0)</strong></em>.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">There was confusion among some students about which was the inverse and converse of the given statement.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">There was confusion among some students about which was the inverse and converse of the given statement.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">There was confusion among some students about which was the inverse and converse of the given statement. Part (c) was poorly done with very few students able to provide an example that shows that the converse is not always true.</span></p>
<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 truth table below shows the truth-values for the proposition</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">\(p\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \vee } q \Rightarrow \neg {\text{ }}p\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \vee } \neg q\)</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>Explain the distinction between the compound propositions, \(p\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \vee } q\) and \(p \vee q\).</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>Fill in the four missing truth-values on the table.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State whether the proposition \(p\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \vee } q \Rightarrow \neg p\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \vee } \neg q\) is a tautology, a contradiction or neither.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>Both are 'p or q', the first is 'but not both' <em><strong>(A1)</strong></em></span></p>
<p><em><span>Note: Award mark for clear understanding if wording is poor. <strong>(C1)</strong></span></em></p>
<p><em><span><strong>[1 mark]</strong></span></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span> <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)(A1)</strong></em></span></span></p>
<p><span><em>Note: Follow through is for final column.</em> <em><strong>(C4)</strong></em></span></p>
<p><span><em><strong>[4 marks]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Tautology. <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">a) The majority of candidates were able to explain the difference between inclusive and</span> <span style="font-size: medium; font-family: times new roman,times;">exclusive correctly but many used “and” and “or” to distinguish between the two.</span></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">b) Less than half were able to find the truth value of the two disjunctions in the table</span> <span style="font-size: medium; font-family: times new roman,times;">correctly. Most candidates did gain some marks but a number of them left at least </span><span style="font-size: medium; font-family: times new roman,times;">one cell blank even though it was a 50% chance of getting the correct value.</span></p>
<p> </p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">c) Most candidates answered this part correctly with many receiving follow through</span> <span style="font-size: medium; font-family: times new roman,times;">for “neither” from an incorrect table.</span></p>
<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 propositions <em>p</em> and <em>q</em>.</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;"><em>p</em>:<em> I take swimming lessons</em></span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;"><em>q</em>:<em> I can swim 50 metres</em></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the truth table below.</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 the following compound proposition in symbolic form.</span></p>
<p><em><span>“I cannot swim 50 metres and I take swimming lessons.”</span></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><span>Write the following compound proposition in words.</span></p>
<p><span>\(q \Rightarrow \neg q \)</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span> <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for each correct column. Follow through in 4<sup>th</sup> column from their 3<sup>rd</sup> column.</span></p>
<p><br><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\neg q \wedge p\) <em><strong>(A1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(\neg q\) and <em>p</em> in any order, <em><strong>(A1)</strong></em> for \(\wedge\).</span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>If I can swim 50 metres (then) I do not take swimming lessons. <em><strong>(A1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for If… (then), <em><strong>(A1)</strong></em> for correct propositions in the correct order.</span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well answered by most of the candidates who could complete the truth table, write the proposition in symbolic form and write the given proposition in words, although the '<em>If </em>' was sometimes omitted. Where marks were lost on Question 2, it was generally in the second column of the truth table.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well answered by most of the candidates who could complete the truth table, write the proposition in symbolic form and write the given proposition in words, although the '<em>If </em>' was sometimes omitted. Where marks were lost on Question 2, it was generally in the second column of the truth table.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well answered by most of the candidates who could complete the truth table, write the proposition in symbolic form and write the given proposition in words, although the '<em>If </em>' was sometimes omitted. Where marks were lost on Question 2, it was generally in the second column of the truth table.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the universal set \(U = \{ x \in \mathbb{N}|3 < x < 13\} \), and the subsets \(A = \{ {\text{multiples of 3}}\} \) and \(B = \{ 4,{\text{ }}6,{\text{ }}12\} \).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>List the elements of the following set.</span></p>
<p><span><em>A</em></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>List the elements of the following set.</span></p>
<p><span>\(A \cap B'\)</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>Write down one element of \((A \cup B)'\).</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>One of the statements in the table below is false. Indicate with an <strong>X</strong> which statement is false. Give a reason for your answer.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>6, 9, 12 <em><strong> (A1) (C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>9 <strong><em> (A1)</em>(ft)<em> (C1)</em></strong></p>
<p><span><br> </span><strong>Note:</strong> Follow through from their part (a)(i).</p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>any element from {5, 7, 8, 10, 11} <em><strong> (A1)(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for finding </span><span>\((A \cup B)\), follow through from their <em>A</em>.</span></p>
<p><span>Award full marks if all correct elements of </span><span><span>\((A \cup B)'\)</span> are listed.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>\(15 \notin U\) <em><strong> (R1)(A1) (C2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Accept correct reason in words.</span></p>
<p><span>If the reason is incorrect, both marks are lost.</span></p>
<p><span>Do not award <em><strong>(R0)(A1)</strong></em>.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The question was not well answered by the majority of the candidates. Many did not identify the universal set correctly and so took 3 to be a member of this set. This affected their answers in a)(i) and a)(ii).</span></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">The question was not well answered by the majority of the candidates. Many did not identify the universal set correctly and so took 3 to be a member of this set. This affected their answers in a)(i) and a)(ii).</span></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Not many students answered (b) correctly. Some listed all correct elements of the given set instead of just one, which shows that they did not read the question carefully.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Although many candidates could indicate which statement in the table in c) was false, often they were unable either to identify or articulate a correct reason for it.</span></p>
<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 two propositions <em>p</em> and <em>q</em>.</span></p>
<p style="text-align: center;"><span style="font-size: medium; font-family: times new roman,times;"><em>p</em>: The sun is shining <em>q</em>: I will go swimming</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write in words the compound proposition</span></p>
<p><span>\(p \Rightarrow q\) ;</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write in words the compound proposition</span></p>
<p><span>\(\neg p \vee q\).</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 truth table for these compound propositions is given below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Complete the column for \( \neg p\).</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 truth table for these compound propositions is given below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>State the relationship between the compound propositions \(p \Rightarrow q\) and \(\neg p \vee q\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>If the sun is shining then I will go swimming. <em><strong>(A1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><strong> </strong></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for “if…then” and <em><strong>(A1)</strong></em> for correct order.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Either the sun is not shining or I will go swimming. <em><strong>(A1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for both correct statements and <em><strong>(A1)</strong></em> for “either” “…or”.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span> <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></span></p>
<p><span><span><em><strong>[1 mark]</strong></em></span></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>They are (logically) equivalent. <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Do not accept any other answers.</span></p>
<p><span> </span></p>
<p><em><strong><span>[1 mark]</span></strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The most common error was poor use of the “If...then” connective.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;"><span style="font-size: medium; font-family: times new roman,times;">Confusion between “and” and “or” was rare, however, the use of implication in this part was a little too common.</span></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;"><span style="font-size: medium; font-family: times new roman,times;">Precise, correct terminology was expected in this part.</span></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Two propositions \(p\) and \(q\) are defined as follows</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;"><em> </em>\(p\): Eva is on a diet</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;"><em> </em>\(q\): Eva is losing weight.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the following statement <strong>in words</strong>.</span></p>
<p><span>\[q \Rightarrow p\]</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, in words, the contrapositive statement of \(q \Rightarrow p\).</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>Determine whether your statement in part (a) is logically equivalent to your statement in part (b). Justify your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>If Eva is losing weight then Eva is on a diet <strong><em>(A1)(A1) (C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for If… then…</span></p>
<p><span> For Spanish candidates, <strong>only </strong>accept “Si” and “entonces”.</span></p>
<p><span> For French candidates, <strong>only </strong>accept “Si” and “alors”.</span></p>
<p><span><em> For all 3 languages these words are from the subject guide.</em></span></p>
<p><span> Award <strong><em>(A1) </em></strong>for correct propositions in correct order.</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>If Eva is not on a diet then she is not losing weight <strong><em>(A1)(A1) (C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for “not on a diet” and “not losing weight” seen, <strong><em>(A1) </em></strong>for complete correct answer.</span></p>
<p><span> No follow through from part (a).</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>The statements are logically equivalent <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span>The contrapositive is always logically equivalent to the original statement <strong><em>(R1)</em>(ft)</strong></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>A correct truth table showing the equivalence <strong><em>(R1)</em>(ft) <em>(C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Follow through from their answers to part (a) and part (b).</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Aleph has an unbiased cubical (six faced) die on which are written the numbers</p>
<p class="p1"><span class="s1">1 </span>, <span class="s1">2 </span>, <span class="s1">3 </span>, <span class="s1">4 </span>, <span class="s1">5 </span>and <span class="s1">6</span>.</p>
<p class="p1">Beth has an unbiased tetrahedral (four faced) die on which are written the numbers</p>
<p class="p1"><span class="s1">2 </span>, <span class="s1">3 </span>, <span class="s1">5 </span>and <span class="s1">7</span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Complete the Venn diagram with the numbers written on Aleph’s die (\(A\)) and Beth’s die (\(B\))<span class="s1">.</span></p>
<p class="p1"><span class="s1"><img src="images/Schermafbeelding_2015-12-20_om_06.18.17.png" 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 class="p1">Find \(n(B \cap A')\).</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 class="p1">Aleph and Beth are each going to roll their die once only. Shin says the probability that each die will show the same number is \(\frac{1}{8}\).</p>
<p class="p2">Determine whether Shin is correct. Give a reason.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="s1"><img src="images/Schermafbeelding_2015-12-20_om_06.22.44.png" alt> <span class="Apple-converted-space"> </span></span><strong><em>(A1)(A1) <span class="Apple-converted-space"> </span>(C2)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for <span class="s2">2</span>, <span class="s2">3</span>, <span class="s2">5 </span>in intersection, <strong><em>(A1) </em></strong>for <span class="s2">1</span>, <span class="s2">4</span>, <span class="s2">6</span>, <span class="s2">7 </span>correctly placed.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="s1">\(1\) <span class="Apple-converted-space"> </span></span><strong><em>(M1)(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C2)</em></strong></p>
<p class="p1"><strong>Notes:<span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1)(A0) </em></strong>for listing the elements of their set \(B \cap A'\);shading the correct region on diagram; or an answer of \(1/7\)<span class="s1"> </span>with a correct Venn diagram. Follow through from part (a).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Correct, from \((2,{\text{ }}2){\text{ }}(3,{\text{ }}3)\) and \((5,{\text{ }}5)\) on sample space</p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">Correct, from a labelled tree diagram</p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">Correct, from a sample space diagram</p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">Correct, from \(3 \times \frac{1}{4} \times \frac{1}{6}\;\;\;\)(or equivalent) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(R1) <span class="Apple-converted-space"> </span>(C2)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: </strong>Do not award <strong><em>(A1)</em>(ft)<em>(R0)</em></strong><em>. </em>Award <strong><em>(R1) </em></strong>for a consistent reason with their part (a). Follow through from part (a).</p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>The Venn diagram in part (a) was successfully completed by the majority of candidates.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many identified correctly the set B ∩ A′ , but listed the element instead of writing the number of elements in the set.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>In part (c) the majority stated that Shin was incorrect giving probabilities of 3/8 (3/6 × 3/4) or 3/7 as being the correct probability. The few candidates using a sample space diagram usually answered correctly, tree diagrams were hardly used. Many candidates did not realize that it was not enough for each to roll one of the three numbers in the intersection, but that they needed to roll the same number. Probabilities of joined events seemed to be too difficult for the majority.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p class="p1">Consider the following Venn diagrams. Each diagram is shaded differently.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-20_om_14.02.25.png" alt></p>
<p class="p1">In the following table there are six sets. Each of these sets corresponds to the shaded region of one of the Venn diagrams. In the correct space, write the number of the diagram that corresponds to that set.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-20_om_14.02.45.png" alt></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p class="p1"><span class="Apple-converted-space"><img src="images/Schermafbeelding_2015-12-20_om_14.04.51.png" alt> </span><strong><em>(A6)(C6)</em></strong></p>
<p class="p1"> </p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for each correct entry.</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The probability that it snows today is 0.2. If it does snow today, the probability that it will snow tomorrow is 0.6. If it does not snow today, the probability that it will not snow tomorrow is 0.9.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using the information given, complete the following tree diagram.</span></p>
<p><br><span><img src="images/Schermafbeelding_2014-09-20_om_08.12.00.png" alt></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>Calculate the probability that it will snow tomorrow.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><br><span><img src="images/Schermafbeelding_2014-09-20_om_08.13.34.png" alt><span> <strong><em>(A1)(A1)(A1) (C3)</em></strong></span></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for each correct pair of probabilities.</span></p>
<p> </p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(0.2 \times 0.6 + 0.8 \times 0.1\) <strong><em>(A1)</em>(ft)<em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A1)</em>(ft) </strong>for two correct products of probabilities taken from their diagram, <strong><em>(M1) </em></strong>for the addition of their products.</span></p>
<p> </p>
<p><span>\( = 0.2{\text{ }}\left( {\frac{1}{5},{\text{ 20% }}} \right)\) <strong><em>(A1)</em>(ft) <em>(C3)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Accept any equivalent correct fraction.</span></p>
<p><span> Follow through from their tree diagram.</span></p>
<p> </p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium;"><span style="font-family: times new roman,times;">Consider two propositions <em>p</em></span> <span style="font-family: times new roman,times;">and</span> <span style="font-family: times new roman,times;"><em>q</em></span>.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the truth table below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></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>Decide whether the compound proposition</span><br><span>\[\left( {{\text{ }}p \Rightarrow \neg q} \right) \Leftrightarrow \left( {\neg p \Rightarrow q} \right)\]</span><br><span>is a tautology. State the reason for your decision.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt> </span><span><em><strong><span>(A1)(A1)</span></strong></em><strong><span>(ft)</span></strong></span><span><em><strong><span>(A1)(A1)</span></strong></em><strong><span>(ft)</span></strong><em><strong><span> (C4)</span></strong></em></span></p>
<p><br><span><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for each correct column (second column <strong>(ft)</strong> from</span> <span>first, fourth <strong>(ft)</strong> from third). Follow through from second column</span> <span>to fourth column for a consistent mistake in implication.</span></span></p>
<p><span><span> </span></span></p>
<p><em><strong><span><span>[4 marks]</span></span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Since second and fourth columns are not identical <strong> <em>(R1)</em>(ft)</strong></span><br><span>\( \Rightarrow \) Not a tautology <em><strong> (A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span><br><br><span><strong>Note: <em>(R0)(A1)</em></strong> may <strong>not</strong> be awarded.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium;"><span style="font-family: times new roman,times;">The truth table was well done by the majority of candidates but significantly fewer could give</span> <span style="font-family: times new roman,times;">the correct reason for whether the compound proposition was a tautology, so many lost 2</span> <span style="font-family: times new roman,times;">marks in this part of the question.</span></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The truth table was well done by the majority of candidates but significantly fewer could give the correct reason for whether the compound proposition was a tautology, so many lost 2 marks in this part of the question.</span></p>
<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;">Alan’s laundry basket contains two green, three red and seven black socks. He selects one sock from the laundry basket at random.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the probability that the sock is red.</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>Alan returns the sock to the laundry basket and selects two socks at random.</span></p>
<p><span>Find the probability that the first sock he selects is green and the second sock is black.</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>Alan returns the socks to the laundry basket and again selects two socks at random.</span></p>
<p><span>Find the probability that he selects two socks of the same colour.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{3}{{12}}\left( {\frac{1}{4},0.25,25\% } \right)\) <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\left( {\frac{2}{{12}}} \right) \times \left( {\frac{7}{{11}}} \right)\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct product.</span></p>
<p><br><span>\( = \frac{{14}}{{132}}\left( {\frac{7}{{66}},0.10606...,10.6\% } \right)\) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\left( {\frac{2}{{12}} \times \frac{1}{{11}}} \right) + \left( {\frac{3}{{12}} \times \frac{2}{{11}}} \right) + \left( {\frac{7}{{12}} \times \frac{6}{{11}}} \right)\) <em><strong>(M1)(M1)</strong></em></span><br><br></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for addition of their 3 products, <em><strong>(M1)</strong></em> for 3 correct products.</span></p>
<p><br><span>\( = \frac{{50}}{{132}}\left( {\frac{25}{{66}},0.37878...,37.9\% } \right)\) <em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(U\) is the set of <strong>positive </strong>integers less than or equal to \(10\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(A\), \(B\) and \(C\) are subsets of \(U\).</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;"><em> </em>\(A = \left\{ {{\text{even integers}}} \right\}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em> </em>\(B = \left\{ {{\text{multiples of }}3} \right\}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em> </em>\(C = \left\{ {6,{\text{ }}7,{\text{ }}8,{\text{ }}9} \right\}\)</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>List the elements 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>List the elements of \(B\).</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>Complete the Venn diagram with <strong>all </strong>the elements of \(U\).</span></p>
<p><br><span><img src="images/Schermafbeelding_2014-09-02_om_17.36.22.png" alt></span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(2, 4, 6, 8, 10\) <strong><em>(A1) (C1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Do not penalize the use of \(\left\{ {{\text{ }}} \right\}\).</span></p>
<p><span> </span></p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(3, 6, 9\) <strong><em>(A1) (C1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Do not penalize the use of \(\left\{ {{\text{ }}} \right\}\).</span></p>
<p><span> Follow through from part (a) only if their \({\text{U}}\) is listed.</span></p>
<p> </p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span> <br><img src="images/venny.jpg" alt width="500" height="316"> <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)<em>(A1)</em>(ft)<em>(A1)</em>(ft) <em>(C4)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(A1)</em>(ft) </strong>for the correct placement of \(6\).</span></p>
<p><span> Award <strong><em>(A1)</em>(ft) </strong>for the correct placement of \(8\) and \(9\) and the empty region.</span></p>
<p><span> Award <strong><em>(A1)</em>(ft) </strong>for the correct placement of \(2\), \(4\), \(3\), \(7\), and \(10\).</span></p>
<p><span> Award <strong><em>(A1)</em>(ft) </strong>for the correct placement of \(1\) and \(5\).</span></p>
<p><span> If an element is in more than one region, award <strong><em>(A0) </em></strong>for that element.</span></p>
<p><span> Follow through from their answers to parts (a) and (b).</span></p>
<p> </p>
<p><span><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was done well by most candidates. The most frequent error was to omit the placement of 1 and 5 or to include 0 in the set of even integers.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was done well by most candidates. The most frequent error was to omit the placement of 1 and 5 or to include 0 in the set of even integers.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was done well by most candidates. The most frequent error was to omit the placement of 1 and 5 or to include 0 in the set of even integers.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A survey was carried out at an international airport. A number of travellers were interviewed and asked for their flight destinations. The results are shown in the table below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAoYAAAByCAIAAABBdIcIAAAav0lEQVR4nO2dzWsbybrGz3/SDb2SQGDjjVZeDQfFC2HCLA54E1AECoyDFwPnQguZG7IId0DCIiFwYGgRExh8yLTIEAaCh8JwCEGhmXvBHETDHK4JTXMxB0/TCyNEUXdRVf3dbSWRLOmd90cvYqnVX89b9VTVW9X5E0MQBEEQZAX407IvAEEQBEEQxtCSEQRBEGRFQEtGEARBkJUALRlBEARBVoLQkjVFxQ033HDDDTfcbnnLtuRbbQwgKwmGAQxQRxigjuBJSIyWjMTAMIAB6ggD1BE8aMlIERgGMEAdYYA6ggctGSkCwwAGqCMMUEfwoCUjRWAYwAB1hAHqCB60ZKQIDAMYoI4wQB3Bg5aMFIFhAAPUEQaoI3jQkpEiMAxggDrCAHUED1oyUgSGAQxQRxigjuBBS0aKwDCAAeoIA9QRPGjJSBEYBjBAHWGAOoJnNS156pr7WW/+rDa7P/xkuXSe56K+1d9Rqk3j3J/nYTlXVveuVmoNxt78j30rrFoVQG1jV9kb2Ne3f+ZFxsnCWTUdc6HjQX1z1xjnlPGJa71s18qaomql+/1RXlWw9uUuj7XRcSaubWNPqxv2rBX6epfBGVlNS2aM8cJZ1hRVU/aH7pSxiTt63iypmlJtHr37Mlu+sp6+tKb8377VvaMpqrbRlZ98Gf7omfGrONLU6m2omqJuzenYt8/ywyDGtW3saUo5v8peHPOOk9tlxXTMhdrGrqLmVNO8Rla1umE7ZjN3NwjlLo910XEmRA0/ewt7vcvgjKywJbOPw8ZmxJJZWCaV6gPz4nMrZepb/Z1Q1Pm2vK6s7t1IRbD2rfUVCIMI/qjHe0i1vuXfsimvdwt9tXTM5crq3tUUVVPu9qyr1Le8QaZqDdP1SLtU3umOcrRY+3KXx5roOAtBZV6gY+ZP1rUMzsh6WXKk61zqEO8zKmXqj4+bpQW1s7yx0arAapuvQBgEUI883q1ta4qqKdttcrns61knVknHfDxyWL/zZ0XVFLWik5Sdyk5Sw3SXcXWrwHroOBOXpPOXna++pDKHybpZctBSVu70LNlU8u1fuvcriqop9fYLmV+i7ocj/qGqKZtN8yNjnm12dqLJ6YYx5IVclvOp1d3if248Hr7nWavyjm7aYZ/Ms8lJr1HVePtOf2m5E8YY88dDvR5Je282T0746Jk8e+JSyzu6QWxR7cxw3uWwAmEgoRfDb578Mvp+N7PKlmOVmrLZNN4G8XBInKl7eiiyj/FuU0bYyEpfUbe6o9/tt71GVSt1iOdZ8ThhjDHm2af9ZknVFFWr6cfBFAffJq+64vNoQC6VFdIxl4ljdg5Pz3La3KE0sk64yhbr36OMcrdWYhWwDjrOBHXMh503H0RlnmphZ9TefkYZXDf5ZmHtLDmY+SXLm38+aFS10sHQmVDb2BVj2tQjnYrIUnj26fPea14409kIeRYhc2D59UPiUI+0S9Gyzb/dbpNLRi+GraoWTWilM1iu2YxeqvjJ3Z51Jf4dmkTxeZfGCoSBgNrG1zrxgseeSkGJNKSiVhrHY//aMQ8qiqqVvtr5artpnA717ZhY2WETDsNU7j368VfXNvZk4y8RJ3xEpLxrjKVYewP7Wvy81CEepY75oKQuKfOdZHV0zIWOB3cfEU8Kl/HcUoU3T6xEuVs3sQpYAx1n4to29tvkUj72xLSAvNo7XgbXUL5ZWHdL5uJJkbgpbnStKd8t3dG80ZLl8fkOSZed8PqiohMvfagbLFleqthfeLDs7RWfd2msQBhwrm1D71lX4WNMF794RSwHHnjmKf54c8OGhfFQN2zKqG3siu5aPE6iNbvIXB4MnYlsdW23yeXqiMhWSMdcqH38gOcUxbNNz97KL7wJsRKWvG5iFbD6Os4EHQ9aTy2fMnZJeFs51sLOq70Tlrx+8s3C2llyYuA6MZylhvsHU4FK93undjDG/WWWzKG+TQbdJ20+fD2rJScyYQmTQEsuxCPtu7KCDqrsxCSvbEvmwZN42vlhI+MhlcuMxUn84BmXa5Pj3n/pfEht6SKy1dExl0ui78tKOaimE5O8cgtvUqyiSEizcmIVsPI6zgL1yKOvRXs6bGHHJnll196JupqzTvLNwtpZsiyuou8iS2nmcgjqWi/0nbCrxOZgyTwBWToYOv/+xF4yWvJnE5TbxBZPQX2GJWeEjYiH1JOPxklwPZEJDfJSffttr1GttExnsioislXRMZ+gmRXf4l4rm+Opwpt8wpmjU+sjVgGrruNMBE2u+JaYPZBReyfq6vWTbxbWzJJlziBYBCVLKR+JyoLy2T2JuvgzLVks0viigWthA+LnOHB9M/Ri+M2TaHEN08bRKvsTLLkgbGax5OACUus3ROt+5QbTVkLHXCaO2TmMtq6yF1YkRGSzWfL6iVXAaus4E9QxH3ayWlpZyyjitXe8rl5D+WZhhS05+aoQ6ttmu1ZOvCokmCBQaRyPfcqoa72xXDp1Xz/tmZZLRcqh0jIdyiJ1cYdcXZyd/YvG01GxHTwaNN6F0sG03rphe3JoJT3ZRCe/O+/PfruWVYPMeoopRa3B2BPxlJ7elXne5bECYeCQTj05MhlO8goXKcqaN9E34jmq+OPNDZuYiNkD1yJO5Apa8Q4p6tv/ILYn2wHlXeOfnlh2uXwR2SromMvEJY93kvOrJ3KSlxSIsbSIuWIlyt26iVXACus4E9Q9Pax9lbDecJKXqA/zau9YGVxH+WZhNS0574Wa9bZhBguHJGL4QlTQ3be2Txmbumf/sD2+MCmyVIlJX1TKO51Tl8Zyiltd6zpYjKSoWuNJT3TTg4perDzWavqAnNvk8Q6/KnPs8yvhi575rOlwWU5k0CxceKNWGv1f0ougss+7NJZcBcSeoRwsiX2oilZz4mmbRjP4duPJ8GQ/tjNjOWETzzGHKatknExZdGBNrTS6Q76uJogu3SDjf5JOXVNUrdYZJoP2tlnVqjz6YINQT2f6Y0uesj8JxMosd2slVgGrquNMxGs5oVfsQxEG/8qqvVNlcA3lm4XVtGRkVcAwgAHqCAPUETxoyUgRGAYwQB1hgDqCBy0ZKQLDAAaoIwxQR/CgJSNFYBjAAHWEAeoIHrRkpAgMAxigjjBAHcGDlowUgWEAA9QRBqgjeNCSkSIwDGCAOsIAdQQPWjJSBIYBDFBHGKCO4EFLRorAMIAB6ggD1BE8aMlIERgGMEAdYYA6ggctGSkCwwAGqCMMUEfwFFkybrjhhhtuuOF2y1u2Jd9CiwBZcTAMYIA6wgB1BI+GA9dIARgGMEAdYYA6ggctGSkCwwAGqCMMUEfwoCUjRWAYwAB1hAHqCB60ZKQIDAMYoI4wQB3Bg5aMFIFhAAPUEQaoI3jQkpEiMAxggDrCAHUED1oyUgSGAQxQRxigjuBBS0aKwDCAAeoIA9QRPGjJSBEYBjBAHWGAOoIHLRkpAsMABqgjDFBH8MzPkqdWbyN4RWf1gXlBxRe+1b0jP7/Ts/wvveTYObtb4sj7Q3c6xyPPBHWtF/qOomqKWmk8/+BO5n8K12wu8QbhVgHUMR+U9gb2dexTj7RLQQynvl1nQOpIXeunV91mSdVKHeLx+sazT/tNLmJNP7ZcesMx1gyQOgqo++HofkVRNaXeNscRn6Ae6VSSb4EGVTyjzLeXHHl2pYOhE1oUdcyH35jO/MvH1DX3l+RYV1b3rqaUd41zx9zXlPKuMV5A+Q8eKVry/KAXw1Y1VaonjnkQlvy6YQOqzsHpOHFHz5ularN7Qmwv+NB5/bx/avssqN/v9qyrJV7l3AGnY8DVf5uvPrgTqex2m1zKry6Jvp38jxlgFc8ocx64nlrPH+oHsuN4PPZp8MWzp9YCLGV5lkzHg3pZUzab5oVHOosr/HIkAC15XlxZ3YP/0O9VEpbsj3r1R7KzBQ1YOlLf6u+U7vdH8U4w/dfZ2cfwEzoe1MsVnXip368vsHQMob+9Owu7cJdE3w6F8856/3kaUZp65NHXC+n/rARzt2TjmeWMjVZFUTWlvNMd+fILaJYsBuo3m+bHBZ8HLXmOUN962uy+d0gnbsl8NKK8o38/JPY8kyurASgd/VGvth1JjeURr9lBAErHPOh4UP9L0MOh7m+/+TT+7T2oo9ZsMZbsM+qQTl1TVC3oO4aWHJioqm10renHYWOT/7nVtaax9HBrQN70GlVNUbXaY+L6Lnmc6n8HRwt3TqZ1ffuXrkxRvODt6jC9vdUd/W6/7TWqkXRUlFhqahBU1rHEuao1TDf5HD7pLhhjnk1OxG5KeUd/aclbyLDkjDuKZmLm2VCAVgX4o17jqeVPvYQlizEPVT5/0/ZBtcIB6XhtG3taTR/wLLJSbXbf5oh1SfT6DM69TgDSMRPq22Sg7x+S3CQntY2vW4vIga4Ki7Fkxph/PhA+1Ld8Gu8lS0fc6FrTcE4Nt2RR5BRVU6pN49wXaT+1Urvz51Jr8P5Vu6RGEreBJfMZAZ7ooPOTBpdROhg6E2obu8G8M1kFV+49+vFX1zb2sqae8eQi7+vzf1ebxnnCleVlJ/iku+A7b7fJpUxzhsmSpCVn3xGNeIxnnz7vvUZLTnNldb/tWVcs9rgiUNd6/X27Vo4N8IAAjo50PKhvyjYr9cfHzVKOWB5p12U9AAU4OmYQ5IwL2sTXtrEfSTMDZGGWLCa1qpqiVlqmM8m35KS3Jcai5c6l1mDsMSZ61Tk7M2obu4oq7C2YG8V7sfxE/KTyONz5qG3spnvJoq0grFocOdjtBkv+pLsQE4sqOvESDydpyXl3xE83/+4doCqA+tbfDkWfKceSxY4O6dRzRk3WFTg6eqQdm/vDm7NpKYPmFyjg6JiHXMZSyewK0/HgLtgJH5wFWrKYhcHXRJ380P9CSxaDwzdYslw1xEduo+uvgo3vKY5TkGpKdk/FkWVn+vMsOfsu5OOyyaD7pM1HF7ItOf+O/FGvVtYUVSvd753OLRsKpwrwR/3Oa1nICy2Zpev9tQeMjtQ2dpWYNOlPePOrHQxoAQKMjoVc28ZeZpuY2sbXsCYHpFmoJbPowpKI/dyCJfMiKn+bMWM+0xQT91JoyXLoez6WzNPDpYOh8+/CXnLBHUXXSUcG2L8MKFVA5tLG/NUU4KaQQNGRt5ZiCw6pbezGW1fU+bn/AqAfM0g6FpI9bPkHGLVmi7dkJtfvRq1L5lnnacmiTMqBa/6nPFF8kTTLOE4WYuBaHFlYYxgoxUf4pLsQj2iGgeuCOxJQ9/SwVg5+/oUArQJu7iUfdkA1xgHpeEn07cioJvVIpxJpV1GX9I+IXDND/fGrwRmcShyQjgVQj3S20gPXf4BRazZvS544pv4wPcWRXgxb1Yh1yS5LqUO862AGcmp6FzchmfPnpS6YliWGLwLn47OcxOs7gukeYT6bT2+mrvXGcjOOkwmfLMZ7nPzIkd7nDUf4lLsI5m/XDduT48/CU4PunWxzZN/R1H39tGfyW7sYtqrZmZhPB2gVkLRk6lo/vRaveqLuu77eJYt4F9vygKQjdcwHJVESqfuu37gnc8bUt812LZg5D/A1T5B0jDBxzIOKfNsadU8P6/uDcbJa/SOMWrNFvVAz3UXzR8+MX8PP/PFQr/PEZ/+d+Z344Z2e5UeWD6naxpPhyX5Qura6J3+XK6Zktnjqmn9tHr1znHd9noJNZlKpz9c4KdH1EvGMbGoJU4TIIqjokT9hEdQsdxFMFNcH5NwWbZR62xz74Qs1Q5POuqOpe/YP2+NPNbaG6gsBWgWkLfn0MMjEvzoDtgKKQdMxUgQib80MWqs3JybWFlg6BvCZ86qs08ys6uvaNnR48/XSzHngGgEGhgEMUEcYoI7gQUtGisAwgAHqCAPUETxoyUgRGAYwQB1hgDqCBy0ZKQLDAAaoIwxQR/CgJSNFYBjAAHWEAeoIHrRkpAgMAxigjjBAHcGDlowUgWEAA9QRBqgjeNCSkSIwDGCAOsIAdQQPWjJSBIYBDFBHGKCO4EFLRorAMIAB6ggD1BE8aMlIERgGMEAdYYA6gqfIknHDDTfccMMNt1vesi35FloEyIqDYQAD1BEGqCN4NBy4RgrAMIAB6ggD1BE8aMlIERgGMEAdYYA6ggctGSkCwwAGqCMMUEfwoCUjRWAYwAB1hAHqCB60ZKQIDAMYoI4wQB3Bg5aMFIFhAAPUEQaoI3jQkpEiMAxggDrCAHUED1oyUgSGAQxQRxigjuBBS0aKwDCAAeoIA9QRPGjJSBEYBjBAHWGAOoJnfpY8tXobwSs6qw/MCyq+8K3uHfn5nZ7lf+klx87Z3RJH3h+60zkeeSaoa73QdxRVU9RK4/kHd5L6fnSs1/kDaR69c2nmUebFx2FjU1NUTdlsmh/ndVBgVQB13/UbVU1RtVpnaHvJrz3SLgUxvDewr5dxjQsBmI6SiWMeVOqGnS5Z1LVe/9BrVDVlu00ul3BpiwGojowx6ttve7xsKvX2i1Gqtrwk+rYsm+VdY7zY2nR5zLeXTD3SqfCnVjoYOqFFUcd8+I3pzP8pTl1zf0mWfGV172pKedc4d8z9jCjxR71aWVP2BrY9bGzeRhUvHAUtOQf/f4Yv3ruUMep+OLpfKXWIF1Vs4pgHleDN75kV/doCSkcJdcwHpQyleMOr0uj+SOx59gBWAJA6Msao83P/6K3tU8Ym7uh5s1Te6Y782A7mA6DN5QRzHrieWs8f6gey43g89mnwxbOn1gI8c3mWTMeDellTNpvmhUc6FeVuz7qKfW8bu+LCXKJva7W+5S+4jhcDFWjJmVz/dvY+bBR6pF2K95/8Ua/+KG7ScACko8Qf9RrfthvVpCX7o15te/GDUssBoI6MJcsmu7aNPS3WYr6yuvchjXYUMHdLNp5ZzthoVRRVUyItHXiWfJP/yUH1W7wwtOSZobaxG2sk8QGe8o7+/RBc14oB1PHK6n7bs2yib8ct+crq3q20FjEgtxKA0zET6pFObBCLj//V9IF5Zi+6Y7NsFmHJPqMO6fAcquw7hpYcmKiqbXStaZABVbe61jSWHm4NyBuRXag9Jq7vksep/ndwtHDnZFrXt3/p3q/EUhRhenurO/qd5zCSw5gczz7tN/mASU0fBJV1LHGuag3TTT6H4C6iHhkcrbyjv7T4RYaH2mwab4NLPSTO1D09rJU1RdVKrcE4SHxS3z77UeymajX92JL9gbQlZ9w7k0NDuRcfBWIV4NnEaDeekGiQiDEPkana0U1gJR+WjtS3nja7I5/nFyOWTG1jV6m3jZeyKuj/kp4xsM7A0jEP6pHOVtiuuraNvbCyzZwFAojFWDJjzD8fCDftWz6N95KlI250rWk4p4ZbckSAatM49+nFsFXVFLVSu/PnUmvw/lW7FE3vB5Zcb5tjn3migx50gPhllA6GzoTaxm4w70xWwZV7j3781bWNvaypZzy5yPv6/N/VpnGecGV52elHwV05OCy/tuoD84LS8aBeDtrycoibNzWuRUaz9NXOV9tN43TIJzXIeofvXNGJF+Y+ZWYlYcl59+6Rdok/QOrbb3vdn/9AlhxO4OIBE4e61uvv27VybIAHBKB09Ee9xlPLpyxpyde2sRc2Unn830LC6BYBpWMul0S/n8gDMjZxrTcDPlsWlqYJFmbJkYR8pWU6k3xLTnpbYixa7ix6iqJXnbNzYG88TSinm/GOID8RP2kwP7lu2JRR29hN95JF9S08VRw52O1TLVkcLXpT8ivXbEY60/KH3P7lDYrLlk+11CEeTZ4iZsn5985PN1tjE2QVIGfCR9cFRL92SKeeM2qyrgDS8co6+k5OHU1Y8iXRtys6CQeUbGMX1uxcQDrmEQyBZDJxyeMdWLPoEyzQkhmjvtXf4WuiTn7of6Eli/HVGyw5bm/R9VfBxvcUx4kW4NS9xJPB4sgJ/5vVkuND2fEB7WxL5udNWrJ8hDYx+t/p9yq5llxw73yuuKop1Wb3bfEILdgqgA9U5Kmfnvy15kDRkfrW3w7DhlTcktOaFqu8hkDRMR9/1NdfjosqpWTDCxgLtWQWXVgSsa5bsGRen8rfZixoSRwn814KLVkOfecdQfbXE5acNX3/0yyZJ6SrD8yLSVEvueDeGWMT13rZrpWTE+NTwK0Crm1jL7dg0/Ggfg/SQgsoOkYXp0Y33hVOppYZHQ/qm9hLXhvoxU9HJ4V+zBi7to17kDRNsGhLZkGfLGJdMls8T0sWVieNkP8pTxRfJM0yjpOFGGoWRxZOGY5n3nSEuIXLC8saLP0ES5YDDzcPXBfcu0TMwit6fwvcKuCS6PXsgWvGmEcOO6Ca4UB1THgwn6kbCXiPtEug1rAC1ZExxhh1yNHfwkmX/vmx8S6rDF6SzneQkkoJ5mvJE8fUH6arOXoxbFUj1iXTnKUO8a6DedSp6V3ck2S7mBe8YFqW6N8ElsytTry+I5ibE+azeV+QutYby804TiZiQlbTOPfFkSPTu246QjyrLR5CJCk+cS3CJ13LPeM54GSrgjcFguHovYHtyvHnRLpaJM9y7939udc1LXcixjAKPBtSFUAvhq1tOdF94pLHu5HhAepaP70WM9ep+66vd0nqXWxrDRwdY6S7xRfDVjUI+A9HrV2cprcW+OOheNFhYuSDT7r8WaxPoe6Ho84jAnWNG2OLeqHmRqrn6I+eGb+GnwUClO7335nfiR/e6Vl+LOe68WR4sh+ItNU9+btcMSUNbOqaf20evXMc+aLE0v3eaXRdafQ9bUHqNJ5nLVoFFFkEFT3y5y2CCpckRZZnxA51p2cazZzb1xqmy6g/Pm6WVE2ptw0ytt8e8unBumn7/zsMHw436cx7Z8x9T+z/s83OjhJfQ5UFoCpAzsbnUpqx26bherP7vVcA1z4C0jFKypJZ3sI/IMDUMeiuxDY5vBEuqa02uycE9Aoohv/tBFIMhgEMUEcYoI7gQUtGisAwgAHqCAPUETxoyUgRGAYwQB1hgDqCBy0ZKQLDAAaoIwxQR/CgJSNFYBjAAHWEAeoIHrRkpAgMAxigjjBAHcGDlowUgWEAA9QRBqgjeNCSkSIwDGCAOsIAdQQPWjJSBIYBDFBHGKCO4EFLRorAMIAB6ggD1BE8RZaMG2644YYbbrjd8pZhyQiCIAiCLBG0ZARBEARZCdCSEQRBEGQlQEtGEARBkJXg/wHW9Kd6qpnwRgAAAABJRU5ErkJggg==" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>One traveller is to be chosen at random from all those interviewed. </span></p>
