File "markSceme-SL-paper2.html"
Path: /IB QUESTIONBANKS/5 Fifth Edition - PAPER/HTML/Math AA/Topic 2/markSceme-SL-paper2html
File size: 1.44 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-02ef852527079acf252dc4c9b2922c93db8fde2b6bff7c3c7f657634ae024ff1.css">
<link rel="stylesheet" media="print" href="css/print-6da094505524acaa25ea39a4dd5d6130a436fc43336c0bb89199951b860e98e9.css">
<script src="js/application-9717ccaf4d6f9e8b66ebc0e8784b3061d3f70414d8c920e3eeab2c58fdb8b7c9.js"></script>
<script type="text/javascript" async src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-MML-AM_CHTML-full"></script>
<!--[if lt IE 9]>
<script src='https://cdnjs.cloudflare.com/ajax/libs/html5shiv/3.7.3/html5shiv.min.js'></script>
<![endif]-->
<meta name="csrf-param" content="authenticity_token">
<meta name="csrf-token" content="iHF+M3VlRFlNEehLVICYgYgqiF8jIFlzjGNjIwqOK9cFH3ZNdavBJrv/YQpz8vcspoICfQcFHW8kSsHnJsBwfg==">
<link href="favicon.ico" rel="shortcut icon">
</head>
<body class="teacher questions-show">
<div class="navbar navbar-fixed-top">
<div class="navbar-inner">
<div class="container">
<div class="brand">
<div class="inner"><a href="http://ibo.org/">ibo.org</a></div>
</div>
<ul class="nav">
<li>
<a href="../../../../../../../index.html">Home</a>
</li>
<!-- - if current_user.is_language_services? && !current_user.is_publishing? -->
<!-- %li= link_to "Language services", tolk_path -->
</ul>
<ul class="nav pull-right">
<li class="dropdown">
<a class="dropdown-toggle" data-toggle="dropdown" href="#">
Help
<b class="caret"></b>
</a>
<ul class="dropdown-menu">
<li><a href="https://questionbank.ibo.org/video_tour?locale=en">Video tour</a></li>
<li><a href="https://questionbank.ibo.org/instructions?locale=en">Detailed instructions</a></li>
<li><a target="_blank" href="https://ibanswers.ibo.org/">IB Answers</a></li>
</ul>
</li>
<li>
<a href="https://06082010.xyz">IB Documents (2) Team</a>
</li></ul>
</div>
</div>
</div>
<div class="page-content container">
<div class="row">
<div class="span24">
<div class="pull-right screen_only"><a class="btn btn-small btn-info" href="https://questionbank.ibo.org/updates?locale=en">Updates to Questionbank</a></div>
<p class="muted language_chooser">
User interface language:
<a href="https://questionbank.ibo.org/en/users/set_user_locale?new_locale=en">English</a>
|
<a href="https://questionbank.ibo.org/en/users/set_user_locale?new_locale=es">Español</a>
</p>
</div>
</div>
<div class="page-header">
<div class="row">
<div class="span16">
<p class="back-to-list">
</p>
</div>
<div class="span8" style="margin: 0 0 -19px 0;">
<img style="width: 100%;" class="qb_logo" src="https://mirror.ibdocs.top/qb.png" alt="Ib qb 46 logo">
</div>
</div>
</div>
<h2>SL Paper 2</h2><div class="specification">
<p>An arithmetic sequence has first term <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn></math> and common difference <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>.</mo><mn>5</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>th term of the sequence is zero, find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mi>n</mi></msub></math> denote the sum of the first <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> terms of the sequence.</p>
<p>Find the maximum value of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mi>n</mi></msub></math>.</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>attempt to use <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mi>d</mi><mo>=</mo><mn>0</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn><mo>-</mo><mn>2</mn><mo>.</mo><mn>5</mn><mfenced><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>=</mo><mn>0</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mn>25</mn></math> <em><strong>A1</strong></em></p>
<p> </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><strong>METHOD 1</strong></p>
<p>attempting to express <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mi>n</mi></msub></math> in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> <em><strong>(M1)</strong></em></p>
<p>use of a graph or a table to attempt to find the maximum sum <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>750</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p><strong><br>EITHER</strong></p>
<p>recognizing maximum occurs at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>25</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mn>25</mn></msub><mo>=</mo><mfrac><mn>25</mn><mn>2</mn></mfrac><mfenced><mrow><mn>60</mn><mo>+</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mo> </mo><msub><mi>S</mi><mn>25</mn></msub><mo>=</mo><mfrac><mn>25</mn><mn>2</mn></mfrac><mfenced><mrow><mn>2</mn><mo>×</mo><mn>60</mn><mo>+</mo><mn>24</mn><mo>×</mo><mo>-</mo><mn>2</mn><mo>.</mo><mn>5</mn></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><br><strong>OR</strong></p>
<p>attempting to calculate <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mn>24</mn></msub></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mn>24</mn></msub><mo>=</mo><mfrac><mn>24</mn><mn>2</mn></mfrac><mfenced><mrow><mn>2</mn><mo>×</mo><mn>60</mn><mo>+</mo><mn>23</mn><mo>×</mo><mo>-</mo><mn>2</mn><mo>.</mo><mn>5</mn></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><br><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>750</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The temperature <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo> </mo><mo>°</mo><mi mathvariant="normal">C</mi></math> of water <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> minutes after being poured into a cup can be modelled by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><msub><mi>T</mi><mn>0</mn></msub><msup><mi mathvariant="normal">e</mi><mrow><mo>-</mo><mi>k</mi><mi>t</mi></mrow></msup></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>≥</mo><mn>0</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mn>0</mn></msub><mo>,</mo><mo> </mo><mi>k</mi></math> are positive constants.</p>
<p>The water is initially boiling at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo> </mo><mo>°</mo><mtext>C</mtext></math>. When <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>10</mn></math>, the temperature of the water is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>70</mn><mo> </mo><mo>°</mo><mtext>C</mtext></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mn>0</mn></msub><mo>=</mo><mn>100</mn></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mfrac><mn>1</mn><mn>10</mn></mfrac><mi>ln</mi><mfrac><mn>10</mn><mn>7</mn></mfrac></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the temperature of the water when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>15</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> versus <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>, clearly indicating any asymptotes with their equations and stating the coordinates of any points of intersection with the axes.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the time taken for the water to have a temperature of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn><mo> </mo><mo>°</mo><mtext>C</mtext></math>. Give your answer correct to the nearest second.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The model for the temperature of the water can also be expressed in the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><msub><mi>T</mi><mn>0</mn></msub><msup><mi>a</mi><mfrac><mi>t</mi><mn>10</mn></mfrac></msup></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>≥</mo><mn>0</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> is a positive constant.</p>
<p>Find the exact value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color:#999;font-size:90%;font-style:italic;">* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.</p>
<p>when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn><mo>,</mo><mo> </mo><mi>T</mi><mo>=</mo><mn>100</mn><mo>⇒</mo><mn>100</mn><mo>=</mo><msub><mi>T</mi><mn>0</mn></msub><msup><mtext>e</mtext><mn>0</mn></msup></math> <strong>A1</strong></p>
<p>so <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mn>0</mn></msub><mo>=</mo><mn>100</mn></math> <strong>AG</strong></p>
<p> </p>
<p><strong>[1</strong><strong> mark]</strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct substitution of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>10</mn><mo>,</mo><mo> </mo><mi>T</mi><mo>=</mo><mn>70</mn></math> <strong>M1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>70</mn><mo>=</mo><mn>100</mn><msup><mtext>e</mtext><mrow><mo>-</mo><mn>10</mn><mi>k</mi></mrow></msup></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>e</mtext><mrow><mo>-</mo><mn>10</mn><mi>k</mi></mrow></msup><mi mathvariant="normal">=</mi><mfrac><mn>7</mn><mn>10</mn></mfrac></math></p>
<p> </p>
<p><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>10</mn><mi>k</mi><mo>=</mo><mi>ln</mi><mfrac><mn>7</mn><mn>10</mn></mfrac></math> <strong>A1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ln</mi><mfrac><mn>7</mn><mn>10</mn></mfrac><mo>=</mo><mo>-</mo><mi>ln</mi><mfrac><mn>10</mn><mn>7</mn></mfrac></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>ln</mi><mfrac><mn>7</mn><mn>10</mn></mfrac><mo>=</mo><mi>ln</mi><mfrac><mn>10</mn><mn>7</mn></mfrac></math> <strong>A1</strong></p>
<p> </p>
<p><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>e</mtext><mrow><mn>10</mn><mi>k</mi></mrow></msup><mi mathvariant="normal">=</mi><mfrac><mn>10</mn><mn>7</mn></mfrac></math> <strong>A1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mi>k</mi><mo>=</mo><mi>ln</mi><mfrac><mn>10</mn><mn>7</mn></mfrac></math> <strong>A1</strong></p>
<p> </p>
<p><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mfrac><mn>1</mn><mn>10</mn></mfrac><mi>ln</mi><mfrac><mn>10</mn><mn>7</mn></mfrac></math> <strong>AG</strong></p>
<p> </p>
<p><strong>[3</strong><strong> marks]</strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>substitutes <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>15</mn></math> into <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> <strong>(M1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mn>58</mn><mo>.</mo><mn>6</mn><mo> </mo><mfenced><mrow><mo>°</mo><mtext>C</mtext></mrow></mfenced></math> <strong>A1</strong></p>
<p> </p>
<p><strong>[2</strong><strong> marks]</strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img style="display:block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></p>
<p>a decreasing exponential <strong>A1</strong></p>
<p>starting at <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>,</mo><mo> </mo><mn>100</mn></mrow></mfenced></math> labelled on the graph or stated <strong>A1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>→</mo><mn>0</mn></math> as <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>→</mo><mo>∞</mo></math> <strong>A1</strong></p>
<p>horizontal asymptote <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mn>0</mn></math> labelled on the graph or stated <strong>A1</strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong>A0</strong> for stating <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>0</mn></math> as the horizontal asymptote.</p>
<p> </p>
<p><strong>[4</strong><strong> marks]</strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><msup><mtext>e</mtext><mrow><mo>-</mo><mi>k</mi><mi>t</mi></mrow></msup><mo>=</mo><mn>50</mn></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mfrac><mn>1</mn><mn>10</mn></mfrac><mi>ln</mi><mfrac><mn>10</mn><mn>7</mn></mfrac></math> <strong>A1</strong></p>
<p> </p>
<p><strong>EITHER</strong></p>
<p>uses an appropriate graph to attempt to solve for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> <strong>(M1)</strong></p>
<p> </p>
<p><strong>OR</strong></p>
<p>manipulates logs to attempt to solve for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> e.g. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ln</mi><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>=</mo><mfenced><mrow><mo>-</mo><mfrac><mn>1</mn><mn>10</mn></mfrac><mi>ln</mi><mfrac><mn>10</mn><mn>7</mn></mfrac></mrow></mfenced><mi>t</mi></math> <strong>(M1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfrac><mrow><mi>ln</mi><mo> </mo><mn>2</mn></mrow><mrow><mstyle displaystyle="true"><mfrac><mn>1</mn><mn>10</mn></mfrac></mstyle><mi>ln</mi><mstyle displaystyle="true"><mfrac><mn>10</mn><mn>7</mn></mfrac></mstyle></mrow></mfrac><mo>=</mo><mn>19</mn><mo>.</mo><mn>433</mn><mo>…</mo></math> <strong>A1</strong></p>
<p> </p>
<p><strong>THEN</strong></p>
<p>temperature will be <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn><mo> </mo><mo>°</mo><mtext>C</mtext></math> after <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>19</mn></math> minutes and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>26</mn></math> seconds <strong>A1</strong></p>
<p> </p>
<p><strong>[4</strong><strong> marks]</strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>substitutes <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mn>0</mn></msub><mo>=</mo><mn>100</mn></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>10</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mn>70</mn></math> into <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><msub><mi>T</mi><mn>0</mn></msub><msup><mi>a</mi><mfrac><mi>t</mi><mn>10</mn></mfrac></msup></math> <strong>(M1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>70</mn><mo>=</mo><mn>100</mn><msup><mi>a</mi><mfrac><mn>10</mn><mn>10</mn></mfrac></msup></math> <strong>A1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mn>7</mn><mn>10</mn></mfrac></math> <strong>A1</strong></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><msup><mi>a</mi><mfrac><mi>t</mi><mn>10</mn></mfrac></msup><mo>=</mo><mn>100</mn><msup><mtext>e</mtext><mrow><mo>-</mo><mi>k</mi><mi>t</mi></mrow></msup></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mfrac><mn>1</mn><mn>10</mn></mfrac><mi>ln</mi><mfrac><mn>10</mn><mn>7</mn></mfrac></math></p>
<p> </p>
<p><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>e</mtext><mrow><mo>-</mo><mi>k</mi></mrow></msup><mo>=</mo><msup><mi>a</mi><mfrac><mn>1</mn><mn>10</mn></mfrac></msup><mo>⇒</mo><mi>a</mi><mo>=</mo><msup><mtext>e</mtext><mrow><mo>-</mo><mn>10</mn><mi>k</mi></mrow></msup></math> <strong>(M1)</strong></p>
<p> </p>
<p><strong>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msup><mfenced><msup><mtext>e</mtext><mrow><mfenced><mrow><mi>-</mi><mfrac><mn>1</mn><mn>10</mn></mfrac><mi>ln</mi><mfrac><mn>10</mn><mn>7</mn></mfrac></mrow></mfenced><mi>t</mi></mrow></msup></mfenced><mfrac><mn>10</mn><mi>t</mi></mfrac></msup></math> <strong>(M1)</strong></p>
<p> </p>
<p><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msup><mtext>e</mtext><mrow><mo>-</mo><mi>ln</mi><mfrac><mn>10</mn><mn>7</mn></mfrac></mrow></msup><mo> </mo><mfenced><mrow><mo>=</mo><msup><mtext>e</mtext><mrow><mi>ln</mi><mfrac><mn>7</mn><mn>10</mn></mfrac></mrow></msup></mrow></mfenced></math> <strong>A1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mn>7</mn><mn>10</mn></mfrac></math> <strong>A1</strong></p>
<p> </p>
<p><strong>[3</strong><strong> marks]</strong></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</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>Consider the curves <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo> </mo><mi>sin</mi><mo> </mo><mi>x</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>-</mo><msqrt><mn>1</mn><mo>+</mo><mn>4</mn><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></msqrt></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi mathvariant="normal">π</mi><mo>≤</mo><mi>x</mi><mo>≤</mo><mn>0</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-coordinates of the points of intersection of the two curves.</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 area, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math>, of the region enclosed by the two curves.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color:#999;font-size:90%;font-style:italic;">* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.</p>
<p>attempts to solve <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo> </mo><mi>sin</mi><mo> </mo><mi>x</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>-</mo><msqrt><mn>1</mn><mo>+</mo><mn>4</mn><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></msqrt></math> <strong>(M1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mn>2</mn><mo>.</mo><mn>76</mn><mo>,</mo><mo> </mo><mo>-</mo><mn>1</mn><mo>.</mo><mn>54</mn></math> <strong>A1</strong><strong>A1</strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong>A1A0</strong> if additional solutions outside the domain are given.</p>
<p> </p>
<p><strong>[3</strong><strong> marks]</strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><munderover><mo>∫</mo><mrow><mo>-</mo><mn>2</mn><mo>.</mo><mn>762</mn><mo>…</mo></mrow><mrow><mo>-</mo><mn>1</mn><mo>.</mo><mn>537</mn><mo>…</mo></mrow></munderover><mfenced><mrow><mo>-</mo><mn>1</mn><mo>-</mo><msqrt><mn>1</mn><mo>+</mo><mn>4</mn><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></msqrt><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo> </mo><mi>sin</mi><mo> </mo><mi>x</mi></mrow></mfenced><mo> </mo><mi mathvariant="normal">d</mi><mi>x</mi></math> (or equivalent) <strong>(M1)(A1)</strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong>M1</strong> for attempting to form an integrand involving “top curve” − “bottom curve”.</p>
<p> </p>
<p>so <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>47</mn></math> <strong>A2</strong></p>
<p> </p>
<p><strong>[4</strong><strong> marks]</strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = (2x + 2)(5 - {x^2})">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mn>5</mn>
<mo>−<!-- − --></mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo stretchy="false">)</mo>
</math></span>.</p>
</div>
<div class="specification">
<p>The graph of the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x) = {5^x} + 6x - 6">
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mrow>
<msup>
<mn>5</mn>
<mi>x</mi>
</msup>
</mrow>
<mo>+</mo>
<mn>6</mn>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mn>6</mn>
</math></span> intersects the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Expand the expression for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x)">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’(x)">
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><strong>Draw </strong>the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 3 \leqslant x \leqslant 3">
<mo>−</mo>
<mn>3</mn>
<mo>⩽</mo>
<mi>x</mi>
<mo>⩽</mo>
<mn>3</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 40 \leqslant y \leqslant 20">
<mo>−</mo>
<mn>40</mn>
<mo>⩽</mo>
<mi>y</mi>
<mo>⩽</mo>
<mn>20</mn>
</math></span>. Use a scale of 2 cm to represent 1 unit on the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis and 1 cm to represent 5 units on the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-axis.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the coordinates of the point of intersection.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="10x - 2{x^3} + 10 - 2{x^2}">
<mn>10</mn>
<mi>x</mi>
<mo>−</mo>
<mn>2</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>10</mn>
<mo>−</mo>
<mn>2</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>The expansion may be seen in part (b)(ii).</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="10 - 6{x^2} - 4x">
<mn>10</mn>
<mo>−</mo>
<mn>6</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>4</mn>
<mi>x</mi>
</math></span> <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Notes: </strong>Follow through from part (b)(i). Award <strong><em>(A1)</em>(ft) </strong>for each correct term. Award at most <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)<em>(A0) </em></strong>if extra terms are seen.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2018-02-14_om_06.23.51.png" alt="N17/5/MATSD/SP2/ENG/TZ0/05.d/M"> <strong><em>(A1)(A1)</em>(ft)<em>(A1)</em>(ft)<em>(A1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for correct scale; axes labelled and drawn with a ruler.</p>
<p>Award <strong><em>(A1)</em>(ft) </strong>for their correct <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-intercepts in approximately correct location.</p>
<p>Award <strong><em>(A1) </em></strong>for correct minimum and maximum points in approximately correct location.</p>
<p>Award <strong><em>(A1) </em></strong>for a smooth continuous curve with approximate correct shape. The curve should be in the given domain.</p>
<p>Follow through from part (a) for the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-intercepts.</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(1.49,{\text{ }}13.9){\text{ }}\left( {(1.48702 \ldots ,{\text{ }}13.8714 \ldots )} \right)">
<mo stretchy="false">(</mo>
<mn>1.49</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>13.9</mn>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mo stretchy="false">(</mo>
<mn>1.48702</mn>
<mo>…</mo>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>13.8714</mn>
<mo>…</mo>
<mo stretchy="false">)</mo>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(G1)</em>(ft)<em>(G1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(G1) </em></strong>for 1.49 and <strong><em>(G1) </em></strong>for 13.9 written as a coordinate pair. Award at most <strong><em>(G0)(G1) </em></strong>if parentheses are missing. Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 1.49">
<mi>x</mi>
<mo>=</mo>
<mn>1.49</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 13.9">
<mi>y</mi>
<mo>=</mo>
<mn>13.9</mn>
</math></span>. Follow through from part (b)(i).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[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">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{1}{3}{x^3} + \frac{3}{4}{x^2} - x - 1">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>+</mo>
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mn>1</mn>
</math></span>.</p>
</div>
<div class="specification">
<p>The function has one local maximum at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = p">
<mi>x</mi>
<mo>=</mo>
<mi>p</mi>
</math></span> and one local minimum at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = q">
<mi>x</mi>
<mo>=</mo>
<mi>q</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-intercept of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span>.</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>Sketch the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> for −3 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> ≤ 3 and −4 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> ≤ 12.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the range of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right)">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
<mi>q</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>−1 <strong><em>(A1)</em></strong></p>
<p><strong>Note:</strong> Accept (0, −1).</p>
<p><em><strong>[1 mark]</strong></em></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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"> <strong><em>(A1)(A1)(A1)(A1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em></strong> for correct window and axes labels, −3 to 3 should be indicated on the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-axis and −4 to 12 on the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-axis.<br><strong><em> (A1)</em></strong>) for smooth curve with correct cubic shape;<br><strong><em> (A1)</em></strong> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-intercepts: one close to −3, the second between −1 and 0, and third between 1 and 2; and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-intercept at approximately −1;<br><strong><em> (A1)</em></strong> for local minimum in the 4th quadrant and maximum in the 2nd quadrant, in approximately correct positions.<br>Graph paper does not need to be used. If window not given award at most <em><strong>(A0)(A1)(A0)(A1)</strong></em>.</p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 1.27 \leqslant {\text{ }}f\left( x \right) \leqslant 1.33\,\,\,\left( { - 1.27083 \ldots \leqslant {\text{ }}f\left( x \right) \leqslant 1.33333 \ldots {\text{,}}\,\, - \frac{{61}}{{48}} \leqslant {\text{ }}f\left( x \right) \leqslant \frac{4}{3}} \right)">
<mo>−</mo>
<mn>1.27</mn>
<mo>⩽</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>⩽</mo>
<mn>1.33</mn>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mo>−</mo>
<mn>1.27083</mn>
<mo>…</mo>
<mo>⩽</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>⩽</mo>
<mn>1.33333</mn>
<mo>…</mo>
<mrow>
<mtext>,</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mo>−</mo>
<mfrac>
<mrow>
<mn>61</mn>
</mrow>
<mrow>
<mn>48</mn>
</mrow>
</mfrac>
<mo>⩽</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>⩽</mo>
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <strong><em>(A1)</em>(ft)</strong><strong><em>(A1)</em>(ft)</strong><strong><em>(A1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em></strong> for −1.27 seen, <strong><em>(A1)</em></strong> for 1.33 seen, and <strong><em>(A1)</em></strong> for correct weak inequalities with <strong>their</strong> endpoints in the correct order. For example, award <em><strong>(A0)(A0)(A0)</strong></em> for answers like <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="5 \leqslant {\text{ }}f\left( x \right) \leqslant 2">
<mn>5</mn>
<mo>⩽</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>⩽</mo>
<mn>2</mn>
</math></span>. Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> in place of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right)">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span>. Accept alternative correct notation such as [−1.27, 1.33].</p>
<p>Follow through from their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
<mi>q</mi>
</math></span> values from part (g) only if their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( p \right)">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>p</mi>
<mo>)</mo>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( q \right)">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>q</mi>
<mo>)</mo>
</mrow>
</math></span> values are between −4 and 12. Award <em><strong>(A0)(A0)(A0)</strong></em> if their values from (g) are given as the endpoints.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">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">h.</div>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows a circle with centre <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math> and radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">Points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> lie on the circumference of the circle.</p>
<p style="text-align: left;">Chord <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="[" close="]"><mtext>AB</mtext></mfenced></math> has length <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mtext>O</mtext><mo>^</mo></mover><mtext>B</mtext><mo>=</mo><mi>θ</mi></math> radians.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that arc <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>APB</mtext></math> has length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mi mathvariant="normal">π</mi><mo>-</mo><mn>3</mn><mi>θ</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><msqrt><mn>18</mn><mo>-</mo><mn>18</mn><mo> </mo><mi>cos</mi><mo> </mo><mi>θ</mi></msqrt></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Arc <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>APB</mtext></math> is twice the length of chord <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="[" close="]"><mtext>AB</mtext></mfenced></math>.</p>
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color:#999;font-size:90%;font-style:italic;">* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.</p>
<p><strong>EITHER</strong></p>
<p>uses the arc length formula <strong>(M1)</strong></p>
<p>arc length is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mfenced><mrow><mn>2</mn><mi mathvariant="normal">π</mi><mo>-</mo><mi>θ</mi></mrow></mfenced></math> <strong>A1</strong></p>
<p> </p>
<p><strong>OR</strong></p>
<p>length of arc <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mi>θ</mi></math> <strong>A1</strong></p>
<p>the sum of the lengths of arc <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext></math> and arc <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>APB</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mi mathvariant="normal">π</mi></math> <strong>A1</strong></p>
<p> </p>
<p><strong>THEN</strong></p>
<p>so arc <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>APB</mtext></math> has length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mi mathvariant="normal">π</mi><mo>-</mo><mn>3</mn><mi>θ</mi></math> <strong>AG</strong></p>
<p> </p>
<p><strong>[2 marks]</strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>uses the cosine rule <strong>(M1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>L</mi><mn>2</mn></msup><mo>=</mo><msup><mn>3</mn><mn>2</mn></msup><mo>+</mo><msup><mn>3</mn><mn>2</mn></msup><mo>-</mo><mn>2</mn><mfenced><mn>3</mn></mfenced><mfenced><mn>3</mn></mfenced><mo> </mo><mi>cos</mi><mo> </mo><mi>θ</mi></math> <strong>A1</strong></p>
<p>so <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><msqrt><mn>18</mn><mo>-</mo><mn>18</mn><mo> </mo><mi>cos</mi><mo> </mo><mi>θ</mi></msqrt></math> <strong>AG</strong></p>
<p> </p>
<p><strong>[2 marks]</strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mi mathvariant="normal">π</mi><mo>-</mo><mn>3</mn><mi>θ</mi><mo>=</mo><mn>2</mn><msqrt><mn>18</mn><mo>-</mo><mn>18</mn><mo> </mo><mi>cos</mi><mo> </mo><mi>θ</mi></msqrt></math> <strong>A1</strong></p>
<p>attempts to solve for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math> <strong>(M1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>49</mn></math> <strong>A1</strong></p>
<p> </p>
<p><strong>[3 marks]</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>Points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math> lie on opposite banks of a river, such that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AP</mtext></math> is the shortest distance across the river. Point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> represents the centre of a city which is located on the riverbank. <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>PB</mtext><mo>=</mo><mn>215</mn><mo> </mo><mtext>km</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AP</mtext><mo>=</mo><mn>65</mn><mo> </mo><mtext>km</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mtext>P</mtext><mo>^</mo></mover><mtext>B</mtext><mo>=</mo><mn>90</mn><mo>°</mo></math>.</p>
<p>The following diagram shows this information.</p>
<p><img src="data:image/png;base64,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"></p>
<p>A boat travels at an average speed of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>42</mn><mo> </mo><msup><mtext>km h</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>. A bus travels along the straight road between <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> at an average speed of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>84</mn><mo> </mo><msup><mtext>km h</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>.</p>
</div>
<div class="specification">
<p>Find the travel time, in hours, from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> given that</p>
</div>
<div class="specification">
<p>There is a point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math>, which lies on the road from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>, such that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BD</mtext><mo>=</mo><mi>x</mi><mo> </mo><mtext>km</mtext></math>. The boat travels from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math>, and the bus travels from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>.</p>
</div>
<div class="specification">
<p>An excursion involves renting the boat and the bus. The cost to rent the boat is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mo> </mo><mn>200</mn></math> per hour, and the cost to rent the bus is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mo> </mo><mn>150</mn></math> per hour.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the boat is taken from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math>, and the bus from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the boat travels directly to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression, in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> for the travel time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>, from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>, passing through <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> so that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> is a minimum.</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 the minimum value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the new value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> so that the total cost <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math> to travel from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> via <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math> is a minimum.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the minimum total cost for this journey.</p>
<div class="marks">[1]</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><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mtext>AP</mtext><mn>42</mn></mfrac></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>215</mn><mn>84</mn></mfrac></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>65</mn><mn>42</mn></mfrac><mo>+</mo><mfrac><mn>215</mn><mn>84</mn></mfrac></math> <em><strong>(M1)</strong></em></p>
<p>time <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>4</mn><mo>.</mo><mn>10714</mn><mo>…</mo></math> (hours)</p>
<p>time <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>4</mn><mo>.</mo><mn>11</mn></math> (hours) <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext><mo>=</mo><msqrt><msup><mn>215</mn><mn>2</mn></msup><mo>+</mo><msup><mn>65</mn><mn>2</mn></msup></msqrt><mfenced><mrow><mo>=</mo><mn>224</mn><mo>.</mo><mn>610</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p>time <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>5</mn><mo>.</mo><mn>34787</mn><mo>…</mo></math> (hours)</p>
<p>time <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>5</mn><mo>.</mo><mn>35</mn></math> (hours) <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AD</mtext><mo>=</mo><msqrt><msup><mfenced><mrow><mn>215</mn><mo>-</mo><mi>x</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mn>65</mn><mn>2</mn></msup></msqrt></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfrac><msqrt><msup><mfenced><mrow><mn>215</mn><mo>-</mo><mi>x</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mn>65</mn><mn>2</mn></msup></msqrt><mn>42</mn></mfrac></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mfrac><msqrt><msup><mfenced><mrow><mn>215</mn><mo>-</mo><mi>x</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mn>65</mn><mn>2</mn></msup></msqrt><mn>42</mn></mfrac><mo>+</mo><mfrac><mi>x</mi><mn>84</mn></mfrac><mfenced><mrow><mo>=</mo><mfrac><msqrt><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>430</mn><mi>x</mi><mo>+</mo><mn>50450</mn></msqrt><mn>42</mn></mfrac><mo>+</mo><mfrac><mi>x</mi><mn>84</mn></mfrac></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach to find the minimum for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> (may be seen in (iii)) <em><strong>(M1)</strong></em></p>
<p>graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>'</mo><mo>=</mo><mn>0</mn></math> OR graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>'</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>177</mn><mo>.</mo><mn>472</mn><mo>…</mo><mo> </mo><mtext>km</mtext></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>177</mn><mo> </mo><mtext>km</mtext></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mn>3</mn><mo>.</mo><mn>89980</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mn>3</mn><mo>.</mo><mn>90</mn></math> (hours) <em><strong>A1</strong></em></p>
<p><strong><br>Note:</strong> Only allow <strong><em>FT</em></strong> in (b)(ii) and (iii) for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo><</mo><mi>x</mi><mo><</mo><mn>215</mn></math> and a function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> that has a minimum in that interval.</p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mn>200</mn><mo>·</mo><mfrac><msqrt><msup><mfenced><mrow><mn>215</mn><mo>-</mo><mi>x</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mn>65</mn><mn>2</mn></msup></msqrt><mn>42</mn></mfrac><mo>+</mo><mn>150</mn><mo>·</mo><mfrac><mi>x</mi><mn>84</mn></mfrac></math> <em><strong>(A1)</strong></em></p>