<p><span>Find the probability that this traveller was going to Africa.</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>One female traveller is to be chosen at random from all those interviewed. </span></p>
<p><span>Find the probability that this female traveller was going to Asia.</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>One traveller is to be chosen at random from those <strong>not</strong> going to America.</span></p>
<p><span>Find the probability that the chosen traveller is female.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{108}}{{250}}{\text{ }}\left( {\frac{{54}}{{125}}{\text{, }}0.432{\text{, }}43.2\% } \right)\) <em><strong>(A1)(A1) </strong> <strong>(C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for numerator, <em><strong>(A1)</strong></em> for denominator.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{25}}{{106}}{\text{ }}\left( {0.236{\text{, }}23.6\% } \right)\) <em><strong>(A1)(A1) (C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for numerator, <em><strong>(A1)</strong></em> for denominator.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{71}}{{170}}{\text{ }}\left( {0.418{\text{, }}41.8\% } \right)\) <em><strong>(A1)(A1)</strong></em> <em><strong>(C2)</strong></em></span> </p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for numerator, <em><strong>(A1)</strong></em> for denominator.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">A reasonably well attempted question with parts (a) and (c) proving to provide many correct answers. A correct answer for part (b) however proved to be a little more elusive as, despite a correct numerator of \(25\) seen on many scripts, the total sample space was not reduced and a denominator of \(250\) lost the final mark in this part of the question. On a minority of scripts candidates simply wrote down decimal answers. Where these were correct, both marks for each part were earned. However, incorrect answers earned no marks – candidates would be well advised to at least write down the fraction answer first so that any part marks can be awarded. A case in question here was a predominance of incorrect answers of \(0.10\) or \(10\% \) for part (b). This, on its own earns no marks whereas \(25/250\) earned A1, A0.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">A reasonably well attempted question with parts (a) and (c) proving to provide many correct answers. A correct answer for part (b) however proved to be a little more elusive as, despite a correct numerator of \(25\) seen on many scripts, the total sample space was not reduced and a denominator of \(250\) lost the final mark in this part of the question. On a minority of scripts candidates simply wrote down decimal answers. Where these were correct, both marks for each part were earned. However, incorrect answers earned no marks – candidates would be well advised to at least write down the fraction answer first so that any part marks can be awarded. A case in question here was a predominance of incorrect answers of \(0.10\) or \(10\% \) for part (b). This, on its own earns no marks whereas \(25/250\) earned A1, A0.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">A reasonably well attempted question with parts (a) and (c) proving to provide many correct answers. A correct answer for part (b) however proved to be a little more elusive as, despite a correct numerator of \(25\) seen on many scripts, the total sample space was not reduced and a denominator of \(250\) lost the final mark in this part of the question. On a minority of scripts candidates simply wrote down decimal answers. Where these were correct, both marks for each part were earned. However, incorrect answers earned no marks – candidates would be well advised to at least write down the fraction answer first so that any part marks can be awarded. A case in question here was a predominance of incorrect answers of \(0.10\) or \(10\% \) for part (b). This, on its own earns no marks whereas \(25/250\) earned A1, A0.</span></p>
<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 fair six-sided die has the numbers 1, 2, 3, 4, 5, 6 written on its faces. A fair four-sided die has the numbers 1, 2, 3, and 4 written on its faces. The two dice are rolled.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The following diagram shows the possible outcomes.</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 probability that the two dice show the same number.</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 probability that the difference between the two numbers shown on the dice is 1.</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 probability that the number shown on the four-sided die is greater than the number shown on the six-sided die, given that the difference between the two numbers is 1.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{4}{{24}}\) \(\left( {\frac{1}{6},0.167,16.7{\text{ }}\% } \right)\) <em><strong>(A1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for numerator, <em><strong>(A1)</strong></em> for denominator.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{7}}{{24}}\) \((0.292,29.2{\text{ }}\% )\)</span> <span><em><strong>(A1)(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> from the denominator used in (a).</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{3}}{{7}}\) \((0.429,42.9{\text{ }}\% )\) <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for numerator <em><strong>(A1)</strong></em><strong>(ft)</strong> for denominator, <strong>(ft)</strong> from their numerator in (b).</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The diagram caused some difficulty for some candidates, however the majority of candidates were successful.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The diagram caused some difficulty for some candidates, however the majority of candidates were successful in (a).</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The term “difference” was well understood by the candidature.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The diagram caused some difficulty for some candidates, however the majority of candidates were successful in (a).</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the following truth table.</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>Consider the propositions</span></p>
<p><span><span> </span><em><span>p</span></em><span>:</span><em><span> Cristina understands logic</span></em></span></p>
<p><span> </span><em><span>q</span></em><span>:</span><em><span> Cristina will do well on the logic test.</span></em></p>
<p><span>Write down the following compound proposition in symbolic form.</span></p>
<p><em><span>“If Cristina understands logic then she will do well on the logic test”</span></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><span>Write down in words the contrapositive of the proposition given in part (b).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span> <em><strong> (A1)(A1) (C2)</strong></em></span></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for ¬<em>q</em> , <em><strong>(A1)</strong></em> for last column.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(p \Rightarrow q\) <em><strong>(A1)(A1) (C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for </span><span><span>\(\Rightarrow\) </span> , <em><strong>(A1)</strong></em> for <em>p</em> and <em>q</em> in the correct order.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>If Cristina does not do well on the logic test then she does not understand logic. <em><strong>(A1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for If…(then), must be an implication, <em><strong>(A1)</strong></em> for the correct propositions in the correct order.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well answered with most candidates able to complete the truth table correctly in part a) and write the correct compound proposition in symbolic form in part b). A significant number of candidates could not write the correct contrapositive, although most were awarded one mark for writing an implication.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well answered with most candidates able to complete the truth table correctly in part a) and write the correct compound proposition in symbolic form in part b). A significant number of candidates could not write the correct contrapositive, although most were awarded one mark for writing an implication.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well answered with most candidates able to complete the truth table correctly in part a) and write the correct compound proposition in symbolic form in part b). A significant number of candidates could not write the correct contrapositive, although most were awarded one mark for writing an implication.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">In a particular school, students must choose at least one of three optional subjects: art, psychology or history.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the following propositions</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;"><em>a: I choose art,</em></span><br><span style="font-family: times new roman,times; font-size: medium;"><em>p: I choose psychology,</em></span><br><span style="font-family: times new roman,times; font-size: medium;"><em>h: I choose history.</em></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write, in words, the compound proposition</span><br><span>\[\neg h \Rightarrow (p \vee a)\].</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>Complete the truth table for \(\neg a \Rightarrow p\) .</span></p>
<p><span><img src="data:image/png;base64,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" alt></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>State whether \(\neg a \Rightarrow p\) is a tautology, a contradiction or neither. Justify your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>If I do not choose history then I choose either psychology or I choose art <em><strong>(A1)(A1)(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for ‘if… (then)…’</span></p>
<p><span>Award <em><strong>(A1)</strong></em> for ‘not choose history.’</span></p>
<p><span>Award <em><strong>(A1)</strong></em> for ‘choose (either) psychology or art (or both).’</span></p>
<p><span>If the order of the statements is wrong award at most <em><strong>(A1)(A1)(A0)</strong></em>.</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span> </span><span> <em><strong>(A1) (C1)</strong></em></span></span></p>
<p><span><span><em><strong>[1 mark]<br></strong></em></span></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Neither, because not all the entries in the last column are the same. <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(R1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Do not award <em><strong>(R0)(A1)</strong></em>. Follow through from their answer to part (b). Reasoning must be consistent with their answer to part (b).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many correct answers were seen in part (a) with only a minority of candidates misinterpreting the symbol \( \vee \) as 'and'. Some candidates left out the word 'if' and consequently lost the first mark. <br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Part (b) was not done as well as expected indicating that some work needs to be done by centres on the truth table for the logic symbol \( \Rightarrow \) . <br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many correct answers of 'neither' were seen in part (c) but the justification was sometimes lacking definitive reasoning. Without sufficient reasoning, the answer mark was not awarded.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Two propositions are defined as follows:</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> \(p:\) <em>Quadrilateral ABCD has two diagonals that are equal in length.</em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> \(q:\) <em>Quadrilateral ABCD is a rectangle.</em></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Express the following in symbolic form.</span></p>
<p><span><em>“A rectangle always has two diagonals that are equal in length.”</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>Write down in symbolic form the converse of the statement in (a).</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, <strong>without </strong>using a truth table, whether the statements in (a) and (b) are logically equivalent.</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 the name of the statement that is logically equivalent to the converse.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(q \Rightarrow p\) <strong><em>(A1)(A1) (C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award the first <strong><em>(A1) </em></strong>for seeing the implication sign, the second <strong><em>(A1) </em></strong>is for a correct answer only. Not using the implication earns <strong>no </strong>marks.</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(p \Rightarrow q\) <strong><em>(A1)</em>(ft) <em>(C1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A1)</em>(ft) </strong>where the propositions in the implication in part (a) are exchanged.</span></p>
<p> </p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Not equivalent; a kite or an isosceles trapezium (for example) can have diagonals that are equal in length. <strong><em>(A1)(R1) (C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Accept a valid sketch as reasoning.</span></p>
<p><span> If the reason given is that <em>a square has diagonals of equal length, but is not a rectangle</em>, then award <strong><em>(R1)(A0)</em></strong>.</span></p>
<p><span> Do not award <strong><em>(A1)(R0)</em></strong>.</span></p>
<p><span> Do not accept solutions based on truth tables.</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Inverse <strong><em>(A1) (C1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Do not accept symbolic notation.</span></p>
<p> </p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the following propositions.</p>
<p>\[\begin{array}{*{20}{l}} {p{\text{: The car is under warranty}}} \\ {q{\text{: The car is less than 2 years old}}} \\ {r{\text{ : The car has been driven more than 20}}\,{\text{000 km}}} \end{array}\]</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down in words \((q \vee \neg r) \Rightarrow p\).</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>Complete the truth table.</p>
<p><img src="images/Schermafbeelding_2018-02-13_om_06.43.42.png" alt="N17/5/MATSD/SP1/ENG/TZ0/04.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>State whether the statement \(\neg p \Rightarrow \neg (q \vee \neg r)\) is the inverse, the converse or the contrapositive of the statement in part (a).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>if the car is less than 2 years old or the car has not been driven more than \(20\,000{\text{ km}}\), then the car is under warranty <strong><em>(A1)(A1)(A1) (C3)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for if …, then …, <strong><em>(A1) </em></strong>for “or”, <strong><em>(A1) </em></strong>for correct statements in correct order. Accept “If the car has not been driven more than \(20\,000{\text{ km}}\) or the car is less than 2 years old, then the car is under warranty”. Accept logical equivalent wording for each proposition, <em>eg </em>“less than \(20\,000{\text{ km}}\)”.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2018-02-13_om_06.56.17.png" alt="N17/5/MATSD/SP1/ENG/TZ0/04.b/M"> <strong><em>(A1)(A1)</em>(ft) <em>(C2)</em></strong></p>
<p> </p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for \(q \vee \neg r\) column correct and <strong><em>(A1)</em>(ft) </strong>for \((q \vee \neg r) \Rightarrow p\) column correct. Follow through from their \(q \vee \neg r\) column.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>contrapositive <strong><em>(A1) (C1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The following Venn diagram shows the relationship between the sets of numbers</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;">\[\mathbb{N},{\text{ }}\mathbb{Z}{\text{, }}\mathbb{Q}{\text{ and }}\mathbb{R}{\text{.}}\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The number –3 belongs to the set of \(\mathbb{Z}{\text{, }}\mathbb{Q}\) and \(\mathbb{R}\), but not \(\mathbb{N}\), and is placed in the appropriate position on the Venn diagram as an example.</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_2014-09-02_om_14.14.57.png" alt><br></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;">Write down the following numbers in the appropriate place in the Venn diagram.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>4</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>\(\frac{1}{3}\)</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>\(\pi \)</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>\(0.38\)</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>\(\sqrt 5 \)</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>\(-0.25\)</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><span><br><img src="images/Schermafbeelding_2014-09-02_om_14.19.00_3.png" alt> <strong><em>(A1)(A1)(A1)(A1)(A1)(A1) (C6)</em></strong></span></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for each number correctly placed.</span></p>
<p><span> Award <strong><em>(A0) </em></strong>for any entry in more than one region.</span></p>
<p> </p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span><br><img src="images/Schermafbeelding_2014-09-02_om_14.19.00_4.png" alt> <strong><em>(A1)(A1)(A1)(A1)(A1)(A1) (C6)</em></strong></span></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for each number correctly placed.</span></p>
<p><span> Award <strong><em>(A0) </em></strong>for any entry in more than one region.</span></p>
<p> </p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span><br><img src="images/Schermafbeelding_2014-09-02_om_14.19.00_1.png" alt> <strong><em>(A1)(A1)(A1)(A1)(A1)(A1) (C6)</em></strong></span></span></p>
<p><span> </span></p>
<p><span><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for each number correctly placed.</span></p>
<p><span> Award <strong><em>(A0) </em></strong>for any entry in more than one region.</span></p>
<p><span> </span></p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span><br><img src="images/Schermafbeelding_2014-09-02_om_14.19.00.png" alt> <strong><em>(A1)(A1)(A1)(A1)(A1)(A1) (C6)</em></strong></span></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for each number correctly placed.</span></p>
<p><span> Award <strong><em>(A0) </em></strong>for any entry in more than one region.</span></p>
<p> </p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span><br><img src="images/Schermafbeelding_2014-09-02_om_14.19.00_5.png" alt> <strong><em>(A1)(A1)(A1)(A1)(A1)(A1) (C6)</em></strong></span></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for each number correctly placed.</span></p>
<p><span> Award <strong><em>(A0) </em></strong>for any entry in more than one region.</span></p>
<p> </p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span><br><img src="images/Schermafbeelding_2014-09-02_om_14.19.00_2.png" alt> <strong><em>(A1)(A1)(A1)(A1)(A1)(A1) (C6)</em></strong></span></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for each number correctly placed.</span></p>
<p><span> Award <strong><em>(A0) </em></strong>for any entry in more than one region.</span></p>
<p> </p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the following logic propositions:</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\(p:{\text{ Sean is at school}}\)</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\(q:{\text{ Sean is playing a game on his computer}}{\text{.}}\)</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write in words, \(p \underline { \vee } q\)</span><span>.</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 in words, the converse of \(p \Rightarrow \neg q\).</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>Complete the following truth table for \(p \Rightarrow \neg q\).</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">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>Either Sean is at school or Sean is playing a game on his computer but not both. <em><strong>(A1)(A1) (C2)</strong></em></span></p>
<p><span><strong>Note: <em>(A1)</em></strong> for ‘either ... or but not both’ <em><strong>(A1)</strong></em> for correct statements. ‘Either’ can be omitted.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>If Sean is not playing a game on his computer then Sean is at school. <em><strong>(A1)(A1) (C2)</strong></em></span></p>
<p><span><strong>Note: <em>(A1)</em></strong> for ‘If ... then’ <em><strong>(A1)</strong></em> for correct propositions in the correct order.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span> <strong><em>(A1)(A1)</em>(ft) <em>(C2)</em></strong></span></span></p>
<p><span><strong>Note: <em>(A1)</em></strong> for each correct column.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The common error in part (a) was not to include “but not both” and for (b), to give the inverse rather than the converse. The first column in the table (not \(q\)) was well done but a number of candidates answered the implication incorrectly.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The common error in part (a) was not to include “but not both” and for (b), to give the inverse rather than the converse. The first column in the table (not \(q\)) was well done but a number of candidates answered the implication incorrectly.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The common error in part (a) was not to include “but not both” and for (b), to give the inverse rather than the converse. The first column in the table (not \(q\)) was well done but a number of candidates answered the implication incorrectly.</span></p>
<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 following logic propositions:</span></p>
<p style="margin-left: 30px;"><em><span style="font-size: medium; font-family: times new roman,times;">p </span></em><span style="font-size: medium; font-family: times new roman,times;">:</span><em><span style="font-size: medium; font-family: times new roman,times;"> Yuiko is studying French.</span></em></p>
<p style="margin-left: 30px;"><em><span style="font-size: medium; font-family: times new roman,times;">q </span></em><span style="font-size: medium; font-family: times new roman,times;">:</span><em><span style="font-size: medium; font-family: times new roman,times;"> Yuiko is studying Chinese.</span></em></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the following compound propositions in symbolic form.</span></p>
<p><span>(i) Yuiko is studying French but not Chinese.</span></p>
<p><span>(ii) Yuiko is studying French or Chinese, but not both.</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 in words the <strong>inverse</strong> of the following compound proposition.</span></p>
<p><em><span>If Yuiko is studying Chinese, then she is not studying French.</span></em></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(p \wedge \neg q\) <em><strong>(A1)(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for conjunction, <em><strong>(A1)</strong></em> for negation of <em>q</em>.</span></p>
<p><br><span>(ii) \(p\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \vee } q\) <strong>OR</strong> \((p \vee q)\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \vee } (p \wedge q)\) <em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>If Yuiko is not studying Chinese, (then) she is studying French. <em><strong>(A1)(A1)(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for “if … (then)” seen, award <em><strong>(A1)</strong></em> for “not studying</span> <span>Chinese” seen, <em><strong>(A1)</strong></em> for correct propositions in correct order.</span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Some candidates found the phrase “Yuiko is studying French but not Chinese” confusing as they did </span><span style="font-family: times new roman,times; font-size: medium;">not realize in this context the word “but” means “and”. Alternative but correct logic notation was </span><span style="font-family: times new roman,times; font-size: medium;">accepted.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A class consists of students studying Spanish or French or both. Fifteen students study Spanish and twelve study French.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The probability that a student studies French given that she studies Spanish is \(\frac{{7}}{{15}}\)</span><span style="font-size: medium; font-family: times new roman,times;">.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a Venn diagram in the space below to illustrate this information.</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>Find the probability that a student studies Spanish given that she studies one language only.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span> <em><strong>(A1)(A1)(A1)</strong></em> <em><strong>(C3)</strong></em></span></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for a labeled Venn diagram with appropriate sets.</span></p>
<p><span><em><strong>(A1)</strong></em> for 7, <em><strong>(A1)</strong></em> for 8 and 5.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{P (Spanish / one language only)}} = \frac{{\frac{8}{{20}}}}{{\frac{8}{{20}} + \frac{5}{{20}}}}\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituted conditional probability formula, <em><strong>(A1)</strong></em> for correct substitution. Follow through from their Venn diagram.</span></p>
<p><br><span>\( = \frac{8}{{13}}(0.615,{\text{ }}61.5\% )\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong><span>OR</span></strong></span></p>
<p><span>\({\text{P}}{\text{ (Spanish / one language only)}} = \frac{8}{{8 + 5}}\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for their correct numerator, <em><strong>(M1)</strong></em> for correct recognition of regions. Follow through from their Venn diagram.</span></p>
<p><br><span>\( = \frac{8}{{13}}(0.615,{\text{ }}61.5\% )\) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C3)</strong></em></span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Part (a) was done well.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Very few were able to answer (b).</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider the following logic propositions. </p>
<p class="p1" style="padding-left: 60px;"> \(p\): Sandi gets up before eight o’clock</p>
<p class="p1" style="padding-left: 60px;"> \(q\): Sandi goes for a run</p>
<p class="p1" style="padding-left: 60px;"> \(r\): Sandi goes for a swim</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down in words the compound proposition</p>
<p class="p1"><img src="data:image/png;base64,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"></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Complete the following truth table.</p>
<p class="p1"><img src="images/Schermafbeelding_2017-03-06_om_13.42.11.png" alt="N16/5/MATSD/SP1/ENG/TZ0/05.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"><span class="s1">On a morning when Sandi does </span><strong>not </strong>get up before eight o’clock, use your truth table to determine whether \(p \Rightarrow (q{\text{ }}\underline \vee {\text{ }}r)\) is a tautology, contradiction or neither.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">If Sandi gets up before eight o’clock then Sandi (either) goes for a run or goes for a swim, but not both. <span class="Apple-converted-space"> </span><strong><em>(A1)(A1)(A1) <span class="Apple-converted-space"> </span>(C3)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1) </em></strong>for If …… then ……, <strong><em>(A1) </em></strong>for all propositions in the correct order, <strong><em>(A1) </em></strong>for “… or … but not both” (do not accept “either” as a replacement for “but not both”).</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2017-03-06_om_13.50.12.png" alt="N16/5/MATSD/SP1/ENG/TZ0/05.b/M"> <strong><em>(A1)(A1)</em>(ft) <em>(C2)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1) </em></strong>for correct \((q{\text{ }}\underline \vee {\text{ }}r)\) column, and <strong><em>(A1)</em>(ft) </strong>for <span>their</span> correct \(p \Rightarrow (q{\text{ }}\underline \vee {\text{ }}r)\) column. Follow through from their \((q{\text{ }}\underline \vee {\text{ }}r)\) column.</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">tautology <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Follow through from part (b).</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Peter either walks or cycles to work. The probability that he walks is <span class="s1">0.25</span>. If Peter walks to work, the probability that he is late is <span class="s1">0.1</span>. If he cycles to work, the probability that he is late is <span class="s1">0.05</span>. The tree diagram for this information is shown.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-20_om_07.11.52.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">On a day chosen at random, Peter walked to work.</p>
<p class="p1">Write down the probability that he was on time.</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">For a different day, also chosen at random,</p>
<p class="p1">find the probability that Peter cycled to work and was late.</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">For a different day, also chosen at random,</p>
<p class="p1">find the probability that, given Peter was late, he cycled to work.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(0.9\) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C1)</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(0.75 \times 0.05\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">\( = 0.0375\;\;\;\left( {\frac{3}{{80}},{\text{ 3,75% }}} \right)\) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C2)</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\frac{{0.75 \times 0.05}}{{0.75 \times 0.05 + 0.25 \times 0.1}}\) <span class="Apple-converted-space"> </span><strong><em>(M1)(M1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for their correct numerator, <strong><em>(M1) </em></strong>for their correct denominator, <em>ie</em>, \(\left( {\frac{{{\text{their (b)}}}}{{{\text{their (b)}} + 0.25 \times 0.1}}} \right)\).</p>
<p class="p1">Do not award <strong><em>(M1) </em></strong>for <em>their </em>\(0.0375\) or \(0.0625\) if not a correct part of a fraction.</p>
<p class="p2"> </p>
<p class="p1">\( = 0.6\;\;\;\left( {\frac{3}{5},{\text{ }}60\% } \right)\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C3)</em></strong></p>
<p class="p1"><strong>Note: </strong>Follow through from part (b).</p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Surprisingly, in part (a) the majority of candidates answered incorrectly. The usual answer was 0.225, resulting from 0.25 × 0.9; the probability that Peter walks and arrives on time.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>In part (b) the answers were mostly correct as the candidates repeated the same procedure, which was correct for this part.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The conditional probability in part (c) was too much for most. In some cases a correct numerator or denominator was found. More candidates could have received method marks if working had been shown.</p>
<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 bag contains 7 red discs and 4 blue discs. Ju Shen chooses a disc at random from the bag and removes it. Ramón then chooses a disc from those left in the bag.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the probability that</span></p>
<p><span>(i) Ju Shen chooses a red disc from the bag;</span></p>
<p><span>(ii) Ramón chooses a blue disc from the bag, given that Ju Shen has chosen a red disc;</span></p>
<p><span>(iii) Ju Shen chooses a red disc and Ramón chooses a blue disc from the bag.</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>Find the probability that Ju Shen and Ramón choose different coloured discs from the bag.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(\frac{7}{{11}}\) (\(0.636\), \(63.6\% \)) (\(0.636363 \ldots \)) <em><strong>(A1) (C1)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span>(ii) \(\frac{4}{{10}}\) \(\left( {\frac{2}{5}{\text{, }}0.4{\text{, }}40\% } \right)\) <em><strong>(A1) (C1)</strong></em></span></p>
<p><span> </span></p>
<p><span>(iii) \(\frac{{28}}{{110}}\) \(\left( {\frac{{14}}{{55}}{\text{, }}0.255{\text{, }}25.5\% } \right)\) \(0.254545 \ldots \) <strong><em>(A1)</em>(ft) <em>(C1)</em> <br></strong></span></p>
<p><span><strong>Note:</strong> Follow through from the product of their answers to parts (a) (i) and (ii).</span></p>
<p><span> </span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{28}}{{110}} + \left( {\frac{4}{{11}} \times \frac{7}{{10}}} \right)\) <strong>OR</strong> \(2 \times \frac{{28}}{{110}}\) <em><strong>(M1)(M1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for using their \(\frac{{28}}{{110}}\) as part of a combined probability expression. <em><strong>(M1)</strong></em> for either adding \({\frac{4}{{11}} \times \frac{7}{{10}}}\) <strong>or</strong> for multiplying by 2.</span></p>
<p><span> </span></p>
<p><span>\( = \frac{{56}}{{110}}\) \(\left( {\frac{{28}}{{55}}{\text{, }}0.509{\text{, }}50.9\% } \right)\)</span><span> (\(0.509090 \ldots \)) <strong><em>(A1)</em>(ft) <em>(C3)</em></strong></span></p>
<p><span><strong>Note:</strong> Follow through applies from their answer to part (a) (iii) and only when their answer is between 0 and 1.</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The vast majority of candidates were able to pick up the first two marks by confidently identifying the <em>number of favourable outcomes/total number of outcomes</em>. Difficulties arose however when combining events and only the more able candidates were able to progress successfully with the remainder of the question. As usual in this type of question, there was an abundance of incorrect answers greater than 1 given.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The vast majority of candidates were able to pick up the first two marks by confidently identifying the number of favourable outcomes/total number of outcomes. Difficulties arose however when combining events and only the more able candidates were able to progress successfully with the remainder of the question. As usual in this type of question, there was an abundance of incorrect answers greater than 1 given.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The Home Shine factory produces light bulbs, 7% of which are found to be defective.</p>
</div>
<div class="specification">
<p>Francesco buys two light bulbs produced by Home Shine.</p>
</div>
<div class="specification">
<p>The Bright Light factory also produces light bulbs. The probability that a light bulb produced by Bright Light is not defective is \(a\).</p>
<p>Deborah buys three light bulbs produced by Bright Light.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the probability that a light bulb produced by Home Shine is not defective.</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 probability that both light bulbs are not defective.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that at least one of Francesco’s light bulbs is defective.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an expression, in terms of \(a\), for the probability that at least one of Deborah’s three light bulbs is defective.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>0.93 (93%) <strong><em>(A1)</em></strong> <strong><em>(C1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(0.93 \times 0.93\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for squaring their answer to part (a).</p>
<p> </p>
<p>0.865 (0.8649; 86.5%) <strong><em>(A1)</em>(ft)</strong> <strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Follow through from part (a).</p>
<p>Accept \(0.86{\text{ }}\left( {{\text{unless it follows }}\frac{{93}}{{100}} \times \frac{{92}}{{99}}} \right)\).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(1 - 0.8649\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from their answer to part (b)(i).</p>
<p> </p>
<p><strong>OR</strong></p>
<p>\(0.07 \times 0.07 + 2 \times (0.07 \times 0.93)\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (a).</p>
<p> </p>
<p>0.135 (0.1351; 13.5%) <strong><em>(A1)</em>(ft)</strong> <strong><em>(C2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(1 - {a^3}\) <strong><em>(A1)</em></strong> <strong><em>(C1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept \(3{a^2}(1 - a) + 3a{(1 - a)^2} + {(1 - a)^3}\) or equivalent.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">In a research project on the relation between the gender of 150 science students at college and their degree subject, the following set of data is collected.</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 probability that a student chosen at random </span><span>is male.</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 probability that a student chosen at random </span><span>is either male or studies Chemistry.</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 probability that a student chosen at random </span><span>studies Physics, given that the student is male.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\( = \frac{{91}}{{150}}(0.607,{\text{ }}60.6\,\% ,{\text{ }}60.7\,\% )\) <em><strong> (A1)(A1) (C2)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for numerator, <em><strong>(A1)</strong> </em>for denominator.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\( = \frac{{111}}{{150}}\left( {\frac{{37}}{{50}},{\text{ }}0.74,{\text{ }}74\,\% } \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1) (C2)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for their numerator in (a) +20 provided the final answer is not greater than 1.<em><strong> (A1)</strong></em> for denominator.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{16}}{{91}}(0.176,{\text{ }}17.6\,\% )\) <em><strong> (A1)(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span><br><br></p>
<p><span><strong>Note:</strong> Award<em><strong> (A1)</strong></em> for numerator and<strong><em> (A1)</em>(ft)</strong> for denominator. Follow through from their numerator in (a) provided answer is not </span><span>greater than 1.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Parts (a) and (b) were well answered with many candidates gaining 4 marks there. The conditional probability in part (c) proved to be more challenging. Nearly all candidates attempted this question showing that time was not a factor in this paper. Many candidates gave their answers as incorrectly rounded decimals, which incurred an accuracy penalty and prevented them from gaining the maximum marks.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Parts (a) and (b) were well answered with many candidates gaining 4 marks there. The conditional probability in part (c) proved to be more challenging. Nearly all candidates attempted this question showing that time was not a factor in this paper. Many candidates gave their answers as incorrectly rounded decimals, which incurred an accuracy penalty and prevented them from gaining the maximum marks.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Parts (a) and (b) were well answered with many candidates gaining 4 marks there. The conditional probability in part (c) proved to be more challenging. Nearly all candidates attempted this question showing that time was not a factor in this paper. Many candidates gave their answers as incorrectly rounded decimals, which incurred an accuracy penalty and prevented them from gaining the maximum marks.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the truth table shown below.</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">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State whether the compound proposition \((p \vee (p \wedge q)) \Rightarrow p\) is a contradiction, a tautology or neither.</span></p>
<p> </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>Consider the following propositions.</span></p>
<p><span> </span><em><span>p: Feng finishes his homework</span></em></p>
<p><span> </span><em><span>q: Feng goes to the football match</span></em></p>
<p><span>Write in symbolic form the following proposition.</span></p>
<p><em><span>If Feng does not go to the football match then Feng finishes his homework.</span></em></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span> <em><strong> (A1)(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></span></span></p>
<p><span><strong> </strong></span></p>
<p><span><strong>Note:</strong> Award<em><strong> (A1)</strong> </em>for each correct column.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>tautology <em><strong> (A1)</strong></em><strong>(ft) </strong><em><strong> (C1)</strong></em></span></p>
<p><span> </span></p>
<p><span><strong>Note:</strong> Follow through from their last column.</span></p>
<p><span> </span></p>
<p><em><strong><span>[1 mark]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\neg q \Rightarrow p\) <em><strong>(A1)(A1) (C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award<em><strong> (A1)</strong> </em>for \(\neg q\) and <em>p</em> in correct order,<em><strong> (A1)</strong></em> for \( \Rightarrow \) sign.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The truth table was very well answered and where the table was incorrect a follow through mark could be given for part (b) for a correct answer resulting from their final column. Some candidates appeared unsure of the concept of a tautology.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The truth table was very well answered and where the table was incorrect a follow through mark could be given for part (b) for a correct answer resulting from their final column. Some candidates appeared unsure of the concept of a tautology.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Nearly all candidates could write the proposition in part (c) in symbolic form.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The Venn diagram shows the numbers of pupils in a school according to whether they study the sciences Physics (\(P\)), Chemistry (\(C\)), Biology (\(B\)).</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 the number of pupils that study Chemistry only.</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><span>Write down the number of pupils that study</span> <span><strong>exactly</strong> two sciences.</span></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>Write down the number of pupils that do not study Physics.</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>Find \(n[(P \cup B) \cap C]\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(9\) <em><strong>(A1) </strong><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(12\) <em><strong>(A1) (C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(8 + 3 + 9 + 6\) <em><strong>(M1)</strong></em></span></p>
<p><span>\( = 26\) <em><strong>(A1) (C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(20\) seen if answer is incorrect.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(5 + 2 + 3\) <em><strong>(M1)</strong></em></span></p>
<p><span>\( = 10\) <em><strong>(A1) (C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(29\) or \(19\) seen if answer is incorrect.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well attempted by the majority. The major error was the omission of the “\(6\)” in the candidates’ calculations. Perhaps better positioning would have helped in this regard.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well attempted by the majority. The major error was the omission of the “\(6\)” in the candidates’ calculations. Perhaps better positioning would have helped in this regard.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well attempted by the majority. The major error was the omission of the “\(6\)” in the candidates’ calculations. Perhaps better positioning would have helped in this regard.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well attempted by the majority. The major error was the omission of the “\(6\)” in the candidates’ calculations. Perhaps better positioning would have helped in this regard.</span></p>
<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 following logic statements.</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"><em>p: Carlos is playing the guitar</em></span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"><em>q: Carlos is studying for his IB exams</em></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write in words the compound statement \(\neg p \wedge q\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write the following statement in symbolic form.</span></p>
<p><span><em>“Either Carlos is playing the guitar or he is studying for his IB exams but not both.”</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>Write the <strong>converse</strong> of the following statement in <strong>symbolic form</strong>.</span></p>
<p><em><span>“If Carlos is playing the guitar then he is not studying for his IB exams.”</span></em></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>Carlos is not playing the guitar and he is studying for his IB exams. <em><strong>(A1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for “and”, <em><strong>(A1)</strong></em> for correct statements.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(p\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \vee } q\) <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\neg q \Rightarrow p\) <em><strong>(A1)(A1)(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><span><strong>Notes: </strong> Award <em><strong>(A1)</strong></em> for implication, <em><strong>(A1)</strong></em> for the \(\neg q\), <em><strong>(A1)</strong></em> for both \(\neg q\) and \(p\) in the correct order. If correct converse seen in words only award <em><strong>(A1)(A1)(A0)</strong></em>. Accept \(p \Leftarrow \neg q\). Accept \( - q\) for \(\neg q\).</span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times;"><span style="font-size: medium;">In part (a) occasionally <em>‘if…then…’</em> was not seen but generally this was well done. </span> </span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times;"><span style="font-size: medium;">Part (b) was also well done despite the dearth of previous testing of the <em>exclusive or</em> statement. </span> </span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times;"><span style="font-size: medium;">Finding the converse of a statement in part (c) proved to be difficult for a significant number of candidates and incorrect answers of the form \(q \Rightarrow \neg p \) were more frequently seen than the correct answer. Such incorrect </span><span style="font-size: medium;">answers lost two marks.</span> </span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>In the Canadian city of Ottawa:</p>
<p>\[\begin{array}{*{20}{l}} {{\text{97% of the population speak English,}}} \\ {{\text{38% of the population speak French,}}} \\ {{\text{36% of the population speak both English and French.}}} \end{array}\]</p>
</div>
<div class="specification">
<p>The total population of Ottawa is \(985\,000\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the percentage of the population of Ottawa that speak English but not French.</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 people in Ottawa that speak both English and French.</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 your answer to part (b) in the form \(a \times {10^k}\) where \(1 \leqslant a < 10\) and <em>k </em>\( \in \mathbb{Z}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(97 - 36\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for subtracting 36 from 97.</p>
<p> </p>
<p><strong>OR</strong></p>
<p><img src="images/Schermafbeelding_2017-08-15_om_12.54.01.png" alt="M17/5/MATSD/SP1/ENG/TZ1/02.a/M"></p>
<p><strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for 61 <strong>and </strong>36 seen in the correct places in the Venn diagram.</p>
<p> </p>
<p>\( = 61{\text{ }}(\% )\) <strong><em>(A1)</em></strong> <strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept 61.0 (%).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{36}}{{100}} \times 985\,000\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for multiplying 0.36 (or equivalent) by \(985\,000\).</p>
<p> </p>
<p>\( = 355\,000{\text{ }}(354\,600)\) <strong><em>(A1)</em></strong> <strong><em>(C2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(3.55 \times {10^5}{\text{ }}(3.546 \times {10^5})\) <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong><em> </em><strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1)(ft) </em></strong>for 3.55 (3.546) <strong>must </strong>match part (b), and <strong><em>(A1)(ft)</em></strong> \( \times {10^5}\).</p>
<p>Award <strong><em>(A0)(A0) </em></strong>for answers of the type: \(35.5 \times {10^4}\). Follow through from part (b).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Rosewood College has 120 students. The students can join the sports club (\(S\)) and the music club (\(M\)).</p>
<p>For a student chosen at random from these 120, the probability that they joined both clubs is \(\frac{1}{4}\) and the probability that they joined the music club is\(\frac{1}{3}\).</p>
<p>There are 20 students that did not join either club.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Complete the Venn diagram for these students.</p>
<p><img src="images/Schermafbeelding_2018-02-13_om_08.15.35.png" alt="N17/5/MATSD/SP1/ENG/TZ0/07.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>One of the students who joined the sports club is chosen at random. Find the probability that this student joined both clubs.</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>Determine whether the events \(S\) and \(M\) are independent.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2018-02-13_om_08.19.04.png" alt="N17/5/MATSD/SP1/ENG/TZ0/07.a/M"> <strong><em>(A1)(A1) (C2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for 30 in correct area, <strong><em>(A1) </em></strong>for 60 and 10 in the correct areas.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{30}}{{90}}{\text{ }}\left( {\frac{1}{3},{\text{ }}0.333333 \ldots ,{\text{ }}33.3333 \ldots \% } \right)\) <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft) <em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1)</em>(ft) </strong>for correct numerator of 30, <strong><em>(A1)</em>(ft) </strong>for correct denominator of 90. Follow through from their Venn diagram.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\({\text{P}}(S) \times {\text{P}}(M) = \frac{3}{4} \times \frac{1}{3} = \frac{1}{4}\) <strong><em>(R1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(R1) </em></strong>for multiplying their by \(\frac{1}{3}\).</p>
<p> </p>
<p>therefore the events are independent \(\left( {{\text{as P}}(S \cap M) = \frac{1}{4}} \right)\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(R1)(A1)</em>(ft) </strong>for an answer which is consistent with their Venn diagram.</p>
<p>Do not award <strong><em>(R0)(A1)</em>(ft)</strong>.</p>
<p>Do not award final <strong><em>(A1) </em></strong>if \({\text{P}}(S) \times {\text{P}}(M)\) is not calculated. Follow through from part (a).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p 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 propositions</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;"><em> </em>\(p\): <em>I have a bowl of soup.</em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em> </em> \(q\): <em>I have an ice cream.</em></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down, in words, the compound proposition \(\neg p \Rightarrow q\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the truth table.</span></p>
<p><br><span><img src="images/Schermafbeelding_2014-09-02_om_17.49.25.png" alt></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, in symbolic form, the converse of \(\neg p \Rightarrow q\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>If I do not have a bowl of soup then I have an ice cream. <strong><em>(A1)(A1) (C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for If… then…</span></p>
<p><span> Award <strong><em>(A1) </em></strong>for correct statements in correct order.</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><img src="images/Schermafbeelding_2014-09-02_om_17.52.20.png" alt><span> <strong><em>(A1)(A1)</em>(ft) <em>(C2)</em></strong></span></span></p>
<p> </p>
<p><span><strong>Note: </strong>Follow through from third column to fourth column.</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(q \Rightarrow \neg p\) <strong><em>(A1)(A1) (C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for \( \Rightarrow \).</span></p>
<p><span> Award <strong><em>(A1) </em></strong>for \(q\) and \(\neg p\) in correct order.</span></p>
<p><span> Accept \(\neg p \Leftarrow q\).</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates were able to write the compound proposition in words, however many were not able to write the converse in symbolic form. While they were able to fill in the third column of the truth table, many were unable to complete the fourth column correctly.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates were able to write the compound proposition in words, however many were not able to write the converse in symbolic form. While they were able to fill in the third column of the truth table, many were unable to complete the fourth column correctly.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates were able to write the compound proposition in words, however many were not able to write the converse in symbolic form. While they were able to fill in the third column of the truth table, many were unable to complete the fourth column correctly.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the following propositions.</p>
<p>\[\begin{array}{*{20}{l}} {p{\text{: I completed the task}}} \\ {q{\text{: I was paid}}} \end{array}\]</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down in words \(\neg q\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down in symbolic form the compound statement:</p>
<p>If I was paid then I completed the task.</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>Complete the following truth table.</p>
<p><img src="images/Schermafbeelding_2017-08-15_om_13.11.00.png" alt="M17/5/MATSD/SP1/ENG/TZ1/03.c.i"></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>State whether the statements \(p \vee \neg q\) and \(q \Rightarrow p\) are logically equivalent. Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>I was not paid <strong><em>(A1)</em></strong> <strong><em>(C1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(q \Rightarrow p\) <strong><em>(A1)</em></strong> <strong><em>(C1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2017-08-15_om_13.13.40.png" alt="M17/5/MATSD/SP1/ENG/TZ1/03.c.i/M"> <strong><em>(A1)(A1)</em></strong> <strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for each correct column.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>yes <strong><em>(A1)</em>(ft)</strong></p>
<p>as the last two columns of the truth table are the same <strong><em>(R1)</em>(ft)</strong> <strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Do not award <strong><em>(A1)(R0)</em></strong><em>. </em>Follow through from part (c)(i).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \({\text{P}}(A) = 0.5\), \({\text{P}}(B) = 0.6\) and \({\text{P}}(A \cup B) = 0.8\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \({\text{P}}(A \cap B)\).</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>Find \({\text{P}}(A|B)\).</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>Decide whether <em>A</em> and <em>B</em> are independent events. Give a reason for your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(0.8 = 0.5 + 0.6 - {\text{P}}(A \cap B)\) <em><strong> (M1)</strong></em></span><br><span>\({\text{P}}(A \cap B) = 0.3\) <em><strong> (A1) (C2)</strong></em></span></p>
<p><span> </span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong> </em>for correct substitution,<em><strong> (A1)</strong></em> for correct answer.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{P}}(A|B) = \frac{{0.3}}{{0.6}}\) </span><em><strong><span> (M1)</span></strong></em></p>
<p><span>= 0.5 <em><strong> (A1)</strong></em><strong>(ft) </strong><em><strong> (C2)</strong></em></span></p>
<p><span><strong> </strong></span></p>
<p><span><strong>Note:</strong> Award<em><strong> (M1)</strong></em> for correct substitution in conditional probability</span> <span>formula. Follow through from their answer to part (a), provided </span><span>probability is not greater than one.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{P}}(A \cap B) = {\text{P}}(A) \times {\text{P}}(B)\) or 0.3 = 0.5 × 0.6 <em><strong> (R1)</strong></em></span></p>
<p><strong><span>OR</span></strong></p>
<p><span>\({\text{P}}(A|B) = {\text{P}}(A)\) <em><strong> (R1)</strong></em></span></p>
<p><span>they are independent. (Yes) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span></p>
<p><span> </span></p>
<p><span><strong>Note:</strong> Follow through from their answers to parts (a) or (b).</span></p>
<p><span>Do not award <em><strong>(R0)(A1)</strong></em>.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Parts (a) and (b) were well answered but very few candidates could provide a reason for the independence of <em>A</em> and <em>B</em>. A number of candidates confused independent and mutually exclusive events.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Parts (a) and (b) were well answered but very few candidates could provide a reason for the independence of <em>A</em> and <em>B</em>. A number of candidates confused independent and mutually exclusive events.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Parts (a) and (b) were well answered but very few candidates could provide a reason for the independence of <em>A</em> and <em>B</em>. A number of candidates confused independent and mutually exclusive events.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Two friends, Sensen and Cruz, are conducting an investigation on probability.</p>
<p>Sensen has a fair six-sided die with faces numbered \(1,\,\,2,\,\,2,\,\,4,\,\,4\) and \(4\). Cruz has a fair disc with one red side and one blue side.</p>
<p>The die and the disc are thrown at the same time.</p>
<p>Find the probability that the number shown on the die is \(1\) <strong>and</strong> the colour shown on the disc is blue;</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 probability that the number shown on the die is \(1\) <strong>or</strong> the colour shown on the disc is blue;</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 probability that the number shown on the die is even given that the colour shown on the disc is red.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{1}{2} \times \frac{1}{6}\) <em><strong>(M1)</strong></em></p>
<p>\(\frac{1}{{12}}\,\,(0.0833,\,\,8.33\,\% ,\,\,0.08333...)\) <em><strong>(A1) (C2)</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{1}{2} + \left( {\frac{1}{2} \times \frac{1}{6}} \right)\) <em><strong>(M1)</strong></em></p>
<p><strong>OR</strong></p>
<p>\(\frac{1}{6} + \frac{1}{2} - \frac{1}{{12}}\,\) <em><strong>(M1)</strong></em></p>
<p>\(\frac{7}{{12}}\,\,(0.583,\,\,58.3\,\% ,\,\,0.58333...)\) <em><strong>(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)(A0)</strong></em> for a <strong>correct</strong> attempt at a possibility/sample space diagram or tree diagram or \(\frac{1}{6} + \left( {\frac{5}{6} \times \frac{1}{2}} \right)\), leading to an incorrect answer.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{1}{3} + \frac{1}{2}\) <em><strong>(M1)</strong></em></p>
<p><strong>OR</strong></p>
<p>\(\frac{{\frac{5}{6} \times \frac{1}{2}}}{{\frac{1}{2}}}\) <em><strong>(M1)</strong></em></p>
<p>\(\frac{5}{6}\,\,(0.833,\,\,83.3\,\% ,\,\,0.83333...)\) <em><strong>(A1) (C2)</strong></em></p>
<p><strong>Notes:</strong> Award <em><strong>(M1)(A0)</strong></em> for a <strong>correct</strong> attempt at a possibility/sample space diagram or tree diagram, leading to an incorrect answer.</p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Question 5: Probability.<br>Some candidates confused the probability of both events occurring with the probability that one or the other occurs. Many candidates were unable to find the conditional probability. Candidates should not answer a probability question with an answer that exceeds one. Only the very best candidates did very well on this question; many found this to be one of the most challenging questions in the paper.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 5: Probability.<br>Some candidates confused the probability of both events occurring with the probability that one or the other occurs. Many candidates were unable to find the conditional probability. Candidates should not answer a probability question with an answer that exceeds one. Only the very best candidates did very well on this question; many found this to be one of the most challenging questions in the paper.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 5: Probability.<br>Some candidates confused the probability of both events occurring with the probability that one or the other occurs. Many candidates were unable to find the conditional probability. Candidates should not answer a probability question with an answer that exceeds one. Only the very best candidates did very well on this question; many found this to be one of the most challenging questions in the paper.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider the propositions \(r\), \(p\) and \(q\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Complete the following truth table.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-20_om_13.45.17.png" alt></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Determine whether the compound proposition \(\neg \left( {(r \wedge p) \vee \neg q)} \right) \Leftrightarrow \neg (r \wedge p) \wedge q\) <span class="s1">is a tautology, a contradiction or neither.</span></p>
<p class="p2">Give a reason.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space"><img src="images/Schermafbeelding_2015-12-20_om_13.51.08.png" alt> </span><strong><em>(A1)(A1)</em>(ft)(<em>A1)</em>(ft)<em>(A1) <span class="Apple-converted-space"> </span>(C4)</em></strong></p>
<p class="p1"> </p>
<p class="p1"><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for each correct column.</p>
<p class="p1">For the “\({(r \wedge p) \vee \neg q}\)” follow through from the “\(r \wedge p\)” column.</p>
<p class="p1">For the “\(\neg \left( {(r \wedge p) \vee \neg q)} \right)\)” column, follow through from the preceding column.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">tautology <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)</strong></p>
<p class="p1">columns \(\neg \left( {(r \wedge p) \vee \neg q)} \right)\) and \(\neg (r \wedge p) \wedge q\) are identical <span class="Apple-converted-space"> </span><strong><em>(R1)(C2)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: </strong>Do not award <strong><em>(R0)(A1)</em>(ft)</strong>. Follow through from their table in part (a).</p>
<p class="p1">Award the <strong><em>(R1) </em></strong>for an additional column representing \(\neg \left( {(r \wedge p) \vee \neg q)} \right) \Leftrightarrow \neg (r \wedge p) \wedge q\) that is consistent with their table.</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Consider the following statements</p>
<p>\(z\,:\,x\) is an integer<br>\(q\,:\,x\) is a rational number<br>\(r\,:\,x\) is a real number.</p>
<p>i) Write down, in words, \(\neg q\).</p>
<p>ii) Write down a value for \(x\) such that the statement \(\neg q\) is true.</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 the following argument in symbolic form:<br>“If \(x\) is a real number and \(x\) is not a rational number, then \(x\) is not an integer”.</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>Phoebe states that the argument in part (b) can be shown to be valid, without the need of a truth table.</p>
<p>Justify Phoebe’s statement.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>i) \(x\) is not a rational number <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Accept “\(x\) is an irrational number”.</p>
<p> </p>
<p>ii) any non-rational number (for example: \(\pi ,\,\sqrt 2 \), …) <em><strong>(A1) (C2)</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\((r \wedge \neg q) \Rightarrow \neg z\) <em><strong>(A1)(A1)(A1) (C3)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for “\( \Rightarrow \)” seen, <em><strong>(A1)</strong></em> for “\(\neg z\)” as the consequent and <em><strong>(A1)</strong></em> for “\((r \wedge \neg q)\)” or “\((\neg q \wedge r)\)” as the antecedent (the parentheses are required).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>all integers are rational numbers (and therefore \(x\) cannot be an integer if it is not a rational number) <em><strong>(R1)</strong></em></p>
<p><strong>Note:</strong> Accept equivalent expressions.</p>
<p><strong>OR</strong></p>
<p>if \(x\) is an integer, then \(x\) is a rational number, therefore if \(x\) is not a rational number, then \(x\) is not an integer (contrapositive) <strong><em>(R1) (C1)</em></strong></p>
<p><strong>Note: </strong>Accept “If \(x\) is not in \(\mathbb{Q}\), then \(x\) is not in \(\mathbb{Z}\)” with a Venn diagram showing \(\mathbb{R}\), \(\mathbb{Q}\) and \(\mathbb{Z}\) correctly.</p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Question 5 Logic<br>In part (a), the majority of candidates were able to state the negation, but surprisingly many were unable to give an example of a non-rational number.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>In part (b), a common error was the lack of parentheses in the antecedent. A further error was the use of the “intersection” symbol rather than that for conjunction; care must be taken in this regard.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Part (c) proved problematic for all but the best candidates.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Ramzi travels to work each day, either by bus or by train. The probability that he travels by bus is \(\frac{3}{5}\). If he travels by bus, the probability that he buys a magazine is \(\frac{2}{3}\). If he travels by train, the probability that he buys a magazine is \(\frac{3}{4}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the tree diagram.</span></p>
<p><br><span><img src="images/Schermafbeelding_2014-09-03_om_06.15.58.png" alt></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>Find the probability that Ramzi buys a magazine when he travels to work.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><span><img src="images/Schermafbeelding_2014-09-03_om_06.19.12.png" alt><span> </span></span><span><strong><em>(A1)(A1)(A1) (C3)</em></strong></span></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for each correct pair of branches.</span></p>
<p> </p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{3}{5} \times \frac{2}{3} + \frac{2}{5} \times \frac{3}{4}\) <strong><em>(A1)</em>(ft)<em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(A1)</em>(ft) </strong>for two consistent products from tree diagram, <strong><em>(M1) </em></strong>for addition of their products.</span></p>
<p><span> Follow through from their tree diagram provided all probabilities are between \(0\) and \(1\).</span></p>
<p> </p>
<p><span>\(\frac{7}{{10}}{\text{ }}\left( {{\text{0.7, 70% , }}\frac{{42}}{{60}}} \right)\) <strong><em>(A1)</em>(ft) <em>(C3)</em></strong></span></p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Candidates showed that they were able to place probabilities in the correct position on the tree diagram and many went on to find the correct probability, gaining full marks for this question. Some candidates did not recognize that addition of two products was required. A mistake that was seen too frequently on candidate scripts was giving probabilities, in part (b), that were greater than 1.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Candidates showed that they were able to place probabilities in the correct position on the tree diagram and many went on to find the correct probability, gaining full marks for this question. Some candidates did not recognize that addition of two products was required. A mistake that was seen too frequently on candidate scripts was giving probabilities, in part (b), that were greater than 1.</span></p>
<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;"><em>B</em> and <em>C</em> are subsets of a universal set <em>U</em> such that</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">\(U = \left\{ {x:x \in \mathbb{Z},0 \leqslant x < 10} \right\},{\text{ }}B = \left\{ {{\text{prime numbers}} < 10} \right\},{\text{ }}C = \left\{ {x:x \in \mathbb{Z},1 < x \leqslant 6} \right\}.\)</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>List the members of sets</span></p>
<p><span>(i) \(B\)</span></p>
<p><span>(ii) \(C \cap B\)</span></p>
<p><span>(iii) \(B \cup C′\)</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>Consider the propositions:</span></p>
<p><span><em>p</em> : <em>x</em> is a prime number less than 10.</span></p>
<p><span><em>q</em> : <em>x</em> is a positive integer between 1 and 7.</span></p>
<p><span>Write down, in words, the contrapositive of the statement, “If <em>x</em> is a prime number less than 10, then <em>x</em> is a positive integer between 1 and 7.”</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(B = 2, 3, 5, 7\) <em><strong>(A1)</strong></em></span></p>
<p><em><span>Brackets not required<br><br></span></em></p>
<p><span>(ii) \(C \cap B = 2, 3, 5\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><em><span>Follow through only from incorrect B<br><br></span></em></p>
<p><span>(iii) \(C' = 0, 1, 7, 8, 9\) </span><span><em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>\(B \cup C' = 0, 1, 2, 3, 5, 7, 8, 9\) </span><span><em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><em>Note: Award <strong>(A1)</strong> for correct </em>\(C'\)<em> seen. The first <strong>(A1)(ft)</strong> in (iii)</em></span><em> <span>can be awarded only if C was listed incorrectly and a mark was</span> </em><span><em>lost as a result in (a)(ii). If C was not listed and </em>\(C'\)<em> is wrong, the </em></span><em><span>first mark is lost. The second mark can <strong>(ft)</strong> within part (iii) as well</span> <span>as from (i). <strong>(C4)</strong></span></em></p>
<p> </p>
<p><em><span><strong>[4 marks]</strong></span></em></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>“If <em>x</em> is not a positive integer between 1 and 7, then <em>x</em> is not a prime number less than 10.” <em><strong>(A1)(A1)</strong></em></span></p>
<p><em><span>Award <strong>(A1)</strong> for <strong>both</strong> (not) statements, <strong>(A1)</strong> for correct order. <strong>(C2)</strong></span></em></p>
<p><em><span><strong>[2 marks]</strong></span></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">a) Many candidates included 1 as a prime number for set \(B\). Most candidates were able to list the intersection of \(B\) and \(C\) correctly with many receiving a follow through for their incorrect \(B\). Very few candidates were able to list \(B \cup C '\) correctly with many listing the intersection. It was disappointing that only a few candidates listed \(C'\) separately – those that did often received a mark for this working.</span></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">b) The majority of candidates were able to write down the contrapositive correctly but many gave the inverse or the converse instead.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Tuti has the following polygons to classify: rectangle (R), rhombus (H), isosceles triangle (I), regular pentagon (P), and scalene triangle (T).</p>
<p class="p1">In the Venn diagram below, set \(A\) consists of the polygons that have at least one pair of parallel sides, and set \(B\) consists of the polygons that have at least one pair of equal sides.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-03_om_08.19.15.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Complete the Venn diagram by placing the letter corresponding to each polygon in the appropriate region. For example, R has already been placed, and represents the rectangle.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">State which polygons from Tuti’s list are elements of</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>\(A \cap B\);</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\((A \cup B)'\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2015-12-03_om_08.21.19.png" alt> <strong><em>(A3) (C3)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(A3) </em></strong>if all four letters placed correctly,</p>
<p class="p1"><strong><em>(A2) </em></strong>if three letters are placed correctly,</p>
<p class="p1"><strong><em>(A1) </em></strong>if two letters are placed correctly.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Rhombus and rectangle <strong>OR </strong>H and R <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)</strong></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Scalene triangle <strong>OR </strong>T <span class="Apple-converted-space"> </span><strong><em>(A2)</em>(ft) <span class="Apple-converted-space"> </span><em>(C3)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for a list R, H, I, P seen (identifying the union).</p>
<p class="p1">Follow through from their part (a).</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the following statements about the quadrilateral ABCD</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;">\(q:\) ABCD has four equal sides \(s:\) ABCD is a square</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Express in words the statement, \(s \Rightarrow q\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down in words, the inverse of the statement, \(s \Rightarrow q\) .</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>Determine the validity of the argument in (b). Give a reason for your decision.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>If ABCD is a square, then ABCD has four equal sides. <em><strong>(A1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for if… then, <em><strong>(A1)</strong></em> for propositions in the correct order.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>If ABCD is not a square, then ABCD does not have four equal sides. <em><strong>(A1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for if… then, <em><strong>(A1)</strong></em> for propositions in the correct order.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Not a valid argument. ABCD may have 4 equal sides but will not <strong>necessarily</strong> be a square. (It may be a rhombus) <em><strong>(A1)(R1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(R1)</strong></em> for correct reasoning, award <em><strong>(A1)</strong></em> for a consistent conclusion with their answer in part (b). </span></p>
<p><span>It is therefore possible that <em><strong>(R1)(A0)</strong></em> may be awarded, but <em><strong>(R0)(A1)</strong></em> can never be awarded.</span></p>
<p> </p>
<p><span><strong>Note:</strong> Simple examples of determining the validity of an argument without the use of a truth table may be tested.</span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A survey was carried out in a group of 200 people. They were asked whether they smoke or not. The collected information was organized in the following table.</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;">One person from this group is chosen at random.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the probability that this person is a smoker.</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 probability that this person is male given that they are a smoker.</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 probability that this person is a smoker or is male.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{90}}{{200}}(0.45,{\text{ }}45{\text{ }}\% )\) <em><strong>(A1)(A1) (C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for numerator, <em><strong>(A1)</strong></em> for denominator.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{60}}{{90}}(0.\bar 6,{\text{ }}0.667,{\text{ }}66.\bar 6{\text{ }}\% ,{\text{ }}66.6 \ldots {\text{ }}\% ,{\text{ }}66.7{\text{ }}\% )\) <em><strong>(A1)(A1)</strong></em><strong>(ft) </strong><em><strong> (C2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for numerator, <strong><em>(A1)</em>(ft)</strong> for denominator, follow through from their numerator in part (a). Last mark is lost if answer is not a probability.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{90}}{{200}} + \frac{{100}}{{200}} - \frac{{60}}{{200}}\) <em><strong>(M1)</strong></em></span></p>
<p><span><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in the combined events formula. Follow through from their answer to part (a).</span></p>
<p> </p>
<p><span>\( = \frac{{130}}{{200}}(0.65,{\text{ }}65{\text{ }}\% )\) <strong><em>(A1)</em>(ft)</strong></span></p>
<p><strong><span>OR</span></strong></p>
<p><span><span>\(\frac{{60}}{{200}} + \frac{{40}}{{200}} + \frac{{30}}{{200}}\) </span><em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for adding the correct fractions.</span></p>
<p> </p>
<p><span><span>\( = \frac{{130}}{{200}}(0.65,{\text{ }}65{\text{ }}\% )\) </span><em><strong>(A1)</strong></em></span></p>
<p><strong><span>OR</span></strong></p>
<p><span>\(1 - \frac{{70}}{{200}}\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for subtraction of correct fraction from 1.</span></p>
<p> </p>
<p><span><span><span><span><span>\( = \frac{{130}}{{200}}(0.65,{\text{ }}65{\text{ }}\% )\)</span></span> </span></span><em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span> </span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was generally well answered by many of the candidates. Many found the conditional probability in part b) easier compared to previous sessions, since they were able to write it down directly from the table. A number of candidates found the final part difficult with a significant number unable to use the combined events probability formula correctly.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was generally well answered by many of the candidates. Many found the conditional probability in part b) easier compared to previous sessions, since they were able to write it down directly from the table. A number of candidates found the final part difficult with a significant number unable to use the combined events probability formula correctly.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was generally well answered by many of the candidates. Many found the conditional probability in part b) easier compared to previous sessions, since they were able to write it down directly from the table. A number of candidates found the final part difficult with a significant number unable to use the combined events probability formula correctly.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">On a work day, the probability that Mr Van Winkel wakes up early is \(\frac{4}{5}\).</p>
<p class="p1">If he wakes up early, the probability that he is on time for work is \(p\).</p>
<p class="p1">If he wakes up late, the probability that he is on time for work is \(\frac{1}{4}\).</p>
</div>
<div class="specification">
<p class="p1">The probability that Mr Van Winkel arrives on time for work is \(\frac{3}{5}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Complete the tree diagram below.</p>
<p class="p1"><img src="images/Schermafbeelding_2017-03-07_om_06.20.32.png" alt="N16/5/MATSD/SP1/ENG/TZ0/12.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">Find the value of \(p\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><img src="images/Schermafbeelding_2017-03-07_om_06.24.40.png" alt="N16/5/MATSD/SP1/ENG/TZ0/12.a/M"> <strong><em>(A1)(A1) (C2)</em></strong></p>
<p class="p3"> </p>
<p class="p2"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1) </em></strong>for each correct pair of probabilities.</p>
<p class="p3"> </p>
<p class="p2"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="s1">\(\frac{4}{5}p + \frac{1}{5} \times \frac{1}{4} = \frac{3}{5}\) <span class="Apple-converted-space"> </span></span><strong><em>(A1)</em>(ft)<em>(M1)(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1)</em>(ft) </strong>for two correct products from part (a), <strong><em>(M1) </em></strong>for adding their products, <strong><em>(M1) </em></strong>for equating the sum of any two probabilities to \(\frac{3}{5}\).</p>
<p class="p1"> </p>
<p class="p1"><span class="Apple-converted-space">\((p = ){\text{ }}\frac{{11}}{{16}}{\text{ }}(0.688,{\text{ }}0.6875)\) </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C4)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award the final <strong><em>(A1)</em>(ft) </strong>only if \(0 \leqslant p \leqslant 1\). Follow through from part (a).</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following Venn diagram shows the sets \(A\), \(B\), \(C\) and \(U\).</p>
<p class="p1">\(x\) is an element of \(U\).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2017-03-06_om_09.16.47.png" alt="N16/5/MATSD/SP1/ENG/TZ0/03"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">In the table indicate whether the given statements are True or False.</p>
<p class="p1"><img src="images/Schermafbeelding_2017-03-06_om_12.54.23.png" alt="N16/5/MATSD/SP1/ENG/TZ0/03.a"></p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">On the Venn diagram, shade the region \(A \cap (B \cup C)'\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="s1"><img src="images/Schermafbeelding_2017-03-06_om_12.57.08.png" alt="N16/5/MATSD/SP1/ENG/TZ0/03.a/M"> </span><strong><em>(A1)(A1)(A1)(A1)(A1) (C5)</em></strong></p>
<p class="p1"><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><img src="images/Schermafbeelding_2017-03-06_om_13.00.17.png" alt="N16/5/MATSD/SP1/ENG/TZ0/03.b/M"> <strong><em>(A1) (C1)</em></strong></p>
<p class="p2"><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Sara regularly flies from Geneva to London. She takes either a direct flight or a non-directflight that goes via Amsterdam.</p>
<p>If she takes a direct flight, the probability that her baggage does not arrive in London is 0.01.<br>If she takes a non-direct flight the probability that her baggage arrives in London is 0.95.</p>
<p>The probability that she takes a non-direct flight is 0.2.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_11.08.43.png" alt="M17/5/MATSD/SP1/ENG/TZ1/07"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Complete the tree diagram.</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 probability that Sara’s baggage arrives in London.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2017-08-15_om_14.22.22.png" alt="M17/5/MATSD/SP1/ENG/TZ1/07.a/M"> <strong><em>(A1)(A1)(A1) (C3)</em></strong></p>
<p> </p>
<p> </p>
<p>Note: Award <strong><em>(A1) </em></strong>for each correct pair of probabilities.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(0.8 \times 0.99 + 0.2 \times 0.95\) <strong><em>(A1)</em>(ft)<em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em>(ft) </strong>for two correct products of probabilities taken from their diagram, <strong><em>(M1) </em></strong>for the addition of their products.</p>
<p> </p>
<p>\( = 0.982{\text{ }}\left( {98.2\% ,{\text{ }}\frac{{491}}{{500}}} \right)\) <strong><em>(A1)</em>(ft)</strong><em> </em><strong><em>(C3)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (a).</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The IB grades attained by a group of students are listed as follows.</p>
<p class="p1">\[{\text{6}}\;\;\;{\text{4}}\;\;\;{\text{5}}\;\;\;{\text{3}}\;\;\;{\text{7}}\;\;\;{\text{3}}\;\;\;{\text{5}}\;\;\;{\text{4}}\;\;\;{\text{2}}\;\;\;{\text{5}}\]</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the median grade.</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">Calculate the interquartile range.</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 probability that a student chosen at random from the group scored at least a grade \(4\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(2\;\;\;3\;\;\;3\;\;\;4\;\;\;4\;\;\;5\;\;\;5\;\;\;5\;\;\;6\;\;\;7\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p3"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct ordered set.</p>
<p class="p2"> </p>
<p class="p3">\(({\text{Median}} = ){\text{ }}4.5\) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C2)</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(5 - 3\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Note:<span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for correct quartiles seen.</p>
<p class="p2"> </p>
<p class="p1">\( = 2\) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C2)</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\frac{7}{{10}}\;\;\;(0.7,{\text{ }}70\% )\) <span class="Apple-converted-space"> </span><strong><em>(A2) <span class="Apple-converted-space"> </span>(C2)</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Part (a) was generally well done although some candidates seemed to be confused between the mean and median.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>In part (b) it was not unusual to see an upper quartile of 5.5 (resulting from (5+6)/2).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>A significant number of candidates had difficulty with “at least four” in part (c), answering 2/10 which resulted from calculating the probability of a grade equal to 4 and not at least 4.</p>
<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 <strong>weighted</strong> die has 2 red faces, 3 green faces and 1 black face. When the die is thrown,</span> <span style="font-size: medium; font-family: times new roman,times;">the black face is three times as likely to appear on top as one of the other five faces. </span><span style="font-size: medium; font-family: times new roman,times;">The other five faces have equal probability of appearing on top.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The following table gives the probabilities.</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>Find the value of</span></p>
<p><span>(i) <em>m</em>;</span></p>
<p><span>(ii) <em>n</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>The die is thrown once.</span></p>
<p><span>Given that the face on top is not red, find the probability that it is black.</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 die is now thrown twice.</span></p>
<p><span>Calculate the probability that black appears on top both times.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>(i) <em>m</em> = 1 <em><strong>(A1)</strong></em></span></p>
<p><span>(ii) <em>n</em> = 3<strong> </strong><em><strong>(A1) (C2)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A0)(A1)</strong></em><strong>(ft)</strong> for \(m = \frac{1}{8}, n = \frac{3}{8}\).</span></p>
<p><span> Award <em><strong>(A0)(A1)</strong></em><strong>(ft</strong><strong>)</strong> for <em>m</em> = 3, <em>n</em> = 1.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\rm{P}}(B/R') = \frac{{\frac{3}{8}}}{{\frac{6}{8}}} = \frac{3}{6}\left( {\frac{1}{2},50\% ,0.5} \right)\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted conditional probability formula or for 6 seen as part of denominator.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\rm{P}}(B,B) = \frac{3}{8} \times \frac{3}{8} = \frac{9}{{64}}(0.141)\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for product of two correct fractions, decimals or percentages.</span></p>
<p><span><strong>(ft)</strong> from their answer to part (a) (ii).</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The answers 1/8 and 3/8 were provided by many rather than 1 and 3. The conditional probability question was correctly answered more often when the formula was used. A common incorrect answer to part (c) was 3/8 × 2/7.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The answers 1/8 and 3/8 were provided by many rather than 1 and 3. The conditional probability question was correctly answered more often when the formula was used. A common incorrect answer to part (c) was 3/8 × 2/7.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The answers 1/8 and 3/8 were provided by many rather than 1 and 3. The conditional probability question was correctly answered more often when the formula was used. A common incorrect answer to part (c) was 3/8 × 2/7.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Complete the truth table below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>(ii) State whether the compound propositions \(\neg (p \wedge q)\) and \(\neg p \vee \neg q\) are equivalent.</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>Consider the following propositions.</span></p>
<p><span>\(p:{\text{ Amy eats sweets}}\)</span></p>
<p><span> \(q:{\text{ Amy goes swimming.}}\)</span></p>
<p><span>Write, in symbolic form, the following proposition.</span></p>
<p><span><em>Amy either eats sweets or goes swimming, but not both.</em></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>(i)</span></p>
<p><span><img src="data:image/png;base64,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" alt> <em><strong>(A3)</strong></em></span></p>
<p><span><strong>Note: </strong>Award <em><strong>(A1)</strong></em> for \(p \wedge q\) column correct, <strong><em>(A1)</em>(ft)</strong> for \(\neg (p \wedge q)\) column correct, <em><strong>(A1)</strong></em> for last column correct.<em><strong><br></strong></em></span></p>
<p><span> </span></p>
<p><span>(ii) Yes. <em><strong>(R1)</strong></em><strong>(ft)</strong> <em><strong>(C4)</strong></em></span></p>
<p><span><strong>Note: (ft)</strong> from their second and the last columns. Must be correct from their table.</span></p>
<p><span><em><strong>[4 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(p {\underline \vee} q\). <em><strong>(A1)(A1) (C2)</strong></em></span></p>