<p>valid approach to find the minimum for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mfenced><mi>x</mi></mfenced></math> (may be seen in (ii)) <em><strong>(M1)</strong></em></p>
<p>graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>'</mo><mo>=</mo><mn>0</mn></math> OR graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>'</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>188</mn><mo>.</mo><mn>706</mn><mo>…</mo><mo> </mo><mtext>km</mtext></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>189</mn><mo> </mo><mtext>km</mtext></math> <em><strong>A1</strong></em></p>
<p><strong><br>Note:</strong> Only allow <em><strong>FT</strong></em> from (b) if the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> has a minimum in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo><</mo><mi>x</mi><mo><</mo><mn>215</mn></math>.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mn>670</mn><mo>.</mo><mn>864</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mo>$</mo><mn>671</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Only allow <em><strong>FT</strong></em> from (c)(i) if the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math> has a minimum in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo><</mo><mi>x</mi><mo><</mo><mn>215</mn></math>.</p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.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">b.iii.</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>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>4</mn><mo>-</mo><msup><mi>x</mi><mn>3</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>ln</mi><mo> </mo><mi>x</mi></math>, for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mn>0</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>f</mi><mo>∘</mo><mi>g</mi></mrow></mfenced><mfenced><mi>x</mi></mfenced></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Solve the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>f</mi><mo>∘</mo><mi>g</mi></mrow></mfenced><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>x</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence or otherwise, given that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mrow><mn>2</mn><mi>a</mi></mrow></mfenced><mo>=</mo><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mrow><mn>2</mn><mi>a</mi></mrow></mfenced></math>, find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>attempt to form composite (in any order) <strong><em>(M1)</em></strong></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mrow><mi>ln</mi><mo> </mo><mi>x</mi></mrow></mfenced><mo> </mo><mo>,</mo><mo> </mo><mi>g</mi><mfenced><mrow><mn>4</mn><mo>-</mo><msup><mi>x</mi><mn>3</mn></msup></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>f</mi><mo>∘</mo><mi>g</mi></mrow></mfenced><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>4</mn><mo>-</mo><msup><mfenced><mrow><mi>ln</mi><mo> </mo><mi>x</mi></mrow></mfenced><mn>3</mn></msup></math> <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach using GDC <strong><em>(M1)</em></strong></p>
<p>eg <img src="data:image/png;base64,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"> , <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo>.</mo><mn>85</mn><mo>,</mo><mo> </mo><mn>2</mn><mo>.</mo><mn>85</mn></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>85056</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>85</mn></math> <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1 – (using properties of functions)</strong></p>
<p>recognizing inverse relationship <strong><em>(M1)</em></strong></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mrow><mi>g</mi><mfenced><mrow><mn>2</mn><mi>a</mi></mrow></mfenced></mrow></mfenced><mo>=</mo><mi>f</mi><mfenced><mrow><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mrow><mn>2</mn><mi>a</mi></mrow></mfenced></mrow></mfenced><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mn>2</mn><mi>a</mi></mrow></mfenced></math></p>
<p>equating <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>a</mi></math> to their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> from (i) <strong><em>(A1)</em></strong></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>a</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>85056</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>42528</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>43</mn></math> <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><strong>METHOD 2 – (finding inverse)</strong></p>
<p>interchanging <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> (seen anywhere) <strong><em>(M1)</em></strong></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>4</mn><mo>-</mo><msup><mi>y</mi><mn>3</mn></msup><mo> </mo><mo>,</mo><mo> </mo><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mi>x</mi></mfenced><mo>=</mo><mroot><mrow><mn>4</mn><mo>-</mo><mi>x</mi></mrow><mn>3</mn></mroot></math></p>
<p>correct working <strong><em>(A1)</em></strong></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mrow><mn>4</mn><mo>-</mo><mn>2</mn><mi>a</mi></mrow><mn>3</mn></mroot><mo>=</mo><mi>ln</mi><mfenced><mrow><mn>2</mn><mi>a</mi></mrow></mfenced></math>, sketch showing intersection of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mrow><mn>2</mn><mi>x</mi></mrow></mfenced></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mrow><mn>2</mn><mi>x</mi></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>42528</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>43</mn></math> <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</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.</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>Consider the curve <em>y</em> = 2<em>x</em><sup>3</sup> − 9<em>x</em><sup>2</sup> + 12<em>x</em> + 2, for −1 < <em>x</em> < 3</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the curve for −1 < <em>x</em> < 3 and −2 < <em>y</em> < 12.</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>A teacher asks her students to make some observations about the curve.</p>
<p>Three students responded.<br><strong>Nadia</strong> said <em>“The x-intercept of the curve is between −1 and zero”.</em><br><strong>Rick</strong> said <em>“The curve is decreasing when x < 1 ”.</em><br><strong>Paula</strong> said <em>“The gradient of the curve is less than zero between x = 1 and x = 2 ”.</em></p>
<p>State the name of the student who made an <strong>incorrect</strong> observation.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{dy}}}}{{{\text{dx}}}}"> <mfrac> <mrow> <mrow> <mtext>dy</mtext> </mrow> </mrow> <mrow> <mrow> <mtext>dx</mtext> </mrow> </mrow> </mfrac> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the stationary points of the curve are at <em>x</em> = 1 and <em>x</em> = 2.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <em>y</em> = 2<em>x</em><sup>3</sup> − 9<em>x</em><sup>2</sup> + 12<em>x</em> + 2 = <em>k</em> has <strong>three</strong> solutions, find the possible values of <em>k</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p><img src="data:image/png;base64,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"><em><strong>(A1)(A1)(A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct window (condone a window which is slightly off) and axes labels. An indication of window is necessary. −1 to 3 on the <em>x</em>-axis and −2 to 12 on the <em>y</em>-axis and a graph in that window.<br><em><strong>(A1)</strong></em> for correct shape (curve having cubic shape and must be smooth).<br><em><strong>(A1)</strong></em> for both stationary points in the 1<sup>st</sup> quadrant with approximate correct position,<br><em><strong>(A1)</strong></em> for intercepts (negative <em>x</em>-intercept and positive <em>y</em> intercept) with approximate correct position.</p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Rick <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A0)</strong></em> if extra names stated.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>6<em>x</em><sup>2</sup> − 18<em>x</em> + 12 <strong><em>(A1)(A1)(A1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em></strong> for each correct term. Award at most <strong><em>(A1)(A1)(A0)</em></strong> if extra terms seen.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>6<em>x</em><sup>2</sup> − 18<em>x</em> + 12 = 0 <strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for equating their derivative to 0. If the derivative is not explicitly equated to 0, but a subsequent solving of their correct equation is seen, award <em><strong>(M1)</strong></em>.</p>
<p>6(<em>x </em> − 1)(<em>x</em> − 2) = 0 (or equivalent) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award (M1) for correct factorization. The final <em><strong>(M1)</strong></em> is awarded only if answers are clearly stated.</p>
<p>Award <em><strong>(M0)(M0)</strong></em> for substitution of 1 and of 2 in their derivative.</p>
<p><em>x =</em> 1, <em>x =</em> 2 <em><strong>(AG)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>6 < <em>k</em> < 7 <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for an inequality with 6, award <em><strong>(A1)</strong></em><strong>(ft)</strong> for an inequality with 7 from their part (c) provided it is greater than 6, <em><strong>(A1)</strong></em> for their correct strict inequalities. Accept ]6, 7[ or (6, 7).</p>
<p><em><strong>[3 marks]</strong></em></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">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>Tommaso plans to compete in a regional bicycle race after he graduates, however he needs to buy a racing bicycle. He finds a bicycle that costs 1100 euro (EUR). Tommaso has 950 EUR and invests this money in an account that pays 5 % interest per year, <strong>compounded monthly</strong>.</p>
</div>
<div class="specification">
<p>The cost of the bicycle, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
<mi>C</mi>
</math></span>, can be modelled by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C = 20x + 1100">
<mi>C</mi>
<mo>=</mo>
<mn>20</mn>
<mi>x</mi>
<mo>+</mo>
<mn>1100</mn>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> is the number of years since Tommaso invested his money.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the amount that he will have in his account after 3 years. Give your answer correct to two decimal places.</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 difference between the cost of the bicycle and the amount of money in Tommaso’s account after 3 years. Give your answer correct to two decimal places.</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>After <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span> complete <strong>months</strong> Tommaso will, for the first time, have enough money in his account to buy the bicycle.</p>
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="950 \times {\left( {1 + \frac{5}{{12 \times 100}}} \right)^{12 \times 3}}">
<mn>950</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mfrac>
<mn>5</mn>
<mrow>
<mn>12</mn>
<mo>×</mo>
<mn>100</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mn>12</mn>
<mo>×</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</math></span> <strong><em>(M1)</em></strong><strong><em>(A1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for substitution in the compound interest formula: <em><strong>(A1)</strong></em> for correct substitution.</p>
<p><strong>OR</strong></p>
<p>N = 3<br>I% = 5<br>PV = 950<br>P/Y = 1<br>C/Y = 12 <strong><em>(A1)</em></strong><strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for C/Y = 12 seen, <em><strong>(M1)</strong></em> for other correct entries.</p>
<p><strong>OR</strong></p>
<p>N = 36<br>I% = 5<br>PV = 950<br>P/Y = 12<br>C/Y = 12 <strong><em>(A1)</em></strong><strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for C/Y = 12 seen, <em><strong>(M1)</strong></em> for other correct entries.</p>
<p>1103.40 (EUR) <strong><em>(A1)</em></strong><strong><em>(G3)</em></strong></p>
<p><strong>Note:</strong> Answer must be given to 2 decimal places.</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>(20 × 3 + 1100) − 1103.40 <strong><em>(M1)</em></strong><strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for correct substitution into cost of bike function, <strong><em>(M1)</em></strong> for subtracting their answer to part (a). This subtraction may be implied by their final answer (follow through from their part (a) for this implied subtraction).</p>
<p>55.60 (EUR) <strong><em>(A1)</em>(ft)</strong><strong><em>(G3)</em></strong></p>
<p><strong>Note:</strong> Follow through from part (a). The answer must be two decimal places.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="950 \times {\left( {1 + \frac{5}{{12 \times 100}}} \right)^{12x}} = 20x + 1100">
<mn>950</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mfrac>
<mn>5</mn>
<mrow>
<mn>12</mn>
<mo>×</mo>
<mn>100</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mn>12</mn>
<mi>x</mi>
</mrow>
</msup>
</mrow>
<mo>=</mo>
<mn>20</mn>
<mi>x</mi>
<mo>+</mo>
<mn>1100</mn>
</math></span> <strong><em>(M1)</em></strong><strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for their correct substitution in the compound interest formula with a variable in the exponent; <em><strong>(M1)</strong></em> for comparing their expressions provided variables are the same (not an expression with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> for years and another with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> representing months). Award at most <em><strong>(M0)(M1)(A0)(M1)(A0)</strong></em> for substitution of an integer in both expressions and comparison of the results. Accept inequality.</p>
<p>(<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> =) 4.52157… (years) <strong><em>(A1)</em>(ft)</strong></p>
<p>4.52157… × 12 (= 54.2588…) <strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for multiplying <strong>their</strong> value for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> by 12. This may be implied.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span> = 55 (months) <strong><em>(A1)</em>(ft)</strong><strong><em>(G4)</em></strong></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="950 \times {\left( {1 + \frac{5}{{12 \times 100}}} \right)^m} = 20 \times \frac{m}{{12}} + 1100">
<mn>950</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mfrac>
<mn>5</mn>
<mrow>
<mn>12</mn>
<mo>×</mo>
<mn>100</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mi>m</mi>
</msup>
</mrow>
<mo>=</mo>
<mn>20</mn>
<mo>×</mo>
<mfrac>
<mi>m</mi>
<mrow>
<mn>12</mn>
</mrow>
</mfrac>
<mo>+</mo>
<mn>1100</mn>
</math></span> <strong><em>(M1)</em></strong><strong><em>(M1)</em></strong><strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for their correct substitution in the compound interest formula with a variable in the exponent to solve; <strong>(M1)</strong> for comparing their expressions provided variables are the same; <em><strong>(M1)</strong></em> for converting years to months in these expressions. Award at most <em><strong>(M0)(M1)(A0)(M1)(A0)</strong></em> for substitution of an integer in both expressions and comparison of the results. Accept inequality.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span> = 54.2588… (months) <strong><em>(A1)</em>(ft)</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span> = 55 (months) <strong><em>(A1)</em>(ft)</strong><strong><em>(G4)</em></strong></p>
<p> </p>
<p><em><strong>METHOD 3</strong></em></p>
<p><em><strong><img src="data:image/png;base64,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"> (M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for each graph drawn.</p>
<p>(<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> =) 4.52157… (years) <strong><em>(A1)</em>(ft)</strong></p>
<p>4.52157… × 12 (= 54.2588…) <strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for multiplying <strong>their</strong> value for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> by 12. This may be implied.</p>
<p> If the graphs drawn are in terms of months, leading to a value of 54.2588…, award <em><strong>(M1)(M1)(M1)(A1)</strong></em>, consistent with METHOD 2.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span> = 55 (months) <strong><em>(A1)</em>(ft)</strong><strong><em>(G4)</em></strong></p>
<p><strong>Note: </strong>Follow through for a compound interest formula consistent with their part (a). The final <strong><em>(A1)</em>(ft)</strong> can only be awarded for correct answer, or their correct answer following through from previous parts and only if value is rounded up. For example, do not award <strong><em>(M0)(M0)(A0)(M1)(A1)</em>(ft)</strong> for an unsupported “5 years × 12 = 60” or similar.</p>
<p> </p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows the probability distribution of a discrete random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a \geqslant 0">
<mi>a</mi>
<mo>⩾<!-- ⩾ --></mo>
<mn>0</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b \geqslant 0">
<mi>b</mi>
<mo>⩾<!-- ⩾ --></mo>
<mn>0</mn>
</math></span>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAgQAAABMCAYAAAASlq++AAASaklEQVR4Ae2dv4vbSBvH9W+odpsuXSpXbtJckyaFi222SHGwhcDFwRUvpBAYAoGDgGHZ6uAQbHNwLJhrAi8G8TYpFsNbhGNxE17C4iIsi3heRtZ4NY9+2bKlecb7DSy70ow0j76f+fHVaKR4hH9QAApAASgABaDAs1fAe/YKQAAoAAWgABSAAlCAYAhQCaAAFIACUAAKQAEYAtQBKAAFoAAUgAJQgIqGwPM8wg80QB1AHUAdQB1AHTj9OpA3QoVHBqoC4J8sBcBEFg8dDbhoJWT9BhdZPFQ0YCKPSRmXwugPcPLAgYk8JmWNSWaUzy8qtBd5zMFEHhMVEecCQyCTkxEVh2YkYsOaAuBiTfragsGlVh4riWBiRfbGQjkXGIJGyexn4NDsR4QIlALgIrMegIs8LmAij0lZHwZDIJOTERUakyGHmA1wEYPCCARcDDlEbICJCAyFIDgXGIKCRPJ2cGjyInyeEYGLTO7gIo8LmMhjoiLiXGAIZHIyouLQjERsWFMAXKxJX1swuNTKYyURTKzI3lgo5wJD0CiZ/Qwcmv2IEIFSAFxk1gNwkccFTOQxKevDYAhkcjKiQmMy5BCzAS5iUBiBgIshh4gNMBGBoRAE5wJDUJBI3g4OTV6EzzMicJHJHVzkcXGCySqi8fZLvecUrR7lCXnkiDgXGIIjC9zF6Ti0Lsro/pz3tJxf0x/hmAbBnO67L7DzEk6Di5bpge6id+SPZrRM9D43f58WFzcZ8KjdYfKN5sFL8npqB8lqQZfBKH386I8/0mL1wKUr376fU+DnP6v8hmbLH+V5a/ZyLjAENWJJSeLQpMS1exw/aDk7o7fjn8j3PPJhCHaXrqecyV1EZ6qD6akj7PKy3G8vXapj59zOMEkHWp9Gs1vq3BevFxQOX9NkfkcJPdBq/isNh1OK100lZ+Z9O5vRvt1yLjAEdtrHXqVyaHsdLClzckuzkQ9DIImJikV1TOOfKRi/gCGQxuZE4nGjD0vofj4h3xtSGK87Vl7dJL1hfaGanXjVbEZUex39QvP7JuPQfAmcCwxBs2bWc3Bo1gNqGwAMQVvlOjzuO8XhzxTGy16nSju8ILz90aW4Lc9tpQ97jCkc7LMWYE1xOCTPnxxlsK2VKu0LB2zwzwxJ7SydNi0+DYNPFM2XdIh14VxOyxDkF4VkUy/J6jNN1Z1PL66vtgq0TuTQWp/I9oEwBLYJsPITWscfaBwuaE39PjtlgRx10/32ktB6+ReFab/l0/Digsa+R4MwJleXubVncoAW+xoC3T9dzOjmMqBhOiWvBt6Ilo3T+PtV4WQ5o5H3koL5t9yBerCvWQ+Qxaj03PwcFh/nclqGIJVWP195SUF0TdPgim6PDDNHsJc/ObReCu2iEN3gsIagC3X3P2f6qOBD9swShmB/Abs4InuW7I0oiG6fjFph8Oii7O7O2a4PO1CLfQ2BvqH0xzRdrCihe7qdnZHvHXtNQdXAX7W/hEuyovj6EwVDnzzPp2Fq6kvyNeziXE7QEBCRXoHpv6PobsdVmw3C2Uzm0GzGclDZMAQHyXfcg79TPH2fax8wBMfVt93ZNos7X9BZ9DVb1PZIq+icPK/mrrFdUb0e1aYPO1iLvQyBHoxfUxh/f9ImMwnHnZ3RZXGmVfufwin8ldzRfDJq/ZiDczlNQ3BC05+qAnBohUrhyg4YAiGk1KOC32iyHXRUWDAE1uEkXyk64ws7s+fatc+VrUfeGMDefVgbLfQd/nY6XU+r539XLRgsr/+bqf0BjaN/itd4QHmtHxkUo8hugPnjh7KMxX2cy2kaAl2ZHHfVGh+Hpvc79xuGQAiyrPOr7DiPPUXa72W72l5KB4n01TT338zZl8lRtNhnhqC0b9q8CeB1MdOclveKrSHIytvX/KXneovvEJR3M2oNQUBnwTsaOv7cTV/fvo1JHyfud2mjExflzgGdDJf0isvvkHYWQ1BGN7mUTRerN0Bek+dV3KEK0rwplP2YHEmLPQxBmQHRjyzGsy8HreQv1+aA1w75Ce/nNJm0+9gb53JyMwQK4vl5RHeP+p33G7orTI9yRWVvc2iyo62JDoagRhzbSTAEdgnoQTBbP5CsaPHhPU0u1Ffs3tCn+YL+s+tX7OxeSGnp+/VhR9JiZ0OQrdPYvm74QKv4ioLhgIaTG1od/rp/qSbp9z9qP0yULZDPfawoWcV0fR1vY0rfogtCmresG5zLyRiCxzikgVptuX1FRLtrvVq3nIkLezk0F2I2Y9QNPP8sjy+oMY9wYct9LnmVYQjyalj5e/2FZumrhh754yndLP+XLSj0ux2YerjYvdvKMbTY2RAQqYE2Csfpl1RVrN4woNmB7/jvIuvTa/Fq7Lqi2BjYywzBDU3SNws88vwxhX/8fdArkZzLyRiCXcR3NQ+H5up1nFrc4CKTKLjI4wIm8pioiDgXGAKZnIyoODQjERvWFAAXa9LXFgwutfJYSQQTK7I3Fsq5wBA0SmY/A4dmPyJEoBQAF5n1AFzkcQETeUzK+jAYApmcjKjQmAw5xGyAixgURiDgYsghYgNMRGAoBMG5wBAUJJK3g0OTF+HzjAhcZHIHF3lcwEQeExUR5wJDIJOTERWHZiRiw5oC4GJN+tqCwaVWHiuJYGJF9sZCORcYgkbJ7Gfg0OxHhAiUAuAisx6AizwuYCKPSVkfBkMgk5MRFRqTIYeYDXARg8IIBFwMOURsgIkIDIUgOBcYgoJE8nZwaPIifJ4RgYtM7uAijwuYyGOiIuJcYAhkcjKi4tCMRGxYUwBcrElfWzC41MpjJRFMrMjeWCjnAkPQKJn9DBya/YgQgVIAXGTWA3CRxwVM5DEp68NKDYGChx9ogDqAOoA6gDqAOnDadSBvVUoNQT4D/ravgGqQ+CdPAXCRx0RFBC7yuICJPCZlbaUw0gCcPHBgIo9JWWOSGeXziwrtRR5zMJHHREXEucAQyORkRMWhGYnYsKYAuFiTvrZgcKmVx0oimFiRvbFQzgWGoFEy+xk4NPsRIQKlALjIrAfgIo8LmMhjUtaHwRDI5GREhcZkyCFmA1zEoDACARdDDhEbYCICQyEIzgWGoCCRvB0cmrwIn2dE4CKTO7jI4wIm8pioiDgXGAKZnIyoODQjERvWFAAXa9LXFgwutfJYSQQTK7I3Fsq5wBA0SmY/A4dmPyJEoBQAF5n1AFzkcQETeUzK+jAYApmcjKjQmAw5xGyAixgURiDgYsghYgNMRGAoBMG5wBAUJJK3g0OTF+HzjAhcZHJ3m8s/FI0H6eyT5w1oHP0jU+Q9o3KbyZ4X61B2zqVzQ5AsZzQq/RTyCxqHv9N8eV8jX0Lr5TWF4TUt18km3yqisXE+3WgeaRWdZw0p+9TkOKJVzdkPT7qn28spTW+WtD78ZJVn4NAqM0pOSFYUXwY0VOz8MU0XK8qIVkSt2P9F4fhFxnREweWCVvUHVZyrm92nwCVZLegyGKUa++OPtFg97CBWQvfzCfn5djia0VIIG/e5aH3f0Gz5Ywce8rO4z0S+xm0i5Fw6NwSbIH/QcvaGvG2noTr7iIKhT55/RrPbMlPwQKv5v2gcLoqD7foLzdKBgjWY9YLC4YCGwazBaLSRruqYLM7JTWeDFYdWFYnc/d8pDn+iYaZRsrqhyfAnCuPvlSEnd3/SdPpXZgQfaLX4SGPfp2FZfag8S7cJznNJ28trmszvKCFVj3+l4XBKsTbfVfIlXyk600ZNmW+fRrPbBoNXdbLj73eeC32jefAy118eX6O+z+g+k74V66c8zsWSIdhcrJ498IM5mZYgoXU8remctIPOdUTJHc0nb2g8+1I0EJ1rmw14HQ1WHFrnl3PkAlLO/oTm9/oWMuO3NYi8wB/037//TXc6e5qcmUrjPPy4frfd5rLR02x7aiB61TC4b9rmqNBm+9W+rjS3uRDR/ZwC36NBGNNj3YU6lOY8E4e03idUzsWqIdAV/2nmILuU7E6/9q4jazSeeixg1QxsYt6YGzZjsQ+ZmrwcWk1WgUl8digLMeW3j16ZiYAhOA7j5JZmowEb/JuMmio6u3v1RhTMoh5n4na/bLfbC9FjHNLAe0nB/NvuFy08p+tMhMvbOjzOxaohKJ8h0Hf/TYNF1jH5bym46GpmIL8uQU9X6+lrj7xBSLG28I8xhQOPzDuu1pyMAzk0I1H6Rjrw+EVdUkOQm+FpvI5NvRicRWzmoPHAzjK4zGXT9vig09z2dJtV1775GVEQ3VqYlavG6jIXIj0T9jPNbi43j1WV1sMJRbXrrar1kJDiNhOt4D0tb6Y09lXdH9FF8JZ8b0hh3OUKMl12N785l34NQW69QLL6TNN0HcBr9ixZD/T5KeYyMbKG4+mBuixPtq+wEFF3ZvnfNWD1M1M/oOjmIwWljyWy1cEd3MFyaDVXKi+pauCv2l95BapejFldqczcS4K7XKoG/qr9RTmTVUzXs2yRqMfbcDF/n3vc5aJU0m8ZvKDx9DOtkoTWt5ebQajyEVuf6rYry20mRJTOQo+ejFnaf6kF0k3jVDu9+jqKc+nXEGzvKjYDsT8OKYrZavPsTtu4+y5TRwPy+njWpjtKj/zKO9Q1xeGQPK9pZqPsYur3cWj1uYWlVg38VftLw1fPrT+ULzAtzd/PTne56PrM62rV/mo9NwtES2aAqg/pPMVdLnr9AL/JyUxCfkaycxWPW4DTTOiB7qJ35PvvKLrTb+FkTBw2aYow59KvIdhFvF0MgV4z8OmKwpHfz2rcxgFMG4KamYaWbYxDa3kaO4cd45HBekHT4Ipum1a/93yFLnNp+8igKHFmIgTdKbnLpcKQZW0oXS9VBODEHneZqMmBiM589ngzHafYPidImEFyLu4ZAm0G0ml7vcCJ3+mYF02HPjJIZ4xUpfBqzAcMAVM92yxbzU60GZAauKkzJF/pevq7ODOgQuONqfz6he5NB5lXbOFaxQLQhktIWe5i9hvOc6xkd7no9QPmNPSmrbygs+irmFc792V1Wkyyt+BOYOEn5+KWITDMgKqS2lHrjxPtW013zK/WEJyfU3AxqnlmpA3BDoPcjsXqbBya3u/K77RDM+4gM25Ng4jiPf2N5vmP5ay/0OXsM3tN1Y4SbnMpM2rKYDe9dsi1Vizf00TQinhnuZTNpmXrl/zxpUhTzGtD1bazTPRbNfm+Kn0LzifPO6dopVeVV1257P2cS0+GQL2n/5q8XT56ogEYA8gDreIrCoYviy45u/vvrsGo50cBnUdf6TH96qJamb2kePo+9zxJQd91MeT+FYRD2/8Mto9o/jDRZloutzhtfUtR9gU9df1PP3Km6Zzn0vhhouzZ6bbdqnb4J11v1/2oN25+o+CX7j7K1abmOssl7cue3vzYfkVy+KtpituIYvkYZ5ls+/XN+gG1GP5D+AtdqI/qjT7SPP7S2Qfp+kDGuXRuCDbTXft06PquP7vT1msKtoOCfkav8+1z7n0k1nf8udeqtDMsewWozN3vU1xNXg6tJqvcpGRFi+l487nbYUCX20FlE7JhCPRbHVvmecbHn4FpK9opcHl628enYXBFcX42Ri+myhsC9TXDjItaFPzHvNvPdrdh4ywX9XnvKMxea1N1Xn3rYf702fY2Ygg5xlkmlHvLw1Of21dfT/2a/X8To+wrn0JEbhEG59K5IWgRI1E6uPKPprQ6U28HbYxPN4MVh9bbRaGgWgXApVYea4ngYk36yoLBpFIaqwmci0xDoFxZ7aeLrWpYUjg+XVwiysnv4o3p5C/YkQsEF3mgwEQeExUR5yLUEKhQu/9Pg46DqPs4ObTjxI2zHKoAuByqYDfHg0s3uh5yVjA5RL3ujuVcBBsCJULJf3/cnTYtznxPy+gDhR1/upVDaxEoDulAAXDpQNQjnBJcjiDikU8BJkcW9Ein41yEG4IjXbXjp+HQHL+ckwkfXGSiBBd5XMBEHhMVEecCQyCTkxEVh2YkYsOaAuBiTfragsGlVh4riWBiRfbGQjkXGIJGyexn4NDsR4QIlALgIrMegIs8LmAij0lZHwZDIJOTERUakyGHmA1wEYPCCARcDDlEbICJCAyFIDgXGIKCRPJ2cGjyInyeEYGLTO7gIo8LmMhjoiLiXGAIZHIyouLQjERsWFMAXKxJX1swuNTKYyURTKzI3lgo5wJD0CiZ/Qwcmv2IEIFSAFxk1gNwkccFTOQxKevDSg2BgocfaIA6gDqAOoA6gDpw2nUgb1UKhiCfiL+hABSAAlAACkCB56EADMHz4IyrhAJQAApAAShQqwAMQa08SIQCUAAKQAEo8DwU+D9dGYBDHg/NggAAAABJRU5ErkJggg=="></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b = 0.3 - a"> <mi>b</mi> <mo>=</mo> <mn>0.3</mn> <mo>−</mo> <mi>a</mi> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the difference between the greatest possible expected value and the least possible expected value.</p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>correct approach <span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: italic;font-variant: normal;font-weight: bold;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">A1</span></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.2 + 0.5 + b + a = 1"> <mn>0.2</mn> <mo>+</mo> <mn>0.5</mn> <mo>+</mo> <mi>b</mi> <mo>+</mo> <mi>a</mi> <mo>=</mo> <mn>1</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.7 + a + b = 1"> <mn>0.7</mn> <mo>+</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo>=</mo> <mn>1</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b = 0.3 - a"> <mi>b</mi> <mo>=</mo> <mn>0.3</mn> <mo>−</mo> <mi>a</mi> </math></span> <em><strong>AG</strong></em><em><strong> N0</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>correct substitution into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}\left( X \right)"> <mrow> <mtext>E</mtext> </mrow> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </math></span> <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.2 + 4 \times 0.5 + a \times b + \left( {a + b - 0.5} \right) \times a"> <mn>0.2</mn> <mo>+</mo> <mn>4</mn> <mo>×</mo> <mn>0.5</mn> <mo>+</mo> <mi>a</mi> <mo>×</mo> <mi>b</mi> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo>−</mo> <mn>0.5</mn> </mrow> <mo>)</mo> </mrow> <mo>×</mo> <mi>a</mi> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.2 + 2 + a \times b - 0.2a"> <mn>0.2</mn> <mo>+</mo> <mn>2</mn> <mo>+</mo> <mi>a</mi> <mo>×</mo> <mi>b</mi> <mo>−</mo> <mn>0.2</mn> <mi>a</mi> </math></span></p>
<p>valid attempt to express <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}\left( X \right)"> <mrow> <mtext>E</mtext> </mrow> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </math></span> in one variable <em><strong>M1</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.2 + 4 \times 0.5 + a \times \left( {0.3 - a} \right) + \left( { - 0.2} \right) \times a"> <mn>0.2</mn> <mo>+</mo> <mn>4</mn> <mo>×</mo> <mn>0.5</mn> <mo>+</mo> <mi>a</mi> <mo>×</mo> <mrow> <mo>(</mo> <mrow> <mn>0.3</mn> <mo>−</mo> <mi>a</mi> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>0.2</mn> </mrow> <mo>)</mo> </mrow> <mo>×</mo> <mi>a</mi> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.2 + 0.1a - {a^2}"> <mn>2.2</mn> <mo>+</mo> <mn>0.1</mn> <mi>a</mi> <mo>−</mo> <mrow> <msup> <mi>a</mi> <mn>2</mn> </msup> </mrow> </math>,</span></p>
<p><em> </em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.2 + 4 \times 0.5 + \left( {0.3 - b} \right) \times b + \left( { - 0.2} \right) \times \left( {0.3 - b} \right)"> <mn>0.2</mn> <mo>+</mo> <mn>4</mn> <mo>×</mo> <mn>0.5</mn> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <mn>0.3</mn> <mo>−</mo> <mi>b</mi> </mrow> <mo>)</mo> </mrow> <mo>×</mo> <mi>b</mi> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mn>0.2</mn> </mrow> <mo>)</mo> </mrow> <mo>×</mo> <mrow> <mo>(</mo> <mrow> <mn>0.3</mn> <mo>−</mo> <mi>b</mi> </mrow> <mo>)</mo> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.14 + 0.5b - {b^2}"> <mn>2.14</mn> <mo>+</mo> <mn>0.5</mn> <mi>b</mi> <mo>−</mo> <mrow> <msup> <mi>b</mi> <mn>2</mn> </msup> </mrow> </math></span></p>
<p>correct value of greatest <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}\left( X \right)"> <mrow> <mtext>E</mtext> </mrow> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </math></span> <em><strong>(A1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.2025"> <mn>2.2025</mn> </math></span> (exact)</p>
<p>valid attempt to find least value <em><strong>(M1)</strong></em></p>
<p><em>eg</em> graph with minimum indicated, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}\left( 0 \right)"> <mrow> <mtext>E</mtext> </mrow> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> </math></span> <strong>and </strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}\left( {0.3} \right)"> <mrow> <mtext>E</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mn>0.3</mn> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p><em> </em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {0{\text{, }}2.2} \right)"> <mrow> <mo>(</mo> <mrow> <mn>0</mn> <mrow> <mtext>, </mtext> </mrow> <mn>2.2</mn> </mrow> <mo>)</mo> </mrow> </math></span> <strong>and</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {0.3{\text{, }}2.14} \right)"> <mrow> <mo>(</mo> <mrow> <mn>0.3</mn> <mrow> <mtext>, </mtext> </mrow> <mn>2.14</mn> </mrow> <mo>)</mo> </mrow> </math></span> if <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}\left( X \right)"> <mrow> <mtext>E</mtext> </mrow> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </math></span> in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a"> <mi>a</mi> </math></span></p>
<p><em> </em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {0{\text{, }}2.14} \right)"> <mrow> <mo>(</mo> <mrow> <mn>0</mn> <mrow> <mtext>, </mtext> </mrow> <mn>2.14</mn> </mrow> <mo>)</mo> </mrow> </math></span> <strong>and</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {0.3{\text{, }}2.2} \right)"> <mrow> <mo>(</mo> <mrow> <mn>0.3</mn> <mrow> <mtext>, </mtext> </mrow> <mn>2.2</mn> </mrow> <mo>)</mo> </mrow> </math></span> if <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}\left( X \right)"> <mrow> <mtext>E</mtext> </mrow> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </math></span> in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b"> <mi>b</mi> </math></span></p>
<p>correct value of least <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}\left( X \right)"> <mrow> <mtext>E</mtext> </mrow> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </math></span> <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.14"> <mn>2.14</mn> </math></span> (exact)</p>
<p>difference <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="= 0.0625"> <mo>=</mo> <mn>0.0625</mn> </math></span> (exact) <em><strong>A1</strong></em><em><strong> N2</strong></em></p>
<p><em><strong>[6 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = 6 - \ln ({x^2} + 2)">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>6</mn>
<mo>−<!-- − --></mo>
<mi>ln</mi>
<mo><!-- --></mo>
<mo stretchy="false">(</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \in \mathbb{R}">
<mi>x</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>. The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> passes through the point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(p,{\text{ }}4)">
<mo stretchy="false">(</mo>
<mi>p</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>4</mn>
<mo stretchy="false">)</mo>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p > 0">
<mi>p</mi>
<mo>></mo>
<mn>0</mn>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The following diagram shows part of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span>.</p>
<p><img src="images/Schermafbeelding_2018-02-12_om_13.30.18.png" alt="N17/5/MATME/SP2/ENG/TZ0/05.b"></p>
<p>The region enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span>, the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-axis and the lines <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = - p"> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mi>p</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = p"> <mi>x</mi> <mo>=</mo> <mi>p</mi> </math></span> is rotated 360° about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-axis. Find the volume of the solid formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(p) = 4"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>p</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>4</mn> </math></span>, intersection with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 4,{\text{ }} \pm 2.32"> <mi>y</mi> <mo>=</mo> <mn>4</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mo>±</mo> <mn>2.32</mn> </math></span></p>
<p>2.32143</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = \sqrt {{{\text{e}}^2} - 2} "> <mi>p</mi> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mtext>e</mtext> </mrow> <mn>2</mn> </msup> </mrow> <mo>−</mo> <mn>2</mn> </msqrt> </math></span> (exact), 2.32 <strong><em>A1 N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to substitute <strong>either their</strong> limits <strong>or</strong> the function into volume formula (must involve <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^2}"> <mrow> <msup> <mi>f</mi> <mn>2</mn> </msup> </mrow> </math></span>, accept reversed limits and absence of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi "> <mi>π</mi> </math></span> and/or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{d}}x"> <mrow> <mtext>d</mtext> </mrow> <mi>x</mi> </math></span>, but do not accept any other errors) <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_{ - 2.32}^{2.32} {{f^2},{\text{ }}\pi \int {{{\left( {6 - \ln ({x^2} + 2)} \right)}^2}{\text{d}}x,{\text{ 105.675}}} } "> <msubsup> <mo>∫</mo> <mrow> <mo>−</mo> <mn>2.32</mn> </mrow> <mrow> <mn>2.32</mn> </mrow> </msubsup> <mrow> <mrow> <msup> <mi>f</mi> <mn>2</mn> </msup> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>π</mi> <mo>∫</mo> <mrow> <mrow> <msup> <mrow> <mrow> <mo>(</mo> <mrow> <mn>6</mn> <mo>−</mo> <mi>ln</mi> <mo></mo> <mo stretchy="false">(</mo> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mtext>d</mtext> </mrow> <mi>x</mi> <mo>,</mo> <mrow> <mtext> 105.675</mtext> </mrow> </mrow> </mrow> </math></span></p>
<p>331.989</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{volume}} = 332"> <mrow> <mtext>volume</mtext> </mrow> <mo>=</mo> <mn>332</mn> </math></span> <strong><em>A2 N3</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{{27}}{{{x^2}}} - 16x,\,\,\,x \ne 0">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>27</mn>
</mrow>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>−<!-- − --></mo>
<mn>16</mn>
<mi>x</mi>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>x</mi>
<mo>≠<!-- ≠ --></mo>
<mn>0</mn>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of <em>y</em> = <em>f </em>(<em>x</em>), for −4 ≤ <em>x</em> ≤ 3 and −50 ≤ <em>y</em> ≤ 100.</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>Use your graphic display calculator to find the equation of the tangent to the graph of <em>y</em> = <em>f </em>(<em>x</em>) at the point (–2, 38.75).</p>