<p><span><strong>Note: </strong>Award <em><strong>(A1)</strong></em> for \(p \ldots q\), <em><strong>(A1)</strong></em> for \({\underline \vee} \). Accept \((p \vee q) \wedge \neg (p \wedge q)\) or \((p \vee q) \wedge (\neg p \vee \neg q)\).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well answered by many of the candidates. It is an area of the syllabus that is well taught and many managed to get a follow through mark even though one of the columns in the table might have been incorrect.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well answered by many of the candidates. It is an area of the syllabus that is well taught and many managed to get a follow through mark even though one of the columns in the table might have been incorrect.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider each of the following statements</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\[p:Alex{\text{ }}is{\text{ }}from{\text{ }}Uruguay\]\[q:Alex{\text{ }}is{\text{ }}a{\text{ }}scientist\]\[r:Alex{\text{ }}plays{\text{ }}the{\text{ }}flute\]</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write the following argument in words</span><br><span>\[\neg r \Rightarrow (q \vee p)\]</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>Complete the truth table for the argument in part (a) using the values below for \(p\) , \(q\) , \(r\) and \(\neg r\).</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>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The argument \(\neg r \Rightarrow (q \vee p)\) is invalid. State the reason for this.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>If Alex does not play the flute then he is <strong>either</strong> a scientist <strong>or</strong> from Uruguay. <em><strong>(A1)(A1)(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> if… then, correct <em><strong>(A1)</strong></em> antecedent, <em><strong>(A1)</strong></em> correct consequent.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span> </span></span><span> <em><strong>(A1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span>Not all entries in the final column are T. </span> <span><em><strong>(R1)</strong></em> <em><strong>(C1)</strong></em></span></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The probability that it will snow tomorrow is 0.3.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">If it snows tomorrow the probability that Chuck will be late for school is 0.8.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">If it does not snow tomorrow the probability that Chuck will be late for school is 0.1.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the tree diagram below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></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>Find the probability that it does not snow tomorrow and Chuck is late for school.</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 probability that Chuck is late for school.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASUAAAELCAIAAAAQowdmAAAe30lEQVR4nO2dfVBbV373f965W5qBhYmfYaf3eTKlu+xmt4xDZnDSjh0yVkY7buPM1p3NQ9eMA07d7jglO/DwELx2J1vZw7MhfoldUkMUbII3cWAhZhMndmyIiPo4ia3BSd0kgIxDB28Q2EviRSDiF5Sr0z+urnT1ypXQle7V/X7+ssTlIrA+Ouf8zvmeQwwAPeJu3c6TDJ5vd3oz/aKWhDL9AgBIGq/HUWmiVaW9VxI2TfjIar2cfj/hG9AxgrNmPa029X+R4Pd5PY7HStsy0B7CN6BjkvTN07VnTU5G+p/wDeiYpXxbmDpX31jOERHRelO3c4Yx5una63+GKPC98/Yzu0t4IqJVJbvfts8LKr1g+AZ0THzfBGeNmfsny+RtxqadbaU8VdQ4bzLGmGA78pCsffN0/dK0r8t1mzHGPKcOb8rlGgen1XnB8A3og4sXL27ZsiXsSQW+7Wh1C9KVUX3zzg2YQyqdRMTvFL8r5cA3oHVmZ2e3bNlSUFBgsVhmZ2flX1IyfhMme7uPVlTzRNF9G7fVr0zbWA6+AU1z8ODBgoKCjRs3TkxMRH41lm/CyIGm0ZtMGD7/TEnO5j1Pt33gGonVvo0PNuTT+g67WkO2EOAb0Ch2u72oqOjee++12+2xronh26Sjcnv33Fdj1uKASEv1J/nC+qO9k7cZY4x5PWeP9KI/CQzCxMTExo0bCwoKDh48GPdCcb471DdheKjNxNfZZtm1wYZ8Mh3o9QjikyZabXp7yGq9LAgfdJg5rnHQPX+iqe+K4HlDVrEkIr6w2TGjzq8G34CGmJ2dtVgsRFRXVxc2VAsnfD1XlLVdgqtlRzknlvhHPm9p5LjC+uP2eYGxhan+DSbiC5/qHxZbP1dXR514O8wHgIzju+56v2lXVUVF/cFnh67eVOeHdHZ2FhQUrFu3LupQLTuAb2ApFi8O/Pz+h6xvHx/49cln7/neig0b35vxpfQn2O32devWFRUVvf766ym9seaAbyA+N6Z6/vJ//tunN8RHvnPdFTk5ey7cStHd5bX+FN1S08A3EJ+P+n6aV9T5mTSgmbnwzLe/dfA/b6fi1haLpaCgYMuWLVncgQwDvoH4jA825NPqnz/5/yd+7/Ux34e99zxQ41xY5k3FWv+6devi1PqzEvgG4uNbvLzj77+3gogob/Vdjz5498qampPn7Z/PJ9elnJiYWLduXUFBQWdnZ2pfqC6Ab2BJvDcnXjrS8BeP3COfpPrhXf/nN2fmv1Z+l9nZ2bq6OiKKXJZlHOCb4fFdd51t2W/Z39z34fCNePNOvknLA/f862/f2tv+zMP/uOaPifL+uPo3Hywq+iFGqPUrAb4ZG5/r00MPrv6Xl45aq2sf+OaK+35ec+5ajOm1uTFrcbAy6fvyyus/up82/sMnX8X/CXa7/d577y0qKjLaUC0q8M3QCJ/V/zin6ZWbPsaYb/61lg1/RHmPxJhec555Mu+bT5/9MvCEt3dPziNxfJuYmDBUrV8J8M3I3JruKaPifb3+LIpv8XJD5Z1EP/zFgWuR8ZSrF575k5AvfXngH7/b/u5iFDfFZVlird+wQ7WowDcjc2u6p4zytu64EphOu37J+oM8yruj0XYl/GLf4oRl23e/kbPh6fo33/33E43/94Fdh1xR+p6vv/66WOu/ePGiui9fh8A3I7N4/eSDd1Lx3cf+K1gnuX7oF3evoLzH6j+LLPj7Fq+eeO2ZqoqKp57sdnwaUVy5ePGiuCzLmLV+JcA3Q+O7sqMyj2jt8yduB7qFYhMX2D7Vt+hq3bV649+dnoyzTBm1foXAN2Pju3C86g6itQ8N/D44DrvW/MSdRNV9w4wxtni9/0ffJ/pG7ZmIHqaf+BFsIAe+GRzhK8dP1xDRmv29XwWMGx9syA/WUXxXLx07ab8eZaJNrPXHj2ADOfDN8Pgun/3nbxP92Z/u/1Bq42787tg9tPHlc7FTN4oj2CAE+AaYb/7NI5u/RXkP/3X/5zcZY2zu0gt/XvTiyI1oFycQwQYRwDfAGGO++XeON37nOyvWrtp1+OX2itUPtp+Otjays7MTtf7lAN9AgBt/uPRq137L7q54tf6sj2CrCnwDSxBnu1WQKPANxEOs9Rsqgq0q8A1ER8l2qyBR4BsIx+ARbFWBbyAIav1qA9+AH0Sw0wB8A8HtVjFUUxv4ZmgQwU4z8M24IIKdfuCbEQlEsNGBTDPwzVig1p9Z4JtRQARbC8A3QyDW+hHBzjjwLcvBdquaAr5lLYhgaxD4loVgu1XNAt+yDWy3qmXgW/aA7Va1D3zLBhDB1gvwTfdgu1UdAd90DCLYugO+6RLU+nUKfNMZiGDrGvimJwLbrWKoplPgmz4IRLCx3aqugW86YHZ2loiKiooy/ULAcoFv+gDtW3YA3/QEjsvQO/BNZ2Atsq6Bb7oE8286Bb7pGGRJdQd8U8jC1Ln6xnKOiMi0veaUc959pnfkZqZfFWPYF1lXwDcleD2OynJua82ImzHGhOGhNpOJKmqcmvCNYdGJfoBvChBsHWaOaxycDj614Hq5slYzvolgrzvtA98UINg6zByZDvR6ZKfsaqY/GQZCA1oGvilhwdVzPy+N3GbCvjhvP3O04sd3tTvcttfqeCLiqo7a5kUzvZ7h1vY6noiIVpXsftvuf35uzFpMRETENQ66RZ+JiHi+3ell3rkBM09E/M5Wd/g52gpBKE6bwDeFTF/qNptERUzba89Pef3Pjw825BMRmbZVHHxvWGDM3drIcXy708uYMGl5POfxmhE3Y17PqKWxnJOpuDDVv6Gc2yEZNTdmLab1HXa/X5Pna1+1J+maH2zwqkHgm3LkjRVfWH9caqzGBxvyg6pIg73rbHywIV826vN6HJUmWm3q/8L/hGA7fN9K6aHYpkk1GLe18rkRL0sB2NREU8C3RPF6Rg48uymXiC9sdswwFss3t6yh8+Nu3c6TzMC5MWux/6Ew1Fnb1lO/srDZMcOEuVPbUluMwQEdGgG+KUCwNzWNhrQ2wlBfda7kWEzfQu2K9I0Jzhozt6PVLQijzbXnv5wbMHPcjlb31dOVh5fZmYxKYCEYBnWZAr4pQLC1lT4bUpwMGW7F60+GVDXdrY3cPcH+JAt0Kcf8ozXxgmMvpaozGYl8Jy91fgKIB3xTgKhQ1V7LB2KZZGHqXH194V+aB1xexmL5Ns0Ez0htFcdJI71pZ1tpzuPHPw5puObGrMW09m/NvROBW3HltU+PqjvTgHRPpoBvChDsTU2jwry9/3lTeIkyWMon4ne+fKVlO+9/ROs77IIgDfaIaL3p+X6pxCK7t9SlZIyJVRPO3KFGZzISpHvSD3wzNFgIlmbgG0C6J33AN+AH6Z40AN9ACEj3qAp884OaQQAsBFMP+BZcUJ/pF6ItkO5RA0P7hrfUkiDdk1oM6hvq4AmBdE+qMKJvKAkkAY50TAna8M133eWwNje//ubkgk/Nn4N1TMsE6Z5lknnffPNv/Xrr/8gT10DlPfzwu1fVWMw0MTGBdbqpAumepMm4b18MtxTf8ZPd9T1vvn3kb376vRWyjHPKwIbEaoC/ahJk2jfB9uJ3t7d++TVjjLEbU7+57xulLSe+Ttnt8UmsKug1JEqmffv6xK/+9+BV6ZHvdzt+uM02He8blIJaf9rAqFg5mfYthNtfnlzHE1He2lW7T7w7n2Qzh+URGQHpHiWo75vvuutsy37L/ua+D4dvxBuZ+eZfa9nwR1J6LO+O2tNjiRcrMVOUQTCruSQq++ZzfXrowdX/8tJRa3XtA99ccd/Pa85dixFdvv2HiyfOfD5/i3198/dvv7H9f+XRI4/9h0f5j8Lydo2AdE8c1PVN+Kz+xzlNr9z0sUDzlffIxvdmlm63bvz2X+/PLen9XMlPwX+wBsHHX1RU9e3WdE8ZFe/r9e9941u83FB5J9EPf3Hg2pLb4cwM/b+isjdc8S/C4YMaB0t5wlDft7ytO67clp65fsn6gzzKu6PRdiX+ty7aX/rB31smF+NcggG6LkD5So6qvi1eP/ngnVR897H/CtZJrh/6xd0rKO+x+s9uRX6D78blT959zf6u9Tfb77v/lbEbMe4bWFWEArRewPSMiLrjN9+VHZV5RGufP3E7MGQTmzg+ZONh/9Wfnn6ygIio+NG/+e1Y1EEeVs3qGqR71K5PXjhedQfR2ocGfh/U51rzE3cSVfcNM8aYb9HVumv1xr87PbnI5qfe27/71X//4Hr0biRq/ctj+tJbldV82Ek90Zi3n9ldwotn+jzz3nCql9cZ+f9R7fk34SvHT9cQ0Zr9vV8FjBsfbMiX6iiL1/t/9H2ib9SeiTOiw+fishGP1Kqocd5knq695Ry3te/jqCKJW7UHCRyTkEoM209Jw3z35bP//G2iP/vT/R9KbdyN3x27hza+fE586Lt66dhJe4w2Df3+1OBu3c6T9Bk3c6G5kOQn9QTxzp1+7K/6XV7GBFfLDvG8ctpmmVJle3UDpnvSsZ7LN//mkc3foryH/7r/85uMMTZ36YU/L3pxJFY5RASLFVKHdICjP3sh+kY5ey5E1KwWrgwH5mqk71LNNxFDrSlP0/pJ3/w7xxu/850Va1ftOvxye8XqB9tPx10eiXmblCIdp+ofM/t9kx7GxOuoKA5aqi7am0f1eoat3btLckLObV8u6VyvfOMPl17t2m/Z3eX4NPZCSiw2V4EwwaSHwaUIUREtXVXae0XF1k1GIumewIHMkcNL6cRZohh9ZmWIPXAKPVFs2WgoH4AwlWok5Zt40E+ssopqJPCBOy8emB7lE0GYtJSV9Sh65cJHVuvl6H+G4FFHy7hJKFrxTXvdiWwiif7kgqvnfq7c0uq6HfMSNVG4eEhw1qwnInqkwhH6tnG3ms0DCtolr8fxWGlbxFSw/+4KfYt7k1Ay75uhhssZQnm9xI8waXk85/GaEXc6X2UYSgpmgrO2zHLkxU25xG8NebUKffN07VmTE2Xphf/uynyLf5NQMukbav3pI+58gFj656qO2sRJcE/XM3xV8O0rDHXWpnIMkxDxwx+Cs7aszekVpy5Mu4KtcZhvsrP7uKrnWsRfzdO1t5yLN9IL800YHmoLHAC40zIa+ybyBQOhSwsy4xvWsKadOPPdt6Z7ysQ3UYXDEzHfvbyqQ4oIpHvC3i1+35jXM1JbzVPwI0PumzB0fFNhyQufzDBpyBdoDAXbkYcUtm9zY9Zi/x/Nc+rwplz5ibYhN/F0/dK0r0s033Pq8KZceQuZAd+MvJwno0xf6jabon3oytq3Ly786i4Kp6LGqe75xgqJrKBIvjHGFqb6N5iIL3yqf1iQ++adGzBzwRNk/S2S34FEfZP9O4ZvgUlL+RKdnYGfnlbfkEEEqUXmGxNPSOeJL2x2eIK+hZ6uHnhGdCAB30QWpt7b2y32FaP7Nm6rXxlnLJcm3xDBziwRTVYyZPqXiEKob4wJH9saeKJVpYf2mx7tD/oma2GS9k1wde79SWHJ7l83vf/ZaMz2LVLvEFT/IyKCDdQj3DcWXG8teSJ28OQTBuODDfkJ9ydDrlyyP8kX1h/tnRSLN17P2SO96elPIoIN1MTrcVTydREblspHaEwqb/gril7PSO3mnCcsogySUe75E019Ecto5L65Wxs5TlzLIri6Oup44ne2XDxpdd4Mu4ngeUNWsaSwFTBq+YYINlAXwdZhDrytwys6wqSl7GfvyOcDpAI9X1h/uHU4MFMXWmWRI63nIiJa3/GhcHuqf4OJiPjqipOjrgEzT+tN3c6ZaDfxCxmtNJV63wwbbQJgSVLsG2r9AMQhZb4hgg3AkqTAt0CtH8uyAIjPsnxDBBuAhEjeN0SwAUiUZHxDBBuA5EjMN3mtX53XA0A2k4BvWJYFwDJR5Bsi2ACkhCV8QwQbgBQS0zdEsAFIOdF9E2v9WJYFQGoJ9w0RbADUI+gbItgAqA0xRLABSBc0MTGBCDYA6YGwZASAtOEfv2FJJABpIKQ+iSX/AKhK+HwAIm0AqEf0+W7MDQCgBvHWT2LuG4DUsnQ+AFtuAZAqFOVxsHYZgJSQQN4U2RwAlknC+5dgn0kAkibJ/bkC6y0xqANAOcnvh4dzAgBIlOXurxw4BweDOgCWJDXnBwQ2FELIQMNMX3qrspqPckhSVITJ3h5LWWnv79Lz4gxCys7rQIhO2yy4eu7nxXPSxOMIt/Z9HN04r2e4td1/fFlxSe/naX6hSpGfz0ZExMc5NVs7pPg8qomJCaR7tIj47ize1+tljM1caC4kWm3q/yLKld7eX921pWFTrtZ9Y0w839REq0p7I44mXRLhI6v1cvr9VOV8U6R7NIZ4qDRJR06LvlHOngu3Yn2Hv/XQuG9McNasj/XBEQ+vx/FYaVsG2kMVz+9GukczzI1Zi4mIqvuGGQv4Jj2Mhrd3X3H2+ubp2rMmJyP9TxV9Y0j3aIUwwaSH/u5lNLLEt4Wpc/WN/tPrpeO2PV2y8+yl7w0e8K2omJQ06vomgnRPpjGob4Kzxsz9k2XyNmPTzrZSf7mIMSbYjjwka988Xb807ety3WaMMc+pw5tyucbBaXVecDp8E0G6J3MYtD8pOGvM3I5WtyBdGdU3aXAbUuzcKX5XykmfbyJI92SCxOslmvQtsvymZPwmTPZ2H62o5omi+zZuq1+ZtrFcun1jSPdkhLjzAYKrZUc5x1UdtQXGLRrzLbBKPuwNE8s3YeRA0+hNJgyff6YkZ/Oep9s+cI3Eat/GBxvypU8i1cmAbyJI96SXOPPdt6Z7yoiIyFTh8IhPCZOWrbwmJpHjv09i+DbpqNzePffVmLU4INJS/Um+sP5o7+RtxhhjXs/ZI73Z0Z8MA+meNDJ9qdtsilaCC2nf/C2bnKCH6URBcVuc7w71TRgeajPxdbZZdm2wIZ9MB3o9gvikiVab3h6yWi8LwgcdZo5rHHTPn2jquyJ43pBVLImIL2x2zKjzS2XYNxGke0AYS0/ehq/nirK2S/wcET9fRj5vaeS4wvrj9nmBsYWp/g0m4guf6h8WWz9XV4d/CZv+5wOUgHQPEMnuOrZWfBNBukclYjUECaH2izTCPK22fBNBusdoGCdcokXfmJH+A0BnZ6dxPl416psI0j3ZjQFzJJr2TcSA/ytZj2FPQdOBbyJI92QNRp7+0Y1vDOke/ROohGVlrV8JevJNxAhV4+wDMz0i+vNNJLtnRbMJLE+Xo1ffRJDu0Tj4DwpD374xfHxqFaxEj4rufRNBukc7YIAdh+X45vWMHHh2Uy4RcVXPtYy4Y10WJa9OpMYWEfhMzSwoIC9J8r4Jk5atHMe3OwU2eeFXdxH/pMUf1wtD2jwjhCT2DFSKkad3MggmSJWQtG/jgw35gSSi11FRHKvJEuwvV3bJAkXeuQEzJ+3iohJI96QT1IqVk6xv/rSfP6Au+hZvf7Ug44MN+ertNyYHcz5qgwWuiZKkb4KzZj0R0TbLlJcFfJMexsPd2sjdo15nMhKke9QAAY7kSNK3MMGkh0tvdCHfEjBtLOPNERh8Ru5pIfaoVR+OahBDJWhSS5p9mxuzFqenMxlJ8p2fedtrdTxFO4dFmLSUlfXEONgpCwl00ZHVSI709icF2+H7Vma2KUgu3SP9vo9UOEKbR3er2TyQkY+PNIMSVEpIa70kI53JqCRavBactWWWIy9uyiV+a418ptEYvmGKJVWoMx8gfGxr4MPfmhntTEaS0OSs4Kwta3N6xf3VTLtaXdJMY5hv8/b+500mcUI/3hoA3YAETWpRZ757ylJNRGE71GugMxmJwsVHft+Y1zNSW81TcOtvuW/C0PFNhSUvfDLDpCFf+CeOnsASOTVY3nquUYt4uFb4Z3m09k07nclI7HZ7XV1dnAsk31j4VqFB3yLm8cVtwzXTnisHS8DVI0vWK6uNzDcmHSbGFzY7PEHfIo99GB9syFfvZCOVQIJGVZL0LbkNQyNJ7S+jHqG+SQ04rSo9tN/0aH/QtxC7dOYbVnunAd284zNLuG+MMWGorzpXFnQQYxDyCYP0rVxbJkjQpA34pgSvx1HJ19nCzQkboXlOHd6US6adllE3Y17PSO3mnCdiZCa0AhI0aQa+LYVg6zAHDiuSDhALfHHSUvazd+TzAdKx63xh/eHWYU0XJ5GgST/wzYggQZMp4JuxQIIms8A3o4AEjRaAb4YACRqNAN+yHCRoNAV8y1qQoNEg8C07QYJGm8A3JUgrs/nqilfetQ78xzRjbN5+5mjFj+9qd7jF9LcsNMBiBXOCWwNyjYPu4Mwez7c7vYGNOpe3BAwJGi0D3xQg2Nrv+pl/pYgw1Fk7OMuu+TcvMW2rOPieGBRo5Di+3ell8YM5C1P9G8qDMYK5MWuxbJXz5PnaV+3JuoYEjfaBb0sjOGvMXFXFK47hEBNCAwGCrcMsru0SlgjmhOQAxTZNWrbitlY+N7L0loIRIEGjF+CbAgJLk6v2Pv3GqLRLV3Tfri8dzJHl3IWhztq2nvqVhc2OGSbMndpWG7peTAlI0OgI+KYMYfj8K9v84dqtfR8LbAnf4gZzAtFbYbS59vyXUnt49XTl4YQ6k0jQ6A74lhALU+8/XuXfrzZef3KJYI6/SznmH62Je+Aee0l5ZxIJGp0C3xTgfsXylr8XKUxatnI/qXHejO2bkmDO3Ji1mNb+rbl3wsuYX8jy2qdHl+5MIkGja+CbAtyn+pqOdIv1fdP22vNTgvBBMKTD73z5Ssv2wIlbooFLBXNCd3Pxzg2YOXPHkp1JJGj0DnzTB0jQZAfwTQfMzs4SUVFRETqQege+6QOcrZUdwDc9gbVaege+6Q/ERvULfNMl2BZBp8A3HZPc2Vogg8A33YO9EnQEfMsGAotOMKjTOPAte8CiSu0D37INrETRMvAtO8FKS20C37IWJAk0CHzLcrCpiaaAb4YASXCNAN8MBHY6yTjwzVhgJ6/MAt+MCNI9mQK+GReke9IPfDM6OGkgncA3EHKSTqZfS5YD34AfpHvSAHwDISDdoyrwDYSDk77VA76B6GDLBjWAbyAeSPekFvgGlgbpnlQB34AikO5JCfANJAC2bFgm8A0kDNI9SQPfQJIg3ZME8A0kD9I9iQLfwHLBlg3KgW8gNSDdowT4BlIJ0j3xgW8gxcjTPRjUhQHfgCoEtmxAukcOfAMqgnRPGPANqAvSPXLgG0gHSPeIwDeQPrBlA3wD6cbI6R74BjKAYdM98M04TF96q7KaJ6JVJbvfts8LMS+ct5/ZXcKTgiuXhwHTPfDNICy4eu7nqaLGeZN5uvaWc9zWvo+jeuTp2lvOEb+z1e31OCpNRFzVUZtqyjGDbdkA34yBu3U7T1S8r9fLGJu50FxItNrU/0XEdd65ATNPRNV9w4wxwdZh5ohWlfZe8ar8Ag2S7oFvRkCyaH2HXWCSb5Sz58Kt8CvHBxvyKeBb+EN1MUK6B74Zgbkxa7FMG79v0Sz66PjmnChX+hvGdJDd6R74ZgTCBItjUdiXpIf+hjF9ZOuWDfDNCCj3jQnOmvVE4phNkK7kGgen0/+qszHdA9+MgPL+JGNsYepcfWM5R0RcVX19ORejspImMpfu8XqGrd27S3JS+lkD34yA8npJCGJbF3PmII0E0j2SctInCPGFzY6ZkGulGg/Rsj4pxIpuqtt2+GYM4s4HCK6WHeVc2Dyb+CSZdrW6bmfmNUcQ3quct71Wx0edrhAmLWVlPYo+JoSPrNbL0YtBgq3DzCnyLc5NQoFvBiHOfPet6Z4yIiIyVTg8jC1Mvbe3e3cJT8RVHerSjGxRkUabj1Q4Qrua7lazeUBBu+T1OB4rbXMuz7e4NwkFvhmH6UvdZlO0VVqy9s15fHMO0XrT88ea3p9K1xRA8gjO2jLLkRc35RK/tWbEHfyCQt88XXvW5PDty/Mt/k1CgW9AxwjO2rI2pzey6xvm27y9/3mTiYiIuKrnWkQzxZVrcUZ6Yb4Jw0Nt/puQaadlNPZNYi9AhW+GgFJBpn+JKPh9Y17PSG01L1vqKfdNGDq+qbDkhU9mmDTkCzSGgu3IQwrbt7kxa7G/E+45dXhTbnBOMuwmnq5fmvb5++GeU4c35cpbSC3+EQFQiOQbY2xhqn+DifjCp/qHBblv3rkBM8ftaHVLjYw4fBUdSNQ32b9j+CaVguXwOwM/Hb4BHSPzjTE27Wwr5YkvbHZ4gr6NDzbkh66PGR9syPc7kIBvIsFiUgzfxm31K+OM5eAb0DGhvjEmfGxr4IlWlR7ab3q0P+ibrIVJ2jfB1bn3J4Ulu3/d9P5nozHbt0i9Q4BvQMeE+8YYE4b6qnNl89RiB08+YTA+2JCfcH8y5Mol+5N8Yf3R3kmxeOP1nD3Si/4k0D9ej6OSr7OF1+vlIzQmlTf8FUWvZ6R2c84TFlEGySj3/ImmvoiMn9w3d2sjx4lrWQRXV0cdT/zOlosnrc6bYTcRPG/IKpYUtgIGvgF94s/CilTUOG+GfHHSUvazd+TzAVKBni+sP9w6HJipC62yyJHWcxERre/4ULg91b/BRER8dcXJUdeAmaf1pm7nTLSb+IXEfAAAmQW+AZA+/hspzty36U0toAAAAABJRU5ErkJggg==" alt><span> <em><strong>(A1)(A1)(A1)</strong></em> <em><strong>(C3)</strong></em></span></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for each correct pair.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(0.7 \times 0.1\)</span></p>
<p><span>\( = 0.07(\frac{7}{{100}},{\text{ }}7\% )\)</span><span> <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(0.3 \times 0.8 + 0.07\) <em><strong>(M1)</strong></em></span></p>
<p><span>\( = 0.31(\frac{{31}}{{100}},{\text{ }}31\% )\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Note:</strong> In (b) and (c) follow through from sensible answers only i.e. not a probability greater than one. <em><strong>(C2)</strong></em></span></p>
<p><span> </span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was answered well.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was answered well.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">A few students were unable to do part (c).</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A fitness club has 60 members. 35 of the members attend the club’s aerobics course (<em>A</em>) and 28 members attend the club’s yoga course (<em>Y</em>). 17 members attend both courses. </span><span style="font-family: times new roman,times; font-size: medium;">A Venn diagram is used to illustrate this situation.</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAeAAAAEuCAIAAADZVFYGAAAaYElEQVR4nO3dsWvlWJbHcf0THTh22tng3FElHWiSSjpwUIjpYLIFFXS2MCs2MDQs2mjBMAo2Gi4sE60GnCkpMCiYoBCzwdBqnAyiKQxqhsJog9OleuWyXfZ7ek/nnPv9hMP0K/lJ+t1zz73SSyYAgErJ2gcAALhfMk1TAgBQSAJ67XECAPAJAhoAlCKgAUApAhoAlCKgAUApAhoAlCKgAUApAhoAlCKgAUApAhoAlCKgAUApAhoAlCKgAUApAhoAlCKgAUApAhoAlCKgAUApAhoAlCKgAUApAhoAlCKgAUApAhoAlCKgAUApAhoAlCKgAUApAhoAlCKgAUApAhoAlCKgAUApAhoAlCKgAUApAhoAlCKgAUApAhoAlCKgAUApAhoAlCKgAUApAhoAlCKgAUApAtqkvu+7rmuaJoQQQsg/yLIs+ZI0Tef/f1VVIYS6rruu67pu7T8LwCcIaAO6rqvruqqqPM/TNE2S5OTkRBJWArpt2+6DL36ahLuQ/7wsyznc5ZPLsgwhdF03DMMB/kAA9yKgNer7vq7rsiwljrMsK4pCEnPfde4wDJvjwRzZMgyM47jXfx3AJgJai2EY6rouiuLk5OTk5KQoCuk8rH1c0zAMbdvOeZ1lWVVVhPUuZKCdO1RFUeSf+bwfdacxNQ/YzHIcI6DXNI5j27ZSKUsoN02j/H6Txoj0Q7Isq+u67/u1D0ovGd7mPtLJyYl8b3mey6wohNA0TfcZGf82+1FCPi2EIEPmnc+cVxTW/ruxDAJ6BXOxLPdVCMFixs2jy8nJSZqmVVVZ/CsWJ1/LnQZRVVWSm/sbfefsLopChs80TfXMw7AdAvpwxnFsmkZyWYplN12CruuqqkrTVJJa+SRgcfNYJck4t+zX/R6kizKvZMhREda2ENCH0HVdWZZSL3vK5c/NNbX7v3Sapr7vq6raDGW18TfX9YaaaZgI6L0ax7Gua7klYqsrm6aR9mhZls5aH5uNnbIsza2XDsMwz+RkFSGqK9MWAnovhmGQezjP86Zp1j6c1QzDUFWVfA9t2659ODvp+37OZaPLBndIz03mdnKh2hppYkBAL6zrOqlNyrKkMBHzTCJNU3PD1ebBe10IlaSWVc2yLNU2aiJEQC+m6zqZ1IcQqETuJSkgFaj+r2gea4uisF7+P9EwDCEEGY3qutZ/jtwjoBfQ9z3R/HT6R7KmaeaQinMa1LatPDPFRHBdBPRO5l6z2qxRS2JaVdNjHEepH2ULytqHsz65vGUOQd9jFQT0lsZxrKqKXvOO2raVWnXd+1+iWRYzSaI7+HJWREBvo2ka2UxKNC+irusVv0/S5ymI6VUQ0M8j7eY0TSNZNTqYcRznZtHB/lHpNZM4TzfHNNXJYRDQzxBCSJKEdvP+9H2fZVmWZfvezdZ1XZZlqjrghkhMJ0lSVRX3wl4R0E8i9/MBggPTh57Dnm7+uVSv63rxD4/KMAyy04NBbn+8BPTNXy9e/dvlu9t9fLY8C8f9fEjDMEgradkRUZrdZVlS9y2l6zppE1G77IOPgP756vyb5Pj86v3CnzvPuGm3raKua+kp7f5R8+IB7ebFzR2PQ64fRMJBQN/eXP1wmiTJWbhe9HOl2uKaW9ciYyTxcQCHWD+4Dmcff/349Pzq5v3V+fH8PyydABqYD+jbn8Kro4VPzziORVEsPr/G1qTLtMXOmWEYWDw4pL2PhTdvzk+PNqfLt93Fi+TF6/D2Zl//5JqMB/Tt38Orl9//6b/+5WixDkff9/JTFLQpVWnb9rkTGuZAq5BSOs/z/TQGf+kuXibJd+H6/TRN081fL85OX4W/72X1SQHTAf3z1flvT8/f3FyHs+ToxcXb3U9S0zRJkrAeqNN8539x7JznQHScVyHP2W436fmi91fnx8np+dXNxwRY/N9Qw25A395c/fDi7I9vb27fX50fJ8dn4ccdP1F2XzEX1kyS9/GWBXMgJWTSU1XVwp/77vL10fFZ+L/ry3+VBFj48zWxGtAfW88bKwZbf9o4jnmeZ1nGLW2CbJS+tzpmDqTKvAaw6J31Yzg7Pvr27Nvj34ef/rncx2pkM6Cl9Xz50+00fehJvbzoftnuw+QaYm+sLfI6lDuPSDAH0mnp83JzdX6aJN+cX/280AfqZTGg7zSe5Gx9WDR4pr7v5cmFJQ8QByHnTmbQ4zjuoVLDYmRms8wzh7dvL14cJS8uOs+9jV8ZC+jb66twfna0eW5k283RNpMducN5UNUuWTb8wx/+IL/fSjpr1nXdIi3p2+7ixUKbAvQzFNBSKf/q+Pzq/fT+Ony30YZ+3jrhvXNkmPO3v/3tq6+++vbbb0ln/WRA3W3CumtL0xZDAb2kJSdcWI+MspeXl/Q3rNixGXV7/ZfvT5d76kG9GANa7mpe6Gzd5nmkB22IvFDw+Sfrx3B2vDFj3mnjlhXRBbTc1Sz0W/f5eSSjbdkqo6MTV0CTzj48dB7njF7lqPBcktG8KvIREQW09J159te6x0dZyWj2TVohW6Spox8SS0D3fc+qoANPmQOR0bbQ63hEFAHNfmcfnt6hIqNtIaMf4j+gx3FM05R3Tlr33PWDYRgYlQ0ho+/lPKCppHyQOdBzd0Yyc7KlKIo8z9c+Cl2cB3RZlpxy63bJWXnjJft2TKCc+pzngK7rOk1TJk2myU27S4eKy8AQGpJ3uA1oSicfFimpmEgZQmNqk8+AZoHIh6UWjnYvw3FI8t47qqvJa0BnWbb8D+3gsOQnX5dqTWy3zIi1yKYdGlMOA1rKrrWPAjuRB4uWraGk68WDxVbQmJr8BbTchAy8pslK0T5+V7CqKu55K2hMTc4CehxHprEOFEVRFMU+Ppl73hZpTMX8/hxXAV0UBZsordv3rrh9NE+wP5E3o/0ENNtdHThMeoYQWKUwZH8zKv2cBLTsq4t5KuTDwfoPeZ7T6LBif2sS+jkJ6DzP2Vdn3SELWxodtsjO6Ah34HgI6LZtaW5YJ4l5yDuQRoctce7AMR/QsnOD5oZ1q2yuyLIszomzRdLoiG2PlvmALssy2gUEN9YqZmXizNzLigifcrAd0LJNMsLOlCeywLtWO5itmbbEdr5sBzRr8Q6se8utOzzguWLbr2U4oJumSdN07aPATjQ0GUIIEa4+2RXV+TIc0Gma8kJR6zTsb41z9cm0eO59qwHdNA17pKzTMwfScyR4Cg0Tr8MwGdBsrXNA20nMsiySosyHSNafTAZ0VE0or7SdxK7rKKINiaSIthfQ2iovbEFOora9E3meU0QbUpal+y139gJaW+WFLYQQFN5aFNG2DMNw4NcDHJ69gKZ8tk7KZ533FUW0Le6LaGMB3TQN5bN1OstnIS/eWvso8FTui2hjAR3P/kevdHafN7En2payLB1v57AU0FQ3DtR1rXwOpP8IsUleyON1O4elgKY/6ID++lR/jY87HCeDmYCWl6R4HScjYWUOVFWV2i45PmflutqCmYDmnnEgz/PV37zxFFQD5uifmW3HTEAz67TOVuo5njW7FEJw+cMdNgKaVyM5YGsOxCVnyziOLvfb2QjooihMTI3xCHNzIHMHHDmX++0MBLSMjVamxrhX27bmCtKyLKuqWvso8FQulwoNBHTTNC67S1Epy9LcHIhXc5iTpqmzSY+BgOZFvdZpfvnG4/zd8L5VVeVs0qM9oOVZe/obptldcPN3w/smTxWufRRL0h7Q9DccsNjfEHQ5zEnT1NPbLrUHdFEU9DesM9rfEOzlsMXZpEd1QHvd2xgVi/s3Ntkt/+PkbNKjOqCt39uY7G9Wa9uWl9vZ4mnSozqgq6ryt/M8NtY3QrAN3xxPkx7VAZ1lmad+f4R8rKpnWebyRTxeefrdJb0BLRvs1j4K7KSua0Pv33hICMF0lyY2nqJDb0B7Ggaj5WMTTtd1rIXY4mbyrTegXb76JDZuNuHQhrbFzfKV3oB2MwZGq+97Nxue8jynDW2Im703SgNals7XPgrsxEcDWripyCIhvw6x9lEsQGlAuxkAY+bpLd5ckOZY398plAZ0CIGCxTofd4hgSmeOjwVqpQHt48uNnLaLakem3ygSIR+bI5UGtKfiK07+tqaxTmhL13UOulJKA1rb8eC5PK0QCtYJbfHRldIY0P6Krwj5izNeTW6Og4m4xoBmxdyBPM+dbWP3MWWOioOLUGNAs4XDAQfFyx0+psxRcTCN0xjQnt4WGC1VV9RSeODbFgcbOTQGtIOJSeQ8PeS9iSvTFgddKY0B7W92HBsHN8a9CGhbHGw30BjQqg4GW6jr2uWGBwc9zdhYDxMCGsvzuszr9e9yzHqYqAtog7OSm6vz0yRJkuT0/E139cfXp0mSJF+f/dBc3659aCvZY6V5e/3rN3z0+z/95T9fJL95ffmPvfxD9zHw9M1Ndxn++/zsxX1fy7vu8n/+dH52/Pry3QpHtg7r/VKNAW2wffn+OnyXJKdnr17/8Ob6dvr56vybJHl50f2y9oGtY19PRd/89eLs6+To1cXbd9PNm/PToyT5Lly/X/4feoD2i/P27cU3L8++/Tq5Z9z6pbt49e3Zb4+S5CimgLa+bEBAL+Ifl69/kyTfnF/9PE3TNN2+u/z+KDk9v7pZ+bhWsp+7Qoa9+Uv+MZwdJy8uugNOU0xcnLfdxYMTi9u3Fy+OCGhD1AW0gVnk595fnR9vFia/dBcvI6+gl74rbm+ufjhNjk7P3/w66L27fH2UHJ9fHa5+JqANsv5QhbqAtrgOc/eWuHlzfnp09Cr8FGsPeg+NP2n0z2OezFEO2oCejDxMSEBvspgnmwjo3b2/Dt8lR99fvpM8fvf24tXR0e/DT/9c+bjWs4fL6cdwdvyxYF6jAS303CkPIaA3GcyTTxDQu/vH5evfJJLIt9dvfjg7Sl58fxlt9TxNe7mcPn7Jt9fNf5yf//vZ1wduQAs9d8pDCOhNBvPkEwT0zt5fnR8nHxydvr647OK5/u+3h8vp9ubtH8+OkiT5+uz8f7uf35wfH724eHv4UVDPnfIQAnqTvTz5FAG9q8fuh1jt+3Ja8TvXc6c8hIDeZC5P7lAX0NZ+jfD23eX3Rx8b0JimvV9Od5r+B6XnTnkIAb3J5K6wDeoC2ti+xdu/h1dfJ2fheu0DUWWvl9Pt9V++Pz1a6zvXc6c8hIDeZGJn5CPUBbShCvrT5jNF9Ed7u5zkgaAP1shoPXfKfT79fj5ZRJWNibNYNulb/6EydQFtvWeESdPltDjHf5pL1vOEgMby9FxOi3P8p7lkPU8IaCxPz+W0OMd/mkvW84SAxvL0XE6Lc/ynuWQ9TwhoLC9x+uOqwzDouVPwFNbzRGNAW/8hXhjbK/lk1vdsRagsSwJ6SdwDDhDQUML6pUhAY3nW74qHcHGaY/1S1BjQ1n6TEHdZf0v6Q6w/NxyhLMsI6CWZeCc6Hmd9ZeYhXv8ux6yHibqAnpQdDLbgdaV3j79Wjv2wHiYaA/rk5GQYhrWPAtvz2qu13tCMTd/3aZqufRQ70RjQ3AbWeV1I4Mq0xUGhoDGgi6JwucQUFVVX1FK8PoDjlYNFXY0BzVKMA0mSOOtTsXxtjoMk0RjQ1l/hisljN8DBfDk2eZ63bbv2UexEY0B77WBGxV+firrBHOuboCedAc1c0gF/O+0czJdj4yBGNAb0NE1pmvZ9v/ZRYHv+GgIO5stR8TERVxrQhn6ZEPcahuHk5GTto1gS2/Nt8dGSUhrQ/ibIEfKUaLTdzPHx2KfSgPY3QY5QnudupkFt23JB2uJghXBSG9AULA54mgZ5+lti4CZAlAb0NE1pmjoYAGPmY5VGsEJoi5trT29Ae32ncFTcPBvt78FI39zMePQGdF3XDhZhI5dlmYPC08FL0WLj48KbNAe0v31aEfJRyIQQrL9zJyrSgHYzdVMa0BOPq9jXdZ2D2pMGtC1t2/poQE/KA9r6T6Zjst+99VSORcLHDmihOqCbpmHzqXXWHwr1VI5FwtMGMNUBTfHigPUnbtlNZEvf957WrlQH9OTrabQ4WR9lT05OWAgxxMGvqGzSHtDOvu442d3z5GORMyp2L7Z7aQ9oNts5YHeUrarKwTbBePiLC+0BPbkbEiM0DIPRLgcbPW2xWwo8xEBA+/vSI2RxLYEHCM1J09RZMWcgoO3WX5hZ3MtBf8MWZ/s3hIGAnmzWX9gkezlsPbFCf8OWqqr8TbVtBDRPrDhg67nQtm3pb9jickOkjYAex9HT7yfFydaWtaIoeD7FkKZpXD7waSOgp2kqy5KGoHVpmppoVbHsYY7XLqiZgJYVAO4Z06y0qni/qC2Ow8FMQE9+B8l4SKtKf6Pw5OTEzdt2YmBreeNZLAV00zSGmpi4l/7i1Gs30yvpR3ldoLIU0JOvFwnGSf/tZKVRDuFyd93MWEDXdW2iiYlHlGWp9o6ytdUE7vd3GQtoOR8U0aZp3iOR57nXbqZL+jtmOzIW0NM0hRAooq3TuarTdZ3XzQAuxVCu2QvoGM6Ke/JaSG1RSPlsSwy1mr2AnqYphGDuzTu4Q1snmvLZFitbNndkMqApoh3Qtp2D8tkWbQP8npgM6CmO2Y17ek6ivBqJ8tkKbaP7/lgN6Mnjy7ljo2cmxN5nW4qiiOTNPIYDmgcLHdBwEuu65tFBQ6JaLTAc0BN9QxeyLFvxJOqp4vFEUU13bAe0jKUxtKIcW7cgKsuSHUGGhBCimu7YDuiJG8yFtU6ivKaSAd4K2T7vfmvdJvMBzRTVATmJh1/yXbe7gufK8zyStcGZ+YCepqmua/ZIWde27YEbHawN2hLnbe4hoCdWC10oiuJgjx7IZJmJlxXRni8nAS0b16NqTvlzyEZHhJNl06I9X04CevqwvBvbDMiZwzQ64pws2yXNqDjPl5+AniIeZj0py3Kvz39HO1k2qu/7mCfHrgKae8+BcRzTNK3rek+fz84NQ8ZxjPx8uQroaZqaponnMVCv9lc0xfaYg3VFUSh5ndZavAX0tP85Mg5gHwOtPLIY7WTZHJYKJpcBzbTIh2UHWtkiEs87HKzrui7m1vPMYUBPHx7hpRltmgy0S+2MXvCjsG+ymMRoOnkN6OnDHJnXLJi21I1aliWtZytkYGY7lnAb0NM0VVUV7fZJN3ZfMGTd2BYWBjd5Duhpmoqi4F131knCbpfRLAzaInMdRtOZ84Beto+JtdR1vUXDSpYiaGVaIWeZdN7kPKAnFhy8eG5tJds29vfAC5a1yzzJMf8BPVFJefH0jGbmZAvp/JAoAnqiF+nFUzJa0pm1ByuapmHL80NiCeiJUdqLL2Z0nucsNFkh6czs9iERBfRERnvxSEazDcAQ0vmL4groiYz24t4gJp0NkTuRx30fF11AT2S0F3fimHQ2hHvwiWIM6Inrw4uyLOU8ks6GVFXF3fdEkQb09CGj6X9Z9+c///mrr756+fIl6WxCWZZpmpLOTxRvQE9ktH2yo+53v/sda036jePIBpvnijqgpw/PsPDqLIv6vk/TVJ5GkfPIkylq9X0vm9NJ52eJPaCnD5dOWZZcOobIk0ebP8sg1XSe55xHbeRkUQZtgYCepg/3NpMvKx7aPzuOIy1ObUIINBK3RkB/NG8JWPtA8Jgvnqa6rmlJazA3nbmntkZAf0JeeMi9rdPTJzrSkqbjuaK2bWVVgFOwCwL6LumXcWFp89zzMo5jURRpmvKs2oGN4yg7ndu2XftYzCOg78HUTJut+5gyJeIn3g+m67o0TfM85+dAF0FAP0hCgTe+r2sYBmlrbD1YDsMgwy2l9F7NhTO3zIII6MfM5QDtjlVI/bvI9qz5oziV+0DhvCcE9BfIzi0aagcmZe+yHeT5MzmVC5pvEArnfSCgn6RtWwqEg9lrtcupXJCcKVbU94eAfipabAfQ9/3ihfPnxnEMISRJQsdja9LTYJPMvhHQz9N1naxZcV0uS8a/JElCCIcJzWEYiqKQPR7E9NN1XSeDKI8LHAABvQ3Z4MHMbinyWsFV2g5z3BDTXyTfFUPaIRHQWxqGQdZGuFh3ITOS1RfuiJ7HMdtYCwG9k/nGpjH9XPNXp2emPB9SVVUsIQqGrnUR0AvgIn4W5V+X/IBWkiRlWUa70jCOY9M0sgyo8zRFgoBejPLc0cDQVzQMQwhBEqqua+VHuyAZn2RJQM/kJloE9MK6rpNuXVmWTJNnTdNYieY72rYtikIKasdPuIzjWNd1lmV0eFQhoPdClhCTJCmKwvFd/UVy20sdarocG4ZB/hDJLzdv0ZJWhoxARVGYPkcuEdB7tBlPIYSoqpK58HQ2RPV9X1WVnFO7NbWMN3meJ0mSZVlUPRxbCOhD6LpOCmrp6zm+GTbzy/eYJH9plmUyCNV1rbysHsexbVv5STBpwfm+FH0goA9HppNStkjx5eb26Pt+7mCWZak8qpY1DEPTNLKwJj/jEkJQsv1Djm0eSPI8DyFEdXasI6BXIBPMufhqmsZopdm2rdTLkstG5/sL6vtewlpObpZlc14f5hR3Xdc0TQhBlmTnUFYyYOC5COg1SYEjvdosy6qq0l9W930v9/98zFRkD+m6rq7rqqrmuMyyTBIzhNA0Tdd1W0TnMAzyH9Z1HUIoy3L+fHlRXwihbVvOiwMEtBZd14UQ5spLWoRKKms5NgllWRyjfbmdruvatpWALopCfuol2SAJ+7nN/49sUs7zvCzLEEJd1wer0HFgBLRGEoiyn1pmqVVVHew+nENEfnR1s7onBfat7/vuPgyHcSKgtRvHUfJ6cyYrM+WqquYC6lmT5XmOfKeauzMNb5qGaTKwIgLaJIlXyVYJ7s8ny4+Y58h3+qEUyIAqBDQAKEVAA4BSBDQAKEVAA4BSBDQAKEVAA4BSBDQAKEVAA4BSBDQAKEVAA4BSBDQAKEVAA4BSBDQAKEVAA4BSBDQAKEVAA4BSBDQAKEVAA4BSBDQAKEVAA4BSBDQAKEVAA4BSBDQAKEVAA4BSBDQAKEVAA4BSBDQAKEVAA4BSBDQAKEVAA4BSBDQAKEVAA4BSHwMaAKDO2oMEAOB+BDQAKPX/YdVYRQEMqnsAAAAASUVORK5CYII=" alt></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>Find the value of <em>p</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>Calculate the number of members of the fitness club who attend neither the aerobics course (<em>A</em>) nor the yoga course (<em>Y</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>Shade, on your Venn diagram, \(A' \cap Y\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>17 <em><strong>(A1) (C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>35 – 17 </span><span><em><strong>(M1)</strong></em></span></p>
<p><span>= 18 </span><span><em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct answer only.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(60 - (35 - 17) - (28 - 17) - 17\) <em><strong>(M1)</strong></em></span><br><span>= 14 <strong><em> (A1)</em>(ft) <em> (C2)</em></strong></span></p>
<p><br><span><strong>Note:</strong> Follow through from (a) and (b).</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><em><strong><span> (A1) (C1)</span></strong></em></span></p>
<p><span><em><strong><span>[1 mark]</span></strong></em></span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This was probably the question that most candidates found the easiest. Nearly all candidates gained either 5 or 6 marks with the mark lost in shading the region on the Venn diagram.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This was probably the question that most candidates found the easiest. Nearly all candidates gained either 5 or 6 marks with the mark lost in shading the region on the Venn diagram.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This was probably the question that most candidates found the easiest. Nearly all candidates gained either 5 or 6 marks with the mark lost in shading the region on the Venn diagram.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This was probably the question that most candidates found the easiest. Nearly all candidates gained either 5 or 6 marks with the mark lost in shading the region on the Venn diagram.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the truth table below.</span></p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAhoAAADECAIAAABWcB8HAAAWRElEQVR4nO2d709U957Hzx/AEx7yoIFkYgJE0jbGpBpD7AONt02QNDGNbWL8ESNmt7HuZqWNiEm33r0tNxhM7uX6YIKL7V66uaxdSVrihZ2r2dRthYhRU5hrTdEKVULpZCQowznffTCoMMx8OGeG78DnvN+vfB8oBYfX+8z3+z6/5tSJlFdwcHBwcHAUOJxIeYUJFyEzoo5ScEwFGAIOrBMFUEcpOKYCDAEH1okCqKMUHFMBhoAD60QB1FEKjqkAQ8CBdaIA6igFx1SAIeDAOlEAdZSCYyrAEHBgnSiAOkrBMRVgCDiwThRAHaXgmAowBBxYJwqgjlJwTAUYAg6sEwVQRyk4pgIMAQfWiQKooxQcUwGGgAPrRAHUUQqOqQBDwIF1ogDqGDOXvPs/Hd03p1f+11mWxI0voj0jv3rBf9K36SraBSKfKDSEkP8mDk7ItzXrZK0Dr/NkrP/3h0/9dSxVlPm+lNT9vpP/eLLvfirgz/kzXW27QASPQkcI+W7igKy2ZiDy2task7UOts5c4trp7TvP3ppZ1Rk4cyu6e9fJy+MrvWO+NuwCETAKNSHktYmDsDY0AxF8W7NO1jrQOtODbds2v99rb5L7xJu++tv1lU39k3P+f2Z507ViF4hgUegJIZ9N/OKHkz/euJuQFNaKZiACb2vWyVoHWGf2Qffh0tJ/7s3xbvYe//pryjNmLnl/dGKZEwjezP0fx/2cZPCS4+NJzxhj5h5PJV4c6T++cuKl0s1t15/6/u2XM13GLihCGt7UwNnmz7LtF3vTQ9EPzg5M5QomaxpBoig8hABbeWbs7vgTH7/UCngtZu6XK/+6cd2R7tGZHN+Asq1ZJ2ud1dBJDrRsdRzHcba2fDsycO7YVsdxnPV7Wv93zC30nw6g434f3V7mbI+OZLzo9O2/NO/ZWOI46z/6+ts/N+7ZvWvrOmfdoc6RZM5/KnWna++WvV13pBPBqZ8HOhvf3vdv//7n9lOnf9+0reLllmsLFqd73XsizvrfXp32u3+5jGkuu6D4SWN2pHP3hp3R27MZPzt7O7pzw+7OkcyvGzmNAFHkH0LgrTwz2nXopb1fjMqVs0JemXhTQ2d2lb5+6vKjbG8xmG1tt05Sg60byisi5RUbWr+5P/h5047qSHlFzYH2a+PB9wB8Y339dccHO4+/UV4RqXr/v/ra68trm2IT9l5tldoxNdZ9yHG27tl/rPXbMddMDbS86Ti7oiO59r/84l/Hu9f1tuOUHetPZPntBloijvPqW42f30h6xpvsfb8sx3caY0zqYW9jpeM4lY29D3MUSup+X3Pdpsavx1KeMU/udr7rOJtOXJlc8B3pit3ZftvvXTmyqWQXlOXT8GZuna0rO9S1aPd5ZrTrUFldtrP5y6QRIIqCQgiylb2HXx+tLHGcTUd7H+Rc+fLzSv8avihZt/fcrWTmIQjOtrZ/dDJ+4WB59RsH3mtq+2bcdZODZ94or67vGC54Nzcndo2St84deC1S1XBuOGGS353eUR0pf+/LcYu3hKxSnUz0H9vgOG+2DEwZY4xxE/0fljlbWwZyHwH4w79OeuJEWgaWhuuORLc7JZVHv37oLfjWPd1j2f4db7KvsXLz0a/+76ujmysb+yazLDbTdzr3lb44R/x4qG2HU/Zhf2Lhm3T6dvtOx6k81PPA5+8vmwp2QfGVhjd5raV+/fPvSa+/6+tbri3NY9k0AkRRSAgBtrL3sL9xS+XR/77xVWNlznP9K+mVFS95I7p3w9JGwdnWtuvETcSaa8qr32j9bn4dSsSaqio2tA7aW4BtGk0Ntr4VKX/r9GB6kb3/5YFXI3UdcXvdWKhO+iBjOZa+01MDLZGFez0zI9FdRT46yT0Jn4527S8peSc6Mr/H5I117y0p3dJ+M8sq4j260rxt3eGLY57xxi4eXret+cqjjEnlPejeV1rx4vzA0+ttm0tLG3oeLvq+dJKRPd33fP7+gVfSse49y2+qpY3uNw3vl781b6xt7H/omfT6W7ux+W+/LFlgfKQRIIoC6sT/Vk5fujjaMzZrvHs9hzcVwSsX3oPufaWlGb8Azra2XSfJwdbfRKqaY8/qzo131Gs9Opk/tCpmNRr7RyepgZbIkgntjkS3OxuO9T87iZf8tmVrWdn+7p+KeO0k51rj/dTTsN7Z2Xl3/k2fethzpHTBHFv4rdNDZ7aV7eu8k/5P03c695VtOzO06ETw09Gu/SXOu51306eL5yb7myqdyO6uu4tn3+y9rn1262RZUgMtkSVLTIA0Ug97Gys3fXI1MZu4+smm7Kf+/KQRIIr8Q/DvNT3Ytu3VZ1cFvNk7n+0uq28byjixtMJeWVnJoxOd29pynbjD5+qqa47Hnm3bqcHWtyJV73/5QOO1k+Rg628i5e+ei6f30NMHXnYvnJjVqZPUWPehBce8ie+j+8vK/qH7pxXYagGundzt3Jn1jHOi/1hZ2fbo9/PVNns7unNd1p0vM3Ojve7lRZclZ29Hd75c135jwUHW5JUTm5yKU1efeMYY79FfP9hY6ryYY89Jn0Te0Tb02Ofvv8xlg1x2AlmXGP9pmPQtCRvrPj37ad3GHDcm+EkjQBT5h+DXK3mr/e3SndGR2ef/YXok+k5p5nWCArwKv3YCs60t18n4hYMvFlw3OXz+YNVrhy+M2jw5ZG/9vf/lgVcjrzw7GCnKhROzOnUy0X9sg5PuD3fs29Y9Zc72D/sLPzIxJpDO0+ttm0sX7Iul8R5fOfmS82bbUNIYY7xfb/5pz/psczjHsUjG8YoxJjHQss0peSc6kkz+0NvyTx/8y7uV2W7C+bn3yMtLLqhILGOa3U4kyxLjP435758die4scUoWrb8L8ZNGgCjyDcGnV45jkUXHK1a8Mknd72t+szJX8jDb2mqdpPff0/3xdPy79oNV1W80941bLROL6+9E7Hht+tDKHf/mD62tLQdes33hxKxKnSzaHSvbeizaP7IC96SkCaIzPRJ9pyTzrZwYaNnmOJVvHvtDV/d//PHIW3WN/3k7y4zyUqPdDet2nLq65PKjN3n11I51Dd3P7ij1Zm6drStxHKdk3dunL/+9/+P1ZVlutJ+72b6lrPLEZf9BLGea1U4kyxLjM42FJIbOfNh+K9ctFT7SCBJFviH480rd7W7YtOnUN0s+QDiXuPrJpkUfBFlhr4yXm+w/sVla2VG2tdU6SZ8dqpgfO46fi8ULvTHIBxavnQyfP1hVESl/7WDrpfjUd6dfsXsRKE3x7+zKvHCyogTS8Sb7Gitf//jq1Isvzd1s31L60onYz/duDgxcH5nw97G15V4nNREfuHEv6Zm52+1bnK2LXtEYY7zZ23/aVrrwmGZ5ljXNYheUVUgjWBR5hrDmvQK/Nsa2tlknmRdOikRx1l833mH7Eydpil4nbqL/w7L8Dvl9EFAn9ejyqe3vfHbn2dG61aqbv4Ftqbv36Erzrn1d8SwfAcuND9NMu6CsQhoBo8gvhLXvFRyIbW2zThKxpqpiLLgZFGX9TY1feG/hHWv2KHaduD9271+f6zMchRNYx/v1Vuexw2eHkp6Zf9OXNHSP2ble5cY76ytKj/ROLvrqk7HeU/vPfCc+kikLvkwX2QWl+GkEjiKvEBR45QPAtrZXJ08fXHi/xv6V6qUUYf11x/tO7qiOHLgwbvuVilsniy+aWDlAyUvnyaOBrtbOnr+0Hdu1rsQpef3Qpx39d1f2pERypOePHx+pizhOydaGlp7nn69J3P6irb3373ksAb5Nnzwa6GrtCvj/wJgZ6QmShnxD0pJvz5pGPlEEDiGgV0BWzCtfQr6t7dRJavD0K88umRTljNBCLK+/E7HjtS8uCNlvFD6CTCk4pgIMAQc+AlIB1FEKjqkAQ8CBdaIA6igFx1SAIeDAOlEAdZSCYyrAEHBgnSiAOkrBMRVgCDiwThRAHaXgmAowBBxYJwqgjlJwTAUYAg6sEwVQRyk4pgIMAQfWiQKooxQcUwGGgMN8nXBwcHBwcBQ4nEjodh9CZkQdpeCYCjAEHFgnCqCOUnBMBRgCDqwTBVBHKTimAgwBB9aJAqijFBxTAYaAA+tEAdRRCo6pAEPAgXWiAOooBcdUgCHgwDpRAHWUgmMqwBBwYJ0ogDpKwTEVYAg4sE4UQB2l4JgKMAQcWCcKoI5ScEwFGAIOrBMFUEcpOKYCDAEH1okCqKMUHFMBhoAD60QB1FEKjqkAQ8CBdaIA6igFx1SAIeBgtU7cRKy5JuejjKvrO4ZdOy9syygRa6rK/XDmuo64HZ+QTciQ6QjgmAowBBxs18nvDnfcSs7/ubmmvLYpNmGMMSYRv/DRYYV1crLh/HDSTf+5qaqi5ngsYYwxbjJ+oanhPOvEDyHTEcAxFWAIOFitk5n4xUvPVtiMOjHGjfdctLT82noHu/FLPfGZ+b8sqhOzWHaFCdmEDJmOAI6pAEPAoWjXTpbUiU2KYZRZJxYJ2YQMmY4AjqkAQ8CBdZIvrJN8CZmOAI6pAEPAgXWSL6yTfAmZjgCOqQBDwIF1ki+sk3wJmY4AjqkAQ8CBdZIvrJN8CZmOAI6pAEPAgXWSL6yTfAmZjgCOqQBDwIF1ki+sk3wJmY4AjqkAQ8CBdZIvrJN8CZmOAI6pAEPAoSh1kvFskqrmWMLS5xfnsWw0ETteu+DxKtY7MmQTMmQ6AjimAgwBBz4CUgHUUQqOqQBDwIF1ogDqKAXHVIAh4MA6UQB1lIJjKsAQcGCdKIA6SsExFWAIOLBOFEAdpeCYCjAEHFgnCqCOUnBMBRgCDqwTBVBHKTimAgwBB9aJAqijFBxTAYaAA+tEAdRRCo6pAEPAgXWiAOooBcdUgCHgwDpRAHWUgmMqwBBwYJ0ogDpKwTEVYAg4zNcJBwcHBwdHgcOJhG73IWRG1FEKjqkAQ8CBdaIA6igFx1SAIeDAOlEAdZSCYyrAEHBgnSiAOkrBMRVgCDiwThRAHaXgmAowBBxYJwqgjlJwTAUYAg6sEwVQRyk4pgIMAQfWiQKooxQcUwGGgAPrRAHUUQqOqQBDwIF1ogDqKAXHVIAh4MA6UQB1lIJjKsAQcGCdKIA6SsExFWAIOLBOFEAdpeCYCjAEHKzWiZuINdfkfPZkdX3HsGvnhW0ZJWJNVTl06jrilmRCNyFDpiOAYyrAEHCwXSe/O9xxKzn/5+aa8tqm2IQxxphE/MJHh9XViTFLRIwxxh3vO1n3USxhq09CNiFDpiOAYyrAEHCwWicz8YuXnu2zL1mF3XjPRVs79EWuE2Nm4p1R1olPQqYjgGMqwBBwKNq1k6yrsC2KWifu6OD1SWsvZ0zoJmTIdARwTAUYAg6sk6BkiLjJwehpy1Ihm5Ah0xHAMRVgCDiwToKy9P4C61Ihm5Ah0xHAMRVgCDiwToKy5OhkuPvcZdZJAEKmI4BjKsAQcGCdBIXXTgolZDoCOKYCDAEH1klQiiqSJmQTMmQ6AjimAgwBB9ZJUFgnhRIyHQEcUwGGgAPrJCisk0IJmY4AjqkAQ8ChKHWS8WySqmZ7n/hLU6SHrNgXSROyCRkyHQEcUwGGgAMfAakA6igFx1SAIeDAOlEAdZSCYyrAEHBgnSiAOkrBMRVgCDiwThRAHaXgmAowBBxYJwqgjlJwTAUYAg6sEwVQRyk4pgIMAQfWiQKooxQcUwGGgAPrRAHUUQqOqQBDwIF1ogDqKAXHVIAh4MA6UQB1lIJjKsAQcGCdKIA6SsExFWAIOLBOFEAdpeCYCjAEHFgnCqCOUnBMBRgCDvN1wsHBwcHBUeBwIqHbfQiZEXWUgmMqwBBwYJ0ogDpKwTEVYAg4sE4UQB2l4JgKMAQcWCcKoI5ScEwFGAIOrBMFUEcpOKYCDAEH1okCqKMUHFMBhoAD60QB1FEKjqkAQ8CBdaIA6igFx1SAIeDAOlEAdZSCYyrAEHBgnSiAOkrBMRVgCDiwThRAHaXgmAowBBxYJwqgjlJwTAUYAg6sEwVQRyk4pgIMAQerdeImYs012R88WV3fMezaeVVj7x2ciDVV5X6aZl1H3I5SyCZkyHQEcEwFGAIORTg6mYgdr41UNccSz9fap+Oxj+uPxxLWXtJenZxsOD+cdNN/bqqqqJm3cJPxC00N51knfgiZjgCOqQBDwGFV6sQYd/h822V1deLGL/XEZ+b/sqhOjDEz8YuXWCd+CJmOAI6pAEPAYRXqxP3h+lDC3okuY4rzDs6sE4uEbEKGTEcAx1SAIeBQ/DqZGmxrj7FOghCyCRkyHQEcUwGGgEOx6mThJeuME18WYJ2sZUKmI4BjKsAQcCj+0UliuPPzy6yTIIRsQoZMRwDHVIAh4MBrJ/nCOsmXkOkI4JgKMAQcVunOLsuwTtYyIdMRwDEVYAg4sE7yhXWSLyHTEcAxFWAIOLBO8oV1ki8h0xHAMRVgCDgU9SErxVl8jfV3cMa9arVNsQmbLxe2CRkyHQEcUwGGgAMfAakA6igFx1SAIeDAOlEAdZSCYyrAEHBgnSiAOkrBMRVgCDiwThRAHaXgmAowBBxYJwqgjlJwTAUYAg6sEwVQRyk4pgIMAQfWiQKooxQcUwGGgAPrRAHUUQqOqQBDwIF1ogDqKAXHVIAh4MA6UQB1lIJjKsAQcGCdKIA6SsExFWAIOLBOFEAdpeCYCjAEHFgnCqCOUnBMBRgCDvN1wsHBwcHBUeBwIqHbfQiZEXWUgmMqwBBwYJ0ogDpKwTEVYAg4sE4UQB2l4JgKMAQcWCcKoI5ScEwFGAIOrBMFUEcpOKYCDAEH1okCqKMUHFMBhoAD60QB1FEKjqkAQ8CBdaIA6igFx1SAIeDAOlEAdZSCYyrAEHBgnSiAOkrBMRVgCDiwThRAHaXgmAowBBxYJwqgjlJwTAUYAg6sEwVQRyk4pgIMAQerdeImYs012R88WV3fMezaeVVj7x2ciDVV5XiUZl1H3JpPyCZkyHQEcEwFGAIORTg6mYgdr41UNccSz5fbp+Oxj+uPxxLWXtKmUboja5tiEy++NN53su6jBYIrTMgmZMh0BHBMBRgCDqtSJ8a4w+fbLoemToyZiXdGWSc+CZmOAI6pAEPAYRXqxP3h+pC1lTdNUevEHR28Pmnt5YwJ3YQMmY4AjqkAQ8Ch+HUyNdjWbm9HPk0R68RNDkZPLzpSWXlCNiFDpiOAYyrAEHAoVp0svGqdceLLAvbrZOF1+IwTXytPyCZkyHQEcEwFGAIOxT86SQx3fn5ZfZ0sODoZ7j53mXUSgJDpCOCYCjAEHHjtJCi8dlIoIdMRwDEVYAg4rNKdXZYp+p1ddgnZhAyZjgCOqQBDwIF1EhTWSaGETEcAx1SAIeDAOgkK66RQQqYjgGMqwBBwKOpDVmpsfhJ+IUV6yEqxOjJkEzJkOgI4pgIMAQc+AlIB1FEKjqkAQ8CBdaIA6igFx1SAIeDAOlEAdZSCYyrAEHBgnSiAOkrBMRVgCDiwThRAHaXgmAowBBxYJwqgjlJwTAUYAg6sEwVQRyk4pgIMAQfWiQKooxQcUwGGgAPrRAHUUQqOqQBDwIF1ogDqKAXHVIAh4MA6UQB1lIJjKsAQcGCdKIA6SsExFWAIOLBOFEAdpeCYCjAEHObrhIODg4ODo8Dx/6KdxWSDoztaAAAAAElFTkSuQmCC" alt></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State whether the statement \((p \wedge q) \Rightarrow (\neg p \underline \vee q)\) is a logical contradiction, a tautology or neither.</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>Give a reason for your answer to part (b)(i).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt> <em><strong>(A1)(A1)(A1)</strong></em><strong>(ft)<em>(A1)</em>(ft)</strong> <em><strong>(C4)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for each correct column.</span></p>
<p><span> Award first <strong><em>(A1)</em>(ft)</strong> from their third column in the table.</span></p>
<p><span> Award second <strong><em>(A1)</em>(ft)</strong> from their fourth and fifth column in the table.</span></p>
<p><em><strong><span>[4 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Tautology <strong><em>(A1)</em>(ft) <em>(C1)</em></strong></span></p>
<p><span><strong>Note:</strong> Answer must be consistent with last column in table.</span></p>
<p><em><strong><span>[1 mark]</span></strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span><span>All entries (in the final column) are true.<span> </span><strong><em>(R1)</em>(ft)</strong><span> </span><strong><em>(C1)</em></strong></span></span></span> </p>
<p><span><span><span><span><strong>Note:</strong></span><span> Answer must be consistent with their answer to part (b)(i).</span></span></span></span></p>
<p><span><span><span><span><span><strong>Note:</strong></span><span> Special case <strong><em>(A1)(R0)</em></strong> may be awarded.</span></span></span></span></span></p>
<p><em><strong><span><span><span><span><span>[1 mark]</span></span></span></span></span></strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Weaker candidates had some difficulty here with the majority scoring less than 2 marks on this question. The more confident candidates were able to score well with most marks being lost only on completing the truth table for \((\neg p \underline \vee q)\). As a consequence, the final column entries of the table were often incorrect but earned the (A1)(ft) mark. Many candidates went on to correctly identify the correct (ft) response to (b)(i) and were able to support their answer with a correct reason.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Weaker candidates had some difficulty here with the majority scoring less than 2 marks on this question. The more confident candidates were able to score well with most marks being lost only on completing the truth table for \((\neg p \underline \vee q)\). As a consequence, the final column entries of the table were often incorrect but earned the (A1)(ft) mark. Many candidates went on to correctly identify the correct (ft) response to (b)(i) and were able to support their answer with a correct reason.</span></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Weaker candidates had some difficulty here with the majority scoring less than 2 marks on this question. The more confident candidates were able to score well with most marks being lost only on completing the truth table for \((\neg p \underline \vee q)\). As a consequence, the final column entries of the table were often incorrect but earned the (A1)(ft) mark. Many candidates went on to correctly identify the correct (ft) response to (b)(i) and were able to support their answer with a correct reason.</span></p>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A group of 30 students were asked about their favourite topping for toast.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> 18 liked peanut butter (<em>A</em>)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> 10 liked jam (<em>B</em>)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> 6 liked neither</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show this information on the Venn diagram below.</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>Find the number of students who like both peanut butter and jam.</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 probability that a randomly chosen student from the group likes peanut butter, given that they like jam.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span><strong> OR</strong> <img src="data:image/png;base64,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" alt> <em><strong>(A2) (C2)</strong></em></span></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(A2)</strong></em> for 3 correctly placed values, and no extras (4 need not be seen), <em><strong>(A1)</strong></em> for 2 correctly placed values, <em><strong>(A0)</strong></em> for 1 or no correctly placed values.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>18 + 10 + 6 = 30 <em><strong> (M1)</strong></em></span><br><span>= 4 <em><strong> (A1) (C2)</strong></em></span></p>
<p><span> </span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{P}}(A|B) = \frac{4}{{10}}\left( {\frac{2}{5},{\text{ }}0.4,{\text{ }}40{\text{ }}\% } \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1) (C2)</strong></em></span></p>
<p><span> </span></p>
<p><span><strong>Note:</strong> Award<strong><em> (A1)</em>(ft)</strong> for their numerator from part (b),<em><strong> (A1)</strong> </em>for denominator.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The first two parts of this question were well answered with most candidates completing the Venn diagram correctly and finding the number in the intersection. The final part, requiring a conditional probability to be found, proved more difficult as many candidates tried to use the formula, when all that was required was to look at the values in the Venn diagram. Follow through marks were awarded in part (c) for values correctly used from parts (a) and (b).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The first two parts of this question were well answered with most candidates completing the Venn diagram correctly and finding the number in the intersection. The final part, requiring a conditional probability to be found, proved more difficult as many candidates tried to use the formula, when all that was required was to look at the values in the Venn diagram. Follow through marks were awarded in part (c) for values correctly used from parts (a) and (b).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The first two parts of this question were well answered with most candidates completing the Venn diagram correctly and finding the number in the intersection. The final part, requiring a conditional probability to be found, proved more difficult as many candidates tried to use the formula, when all that was required was to look at the values in the Venn diagram. Follow through marks were awarded in part (c) for values correctly used from parts (a) and (b).</span></p>
<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;">Merryn plans to travel to a concert tomorrow. Due to bad weather, there is a 60 % chance that all flights will be cancelled tomorrow. If the flights are cancelled Merryn will travel by car.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">If she travels by plane the probability that she <strong>will be late</strong> for the concert is 10 %.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">If she travels by car, the probability that she <strong>will not be late</strong> for the concert is 25 %.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the tree diagram below.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that Merryn will not be late for the concert.</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>Merryn was not late for the concert the next day.</span></p>
<p><span>Given that, find the probability that she travelled to the concert by car.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span> <em><strong>(A1) </strong><strong>(C1)</strong></em></span></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for 0.9 and 0.75.<br></span></p>
<p><span><em><strong>[1 mark]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>0.4 × 0.9 + 0.6 × 0.25 <em><strong>(M1)(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their two relevant products, <em><strong>(M1)</strong></em> for adding their two products.</span></p>
<p> </p>
<p><span>\(0.51\left( {\frac{{51}}{{100}},{\text{ }}51\% } \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C3)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their answers to part (a).</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{0.6 \times 0.25}}{{0.51}}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted conditional probability formula.</span></p>
<p> </p>
<p><span>\(0.294\left( {\frac{5}{{17}}{\text{, }}0.294117...} \right)\) <em><strong>(A1)</strong></em><strong>(ft) </strong> <strong><em>(C2)</em></strong></span> </p>
<p><span><strong>Note:</strong> Follow through from their tree diagram and their part (b).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">It was pleasing to see many correct answers in parts (a) and (b) with many writing their answer to part (b) in the context of the question and writing down a percentage. </span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">It was pleasing to see many correct answers in parts (a) and (b) with many writing their answer to part (b) in the context of the question and writing down a percentage. </span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Conditional probability is not an easy topic for candidates to understand and many simply wrote down 0.6 × 0.25 = 0.15(15%) for part (c).</span></p>
<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;">\(U = \{ x|x{\text{ is an integer, }}2 < x < 10\}\)</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><em>A</em> and <em>B</em> are subsets of <em>U</em> such that <em>A</em> = {multiples of 3}, <em>B</em> = {factors of 24}.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>List the elements of</span></p>
<p><span>(i) <em>U</em> ;</span></p>
<p><span>(ii) <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>Write down the elements of <em>U</em> on the Venn diagram.</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>Write down \(n (A \cap B)\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>(i) 3, 4, 5, 6, 7, 8, 9 <em><strong>(A1)</strong></em></span></p>
<p><span>(ii) 3, 4, 6, 8 <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Follow through from part (a)(i).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span><em><strong>(A1)</strong></em><strong>(ft)</strong> for their 3, 6</span><br><span><span><em><strong>(A1)</strong></em><strong>(ft)</strong></span> for their 4, 8, 9</span><br><span><span><em><strong>(A1)</strong></em><strong>(ft)</strong></span> for their 5, 7 </span><span><em><strong><span><em><strong>(A1)</strong></em></span></strong></em></span><span><strong><span><span><span><strong>(ft)</strong></span></span></span></strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C3)</strong></em></span><br><br></p>
<p><span><strong>Note:</strong> Follow through from their universal set and set B in part (a).</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>2 <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from their Venn diagram.</span></p>
<p><span><em><strong>[1 mark]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates were unable to write down correctly the universal set which was integers between \(2\) and \(10\). Some candidates did not read the direction “on the Venn diagram” so complained of lack of space for their answer. It is important candidates read the directions carefully. Many candidates listed the elements of the intersection rather than answering the question to specify the number of elements. The empty set for \(\left( {A \cup B} \right)'\) was awarded a maximum of 2 marks as this has simplified the problem.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates were unable to write down correctly the universal set which was integers between \(2\) and \(10\). Some candidates did not read the direction “on the Venn diagram” so complained of lack of space for their answer. It is important candidates read the directions carefully. Many candidates listed the elements of the intersection rather than answering the question to specify the number of elements. The empty set for \(\left( {A \cup B} \right)'\) was awarded a maximum of 2 marks as this has simplified the problem.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates were unable to write down correctly the universal set which was integers between \(2\) and \(10\). Some candidates did not read the direction “on the Venn diagram” so complained of lack of space for their answer. It is important candidates read the directions carefully. Many candidates listed the elements of the intersection rather than answering the question to specify the number of elements. The empty set for \(\left( {A \cup B} \right)'\) was awarded a maximum of 2 marks as this has simplified the problem.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">When Andy plays tennis, \(65\% \) of his first serves go into the correct area of the court.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">If the first serve goes into the correct area, his chance of winning the point is \(90\% \).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">If his first serve does not go into the correct area, Andy is allowed a second serve and, of these, \(80\% \) go into the correct area.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">If the second serve goes into the correct area, his chance of winning the point is \(60\% \).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">If neither serve goes into the correct area, Andy loses the point.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the tree diagram below.</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>Find the probability that Andy loses the point.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt></span><span><span> </span><span> <em><strong>(A1)(A1) (C2)</strong></em></span></span></p>
<p><span><span><em><strong>[2 marks]<br></strong></em></span></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(0.65 \times 0.1\) (\( = 0.065\)) <em><strong>(A1)</strong></em></span></p>
<p><span>\(0.35 \times 0.8 \times 0.4\) (\( = 0.112\)) <em><strong>(A1)</strong></em></span></p>
<p><span>\(0.35 \times 0.2 \times 1\) <em>the 1 can be implied</em> (\( = 0.07\)) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>0.247 <em><strong>(A1)</strong></em><strong>(ft) <em>(C4)</em><br></strong></span></p>
<p><span><strong>Note:</strong> No <strong>(ft)</strong> for any probabilities greater than 1.</span></p>
<p><span><em><strong>[4 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question proved to be the easiest question (along with question 1) with many candidates gaining full marks. The probability tree diagram was completed correctly and then most could go on to find the required probability. Very few added the probabilities instead of multiplying them.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question proved to be the easiest question (along with question 1) with many candidates gaining full marks. The probability tree diagram was completed correctly and then most could go on to find the required probability. Very few added the probabilities instead of multiplying them.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The following histogram shows the weights of a number of frozen chickens in a supermarket. The weights are grouped such that \(1 \leqslant {\text{weight}} < 2\), \(2 \leqslant {\text{weight}} < 3\) and so on.</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 total number of chickens.</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>Write down the modal group.</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>Gabriel chooses a chicken at random. </span></p>
<p><span>Find the probability that this chicken weighs less than \(4{\text{ kg}}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(96\) <em><strong>(A1) (C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(3 \leqslant {\text{weight}} < 4{\text{ kg}}\) . <em>Accept</em> \(3 - 4{\text{ kg}}\) <em><strong>(A1) (C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>For adding three heights or subtracting \(14\) from \(96\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(\frac{{82}}{{96}}{\text{ }}(0.854{\text{ or }}\frac{{41}}{{48}}{\text{, }}85.4\% )\) <strong>(ft)</strong> <em>from (b).</em> <em><strong>(A1)</strong></em><strong>(ft)<em> (C2)</em></strong></span></p>
<p><span><strong><em>[2 marks]<br></em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Very few candidates could draw a frequency polygon correctly. The word ‘Draw’ means that a ruler should be used. Many managed to draw from the mid-point of the bar but did not extend it to \(0.5\) or \(5.5\). Most could answer the probability part of the question.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Very few candidates could draw a frequency polygon correctly. The word ‘Draw’ means that a ruler should be used. Many managed to draw from the mid-point of the bar but did not extend it to \(0.5\) or \(5.5\). Most could answer the probability part of the question.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Very few candidates could draw a frequency polygon correctly. The word ‘Draw’ means that a ruler should be used. Many managed to draw from the mid-point of the bar but did not extend it to \(0.5\) or \(5.5\). Most could answer the probability part of the question.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<p><span>The sets \(P\), \(Q\) and \(U\) are defined as</span></p>
<p><span><span><em>U</em> = {Real Numbers} , <em>P</em> = {Positive Numbers} and <em>Q</em> = {Rational Numbers}.</span></span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Write down in the correct region on the Venn diagram the numbers</span></p>
<p><span>\(\frac{{22}}{7}\) , \(5 \times {10^{ - 2}}\) , \(\sin (60^\circ )\) , \(0\) , \(\sqrt[3]{{ - 8}}\) , \( - \pi \).</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span><img src="data:image/png;base64,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" alt> </span><span><em><strong>(A1)(A1)(A1)</strong></em></span><span><em><strong>(A1)(A1)(A1) (C6)</strong></em></span></p>
<p><span> </span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for each number placed once in the correct region. Accept equivalent forms for numbers.</span></p>
<p><span> </span></p>
<p><em><strong><span>[6 marks]</span></strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-family: 'times new roman', times; font-size: medium;">Very few candidates gained full marks in this question. A common error turned out to be that \(\frac{{22}}{7}\) and \(5 \times {10^{ - 2}}\) were not considered rational numbers. Also, \(0\) and \(\sin (60^\circ )\) were often placed incorrectly. However, it was encouraging that very few candidates placed values in more than one region.</span></p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Music lessons in Piano (<em>P</em>), Violin (<em>V</em>) and Flute (<em>F</em>) are offered to students at a school. </span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The Venn diagram shows the number of students who learn each kind of instrument.</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 total number of students in the school.</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>Write down the number of students who</span></p>
<p><span>(i) learn violin only;</span></p>
<p><span>(ii) learn piano or flute or both;</span></p>
<p><span>(iii) do not learn flute.</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>Explain, in words, the meaning of the part of the diagram that represents the set \(P \cap F'\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>145 <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) 56 <em><strong>(A1)</strong></em></span></p>
<p><span> </span></p>
<p><span>(ii) 85 <em><strong>(A1)</strong></em></span></p>
<p><span> </span></p>
<p><span>(iii) 89 <em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>The students who learn the piano and do not learn the flute. <em><strong>(A1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for students who learn piano, not flute, <em><strong>(A1)</strong></em> for and</span> <span>(accept but). Accept correct alternative statements.</span> <span>Accept “The number of students who learn the piano and do not </span><span>learn the flute”.</span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The most common error in Question 4 was to omit counting the four non-music students. Explaining in words the meaning of the set notation was difficult for some candidates.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The most common error in Question 4 was to omit counting the four non-music students. Explaining in words the meaning of the set notation was difficult for some candidates.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The most common error in Question 4 was to omit counting the four non-music students. Explaining in words the meaning of the set notation was difficult for some candidates.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>In an international competition, participants can answer questions in <strong>only one</strong> of the three following languages: Portuguese, Mandarin or Hindi. 80 participants took part in the competition. The number of participants answering in Portuguese, Mandarin or Hindi is shown in the table.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>A boy is chosen at random.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the number of boys who answered questions in Portuguese.</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 probability that the boy answered questions in Hindi.</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>Two girls are selected at random.</p>
<p>Calculate the probability that one girl answered questions in Mandarin and the other answered questions in Hindi.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>20 <em><strong>(A1) (C1)</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>\(\frac{5}{{43}}\,\,\,\left( {0.11627 \ldots ,\,\,11.6279 \ldots {\text{% }}} \right)\) <em><strong>(A1)(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct numerator, <em><strong>(A1)</strong></em> for correct denominator.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{7}{{37}} \times \frac{{12}}{{36}} + \frac{{12}}{{37}} \times \frac{7}{{36}}\) <em><strong>(A1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for first or second correct product seen, <em><strong>(M1)</strong></em> for adding their two products or for multiplying their product by two.</p>
<p>\( = \frac{{14}}{{111}}\,\,\left( {\,0.12612 \ldots ,\,\,12.6126\,{\text{% }}} \right)\) <em><strong>(A1) (C3)</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Maria travels to school either by walking or by bicycle. The probability she cycles to </span><span style="font-family: times new roman,times; font-size: medium;">school is 0.75.</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">If she walks, the probability that she is late for school is 0.1.</span><br><span style="font-family: times new roman,times; font-size: medium;">If she cycles, the probability that she is late for school is 0.05.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the tree diagram below, showing the appropriate probabilities.</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">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that Maria is late for school.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span> <em><strong>(A1)(A1)(A1) (C3)</strong></em></span></span></p>
<p><span><strong> </strong></span></p>
<p><span><strong>Note:</strong> Award<em><strong> (A1)</strong> </em>for 0.25,<em><strong> (A1)</strong></em> for 0.1 and 0.9, <em><strong>(A1)</strong></em> for 0.05 and 0.95</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{P}}({\text{late}}) = 0.25 \times 0.1 + 0.75 \times 0.05\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(M1)</strong></em></span></p>
<p><span> </span></p>
<p><span><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for two correct products from their diagram and</span> <span>award<em><strong> (M1)</strong></em> for addition of their two products.</span></p>
<p><span> </span></p>
<p><span>\( = 0.0625\left( {\frac{1}{{16}},{\text{ }}6.25\% } \right)\) <em><strong> (A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Part (a) of this question was very well answered with many candidates gaining the maximum marks. Many candidates were less successful in part (b) and it seemed as if many of them either gained 3 marks or 0 marks. This shows that students who knew how to approach part (b) were also able to correctly substitute in the formula they used and reach the correct answer. Very few of those students lost the last mark for wrong rounding.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Part (a) of this question was very well answered with many candidates gaining the maximum marks. Many candidates were less successful in part (b) and it seemed as if many of them either gained 3 marks or 0 marks. This shows that students who knew how to approach part (b) were also able to correctly substitute in the formula they used and reach the correct answer. Very few of those students lost the last mark for wrong rounding.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the following propositions.</p>
<p style="padding-left: 90px;"><br><em>p</em>: my Mathematical Studies homework is due tomorrow<br><em>q</em>: today is Wednesday</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down in words the compound proposition <em>¬</em>\(p \Rightarrow q\).</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>Complete the truth table.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State whether the compound proposition (\(\neg p \Rightarrow q\)) ∨ (\(\neg p \wedge q\)) is a tautology, contradiction or neither.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>If my Mathematical Studies homework is not due in tomorrow then today is Wednesday. <em><strong>(A1)(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for If… then…<br>Award <em><strong>(A1)</strong></em> for correct propositions, <em>my Mathematical Studies homework is <strong>not</strong> due in tomorrow and today is Wednesday</em>, in the correct order.<br>Award <em><strong>(A1)(A0)</strong></em> for “<em>If ¬p then q</em>”.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAigAAAC1CAYAAAB1agQxAAAfCklEQVR4Ae3dD3SU1ZnH8V/+gAbS2IiIiEFKioHljyizDSziZlGKVKsHBM/B42LX2qrBJsfdpK3HbdfqutSGszSURra1Vuiu7DZBqliUtVaqZE3sgFihkgqIICAECMbEtCSZ7HmHmWQy/8iEJHNn7pdzODNz5515n+fzvJl55s6dmZSOjo4O8Q8BBBBAAAEEEDBIINWgWAgFAQQQQAABBBDwCqT7HVJSUvxnOUUAAQQQQAABBOIm4Ly509mgOFHwbk9oLZzGDZfuLph093AuYRJqci4jeMamh1dsXmxttoBzPDv/eIvH7DoRHQIIIIAAAlYK0KBYWXaSRgABBBBAwGwBGhSz60N0CCCAAAIIWClAg2Jl2UkaAQQQQAABswVoUMyuD9EhgAACCCBgpQANipVlJ2kEEEAAAQTMFqBBMbs+RIcAAggggICVAjQoVpadpBFAAAEEEDBbgAbF7PoQHQIIINCvAp4T72rz0xu0vdnTr/sx985PaXvlf+v1g80DEmLSezfvUOXTr+tgy7kfTzQoA3JIshMEEEDAPAHPCbfWrv29hlz3RV091Nang89q6uyJOlb1Yz29vV7n/rQauc5WeA+dqNn5J1W1/BltP9EaGaMH19h6RPaAhk0QQACBJBZoeVfrK7Yp947FmpUzNIkTPXtqqcMm69Z7F2rE1me1+UA/zaRY4z1IwyZ8WffeOVxb/+u3OnAOMyk0KGc/dtkCAQsFmlRX+X09/LRbJ/rzJaWFsmakfFoHt2zSbtc8zRw+yIyQ4h1FxljNnT9a7jWv6WCfH/O2eacqY/Tfaf64nVqz5cNez0p1+7HAeB8f7B+BcxVor6vUtyu26rSkwdfcrdIpH+mFdS/q7YZ2pY2Zra8t+ZImDEuOB+T+zTVTeTfdpvzVT+pHT7foq4tnKiejJ69nWnWiboue85oPVu6CW5T7WqVeGXWHHr3rahn7Or29TpXfrtDWMweO7i2dpAMvVGnT28eltDG69mtLNH/CsCg/Xtaq+td/qmVVDZpRWKxFeZk9OJTjaNW8Uy+/3C7XA5dEyakHKQz4Jk7jvErrmq/XN5a4NKwnh2QMMaaOmiiXntTLO2borqs/G8Mtz7JpwnqfJa+oVw/WqEl/Ja34rXZcu6RXbyHSoEQF5spEE0jLW6Sy716iFY9s0Mcf/k4vpP6tbvnuci1+b4Mer/idqt68Sg/NG51gD8rhqxB7ru068foTeqTqvfB3GHG0Sis+PtmD5q5ZB178mX740mHl3HC/vj/vYh2oLFfF8TSNKbjM3ObEyTstT4vKHtIlK8pU9fEBvfzC+Zpzy7dVvniPKh//qV6relNfeGieciI9ITa/o40bTmjClUP0xi9f1/Ro23qd42nlUXPdH7Qze7LmjBocseq9vSKhG+fUSzTJlamXd+xT89WBDbVHLXUb9Pg6afG35isvXLPu+Uivr1qtt666V/fPCmz8zPb21L+uVcs26OSMr+lbiyYooweFdxb6vvzcmQY+Lfcm3Z77ln7xysW689HujYi34ct+QzvqGnV1Lxo+GpQeFINNEknAo+YP9uqgpKzLrtPiW31/cJd9TqPTXtO7TS3qSKR0osYaa65pGjbrfpXPinqnoVe2HNDr69Zo9WP7dM3tC3WTKyfMg5jzAP6Snnppv7Ku+ZrunTdWGWrXRZdcIGmQxo/pw1ejoRH2zUjzh3rv4Gkpa4zmLr7R9yQ0Urmjz9fWd5v0acQDp0l1m17Uzkk36tGvXKrtq1ZrQ/VVQU9SgSHG26pRdTv+JI2aogsjNVyB4cZ4Phka5/ZDR3XSI3WtG05VRt5cLZ64SuteqAvzRN6q+upnteHjfD0wM7A5cfBM8w4s6Cnt2PiyTk6YoAve2Kgt03M1Lyda0+pRy4GXtfqHm3Qw50v6p+9fr+EHfqXHKw5JY2bo8i6wgJ206NDRRnn02ZhfGBrRoLTvWqO7H9usv0g6b26p/s11SJU/+aVq6tuUnneLSgsXaLK175O2qn7XZq3zepyniV+5Q+M3/0zPXb5UFUX56slEcsCRYu7ZwCn2nkQ5ZqG++8AsDQvZ9i/6cO9+tadN0c1fyut8IvWcPKpD7WnKysxQSshtBngg0XLNGK1Zd90jObMLv3hOl3zuPs0altYdraVOL6yrVkP2TBXe5Hf/RB+8d1gafJXGXhrtQa/7XcV6KfAV+9lvO1hjFpbqgVkXh2za/uFevds+VFfefF3XK2RPo44e+rOUlakhEQ4cT/1b2vxmtuZ/c7KGpqbJNXeyXvmPl7Tj6u6vJjt3GEcrbwz+nEZ1RtTHZxK5cU7XhSMuVlrDUdW3eJTT7Qk3U+MKZurCZc/qhSlBb+N5Z9AaNOOeJaGzbMZ5+8vtNMqv6PmdY3Xzo7crZ/uT+sGGWrnun6XhkRpX59h9arP2Z12rwnvnaLQzk3TRxbpAaUobf7my/XftP03N0ohRg9Rw5LhaNDrmWVQjGpS0iXfq5+Wj9L3itTq5f7Mq0+Zq8Yqndfe7z+jBx36tp7d+QWXzPxdz9+U3StzTJr2/oVz/UrlfuYu+oyfnj9D7ax7VY0fSlDdvdPI0J06BvFPs5VrUg2J5n5A2RdjQU699uxuVNmmK8jofXJr0Xs12HU/7vBa6Rsb/OEq0XH0zKFUHL9U1f3+LXMHNiaT2Azv1ZoN00Q1/rXH+6e/mfdqxs1lpk3J1WVA/E6F6vRr2vmIv78mR06K6yn9X+EPntA7ve1+n067Q1LwsXxwetbz3e9UeH6zchVdpVNgH7TOvQD+efXfnYlPvK+0Zq7RuU50mhJkyj6dVVGAa5y6e9mM6erJNGtq9sU4dnq/5c97Qis1vqWCc/4ncN4M25lo9OC6Gl4zx9vYck3vzO7pw/r2aOnSwUl1/py+8sk4bd0yOsP6mSXUvPKutDcN0TeFcXxPvb0azNGPs8IiPraEzUl3U0c4Z0aBIHjXtq9NeSdljbtTdd0zWECfqy8cpN32T3mr8NImm5aOVI/A6jz7d9Sv9sLJO2XNLVTp/nIaoXRePcuYMBmvK5y8M3JjzfoGGD7T7+PmadONYX7fuTElWa9Mbnyh3/lc7n0T8myf0acy59nYNirNOdLbufSjSAuN2nTp2VKeVpfGdD1JnHrTfbh+sMeMMX3/iPQhOaf/ueqVNur6rsW3Zry2bfq/G3Bu1NGTa3rmR7xXogSu1ePFlAQ/OvlfaP3hV7oLPa1a32V+DrWicux4O0i7WiAvDPT0OVk7BlzWj9hdaVz1O98+6WH+p26x1WwdpTkl+5JmHrnvuOhdXb4+ad7zU/S2pjDzdtPhKPb7uFdVNCLPOpv2Q/vDmMedViKZ3NmJn3r5qT7tCuZed15Vb0Lm0USN69XZiuAoE3fVAXPyzPtj9J7Wl5+v2WyeeaU6cP//jh/VBW7ouzBoS/2n5gWAI3Menu1T5k/9V/fAv6qFFfpNG7fvjfum8GboiJ/LBEHg3dp33d/MepTX/WR61quHdTVr709/p4ym36xthn2QSVag3uca4BqVln15c/aRqL5h3lk/xpOj8oZlK04c6cuxjecZ9qrrnfqud7UOUlmjrT9Ka9alHymh4RxvW/pde+3iS7vzG9PBPPN5XoH/U6Ju/0fWWkO9w8r7Snv2GVmx8R1d3+/SSAVbeaffz++/AT4bGOXuEhvtnAoOlMj6vgusu07INL2nHVQU6+ssa6Zq7VBBp7YZx3pJa6rTp+Y80Y/HCgLekUpUxbqauu3C1Nrtnaly3hb6STh3Th6elwePH6lLvbKKvQX+7WRqTG2H9iYOXruyRF3W+3R7MGe2yGQ2K56j+9IcGpbtcmpjpn0dt1Lu/+z8dSZ+ku/4m8NVJtHSS57r297drS700ctFMTRjiM2n6k2rdjUp3jdfl/ThlnriKvvUnatHeqmV6oMqZkrtSN9zxgAquDrewM3Ezlfo7V2c695eqzV7Qg49zpmrohGs1Z8xuvVS1TCXua3X7wgJNqfmxtl6Ur0n98EmRvq7cmfUnUvveKv2r98C5SFfecJtKCqZG+Hj1mUWRz6tA35wabgGw75X2489pU90VAR87NsEqS3lTr5B+HbwQtC9UE71xbtPJo8fOsoB4kIbPvElztvxIv1q+T02NE3VHwHq3UEXTvFtV735Vb47+oh4O/jh86iWaOT9fW1aEWUN1/lBdkCYdPHJMJz1jlVr3G/12Z4suSIuw/sSB8K6/kUZNzQqYYQwVijRiRoNyYq/+cGSIXLdd4VtX4dGn729R1SunNHHJA5o9Ijm+tyJSEULH23XyyBH9RdmacsUIX2EbtWt9lWrazlPeXyXZ+pNQgKgj3jUHeWE28a8/ufJOs79zI0zokYbil2um8hZ9Ww9HCix4PGOs5j3wfc3zj3sO6EVnLVAvp3b9d9O3pxnKW/SQQg8d//qTq0I+Jhl5/4M0fFahyqJ9IipjghY9PCH0LuJulaqheVM06T9/o52HrlNOpFf+oZH3YCTBG2fPR9rpbgp4izhCyqmXqeC26aqt+L3GLLxBUzvXu4Xb3ixvT32N1j0v3ews6g4TbmrOLN0Wbg3V0DxdPydXO1+q0r+WuL2f6Js3pUbf23qJZk8K/uTSmTv2HNold8NY3di5rivMDqMMGdCg+NeftCvvkxZ5lKkT7zyrirJf62T+ffrn2Zf2qvOKknMCXJWijM98Runaqw+PnJJnQrN2/fcmbfdkKp31J5Hr13JcRxoC159E3jThrzE915BpfpPFP1X9kVPd158MZLjxsBo6SXPmvKqnd36kuTmxfy9QsjbO3idUzdBXws6KBR4UzseOb9XD5bcGDkY+b5B36vBZKoraWUd6cTJUo+cV6d87X4Wc1sEXnYXlkdbrnNahnX+U5iw6SwMXmc3/fkrkLfr9Gt/6EzVr11MluuP2O1X85FFNWfqIli2dEf69336PKd47SFXm5C9qfp68Jl95dLOa/uYGuVJPqm2kS1eNZv1JaIVaVb+9RjvbL9W4yz8TenVSjRieq6de2zdu0X4lRi089e9o685W5cRjMW/crJy3oL6k8e7n+/a3Z/yN81T/InXD/vD8zWC4+DwfqXrDHzX+tlkB6zL6Kv5k9PYvLA/8xGSXl6e+VhvcY3RbQe+XaMR/BsW//mR6cXJ9r0dXnXp3bsg4zf+Xn2q+/9ae97XBWadz+aW6yIC20h+WEadBH9ereuQ7eu/Ob0b4qJwREfc+CKNz9ah5+1p9Z81bavdmeFxVjzwhfTfM96b0XqAPb+l87PhxVWxtOHOfVY/pH98bqLcHDbDKmKBbC5u1tuLnevHOf9C80eEm/GPh7mqc55v4IiGgGVwYHJ/3o/TPa+81S7QkeF1GLATRtk0q71ad2P6/emW/lLMw+FN6HrUcrNa6qoO6pnBRyALyaETB16V0dHR4vx8xJSVFvrPB2/Tv5aZarSz8ubR0mYryQ77mpX/33YN7j5tLcGz1v9H3iquUXRx/J2NMgo3ieBmTvsXHMzbPc/Jynpz/Z5uGLrqlV7+X4o00qHGWhupKY14kBDeDTsTjtLCzcT6l7ZWbVD9lrubkRfu9pdhqEnHrRPdu3q6nvrNGb595FeL92otuX37YvEOVlfWa8uUC5fXyd8/8x3OcG5RWHf3NCpU+5dGS8lJdP9y8j6b4oSIebANxheeoap/4gcqrh+suA5yMMBkI9xj2gUkMWD3YFM8eIAVsglcABmcTXsB/PMevQWnfpTV3P6bNzvfbe/9laboBswP+aPynfij/5YE99aip9gkVllerrXPHU+LepMTXpBPCqDOY9G058IzNE6/YvNjabAH/8Ry/BsVsn87o/FCdA5wRJqEHASahJucygmdsenjF5sXWZgv4j2eWW5pdJ6JDAAEEEEDASgEaFCvLTtIIIIAAAgiYLUCDYnZ9iA4BBBBAAAErBWhQrCw7SSOAAAIIIGC2AA2K2fUhOgQQQAABBKwU6PYpHisFSBoBBBBAAAEEjBJwvji221fdx+WbZI0iCQ3G/3Gn0GvsHcEktPaYhJqcywiesenhFZsXW5st4BzPzj/e4jG7TkSHAAIIIICAlQI0KFaWnaQRQAABBBAwW4AGxez6EB0CCCCAAAJWCtCgWFl2kkYAAQQQQMBsARoUs+tDdAgggAACCFgpQINiZdlJGgEEEEAAAbMFaFDMrg/RIYAAAgggYKUADYqVZSdpBBBAAAEEzBagQTG7PkSHAAIIIICAlQI0KFaWnaQRQAABBBAwW4AGxez6EB0CCCCAAAJWCnT7LZ6BF/CoqfYJFZZXqy3qzrM0vXiZivKzo26VNFc21WplYblqoqMofXqxKorylZk0iZ8tkQbVrnxQ5TWNETe0zyQihdS2TcvHu1S6N8o2knLL3NpdMq37D3NFv4k117ZtW67xrlJFJFyyXofXLNBIa0TsSfSstfdSFKjMvVEl0+x5FB7IIyDODUqqMvOXau0zS305+xuWd+SyqSEJrnhmvorWPqMi/7ivYXG7bGtI/ABBp+kzVVxxn/IzmQAMkuEiAgggkDQCPMInTSlJBIEggfRpKtnTIedXyp3/re4y5Tqb5JbJ3do1vofZkyC4MBeDzPymHcyehMFKjqH0aSXa4/vb6ej4RO6yAm9izoxja+f4q8ye9GO5aVD6EZe7RgABBBBAAIHeCdCg9M6NWyGAAAIIIIBAPwrEeQ1KP2bGXSevQFu1yr9eHZIfC2RDSBjoK4G9pXINKg26t3u0/vAqLRjJw2gQDBcR6BMB/rL6hJE7GVABFskOKDc7QwABBOIhQIMSD3X2iQACiSXgLJLdXaJpPGImVt2INqEFWIOS0OUjeAQQQAABBJJTgAYlOetKVggggAACCCS0AA1KQpeP4BFAAAEEEEhOARqU5KwrWSGAAAIIIJDQAikdzlciSkpJSfF+22RCZ9MPweMSiooJJqECfTvCMRabJ16xebG12QL+45kZFLPrRHQIIIAAAghYKUCDYmXZSRoBBBBAAAGzBWhQzK4P0SGAAAIIIGClAA2KlWUnaQQQQAABBMwWoEExuz5EhwACCCCAgJUCNChWlp2kEUAAAQQQMFuABsXs+hAdAggggAACVgrQoFhZdpJGAAEEEEDAbAEaFLPrQ3QIIIAAAghYKUCDYmXZSRoBBBBAAAGzBbp91b3ZoRIdAggggAACCNgg4PwKT3pgor6f5Qkcsv68/zcBrIcIAMAkAMN3FpNQk3MZwTM2Pbxi82JrswWc49n5x1s8ZteJ6BBAAAEEELBSgAbFyrKTNAIIIIAAAmYL0KCYXR+iQwABBBBAwEoBGhQry07SCCCAAAIImC1Ag2J2fYgOAQQQQAABKwVoUKwsO0kjgAACCCBgtgANitn1IToEEEAAAQSsFKBBsbLsJI0AAggggIDZAjQoZteH6BBAAAEEELBSgAbFyrKTNAIIIIAAAmYLdPuq+4EP1aOm2idUWF6ttqg7z9L04mUqys+OulVSXdlUq5WF5aqJCGOhiRpUu/JBldc0Rix1+vRiVRTlKzPiFhZd0bZNy8e7VLo3es65ZW7tLpnW/Xcvot/Emmvbti3XeFepIhIuWa/DaxZopDUi9iR61tp7KQpU5t6okmk84vTHkRHnBiVVmflLtfaZpb7c/A3LO3LZ1pBEqC5PuGFg0mequOI+5WcyARhGhyEEEEAgKQR4hE+KMpIEAmEE0qepZE+HnB8Bdf63usuU62yWWyZ3a9f4HmZPwuAFDQWZ+U07mD0Jgkqei+nTSrTH97fT0fGJ3GUF3uScGcfWzvFXmT3px5LToPQjLneNAAIIIIAAAr0ToEHpnRu3QgABBBBAAIF+FIjzGpR+zCxJ7rqtplxfrwlOxsYFsgEGbdUq/3p1wMCZs6zXCSFhoK8E9pbKNag06N7u0frDq7RgJA+jQTBcRKBPBPjL6hPG/rsTnnTD2LJINgwKQwgggEByCdCgJFc9yQYBBPpDwFkku7tE03jE7A9d7hOBsAKsQQnLwiACCCCAAAIIxFOABiWe+uwbAQQQQAABBMIK0KCEZWEQAQQQQAABBOIpQIMST332jQACCCCAAAJhBVI6nK9ElJSSkuL9tsmwW1k8iEto8THBJFSgb0c4xmLzxCs2L7Y2W8B/PDODYnadiA4BBBBAAAErBWhQrCw7SSOAAAIIIGC2AA2K2fUhOgQQQAABBKwUoEGxsuwkjQACCCCAgNkCNChm14foEEAAAQQQsFKABsXKspM0AggggAACZgvQoJhdH6JDAAEEEEDASgEaFCvLTtIIIIAAAgiYLUCDYnZ9iA4BBBBAAAErBWhQrCw7SSOAAAIIIGC2QLevujc7VKJDAAEEEEAAARsEnF/hSQ9M1PezPIFD1p/3/yaA9RABAJgEYPjOYhJqci4jeMamh1dsXmxttoBzPDv/eIvH7DoRHQIIIIAAAlYK0KBYWXaSRgABBBBAwGwBGhSz60N0CCCAAAIIWClAg2Jl2UkaAQQQQAABswVoUMyuD9EhgAACCCBgpQANipVlJ2kEEEAAAQTMFqBBMbs+RIcAAggggICVAjQoVpadpBFAAAEEEDBbgAbF7PoQHQIIIIAAAlYK0KBYWXaSRgABBBBAwGwBGhSz60N0CCCAAAIIWCnQ7bd44iPgUVPtEyosr1ZbpADSZ6q44j7lZ1rSTzXVamVhuWoigpyBSp9erIqifGVGckuq8QbVrnxQ5TWN0bOy7ViJptG2TcvHu1S6N9pGUm6ZW7tLpnX/Ya7oN7Hi2rZtyzXeVarofAUqc29UyTQ7/gqtKLwvSeof/2ob0KD4EbI0vXiZivKz/QP2nmbmq2jtMyryC/gaFrfLpobEn7z/NFv5Rav1TCeKr2FxT7arefVzcIoAAggkuYAlUxJJXkXSQyCcQPo0lezpkPMr5c7/VneZcp3tcsvkbu0a38PsSTg9pU8r0R6fXUfHJ3KXFXi3c2acWjvHX2X2JKxe4g9S//jXkAYl/jUgAgQQQAABBBAIEqBBCQLhIgIIIIAAAgjEX8CgNSiNqilfqppgExY9BotwGQEEEEAAgaQXMKhBYZFs0h9tJIgAAggggEAPBXiLp4dQbIYAAggggAACAydAgzJw1uwJAQQQQAABBHooQIPSQyg2QwABBBBAAIGBE6BBGThr9oQAAggggAACPRSgQekhFJshgAACCCCAwMAJpHQ4XzEpKSUlxfttkwO368TYEy6hdcIEk1CBvh3hGIvNE6/YvNjabAH/8cwMitl1IjoEEEAAAQSsFKBBsbLsJI0AAggggIDZAjQoZteH6BBAAAEEELBSgAbFyrKTNAIIIIAAAmYL0KCYXR+iQwABBBBAwEoBGhQry07SCCCAAAIImC1Ag2J2fYgOAQQQQAABKwVoUKwsO0kjgAACCCBgtgANitn1IToEEEAAAQSsFKBBsbLsJI0AAggggIDZAt2+6t7sUIkOAQQQQAABBGwQcH6FJz0wUd/P8gQOWX/e/5sA1kMEAGASgOE7i0moybmM4BmbHl6xebG12QLO8ez84y0es+tEdAgggAACCFgpQINiZdlJGgEEEEAAAbMFaFDMrg/RIYAAAgggYKUADYqVZSdpBBBAAAEEzBagQTG7PkSHAAIIIICAlQI0KFaWnaQRQAABBBAwW4AGxez6EB0CCCCAAAJWCtCgWFl2kkYAAQQQQMBsARoUs+tDdAgggAACCFgpQINiZdlJGgEEEEAAAbMFun3VfXxC9aip9gkVllerLVIA6TNVXHGf8jMt6qeaarWysFw1EVGyNL14mYrysyOpJdl4g2pXPqjymsboedl4rEQTadum5eNdKt0baaN7tP7wKi0YacBDQaQQ4zjetm25xrtKFZFvyXodXrNAI+MYI7vuPwHq33+2Pblngx6VbHvC7Ul5pPTpxaooyldmzzZP4q2ylV+0Ws8U+VP0NSzuyfY1r34CThFAAIEkFjCoQUliZVJDIO4CBSpzb1TJNFrdXpUit0zu3SWaxiNmr/gS/kbUPy4ltOg9k7j4slMEEEAAAQQQ6IUADUov0LgJAggggAACCPSvgEETlo2qKV+qmuB8LV/02FZTrq+HoLBeJ/gw4fLZBLao1PUZlXbbLFdL1r+qNQtyuo1yIYzA3lK5BnXXk1hgHEYqOYeof1zqalCDwpNuuCOARbLhVBhDAAEEEEh2AYMalGSnJj8E4inAItlz0meR5DnxJfyNqX9cSsgalLiws1MEEEAAAQQQiCZAgxJNh+sQQAABBBBAIC4CNChxYWenCCCAAAIIIBBNgAYlmg7XIYAAAggggEBcBFI6Ojo6nD2npKTIdzYugZi6U1xCK4MJJqECfTvCMRabJ16xebG12QL+45kZFLPrRHQIIIAAAghYKUCDYmXZSRoBBBBAAAGzBWhQzK4P0SGAAAIIIGClAA2KlWUnaQQQQAABBMwWoEExuz5EhwACCCCAgJUCNChWlp2kEUAAAQQQMFuABsXs+hAdAggggAACVgrQoFhZdpJGAAEEEEDAbAEaFLPrQ3QIIIAAAghYKUCDYmXZSRoBBBBAAAGzBbp91b3ZoRIdAggggAACCNgg4Pz0TnpgovwWT6DGmfP+3wQIvcbeEUxCa49JqMm5jOAZmx5esXmxtdkCzvHs/Pt/5mApVuPwWLMAAAAASUVORK5CYII="> <strong><em>(A1)(A1)(A1)</em>(ft) <em>(C3)</em></strong></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<p> </p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>neither <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C1)</strong></em><br><strong>Note:</strong> Follow through from the final column of their truth table.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p><span>The Venn diagram shows the number sets \(\mathbb{N}\), \(\mathbb{Z}\), \(\mathbb{Q}\) and \(\mathbb{R}\). Place each of the following</span> <span>numbers in the appropriate region of the Venn diagram.</span></p>