<p>Give your answer in the form <em>y</em> = <em>mx</em> + <em>c</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of the function <em>g </em>(<em>x</em>) = 10<em>x</em> + 40 on the same axes.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAdwAAAGWCAYAAADSYDL/AAAgAElEQVR4Aey9C3Rc1ZEuXGq1Wu+3ZFsIIYxDjGOMsTEGA3HAEK5DGJKQBIZwE5JMhtzcrPmZ/H8m80hWhrmTmcmayZ1hSAghAUIgGOMXxvht45dsy0/Zer8ly7LeUqvVarVarVaff311erdastRdm0hgoGstu1un69SpXVW79jn71P52jGEYBkUpaoGoBaIWiFogaoGoBWbVApZZlR4VHrVA1AJRC0QtELVA1AJsgeiAGw2EqAWiFohaIGqBqAXeBwtEB9z3wcjRS0Qt8KdY4Pe/+z199vP30r133x0UMzw0RNd98jr65XP/HTwW/RK1QNQCV7YFrFe2elHtohaIWuBbf/ktysiZQ1975IvU0z9AuZnpRPGJdOeqVVR2vipqoKgFohb4kFggOuB+SBwVVfPjbYEbbriWPD4fOXq7ecBNtFror77/FNXW1n68DRNtfdQCHyILRKeUP0TOiqr68bVAQlISpSQkUF9fPxvB5/PR+j+uo6985SsfX6NEWx61wIfMAtEB90PmsKi6H08LJCWlkDUhgewuOxtg5zvv0CNf+3NKTEz8eBok2uqoBT6EFogOuB9Cp0VV/vhZICkhgRLwhNvWTy0tLVRRW02333570BA9PT3B79EvUQtELXBlWiA64F6ZfolqFbXABAskp6ZSotVKTqedXvr97+hHP/xR8Pe9u3fTjZ/6FJWVVQSPRb9ELRC1wJVngZgo0tSV55SoRlELTGWBm29eTjarld548w1asGABs/T399Ott95KjY2NtGrVbXTkyFGyWqO1kFPZL3osaoEP2gLRJ9wP2gPR60ctILRAQX4e/fzf/z042OK0f/uXfybf2AilpaRRfX0jPf/rZ4XSomxRC0Qt8H5bIDrgvt8Wj14vaoH3YIETJ07Qn3/tEVqzZhz84syZMvrlL5+nf/v5f1J6ShI9/bOf0dP/+M/U0dH2Hq4QPSVqgagFZtsC0Snl2bZwVH7UAu/RAmXnz5OfiJwOBx0/c4J+9MO/I3WHPDw8zFPIa+5eQz/4m/+PVi5fSTUNDfSdb36D+gcHaffOndGp5fdo9+hpUQvMlgVU/50t+VG5UQtELfAeLfCNb36T/vzPH6EDR47Q34UMthD33PPPU1//AP39j39MGJXjLEQW8tO//+IXVFxcTNu2bX+PV42eFrVA1AKzZYHoE+5sWTYqN2qBP9ECu/fupySblVaHYChDZGV1Nd2xciW9/sYb9OCDD1JrWxutXL6c6hoaKDU1lV743e/oH370I6qpq6Pc3Nw/UYvo6VELRC0wUxaIDrgzZcmonKgF3icLPPrYV8nr8dPGzRvJarHwgHv7XcupoqSBMjNTyTfio9WfuYvW3Hcf/exnP3uftIpeJmqBqAUiWSC6fiCShaK/Ry1whVngqe/9gBYuXsCDrVItxuUntRrIGm+lNzdupL7+KBiGsk/0M2qBK8EC0QH3SvBCVIeoBTQscMfqO6bk9gVLqogKCgr435SM0YNRC0Qt8IFYIFo09YGYPXrRqAVm0gJ+GrNYyco1zTMpNyoraoGoBWbSAtEBdyatGZUVtcAHaAEf1hBFKWqBqAWuWAtEB9wr1jVRxaIWEFogsCwo+oQrtFeULWqBD8gC0QH3AzJ89LJRC8yUBXyBXuyzREsyZsqmUTlRC8yGBaID7mxYNSozaoH30QJWstCIzU9Wn+99vGr0UlELRC2gawHxLbHP56PBwWEi8lFCQiolJk5/6uDgIIEfhJ1LUpOTiSxTj+2m3MGg3tjzM9ym2qGycVJmZmbw3Mu++P3UPzAQPKwrGyAC4XZewU4tiridqanqz8s+PYPDNOzzBI+nJqWTNX5qm4BJR/ZkG0bSe3BgkHz+EP+E0VtbdqjvLVZKTZ/eJpNlJ9qSKSHZFrTR5C86vp8sW9f34eLqT5adnj5tf5js+0h6Dw95yeV0UpzbTw6XkxJTk2csZn0jIzTodgfdEDmuBsjnN18kR+oPk20YUXZIXEEhHf+kJiWRNT4+2I7JX0LjCj0yPUxOmax3ZP8MkcfrDV5SR+8Em40SkTunIcB7ejzjOSUzXFz5/dQ3NEiWwIt+Xdk6/plp3+vkQphK8Ye1xzQ2ne3D04+ak64M565b9zJ5PD66555P0/LlK+nokSN08vRp8o+OkiUujh555BFeilBUVETV1dVktVooJSWNnvif3yJrPPHawEsXL9LI6CjdvnIlrVmzhhDsL774ClksZkddtWoV3XHHHVRWdp727Xs3KHvt2gdo8eJFDFtXXl5ONouVLDaib3zj24yuc+DAATp37hzzL/jkJ+nhhx8mz4if1q17lXVGc5Ts1tZWWv/666wzdL9z9Wq+5sljp6m08hwlJFj5nG9/+9vcsZ977r/5b/DOycujJ554gq3z8ssvB620aNESeuCB+2lgYJB++/xzQdnf+e53WUZZbSUVHT7Menv9Pvr2k9+h9Ph0euP3r1GnvZv1tiXG01NP/eAy2fPnz+f24If/+PnP+XfYG23Eb/X19bRz506yWKzk9/voG9/4BiMMbdu2jWqrqoK6/M3f/R2fu2HTBnI4HPx93rx59Pjjj/P3UNn33nsv3XzzzQRbbdmyhX3p8/mD1zx04ACdDdgbujz11FOc6Pft20fNzc0sLyUlib773e/x9+eff55vfuLj4uiWW2+lu1evJmyavm7duqBN7rvvPlq6dCkdP36cjh05EtT723/5l5SdnU2nT59mH0MgfPT97z/Fsl9//XVqb21l/ttuvZXuCpGtfLls2TKOt1OnTlBR0TG29ygRPfboo2zD4mPFVF5pxpXP6qfvfft7lJCcwHY9X1ZGcUS0dPlyuv/++wl94ZVXXmVbQwEVV9W19bT9rc1Bve+9fw33E6U3dEHu/c53zJg9dOQInT19mvvDgvnz6dFHH+X2hMas0rujo4Ntpfqaamd55Rnaun0nDbq99NIf/kDf/+532ffKhhRPlJaUHvTDhg3ryOUyk/SCBdfQF7/4VU7azz33HPnGhskam0hKdv3FC7Rz2/ag7x955GEqKJhPJSWnaM/e/WSLi+dz/vZHP2G9t2zZSr32Xv6ek5MT7CccVxjvRogW3byIHlz7haDvkSMQVw8+uJYWLlzMsbNh4+usB/RRskPjKtT3//FfP2e5fouPrs6fz7Hc1dFB6zdsCOr9mXs+QyuWr+B8VXz2uMkfT/TUk39FCcnJdPjwfqqtbWK9k5KS6HvfM2P2dy+8QA53P/OvuvsOuuv21ZzMX3311WCOWHXbbXTHXXdxzBYdPRDU+xtf/wvKy8uj02fPctxCOPT+3vf+iiwWC6GNrRc72X6rbl9Nq1ev5riC7/1eIuSIxcuW0to199H58+dpz97tQdkP/dmXadGiRdwXAOMJstgs9M3/+U3ONbv37qXykhKC7xcu+BQ99NBD/AC0Zf0G8rjcLBvnP/DAA0F7W/xW5r/zNjMXVleX08GDRSwb/33ta1/j9qi4gr3nzS0I+njTpvVktzuZX+UrDHwvvvACy4XvlQ2RH5CbFEEP6APZaA/8npKYTt//q79ili1bNpHDYcqeMyeLHnvs65xrkJca6+qC8lV+w3Hkt28++R3KTk1Xl7kyPrEfroSczmHj2WefNTo7L0nYjaamJqO4uFjEC6Zdu3YZdrtdxH/x4kVjX9FBES+YDh48aLS3t4v4ofevf/1rY3R0VMT/7rvvimXbnQ7jnXfeEckFU1FREdtResKmTRukrMaOHTuMPXt2ifnXrV9vjHrGRPx1dXVavt+8ebPR63SIZF+8dMkoPiaLK+j74osvGlU1VSLZ8P2xY8dEvGDat+9dcX9A/CHGpVR0uEgcV1VVVUZGWoa4/5w8WSyOq+HhYWPjxo1StY2SkhL+Jz1hwwZ5zB47dtjYrMG/fv06A/pLqOnCBQN2kdKWLVvE9obvDx+W5SvE7MuvvmKUlp4TqdLd3a3Vj5GTEecScjqcxtatW4zRkREJO+t8oU4mG7n+mWf+U2xD+AZxLqGRsTFjy3p5XElkzhSP+Ak3NdnGT7B40pAQployM2W8kJeVlRF2Kiz0mpA9N12OEQudcY6EwFc439zcW8IPvaWyrRTP7ZTIBU96egpZrTK9wZ+bmycVTfPmzeGnLekJBflziWIxCzH9NLiSBXuk58rvLPGUnSCQC/k2i41SU5LUpcJ+WuNMAIikpLSwfOpH1jvMdKLiU5/Z2Zlks8l0gezc3Lnq1IifmdnZZLFGtjUEYQoPG9NLCa8zpDGLqcecOXOkoikpK4lsPrku+fn5Ytnpabnk88tsAqF5eflEYzL+lIQEGk6Sx+zcuXPF+Qr+yc6W+R6vmQrzCyhV+GQGP2ZlZcltmJ4q9j3Fx/NsicU2/Wue0AuzzjaZ7xNtNsrPny+2YWZaNtmSZX0NGmTnyceH0DbM9vcolvJsW/jjKh/v8qZ5b/9xNclstbu1rZW356trqOPXK7N1najcqAWiFvjTLCC7/Qtc49ChI/zu5U+75JV9Nt4p473lR53wTlAVF8xKW6+QwRa+hE8/yoRCJb/fTx914IuPU98cDCn2/CjGLuogVK3HR7F907VJa8Ctra0kl8s1nawJx1H0hAIVKe3fv1/KygVZhw4dEvOfOHGKfCGVguFO7O3tpb1794ZjmfAbChqkAxf4Nm3aMOH8cH/Ahh1tbeFYgr+hevKNN94I/h3pC4oTmpvrI7EFf4fs0IrI4A9TfMFgXl5ePcUvUx964803xTYc9Hi5aGdqSZcfRTHdpUuXLv9hiiPwJQo3pKQTg80tLbR3726paDpz5ozY3lwIQ14SzkBzQSIK1iTkGfLQ66//QcLKPJWV1VqJVEc2/Lj/gLzfv/HG6zQ4MCTSHX0T/pfS1m3bCHEuIfSbM6dOSViZBzHb3GIWHkpOAr+UThw/xf6X8r/9zttSVpYL/0sI48i2bVslrMzDuVBob+RCnbgSKzEDjLIJ98CFrFbZXD7YMaMYGzt9Kf5k3XUeiFDRjDt6OelNb/o11jOaesvMiHc5IyNjYrXRRJ2VlVomIdJ6h6sr2zBGxO3ExunoJBKyjI6QThxCJuw+G6QTs7i+rg2lOqM/cJWp9AQdvlgwy/u9rk10ZNvISlaLLE7MJloIxbcSQvzp6G6Myfsxrh8Tizp3GenGq47eKJXQicO4WA4AkeKmXHm/R3W6DqklZ7Jz5DErkzczXFpPuDqOQhCMjcmNrzOA+slCFqwJEhLK8H0jcudatBO0LAmgU+uKFuYLtoRWx0MalZtQKxkJ3RJkw42ZNMnAizpxiItIB3NTIXmX0NLD7581G/r9FrIE1lUHjRrmC+wttcnoKF7Fy/uOlk3C6DjVTx6Lj3zSEZTjxEtWoUKIPyErq2aVm4RjWzcX6uiiw6vjSzQUsSUl5J+YGJ2HLHl2Qxux97OUNFilImeEL1o0NSNmjAqJWuCDs0BrWxvduWIFldbUUWYYoJEPTsPolaMWiFoAFpDfMnxM7IU7fxRnSJ8APqxmGRz08EL7D6v+Ur0/Dr4EatiIz09+jSdRqf2uJD68C/2oF8DB3h+LmFV5Vufx/EoKxveoi3jARYJ+8803xFXKXa0dJH2Bjrmc4ydO0YCwMq+nq4vOnTknbnJp+Xmx3qhqXbfuj+IpaKBb9feNQzyGUwodSacoB4habRpFU0eOHAl3+Qm/FRXtp6KiwxOOhftj/4ED4psQ2BBIY1KC3tJEimKfyvJKkWivz0cbNmxgJC7JCWaxV7mElXnOnj0nLvZCUQ6K96QE30sLm7xulwmp6B2H+Qt3ner6amptkRXjYZDD6gQp1dfWiu0NmToxC4QrIE5JCXrrFPrpxCz6sTxm+6m8vFSkNmJ226atVFFRIeJHXJ3SKMiCHtJiL5WvpA8f9fW1WrJffvlFklZjwzfSqmboe+SIvLhOZOgZYop9+umnn5bI8nqHqbj4KNlsCeRyuyg3x1xYDCMARgv/sAg7Li6OjV5RX00Ou53GxsYIMG8gOBpVwOCFUZKTk7lDVFaVUdulDnK7h1gGjsPZ7e3tQdkKgxTJvL6hgTq7OoOyY2JiODl1d3czPzoZsD9xjcrKSrrQ3Ewez0hQNkrSUfGo9FayoR/aA17DSjQnK5sssbGcVDs7O5nf7XZSWloGtwdJsaWlmdzDw/x+ITUtja/Z0tISlA098A4ZyRMQjNAf76vT09P53Q46jJINTNz0DFN2aXklXWq9QENDbvJ6fZSdbS5un8resFVNTQ1dutROI6MeyszIZNnT2bCxsZG6ujr5ndWYMTalL/FOKz4+ntveUNdAFy40k5/8lJacQrb4eOrp6qPunq5gO5UNa+sbqb35IrV1d5M11k9ZWabv0W673c78MB7wsqFfVVUV29DrMyg5KZGPh9oEPlI2hAzI7+7tpDHfGC/KnxxXSjZioKqykvVHWwDZh7iaLDs0ZuGf3t5u8nhHaS5idlJcqZhVcXXxYjO53cNsa+g42d7Khoiryupa6u3rojHfCKUlZ5HVNjGuVMxCf5VcBgaHKM4SQ2np6TQ87KNLl8bjSrWzp6+fqirLaMO6N2ntA5+jjIw5FB9vndBOVIQi3kCI2ebmFhoeHuK4xHG0JzRmlU1gq9raOmptvUCGASCWy2MW/lG+Z70vXqIBRz9Z/BbKzDZxzkNjVtlkeGiIqqrLqenCRbKMGpSYksTxNtmGSjb83tfbRS6Hh2LiLTRnivyDl+SJALDw+qiurJIaLzTS6Ogo+x7xNtmGwbhqaaPGpgbuhyMjIwRQC9BUMQtblZaWsr2QR9AeyEGNSEvrhWB/UDZEv6+urqTu7h4KlR2aC3Et6AfZNdXV1OdykIViGKo1IyM9bFwhZjs7u2l01EvZmZmcr3BNlQshE3GPz9raWmptbaf+ATslxCew3pNzodJF5Svkt5gYC6UkJXG/D+0/k2O2ta2TfUQUwzGBa4bGlZINGdAb+R6y09LSgrkmmAtDYha8zc2NNDjo4nYo8KXQuFLtRPwgFzY3X6AlS5bgklcUyd9aM5psoGAlpBZqcHCA4uIuf1GO2S1eGxhSiQajwEmYRUhJSWFDGIbBL+ZxzOcbB/kGL2RPrnTGcRBeikM+/mFA8/v8QdnoBCB8Kn5TvnkujrndnsuKWIK8hKrPwEW46MbL/CzUP7HSCHK9Xm8QtB08obLR4ZU+4PX7vTQ8jEpbU0dcEzaZTKjcVTYB3qyiUHsrffEbeMfGhon8RKqCcjrZPq+P+Vmm2tstRG/zugE7W6089cw+Zv0DulhMeyu9kHCAkgO9veSlBMbInah3TIxZ8RiqN86PiYnj85RSiAPYEAQ/h9oQ8iE1tGYF9lM2x80Jy8QIgfM5BrzBOAi1SWg78d2LaVkI5jWtfr6JCpWNJBpK4GX+kIMqvqE3viMZg2zcjjHyek074Rh0Bc9kwnGcz/+CVXajE3iVDbEHrsdrIZvNxGm2Ws12ezzuAL//8qputM83bhNcP1RvpQ+u4feb1bjQCX1V0VT8MAb8A+94fOObHkzZj1kHM148kwq+lE1CbQu5Pp+FrDZfEIB/st5q6V8c+WkIfSFAylZEsCH0Go9LsPjI7A+wdyhBD+ULfIIC4cHnhPIi9pXeocf52shPaO+IWY2v8pLiV59wOIqwgYdu5jVTEmRM1+/BMWaMmHEYaAB0hUzYT+UZFByZ/vSSP6TPj8tGFbXJA5kmL2LQzKGqkNSMK9OG0DOU/NicxWILXhO/Tae32Xe8E/oPrhm0RYhgHCeyEp7+QwmyQchNqm+q9obyXVHfpRiRwCR99Y9/NIDdKSHgHZeVnZewMs/hosMGsDslBGzS06fPSliZ5+Tpk2K9gTP629++KMZgPXlSLtvpdBqHDx8W63327Fnj0iUZdrUxNmbs2rNPLHvXrj3Gnn1yfuAuS/GlgUt7/nyZWJd9e/YYsI2E2tsvGufPynBmgQELLGVgO0sIMXvurDyugLts7+2ViOb4O3asSMQLJsS3tK8BYzZtTpqYv6KszEBbJQQb7tqzR8LKPMCtlmLe4oR9++SygQO8frMcIxcxK8VSBkZ3mTCuoPfBd98Vxyz8ePbsaZkNx8aMP77yRzGWMjCJjxXJc0rZubNi3wM//9135f2+pqbOuHChQdROh91u/OIXzxr4lFBpxTnjohAD2syF8riSXH+meKJVypNuf3A3hSmP3NwrE4tzkrrv+U9MveD2MjUw1fieBV3hJ2JqDLMpmLL7qFJbSwutWHk71dXVhd0O8cPefoBY4MlcTVV/2Nszpf5+P/UMDFJKgu0jHbPIs8hBmAG64p9Kp3TUezuoMaX83i7wYTsLzv+oD7bwiZrq/LD5R1ffj4Mv/YFXDhMn3HQtdeXzp6Zjb9jp94e98lsg0NBiodxM+SYKAolXJAvyrHo/f0UqOEtKTXprEf4qv/vdS+JKMV1oRx3YOxRn6MDqnTh+IvgOL3wLidv30ksvRWIL/q4H7TioBb8IG6JwQ0K4Y9SBdsSekaj6lBKg0jxD4+/Yw52HghDoLiUtaMdBD53XkP37P7wmrprVhXbUqYREgYdOjOtAO7pd5vvakFf9YU0P3+DJX0J4p6YDk6cKviSywfP663I40uraaoI/pQTZPJMjOAGzWlrQjlu3iityPcM+LZjbN998U6v/HDggh8U9evSofPUIEelAO2JVitSGiL//+K//K/CMyQK5yCsSQp7SiVmJzJni0RpwUfAjJbwUn1zwFO5cvJyfLcKG4tJtuqDDbEE7ojxjcmFGuDZz0YjGCcwfTuCk3zTcaSJ7ydHpJl0p/J9mQYz0+WxUyz+AAjSLLsLr8F5+9WugHkE+CvukpOF2s8AmWFwlvYKczz+pUDDcmboxSCTPKTa/LrSj3N7h2jTVbzFjMVMdnvIYqvW1SNOIOrnTZkuk0dGQqtcIisXGyDs90LR04haV7LNBXLypgUQ4GzpMJ1OrxToYtjC8DpzZ5MrB6RR+L8dtgL6Txw1XtupdRzpYXF7VGu46sKHObYgubJtOTPLN1mg4bSf+ppMzdKAdieK03vkAChAYvBJCtSOWPknJooXrGyi5FgrXsR9E+hNQMi0TDnujClZCgHa0auAY6iRc1ltjMPdasRpA5kvI1tFFZo1xi/nIK84TwACO1cBSRjYRuocVmlwtPK7l5d9U1fnlv0x9RCenQGedh6zQ1RdTX/29H9Wx33u/iv6Z4nW4EI3S8Kvz83nNVMRLWeIoLTVV/K4wLs4aXCsYSTbm/1EIo9YWRuLHWlqsw8TyoUiE8vmE5GSaF1iLF5HfGkOJiRkUFxdZNtYo22w2+TtiSxwlJ5vrEyPpgbZZrXFi2Qj23NyrKCVF9k4sNi6R5szLJUtM5Dt7+MeWkEQpwg2j4Xtsog37RCJgqfspltJSzWVlkfgTbbGUmzdPVICCpmWkZ4hj1mKJFcegitmMwDrrSHrDFlg/KYlZt9NFLz//Iv0/P3hK1DfRTrzDl9rbZjM3Io+kM363kpUSkhJE9gY/ljNJ37NbrfGUnppEublzJKpwf5DGFaIaS0tgcwnFJydRRqq5fjQi/5iFYq0WcVwlJtgoZ06euP9YrPGUkZ4WUQ0wxMZaCDEobafFEkdZWeZ66kgXiI2N5XwlkY24TkqyUV5efiSx/DtkI4cDGyASQTZyijSuIsmbyd+jVcozac2orKgFPgALtHa00aqbbqbypguUmSobMD4ANaOXjFrgY2+ByI9lARPhPRgKeHwjsulTIJigEEFEKIXv6RG/a9OSTcR64BwJdXT0mMUtwjkJ1ltoE9hQWqwCXWE/IPJICIvqO/plRQWQV1JSQqUlZRLRzMPtFNoEhSpi3wcQyKTvWXV8D5nYK1QKj6kjG0aBTYBqJCHI1va9MGbdLg+NABQgBDgmnE4cV0LZsGFXlwwGEteEbGmhEvilhTDgraqtpRMn5Hts68jW9X1XV9es5CvY++iRQ/JiyZH3kFM0fM8xq9HvYUcJIUZ2794rjhWOK+HexrChTl+T6DtTPOIBd3homLZt20I9dll1Y+fFi9TQcEGkJ96f6ODS9tq76ezZsyLZYCotPReEFIx0ksfjosbG5gnIUeHOATap1CaDg8N0/PjRcOIm/AYIuUudnROOTfeHNY7oxF755unt7Z3UYW+fTtxlx/ejElLY8QDPBlxVKRUXF4s7HqBBa6tlWMq4PsO/OV0iVaA3oEClBP84+7tE7IBA1InZ8vJKccz6/F7G3/LQ5ahVUykHiD9Am0oIN3JFRcUSVua5cOECNTQ0iPl1+oOjr4tahFX7UAArGaZCLppKOd2YPXmyWIz9Dt9LsZRR3NnS2kZ9fX1TqXnZsX5nP507J8+FtbX11N5+8TI5Ux3AoHjy5GnyCvs94BcB1SkhDIqoaMenhJqaLlB7p2w8gTxgv1+JJJ5SxuYFf/zjS5SWkUO52em0Zs19XLzy+uuvMxQZGrd27QM8b45lB2rjgszMbFp7/31cwYAOgKcNGHnJksW0fPkKviPevXdvABKOaPmKlXT9ggWcKI8ePRKEFnviiSfYfhiYGxpqCH5KTk2lBx9Yy3ogmQHwG4VdeXlzac2aNdzZcBc1NDTE+9Dietdffz3fVePJR9Hjjz/OX4EzW1VVwVBhwD390pe+xO91UJKO9qBwKDsjgx74sy8w/7Zt22hw0JR9w/ULaeny5XzNjRvf5IINxOkXv/gwv7sBHmhJyRkes/Aq+YEHHuTjZil9CctDwc7XH/86f3/r7bfJ43bxOzy851i9ejUff+21P7AMtHPNmrspLy+P2xO6TGrt2rW8xg2DTehmCaqdsLfb5WQbpmVkmP4hIsjGPsNo5+233xG0VVC2hei+Nfexj9EWDE5mhaSFHn30q+wHLJXp7rYzbmxubibdf/9a1nvjxo0Mk4c3sIsWXU/Ll69k32OpDHyJIts77riLCgoKeGkBEhRkYz/OBx8023Pq1AmOC+y5mbDcQesAACAASURBVJJiYxtC+O7du6mPN5AYl41ksXPndvYlqjJvvGk5LV60kDv5mTOngnrfvfouyi8o4GUY8AWKPmJjDfrCF77A7cEyipYW4F97aeHChbRy5e3s4307dpHb5+H9P2+44Tq66aabqbmlhZ9O1F7NF1sb6c8ffZxhJ9UyKavNRmvvv599b8ZVJfcf4PcqW+3cuZO2v/0W/f6VPxKW+qB2ApXzk4ucLUl+sngsfBx8v/rVb+ihhx9i3yvZsE9KShJ94Qtf4pqqHZvfIpfXhDUtnH893b5yBWHZyuYt6MfopjZyOR10+513UVZmBt8gqnz74INmzCJRmjY0Y+XrXzf75t69e3mgQHzj/RlyBMiMKxQ7WWj1XXdQQWHhZb4HL85pbWuhI4fMm1LkCdXvEVdtbR1s77S0cd+by4oAyemjFStW0qJFi/jmbfv27XxtdMTbV66k+fPn8zVhWxM6kejRrzxGCck2OnHqDGP1ooo8IclGX/7Sl/lcyMDAh762ePEiuvnmm9n3b731VqAPEn1q4U205ObFXIT2+uuvBfuPyoXVFbVUVlnCesfGjrEf8D4fS3kwm4a4WrzYzIW4OdizZxeNjhk0OjJCCxbM53hrbMSTfQnzwj933HE7twfxWlFxnnXBu/DPf/7POF+hn9TXN6P0ivLz8+nuu+/mnIu2IxeC0B7ELGYB9u/fa65CID/nZRyHjxGzk32vciGqy9PTswkxAdq5eydvRAD++fMX0O23r2Q/bN26JShb9XtcE/7Ee1lg7Svf43rl5dj0BHCkyCmPsez9+w9QT495Yzt37nhcYexRtGABrnl7MK5wXJ2veK6ITylkFWC+fvWrZ4z2S5cmwKU5HS7+GxBqCvoPn4DTO3ay2BgeGQleYtg1Ygw7TX73yGjwOODj3nnnHQOQjaEyIFPxK2b8DvhFQMKFwra53aPjeoRecxjwZPsYzkzJhixACbqcTsPpcivRfG3o/evf/sYYHByccJx1GR42nMMh7RkeNgAfB5g8JXvUM8Z6wF6hNoEwQLxt3bplgt44D3oo+eqiOH7w4EG2o5KN3xTfZNn4e9OmTZfJRjvxWyh0IuTt2LGNdYftFQ27TJ2nlL1ugzE4NKRYub3gwzmOYVfwOI4B2g8whlPq7RqPE5wE/s2bN7JtFD8+cRy+GXaNy8ZxwEYWFRVNaCfzTmHvQceQ8corLxvnyyoMwL2BgrIDdgm9Jnx/+PDBibIRs2gnt3XcViOjo5f7PqA3+9M1bCy7Zalx9uRZviZiZNcuE2oweE2Px1Bxgr6hCL/v23fQOFdzzui1241uu50/O7u7jd7eXqPd0cmf+I7f0M8y0jK4/ygZHrebdXagv7mG1WHuj4CkRFsn+D7QRuj+yCOPGL/51a8MWAzQgevXr5tgE2VDZRclHG0A1OnJkyUT+BUfdFFthz9wfANidmTEQL8BKdkqbpVs/H7s2GFj07oNE2W7zPZBVlB2IK7WrVtnOB2O8eNjY+P2Hh63CXThfHVsYlwFfQPZHo9Sha//zuaJ+Qo/qnayLiHtQb5CX8ZxRWizyp2T9X7llVeMsrKyoN74fYIuo2buxHHkzHd27Jgg2zXq4X6jzlHXBD/6ZUVVzQTZ0Ev1NaULPpGv3n77LWN4aOgyftVWJRu+LykpM+oqKoK8+C0o2zlRBmQ/++yzE2IW12T+QN9UsnEcsJ6wCX5XpHgRK0pvvubQkLFu/XrFdkV9ApBcRGgQAsftHh+gwp0IPnRWKXV32ycYLdx5urKhh1RvBDAGc5UAwumB3yA71Nnh+MGHQJOSw+EQ6w2ZOrKB7XrubKlUFaO9V4jpHLiZQTKREvSW2lDH90jh7777rhiPWkc22hbJ9zkZWUavy8RaRvvsvfL+oBOzGCzmZOXwoCyxeSTZ3//+941//Md/DIrSiSskP3fITVJQyDRfdGRXlVfxgD6NqMsO42ZF2o/he52Y7XR0imOWfa+RC4G33tQkwySGbNx4SUknp0C2jn/ge5d0fHC5jHd27ZjwIBCuDfbe2cuF4a4707+Jp5SviMfxqBJRC3xILIAp7euuvY5aL7VRQqKNp7oam5tpxfLlU7YAxSbHjhXxOuBVt9055RISTLGeOX+Gett66NN33EXpuYHt79pa6TMrVlJpXcOMVCljx06Ho4+eeeaXU+oaPRi1QNQC780C4qIpiMe7AWn1aUdHG79zkaqlU2SDCjS8oJdSa2uLlJX3zJQWLEAo2imtzAOfepcnUQiypRs0o7hFR7ZOpSp0xbsbaYEDBhvoLiXoLbchKhBlhUq4fl9fF/tUogt0lkJpQl64GKytr6e5+bnU0dlGP/3pT+naa66hH//9j6dUA+/a/8dnP0uv/eEN2rl9N61adScdOnpggr3hr0e/+lX6l3/6FzpafIyWLb+Jjhwx33UCl2LE5yds1SchjitsXjENFeQXUH+/k3+Fz+F7KaFvSnMEZOrIRoz0SVc+qJgdkaEq6cZsTVmFuNAPNtTJQcg/2LtXSuHicLIM1CPo9M2qmqrJIqb9G3K7umRFtbCJTiVxpJgNVUo3ZkPPne3vWgOuTuUkjNnWJh/oWlvlCbrX3kstLXL+ttaOCckrnFE7O1tp69at4Vgm/IZ2ejyyzoGiCLMoYIKIaf9A8DpcsgpbS7xFXglJRAcPHqTq6vJprz35BxRoIJAlhA3P7XYzYUv4IVtaTerzDWsNitu376aLF2UV07B3a6t8aRWS13RUX19N8+ZdRRlZWfSDH/yAUJyGYpDJBJt+++tfp4JFhfSH135PzzzzDH3xoYfo8a8+TkND40ss/uZH/y8nKBTs/PznP6dnn3ue/uzzn+MiMtjba8NGqpOlT/032hnOl3nz83kzdpwNvsrK0qkFTXEUiRFVuVLSkY0K6O3btklFs95DwphFO3UGgJqmJoLdJQTZKCSU0v79+6m+vkLKrpULdQZFKNAkXGkCXthPuoQMNxWvvPJHcRsRs1J7QyiKvq5E0hpwpXBwaCiq1XRgvsTZImBFLV1Qwjmm1VRNX8kGIgiVoPuEXlwKZGfawxZ6asTvXjmMLcsCCpeUdGA9TahBqTJ60I6AprP4J24cP10bAO3oEy6tmU6GOt7a0kZ4UsxMT+eq4czA9K/6XX2+/dZmOnTsGD3x5W+pQ/T41x+n9s5OWr9pPR/DNPJLL75C33riCa6cxsFP3/MZrkj95XPPmee5UGIcFBH2C9wYbsC99qqrqadvfBZBB0sZNtQjecwColMHfperxYU3IbCHTr4yDDnOKaqSR8fk/Hr2gy+lfceUrOOj2YJ2BBqUTe56XZNwRbf2Se/DCcIuqq8JnKoDkq3Kz6VXEud+P6bafIDgFZNfFyNXiNULBXQ6KidGodbSgTlUnE7Asy66Tgq9WJjvJui5rPf5LaNaCQbYu16LLCFBD6sGVm84bPGG+mYqLCgItnq6m5VX/riOeVbdeVuQF0tbADOI5TSgPVt38+eyW28N8qSnplJ+YSFt27yZ+KYC66qEg0tQyDRfCgoKqadrfB2ouK9NI2+mDvss8mlzdU3pNDsPijqg/rHyGwsM5haNvgPsZR3SwiT2+7Qw7rEsT0q6OV8qV5tvVh+utLWZcIJW0RSm/RCY+BeJ1B20hBeywC/lZX6vl7CmUUJasv1+8ni9nPBmXDYRT50imUoJ72ax+4WE4B+pbMgFzYZsyNWxuU4bWWkkJOEowHqAV8APXraJIL4jtRHreB966CH6i7/4C5a5/KabKK8gn3bs2MV/8/l+P92wYAENOBzUM+nd5Cfmz6c+h4P6+/rosSeeoC3r11PTxYuUn5cXPP/zn/8c7dy5m+oaGujeu+6ic3U1lJ0aeS9VeN4fIa4woA8E3vNqxZWmDXVko+HYeg1rZyXEspEjBL6HPK2Y1cxXEn0VD/fNWKxFjZxnWe8IvlRy8cm+19DdN+wja6JQj1n0PXyD9eiyTEjkHfGTTZg3Q+0z29+l+rMeSObSIACflBfCdXiZXzjYasvG5gUaA6Ku3jqyWXeNoNGRjYFWOthCDx3ZujbX0QOypQk0qIcw4c5UzCJhNrc208JFC1ld/s+GzSUmdjfAQg65XZSdmzvOF/iWlJnK3/oHBsjR2cv2t01KwEpeV08XA2PYhOkIWkSyOTYHUcVPOr7XtaGObBhEOtgyL/qx0Pfg1+nLOrzsSI3/uG9O8nW40yP5MvRc9r2ObOFgi2vMpu8he2LvCW3V5d+vxMEWWorbgLtFIPeoTnh5EyceAZpItRSCz+/nCmhUCkqop6tHqyK3tLRcrHdLfTM99/zz4s3WgbgktQnad+qUfNN3VO92dIy/SwtnG9wBhqJKhePFb9t37mR0mEh86vcTR46SV1iAgkpfQMhJCXrr+L68VlYEhZh96aWXxAUUfR098phlPOqpfe+P9VNPawctXbJ0ggnc7olThXHkp7hp9oF295t9gRMNHtKANjVBGp7IzCM+r5+GvD5x4Rn6ZSSc4ey8XGpra+WnPqACSQkV10BVk9LRo3I40uPHjxA2Z5fSoSNHxDaBPXT0BiSlOGb7eoLIe5F0x83aH/7wB3F+Q+5BDpKSxPdKlspX0noZVEtHiislG3r/x3/8lzh3Qm8pJjpyoU7MKp3ej0/ZXAERjY6MUX1zI1deupxuKig0t1WCgZEU0EhAs+E7psEam1vI63FRSkoaw/WhMTAy+PAPd9DYIgzf0UnbO3vJaq1nyLLMzExeJoJqRyQa0NzAUwBAw4Gn2t3ZTamp6TS/sJDvYpVs8EIHyIBsJH9US48FihaUbFXxBh7AI4JQZdfR30MZaSnU2t7CukAWAs/tdjN8G7bXy87OZv7mxhbq7Ozm+xZMQ+fNncvXxNIFQPEpPZRN2jo6eXlAZlo2zf9EIf8O2RgYoAf41JZSkH2ps5tcLjcBuy+vwNQR9lZbtmVnZJM13tSvu7eXZTc359GcefMoOTGRbeh0uYK6KNkIXOhnS7CxLdW7RpYdsHdaSgpvsYZlSb12OzW3tVJm81y65qqrKDE5eYIvQ9sJGbC5y+WgpISkYJzAtmo6CxW7Sr9L7e3U2trMW4bl5edzkRFs4vQ6yeozfQ974xqQjX+Ozm5qTUhgiEDlN0DkYXM4bOGFuMISks72dn4yRGwgJjOzs9mXsDcINg/GbH8/1bc2k8NupwToXVDA18S5uNGAvZKwJWQgZtHGixcvUYI1iTDg5c7N5msirvDPEzJtxzJcHhpOGeRYV7LHDIPScjMJVfRoM/QGQXZHby/l5eSQz++jwquvof2u/Zxw1B0y+k/PQD+3zxIYinFeSmo6YXs3M2ZRKW7leFG+b6yv5+V6gCQFIfZhB9V/lC+zMnKosrqW4uMTuXK7ubGR7Y3fYVv0TXwHKdnox0i6eLcNW6npb/gMvLgOtoZLDMQm8JxRNYuB7uqrrw4eh/0m9wcUoXk8XrJZbAyhyf2eiNr62jhO0CfwtBzMKQ0t1IVlXo0tNOfaHEpPzmaZXQNd43GFfGWxUEdXF9vc4bCznoCBBKmq5VC98R3tBMxkRkoW5ebNpdxcU/ZkG6LNeBfe2tZKnZ3tlJSUwDkFssHr9rtZF/gSW9pBdkd3K1kTLOR0uAi5DpCfyt6q36elpbGtIAN5FrkQa7wL8/P5NRuOewMVkchXwVzY0katLa0mHK3FFoxZ5AjEVWg7UUXcEchXsCkgcdGe0HwFe0M2CDkZ8afqGlRcwYZKb9U3IQMxMWdOBn9abAmUnpw4rWzAfcLeAz0DfC3AVYJUXOG78r1naIg6urv5N2a6wv4TD7jE1Z4WcrmcFB8fRz5/HgerWhOJCj81iLo9XnK7HFypjCBGggGhI/X39zG+Lfl93DlGR0fJ2T9AY6PDjDkLp4OQFNGpgWmMWSE14GLgA9ar3+8hp9PFmwyg03jcXurpM5d0IEAQCAiQrp4exvB1Op0T7nYx6EAuNoZWAy6u6XTYmR/v1FTHc7s91NXVwXrbrOMDbv8AZHsJslXSge7o6IpUQPrIT3b7ANuk39lDhVTILLgmkg4IRQdKjsvtJJ/HTR6rhZweJ+WRuino4mpKFPhwAMebNy19PV1k8Vl5jeq8efOCsqEL2ogbDiXb4XByG0dGRrm9FPCP3e7gQjdUUqMDIjGigKO318GJf6C/j3xzrmLZ8FN3d2+wAGNctp2we43X6yOnCwnf7BzdvXb2MZ9MfkpOzOcO3t/XQ7GxidTb2x3UDzFm73Wyf9BOJBj40uvxEuLJ7feR3eGkAtOEHAewI/wJnFz4PyYmhnr6gFWLuHPye3lcO9Te+FslDfC4ECPko/6+/pCY9VB/v2lzVINiwAUhjkG9TjulZmJLvGzyeb3sy5OlZxkP3Olysw1xTQ+eRr2IAQfNyy/gMjuX00W33XIbvVz+ClWWV9Ltd9zOMusb68ntctGyBx8gl8NNt929mp7/7W+pFPjSgRn19NRc6m1po1tvuYUTM2arHY5eImOMZbAN7U72T2JictC2A4MD5PX6OWahFwi2RQyiD8Pe6Me52bnUfvEiFeTnMc51l8NF8+aNMC/6cWjfVL7ndrIf/OS09wYHXOQIJTshKcmMK5+P/QZ/wZY5OTnB46YuE2PW7XVxfnB5XTQwgF3ITOc7Op3sYxSOzZkzxxxw/X7qc5i+7xjsoxxPDlEyEXKNvd1JhjHCfYJvnDl3uNkew8OIr/ElTfg+PDwUqF72UyJidsTP+hqxsdTr6KZUnvo3bwhD+4MaAJA37XY7xzrkod/A3ohjl8vL9s7NnRvc+7i7w0F+r4WcAw6+wYB/3G4ny8CEJPyDQRR9Ez5GnvXiBsjuCBbpwQ8qLwPLXuVCzlc+H9vR48WSpmx+iOgI5kIUgpntRF5zOAbI6/MzPwZ99CszF5qxYrNZggOu0+Hg36xWP3k8bo4r/Id4B0HvuXPzTf9w7ugmr9tL3d3dVMgPE4nBvqliReVO5HnErIPclIy4Cgy4sKcqzAUv9EMtuLmTU1CFK+uLFLoKuJUvv/yyGOoL2LEVFVUi8YDgA8YnoMEk1N3ZaZw5UyJhZZ6yc2VivQFf+Zvf/HoCzmy4C50sOS+WDRsCq1dK58+XGRcvyCEV9x18Vyra2LFjh7Fvzz4xPyASAfUmoYb2JrHvIQ+ygfsqIUDNnas4J2FlfV988UXGdpacAFjPsnPnJazMU1x8ckr40mefedZ48sknJ8gBrvJ9n713wjH8cfHiBSMhIcH4zYsvBn/buG4dHzt97jQfAx5wTk6O8U8hcIuVdZXMs2nLFqOmpsbIysoRx2FZ2XnG/w5ecIovT37nSeMf/+lfuB/s2rMniEU9BeuEQ1UVNYxLPOFgmD+Acy4lYCmv37xBys5xFYoXHe7E9s5OA3aRUlHRQXm+6u42AKUqIeRC5NmKigoJu2G3Ozl3ipgNg/vCxUuynIJ8jHZK+z1yJ/5JyO50Gc88859T9p+pzgc+e9MFmezRsTH2/VRyPuhjWlXKV9atwuxogzs5bAGXNyc/YmHJ7Gjw/kjFkyXmEvAkM+OkUUU849eeJBDTXJjGxN3v+0U//OEPKSMji37yk38IXvLGG26gnKuuokMhu1SpH3/2r/9K6159ld49+C5PRT/6hS/T2gcepP/zf34aLPrBzjXf+vrXaf/hI3RNwdX05JNPUoLVSr9/7TWesrx9+UqquTBzG9D/5Kc/Jbezn/7zCoJ37O/pJ4/PE5yRUvb7qH1iqjQhJYkyBRXnH9a240kf7cTsIp74Py708Wmp0KOYqlFT4MJTPpRsmbMx0CpLaFSGqlNm6/OD8GVldSV97SuPcJPaWtroD2+8xrUILrudnnvuOfra174WnIoD00/+4R8oP28uff7PvkB4d/6Dv/17euxRc4s4ZRdsg/bamxvp+//7u1ws9dXHvkpPff8pTlZYHhdvQ1GVHIBFyZ3uMzc7m041yuFTp5Mzk8enAw+ZyWtcCbLUK64rQZfZ0gGD7AfRN2erPWK5Oo/Y69atjzgVpeRVVpbzdkrq70ifOlOt5lZaxyKJDP6O6RzptAimwtdrbO2Edjodsqlw8GF7PilBNqY5JYT2bdkil71nzx6jtFQ2NYvrT95WMJxOmPatqakLxzLht107domnljDNVVVeM+H8cH9s3rzZaGiQ7bwCe58+fTacuAm/YUp5Klp4/fVG0bGiCT9hGu/YNPwTGAN/wDehW5FNxaOOoT9kZGTxNo/qWLhPtBM7BoWjV15+xVi79gHWQSdmoQv6kJR0YrauocHYuPktqWjuD9LXVLAH7CKlXXv2iafw4UdsLSelt956W0sXvI6T0tmzZ7Vk79snf00F+0n7PXIEXvdICbLFuXBkRCsXSnWYCT5V9CgaoPGSXhU1RToBfCg4kJLHq3d3HvpiPtI1fL4YLnaIxIffoTeKQqQEflSSSgh8KDqQEgqPUGwlIdwxwj9SQmUiihakpKM3bDIyIvc9iovMKmOBNnHxNOxB0YyMUBEJfSQEPrcGTJ7XO14couT39A/QwMAgFaqKrsAPKKhyOeV4ulKdIR68eL6VRQrQzmInFBAq3UM/8woLqG/QLAxzueQxC110dNeJK4vXT8NDct+bRWEyiDksfUF/k9LIsDyusNJCJxeCFz6Sko7eKIYyjBipaJoqxqc7GTrrtNOpgbeuE1OonlQFgdPp+kEd1xpwdZTEa7yYGDn82XTQd1Ne02chyzTrF6fi9/tHyaaxgHsqGeGPSWfmsUQjvKTQX8GLnWAkhITB2LES5sACbIsMsIclwp9SUssApPyoGpXqbhkdIatNjtQl1UHxWQNrW9Xf4T6nsokLVdRuF+XkmdXZwfN1HE+6OOREfosVq8dEhMrOSO/N5uVkkaPdwZXXRPIbM5ECE5jksr1WLwGqU0qoKo+zmFXbknN0MIan8v1018CSMr9P3vHBiapeKaHSW0rgVUskJefoQDtCZ60w1+jGOvZGu8Q38BIjzCCPPHqJ6JZblnEBiuT6KN3WeQqdPz+wxkMgPGtOBpFVHmSFhQVc/i4ZCFBgs2zZMoEWJkteXj4lJMjMCD7g5EoJZfRYKyshtG3JErls6JGRkSYRzTw333xTxCSthGG5EnSX0k033SyWHW9LpFwN2fBlVlaWSBXonJ0pf5orLDTXa4YKb2lrpoULF1LiJFQpxJVaZhbKP933OXOyxDZJsNnIaiOadMnpRNPcubm89GdaBl5bO5c8wwM0asTQzTevDMc64Tcs74k0mIeecNNNctlXZVxFS5fIB6Lly1eSIRwBELNZWfL+cOONN0a0oWon7FG4QJ7fbrr5Zq2+uWBBCKKZuug0n4WFC7T8s3Dh9dNIuvwwcqF0IwUsPcOSOClBNtYxSwj21olZicyZ4olWKc+UJaNyohYgYmQroIm98MIL75s9AKyw4qbl1HChaUarsVMTE+lie/uEAq/3rVHRC0Ut8BG0gHieA3PoKOOWzqVjeQ3en0kIi8l13rUN+UbEsnF9yMY5EgIyCmDbpHBmOnrDdkCBkRJkw44SMhfky2WXVVdTvQb8oo7ew0NDWv6B7FmJK5+PIUMVYlAkO+rELGRN5fuW5ma64frLnwrQPvBLyfS9bBYHKGeYy5PaUBpXQItyuQFWI48ryNZpp47s5pYWrT2fZyuu4EMd2b4RjXzFMLdnxEhJnFOAGiacc5X6Hm1k2Rq+R/+R5ivoAajOwUHZjBLrPSSrC9HVW9onZ4JPPOAOD/toy5YNQbizSBdvb79INTUNkdj4d4BvHy46LO7Yjo5uOnnypEg2mE6fPk3OHlnBCgqmgL0sHXCLi4+JbTI4OKyF8Xnu3FkC/J2I4ogOHNgvYgVTe0sz1Tc3i/n37t0tTuh4KhLjaBPRwYMHxUkaa6TLy+UbopeXV/K6aklDOzs7tWTD94DxDKXisydp0Y03hh7i7xj0jxUVXXZ8ugPnzpWSw2Eip03Ho477PF5GPJMOuNXVdXSppV2dPu3ngkWLqLm+mXbvN7cHnJYx5IeGhgbCPynt1ZDd0dZCVTV1UtG0e7c8Zju7u7ViFli9ajelSAr12O109uzZSGz8u9fvp9rackZLkpwACMbTxQeD67UjnVNZWUmIcwmpfCWNq9raWnG+Qh3j6dNnyeeTPVAgnzRdlOVC1APt3rtX0sT3nUc8pYw7jPXr11Fubh6lpaXQ6tWr+V3Ahk1bgi/K7/nMnZSdPZeBuquqKig21qC0jDl09+q7mBcg9XA2bsYWLJjP70pxp1hUVMTVbXFxibRs2VJ+14W72WCQ+v30la98hY1z9lwpNdRV8XfAlq1Zs4Zlnzt3jhoa6hiyDdCGd9xxB29AcODwburvH6LExDi6ZcktVHj9fB4gDx4uolhjjIyYWPrKVx5meeXl5Qy6j5f/KKB44IEHGPqvsrqaKsrOU3xMMiVlJdD9993P/Lu37ab+oX6KS4ynRYXX0+JlSwhYntv37KGx0RHmv/dz9/A0H7BoyysraXCwn5KTM2ntvfdSQmoy1VbWU3ltOQEPd8yIoa9+2Vx/uX/3Xuob6OP9WfMK87k9uOibG98IQM1Z6M5Vt/HCcSTzomNFNDw0QqmpyfTpT3+apwEB+nDy9GkyxkbZLg8/bLbz0JGj1NHWStjQO3NuJq1Zcx+3Z/PmjVzBGBNj0PLlK9gPgMYsPlZMQ0OwYTzdc889LLu0vJJq66spbnSMxuLj6IsPPhT0cWtrC18vIyuH7ltzN8veseMdApSkYYzRpz51I7/Lhu8PHy6ioaF+SkxMpVtvvZXX5p0vKzOTdgBOVF0TPm5sbOaCEvj+/vtNPxw6tJ96ueLRQp/8xLWEd8KIVwzk0Ds+Pp6WLFnCeLDA7T1//jzFxsayLnfccRfbEMni/PkSjk1A/qm4OnXqDF1sv0AxowZd94lPcMyiAvLQoSM0MNBHMXHxtGTRIm5Pa1sbAeDi33/xC35vvGKFacOasgqqPMNyYAAAIABJREFUqKtjvePi4+mBtWZcIYkArxiUk5NFd682bbV//27q6Rsgq89CN9x0A+sOW+GGKibG1FvZsLm1hfbu3k8/+eEP6dnfPEtr1z7I/sHGF01NF2lsbJhti1gG7d69lwYGegh97dprr6Xly5dzYdTW7dv5d/x3b8DHjz76KC2Yfz0tXrKYkpPj6J57P0fpqcmMfYwbGfQTwIaquDpw4AAPFLB3Vk4O3b16NcvcuPFNjlkU7Ny26jYqyC/gm+sD+/czTnVcfCLd85lVnDswi4YZJhDaqmQfOXqEOtt7GcoP2MXK94hZlGdjBQBiFpi/yveAgExOHo8rHMcGLHjHh4raBx80/VBSUkL19bWsI94TKlvhJhMV9KBFCxfR4sWLuPp1+87dNDoyzHG1eOFiWrh4Ia+C2LpjK+fC0ZERuv/+tewHxBs2F4CdgC1+/9r7+fpH0Z7uXpZ9/YLraenSJeyH3fsP0OBAP8XHJ9P8+QUcb5g1OX3uHPPiv1tuuYUx5Ctrq6mmpILGYmMpLSGB7r5/Decr9JOmJvOmB+8+kQsxA7b/8F4a6O/ndqItqONA7jh8+DChz4NUXEHvyspSGh4eJcTs//jsZzmPlVfWUm1tJfNmZaQFc8f+A4eoB/C38Ym0YH4h6w1779u3j3mR8z/5yeu4b7KPjx4lrExBXr7nnnvZVugLldXlFDdqUGxiPG9viQ555Ljp+5iYEcqdW8jjCYRi7GHMDD/Rtddew/43c8phftJ+7LHH+NpX0n9aA+6rr75M99//AGFAU8g9PT0dZFay+Sg7Yy6D6WNaAQ4DhiiCQ/HCGLzjjN9LSUlpE44fO3qUlt58cxBTFTKAUQyMVNwNqcXgmK7EYNx+qZ2WrbqV0m2pjAgF56pScHQohcOJa+JJEZtqK4B0c8qhh4HdsTl5frZZ4IPjVVVVdPJkMX3xoa9Qbm4m3zkq2X6bn6xeS3A7tb7BATpbXEzz5y8I2gSFol0KrN3qo9xUc0MHbMXW29XBuwUhmaempzMWtdlOPH2b2xmqjRFwzdOnz1HOnCzuXMqGanoUVXi4uUFboTf4kZAxeIIXxzEr4XR2cQUweJQNwfvuuwcpKclKq1Z9OugHyAYfzkVRA2MpK9m799Jda1dTdqA9Q0MD5A4sK5osu762kTxeNw8USm/4Af6BbIUzq/TGwIjBVqHOYJAEfmwwrgLthK0AHA/MWhTwhco2wdqxKUZGEAgeGy9s2b6Nli1ZyskF7YEMzGLwDIbFwkAT6nhtfSM5Hb20ZMnSoA3xFOMNwRwOjSs84S5etJiwWQRk4AZnxfLldOTEccpKywjaEH64dAm76NTSqlV3BmWbcWUuQbNaEigz2wSCN31/kmP2qquv5o0eYCvYUPkn1IbnS87QZz/3OSopOU8FALAPAZlXyUbhHUNGefk5ysiaMyGugD+Lvga7qLj667/+a0Lx1ic/eSPde+89vLEERhTY0OG2k9VvY31C4wo3p6jKxQ2O8g/iykseslFC0Cbjvj9M99zzGUpNSud+DFu5XOasAXiCsgeG6FzpSepq66O1D64NysYMA/gwVadiFn0QAwsGzNWr7w5umAA+tB8U2n9UXAHPG75XPu7pAa+HbRLMV34/YctE9DUM8DnAb04GljYwfNs4ZmF/yMAnZPMGHS3NtGzZLUHZuFkzY5YowZbE+QAyoPeWrdtp6dJFdP2CRZSanswynLykDKsc/BzjKmYx41NaWkqrPvNpSk9O5ZxixpU5Vat0wcDVPzBE5eVnGQUNNyaQAZvAP+ADqbiCH3p7OwiD96fvvNPMV1Yrmf1eLYcb32wFetfW11KSNYkfapTvMbjyBjR+L6WkZQVjGce3bNtCDz/0cEi/D+QUix9l90H8b7QHD185GTlcfKZkm2MPYtZCKRhP0s0NINBn9+/dTY8+euUNuCRdzAtgBeAXu91u0SngAwaslLq72w33KJBEIxNkR1q4HyoFvG63DAcYi6vffvttY2xMpgtkS0E1wIcF31Iy9ZbZGzKlC8PBC9CGYyeLpaoYl3ovGaMemU10/QO9pTbUkQ194UspEIOObBhusn8OHz5sLFhw/ZRtcY+MGvbe8GAToc6YLDv0t8nfq2qqjDlZOUZvBDALdZ6912G4XC7157Sf//rP/2z8+O//Xiuu0OelYBO4sE7MAhP93YNy7GUd2bq+Rz+ejZiFTfbs2WHU1cnAXaC3bk6R+B56oH2woazXG+x3h0eW850ut7Fh/XpxrDicTjGvMTZmNF24MG1cf5A/iJ9w+fYn+l/UAlELTGuB37/0Em3dto3efvvtaXlm4wdMZa9cvoKqGhooM9V82pqJ67z0wgt0/NQprryeCXlRGVELfNwtIC6agqFOnToRnJKJZDhssYU9DKWE6TYpYQoE+25KCe8UpYQpFs+QfDE+2olpIwmBD+/WpATZmE6REPTGu0kpAfkIW+9JCbJxDQlBZ+guJdhEx4ZdXXgdICP1mkHCDZ1bWlolrMwzOQbxGgVTdVMRpjJ1YhwxK7U3pguBo3z5FvVTaYJ9RGUxmzkvl1paW7RiFr5R07ZTX33iUZ3+AHv4hmUxiKsgZqVxhZjViStMnev0TZ0c5BnWQ+uaHIcTLTzxL/Aif0qpqsasl5HwI66kNoQvdfumjr11cqGkbTPFozXglpZWTtgvMpwScCo2fpdSa6t8cO6191JLizyht7W2iZMX3sO9vv41qdocvB6PLAkgwCorq7Vkh+7PGe5EvIPRqd7dtn07lZ0/E07khN+gt3QAwDtSacfDRSBb2vl8MbHU1iq/2XrzzTepulpmc8Rsi8aNwuTBubqxmRZPAz4CP6LgS0qwn9Te2CMa+4VKCe2UwJfOycyhpupmrZi127vFOQL6lpfLfANe7BP82qbXpc1kvbEvsoRga52bxIa6GpENcW3I7u6WrZIA/9vb3iQUnUqppUWeZzt6sLG8PHdeaLggVYPsdqdYNm7Knv/l82LZ6A/Yr1pKOnlWKnMm+LQGXB24LDw86UA76sg2QWPlT6H+Wd/+STbgwmGoVpQSP4AKkXLQqVXhg1i+3IQsUgd+UwcmD7zSwSVudIQsVhniDJT2W4irsaU2sUnxEQMbwYfKbawvpdW3m5XGocfVd6ErmR11I1IC3rZOR8YG3xJ7Z+fmUr/TrgWTpwMFaLZPHoRWi1X8FK9kY9P52SAdPGL0S7VRukQXn98SWIkg4QaPDOkOnBavV0+2RiCijToxTvJubBpCKpxhbqW2e3/55J6CW4EfJ6Tk5GQaHBwQchMBWk1KqKSz2YQwbH4/ATFHSugcCSnySEhMxDszmRkhOz5eDkoO2TLJgPWz8HIjaTuTklK02pkCmwgDHu2MidHAsI2PpQQhPvJoXDzFx8tvWrLTM8kvDFssxfAlyZ6IYOeEhPGYxQDW2tJFCxYumNIFHFch/FMyhRyM13gXayVgi8uHXPgGfSgSpWSkBeIvMq+SZbOZ1fbq70ifKSnCfozBwkqUmGxWckeSi99N2fJYge5SSktLE9/gIjaQD6WUmZ6u1X8QW1JK1pQdGuORrmHmwkhc5u/QOS1J7nsd2X6LResmUabxzHBpFU1hKiolJZMSZ3UjgJlpWFRK1ALvpwVOnDpF/+vJJ7Xeo8+Ufrwc6a4V1FDWQKnpqTMllvoHh+iTN1xDp46foflT4EbP2IWigqIWmGELYMpaLe+aYdF/kjj5bTEDmueKB1sUKwwOyKC4MHs2OCDf7oplC4uJYB28bJcWT4APNxaMgCAwLWRLpucgCnw6BSU6eqMASkc2eKVIOdAd/Fg8L6EhDVjPoGxhQZaW7/1+9qWO76WFGdA71PdnT56mcEDv8L2ubKyFlJLfiW0iZdxmXEWWjYrnRL+N2jTqKyBbp506MQu5/X0Tkb3CtZhjdjbiSvUHoWxd3yP/SGNWV7bpe1mRp26+gs46emMtLq4hIR29Ie9KHGyhl3jAhSEBZwYwAQldvNRO1bXlElay+P10+Jgc2hGLvU+flkM7YtG0tPgISFibNm0iQKxJ6IqBdvT7taAdi4uL6WTxMUkTmQcgAiScnWu/eJEAISclbWjHUplsz4iftm3bRhcuyAo/TGjHcUSfSPofO3YseJNTXVVB118//a4tSKJAA5MSwAx67bLiFhRAWayYRlOABOGvwvB+7bJCmzmFBbRz+9bwAkN+1YV21IEjBWDH3v1yyL7ZhHYsKjpMA8JcCN8HUfNCbDXVV9zUbt+9U1zRjpsK6CKlc+WlGtCOg3TsWHFgi8bIV9CBdsQAun79BvHNWXVlNTXVy/oxBvHSEnk/jtyymeOIffrpp5+WiPN4xmjfvh1EMbG80XlmZha/Nzp05AhdAPJTW1sQ6QVVcBeam6m/304+3yhlpuWQxRrD1aIopwe/4ffzXQgG8tKK89TT1U1jY36KjY2h1NQ0rnYrL6+gxuZmutTWRnFWCx9HeX1j8wUacAyQ1+uh7Owc1gMIRKXl5awHntzm5Oby3VNFRRm1t7fRyIiX4uJiWQaCFJCH0BnyYy0WSk9PZ6SgxsZa7kiWGAvrFxcXR0ePH6VLrZcY5QjYpQr9BqXnnZ1tvHH12JhBmZkZfId38mwxXWxqoaaWFsqbM4escXEMRt7cXEvd3T3czvSsHIqLtRDDyjVWU9ulDl6CcU3BNewOJRsbdAN2DfYGTWVvtAdwa93dfTQ6OsxIMtAb1bmwN9rZ3FJPhdeY28mhArKj4yK53X5+pwwbKtmXWlrY3taAvdExAPHW29tPIx4XpaVlMKSdsrfyPWyC94hY+tJysZVcLgdXzs6Zk8uysaSsvrGJdcEB2BuyoSNwt3F/A0hAvOuCT2qqq9neWGOam5NDaA9839JykXp7WmnMH0tKdllZGdUDx7WtjVGOMjIzWTYwaYFKhUpV+D49PYN9jAEH1wiNWSyXgOz+/kEaGXEH44oh7qpL2T+opAYSGMDoyyoqGFnI4/FSfHwivfDy72jFimU05vPzNTDNq2wIvZubL5C9D9CEPkZTg60A2VdVXc2fjoEBmjt3LtsKS2W62jsZ7tRqTaC0tFRuz+mTJ7mNOC8mELN4SiivrKbNGzfRZ+67h+bNmce2UjbEZ3dXB+XnXz0uu+sSOQadZImJ4bhCgjp6/BC3EfyqPyCu3n5rK6WlJNNVVxewb+Aj9O/S8gpqCtiwoKCAZSOu2ts7GE7T6/NSbo7pe0C6wh74p2yofN/a1k5kGOx7IB/hmqfPFpv9oa2ZrrmqANWXHFeXWjpo2DPIxZjYYhAE2bAH+pozYEMlu7OzncbGvGSzJUyIK8V/dX5+IHc0UvOFRurpdtDI6AjNC/gBfbO2vp7QJ5S9ka8QP8gpPt8Yv8cF8pGyt5KdnZXFbVK+7+vrIb8/hrKyMvmagC9tamw08w/6Q4aZO2rrqqiro41iYmxks5kxC3sjFyob4v07+gmONzbWUV+fncbGfJSWls6+h851tbUse9jtZsQm+Bi5sLsTceVhCFfkK9ibIVMDvoRN0Tdxk4Bc2NnZQaO+MUb2gu/RPhWzzr4BmpNnxix839Z2iQYHXbzfLnIKbHWsuDg4PgBlMCszk6+Jwdlu7yCr1ezzCqntXGkp27tzUsy2d7SRZ9RLYz4g7F2erxTKGPJPW1s7VdfV0ZIpMM05aD7A/8RPuERmtV9jSws1NDQFCwbwdIp/6Ejq5X1PTx+hVL2rr8fkjTcvA6czPxoceILEsfraZurtdVB1bT3hXCa/CVkIfkDrqYKtjrYudnpPXw8vEwBuKUjJxvpSYyxQsDNmoeraasYsrW9sHpeNR3u/n+/c+DMwrYF1wyh8ASEgIBNk8Vu4fXjmDX3uRcfr7nUQZCP4FXldWBdpkvrEE3ZtbQtvTo7zfCOBaR3YwWcjj9vLOikZLLvbQW1tbRS6ZIrtB3tjh5gAOZwOqq5uJpfDSZXVjawr/wTfELH9/L7xyiH4r7vXSXZHLzXXjz/psK29pmxLoFwGT0+VlY3kcrmpvr55wkxBUJcQ37e2Qt826ujoosbGeqUiD74Wn+knhvcEaJ7Hx8kLNxWNjY1B2dAZfoTt4HvlB1NmI+Mm19SML5vA714f5HlQ2cfXhOza2mby+r1sw+6OQFxhxarHx3B9zB/QMBizPR1UXVs7Hp8jfoLtmDcQs8NjBtUirgK+RyJsa2iiRYuWMh944U9FSm/YEPB3SEQgbp/Xz3CnMf7xYrrq+npq7eygxmasaxxfLofqVchFVCqbOB1Oamyu5RuNxvrmoO+VDeGj0ImsCxcuUltbH7W19rCfWJExC/k85m5D4FeysdwIBWoA38eNm1pK5PPCJmZfdgdgLyHHlN3Kvr8QwPLFcbYHbBLiS/Z9dSV5Xe7LZJPfyrHhc/mDhXqtbR3U1dtBdrubaiom+d4bqNIO+AfXQf9xuTwTYlbZBLFi2oVbT2ZOgewuag7ZQQsxyP3H6w+uWVeyAWtaj5i1m3jISjZ8Eyq7v3+AYxu4yYhZVekfGxNj5h/YJ9CXcWOI2PO4/ByziBsQKr9DbWhqTZzPGhvbOHdWVtYH/aZ0CdUD58A/Ks5D8xVk4xx8KkJ+Rb4CvC5yofoN0QTf4dPlH+eHbMBuIl/BniDI5H8q1waEI46Q630+bNRQH8SrRtxx/AXiXOnCsru6qA03bSHr5MGL5XCwnxp7mlta2fd+6fsVdZH361MKczU8PGz89re/EcOIXahrMoqL5dCB+/bsE8M1Aqrv4MHDUtWNw4cPiiHkmpqajF//+tdi2LaDB981Ojs7RboAru+dd3aIeMFUVHTMgD5S2rJlk5TV2LNnlwGbS2n9+nViuMu6ujot32/evNmw250iVeD7w8WnRbyApnvxxReNiioZTB5sXXTspEg2mPbt22f09nYavQ67kZaSEhb2FBB5u3btEssuOlwkjtmqqiojJyND3H9OniwWQ9/927/9m/HFLz4s1rvkbJlRUlIi5t+0aYOYF/kEsSKljRs3G8hbEoLvAV0rpS1btojtDd8fPlwkEz02Zrz8yqtGaek5EX9vby/3ZREzQ7oWi3MK+uQ777wjzoXQGX1fQoD//M9/f8bodcqgIE+dKjFqKqskopnnnR3yPCsWOgOM4npyTGP85V9+V3wfkJKVRoUay2sK5xeIlipAgbSUFCosLBTrgs0FMOUgoYyMDLr11tskrMxTWAjZsmUTmHq67jpzylhygcLC/AlLTyKd88kbLt8WbrpzgIgU8pA8HVvwOHbgAbC9ZPlJTk6O2N64AHYtSUiQhSL8U+gbf3oMKjjFF9z1Llu2jObNyZji18sPQbZNY4kFdrxKSEjhXaAWLlzIYPCXSzWPIP7CveOdfB7iWxqztqQEslis5Bcu28vPL6SkhPEZj8nXDv07Py+PsMuPlK7On0MaGBx0w6dukoqm/Pw8SkoZX4oV6UTsTqOefCLxZmRl8SuASHzq9xtvvFGcr+DH+fOF+cpioVuWLaW5c/PUpcJ+2mw2rbjCJi7YEUlCqamJdN1114ptiJ2JpAS/fPrTqyhJGLNXXTWPdJZtPRjYHUuqz/vFp7Us6P1SKnqdqAU+TBb4r//6b54+/9WvfvWBqI0p7VXLl1N1U1NwF52ZUuTIkSP006efpkMHDsyUyKicqAU+thbAFLuYtm3fycU/khPw0h0FHVJqbB5/lxjpHLzoR5KREusReL8T6Rzw7ty5MxJb8He00zciewLAuzsU4UgJslEAIiG8/2isrg++O450DhKpDrYvipuky4KgM3SXEmyi3mtGOgft1JG9e+9OcaxArk7MtrSa7+1hG2xHF44Qs80tcmhH6KHepYaTi988Xg8N46WakNBOqb1REFUvhMbE5fv6usQxC361t6pEdfR57OcrJeyvKrUh7KETV7oxqxNX2FdYp2/q5kKddqI4UkqQK5WN/rBly5tS0SxXJxeiQv1KJK0Bt6OtJfjyPFJjOjpa6dKlzkhswd9bNDYjwPINFNlICRWoPiHCG4oDdDoHig8G3bJBEcUGJSWnpGpzIZbDJcMPxRTNiZLjXKQguQCWVvVrIIFhc3ZfjOzGAkURqA6WEjboVkUZkc7B2tTQgo9I/B0dfeR1jRd3hOOHzjqJriVQFIYN069fPPWmBep6jKVcL09e3Z3d4sHC5/WRPwF7iKqrhf9EYYsqgArPae4xi1iREjCDdfjPnCmTimadUe0rpbLzJTQi3FgE8Qe7SAlVudKlhhj0Q4t9Il0Dg5b0hgiytHJhY6NW3yyrkPsH/VLa72GTxsb2SKYI/g7Z0phFQW5/vyqSDIq4Ir5oDbiqUliieWxsIhmGWUEs4RdnC4aYtGq9V8JgZBGuIYWuwrzFzTIfnGXvH/F60OeTmxyyrUJlzDt52Xs55Q+L7FVogN0SrNxV54f7HBuT+14LcztujFAlKyWrxUc+IR4sdJa+88P1LVYbL3Ho6+miwjxzyVU4vXTwwscM4R0i9ED7uKI33NXHf9NAgSQsS0L9hs5N6PiVIn/T0QV3k9InVlwZNQfSSDHrEyLrqzjGjPGqcnUs3GdsfHy4nyf8hjYC71pKOu/YEbM6uM6xMRqJk4h0+r1NI10JJyhNkzG0ozzPSu08E3xaWi1duoxQWCIhHadCHgJeSghIi0XuLX9sPPmFKElo3y3LlklVCcALy578oLdGTQ7rIJOM5I9BXz6ColApv1Be5CA2yHtgxIAhTaTWUT9ZbfKwXbr0FsrKMtcwR1INIagDvo8BFLtWxfqJCgvNtajTXoOTwLS//kk/2AKDohC0h5O51N6440tPSSHMWElIoxuzOJ+wAA7MV2XNizh1H6qjzmCOYkAd3a3Cm7igPhqFZ8uXL6esLDnOMArmpKRjE8jkmzmhcNhPeqOAQjKd4lShCsyGm+Yl0+zapSNnNng/HkVTiATdSJsNa0dlfuQssHHjRnrxxZdpz55dH1jbmtta6TMrVtK5uhrKTk2fcT1W3L6Sfvy3P6YvfekLMy47KjBqgY+TBcSPCrgjxrsF6Z0x+KS8MLj0HR54tWUHQBQkju3v6yOgIkl119msHjK1+LFJvPDJnG04JH/Cra+pZ8AOiU1Ydsii+EjnsH909NaVLXyUgx54Pywt5GC9hbKVTQCwcNutt0QyiRmzGuuwECfAx5YQABqGPV6yChf7A3gEbZVS/txcsgvf474XG0r1aGltofJKGVwsZM5qTpnFmMV7UwUeEck2yA8KSCYSL9sEOUXoe8iW8kK2ju/xjvr48SMkxQvXkY2pioFBGY6/xGYzySMecGGg9evXi5MXKudKS2WdA44FTjMq1yTU0dVFKFSREpJul7Bi2uF0MtSZVPaJc8cZ4k/CDxseKtovYWWeU2dKqLVTVmiD5Lz/oLwyr76pkZoba8W6vLNjh7jzoRq3tKJULHv33v00oOH7kjMlYtlnz5VTd69s82+8pzxz6oxY9olTJ+jQ0QN0y22R120DEvTQEXnMllWWUE+XidgTSSGfBzda8veV50vOECAzJYREBwjQth6ZLuXl5QzXKZENnn075DMDHW0dVF9VIxXNqw2kg25rSxvfnEmF7z8gz1ddfW104oSsWBJby507fY56+mQrPAbdA3TowH5xfUV1WZm4an/YO0R79+4V93ugRkmrmlFAevr0WfJ4ZAWnGEuksjGeHHx3j9SV7yufGEvZ6zWorq6MnM4hrs6bm5PH+Mi7d+6kusZmam6opbT0DMb4rK+tpvKKSnI6B8hu76WCAD4wnhzLy6uooaGeX9zn5s7hJQRFRxG8A9Tba6f4eFsQ17j42DFqaGmhmppK+mQAGL68vJRqa4DDCdl9lB/AQ8XSDGxo0NzcRP39TrrqqjwOlP379zKcGSDN4uKsjI+MJ55jx4qourqGmi5coE8sMPcwhYzq6nqyWGK4SOTqq6/mIhpUrp4+fYYAzN7d2U4F15iL2FG+393ZS319vYyrmpuby3fV+/fvp7q6KmpsbCYlAzcgp8+eJkf/AFfZAtsW7xpCZQPC7LrrzOIb3IBgAGjv7qIRtyeI37xz53ZqbGyimroayszIZHujPcXHj5Ld7mSMV2DyAvcU18QGBfUNjdRQV0efuN6spEXn7+6+RF7vGA0M9Af9g1L6moY6utDUSDZbfBBTFbYadg/RpYutlJObR4mJ8VRbUU8nSk5SU1MzNTXWU+HV13E8wMdNjcDR7mY4SPgHhHWcNbW1LD/G8DMeKm6wDh8+TEOuAerq7qKUlFReR1pfU0Unz5ym5oZ6qm2op4K8ArLarFRWeZ6aKuuo2w6b91Bh4bUs++iJE1RTUUbVdTUUZ7FSZlaWGVdFh2nM5yPXoIPbgx1E0Gmx4QTiBP7HMeDSwg+VlTXUZ+9lOEXELN7rYQA5e/Y0NdbX0bBnmObOncc+hn+6u/ro+edfoP/9nf9FV///7L0JeFzVkS9earXa2iVrlyVZyEIIIbwbE5Yh4GQYwmNIIBNIwjePx/DPNllIYJKQTCYhGZLw+DMkQMISCEsIYbVZjI33XZZXyZv2tbXvarVaLanV6vu+X92+rZbU6q5DbGMSnw+j7tvn1q1TVafOuefU+dXCbNYXEhrU1tdSQ30DhYeHM33QPnGigoaGeqmjo4NxjVn31ZV09MhxqqmvoP6+fsrO1veBfbrv6KQwLYxSUlO4Pdt3bqGG2gaqb2oibWKcklNSObJ2Z0kJbVr/AV26YhllpqczAEclaB86zHVbrE2Ul7eIZYVkAYBR7e1sI5d7kvGb8Ya8cetmry6rKClJ1zHsr6S0hGqrKhlO9dZbb2WbhQxLDpZSY30D6/OiC3W7Aq4x2tfX18N+Ijtb1z3sykhqAFkDAAa65wQADgf3h8TE+ZwTG7a8e/dOtvHa2moqKLiI+YZdtbS00rjLTTb7IOV6+yCSatTUVHN9Q944PgIawPVFdGtkZJQPu3vn9u0sk8a6GsrKzuH2cL+vPkX4nDqYAAAgAElEQVT9/YPU2d1Li/J0u9q1bx/VVp6iqto6CiPdZjGAQ4a2wUHq7u5mnG7G13a7aeOmTYwvXV9TQ8kpKayHpoYGOnG8gnHlUR/HrGBXhw4dYttCPw6jMB2j2+Wikn37+NTD2OgoeTwa4yCjHyPZCPpwY9NU34RdlZcfI4djhLp7ethHwK7gI8vLT1BjYx0NDdop0+sLd+3aQZ093dTT3UMREfMY1xny3rt7N8uktq6GzOG6j4SOy8uPk90+yHLPzFxI8+aZqaGugQ4c1n1Kbw/aowP57Nu3n6zWOhoYGPDxDT0gMYmhe02b5H4Puzp8uJTjcPr6uiklBVnoovx8YTU1N7f5fCFernAPsLHRVsOnbNy0kX0E9AOMZWM82b13N+s+1FE9Nqyz/D/5bjtNEIDa8/PzGXzd7MVHLiwq0lk2mXzIOBkLsmloZJycDhujoGCWDEMA4lNqqoPrGyg6EPTixUvpwNFDBOQeIygLfwuLi2fN3LIXoDOYuCMh8McoGRkZFIkk9h7PNASY5ctXcqaOhXnZlJShB3whp28g1J+FCxfQyOg4HS9vpauvvIZ5Bv2UlDQfljPaYRQo9OjRcg6YwfNR8DtQh3jP2OPxo5FCBfkFVFGBM5tLp66nZfhoG3Txt6iomFyuk5SUlEh5eVMRsEXFi30yMWSIQQM0kdhg6dKlPsQjyLCgcEpGBv3CggLCKoHFEjFNDsy3t5KhB8iKae/aRctXriSgz6CkZaWQJWZKFiavPUCuiIR02O3T+M4vKOAJEJZU4r2Bd3C84BfOBHwaz0xJzyRzlDdht8dD2jw9QC4vO4+Ammvu7WP5GO3Jz82lMS/gvEGD7ap4MWeXycsvYJtFfaBg+WRoMvlsJSNjAQ0PYzI5wO01aEOvsfF6AEss7IsTz0dScfFi2vj++5QIBKliPUsQns39wbsUjGehgPaYa5xarQjmWDyle7RzXhTbin9CeEP3QFbKyF7ANKIsUVRU5EVl8nh8skJAWFF+HoPWLi4q8gFfZKVj0IxhW5lus0vZIccnpvBkEMTNFgsVG3bCMtH1ivYsLl7ME5ixrq4pvlNSaDEVcQSw/xIZ0Muw0gKMW/9UhYHsCrqHXZWUHOS/CbH63jNsGu03+g83nojtFJjbmGgVGbziuvHZTyZRlhimiYkLnmHoATbh81fevqrrJ4OP4TgdTiosmsr4VJCXRy5sA5hMlOi1gUiLhWkePHiQ+7l/vy82/JGfXaUtWEAjzlHq6u5hRDVDF+jTmKCjGP0YvxUU51N3azulpS0ggzbblZ9PMWwcdgXFA+uY7SpM7yfZ2QspNtZrs16EPdCGLCpOVlB8Yjylpem2iWf7+1mDtiGzsrIhWrlypS8ta1JKEhVZdDs02oI2QN/4jlAZg2+fvL39waCNv9Dbti2baPXqVRQdqSNfsZ+1RM6yWb0/HOcJGXyoUdhOvF+MvolnwqdA9+dkkcJDjjrGtd07d2s2uwzzFrjBbW0dUvJaY319UCxaf0IDNpsYDxT3NTe3aMDulBRg9QI3eGJyUlJda2ysF9N2Op1aba0M1xcPBy8DfX0iPlCpuvqUuC7wpcX4rpqmAa8X2MSS0tPTI8YBBj3QhmwkxW6zaW0tMruaGJvUXnvjNa25XoZHDZuFrUjLk48/oV3xD/+gaQJbgf0p635gQMQKsKLTklI04OpKCrB90VZJgc5ffP55vZ2CG0C7rUOGLQ5yFRUnBVT1KuUHD2sbFPCoT52S26xtYEBrbJHrvrq6Vm6zdjv3ZWlD33j7La2iqkJU3eF0avVC+wbBlpZmse6dzgnWj0q/7+qR2aDd5tBefPF5se8E3z1dMtrw3CdPHhfJ72xX+vuIUlac6hhv5Iq3ffyq/x1Eb0vxnz+M8n76k59Sj91GTz/++Ie5/bTdgyXHT1yziqqP1VNcQtxpo2sQwvLiP33qU1Tb2Ghc+kj+cpjXqJvMUVMrKx8JI2f6oQhqwqvi3/jJCuy1GiulZ1qk5wp9/xWhkDwhT6cUXgt7A1h3lxY4DWnB/o9KfeZDGPEJHvyXSkLxhHZKI+0QNHXGoB3HPUrBKtwuhQ6NfS5MRCQFNgK5SIsKTB5krUJbkmzB4FPVZpGybqWxjGgQmePv8NDQGYN2hGMOc3jILdSnbrPe9JBz8Gtc5qCpsTHqFuoTfVMaAIdnwK6kBcOsymCrYrPomyp2pWKzkKGKL+TD+kJdQnaqvlClnZhsSQvoqtBWGWxBVzr2QN4qdiVt3+mopzTgHjx4VAzbhmAFJF+WlqqqCmlV6unpoLo6ObRjq9UqhnaEgT31zDNiXgAIII20+1DQjnYZtCP2UAG/KC3r1q3j40/S+seOHRMPuIBgU4HJU4F2DPOMK9F+4YUXxJ0PPKs4mONlR+jTN1wvEmHfwADnfRZVJiJE5EonONgvH3G5ySzEVVKBdgQPp04c431GicMD7OqAzSZtJiHJu7TAib700kvS6gSbxUAqKXaXXQxLCHpnEtrx5Vde4VgPCd+o06AAi9vUZKWenh4paVLxy/D5+CcpnYOd9JtHHpZU5TqgK4Z2JFLyhWImTkNFpQFXBZoOL5RS1BG0QwkthRAcIHvbAm2cZjSCeiQyU0nRpqdYli1xfShoRwnDaCO/fSqpk8gsr6+CBAaWEQUpLbAT6eAywSkCpZRhVyYOtJLfIauJN7n2ri4OBJTdgVryc9KkiGSkkrpM4eWJm4a+nJ6VRTUKiTekMlFZgZDSNOqp+Cuz26wEeaiwYMbsRETJ+wP8jwpSH7C0pcXkcdPkpBw2VA15Te7zLR4LkRJ8pbSFej0VvtUo/3W15R6Xl1rlcIpwuCq4miodz8VOVzbIGeLRByTj2+n+KzN4DCp+Qc4hmYBjlFHWSanA5OEOFSxlVSetontVDGNNCwspO18Fj5mEqV99t0g+bNm2jQqKpiImQ96jCB2o6tBdCk5XZYJjtCs/K5fqquTnto37Qv1VsVn4CBU/gUm8S5jOQ4Uu2hQWpoClrJlpYlz2pg3a6PMqLysqW2Aus0mJtgq0o4rP5wm2EKgllA3N+p3nEwqT21kEztwFpaApLLelZWRQTJR+NCQYW9jHwcCYmpwcrJrvN5yTTU2V1cXSFs4OzhfSxtsIjiGoGKaPsRAfwAtC0SW0YWRYzkNycUnBvh+ObIC+pGCfKDNTlrhaQs+/Tmt7K+UgwbRg5MUy3hj0kyCDGQTfOCogaSdkCJnjKNTpLmxXbreI9ne/8x0iTaPfPvGEiI2RkRFyOhyU6j2+FOomFbvCHt5Vq1fT8epami8ImlLpD5B3Z3cn/frBByk7K4d+/JOfBGUdfKOgv0lKa2e7bleSyop1OtvbWd6ivjnuptGxEYo7AzbL2WuGhkR2pdhEro79TeOIUaj74VNwdEvaf1R8ikr/CcXnzN9BG3qU+AjcC2CXHC8GwExaH+V3pQH3o2T0bD0bDgb//M9Fnq1nn83n4AA/DFjijM4mX6f7WWeindiiWPPpa+juu79G//qlO043y8r0zjSWMhj6xYMPUkdbGz399NPK/J2uG7hvjnsoMka+0na6nn026ZwJmz2b/EufhXb+rfvZmbIQLykPj7lo26ZtYvhFzLpUIvMACzYyMjSTv4DfMUNHjltpASKLMfMOdQ/eFl599VUxDqsKbbz5IdhCWtDG3m5ZXkc4o2Mn5Lkrd+3bRbt27fOBaITiCRHqCOOXFOheJWAOYCDS4BboXkob/L765iviQKihXthV6EC/keFhqquoo9S4+WK7gv3BVqQFupfa7JjdQcPOMSLhsjLaCDlKCuwKus9KThf1Z/R5lX4P2tKC4Lot2zdKqzPf4F9SVOwK9BDAhVULSUHeaam/gs2+++7bBH8oKR/GrqS6N/yVtN8jsKm7V+avBgeH6dlnnxXbIfp8d6fs5INhsxL5ne064o3QiIlxqmmooMSMJMocG6Ms79IlOkx4uJ4zceHChT7YNiw/2+12flsEnBkKjM7p1HFfgaCUmZnFR2q6ulo5Gm50fJzy80w+Gh0dSGDv4U3+JUuWMQ3dmbdSR0cbIzRhCRVvae3tnYwShICAhIRkRn+C4LG00NBgZRShvPx8XuaEkYIXfZ/EQ8VAtCLikHbQx74FBl6gwYA2DAmwieDFEmlhxCjUR52auiamjTZiWQfPxKBqyGTRokJGaYGRwxGhowIBCPVBG8/DMjP2P7Baa6BnGbSTEuPJ7XH5looNeU9MTDDqF5bu0DEQHdpYX0sJcXGM9IKlF8OJoJ2Tk6O0ZMkKbif4GB0ep3nzXIw4ZSxDG7Qhw5ycXF52Mmgz3zFxlL1gAS/rgEZvbze3E7wsW6brB9fBO3SP/MkGbaDhgBbaCZQbyMqgferUMQoL01gmaI+/vMHwokWL+JmG7gEdiGA1w64wkLlcsJNxSk/PovR0XQ9NLU1k8phYxkDOwTIaaIC+oXt/m61pqCG73UZms8kHk4e2IJk19JmYmERAf0KSbURMuslDrQ1WyszNYtqGvNFGBL3AvtFOXEd/aGlpYZkYujfaCb5jYhIYac2wq7q6JoYkNRCJICu0E3u7oI/0baAPW4bMzSYTtbY2UXR0AtvbFO1RioqKI6BAGbQBwdfZGc3XptssAns8Pnlj+bGrp4dqaxuJok0+/GXIEEnm0UbIsbhYRzODrMCjkTfb0D0SPEBfaGdObh73QUP3gFKNi0vw2exU34ygmXZltztoaHSU7cvQPSZrho9Iz8yh9NRk7oPgBb+FR0TRwuwF7FMMGRq6BwKW0QehH5sNfdzfrupodHSEdQ8UJMOuQBt9HPxlZmXxttlUv9dleMEF2axTJENpsnojg01myvNuJ+F5w8ND0+wKNDp79Oj0/v5u6u3V+4lhV4ZPWbBggZ+9tc6yKwxOdruT5e3vC2EnON2RFNtP+UUFTGNK3jrfaWlpPpttb++g+vpGipoXRTm5ubN9ocXsQ6qDTKzWVvadJir09e/GxuYp/Xj7pm6zrRQdbWFd4i0X/qq7u5dx6aEff18IvjEBiY6NJQ+5fT4F/sroD/GxsZSTm+PzKdC9MWaw4Z8j/xO/4Y5isLFEkq3PpicC8EZ12GwOxiAF5Jrx/gNn1NPXR06ng3p7p4DjAQ0JEHdgljqc+swTxzxaO1vZeJGRZMzpZNFguQEOHXVhPEaxDSB8f4Cw346jEzSpN8HlQv1exu8dGdbhI+GEOttxbMdJtoE+GnPodGDYAwPgG0Y9NdMH330DGCiip4W3w5mDb9AfGZoC225tbSe3a5hsAzZfyDpo6zLpZd4jTJPMOq53dPSwgWCAnfC+LYI3h8PJ9Af7p3iBkY05HWTvG2Dsal/7Wd56O0ETBbLChGN8fILawZP3OvZqBgZs3E6bbcwgwc7S7R4jh2P6+UDIGW3EX9A0aFutVuYbsjRoI0gH7ewd7Oe2G7qHvuGMoevOzqnjB9Cj0+mk7sFBcjr0o06gBeeADgacVOOZbrch70GWi8H4gN1BfT3AaNZ1bVzHJA6DIvh2OnXaOK/b3ttJFlMkwVEbRwrwDJtNlzd4QiwACn632WwE+EC2Ky9x1NflAv512njTuuzyywl8tg10eB01/IpHr9ut8+Lx5nrl/sBHMQBJ2unTvWFX/nzjsXA8Y2Pgx+7jG7KCvCFDxDvg2TrfY9Q/2M/7ch09feRx6/ap0+4mu93NOOXe5hBsFvLD0R201yhTMuklt0un7XJ7uB9gYEXQtNM7gQYv3d39XjufSmqA/gr5ORzTj9jAptB/0E4ybJN1jyMkiGvo9NP9VP9BvzAK8J8djiEyQQ79U3zr/kS3WffYVP9GnuKIiAjq755J29D91NsS5AoM4NFR4JxPYQcMDQ0zz7rtTtks+IX8u9hf6f0EAzfaZ/gJI0rW4XRyH4Qd9XZ2+/qPYVeg7XJNtRP9AcFeDofLZ1f+dSFLow/CPjD5xItKZ2e3b7XKsCvIz/CF8JOYhCG2os9h55cTyBa0dF8Ivwy7m+oPwKofHx+l1nYrjY6Msyq4b/aibr/35UnXkI39eh85bQ72h7ga5gmnwf4p3Rv9B8/s6mojIgvL3WgPfLjhlwf9sv3An8Cu4MMx2TUK9Gb4Tkx+UUDL8ClGvXPqrxTaatQxqv3hD0+LIfsaGxu1ssNlc5OfAYe3fft2MeQY4ONKSvbOTXvGLyUlpRrgBiUFfD/55JNiGMPS3SVal5A24P02b94sYYPrlB48KIebm5zU1m9YL6a9YcMGbevmreL6H7y7QRufobO5boYMjx49PNfPs66DF0C9SUpLW5t2tKxcUlXTJia05557TqutrhXVB5RmaVlovu+55x7t8d/+VivZvVcMpwj7275dLu/SklJxXztVXaklxieKeSkrOyKGGhwdHdXeffdtraOrS0tMTAzZR08cr9ROnDghkjcqvf/+e+K6JSW7tbVr14rrv/POOg38Swp0D7lIy+bNH4SUhUELui8tOSiCAAUs4YsvvqgdPy6zcUB07ty523hUyL9lZWVi3dvsDg3tlEI71lfWatWNsr4GiNZHH/3t3DKc4WuOHTuiVVfJaEMI7733TkhZfBQV5EFTHg8Nj7goLk4Hmg41a8C6vwqSCGYmmCVKi0p93oMIn0okEOwZWO7ADOmiiy4W8cOzM5OJl/SC0eXfPB5+E5G2k2krIF+pyBxt9JjNlIvIY0HBzBjA7ZKiyjdm8JbISOEBDn0WK5Eh5rzVlad46VUUlSnUz6WXXkpP/uFpWr1qNVksFhHfKjYIGavYd4O1iRPQn2xspvlx3qQPwRQlbKdBwrCreRER1NzS4lvSM36f9he0J0jc91Xa2d7eS07ngG8Zc9pzA3yBXakE5RjtDEBq1iWsjOAEgaTADj3S+h4P1TXU8fYFlvslRYUXVTtUkaGKLkfc49RY1UgXXniBKPIYfANLQboki3zS52JwnXzAlWj+fJ3zEvgblwCW9C668CJC+jtjj/KjbjLiFK5YtoyqGhvFx3E+DM9Lll1Mzz/3Gq1ape/Xfxga5+85L4G/ZwlIJwwsI+SBhMORlFZrEzUIIj4NWsg7Ki04X6cCOVbT0ODb3wj1DLRvz549oar5fsebIt6KJQX19h2QJyEHbQRMSApmlyq0kY/TKo309nho/4H9vr2jUPwYQR6h6hm/I9epVIYIfGlXwN2GLv335YxnBvqL4JZQkcQVNScpPSuVg0KqFCLOYVfIUyotTQ11vN8mqT/mGqNRfQtLUp1XcMR25XLRngP7mW5ubhH1dAeH7oPNSn0EiO7fp9OWMA49IueutBw4cICQV1ZShkdGOJBSUhd1ysvLlfpmXbUs6hi00UbsE0uLki+sq1SiXXZSDr0J3Te1B7cPo00IyNu0ZZPxNeRfVV9o2GxIwme5gtKAi+MERvBJKD7tCGzplhsNAi6kxe5wcNCGtP5Qfzcv5Urqo30qCQbguIQnD/QN/Sa1JA1SeSNAzNogp93W1sbBNhKZIGTQ2tQkHnCNIA8RbSJqaUEydNnxDXdYOLV3ytuJgC9ETEvK8NAgByQFq1t+sIIuv+xy3m7o58j1YLWnfoMeVZxo/9CQeJJITg95TDL5gSME6kgLAu8QiY1SXFRIdfX1QW9FEIvUZkEIkxxpQUCOSt9saKihcSFkF4I19RMUMm5aWpp9gV6h7sBk2DE+FRgVqj4ifhHQKS3IbS0tQ4NI0iCv32HFSRFZgS8c7pe9kGGLquKkPHEFbBZ+RVraFV72pDRPRz2lAVcFhg1HAASgRL42qGD1AoZNBSfV5ZHvDfsYUvogd3ZGaL+EPHwFBlJJ4cTfsqo+ch4F9DMj6tJ3c4gP0L+0MG0hM6aJcYqM1BPBS+ir2JXum4ML8UjZfrp2zbX8aBUbxA3GcRkJ3yp13CY3md2I9w3Ou0ETJoVBQFQ4yF43FCyhS1cLRLS5ktwIXWZ5XZA2mSw4MSQqiAlQwS9Wghf9ENCOIqa9leQ7m0Quz6iSX1aBdkT/0Y9cybi3CH2bjJpfLcQReE8I+F09Jz7KeqiX1aKiYs4aIuF8fmomL7tJ6qJOZqZ+VldSPzo+ls9bSuriqEaWEDIS9GJjY31nFiX0589PFwcT4azZBRcskJDlOsnJ6WSOlAWpwWHk5spluCC3gNIzZUEZYCY/L18URIa6kZZoPuMnbShkgnskJTwigiAXacH50/j4eFH11NT0kPCi27btojXX6hmCMtNlAWd4OOwqPV0GXYr66cmZviNvoZiH7k2RZjJ7ZIMobFYSdMbPDSfKz9fP2WZfkB0y8xIgOtFWacnJK5RWpaTYDMrPl+NX5+fnUaQwQQfkkZwshwvNW3iBOCArcp5JyRcW5OYr9Z90IVwoBJ2VmkVxyfJ+j/P40oJ+GR8v68cIZiv0nt+W0E9ITRXLG7rML9SxFSS0z2ad80FTZ1Pa55/1sZYAljPXrFnDIBbiAesstBhLkFesWEHiKOUPydOB/fvo/3z1q1R9qvJDUjh/23kJ/H1LQPyGi7BsrKFLl6JQT1oXKlBZn1em7QU3kKga+xAMkSjd+1HYVwDfCFeXFgZlEPKhKkMgbcFRS8sZ1Y+iDKV2hXpABBIHCIWw2W1bttCyFSt8b4dnVCawWaHux9wumjSZiVyyPS7l/uPVT2p6JvVa24Ou0mIvXqofVZvFcnaooDZ/ez6j+jnDNiuFSFTVpYpPAe0zJUMEP6rkK2abEvYHVbvyt5kz/Vk84I5qbnrppWfFEYhw5tLIYwhz3/79YseIKMj9++XRvmVHDon3nuw2G5WWlIqdBhJoS/e1YGR7SnaIdXqg7BBZhYMi9ip3bt0upl1T0xByedCf2Natm8UyabI2MY6t//3BPu/YsYOArSopkPUxhaTlpaUHqaNrCvEq2DNAGyhSc5VDFUfo8pUrfT8j0lsakYtBf8+eXb57Q304UXaEYTdD1cPvrjE3AaVnTJhvEW2U2iwc7rZtus1iad4SHR00SrymqkrJrqB7aWlqqqOyk3K88PUbNogHDMhD6q/A784d25X8FSLxJcVkNtPRg+XULQwMhF0hqpkHJMEDTpw6JQ5UY3+1Z5eYdm1ttXgSD7vauXO3WD+AcZQGzEEW27bJI6AFYjttVcIfeOCBByTUXCNOOlp2jCYmJgmQX8AQRVZSOBGrtZn/xccDxzWKZ6E1NbXU3d1JIyNOwh4DAp0gtJqaaq7r8Wg6lufQMO09UkKO7gHq7OmmyGgLJcQnMlRZefkhQpQp6OfmXsBsAtMX2Kx2+xANDAxRWloqv3Fg5ltRcYrrOp2jvGcCwe/as4t6e3poYGCQwsIjKGl+IneUw4cPUmtrBzU3N/hoI8F2Fef8dFFP7xDj5mLpEG+DFRXVXLe/t48yF+j7sMaRk77BLpqc0PiZMCQcR2hubqSmpmbGiAUNTEAOHz1MjuFRamuzUlZWNvMN/NETJ8q5bkdHhw8feN++/dTd2UG9/XYaHrfTgnQ97V4geaPT7du3hwaHhhiXGfKeN28eDwZHjx6m1tY25seQIQYK4FePjbnJ6RxmXiBc0DbqWizz+EwnBpSDB0sZHhBOyaANLFgcczHqZ2UsJJM5jI9LNNQjMniQBgftlJ2t73PqMmmmxsZGCg8Pp4SEBNZDSUkp29PgYCdFR8fxMyHvkydP+PSTlJTM7YHu8c82BN33UU7OQrYJDCB1dbWse5NJp41jRqWlJeRwjtL4qJNh/gB+AT0cP17uo+1vs9Ax6PrbFY5c1NTUU3NzHT3z+LP0jW/+O+NJ7ykppZ7uLm/Ep0bJySl+8oZd1TEUKrChYZtoD6ACu7u7fTjN0+yqv48yM3W7ggO1trWTbXCIJiZdlJqSysemoAfYbEuLlfHF589P4oGzZP9e2vL+B7R65Scoc0Emy8qQIfpOd3cPZXlTle3atYch/Hp6ANs3xvrkCe++PWyDbW0dNH9+ItPobO+mw0cOMAQkIlsXXVhATz35GF155dX8XOgS0bqGXYFvRL8PDQ3S0JBtml2hL6BudHwcxURFs+5LS0sZIhCQg9AxfAegQg8fPETgw79v4hiOtbWdJuyj5Bgd8fUT3Wb1uobu0QdxhHHEMcL6iY6Mo7j42GkyBO309Azug7CpkxUVNGSzMUZ7Xt4itisMkk1NLcyHxzNJkDdoQ4Y22wB1dXVTeFgEJSXP50EJfdDwKYlJyRQ5bx77L/g99M2uzg7KzVvEflMfQBqZttszSUle2qX799HouJMTI7jdGvs39Lvjx49zH0Z/A2SlYVcVVbXU16vDi6JvwtdgYKqoOMn9YWhohNLT03z89fR0U19fP2OXw2bhO+ALDR9uyNBqbaAjZadoyNZPPT16+j/4lGA229KC6OpBmoTNpqaxrPBiZPgIQ4aQ92P/8z80OGyjmOgYSkpKYt1P0a7jiH4DLxv+qq2tnXr7+vjEgWHLhi+EbU2MT1JyShLruKSkhHr7h2npkktZj+fS/8R7uMPDY/SnPz1Da9ZcTwCC5zy3c0SZYWYEoTrsDioqLgoeMODxUDfeWA8coGWXXkoZXnD8uYSE81vNbVbqbO+g5ctXBqfNRyD66fDRo5Sbk0MXXBAc1QR8w1gx073mmmv0fIpztBH8YTA6erScg5Wys7ODgg6AdkdXF508fpKuuuoKnmwE2wcEbfCBIJT8vFxKmD93wM2oy02OIf0N6uprrqXk+fO5480lw6GhISopLeUI6OXLlweVIZwxeMHACL5Tk5LIPA9A54ELOjADwdtttHzp8qDBH6DdPdhJpbsP08qVy30A9oEpE3cmvD3b+uxUVKwDpM9VF8uxOC6BSVFhYT7l5xcG1Q8GaBwjAaYwwPhnovz0Dw/ShQsXUUdHLycHgEzgqBBIiP4ABzhXge6bm5upqamVli9fzLRD6R4OFo5FYleY+PzTP36GDh055Eu4MRcv4BuTiNjYeK4bDIEL+oGzh9O85pprme8rr7ySfvqLB+imG4pfTrMAACAASURBVG6c9Yje/kGqq9GPeiAJRyja4GXfvn20Zs01FB2NAXfu0wSwWUyUbA4HXXHZ5bP0488Mtr8G7f086KI/JIXItQzaGGCAN15UVBCUNuyqu7+fV8EWL11MCzIygiIlGbpvb+2kxcsXUzpyeIfwKXjrz83Lp6LCPE7E4t82/8+gjQkOEoNcfvnlIp+ClxWsVCCYMJTNdnV08ETksssuC2mz6PewK5wgQMKNmbqHLR04coBe+9Nr9PLLL9Hyy5fTpZesoPu+d0/Ifg/asHGpzeJIFSZFt9/+JX9xnROf57bwGeyhM1x22eUhHQBuw0w1LyePxtxjwY0XlU0mnmUvW7IkpOBRHQmiL6Bcio+dH5o2ESUnJ1NRYREhOxH4ClbwO4wQwPF4gw/WMUAHTrmwsCCkw0Vd0EbnBKD9TGceiCfUQURmfGx00MGWaVvMFJWaShdfsoTSBXBweLvEUYJIizkkLxgYcBwEDhQ8BRsowAs6GjpXpjtzVqeb2U7QykrNoeJiB2Vk5AR1uLgXusnLzaOehL6QfEN38+OTyeV0UVTM/KDOxaCdm5tPycn2gLT3btpGn7jySh+PkIVksAVt6B4Dp5GFaKYcZn5n3RcVUUp8fEi+dZtNIDITJaWkhNQPaLvdhRzxOdMpzuSDdZ+WxVlXDFStvLxc6rQG3vtPxZteXh6TEdHOzCTAZEqizmGzFnM0ucf7A+rHn3dAyur6KeL+EMpmQTuHI4NtIWmzv0pNpYsuWhRysAVPhu45Sl3QN2GzOMsUFxMTdLA1aGdk6G/paG+ownaVX0ixsZEiu0KGoNFxfbUwlAyh74ICPeLcX/cYLP/0wp/o2eefJSRn+drXvkKnKispNjaR3nrtT5SYmBLSL4MeJswWi1nkU1LTs2hp0eJQ4vhIfhe/4X4k3H0UD/V4GOFHBYP1o2Dzr30mBkUcUbQo4Ff/tc/8KO5nDGi0MchbhYSvr3793yk7I4N++sBPJdXPap3W9la6YtmZj1JGo+6//36yxMbTL37y47PaRn4Y+uao+5zEyD2dwsCyNQa4UIPc6Xzm6aa1Z9cuzne7ceNGuvaGNXTX7XfRp/7pU9MGVwTY8Vncv7Jvnm7ezyQ9cdAUmMD+lxSCDzMb/JOWXgW0FPDQrYCW0i+Eo2ReTSbxeS/UBy8YvCQF9QBLKS1Dg4Oc31FUH4hAwgAr0ENnVhlsQVvaTix1Se0EvGDZEvdICnhQoc0JF4QdGvtsAW0W0Jb79tCVV39iGou9/bJk27gJPGMJVVqQR1Uqb1gfgm2kUc1oI9IXSgrbrF/Kuvy8POpumBumEO1U0Q8mC+KCvhkjSxgAmqAtlSHkMTws91eqNjs4JKeNyb7KYKtih6p+WQXFytpgpd889hitXrWC/u3uuyk3N4/KTpygta+upZs+d9O0wRb6Yf+j0DdVfISKLxTb32moqDTgbtq0iXOdSp4L7EuVEP5yBSzlrrYuDpyS8IE6DU1N4mg47D/+8Y9/lJKmhoYGsYOBI9qlgNNsbbVSn20qn3AwpoA0tWePPHJ73bp1VFZ2KBjJab8hIETqvJBnFQEQ0oLgB8zqJQWOsamhRlKV67zw8ktUU4ME6KFLR1sHVZycXbe9s5O629tp+crLphGpqpDjfyOn59GjR6fdH+wL9qql8h6zO2jYOUZCjAfGUnY6ZZMF8LBt2xYfq4VFRVTTOrdusaeItkrLrh1ym0VcyMsvvywlTXt27SP3uGxiAXk0N8thDBEE6J9POChTHg/VcDBm0Fq+H199/VWlKP/j5eW+e0N9gAw7OuTtPHogeHQ1BkHszX717rvpklUX0dtr36af/PQXVN/QQA/+6kGOnQnEEyafjz32m0A/BbwGaFmxvCdNtGePPPo94APP0EXxHq7q83FkSgXmS+oswIcbIHY4dygsODIjTS0nJPkhq8l5xgMgQ7MQmk5fMpWf8WX6CtVVoR1VBOQRQhIyzQiTGLsa9S0e7IjJ5pWAowwk7pNVFVRQWMDBaP7tUjgWyLepQDuq0sb+lkoR63NyUodI9BLHXn5jVZPKo4LWNQmPMjERQFIGUtCcT3DRhGeCIik0WhtgIFXgSMPCcUZDVjAZRmSxuKj6ToVtIY/Jo9ROCg/MN96Un33mGfrTn/9MjsFB+v+++W1685X1tGBBGi1bJssmpQCPIBYdVwznzTK1e85SbZkn+hDMRETMU8ImVcG8xXILgo+kxUV6HlpxfeESMejpKyJSZ4eJgpQLvZ5sfq6Pzowdq0DeI1+d40AOBdLS1U0mGREeIX6bo4lxMisMLiZEEwkLBrlApA/s20/X33DzLCrK8hbiReNB4RQ+63nBLoypjUTBSE3/LRx8TPU1BK4N2W3iLYDpxAJ9kxuhxWMms0KSBhX9wP+o9E1tUgvUmDmv4diKtOAIpcrgLwaMhr9yq70I+WMpY7Vjz44d9KW77qBLLrqIDh4tpwcffJCq6uvpJz++n7Kz0wh+X1qE6YSl5Hz1lOZkvrvO0geVrPflx49rdrtddEtPT4/W0dEhqotKLS0t4roDAwNK9fs6erSJiQkxfZWK4MXpdIpuAQ+VlZWiuqjU1dMnljfqn6qsFtNWrQi+pTKEPMC7tNTW1irJsKOtS0paqR54DmSzxcXF2t7SvbNoqdgs+k1jY+MsGnNdQP+Ryht85GRkaAM2Wd9EO1Vs1t+uxicmtMKCAq2i4mRA1tEf8E9aVPqDlKZRD3xL24l6kLm0NNbXi2mDZleP3BdKeTDqNbe0GR9D/oUvVGlnfWMz94nfPf07bfnylVp+foH2ox/+SGtsaZ71LFvPgBLtWQSCXADP0rEHZM6kXQVhM+RP56OUZ05skGnC41EKWphJ4uPw3T3qJnOQc48fhzZIeORISIUlt5k0ERyz5JJLqLKxmVLnJ8z8+Zz43tTeSp9ctZrKa6spOe7M83jtmjX07Xu+SZ//7OfPavuhS9OkiXDs52+54BwxhX+0PggQtMeqyuipJ56i9957j66+5kr69je+TWs+/enT5hvxxqwSHPa3oHOx5Y4NjzISUcAozgCSwKY4nJWkwMAQYCWNQgMPCG6SFtSVRk62trfT66+/Kl7iBN9S2mgfsH2lBYFHUnljDVeF9p7SfUpQg6AtDeKB7hE0Jy0I5FDRvTQCEfy+vXYtB7ZJeIGsZ/K9bdcOzmqSmjAb2ELFZmEjKkGE0L3UrtzOMRoec4mxlCE/REFLCmQI/fiXrPRMaqhp8b/k+4w+L+33uGkmbR+hAB9OnThGW3bKIfuAiS61WeheJV9xRZXcX0GP0iBC8PvOB++I/ZtOW+4Lofv+ILoHvYd+9Qu6+pNX0i233ELRkbEMd7r+7fV0/Q03BB0ggRgWjLa/SvGcl156Sezf0C+lUf6BbNb/2R/lZ/EG14SJGO0DKczQIOOgtf/Ah0PYOOgNYUKxSPyNGYxRFx3RiEaNjY6n1PRkptU70EvA9nW7PT40KNDwj3YEegkKOgYiIaFchM8bB/KhDCPxtXEdfOI6HJ3T6aSFCxfygW84966uqUg9f9qo73LpCDugDf7xTCNCDt8NyDG0p6nJynyj7TigjWf6Dwioi3tGR0aoraOD6usbaf78ZJbJLNomE+GwOQr4aGiwUnx8P6PCGIfJA8kb7QF/QKbypz2XDEF7dHSINC2Cn2Pox5+2gZ5k0K6srKW4uAQfLCFoGPIGv4YMe3sxaOm6B+qMQRvXIBsUoGcZsgKdiooqlhHAIWA//vJGfUOGhu67+7tZ9xLa0DucQFpaGut+Jm1/m0X7BwZsDMnIACImE5WXHOYBF4nSAV6AZ6IdoAP9wGYNNKiZ8jZkiOuNzS0M8we0HNCYqXvDZtFeyKSpwUpDziHKzcin+ckJPCHxt1lDhtBPe3s3mchFfX02BkuYSRvf/W0WkfWx8fGUD3CQADablrOAYszzaHhkhGwDAwwyj+cZfGflp1NjzQnfoDCle72vITgMzzT0E9iu3GSz9dKpslNsD6Bv+I5A/R4yGbDbGR4TnwPRTkxKovkJCbpP6e2lmqoKSk5IoJS0NKY9s9/72xX0axvo431cw6cEs9nqyhNcN3vBArarmf3esCvYSUtbB+HYI/qDQdvfF8YnJnJAnmFX4yM6JCXsB/oJZlewiZrKSl9/gNwhH6NvzrRZ+MLExCSyWCzTfOHJspO0duPbtOm99wkrGPfddx+tWrGKTlZUUaQlUl/1M5mm9c1ZNtvURCZzJMP4BrIrf5sF3x6Pm3084gKC2Sza09DQRNHRSP0Hu9LTKPrblX87UR+TLQT4nWtFPOB6cEjZEknA/h0c7GcUHyzt+M/agR6CTtPT00dtbS00Pj7BvwM9BXUxgxwY6OGox5ycTB5w0QkA2wXHCNpQIjowBhAIGYmEEcxgdGooCg5jYmKCamrqfE4AGLjAXUbJzMzyGTZm0MCwdbt1hUG5MEZ/vg3afT09HDKPoJyTFScp05tnEk4YsH8oUKzhvKpqKmi4f4gavOF2hpH50zacbp+3PcPDI9xeQOXByNBOQLOhjQjyMAZc8A05Ox12Hw4wnm/UNXiBvJ1jY4y1iqAfyPKKK67izoR2BpJhXV0DOZ0IhHGxHAzn5c836BuyAk0k5z5ZdZLbj3baHHZqqKnz8m2mnAW5rOOOjgZqaWkjmpzkZ/vThkNBG3Nzs7yORNc9AkTwbMgW7enr6/E5c/BhyNDQ/eTklO7xe2trO9sPEsJDl+DPsCvYE+wxNbWP2zPTriKjo/mZXT09bLOwq6qaKh0e02KhLbu20ffuuYca6uooMytHd/QTupyHh4eoocHFCFJxcYXkGHNyO9BGIwE2ZAjardYmGh0Z4jc68Afd+7czNjnFZ7OAF+0f7CeHc4xiLDE84EJ2NQ11ZOLgnikZoj1Wax2ZyEInTpyiBd4BwN9mIQPDZtFn+vt7yW630byICJYVZOive8ib4ubRmNPJ/QC/nzxZTldcsYbi4syUn1NEf9z1AtXV4c1Kl7lBo6/PTlrYBM0zR/kGRcjTYo5kmcRGR7MenG69H3jMbrbZyy+/igAEhwm5v40bfROD32BvP5HHzfCrhl3B6bpcLoYpzS8o8A24gMZEOV5RQctNJsrKySH4MP/+kOPFl4ZddbS10OjoOMMTGoMi/JHTaZ9ms9AD+oOmhVNTQx0/1xgw0E6zN/JKR1Aictoc1N7aRCMjOtwt+IbuWzs7ydan+8KsrHR9wCWiivLjfAIDNpuQ0MX6GbAPMGQmBjPYOPTJdtXVwbIYco6xXRky6evsofaebq4LXRrXMbHFBMDhcFFcXAzZbNH06iuv0GNP/Z7iYqLomiv+gT7YvJVWrFhGOJYGHzQ+PsI2cEV8MuvesCucEomMnnrhgf2AZwzkbVG6XbHN+vk2o987HDa2HbQD94FH9An4cPh29B+007BZ6BhnjSNsdg7eTE3Vz8P7yzsvL5/biX4P3XvcsmOGbCRn838hd3m9Fez2Ue3ppx8PGFQSiAYCRI4cKQv0U8Brmzd/IA62aGlr03bv3h2QTqCLJSUlSnw//fST2sTYZCBSs65t37lbHChgs9m1DRvWz6Ix14WSvXu1xvrZwQmB6oPft9+V0/7gg83a5s1bA5EKeO3tt9/VJsbHA/4282JtVa1WevDgzMtzfl/79lrNLgz4QVDTwdLSOWn5/4AAn+eee04cQAGbPXjwiI9ES0uztiAjY87gpe3bt4t1D763bt3uox3qw+7de8U2e6q6UkuMT9T6hMFK6JfSAK5R54T21ltvTGN35/at2mVXXa5pk7P7yJGyY9qJEyem1Q/2Zd26t4L9PO23kpLd2puvyeu/ufZtbXR0dBqNub40Njcr+av16zeI/RV0L/VXkOiLL76olZeXz8XqtOsIUNu6dfO0a8G+QIZ//vNr2r/cdpuWmJio3Xzzzdr2rVsDBoChT27YsGFO+5/5HAQqVdfWz7wc8Dv4fuS3j4plCH9SX1sbkNbMiwg2hL86F4tS0NTQ8AjFWKJEQQsIPMK+ImZzkqIU3KIY2ISZlpQPLN9gyRrg3qJ7wAsWOoRnCjCDx8xOVBRpI9elWRhrj1mjJTKSsjL1LESh+FHhG3vyZhzfE8pERT/gk+H9JAFfHg9V1NQw5i1m0KEKB6uEuX0yfOyxJxhc/803Xw94K/OtL00E/H3mRZV2qtSFLj+xajVVNzbS/AB7zTP5wBEYzwSJ+jHunRlg12RtpU9eeSXV1jbMRn5S7JtiXWKpvbOXbA4b982ZbQr0XaU/wFepBEuq6Id5gz8U9oe6mhpeBpfYLOtH0O+xzPrMs8/Qa395jZzDI3TP9+6hmz/7z4Q3wzmLokxUZAhAEmRmu7BwEa8wzcmD3w8qMocfxyrAuVaUBtxzjfnz/JyXwJmUwC2f/yytueYG+vY93ziTj/mraWO59arVZy9KGQwnxMVxli/x5PGvbuV5AqoSwAAFlLA333yT1q17h9asWUN33nk33XTzjUIoGNUnnq8fSgLiKGUQQn5I7AFICvI9SpMug96WLfLoQ+wtIP2StOzfJ0/QjPYdOCSHPORcl0KZIMk6IqClBbSlWLPoXK++KqcNGcJRS8urr77iC3gLdQ/SLR47dixUNd/vr77+ulJ0I+QiLWVlZRxEIqkPunu8UHaYIR85VEafvvEf5rx11y55Qnm8harYOHL8GgGGczLg/WHM7aJxt5sihW4U7cQbj6Qg+vmVV16aVRU4uUg4PrPArtBWaQlEe657wTP0KS3oD9CjpCCwTsWu3n77bXE0Nt7iVXzhiRMnOChUwjfqIPevf0G//v0TT9DFF19M37r3u5SZnkm1tbW0du1aSkuJ52Ay//rBPr+7/t1gP0/7DfKTyhB6Qf5kaYE/kUa/wxeq+B8pD6ejntKAe/JkhS9aN9TDsYKiAu1IQmdhPBeb6uIC+KBJWVMRhFKhgOuMdsqLGDeKSeq0ZXxjuUoFrQuOsbdXdmwLzIihAFGXg6PkUrF4hG30ktTcchQmRG77R72G4srsRWwC/nZUTAwVFcydxFq4Quh7pEcBDUrFrtxjLpa5iilK65omxjky1NcI7wfkI66omo07PbNe6O9ypCnoEflcpUXJR7CNSymf2XonKyoIwWfSggAmDDLI/fzZz3+WVi1bQdv27KA/PP08HT9cTg/+6le+wCmTOYqDWaW0w8MCQzsGul/F52MyWVpaGohMwGvc1xQ6BQLEzsUi22D1cq7i0CEglwudVVZE+6VeUip1eR8Zu6xyu5Ex7K2lO125GBVshp8gpsyEFQd0hTkLnJeS3BWk6DYhelk46EbMo0nPiAJ1PTOS5AZ9gujgqu+sW0e3fu5zIW6TDxYgZLYI9+6x/a06AYXTFY6iMBWhtCk8IiKgbvLyCqjiZBXR7dNFpGrf/rCR0ykF+KaIpYxoV2nHh2+TwhJCzOFhcixljmcI0Jy5LiEeRNNkvhNvfX984QW697vf5RWRO7/8v+mRRx6lgjn2Zj0eYGPLJ6z+0I5z8WtcRxdWgaREfmhpgV255dWnwZFKn3E26on9OZjBcRvpnk16JsLw5R4dQUrSgjByKR9488vKydczAQicOuime48DSfjJysokS5zM8WITXwrszfLOyqHoSBltDIarV1wpYZnrQIYJyXJUolWrV4tp47ydyuC8YsUqsT7jzCbKypXbCo54SG0lLS2FkpIS+W3hvXfeoV89/FDQNufl5QT93f9HyFul5OTq57cl95jMFgbJlfqvrKwsPoIloQ09BrJZHKnZf2h2JpkFCzIkZH11Vq2anvLQ90OAD4nRiZSZGTr4zbgVfFvMMsxjHEmTFvj9xUuXimUIujk5+vl6yTNwHBHH4+YqOPpSUlJCr7/6Cq3DudlrrqGf/ffP6Z//+bMhJ1K5CnaF5xcqJHKHzzcFTP8xuyVmM46qLZj9wxxX8rJyyRQpHK4mTQS8iHOxnJagKU7yLYyOPReFcJ6n8xLwlwD2wJYtW0H1tdU0PznZ/6dz8rMRNHW8ulYUpXw6GvH+xvfpFw/8gg4pxDucjuf+3dLweAi5ad944w164vHfEc0Lo/9925fpK1/5GmVmyU4a/N3K7hxquNJLeiC+sfn96evX0Esv/JHfDIw6/f3dcqg05Iusa6CRkSHj9qB/EdikEpihApMH2ghw4CMiQbnQf8RBemlgBmamKvCLKtCO2MNR2beoqKgRw82hpaCNZ0gKgltmQiQGuw/7yZCNpEA/UtrgVyVoimlbrXwUaPWVq0IOtji0L+UbNuIPLhGqrSo2i3aOIp+wR6YfDNDSoCnQDhQIszA7m7rap5DjjPZgiVMa3IJ7VGwWeoetSIsKtGNvdz8DqEhpq9gsdK8C7Yigqe7uqaC2Hdu20S1f+AJdfNHFHND59FNP0cnD5fTTBx6g+MR4BvOQ8g0Zws4lBbYNoBRpvwf632CvnDaCpqT9B3xLbVbSto+qjnjAhdE8++wzszpTlCWGfvAfP6bfPPYYXbvmWtqxQ0/86xhwyh3jBFFTQxW5XLJNKAejUsmxeoEYY0CdhRI0gqbKkdBZuOdrtTaIaSNQoLk5MAZtIL4A2acS8NNQJ0/M3t7eRDVVcycSn8nPiVMnZl6a8/uAzSafbHnxdKURudCj1do+57Nn/gBd2vtsMy8H/A7dIyp848ZtdOvNtwas438RfOAeSTFQvyR1UQe6t9llgTOQncdkZnQeCf329naxzcLZ1tY2ziKLJdIht30WJjNQm/BPWqqr5djicLonTsnrA9pROlg4XA7qbJf7FERoi32Kw876lMgES/iHjx6m48cP068efpBWLFtGX//Wt+gTS1fSsRPHGBnq09d/mgP6QA8IfQYKnoQ+7Kqnb0BSlWXH+hFuzGOS0GfrE9GGzR48eFgciQ+Uwr5uId+jbtq0aYuIj7NdSbykjAH3xRdf5D0uYOreeOONZDKbac++HWTy7mbv2LOLnn3qGbp0xTL61Cevo9TMdEpOmM91YUiIGAXWLlLIA7YL+7ag+97779GY00WRZgstXr6YlixZQp3trVRVg+MFmLWbqaiogKHv9u8/RHV1VWQyAWoymj772Vt4jw5weJi5owDKbPHixWwwa9e+SWMAdiei5cuXM23M8MqPHgdZJp+Xn8uQgPv2HWDjRQAFIMrQRhw+37NrH7k5KtpMsbGRtNq7n/nKK6+Qc8zF+6yAoLvyyit5xoboOwQ+4CD9FVdcwfsxgIMD9B4MDXuKN998Mx/MPnLkCGNOQ5bY/wDkIwpoG84CssIZOhRjQoPPaA/4w9s+ZosG7RtuvJGh4nR5T82UDRrI/oGjOxYv3i3aiYJjLmg7eC8oLGR5420Fz3Q5XWSJttA1a66hnMwchpQz5I17Ddqoa1yPjY2mz3/+C0x7/749pKvBzbKGvDBj3bJlC8NMRkdbaMWKFYx/ivb4r2BcdtllLCssXxpvOICVu/0LesQO3mKNgQ90/WmPjTkI+0WFxUUMDgG64A+yhU0CbxX2AvnBhsZcHvrBvd+hE5XVlJuTxc+DrPDymJWTSYVss2O0cdO75LA7WJewNdgs2gOZM8CBm6igMI/37sB3XVUducjNtnLjjTdxe4CX3GRt4PrzY+fT8lVLWVavv/k6jTl1aDrwB3tDPzl8+LA3YnhKhrCrLXt20IP3/4Ie/u0j9C+33uqzCUOGsDfYJgr6g8Ph5M+GXUEWiHA1iiFDyAnXDbuCjrEnjjcZwIP+r3/6DP32ySfp7rvu5FthV8bbE2Rq2JW/zeJ+tMnQvUH76quvptzcXD4eZsAygug0u2pqJZfHTfHx0XT77V/iZ27bsYssZCI3uSkxPpFWrFrBS694KwR8aTC7gkwgG7QRssK4AtqGzUJvxqBqyATt27hxI8NUAjN6yZJLafHipXy/IW8wZvTNsiPHCBCwLoeT4lMS2V9N+UK9bwLOtSA/n2X31DO/p+07d9O+HXvoisuuont/fC9dtnI51TQ0MawnaBs2izdh2BtkCF/4hVtvpsiYGKqqq6Pe9nZye0yUmZnK9XE0acvWjfwMBELl5xeyTSCJBeAvARmKBazcglzKz82jyupTVH7wOI25dX91/fXXcz9BG/V2TveF77z3Pg32DxJ2FhHrA73h7VWPRNYdrSFDw64wWQA+MvSA35g24HndCDAkny985533aGhIf3MGJPCaNdez7v3typA3/AlsC0TuuEO3S658jvxPuAsNbvVXvvz8AoqP1wMM8Hps9pjJ5M3afd8936Pvfe8++uV//zf/u/baa+lH//Wf+pEcsx4tGskb32ZfUA2Mb9mSFXSi8hjl5eRRaqq+Z4aITqMuno56KDk56YyT2TegI84Y1/HXCI4xruEo0KWXLqPa2kreRPfRRt1obzCSZYp2fn4uud1jvPQHJ2rQi4xG2L2+GOCjTUTFxcXU0FBH6emZlJmpb9JHRET47vMXbkbGAsZThbFhomEERWBgN57jH7WHgA/MopOTk32Yomi/UZeF4f0fgpTAS1VVBRUVFVO0F8kKdQPVLywsopGREYqMtNAFFyz0kQIvU0VfbUAwCWgDW3rx4mJKjI7nKjNpGwNYXl4uD04ut4suuCDbR84SGUtkwiAypXuDdkXFcSooKGRMVdzgr0vjO/5CxsDNtdkGCFGyRvGvb+iHaS8upvKj5YyBnJulBzihzahj1DP+5uRkMe2N779Defn5lJaSxOTxOyYmmJwZy0FRUWYqKiyk+vpmyshImrJZPxskP7sy+AbW7IUXXkBmsx4QY7aYfPoJj5yKer30kiVUWwu7SuIzlEY7p3Q5xX92xkIqzCtk5oqLptDRwLdR3/gLOpdevIzqmqoISRQQQGMU/zqGTJBgBANBnbWJiguLpgUJIQK4aGkx2Xu7DRJUVFSoYxVPIAnJlF0FpO21K0ygMIDEx+t2hWh1//pM3OOhnIJccjodNNQ/wvWNh8bHAqPZA6siXSa8LgAAIABJREFUYKCjxHtpw67AU1KSHrDmLxPUM9rJNuvxMG5ydvYU3/71jbrgDZP/ujoryy8pRQ8S86/rTzszK5WcY7mcFIP7A44n+nyhHrU+PDRIjzzyCP3huec4ycmqVavpL6/9hVavXsUTNgwgFgR8zgj6hD/DQNXe3kqFhYU0OU9vfyTs22Lh9wlM5FEi55nowgsXUXNzG0VHI2Api6+DJts35GEhioTh4qUlOZ3yCwvJaq2hwsJin0782+mvp6WLoXsruT1uwhlto0zVmbJZ9M38/HyeQMLPwn+hMG34IO47Rm8jyi8sIGtDHUVagGPv5XumL/RGDEKXSFSislVh8HpW/krxJoFPuXvnbnES4N0792qf/NR1WlpKivZ/f/3rkHic6zfIsUlb2lo04NhKy86dO8W4tMCYZSxlYcL67dvltIEfCgxWadm7t0SrrZJhk4LmG2/JcWaBXQ08ZWn5y2uvhdShQau2vl47eFCGd4x71q4FlrLNuD3oXyRb37t3djL4QDdNOL1YytWVgX6edQ26//Q//qP2/fvum/VboAvARgZOrqSgHmQuLXt3y+0KGLbAUpYmfi8tLZVjKY+Pa+tem46lbLThhz/8ofbk735nfOW/ZYeBpXxs2rVgX96Yg3age4AD/NrawLwEqv/nv7wmx1JubNQOHZJjv7/zzjqxvKF7+KCZBRjIn7v1Vi0lMVG77YtfZkxkp9Op/eXFP2vHj8uwlJGYXQWjW0X3A3abtn79ejGuPHiuFeIdDwzYtd/97rdiGUI3ldWnZopwzu/HFPC85yRyBn4QLymrjv7GciiWTO//wf2cJehnP/sZ3fKF231vCv40gXtKmlmE74qAJtCPjPF/I/OnNv2zsWw1/Wrgb6A7OuqmuDjZmUkV2niiSn1DhsbsOjDHU1dVaKMu6J4J2uAb78fGzHmKw8CfVPieiXccmOLUVaaNWfOMt4OpGn6fPB66sKCA3np3LS27dJnfD4E/qvLt1vRML4GpTb+qovumVit9cvUn6HhtPc2Pi5lOKMA3Fdq4fa52PvvMM7x8+egjj/ieokzb5aLIaSsrPlKzPoA2MHgjY05/32Ta8ClCnHPIxBxmkfkrb7Ah+hr2od944y16+eWXyOX20Jdv+yLdede/Tjs2xLSlfdPjIT4losL3GaKtpHuPh4ZHkLVIpksl2rMs59y5oDTgYmkDe4ZSJ+3fzNdff5P+62f/RWkpKfTbxx+lFStWBxx4/e85//m8BM6mBI7VVNG/3HgT1TfIg8nOJn9zPau1s52uWLKMqhobzypg+7Zd2+iBBx6gfbv2zcXa+etEvJd59PhRevapZwmAKoiD+NpXvkE33XTTefmcIQlgr12a/OEMsRCQ7NRCecCfp19ct+4tX0DM9F9mf0M4OaLqjHL77V+g4+XldOe/3kn/eN0/0Re+cMu0KOY9e9RwaQ8EOHRvPGvmX+DSGjOkmb/N/I491tdfD5wdZmZdfEc7jUCRQL/7X0Pgy7vvvu1/KehnHCGSHrFA+1RoI7gg0HGPuRgCbcy8JQUTM5XjT+9v2iSX4ZhLifa6des4GErC9/NPPEU3fOYzkqpcR+UMqh4oIrdx6EYqb6fdSaNA4pEF+bP8+oVHQ8DDXHaVm5NHFQg+9Cv+wYt+l+f8OBftQDfUNTTQ22/K+w/wjqUyRB9WsVngYuvBOYE41a/h94cfeohWLl/JQV7FRUvpVGUlrX93Q9DBFsFn8CvSsn+/fMJzqKxM3B/w/C075NG+kB/0LyndQ930wh+flVTlOqq+8P333xPTPpsVlQZcHSpNxt74+DBNjE9HeUGg0Fe+9hWqra/lSLhVK1YxJNng8BBHyMko60tcTocOwSe5x+WSp+fDwGVEJkpoo516uHPo2qDt9Eafhq4NaEzZuUrQwqqDEX0qoY02GknSJfVV+EY7Jyfl8HEj3ghECR/A9gV9acEkR1KwVLllxyZaunSxpDrXGRvTo30lN4Bn6bE30FPRPeARPSY3mYUoP6ANvGtpcTgCH09KSkzkFI/+k0K0U0U/DodsEgdeTS4P2cYC8xKoLdDP+ORkoJ9mXQPPSCovLWNjgdsJOls2bqQv3fEluuSii+h4zXF66JcP0dpX36Qf3H/vtADIuZ41MjrCid/n+n3mdSVbGcOWmRwa1eWU2wn4kPJidhMN9Kn1n5ntnvP7pEm0gzTn/WfwB6UBVwUMPDw8ak5cTRwZePiRR2nP/gN82PzSiy6mt15/VXwIGmHtKoM/QjilM111WUOEcqNUoY9tR6nz0oE61PjAtrm0CI/i+chJsWBxQ1jYPPEZUk/EPHIrTERAXyLDusY66u/spYKCYl8bTvcHlf6j8mwkljB5EEYt687Caj4WPJ7AsRIJCQm8bNfQ9NcswcuN0GV2ESkkuoBczELDxYR1ghM1+Jod9INnxuQGKxi/eeQRWrZqBX3r3nsJJwGOVZ6iV154la7/X9dTxDzhwf4PgaM9FT8flGX+0U1yeeMGFSxlYFFLZcjJUMzCJRnVxBLhHEESWhgfQY3wB7AJIywAvcY5OuNIS7DbgO2N8POEBD3kO1DdlOQkuu322+iqq6+ml156iR594jHKy72AFi1aFBAw3aAxqYVTTHSkeI1e09yUnCzDso1LSKBLi4vF+9SQCc6S4TiQpFgskZSWliqpCoh0ioqLpqh5oQMLTOYwHrjS02W0cc52QdoCwn2SEh5uZr6lSQYiIswUF6cf9QhFf2JygtLTMvjsc6i64aSRKTxMTPvSSy+l1PR0CtXKZ5/9I2VkZ9E/33QDzZ+vHwkKxYvHE0bz589t39PuN5loniVCbIeaFkbx8XFB+4FBH5PJl5//I33l29+kaImtmMI5OGjevHkGiaB/w8M1Sk+fjZEMW3hn/buUm5lLS5frZ4hBCP1B4iNQF5Mtqc2mzk+hxcWXkClc9iYKm01KThL3TRzLk9qsZ3KC6wJY5Yc/+hHdd++9NBmu0S9+8jN6+OGHac1111G8n/2Hh4eL99cvLriEUtNTRbqHDDXNI/aFJlMExccnUmxs6OA63SjC+Gii/jn4/w2fL5FhTEwMrV59mbiNYWHhFBMTTRKb1X3UZECbDd6CM/+rUtDUmWQHbyGbNm6i7977XVqQkUEPPfQQXXn11Wfykedpn5cASwC2d3FhIb34ykt09Sc+fjYHdKzVK1ZTfX0txcTFnVWtfu0b36Cs9HSGGTyrD/4IHzY4NES/f+x/6LU31tHwyCjd+93v0Oc+dysDpUhXGT5C9s8/+iOUgGwNyrssd/RoOQ1L8Y6Hh0IGFRjtxgJAe387feofbyCgzNxy6+fp81/6An3pjjuoJsAmPPbl/PeNDDpz/UVdKWYn6r733js0NiJbelGhDR6w9CQtoC3eg3S7lWgDXUclKTajywiX5wb75bqHLEBbsuyLupBHqGAVQ76giQAUHRnHuDr7b9mx/TTq9FB+br6YNqio6F7dZnvF2OJOh5M8Hjc5FYLaoCNJgQyDye/iwnyqa5hKOA/dSPWD5wejPZM/oGr5owvN/H3m99NpV5DDxo2b6F/vuIMuvvBC2rRpF/38Zz8jwKnec889OojIHGv1AJnp7JxCfJvJp/93IL0ByQoY7ZICn9LeKc9rDd1IfYrhr6S48gg8Uwkgff31V8W8gG8pbbbZVjlMp0TOp6uOPxhSUJqjI+N04MAeBsumNCy9xPEuRndnJ0M84uZk75EhVlSTlRGBIiNX+pZSILAxGiP8B7QR0IBwhoeG6MSBKlq2AlBkmfS9e79HX7zjy/Qf//FdWrZkCX3vnnvo2/fcw7/BWIDVam1q4mUxI/QbtEEL/3CWDtdhKEOuYU5aDdi47OxsXuoCf3rQkB5MhT1lFNAGnd7ebhoeG6bIGB31CtcBQ2ZAPgL9CQV14QTy8vIpe8ECxjfF82EcQHhBYApoY38IzwT8IAY5o+24zrSBhQuoQYuJEV4M2kCOSklJYzQZyAoFTh734TkGbXwGHUQrXn/9DSxX/2ca9SFbFNQF5CGgevE5EG2gv2BZ0KBt8G0cC+sfHiS3U5+UQC7+tFvbZ+seMgEtFKP9Bm0sy4FH0MBflonTzknvsTwEeRvXu7payWrtoMsvv9zHdzDag4P9NDI4TKMZo9wegzYC3cA3ZPj+ezvoxhuvJSTcQOLvpUvNviU6w2YRsBMZHU8JXpsdGh2h8vKjVFRYRBnQfVSUT8fGsjvQk4zrXT09VFdTRZGRV/n0w7x4dR8dHUsJCbqO8cyamgpCGr3sbItPD2gn5IACG4feYFeDw4OEzmhz2JlvQ1awcR0yVIc7xX2gDbuKT0whc6SZ4mJiWC+IWoYNor5/P4bdHzh0iNGA8DzQNvoP6F2QV0ivv/YW84T2GAOowR9+8LfZmXaFEwS45k8b/cSQoZEqE7TBe+9gPw0PDVOcV1bBaMNmwUcq7Mdi4XZy3zSZWPf+NtvQZCW7bYDbZ/gU1O219dL29dvpqT/8njxmM9160820b/9+qqipopVLl9PExIRPJ93dU6hbhs1CVh0dHdTaCn912XS7GhvjdmIJHu03+gNsFraYsSCDYvztyqt7IGn57Kqri/UZbbnCl2wDcnK54K9M0/ra6MgI142NTWQELoOGbczGPhm6jY6N9T2zz95Hhw+X03WfjKa48ARuJ/Rg2BXO2RuywjORnAMwqqBjtEeXN16pzLzVYFyHjoG8hr/gw7BZTBphh5bISLZD2A+eCZsFOppB27Arwm7bGDHfvr45PExH9hyivDvkKRHZgM/C/8R7uM6JUaqpqqYh2zD19/fQBYvy+Rzt1q1bqcXaRM3WFspITyeszdfW11NNdS0Lc2hoiHLz8ngPDW/IDSdrqbG9lSwmM6Wlp9Gwa5T27dlJdswCO5ooNn4+zU9MJNvgICXHptA1111Dmz7YQD9/4L8pPAJgChZqbGoiO950BvspL2ch7+nU19cT6Le1WWlsbJIhwDw0Sfu27qB+2yBjtEKx6AhQMo4hWVvbqK2hiYou1QNlGhsbqbKymrD/2GJto0WL8ljB9fWNdPToEepFMoHBXlq0KJ9Vs3PnThoaslFfXz+5TWbKTE9jeEBcb7Zaqa3VShdeqMPttbW1MZSZyzXBb6KANoPx4JmHjxyhntZ2amrvoqLCi5j23r17yWYbpp6eTnKOTdDCHB0mcdOWLcxzS3sL71FA3v39/bRz916a9L7lLvAOAJiYlJYepOYWK7W0tlLxJZcw7ZKSvdTbO0CaBgcMmEQdim3z5q2+uvFxcdyZ4ER2g/bkBLW3d9GCBfoeflNtI50sO07NrU3U0tJOl1xciA05OnjwIDU0NdHYqIuGhu10Qa5u9Nu3b+fEDe3tbbwPg4EOtgFZjY+PU2dnNyUkxBMCcapqaujU8SqytrUw37kLF/I9lZWVVFVVT0PDDrIN9tCiRRdye0rxzMZ6amudoo2lvh07t1GE2ULdfT3cqZGTtqWlhQ4cOkZdVis1trdRWmIi/ft37qH/89WvknN4iPr7bWSz9VJWRi6ZLeFUebKCqo9VUUNLB4VpE5SZuYBcbjft27Gbhh126uruI7M5gve3Ie+DB0vJ2tpCba0tFBUTS8lJSVRbW0+VFadoeNhJXV2dLG9D90ePHKKOjm4GhsnLW6S3p7SUMEB3tLczbGpGWjrLau/eEmqyNpK1uZXmzTNTamoaTz4P7D9A67e+R8svXkm5eQu5rbDZsrKj1NRcT7bBIYbSA3HI22YbIttgH3km9YkSJh7btm6m1qY2arTWUd7CRTQvch7TxiRuwjVJbW2tTAN8w5b37T9A7Y36ysSfX3qRfnD//bR7927GWR4YGGSdAqsZxd9mwTOcLnS/fftOHrCw6gM4PtgyknWUlB6k1pYmam6ZstnSg4dZHpMTHhoY7Pe1Z+v2rdTUbKXWthaKjorm/g34T/gll2uS5R0fN58SEuMZznTHrl3UYm2llrZWKrzwQvYdpyqrqaW5luEXMUBk5+XT4f0l9NWvfJN++YufU+9gD91733/QE7/5DX3yumvpYOlBco6MUFtbC8VAx8nJPFhu3rqV+zz8SnraAoqJiaLm5mbGOx4aGqbO7k7Kzy3guImDhw9TXX0ttVibKZwslJ6RRp5xD+3eu5s0zUR9AwMUpk2yvYEGVv4aGxqotbmZ5iclcT+BzwOW8siIkzq7uhiLGvqprq6msmOV1NHZSq7RMcrKzmZc9x179pBtoJtsNjvHS6AP2mx9VLr9MFk7WtiPR5jD2a7wzKOHysntHqGOzm7KyF5IUfMsBLs6duwwNVtbaXBggONtoGNgJqNvY3DUNI0nz3iz37lzN7W0tVNXazeZzBqlpaUTkmcAFxz7sfAvmLBGR0WxL0R/gK11NLVQ4SVFbD/o3x2dXWQbxGBv53bih61bP6CO+h5q7WgkU3gEjz+wq107d9KEZ4Lx9JnAufQ/KXqV3T6qPf7441pXV5volvr6au3IESFU2uSk9kEIaMfSo6XajTfcoOUvWqT98v/+MiBU2lyM7dw9NwTf5IybAO/35JNPiuHMtm7dqnV1dc2gEvir3W7X1q1bF/jHAFd3796pNTY3B/gl8KW33not8A8Brm7Y8IG2efPWAL8EvvTmm2vF0I6QISDkpEUJ2rGtRSstPSgiDTjS5557Tquurp6zPmDxiouLuW3gu6REzjeg+QCtJymq0I4lJXvFsJGnKqu1xNh4MUyeCrzf6Oio9uabbwZtYnZ2to9XQDuWlQn7PcN6Bqft/2DwDVuRltde+4sY2rGluZmhN3/+s5+zPWQvWqg9/pvfaI2NgaFV1617Syxv6B4wrZICf/T8889rgOuUFB3aUd6PS0vksJ42LxQt+pE2OdNTzubu1KlKrVIIowoo10cflUM7Aiq2unbufjyTmzfekPvCmfeeye+YjcjK5KTW19cndrpO54QGXFBpwWDEig1yA1SOgeKylcu1pUuXah+s/0CbEBiChLbx2J6+Pq30cKnIwHCPCm20D/WlxW5zaGMKMgQ+qbTUVtdq9fW10upi5wKC0LvT4VCiHUr3BrGJsQkl2qWHDwcdFP/t3/5N+8/v/4jJw2aV9COwWR/fqroH7bEJ4/agfzFRSEtK0aT6h12p9M1QGM2fvO4630SSdX+GbLaluUU7Xn4iqCz8f2S+Q/gH2N0HH2zQvvzlL2vxsbHaF2+7TduwYUPI/n8m+/3Ro4d9Exj/9gT6rOpTdP3I7Aq0Q+nenyfQltos6u4tPSjuy6jvULKrAX/WzpnP50yUsupb/7PPPku//v9/TQULF9EvH/4VrVqxWpXE+fp/5xLA/toFixbSnj37Oe3ex1UcepTyKt7KwXLt2S5fufsuys0roJ/85Mdn+9Ef+nlYxgYK2RNPPMHbVF/84m307fu+R/PjEj40zfM3KkoAQZhzBJopUvrYVBdHKaNFR46UceCCpHXImYmkwdIijcoDve7efkJ+xuOHy+nmz99Cn/nUZ+jzt0yHivR/LgDDpQWb/8ivKi1oJxy3pKCeCpwiaGNPRFQ8Hjp2bApKM9Q9SIvWrpDIHbSNoKdQtMEzeJcWyERFhkh0LS3QJfblApV1b71FxYXLfYMteFaJIm9SAHwwgkoC8RHoGmxWKm+A17stHg6cCkRr5jUVmwUPoewqt7CIaupO8mMga7RVWkLR9qcD2ip9E7T97Qpt2bNrF91yy2c5GBPBYMjxffTUKfr+D3/IOZ/9nxfs86lTJ8R9E89ttcpPJyDPrUr/UbFD1J2rPwRqb2V1ZaDLAa+BZ2nfhI/Yf+BAQDqBLoK21BdKbDbQM87GNaUB9+jRgxxwJGEMSm1vlw90TU0yDE48e2Cgh2A4AKn45je+SZX1tVRQWERLliyjr3/967OODGHghxIkBQFVRznRt6Q2sfEC5k1SAFBQXV0vqcp1IEMbQokFxT1BvuTsgup6YvV++aCIAVoqQ0QxSjseeEVQkfRIC3jo6uqQNJHrIKgE9hKoPPPMM3TH3Xoic/wOeasMuFYFJwq7UppUdk9FdQfi3f+ae8xFbrtbDDiEdkJHkgJ5I69ssFKYX0BNXlkg6AltlZZQtP3pgHZFRYX/paCfkRM1LCyM/cGDDzxAq1aton//1rdozSevY5z3V195hZD4PsqsI9GpDHINDQ1KMuztn4pgDso06f1Ypf8YkeGh6OL33u5epcG8ubFZQpbrwK66u2U+Bb5QT04vIw95SG0WFM/VfLhKA64KnCJWC8LDZUg2usiVWEHyN5+mEPb/0EO/IswMR0ZHadWKFZzFZGqmbSKa8FUP+cFI2hyyoq+CbMBFdU2TMwIZis9tRZAYHtFgW861lzaSZwsLYN6khWHePLJzz0QRFBYmw8fF8xkG1DMbqQtwhCcrKujmG6YytrC9Cs8ag7YZGbsVCiJIxUUuaiapbrNiTmguaEeDAhLfdzR0fkj4VDUZGs8M9RdvtsdPHqQ777yL32bLq6rooV89RCdOnaJvf/e709LhhaIV6PewMBmynHGvCk4zJjkq/cdkktsVDugomDhqG00I+VfV5wPZ68wVqT85cxwEoqzU4vj4WD7KEojQzGsI8VdxjICBlJZoi5ksltms4xjCyy+9RFu2b+PjKQAPx14vY9jOm10/0PPgFHEmUlqiomLILDR40Aa0o7RAhtJBEV0uIUEG64jno40Ws5yXhIRkjHWignaq6H5eVDiZTTJeGEETuMHCEh2bSHxWb0b9ta+/SbffdhufwzV+As+R0dHG15B/LQoOQ9e9nO+oeVLoPQbfJY/CkjJsVqXExwfXzUX5l1BvXwcv36Kd+CctsbHBafvTwZla9Im5CgYqrFA88sgjVHzxJbTuzfW0dHExZ+hZ+/rrdMONNwRNCWqxyPnG2VmVdgbyV3O1A2dbVfqPxSK3WeheRf+RkXLaKj4fssO5WmlR4RlTBBXaUh5OR72PbdCUpPEHjhyg73z9W2RzOOhHP/w+3XXX3ZLbztf5G5cA3n4WLlxIH2ze8DcRbNfe2kpXrF5NFdW1PkCIs63CFatW0ZNPPkmfWP3RBC9u2bSJHvv972n/nn100+duprvvuovBUXD2/nw5L4FzRQKy175zhVtFPj6x6hN06MgRevjhR+n3v/89rVi1gt5ZGzyfJjbmMUvGbPlvuQAhrH+OYKK/lXYbbzwzgy3ee+cdysnKouKiFX8TTR1ze2gcqdFM8uW/093wy1aupOMKsQ8f5vnYIgKylFEQWPbATx8gJKi49/4f0LVXXUWVlSd4levaa69lABCj7sfpL/zPTJv9OPEv4RV9UwV6U0Lz41BHPODCAF544YVpBh+sgRAmIPskBUg3O3ZsE0c3tra30z4kXRZuRqSlxNMHH2ymb3ztG/SD//wRrV61mnbt2hVwUEVgxsaN70vY5jpArEKwgKRAhps2yRM6A+WnySoLPIMBb9iwXsIG1zl+8jgdPirTD254+913A8or0AOhe0SASguwY6f224PfBWekkvh9y5Yt1NPWNY3oi3/6E935lbsoKmr6EqJOWx45CTxqqe4xUOzatWcaH8G+HDhwiDo7ZZGtrjEdS5mEaQuhG2mgDYJbgEcdqlx80UV0sqqKkY8QqCYt770v72tVVScZS3nThk30r3d+iS69ZAk/89FHHqFTx07Q9++/nzKzdHQrPP/99zeK95Wh+6NCfwXa6MdSm4Xu9++X2RX68bYduzgoVCJD2B98p7QA7lKqe/gr9B/YgKQgSXxNnSxVI2gDsx5/JQUQoNLk9pDhe+/J7Ury/NNVRwztCLg0OLqwMI0c9hFKz0hnHsrKDnFEKmDtsIYPuC6r1UqAHYNBjo+P+tIkAWuztbWNIeMmJzVOPwaBnzh2jDp7emnYZqeY2BimM9Q7SNV1NVwXtDMy9PRgdTV11NBQT47BMXKMDlFqYhqZIkyE2W5TUzPXHx+foMTEBB4gjhw5RF1dPTQ8PEJXXnkF/eD73yeXa5y+/tWv0/atW2h+QgLlLypkuLWmplZCtDQmAHb7MEOOhZtMHNXX0NDItAHRlpKiYyn/P/a+BLyq6tp/5eZmIPNAmBGRoiIKiEgpWuujPP+UOo9Fn/KsbS21lj5rrW19fT61ffY9a63iQBUVEZB5nuchQAghEDLP8zze3CQ3Nzf3/L/fOjk3J8lN7toKFS37++DenLvO2muvtfY6w177t+C8elYmtkGgVFs0r2MhkxIyl5cXU1zcUMZLxaRLSztHtbXV1NrawmXasI6BzMiCgnyqqKikuroGT+m+s2fPMexZU2M9uVyap09sdQBvs76h56SzyVRbXcvwdYBHhB1wPCurrw6B/wwcUyKth33MvAMC/HidFzwAK1dfhyzBZoqKimbe0HdRUSHLbbYPME+LCgoZgs3h6LY9tv5gjKBFqS2UB4PtcVNWXV1JDkc7P5HAh6ATQ9+gj4wcTAEBFsZqzSsopKbGRrK32mn4MB0b2uxXZt4Yp621ndpcLRQ6KJQhBU+fOkWvvPwyvfDb/6TaumoKCdF9FuPJyAIMYh21tNgpNm4IwfbIhi8qKma5DZ/FhNb9SteJv78fl6HsrW+UZMN4wDsnJ5chUaFDlIo0bG+Ms6WljWJiorvm1CmGv4N+LORPUdFRPfwKOtG0Ti4Ph4B78tRJ2rR+C930LzfRkMFD2D5mHfb22RrMtaZm6nSj9Fo0zxMkHIKvru9ILmlXU1VHaekpVFOj+xWgMSE3+kTwAy1sh9J9Da02+uiDD+nGG28gm62JXK5Oz/q42a/gl3jNa9i+HgU6WlsZqhC/AVc9IzPTIwvPe7ebjh4/Th8uWUp/++sbtGPXDrpj7n300dIldMPUyRQZFUuVlWWEUpnQd5vLTcmnEpgHiq0HBw/Sj7e1cZazMU6MB5jNBXkFlJObQ/V1sH0zwynCELiAlJWVMx/Dr3DxQfAvLy+ltjYUUA+gqKiIPjr0xMKSMsqM5kMsAAAgAElEQVTNyaaGhlqGgR05UodoNftsJ0oxhoeRy+mkc6mp1NhUT+5OJAb6s0+Y9Q3ZDR3Cr7KysqmpyU6NtiYaFhfHUJU4jliI+ON0uj2x8MyZ01RdXU31jU00KDjEE3+xA8HQCXwZcJVGvKqpqeZ4GRGhxxSzXzU3N3nKTeo6qSRbUz3boXcsBH+zz6LP9nYH/4uJie3js+ZYiHlcWVnL88ccU8x+1dHeQZFRkexXoC+rKKPJk7pLRp6vC+YX5dPzFn9AbgGc8RkVFUMxQwbrT5cWC40erePw4lRjvQSg7WERqBPayOD7KCJgDbLQsGEjGGsYFzQkQBjnREfFUWV1JcUMjmHQahwPDAtm8HYmMv2H/huaAM5dq1/Mup5SAPJvLPAjKKAhc3No7HCqrq0nJHwBNB+/LfjZz+jue+6hjVs3049/+jOaccP79Ke//h/Xh0WSjauiigCabjz+o09PRqopqXL48JFUXV1PETFDmDf6DLAEMdYngrK5QSdRUYMZxxQXYUPGHrxNJ8TERPGFB4v/kN1oALTXm4ssg3RhoMvRg0dSTUUFy2216utWON5Nb3AgtkleXgkhSQT9G2306OGeggFICkEDD+gCd8W95Tb0bZyPT7ZPQxNRayv3Y/w2evQYvpEx2x46AG9g88bExHh8ordOjFLDsHEDeLuJ4mK7E8QGDx5BUVH6XXgPv4qII3Ll0ZCwKA/vt999lx6ZP5/Gjh+nF4zo8hXoOSYkjGrdLoqOjKPArg35uIBFRMX0oMWYYHsEkZjBgz0JGsHB4T30DX9D020YQTZbax8dGn5l+APoh8YNperaRp5DYVF6YgnqLcOWuEBAh2b7wC5w1mGDh5Fh+946ZEG65IYc8KmoKN3G6NvsJ0Zt55CIEJYX259QU9iQMSwsmtgN8Qq7qyD85SNGEegAXh8cHMgFCYw+zbwN+xi2h1/BBwze1sDQHrJs37qV3n3/fX6yvfnbN9HTC5+meY8/QuNH63jmmOOYa5irhr4DCEUphvI2LHwafRo6RF/m+QkdY37ihVm0ya9gY4PO4GH1C2TexeXlXAAiIqKvDpEZb8TCmIgwqouIIIejlX3GiIVDhgxjfGMA9Ru8LYGBFBEVRRYuOtA97zEuw/ZOi9NDb/gVCkygRKIBIhETM5hjoaFT2AF6io2No9raeraNkaQKOb3ZBzIhXtXXoyBGrGc8Zr8y84eubDY7hQSGdNuhVyw0xonxYL7jYQBz2uBj5m34Dj5BU1XVQIHWEBo8pLsus1nuwAg9FmI8kDcoQL510NzXBf8uxbwCpuq2bVvEUF/VlZUaIOekLSUlRQPknKQBbkyKNQp+2dnZ/cpdWVut/fb3/6mNGDZM+8HDD2sbN27U3nvvHa3N3i4RRctMz9QaG2tFtBhfSnKyiNaQW4rVC/qkpCQx7127dmg7dsgxWE8nnfYJd2d0Xl4K2xcbf/r8PJ14WrMJoSBh++xs7/i2vTsCNJ0ZSxm6jImK0jKzvUNa4vfsXLnPwgel0Hegg49L20A+25tHZmaqFjEkQquulsHZYV4C31fSoEMJdjWgDocMHqwdOnRIKyyU296bzxYXF2qvvvwyYxoD5/q1//kfrby8VEs4fkRbt3q1RGymSUhIEGMpw/b5uTK/AvPkpCQxDCjHq0wh785O7eOPP9bOnpXFCegdfuUb6VhXW35u4YBQp2bl2ttbeZwdDhn34uJiMa48dKKCpZxbmK/hmiJpkDYxQYa3LuF3Pmm+1lnKKncreMX129/+hpYvW0XzH3+Ea1yi7N6l9vXRwEsv/Ymyss7R8uUrvz6DIiLkNEyfOo2ys7+8LGUodNK1k+iNN9+kWbNuVdYvMsdRxWrJR0tp++bNNOu22+ipBQto9uzZyrwunXBJAxerBoy3piL5pEXZwQyvYozXMRLmqrR4rSZtEt7AoF206B1KzUzl11NTp06jeY88wutvA/Uj4W2cD4mlCQg4B7ylxZ9Br8y712tvQ05vn0q83W4l26vwxns/FZ0D9hB6x/rq4rffogVPP+VteHyM9a2gExU5VG2pwhs68XfLkaZUeUvt882bvkVp5wZGpeqt/LKqCnrppVdo4uSJ9LOf/4K3FWVmZ9OGdev6XGwxF1AaUdqkcoMf20eBN9Zb5RFI5y+Wu80lTgg1ZJfyhtwq9lelVaFXtY90jKBT4a3C94vSKl1wl366RJzhhoQDLKRL28HDB6WkLMPBg/vF9EhukjqC0+GgiddNppOnz3DSB+AiFzy1gCrKvGeMYpwI5pLW1NAgyvg0eKWmplJNvQwqDTcg69atMk71+YnM05QUOWb0mjWrSHrDVVdTwQknPoXoIkA2KRJDJK25xanEe9XKlZSVkUEbN26kcePHEbaK9ddgyxMK+K7IIpe2kooy2n9InqGecvqMOGgA8q7NTeQSXgEwTrG+nS6xX02ZMIE2bdviM0ZgLm7esI7uu+8+uvryK6ggL4f+/s57lH42ld8sGYXhe+s2Jz+L1iyTv53YsGGDOAsWb7igF2nbsm0bYWudpCH4q8TCTVvX0JmUFAlrpsFOCVFzu+nk6dNK49y2Y5uINYigP8QsSYP/YaumtIE3MsklDTcVsP3F2JQuuEaCh2QggMlTeAj1JChJePPF02LKXvJxEi/KK8ASgt34sWPozTfeoDOnT5PT4aRrp0yl5559ts82HX2M8tyzTs4+9CGw6Wc9HcR0oJ+v+hO/XCdg41RAP2PbC5GmANWoYvvOznZOBupnaD0OuwM6ySnc/mKc2NneTn948UV68aVXPAkaxm99P+VTQmWM4qthl0BduUh9xevniNviIgXgq3649D0c0AkoUplfXT99BhViW0g/giDj+8+vvML7Zl/875fp+usn06tvvEkfLV1Ks2ffRtaggecRJ4wNTNJjAGwfoZEQU/z9hQ7OkKE9uvL5hwpvJKIpFdERIt2BKbxbqBIek78ChCX4SiEpgf6nBEkJmFspgpnFQi6XQnDzab3zRyCPLvzaRT6Ijg4EUbmg0rtzcHQTHEe2Nwz0fIGWz6UeQo8ZO5aWLFlCZ06dpqqaGpo6ZQo99+wznn1y+hhlr7ngMCrODkGswqcWHUtXbh/wDpTF0W59KAgvnXhgrmNuC3XY4ebs6m6hBv6GjNH3Pv6QhsfF0i233DwwMWdzKjitT249CZwKTq6Hxp7nD/SXVaa+gVh4/83fH7dm3n/rdXT8+HFUVllJFke30+LJcf/evXTPAw/Q9KnT6WTyWXrnvffoZMJpeuGFPxCyeFWaS+lFrpPcwiCNudnRIcc51zQ/FbGVaF1ut1qcwHKCsOFFuMrcxPyRNvBF3Jc04PKr8JbwNGggsQruv3HeP+RTJQMLGYXSrEwUDJZmHUMGZNtJG4qyq9BDFmlDAeXa2v6z4fLzC7WFC5/WgoNDtAd/8LCGv5HJKWmfp6Bza4csQxD9SwuQ67T157UIuXn8GKeKzuFTUh1qnZ1KvBvrG7URl43SNmzYYBbR63f2Wfihj6Llxskq/o3xqfqsVCf5hYXa6GHDtPpG2RzCOKW8oQvpnMdOhnGXX64lJBzXKquR/f9b7aoJ47XLLr9CW7RokYYs1t5NyhvnQW4VeswH6ThBp+KztkY5b0P23mPv7+/GxkY1WRRiZ6vdrsRbJaZAf1IdQt8qOzDAV2pL6FXFT/qzw4U4filL+XPe1mD/4F9f+19atXot3X7nnfSrpxfSNVMmfU5ul067UBp49bVXaefmnaSSI3ChZLlQfLG2BfS07OxMLll5ofrxxRdvkmbeejO57A5eern7B7fTvDsepdvmzPbsEfXF49LvlzTwddaA+P0ZJhNqQJoLOg+kGLxKkiZm4P0JkE0uCO+uOqfNTS0Diev5rayiiuHMsPA+UBs7diy9+fa7dPDwMX7J/e1/+Q49On8+nTp9ut8ELeiwoKJAvIgC/QF5R9KwhguEL2kDatjZ0/LEjJKCAnK2y14vNdTVUV1dnVQUKikq61dnvZm0tLQwAlfv497+RjLbW3/5Gz3zzC+9/dznGPusgtzw2RaX7BVaW0sLlQmTbCBYWU2VeD4gE9tpaWUghT6D8nIASyMtQkg9+CzsM1DD2uxfX3uNrr7qKko7m0ZDBw/mLUofvbuMbpt724AXW2kiDPpPz8mhY8cw32StpKhI7FdK8QpbsUpK5LZvaxND4iIW7t67n0FEJKNEzJQmb4GfSkxh25fIYwrmG/QoaaBDsqSUvqauhpB0Kmm63LIEKwm/80kjvuC2tbTTzp1bGcrQnHLd1NJCTY4WcrQ4PM6NAReWFjPSi5kW30Hf3NJGrnY9UIG21emk5OQkLlyNv9Hw2dzsIAf4N3dfLJEpW1ldzZitZt5wvGaHkwNJW1dSDdZCQAOor0YbIBJ78XY4uA9DoY42F7XabVSUV0AIYkbDeeBj/DOO4++KiiJ68cWXKD07m8aMGU3f/9f/R3fdcQehUhGcydwnHDL1WEoP3m1tLh4jbgigF6OBNyAiS8vLe2Srgif+4Xczb0BvAm6w93GDFp9GA019dS1V1Pfm7WAZEIzNvEF/7ORJcnY6PEHd2e7Sbdmsn2MsOoG2vLqWsrIyesgNnvAR2N9se9AnJiVwprfRJ6D5QG/Y3zjOti8v5xs/nGc0fAe9zrvbxn/7298oOjaWxo0f32M8Bl/4lcEbn8Bczkg710Nu8IZd4Ictzp72OXcugxqrKnvwAD3k6D0fauvr6VxyMvM2blvgs8y/y57m8eSlZTD6mlk+1l9zC58Dv0HD762tDnK3WshuA9Sg3gbinZOVRcVF5Z4tNpgnPIebu+Zm1zzBHIB8R48d5k+DN/qEL2Nt9o577qApk6bSscRE+vv7i+kPv/k9WQeFs94NevAw/nnG0+7meXA8MaEPb9aJw8k6N/NorKriCx1+Nxp0Atv01jdojp041mcOMm/MNYfTc+OLY4gpQD7qwZvjgz7fPHJ3xYKkpCSy1VR7bA95+publbXeecP/0B9sZTTovKaqjOrqqjy80Tey8405YZalsbGREpOTqdWsE8iNMZr8CluqwJuhXqu75QYv9iv4d695DxufPn2aC78b2xMH8ivceBUWFvaQG+PT50MLeeJylw5Bjwx7gzeP0xTfPDpxOCgvp4CKS0t72Mesb0OH4IF/RxVuzIx+/hGfYizl1o42SjuXzlicNQ11NG7sFSzfmlUrKSczl86lptDwscMpfFA4paamUNq5NLLZ6qi+vpHwNIh29OhRSk5KosyMFHJ1ajRixAjG/t22dTM5HE4qK6ug0NAQxiTGK9t9+3ZQWno6FeTn0rXXXsc8zmWkUEZaJuO1FhcX0je+MZ4zXIH3eyL+KGVlZ1OzrYHGjLmc3B0dtHPXLmpoaKTi4mKGw4uNjeUnpN27t1Nq6jnKzs6iSZP0V8EZ2RmUcjaJggYFM0bp+CuuImugPxe2P3ToCGVkpFNldRmN/8ZVLAsAzOvr65l3QGAw/dvDD9PDjz1K8ceP0H8+/wKtXL2Chg8bQRMnTuSnz6NHD1O7q4MvGKNHX0FBQVbKzc2ivfv2UH5BLuVkp9O11+qyADQcOM3Aqm1tbSPU+kVbv34tZWZmMS7zsGHDGR8YT5Pbd+6kDmcn5efnMVQbIM7wxLt3737KyEihrKw8mjRJ1yG2EdQ31lNbi4MDp2GftWuXU052DmVkplJoaDhBVzV1dbRr53ZyuzUqyM+n4cOGsR7PpZyh+KNHKScng7KzMmjCtdeRxc+Pn0CAHdvcbKPa2ga64grd9lt37KIzZ09RXk4uaUSMjd3U1MSFIpzONiooKGJoz8iISEpLOUvxx45SZuY5ysjMpdHjLqeQoGCC7dPTs6i+voYqqipp/DfGs04A3n7mLPziHPlbLYztm56eTj9+4gn65cJfk6PdTv4BwTQkbjAHnIMHd1NWNvSdQUOGDGUdwmfPnEuh5mY7P42MHjOGrH5+dCIxkU6dPE6paakM7wgsXASRnXt3U2N9FRUXl1NgIOD+4hj/GIUvcrJyKSMzxaND8E5JSaOW1mbKySumsaNHUmBQEAF3+uDBI5STk0nArB037hs8nt27d1JNbR1VVdYQdDN8+AiCrrZu20xZmdnsh1arm4YOHU4ozbdn3346uHsnXTnpahozegzD8Bm8s7IyeS/51VdPYN4ocNHQUE9VNRXU7myjkSNG8TxZt3o1ZefmUnZWOl12mc6jprqc9u07QprWwfMEc6qx0UbPP/9rWvj0L2jVmjU0ddIUWr9xA/3w8ccpKyefGuw1tG7Vai6NN2bMGO5z5crllJmZQxkZmRQbF0OwcVNzI23ftoncLo1vzGNjIxgCs6qqilDMIisjhef+5MlTmAe2YJWVl7EfVlRVeGy/Zt0aSk07R6lpaRQ0KJRtjJvPTZs28D1gfn4uRUfHMFZzU1MLbd68lvLyc3m/8FVXT+DM15Rzqfx3U5ONEFPMukpLS+endWDIAzPa4N3Rgdq7VWTR3DRk6FAO8th6lpmZTWlpKTRq1GjGbwbmdGLCSb6w5Obn01VXXsnximPh6SSuboSEx2FDh7Ff7dm2gzrcbqqrq2cIT2yRwpvF/ft2UGZWDs834BoDq5h99sw5amttobL8QhpzxVgeDy6Sx08cY+zxlpZWLkXppk7au2cX1dbWMD60MR7oG34Fn83OyWYI2yFD4rhP6Bw7AnJzs2nMN8ZScKDus4cPH2GdlJWV0ZVXXsn22b9/P+PkAyseeMeYJy0tTtq4cR1lZ6ayLQO65ib2Xh/cf4DjCPQ98rLRFDJoEI/nyBHInc3LI0bMP3r0GPsweNfX19HYrmuPORYCd3rEiOH8RnD3nj3U7mglw3dYwIvlP+nCsM3Wpi1a9IYYEq4wO5+TJ6T8t2yRw0Yi+WLfPjks4b74A2K5AXv3zjvviRfodxzYo1VWlvYZJhJkFr35JsPT3XjD9donn3zCSQJbtmzrQ9vfgSNH4rXsLDkk3Lp1q/pj1ef4DoZ23NXneH8H1qxZI9YJYAmPHz/eH6s+x9etWydO+ILt44/45v2Df/uB9uRPfsLQjumZ6X369HYAto9XkHvPnj1adbUMIhFQioDTlLYjh46IfTYzM1OLiogSJ4ogqUkKu4pEqBUrVmjbtmzSHnzwQS0qKkp77LHHtF27vM+/M2dStOCwYHHyzIZ1vpPZDJ3FHzmirVkjp1+zZp0Y2hGJZ9CLtGEeSxNzYHvYU9KQIglox2QhBCwSj+BX0tTK48dPiW2PhCnEZWmyUmpquiada4iPr//vG2IdwjaZGbJY2NHaoa1at06i7n84DUl7hNKLS0vFyge9SoYtsIulhgWdFOsY4+tolfPWHXiP2IE72ts1X1ijH3/8iXb95MnasFHDtNf//Gdxdh6CnVQnGGebvU1qTsZqTU46K6a32WQ416zvjg41udvkciNrFhivA7Vtmzezrhvttdq+fYe00lLZRZH9SkEWto8QZ1b3Wfk4VWyfmZutDYkZrNXWy7CU2x0y+2RnZ2pvvPEG6xKYxv/9X//lM9Ma4/zWN2/SduyQ3VzgRl7asjOytQSFGyLVLHKVmKJiHxW/6ujs1I4cOuQ1o9ubnhB7IIu0qWT7QhaVmIJx4p+kIVt6x54dPv3J4NWuwBvn2BUyt40+/hGfl7KU/0GvGrCuABSj//qv/6bUM2fogXkP0O9//5/8KlK8ofsfJOtXuRus5dxw/fX0m9/8muY//sRXeShi2UvKSniPa3puLkWHh4rP80aI1+WHDx6ktxa/TUcPHqM5c+fSUwuepBtumNGnfrC383HsFz9/kiKi4uiVV17pj+TS8Usa+KfUgDhpCtpBTVNz8s1AGkM2HLI4pa2kTC0bTiW7EXIYC/O+5EGigArEG8ZpLNgPxBsX1RtmzKS//30R7TqwjzrIQtdccw098sgjhELm3hpnFJqSnbzRGMcwvrSsDONPn5+oxwn+0ob6lbhpkDT4iApvrHNJdIi+Xe2uAXn/xy+eoXETr6L58x9nUWFL2FTSILOSzwqh5tA3ZEBegrSxzwr17XK6yO12kVUIgIBx9tY3aqi++MIfaNq0afTMs8/SnH+Zy9Cfy5Z+RCPj4sQXWyT7jBg1gZMaJWOFX0mb6txU8VnoQ9VnkTEvaZg3Kn6lOjdVY6HKOFV8FnylvKFv1FKXNvCVXnugbxW/kspwPuiULrgJCUmcyCPpGIWKMYmlLSsjS0rKdUiziuT0BSVFZBEiTSHr7/jxBLEsGKfDIbsQuVpa6OTJ0zRl0iRavGgRJ1hcNX48PTb/Ebrl5ptp2bJlPZwKSQmNdptIFmsAUcppOTbyuXNpnKwiYk7Ek0N604KnJMgubcCZxTmS1uZs6xfXGk9mmzZupjdefc2zFeVsIopXV0pYU0VFiZJOkMwibfArBFJpg/6kNzjQHYNYCaHdwJvxl9vaaPvWzXzTh+SnrIIcev21/6WU1FR66hcLCDWMIcPRk3K/Qn3o4SPDGb9aIj8SfKQNdkxITJaSs8/2vrHo72RVn81MSSWbTTY3oQepD0K+k6dOK80fJC5KW0FeAdfZltKnpMq3DmL+oFC8pEF3hw4dl5AyjeGz0hNQnP5ibEoXXOBfShtQAHXIPukZCiCpgDx0BXrS+n31wHWyFWAJffHr+7vwgut29YC7HDo0jl565RXKyCmiJxcsoLfeeouuvvJK+tMrr3j24UmhHV0dUIeSOZWgHRkqTXjTggAjjP2sSuDMSoIzEwcEkcsLRGJNVRU99Ogj9MZ7/8vbgAwbOQmyyPQC/QlJmb0KtjhOUIGbC1DA9QVvdzCKwRuj7v8Teq6ur6W//e0tmnDN1fTss8/TxInXUWZ+Pq1cvpJumzO3D665xSKf9+j5uonXMwyq7M2CbO6AL+xoUZrHgai83r8yvsAvLgXIQ6vFIoY8hEiQWA1+UQGj1eJWissBCljKRBbSNNm+dNjS2zzuzyQ8L4W2xzRQuVb11+eFOC6LRF09qwQYFVxNsFfC1TSkVomOQu1ZUBkL/yk06xec1IOsFn7KwKb+Tdu2UV5BEV199ZX0k5//lPe/ikQJUNShiGkvIqHD9zpL8KdhUAFpRztZA/sG0R/96Ed02+xZdN/t83owkV5se5wk/EN1UqvQd2pyXF8W1+5GvOu3Achl6/btdM99d9EDd91HRSVF9OnSZZSYmky/+93zFBsd3e+50uIFBgNsWYkbOpTyBK/QVW5CcJ/lzfZGv30/nRQguQth6Jq+Zw90ROVhAvucVehR/AEFPaRNcJ/VzcoaqMSbFG4sEB5UxhncT5GLbmG7v4G3awD/7qbUp4GKX5nPvdDfLyVNXWgNf07+2JO8evkyev/DD1Emgx6+/356/MkFNHL40M/J8et72u9+9wId3L+X9h04wHtQv74j9T4yrOHdNH06nc3MpujI8B5EWNZZsvh9WrtxI1ktgfTYj/+N5t37AA0fqe/r7kF8Hv/45S9/SRPGj6cnn+q//vB57O4Sq0sa+EpoQHjP8JUYy3kRUjV54rx06oXJyJHD6T+ee47SMzPp9ddeo8Sz5+jaq79BDz30EO3cKYdE88KaD+F1X0OdDDayPx4Xw/Hly5bRipVLacmyj7xebJFsIV3HuxjG83llaHd2l+fDeD1rs1OmUVZeAb2zaBGdSTlNzzz9zAW/2GIM1113Hdde/bzj8XYekmZkr6m9nf3VOIY8iZqmr7/PYmkDc1O8lPTVMJ9PKcUXXDj78uXLxFloRUV54kxFKB3oR9LJhIw/1ULh0uy52tpKWrt2vTiJB6+BpbyhQyCySNvZ02eoqKKA5syZQ5s2rKPswkK68cZv0i+ffY6u/saV9Lvnn+dsPOgP/4BOJW1IDEtKTpSS8+tI6eRAZuO5c+fEvCG3NAOxrKKETp3SE212795LzzzzDK1YuoYmjNeRlMydOlHofPNmKiwuNR/u9zueFFWSeFRsDx8BYo60nTx1UpzZigQoh9VJhXl5vP6Ptdnnnv8dTZ8+g9JzMwlIT7fcequna6DASTNbkUwERDVpQ3Yo/l1//fUif1Tx2XPnkunAgQNSUWjrzp3ieQx9qPjs/v3yeAXbA7tc1AKIdq/fSrm5hSJyxExxAXpOfjwltr0Rr6TzXqVIPHh/9tln4nl/9uw5KhAmKeKmRcVnRYo+T0RiaEenU6OEhKNktQZTS4ud94/CEIAXA4RfZWUJRUREUUBAAGcn5+aWUGNjPXV0dlJ0eAxZrH5cQ7a8vIoqK5GBqVFERDg/fQCGr7ISd3WtFBwczJBocCRkddbW1lF5eTlDAWLMwN8sKCjkixzqV8ZGxJIlwMKwkIWFeVRRUcl1LSMjI/kiBMjH8nIURmingAArw/jB2MD6hdyA1BsyZAirE5MuL6+InE47+fn5U1xsLFn8/Tmrr6Agn6qqKslua6aY2FimxwQtLS2l9i5caKNPQyfgHRMZSYBuQ1IP4AQrKys4CAwBbxyvqaG8vByqr2+g6upaAqwaGnjnFxaQo6GDNIubodxCBwH2Moruv/deuubaiZSTm0vPPfMMrV+/ngoKC8litZDFz0JhYWEUFBTENzC6DnuOMy0ng2oqq3jlyuXqZFuiT2z7gr4hE+wIeEjYITMzkyo5G7uNACsH3rjpgS0M+pjIwWxjbPHBBbehoY7MvDEZQYusbovFn20MO8D20HtnZwcFBgbxcdAUF5exn8CekZGDKSDAwolkRflFVN9QQ4ePxtPPF/yUPlq2jMZeMYbKyyuppqaWNI0oLCyU/SojPZ0hEf0tfgy/GB4e3kPf6CckJNQznpycPGpoqCWHo51hLbH+C9mKigpY9o6OTvZZ+H1achqVVhRTe7teSBu+DF3l58M3q6myEpCPQaxD6AoYtnV11dTW5mBbYpuYMU7Qt7Q0MwShYfvysnJqa2kjP4sfwxLiqRVwjfBB+K2fn5tCQ8N4PKtXr6Xtm3fRp59+QjxstyYAACAASURBVCNGjqSX/vQyLXx6IY0cOYJa7S2MUQ6YTuZ9Jo0KSwoYUlXr9KPomCieJxkZ2Camyw0bw/6AcE3LSKfqylLC2KOi9PkN/wBUKuSHLIbP4kLL+Li2ZrIEBNCnH33EBT3MfhIQFESDgoM50GamZ1JxWTG5Olw87+Fv8AnwqatDTCljOEXIjTlSVlZN7e0OhjwcOlRfWklLy/DIbfgVMLfT0lKprLSEYwGgN0NDu3wiI80Tr2Jj4zgRC2vNhQVFbJ/W1nYaNkznDV8uKyth26P+LfwKtkdMKSgpJJdTX2fHvAeOJGBoa2rqWG5Dh4btAUsIiFZANaJhjuB1P+aE2a/gsw02G3V2dpK/n4WioqPYr3T/0XUSEjyIgoKDOebl5uZQRW01OdvaKDp2MFn9/ZlvUVEh+4rT2cH+wz4LbPbSMp4byMeBz/aOhX5+fl1zED6bQdXVkM/piSmwOXjgE+PBej0abFZaipjfhCQY9iv4bHZ2LtsHPgM4SfisHttzuG9sZ4uKiu6ag2VkxFnEQ8ClGryLi/PI1tzG9jeOI14hPsBX2tscFBkVSc0tLZSZmU6gnzRJhwVlJhfJf32zT/oVTHcu5CkhWMCA+AyPjO7KFg72nGmxBpPV4iYH9gZaLIQtK2hhYVFEhFT6YAoJ7s6sA5/eSQI9eXtYk9Wi9wOHAW8K0h/SQ0KCyenSZcFNARr3bbUyPigMG9xVcb1f3l3Fqt1uK++TNVJWg0PCKDrSRUilMngYEnnL2+rWCVdX12UJRMFlJDbp2ZYdfv6cjWiWBd+Nhu+BSA4KMY7on7ghQbvlllvowQcfpL/+9a+0fu162rx1M7379ts0dtw4euLf/53uf+ghniQ9ZOliFUJW6tQ6yeXo7g8/mWkNWYxPP78AsgYEs81BCzl60HfZQR+grnPjXIM3EneCQ0I8PIzfdR1aPMeDg0MoJMRJZAlh3wqwdHLuJujc5KadO3bQurXradE779DcOXN6PAmyzogIgcNiDSSnUy/ywL7SZT9DbshibswfGSid3S9+zOM0ePM5bAadTpdf1wn8kBsOGj9AehQ479TI6gfd6HqHX4UARL9Ln/qJOi3L0i0GXwBZbhC53VRSUkZv/+0tWrF2Lbnb2ykw0EJr1m2gb3/7Vt4zi6Bm+IrRH061BEEsq57x2zUF8btHbs6Q1SeslSwUZhlEfn6DWDRchNHAl/9Bf70S6cDLYgnmYBk7cjilZZyjceOu0uksFvLkuyEj3IrD+iDNskYiiDPfLl3qQ+a+kdlqHo9HbovFMzcRb+AnLuwK6NI9Tob84eGRzId9S/9GIcHBHlOZTMZjtCJmuN36XOyix8egLl2EGD5ksTA2MJPAb7say4rsaksgWf0CPXEzLCRM9w+3u4fucRreKiCJFDfQaODh0Ql4dwlpyBpA/hRiDdHjIcfZCH2bmNmvOjG/uoTiJFX9O3gb88HoC5+42QwOjKCOTr3qDm6G0OCzwY6ueWwIwL/gnEA2mzVQlxv69tiHx9Ed83EK5iZfK7oEg04ckXrCqjFfQQcZLaTbyBx/zfMhLELXeaBHNz376hLxy/+QwlkBPmz1is/EsITAD5XitQKeDBis0gLdwDA9ezZZKrqWnp4uxuyEzO+8844GyEZJSzmTIubdam9XwmtNT8/WqisrJWIwTXz8Ee3NNxdp3/nOd7SIsDBtzpw52qcrVmiFhYV9eGzbtEvbtU+OpZyQkKB1CguzV1dWa4AFlLaE44maBIYPsHQv//FlbdiQIdq+Q/E+2QNm7oMPPtCA7Sxp8FkpLfilpKj5bEryGYkYTJOamd3HrzA/du3Ypt3/4P1aRESUdv+DD2rAFwaW8pDBg8VzE7aRFv+GDuFX0pZbWOyBJfz3f/+h9vrrbwx4amKibzsaDOLjD2nA3ZY2+KwUarC6ulbJZ5MSk5TiVXamfD4AS1ka3+ATiJ3Slpmbr2F+Shp4JyUlaoBTlTTgnHvDlfd2LmI4fEOKR52fnyvGFkd/Bw4d8tbtl37sUpZyr3sePLmjdmk4XhN9hRte4ezeu5df66Hizfhx4+juu++meY/MY0CDdncH4cHRuHO92IeKV3A/+9nPqKKiijZsWOepQOVLbrwywxj5ScMX8UX6OyoCvbt4MS1dupTL3j35xBP04MM/oLhY/ZVbQVkJfXvKVDqXX/iFoR3PpwoWv/02HT1xjJYtW35e2PLcbGvjZaHzwvAiZQKftVoHidG9LtJhDCgWXiQ5W1rIGhT0lZ6bAw7Sy4+XLrhelPJ1O4SL7/GEBNq+aQut27iRYuMi6Vs3fpNmz5lLd95++0UdwPBq9H/++EdatnQpPbVwIf3qV7/6ytwkfBE/wsVlw7p19PGnn9Cxo8fokUfm0f33P0g333xznwCFdWZsC0rLzLyobhSxdvuvs2+jXGGyyxfR16VzL2ngq6AB/WW7UNJ3331XjAcLaK2TJ08IORPt3b9XTIsFetRAlbYTx47x2omEHk9S7y9ZIiFlGowTFwVJA93KlSslpEyDpAAEU0nDHeOyZUu9kiLJABfW995fTDU1VfTh3z+kVreT/vKXP9MVl11GN988kzOe123Y0G9/4I21JUlDoghkl7ZVq1ZSnUmHuNgcPXyYfv7zn9O111xDJRUVtPfoQXrhhRfI5fJjjF8pbzwVwl8kDTKjBqi0HTx4UErK82bnzp0+6ZEc89KLL9H4q8fQ//z5/2j2rbO49uiiRe/Qrbfe2udiC4Y2eys1uxzkEgKw6MkmMpxz2Hz5cu9+5W0w4I05hDZ8+Ehqsdmooqz/vvrzWW+8YUfYU9ogN54WJQ01pVXgAPGWBX4uadChSixcvny50vxRiYWHjx1V4o26wtIG/UnnPXT3l7/8Rcqa+UpjIXJFVPxKLMR5IDQto/vmhmw/laaCOiIEhOHuGZXKIpfFbc4WkAxACBoPVvoavVyNvfIMJNKIaNycxCbTycybb6bK6nq6fOEQmjBpGh0/epS3z/z5j3/kovWDwkLou7Nm08yZM3l7x8iRQ/VkiAskPPJjGuurKSMrjXZu3Ukrli3nvKX77rmHjp48QWNH64XMoQgkUBmJNhLFuAeCX/LCQIW3qjr6o8dF4Xj8EXp38ft09OBBmj13Lv3uVy/So4/Np+BQ3za1WlxkcVvFxQswbJVX7G63bxkMVZohCZEINX7CBC7O8dC8hwySHp9KiEBKjwd6Eg+RDI9UFZGsV65YjzF5+wPwpdKmYhvwRBKctAUr0IKnSgxXQRfEGK2KSFNSvbi7ktSkOvlH0skthUotLjmmKpTvdMqBFfoLRl6VYQkmC+cMe/21z0GEC+zNkl53sV3nQjXViWpkJPqSR11mF7ldFhoUaKVZs27lf+ijpqGJSgryKCkxkZKTk+mPf/4j1VXUUUhYCD9djB8/nq4eP54mTrmWJk6YTLGx0Xp2JLLRobeuAfaYqG7kjOrN3e6mNlcbpWWlUWJ8AgPlH9m/n6rq6xkO8OEf/IBWrFtJkydO9vrquMPtlqqEO7RQz6zWLjG8fkB0JT/kPHOvrPoe9MKY7/L/9n+0fv1GCrYE0n/85tf05jvv0ejhQwkFHcjf0FpfduYjLjf07hILr49TdvXq6CAKDJTJYZbJ+D71+usp6WwS9X/BNShln1YFvHAdShO7K7qznWW9+KYKCtKzdn1TGhQyfYPajfmipHIF3mRR4q0CuYudJl7c3FBAn0+n/HKixFcNb7uPWBf0gNIaLsrITZgwwbM/6oJK9iUxx96x8spqGje2+6nqSxLlgnaLYI9tMdGC5LCGmgauJION53kFeVReXkaZqTlUWJ5P+A3bKrDHNSwmikKCIyg8MogvRcaE6uhsp0abjez1jfz6HU/jo8eNY9D8SROuoisnTqSpU6bQ6NHnH24Qr6GwfxTyXQwNr8s3r9tEH634mE4eO0F333s3zZv3iNe1Wam8eIX7nZkzKTk7k2KNbS/Sky8w3cpVy2nJko9oL8AzVKKxF7nwJgBVly6En3jp7ks7hLmJvfQXi89eCEVgHmBujh079kKwJ9SIHn2B4Us/j+BKF9zP08Glc77+GkAgrK2tpbqqGqquq6Fmu73HoK3BVhoZO5JiR8bRqGEjvD659jjha/gH1mbXrVpDby9ezHjYD9x/P/3oySc9wAFfZMgIXNOnTafc3GwKvUhuLIzx4OIxddIkKiqtokBjr7bx46XPSxr4Z9OAdGMS9rNhn6J0X1tufiHvU5TwB89Dhw6I92RBDuyxk7YjCfHifYfYS/bZZ59p2HcsafHxct7Y17Zv3z4JW6ZJTEjWcovzRfTQ4a5d8n21h/Yd0o7Ey/dAgrfU9tAh9j5L2649e8R7Gtn2SUki1thLjX2b0v3gkDtJyBsC+LJ9q92u7dqxg/dDR0VEaf/6//6fdvz4cZEeIUd5tWwPdmZmtjZ4cJTYx1OTU8V+hXmwbdsWkb5BhL3JvW0/btz4fve4qvgs9oSq0G/ZsUM8j2F7yC5tmMfSPaTY8xwff1zEGnNs06ZNGmwqaZABsVPaoEOMVdKMeCWd95BZOtdqbY3axx9/ojXW10tE4b3G0j3ykFe6z1zU+XkkEr/8x6vW9etXM5Sc5KYEa2ctLS0SUl77a22Vv9B3uZ3i4s8QwNWqow1JhMGrjsbGWnFSCTIQcY6kgay5Wb6uDYhJi1O+mKPC2+5qJZut55PoQGNoamgiElaMg06UZLHZCK+ZJQ26hj0lDTWCkRkOeSQNvB2OVgkp09jt4NtXbsDePffLZ2ni9dfRs88+Q/feey/tObSPnn/uOZoxY4bIt1pbWwnZlpIGFDWkV0iTSpodzUp+pTQ3WYc99X3TTd+indu9Z2g3NMmyiKEHR6uD6hrk9C1Nst0D4A3bq/isCi37rKunTvqzK2xYU1dD7e2y2Am88FbhfECfTqdbHK9Aj3FKIxBkxlglzeJyM/TvheCN/lXwpSXyni8a8Svl5mYHffzpEiKHi6whwfTjJ57gCf7nV18lAO8FBQQw1CDWVw4ePsxJN9SpUURcOD3+qE4LzN+c7GzOG71++nSaPWsWB8QPUYKOiNo7OujWW27h7FikmO/bt89z/J677uL1490799K5tLMUCHi6QKLHHvshr3WgKMCJkyc5J3H8NdfQ3XfeSQ6nk95/+11yIqGEiG648Ubmj1dwy5YvZ5nNfe7evZPOnUvjrD8Esccee4zXq99++2/kcLjI3dFBQ4YPp/nz5zM/c1o71rbnzp3L2xDeevttD+8FXa8NUWwhPj6eM/MAT/fDH/6QXyd+tGwp1WLbRBBRoCWIFi78jz68sc6BoI32yquvghQ4dYypjN+wXWLrzu1kJStB7ocffpgxWwHcDzxYo2EPK9qSJUt4LQzfhw0bxrV48d08nu9+97s0ZcoU3uIBu1kCLeR2ulkO9In1/MTE7uIHCxcuZH9gXOeubSFhYSH05JMLuM/Fi98lu12/mH3rW99iG+N144oVKzz6nj1rNk2+fjKhKED84cN8fYdfGXbYuXs3pXUVRQgOttJTTy1k3thGUVRSwjo3bGzwBh1sBzD9WbNm0YkTJ2n/wf0e+8x76CFeR9q+fTvrUYc9dLPcyLLF8bSUFK6RfP2U6XTbbbdRc1MTffjxh54C2t+88Uaa8c2ZtOST9+mtt96ivJwCmnjdZHp6wY9p/uNPcMEKJKAhKxNZ0D/6ke6zGOfx48d5DKNGjeJKUPjD7G83TJtBs2bfyltQoCujGTo8efIUrd++lhb/ZTEt/M2vCKAYwOvFtqqExET22YjoSI8d3n7rLZ4X4GP4FS7s//v668wa+jZ0mJWVQ1u3bvb4LHwQ55w+fZK27zxIg4L8ec6iiAaa2a9iBg+hx+c/ysfvuOsuKigoovnzH6WJXfPEsA8TENGcubfTxAlXsb+tXLXKYx+Dt9mvoEdjnvzfq6/yXACu+pjRo9mXMb9Xr15NFreF3BY3ffumb9P0GdP7+NVPf/ITfgVvnidmv8J4ausqyOo/yKOTqqoy+uTTzygk2EpNzW106803E7L+YUvEPegPMeXx+fPZDuZ5At5PPvmUZ54Awxkx5VszZzJUa3NTC3348d/ZRzCPUXEJ/oatNlu37/TwNmKhYWPoEH7105/8kPdhoyAEsNghB7bV3YlY2OaipZ+8zzefiD9GvML6P3QLORBYbvqmHn+xjenIkXjDPJ7YbowHvEeaYiF0hRt4yD1m1CiGlsXNLgBbkJ8NbG3DrzKyMmj71u0e3oibkMesQz9/jZ755bNMY44d5nnyJ9i+17UHsaCyspJGjBhB8+b1rI3t6fDL/CJ9WrbZ2rQ333xTyy3M8gnDBwi+9HPpDAnXWG8bEBoMoGF4LbJ+40attLhYw7kDNfyelp2h7di1i19DAhZyoIbXInv27NHyc/NFvM+eTdfee+8drbqy1uerP8i9Y8cOhgNEPwM1vObAq5y1a1eLXkWBN+Q+e/asz9et4A09r/hsBX/6egUEWfHaatOWbSLetkab9umnK7TqWt86AW/IfODAAd+8HZ2si3Xr1ohtn52Rwbzr4VcDtI7OTq2+tlb7+98/0JKSUnzb3t7Ocu/bh6UNm0/b19rs/Kp1164d2n//18vasFHDtOuvv0H748sv9xk3fDY7N1fbsmWL1miz++Rta2zT9u3bo2VnC3zW3q4lJSZqeGUN//Jp+7Z21p/Ur/BqbsWKFWwnn7xtNu348QSe9+b5kHA8QRt3+eU9ZAMv+DjmA14rSnjv27eLl3t82p55w2c/1iqrq33yxqv/5LPn+NWsWW6v7gW/qrdpq9eu7fLZDq9kxkG2fXY2z2VfcgNCsb7RpgHaMTHhuNZoHzgW2jscWnFhqe5XdpsGnx+oAT4V81Ji+9ZWxKtyto8kFrbZ7bzMl5iSrOFaMVCDrRHr33jjdZnP2tpYbiyz+LIP+oZfffbZioFE+NJ+E+9/CQ8NpNtvv52GDRntE3IMUHphkWHU4W6nyOiBs0PxThuZsthegmpDvqAG8XtsWCTZwiJEWXzI9IsIC6GwiDAR7+joMM5qjRuqV1cZ6GYIlTIiIiIoYnCMT1nwqgjZsrGxQ0WJMuAdExPDtL6yFcEbekZFGF/6xnjALyomioIpUCR3eGQ4xcVFU2x0NIOaD6QT8A4PjeTKID7lDrJQdFA0RUGHcUNpkKmghbc+dL+KpIhWO0X78CuAnwOeMzo2gmBTn34VGkiRQyPJz+X0yRvQnwlHDtArL71CGVk5dOedt9OGDRto2pRpXl/rom+MMSYmiiLDQ70Nrcex8MhgLvQRFSWTOyg8lLdmIbPV12vl8OBAio2KoKjoaJHtMTcjoyNFPgt7R0aGsyxm2183+Tqqqa+lsrIyGjNGz/6HnPDx8PAQYmD+Hhro+wf4RUUMJqfL4tM+Om/Mh+EUGR7uUyeDQkM5/vi7nT51gkxr+F50ZDRFRCFeDRxC2fZRUdTQ1OBTbvAODw+l2PBo1klk6MBbj0KtQeSMCKGYqAiKDB04zkKj4ZGhFBGF+eDb9hhXXAx2HISTJBYGh4ZSWHQYRVrDKTx84G1YsE9sTAxFReFflE/7gB+uD2GCmK/3HUyzZs3u60QXwRHxK+WLQNZLIlzSwJeqAZRuXPzuW7Rx61audvXUUwvo9tvv9pRc+7KEK6koo5umTqOz2bkXFZayWR9AyfqPX/2K7rrjDvPhS98vaeCfSgPipClopayggJra5Uk/X0VNYosL1oC+7q2srIgamr7etoQNYUvY9PM2JAtu3riR7rnvPrp5xjSqqqmh9xYtojNnUujHP17wpV9sMS6Xw0ntKFvXlavwecd6Ic+bPWc2JSUkfKEu/mnmZkWFGC72Cyn0SzwZ88qAAD3fYiBx62KN4UoX3K2791N9eb1IP1joV8EP3bt3t4gviJAkhMV7aUOijDR7DvtJkXQgbRinHEu5mYAbLG3gLXYct1sJ8zYhIYkK8rKkojBvFPaWNCTEpKWlSUiZhrGU6+pE9Ejeg16kDcl05eXFInIk6iFxA1A8CAav/ulV+sYVV9AfXnyRbvrWtyg7P5/RtmbN1l9XHT58TMQXRAVFRYSkPGkD0pQ0u7rV4SQXoX6wbDpDfyhoIWmOFocS/jfmprdAesvMW2j9xo19uly+XD4fSktLOQGtD5N+DqxcuVx8swV9oJi9tK1bt0YJSxlJk9J2cP9+LiIvpVfBUj567IQYWxz9b9++VSoGY5xLdWi32zlZS8occxNxRdQ6iI4elV8fRDzPE5Fshno6kwVckAOarAe8n4fHF/8CdDcV6DMVeLLPJ93A6zjdPGUp8wY9xuhrTc6gdbFC5Ji3OM8tN6eO1yqHg6XOTuEeoi68VsDZSZv05gn8ApG5LcRTxvVq99799P3vf5+mTJpEyCJduWkNHT91mp599lkv63tymZUctmv+SPUBLGUCvOMFaB3+yKxWcJR+ZEAWKtZwpRf6ftiI54N+vjy8YZ51dLT3122f40FBvtfizScFBfHeAvOhfr9L57zBQAVLmSwupXGqYIv7+w9S4q0ktzFYwac7QM/aFpD+w0mUZqnVKg/owFJ2OFReWcpFwZYglSCgEMvZAAphVNlgKrLgAiC9uGCSqugEgivUf9ALBqgIr6AZYLBKgwyKF6hMVDz7+Wp4IluyeDF9tmYNBQ8aRAsWLKAPPvxQ8LrYN29z326X3LOED6vMHkHRcoFeJwcQ9m2aR/H5vqNiFRKm8AbhrrvuMjGRX8zhI9L5YOpA9FVuGZ0dfFbaIHd7u5weN88qDyvYiiNtuDdT4a3ysKKKpYztSRei6bdZcr+6EDL0y/NC5UdjOwFQgaRNin4Cfkj7VqFXQciSymvQ1dZWag4fW5kMWqTD90bhMX7z9llZXeszDd58XnqmHN3JfJ7ke3Z6ts/tFQYfbIVQQXoBggzOkTTosLxShsA0ED+73a5t2rBBu/Peu7WYqCjt4X97TNu2ZcsF81lsZwD6mrRBf762yhi8MBdGDxvGW0qMYwN9wq9U9K3iV+CN+emt/fTJp7Xf//73PX5KTc/s8ff5/ANzDdtbJE3ZZ3NzxXOTfVYhFkrkNdMUFpea/xzwe215tdLcLMyV+yxsrzLvBxS014/g62tLUK9TLso/L2Up97oVwR10c3MbRUeGitfEerH4SvyJtVCrVfO5XeYrMZgBhESiDbZm8BO0200lZWX00ZIl9P77Syg0OpIW/mQB/eDRh0XbXgbo5kv9Cev8U2dOpfzUfN7G8aUKM0DnmzdsoNff/isd3Pv51tewpg2AC/OWowG6+8r+1MNnv7KjGFhwxFkkTn3dbdlbC+JFDjgBklukazBY4DajHPXu2Pw31u/OnD6tmOAgT8pBkog0sQnBa/XqT8gpfH0KRBcpb+jw9OnT5qEP+B0JKNJEAZQfBNKWtB05spcOHTgiJedXgdLXeRUlFQSUImk7duykku2zhAXlkeQFxCH44YZ1a+i73/8eI+9UllXQqg3LKfXMGVrwi6c8F1v4NnQubSq2h4+cPXtOyprlqBEmkqEAvcsmh6WEPqR+hYvcyRNyvyoqKCBUlfLW/vX7d1ByQnKP18JIaJQ2HeFKnnh29OhRceIZbC+NV5AX8xjzWdJge6lfYY4B+Sk1NVXCmpqamhhVSkRMRFkKtsf4Tp48KYZ2LCkp4nV6iSzg/eGHH4hjZ05OFpWUyJKmoEOVpFqJvOeLRr5wSgFUW1vNGYh2m43GjhvHMpgzEgETiKeJuooaKijIYSg/PFkADg4Nk9zIvMQmfazr4C6ntLiY8otLCbigqLeKjdkwCDKGjWbwqCqpoIKyIqqtrafAwEDmjT4wYZD5hgZIPsDbQfEF2QVUXF5OjlYXjR0/huJi9T4B/2U0g3dFRRXLGBYWRQjqSPQAb0wYlAVDw99GeTBM0IKCPL7rxriMPs2ZxaBlHnV1/HQFeugI4+zLm2j0aF1XCFqgxeZwjMPo05u+m1uaqLy4nMpLiyknMpJGXXYZ99GfDvNKCngswKTOK8ihcWPH899m3oMHD+a7T/AoLS/nrEnY5XLwDg3toW+cbOgQYy8qyiPg7wZbLTSmy09wHONAw2Z38ILtiwsLqaQkj+vtjh0znCIjY3voG/SGDuE/eUUFZG+0UWBwsKdPs18ZvJ3t7XQiKZ42bt1Mf3jhBYobGkdPzH+S3nvnHbKiCDeedktKGNqSfRYBNyuPGm21FBwYQqPHjmYAB7NfGT7LflVQQEVFRWx7/A1f7q1vQ4e4cBbkFFBldSnv3x09aiwXljf7leGzGC/sAN6AkHQ6HDRy5EjWldlnjXGCB7CbUcu7qKSMAsMiCIAJZt69fRbJYBFhYRxIAc8H+c0+a8xj8ECfKMkIAARvPgt5DdtDbvwDnKI1MNCrz467ahzt3rmT/uW736XCvGIqKsphUINRI0awX/XWocEb8jXaUcPZxX0Yx80+GzU4hqLDI3k8uOErKyuhuJgYhmM1/M2sQ7NfgY/dbsNweJz49Oaz0FVeXhbl5xeyD40eM4Zt358O4T/gXV1dzW/MJlx1Ffdh9tnefgVfsNlsVFFWRsNHjuzXrxBni8pKqLi0mGPJ+MvHk3VQz1ho5o15WVRQRhEhgQxgM3To0H79CnKXVVTzvMdTKPQNucx+hfgL30TLK8pjHw8JCSHULB46uq9fmX0WugXQUV5BEV1ltXKsMfNGxv3YLpAU6K+goISsgXg+9B4LjXF6Ygrgci/CpnDB7SCXy8pOGRDanaEHcGskSJmbzeUgu83BF1AzQD6c0nzB5XPc/lTT1ECdHW1kdzjIjSIG0XqyEIDke2fJ1TtbyW5r5AQhTE6jmXkjwKDhs8Zew/sU7a12cjn1gG/Q9n6IdbmcPD6nE6+VzbydDBCORBY4ndHgIOBRX2/zPCXhNwDPW7qyXvAKDHIgEaK+vpGcLjc1NNRRZ8fl+nGTTgy++MQeWciBaTqxWQAAIABJREFUC310dJznJwM0HTrHONBcTjcBBL69vYP3iQJvlI974+12k7PBQXZ7G/n7u/lGhIk9cusZfs4u4Hz00VBXw+OsaWgggzfOMWxp9IVxNrQ2kN3uJOiy3uEgo6ow5Pbz8+euPHK7XFTVtRfYVl9PzpHDu37v1jcOGDpsxZNcq4P7he6NoAs5DD+EjhPjj9BbS5bSsYP7+cbwhT/8gW6//U4aPXok3yiYb+QMWWxO9NlIyONoaKih0WNGcoCEDxrj7G379o52amy0UXScgwwLGbSQG9t1UC3P3tpKNns926euqYlGje1K63ACeL7bV3jwsH1XwQX4LPzFaGbehtz4rKmpIpfbQvX1tRTY9TyC49AJEmQCA7uneVNdAxdFaG20UaupjCJ4w5d7J2vVdT1lNzQ0UUd7d3KbWRZDvoYGG8Fv0Let0UbUVd5YLwihj3nq5Bto996D9O1v/ws12FBcwEJVVTU0BDfrXYy88W5tspPL0UAWt34DbLa90T/2I1M4Ubu7g5qaAaTvpKraRooxocZ54223Yz5Adhfr3uAHWrOe+bjbTXU1zYQEIbxZMPjB943vxvn4hP0aOV4RtTQ3MD+OB11zE5nRuFgYDbEBJgfuuMOpFzyADOANWvO8t3ERl3qeHy2g7dpFYNCDJ/pCQzxqamghp7OV6slNI7uKdIDW8BPY3hivw+Ume2Md67Cupo4uv/xy5mOm5wNd/9nrmvnm0EVWanDYaWjXvDXrxOCNUzBPLRYXx3KDD34HPfzQau32ezxIOVkXlh71kM1yG3MTPGrqmshq6T7f4H9RfEpXllGm64MP3hMviiORIyXljJS9duTIEa2xsVZEj6QZlfJ8oJUu5qO8FPB3peX5VHhj0X/PoT2iMYIIpbRUEs927JLz3rFrh7ZHgZ7L8wkTUIoLUZpRbvt9CuX5YMek5L7l+eBvSMgZNWqUNnHiRG3Re4u06tp67YMPPmCsa4nSwSMpOVlCyjTH449otbWNInrIHR9/REQLosTEJLHPZmZmMpYyEvgkLSklSSstlSXaYB7s2CEv+4hEpYESA9euXqvd9J2bPGLu2ifnHR9/iMstek728QU+K53HpeXFWkqS3PZ79u0TJ/GwzyYl+pC26+fOTsZSPntWJgsS1NivfOAoG50npaRqxcKSn4hX+/bIy4kCL7ywMNfoasBPW2Oj9vrrb/SbYNf75PTUVC03V1aqFOdu27GtN4uL4u9LSVO9bnvwSgLl+YYP77o97/X7F/7T22PEF2aqzgBPUWh41fZVbbibXbNuHX368cd06tQpuu/ue+nhJx6lGdO6S+DhtVxEVBiFhkZ+VYfpU+6CogKaOX0mpedevNCOxiDgd6NGjaDS0nJl32tq1p+i8Pr+69zwOhdPbF/nhCJ+Eq2p4dfxxlP419mmxti63zUZR/7JP7GeN2jQBbrYQre939l9Sfr+Kl9os7KyaNXKlfTxR0tp2PA4mjfvcfp0xQqvARxrYF/3hjXpAAtd1NCOhg3gdzfc8E1KSkqk2bNvMw6LPlGIgN/Ri6i/ukRf9xsKWAYXWeS8/LM1cZYyFIO6hOYkhYGUhcxgFWhHFdg7ZPwdPHhwoO57/IYsS2kxb4wPtR2lTSUDGnf3q1evlbJmCENzMstAJ+KOceVKOUweMiFVMkQBk2dejxlIFiSEQC/StnbtWjLWCvs7B7rbvXM73XHHPTRzxgzKyMmh9ds20LETJ+nphQu8XmzB66OlyygvQ5YxDZmPHpXDNaoUuQa0486d8gxbPLFL9Y21xGaXg1xCRC2ME09RkgYZli9fKiFlGsxNXzHie7fNpq1d9VBVfBa8ly6VywLe5lyMgQYBfQA+UNo2bdogz/RucSrFwuUrVyrNHxVoR8x5lbm5afsmqUoYGlOqQ+jbXH/bVycq0I7YnaDiV776Pp+/Kz3hqiBN4c2pCqIJkiekTQX9hHliAb0reUDah5QO41RpKpCHnDyg8ESMJBGVFigHDlNhy7SqevEG7Wi8dvrrn/9Ca7evp4iQMHryqafo17/5Nd1y80yRTIA9dABeR9gs4k0QYKgwfdxupZcbCmbnDGUMEZnKF6bJHUVi9xtmzKBf/OLnLKqSz1pRoEE+SBXkNTxxqehc0/zEqrYGyWUGUwWvYhlUkNd0ncjt6Q+cRGFTQZrCfLdeIIeFvlVsLxzeeSFT8gTJZDKkgvOqwp8Z5/r6tLoDPdl0vmjxO8utIDy2J0mbPknlU0RlUoNWLInFQio3RNLxGXS9s8WN4/199s5c74/O23Gsoy9dtoy+f9cdjGnc6nLRJ598whV6Hn94PoWFKOjbFSy+lcMNolPpgiu2Dg9TBdpRwV05q1U5SntTvJdjHaw9+Y2c5Gb4xhtuoIaqOn4SVvFZqyuYXErZp9j+JQtxuLlTeUDQNM2LtrwfcslhxZmBW9GYStCOlkA9HnoXtc9RiT2Nk+Czfn49d6wYv/X+RNZ010aI3j+dl78tKri156VHGRP/F1988UUZKfbRltJll42RLeZbAigCxcix7iJouMOMjJQltvhZLbyXE8XfJc3f359CQ0M9W3UGOgeFy6OjIykubshAZN2/Wf0pKjSELIIn6ICAAAoICOREgW4GA3yzBFB4aAhJgM8tfn4UbA2m2LjYARh2/4S7y7i4ERQW1r3Fq/vXvt8GDUIR6FiZDq1WCgiwss77cup7BHrBntXs7Gxa9OYimv+j+VSQm0v33nEXfbh0Kd1zz1102ajL9BOxVhkYQmGhIX0ZeTliHeRHw4eO4H3JXn7ucQjbpKIjY8Q+a7H4i30WfoWC5VIfh06kPttib6YPFy+hX/xyochXCH4VFkrow1fzJ43Cg8IpRuxXAZzwg1yI/hp+27JtO40dezldc+0kGhI3uD/SHsctVj+KiMD+fdncDA0YRIOHDRb5LC4AKj6LfcZD4uJEOrT6E1n89b2mPQbUzx/BwVaKixsqnj8WaxBFRcpiIUweHhkrnj8WSwDFxMgSKwMC/Fhm+K2vBn1HR4fS0KGydVw//wAKDRkk8m/wxvXkYlwLv5Sl7MszLv1+QTUApJz4wwfptTf/Rmmnz9HcO++khb96mq69+lrPHsILKsDXgDnW+W+aPp3OZmZTdKTsBvfLHvZfX3uNCgoL6c1Fi75sUS71f0kD/zANyN63AFyhC42mrU32Gg30eDUobUhuwDmSBjppMgT4qfCuqaqh7Xt3EqASJa1FUW5pIgz6Bq1UJ8Y4JTKDBtB0p07Jk0RU9I0ENV+2BwzcL37+c7r22mvp+d/+lh55+FFKzUynjz5aQlOundLvxRb6aBf6FWhRDxdJXJIGel9ym/kAj1pqH9Cp6FDFZ1uhbwAGCNfwVfxKVW7wlujw9rvuoJWrVokTw6D3rMwsJfhSFR2q2/7CxCvIgYTQoqISs6v1+x30iEHSpmp70EvfQcPukEfSYJvt27eL5wTLLXwHjcgN4BOp3BJ5zxeN+ILb1tJGmzevp8ZGWXYjILvOnTsrkhMXt/j4Q2LlA8ouKSlJxBtEycnJ4qxMoPuU5BUQ+ckcJyExUcwbRRH2bNshlhtZ3r4yPg1mcPRdu3YZf/r8rKwsp8b6buhMXyegELV0bTsnt4jOnu1re0zIpcuX0fe/9z2aPnUarz0im/DFl16he+9/UPQKqKKqjBITk32J6/kd+jNgOT0H+/mCJ0UVvzp+fH8PZKJ+2PJhZGXGx8cPRNLjN+hPmknsdjrJDbhK4Yo/Mj5V/EqlCDkyiTMzM3uMxdsfw0aPpciwMHrj9Te9/ez1WF19FQGrWdogt/QCUFRSQsnJ8phy4MABcbyCHaW8sfRQUFRCTU11omHW1VXR8YREES2ITp8+JbZ9c0sb7dq1Q4wrj+16Kn4F+E2pfZBZDRxoSXO3uWjv7s0XzRZMs8ziV8q4I1mx4jOKigrjLRizZs3mp5Dly5eTsWg/Z85cDppQDiYeFtGjo2Npzm2zefC4c0MRatBPnDiRpk6dxgFr797dpGkBnGQ1bdo0xjKF4Y4ePcy1T2GU+fPns9xJScmUna1PaGD63j53LsuBQGlMdOB73nrrreRoc9G27RsYsg0JSOgPeLB44sGTj9EeeeQR/goweoCGc7KS20IP3XcPY8IiQKWlAdTezeu7c+fezvTYGtDa6mD6b1x5Dd1w/WS+Y1+zZhX/joSQ22+/ndcEgS198uQpz02XcRx8z5zRCxq4yU2PPvIon7th0yZyMrQlMV7pLbfcwsfN+sY+Ruxlq6qpoYP793LdUiwl33bbHLYRdIj6o0YzxomxV1VV8eHI6EiaO2cuf1+2DFsugLPqpunTp3t0Zd6CNXv2bLYxtq1kZaGABAK9hR566AG2A0DDcUOEG924uGiCnwBzGqkCO7dvp7jBg+nBRx6h3//+9wwFh+1g8BPofObMmxl/t1vfuuRz5+rjQXGGooIchvtkv5qj7+PEdpu6OsBsOmny5Mk0adIUam5qpl179rBPgf+UKVMYGxt+eerUSdKTKtw0a9Ys1qHhs5oWRCFBGt122x2Md3zs2FEqKChiQcaOHcMy4gl+w5Yt5Kf5MdzexIkTuM+CkiI6dvgo6wOyTJ02gyZOuIq3YcDOSMrx8+sgzBPkNujjTOP5AFxb2A0NW2ZaWppYL1ddNd4zT7Zu3cxym8cJG+/cvZuef+5Zeu2NRXT/3Xey7Q3e4BcWFkJ33XUP8zZ8Fn+MGzeO7Yynhw0bNhAyRzE3AYOJ/bIlRWV07MRhj1/B7yG3WYeQ5dFH9bm5e/du3t4FW2L9DLZHg1/pmbQWuuUW3cbY5vW9732Pxo4ZTXffey/T4pyykhLaf3C/xz6Gz2ILVllZRVdMCSdjDi5fjq1wutzTpk1nGzc7nLR1wzruG//NmDGDYUDRJ56qMEb4xEP3z2Mbnzh5iooKstivBg0KpbvvvpPP3bp1K48H83jChHE0dep0nt/QldGunTCJrpsykXW3fPkyzzhvu02fJ9AVbOHvH8DY77ffrscrbOWpqABkqtMTC2EH6LCtrYXlGzduLE2fPoPnD2IHIaXPTXTzzbfweOCz2dn5XGsX677f//4dvH6OG/WcHNyYuDl2cCxscdKu/dvI0epgP7zyyivYZxELEX8xHzDvEZcxfyA3+KM/NCNeYSx4kIJO4As4jrZz526GrHW5XXTV+PEsN64ZGzeu99hywgT48nTGiD58VK8YBf5GTEF/587pcRY5Jg89NE/nvXs3NTXUsSzDhyO267EQW8QgB3R41fgJNH3GdL6eGNvv5s3Tz2cmF8t/UrwrwHwtWvQG16FtM0H8ATrN+GfU78Qn4N2OH4nvAa3WZjfRtrd7usb527ZtYhhDMw+DLz6Nht8Bv7hv354evHHcZm/V2uz2HschK2gB29eDt92u2VramN7MG7VZ33nnHa2tpUXr7PoB53mTBcd27drRk7ejswetp09HJ0P1bdy4vod8LLetWy9mWQ4cOKD1rkNrlsPgrXV2ai1tbdratZ/1y9tcSxLnbduyQwOsnoeHpulyd+nPc7yzU4MOP/tsBevELB9kMXRuPp6amq7t27dLW736M+273/2uNmTwYO1HP/mJlpicqNlsbX36XLdunVZdXe85jr4NO9ptNoO1hnFm5+YzlB36Nlqbvd2jc4/cmqY1NzcztCN80TjOvOGzvcaJ47D9oUMHtDaTb3a0d/M211ZF/zt27Ojrszbd//C7uc/C/HxtRy+owQ6HwyM3xmA09Anbw889PPrzq44OLSUlRRscFdUDBpTHiTF2zTmDN+SKjz/OYzXrEP6Bv81yQ9/1zS267U36Zt6mee/hbW9nyNWEhNPMx3PcoLXbPePBb+998I42efL1Om0XNGEP3vZuG3c4Ohn+9bPVq73zNukbchs+C+jD/nRoyAfeuenZff3KkNvMu2uebNrUFa9MkIqG/sw6RN+wI+yJ40ZrR7xq1H3FkA+/gebjjz/WzpxJ6Za7V/wx6PEJ6FfAGJp5t7a19/Fv8AY9YCBRg9jMA+diPtja2j3HoUNAUm7atIHnfR/6Lt0Y44HPJiYmatmp3byN8TB/kw6hb/B+441FfX0WMaUrHhq8IQvkTklO7TFOgy8+DfmMPhGvLsZGUqEwIARSu7BQOCawOcj76qe8tLKH0gaiR7Ho8srqgUh6/AbjSgtul5aXa5hM5gDYg1mvP3ChkPKGDsFf2upra7XGVu/FvPvw6OxU4n3kSLyWkBDfh01/B4C9a9yA9EeD4+fS0rQnn3xSGzFsmPatb35T++DjD3xiAiNomCfMQPyha+hF0sATtiwslBXRhr/2VzzdW38qfsU+q2L7erlfpWama0NiBotlxxjFc7OzUysW4i5DR42Y940yfGnIEBwc4k21Xo8Bn3vfPjm2L/uV6YLolWnXQcQ1FduXlpdquGGSNNi+ulYWr3AxAgZ0dnamhLWGm8DqShmGNhhijHa7XcQb8wc6lMx7MIQ9pX4FOlwUpfT11fXyWKhpSj4rUsZ5IhK/Ur5YnsgvyXHxaaCupY52b9xNn3z2KZ05cZLuvPdufs148803X3zCfg0lwtrz9GnTvxJYyr3Vj9edTz31FD3wwAO9f7r09yUNfO00IE6awsixNoB1EElDggze4UubCu2F5i0dI8amkpmHtWhV3uKs8HaU/ZPZBnKDFrJLG+jNCQ74jnWeV155iSZdMZX+7y9/oblzbqP84mJ6++136YYbbpCyZlnMvAc6EXSqckvpQafihyq0sKMKPWilmfLQl9viEmMpY5wq+lbxK/CW6htyY30Va9OSBr41NWo+rjJOFbl7z4cB5Xe7qbmpZUAS8491TWpzU9WvVMdplm2g7+Ar5Q27SJMC0Sf4qthSxWcHGtP5/k3pgnv2bJo44xMZaxkZSKqRteMJCTJCIiosLKTERDk95JAaCwWqgTMsbTk5WeJAiolhLOhL+EOHjY2yLS2ohbl9uyxwoW9kWZ49e04iBtOANy4ADqeTVq1cTnPmzKGZM2dSWUUJbdmxgW/Gnn5qIQNMYCLl5haKeUMn2I8rabhwZXACm4SaaPPmzewvEmroW5pZD37SzFPQVlaW0PHj8ixl+JVLkyE8oV4o7whCtpKgYZzSgIR5o+JXmJvmIu++xEFR8YSjx6i5xfeugMLiQiVZcCFva5fBPKESEfQibUgklF4wnG43ZWTJ59rurduVZFGJhUjeUxmnkdwk0Qv4wm8lDf4H9DhpA++KrkRPn+d0qMVCn/zOI4EcIw930W5ZADDkU4FKk4WKLs4WZLXK8UCNTDtDrvP5qcIb6Ccq9JAThcVFjbF65ToBTxUs5crKWnrut8/R5i3raMTQkfTEkz+m5StX0dB+EIg0rV0kNoh0GEjfARe07oBOsihisELv8ibUNzNU4SuXgCmlducCVG5yWV1IShU14XWZeXXIrleeflX9e+KE6+jd+sVUWp5JE8Zf6+Hj7Uug2ypFauTTkRltccv8ClZXiW/IxpU2t6IOddQrGUQiZFDROcaoEjv9/XyjkZn1oBTzeSub+eyBv2PLlKTp8M8XcG5KhOiHRkkqpGBLG4KowyF7apHyNNMZW5HMx87Hd28g+gPx1X1Apkb9KVvtpkXGmYg6Zc5oHouvkMFP5Nu304crPqFj+w/T/Q8+SJ+tXMOvAc18vH1XCQL6lUI2UmuHm9QKDOigLd5k/OLHfGnQ1IMFgOqmv318xRYxaQPOtdUl0x94qsihoz/K570K9q4xvofmzaOt67bShOcHvuCiCEWgS+7nuHA5yE2+gQZ1HwkKkqN0BXKxA6EsfsBpll+4MMQLhkNvHaRkf4smv1tALFSR+/P4iuEzA33qVhHaZiBGF+A3paQp7BMLxmOR4E7DeIUrfboAvZTW4zECOaAzJd5dCE8oAC1uiGBSWdrdpFI9BK9xpfRsH6Hcxvpgb97QVUFBHn20bBl9sngJDR46nH781BP02MOP8b47sU4UCNlXOi3icarYU4UWIqvQK9ECuczPxfu6JapR4e2BdkzPpuho2UVDxa9UZGG/8kclGNkNAOh3H9pNLzz3PJ0WlMfDkgbHIIESsV+a5ZDOTYUYpKI/Zb+CryjqsPc87k89n8c+F4q3aryy4p7lAtiyP11diONKF9wLIcAlnheHBhBUV61ZRe8vfp+Sk5Lox08+Sff/4H6aNnU6SV/lXBwj+eeToqSshKZPnc6AMOHCAiAXk5awFnrtNdcwbOPYsWMvJtEuyXJJA+dVA+LnbtyNACpNmmxRU1VFOUIYNtx1AeVJmm1XU1fHGbJSTSCbVip3Vk4eLV78rhjjFXLXNcvgLptbWhjDWEVuAxHK1zkut5tOnjrpi8zzOwpLb9+9k5G1nn3mOfrG+LH07lvv8vaMwuJieu2112jGtBmeiy3QeDxvFjxcvH8Beo2OdOP9995HT54+IdY37AjkKkmDzy5ZskTsKwj8Ut7oX8VnITfopS1DIbHJZmslp9NBreQQsc/JyxMnoOBGzIxW5quDvKICKiqRwy+eOHWSUakmTZtCBw93o7956+fYscO0apWO4ubt997HTp48KfYrVdsDi1war2B7xCBJw0ICfBaoS5IGGeBXmP+SlpWXI0724nh16pR4cQMoYWVVsiRP6AQF6PEpaUBUK1PARIftL8Yme+/Dadkd/Kpx2LARhKxIQAqiQWHGK6ewsDA9S7WujgOuw2mnYKuV4cWwngJa4PG6XS4KCQujyPBw/rustIjyCvKoo6ODIcsAK4c0cGDg4pUQ+Bv9IZjDsJW1tRQYHExjRo7k13TM29nKUIOBgYEMTYfzCvKLWG4jXd3gjTGgmXnj4gYIscDAYMYEBQwk+odTt7baGPoNvFGmDq0gL49xTzu1DnLFuWjo8OHMD5MX6xNITkB/4AH5ykpKWRaUaBszejTLbfAGRCJ0ZJSUgoPhVaE+LjeNHq3rG+M3dAJafG9pa6Pq0lLKyyuguNg41hVeiZt1CHkN3nk5eZRwIoG2b95OJUVFvG929cpNNO6qsQxRB53gXJRRY97l5QypGBkWSZddeRmFWoOouamJM5ZBCxkM3pAPsjscrRQcEkijR45kXUEnaKCPiopi3m0tLVReWUmFueUUbA1hWEfoCzrBxdLgbegQvEvKyshWXct9Gk9DBm/wx7gBOdfmclNpSQkXuYYOQQMZWd8AZMdaJmSJjaNBgVb+/f+z9yZwclVV/vi3qyu973uWTtM0IcYQsoCRTcQYEBgHcUFBB9Hx7zAojCK4jOO4/MZRR2VUBDFABAyLAmIgkJB9XzvpTm/pfd/SW3V1dXV1dXV1vf/ne1+/6kqnu+tcTDAwOZ9PUtWvzjvv3HPOPfe9d8/9XurtdDqU7Fz6Z9xv1IXf+Y+6UC/6prm5WcUseSmbNnO53Uouea3+wOtTdltbC+Li4pCblwfOAVq6UA/qTdkk4vrSL7RxXn4+sjMzQ+LKvEemHLaTMro629Wute21rUhalIrY+Ch1nDFOPUiWf+rr6xUeMc+nJEJKsj20D3n5nbz83t83gF5Ht9Ins7ZW9U0eny6u2MbmxnpEKXjQCd/Tb9b2lUnjOYIy2po70NbUgsbUdAUR+NprG3H7pz8Ll8sBsCgy4EN2thk/hJn0eHwqX9DueXl5ql3tfe3j89d+JCWlqbjiq+Tm9nawrcnJ8ciZM1/lmtB28mQrrvhw0FjfDKfbCbstCvkFpuyp4ooy2E5Ou7C/0vfMBzxOXGP2+VAbUgZjhXHO3FHAJ3jmwr4+dYPEufeEhBjExyer8+j3uLgElftoN+a9UHtTttV/GFf1jY3oGI8rK6fwuJc3X16oeGO+4XnsO8219ehLMbfyC8asy6FyG9vDLU/Z7ymjo70Njc2N4FsTtpMxqmLW41F5IjQXUo/25kbYouLALYupt2mTCUxoK2YHmAvb29VWi7QN5fKalO32u2HzmVMS6enZpo/b29FYXY+YpDh100/oXlJoXMVZ/X48p1AfwtOeayQecO3qBTpUQomcFa0cYDa6XVWZjo6OID+/QLXP63HD43XB6/WpwJmbm6uOu1xuBcptVqUGVCfgIOvs78foyCjcbpdyEpmZ5BwOZ3AS3hpwmcjdHi/YqTxuF2CYncPn9aHX4VKv+GNizIGOATTo7ldYykyElGkRHW5NB1iy4QsoHeLiGFgDwSc6XrO316VOjYqyBwdcp4vJ1QeX04v05IliKN4o8IaTBQRMulYic3gHFC5tX18PcnLnKBRi6mTJJr+VGJkseV22weN2AjAH3J4eEwOZylA2k67P60UPbxQCNnT29CAny9wv1LShA2Njo/CPt23Nmiew7qlnEB0ThU988jZ8+vZPBwOTOKm0CXVnQmMnULL7etTG0gOuPmA4A0iMhtvtRU9fp8Jlpd6pSelqDtbpcKkYoX+4OYI14Pb2dqvByaxiDCA2dq66K6ctWNHM9rKDkohP3dXVHpRt2dDn88PtcsIT8Ct+xQyo78pf4wMLbWIbHVHYruzMPM+STZtwgCKxkIXJDlHmIOpyuTA0NASn04XxkFXxwCdI0zdmAuC5/f19GBkdUbrSTyReg7LZRvIT95U2ZHscDgdGx8bAa4yx9NduD7aT5yYmJgcHXNqEMj2eGDPGMzOV7eh7SzYHIraT7XG6XGojiF41UI0pXXjcihXiA1tx5fF41Dn0s4c3ndlmm6y+xr7JhM6YZeZUMgJc492HefPmqeP0FfnZ5ynHks3+6/MF4A14lZ8wnhgt2VQsKteMK9rKNeRSsUks8FtvvBXf/873VL5wOHh8RLXVGnC9PlNv9k3a0CJHh/mdenCwo71p3r7xftLfP4SUJPdErnE6FfYw+dUNTiAAt9cHt5e6++BwO5APM6ewHw8PDyIyMhZpaUnK3ryuq38APn8ALsaiJ13lA9ortB9bfZPtpL2YJ9xup9pegknX5fHA5TRv+gP+NDXgcurG4XLDZvPIGqoxAAAgAElEQVSrmPV4zZzCm33LhvS/NUDR3l6PByOjYxgY6GenVWZRubDXqXzDOOKAS9lul0vdsPCc0Ji19ObJLEZl32T89DkGMWZEKjzpeXPmKNk8r7eXm57YlB7Ww4dP5XwfWCxvycYYFC/zD+OKshmzfBZnH2M7eIPL3IRYs9/3djPXmXO11oDrpJ39XnjdfiQ7XeoBjiymTYaVf5KSzBtQphD2H+nbOPNib+P/UsQq4lU+/fQfjJNCGDHihxIPVEKEDiPesRRara2lxSA0oZQK9x822nrbROzUm1jKUqjBvXt3h4UutC7scrqM7Zvk0HQHDx42GoSwhISEI6bqZGI7nv7jH43VN65WmMZf+9rXjIOFB4033thgbNq0dTL7tH+vf229QbxUCdGGx44VSlgVzxtvvKHwUyUnEBP72LFjElal75NPPqmwYyUnUPbBw3K9ibtMeEcJkY8xLqXDhw+egjM703nEik5JSjF6hZCX9A19JCH6/JX16yWsioe4zqXl5WL+119/zeQdGzOu/MAHjOefnx4Dd//+3QZxt6U0Gbd8pvPMuJL7nvCL0nxFeET2ZQmxv/7xj88bJSXFEnalw86d8pxyrPCY0SLMKYRd3Lp1kzgXlp44YbQJ44q2I5ay1IaM2ZqqOpFNiL2sE7MyoWeG6/9O0ZSwkpivNbhwn68r1V3+23jzc6Yuxbvq8hMn8OKzz+P5l57D/LkFuO22z+Czn78d6eOvLVtbO2G3BTB7/CnkTF37XJPDOdmcnAwkJpqva881/c6EPpw3/eDlK1HW0ITURMkimDNx1TMv46c//jGOl1Tgzy9xB6DTqb2zS+2gZU0lnM7x7jhC8IiMjKzgG493R6tObQVzFPvm/AUXqimqU3999/71f2fAfff6MNgyzrvs3bULT/zhDzh66BBW3XAzvvnv96sN3YNM57+86yzAubkrly1DZUND8LXnO7GRtY3NuO6qK9Sc8Tv1ZvedaPfzOr99FhBXKVOlF174syoAkKh34kS5VlUm97uUEosWuE+plLjpslp/JjiBk/g6lZBsZ3+/DDOaAyL3I5USZbMwYCbinWJrazO+8fWvq6UV3//RD9Rm7qVVJ/Dcc89MO9hy383j5bJKSF6fenNeR0IsFKHuUuIepbSNhPgGQkc2YTpZeS4hyi06au5NLOE/cOCQhE3xMK527Zq5CjdUWOnxUrG9ORc7HCAqWaiE6b+znaEFQdNzmrUUOjHLpxa2VUqhe8suyM9DXl4udmzbNuXp9bW1WL/+5Sl/m+ogZQ96ZDHL+NOJq20b39SyoU6FOuFIdXTRyYVHjxZpyd6ybctUpp3yGHXmpvISYvyxGltKlMu6DgkxJ4bGleSct4tHa8Bl9SAbIyHDiFQFKBJe8vil2YIFVT6vKiqQyvb4ArBFy5rK9rHASkqmPWQ2ocyREbOoRSKfxT7TESsXn1m3Djf9401YcekyeGHH3ffcjePHS/HFu+5U1crTncvjqpDDN1HoNRMvf2Phj5RoE/pfSsRR1oHVM8YMqWgMDA4hSgjDR709wpsKKuD369mERTlS8ilwZBm32jiemxfIQlz1HZ0nSBbISYk2NPuE7IzJcXXzR29VcT3V2Vz6Mtgv33CDxTu2MRlSks/mw9iYPGbdIYV4U+l6yjGDld3yzQvYt3V0YaGalPx+n1bu9Hmnz0GTr8k+r9NOj0ueZymXiGoiGtXLVyKZZ4hJ2ALzajoYnKwyZCWglHQhFVklJyU7AmqphpRfLtmSKC72hqEBlUbpk9fXHS8txfe/931cePGFWPPoGtz60VvVDj2/+/UvUVCgBxqgA40tXOZnGURVmQb/CPPFrFqX2nAWRg35TQthID3ClYTCaf5ga3RtAsghEuUp1FSH1aFSYr+UDoqjBNLUCRSpEkG+U29Cbrnlo9i2ZQu4mcCUJA0TVXErBwHl8hzmLClFRMgGcsrjAg+dWGGf18Ei5yCqQ2Z/k52hA79oVa3LJAM+4Y2wVF6QT6Fo6tkkeO5Z/hL5wx/+8IfSa0REBDB79hxVeh/uHJstErGxMUhOTgnHqn6PiDCQmpom4rVFBBAdHYe0NFkhjGGMITExSS2xkVyA5erBpUJhTmA7uVRhlgk6G4abkWAgJycnDJ/5c0REJBLjYuEZHgZf7Xzlnq/glz/9KbJmz8cjv/sN/uM738HK978f0dEm0HlERDSyszNFssmUlZOp7CI5ITLSjqysTLEN6Z+EBFkBj98/gpyc2SIbRkYCY/5RcVxxWVVOVjbi48PrQnsnJCQiOdlcpxjOLpGRkWrJRTg+6/fo6Eikp2dYf874GRUZifiEBJG9uSzomaf/iHvuvQ+xMeFB7xmzjHErbmZSJBIGIiNtyM6WxSxlcb0ll+dIaHLMcl0waxCWL12CCy80lxlaciIiItRaVmnfBMaQmZkliivKtttt4v4QEcHlgWkiG/JhYtasSLHsWXZTNnOWhLi8LSUlWcIKwzAQH8+16jLZQERwGWS4C7A/MOdLZLNf2qLsmD/PXDIaTjZzOPumJGb5pBeh1pjLYzbc9c/U7+eLps6UJc+CHM7N/uJ/foG/vvqqWnv21a/ehxtvvhGZ48AbZ+GS50W+Ay3wbimaskz/i5/9DM0tbXjkd49Yh85/nrfAu8IC4renfAVFJCbpqyjyeYfkj/UsyNGSrTHXpiObk/ksQpDqoiNb2SSM3py/WbduHf7hppuwcsXlCNjseOmvL+HQoUO4887PzTjYUhcpcY/gWmGBA2XqyH5Lvidgu4B0ZJP3yJFD4uIWiX9CVTzTvn+rsqnHsF0+d3rW9daYq54qrm795Mexbt0zILRgKBGNTme/YsqWRZX5iv2cyFeEaD1yNGyxpGWXcylmqQv/SYjFjwf27QPR5iRE30hl0+dTxZXkOmebRzzgciB4+eU/iZNXfWMzSitkFZ+sIN62a4eC9pI0uL2zXQvflYOVtCqTxUQ6G7NzcJbKpg03b950WhMZSMRa/f73voeLLrxQYTnffOstWPfCn/HA1+5TmMannTTFgQ0bNkxxdOpDhA8k/JmUWPUnDXhWkUt9z+uzSnnQN82c3SQFWbVdVFYknhQrK6sYR8aZJGiKP1lde6RIFrM8nZX10upqxohOJf7Ro0fFeMfwBhDw2sT+IaJYY13zFBY4/RB9rlOlzDguq6g4XdA0R17dcHrVfsGChShYuBBvbtx4ylmd7T04UVtzyrGZ/mDMEilNQvS9Tsxu2vSGOF/R97zxkxA3q6+uLlMPNxJ+xp9OXNH30ipyK19Jb0TKy8vFKwJ4J3TwWKGCh5W0s7TyOLgJvYQCPp96Kyjhfbt5xK+UBwe9eP75J5CemYu0lCSsWrVK6friy6+o4qix0RHccMONarF2RWU1ykuLEDErGhkpKbhu1SpV4kQQdIJKkAryC7B0+VK1pGb//u0YGCB2bzSWL1+uQCcYFBzMTEiwAD71qU+p844Vl6Cu5oSCfYuPjsb1N31EAVSUHC9BbQOXf3DOLgvXXHOVesLetnMjhoaGlZwlS5aA+MjsAHv37lXyONH/mc/cob6zdJ/LGkZGRtRcwc0336zmuphE+I+8qemZuGH1asXPgYIVtpxXoFzK550VE5RZmBDA9R++CYnJ8QqrtbjsGEaGx2V/5GaMBkbx/LN/xNq1T6ly+muuuwo//Z+H8N6LL8auHbtAyLvY2FnIypmHa666Ql3z5VdegTE6hsjoSFx95fsV1qxqz/69Sjb5P/jBDys/0IaHCwvVefSP1c49e/YoLFP+kJk9G6tXXad4lC/tAUSOGFi28nLlB77VOHz4sKo4Zzs/9KEPKdnsuHUNDeo8lqbccsutyg8EmG9u7cSsyEikZKRh9XVmnLz5+kYFz8ZKw4svugCXXrpMDVbbd+7GyPAAYmMT8b73vU9BhrIwrK6uLij7wx/6MJJTU1FcXKzwosfGhpGamokbbrhB8WzbsQ0uJ7GugcWLF2LRosUqGe7cuRNDQ4OIjo7H4sWLsHDhQuXf48eLVPxwH94rr7xSzdfTvwSM55xiUlIUVq+6QWFdEwS9ra1NyS4oyMPy5ZcpH+/YsUP5flZ0LBYv4jUXqURWOG5vxsrKlVcoG/JtQkVlLUZHTHzqG6+/HjHx8SqmeF0S4RStPrVt25vo6RuA3W/Dey59j4or4s9u3blT8TLGLRvSx6+9uRHfe/BB/O73j+PGG80+yGtWVpoJilCnN9/8UXWuurkZHFDxecEFF2DFihUq6W18/XX1O+cbP/zhifg5euAQPH4/YuOj8ZEPX4/4xERlQ2uZS2j/4XKenj4u7/IrQJVrr7lWySSQRURkNIzREVx77XXK3hwodu7eieGhEUTHxuIDH3o/slNnqye7/QcP4qUXXkBvfw+2bzOXC+47cAjtrfXw+4k3nh70/SvrXwkWJC1ZvBALF074nnCH8fETccWnqq1btyqdqPfHPvZx1b+5EQHBJgibyHoM9nsSl86pav6QuGL/pg2tHMGYWrx4sdnOP7+g7ErZVi5kPuGyRMomLCxls0Kcg2Rvr0OdF8wdPh92bGNc9auYzc/PVfmQN7CMfRJlX3XVNaqfVFRUoqr8BHwBn6pRYH/g3Dx5eQ4pKyvHzIXDfuzauw2MIxL7H2OWuWP37r3BAlce4z/qXVZRZuaUxHh88OoPmLm9ohLV1ZXK5oS7XLXKzIVbtmxTUJeRY2OYf9HFuOyy5aoPWvZm37z44gvVdbs6W7H34DEMDw0o/1g5pbq6AmUV1WqssNnsuPXWW5SuzFedne3KbumZ2bjuWjOuuOTPory8fHVNxtXe3XsxMDSAOz93p/XzOfOpNeA+/fQTuPnm65GWNje472ZPj7VO1AR2ZzDxzqi+vgFOZz+WLlmiwK/ZYhpDPerHAHF2c/MCeq5/YAD79+/C0qWXIyMjQxVcUAaDncS7bKtQgq8gCErf3NKEy678AJIT45WDiIFLrFJuAhATY0dysrnBQP/gEAoP70d+Xj7mzctHbKypH2VTLvW1sGCHhwlMXoODB/filo9+Cqnpyep3dlTyc6Lf2hjBbM8gDh/erxI59SZOKIlBrJ4GY4DMRBMInn/z6Yx3unNz87DmySewZcPr4N38l++5G9dccYUCDrewSXnN4uJjSErJQEF+XojsTnNPyIBNdQDqT9nk37ZtG1avXq14LT9YNqFeVjvJu3fvboU9e/XVV54qG3b47X6kxJgbDFiyt2x5E9ddex3SrQ0ThobUhg60N6tYLcxbyuamDsTDvex9y4OyCezOt01M6Bb4uiWbAyMHW/p4Qm/63nw9xcHVOs5EQixX3phZ9mZcURaJCYfH+TePc4erxUuWq0GRhTwTceWHzxZAWpwJeM/jSnZ3N5YsXaoGeL7+YXtM3wcQFRWnbM7rcO11YeFBFBTMx5w54/jAI370uLsAn03pSzxd65octJnUr7zyaqUf22PJtvS2Ni/g8cLCY5ibn4t5OXMQHxur2tPX16c2xeBNiwUy7x8ZwfGyCtx0/YfV07m16UKobF7L8j31rqgoU8DxRGyybGiucbTDb/OpgY/n0IZ94wnswx/+UFBvy4b0JfuEJZvXrOCOSHHA4vzFwX5PvclLsmwS6nuVcNl3eM0RP/pd/QrDetmly3Cyu1vZkLKLiwvR09OnBjNLb/Y1xgnlW5sXmP7pB2OWA3xovJGfbSNZmxdYvu/u7sbSpUtDfGzmK1bqxsVNYCkzrjhILb1sKXIysoIFYla/p/xQ2W1q849GXHbZZUHZrMLm0zf7TlRMAlLHt1XkgLj+9fVYvGgpFi5YqG7WLXvTZpRt2ZDHTzp6UVlSouIqNH5UzNrtiImyBXOhaUMzpyxcUBCMTfKaleh2VfBG2zIXOh09OHBoH1Zdt0r5ktemDGI7WytWQn3Pm7yYmDh1kxnaBy3Z1JvFi2wHc+Frr7yGWz5xS7DfM4cT65u/R0XZYGEp85p865gQE4eChQXBmLUwCkL9Y8XV9u3bgw9pytnnyn9ShEhifB4vOm64PR7RKcThlOLMUmBbR4fhEcqmDsQnlVL3yW6xbMp9+eUXjdExIjyHJ/JL9Ha6XMaTf3jcWLp0qTEnJ8e47/6vGYWHZ8ZXpf1oRylJMVIpb//+/Vp4x1JMZ8pWvhfi+pKfekuxq2lraVwRX3rD5vVGU5MMg1U3Zk3fj4rcQ721Yra723C7nSLZVVVVRlpKhtHrcIj4deNKirvMixMbt7tbpgf5Z4rZ1TfeYPz+8SeDbSovPWFs3yrHoyY+sjSudH1P2ZJ+T+V1Ypb8mzdtMmpqqoLtnunLW4kraU6h7dhOWSY0fe9wyWLW5Ro2Xn7lRXF+I4a/wymTTXuxT5yLJH7CPVduEN5JevBui69mXvjzC3ji0ceQX5CPz33uLgVQYd1lv5Pac17Xc9MC3ID+6stXoqSm7h2NpTzZuo8+ugZ/ffUlbNsyNfLUZP7zf5+3wLluAXHRFBvC16F8nSIhvnNvb7deN4c/g3u5SomvbrgfpZRam+WyOUhKYSB5fbaTr3ZCia/Nn3vmOay67jpcc821cDtd2LR9KzZvP4APfPDq4Cut0HOm+k7Z3BNVQtRZumk15VFHtlVKnLOV8vMVEHWXEvWebMPpziWfjmxuExic5JtO6Phxym1ulsMS6sQg+w1fKUuJS8Kk9ra8GBh/BR/uGmyn1N7Ugb6XEvumNEdQ5kyyP/vZT6Pw4GFwv1oSdZHaxJItbaduXPH1KeNcQtSZ/pSSd1jNvUjZtXIh41un/+hATFJuV5e573U45ZmvvBrV7JQttTevraYuwynxd/hda8AtKalQ+1VK9GTHa2+XB5lO8up19KK5WZ7QW7vG51QFirMI5ZlnnxJwmixsp3cc/qy0tBxf+cq9KFi4AE+sXYMv3v1l1NXV4H9//WtwPirg4/yZWSQjuQBlO4Uwk/Zom9aSCRZ+lJbKK3KptzTZcU6Ic7hSqqlpUHM3En7q0N05vmem4ARWelcIlz8xWbS3ywdcncGZe6vq3FRSF6m9vS43Br1exAjR1xhX9JGEqENFRYmEVfF0d/eKcwRPmKk/cE7ylls/gaeefV7Jrq2vxXPPPSfWhXoT0EJC+jFbo2XD7m6zQEqiy6uvv4TS8lIJq+Jp1LhJ1BkUKbyhoUWsB/u8dDAfcPfg0d/+Viyb/UEas6yqfldgKZuT3zIbsSpPB85MBwaSGoh1YWGHxpOcrHUTXNwk+uVXnlfFSjd95HrYjAD++pe/YteePfjinXcFiyR4hl8KdjsuXsd+ZnKWQwfyEjqIfbr+0YHJI69VVDNh2em+zUKEXQ7BZ1OFPdLVmNNdc+rjujbRmUaYFanw6aa+8BRHo+x2aEDqTiFh+kOBgDyudG0CzLxW/3OfuwN/fGqtuvmIChCkVecZIQqj3I1eQPQNK4ClxI3ZpcTN33VkQ4oZbCmgkyiA8RUU1skzf+pAO+rA+bLwT4yNPLOKp/3Khw/x+HDa2Wf3gAYyKYsI5R2PAcwyeCmx+ldKcVGsRJZBRrLenUsZMGZjQW1Yot4JCXEz8nFw49zsM888g7Vr1iAvfwG+et89uP3224MVi1MJ4BNIYqIMgo3nx8bGS1RWlzL1jpnqslMeY8WgPU7Oz+pfXkNC5LNr+DM+MVUsmwiaNo04TE1PBeNFQqygDARkT0SUx6plKdEmOv0hIlK+QYPSIQDx5gWMKx1KSpLHifK9ME6oQ2LizFCkH/jgB9Hf1QUuFaMvuSpBSsnjlb9Sfh3/JLH/CNtJbGQJtKilJyvbuZRNSnFxCVJWxERFISJCjkXOqmMp6ehMmVlZwhxu5UKhvSnbqqKW6v528WkVTfFVVGpSKuzRsgT2djXi7boO5wPXPvMMXnjuORQfO4Z7vvpV3H77p3HJpcvAu9jzdN4Cfw8LENpx5YoVqKmrCy6Z+Hvocbau+a0HH4Q9yo6f/ORnZ+sS5+W+yyzAOgJrmdS51DStUYJrrqSDLZ8CVcGKsLU6RTyUrTMprit78uR8UdFx3HvvvbhoYQFeWLcOd33xTjS1tOBnP/sZ3nvJpeKinLOpN82saxPvkAyFJyhb+OqKftf2vQ60oxA9iHMaBGyh3SV0Nv1zNmWznf6oAHE8RKTbH3TjSmpvKiuR/cUvfQlPPbHWXMevGbNSXZR/zhEo2ndqzNKGYnuzaGpo6LTd0KYLYJ2YpYxzcbClXuIBl1V8OlB2hHYsOi4rymHF2q5du8RVaFzwrLPpsg60I4umnn/+WbUw+7kXXsBHrr8e//gPN2F0ZATrN2ww52bv+lLQofv27NGCdty06XRox+mCjPB+FmLMdDzWcdpww4ZXrT/DfhIpac9+E8UnLDOgihAmbxU43Xn1Da04qgGRqNCPpNCO7e04IqyaZbXniy8+p17/T6dr6HH6nji2UtLpD3w7xBiXEn3PcyTkcnsAt1/tEy3hLyotlUM7jgT0oR0JfiEkbswRjhZcuBB5BQX4wX//AK++Hp7fkqcDR0rf60A7EqJ18o25dd3Jn/SjFNqR/Xj9+hfEm8TzSe5sQztKb54J7dhcK1sRQijXR3//uHgVBlcycBpPQsxTZcfl8KISmWeKR7w9n9c7hq1b3wAht9xul9pKjygzLA5qa25GW3t7EAGFlWpNjY3o7+eG9aNBXsLYVVRWoqm5GUYgoAYtDuSVVSfQ2dmMkRGvmhfh9k6UUVZWDmL+trS2IjYmRs2DsLy+ubkFDgfRayLUFn3Uo765FidKK9DS3Iwhj0eh3/Buq7y8FB0dXAbhVihRlM0gPVZSiJaGZsUfYSMaS7Iqrz906DDWPfsMfvj9/4fa6hp84Z+/iLv++Qt43/tWYnRkFF09fZgz29z2iUsaOjpa1IbO3F6QWxGyPYT3YwfmPyJQces+3iQ01jeiu+ckRke9yMzMVig9hJWrrq1FR3s7mlubMT93vvItZbNidnjYi9CtC6eyN9tTXVOOzq5uGAHqkayuadmbsombfEFenpLNUv/OzhZ4PNzmcGLLON480H70pbVVGZMKqz37+vpVAQrnl/iPNwIlZWXKl5RPlCj6gUtfWtpb4Rroh8c7gpzsbHVNJhyij/H1J2dJqSNlU0faMOA3FEQm57qoa1VlpfqkbMuG9H1jUz36u7sxFohQ2wVSeGlpKSqrq1UcWr6kbNqEVbOsVOX2aPQPfVJRURGUbaH2sEqecTU46ITXO6y20TPbQ4i7CuUfbk6fkZ6ufMxlIZRNf1tbrzGxlpSUBGVbNlR6Nzahr68Ho6N+1R7Kbm5sxInKSvXpHBgAt6Yz23McXV3dyj6REZFITjFtdezYMcVL/wT8fqSkpqq4Kq84gVf+8iJWfYQ7SSUjKirmFBs6+vqCSG1MXN3tLfCMmFXK3BKT/WTPvn1BX/r8fqSlpqKnvw/1NRXo6OoF1LZu8cpH7JvFxceVL4n6RnQrEuOqo6MTg4P9GB0bQ2aGOT/LmGWfpy+JsJSVmRn0fXdXq+rHhA1lXIXakOcwZm32CLS1tOGNNzbg6quuUPCb1jaUhItlvJDXNW5DK65OnuzA2JgP9qg4JMTHnWKT0JhVvm9tw0lHN/zekeBWhFbfpL2NcXvT34yfzs4OjIx4VAESUZVCfUl+oluxTZbvHY4ejI1FICsjHYiIQAXhS+vr1XljfiA1zcwd1TUn0NXVi0BgDNHRUSpmrVxo5RTWU7Cf8HhjYxO6u7tUXFn9nvmkprpayR7x+dT2evRxFfNs+0m4h0xEvtTUFDMXFhaqPs82WP2HfiB2cU9PN0b93N7U3BovtJ2uvgFkzM5W/Zm+b29vg3PIDUQYSEtNU32DMJ2W7624Uvmqsgr9/Sdht0erttD3bF9xSclpuZAx29HRgaEhrnywB7dlDY0rqx8z/7S3tKKqphyX8O3jOUbiJ1xgVFWVcVCoq2sIFgywCpRvsmhMax6T8GutrY3o6RkAl3xYxQV0Oi8YZZsAWucxJl2ny4fq+lYF3aZsFLCrdVoEouY/a5Pl1tYuNDc3w+n0oKqqXDmV/ARvpx7q5aFtvChgzIbK+lq4et1obG4PymayC3gD8Adsip+vK5544gl88rbb8K//8i9IiE/Gt/79m9i8fSu++MUvIi4qDl6PuVtF6JbWvHlwO7xKn9bWiWVKlMd/tIlFTocL1bXV8Hp9qKyuD+rN14G0ibJNYGJunDZxudwK87i1dWI9s+Ilf8gaNqfLiYrKRvj9AVRWVEy8prNk+3ywTaiChoYmOJ1+BdHWWDuxdIssPl9AybaKDliKX11dD7fbqzog22URdaFc6mL5mHZob21VA3RLU5PFCt/4aRwoLLuwzUxe1Luxuj64nETFB3Uebyf5SJ2dXait74TT5Va+t4Qr26kYNO3I41yqVV3dqDBi29vbg7i1fO/q95pxGNoWxizjijFLDGLrmpZstpH6kDiA0z/EDa6tZ5z3jf9i+TGg4sU6aOrdCLfHi/ra6qDvrX7D1oUuX6lViW5cn/4J2SoGx/ua9fbY2edEc3MjAn6b2v2J/iNZfcy04YTPmppa0NXrRnNzF1rH18mz3ypfjtvbaqfP41Wx6veZfrKWZfjHr0FoQl9IHCrZXV3o6elHU93EchJVKT4e49Hj+0bT9vS9z2dTMaue0plOxyElrXMsG15z7TVobGxHS3snqk5MLJmxfMmSS8tnlmyvN4Da2ka4nOaSnNC48vk9sAqYVU5pbIS7z4Xa6on1/ZbvGbOWvS3ZbHdjYyec47JDfRkaV/3jMcIcVF5VCv940XQgIkL1AzOyzf9VXFVXw+MNqPWsjBsSq3kZf5QbKptxZ/Ybt8otVvtNn/tUbrOOUQ7zNh8YmE84WFvEq7NPsg0Wf09fD+rrQ/u9qeMp7YTZjyhH+b6/X90Ato8v2VQx5Tdfo1q2JC/jiLI5eFL/YFyNjw9sK31lkRlXXNtPnSaecq0YoU2s/MMlUszLZ6sC2hJzzu0AACAASURBVNLpLX9K4a+Gh4eNxx//vRhWr6qmzjh6tEgq3ti0abOChZOcQLix7dvlEG87d++cElavsLjQ+PbXHjBy5uUYH/zgB43HH3/cKCkpMX7/+9+JIeG2bt86peyp2kHYuw0b3pjqpymP7d6939CB1Vv/4itTypnq4BtvvGFs3iy34fN/+pNhCOEua2pqjIMHD0512SmP/eUvfzF6hZBwhEfcvX//lHImHyQ855NPPmmcOHFi8k9T/k1bE/JSSlu3bjV6hRCW1Hvz5k1S0cbevfuNjo4WEX9VVbmRkpMm1uXw4YPiuBodGTFeeukvIj3IVFRUZBQdOy7mJ4yqlL70hX82Pnv7p6Xsxp/+9LzBvCUhQkzSLlJ69dU3xPmKvt+5c6dUtPHsH/5glJQcE/F3OBhX20W8ZNq/f6/Y906Hy1i//hVxLiwpKTYaquQwqv/7v78W27CwsNBgXpHS+pfXS1nfVj7xK2XeQVx22eXi8vZIG1/j8VWtrPTbMPxISUlVr33D3T3wLis+Ll69tgnHy98jbZEK7J2vePg64/XXX8d9X78PD//iEczNn4PH1vwe33rwWwpcnMuT4uLi1es9PgmHo0j7LCQnJanXR+F4+XtU1MQr3HD8vHxcXJzY5mN2IGv8NV5Y2QTAz0hGRpq5yUM4fntkJFLT0tRr43C8tFpCYqJWxWxmWrp6DR5ONp824qJj1WvWcLw2w1Cv7/i6W7osIzE+HolJSeFEq98NIwIpKfHqFa7khNjYic0PwvFT9fjEJDWVEo53cGAQzzy+Fv/2b19HTGz4JTw2W2Rw+iec7IA/AgFwcwpzGiUcP39PSIwX+96IsCMrM0MiFlExsXjk0Udxzz33iGIlMtLctEHSj/nEGc2+nCLLV1xzmpmZJdKDjWM/5ivfcMTcZkREYM6ceaKYtcOOyEhDTYGEk83f7fZZYt+PzQKiIqODUzfh5DOuomLNV8TheLnuPjLajty580Q2HBsbRUJCosgmvPZ73vse9cQuX+QXTuMz87vWsqAzc8m3XwpfZ3B+4Fc//xX+8spLyM3Lw333fw03j29l9vZrdP6K5y1w5ixALOUrl61AWUPTuwpLeSoLLVt2qVoeZG2hNxXP+WPnLXCuWiD8I1yI5q+9vlG9ow85NO1XTrpb2ydNyxTyA+fPpMSnVA6g4YgFDk88sRY33XADVl6+ElHxUXh10xs4cOQQPnfHHcFK41A51JlVs1JiO3kdCZFPWmlHeZTNAhAJ8aaC84pS4h6TOti+lG3N74S7BnWm7lKiTaQ2pA46sl9/801RrFBXym3lvJlw+ZMkBi0bcAtKacU5z2EcSu3t9XgxTOCL4EyjddWpP9lOHXtLN/7m1dg32VYpcQ9UKdHeV7z/avzy5z8XnaITs7SHTlzpxqxOLuQKAh0YUJ04pB467dSJWcqVymac/Pmll0R+JBPl6uRCbs14LpLWgNvZ3nzKpP1MDWKhirXZ/Ex81m86A1F3d8eMAxeXpHz3W9/B/Pnz8dxz67Bk2TLUddThl7/8JS5fsSJY/GJdO/STE/A6nYPFBxaWcqicqb6Tr6joyFQ/TXmMsp0uGSYxC19mAoKffAHuKTs4KE+MlC0dAFgEwb1FpcQlMKHFIDOdx8QYWvAxEy9/6+/pFMtmzLY21pr7DYcTDIwXfggYATgdDlV0JuM2N8WQ2lvKZ12b7bQKVaxj031SNv0jJfZ5tlVKR49OFECFO8ftcWPhe9+DsrIKlFaWh2NX/UF6Y8F9WGkXKXEJDPGxJUQbdnSclLAqHg4uQ0PyvhlaSBTuItyrmtX1UqrUwHTu7GzFyZMy2comTW1SNVSfl8YshbJw71wkrQFXB9qR8486+KGC6dKg/exTYLvyjumll17Ctddcg3/8yEfQOdCFfXv3qrWPn/70p5E8y9wcPijkjH4xK/jCiSQymd8vNzkftCbqlmeWzrkf4YNZUJBMa5NdVzbnXKQ0axZxt9kCGRl+OY6tn/i7GqDRZr2uTA+d/kCJOvwa5jDxhUPL0MOor9PXRs1a8TAS/5afZ8ZSniw5KyMDt33qVjy79unJP03xtzymGH+s8ZBSpAbWNetfdHLhjE8EUygojhUy2u3QwTkPRMgxvSMjY7VkI3y5QbC14jYyD6qz9OIqeKGz/EWaz5UaS5cuFxcq0UDcwEBKOmXcflsgWAbONWe/eugXePUvbyBvYS7u/+rXsOoGrkdMDV6aCYbl+HaBOlw/t3z58uC54b7otJF3dRpwoGpJi3RQ1Bmw2KZFixYhKU5WHER+HRBz8kdECIw9blwT9Fx6IzILETb5YH7Z8qVISZMX/OiA4+sM5GyqDr/O5gVRMXbEwh6ySGPcsNN8MGYZixKyjY6cVVxaa/mZRJe0tCwsWbIEV1xxDa64fBn+8wc/mLE4SyencFAcGZFvXmAY8hhU/V6I5007LFq4CNnZsyUmUTySorBxRnDxj07O0un3OpsXcN3s+y97v7iNOozcyGPZspU6p7xtvO/Ioim+y3/x5Zfxp3XrUF5Whjvv+hI+cfutuOLyK942w52/0HkLnCsW4Bze1StXorimCukam2OcK/q/FT2uv+kjuHH1DXjggQfeyunnzzlvgb+LBaSPFeqOmK9tpXfG5JPysuXh5vAoq+j4cXz/e9/DxRdeiLVr1uITn/kMGlpa8PNf/mzGwVZnQ2e2UafYIpzeoV5lG3T4qfeZtGGoLkzS9Rr7aOroTZ3Plt46sslbWV6N/hDwiFAbTP6uI5vnct9NKVG2Dr+OvT1+P0Z8ftj9sleoZzOutG0YAqQSzpasraivr1Zs9/7rv+K5detmjDMdG55NvXVlE8Wsp2sC8GQmuxAKkvKlpKVLIKCVr3Rkc269rKxMXLxHYA62VULk09ncXiLzTPGIB1wa6OWXXxRXoTGhl5QIMVUDAezat09VOE5umKpme+EFXHvtdbjlIzfB0d+HdX/+M37ysx/jnrvvnnE7PEvWkcJ96OwyUVusY9N9shBCB/P2yJEj4iIr2pAViFIqOnZAXGHLYN+yZYtUtAr2Ro0K0Q1vvCHu2KxsLCqSF9ps27gNfcICrs6uThByT0oHDu9Dd7esYIUJXYp5y+sfOCzH0e7r68Oew/ukaiv7iYv3fJ4gUpDkApVVJeK44qBFSEUpMYnqVMvrxGxjYy2Ki81K/I997OPweHzYtm3btKq9/vpG8YDR2tyuFbPsx8xNEmIRFPOEhNiPjx4tQmdX+FUYlNfnJUb3HoloxcO+I61q7h8cwp5dO4LIcOEuQnhHqWzG1Y4d28T+qSgrQ23TBMrUjLpEBrDlTflKkxllneEfxcAXhDIrLy9D/4ALzv4BzJkzW8HRvb5xAxpq61FTX4uM9Aw1ANZWV6LiRC0cji44nf1qcTPxQw8dOYSqiipU1VbAP+pXC8f5enjvvgNwOvrR0dEM7u3IBeL7Du3D/V+7H9/9znew79AhfPNb38QvfvkLvPeSxXD09qO3twv9/U7MnTtXgTFUVpThWFEx6urqMDQ0jJycbDVAbNu2RXWM7u4eVRTBOVp2gL27d6OmsVZBvy24qECZlYmCcHOcdu/p6VWyObfD5TOHC4+guqYWvT09QezYbTt2oburTcEGjhE7NjNTBRBL0hsbG1BZWaUqpSmDgVhYeBgDAy5VDTlv3jw1D83B6eDB/aitrVHnFBRcpHThsp2u7i509/bBMzQUxMIlaEddQx3q6xqRnJykFoKzPfv374fL5VKY1GlpsxEbSxzXVhym7IZG1NRWY8FFC5TsA4cOoetkBzzDwxga8mLevLnq+MY3N6C+xvRlTHSM8oNlq9HRMbS0NCIjI1P5mHfhhceOorGuEdV11ci/IF/5gQNWQ0MjBgc9IH5s7jg2NDtXZeUJ1Na3wBYxhrS0dAz092Hb7l0Y8jjR1dGF5MREBZhRXV2LoqOHUVlThab6ZmRlZynflZWVoLaqAV3d3eh1dOKCvAuV3ocOHEJpZSlqK6sV0EV6erpaQrB//14MDXsx4HQjJiZaLQML2ru+DrU11QpshaAYvGZ5eQkGBgbQ3d2HeXNmwxYZqSpdS48XKV3G/IGgjwkYz0pIxmEAkchIT1M3Xvv37lV9gbESa49Bcmoy6mvrUXy8EB63B21tLZg71/R9bdUJFBYVK9/0O/rUcTZI+b7rpMIlHhszFPBA/8Ag9u7ajsqaajTU1sCwRSI9LU35eO/+g9i4cQOWL1+hAFuIS8vkR//UNzSipbkR+fmmreiH9vZO8AaAfZr4zYTS27h5Mxpqq1FTX4eM9BwVPxzwGZsej3fKmGWM19Y24KLx/rNv3wG0tTXC6XTD5eoPtufNN99EXU0V6mprEJ+UjMSEBNUnd+/erWKW1cH0mYWlvHv3ToW7ze0GF1xk9gduKtHc2oER76CKrfnzcxEdZcdPf/JzXJifq/wTaY9BWmqK8v3OnTsxNORW1a0xMbFB7O7tW7eidrz/MO7ZN9nvK6vKFRxpZ1cPLsy/QMUVfVxReUL1+1l2u4ofa6Do63Mq3wMRJlbxSABvbtuExrpaVNbVInM8F1bX1qO8rBQOh0PpMn9uvsKGPlB0BBUlZaipqQICkUjPSFMD2949e9TqAUKpAoaKN6sfm/2hFTGJkUhKSFF5qfxIGRwDDpXTCPDC9pSUVeB48RHU1TUpP8yePUflwl27dqC3tw9dXV2YFRmJtPR0dR77SXVlFerrakAgH+60w35SXFSIfqcLJzs7VZywqEzlwsPERSeGc2ewf9NWrMQmdOSob1gBpXA3si07tqBa9eN6+A1bsJ8UFhYrvGiHozeYUyj7YOERlT+IM31RgZmXDx06goaWWrj6XBgIiavXN25EXW21ipVh9zCyc7Kh+sme7XC5htR8v3LkOfSfRtHULPh8XixcsMAEXx9vxOLF49vT2WwgqDYpZ848DA4Nw+V0YsGChQiMY7UW5C9QGx+wcihhfGNjdrLFixepJ4t58/KwceNreHH9aygvKsXn7vgM7ln3DBYuXBQc5HiNgJ9FU8CCBQuCxVM58+YjZnwjZksPBt/y5ZeBoO95eXnIyMpS+nHCfuGiRebyj5DytwsuuEC94qioqFRFRTyflJGRBXtUjCoDtmTz+NIli3HsmA95ebnIyTELc3jOosVLgiXDEzIysGDBYrURwNKlS4N68wZA8bOKNaR8lEVNPp8faSlJyM/PV3rwv8WLFwf1ZjtI7CCUuW/fPixZchkSE2PVccpesGhxUBd1kEUZCxYqrNbE2GgUFEzIXrRowpc8l5SQkIqly5erHUmWLH4/EuPMam/6WNnbst+YTZVU0982eww8bicW8drjtGDhIvMJORAIFt7FJybjsqXLcfDgQSxmEdf4NbOyMhAVExXUmzFCuuCCC0F0p95eBxaHyM7Lz0O2b7bit/TmOYwbJpeL5l+gYpYyMtLSgvbm35Y/58zJwdDQIBwOJxYuXABbFNF5oW66klNTlWzL3vTpkiVL1Q0U25uTY8YVr23FFSMnIc0sSsvKyYLPv0gtI+J5wZiYPRf26FjlT24MbpHl+7lzZ4M3ZqTE+FjQhopsNqSMo2FxY4cFBfmIskWp3wkyT5o9Nxex8YlKb3uIbF6/rKIMKSlpQdn8XcUVTwwEkBhn6pKSkql8eOxYsYqvoN4ZGaZvGa+W/wFlN4rg4fx8M1ny74ULF5oHbTYkJZg5gnoyZpmo+Wn5gTYO7T88n7RgQQG8Xjd6egLB63zq9k+rG/KhsTFcfsmlCk2OvEQLY+EjBxi2lzYiMSYWLVmivlNvqz3su8OjI3A7T43ZAuYu4riHxGxUTIySyd3KTN+P9/tomyp2Uo0Piat5czIAbwGaO9uVje3R5kvFhXPz4U7NVBW1CeO+ZLHPksWL1aCVk5MRzCnBfkzNAwEkxaWpNuTkzFEbvnGgYjGZPcL02/w5OUhKMDeOnxyzFWUVSEpJQtZ4vuLvwbgCgnFFm/BpmzcjjA2rD06XCxctWgquqSai1rx55gYs3MqVBWCWTayYVe1ZkI/OzkZlw5gYM2YzsnIQExWj7G35hg3lmOP1ehAXk4D8fHMDFh5fsmiRGltoE6vfs58sXXqZ1g5Kyphv139SIEliqu7evdNwuVyiU7q7u42mpvBYsKOjo0Z5SYnx2c9/3shISTGufP/Vxu9+9/sZ8Tt7HQ6jSgNXs6aqTqw3cZqJwUq9JER8T5fTKWE1PB6PUVoqx5klti9xWKV0/HiplFX5cvfu3WL+o8eLxFjKJ0+eNBrqGsSyib/r8cjs7eh1Gg0NMrxW+vBPL74oxo7t7u3V0vvEiRpxXFHvqio5Fix97xDiNJefqDLS0lLEuLTEDe7u6Bb5h3jUxYUyXF8KZP/hPymVlspj9tixQoMY4KH0ox/8wLj7//vX0EPB78Ryl/ZjR7dDHCe8APVmf5aQ0+XSkk1scSluMPOxTlzVNdQZ3Sd7JWobw+4Rg/jIUmKuOnlSFlfDbrfx+B+eFPcfjiUcU6RE7OVzkf5uVcrDQ0N45ZVXsGbNGlRXVuPOu+7El778ZSxYuPCUJ72368bDuo6amI+cuPu1jp//fIdagLtZjb9heYe2IKza3PLw6ssvR0lN3bse2pH903pKpGH4OvqSSy5R86+hT9VhjXYOM/DJMvQJ7xxW9W9STfmSy3xD3uz9TQLfASeLi6bYFu5LKIVt49zfVEUfpeXHce+99+Kiiy7C2qfW4Z6vfhVVTXX42v33m69xBcZnsYJ0cp56Uw81kAocws6sE+xsJ4uhJEQ+HSg7ytaBM9MpVpHoG8pD2UwEEqLO1F1KujB5OrLZmaVBTrlTxex07dCJwf6B/rMG7Uj9uKnD2YJ21IkrnZil3jqyyR862PJv1nDcfMuteOzRJ/jnKaQTs+ybOnHFmNXpmzpxpZN/2GCdOKQeOu3kXK6UKFdHtvKlIN/z+pSrY2/duJK28W/lk+YidZ3Dh4+JYdsIv8fNl0kcINetW4fVq1fjpn/4R9hgx4Zdm7FjxxbcQUzjxGRUElJPSISP04EzI06zTQiYwgBbu3atUBMTgk+6/IB8JSXmsgbJBbSgHe12LdhIvl3QqcjVhXbUgV9kRbPUhkyMne2yCk7a+KmnnhIndeqsg2HLjcul5HQ4tbCrqYv0BsftcmFIuCSI+upCO+rAkRIylP+kpFNxziT61DPrThP9/e99F+ueWXta1XBR0XHxzTDjTwfasaKyWgses1VjCd5zzz2nHm5Oa+g0BziHK6XGxmYt2NXSswTtyAH0oYcekqqtDe2oA3MrVuIMMGoNuDpIOaylqKiuD66bXbPmMdx5111or2/Ew4/8GisWXnqK+rbxTa1POTjNH0Q/0UGR4SOOb1j2dMZLylZ7hSonqz3jnevYmOxpWOmhAe1oJmeZHpbmtoDc/bpIVjpoNjrIR8Ass1DCakSYT6LwSNGjqEdAAyJRDrwZRsmpftbwjZ3wlVF+ceAKHypCtJoo6Ao5eEa+ilGSeDXW5U3hHxbVXLvqWvzmV785RScdlKRTThT8EaGBNEVxs2KFd/wKAlSvH8Mm52d868CuRmpCOxqGHK1LYOYgC8cTomRJye+Xr5EPlcmHQ+kby9DzpN/lGVeIBTswNIzHHluDL3zh8/jWv92rSt33HDiAXdv34a4771RYnlMpp5MEmEB1+OmnmFh5UGoZRTVGNpibg6JcOtsok2zNg8hlU22bVh71A6xEFpIOXit5xa/RZtkQ8ImtogbbOKHaSo+APE40vKOspgNjGNBILj47QS+i1IAkdI+cbYys8uQVUrQsuoZOYowK2EFs7Kno/vu/icfWrDnltWMgoBEngYBWTmG1vJQY2yPD8oGIeULLjhrtjIJWp9eCdNXCi1bjibBjjhvaLp4c4rSwXjstX/7nf/4nrr7yShw5WnRKBb71+9/8qVPJxepGt9s95SkHDx82vvrVrxpzsrKMG6//iPHHZ582TmpUlUkr53hxVuZ1dzum1GOqgw5Ht8FqSwm53ayClVfYUhdpJST5dCo4KVtaCcm2dbS1SZqoeJpa2gyHsLqaJ7R0yGVTZ+ouJVY3SttJGzocct+3tTWJdaFcHdmsapYS26dTca4TV4zXuRkZ4nbqxJWKWY24omwd37doyp6p/9xw42rj1w/9KugSytbpmzr9QSdmjbExw+GUxyxl69hQLxc6tPq9bsxKbcj+oJtnpTmCAdCmUSkfDBjDMHp7e437H7jfiLLbjfvuu0+8UiBUxkzf/6YqZb6H536j69auVVuPffKTn8Td992DxQsn1l/+zXcE5wWct8B5C8xoAW5Av3LFSpyoqUFq8tncFWtGNf7uP+7bswe33fUZ1ByvQmJy8t9dn/MKvHMtcOTQIfzrvV+By+nCw7/+NW7+6EfPSGPEz/R8r80iG77jPl5aiq//29dxycUXY+1ja3D33XejpqEBDz/ySHCwHejph06hAJFxpO/OqYNOwQoLYaQVbo3NzarQhug7EmLBglQ228d2SoltFGOq+v3KL1LZ27btwLZtu6TsqohDWsTDGzGrYE5yAQKN6PheKpv6PvXMMzPunRyqnxlXZqFf6PHpvuv4njGiV9xSL44rIlix6CcgnLdqbG09rcBoujbShlydICWiWOlU5OrIZv557bX106pyzbXXYkHuQrz4pxcVD2VLY7a/r08vZiur5TE7OCDOV9T3z39+AewTEnorccU4l5CVr6QrPFjoR6QpCfX3D+Kxxx4VxyH7PPOKhHRjdiqZK6+4Avv37sfn//kL+ORtt+G2227TiuupZPLY1BMiU3Bz89//+u//RmtzF6ory5CXn48v3v1lhfjDwWn9i2aQ81Svz4+uvj54PC7k5y1AzAxXYXGl3+dFRW0tCubNU9B+LAKwc/6SRUOTPhHwo9fVj672boVgw/kRi0c1aJzfagJl1zbWY3ZGFlKIGDReYDDVOXSUs68HJ2qr4fP6FPrNVHzWddjO2vpazM7ICMq2+Cd/Um+3x6uqq4mqpJCrLCWn+KTeTIwJcXHIzJ6r2jgFm3koYG4WUFJZiaVC2ZW1tWA5UXNjPWKiODdmirL05l/8zjaSisuKsWThUsSMoxBN5rPOZzubO7vg93qQl5ev5man5YXp+2NlZVh80UVISJ7YUnGqc5R/BvrR19uLgoIJlDFT89P/pw0Li4rQ3tqK3Nmzg74/nVOtq0FnT49CG8ovWBC0iaXH5E8zrhoxNysLSXyamiGuVMz296Oz4yQWLVwg9n1qQgJS0jNnnt+mvbs6Va3E888+g6SkdNU8S1/+EfqdNmxsrkdiTBwysk0owCntwYMBv/I/8ZGXL10S1DtUXuh3ym5ub0Q07MiZmxu04WQdrHNow5KKSiwlShJv/WewoaW3c2BQ3YRO1e95nSsuX4Hv/fj7am1nYXExli9eFESgm1YPvx89fT1wOd0oyM9V7bR0nHwO/6beFZWVyGO+Sk4N6x8nfd/dqxDBJP3+cNFx1FZW4tCBvBltyL7pHRpEY0ubPK7aW5Eal4CMzMwZ7a3yFW8SW5qwaOFihCKh0QaTif4hznm0LYCs7LlKtmXDyZ+U7fIO4eihQgRGRoP93uKj7NDv5K+tb0RiXEwwZkN/D/3Oc1W/LynDB97/vmBem6xvuL8pk1QwNxfffOAB/Pa3j+LSSy7Fmt//Dp+47bZwp0/7u/iVcmtzMy666GJcs+papCQkzLiZNgsh3B4fDAwgPiYTUSHQclNpQkxXDtCpifGIi0uasXjBkj0yMozU5GSR7L6+fgV3KJHt9QXQ09+F2enpiIkxoROn0pnHqHdPfw+S4xPD6s0iCI/Pjb6eAczOntkmLFAlpFyfswf2yBikJqcqnOKp9CCvLWDq0t7TiVyVRKcvGLBk9/QPIMpuQ2J8osiGlC2xCf0zMDioVKVse0yU0m8q3S0bWr5PSJh5f17L9yxukuhNKMDOvj5kJqYjLiEGthmqOS3Zw6PDyExOnjG+Lb3p+9TEdNij7CAs33RE2T5fAP2DfchMlfme/iH05kwxqwqZ/UBfXw+I4bz6htWYyYam773g04XNbkNqcvqMfY0x6/O50SWIWbad7ezvH1CyiYttt08fh5YNiV3M/kDemQohLdm+gO8UG1rxz0JKK/EWHyvEyOiYWqObnckckRBWNvOVFVeEmZypKt/KV+kcbGNsClZzOt/Thm6PC0PDI0gX5iv2NcZVQlzUjDakLfzegML/Tk9PFfXjvgGz30t8L81Xli+JQz4rOjas3pZN3ty4BTfffMOMMTs5rqQ5pae/HbOzC9RDxXS+mem4KswdL1z0+n1487XX1U3tt//j2/jZj38206kz/zbTBG/ob4RTTElJMcrLT4QenvZ7Q1OTcfxY+bS/T/5h+/bt4oIVTuTv3793sohp/z548KC4gIsT+b/73e/EMIb79+8XQ465XS5j69at0+o5+YfDh49qFVm9seFU2LvJ8kL/3rx5k7F5s1yXTa++YcjKzgxVDKEDM0m4PmmRCH1/+JgMapD6Pvnkk8YJIaQiC3KOaUDC7d27XxVZhNp1uu/UWwdKc//hw8bJk7JCtaqqciMtLUPcf44WHRfH1cjo6GlwitO1kcdPlJwwyiuqZmI55bdNm+Uxy35M2MNwtHvnTqPgwguNV1991RgeHg7Hrn6nf1j4KaVNmzeJIV1ZPFp4+KBUtPH000+L8yyL/LZrQLSWF5UaDS1NIl1c7hFj69ZN4lx44sQJcSEU+1pSQoIhLZo7fvy4WDYbt+Gvm0RtDMd0rKzYuPrqq42ceXOMZ599Phx72N8RlmOcgQlxzpz5Rl2dsDONjYkrBHkJaTWhpe+oV5r+9WSznRUVZYZUPvWWa2IYTGBSGqMNz1I7iU06U8XnZB2HR0YmH5r+b13f68jWiBXajjizTmlV8zmiNw2r4/e6JrNKudc19QqCyY5SfU1Ytc9zdXzPvqDTPBqThAAAIABJREFUl4nRLiUOinVCjO4bb7zR+Pdvf1sq2lzFoGETnTZSiRGNfsyY7e09KdddI6fo+l7HPzo2oS9TUtKMk92ydurG1bCGTaYyNCui//3b3zTi4hKMu//lX8Q3s1PJCj0mfqXMyfnFF1+M3QcOnLJ7zczPz+d/PW+B8xY42xYglvLlV61AXWkdEv8PVymH2vnQkQP45Mc+ifITJ9RuWqG/nf/+97cAC6Auee97UcXKetbWnEPE7SQffPBBBa70yCO/xqpVq86YduIqZcyKxggCYgi+1uZGNLa2ixWVVuVRIKsguR+rlGrr68WLmBkI3I9USqyeGxzk3pXhiRs27DtyIDzjOAdlSysKuVJ+zwH5BufcEFta7Ut19h3YJ6/4VFjX8mpfVp8ODg2J7MLKSZ3q9z2H9qCrSxaHLFIjRq6UTlTLIfUYV9zPV0q1jY1ie6sKZZdPDHxhxqw5zx5OH5/fj0MH9GJWWk3Ka3NvZimx3x8Q6nLFyqswNy8Xv/3NYyLxfKDQ6Q9Hjx4R900WFNU3y2FA2UZWe0tJKxfWVqO1Uyg7EMDRoiKpGsp+Ur0ZV16vbCUIFdDJhbS3TsyGNvBXv/oVPnPHbbjllk/g2LHDZ3Sw5XXkA+7oCKJhw/CwrKO63F50aWDeSpMilXY4XeLyc/J39XWJEZtYja2TdDkg+v0yuEavz4eOpo5Q/874nbLdHs+MPNaP/lGgs1WOMdzW1oaeni7r9LCfHOQYyBLiAOByyfSmPC7bki7D8kdEoqdPmDCIG1zdquJFovdAX5946QHldUsTF6Bwd7u6ZEsmKNvjdIrtDW8AfqusUtBQxhV9JCFuilCvgXPudnvEGMO8fmO9/KaFfZMbukvpjs/cgYd+81PR4MXYZnGllDo6usU25M1wT7vc99yMoK9P3jdZeCalvr4B9Ev7vc2G7pMnpaJVn5fmFB+XsLF6Skj0jTRmKZLLO98Kcc9t3gT+5Cf/L7gHMOXwRn/bti149NFH1b7jluwd27Zhzdo1Yt3EAy6rtkYVguDMlYeWIqz4m6nq0OJ7K5+srpWuOaR8uyrPlDtXX6fpK1QnyzI0MFg14pEQwzrxO1mtM/43/S+lWbOixUCGtlHCQMpikNf3iW+1AOohBiRWfUHaQpNPB4t8zFCYiqILBOw+LZRJhRktkmwxye1tnSH/lMvmoDgVlvJ018rISMOq1TfgoV/8dDqW4HGfzQcd/G+d+OYG9tHxcizloFLCL7p5ViuviHsmVJW3ji7BpYTCdkrZmOl1+lqo3I9//GNBLInQ47NmzcLsuXnYsW2X2u2Ov3FDnptuuglf/8rXxWt0xSMF12ySbFGyU9JTM+HVsGg210kKKSUlBf4R2dMWRap1rELZCQkJWLBggZAbSM2cjZgo2X1LbEy8WpsqFZ6ZmY24GFlCsttsKCjIl4pW8/BJSWka/AUzrzcMkcRlFenp2SFHZv6an58vXhAeOWuWlmz6UtrOpKQ4RGkM5rNnz525YSG/JiQlYbZGjGdynaQQuzoqKs5cwiq8p2Q748Is1QtRHQsWyOOKfVOMiw0gf0FB6KVm/J6RkYHcPHnfXFCwCP/781W4auUKfP6ee7Bs4aJp5SfZU+FLkT31UwiXSDLOJWSPiEJK0sxL3kLl5BcUaM1rZmr0tWy1BEuWr6hTTq7c98z5fuFLU7WOWmY+ZRqVZ4W5kEv0Cgqm93WoraXfqe/iRQvxy//9GS688CLs2LFDvQntdThQXFwsrmvSKppa8p73YveuPciTdkDeSunc8khbfy7x/V9o47lk7/O6nGYBFk1duWwZyhqa3vUb0J/WeMGBb3zjG2hursdfXvrruz8fCexxLrBwnv8973kv6uqERVPnUJ6dO3s2cvPysHXrViQm6kGpym91AIzY/PATZUFAfP3DVylS0nk/r2QL5xN5fSVbqAuLJ7gnLq8hIc7LSt/lUqZOO8kr1YPwazqyWYDS3imfJ9KR/Zb8IzG2AlcwUbUk7Iw/Jlr6VEJnVe+RgNiX1JVFJdL+4/H5MEZQDyG0o3dYbkP2YB3fsz9IY5bt1JHNJK0DG2nJ/tGPfoQDR45iz67piwrPqu/pS2E+ob2Zf85azOr4J6CXU7RsGAiA9QFSu7AvSHl140qSG0J5Vt9wA+Li4rQHW8oQD7hsrNftFVeWNbe2o6JCVpVJ2QcOHRBX/fV0deHAEXl1Izc47+ySDS7cPHvLljchxQ89evSQQskKdch03znxvmePHL/4eHkpWptlFbacw922Y8d0lz7teHFxCSpLZP7hyZs2bxYHPFHJisvKTrvmdAf4ekZajc2EK9603O9XeNEtbbJCNS3ZAA4dOSIusupzdmLfPnm17/GiIjDOJRTgjZnPOyM6UqicyqoScVz5vF5s2bIl9PQZvzfW1oIbxUtp2443payora0ENyiQ0ubNm9SAzqeQH37vh3jwW1/H8DRbO9L3ZcflMcuVDNKY7ervxFFu9yYhrjbYs0eMvdw31GfGlfCBorKiTHzTwpUDzFfSga6mpgos+JIQ0Zu4faJ1UxTuHG4o38jVJgJiAeaWHdsEnPos9Hl1dbXCupbeFIVeJfKHP/zhD0MPTPedhtm4ZSMuvmgBCKs4e/YcxUqHNDc3qX9JScmqsoug+3W1tejr68PgkAdzxueuCCZeXV2leAMBQ81TUGm+A+862YWBgX7ExMSqO4f2znYcLy5Ca2sHmprqkZd3gbreidpaNDU0oKfrJIaHPEjLzgbnL2urK1FxokLJ9niGwTkwBsqhQ4fQ3d2D/oF+2GfFICU5SXWUw4cPo6XF1NuSzTtLVkGO+b1wDw1ibu582CIiVPCXlZUq2X19juBcHGVzIB/od2FszI/09HQVQAcO7FO8tEt2do6a02KHLikpVtB3hOKzjjc3t6K0tFjxs63z5+eqdnKpTFdnJ3oHejE2Oqbawx8sezc2NiE52bQ3g+DY0UMYcLrQ29uNtLR0REdHo7OzR12zqakB5L/gAtOG6gakpxP0gcfjPsWX5Gtr68CsWXblB8ouLDyMAWc/nM7+oGxWFpeXlyi5tGNu3gXgDqHHS4+jubkNA/2s4vQjJ8ecyzVt0qZ8GQiMITU1Td3FHz58EH19vXC7hxEdHaWuyfix7B1qw8rqStTX1So9BofcmDMeg2xPbW2NsiEQiZSUZAx4h1BUWIzBIRcxBzErKkrZiwmBfrDiKjRmK2tr0N/ngNPRi5y585TvueSisvKE4h8Z8SA9PUPFFZdVdXechGvQCZttlromn8COHStUvC0tzYiIiFDXpI8rq+vQ7+iGwzGArCwTH5ntrKioUjZxOgeDtmJybm9vQ38/K1sNZXP2k4MHDyrfsD9YNuSgfOjwYax/bT2uuupqZGdnK9+H2rCrq1vBHDJ+jhw6grb2dvS5exEZMJA23p59+5jkTd+npqYoGZRdfPw4HA6H0sWKWcuGVr+3+g9vhJqaG+FyDWJ4eCTYHitmyR8XE4v4hAQMDPThyJEi9DvcqiLX8gM3ESg8eiQYV5bsiooKtLe3Y9g7Bq/Pg7lzzPlzLqFhW1tb24L25qB6cP8eOBxODA4OIC4uHu973+V4/InHMdjXA25lS/9bfuCqBG4s0dvXB4ejF7m5880+eOgQ6hvqTokr75APh44cRHd3B5xOF1hMw37IXEMbWjax+iBtVVfZiN6+bpzs7sYFeXlK9lS5kDIOFh7GYL8TI75R1R7mFOaO4uJjQZvEJMQjIS5etbvuRD16ersx4HKpHMG5xulyIZcydXR0wOHoR2RkhOqDVv+29LbZIoP9hMvYenr6MDQ0BM7NM6eExlVfvwOzc8zaG/ZBrnyg7LExAxkZE7nQiquxMZ+6JvvJ4SPHUHj4CJYtvxRZObMRMy7b6g+Mf8sPlN3V1aty4cjwsMqdk3PhmGEgLTVV5ZRjRcfh6O3GJZcsUbY+U//RPw/96hf43D99Hk+u+T1u++ynkZGWocYTPvFKSFYBBSA2KhZ3feYuVUCRnT1XPQHao21gYY9FVhFBSkoaUlL64HLZMDvbBFMnT2pq+nglKIIFB7GxsWoAY+dIy8gBi5ZIcTFxQdmhN2+z09Lg5rIGnxcstIoZnyNOSEhD5vgbbEsGB+Lc3Fw43S7MSctBWopZuMCgZGKaTAwq8hDsXhXE8MI2m8L6tNoZFTUx0z937lzVqdPSUlRAUh5lW7z82zAMdRnqlJMzR5XO5+bmBQtL4uJiTuG3dOL1Xb0eJKUlBGXzt1DZvBaJds/NK1BLD0zZsePH7crm/CN0Kp2yO1q6YcwaRWb2RLHahOxA0D+m7Hx0dDgQqndSUgK83uygXOtVSXZmNtxuL3xeG7KyMpQe/I+yGbAkC+/XHhuvZHZ3O1QHtfzG3yd0mbBhTlYOhoeG1QDA61jEuIqNjVd/xo1vrhBvj8bc2dmor69GTEJSMK7YHks23WvZkDGbltQHZ8CGubl55jSB8j0Ly8zWWfHNC5m+70VKWhpoC1KobG7GbbWHvzOuPG4n5s6d2DCA7UxPN9cihspmYYvTSdlZSEowC9smx6xlw5i4OBXLNtgxZ86cYHtCbWi1kTrOnjsbLrcLaSkpiEsZ98/YRD8mhrDFH5eUpNrZ1dV5iu+ZXCwbqoaP/8f+6HK51ablk31v8dnjzP4TH5OM3Ny56GlvR25efjDe7FFRU8pOS0tDZ2eCWp4xOyRmQ0ETLBvOskHpe/Ikb47nKtnMMw//+mF87GMfx7WrbgCxh612st+npGXAbneq8yxdU3nTPr5rGPspiTmPvueN9rysOYhJMBMtZYXaJFR2UkoCfH4PCvLzg3EVmgvj4sz44Tl5c3PRWN+o9KFepNC44t9R45jg1HlwcAguN/XODbYnISnl9Fxotytb0D9JSUlgvJNC9WZ/sGyYkJKErKwccJkXH15oP1JoXFm8PK7ylduj5DEfkuwRp9rEiln2i4svuhAPfPNrmD//giAOOX+3+oMSMP4fZXN8iItJQUZGVvCnUHvHjRewxUZFgf2nvf2tLQsKCg/5wjcOxUeKMeQfwDVXXIP3X3216ttvvrYFFSUVuPbaa9XDVsgp038NhZ2a6TsxSYnZ6Zpi03JuOvyjH/2X0RGySfnJ7l6tDbdraqrEm5C7XA6D0IRSamioE2P1Ekv5ySd/L4bW05HtGR1TsJFSvVtamrQgxcqrZDjXvP6mrZuMrdt3S1UxTpwoF0P2OXr1fE8M1lGvV6QLsWNbWjpEvKOeUePZZ/8ohiOl7A6NDdEJM+h2y+AUCRnKGJdSS1OTOGbp97SkFIN45xIirB59JCHC9dE/UqJs/pOSTswSS/nVV/8qFW2UlBSfFrO33nKL8c1vng75yLzW0CDDGKYChF+UbohO3zNPSGh0bMx4/tnnjbIyGV44dZDCXfL6OjmFvifMrZS6u7vFkJS0ycMPP2w4HC6ReJ2YJQxkZYlc73AK/OEPfzDmzZtnvLFhQ5D1gQceMN532XKjvEq+XwBPFlcpTz9kA9948EH86qGH1KvhZcuWzcT6jviNhR/htqN6RzRkBiXV0yafZjSWh8wg7pz9iVMhXJbBJ5N3K/G15dUrV6Kkpu5dXaXMF1i+QT9iEsUv5k5zeXN7K1YuW4HNO7di2SXnYK5icRAfNcds7+qYpWNYGBjFV2+hr99O89i764BWFpqqeu7NDRvw2suvKKuELjYe6O8XFxXwZGlRE3k5n6XD38O5MAaxkHQG2/7BgeCr0nDiOcgxOUqJ8ysstJIQi7xaNV6j8FWSzmBLva1XwuH0oc7UXUo6sqkDY0tKfO0lHWw5z6+jN+eipMSY1eHv75PHFRPWKG+ehCAFKq6mKR6a3B4VsxqIcWwn/0mJS5qkxGSlM9i2tp8es3xle9999+Fb9z54SjwPD/sxOCiPK86rivum3y+PK5tNvZaVxixtpxNXPayrGRiQmlwrzzKupL6vqK7ADatXIyIyEtzK8cEHvzGjPVXMSnNhQC8Xio1xBhi1BlxWk7KK1yIa4dEnH8d//OhHap7LZpsAaWjrOKmquSzecJ+snpPSybaT0OGvr64VL7HgTcXatWulqqC5Xl7Cz2Bk8ZCUmpub0et0iNht0Tbs2SWvgH7llVdQVHREJJtMu3bJK6CdTqcWLu3Bg4XoGZQNXkyMza3y+Zmn1j0jhursaDuphXfMQh4pmQvkj0nZ0dhaf8qAMNOJbpcLHnjFIFmMK8+gDGqQA+6uHfKYZeFMaI6YSW/+tkujmpTVz+vWPRVOZPD3Pbt2TAmQ88B3v4emlhb8+aWXgrweTx+amuQwhiyYZJxLiDZsaGiQsCqe5557DiyqkpIORnd9dT3qGxulonFMA+uaeMcsqgpHnZ3t+O6D38FVV1yj6jE+8alP4aGHfoVnn3922lMZs1J7s0hyzy75ioBpL3oWftAacEM3ZWYQfeGOO/Dj//qJ2sh8cm/XhXYMlR2unQHhWuAJOVrNnDhN8M18GyJ9xWXXedBWV7cLH8y5pg1ivCazYQE5djh4M0WfS0kLJs8YQQwmitFmukZg1hh8GghmfOqT6s2YtYpdZtLB+k33TZjGSxYENNpIfez+KKu2y1Jv2k/qHVC710/LcsoPNptGoAifsq0LhN6kW8em+4yCHf6AtK/xTWUURqfoP7F2Gx5+/BF85xvfCC69Iq8OXKOu70dH5FCdjEGd/iN2PB+L5OYz3RAph6RkfEdEEB51ZnL0u/DwI48gMztTrVR5+OGHkRATg+pKOa72jFew2c7Zt9RveSTiU+CnPncHll46UXod+kqZxtcLGnkkcHDW6ag27QF6RndO8aN0IPJrBQI7tVQylbJpZoGQFxJTtOnUQ7o21ElesyJnideQ2kcD4zd4p+o33V9M0EzUEjIHxLfcJSSXEPNouhK2gE6kiNUA5OOEEqozkGtooVgJuqODpWzmIyLAn043rr4B1924Gv/13+Fxlk8/m5XzkVMdnvZYdHz4gcg62Y+A5uAvj1mdmz7qo9PviUUu6feL37tIAUdYslkBbY+JwapVqy0T/G2fo7yh1LlJ/Nsup3V2sOxK8KW4pERVThaWlxqfvf32YAXgs88+y7UvRnFxcVAKK9Z0qhV1NkM3K1XlVcrUQ2dz5GAjBF+oi9fjEXCaG3PrVHyy0pvVfFIqPyGvgpXKtPgoW2pDVk7S/1KqqZFXfFKH7pOyTaul17f4HN0Oo6VDLrutTc5rVqo2WJcK+0n7Se3d0tZm5ObkGA6nLFYYV9IKW+qgE1fsD/wnJZ3+IJVp8VFvrgyYjpgXMjIyjN07dyp76MQsVzNI+yZtqJMLp9N3uuNNLW3T/XTaceqh006dCmjK1ZFtKffqK68Y93/7mzPGu24urKo6e7nQ0vutfAarlMvLy/Hyyy+HHazvvvtufOXef8Ufn342CG3FOYd/+qd/etdUKYc1wnmG8xY4hyzAwqMVy1agoaEu2CfPIfXOaVWeeOIJPProbxUSlM50wjndqHeIciw8e+yxNfifn/63err9w9NPmvgH7xD934qawXcReXl5uOWWm6f9d/PNN6hF+0+sfQb7dhzCBz/0Aay4fJn695/f/a669u2f/CTuuO2T6vtAT7+4cIYVtkR6kVb9sViLxU1Smqq6erpzWTH70kt/CS54n47POk7EJWllHtt34kS5dWrYTxYgEHlHRIGAghsT8QLYsWOPeDNvyjxeWioVraomdTbzZjGMju+J3CQhgha8vP4Vhacs4VdxxSpy4Xs3nZhljJBfSmyjtGrW4/aAu3n5fLI9iAnsIo0rzn9XVMihGplE+U9KOjCQRceLtGAmWXgUbv7+y1/+MmbPzsG9//YVdGps+k54P2nM0veSYiLajPpu3LgR1dW1IhOasuW5kPmNcS4hto8oXOFsaMliMRTzvoSoN292lixZjNWrV+PNLW/iH//hY9NWADCfSKuxqa9OXEn0PVM8wckt4o2uWLFyWrmDA14UFhbiipUrkPvLnyBuHBGKJxzctw+/eeQRfPnue7B4xaUqEOs7m+FxeRSiyUw7KtA4gx4mo0a1z2lOTk4Q1WQqZegoVkHW19crBKZQpJnJ/Er24KDi5XfewVqIKZN5+Tdl85/b7UD/wADSMzNnBJtm4NbW1ypMUJ4/UzsJj0aIvJqaBnUXR96Z7qj/f/beBLyt6zgbHoIgCIIkCO6iJFqmZXmLLdv6bNlxZCexnXxJm2ZpmrhumrhO2rpumjTN069f/7/f/zV9kjRN4ySO662J49hW5EXWvu8SRZEUJZEUdxLc9x0kQQIEQBD3f965vCBIUcAcR7JlR/M8EkDcuXPnzMyZc+89c94D2Z2dvTThmODlO9Fko23Qt7b+PC1fvoz1iCYbbfQFp4h8Fm5vLNngb2txUl5uLiOqxJIN/Gevb0rm+8lJrsgE+kxeTh6ZE8MheYGLoEf/YD+NDIwQ0Gxi6T0xOUnTk9M0NjFNOdPTUX2P5IJkNO5ykSMlJer2aPNxhWppE61cuTKm7IGBAWpu7mSkHInvMTgvX7mS8vMslJqmo2hdYJC5jbEBk+ijACN8paXpcb4UL35DXLW2tzKCFZaFRbMhYAwnvRNUWyuLK8g2boThz2iyDRvWn68l9PlYNoHvgZIEZKWxsUlKT7/4Li2GbCRdoBEhR0SiIi22zY9+/BR99CMfoQ/fcz999rOfEfm+traaLBYL6x41p0x4aGBogB8+gO4kyVejY2O0fGKCJic8MX2P6ve66mrOham2tIsugcNDzURAH/ihB+wRTW/0h5GRce6bWRkZlJqWJshX3Sx3tVWHhV1sZ+NvbK2KimOgY9177730uS98gR776lfpzTff5FUcG+7bYLDyJ3yPXAi0L+gtiSs8INx886Xdom+BUu/wDzGWcmAmyK+M4aRV117LG+/eeuutNDAArONeKiktph/9+Ad0/0ceoLa2DmptbqaJiXGaBCZxbj6ZzHH82qa6uopaWloI0HfZ2TmM03ni1EnyTrlpZHiEAwfYpEh+wI4Fr9NZT2vW3MhNdDqdVN9YTx6vhybGJxl7GMVCdQ1NVFF+jvnd7nHGB0ZxVXFxMTt3aGSIUlNSOeBxp1RUVMS8kH/99dez7K6uLmpsdFIoFEeDg3205rrVZIqPp9bWZjpz5izz9/X1MK4zih9Lioq5jUMjA5RoAWRgNvk8Ht5EAHLxz8C2HRwcJNyhB/wz1NvfQ9cVXMcBjAQFXGfw4pXg6tW6LsXFwBgepslJL3lmApS/XMeuPnBgD7W0tDE/7JScnMyY1WXFxRQMmtgfgJ7TsZT7uf2GLkY7y8+WUW/fKPl9fnJPeejaVTp27IEDB1gu+HE+5AMPu7SkhLzTPhoZHKTs3FwueGiobaDyivIwP3Ca4YfyynLq7u4gn2+GJiZcYQzsY8eOUFOTk/k1bZYxiScmJqj45EnGjR1xjfD1ADuHwebsWd2XkTZsamqgtuZ2mvRMkMs1SgUF17HfsNSqrq5+gWyPJ0BFhUcppM3SmMvFcHZIdrB3aWkR4c0EZCenJnNcIGYbWxvIO+WhkZFh1huvfypqa6mqspJ5p/xTBHhJxBVic2xshLGR4xNMlJ2VzU92iDfD3vHx8RxvkN1UV8+4zsOjw7TqGh3aEzqcOaP7fmgIGL4ruT2lZaU0PuiisXEXWZISKTsLEH6TdPz48bBsw4YYyMvOnqNDew7S2tvvoOuuK2DfRdoQWNeGrYqKi2h8zEMjY4NkjtchTjFAYYMCQ28jZofHhuh0aQljYvcP9i0ZszjHiKuys2U0PIS1mKM8+Bu44JFxhXhFwoTvT5SeIr/fR+hT2XkrKTnJyk8xS/XN8vJKGujvo2m/l2Z8HrpmDlsdG400N+t9zbB3IBDg/UpnZ000ONjLsYZrLrbhyrxryGyJp9GhIfIFQvSrl56jm2+6hW666Sb2AzabqK+vY7sY9mbZJ46Rb9pPExOTZKJ4ys7R8bUjbQgMZOTKvv5eqqmpoXH3JE1ikLnmGr2flFfS4lyo56simgn4adzjp3jLLOXmLKPO3k46faqEWlpbWRfDhoir6vNV5AtM04h7gq5blc/5Cm8kKub6ppELTSaNSk4V0diYh4aHB8mWmECZWdkX2NtoJzb8qDl/lqZ9AeoDtOfKfI6rpXIhjAXfI3+PuNykUZAxlgE6c+TIkXBcGbIHhwcJuM5+/xSNjo3TirxraO3aW+nFF1+kNTfdSJ7JqQW5ELKHBvsZQx2Y60vFlTGeIK5OnjpJM/4A3XbbfEEvO/RK+E868Ts9Nc1QXAMDF07QL1U0haKCc+cqROJnZ2e1wwcPMyzYxUsc5kWhSKSw8Pj8D1G+zfhmmZeLFmajS0dxA/R+/vnnNc/0dBSp84eOHz+sDaCIJ4ZsnIFikt17d8yfHOPb8cJC1kciG7qHYe8EuuzfvV87eHC/SG9cf/v2nRrgPSXkbHBqxcWlElbm2bl1t7jgB8V1paVlIujN6Sm/9tJLLzE0IewTi+D7ouJinU1gw6NHj4qLRBB/sLdEDyhQWFqq9QghElF45LA7WBfEeywqKyvV2jo6YusyO8s+37JlsyxONE2rqKjQqqurY6mgH5+d1Xbs2KZ/F/inuKhQ27p5swb4QwlBb8SsxObOlhZtzY03at//t3+TiNb27t0r8j00he8LCwtFMQs40tdee41hKSX9fmRkRO/HAvtBHvu+rU2TWJDz1e692ozfL7IJ4F9RACkhyH7qKUA76gV2sJHVYmXoyaXOh96NQtmwIcfsUoLe49/CRVOxBn/jNc1Sr36wddLLv32d/p9/+BblrdB3uwE/KNrrx8hrYr5NBflIhR+vU6TILfzKrbWd7lp3hwhyDLK5nULoQBVdYENswCBdS4Q7ymivziLt3drcyst2Vxesjvz5ot9VZMMiJsyDCte2sC+xEYOUf2564KLKRhyoOFdBBasLor7Ki2DnuXtpHOKJBP9GB0kJAAAgAElEQVTEMa4Qhyq+xw5XD913r3gDehXZsE3AHyKLNL4V+z1eW1uT5wFzIn2x+Dveek1NTNHNt8peFarELK6Ftx8b7ruPATE2bFj4WnOxLmzDuc1DFh9b8m+F/lBRfZ7yc/P4bdKSshb9qJRTVPOVQl+DTUCx+gPGi4a6Bu6Xt99+O78JeOGFF3j7vf986qlFrZv7cw7yMpZs42RV3xvnXe5P8YB7uRW5Kv+qBa5a4J1ZAFXK69etI2fL1Srld2bB+bP+64Vn6b+fe5HOlpVRUvLF587nz7j6TdUC3/nOd+gXv/gFff7zn6c//9qfUUdTK3UPDND3v//9qPOzqte5EvnDVcoS5bBHK54AJYQKQfBLCXMxUkIxBOYEpQQYNuPuK9Y5aN+5CuFm0URcVCC1CfjeeOONWCqEj8OGuKuXENqnIhtFBagqlNKmTW+IN4tGlSp0l9Jbb70hrkDEPBz2x5TSufMVYtnQ+eRJOYzhCQUoTTw9qcR4xbkzYnvjDUEAaFBLoCotZSc8YUgrPmFvlbhC30RbpbRp06tSVtYZe+5KCTEL/SU0OjpINTUN9K0n/46Lbb793e9GzRlvb90qrsbG05ZKLqxW7JsqufDU6RKlvrlz906J+ZgH/UfS73/4wx/Ss88/T4GAj1D09eXHvkpPP/101MEWMSvF3UYuBP+VSEoDblVVnRjPEihTwtUVbBcV5CjdkEqqi22P6jkUyUhJpY2QKXxrypdn2QonBINydJW2lhalAVeczaWGi+BDO6WvinQbXrySOUIsf22oqVLC9iWLXLaCaxarFfPvUNT6+IWnI6GHfJh6WPj7xf5S0RsbrKug9qB4RY1kr5MhE6sTVPCrDSQjiT6R0I7PPPM07diyjY4dO3TRUxMT5EhTJrMapGtNXR2NjLgveu0LDijgNWIvXZWcFR936aEdUfT15T/5E3r44U/RE994gvLzVlzQpKV+4Om1pQ4s8ZvKUrYlTr9sPwm7qH59lY4HiC+Vjq2a0E0KQaZqPeGDAovV2yhP0irBjgvIJasNWqo2UfOleCkrq8FJXUEh8EsJ0I7SwRw3iZa5eSiZfBXvEAUUnK9qb4vZRIrwy6ImziyNjHjRcwHvd6VQ6B3CXWLD842vbKSvPPpXF10/q83EiZsJnHOT9G5ors9rmsKNi0I7EYIqsaVy0yKFdhQb7ndilD98/E6XUTxZKWPk568SF+Xk5uVTSOGJ68Yb9WU/Ev2xbg/r/KQEUA9plKHoKC87WyqaclesoFSb7C4dBWcq+wWjAM1mlcnGXfRdd9wr1jsraxklJqaJ+e+4Y5144HI4HGQyy/SGAiicsFllmxdgqUVGRoZY7/y8XHHM5uRkkd0uj6uCglViPRxZGXQnyZcpoK9JbxQYQxtvCYS3z+ibKSk2ke6pyRa6Y51KXGWJ7Q0F1qE4UUjo81iyJCXoHW2taaQc9HsspzPoU3/0KXrkK1+kb//t39H23bsv8MUtd9zCSxgN/mifkL1qtV5MGo3POJa3YoVYb5yzeo2siAy8q1blX9AW47pLfd5884eW+nnJ39B/pASbrFy+TMrOxbjSXBiaNVF2vjxOxEpcAsarRVOXwIhXRVy1wHtpAcxt3XXfOmqpbqHUtIsDQryXOr4fr425QAAzfOYzn6Hvfe9778cmXNX5CrOA8J5YXWsUZUgh3hDYWKgvhUpD8ZFKYQZg1aTFE5CNAgdjuU+slkNvqWy073JBO8KGKvMWDQ31F31dtlSbGdpR+EoUvr8ioB2DQUKRjbRASI8r+V67Kr5HjIBfSioxi6KpkDtAQeGrRcBGqkA7SgphjHapQjuqyEZMoShLSpCNfiEh+H5xzOINw1tvvUUvPPccAzhEyqlrUoAjnZgQ9zXkHZWiKcQVAFSkhCJMaX8w8pXUhijCHBNCO0J2SUmJOOerQDtKbfFe8IkHXDh206aNYmd5x6cImwZLCIHd2tpJU1NTEnaa8nqVBlwkGKlsFE1VomhKOE3IawOFeqO4pa2tS9RGMPX2DtLIqGyTa/C3KiT07u4uamqIvVm0oWyLs4WCwgEXNuxVwKVFEoVtJAQ/dvfLKrchD76UbogOvQcVZANuTkVvlcQI34+7ZYUz0AHzt9LEODjYzdWhEntDJuBIpQTkK/yTUovCxuxIuufPy7HIcQMqtcnFYnb16tX07H//N3318ccWxHRbbaM4p/i8XvFqA+AFnK0sI5dL7vvmpjqpuam3t1eut89HXS1d4um4wcFhGhkfEemCmC0rOyvuP8gnI4MukewAkNMOyFe9iIReIibxK+XJSR+98sqv6JprVlJSWho9eM8DZE4yM4Saocudd97JAANIoOdrqykUCFJeXh498MADPG8AiDPj7go4mmvWrOGnw8LCQoYQxBzNLbfcwmX5/b2D1BARSMDFhKzKMxXU1t1OPp+XoRQfeOBjPGcEkG1jCQ0gFgHrBaeePHmC+geHKcVmC8vG3SwPqnOKFxQUEP7haQgYzW63i7Kz8+jjH/84l6pDRnCuIgU6rl+vY07v2LWLPBMTZE1JoYJVq2jdunV8xwbYP4M+/OEP83xMQ0MdNTe38rIqQAwass+cORPuAGazidAe0K5du9g2ZouJVq1aTffOXfPYsWOGaLrtztspOz2T2w3b4unCkeeghz/yMMMkRtobJz344IN8LmTotgpRQcFq9g8ORMo27A1/6TCGo5Senkl33303+yHS3pGysQQLNgRlZ2fSJz/5Kf4eaUPD3vADYPzGxnTZuCZiAm8vIt9g4JqY/z5Xc546na3s18zMFPrUpz7HsuE3JExQpGzo3d/fTSkpDvY9YgJJG34wCL8hXiDDAGqH7I997H9yXCGWjTc1iD/oiJvP0tJi6u8f5FoCI2ZhK9jcoDVrVhPmYisqaqi93ckxCxvef/+DlJpqXdBOxAT6DwjLh4aHR7nPQDZ0xDWBZW6Q0c6m5iY6dfIU/dN3vkPPv/IKffLBB7kPRtoQ82X33XffAtkWi4ny5+IKg9LJkycN0WEbIkbQT0YHRyklx0YP3/cwpWdnUn9vNzVEgOtHxpVhK8yHfuxjeixHxhWgQW/70Ie4HxSdOkaDQ1OUm51O99x5N+Xm53F+iLShIbvk9GkGRkC/z81bQZ/5gz9gfSNlp9jttP6uu1gGbDXYO0iZuZl084c+RGtWr15gb5xs5CX0QbQV+SIyZrlver1cuPiTn/6YaEajlzdu5P4wOjFGmWnpBB9jnjPS3pBt5EK0BXC0hmzs+YoHjMi+GZkLi0uLqbe7l2Nv7dq17Pvuzm7GbDccZPRNbKBQW19PU243x/D999/P/SSyb2Zn5dFta28m33SQSkpPcMzi+uhnyFcXy4WQgdhHHGZn2zlmDWhUo29G5kL4ITK3I97wFBuZC42YRYzAP3giRoEabAUbtLd2Unun3jcjc+GRI8docLCfTBYz5a/Iow33PXCB7w17nzp1inMB+sujjz5qmOyK+RQ/4UJjVLclpSZTlt1BNIc8g85s/IMjQXBEWnIqDzQooDEIxxfz4je9CCbEiQLngjDQGLz4NGQ7stM5qFDGD9mapl9zSdlxOg+KSZCww7Ij9IiUjWSIknWvN7SgIGIpPaBjTlYWYflG6hw+LH5DBW0kPzeGiIH8cX0UuGRlZYXbE8mL7waBB5XbqclplJY6Py8XyW+eq3zEb1yoZDJTniMvvBF9JG+kbMMnIbP5ou00qsZhV+iCGw58GnIWyzaeJIC/jI6ZmJjEQP1Ge1JS7GG7GL6MlI1B0SjkifQlrmPwZ6akUTI2qzYnkcORZ4jm44Y+Bi8+U2x21jsxKVngez2uEq3gzQ1fM1IXQzYKcdAe2AhtXSquLBZbWEZ6ug7kHwrBlhlkNmP7aL2q3NA7PqLyWvfPQtngN3gjbWKHXVNSKGg2c5wYOkbqDX6DMjJyCMksOVpcRfRj6BKyBGlFegGFl0yZFvZNQzbiA7bBP2BiGxSpt9WiF9NBv6zMPLLO9QeyXdiPI/VOZ/B8pCsT5WTNF80hZsLy52Tjb+jtMwX5M2Wu8PBiNoEPoTPsYvQN6M78Fgsj4D311LM0OD5OP/zh9/X+GzSx35fyPa6Pc0GQh9yDVRUse1ZPuUvpwnFlc5ApGKIki40sdr2wzToH2m+005Bts9k49+BvPa4utKElcZb1sCaayG7P4HZCH/wzyJAbqTfsirbBJhlZeTrinWGTiJxvyIDvE5OTKTk5kfuE8ftSsqEvZE9NefnTbr0w56P/GJSRYed8kpyYRJn2ed9HyjaKYhF3KkWVxjXetU8ptCQwSYEFOz4+LjqlpaWFcTslzMA63b9/fxhXM9Y5XV1t2tGjhbHYwsePHy8UbwANPN0XX3xWhHuKCwBPl3Gaw1e7+BcDm/TiHAuPFBUVa20tLQt/jPLXlje3RDm68ND+g/u1g/sPL/wxyl+/ff1NESYtRDjrnGLfg3/r1q2aWxhXwNEuLpXhNCOugKUsxXeF74uL5XF1+LDc9waWchQTLzhUVFQqjitgKWc5HOL+U1pcqmN0L7ji0n9Me2e0t99+e+mDS/wKLGX8kxJ8LyX45nWFGH/zzdfF+N/w/Zkz0fXu6+vRVl27Unvttd8yBrSBAxxLf/j++HEZ9jtkvfTKL7Xq6vpYYvk4NnxnTHQRt6YVFxeJfW/kK78Ep1nTtMrKSq2tUZavIPupp58WxyxjKdfIN5WHLlciiV8pq94B4HVCMBCKur1UpEy8AtDvMvW7tMhji79PB4IU9E8vuEtbzBP5t6rsqYkxfkUTKeNi31Vk4ykQ/LijlhB4cTcIu0gIr4eksifGxghLiSLvdKNdg2WnpYnmc9j3waCSbOhh3LlH0wNbe/kDk5ScKrMhXnPhblpiw+npIAWDlyeu4HvYRWpvFd+3d3fT/evWibGUPdPTZKIESkqK3dfgC5W4QhtBEnurysZ2dcFQQBzjKnp7gn4KTQdi+ufYsRP0yBe/QNv376Z777pXFrOKvh8bHSM81UpsqOeU6ajbFbJD5v6DDfH2UC57kvB2wXiCjJS1+Luq74HulZaWKbKhit6L9bqS/lYacJG80u3pUfcsvZIad1WXqxb4fbDA1WVB766XAbT/06eeotLTp8U35u+uhr/fV1N9sHk3raU0h7tjxy7q7pNViGL5S2TxQ6xGoahGSu3tzbxRsZQf2LtwgoRQPIGlAFJCO7EhtoTw1LJnzz4JK/M0NTWHC3ZinYT27dy5PRZb+Dj27lRZkgHZKPyQEG7MoLuU9hw4wE9REn7YsKlBvrxm27ZtXNAikQ1fonhKSiiqkRLi6sSJ+cKkWOfBN1J7owo2MB4QQzvqMSvDRIcOKnEVWbATq404riob/pQSZKPYU0LY9xl2kdCTTz5Jq2+4if70S18S5RXYUCUXomBSqgv0xX7QUkIuhI+kFFmUFusc6CyVjRzx61//OpbI8HHkk95h2diDk/bt2xU+90r6ojTgqkA7alo8by4vbaxRBSzh9/mCvGG0hBc8PNjOFSvEOge80iVEYdkkG8wh2+OZiKVC+Ljf7xF1aJyA17FTU7KlBOBHG1Wwl71eWeKCbLQTuktpckKW/CEvwZRAHhXZk5PigQt6q7QTFbNSguxAQI1fRTamB6SbF0AX/JOSSlypy1aLK+O1pUR33Zd60ZCEHzlLSn/z139Jw243ffOb34x9imam6Wl5f0AbAwG5f8S8oRD5ApjakOuiEuPQA7lZSipxBZ1NQdkUiH59OdKdVN9Lwac04JoV4PpUsZSxr6iUeK4vJMfK5OQiXFcr1WEhnzQQ1IDDYRLJvCZ0QRtDIbUgC8hNuLC5l/ivhHg5QL4/NKuELw1VpTaEvVVwZpXMYDIpgcZTSKVr6vvyKsD1ilVXxVIWCw4zyoMQflS5UcADgkl6F0JEyFkq9NamV+jo0aP085//NDp4eFyQ4uPlCShIIVLDpBbGislEkA3McCmFFOIQOqtgQF8p+Udqi0vBF/89RcwyrEWUTLgTxfPSCbt9vvw8msJxcRqlp8+XfEfjNYVMlJRsFfObzQmUbLOFl8tEk41jKDdHOyVkMsWTzWbl5UCx+RHscZSbK8MQjYuLp8QkKyVFLOu42DWw3CgublYsG3KWLcum1NT55RsXk43fsawhJydbbMPERCwrkO0nqmlxlJWVTZa5ZR3R9DDHmygUR2QX623ieTYs94pF8fHxvOwoLWIpW7RzQqE4Sk+fX/YWjZc0jaxWC2VmyvBmQ3Emsqfqy8iiyiUit9tDr732En3rm9+iRFGsxHOMJybGTrzx8VjqlsS+j6WHcRzLVWQ5Qj9D2h9wU67SNzGwZGRmiPpmXFwcxcebxP0Bg//y5fn02c9/nh7788fohltvpJtvvDimMfqyNBcmUBylZ2I5kaxvapq+hMywf7RPS5yZkmwWsey4OKLMzMxoIsPHNI04F0r0Rr5KSkqgFStWhs+P9gX2S062kSRm+fYjLqSUC6Nd+1IeUyqaupQXvirrqgWuWuDSWKC7t5vWr1tP9U4npV/FUr40RlWQUnLqFP3hH/0R7dy+nR6YA/tQOP0q6++RBYTvIvRXluXllbysRWIfFLegLF9CeJmMSXQsy5AQ5jjALyVdtr5cIdY5QEHZuvVt8asrFdl4HaaiN+zn8cjmW4DBOqhgk1MlJVRyWl70A7tIoR0nPR6x7+EPli2cU4TvpXEFe6MApXMOvSaW71ViFrJUfK8as2gjzpGQd8pH2IouFJTNEUM22ioh2BD+kRJkS/0DmSqya2qqFqChxdJJJa7Qz1T1Nl5v37dhAz377LP0yFe/QnUN80hjhn4qMYun+H379onxkd9JXF0u30OuVDb43njjLTG/aswaaFiGD66UT/GAO+3x0+nTJxmXNlblHwbOnp4eApxhrEpLBK0HsHVlZ8nl6o050EFeT18fVVVVsexoM7+QDX7wDgyMxJSN9b1Yn4qCIgSE0aEu5izIrqwsZ5vESo6QhQR94uRJUZAZsrvau8gTiJ54IXs64KGiwkJddoz5cMh2j7vI5x0X+Qf8J06cIJ/QJq3NrWLfQ3ZxcSlhTZ7E3j2dfYTEGysG2SY8OI/SlBfrtqPfzBkxi2pS6BSNcHMDHgOnOZbvIRv4wmfLz5LP44vZTrQNbUQf8k1Hn+NEO1GIh/sVrzcgkD3JvoEdfTEGdMhGP8AKAkkihU1QpYp/MW3Isn1cYYv2Snw/MYGb+FGRbFwfMTs5IevHnZ19vLk9/BONDN8DB3hwcJCwcQToK1/5Cn33m39Pn/vM5xfcRKBdPX0DnCckMYuBf3JygiYmRmP6HnEHSNOysjI9rmL0e1y/rq6O+vq6Yj7cQG/kK0C1YrCL5R/EB6Am2zq6RP5BjnW7h+aKN6P3TfgSekvjCnY5d+5cNDe+Z8fEc7g+v5+qqysZjsvlGma8VWi9b9cOamrtoMaGesrJyeG5m5aWJsbhHB11sbNWFRQQtms+feYcVZdXUGtzC3lmfLQsJ5ef4I4fP04e7yT19g7xe3qAN2AZRXFxMWFXDmdjExn75SIhNjU2kmvcRcMjg1SQv4pM8fFcdl9eXs7XnZiY4L0tcbd44MABDsrh4X6yWBJ5PgKBVHS8kJwtDbx85YYbbmAHOBtrqJGXs8RRZ3cv3bTmepbd0NRA5afPUqOziXoGuqhg1XXMj6U1Y2Mu6u8fIpMJc7O5HGz43Ug82LsX8w7YyAH4obPBAHV0dFLBNQVktpj5+udOl1Gts4F6WjrpujWrw7IxNzcw2EvTnmnGGsWBHbv2UEdTCzU2NzEAAOYmsaQBNkTVMWQvm5tnxx1+0fGjYf8YNgRuLnzj84VodHTel3v27GHc15aWFi40gh+QVCB7dnaWOru6aPny5ezjpvoGOlVaSm3NrdTc0kwFq1eTKS6OdFzaLpYPP1x77bV6e44co6b6Gmp2tlJwNsjzqjh++PBh8vn81N8/wHCAgIZsaqqjcyXnuI2NjY18TdiQfd/cSBMT4zTiGqbV1+m2wq4juKkCZq2maQy9h8QFvYk06usfpKSkeIaaxJ1vYXExdbQ4qb6ukef4YEMjZicmxqivr5/jG/NMlRWVVFVeyb6HTMztB0IzdOzoUdJ5B8liSeD2wN7FhUVU7Wyi5sZGnpOGDSEbunumPNTd082yMQcYjquWJhrpd1H+Kn0+q7DoCA0PDdPIyCiRNku5y5bx0rPCo0c5TtoibNiJflJSSvuO7KLbb72DrrnmGvYPcHARb7BlV0cPXbdaj1kU+QwODtHYhIv8oSAtX5bHyRS+BwY2zjP6cW93PxWXnKJgcJbjd+XKlRzLsCEwchHj4I+Mq97ebhofHyO3e5J4H2oi2rNvBznr2qjR2cA+BvgHfH/06GEKBGaos7Odli3LIpsthQcr2HBx30Rc9fR0MVQn+i82FQAd2rOHmp0tVN/YELZ3YDpA+w7so5mZaerp7QvHFQaF4wePUm1zAznrm2j1dQXh3AEfuVwu6u3rJSMfHDtxjJpqG6je2UyhuZgNBP38BOrzTfNNlCkhgbIBfeoP0bTPSz09g/R/v/9/6ct/8iXGM29ubKLauhqanHRTX18nXXf9DdxPMJBhVyAMUtMzfs6FyFeIWfQH9P3Z0AzHG3Lh8aJCgt8bGudtiH6Kmz5UEvf0dtK1qwq43yLWSs+WUUdjK7k9kywDA+bx40doZGSIhofHCVjawBA3cmFjSxPV1zm5xgRzts2t7VRRfo78fj/nwlXX5LPvwzHrbKK+vr5w/0auhn8mxsc5ntBPMFAe2reHmlpbqKWhjQI0QzlZ2ZxTED8mUyINDPTP55TmViopPsVxiNgC3jMIb+P6+3pocnJKH0+wv/kc3rwRs4FAgPOvHldHaWZmhnGomfFK+k8Kf+V2T2vPPvu01tXVpc34/VFPA6Qe4PRKS0u16anovBAEnt3792p9AwOx4QNnZ7W2lg7t6NHDMfWAbOgCXkACarOzIr2ff/55ESQc7AB4P7aJAP5sYMSlbdu27aKyI7Wb8c1qhYXH2Y4z3pmYeqOdb27ZLLI3ePfu3avt3n9QiyXbsCFg8jzT01qkjkspBdmAGiwtLorpS/DiH+D9XCMjIv6Ojg6Gp4sVg9ANcKSAdmypd8aG6pydZVsXFup6w/7RCHoDUg+wffgelWZnOUYQ49A7Fj+uXVRUpLV1dMTkRUzX19ZqDrtDBAWJawPeD/1TYsPJyUkNvo+lM9oPewPWsazivCyu/H7tzc2vx/YN+vEs+kMhx4oop3hntNfffJOhaCW6O1ta9LiK5cu5nLJ9+05tYAnf41pf/4uva/fcc4/mdru5vyA/HD16XGRvtO2VV17RqirLY9oc1xoYGNB2796t+WPEK/wDfuTkFvg+VjtnZzXARu7cuV2kN2IWOqPvx5StaRpy4dNPPbOkDRf3pdnZWa24qEirrq4WyYYNX9/8+mIxV8Tf4qIp3CHhDj4rC1XKsZfB8Gu2UIiSBNWhuAHB3ScqGyVLOKAL5KvA5Ell444Pd+3Y7UKii4reWBeC+U0VvU1JFko2x64mhQ3xOjxNCBt5vraWbCaiG265VXT/h9dKYog3D0AYZtmfEuGQDZtI7K3iezx1lJSfpNWrb6QVubGrzhFTmKfGZhQSUvG9it64topsPA1suPc+qm9ro0xB0RT3zcsJ7ajQ7wEak54uW8nQ3NxOY2PD4d26YvmIY1bYH1T9Ey1mIeuLX/gCr9J6ffNmrpJWyVcnSk7RjatWU96K2DGrqjfiCv1MUkVuyE6yJBO2DYxFeg3OjEg23hYVlxXT/R++X8SvIht6quTCWO26lMfFA+6lvOhVWVctcNUCl84CqFL+8B3rqKGtTXwzd+muflXSUhbAYIXKZYum0eY9+ygJW5Zdpd97CyhFwZkz+gS6xGrY61BlE/Jmhc3T8RTa3j6/p2ksfQDuLiXcuarA+6Gd+hND7CuATwVOEbJxRyolFdl4iu/t7JWKpvPnz8csnDCEQWfoLiXorWJDbHQtJfgS8SIh6Iz5MimpxCDiSiXGsW8vkraEfAHMjgHUQNad0U48YUgo6Pez7yW84IGt0VYpIa6kBNnnz8uLYVTiSjVmAWMYrW/iKRIwlGPuKfrrr36F92GWthNzuyr9RyUOEd8qsusb66Vqs1xp34TtUHshJegczd6RctBvVHJh5LmX+7ush85pUVNTF97oO5ZiLpdbKci6u+VLD0ZcI9SpMFgMdneLkxdX/UVs9B2rnUgCUjgzFBFgoJMSghebS0sIr09rauSyocfgqHxQBL90AEAFosulbwgv0d3pbBPDaQbj4qmzW36zhQKSoRGXRA2CvVUG3M5O+eCMuGptbRfpASYs8ZLaO+gLUCgYILMQVQkx6/XKlhAFNY3q6qrEeiMxoq1SUpE9MjJClVXyGEelNwAtJIS+iZwlpZaWjpgxi72b9+7cTQ3dzfRP3/1HoXeI6mpqlPqPyhKY3t5eJdltLR1Sk/DN1uCgLKfA3mXFZUqykVekpJILpTIvBZ/SgKuCvasK7UhCPGJudLS1QEtYBdWmKmSZ2zxafo7sSYSQEhV0h9pSycTIcdGXkMjbcyEn42gL8ahx9uzszIVCLvLLzOyMaP4WpyfM+Mlint9Q/SIiwz+HyMRz1eEfLuEXxbBSgo2Mj5PN2xvNCZnMFFSILeM8yacKZKgaJCGurgBHaiKyKLyaNZksXK0qaSOeSGdm5NCOs7PRl+oZ10zLTqf9uw9SZcV5evyrXxXdRAEXW6X/AAVOSlivrSZbHlTIbSqwkSTvxpw3AUspIk49ly8XinS4CJPSSORwZIgTY1JSMplN8s4kgfUz2mC12ZQ6nrRwC/LR8bB/qpS4ncIBGmyAgZRSYmKyGDcYXS4tLVsqmpdgWMw2MT/2rdQH9dinwIZmAUyjIclhsxEGDBElYB9XWVET5GWmp1FQmKSxPMicLLeJ1Srnhbg+VeQAACAASURBVE1U+OPj5aD7/CbZzLdzIhOq2A8C7XZ5zLLvhf0BslNS5LJtFlmxj2GE5OQ046vo02IRxiD3Ndk+rrhwqiWVXntjE7/d+sbjj8ecPklKTVbqPxaLPA5hE+QVKanELPoP4GUlhDix22TQlZCHmLVIR6tEQHTKc6FE30vFc7Vo6lJZ8qqc380CuD1WfWT83a74gTkb++F+5K67qM7pvFo0dQV7FXPbn/7DP6Jsewpt3r5dVJ17BTfnqmrvwALSe4Z3IPr9eQom5jGPJ50/e3+2UofUw1zeFUOXYbCFD+FLabHFFWMLRUWwLZo/oLblnuIlrgj24dHRBShOV4RSCkoABIXBPuLi6Mtf/vLScRkK/V7ELPom5p4/6Hl2cXiIB1wkrVdf/Y044JHoULQgIRgdmyhLqxuxHhgV01ICr3RwQWEGUHekdPr0GbFs2BDoNVLCZtHSIh7Y8NixI1LRVFlTRWfLK8X8Bw4dEncOdKS6OnlxCza5lg6K8H3Fefkm8UD9AkSihGDrigpZzEIefA9ISgkh/lQ3CpfGbDAwRQFhRTN0Rb/sFhYdorjlwBF5XKG4TqUw8MgReX9obqqj0lPyzdYPHToQE2bQ8B2KiaT5Cuegr0ljFn5EXwZxIdXu3TwL8IlPfOKCnBecIYaklFYeI2eqxBWKCKU5Be0DrKd0UEQVPhD1JATZu3btENsQ+URaHAZ9VWJWou+l4hFDOwYCGp09q5dxu6c8tCw3l3VAWT9wYvEP7/B1GMN2amxspfFx4J5Oh7dJgkO6u3uYd3ZW4+2qYHgEel/fCLnd47xlU0qKnQZHh6nF2cy8wP7My1vB18Mi/9bWJhoZGSO/f4YysjIp3mTiiuj29g7mx+8ORxrjnJ4uL6ehgX5yjU/wNncAWMA1kRQMvQG/CIJDoaPf7yOvd5pyMpeR2RLP5e6trW3MDzzXrCx9uyoM5BgAAPFH2FIrPZ3nZ4D7CdnQOzs7l7e06+3vp8aGOhrqHqZJL2Rk8XwxqjoN2aOjY+Ft0NBBe3qGaHwcGNCAK9SvWVFxhqtpI+2NTldVVUlDQy62ucORzn7A74COW9xOtvfAEJHfTyhYMrZHi/RlXEI8pdiSOSFUVVbR4GAfTU1NkiEby1YMe0P+spwcorg4tiuSxcBAH9sE8HEgdJi+vl7WRdNmeXsw+AHQdH19PSzbZkvmGIq0CWzocORSQoKJfdPa2kIjw6NkQLlBdmRcGbInfB46f+4cTU15mBexCd8j+SGGDJskJydSYmISLzODbMD7YWPs7Owc9hva0tnZxfwoqklLc/DgVl1VRR0d7Qx1ii0X8TvsDV0AUwn5vN1fcjLHZl1DI425JsjtHuMt+jCHFdlOj2eaMjLS2VZVVUiKneRyjXGVbWRcDQ0NsHyjnWhP2dmztHvndtrw8Y9RdmYW+z5Stss1wu2BcMRsX98ADbtdZI4zccwiQWEpCmyNSm3AayYkJLCt6upqaKCvn5cRGTG72IZG/0EyB0wj9AYUqOH7yLhCfgDoguH7/v4uGh93sx44ZsSsoYshu6GugXp6B2jSM0UzZKbly3LYVoZs8GO/bvgZS8zOni2j/v5B3mzdak0K/15TUxnuP2gPCirR7xvr68k1Nk6Tkx5avlwHnMDSn97ePvYltofDdpO4AeEb4d5+mhx3U5w5nhxpaQztWF0LzHbd90lpiWRNSCL0+3rYcGCEcwpk45rr7/kwHTq0n37x86fp4f/5EGVlZnNcVZ4/S2Nj4+T3+igh0cJ2WWxvw4at3e3krGuioWG0M8Dxg7iK7JvYuB3bnsLH589XcB90uUYZ5hZ+XpwLEcvJyTrEJnwPG3q9PkpLs18QV8B8NrabxPK7nh5UQI9QKDTLv8MPRi6EXSJjtqGhiZBLZ2cDZLencUxExizi3MhLyFcdHW00Nuam6emp8O+RuXDGP0NpDr09nK8GuunWW9dyjFxJ/8mrBGiGsBkxCqeyMub3rV2xQh8I0SgDvcRud3AxRCBgpoysHA5GIJUsW7acHQ/nY19L4xwMSt0DvZSVkUO2uYn0zJR0MuejKs28YG7P4XDQ2EQGeX1ByshwhFceZmXlcFFKyBIiy9xG7Cjcyc/NJdfIOGU4HJRi04sLoGd+fj4FTAEyB+dNkJGRQQ5HFg0PjzIup3kOUUsvFtMLwBDQBuEmYGTERXZHFqXY9QKABFMiY8iijZG8DrudbQdsYmAuG8ciZZtM81V4sAkGUBRw2e3zRVwFBWvCd5yGvfU9QlcQlqlAJ7M5iVXE70u2MyuHktrbKN5sJUfG/P6s+fl5RCh0C4UIe5qCICM3L5faO9spOyMvrDfsDexbEDBgQyYT+4L9MzbG++fa52wCnuXLl4X1NorSoCds0dPTxzjHRkwgfixWG4XmbJgwt3e3w55FYykTc3E4vw9tVtZycjh8BPtZ5+IH6Fy52bnU3t5J8KshG9c2Yhb8ZrOOcgQ/2FIA0o7BSb+ZhN5oJ24AQYYMvBZCssY6c7vDHnE8NXxjCNmGfXA+4g+7+mTnztsQv2OQMGKBL0LEcd3fb2W9YU8QBkBDb/xt2JD9wzc1Zspy6Ddx+nE794fFcYj4cLu9HFO2uT6I60M2PsGPa4GsFhvbAk8tkTFr2BBtjNygHLoODw9ymwy9IWcF4ipkYvmGDXEtyMQAbVwbvLgpQswuJkeGg6y9qPJPotyM+WIbnMurEEwmMtoD/dHO9vZuys7MI2PVAX43+g90NwjtcWRkkNvtppyc+f6Ql7eKgkEf6234yBxnmbNJN+Usywn3TeQ3YEejL4CSTXrBlt1m4/wAuyJfGYTv2C3nxz/5MT388Kfo0L4DdPOHbmZ9OWazs8I+hn7zsudzZ1aKgyYcY+T1eVlvQ0f0E6PYKdLe6WnZNDIyTg6HnX0LXZBDDPtDR4MfvodNsFQqMzM9nNsRs5C9OK6yM3PZfsgb6Esg5EIjp6AvGzGLTyOn6XlbHwuMXGi0w7AVeHAjCNn4blB+vo4dDV0M2WhPZnYmdXbLl+AZ8t6VTynAJHBSt2zborlcLtEpwJh1OhtFvGA6W1bJuKeSE0aGhrTq6loJK/NUVVWK9W5ra9NefPF5EWYnhKvIdo9PaWXllTExnY2GVVXVMp6p8Xe0T+CNAidVSnt3HtSOHj0oZWfZwLOVUE9Pj+ZsaZOwMk9xcTHjzkpOAL6rs1EWV8B0BZYy8F0lBGzcxnqZbMgDtqu0P4CvvPysRA3mgc5DIyMifvACSxm2kZCzsV7r6xmQsHI/KCoqFvGCCf0HWOdSKi0tk7JyDG7dvFnMj7jyx8IMnpPG+aqxRSy7rKxMnK/ge+SJi9HPnnpKW7V8uVZYVMyY0a+99nJU/kg5wGs+X14ZE+PcOKcevu+TxQlyfllZKetknB/tE5jRXV190VjCx2ATYPNL+09jo5PxyMMCYnw5XiiP2RiiLunhq1XKi25rcLeE1yx4jfdBJr/HQz4yUVqy/jT8QW0rfIm73sV3zR+k9rb3dtNH71pPVc4WSk+VL/l4v9kAeLrBoBxD/f3Uvldf3Ujf+c63aePGjfTRj36U31JJMOvfT21crCtwtFNTP9h9c3GbxUVTOBHzF0A0khAGLvyTEmRLSVW2ih5IzCqDrYpsvKoFDJ+UWLYCUoaKDROTk5UGWxXZqv5RkQ3bqdhcuimCIVdFtm9aHt+qNlHRw0wm/fW7EBhARTbsouIfyJZlCL0XqMjGAAR/SklFNjatULGLDxt0KFAs2Y899lXau3s3Pf7Y4/Tyyy+TMY0iuUQs2ZEywKvEr5ivVGRj0wrpjbCKXLRXxfeR9rnc35UG3I0bN1F3n6wKDQUHRmWepBEqlXYoejmlUK147lxFeKPoWLqgCGrfvn2x2MLH0U4UekhobNJDO7e/LWFlHsjGGksJISC3b98uYWUe7ImLAh8pbd36ljiIUeRRW1srFU07d28X2xBPrLX1ctn7DhwSVzdCZ+y7KqVzc0WEEn5Uhh45dEjCyjwoBpImDZ/XS9MhEiNNIa7gIwlBB/heSk1NzdTZLp8/U5ENGx44IF9B8Pbbb/HbKonukxMTSjF78Mhe8YoN3JhJcuF9GzbQqdMl9NTPfkZPPPlN8cCISmIplZw5rdTvdx/aLxVNiCv8kxBy5ltvyeMKfRO5WULIhSpxJZF5qXiUBlyG9xNeWRXmS+FBjjVQg2uUgyogwUgdC0WU9A4F1fhxAYX1qSr+wfKn0dEJoTehhhw1DEJVIP4AYyi/g00gk4LRR4d7KeSTP4mKDQLfKz3LEZmEiFcqOoA3AExHU5Ck4hXMx6qoQDtGFiNJ2qEiG1i6/YOym1tcGwVpgPZ8r8kcj+IymRY3rllD3/s//4cqz5bRw3/0oCgXSWVDA6sC3CX4E6XwcnO5UArtiP6ur2SQ2UWJiw2ilq+U5P8OzErRiACWEsYJ4ClLSWFc4dcQKrjOAYXEaFQZquk9X7kc6zyVGwWVjkSzJuVBUQF9UZwwjPar+B7LbaSJOpQwSwozFRQMmclnUhlwlbqE0VzRp+pNi0go7skwrCg0UaWv0SxutuSvTyOrliX6K+liIrIqDKC4AU00xUvUUOaZ0eRy8brarAAbiRUPL738El2/fA2tv/deOl8Rfd259LUsGhkMyX3JRomo5o5lJNWcr/C2OtalFx7HionL140XXkvxL/E6XENuXh42oJcU2mDdmp3X2hrnRvsMBmfCa7qi8eEYBsWkpJTwusVY/JZ4MyVbU8lkjr1zCJayoAQf6/kkZDLFMz6ysZQi+jlYbqGRsbYwOi+WtcZTqi2JEueWb0TjR9uwzs1YuxaNF8egA5ZOyPQGKLmJcnL0tamxZON4QgLm2+aXb0Q7B+DrOTlYazu3/icKM+YrkUOlsq8vuJayMzLJLJCtr7W08TrUKCqED4VCWHs9v9QjfOAiXyyWeHGMx8Vp3EbJDdqU10u/feUVeuKb36Ika+xNDxCzWP6B9ZwxyYQB1ySOK2zOg+UbshyBq8tjNj01nZZfv4KSrbK+GReXSBmZDlFcQROzGRi8sphNiMfyrUyZDYko3hQvnn9G/snNzacvfuFzlJqaTH/x2NcpNyeb1t55Jy2VwTRNE9edmM0JlJqKZZsyGwJfIDNTxwCIGSuk53yJ7ERzEt3yodXhpXOxZCO3paSkiuyNeMU6cGmejXXtS3n8apXypbTmVVlXLfAeWABzm+vvWk9OZyOlpqkB9r8H6l69pKIFUK/yyCOP0qOPPkLf//73FW5mFC90lf2yW0D84I137ihWkm4UjuIWaTERWokiDuk8HnRQkT02OibWu7d/kAAHKC1YUdEb7ZMWq8AmaKPU3pgiUpGN4qCqimpxgKnMa097PEr+ARjI5fA9ZB45dkwMZacaVyq+h+zhYfn8o4rvUfkeMHkJry4lpCIbNlTxPWSj70tJRXZDQ53ipuX9Yptcbt/DLiIKhejQiUMLYnbDhg107txpqjxzhj7z6U9Tc/v8ftBYKqXS71V9rxLj8Ls0X4EXxanSWFGJK/QD6b68Ip9cQibxgDvt8dOhQ/sIxTbhwSgUoolJD3kmJ2nSFwgnzWAgwPi1zU1N87xzpdow8ITHQ8FpfS4BHRryysrKaHR0dF4G1sN6ArrsyfklQyjHBzYuIAHDekTIxm+G0w3Z5VVnWW/8DcLn5KSPJj3T5PN4wubEud4pN8P8Gbxh/gkPtxFtNQj8VVVVnJAMXYxrop2RwYTfR8dGGffU4GXZfj/rAShCnyeinT4fQ152dHQsaKdhP+hu6IjPgM/H+K6QHfk7+PFbpC742zU0Qv2uvgWy4UvmnfAskIHfTpw8yRtuG7L909PMC3sstklLWxuhWhXnGQQetA9641xu+5zvi4uLeYBeLBs6L9YbvgcsZ6Rs1tmIK/+8j6cDQepsB8To+IL2wPfwO9prXBOfsDUgKBfLht7sn7mYhe7gqawsZ99HytB18fHxyN8HhoaosrJUlz03MCJZQo/JCd3uhq0gA1CdOCdSBusx5yOca9hwaspH5DXRlHt+U3lP0B+29+IYB9we2rpA9lyMRNobx32T0wT/QCdjSSB+N3yD3w3Cd9yUL/ZPJO/ia2J1AsuO6JtGrCBPGAQeQJ92d3bqNpw7ANk4hs/Fsk+ePEaoPl78O+yNfGUUJuD8nr4+hiHEd4MMuUvJRn9YPBhdrJ3ImeXl5Qv0NmTj08hXuK43EKD+5kFG7IrUOz09k7bsO0A3rr2FNty7gY4cOcLtcrl6l5btmeZ+GfY9liT6fNRQV3OB7y9mQ6yTNbCUDV2Mfm+cE2krrHpoaWm5wN7wI/RAfwRBFnRpbm8mr9dtiKDpYCg8lizOKYCoXZwLjZzJudCv1wtBNsafwiL55vZhBd6FL+I53MCMnyorqxgrc8g1SqtXXcsVtFu3bCVncyPV11bTypV5lJycSrV1NVRXV8vYpNjhY/V113FT0LnKyyvY6VqcRnl5yxmjdc+eXeT3BxjmDXMoWAfb3dpJh4/uJmdzGzmdtXTbbbezjJqGamqobyK3e4K6ujro+uvX8BwT8GeLi0uorq6aPJ4pWrXqWp7r3b17J026PdTT00WJSSmUlZlBeKI6cGAXtbY0U01tDd1++x0sG4miuvo8z2+1tXXSddfp0GG1tdVUXFJMzsY6GhoeoOuvv4H5cYeGZA7ZmkaE+W1g/GI5gtPZzMnn2muv5XkHwOMVnSqmmcAMv/qDfphDwxKX4lOnqKm+gZpbGsL4nwcOHaGhwV6GNEOHNODutmx5k5yNLdTsrKWcnGU8L4QblQMH9nH+aG1tZag2zKHhmtgYAPo7na20du1trDc6kWvcRZ5JH42Pj1FBQQH//vbmTeR0tlBjUw2lpqYxtCBsBRB4LTRLLS3NlJ9/Db/SOl9VxYm4odFJjU1OunXtbTy/BB93dfXS6OgwjY2NUkGB7vv9u/ZQVV0dNTvryRSvzwlOTEzQvn17KBCYpc7ONsYjBiRgfUMdnThRRE1NTmpudtLKlSv5mnU1dVTfUM94x/2DPbTm+htZbwDJV1VVc1zFm3XZHo+HDh/azwV2wPYFrjGwfdFxT5w4RE3OFmqor2K4UazthI0aG5tpdLSfBgaG2N4oRjl9+jSVnS1j/wQCftYFyQJvQSYm3Oz7+HgLY2ADAB/taWlpotraGrJYkyknO4tlV52vJK/Xz0uUluevImuihRoaqunkqWK2t2t8nK6bsxXsDcjQnu5ujmHEFWy1Z+8uanY6qb6+nszmEOXm5lFvdzcdO3GEDu0/SDfdfhOtyl/FtqqvrqWi4iJqbKimzq4euvnmm9lWe/fuprExF2ORe70ejhXA7r29ZRvbGzbPz9ftjfYcOYbEHqLm5ka64cYb2J6wIWLI6dTbafSfEyeOUFfPALknXAS8XsP3iNmmplZqamrkmAKGL7dn3z6aCcyybOQC1E309vfSwYNHqKGxmpyNTlq7VsfDhR/w6lwjot7BQbrh+uu5Pdu2baH6+iaOE+ypDR+jD+7cuZ0wx97W1sJYwvo1PbRr1xZqbWuhupoquvGmm7k9VTV11Fhfxzd9yCk33TRvq7q6enI6nYQ5ddRHGLLRH4AlbjVbKSsniweRHTt2UGNjIwGDeOXKfG4PbHXu3BmanvZSc2sb3XjDDZyvTp0qoYqKcqqvbyQKaZS3PI8HocNYOhY/yzE+MxNiXGdgPR8+fJSaGmpoVf519NH7P0Lf+tu/pcqaGrImJlEg4GPZyLOI2YqK81RacoKcza3k8XrpmmuuocDsLB3Yv5dGRscY79mwld6/D7Ee6GtGO5FHSkpO6rKbm6mg4EZKTDRTbV0dFRUVsU2AfbxmjZ4LkWc6u3toeGiI/P4QrViRx7l9x45d5Gysobr6ekqY65uIK8SP1ZJMvb0DlJ2dxbZqqK2iU8Ul1FhfRR2dnXTLLR9iH8NW3d1dNDQ0xDdWmOMGvf3GG+RsbuYYD8zM0IoVK/kG69Dhw+T3TYdjh5mvlP+kuFVu97T2zDPPaAMDPaJTGp0t2rlzFSJeMO3eu1cM8wUIsaNHD4tlFxYe1wDdJqEwtKPfL2HXjh49KpbtHndr27ZtE8kFEyD1oI+UtmyRw97t3btXO3hQbsO33t4uhqR0Op1KMJNbt27VYBsJwffFxTIIyxmvGrQjbF1cVCRRg3kOHz6qDQzIIBIRf/v37xfLLiosEscVoB2zHA5x/wEEqDSupv1+7c03XxfrXVFRoVWUnxfzq8RscXGhpgLt+PbbWzXAE0oI9gCMoZTQj6WwhPC9CjzmK6+8otXWRocjbWnp0D760Y9q99x9t/bKK69J1eZ+KfW9y+XWdu/erQRz2yaEXXW5p7RnfiaHdoRvAO8oIUC6vrlZHrMSmZeKR/yEG59gomtXraKs9BzResJkWxKlpqaIJ/izM7Io1Z6qA5HHuBvR785yxLKxG0W6PV2kN55epqam6frrbhBVNeOJDE/kkmrSeHM8LV++XKw37Jdis1OiVbYcCzvcSKursdMH7AjgcgnlZGdSYoJNZBMdwNwhbic2AlDxPSqDJVWwqGYeGh2llStWiCqPUbmbnpEhkg2bQQ/4X+J76JudmU1JNkmFP/HOJ/ClpHIbb1l+9epv6G//5luULIDqRGFVsjVFFFfm+Hh+spPGFUDkc3KzRXrDhioxi00XZimOCq7Vn3BixS38g7cXEv/A99jxSRJXuC5iFk/NEtl46sROUBLZeCUKf2ZkpEWtaMfmB3/xF39BLa2t9POfPkUrV+TRTTffElOf5KRUcqTru0HFsl9CAqrqM8XV1djtKyU9nSyCFQHBgJ+GR0dozZo1ospje0oqpWXIZMMn2bzpyPymL7Ha+m4dv1ql/G5Z+up1rlrgMlkAr1o/sn491Tmd4uR4mVS5KvY9sEDJ6dP0Z48+QvfctZ6e/+UvKfMDjgP/Hpj4kl1SXDSFK2J+c2xChk6EggKVCkTp5sLQAxVrSDJSUtEDsjGfJyW0M7LoIdp54MM8sZQgG8UJEkJBS0NznYSVeVDgAPlSgt5G4USsc6CzimyV6nfooCIbUHPwqYQgVyVWVGIQOqjEOKrlpfb2BoPknytIkbZTGrPQ4XLFLHRVkQ0bSqEDDdlSG8IeKnGlGrMqcYW+OTg8KnEl8+SvWEGVFecpze6gtXes5fnri50MPVTaqRKzkCuVDXtjP1spQa44FyrGrFSHS8GnNOCWlZXTuMslui4m1LHRtZQwSS8lbGaswo/iIWnHw+ucsrKzUlUIBQB4DS0h8AEjV0qwIeDsJGROIKo4I79RqKmpo9ZWOeYt9JbakCH4+mUY0GgbcGalNkRH7e+V32ydPVvORSISG8KXKgkGm9NLCXGlgl2NNkrtTQEvBRQQgVTiCpWjKokRFbn4JyVsXC4l9PvyskopO+sN/SWE+IP/pQRsX/hUQvAjdJcSsN8H++UxjlyIaa1f/vpX9F9P/Yz+9tvfpm/81RNLDn7t3Z00MCD3T7XCwwfiamhIJhs5orCwVGoSUolZCFXJs2IlLgGj0oCrgtWLlQ8q8H6SuZB33l6lZipdRocQU4F2lIuHDaVJFxvAE6nBtqlBO8oSl9E6KaYq+MErbSf4VaAdwa8CfWfoL/uU+x3yVKAdE+Jjo24ZOgJO0SwcWIxzpJ8mht2U1RBApnApcMTl5X2Tc4SCydneMzJ4WaDXqcEBKvQHzUyALxWT6Z3YUZf+x1/6EtWer6bxkSG6e/06OrBv3wJgW1MwSJom1yUhTiUO1XI+qt9VSLrOHDLV41BFk3fOK4/2OTBw6aVUwOt1mXLjW8hMoZC+pkuijxSnVyLrd+VRGYhwLelgoQP6yxMjZKsMAGaFRAfZKjdb4DUpXCBRBC2q7in1mJXHILRRuWGd1WbEDQBAf1ABY1glBuMTEpT0Vhu00ES1m0RVrHOpETGYqyTphARZ8RtfPy6otJmHiUxK/IvbiKfdrdu307P/9QI9/sQ36Etf+AJjHIDPhA0d5KmWSOHNiWr/sdmUhh8yS4NrhlesLjbLFfH31aKpK8INV5W4aoF3bgGjaKqq0UnpafL9Yt/5Fa+e+X6xwOjoIP3rv/6I3nprE/3g339Af/VXTyjcmr1fWvn+0VPtFuP90653rKlRPKFyE/iOL/YenogCFGkx0Xuo5u90aRSSodgCPv0gE576ZhCwCm993o/2QNHMBz1m4ZdLGbOZmbn07LNP09a336YXnnuOPvbABjpz7tx77n5MIaGAS2Uq6T1X+hIoIB5wEeybNm1cciJ+KT1gTMDkiSgUotOnz4ir0PoHh6mqpkokGkwoypFWzw0MDdCWLdsoJNw7Cigy0iQAG5aUlIj1rqmpkRdyhEJ04sRJsezi4jKGx5SeANnSzoEnLpXq05MnT4p9Dz/WSH0fH6Ide3YxFKiknYhZ2FxKlZXnwq/qYp2DGDl9Ws330pid8nm56Ez6uhX9UlphDShVlbhC9S7+SQm+l1JNTSUdOHRMyh6GOpWcAN+rxCz6sbRqdngUMSuLK/QxINhJC+wQV2fOnI7ZxAc+9jFCMdb6ezfQJz7+cfrud74TMyca+Ura76Ez7CghyN6yZYvYhk0NTeKCxkAwSCpxJdH3UvGIgS8CAY1KS0t4kbLbPcVQdpgMAGRXX18f45wmJelbfnV3d1JDg5NcrgGGhQPcGqizs5U6OrqYd3Y2wFthwfD1DQ3U0dVJnqkpXhyORfYIJC6PHxygwcGB8PZgTe3N1NXWSv19AzQzM0PpmZkUbzJRb28/w39hU2Ofb4YcjjQeIIB13NXVTdPTfkpMNPGWgbhmU1MDw9sNDw/xtnPQD0kIcI/T0x7yzYYoOzOT51BRIQe4QvBOTIyFF6SjE3V2dhFAJEIhfYusoN9PDU1NvLnyyMgor4sEeAECEdWEqGwNBme5qhDzs0iqra3NBN7h4VHdrkTcQVFd7XYDB3g2vEUWQJ3p/AAAIABJREFUlmaBFzaHnQAPCVvVNzRRZ3c7BWeCBPAB43fYcGRkjHXH9nogJJaBgS6G08T2W4Z/UNkHvNq+vl4+Hwv1x0YnqLGpgdramkjT4sKy0R60BbrA5rnZOdhPkJMtfh8aGuYtsgzZWM4xNIQ2DjF8XHJyCne22tp66upqJ59vmqy2ZEq22bgiEfYeGOimkZFxBlCBDSG3tbWNZcOfy5blcnvQxoGBYebHVn+wCzZQQFyNDGF5zQxhUT5AEObtrdsEbYStED+NjXUMSQgIxqysTAYRQEx0drZzO2dmZnm7SSQgxFVnZzd5vT6KiwsxaAL80NbWwW3EdeLi4lgX7g9NLTQyPEwezzSDIMD3RlwNDKAaXf8dDdLjqpMmJiYpPp5YNp7SAd6vx8nwnC+SuT3nz1fRzr2b6aGPPxzeMi5S9vj4JLfHkA17AxoVvsd8H9qDpXDoZ/gHoBjYG7CsTU111NXVxTzgXRizgAnsDffNmro6am9rIbd7kiEQDd8vFbPog9XV9dTb3sqwgwCegC+AfdzQ2MhxGCm7qbmZ+7yfVwQAZlH3vS5b96Vhb9iqurqWYTcDgRkGeOGYCNsQendTZmY2+7i9tZNa29q47X6/PywbNw69vYjB0bC9YSvcZHd397AvAQhkT7WHbYi+Btl2u74tYG9/N7U0NlNvXx+/aQFMJwjV8IgL2Bu5A7EJ2eibg4NYrhcikzmR0h1p3L/b2to4P8AmFksi2woxC7jVgYFBzlkAEcFcNPpmV1cPDQ+PkN/vY4AOXjbYVE/pjlR68KFP0vGjh+jffvTvRCaNbFYb21vvm3rMQgZyZF/fIM3MBCL6fS/19PRy7Hq90xw/aA/0BtQl8kdcvInSHQ5ub0uLk/sr+oOePyJz+wjHt8ORzn0Q7e7s7JjLnWPhXAjZLa1O8nj0G8vFcYX8Ewxq3DfR73FD2dHRTrfdpkPZssGvkP8USmFmwpuEWyxmBjI3J5p470tMZvMmy3OFL1azjSv+zGYrd1AEEjqqzWanEJm5hMxqsbIJ0LFxjDfRjpgUx2+paekXmCnFYqUxsvA5OGiZO8dms1IgYCMym8gypwdk4B8QlUBGkVBY9qLqAfBZLDbGUk61JIWvYbWlkA1g5yhiWlTaazZDFwufwwzx2B/Xps/ah0JhxB0kFJChC3QAReoSWTc0f3y+reBnm2BDa5NpXj+Lhe1tVLbOnztnw0XtxHEUzsCPFJp/yZGGBfPgNdnCss0W/Xhior5/piEb7TF0wcVRJQ1ODHh6uy7UG6DixjH+nNsoGsUWJrOVrEb8GPY22VgfxAgIvgHB5fC3QSl2B/m83gV6x8XHcxus7JuUsF5Wi2Veb0PAnEz4MRTy6XaZOxbZTrYX85rIkmBhRcymeb3AG6mX4XOb2UYWs4lM2izHZtiGc+00w94RcYXjaKMe2rr9YYOwvdkWhp3NZDFbiQKI8Xmbh2MWsuf6iNFc+EiPW10GCtbS09IpCL6IWMF5SUnz+6Zi31VQpE2wJbxB4Nf9b57vDxExO9cgZkcbzdYQxSUmYmgJ88MOiEMUAYbg/zlCn+ZzFhUSpqZnhsvWDbvCVmgK9sMFRf4etmGEbKs10t7GFfV2sl9CoQUxkZiIgin0wch4j+hrEbLhG/QNzhEWCw+q0Ac3xYY9jDgx9NR9YyErLjCnP+cU/iMl3J6wWyF/Lp/O8+t+CctO0O0A2Svy8+ilVzdRU10N/fM//xP96oVf0b/8y78QdiUydMDAbbXYaXZWX56EmyEQ4srqC5DVdmFcQTZ00qMKe2InkNUa4UPkmzCZyG63EpnmYxb9y8idkTELnUI8RlgI/degeV+awv4JJeibz4dtYzBfKZ9SjEhgkr65+U1taGhIdArwQ+tbouOBRgoCVqbbLcPThQ6VVZWRp0f9fv58tRj3FDijL774vDY9JcNSLi8/K5aN9pWWlkXVNfJgVVWt1tcjw67GecCMltLBg/u1/fuPStm148cLxZiqPT09mtPZKJZdVHRcc49Pifjh+1g4s4YgYKq+9NJLWqMQ35Vjtlaud0XFWW3EPWJcLurnkGtcqzh7NipP5MHq6krNNeKK/Omi31WxlOtr6sU4zbDhcYW4Qv9pa2m5qK6LDxQqYFczlvLWrYtFXPRv9AcplnLfwIAGu0ipuLhYKV/BRxKCvV977WWttrZWwq6Nj48oYdbX19cu8D2u9/Qzz2g5Ocu0P/3zP9WAg26Q2zOtFRcXiTHU29paNPR9CY27XNrPFLCUnY2NWkdHh0Q067v/4EEZ77vMdXmrlPlpSb9Lu1JuMGLpgadxvJLCK54PMvFWWTN+Skqef4L5ILYXry5xd27cuX8Q2wgwg/vX3UU1bR2UnvrB9Sfm5rA93Ae9b3LMWixkTtSf0N+NmMV0yE9+/CN67rkX6KuPPUb/+q//Gp5quhzXR42fZ8JDqalJ4Sf9y3GdK03m5R0Nr9jn+ou7AYn5g96h0foki/kDP9iinfDlB3mwRRvx+m0Wr4kXQBxcPMbfr0fwWvn3oW9yzL6Lgy3iAfPz//4f/0nnz9fya+9bbrmF/t9//ufLVuGPgSc1Lfn3arCFnZUG3BdeeEFcKYYCHEn1nNH5sQeolBqaGrgCUcqPvTTx5CohFDO88N//LWFlHrQTd4cSAt8bb7whYWUeFIRIq0lRFLFp0yax7C1vvaUE2bdx46ti+EUUXEB3Kb311hs0KrShXmwjl/3qq6+Kq0+h80lUkUfMY0Zrw4kTJ6IdXnAMcbXnwL4Fv0X749w5OdwldtHxCavqcU3ELIpYJIRN7+F7KcGGKvCYKrJRPAN/SgmyES8SQvzBLlLavn27uCLXNx1UyoWb3nhDqf9gM3oplZScjtrOgtWr6MUXX6TDxw9TXVMdrVy+nH7+i5/S2GhsbGfYT9rve0d76edP/adUbZaLvCIh5HqVuJLIvFQ8SgOuUfAjvbgKoo1RbCOVjQKRy0VG0ZVEvv4QH1kMIDlLgUf6loDrimQ3Fbi6KSGB5NwouLh89kacYBN0KaHaUYVQlCMh6GFWmgZR87tR4CfRRS9Bk3DirhkVrfKV49KQ0q8+Gy42lGijijZkFDJKZKvycMxGFAVGO18WIfMSVGAGzfEh6T0cXyCyYGj+ihf/pvIGB7GCqvxYdMetd9DO7bvp/37ve/T2W9vpzrvuoF/9+jdRb2AQV0ahWiz5VrJSKE6O1iW8B9YvO6sXTsXS4b04rhRnKo1Gx1PBD1UZcC0hJDo1SLjLa1zZYIGOoWJD5hWeoKd++aAI/F2TggmFaoTNrMLP0I7iUSCB4uJmw9eRfJFCe0KPxZW60eSbTDK/swxF6EAVSD2Wjz4hNLqQjcXOMKazQqBEM9jveIz7j/DmCZcClGYo9tjyjrRC1bmUMDir3EBJ5Rp8YphbON5sISx9ktLq1WvoVMkp+u3GN2jzpt/QbWtvoR/84AdLvmrGDasUp5mxqxWAWsTpAQ2Lx82nPBdKbXEp+MTrcHGxyYlxWpmfL9rkPCHBzJs0G+XksZRNwRrMFFnBR4LVwmthsbZOQsZ6VQY/j3GCyUp0TXY+2dPTYnDqh7G+E/IlsuPj4ykz28HbaEmEQy6WDxjLYqKdE4qLo5xsbLgt0zs9PY1yVuZRUuL8so5o8rOzs3j+TNJOszmJHI5U0Z00rpmZCb2zKCEhdhLDulSrJYWSIpYFRdMbG2gvy80iS8SyiYvxw5fZmWmUZJNtXI1NsZOwBExA2JQb67qTsRxEQFiTnGS1iuIKO69seuU39MTffZuSrLFHGMQVlotI4irRFEfpWTmUZrcLtNaX0mBph+QpCgIz0x1kT5PFLN6wLc9bxutKJcpkZ2aTwy7bJB62QK6S5qv09AxKS5PFLJZdpaXZ5TbJzKTM7Bz2v6SdDns6JdkET4tYF25LIkdGhlh2erqDUpKT6ZprrqGvPfY43XLLOnrjjdfo//u379H0hJtuu/32sM2Aw5Caag//HU13PMWvuGZleB1vNF4cw9pjaS5Ejpqa8lB+/spYYt/145e3Svldb87VC161wO+fBbp7u2n9uvXkdDZSqnDw+v2z0tUWX0oLnDl9mv7tRz+kM6dO05NPPkGPf+NxKihYfSkv8YGUFfuRYq7ZmIjGpLW0+AjFPioQbyUlp6LOD0RaH4gklZXlkT9F/a4C7Yg27tu9k7AEQUJVVYCNlBVNoYBDBdoRBQjdnbI9OlE0pQJnhkKyM6flmKrq0I51EvMxz6lTct/3Dw/KYfKmg3To0CFx4Rl8X1Ulg+CD4igKlBbMoUhJpYgQ+xWLC5u8PvKSl8FnJEavqauRF/z4fErQjk1NTUr9XiVmq+vqlGIcMSvdZxm+R1GWlFShHaVxhfx64NARceHZ2OgYnRZAOxrtAgoT2iohI18Fpy/MhevvvZf27txNp06XUGtnN92x9i760he/SKdOnxKNEZC9bds2cc4Hypq0gBRTKxOTHkkT33Ue8YCLtanbtm0WJwEEzqigsg0tBq9r3C1yFPgDAR+NTQCaTkZ45Sa9UUAH7ezpE88UjY4CelG2AT1WbQwPD8qUJiKuPhXKBuqXimyXy0VTXpdYl/5B2cAPgb5JH8MSSoUPDQ2J/RP0BRhKUyI7GB/iTgr/Swi+93jkccX+YajB2NIRf9INyyFtcnJMPFhAtjmooxjF1oQY9nJqwithZZ5BBd97vV6S2hvCBwfl/WFqYpRGFPhV9Ibvx8ZiV+IaRsNG64GAzIbBQJAmJmSy8ap1sL9XHuOhILnHxw21Yn4ib3q97ph8BgPnlChb4t64Zg1t2vgqYaP6Ffn59Ief+DQ9/PDDtGPHDkPEkp+IWUCjSvMyYE6lcYU58wMHdi153ff6R/Er5clJH/32t78mny9IdnsKPfbYY7y+8d//4z8ocQ5678tf/jLl5+fTqZISKist5bY5HI4wL+5oWp1O/v1/rF9PDz74ID8hvPzyy2E73HP33bThgQcYDxNPmiBU1H7iEw/R2rV38BMLsGYtJjNQwehrX/s6zy0eO3aMyisrKTQzQ2tuuIH++I//mAAl+F/PvRDeO/fDH/4w3XfffZyEN27axHr7Z2boYw88wL9jaRKeLCA7EArS1772NV78/dxzv+B2Q3ZOXh63B3r95D/+g3XD95tvvpn+4A/+4IL2fP3rX+d5CjxRFhcXk9lsYnxp4/ffvLqRXCNDBD2SkxLp7//+H7jNP/3pT/kT/xUUFHB78B32BsHmaCOO4c4cgOcG/dmf/RkBs3XXrl1UW18fbifW1YF+/etfh5P/smXL6Ctf+Qr//pOf/jR8o/HQQw/RHXfcwXfa8Bts4qNp+vynv0RrblrNTxrwM/SA7v/0j//I8bBl2zbqbG9neSkpNnriiSf5O5aUTU1MsL0MH+NO+7evvkrmxCT20cc//lFat+4ufgtQfPIkYUdYyDf8cOTQIaqaA4EHHN83v/n3LBvLoTq7u5n3f9x9N/sTsl9//XUCH2L2zjvv5HjDJhnHThwL6/3oI4+wDWE/2BHFeyiyeuIvnyRrspXter66mpBzbl+3jj75yU/S5MQkvfzKS+xHKGBc0/AD7AH61CcfpHXr1vMTS11NFdswZArR1772l5Senso2PHv2LNtvdUEBPfLII3xeZLwZ/cRoD2IQ/cGw4ZkzZ3iDhv/6yS/of//L/6ZvfOMb7Hs8gcGGlEhkt6Ut8AMGRZARV+gn//mzn/FvsPd8e5po37494Zg14q2i4gwdP17EesMu/2uJuMrKyrqgn0D3D61dy/3EaA9flIh/Qx/CkqI33nor7B8jZre9/Ta1d3UxO/rQUv3EiGU8CW3evJm4MNAUovs/cj+tv3c9x9WJkyfDsgHgj7ls9BPjbRzmn598Uo9Z9JPB4eEFcYW3Dq+99hrHCYqVPnzPPXTfhg0XyH78scfYD3iCh49BiMUnnvgm9xP0qUank+PqnvvuowceeIDj6qXXXiJz0MT5B1jAiDcstzl69CjbG3K+8LnPcb5BW8rnZKOtf/PXX+cpBbzVQY5EHN56yy302c9+lrA06dXXfkUBb4BlG/kK9oYuBhk5Ev2kuLjI+JmMnIK4Kp3L7Ya9wfSbja+S2+WiCY+felqb6fTZMvJ6A7Tm5tV09513UlpaZjhmYWvY3CDkTehjxCziOy5eo+9+5x+ZBbnDiNmVK1eG+0lkLjTGHuSCgYEBWr58OT366KPGJa6cTymylds9rT3zzDNaW5szJpSh1+vV6urqGBbM5XLHhAZzj7u1vXt3a11dfRrOjUY4Dvixo8cLGVptxjcbjZ15jh49rAFyTiK7rs6pvfzyy9rQyHhMKMMR95R28OhBraOtTRufiq43INS6urq0vXv3xrQfGgSbAJoOdowFeQnZLpdL27Fjmwad8Hc0grzdu/dqhw8fFsmGLpu3bNFcIyMi2TVVVXO+jw5NODM7qyE+du7cyXBzseA0Dd8XFRXzedHaaNjk5Vde0aqq6oW+r9MKC4s0VywbQm/4fv9ehrKLFVe+qSnN2dahIQ7HXW4N7Y5GLte0VlhYqDlbWmLqjXaWny3XshwOjq+Yvh8fZ99I42pkaEh7e+t2jq+Yst1uraysjP8Bui8aGf6B7xGPsWXDJse1zZu3iH2/ffvbDEUbW7ab+xlgV9GPopGhN/ox+rN3JrovjZgFNCrnwijCkctgi9df/61WXl4u6pvQYf/e3dr4VOy4mkJOKS3itsaKWbTTyFcjLpfAP26tvLxSc9bWat4pHab16P7D2kMPPaQ5HA7t77/1D9rZ8nKWY8j+5S9/KYtZt5tjtqqyJqZNME7Bh2+++XoUS793h8SvlJOSzPSZz3yGli0riFlZhkq/tKRUSk1J5zt5A6T7YrcZqWmpZLOnkD1F3zHkYnz4HbLtDgdZrRYdRSgxehOA2mJLcXCFW6wKRBxPTbWSzW6j7PTYCEWZqclkt9rJlpJCacnRqwSxpAFP+6iWBapLLIJNUJUH/WOh60A2ZEJ/6IS/oxHkZdntfHcvkQ1d0qBHWppIdhLzwvfR24nXZ3jSswH0P91O1uTopfxoH2ydYoMNo0Nvsk3S0ig1OY3S0iwxKyd136eS3W5jeMSoNoTeqcmU4sjgnVZwbjRKTE4mR4qNzFYA86desJnA4nPT062EtwMOe+yKT+iZlJxEQWzokDIPbL9YpvE3fIhKdmlcpaWlUYrNxr6MapM5VK/U9DRKT0vjDQiMay71yf5JTyerDZWtsfsa+mWK3U6ZaXM5ZSmhc7+FZVvtQtl6H0tOTowds3N9DfnHYXdQUozlQYgN9HuOq1gxm2ii5NRU3jAiOVnW7/FEnpGRRWnJseMqGTnFamObxIpZ2BC78pgtZu77It+nJpHZZgsj2D34qYcJoBwVFec5p37+039I9927njZu3Mh5BBt9wDYi2WnplJb2/7d3rcFRXFf6aDQaPRACSchCFopKUbQYGxIMikzAIYRgnHWI1y7WRaVSKf9KxSlvlTcvb7Y2tV7HW1vZ3Uo2/pMtCscOcRzMYhvzMCCQeEpYCJBsMERCKCOhBxZ6jKSZkUaa19Z3eu6oNUgz58aAhdK3CkbTc/r0ud8599Hd537X2PErjuu5/0a/s/rhtfHEPrXfxI+UPzULrQtbCFgIxEUAj1DXVFTQpStXuDONK2z9aCHwKSGARKnK6mr67datVF9XT//0zz+h5583XnN9Sibd8cvGvz2MMQf72SJ5ajYXBIU4G+4uBqKrq0ucYXsXV5N9CZ/O5oLEE3+IKBB9Az87aws/og+a7QXvt2djzOJJxt8/8QQdPHiQTp6uocLC4tvjypCRLHl7lH8yrVoD7qFDh/mFtOSSWNKiswyiquqoRC3LIDkFSVLSAv5QaTZcX18fHTIlICW6BuopXRricnu1uJSRLNFxXZ4drMOlfObMGXI6WxJVL/r7G29sJ59XxjiEDuPSJfmyoLd37BJjiOQ9KV8rjEecdHZ2RusR7w/orak5HU9k0m8nT2pwKbe306FDcr7weg0u5ZFxH2c0SzcvQD3FS468Xi2ObrRNHS5lxJW0dHZ30tHjcv+At1w6cKEN63Ap79lz+7iUEbNOp3xicfSonEsZd5Y69VSJqxIfIa6kuu9ZsID6+j6WqGUZ6EW/IinjISyRrJGI3nEZrQFXh08XLGJ6XMpyLljjmb+GvC1EFJRXFcwwOsUe2XQ94TmBcaabSyhnEhBT5GLDbg2qNFzi5tV1pgvH/Mmct3GWB8SIUzBoZOrGHp/q+zgFaFzIM2kjv3jypK6V6B2RksOnPErMZwn+Br2fhvIErwYnXdARMDL2Jx28VV9A7aURKTq0kYaJ8d/bx1ZDh1IR1I63q+jUE1zKOkUnXqFXhxYXlujEYShJ3uiBiZRhDHZr7LehAx/ZuK3pYa51gU8grNEFiKla2Rw4Fdy00qITwIFQQER5p649jlrK40adJvqE3QGhb2GGDlk7MJQOiszXKh34mWdWj0s5EBhPmOwjAmwKIfBu2wOySU4oBdSFQsAj15I+3cAEEYO/vMhsZn2aXMpa7cEW0EREXkNDUj4o6nTm2laE7FqTLbQ1IX+NrimEPkha0DZDyGqTFh3nc1uW2wIT0JalRcpDDn1oxzo8zQ55WEnNNeRsWHqph4neBf5yaS0u5ZUrVyTM4ouaYkuhLEGGrZIHlykyIiXFnuKgzDmZYvl0u4Pmgnc5KfEuM8hwW7FihcQMlklKSaa56Wlkj6xFjnciZJBVCH5fUbGl0Nw5Ql5am40yUuZQbl6OSPX9999H9y4qFMlCyJGWSrk5uaKJDmboqalpIs5t6AbvNjCRcPsmU5gzvcEHLClYS4xsS0lJTg5R9rwcceKRzZYkjkF7cjL7PlHmtrITWEg5ukHa8Put2+gfnntOdoeBuMqcI8Ib9qSmOsQYwvdY25ooC3ainkY2rPoe7zMnL5fXhseTMf8GWwoK8kUxi/NgtzSu0tIzKW+BLGZhR0qajTLnxM+sV7YvXbaM8vMXqq8JP232VJo/T8Z1jW4qa/49lDlHyAFuS6X5OfMT2gABdK9ZWVkiDIHzqlVfEumFEHjopRzd4FL+wheWi3XfSUErSzkGbcyMkBiWaLlMzGl33Vf1PjbRUpy7rmIxBmMwQoeHf7O1IMmvoryCPrraRLnCzSvuRiyw569/bGzWt023b5yXG83mmEX8/TW0zdh2Jn7OgeSDvXvfFSdb4AW3NHkCgxz4jqUJDkj40EnKAXuUNLEJnddbb70lptUDo4tUN+pXX98Q64Npv4P3VEp9h8dWdXXyRIGTtUfp9Bm5vE7i2fWO69TcLE/Iqjt9mrzCTGL4vkWoG3GFRDJpHEL3ny7J+XTBjyv1PeQQ49IC37tcsk3iwcKDzovGZY/RwPQjTUABhmAAkhZgrVibJOfoxOyFDxro2LFqiVqWAT874yI4g+OqRR6z5+rrxf0VfH/hgiyJEHjv3bmDLl/+SGA10dDQkJhbHAovNzeL+3C310tgMpO+wEHf2d4hS/IEJtu2bRNj2NLSTB0dsqQpYAhmv5lYNKb9KdTR0U4LF97LnJaghUMxd2ag+sKjpJ7e6+Rsbadhj8HxqWTRyFUDAKkDHvXhbrLz2jW61vkxv5orKS3lx9YYnJAxrIpZB6gD+wYGyOHIoJKSIr57QYNRXJt4NARqQwCPxt/R4aTRUS9BN7ZIwzVB/6XKhO4e7oiQbIF6lZWWkt3h4E5V8eBi1gn6ShTohpzf7yffyAgVFBbyNc3LiiCLc2Af6t/R0Urz5qZTaVkZH0fgKd1kt1FJkZEq3wrd7U4aGnKRbzxAxUXG49+p8AZW1zqvUXf3AIE8fuGizzARx3QYQseQ100pSanU6nQSaAVRzLpBzYe7fEN3N3V3d1Jzczp99rN/wz42441zFYbtHU7ecAF8rVjYrrACJvAHCha749Eq/NDW1kbtHe1MalBYWMjHJ2FCxDqAoYFfB/X13eDsprKyMtZnjquo7kCI2lpamJbw+vUu3pIMvo/VrWK2nwfyVhoc7mMyBrPfVFypmEU9nK2t3B6C/jEKFBdzLMfirTDEZhvt7U7q/vgGzZ3TzFjFxpWKWVTI2eLk5S9DbjcVFweosKDgpphV9XQNuZjWMmAfJ2erk7CFHfxmrqc5ZpsjMZsV2SZQtRNzzCpMoKO7u5vr+afmXCorKbmpPcBe5XvEj4qhNIeDioqNWFbHIKswge+72zqp1dlBudnNtPDee6PxNlW7h319fQPk9rqppbmVyhYbO9OYdStMsPFISxPafQfNn5/DfYGKN3O7Vz6+3tVDzvZWGhgc5DwF9BMoU8UsfN/a2kx/vtZN2LO4uKiE8vLzb2r3CkNQQ8L3fTduUHqqncoWL2bdU8UsKDadbR0UshENDAxyvMM/08UV2iD6iO7ObvaL8o+5bUZjdixEHZ1O6mxvp8Feg9dZ9b9mTBSGE/1VO7f3JYsX3+T7STHrdFJraytlZqYREtumiiulG/XB+IB3uK3OdlqCR/np6ZNi1twXGnHVQXYH7g8D0T7F7HtVTzWeQO+qVasY65n0n8aAa2SdejwjlJ4+QX6N2XXsHqnjvgANeAbJTjZyuYapqCjAgwuC1TzgMhChZOodcpF/zEvDnshMnV/sB5jAGy/izcUTmc1Dl9uNwDEGP3wfGfFxBh46GBR8gvd2fDxAIx4fhSIbASg7YnMTkEwAHfa0TOrvd1FZmfEAwOcz7II8BhFV3ENDvOf34ODApHfbBiaQsvFgbNhjp8GBPpbvGRqiz/j9N2FiTgZCZxuCPYPD5MsG3saA63YPcfY3J1RFBjDGwuUmv99LGDg+s8jYB1LVU9mrPjGApCSlMFYjngkCdoUf5HCu+hxy9XI9XC5v9Dh+U75UcqgncAapPzaYBi5qwIXdSUnIeJ2sG4Txyckp3Jnm5+fz7+yvSFwBc0xooBuTGo9nmP2Jx26qwG5az59MAAAR/0lEQVT4CHGIc1FCo16e/aNT8PlC5BsZJ8o1rq3shm5VT8+Ijzwjw5wA19vbH7UbPMwK8+ieukEbwT84d3DYQ3kj2BzBeE+sdMMG/I3BD5tteIaHKegfpX63mxb5eR9wIy6naD8ur4t/840M07hpcwTog83wvaonE+O7+iktlEYDgwPEvTVngKKtwQ/YS3QiO8XtcjHHOHBUEwllKwMX8x/uoKDD1dtPo4sW0dyILnM91SloM+PjyMQHLsORlomNGIY4oQZ6VAF2XS6Dp/i6y0UYoFSZSrdn2EMhCvEk27zBhFlW+TI0FqCh4X5KSkqhG30Dk94/m+XV9YbHPTTiGaZQIMQbrqgBF7JKp/oEGP29bgoHR8njGY/uKsbx6UNbQp8xUdGAz8dtAv5SMQNZ6FO2qE+sjugZ7Od3lT7fOHkivoeswhA2K1vgX7Q3tA+vZzSafmzWjWtxSSHC5Ax2eAi+HyGkNkAW7QfF3Kf4AiEaHBgk33iIJ3ujeJTvcHBMKXuBlyro5zFhGBy0UV6esVnIGAWjfTLklN34HBwZpszMBYw7zqP09KgtsMMemhiaEKdoQ8AWNyeqTzGPPWjn6hrXe3rJjpUpM7FIWSVHR0fDv//DH8IDffG5RpU+8AufP39WfU34ebCyMpyIf1UpAccneFWl5f0Tp8KdfZ0icXAu/+Y3v0nI/6yUgfP2xo0b6mvcz8FhT/jgwT1xZcw/nqqtDbddu2Y+NP3fwWB4z5590/8e80tl5cHwkfcqY45O/3X37j3hYAIOYHX2latXwufONaivCT9379mXkCNVKenu7g6///77Iv+As/WVV14JX266rE6P+wnfv3/2TFwZ849HqqvFvofd4FKWltozZ5lfWiLf1NQUnp81PyEPsNL1/pkzzGGrvsf7RLt/55234olM+u3ChQth/JOWd959Vyoarq09EX777bfF8uAWh/2Scq2zM3z2bK1ElGWknOgQhu9ra0/JdAeD4d+9Cv7vRpE8eIN14krH9+B1rqzcF/aPxOdmV4Zevnw5jLYvKcODg+Ff/devxTHb0NAQbrp8VaKaZd59Sx5XYqW3QNBKmoqZBeGRBLa7ys3JJ2x5N1sLHheiSLNm71YcrncZj5OlWbN3Yz2dHe20ank5NbW1Mcfz3VgHic14ooS7voLIkxDJOXejTG9PD/NiSzOm78Y64i4Xj62Zr1ndhd/iiuAed6b14NaAe4udbKmzELjTCOBdI3MpNzXxBhN3+vrW9SwELARkCGhNALZu/d9oUkQi9aD50qF21KEnA33c8eNyWj3s7ajeOySyGy/isQ+mtIByTN0tJjrH5XJrUTsCQ3SmkoJ3pjo0edgDs76hXqKaZW4ntePOnTvEGCLhArhIy/bt26m5WZYhCr0zhdqx4Zw8ZpH74EZ+Al5+CQrqibsLSUG70Ymr20ntCN1vvPa6xGyWef317eIsWOAhpSWE8t27NagdfT6qO63R1nbs0Ipxnb4Tmds67WfPAWNPcgno0CvV3dPTRb98+X8kalkGepFoJilYPqYTsxKdt0pm4s20QKMutWNS0uSEp3iXwIAhLSHtBwUhQtbk7SgGE4sURjBkadQzRGJ2JwM/qR0GEkI2RRZmhiwNijodakfEiQ4NXzhgJF9J/WkLTSS6JTrHZkp4SSQb7/fYCR4SQ2LHQyWDxJZocktEqU6Mw2Ybkkw02lA822N/C4XkbUfXBB3dSIoLaLQfUB6GYkGPrVzkO/AXikbOkLdjnJA6R051h20r9YpcnjHRMD05JLcbvo9Ncp2uHtyfyFaxsQqduAJ+Oox+09l4O47LPcUUYnJPIWbCYTm1o07ljEFLbgt0g9D69hRAKIsccC4HNCjegKFMsxqYtdxJNnk/agyIGnzUOlgnB4PIKZedkpJKwZBXJouYRUavcGZhUDvqxMnUNmP5XH5eHi+nwLtj/DtaNZlgfvtvt9Ha9Wvp2e9/nx5Zt+6m33X6XLQHnnDpnCRE0I+MajGhN26ydfCD/ES2ucSk2BUR8c6BrF3Y7vFOUYf7PSUl/h7IZrswAIyNyvtC+FJoNl/mNrg9ar6OPzHY+v3yejo0DNcQZdt18ItW9g78MXWPMc2Fv/jQQ7yecZqfJx2eM2cepabK6PdwYna2jH4PslmZGeSbJ6RH5I2x54nviRfk5NDKh1ZOqku8L9jMO/buZFp5G1FBgbyewDDNIbs7w0w+Ly/+hu9mu5Yte4CysmQ0kDgvP7+I7OmycEGKPmyXlnkF2ZOWrsQ7z+Yfo+xcY/lQPDn128Nf/CItuGdiyYk6PtVnWpqd8jLlcYU1h1OVf/23f6fnfvQDys02dGG5x+NPPEHt7cbrAexi88MfP08fXLjASxx2H9hPTz31FJ1raIiuaZ2bIccvzZ5BdjD1Ccc6nZgFFaCYipTpETOYInEqXKY6lp8vpxe9Z+FCWrnywanUTHksPz+PQphxCQpi1sHrPAXC6IOy5PVE29TBsLx8BWXNXyAzhIjmafaF5qWNiS6CdczSAgwzMmSzeKybXfMVObUjEsiwdl1UglgHLO9nRTpvkZCVNHWLgLTUWAgAAWyr9rOf/oze2LljSkBGvV564MFl9OU1X6Htr70WlVm6dCmVlJXQvt37osekf3R0ddGa8nL68PIVys6W8fVKdVtyFgIWArcOAdn0L7KI//DhQ+LkFjyiwRIbUQmFCPuc4hxJgRzkpQW0gVLdSJ7APqeBMdntgs+rZ7d6byex3eedTDSR6BwkFEnLxQ8u0aWP5DSGrFv4nEbL90Q05PWK3z/q6IYsaAmlyRaQ1/KPiRhB4f7aa6/T0dMn6ZlnnqHTNRPUmUr3+fPnmUmqfPlkcvU1a9ZQzfEaut7Tw6pgB86RlBGfj0aZJEEmj5gFG5OkoB0gDqUFdo8K902GThDTSAuYjBobG6XinDAFylNJAdZadqNPEfYR0C1um6EQ1Zyuo64uWYIQdEtpUYGDTlxBt057QH+PcyQFstj3V4oLuN91bJHqldh6K2XEA65/LEjgs5RWGtm+Fy9+KLPVZqNTpw6LwcfaysZGOVfm2fPnxVmZYDVBNqR0O7+aMzVi3QgCTFqkpf58ozgrHIGuo7vrRgd1dcoyoGHvgQP7xe/BQRf54YdC3xPRkYOVzAolwQWDZ2PjeYkoD+Lw5cDgBDNavBOREd6gkbmNiZk5Qx1to6urg/Lycmnr1m205stfpi1btnBcq4nc8ePGIHzvvQYbmLInP6+AWXR6Inyx586dE08UKOCjANnJR7JJ6AcXPyDQo0pKIClAe/bvlYiyDPBuuiLLCscJR6qPiHUjs/XK1ati+QMH9jL7keQE+L7xopzn/NixY+QeGZKo5v5BGrOYILQ7W6m/35h4JbqAa6ifTtXWJhKL/o5MbDMlYvSHKf5wu0epsvKgGEPQykp1o62Ai1w6QF+41CDWDZ3or2ZiET9SHnJ7qfrIEcrJzKR1GzdwXfbs20OeYdCZgXLNwe+h8AMIr9vb23nfxcLCIlq9ejW/58RSHiSUIINscVkplVdU8Ay3+tgxGhvzssyKFeX8HguOq6k5yZsrA8Cnn36ar3m+sZHa/nyVKcqy5mfRo197hJ/t486hqamJZcDJu27dOsKs6PCJKhp1u5n2r2J5ORWXlXBHVlV1GJvOIZ2KvvMdQzc2IsAsGkkL4XCQvvGNb/L7KAQpyOQhi/clmzZt4uscOrSf+l1e5g697777aNmyZTwh2bVrZyTj0UGPP76J6f1QH7yjQ7aqw2GP6r5woYEuXWrmayLJ41vf+hbrhn29vT1c/5KSUqqoqODjIONXG81v2LCROUu7ejuo4eQ58oz7GIsN69czocUEhg5OelL1PHn0OPUN9nEGZ05WDq1fv451YxmFsZm1jSoqyglcxdBdd7Le2EPTbqeN6zewbgwIxnIbvNe10ZYtT7H/ak7XUEd7O2cr5uTMp/XrjVjZtWtXhI4wREuWlNGKFRXU73JRTdVx8oV8hISyilWr+J0m8MZkzciotNGmTV/na57/sJHaLl+lcVuA349u3Lgx4odDTMWJOFS6ced04tQp8o37KDnJT0uXruD6YEA4d66eYxCZ0evWb6CiwkImi//w4iVKSU6mrIxMWrthPaXZ7VRTV0fO1haWLy4rpocrVrOPq6uP0PCwh3153/2fpweWLOYlXCdP1rDvBz0e2rnzdTpRfYq+9NBD9KOf/Ijr/8c336T9e/fSsRMnKDc7jz766APG9vChA/SHP/4fVVZXc/oYfP+Tf/whjQUChHfAoUCA70rxiYL3ZebjoBB85Xe/p40bDf+omEUdMzIzaPOTT/F57723jylUwXdbVFTMcYV2suudHYRVCKA33bTpccYbgxCW9oGuMT19Ln31ka/SvDlz6dKfmgkbCUAWPvr2t7/NuquqqnigwLH8/AJau3YtHzfH1dqHVzPHMiYqWM4CqkG0B8QJSFhwzePHj0b9o2K2pqaGerp6KJicxFvAfT3SB+F9uGGHg1asWE5Lliwh0H4efm8P60Z+BTh1QQeIax44cIBtwn+bN29mHBsaGvhmAhSj6emp3Dbx+/79+6MTwQceeIC3BsRAAQzRJ6GeeBWAa6Kgnijo3+AHkDqAbx2bViAhKz09hR599G+5nQArcGwbMbuY0O/hqUPV4UMEWkckEZaUFNKDD65k7ua6uomNL9Cfgr8aOQBtf25jnvisrEz62tce4frAZy0tmFCFSPWF0F1deZAGPSO88kHZjQks+hrYjAQp1PPzn1/OdmMDBaa6dThI9SkqrqA7O3sePfaY0Rcerqoi95CLk72Ki4uoomIVTzT37t3PfQ8eNDz44BdYN16BnKuvo3A4TP5wONqnYOnPxYvoZ0PMgb5li9EXIh5AtxpOTqJFCxbS6rUPM85Y8mesnAlRaWkp+3nI5aLDR49yP6v6UhaeIf+JB1zYq+5u0dij35Fhmmws01DHEYz4p4o6rs6nYJBsqankAKdoKDRpBoUGgn/T6cCAZX5MpHRDfnTMTynIHElO5sCLtTFsd/C2V4gKrNVSxaxjKruns4XrE6k/MhHVS30cR3YnEk6mq4/5+OhogGVhj7IlilXEyKmOR3WMhSgQltcnnm6/P0gpKckTdsfqRuJCZINn4OIPhhnztMj+tGb/YECAj1HM14zaLfF9MEhR3YniKsKfDf3SuIraMo1uPJUAqX0IE6W0NDKqY49wBhuPK6FD8UAHxsai7QEx8ePnn6eXX36ZTpyqpYryFfTss8/Sq6++SrW1tTzYjY2OUnJKCv3iF7+gF198kQfiVZHJlcGnPdGOIqEw7QcGLF7+pvxjsiVe/Ezrn1hMYn3v9/OeulPphs5Jx/1BInNcxehO5AcMGDzZiLS3SbpxsWCQ7KmpHLex7fsm3ZwVn0xpc4x+LG77hmq/n1LT01k3PG7mt1a6xRiqvhOP3SPL7DDwKCa0aDsx1Qf2cd+GUUuKYcT3Ovahz0pPT9D/xvjtJj+gDaq+MKafVbbE4j3p+NgY+ZOSKcVmih8TVjfFVYzvzbqVbRCZKUVrwJ0pRlt2WAjcKQRwJ//mm28mvNx3v/c9WhzZvcgs3NvfT/d/7nP0q1//mr7z9NP0Hz//Of3LCy/Qu3v30t9985tR0ed/+lP671/+J108e5GWLl8aPW79YSFgITB7EJCt85g99bVqYiGghUB5eTnh319asCVgXkEBZecWsIq1eAz+wgv0cWf3JJV4p3rP/AVUGNn6cdKP1hcLAQuBWYGAOGlqVtTWqoSFwB1GANvbYW33VyJrDleVl/N7MvPG63gMVlN3mp7cvJmyc+Xrb+9wVazLWQhYCHxCBKwB9xMCaJ1uIaAQQJb4M9/9npFdjKVuQ1566YUX+XEy9sVFwfuql156id55511CNjfeCW7bupUpxXDcKhYCFgKzFwHrkfLs9a1VszuMQGZGJh2qOkA73vwjbXr8MSpfvZa+/4PnqLS4eJIlTz75JAVefZW2bNlMGWlZVFpaRIerDkzaKH3SCdYXCwELgVmBgJU0NSvcaFXCQsBCwELAQmCmI2A9Up7pHrLssxCwELAQsBCYFQhYA+6scKNVCQsBCwELAQuBmY6ANeDOdA9Z9lkIWAhYCFgIzAoErAF3VrjRqoSFgIWAhYCFwExH4P8BlHfANzk9MEcAAAAASUVORK5CYII="><em><strong>(A1)(A1)(A1)(A1)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for axis labels and some indication of scale; accept <em>y</em> or <em>f</em>(<em>x</em>).</p>
<p>Use of graph paper is not required. If no scale is given, assume the given window for zero and minimum point.</p>
<p>Award <em><strong>(A1)</strong></em> for smooth curve with correct general shape.</p>
<p>Award <em><strong>(A1)</strong></em> for <em>x</em>-intercept closer to <em>y</em>-axis than to end of sketch.</p>
<p>Award <em><strong>(A1)</strong></em> for correct local minimum with <em>x</em>-coordinate closer to <em>y</em>-axis than end of sketch and <em>y</em>-coordinate less than half way to top of sketch.</p>
<p>Award at most <em><strong>(A1)</strong></em><em><strong>(A0)</strong></em><em><strong>(A1)</strong></em><em><strong>(A1)</strong></em> if the sketch intersects the <em>y</em>-axis or if the sketch curves away from the <em>y</em>-axis as<em> x</em> approaches zero.</p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>y</em> = −9.25<em>x</em> + 20.3 (<em>y</em> = −9.25<em>x</em> + 20.25) <em><strong>(A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for −9.25<em>x</em>, award <em><strong>(A1)</strong></em> for +20.25, award a maximum of <em><strong>(A0)(A1)</strong></em> if answer is not an equation.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct line, <em>y</em> = 10<em>x</em> + 40, seen on sketch <em><strong>(A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for straight line with positive gradient, award <em><strong>(A1)</strong></em> for <em>x</em>-intercept and <em>y</em>-intercept in approximately the correct positions. Award at most <em><strong>(A0)(A1)</strong></em> if ruler not used. If the straight line is drawn on different axes to part (a), award at most <em><strong>(A0)(A1)</strong></em>.</p>
<p> </p>
<p><em><strong>[2 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.iii.</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>Consider a function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span>, such that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = 5, 8\,{\text{sin}}\left( {\frac{\pi }{6}\left( {x + 1} \right)} \right) + b"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>5</mn><mo>.</mo><mn>8</mn><mspace width="thinmathspace"></mspace><mtext>sin</mtext><mrow><mo>(</mo><mfrac><mi>π</mi><mn>6</mn></mfrac><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mo>)</mo></mrow><mo>+</mo><mi>b</mi></math></span>, 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span> ≤ 10, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b \in \mathbb{R}"> <mi>b</mi> <mo>∈<!-- ∈ --></mo> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> </math></span>.</p>
</div>
<div class="specification">
<p>The function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> has a local maximum at the point (2, 21.8) , and a local minimum at (8, 10.2).</p>
</div>
<div class="specification">
<p>A second function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x) = p\,{\text{sin}}\left( {\frac{{2\pi }}{9}\left( {x - 3.75} \right)} \right) + q">
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>p</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>sin</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>2</mn>
<mi>π<!-- π --></mi>
</mrow>
<mn>9</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mn>3.75</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>q</mi>
</math></span>, 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> ≤ 10; <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q \in \mathbb{R}">
<mi>q</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>.</p>
<p>The function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> passes through the points (3, 2.5) and (6, 15.1).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the period of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>(6).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> and the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
<mi>q</mi>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> for which the functions have the greatest difference.</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>correct approach <em><strong>A1</strong></em></p>
<p>eg <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{\pi }{6} = \frac{{2\pi }}{{period}}">
<mfrac>
<mi>π</mi>
<mn>6</mn>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
<mrow>
<mi>p</mi>
<mi>e</mi>
<mi>r</mi>
<mi>i</mi>
<mi>o</mi>
<mi>d</mi>
</mrow>
</mfrac>
</math></span> (or equivalent)</p>
<p>period = 12 <em><strong> A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<h1> </h1>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{max}} + {\text{min}}}}{2}\,\,b = {\text{max}} - {\text{amplitude}}">
<mfrac>
<mrow>
<mrow>
<mtext>max</mtext>
</mrow>
<mo>+</mo>
<mrow>
<mtext>min</mtext>
</mrow>
</mrow>
<mn>2</mn>
</mfrac>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>b</mi>
<mo>=</mo>
<mrow>
<mtext>max</mtext>
</mrow>
<mo>−</mo>
<mrow>
<mtext>amplitude</mtext>
</mrow>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{21.8 + 10.2}}{2}">
<mfrac>
<mrow>
<mn>21.8</mn>
<mo>+</mo>
<mn>10.2</mn>
</mrow>
<mn>2</mn>
</mfrac>
</math></span>, or equivalent</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
<mi>b</mi>
</math></span> = 16 <em><strong> A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<h1> </h1>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to substitute into <strong>their</strong> function <em><strong>(M1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="5.8\,{\text{sin}}\left( {\frac{\pi }{6}\left( {6 + 1} \right)} \right) + 16">
<mn>5.8</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>sin</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mi>π</mi>
<mn>6</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mrow>
<mn>6</mn>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>16</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>(6) = 13.1 <em><strong> A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<h1> </h1>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid attempt to set up a system of equations <em><strong>(M1)</strong></em></p>
<p>two correct equations <em><strong> A1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p\,{\text{sin}}\left( {\frac{{2\pi }}{9}\left( {3 - 3.75} \right)} \right) + q = 2.5">
<mi>p</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>sin</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
<mn>9</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mrow>
<mn>3</mn>
<mo>−</mo>
<mn>3.75</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>q</mi>
<mo>=</mo>
<mn>2.5</mn>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p\,{\text{sin}}\left( {\frac{{2\pi }}{9}\left( {6 - 3.75} \right)} \right) + q = 15.1">
<mi>p</mi>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>sin</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
<mn>9</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mrow>
<mn>6</mn>
<mo>−</mo>
<mn>3.75</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>q</mi>
<mo>=</mo>
<mn>15.1</mn>
</math></span></p>
<p>valid attempt to solve system <em><strong>(M1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> = 8.4; <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
<mi>q</mi>
</math></span> = 6.7 <em><strong> A1A1</strong></em></p>
<p><em><strong>[5 marks]</strong></em></p>
<h1> </h1>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to use <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left| {f(x) - g(x)} \right|">
<mrow>
<mo>|</mo>
<mrow>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>−</mo>
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</mrow>
<mo>|</mo>
</mrow>
</math></span> to find maximum difference <em><strong>(M1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> = 1.64 <em><strong> A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<h1> </h1>
<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.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>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is defined by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mrow><mn>4</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfrac></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi><mo>,</mo><mo> </mo><mi>x</mi><mo>≠</mo><mo>-</mo><mn>4</mn></math>.</p>
</div>
<div class="specification">
<p>For the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></p>
</div>
<div class="specification">
<p>The graphs of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> intersect at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>p</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>q</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo><</mo><mi>q</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>write down the equation of the vertical asymptote.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>find the equation of the horizontal asymptote.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mi>x</mi></mfenced></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using an algebraic approach, show that the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> is obtained by a reflection of the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-axis followed by a reflection in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> and the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the area enclosed by the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>.</p>
<div class="marks">[3]</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><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mn>4</mn></math></strong><strong> <em>A1</em></strong></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to substitute into <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mi>a</mi><mi>c</mi></mfrac></math> OR table with large values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> OR sketch of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> showing asymptotic behaviour<strong> <em>(M1)</em></strong></p>
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>4</mn></math></strong><strong> <em>A1</em></strong></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mrow><mn>4</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfrac></math></p>
<p>attempt to interchange <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> (seen anywhere) <strong><em>M1</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mi>y</mi><mo>+</mo><mn>4</mn><mi>y</mi><mo>=</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>1</mn></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mi>y</mi><mo>+</mo><mn>4</mn><mi>x</mi><mo>=</mo><mn>4</mn><mi>y</mi><mo>+</mo><mn>1</mn></math><strong> <em>(A1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mi>y</mi><mo>-</mo><mn>4</mn><mi>x</mi><mo>=</mo><mn>1</mn><mo>-</mo><mn>4</mn><mi>y</mi></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mi>y</mi><mo>-</mo><mn>4</mn><mi>y</mi><mo>=</mo><mn>1</mn><mo>-</mo><mn>4</mn><mi>x</mi></math><strong> <em>(A1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mrow><mn>1</mn><mo>-</mo><mn>4</mn><mi>x</mi></mrow><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfrac></math> (accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mrow><mn>1</mn><mo>-</mo><mn>4</mn><mi>x</mi></mrow><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfrac></math>)<strong> <em>A1</em></strong></p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>reflection in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-axis given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mrow><mo>-</mo><mi>x</mi></mrow></mfenced></math><strong> <em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mrow><mo>-</mo><mi>x</mi></mrow></mfenced><mo>=</mo><mfrac><mrow><mo>-</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mo>-</mo><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfrac></math><strong> <em>(A1)</em></strong></p>
<p>reflection of their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mrow><mo>-</mo><mi>x</mi></mrow></mfenced></math> in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>f</mi><mfenced><mrow><mo>-</mo><mi>x</mi></mrow></mfenced></math> accept "now <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>f</mi><mfenced><mi>x</mi></mfenced></math>" <strong><em>M1</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mi>f</mi><mfenced><mrow><mo>-</mo><mi>x</mi></mrow></mfenced><mo>=</mo></mrow></mfenced><mo> </mo><mo>-</mo><mfrac><mrow><mo>-</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mo>-</mo><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mo>-</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfrac></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>4</mn><mi>x</mi><mo>-</mo><mn>1</mn></mrow><mrow><mo>-</mo><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfrac></math><strong> <em>A1</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>1</mn><mo>-</mo><mn>4</mn><mi>x</mi></mrow><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfrac><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mi>x</mi></mfenced></mrow></mfenced></math><strong> <em>AG</em></strong></p>
<p> </p>
<p><strong>Note:</strong> If the candidate attempts to show the result using a particular coordinate on the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> rather than a general coordinate on the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math>, where appropriate, award marks as follows:<br><strong><em>M0A0</em> for eg</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>→</mo><mo>(</mo><mo>−</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math><br><strong><em>M0A0</em> for</strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>−</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>→</mo><mo>(</mo><mo>−</mo><mn>2</mn><mo>,</mo><mo>−</mo><mn>3</mn><mo>)</mo></math></p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to solve <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mi>x</mi></mfenced></math> using graph or algebraically<strong> <em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mo>-</mo><mn>1</mn></math> AND <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mn>1</mn></math><strong> <em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>(M1)A0</strong> </em>if only one correct value seen.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to set up an integral to find area between <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math><strong> <em>(M1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><munderover><mo>∫</mo><mrow><mo>-</mo><mn>1</mn></mrow><mn>1</mn></munderover><mfenced><mrow><mfrac><mrow><mn>4</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfrac><mo>-</mo><mfrac><mrow><mn>1</mn><mo>-</mo><mn>4</mn><mi>x</mi></mrow><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfrac></mrow></mfenced><mo>d</mo><mi>x</mi></math><strong> <em>(A1)</em></strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>675231</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>675</mn></math><strong> <em>A1</em></strong></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></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;">
<p>Candidates mostly found the first part of this question accessible, with many knowing how to find the equation of both asymptotes. Common errors included transposing the asymptotes, or finding where an asymptote occurred but not giving it as an equation.</p>
<p>Candidates knew how to start part (b)(i), with most attempting to find the inverse function by firstly interchanging <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>. However, many struggled with the algebra required to change the subject, and were not awarded all the marks. A common error in this part was for candidates to attempt to find an expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mo>(</mo><mi>x</mi><mo>)</mo></math>, rather than one for <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo></math>. Few candidates were able to answer part (b)(ii). Many appeared not to know that a reflection in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-axis is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mo>-</mo><mi>x</mi><mo>)</mo></math>, or that a reflection in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>. Many of those that did, multiplied both the numerator and denominator by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math> when taking the negative of their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mo>-</mo><mi>x</mi><mo>)</mo></math> , i.e. <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfenced><mfrac><mrow><mo>-</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mo>-</mo><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfrac></mfenced></math> was often simplified as <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>4</mn><mi>x</mi><mo>-</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfrac></math>. However, the majority of candidates either did not attempt this question part or attempted to describe a graphical approach often involving a specific point, rather than an algebraic approach.</p>