<p><span>\(\frac{{1}}{{4}}\), −3, π, cos 120°, 2.7 × 10<sup>3</sup>, 3.4 × 10<sup>–2</sup></span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span><img src="data:image/png;base64,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" alt><span> <em><strong>(A1)(A1)(A1)(A1)(A1)(A1) </strong> <strong>(C6)</strong></em></span></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for each number placed once in the correct section. Accept equivalent forms for numbers.</span></p>
<p><span> </span></p>
<p><span><em><strong>[6</strong></em> <em><strong>marks]</strong></em></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">About half of the students answered this question correctly. The placement of cos120 and </span><span style="font-family: times new roman,times; font-size: medium;">π appeared to cause the most problems.</span></p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The grades obtained by a group of \(20\) IB students are listed 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>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the following table for the grades obtained by the students.</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 modal grade obtained by the students.</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>Calculate the median grade obtained by the students.</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>One student is chosen at random from the group. </span></p>
<p><span>Find the probability that this student obtained either grade \(4\) or grade \(5\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span> <em><strong>(A2) (C2)</strong></em></span></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for three correct. Award <em><strong>(A0)</strong></em> for two or fewer correct.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{Mode}} = 6\) <strong><em>(A1)</em>(ft) <em>(C1)</em></strong></span></p>
<p><span><strong><em>[1 mark]<br></em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{Median}} = 4.5\) <strong><em>(M1)(A1)</em>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Note:</strong> <em><strong>(M1)</strong></em> for attempt to order raw data (if frequency table not used) or <em><strong>(M1)</strong></em> halfway between 10<sup>th</sup> and 11<sup>th</sup> result.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span>\(\frac{7}{{20}}{\text{ }}(0.35{\text{, }}35\% )\) </span> <span><strong><em>(A1)</em>(ft)</strong> <em><strong>(C1)</strong></em></span></span></p>
<p><span><span><em><strong>[1 mark]<br></strong></em></span></span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Parts (a) and (b) were well done by the vast majority of candidates.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Parts (a) and (b) were well done by the vast majority of candidates.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Part (c) caused problems to many – with (1) the mean of the two grades not being taken (2) the mean being calculated instead of the median.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Part (d) was successfully completed by those candidates who did the question by counting. Those who tried to use the probability laws were not successful.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Much of the question could have been checked by inputting the data into the GDC.</span></p>
<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 probability that Tanay eats lunch in the school cafeteria is \(\frac{3}{5}\)</span><span style="font-size: medium; font-family: times new roman,times;">.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">If he eats lunch in the school cafeteria, the probability that he has a sandwich is \(\frac{3}{{10}}\)</span><span style="font-size: medium; font-family: times new roman,times;">.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">If he does not eat lunch in the school cafeteria the probability that he has a sandwich</span> <span style="font-size: medium; font-family: times new roman,times;">is \(\frac{9}{{10}}\)</span><span style="font-size: medium; font-family: times new roman,times;">.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the tree diagram below.</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">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that Tanay has a sandwich for his lunch.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span> <em><strong>(A1)(A1)(A1)</strong></em> <em><strong>(C3)</strong></em></span></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for each correct pair of branches.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{3}{5} \times \frac{3}{{10}} + \frac{2}{5} \times \frac{9}{{10}}\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for their two correct products, <em><strong>(M1)</strong></em> for addition of their products. Follow through from their tree diagram.</span></p>
<p><br><span>\( = \frac{{27}}{{50}}(0.54,54\% )\) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C3)</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">\(U\) is the set of all the <strong>positive</strong> integers less than or equal to \(12\).</span><br><span style="font-size: medium; font-family: times new roman,times;">\(A\) , \(B\) and \(C\) are subsets of \(U\) .</span><br><span style="font-size: medium; font-family: times new roman,times;">\[A = \{ 1{\text{, }}2{\text{, }}3{\text{, }}4{\text{, }}6{\text{, }}12\} \]</span><span style="font-size: medium; font-family: times new roman,times;">\[B = \{ {\text{odd integers}}\} \]</span><span style="font-size: medium; font-family: times new roman,times;">\[C = \{ 5{\text{, }}6{\text{, }}8\} \]</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of elements in \(A \cap C\) .</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>List the elements of \(B\) .</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>Complete the following Venn diagram with <strong>all</strong> the elements of \(U\) .</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(1\) (one) <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><span><strong>Note:</strong> \(6\), \(\{6\} \) or \(\{1\} \) earns no marks.</span></p>
<p><span><em><strong>[1 mark]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(1\), \(3\), \(5\), \(7\), \(9\), \(11\) <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><span><strong>Note:</strong> Do not penalise if braces, parentheses or brackets are seen.</span></p>
<p><span><em><strong>[1 mark]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span> <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C4)</strong></em></span></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for the empty set \(A \cap B \cap C\) .</span></p>
<p><span>Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for the correct placement of \(6\), \(5\), \(1\) and \(3\).</span></p>
<p><span>Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for the correct placement of \(2\), \(4\), \(12\), \(7\), \(9\), \(11\), \(8\).</span></p>
<p><span>Award <strong><em>(A1)</em>(ft)</strong> for the correct placement of \(10\).</span></p>
<p><span>Follow through from part (b).</span></p>
<p><span><em><strong>[4 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">There was much confusion amongst candidates as to the understanding of the words <em>number of elements</em>. Many candidates simply wrote down \(6\) or \(\{ 6\} \) and consequently lost the first mark.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">There was much confusion amongst candidates as to the understanding of the words <em>number of elements</em>. Many candidates simply wrote down \(6\) or \(\{ 6\} \) and consequently lost the first mark. Part (b) was done well and many successful attempts were made at completing the Venn diagram in part (c). The most common error in the last part of the question was the omission of the element \(10\).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Part (b) was done well and many successful attempts were made at completing the Venn diagram in part (c). The most common error in the last part of the question was the omission of the element \(10\).</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The probability that it rains today is \(0.4\) . If it rains today, the probability that it will rain tomorrow is \(0.8\) . If it does not rain today, the probability that it will rain tomorrow is \(0.7\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the tree diagram below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></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>Calculate the probability of rain tomorrow.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span> <em><strong>(A1)(A1)(A1) (C3)</strong></em></span></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for each correct pair.</span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(0.4 \times 0.8 + 0.6 \times 0.7\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(M1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <strong><em>(A1)</em>(ft)</strong> for two consistent products from tree diagram, <em><strong>(M1)</strong></em> for addition of their products. Follow through from their</span> <span>tree diagram provided all probabilities are between 0 and 1.</span></p>
<p> </p>
<p><span><span>\( = 0.74\) </span><span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></span></span></p>
<p><span><span><em><strong>[3 marks]</strong></em></span></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Part a of this question was well answered, however part b caused many problems. Candidates did not seem to know how to find the probability of the combined events.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Part a of this question was well answered, however part b caused many problems. Candidates did not seem to know how to find the probability of the combined events.</span></p>
<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 school offers three activities, basketball (<em>B</em>), choir (<em>C</em>) and drama (<em>D</em>). Every student must participate in at least one activity.</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">16 students play basketball only.</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">18 students play basketball and sing in the choir but do not do drama.</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">34 students play basketball and do drama but do not sing in the choir.</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">27 students are in the choir and do drama but do not play basketball.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Enter the above information on the Venn diagram below.</span></p>
<p><img src="data:image/png;base64,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" alt></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>99 of the students play basketball, 88 sing in the choir and 110 do drama.</span></p>
<p><span>Calculate the number of students <em>x</em> participating in all three activities.</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>99 of the students play basketball, 88 sing in the choir and 110 do drama.</span></span></p>
<p><span>Calculate the total number of students in the school.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt> <em><span><strong>(A2)</strong></span></em></span></p>
<p><em><span><strong>(A1)</strong> only if 1 error</span></em></p>
<p><em><span><strong>(A0)</strong> otherwise <strong>(C2)</strong></span></em></p>
<p><em><span><strong>[2 marks]</strong></span></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(x + 16 + 18 + 34 = 99\)</span></p>
<p><span>\(x = 31\) <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Choir only \(= 88 - (18 + 27 + 31) = 12\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>Drama only \( = 110 - (27 + 34 + 31) = 18\)</span><span> <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>Total \( = 16 + 34 + 18 + 31 + 12 + 27 + 18 = 156\)</span><span> <em><strong>(A1)</strong></em><strong>(ft) <em>(C3)</em></strong></span></p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<p> </p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Venn diagrams continue to be a problem area. Quite a good number of candidates managed to fill in the information on the Venn diagram accurately. However, finding the correct value for <em>x</em> and calculating the number of students in the school posed a big problem for many candidates.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Venn diagrams continue to be a problem area. Quite a good number of candidates managed to fill in the information on the Venn diagram accurately. However, finding the correct value for <em>x</em> and calculating the number of students in the school posed a big problem for many candidates.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Venn diagrams continue to be a problem area. Quite a good number of candidates managed to fill in the information on the Venn diagram accurately. However, finding the correct value for <em>x</em> and calculating the number of students in the school posed a big problem for many candidates.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Shade \((A \cup B) \cap C'\) on the diagram below.</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>In the Venn diagram below, the number of elements in each region is given.</span></p>
<p><span>Find \(n((P \cap Q) \cup R)\).</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>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>\(U\) is the set of positive integers, \({\mathbb{Z}^ + }\).</span></p>
<p><span>\(E\) is the set of even numbers.</span></p>
<p><span>\(M\) is the set of multiples of \(3\).</span></p>
<p><span>(i) List the first six elements of the set \(M\).</span></p>
<p><span>(ii) List the first six elements of the set \(E' \cap M\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>not shading \(C\) or shading \(A \cup B\) <em><strong>(A1)</strong></em></span></p>
<p><span>correct shading <em><strong>(A1) (C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Identifying the correct 5 numbers \(3\), \(4\), \(5\), \(6\), \(9\) <em><strong>(A1)</strong></em></span></p>
<p><span>\(27\) <em><strong>(A1) (C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(M = \{ 3{\text{, }}6{\text{, }}9{\text{, }}12{\text{, }}15{\text{, }}18\} \) <em>brackets not required</em>. <em><strong>(A1)</strong></em></span></p>
<p><span>(ii) \(E' \cap M = \{ 3{\text{, }}9{\text{, }}15{\text{, }}21{\text{, }}27{\text{, }}33\} \) <strong>(ft)</strong> <em>from (i)</em>. <em><strong>(A1)</strong></em><strong>(ft) <em>(C2)</em></strong></span></p>
<p><span><strong><em>[2 marks]<br></em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question proved to be one of the easier questions with a number of candidates able to shade in the required region and finding values in a set. They still had problems with part (b).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question proved to be one of the easier questions with a number of candidates able to shade in the required region and finding values in a set. They still had problems with part (b).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question proved to be one of the easier questions with a number of candidates able to shade in the required region and finding values in a set. They still had problems with part (b).</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The table below shows the number of words in the extended essays of an IB class.</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>Draw a histogram on the grid below for the data in this table.</span></p>
<p><span><img src="data:image/png;base64,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" alt></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 modal group.</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 maximum word count is \(4000\) words.<br></span></p>
<p><span>Write down the probability that a student chosen at random is on or over the word count.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span> <em><strong>(A3) </strong><strong> (C3)</strong></em></span></span></p>
<p><span><strong>Notes: <em>(A3)</em></strong> for correct histogram, <em><strong>(A2)</strong></em> for one error, <em><strong>(A1)</strong></em> for two errors, <em><strong>(A0)</strong></em> for more than two errors.</span><br><span>Award maximum<em><strong> (A2)</strong></em> if lines do not appear to be drawn with a ruler.</span><br><span>Award maximum <em><strong>(A2)</strong></em> if a frequency polygon is drawn.</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{Modal group}} = 3800 \leqslant w < 4000\) <em><strong>(A1) (C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{Probability}} = \frac{3}{{35}}{\text{ }}(0.0857{\text{, }}8.57\% )\) <em><strong>(A1)(A1) (C2)<br></strong></em></span></p>
<p><span><strong>Note: <em>(A1)</em></strong> for correct numerator <em><strong>(A1)</strong></em> for correct denominator.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">A surprising number of the candidates did not appear to have brought a ruler/straight edge and so lost a mark in this question as they were asked to <strong>draw</strong> a histogram which means the lines must be drawn using a ruler/straight edge. Some candidates drew a frequency polygon. Parts (b) and (c) were generally answered well though \(20/35\) was seen occasionally in part (c).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">A surprising number of the candidates did not appear to have brought a ruler/straight edge and so lost a mark in this question as they were asked to <strong>draw</strong> a histogram which means the lines must be drawn using a ruler/straight edge. Some candidates drew a frequency polygon. Parts (b) and (c) were generally answered well though \(20/35\) was seen occasionally in part (c).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">A surprising number of the candidates did not appear to have brought a ruler/straight edge and so lost a mark in this question as they were asked to <strong>draw</strong> a histogram which means the lines must be drawn using a ruler/straight edge. Some candidates drew a frequency polygon. Parts (b) and (c) were generally answered well though \(20/35\) was seen occasionally in part (c).</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the following Venn diagrams.</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an expression, in set notation, for the <strong>shaded</strong> region represented by Diagram 1.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an expression, in set notation, for the <strong>shaded</strong> region represented by Diagram 2.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an expression, in set notation, for the shaded region represented by Diagram 3.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Shade, on the Venn diagram, the region represented by the set \(\left( {H \cup I} \right)'\).</p>
<p><img src="data:image/png;base64,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"></p>
<p> </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>Shade, on the Venn diagram, the region represented by the set \(J \cap K\).</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em>A' <strong>(A1)</strong><br></em></p>
<p><em><strong>Note:</strong> </em>Accept alternative set notation for complement such as<em> U − A.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(C \cap D'\) <strong>OR</strong> \(D' \cap C\) <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Accept alternative set notation for complement.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\left( {E \cap F} \right) \cup G\) <strong>OR </strong>\(G \cup \left( {E \cap F} \right)\) <em><strong>(A2) (C4)</strong></em></p>
<p><strong>Note:</strong> Accept equivalent answers, for example \(\left( {E \cup G} \right) \cap \left( {F \cup G} \right)\).</p>
<p><em><strong>[2 marks]</strong></em></p>
<p> </p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"> <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"><em><strong>(A1) (C2)</strong></em><br><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>All the children in a summer camp play at least one sport, from a choice of football (\(F\)) or basketball (\(B\)). 15 children play both sports.</p>
<p>The number of children who play only football is double the number of children who play only basketball.</p>
<p>Let \(x\) be the number of children who play only football.</p>
</div>
<div class="specification">
<p>There are 120 children in the summer camp.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an expression, in terms of \(x\), for the number of children who play only basketball.</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>Complete the Venn diagram using the above information.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of children who play only football.</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>Write down the value of \(n(F)\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{1}{2}x\) <strong><em>(A1)</em></strong> <strong><em>(C1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"> <strong><em>(A1)(A1)</em>(ft)</strong> <strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Award <strong><em>(A1) </em></strong>for 15 placed in the correct position, award <strong><em>(A1)</em>(ft) </strong>for \(x\) and their \(\frac{1}{2}x\) placed in the correct positions of diagram. Do not penalize the absence of 0 inside the rectangle and award at most <strong><em>(A1)(A0) </em></strong>if any value other than 0 is seen outside the circles. Award at most <strong><em>(A1)(A0) </em></strong>if 35 and 70 are seen instead of \(x\) and their \(\frac{1}{2}x\).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(x + \frac{1}{2}x + 15 = 120\) or equivalent <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for adding the values in their Venn and equating to 120 (or equivalent).</p>
<p> </p>
<p>\((x = ){\text{ }}70\) <strong><em>(A1)</em>(ft)</strong> <strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from their Venn diagram, but only if the answer is a positive integer and \(x\) is seen in their Venn diagram.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>85 <strong><em>(A1)</em>(ft)</strong> <strong><em>(C1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from their Venn diagram and their answer to part (c), but only if the answer is a positive integer and less than 120.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The probability that Nikita wins a tennis match depends on the surface of the tennis court on which she is playing. The probability that she plays on a grass court is \(0.4\). The probability that Nikita wins on a grass court is \(0.35\). The probability that Nikita wins when the court is not grass is \(0.25\).</p>
<p>Complete the following tree diagram.</p>
<p><img src="data:image/png;base64,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" alt></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that Nikita wins a match.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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" alt> <em><strong>(A1)(A1)(A1) (C3)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for each correct entry.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(0.4 \times 0.35 + 0.6 \times 0.25\) <em><strong> (A1)</strong></em><strong>(ft)</strong><em><strong>(M1)</strong></em></p>
<p><strong>Note: </strong>Award<strong><em> (A1)</em>(ft) </strong>for two correct products from their tree diagram seen, and<em><strong> (M1) </strong></em>for the addition of their products.</p>
<p><br>\( = 0.29\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></p>
<p> </p>
<p><strong>Note: </strong>Follow through from part (a).</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Question 1: Tree diagram<br>This was a good starting question and answered correctly by the majority of the candidates. However, some candidates were unable to interpret part (b). The weakest seemed not to be aware that the sum of the probabilities on the branches should equal 1.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 1: Tree diagram<br>This was a good starting question and answered correctly by the majority of the candidates. However, some candidates were unable to interpret part (b). The weakest seemed not to be aware that the sum of the probabilities on the branches should equal 1.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A group of 60 sports enthusiasts visited the PyeongChang 2018 Winter Olympic games to watch a variety of sporting events.</p>
<p>The most popular sports were snowboarding (<em>S</em>), figure skating (<em>F</em>) and ice hockey (<em>H</em>).</p>
<p>For this group of 60 people:</p>
<p style="padding-left: 120px;">4 did not watch any of the most popular sports,<br><em>x</em> watched all three of the most popular sports,<br>9 watched snowboarding only,<br>11 watched figure skating only,<br>15 watched ice hockey only,<br>7 watched snowboarding and figure skating,<br>13 watched figure skating and ice hockey,<br>11 watched snowboarding and ice hockey.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Complete the Venn diagram using the given information.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAxMAAAHFCAYAAACJoqRLAAAgAElEQVR4Ae3dD7BW9Z3n+e9N3JmFODairkoDQbQBbUaQIKEXGGibXMTYC4uyXTI0OhGdlINO2dWgg6SECbAKVtMNhHUAU0hY2TTxFlTbIoSw2MAMQUQwbBA6KggBXRQJzWBvl83d+hxz8OHc+zz3+XP+/H7nvE9Vwr3Pc/78fq/vEX7f8/tzmlpbW1uNDQEEEEAAAQQQQAABBBCoUeArNe7P7ggggAACCCCAAAIIIIBAIHBZ1KGpqSn6Eb8jgAACCCCAAAIIIIAAAoFA6cCmNsmE9ijdATMEEEAAAQQQQAABBBBAQALRjgeGOXFfIIAAAggggAACCCCAQF0CJBN1sXEQAggggAACCCCAAAIIkExwDyCAAAIIIIAAAggggEBdAiQTdbFxEAIIIIAAAggggAACCJBMcA8ggAACCCCAAAIIIIBAXQIkE3WxcRACCCCAAAIIIIAAAgiQTHAPIIAAAggggAACCCCAQF0CJBN1sXEQAggggAACCCCAAAIIkExwDyCAAAIIIIAAAggggEBdAiQTdbFxEAIIIIAAAggggAACCJBMcA8ggAACCCCAAAIIIIBAXQIkE3WxcRACCCCAAAIIIIAAAgiQTHAPIIAAAggggAACCCCAQF0CJBN1sXEQAggggAACCCCAAAIIkExwDyCAAAIIIIAAAggggEBdAiQTdbFxEAIIIIAAAggggAACCJBMcA8ggAACCCCAAAIIIIBAXQIkE3WxcRACCCCAAAIIIIAAAgiQTHAPIIAAAggggAACCCCAQF0CJBN1sXEQAggggAACCCCAAAIIkExwDyCAAAIIIIAAAggggEBdAiQTdbFxEAIIIIAAAggggAACCJBMcA8ggAACCCCAAAIIIIBAXQIkE3WxcRACCCCAAAIIIIAAAghcBgECcQk0NTXFdSrOgwACCCCAAAIFFmhtbS1w7f2qOsmEX/FyvrT8x+98iCggAggggAACTgvwcNLp8LQpHMOc2pDwAQIIIIAAAggggAACCFQjQDJRjRL7IIAAAggggAACCCCAQBsBkok2JDn84PM37bmbmkzdhl/+7w/tuTfPXazs528+ZzeVfH/Tc2/a5xe/5QcEEEAAAQQQQAABBNoKNLVGBrmrsRn5qO1RfOKhwD/a4R9Osb4PHrQpL6y1H3ynv10eqcWFX7fYQyO32rdf/wub8Lv/IvJtx79y73RsxB4IIIAAAgggUFmA9kRln6y/jcaHnomsI5L29a//Y7v/3lvaJBJBMf77P9j/MHOaja8jkUi7GlwPAQQQQAABBBBAIHsBkonsY5BOCS4csR0/3mH2rcF28xXthf0f7Vc7/pv9Tq+rrb1v0ykkV0EAAQQQQAABBBDwSYB2o0/RaqCsF371X+3Hm82aR95i17Z7nnN2/Fe9bMzgru1+y4cIIIAAAggggAACCEQFSCaiIrn8/YKdO/4r+4X1tW8N6N5+z8PZt23T2/+Tdb+cWyKXtwCVQgABBBBAAAEEEhCg5ZgAqnunPG17Nm22k9f/gQ36vc7tFO+Cnd2zzf6fCf+z3cQd0Y4PHyGAAAIIIIAAAgi0J0DTsT2VvH32+VHb+/KbFeZLnLW/3/v/2qhyvRZ586A+CCCAAAIIIIAAArEIkEzEwuj4SU4dtV+8a3bjv/66XdNeUc/utb9+vmuZXov2DuAzBBBAAAEEEEAAAQSs/eHzwORM4Gtd7Lrrzc6f+o2db1O1M/bm8iW2+7vjbUi7qzy1OYAPEEAAAQQQQAABBBAIBOiZKMKNcMVg+3dzv2O24Fmb9+JuO3nhi0pfOPmmtTz3H+2P//bf2HPfHdz+uyeK4EMdEUAAAQQQQAABBOoSIJmoi823g66wft9ZZNt+9idmq8Zbt682md5e+NVvLLb3ev072/Y3/9G+wSpOvgWV8iKAAAIIIIAAApkLNLW2traWliL6iuzS7/gZgUoC3DuVdPgOAQQQQAABBKoRoD1RjVJ2+0TjQ89EdrHgyggggAACCCCAAAIIeC1AMuF1+Cg8AggggAACCCCAAALZCZBMZGfPlRFAAAEEEEAAAQQQ8FqAZMLr8FF4BBBAAAEEEEAAAQSyEyCZyM6eKyOAAAIIIIAAAggg4LUAyYTX4aPwCCCAAAIIIIAAAghkJ0AykZ09V0YAAQQQQAABBBBAwGsBkgmvw0fhEUAAAQQQQAABBBDIToBkIjt7rowAAggggAACCCCAgNcCJBNeh4/CI4AAAggggAACCCCQnQDJRHb2XBkBBBBAAAEEEEAAAa8FSCa8Dh+FRwABBBBAAAEEEEAgOwGSiezsuTICCCCAAAIIIIAAAl4LXOZ16Sk8AgggkLLAZ599ZseOHavpqldffbV17dq1pmPYOX8Chw8frqlSnTt3tu7du9d0DDsjgAACaQuQTKQtzvUQQMBJgTBJOHXqlH300Ud24sQJ++CDD4Kybtu2zd54442L5Z4+ffrFn6v5odzxXbp0sX79+tnll19uvXr1MpKOajTd20dJwvnz5+29996zc+fO2YEDB4JC6vMNGzZcLPDUqVPtyiuvvPh7Rz+UOz68b3R8//79jaSjI0m+RwCBJAWaWltbW0sv0NTUZJGPSr/mZwTKCnDvlKXhC8cE1Eg7cuSI6U8lDAsXLgxKqCQh2lDTF3E28sOkRedVGdT4DBOXMOlQo/OGG24IEg01FuO8vmOh8Ko4ul+UbL777rtBwlAaLyUJQ4cODerTu3fvoIEfdyNf19cWJrxh4qLPlbSMGzfO+vTpE5RDZdB9Q8+GV7cYhf2tAO0Jt2+FaHxIJtyOl1eli95cXhWewuZW4Pjx43b06FF76623bP/+/bZy5UpTY33AgAFBw0s9Aj169LBOnTo5YxBttCrZUUNxyJAhNnjw4KAXQ41GtuQETp8+HSSab7/9dpA4lMZAvUkuJnnhva6etV27dpmSHW2jRo0KEgyV2bV7PbkIcmafBWhPuB29aHxIJtyOl1eli95cXhWewuZGQI3AgwcP2uuvv27r168P6jV+/HjvG+FhQ1FJ0ZYtW4In0epJGT16tN1yyy08gW7wDlaP0aFDh2zHjh2X+Kq3wedGeGlStH379ovJ9IgRI4IEg6S0wRuHwxMRoD2RCGtsJ43Gh2QiNlpOFL25EEEgLQE1tLdu3WphY2nevHlB8pDnRnaYNIXJhayVWAwfPtwGDhyYFr3X15Hhnj17guRBPQ9KzsLkIa+N7DBpUo9LS0tLMMROyfbIkSNt0KBBTvXQeX1zUfiGBGhPNMSX+MHR+JBMJE5enAtEb67i1JyaZiGgoUCbN2+21atXW7du3WzChAl26623FrYhrYRq9+7dtnHjxuDpsxIqGoht78ww8Qwb0lOmTLHbbrutsA3pMKFSUvXUU08FCZWSUvVcuDT0r20k+STPArQn3I5uND4kE27Hy6vSRW8urwpPYb0QKG0IqsBKIO644w6G+ESiFzYQ161bF8wTUYO5yD0WeERukDK/qtdi7969wRBBJRYkpGWg+DhxAdoTiRM3dIFofEgmGuLk4FKB6M1V+h0/I1CvQNjAWbVq1cWGsYZlsEpNdaJqSGsirnpwtCmx0ITcIrz3Yt++ffbqq68GT9zVML7rrrsK23NV3d3y5V78d/elBT+lL0B7In3zWq4YjQ/JRC167FtRIHpzVdyZLxHoQECN4JdeeiloBKvxq9WMhg0b1sFRfF1JIBwa9uijjwZPne+9995gRatKx/j2nRrBGuoVJk+PPPIIQ3YaDKL+W3zllVds6dKlwSpoDzzwAP8tNmjK4ZUFaE9U9sn622h8SCayjkiOrh+9uXJUNaqSooAavFq+VU/T9RR90qRJhXiKniKxRRvcmnjse6IWJp95TpTSvEfKXWvnzp0W9hI++eSTNnbsWOZWlMPi87oFaE/UTZfKgdH4kEykwl6Mi0RvrmLUmlrGJaBGSvjyOJ4mx6Xa8XnkrheeKXnzsXFYmnxOmzbN7r77bpLPjsPe8B6lvVxLliwh6W9YlBOUCtCeKNVw7+dofEgm3IuRtyWK3lzeVoSCpypQmkTk4Ql5qngxXqy0Ue5DUuFbeWMMlVOnKu0RIqlwKjReF4b2hNvhi8aHZMLteHlVuujN5VXhKWzqAiQRqZNXdUHXG+mul68q5BzuRFKRw6BmWCXaExniV3HpaHxIJqpAY5fqBKI3V3VHsVfRBMLGoP6kJ8Ld6Idx0vCnRYsWZT6nQo3V559/PniruQ89J+5GNtmShUmFJsATp2St83x22hNuRzcaH5IJt+PlVemiN5dXhaewiQuokfHMM88EY/Pnzp1rzc3NiV+TCzQuoKRixowZwYkWLFiQ+upPmiyu92Xcf//99uKLL9rEiROZ8Nt4WBM/A/+9J06c6wvQnnA7vNH4kEy4HS+vShe9ubwqPIVNTCBcOeiee+6hMZiYcvIn1rC0xx9/3PSOj+9+97upTHLO4prJSxbrCmEyes011wQ9kX369CkWALWtS4D2RF1sqR0UjQ/JRGr0+b9Q9ObKf42pYUcCemnY7Nmzg6fZGvJQhBeldWTi8/dhL4HeN6B46g3kSWx60/nixYtNDdEsekOSqFPRz7l582abNWtWsNzzgw8+SO9S0W+IDupPe6IDoIy/jsaHZCLjgOTp8tGbK091oy61CajRqXH269evt+XLl/PW4dr4nN9bjf05c+YE5dS8l7ieNpf2Yr388suJJSvOA+e0gPy9kNPAJlAt2hMJoMZ4ymh8vhLjuTkVAgggYHoCOXLkSOvevbu9/vrrJBI5vCcU2xUrVgTzFyZPnhy8bVoNxUY29ULcd999tmvXLvvkk09IJBrBdPTYTp062cyZM23NmjVBj6Xm4mhuBRsCCPgtQM+E3/FzqvTRTNWpwlGYxAXCp467d+9maEri2u5cIJxoq2RAw5+UaNS6aeUfHcvE/Frl/N1ff19oYr3iTu+lv3FMquS0J5KSjee80fiQTMTjylnMLHpzgVIcAc2NePjhhxkPXZyQt6mpeqTGjBljtQxPKh0u9eyzzzKnpo1q/j9QEqreLU3s1wR/9V6wIUB7wu17IBofhjm5HS9Kh4DzAnqqrERCTxenTZtGY8D5iCVTQC31e+zYMdu4cWOwlGxHw1eUfGgC99ixY4MhU0zOTyYurp9V8200HFKbhrkpwWRDAAG/BOiZ8CteTpc2mqk6XVgK17CAGotPPPFEcB6eKjfMmZsTdDR8heFwuQl17BUJe7c2bdrEe2hi1/XrhLQn3I5XND70TLgdL0qHgJMCGtZ055132ogRI3iq7GSEsiuUhqlMmTIl6KlSj1VLS8vFwuip82OPPRb8vnbt2thWgbp4AX7wWiDs3Vq2bJnNnz/flHiyIYCA+wL0TLgfI29KGM1UvSk4Ba1JQI1DvcmaSZM1sRVy53BOxA033GBDhw4N3k2R5PspComcw0qHvVfvv/++Pf3003VN6s8hS6GqRHvC7XBH40My4Xa8vCpd9ObyqvAUtkMB/oHvkIgd2hHQfTN16lT76U9/aj/60Y+CSdrt7MZHCLQR4MFFG5LCfEB7wu1QR+PDMCe340XpEHBCQA1CDU85c+ZM8Gbiepb/dKIiFCJVAd03L7zwgnXu3NnmzZtn3/ve94K3WqdaCC7mrYAm6Ovllxout3PnTm/rQcERyLsAPRN5j3CK9YtmqilemkslKKChKvpHXePgtVoTGwLVCIQJqPZdvHhxsMqXGoTDhw+3HTt22LBhw6o5DfsgEKzwxN9BxboRaE+4He9ofOiZcDtelA6BTAW0Bnz4dJBEItNQeHXxcKL1gAEDggn64bsDlEBo+Vi9T6B0YrZXlaOwqQuoJ1TLx+7fvz94yZ0SVTYEEHBHgJ4Jd2LhfUmimar3FSp4BXiKXPAboM7qV9OTVc0+dV6ew3Is0F5vV46rW+iq0Z5wO/zR+NAz4Xa8KB0CmQgokdDT40OHDjEcJZMI+HnRMEnQOPdKPVnRJ81+1pZSpy2gHi4NmVOPl+Zw0UORdgS4HgLtC9Az0b4Ln9YhEM1U6zgFhzggECYSGobCRGsHAuJJEUoTiWrnQ4RPmtU4rJR8eEJAMVMUWLp0aTDsKZyPk+KluVQKArQnUkBu4BLR+NAz0QAmhyKQNwESibxFNJ361JNIqGThk+ZwLHw6peUqeRBQ8kkPRR4iSR3yIEAykYcoUgcEYhAgkYgBsYCnqDeRCKlIKEIJ/qxVgISiVjH2RyAZAZKJZFw5KwK1CVw4aW+++IT9YVOTqfuw6Q+fsB9uPWxnD//IZrYcq+1cdexNIlEHGodcXLJTcySqHdrUHhsJRXsqfFaNQJYJxedvPmc3hX9nl/1zsD2x9eNqqsI+CHgrQDLhbegoeH4Eztibf/GQDV71VXv00G+stbXV/vmle+yrmx613+n7N3ZT/2sSrSqJRKK8uT15oz0SURgSiqgIv1crkFVCcdk3/tx+9Zuf2YzrzWzKy3aitTX4+1t/h7e2/rP9w8FVNuXGZhszuGu1VWE/BLwUIJnwMmwUOlcCn79r//fzf2s3fvse+1/6XBFU7SvXD7H7n3rCZvQfYgN6/4+JVZdEIjHaXJ847kQixCKhCCX4s1aBrBKKCx8esX0nr7fmkbfYtZcU+it2eZ9v2h3/odkGX0FT6xIafsmdAHd47kJKhXwVOH/wqH10oaT0nX/HrvtfB9nvXVbyWYw/qkGo5V81RIVVm2KEzfmptALTnDlzgtWXGhnaVI5JCcWzzz5rq1evNiW7bAhUK/Dggw8Gu77wwgvVHtLgfhfs3PFf2S9suP3J8F72RYPqgp3dusgWvXnO7Cv97P7HR9kXj4gavBSHI+CwAMmEw8GhaAURuOxG+8PvfttO/nCaTf5PLXb43G8zisu+YY//5zsS+YcoqSfLBYlYYatZupTrlClTEnPo2rVr8IZsJbskFIkx5+7E6fdsnbY9mzbbyeY7bfhN6kG+YOcOr7d5z35qA36vc+58qRAC5QRIJsrJ8DkCqQl0sW/82Qr7+V98yw4tuMdG/Yf/w3af/KfErp70k+XECs6JMxfQE98rr7wylXdCqLdszZo1Qe+Zkl82BKoRSLVn68LHdmTfCbPND1rfr2rxjK/av+p7jy2wXtb9cppX1cSLffIhwN2ejzhSC98FvnK9DXl8iW194Ttmq6fZNyf977Y1oYTi6aefDtZnT/LJsu/hoPxtBTTsSO+D0BCntLY+ffoEw/AmTJhgp0+fTuuyXMdzgdKercOHDydWmwu/+q/2481mzS8ctH8OJl3/f3biZ7Pt298aYL1pXSXmzondE+B2dy8mlKiwAldYv+8sChKK67fNtsl/ucPOxmyht8Z++umnFo4tjvn0nC6nAhpqpHtHiaie/Ka5aV6GEt8nnnjC1KvGhkA1AurZ0nywyZMnB0sYV3NMbft8bh8d2G2bra99a0D3386X+Bd2bfd+9keDvm4JTXWrrYjsjUBKAiQTKUFzGQTaCmii3gp78fA/lnx1hfW799/an15vdvLlvfb3n5d81eCPahDq6bImt6bdIGyw6ByeoUA4UV9DjrKaqK+VejS8Kr2JtRmCc+nYBJSI6t5Rb1r8iegZO/jzPWbX/4ENKpkf8ZU+f2KP33F1bHXgRAj4IEAy4UOUKGNOBTR5b4P98vi5dut3/T3xreRU2iDUEAA2BKoRUANMjbG5c+eahhxlualBuGXLFtu8eXOWxeDangmoVyuRRPTs27bpR2+afWuw3czSr57dFRQ3bgGSibhFOR8C1QoEk/f22oLvL7QX3zxpwRpO596xlnnP2oKT37Y/+98GxbKSk0sNwmpp2M8NAQ0TGTJkiDU3N2deIPWmaajVmDFjEhq2knkVKUBCAvEnov9kv97SYj86eaNNGXe76Z11bAgUWYBkosjRp+6ZClz41V478u932m/+yxj7579+wL7a1GRN/+pmm/bhnbb50Ev259/oEkv5XGoQxlIhTpKKgHoAdu/eHaymlMoFq7iIhllt2rQp6C2Jf9hKFQVgFy8FYk1EP3/TnrvpX1r3e35gJ+1dW31PT2u6v8VOeilDoRGIR6CpVe99L9mampqC18GXfMSPCFQlwL1TFVOqO6lBuGzZMlu7di3zJFKV9/tiGhbXo0cPO3bsWGbzJCoJzp8/P/h65syZlXbjOwQuEeDvw0s4nP6F9oTT4bFofOiZcDtelA6BugXUIJw1a5YtWLCARKJuxeIdqCf+GhaiHoCsJlx3pK6X2anXhBfadSTF96UCGq6nuT9M5C9V4WcEGhegZ6JxQ87wW4FopgpMtgIPPfSQjR071rRGPxsC1Qpoxa8DBw4ESWi1x2Sxn94foGU/X3vtNWNRgSwi4Oc1lSyPHDnSli9fbgMHDvSzEgUoNe0Jt4McjQ89E27Hi9IhUJdAS0tLcByJRF18hT1IDXRNcn7yySedN9ATZq009cwzzzhfVgrojoDmTyiRePjhhxNYLtadelISBNIUoGciTe2cXyuaqea8us5Wz/Xx7s7CFbxgemJ733332SOPPOLE6k3VhMPHMldTL/ZJXoB5N8kbN3IF2hON6CV/bDQ+9Ewkb84VEEhVQOPdX375ZWfHu6eKwcWqFli3bl0wntyFZWCrLbSeMmtOkOYGnT59utrD2A+BYJWy9evX2759+9BAAIEGBUgmGgTkcARcEghf6MXwJpei4n5ZfBreFNVkuFNUhN+rEQiHO82ePZvhTtWAsQ8CFQRIJirg8BUCPgnoyaye0E6fPt2nYlNWBwQWLlwYvOXa14nMEydONCVEPGV24GbyqAiagK1kVL1ybAggUL8AyUT9dhyJgFMCzz//fDAhVf84siFQrUDYm+XT8KZo3fSUWU+YecocleH3jgS02IAWHdBcMzYEEKhPgGSiPjeOQsApAT2V1fhfPaFlQ6BaAU1gzktvVviUeePGjdVWn/0QCJYVVkKxePFiNBBAoE4BVnOqE47D2gpEZ/e33YNPkhIYP368V6vwJOXAeWsT0BNZbVpiNQ+bhvpdddVV9sknn/DuiTwENKU6hKuCaYjosGHDUroql6kkQHuikk7230XjQ89E9jGhBAg0JKBhKtdcc403y3k2VFkOjk1Awzr0grpJkybFds6sT6Q5Hy+++KJpyB8bAtUKhMPkNHdIiQUbAgjUJkAyUZsXeyPglECehqk4BVuAwmhYh4Z3+DrpulyINNRPQ/409I8NgWoFGCZXrRT7IdBWgGSirQmfIOCNgMaHjxo1KliRxJtCU9DMBdTQ3rZtm40dOzbzssRdAD1lVpK0cuXKuE/N+XIuMHXq1OCN6vRO5DzQVC92AZKJ2Ek5IQLpCOgfvGeeecb0DyAbArUIqKE9d+5cU8M7j5uSJCVM9E7kMbrJ1Ukr4enhDJP4kzPmzPkUIJnIZ1ypVQEE9A/elClT6JUoQKzjrKLexaBGts9LwXbkoSRJk2k1Bp4NgVoE1KulhzT0TtSixr5FFyCZKPodQP29FAh7JfI0edbLQHhYaL2LoQgvNtSqPKdOneJFdh7eo1kWWXOI9JCG3okso8C1fRMgmfAtYpQXAbPgHzr9g5e3ybMEN1mBcNhPUZa/VNL00ksvJYvK2XMnoIc09E7kLqxUKEEBkokEcTk1AkkIhL0SercEGwK1CGiuRBF6JUITJU3MnQg1+LNaAT2k0d+v9E5UK8Z+RRcgmSj6HUD9vRPQP3CaJNi9e3fvyk6BsxNQo1orOBWlVyKUfuSRR1jZKcTgz6oF7r33XnonqtZix6ILkEwU/Q6g/t4J6EVjrODkXdgyL/BPfvKTYMnUzAuScgFGjBgRJFF6SR8bAtUKhCs77d27t9pD2A+BwgqQTBQ29FTcR4GdO3cGb7vWP3RsCFQrcPr0aXvqqady+V6Jjgy0stO0adOCF9l1tC/fI1AqoLkTrAhWKsLPCLQvQDLRvgufIuCkwKpVq+yBBx5wsmwUyl2BV155xZYsWZLb90p0JH/33Xfbo48+ynKfHUHx/SUCeiu2Ni2nzIYAAuUFSCbK2/ANAk4JaJjG/v37Czfm3akgeFgYTdhfunRpMKHUw+LHUmRNqJ03bx4TamPRLNZJNOfm1VdfLValqS0CNQqQTNQIxu4IZCWwfv36YLhGVtfnun4KaMw3E/bNNKFW843YEKhFQHNuNERQQwXZEECgfQGSifZd+BQBpwT0dFkNIQ3XYEOgFgENjRs3blwth+Ry33CeEUNWchnexCqlOTcaIqiV0NgQQKB9AZKJ9l34FAGnBMKny7ykzqmwOF8YPU3V0LhBgwY5X9Y0CqgXPe7YsSONS3GNHAk0NzfTq5WjeFKV+AVIJuI35YwIxC7A0+XYSQtxQk28VgNaT1fZLBjuxURs7oRaBejVqlWM/YsmQDJRtIhTX+8EeLrsXcicKXBLS0uhJ15HAxFOxObdAVEZfu9IgF6tjoT4vsgCJBNFjj5190Jgz549PF32IlJuFTKcG8Cb0i+Ny8iRI23Dhg2XfshvCHQgoEUMmMDfARJfF1aAZKKwoafivgisW7fOhg8f7ktxKacjApobMGHCBEdK404xNH9ELyJjdR53YuJDSdSrNWDAAN454UOwKGPqAiQTqZNzQQSqFwiHOIUvT6r+SPYsuoCeot5xxx1FZ2hTf80f0Tsn1OPHhkAtAhMnTmQCfy1g7FsYAZKJwoSaivooEA5x8rHslDk7gcOHD1u3bt2MIU7tx0BDnUgm2rfh0/ICgwcPZqhTeR6+KbAAyUSBg0/V3RdgiJP7MXKxhLt27WKIU4XAaKiTXkSm97ewIVCtAEOdqpViv6IJkEwULeLU1xsBDXFauXKl9e3b15syU1A3BLSK09ChQ90ojIOl0FCn6dOnG6s6ORgcx4ukN2K//fbbjpeS4iGQrgDJRLreXA2BqgUOHjwYjO3mHQFVk7GjWTCx+MSJExaujQ9K+wKjR4+2t956q/0v+RSBMgKah6RknQ0BBL4UIOyAcfcAACAASURBVJn40oKfEHBKQA0djdFlQ6AWAc0FGD9+fC2HFHLfW265hfHvhYx8Y5XWPCQl66wG1pgjR+dLgGQiX/GkNjkS0Go8avCwIVCLgJIJTTBmqyygRqEmqR8/frzyjnyLQERAyToT+CMo/FpoAZKJQoefyrsqoAYOq/G4Gh23y7V+/Xq7+eab3S6kI6XTUKdf/vKXjpSGYvgiwGpgvkSKcqYlQDKRljTXQaAGATVw1NBhQ6AWgTAJ1aozbB0L3HbbbTxh7piJPSICStaVtLMhgMAXAiQT3AkIOCigLnQm0DoYGMeLRBJaW4BoFNbmxd5fCITJOkPkuCMQ+EKAZII7AQEHBfTUi/kSDgbG8SKRhNYWIBqFtXmx95cCmjfBELkvPfip2AIkE8WOP7V3UCBcJYS3FzsYHMeLtHv3bpLQGmOkRuHRo0drPIrdiy6glfb0pnk2BBAwI5ngLkDAMYEPPvjARo0a5VipKI7rAkpCN2zYYCShtUWqX79+vG+iNjL2NrNevXrZ/v37sUAAASOZ4CZAwDmB9957j7cXOxcV9wukJFRvdWarTaB///40CmsjY2+zYE7bypUrsUAAAZIJ7gEE3BPYtWuX9e7d272CUSKnBZSEqmHMVptAjx49jEZhbWbs/YXA1KlTGerEzYAAyQT3AALuCWzbts169uzpXsEokdMC77zzjt14441Ol9HFwnXq1MnGjRvHy+tcDI7jZRowYIAdOXLE8VJSPASSF2DORPLGXAGBqgU+++wze+ONNyxcZabqA9mx8ALvv/++XXPNNYV3qAdAyzB//PHH9RzKMQUW0ItFP/zwwwILUHUEvhAgmeBOQMAhgWPHjjHu3aF4+FQUDdXh3ST1RWzo0KGmYWJsCNQioGGFBw4cqOUQ9kUglwIkE7kMK5XyVUBd5gxx8jV62ZVbL8/SUB22+gSuvfZa0zAxNgRqEbj66qtNw1LZECi6AMlE0e8A6u+UwLlz50xd52wI1CJw/vx5eiVqAYvsq+FhZ86ciXzKrwhUFtBwVA1LZUOg6AIkE0W/A6i/UwKs5ORUOLwpjIZasJJT/eHSik4LFy6s/wQcWVgBVnQqbOipeIkAyUQJBj8i4IJA586dXSgGZfBM4PLLL/esxO4UVys6sSFQj8CVV15Zz2Ecg0CuBEgmchVOKuO7gJ6O6ikpGwK1CNCjVYtW+/vyhLl9Fz6tLMAk7Mo+fFsMAZKJYsSZWnokwFNSj4LlUFHp0WosGDxhbsyvqEfTI1jUyFPvUgGSiVINfkYgQwFW5MkQ3/NLq0dLK8uw1S+gVdR4AVn9fkU9UskEK4EVNfrUOxQgmQgl+BOBjAVYkSfjAHh+eV502FgAtYqaVlNjQ6AWgV69erESWC1g7JtLAZKJXIaVSiGAAAIIIIAAAgggkLwAyUTyxlwBgaoEeGFdVUzsFBE4fPiwafIwW2MCenGdJrKzIVCLAC+uq0WLffMqQDKR18hSL+8EeGGddyFzpsBMHm48FHpxHRsCtQrw4rpaxdg/jwIkE3mMKnVCAAEEEEAAAQQQQCAFAZKJFJC5BAIIIIAAAggggAACeRS4LI+Vok4IIIAAAukIaM5GuJ06dco++uij8NcO/9SymloNJ9w0/pxVqUIN/kQAAQT8ECCZ8CNOlLIAAidOnLA+ffoUoKZUMU6BAwcOmN7Cm8T22Wef2bFjxyxMErSe/pkzZ2zbtm32xhtvBJfU5O/SORtDhw6tuihKRLZs2XJx/9LzTp8+PfhcdVPSoT/1Yr7u3btf3D/OH/Tmeb2vY8GCBXGelnMVQOD222+306dPkwgXINZUsX0Bkon2XfgUgdQFPvjgA2tubk79ulzQf4E43sKrlyYePXrU3n33XVOCEjbs1ajv0qWL9evXz0aOHGmaqPzYY48l1qhXNMIkRj+rLFqcYOXKlabkY8OGDcHqVQMGDDC9G0JJRhxJOG+e9/+/g6xqMGrUKPv4449JJrIKANfNXIBkIvMQUAAEEEAgfQE1zNVQ13KoShy0jR8/PkgaJk2aZE8++WRmjSM17MMEIfwzFAoTDS2lrDps3LgxSDTUQzJixAi78cYb7eabb86s7GE5+RMBBBAoigDJRFEiTT0RQKDQAup5+OUvfxkMK9JwnrDxPW7cuEwTh1qDEiYaSjLCnrwVK1YEiYWSI/VcDB8+3FSvCRMm2K233mp9+/Y1eh5qlWZ/BBBAoDoBkonqnNgLAQQQ8E5g3759tmPHjiCB0JycKVOmBI3sOXPm5K5xreRC/1MCoXkPYc/LD37wg6DnYt68eTZ48ODgf0zy9u5WpsAIIOCwAMmEw8GhaAgggECtAmECsXr16mBOgRrXS5cuTXSOQ61lTGP/0uRi8eLFtnfvXnv99ddtzJgxQa/MxIkTSSzSCATXQACB3As0tba2tpbWsqmpySIflX7NzwiUFeDeKUtT1Rdq8JUO3ajqIHYqvEBLS4tp8r6etuse0qRk9UBoUihP4NveHppzESYWTz31lKnHQhPLBw0aFKwWxb9/bc34pLKA/u375JNP+O+tMlNN39KeqIkr9Z2j8SGZSD0E+b1g9ObKb02TqZkahdr0JJkNgY4EwkbxX/3VX9n27dtNDWNNoE5q6dSOyuPj96HhqlWr7Oc//7lde+219uMf/5hGoY/BzLDM/NsXPz6m8ZvGecZofEgm4tQt+LmiN1fBOWquPslEzWSFPEDr2b/00kumYUzqfdATdT1p5/0Ijd0Of/d3f2ff//737Te/+U3gqgncw4YNa+ykHF0IAf7tiz/MmMZvGucZo/H5Spwn51wIIIAAAskIaELx/Pnz7c477wwu8NprrwUJhJIJtsYFrrvuOrvtttuCeRVKJLTilXp6Nm/eHLz3ovErcAYEEEAgnwIkE/mMK7VCAIGcCCiJmDFjhk2ePDl4B4QmEU+bNo2hOAnFV0vIqkdi/fr1QbKmN3RrToV6DjUsig0BBBBA4FIBkolLPfgNgcwE9BZjLd/JhoAEwiRCiYSelO/evTuYT9Pe+xK0L1tjAqdOnWpzAi2IoOFja9asCV7uR1LRhqjwH2jY4e233154BwCKLUAyUez4U3uHBHr16hWsyuNQkShKBgLRJEJPyCuN3VeDVy9qY2tM4KOPPrKhQ4e2exKSinZZ+NDMPv7442CODRgIFFmAZKLI0afuCCDgjIDeUB0OZxo9enQwzKZSEuFMwQtUkPaSip07dxZIgKoigAACbQVIJtqa8AkCmQh07tw5GNqSycW5aGYCGoev90P06NEjeDKuORHNzc01lUfDLDTcgq1+AQ0x1FDDarbSpCKcqM1Qs2rk8rfPkSNHrEuXLvmrGDVCoAYBkokasNgVgSQF9H4AhqskKezeubVSkMbhnz17Nnjpld4x0t6ciI5KriViNdyCrX4BvfhPQw1r2ZRUaBjaI488EkyQ12pbJHW1CPq/77lz54KFEfyvCTVAoH4Bkon67TgSgUQEWDEmEVanTqohTQ899JAtW7YsmNw7c+bMhldnOn/+vFN19K0wn376ad1FVk+SepT0QEBL94bvjKn7hBzojYCSCTYEii5AMlH0O4D6OyUwffp0O3bsmFNlojDxCShR1Mvm1AMxduzY4Km2nm43umni8HvvvdfoaQp9/MqVK62RWKhHacqUKUFyuHHjxiBZVNLIlm+BAwcOWP/+/fNdSWqHQAcCJBMdAPE1AmkL8IQ5bfF0rqcx9ffdd5+p8aEXzimhiHPjCWn9mnH2BiohWbFiRZAsah4MvRT1x8WHIxvp0fKhfpQRgWoESCaqUWIfBFIS4AlzStApX0YNSr10TmPr9d6Crl27xloCPRlVksJWn4B6A9UrGOemZFHnpZciTlX3ztVoj5Z7NaJECNQucFnth3AEAggkJaDVZFgVJind9M+rYS5z5swJLqzeiLiTiLBGrAQWStT3p15Yl8SKPJpDoV4KJZPqpdi0aVPNK3XVVyOOSkOAF9alocw1fBCgZ8KHKFHGwgjw4rr8hFrvHwjnRqhBmVQiITFWAmvsvtEL6/r169fYSSocHfZSaMK9VnyKc1hVhcvyVcICvLAuYWBO740AyYQ3oaKgRRDQ00utW8/mr4AainpvxOOPPx5Mxo17bkQ5malTp9KrVQ6ng8937dplvXv37mCvxr5Wwrd27drgJJo7w+TsxjxdOJrJ1y5EgTK4IEAy4UIUKAMCvxXQijC8gMzf20ENxMcee8z0zgItFdrI6kC1Ktxwww2m4TpstQtoaOHVV19d+4E1HqH/vrUMsObO6MEBb8+uEdCx3fWiw+uuu86xUlEcBNIXIJlI35wrIlBRQC8gU2OUzS8BNUjVCzFixIhgknU9L59rpMYapvPuu+82copCHqueJL0sUj0HaW16L4UmZ6v3Sr1YbH4K7N+/v+YXHfpZU0qNQGUBkonKPnyLQOoCrOiUOnnDF9SbrLVa06JFi4J3DTR8wjpOwIpOdaCZBY36uFdyqqYkSl7Ue6UGqV5gyDyKatTc2oeVnNyKB6XJToBkIjt7roxAuwIau60x3Gx+COjJ8qxZs4IVe4YNG5ZZoTVMh/k2tfNnOe5dvVeanD9gwIDgHSTMo6g9flkdoZ5IzVNiQwABM5IJ7gIEHBPo2bOnbdu2zbFSUZyogJ4kz5gxI3iyrCfMaQ6TiZZFv2u1qHHjxjGxtz2cCp+98847duONN1bYI/mvpk2bFsyj0DA5loZO3juOKxw5ciRIAuM4F+dAwHcBkgnfI0j5cyegRmG3bt1oFDocWSUSmmitdxMsXrzY0p4fUY5myJAh9stf/rLc13zejsD69evt61//ejvfpPuR5lFomFzfvn2ZmJ0ufV1X27Nnj9122211HctBCORNgGQibxGlPrkQoFHobhjDFZs0NEUr87iSSEhs8ODBPNmu4dbRS8e0Zd2rFBZZw+TCidms9BSquPmnK0momzqUqmgCJBNFizj19UKARqGbYVIioaEoSiQ0NMW17ZZbbrEtW7a4Vixny3Pw4EEbP368U+VTYqM3ZmulJ03sZ3NPwLUk1D0hSlQ0AZKJokWc+nohQKPQvTCFicTcuXOdTCQkpoao1r4PGzvuKbpVorfeeivozXGrVF/EUQmFJvazdKxr0THTECfXklD3lChRkQRIJooUberqjUDYKGR1FzdCFiYSGtOuse0ub2rk6Ik7W8cC6sVR4u7iFvZQrF69moTCsQApmVDvMRsCCHwhQDLBnYCAowJTpkxhMq0DsSlNJLJc+rVaCjVytLoUW2UBxVW9OGq0u7qRULgZGc2XIJlwMzaUKhsBkols3LkqAh0KaKUQPQFjy07At0RCUmrkqLGT3XbMWu6/yZqamqyp6W577s0zZhdO2u5F91u3pia76bk37fPsCnfxylr1Sgm761tpQsEciuyjpb8TtNqeVt1jQwCBLwRIJrgTEHBUYNCgQfbUU0/xZtyM4qPlXzXZWhOtfeiRCJnCpYWze19BD5vw4q/sn4+/bN+5/m/tL/56k/30r5bbgbFL7ERrq/3qz79hl4WFzfBPDXHyZWnPMKHQHApWecrwpjGzrVu3Bn8vZFsKro6AWwIkE27Fg9IgcFFAS47qDauHDh26+Bk/pCMQvkdCT659eHodVVESlPVb1L/yu//G/u2ffsNOLphr/9fXH7AH+l0RLWZmvyu+elu4EnZftjCh0CpPJBTZRW379u126623ZlcAroyAgwIkEw4GhSIhEApMnDjRduzYEf7KnykIhImEq8u/VkNwxx13BMuLVrNvcvt0tcFjmu16u9mG9b/WXPrHZu/evTZv3jyn3hFSTRyUUKxZs8aGDx/O+0SqAYt5H62Stn//fhs4cGDMZ+Z0CPgt4NLf735LUnoEEhDQ+Het5sKWnsALL7wQXMzF90hUq6BGpyYXa3x3dtvn9g9nzprZDvvxjiN2IbuCtLmyJqj7OoG2T58+wQOGyZMnZxzfNqy5/0Bz2Hzsqcx9YKhg5gIkE5mHgAIgUF5A49/1hHzfvn3ld+Kb2ASUuOnJ4+LFi2M7Z1YnUqNH47uz2i78+hX7/t/+S7tvlNkvDp2wc1kVJHJd9TxpLpKvyYSqozk84ftOVB+2dATWrVsX9AqlczWugoA/AiQT/sSKkhZUgKFO6QRe49D1grCnn37au+Ev7QnpfRh68Vkm24Wjtv77P7fm//y0/fs/HW4nf7TF9vx6ly2aucF+nXEXhYY4TZ8+3fvVeBTf0aNH22OPPZZJiIt2UYY4FS3i1LcWAZKJWrTYF4EMBMKhTjyBTA5fw4E0Dl3j0TVEKA+bhsNoS3VVp8/ftOduarKmP/ovZn/2lE343cut24A/sFEnV9n3F5+wb8/8Y/vdjP/V2bBhg40bNy4PIb74Jnbekp18OLdt28YQp+SZuYKnAk2tra2tpWXX2uCRj0q/5mcEygpw75SlafiLhx56yB544AGvlihtuNIpnUBJ2siRI01vt/ZpCdhqeDRs6+zZsxcbndUck+d99HT5qquusvPnz+ei90mxyvP969K9qDfLz549m8nXKQWF9kRK0HVeJhqfjJ8R1VkLDkOgYAJKJPRElS1+AQ1r0vyCvCUSkrr77ruDCfz0an1x3+jp8pIlS3KTSKhWWkJaw9nUs5bthPv4/9t05Yxh7x6rOLkSEcrhmgDJhGsRoTwItCOg9fDVENKTVbb4BNQI+/TTT+3BBx+M76QOnSmcwK95AmwWJFZqdOdt09C8TZs2BT1QJI7xR1dvHmcVp/hdOWN+BEgm8hNLapJjAT191D9mr7zySo5rmW7V9LTxmWeeyc2E63J69Gp9IROuiJbXp8uakD1kyJBguF65e4HPaxdQcvboo4/aqFGjaj+YIxAoiADJREECTTX9F9CYXSZaxhNHNRC0Tr/mSeRlwnU5mbBXq+hDYF599dXcP13W27F3795tepLOFo+A3nitFxyql48NAQTaFyCZaN+FTxFwTkCNXr1zQkuYsjUmoCRCyVke50lEZdSrpRfwrV+/PvpVYX7X8EC9W2Ls2LG5rrNirQcOs2bNYv5ETJFetmyZ3XXXXTGdjdMgkE8Bkol8xpVa5VRAQ1ZWrVqV09qlUy09tdXTWz3FLcqmidgaqlHU8fQaHpi3idfl7l09dHjyySdtzpw55Xbh8yoF8j40rkoGdkOgQwGSiQ6J2AEBdwT0JP3UqVPpvjvAneo3XBI9odZT2wULFuRqRZ+OYDREQ0M1Nm7c2NGuufteCZSe1qsnqijbhAkTgqpm9tLCnEC/9NJLwQsOc1IdqoFAYgIkE4nRcmIEkhHQROyVK1cmc/Kcn1UTrjXkJ3yhW86re0n17r333mDCedF6J5RAafJs3ufGXBJss2BhgXvuuYfhTlGYKn/XAg1aQU9zjtgQQKCyAMlEZR++RcA5AY371j9yRZ9QW2tgNNdEDYSJEyfWemgu9lcCpUZ10ZaJ1Yv7pk6dmosY1lIJJU8vv/wyw51qQSvZ9yc/+UkwXEzzUNgQQKCyAMlEZR++RcA5Af3jpjHRRZ5QW2tQ9DRecySKNrwp6qRG9cKFC6Mf5/Z3JZBKoorYE6WghsOdWN2ptltcwyH192veJ+zXpsLeCJQXIJkob8M3CDgroH/k9MSVl9hVF6IXXnghGDNf1EZlqBQ2rIuyIpgSpyL2SoTx1p/Tp08P5gnxd0WpSuWfNVdCD2zolajsxLcIhAIkE6EEfyLgkUDYO6F/9NgqC2hokxKvIq3eVEmkKL0TRe+VCO8BJZCaZ/X888+HH/FnBQElXfr7gl6JCkh8hUBEgGQiAsKvCPgiEPZOqLHMVl5AT6fnzp3LU8bfEoW9E3ke+qJhbfRKfPnfxIMPPhgM2+Hvii9Nyv2kRRrolSinw+cItC9AMtG+C58i4LxA2DvByk7lQ6Wn01pKt7m5ufxOBfxGvRNaIjevKztpBacwaSpgeNtUWX9XKKEu0nyZNghVfKBkS4tb0CtRBRa7IFAiQDJRgsGPCPgmoH/09I8fTxzbRq500nXbb4v9iRraWtkpj++dUNz1dLnocyWid7gSaiXWRZkvE61/Nb/rwQy9EtVIsQ8ClwqQTFzqwW8IeCWgJ46LFi2yGTNmeFXuNAobvl9ADWe2tgKPPfZY0OjO28TcdevWMdm+bbiDT7SameYO5bVHqky1q/pYSZYeyoQrYFV1EDshgEAgQDLBjYCA5wJ6K7a2PI+BrzVE4dNpNZjZ2hfQewg0MTdPk/iVGN1///323e9+t/1KF/zTPPdINRJa/X2hIWBa+YoNAQRqFyCZqN2MIxBwTkBPHPM8Br5WcC0Fq4Zy0d56XKuTJuZq5Zq8DJPT8Ca9qK1r1661UhRmfw3/khO9E1+GPJxjEz6Y+fIbfkIAgWoEmlpbW1tLd2xqarLIR6Vf8zMCZQW4d8rSpPLF/Pnzg8azGtFF3vR0+qqrrrJPPvmERmUVN4J6tDQ0aMWKFVXs7e4u+/bts9mzZ9vatWtZuauDMGlY5NChQxnSYxa8q0d/Xxw7doyHDx3cN2l+TXsiTe3arxWNDz0TtRtyBAJOCmhox9KlS3PzlLleZA3bWbJkCYlElYDhSlctLS1VHuHebnrK/vDDDwfJhOYRsVUWoHfiSx/10rz44oskEl+S8BMCNQuQTNRMxgEIuCmgoR1FX/5RvRKPPvqoTZo0yc0gOVoqjRVXo8rXydjqWdHqVAMHDnRU2K1iMXfii3ioN0tD/CZOnOhWgCgNAp4JkEx4FjCKi0AlgTw8Za5Uv46+0zK59Ep0pNT2ezUup02bFiQUbb91+xM1BtUjpyU92aoXKHrvBL1Z1d8r7IlARwIkEx0J8T0Cngk8/fTTds8999jx48c9K3ljxVXjQE/Xx48f39iJCnq0ns6qYe7TqmCKucb/q0eOSde13bhh78TevXtrOzAne2tJbf1dQW9WTgJKNTIVIJnIlJ+LIxC/gFYw0oo2c+bMif/kDp9x+/btwVAXVnCqL0iaaxCuCubLcCcNb1KjOOyRq6/mxT1KwwGL+FZsDW9av3598M6N4kafmiMQnwDJRHyWnAkBZwTCFy/5PKm2Vsxly5bx1uNa0SL7+zTcieFNkeDV8Wv4VF6N66Js4fCm5cuXs+pXUYJOPRMXIJlInJgLIJCNgIY7adiPGl1538LGkBrDbI0JaLjTp59+ai4nomoQTp48OXj7O8ObGou3Jt/n6cWFHWno70Utnx0mUh3tz/cIINCxAMlEx0bsgYCXAhruo7HkGlOuxleeNzWGHnnkkTxXMbW6abiT6/NuwvHuvGSs8dti0KBBpoULfBna1kiNNR9ID1f0skY2BBCIT4CX1sVnWfgzRV9iUngQRwD0MjttM2fOdKRE8RZDjSC9dOr8+fMMW4iRVg0vDR1z7SVwrpYrRvrUT6XVsK644orgiX3qF0/pglqQokePHrycLiXvRi9De6JRwWSPj8aHnolkvTk7ApkLPP7447Z7926vVumpBe2VV14JloPlZWW1qHW8ryY1DxkyJBhK1PHe6eyhBuGYMWOCpWCJd3zmWtVICUVeN/XMaunjTZs28XK6vAaZemUqQDKRKT8XRyB5ATW61FCYNWtWLudPaGw/q/kkcx+FiagL8yfUINTCAjQI44+1hkQOGDDAdu7cGf/JHTijhu2NHj2avycciAVFyKcAyUQ+40qtELhEQI0FjTPXpNU8jY1m4vUlYY79lzARdWEifzhxlsQx9jAHJ9TE+9dffz2Zk2d41tWrVwcLCjBPIsMgcOncCzBnIvchTq+C0TF06V2ZK1UroB6K/fv32+LFi3Mxv0D16datW/DEuloD9qtdQE+s1UuhHoos3uORt/u29ggkf4R6fjp37pyruUdZ37fJRy2/V6A94XZso/EhmXA7Xl6VLnpzeVX4AhVWqzv17NkzGEPse7U1pv+1117j7ccpBFKJxMaNG1NPRMMGoZ6aM08i2UBrsYaRI0daHlbJ0vwaDYtbs2ZN8GLDZOU4e9wCtCfiFo33fNH4MMwpXl/OhoDzAnoztnon1P3v86YhThrnzXsG0omiGmbyfuyxx9K5oJkpxmGPCIlE8uxKJFatWpX8hRK+goZy6n7V0E7ePZMwNqdHwMxIJrgNECiYgBplGn+uoSM+T7jcsWOHaZw3W3oC4bhz3TtJb3qy/PDDDwcNwiyGViVdPxfPr3dOrFy50uv30mi41hNPPBEsc5uHHhYX7xPKhEBUgGQiKsLvCBRAQI0zDVvRU19fEwr1rAwePLgA0XKnikpENd9GPVtJJhThEBU9WaZBmF78Fd958+bZ3r1707tojFdSIqGeM/WgaSlYNgQQSEeAZCIdZ66CgHMCSiiWL19uw4cPNzXefNoY4pRdtMKeLSVzSSSiahBqKN6UKVNIJDIIs4Y6+bqqk5JPbSQSGdw4XLLQAiQThQ4/lS+6wMCBA03DhTS+2KeE4u2337YRI0YUPXyZ1T+pni2eLGcW0osXvvnmm+2pp566+LsvP6in7P333w96znwpM+VEIC8CJBN5iST1QKBOAQ0j0RM9nxIKDdEaOnRonTXmsDgE4k4oSCTiiErj59CCBlOnTg0mvzd+tnTOoEQiT0tep6PGVRCIT4BkIj5LzoSAtwI+JRRaqeXEiROs0uLA3RZXQkEi4UAwS4qgXj/1/vmwkUj4ECXKmHcBkom8R5j6IVClgC8JxcGDB238+PFV1ordkhZoNKEgkUg6QrWfX71+27dvr/3AlI8gkUgZnMshUEaAZKIMDB8jUEQBHxIKTQ5lFSe37s56EwoSCbfiGJZG72ZwfYlYEokwWvyJQPYCJBPZx4ASIOCUQGlCcfjwYafKpsKsX7/ebrnlFufKVfQC1ZpQkEi4fcdMnz7dDh065Fwhdd+QSDgXFgpUcAGSiYLfAFQfgfYEwoSib9++iSz/2d41q/lM8yW0qeHK5p5AaUKhBl+5TSuHaQlS3gdQTij7zzXUEgWEfgAAIABJREFUybV5E2ECymTr7O8PSoBAqQDJRKkGPyOAwEUBJRR6MqkX223evPni51n+wHyJLPWru7YSitdee63si+3CF9LNnTuX9wFUR5rJXv3793dq3oQeJIQvpNOLE/W+EzYEEHBDoKm1tbW1tChNTU0W+aj0a35GoKwA905ZGq+/CBt/eolY1i+D0ovSLr/88mAZW69RC1D48Cmyqho2/vSSO70kUe82UbLK5q6A4te5c2cn2gMu/R3kbsTyVTLaE27HMxofeibcjhelQyBzAT1p1qRnDS2YMWOGqZGR1aYVZvTElM19AT05VhKhoUz33Xef/eVf/mXQy6XeLhIJP+Kn901kPW9KCajegaN34WT9MMP9qFFCBLIRIJnIxp2rIuCVQNgw7NKlSzDUQE8Ks9i0wkyPHj2yuDTXrENA982DDz5oX/va12z+/Pn2/e9/n/eD1OGY1SFKBI8cOZLV5U0vp9Qwy+XLl5OAZhYFLoxAxwIkEx0bsQcCCJgFY5RnzpxpY8eODZ4U7tu3L1UXJTDjxo1jrHSq6o1dTDHTOPff//3ft7/5m7+x733ve0EDsbGzcnRaAloiNoueCfV+KvncuHFjcL8MHDgwrSpzHQQQqEOAZKIONA5BoMgCGnKgJ4UPP/ywaQ5DWtvRo0dtyJAhaV2O6zQoEA5PUfKpJPSb3/xm0DBUAzHr4XINVq0wh/fq1cs++OCDVOurBFTD4rRpmBwrt6XKz8UQqEuACdh1sXFQewLRCTnt7cNn+RHQ6ipPPPFEUKFnn33WunbtmmjlNORBm5IZNncF9FT5hRdeCBLNNWvWtBnW1NH37taseCVTrNKchK1V48aMGWObNm2y5ubm4oFT44sCtCcuUjj5QzQ+9Ew4GSYKhYD7AkoeVqxYYSNGjLA777zTkh72tGvXLuvdu7f7MAUuYTisSU+zNWlfw2Sim+ZRaCKtJtROnjyZYU9RIId+V6xuv/12C9/vklTRwmFNy5Yts2PHjpFIJAXNeRFISIBkIiFYTotAUQS0ZGw47EnjnNUwSGLT2G09JWVzU0BPlTU5XsOaFixY0OHcFq3opN4mDXt66KGHEm+wuqnmfqlGjRplH3/8cWIF1UMIvcBQ29q1axnWlJg0J0YgOQGSieRsOTMChRHQBEk9idam8c5JTNrcsGFDu0+6C4PsaEX11FpzINatWxc8Va5lGJrGw6t3SwmIerdceTmio9SZFKtnz5524MCB2K+thw6ac6W5V3oYoXk16glhQwAB/wRIJvyLGSVGwEkBNQTUIJg9e3YwfGXp0qWx9VKowarhFmxuCahnQUmA3v3RyGRZJSCaX6FhLkpMNFyKzQ2Bbt26xV4Q9UbooYPirIcQrNYUOzEnRCBVAZKJVLm5GAL5Fwh7Kc6ePRsMX9CqPo1uGmah4RZsbgioEaihSeHSnRrq1uhTZc2vWL9+vQ0dOjQYLhVOuHejxsUtheYpab5SHJseCmgopHoj9NCB3og4VDkHAtkLkExkHwNKgEDuBMJeCg1fWLhwYcNPm0+dOmV6YR5btgLh0BT1JGhokoYoxb10p86tSbhqwI4fPz6RIXPZKvp19bjmKYW9WFdccQW9EX7dApQWgQ4FSCY6JGIHBBCoV0C9FJpUGT5t1hjpeiZof/TRR9avX796i8FxMQhoPoMmyqpX4rXXXkt0iV4lKJrEPX369GDInIY+Jb2iUAxEuTzF1Vdfbdu2bau7bpo/paRQvVgayqaVvBrtxaq7MByIAAKJCJBMJMLKSRFAIBRQw0FPmz/55JOgIaoGKUNYQh33/wwbg5pgrcaghqYk/U6RUEUrPmlMvZLRq666KpiwW08yGp6PP2sXUKzfeOONmg9U0qkkUMv/KilUL1Z7SwXXfGIOQAAB5wRIJpwLCQVCIJ8CapSoIaoGaTiEpdr5FLxjIv17QkmEGoP6X5aNwdJkNJyHo2SUpCLde6Jab/UgafEFPUBQEqhkUEkhGwII5FeAZCK/saVmCDgpoKeT4RAWzafQEIhqkoq4xm47ieJQocIkQk+U1RjUMDUXGoNKRjVEJkxGwx6uahu5DhF7VxQlk5rHUmkLkwj1IGkLh8IxpKmSGt8hkA8Bkol8xJFaIOCdgBqoWr1HDZVakgrvKupJgaNJhJ4o6+mya43BMBklqXDjxoomERrOqKQvraFwbihQCgSKLdDU2traWkrQ1NRkkY9Kv+ZnBMoKcO+UpeGLKgTUO7Fq1SrTyk1aalSrBYUN2SFDhgRPOmmgVAFZ4y6V3Gs8VSa7Kwn6yU9+EiSmum8mTZpEQzbmSGio29SpUy+Z84B7zMic7hIB2hOXcDj3SzQ+JBPOhcjfAkVvLn9rQsmzFFAjZeXKlcEKMmHjUEMneMgRX1Q0NEir62h1LW3qHXJhKFMjNdQT8pdeeskeffRRmzdvnt17772XNH4bOXfRj1UyoSRNq7OFyef+/fvtySefvCTpL7oT9Y9PgPZEfJZJnCkaH5KJJJQLes7ozVVQBqodk0DYOFSDV6vJ7NixwwYNGnSxtyKmyxTqNErUtMRrnhvc0UTpkUcesREjRnDfNHCnayWmX/ziF8HCCQMGDLAHHnjA++SzAQ4OTUGA9kQKyA1cIhofkokGMDn0UoHozXXpt/yGQH0Cahxq8rWGWehpqHormpubeepcJaeSsldeeeXicrzy09vEizBkbN++ffbqq6/aU089FfRW3HXXXcHT9SrpCr2b/rvbvn27aUlgvWdC98zTTz8d+0sKC41M5csK0J4oS+PEF9H4kEw4EZZ8FCJ6c+WjVtTCBYHw3oo2jDVB+I477qCBEwmSnPbs2RM0BEnALFhGNmwYhx7Dhw8nsYjcN0og9u7dGyznGiZgWjVLL43Upv/e2BBIQyD8Oz+Na3GN2gWi8SGZqN2QI8oIRG+uMrvxMQI1C7R3b+mlWFu3br34xF0NnVtvvbWwDUR57N69O5gLQYO5/C3WXqJ12223FXYIXeixZcuWYFU1zTdRAlE6pDB8ySTJRPn7im/iFWjv7/x4r8DZGhGIxodkohFNjr1EIHpzXfIlvyDQgEBH91aYWOjpsyZvq0E0ePBgu+WWW3Lba6FG4MGDB+2tt94KJlJ369bNRo8ebTxxr/5GizakNZROq4j1798/t8Po1Ptw6NAhe/vtt4NE/MSJE8G7XqIJRKkiyUSpBj+nIdDR3/lplIFrlBeIxodkorwV39QoEL25ajyc3REoK1DLvVXayNbT1rCx1K9fP68biUqYjh49GiQPqteGDRsKkTSVvSli/qK0kR0mpVrlSi/u6927t/Xt29fLSdzhfw/vvvtuMAdCyXZYr2qTJpKJmG82TtehQC1/53d4MnaIXSAaH5KJ2ImLe8LozVVcCWoet0Aj91bYmNITfA3/UWNKT6C1Ko2e5qtBdfXVVzszIVmNWr1t+MiRI/bhhx/agQMHguEn48aNM71vI+89LnHfO/WerzS5iMZAiakSDN033bt3r/cSsR+n1br0nhbNcdi1a1cwcVoX0eRpJUXVJg/RgpFMREX4PWmBRv7OT7psnN8sGh+SCe6K2ASiN1dsJ+ZEhReI+95So6u0sa7VarT8rJ7YalPDS5saX9riTDbCZEHnVRnOnTtn77zzjp05cyZo/IXl6NKli4W9KT169PDyqXiAl6P/C3uH9JRfCUZ43yg5vfLKK4P75fLLLw8SDa1Apv/FmWzovtUWJgzqdfvggw9Mn6unSuW44YYbgvtGyU7Pnj1jSZJJJnJ0E3tSlbj/zvek2t4UMxofkglvQud+QaM3l/slpoS+CKRxb4WN/LChpka+GozawkZj6BU2HsPfO/pz4cKFl+wSJi1q7Kl3RA3QXr16xZq0XHJBfklUQI358+fP23vvvRdcR70C2sJGfnhx9S716dMn/LXDP8vdd2GiqRMo4Y07aYkWjGQiKsLvSQuk8Xd+0nXI8/mj8SGZyHO0U65b9OZK+fJcLscCrt1b4RPiasnpWahWKt/7qWdDSUe1W5w9YtVes739SCbaU+GzJAVc+zs/ybr6eO5ofC7zsRKUGQEEEMhSoJany1mWk2u7JRDnkKc0a6Zeuuuuuy7NS3ItBBDwSOArHpWVoiKAAAIIIIBAygIa7qdheGwIIIBAewIkE+2p8BkCCDgloDkKtQ4tcqoCFAYBBBBAAIGcCpBM5DSwVAuBPAlopRw2BBBAAAEEEHBPgGTCvZhQIgQQQAABBJwRUK+gVoxiQwABBNoTIJloT4XPEEDAKQEtoap3MrAhgED6AnqHha+Tx9PX4ooIFE+AZKJ4MafGCHgnoHcxaEUZNgQQQAABBBBwS4Bkwq14UBoEECgjQDJRBoaPEUhQQEOc9LI9NgQQQKCcAMlEORk+RwABZwT0lt/wbdTOFIqCIFAQAd6rUpBAU00E6hQgmagTjsMQQCBdgU8//TTdC3I1BBAI5ippzhIbAgggUE6gqbW1tbX0y+grsku/42cEKglw71TS4btGBbi/GhXkeARqF2hpaQkOmjBhQu0HcwQCdQrw932dcCkdFo0PPRMpwXMZBBBoXOCzzz5r/CScAQEEqhbYtWuXXXvttVXvz44IIFA8AZKJ4sWcGiPgpcD06dPt2LFjXpadQiPgq4CGF15zzTW+Fp9yI4BACgIkEykgcwkEEGhcgHdNNG7IGRCoVWDlypXGBOxa1dgfgWIJkEwUK97UFgFvBfSuiQ8//NDb8lNwBHwTOH78OMvC+hY0yotABgIkExmgc0kEEKhdgOVhazfjCAQaEfj444/plWgEkGMRKIgAqzkVJNBpVDM6uz+Na3KN4gho8nXnzp0tsgBdcQCoKQIpC7CSU8rgXO6iAO2JixRO/hCNDz0TToaJQiGAQFSgU6dOdvvtt5uGXrAhgEDyAlrJqXfv3slfiCsggIDXAiQTXoePwiNQLIHx48fb0aNHi1VpaotARgLbtm0zXliXET6XRcAjAZIJj4JFUREoukC/fv3s3XffLToD9UcgcYGwB7Br166JX4sLIICA3wIkE37Hj9IjUCgBTcLevn17oepMZRHIQkA9gOoJZEMAAQQ6EmACdkdCfF+1QHRCTtUHsiMCNQjoPjt//rxpDgUbAggkI7B06dJgJafm5uZkLsBZEaggQHuiAo4DX0XjQ8+EA0GhCAggUL3A1KlT7dChQ9UfwJ4IIFCzwJYtW6xXr141H8cBCCBQPAGSieLFnBoj4LXAiBEj7O233/a6DhQeAZcFTp8+bSdOnOAdEy4HibIh4JAAyYRDwaAoCCDQscCtt97KvImOmdgDgboFDh48yHyJuvU4EIHiCZBMFC/m1BgBrwUGDhxoK1euND09ZUMAgfgFXn/9dRs8eHD8J+aMCCCQSwGSiVyGlUohkG+BefPmmZ6esiGAQPwC69evJ5mIn5UzIpBbAZKJ3IaWiiGQXwE9NdXTUzYEEIhX4PDhw9atWzfj/RLxunI2BPIsQDKR5+hSNwRyKqBkQk9P2RBAIF6BXbt22YQJE+I9KWdDAIFcC5BM5Dq8VA6BfAroqemAAQNs3759+awgtUIgI4GWlhYbOnRoRlfnsggg4KMAyYSPUaPMCCBgEydOtB07diCBAAIxCRw/fpwlYWOy5DQIFEmAZKJI0aauCORIQEOdVq9enaMaURUEshXYunWrTZkyJdtCcHUEEPBOgGTCu5BRYAQQkABDnbgPEIhXQEOcmpub4z0pZ0MAgdwLkEzkPsRUEIH8CjDUKb+xpWbpCmgVJ219+vRJ98JcDQEEvBdoam1tbS2tRVNTk0U+Kv2anxEoK8C9U5aGLxIS0IvrrrrqKjt//rx16tQpoatwWgTyL7B06VK74oorGOaU/1B7UUPaE26HKRofeibcjhelQwCBCgIa6qQX2G3fvr3CXnyFAAKVBD777LNg/tHdd99daTe+QwABBNoVIJlol4UPEUDAF4GRI0faunXrfCku5UTAOYG9e/faqFGjeFGdc5GhQAj4IUAy4UecKCUCCJQRGDZsmO3fv9+0rCUbAgjULrBq1SobN25c7QdyBAIIIGBmJBPcBggg4L3AtGnTeCO291GkAlkIKAlXMq6knA0BBBCoR4AJ2PWocUy7AtEJOe3uxIcIJCDAROwEUDllIQSYeF2IMHtXSdoTbocsGh+SCbfj5VXpojeXV4WnsN4LzJ8/3/r162cTJkzwvi5UAIE0BMIk/JNPPmG+RBrgXKNqAdoTVVNlsmM0PgxzyiQMXBQBBOIWuPfee+2ZZ56J+7ScD4HcCmzbts2WLFlCIpHbCFMxBNIRIJlIx5mrIIBAwgJ62ZZWpNm5c2fCV+L0CPgvoOVglXzzxmv/Y0kNEMhagGQi6whwfQQQiE1g0qRJtnDhwtjOx4kQyKvAxo0bg+SbN17nNcLUC4H0BEgm0rPmSgggkLDAwIEDgyvQO5EwNKf3WiDslZg6darX9aDwCCDghgDJhBtxoBQIIBCTwPTp0+mdiMmS0+RTgF6JfMaVWiGQlQDJRFbyXBcBBBIRCNfLp3ciEV5O6rkAvRKeB5DiI+CgAMmEg0GhSAgg0JgAvRON+XF0fgXolchvbKkZAlkJkExkJc91EUAgMQH1Tmhi6ebNmxO7BidGwDcBeiV8ixjlRcAPAZIJP+JEKRFAoEYBTS6dNWuWqQHFhgACZuvWrbPx48cHiTYeCCCAQFwCvAE7LknOY9E3IkKCQNYCM2bMsP79+9uUKVOyLgrXRyBTAd52nSk/F69RgPZEjWAp7x6ND8lEygHI8+WiN1ee60rd/BCgAeVHnChl8gIk1skbc4X4BGhPxGeZxJmi8WGYUxLKnBMBBJwQ6Nq1q7388svBm36dKBCFQCADgcOHD9u2bdts4sSJGVydSyKAQN4FSCbyHmHqh0DBBcaOHRs0pPbt21dwCapfRAHNGVKvxKJFi6xTp05FJKDOCCCQsADJRMLAnB4BBLIVUANq+fLlNnv2bCZjZxsKrp6BgJaC1cpm4ftXMigCl0QAgZwLMGci5wFOs3rRMXRpXptrIdCRAGPGOxLi+7wJHD9+3Hr06GHHjh2z7t2756161CfHArQn3A5uND4kE27Hy6vSRW8urwpPYXMvoMnYd955p61Zs4alMXMfbSoogYceesg0zG/ChAmAIOCVAO0Jt8MVjQ/DnNyOF6VDAIGYBDQZe+7cucH4cd49ERMqp3FWoKWlJSgbiYSzIaJgCORGgJ6J3IQy+4pEM9XsS0QJEGgrwHCntiZ8ki8BhjflK55FrA3tCbejHo0PyYTb8fKqdNGby6vCU9jCCDDcqTChLmxFGd5U2NDnpuK0J9wOZTQ+DHNyO16UDgEEYhbQcCctkzl58mRWd4rZltNlL7B69eqgEAxvyj4WlACBogjQM1GUSKdQz2immsIluQQCdQssXbrUzp49azNnzqz7HByIgEsCejmdkuTXXnvNlDSzIeCrAO0JtyMXjQ89E27Hi9IhgEBCAg8++KDt3r3bNm/enNAVOC0C6Qlo+J4SCb1ThUQiPXeuhAACZvRMcBfEJhDNVGM7MSdCICGBcKLqoUOHWC42IWNOm46A5kkMGDDApk2bls4FuQoCCQrQnkgQN4ZTR+NDz0QMqJwCAQT8FNCLvHbs2MH8CT/DR6l/KxDOkyCR4JZAAIEsBOiZyEI9p9eMZqo5rSbVyqGA5k/s37/fVqxYkcPaUaU8C+zcudMef/xx5knkOcgFrBvtCbeDHo0PyYTb8fKqdNGby6vCU9jCCzBMpPC3gHcADNPzLmQUuEoB2hNVQmW0WzQ+DHPKKBBcFgEE3BJYvHixbdmyhQnZboWF0pQR0IRrLf+qYXp9+vQpsxcfI4AAAskLXJb8JbgCAggg4L5Ap06dTMOd1ED72te+ZsOGDXO/0JSwkAKfffaZPfHEEzZlyhTu00LeAVQaAbcEGObkVjy8Lk2028vrylD4wgrs27fPHn74YWtpaTFN0GZDwDUBhuS5FhHKE7cA7Ym4ReM9XzQ+DHOK15ezIYCA5wIDBw4M3pCtHgqNSWdDwCUB9Z5p03tS2BBAAAEXBEgmXIgCZUAAAacENMRp7ty5wZAnEgqnQlPowoSrjml+j4blsSGAAAIuCDDMyYUo5KQM0W6vnFSLahRYgMZbgYPvWNV1L2qBgLVr15JIOBYbihO/AO2J+E3jPGM0PvRMxKnLuRBAIFcCegmY3ir82GOPmSa9siGQhYASCb2YTn/SI5FFBLgmAghUEiCZqKTDdwggUHgBEorC3wKZAiiJ0P9YECDTMHBxBBCoIMAwpwo4fFWbQLTbq7aj2RsBtwUY8uR2fPJYurBHgkQij9GlTpUEaE9U0sn+u2h86JnIPiaUAAEEPBAo7aFgUrYHAfO8iCQSngeQ4iNQIAGSiQIFm6oigEBjAmFCwbKxjTlydGWBsBfstdde410nlan4FgEEHBBgmJMDQchLEaLdXnmpF/VAICqwefNmmzVrFuPYozD83pCAJvkvWrTI3n//fWP514YoOdhzAdoTbgcwGp/L3C4upUMAAQTcE2hubravfe1rwXso1PjTeynYEGhEQImEVg3TRiLRiCTHIoBA2gIMc0pbnOshgEAuBJRALF++3B5//HFTTwUbAvUKaA7OfffdFyxDvGLFCpZ/rReS4xBAIBMBhjllwp7Pi0a7vfJZS2qFwKUCaghqLsXo0aODPy/9lt8QqCywb98+e/jhh+3JJ58Meroq7823CBRDgPaE23GOxodkwu14eVW66M3lVeEpLAINCDBEpQG8Ah8azr1hqFyBbwKq3q4A7Yl2WZz5MBofhjk5ExoKggACvgrorcQanqK3ZY8cOdIOHz7sa1UodwoCSj7nz59vy5YtCybxM+cmBXQugQACiQmQTCRGy4kRQKBoAhrupKfMkydPZh5F0YJfZX01LE4Trc+cOWNr165l6dcq3dgNAQTcFWCYk7ux8a5k0W4v7ypAgRGISSCcR9GnTx+bM2cOE2pjcvX9NOGwJuZH+B5Jyp+0AO2JpIUbO380PvRMNObJ0QgggEAbge7duwdPnXv27MmwpzY6xfugdFjTmjVrmGhdvFuAGiOQawGSiVyHl8ohgEBWAppHoWFPWj5Ww55Wr15talSyFUtA82c0j0abhjWpt4oNAQQQyJMAw5zyFM2M6xLt9sq4OFweAWcETp8+bc8880wwMXvBggU0KJ2JTHIFUeK4bt06W7p0aZBQDhw4MLmLcWYEciZAe8LtgEbjQ8+E2/GidAggkAOBrl27mpKIRx55hF6KHMSzoyro3RHqjdDcmddff91IJDoS43sEEPBZgJ4Jn6PnWNmjmapjxaM4CDghEPZSbNu2jSfWTkQkvkIots8//7ytX7+e2MbHypkKKEB7wu2gR+NDMuF2vLwqXfTm8qrwFBaBlAX09Hr27NnBkCet7qPeCzZ/BVpaWoKhbJonM3HiRFbw8jeUlNwBAdoTDgShQhGi8WGYUwUsvkIAAQSSEtDQF03IHTp0qF111VVM0E4KOuHzKikcP3687dq1y7RS05QpU0gkEjbn9Agg4JYAPRNuxcPr0kQzVa8rQ+ERSFGgdHgM7yBIEb6BS2mVppUrVwaT6qdPn268xboBTA5FICJAeyIC4tiv0fiQTDgWIJ+LE725fK4LZUcgCwEaqFmo13bNaOI3duxYeiJqI2RvBDoUoD3RIVGmO0TjQzKRaTjydfHozZWv2lEbBNITCOdT6Io89U7PvdKVlES89NJLwXA09R6RRFTS4jsEGhOgPdGYX9JHR+PDnImkxTk/AgggUKOA5lNoRSAlEgsXLgzG5O/cuZOX3tXoGMfu6i2aP3++3XnnndatW7dgqdcJEyYk0hvx+ZvP2U1NTaZ/qC/+7/4WO6mKnGyx+0s/1883PWdvfh5HLTkHAgggUL8APRP123FkRCCaqUa+5lcEEKhTIBz+pOVk9VR81KhRrP5Up2W1hyl527Bhg4XmqfVEnN1qT/T7I1tg37EXti6y7/S74ssiX3jHfjj2Dntw87+2//SzH9rcO37XeCL4JQ8/5UeA9oTbsYzG5zK3i0vpEEAAAQT69OkTvPROScXmzZuD1Z+WLFlizc3NvE07xttDb63euHFjMJRJp1XP0Jw5cxLphShb7P9+xj48eb01vzDdHihNJHTAuRN26Bcn7foZa+xJEomyhHyBAALpCvBQI11vroYAAgjULaCkQu8x+OSTT4IhN5MnTw6GQCnBUEOYrT4BzVFZunSpde7c2d55550gcdMwM63Q1KlTp/pOWtdRF+zswT32U+tmA3td3abX4fO/32svn7zRvvXN37OS/oq6rsRBCCCAQFwC9EzEJcl5EEAAgZQE9II7jdvX/9QQfvXVV23MmDE2b948u+uuu0xzLtgqCxw/fty2bt1qetmcNr0fQklati8PPG17Nm22k9c325jB0ZcY/qO9t3+3vWuDbGb/aypXjm8RQACBFAWYM5Eidt4vFR1Dl/f6Uj8EXBLQakN79uyxdevW2f79+4PG8fDhw0ksSoKkBGL37t3BUKbQyKmhYhfnRARTrktKXvLjjQttzzt/bt/gUWAJCj/mTYD2hNsRjcaHZMLteHlVuujN5VXhKSwCORIoTSz0YjX1WIwcOdJuvvnmjJ+8p4+snpu333476IE4ceKE00nWhcM/tLF9Z5m9sNU2fqffpcOctJpTt3vspzN+Zu88ewfDnNK/lbhiigK0J1LEruNS0fgwZ6IORA5BAAEEXBbQUB09cV+xYkUwdGfw4MHBkqZXXXWVPfTQQ8EEYzWy8zjPQr0PmkOi5Vz1D94PfvCDIFQLFiwIeiU058TNYWCf20cHdttm62vfGtD90kTCwrkUzJdw+b87yoZAUQXoKC1q5Kk3AggUQiBMLJRczJw507Qi1IEDB4IXsOkdFlOnTrUBAwbYbbfdZl//+tete/fu3rgoGTp27FhQn127dgXLuOpdEKPKxuYjAAAGdUlEQVRHjw56YrKfA1EL5Rk7+PM9Ztc326Df6xw58Lz9/d7/ZidtkI1kvkTEhl8RQCBrAYY5ZR2BHF0/2u2Vo6pRFQRyKxAmF1rFSPMJ9G4FLYnas2fPYMWo/v3729VXX5358CiV89SpU/bRRx+ZEgf9HpZVZbz11luDMmc7gbqB2yR8v8S3XrYTL06w60tPFc6lsLl2aON3rA9jCkp1+DmHArQn3A5qND70TLgdL0qHAAIIJCqg5Wb1v3ArfdqvOQbhE/833ngj6MW48sorLyYaOkYN+XCrJ+lQUhBuYbKg33Vdbeo90aYelBtuuMH69etnkyZNChIcLd+aj+2svfOT/9N+pPdLjLzFrr2kUv9kJ7f92H60+aTduHCA9SaRuESHXxBAIHsBeiayj0FuShDNVHNTMSqCAAKBQNjwP3LkiJ07dy74n4ZMhZveFq2ko5ZNSYISFG1dunQJkgX93Lt37+C9Dz169Ej5XQ+1lD6GfX87sXp16amm/LZ34vM37bl+g236uyVfsppTCQY/5lWA9oTbkY3Gh2TC7Xh5VbrozeVV4SksAggggAACCDghQHvCiTCULUQ0PnSYlqXiCwQQQAABBBBAAAEEEKgkQDJRSYfvEEAAAQQQQAABBBBAoKwAyURZGr5AAAEEEEAAAQQQQACBSgIkE5V0+A4BBBBAAAEEEEAAAQTKCpBMlKXhCwQQQAABBBBAAAEEEKgkQDJRSYfvEEAAAQQQQAABBBBAoKwAyURZGr5AAAEEEEAAAQQQQACBSgIkE5V0+A4BBBBAAAEEEEAAAQTKCpBMlKXhCwQQQAABBBBAAAEEEKgkQDJRSYfvEEAAAQQQQAABBBBAoKwAyURZGr5AAAEEEEAAAQQQQACBSgIkE5V0+A4BBBBAAAEEEEAAAQTKCpBMlKXhCwQQQAABBBBAAAEEEKgkQDJRSYfvEEAAAQQQQAABBBBAoKwAyURZGr5AAAEEEEAAAQQQQACBSgIkE5V0+A4BBBBAAAEEEEAAAQTKCpBMlKXhCwQQQAABBBBAAAEEEKgkQDJRSYfvEEAAAQQQQAABBBBAoKwAyURZGr5AAAEEEEAAAQQQQACBSgIkE5V0+A4BBBBAAAEEEEAAAQTKCpBMlKXhCwQQQAABBBBAAAEEEKgkQDJRSYfvEEAAAQQQQAABBBBAoKwAyURZGr5AAAEEEEAAAQQQQACBSgIkE5V0+A4BBBBAAAEEEEAAAQTKCpBMlKXhCwQQQAABBBBAAAEEEKgkQDJRSYfvEEAAAQQQQAABBBBAoKwAyURZGr5AAAEEEEAAAQQQQACBSgIkE5V0+A4BBBBAAAEEEEAAAQTKCpBMlKXhCwQQQAABBBBAAAEEEKgkQDJRSYfvEEAAAQQQQAABBBBAoKwAyURZGr5AAAEEEEAAAQQQQACBSgIkE5V0+A4BBBBAAAEEEEAAAQTKCpBMlKXhCwQQQAABBBBAAAEEEKgkQDJRSYfvEEAAAQQQQAABBBBAoKwAyURZGr5AAAEEEEAAAQQQQACBSgKXVfqS7xCoVaCpqanWQ9gfAQQQQAABBBBAwFMBkglPA+disVtbW10sFmVCAAEEEEAAAQQQSEiAYU4JwXJaBBBAAAEEEEAAAQTyLkAykfcIUz8EEEAAAQQQQAABBBISIJlICJbTIoAAAggggAACCCCQdwGSibxHmPohgAACCCCAAAIIIJCQAMlEQrCcFgEEEEAAAQQQQACBvAuQTOQ9wtQPAQQQQAABBBBAAIGEBEgmEoLltAgggAACCCCAAAII5F2AZCLvEaZ+CCCAAAIIIIAAAggkJEAykRAsp0UAAQQQQAABBBBAIO8CJBN5jzD1QwABBBBAAAEEEEAgIQGSiYRgOS0CCCCAAAIIIIAAAnkXIJnIe4SpHwIIIIAAAggggAACCQmQTCQEy2kRQAABBBBAAAEEEMi7AMlE3iNM/RBAAAEEEEAAAQQQSEiAZCIhWE6LAAIIIIAAAggggEDeBUgm8h5h6ocAAggggAACCCCAQEICJBMJwXJaBBBAAAEEEEAAAQTyLkAykfcIUz8EEEAAAQQQQAABBBISIJlICJbTIoAAAggggAACCCCQdwGSibxHmPohgAACCCCAAAIIIJCQwGXtnbepqam9j/kMAQQQQAABBBBAAAEEELgo0CaZaG1tvfglPyCAAAIIIIAAAggggAAC5QT+f5Yv0z+2hUJ/AAAAAElFTkSuQmCC"></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>x</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>Write down the value of \(n\left( {\left( {F \cup H} \right) \cap S'} \right)\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"><em><strong>(A1)(A1)(A1) (C3)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for 4 in correct place.</p>
<p>Award <em><strong>(A1)</strong></em> for 9, 11, 15 in correct place.</p>
<p>Award <em><strong>(A1)</strong></em> for 7 − <em>x</em>, 13 − <em>x</em>, 11 − <em>x</em> in correct place.</p>
<p>Accept 2, 8 and 6 in place of 7 − <em>x</em>, 13 − <em>x</em>, 11 − <em>x</em>.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(4 + 9 + 11 + 15 + x + \left( {7 - x} \right) + \left( {11 - x} \right) + \left( {13 - x} \right) = 60\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for equating the sum of at least seven of the entries in their Venn diagram to 60.</p>
<p>\(\left( {x = } \right)\,\,5\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (a), but only if answer is positive.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>34 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C1)</strong></em></p>
<p><strong>Note:</strong> Follow through from their Venn diagram.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br>