<p>Those that attempted part (c), and had the correct expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo></math>, were usually able to gain all the marks. However, those that had an incorrect expression, or had found <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mo>(</mo><mi>x</mi><mo>)</mo></math>, often proceeded to find an area, even when there was not an area enclosed by their two curves.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.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.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>The following diagram shows a semicircle with centre <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>O</mtext></math> and radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>. Points <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P, Q</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext></math> lie on the circumference of the circle, such that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>PQ</mtext><mo>=</mo><mn>2</mn><mi>r</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>R</mtext><mover><mtext>O</mtext><mo>^</mo></mover><mtext>Q</mtext><mo>=</mo><mi>θ</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo><</mo><mi>θ</mi><mo><</mo><mi mathvariant="normal">π</mi></math>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAacAAADgCAYAAACnxan4AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAC+ASURBVHhe7Z0NcFXltfcfW8erbRXwvhfQklgNkQ+NM4USQRHvKx/hIxZKEoMEGU1CFexYEm4/vDMloTNvtbc1QV8JchOwNxpuJRwc+RCTIFYJIQahLYHwLSWk8Gp7CxGpthV481/ZTzjEJOYk55z9PHv/fzOZfc4+GU3I3vv/rPVfz1pXXGxBEUIIIQbxJedICCGEGAPFiRBCiHFQnAghhBgHxYkQQohxUJwIIYQYB8WJEEKIcVCciDEsX16kYmMHdfg1e/aDqr5+j/OdhBCvw31OxDjGjr1LJSTc0SJWL8j71avL1FNP/UxeV1fXqD59+shrQoh3YeREjKNPn77Oq1Zmz85Q06Ylq+bmZhEqQoj3oTgRq2DURIg/oDgR4/nxj38kEdPYsfdIFEUI8T70nIhxTJs29bLiB/hPGRkZFCZCfAQjJ2Ik8JgaG5tEkCBUsbGxzieEED9AcSJG8/TTP5fICak9FEQQQvwBxYkYD0rKIUzz5z/mnCGEeB2KEzGO5uYzl0VJSOk9+eS/q+rqbdyMS4hPoDgRY9AdIhobG0WI8HrTpo3yGbwnfOE8CibwRQjxLqzWI4QQYhyMnAghhBgHIydCOqCp6YQ6caLJeddKbe0O59Ulzp8/r/72t7857y7nK1/5ivOqldGjxzivWomJGaQGDYpx3hFCgqE4EV+xY0erwDQ07FMfffSROn78uHyBAwf2q3PnzsnraPPVr35VxcUNVl/+8pdEsG688UY1cOBANXz4bfL5mDGXCxshXofiRDzHvn37JPJpaGhoiX5OqGPHjnUqPFdffU1LBNMavfTr20/17dvadPbqq69W/fv3l9eaf+n/L+qf/umfnHehgejqTx/+yXnXyocffqg+/fRTeX3mzBl1+sxpeY2f+dNPP5HXwWgBu+mmmyTq+uY3R4iQ3XZbq4AR4iUoTsRaEPlAiJBuw/EPf/iDOnTooPNpK1p8tPCgcSy+rutznbruuuuc7zIT/H4fNX8kZfX40gLWkXjdckuc/J4JCQnqnnvGiWCZ/vsR0hUUJ2INSMlBiOrr61vEaK86deqU88klEbr5Gze3CVBvIh0baDrR1CZcx/5w7HOihchv2LDhbYLF1CCxCYoTMRJEDTt21IggvfrqOnX6dGvKC0CI4uPj1Q0Db5ANul4XoVDQ6UPsFTv1/06pP/6xSf3lL39xPlUqLi6uRaTuUvfee68cGV0RU6E4EWOoqHijLTqCX9Seq666SqXMTFVDhg5xzpDuAKGHYKHw4+j7R0WwNMFilZQ02TlLiPtQnIhroGihoqJCBKmyssI5q9Tw4cOl7HrQoEHqpz9dov75n/+X+p//+bO65ppr1CeffKK+ff90NWLkCOe7SU9AShDR1b6GfZeJ1Te/+U3pCD916lSWuRNXoTiRqILChfLyNSJK+qH49a8PEj8kKSmpLdWE1f7o0Ynqs8/Oq+ysbPX8sv+r5s9foH7zm7fU/v37VeKoO9X4CeOZzgsDSAVCrA4ePKiOHD3clgYcMGCg/E0gVvSrSLShOJGIg3SdjpC0ICE6Skt7QCKkjkqhk5ImighlZ81Tg2IGqeLiYtn7EwisU7m5OWrt2nIRtfT0dPomYQYpQBRX7Nq9q+3vhTL2CRMmquTkZKb/SFSgOJGIoCMkfJ09e1bOTZqU5ERHSNl1njLS4hOcvnt90+uqbue7MoAQ4L+7aFGuFEfMyZgjAkbCD6KqI4ePqAMHD7R1g4dQ4W85a9aDjKhIxKA4kbABD6m8vFytWbOmbcWtBQmr7e5EOFp0kLabGtR5fN/eFrFbu0a98kp52wMRApiWlqI+/vhjNWlikrrr7rvkPIkMHQkVUn9TpkxR3/3ud+lRkbBCcSK9At4Q0nYQldraWjmnU3YQpVAeWBCbKVOSJF03d+7cy/wk/H8KCp5ROTm58qXB+czMh1VdXZ1MzEXaiT5U5NFCVbOjpm0hgvL+xx6b3+2FCCFdQXEiPQJCsnJliQgT0nbXXnutCFJ2dnaPVtDBBRALFizo8OH23HPPqhEjRqpVq150zlwiPz+v5fxKEbYZ02fI3icSHfC3e2/ne2rvvnopptBpv+9+91G2ViI9huJEQkL7SDpKwkMoLS1NVsu9oX0BREfAd9rXsLfl+y5vUaTBz5WXt1idP39BpaakqrjBcc4nJFocPXJU/e73v2tL+9166xD16KOPysKFkFCgOJEvBCtjREnaS0KUlJ09T0QpHD6Djnq+aP/S7l271foNr6nNmys6XZEjosvKekSdPHmSPpSL4JrZW79Xvbdrp0RTX/va11RmZpaaNWsWvSnSLShOpFNQ4FBQUCCVcwBeUlZWdlhXwboAAn5RSkqKc7ZjUOK8rOj5lugoX36OzqAPZRYoZkE0dfjwIXn/ne/MVD/4wQ8oUqRLKE7kc2A/EiIl3bUhNTVNBCncZcO62q5Pn76fK4DojKefflqNGzdOlZSsdM50Dn0os8BG3z179siWADBqVKL6t3/7AcvRSYdQnEgbEKXCwmfa/CSIUm5ubkRWuIhuJk2aoE6fPqMyH8nstnAEAgH15z//Sb377k7nTNcE+1DJ05LVbbfToHcb/O2rt1WrPfV7pIv6t741qiWS+iFFilwGxYlcJkraT0LaLJLlwKmpMyXt9tCcuSEVLmjfqaZmR7dFExHawoVPSHuecffcq+4bf5/zCXETlKPvem+XemfbOyJSI0d+S/3whz+iSBHhS86R+BCI0gMPpKr09DR5gGP/0I4d78oxksKEdBuECQULoVbU6em0+Nm7C4onAoFXpf3OO9veVmVlZfJgJO6CNC4KVnJycuRawDWIazElZWZIf1/iTRg5+RA8BJYsyYtqpKQJpQCiMyBuSDkWFBQ6Z7pPYWGBfF1//fXqwVmz6UMZRPtIip6Uv6E4+Yj21XeIkKIlSqAnBRAdgcjn3LmPW8S1zjkTGtg4vHDh99WFCxfpQxlIe5FCxPvTn/6U1X0+g+LkA/Q+JUQMIJKFDp2BnyEl5TuqsfFESAUQHVGzvUZVVlWovXsbeiys9KHMByL15pY326r7sE8qN3dR1BZTxF2+nN+C85p4EKTRHnooQ7399ttq9OjRqrh4Zcv7h1pu8D7Od0SH+fMfUzt31qnvzPiO+sbN33DO9owrrrhC7f7tbhmMN3jwYOdsaMC7mtHysxw6dEi99Zut6o9/PKmGDBmirrzySuc7iNvgbxF/a7y0rPr443MS8f7Xf/1Khk6OGMFhk16HBREeBYby5MmTxN+BEKGb95o1a13pdYaIbcuWKolQwpFC0+2NemuaYwWOPn1Ib2KDaGFhoWz0JWaBvxP8SbS26tu3n1qyJF/6MLJowtswrecxkD5DwQB8JRQ7IA3SVTeFSIPV7rx52So+/laVkZHhnO09GD74ta99VVVVvemc6R140KHtEcZvpKU+QB/KYLCdoLKqkn6Ux6E4eQj4ShgrgS7h8JXy85e4mp+Hr4P9TCh8ePTRx8LaQmjrm1ulLLw3vlN7UDCSmfmIOnDgwOfmSRGzgB+1vXq7XAPogo6qPjcXYST8MK3nASAC2K+EdEdMTIyk8FBm7aYwIYJDwQEq4lCyHU5hAjfddJMc8buHC6y+165dp2bOTBETHtEZ90OZCa4nFLE8vuB7bak+dBwJ5/VA3IUFEZYDP+d733tcNTc3q8cf/55atqxIBMptwlkA0RFYLVdXb5PfNZz7YPDQmzx5igj7hg3r1XvvvaeG3DpE/n/EPPB3GTlypLru2j5q929/q371q9ZZX/BWw70gItGFaT1LwQpx0aIc1dDQIFV4iJRMybvrja6RLtFGZHPjjTeqQGCdcya80IeyC0TrGzZskOIWXBeFhc9yA6/FUJwsRD/8TSh4aA8e6GhBE+4CiI7A8EGk3xobW8eER4L2PtT4CeO5IjccDDxcG1irPvnkr9wbZTFM61kEoqW5c+dIugnR0ssvl6l//df/7XzqPniQowPEl7705RbBzIr4nqG///3vLZHjvpZ/izERS2WiDH/69Bnqww8/VFVbKtWxY8dahDeeAmUwaE01atQoSXWjWnTr1jdlr5Tuy0jsgAURloBKvClTktSJEydk2B72LJlUPouUCiIMpMCyWlar0Xh4x8S2/v61tZHd74JVN9KmzzxTIJOAi4qKZDYRMRdcf9gbhenKx483yr2DbAOxB6b1DAcP/ezsTGnSikm0GLJn4p4O9Kpbty4QdW/mueeelVUxNtNGA0SviA4hwl80Vp6YQbAXlZiYqJYufZb7oiyAkZPBwL8ZM+ZOESZ0MXjjjUojbypEdRAmeDLRLhoYHBff8u9U47yLPKgCQ8PZYcOGyVwp+F4sNzcbRL7wPzGWQ0a1TJoo6T5iNhQnQ0EKAoUFAPuWIE4mAgHFHhOMQndj0+rAgQPVuXPnorq/BQ+7iooq2eiMgozS0lJZnROzwewo7Iu66qqrpGsJOqkQc6E4GQYecthQC3FC0QOG/5laDosCCJRaX331NTICww10IUSkfaeOoA9lH+iGj24lmCe2atVKlZQ0Ua5jYh4UJ4Non8ZD0YPJJbDRLoDoCDxsII74t3ODtLQH1ObNFerKK7+sSlYWyzgPYjbBxRL79+9nms9QKE6GAN/GhjSeJjc3R/b+4AZ3e5osSrvr6/c476KP9qFgtmPOVCAQoA9lAShmQZrvs8/OS5qP1XxmQXFyGaTx8KCHb4NqPJPTeBrMiELXcxRAmFCtdvM3blanTp1yNT2DCBd9+bDpE0IJH4rjN8wHC6ucnBzZNA5xys7Oon9oCBQnF9H+Eh70MNdRjWdyGg+0tk3KlQIIdEswAe07uZXaCwad4OFDNTefUateXCXdCojZIM2Haj6026qsrJCtAvSh3Ifi5BJ4yMNfQm88PMxgrpsOxBQ3Ljye9PR013ym9ui0ogniBOBDlZcHVL9+fdVLL5fSh7IE9IHEPj3tQ0WzApR8HoqTCyAthogJwF/Cw8wG9ObTORlzjIvwkJapqdnuvHMf+FCVlVvoQ1kG9unBhzp//oJ0lcC9StyB4hRlUPiAtBhSUajGs6VrMnwxrChRAKHHpJsEfKeTJ08alY6hD2UniMTnz58vqWvcq9wP5Q5s/BpF8IBfvrxICh8gTJFqVhpusHpcurRQCiDG3TvOOWsWV1xxhdr9293SBHbw4MHOWTNAc95BgwapzZtfl5lD/fr2YxNSw0HK+vbbb29rHouelklJk51PSTRg5BQF4NWgCsimwgeNiQUQHaGjOVN8p/YgdYsoKjY2RpWvXSNj5onZ6P1QWJTh3sWGXVbyRQ+KU4TRFXmoAkJ6x4bCBw1+dt0BwqQCiM6A77R9e7XzzjzgQwUCr6oJEyaqd7a9rcrKyuhDWQDacukNu/BdKVDRgeIUQbQw6Yo8lBnbRGbmw+LjpLVEezZEejcMvEEdPHjQ6IcH/h3RQR2brNEle8WKF+hDWQD28+lKPggUK/kiD8UpQuDiTUqa1CZMtlTkaWACSwfniUkqbnCcc9ZsbrrpJjlGs0t5T4E4FReXSOSE/VD79vJhZzqo5INAHT9+nAIVBShOEQAXLSKmjz5qlgeQbcKEAgg0xURzTHRytgXtO2FBYAMw2OlD2QUE6pGHM6XUnAIVWShOYUYLE0BFnm0VPvj58/IWSwFEcnKyc9YO4Inh566uNtd3ak97H6q4uJg+lOGg1DzzEQpUpKE4hZH2woQHj03oAgjcdDOmzzC+AKIj4m6JUzt31jnv7CDYh8L4jcLCQvpQhkOBijwUpzBhuzABXQCRmpLa1hLINgYMGCBHU0vKuwLihI4hGL+xrOh5+lCGQ4GKLBSnMOAFYUJHZtsKIDoiJta94YPhAB1DKiur1NChQ8WHwhh4Yi4UqMhBceolXhAm7ICHOGGfkE0FEB2BFNn1119v9H6nL2LQoBgplJg5M0XGwNOHMhsKVGSgOPUCLwgTfoeFC78vD/TU1NbfxXYGx8Vb/4CAyC5d+qzKy8unD2UBFKjwQ3HqIV4QJhRALFz4hLpw4aJ6cNZsKwsgOgL7nc6dO+eJB0RWVvZlPtTuXbudT4hpUKDCC8WpB+ChvmhRjjp79qy1wgQQMaGjQvK0ZLmxvIJuqmqr79SeYB9q/YbXxIdims9MLheoVA4t7AUUpxBp35LIVmGCx7RlS5VM/8TGQi+BBwT6AdpYsdcZ8KEwHwqNg+FDlZaWyrVIzEML1Mcfn22JfDP5d+ohFKcQCRYm2zo/aIILIDD904vEx8cbNXwwXKBxMK49+FBFRUWq6UST8wkxCQhUcC8+ClToUJxCAPOYIEwwqW0VJuTBvVYA0REYPoipvV5Mq+Da27y5QnyokpXF9KEMRffig0BlZ2c6Z0l3oTh1EwiTnscEk9pGsHrzYgFER+hBjl5K7QWDdHJtbZ0aNmwYfSiDgUAhdV5bWyvPENJ9KE7dAI1QtTDZNI+pPYsX/8STBRAdoX8/r4oTQLl5RUUVfSjDQepcDyxEOp10D4rTFwB/BpNgMVrdtnlMwaxcWaLWrQvITeK1AojOMH34YLho70MdPXLU+YSYAgYWoikxxAmLXfLFXHGxBec1aYfey3TddX1aRMqe0ertQfSQnp4mN8e8efOcs96nZnuNqqyqUDU1O6TazevgekXjXvRHRBsq27t9eA2kXRHdNjefaRGogLWVvtGCkVMnID2SnZ0lr0tKVlorTCgI0KPW586d65z1B7GxsXL0y2ZIPOxQbp6YmCiiHAgE6EMZBDxedPvXm3SZgu0ailMnoLoGaRKkTGxd4eDiz8x8RKrWsjKzPF0A0RF6+KCXfaf2YBGFvnyZLX/v+vo9slJn2yNzgBeaMTtD7kkKVNdQnDoAI8pRXYMRBrYNCwwGBRAHDhyQclavF0B0hl98p/bAH4UPhRQSxsDThzIHLJp0iTmeNaRjKE7t0CPKUQEFcbIVPxZAdMQNA2+QCkU/rlCxHwreRr9+fdVLL5eKB0fMAPekruDDvUo+D8UpCHgTWMnYXpmH32PJknwpgECVkJ9BE1iwY4c/H8z0ocxFV/DhXvWLLxoKFCeH4AKIZ54ptLYAAr8HctkogEhPT3fO+hftO6Gzh19p70OtWPECfShDwD16zTVfof/UARQnB+zetr0AAuAih9k6J2OOtQIbTlAEgtVpdbX/fKf2IBtQXFwikRN8KI6Bdx/co7pAIjPzYecsARSnFpDzrayskJWlzQUQEFiYrN++f3pbxECUirslTu3cWee88ze4vhFFxcbGyBj4rW9udT4hboF7FfvS6urq2EEiCN+Lk/ZnbPeZdIslmKwjRo5wzhIwYMAAOfqppLwrkBkIBF5VEyZMVO9se1uVlZXRh3IZbJhGZSnEiddpK74WJ+0zXXvttbLR1lYgsGixhPTV+AnjnbNEE9MSJQCvDB8MB0gnrVr1olSkHj58iD6UAWBKAPynnJzv039qwdfihMo87TPZ2t6mfQGE3zbadgc8iDEixI/7nb4IiBN9KDPAvZuakirtp9jB3MfihIauutO4zT4TCyC6x+C4eJbrdgJ9KHOIGxwnIzbggfu9QawvxQnRBlYmSIPZ7DMh8mMBRPfAfqdz585RoDqhvQ9VXFxMH8ol7h57tzyb8vIWe3JYZnfxpTihb97Zs2clnWdrtKE7WSQk3MECiG7Qv39/OdJ36hztQ2HSM9LdhYWF9KFcQDeIRUYEU6v9iu/ECWXjum/emDFjnLN2gdU/VlVYXSUnJztnSVegtyB8OVZCfTGY9PzKK+UyBn5Z0fP0oVwA16suL/dreyNfzXNCiJyUNElGeL/xRqVz1i6Qkpw0aYI6ffqMynwk07cNXXsCWvccO/a+amg44JwhXYH7BV3t0TwYWxT83grLDZBePXPmtKqq2uKLmWTB+Cpygs+EdB7aE9kKdpGjmgdVPRSm0Lj5GzdLqsTPefxQwMMQhRIzZ6bIGHj6UNEH6T14pX5M7/lGnODR6HSere2JUACBMB/hPqp6SGggYgZM7XUf+FBLlz5LH8ol/Jze84U4IRWGBzs8GlvHYAQXQHD8ds/QkSbFKXTa+1C7d+12PiGRBvc7nl2//OUvfBX1+0KcdDoP1Xk2wgKI8OHX4YPhAAVElZVVaujQoWr9htfU65teZ5ovSuj03uLFi50z3sfz4oRVMja0YbOtjdV5iPqysh5R589fkAuUHSB6B3ynU6dO0XfqIfChMB8K9xN8qNLSUrlGSWRB1I/NuVu2VEkDAT/geXFC1ITeebZutoURigKI5GnJLIAIA7GxsXLkZtzegSwExsDDhyoqKlJNJ5qcT0ikwOZctOFavPgnvlgQeFqc0OEXNw+EycbNtvj5sVLCisnPo9bDie6kQd+p92AM/ObNFeJDlawspg8VYZA1mTY1WSJ/PxRHeFackLYpKSlWo0ePlpvINhC6Q5zgkdw3/j7nLAkH9J3CBypfa2vr1LBhw+hDRQFU6erRGl5PTXtWnPLz86UIIi/PvnQeUk5I5yGERxt9El5uGHiDOnjwIL2SMIGsREVFFX2oKHH//ffL0et7nzwpTroIApNtbdvThJt64cIn1IULF9WDs2azACICoAks2LGjRo4kPLT3oY4eOep8QsIJFgN675OX09OeFKclS/KkCCI3d5Fzxh6wGsKqngUQkUP7Tg0NDXIk4UP7UNdf30+99HKpqtnOBUAkGPmtkdIrEgtZr+I5ccJmVTx0srPnWVcEwQKI6IBoFHvGqqvpO0UCZCtQbp6YmKgqqyqkpyF9qPCCa/j+5Ps9XRzhqcavSImhsSvYsaNWjraA8Dw9PU3MzoyMDOcsiRQYqIe5RY2NLIGOJOjMgs4mWAxgnx6zAeEF/Q6bm89IUYqNFcld4anICSsI5Ltzc+1qUYSqG2y0RZjOAojoMGDAADmypDyyYBsHfCg8QDEGnj5UeJkyeYo0M/Zi9OQZcULUZGPpOH5ujCXABZaVmcUCiCgRE9vaBJbDByMP7sfy8oDq168vfagwA/8U2Zb//M8Vnist94w4YeWA0vGcHLuKILDbG/Ny0lIfYMojiiAFglJ97neKDvShIse94+6Vvnu//OUvnTPewBPiFLzh1qb+eRDUdesCMsiNBRDRZ3BcPNsYRREsCDAfCls86uv3qBUrXuD4jTCA6AnPEDxLvBQ9eUKcCgoKrIua4HUsWZIvRjEnjLoD9jthxUmBii7woYqLSyRygg/FMfC9Z+w9Y+XopejJenHCSmHt2nKroqbgAoi5c+c6Z0m06d+/vxzpO0WfpKTJEkXFxsao8rVrpHqS9BxEpV6LnqwXJ0RNwJaoiQUQ5gCPDwsEVuy5A3yoQOBVNWHCRCnrLysrow/VC3T09Itf/EKOtmO1ONkYNWHfBwsgzCE+Pl7V1Gx33pFogxX/qlUvyoTqw4cP0YfqBTp6evXVdZ6InqwWp/LycjnaEjWhewXElAUQ5oDhg4hivZIKsRWIE32o3uMl78lacQre12RD1ATTfdGiXCmAGD9hvHOWuE1MTOt+J6b23Ic+VO/xkvdkrTjZtK8JQpqWliL+Rnp6On0mg6DvZBbtfSi056EPFRqjRo2S469//Ws52oq14mRT1ARhQupoTsYcWdkQs0D0xM245qB9qLy8fGlHVlhYSB8qBLDgQtcILOCxMLYVK8UJ3g2iJhvaFOXm5qj9+/erb98/vW1UAzEL+E7o7kzfySyysrLVK6+Uyxj4ZUXP04cKAd01wuaee1aKE8rH4d2YLk7BBRAjRo5wzhLTiI2NlSNTe+aBzEhlZZUaOnSo+FAYA0++GCyE0Z5r9eoy54x9WCdOeIAg1M/OznbOmAkLIOxBR7TsFGEmgwbFSKHEzJkpMgaePlT3GH/fBPXBBx/IItlGrBOnwsJnZMqtyVET8ry6AwQLIOwAOXr6TuYCH2rp0mfpQ4UAtqvgGbR69WrnjF1YJU7wBGpra6Xk1OTCgszMh9XJkydVWmoaCyAsAb4TxuPbbCD7gfY+1O5du51PSEeMu2ec2rXrPSuzAlaJU0lJq7ln8jBBdICoq6tTkyYmqbjBcc5ZYjqXhg9y1pDpaB9q2LBhav2G18SHYpqvY25PuF2OmPdkG1aJE3KnKB9HDtpE8PNhJHVCwh3qrrvvcs4SG9C+E4si7ADPgIqKKpWamiY+VGlpKaPeDkDmBs+jysoK6/59rBEn08vHETbn5S2WAojk5GTnLLEF+IL429XX1ztniA0UFBTKGHj4UEVFRarpRJPzCdHcmXinlJVXVLzhnLEDq8TJ1EIIXQBx/vwFNWP6DBZAWErcLXFq58465x2xBTwTNm+uEB+qZGUxfah26LLy5cuXO2fswApx0oUQpkZNugAiNSWVncYtBsMHAVN79oG2R7W1dfShOuFbI0epI0cOW1UYYYU46UIIE/c2sQDCO+iFBYcP2gn8FfpQHWNjYYQV4lRRUaGGDx9uXCEEcrgsgPAOeLgh/cH9TnYT7EMhlXX0yFHnE/8SXBhhC8aLEwQAFxn2N5gEwuOFC78vDzMWQHiHwXHxEgkTu9E+VL9+fdVLL5eqmu3cIjB0yFApjLClY4QF4tSq9Nh4awpIFSxc+IS6cOGienDWbBZAeAjtO7GVkf3Ah6qs3KISExNVZVWFCgQCvvahdMeI9evXO2fMxorIadKkJKM6LSBiQjeB5GnJLIDwGDGxralj+k7eAM8N9OXLzMxS9fV7xIfyc9ujOxLuUG+//RsrvDijxenS3qY054z7FBYWqC1bqtS4e+7lqHUPgocZVpfbt293zhAvkJ+/RHyo5uYzMgberz7UkCFD5Pj665vkaDJGixNSetjbZEpKD1EcxAlNQu8bf59zlniN+Ph4Rk4eBD5UeXnA1z4UKorhk69fv8E5Yy7GihPCTlSWmCJMwQUQqampzlniRdAEFpOL6Tt5D/pQSt1+W4Kqrn7H+NSeseKkW20kJSXJ0U1YAOEvMLYdNDRQnLxIex9qxYoXfOVDJSQkyNH01J7B4mROSm/x4p+wAMJH4G8M34mdIrwNfKji4hKJnOBD+WUMvL6+TU/tGStOGF1ggjBhBv+6dQEZtc4CCP+A6Imbcb0PnjGIomJjY2QM/NY3tzqfeBtU7Zme2jNSnJDSQ5Ue5ra4CVbOS5bkS7fqqdOmOmeJH4DvdOrUKenrSLwNfKhA4FU1YcJE9c62t1VZWZnnfShdtaftExMxVJzc33iLh5IetT537lznLPELsbGxcmRqzx/Ah1q16kWVk5OrDh8+5HkfClV7eLZt3WpupGikOOGBgKGCbm28RaibmfmIVGxlZWaxAMKH6OGDrNjzFxAnv/hQ2DLx1lsUp26DhwF66bkZNaEA4sCBAyot9QEWQPgY7Gej7+Q/2vtQGL/hRdBr769//aux2QHjxElvfnSrhJwFEEQD3wlVmqbvByHhJ9iHwviN4uJiz/lQulXXhg1m9tozTpxg0KEAwY3xGCyAIMEMGDBAjqgcJf5D+1B5efmSzSksLPSUD4XfD886U69vAyOnWleq9LA6ZgEECUb7TiyK8DcY1/PKK+UyBn5Z0fOe8qHibolTR48eNTI7YJQ4udkVIi0tRQog5mTMYQEEEXAdYGVZX1/vnCF+BQvmysoqNXToUE/5ULfeeqscTYyejBInvUIdMya6U2Vzc3PU/v371bfvn962WiYEYGW5cyeHD5KWSHpQjBRKzJyZ4hkfSj/vTJzxZJQ4oRgC49ijWUKOsRxr15ZLAcSIkSOcs4S0oocPMrVHAJ5NS5c+e5kP1XSiyfnUTlCVWlf3rvPOHIwRJ+Q8Gxoa1OjR0fObULa+aFGupG7GTxjvnCXkEnorAUdokGCCfaiSlcVq967dzif2garUDz74wDjfyRhx0psdo1UMgT8EfCYUQKSnp9NnIh2ClTLGpHC/E2mP9qGGDRum1m94TXwoG9N8l7qhmOU7GSNOemUaLb8puAAimmlEYh+D4+JVXR19J/J54ENVVFSp1NQ08aFKS0uNrHzrCu07vfXWb+RoCsaIE1Qb6bVoCEV+fh4LIEi30b4TWxmRzigoKJQx8PChioqKrPOh8Ow1LXVtUOQUnf1NKIBYtWqlSki4gwUQpFvonfT0nUhXYAz85s0VVvpQqEp9//2jzjszMEKcouU34f+Tl7dYVgnJycnOWUK6BtE8vMnt27c7ZwjpGLQ9qq2ts86HMrEq1Qhx0uOwhw+PXC875IHRAeL8+QtqxvQZLIAgIYEOzoycSHfAYqa9D2V62yNdlfq73/1WjiZgVOSEVUekyMx8WJ08eVKlpqSy0zgJGZTbooCGvhPpLtqHam4+I+M3jh4xK20WjM4O1NSYU7FnTOSE+U2RAgUQqLaaNDFJhmwREioY2w50lE9Id4APVV4eUP369VUvvVyqarab20QY1/iBA/udd+5jhDihGCJSKb3gAoi77o5uWyTiHRBtY2XpVk5++fIiFRs7SL6mTZvashpvdj4hpoOMUGXlFpWYmKgqqypUIBAw0ofSm3FNwXVximRKjwUQJJxgZenGZtz58x9T27ZtU42NTWrTptdbjsfV6tVlzqfEBpA2Q1++zMwsVV+/x0gf6tKIGDO8VdfFSadJwj2/iQUQJNxgZXnq1CnV1HTCORN5EDHhYbZ69X/Le2QAxo69R23cuFHeE7vIz19irA+l95jiejMB18Wpqal1s1q4y8gXLvw+CyBIWLnU5iU6K0uk7oqKlqmMjDnOmUvg4UbsxFQfSj8n33//mBzdxnVx0p0hwklhYYHasqVKjbvnXhZAkLChu4lEq2IPqTsI1OzZGc6ZVhobG51XxFba+1BlZWVG+FDoUL53rxnzy1wXpxMnmlRMGFsIYWAhxAn/yPeNv885S0h4wHUVLd9pz57W9EpCwm1txRD4QtoF6T1iN9qHysnJVYcPH1IrVrzgug/Vr28/dfToEeedu7guTuhFFa5mr1jRIp2HLtKpqanOWULCB3yngwcPRqW5Z3X1NjV//gIphNBfy5e/IJ/pFCOxH4hTcXGJRE7wodwcA9+3b1917tw5I5rXuipOOj0yaFDvIyf8Yy5c+IS6cOGienDWbBZAkIhwqaIpsj4BUndI6eFhEQyq9gCrT71FUtJkiaJiY2NkDPzWN7c6n0QXveiJVuq6K1wVJ131FI5KPURMWNEmT0tmAQSJGNp3inRRBMrFQZ8+feQIIFabNm2Uaj2m9bwHfKhA4FU1YcJE9c62t13xofSiPpoVqZ3hqjhh8i3o7R6n4AKI226PXAskQnDzooCnvj6ypnGwKGl0gcSTTz7pnCFeAz7UqlUvuuZD6YX9oUOH5OgmrooTbjSg6+t7AlawLIAg0QTjBXbujOzwQURG+NL7mSBMTz31M/X00z9n1OQD3PSh4NkjC+U2V1xswXkddR54oLVoYc2atXIMFYSekyZNVJ99dr7lj5lDn4lEBWycxP4UFCtcffXVssgK7rmHNDW6ScBLRVuunmYGUJWH7hDwn+AFLFjw+OfKyom3aS3yekLEInHUnWrqtKnOJ5ED6cRrrrmmZWG0yTnjDq6K0+TJkyRq6ok4oQAiNXWmOnDggHp8wffoM5GogWuvoOAZ510rwY2L0SsymGuvvVYM76SkJDkSEgq43hYv/olaty4gKeW5c+dGdCGOGVT7Gvaq/fvdjZ5cFSfs2UD4iq9QQQEE/lhpqQ/QZyJR57nnnpXKPczt6QyknBFR4YjqvrNnz4pQZWfPU1lZ2b1KZxP/sXJliVqyJF8aEGdlZkVsQY6OFdgYjK0LbuKa59SbOnr8kSBMCHMpTMQNBsfFt6wsux4vgJZcEKGSkpUt4vSu9FRDug8e6Zgxd8p1TEh3wbX0yivlMgZ+WdHzEfOhkKoGbpeTuyZO+hcfPny4HLsLVqFYPSC8jUb+lZCO0GOtu3sDI0pCT7U33qiUBwxECtcxUtsmlO0SO8CCp7KySg0dOlT2QyEFF2769+8vx94EEOHA1Wo9cN11ny+Z7QzcxOg0jrAWeVdC3CImtnVvXk9Gt+MBA5FCOhvbKZKSJknbLUK6AwpusGF35swUGQNfXFwckf1QH33k7sww18RJVzd1N+8OFc/MfERGZSPfyso84ia4brFI2r59u3MmdCBOmzdXyAJt3rxsGYxJSHfA9bd06bMqLy9fWsAVFhaqphPh8Yj0RnO9D9UtXPecultmi1HrqMxDAQQr84gJxMfH9yhyCgbXf0VFpaS3Fy3KpUCRkAj2oUpWFqvdu3Y7n/Sev/3tU+eVO7ie1usOuGHXri1nAQQxCjSBRSTfW+MYq2Bsp6BAkZ6ANHFtbZ0aNmyYWr/hNfGhepvmQ1YAEyPcxNWCiO7MccL34YbF946fMN45S4j7oKgBBG/A7SnBAoUsQW8Fj/gLXD/Y1pCamiY+VGlpaa8KGnBtY1irm7iY1mtu+QfoWpzwj5uWliIqnp6eTp+JGAXSy7g2w9UEFg+YZ54plNeLFuXIkZBQKCgolC0L8KGKiorC5kO5gdFpPQgT0iZzMubIjUuIacB3CufwQXhQubmLxIzGfihCQgVbFlBo01sf6h//+Ifzyh2MFafc3BzZ5Pjt+6e3VY8QYho3DLxBnTp1Kqx7lWByox1SSUkx90CRHoFFTm98KFzXe/b83nnnDq6JE/qPoSlmRwQXQIwYOcI5S4h56OFs4UrtaXJyFkm7o4ICRk+kZ3TkQ3V3/IbuEuEmrkZOHc2sYQEEsYlIDR9EBRaiJyzS3N6pT+xG+1DNzWdk/Aa66tuAUWk93IS6AwQLIIgtYJYYxluEG0RPgKXlpLfAhyovD6h+/frKuBc0dzUdo8QpM/NhKV9MawlDWQBBbAH7nTBvJ9wRDqInZBAoTiQcwIeqrNyiEhMTpet4IBCISNujcGGMOGFvR11dnZo0MUnFDY5zzhJiPpd8p/CvRjEDCpV7TO2RcIBFP/ryZWZmSbTfmQ+FcTAg3OnqUDBCnLAyXLVqpYyfvuvuu5yzhNiBbqcViRsZ0ROIhPAR/5Kfv6RLH8oES8UVcdI3MXbDowAiL2+xpC+Sk5PlPCE2gRsZ129NTc+bwHbGmDGtizW3m3AS72G6D+Vq5HTllVdKAcT58xfUjOkzWABBrCXuljhpTBxukIaB8LGdEYkE7X2osrIyY3woV8XpP/7j51IAkZqSyk7jxGr08MFIpPbQ5svt2TrEu2gfCiNcDh8+pFaseEGdPn3a+dQ9XBUndIBgAQTxAnq/U29HaBDiFhCn4uISiZw2btrgnHWPKy624LyOGlhdpqenOe8IIYSYCGZF6aKcaOOKOKFf2EsvvSSvTWiTQQgh5BKffto6aPChhx6SsfBu4Io4EUIIIV1hxD4nQgghJBiKEyGEEOOgOBFCCDEOihMhhBDj6JY4TZs2VcXGDvrc1+zZD6pNmzY630WIv8C1P3/+Y5fdEz/+8Y9UY2Oj8x2E+ANc87j2g++F3upDt8Rp06bX1dNP/7ztdWNjkxybm5vl5qyu3iafEeIXnnrqZ44wxcr9gK/q6hq5SadNm9Krm5IQm8C1jmse137rPdB6P+DewD2yfHmR850hglLy7rBx44aLMTFfv7hnz++dM5fOPfjgLOcMId6nrOxlue5/9rP/45y5nKlTp1y8/fbhF48fP+6cIcSb4BrHtY5rviN+9KMfyr0CrQiVXnlOY8feI0dEUIT4haKiZXLMyJgjx/ZkZGTIPaG/jxCvgmsc1zqu+Y5YsOBxORYVhR499UqcGhuPy7FPnz5yJMTrYEAb0hdIWeghg+1JSEiQI9PdxOvoa1wHKu3R94m+b0IhZHGqrq6WY6sB9mN53ZlqEuJV+vTp67zqHGYUiNfR13hXAYq+VzDYMBRCFicYwajEGDv2LvmfoVBi2jQOCST+ojs3GjMKxC90tRDT90p3FnTBhCxOulpPVyfNns2oifiHhIQ7JE2BzEFnaYr6+no5ctFGvI5O53WWwoZo4aurNHhn9MpzIsSP6EKIzgoeME0UUZM2gwnxKtrSwTXfEatXl4k49eRe6LY46VViV+EbIX5g/vwF8oUbDxsPNbhHsPEQhUKrV/8303rE8yByevLJf5eCh9Zr/1I2AfdG637ABT3KsHVrZAY6ROB/rkG6YvnyF5x3hPgTbD7EijE4pYEbEatEChPxEx3dC0iBI7LqqfXDeU6EEELCQnA2AREVFms9heJECCEkbCC1B4FCFIW0H6KnnhQHUZwIIYSEHVhBGzdulJQfBKu+fl9I6W6KEyGEEONgKTkhhBDDUOr/A1Q1Zm59oDg0AAAAAElFTkSuQmCC"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that the areas of the two shaded regions are equal, show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>=</mo><mn>2</mn><mo> </mo><mi>sin</mi><mo> </mo><mi>θ</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence determine the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math>.</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>attempt to find the area of either shaded region in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math> <em><strong>(M1)</strong></em></p>
<p><br><strong>Note:</strong> Do not award <em><strong>M1</strong></em> if they have only copied from the booklet and not applied to the shaded area.</p>
<p><br>Area of segment <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mi>r</mi><mn>2</mn></msup><mi>θ</mi><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mi>r</mi><mn>2</mn></msup><mo> </mo><mi>sin</mi><mo> </mo><mi>θ</mi></math> <em><strong>A1</strong></em></p>
<p>Area of triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mi>r</mi><mn>2</mn></msup><mo> </mo><mi>sin</mi><mfenced><mrow><mi mathvariant="normal">π</mi><mo>-</mo><mi>θ</mi></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p>correct equation in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math> only <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>-</mo><mi>sin</mi><mo> </mo><mi>θ</mi><mo>=</mo><mi>sin</mi><mfenced><mrow><mi mathvariant="normal">π</mi><mo>-</mo><mi>θ</mi></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>-</mo><mi>sin</mi><mo> </mo><mi>θ</mi><mo>=</mo><mi>sin</mi><mo> </mo><mi>θ</mi></math> <em><strong>A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>=</mo><mn>2</mn><mo> </mo><mi>sin</mi><mo> </mo><mi>θ</mi></math> <em><strong>AG</strong></em></p>
<p><br><strong>Note:</strong> Award a maximum of <strong>M1A1A0A0A0</strong> if a candidate uses degrees (i.e., <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mi>r</mi><mn>2</mn></msup><mo> </mo><mi>sin</mi><mfenced><mrow><mn>180</mn><mo>°</mo><mo>-</mo><mi>θ</mi></mrow></mfenced></math>), even if later work is correct.</p>
<p><strong>Note:</strong> If a candidate directly states that the area of the triangle is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mi>r</mi><mn>2</mn></msup><mo> </mo><mi>sin</mi><mo> </mo><mi>θ</mi></math>, award a maximum of <em><strong>M1A1A0A1A1</strong></em>.</p>
<p><em><strong><br>[5 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>89549</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>90</mn></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A0</strong></em> if there is more than one solution. Award <em><strong>A0</strong></em> for an answer in degrees.</p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The height of water, in metres, in Dungeness harbour is modelled by the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>a</mi><mo> </mo><mi>sin</mi><mo>(</mo><mi>b</mi><mo>(</mo><mi>t</mi><mo>-</mo><mi>c</mi><mo>)</mo><mo>)</mo><mo>+</mo><mi>d</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> is the number of hours after midnight, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mo> </mo><mi>b</mi><mo>,</mo><mo> </mo><mi>c</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math> are constants, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>></mo><mn>0</mn><mo>,</mo><mo> </mo><mi>b</mi><mo>></mo><mn>0</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>></mo><mn>0</mn></math>.</p>
<p>The following graph shows the height of the water for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn></math> hours, starting at midnight.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The first high tide occurs at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>04</mn><mo>:</mo><mn>30</mn></math> and the next high tide occurs <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math> hours later. Throughout the day, the height of the water fluctuates between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>2</mn><mo> </mo><mtext>m</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>8</mn><mo> </mo><mtext>m</mtext></math>.</p>
<p>All heights are given correct to one decimal place.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mfrac><mi mathvariant="normal">π</mi><mn>6</mn></mfrac></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the smallest possible value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the height of the water at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>:</mo><mn>00</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the number of hours, over a 24-hour period, for which the tide is higher than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> metres.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>=</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi></mrow><mi>b</mi></mfrac></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi></mrow><mn>12</mn></mfrac></math> <em><strong>A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mfrac><mi mathvariant="normal">π</mi><mn>6</mn></mfrac></math> <em><strong>AG</strong></em></p>
<p> </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><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mrow><mn>6</mn><mo>.</mo><mn>8</mn><mo>-</mo><mn>2</mn><mo>.</mo><mn>2</mn></mrow><mn>2</mn></mfrac></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mrow><mtext>max</mtext><mo>-</mo><mtext>min</mtext></mrow><mn>2</mn></mfrac></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>2</mn><mo>.</mo><mn>3</mn><mo> </mo><mfenced><mtext>m</mtext></mfenced></math> <em><strong>A1</strong></em></p>
<p> </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><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mfrac><mrow><mn>6</mn><mo>.</mo><mn>8</mn><mo>+</mo><mn>2</mn><mo>.</mo><mn>2</mn></mrow><mn>2</mn></mfrac></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mfrac><mrow><mtext>max</mtext><mo>+</mo><mtext>min</mtext></mrow><mn>2</mn></mfrac></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>4</mn><mo>.</mo><mn>5</mn><mo> </mo><mfenced><mtext>m</mtext></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>substituting <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>4</mn><mo>.</mo><mn>5</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo>=</mo><mn>6</mn><mo>.</mo><mn>8</mn></math> for example into their equation for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>8</mn><mo>=</mo><mn>2</mn><mo>.</mo><mn>3</mn><mo> </mo><mi>sin</mi><mfenced><mrow><mfrac><mi mathvariant="normal">π</mi><mn>6</mn></mfrac><mfenced><mrow><mn>4</mn><mo>.</mo><mn>5</mn><mo>-</mo><mi>c</mi></mrow></mfenced></mrow></mfenced><mo>+</mo><mn>4</mn><mo>.</mo><mn>5</mn></math></p>
<p>attempt to solve their equation <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>5</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>using horizontal translation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>12</mn><mn>4</mn></mfrac></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>5</mn><mo>-</mo><mi>c</mi><mo>=</mo><mn>3</mn></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>5</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>METHOD 3</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo>'</mo><mfenced><mi>t</mi></mfenced><mo>=</mo><mfenced><mrow><mn>2</mn><mo>.</mo><mn>3</mn></mrow></mfenced><mfenced><mfrac><mi mathvariant="normal">π</mi><mn>6</mn></mfrac></mfenced><mi>cos</mi><mfenced><mrow><mfrac><mi mathvariant="normal">π</mi><mn>6</mn></mfrac><mfenced><mrow><mi>t</mi><mo>-</mo><mi>c</mi></mrow></mfenced></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p>attempts to solve their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo>'</mo><mfenced><mrow><mn>4</mn><mo>.</mo><mn>5</mn></mrow></mfenced><mo>=</mo><mn>0</mn></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo>.</mo><mn>3</mn></mrow></mfenced><mfenced><mfrac><mi mathvariant="normal">π</mi><mn>6</mn></mfrac></mfenced><mi>cos</mi><mfenced><mrow><mfrac><mi mathvariant="normal">π</mi><mn>6</mn></mfrac><mfenced><mrow><mn>4</mn><mo>.</mo><mn>5</mn><mo>-</mo><mi>c</mi></mrow></mfenced></mrow></mfenced><mo>=</mo><mn>0</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>5</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>12</mn></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn></math>, graphically or algebraically <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>87365</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>87</mn><mo> </mo><mfenced><mtext>m</mtext></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to solve <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>=</mo><mn>2</mn><mo>.</mo><mn>3</mn><mo> </mo><mi>sin</mi><mfenced><mrow><mfrac><mi mathvariant="normal">π</mi><mn>6</mn></mfrac><mfenced><mrow><mi>t</mi><mo>-</mo><mn>1</mn><mo>.</mo><mn>5</mn></mrow></mfenced></mrow></mfenced><mo>+</mo><mn>4</mn><mo>.</mo><mn>5</mn></math> <em><strong>(M1)</strong></em></p>
<p>times are <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>91852</mn><mo>…</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>7</mn><mo>.</mo><mn>08147</mn><mo>…</mo><mo> </mo><mo>,</mo><mo> </mo><mfenced><mrow><mi>t</mi><mo>=</mo><mn>13</mn><mo>.</mo><mn>9185</mn><mo>…</mo><mo>,</mo><mo> </mo><mi>t</mi><mo>=</mo><mn>19</mn><mo>.</mo><mn>0814</mn><mo>…</mo></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p>total time is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>×</mo><mfenced><mrow><mn>7</mn><mo>.</mo><mn>081</mn><mo>…</mo><mo>-</mo><mn>1</mn><mo>.</mo><mn>919</mn><mo>…</mo></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>.</mo><mn>3258</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>10</mn><mo>.</mo><mn>3</mn></math> (hours) <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math>.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></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>The following table shows a probability distribution for the random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}(X) = 1.2">
<mrow>
<mtext>E</mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>X</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>1.2</mn>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_06.18.09.png" alt="M17/5/MATME/SP2/ENG/TZ2/10"></p>
</div>
<div class="specification">
<p>A bag contains white and blue marbles, with at least three of each colour. Three marbles are drawn from the bag, without replacement. The number of blue marbles drawn is given by the random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
<mi>X</mi>
</math></span>.</p>
</div>
<div class="specification">
<p>A game is played in which three marbles are drawn from the bag of ten marbles, without replacement. A player wins a prize if three white marbles are drawn.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q"> <mi>q</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the probability of drawing three blue marbles.</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>Explain why the probability of drawing three white marbles is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{6}"> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The bag contains a total of ten marbles of which <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w"> <mi>w</mi> </math></span> are white. Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w"> <mi>w</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Jill plays the game nine times. Find the probability that she wins exactly two prizes.</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>Grant plays the game until he wins two prizes. Find the probability that he wins his second prize on his eighth attempt.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>correct substitution into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}(X)"> <mrow> <mtext>E</mtext> </mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </math></span> formula <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0(p) + 1(0.5) + 2(0.3) + 3(q) = 1.2"> <mn>0</mn> <mo stretchy="false">(</mo> <mi>p</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mn>1</mn> <mo stretchy="false">(</mo> <mn>0.5</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mn>2</mn> <mo stretchy="false">(</mo> <mn>0.3</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mn>3</mn> <mo stretchy="false">(</mo> <mi>q</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>1.2</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q = \frac{1}{{30}}"> <mi>q</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>30</mn> </mrow> </mfrac> </math></span>, 0.0333 <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>evidence of summing probabilities to 1 <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p + 0.5 + 0.3 + q = 1"> <mi>p</mi> <mo>+</mo> <mn>0.5</mn> <mo>+</mo> <mn>0.3</mn> <mo>+</mo> <mi>q</mi> <mo>=</mo> <mn>1</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = \frac{1}{6},{\text{ }}0.167"> <mi>p</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>0.167</mn> </math></span> <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P (3 blue)}} = \frac{1}{{30}},{\text{ }}0.0333"> <mrow> <mtext>P (3 blue)</mtext> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>30</mn> </mrow> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>0.0333</mn> </math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid reasoning <strong><em>R1</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P (3 white)}} = {\text{P(0 blue)}}"> <mrow> <mtext>P (3 white)</mtext> </mrow> <mo>=</mo> <mrow> <mtext>P(0 blue)</mtext> </mrow> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P(3 white)}} = \frac{1}{6}"> <mrow> <mtext>P(3 white)</mtext> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> </math></span> <strong><em>AG</em></strong> <strong><em>N0</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid method <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P(3 white)}} = \frac{w}{{10}} \times \frac{{w - 1}}{9} \times \frac{{w - 2}}{8},{\text{ }}\frac{{_w{C_3}}}{{_{10}{C_3}}}"> <mrow> <mtext>P(3 white)</mtext> </mrow> <mo>=</mo> <mfrac> <mi>w</mi> <mrow> <mn>10</mn> </mrow> </mfrac> <mo>×</mo> <mfrac> <mrow> <mi>w</mi> <mo>−</mo> <mn>1</mn> </mrow> <mn>9</mn> </mfrac> <mo>×</mo> <mfrac> <mrow> <mi>w</mi> <mo>−</mo> <mn>2</mn> </mrow> <mn>8</mn> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mfrac> <mrow> <msub> <mi></mi> <mi>w</mi> </msub> <mrow> <msub> <mi>C</mi> <mn>3</mn> </msub> </mrow> </mrow> <mrow> <msub> <mi></mi> <mrow> <mn>10</mn> </mrow> </msub> <mrow> <msub> <mi>C</mi> <mn>3</mn> </msub> </mrow> </mrow> </mfrac> </math></span></p>
<p>correct equation <strong><em>A1</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{w}{{10}} \times \frac{{w - 1}}{9} \times \frac{{w - 2}}{8} = \frac{1}{6},{\text{ }}\frac{{_w{C_3}}}{{_{10}{C_3}}} = 0.167"> <mfrac> <mi>w</mi> <mrow> <mn>10</mn> </mrow> </mfrac> <mo>×</mo> <mfrac> <mrow> <mi>w</mi> <mo>−</mo> <mn>1</mn> </mrow> <mn>9</mn> </mfrac> <mo>×</mo> <mfrac> <mrow> <mi>w</mi> <mo>−</mo> <mn>2</mn> </mrow> <mn>8</mn> </mfrac> <mo>=</mo> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mfrac> <mrow> <msub> <mi></mi> <mi>w</mi> </msub> <mrow> <msub> <mi>C</mi> <mn>3</mn> </msub> </mrow> </mrow> <mrow> <msub> <mi></mi> <mrow> <mn>10</mn> </mrow> </msub> <mrow> <msub> <mi>C</mi> <mn>3</mn> </msub> </mrow> </mrow> </mfrac> <mo>=</mo> <mn>0.167</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w = 6"> <mi>w</mi> <mo>=</mo> <mn>6</mn> </math></span> <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}(n,{\text{ }}p),{\text{ }}\left( {\begin{array}{*{20}{c}} n \\ r \end{array}} \right){p^r}{q^{n - r}},{\text{ }}{(0.167)^2}{(0.833)^7},{\text{ }}\left( {\begin{array}{*{20}{c}} 9 \\ 2 \end{array}} \right)"> <mrow> <mtext>B</mtext> </mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>p</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>n</mi> </mtd> </mtr> <mtr> <mtd> <mi>r</mi> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mrow> <msup> <mi>p</mi> <mi>r</mi> </msup> </mrow> <mrow> <msup> <mi>q</mi> <mrow> <mi>n</mi> <mo>−</mo> <mi>r</mi> </mrow> </msup> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mrow> <mo stretchy="false">(</mo> <mn>0.167</mn> <msup> <mo stretchy="false">)</mo> <mn>2</mn> </msup> </mrow> <mrow> <mo stretchy="false">(</mo> <mn>0.833</mn> <msup> <mo stretchy="false">)</mo> <mn>7</mn> </msup> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>9</mn> </mtd> </mtr> <mtr> <mtd> <mn>2</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p>0.279081</p>
<p>0.279 <strong><em>A1</em></strong> <strong><em>N2</em></strong></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>recognizing one prize in first seven attempts <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 7 \\ 1 \end{array}} \right),{\text{ }}{\left( {\frac{1}{6}} \right)^1}{\left( {\frac{5}{6}} \right)^6}"> <mrow> <mo>(</mo> <mrow> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>7</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mn>1</mn> </msup> </mrow> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>5</mn> <mn>6</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mn>6</mn> </msup> </mrow> </math></span></p>
<p>correct working <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 7 \\ 1 \end{array}} \right){\left( {\frac{1}{6}} \right)^1}{\left( {\frac{5}{6}} \right)^6},{\text{ }}0.390714"> <mrow> <mo>(</mo> <mrow> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>7</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mn>1</mn> </msup> </mrow> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>5</mn> <mn>6</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mn>6</mn> </msup> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>0.390714</mn> </math></span></p>
<p>correct approach <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} 7 \\ 1 \end{array}} \right){\left( {\frac{1}{6}} \right)^1}{\left( {\frac{5}{6}} \right)^6} \times \frac{1}{6}"> <mrow> <mo>(</mo> <mrow> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>7</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mn>1</mn> </msup> </mrow> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mfrac> <mn>5</mn> <mn>6</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mn>6</mn> </msup> </mrow> <mo>×</mo> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> </math></span></p>
<p>0.065119</p>
<p>0.0651 <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[4 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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.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">b.iii.</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 function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = - {x^4} + a{x^2} + 5">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>a</mi>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>5</mn>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> is a constant. Part of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f(x)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span> is shown below.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_17.47.40.png" alt="M17/5/MATSD/SP2/ENG/TZ2/06"></p>
</div>
<div class="specification">
<p>It is known that at the point where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 2">
<mi>x</mi>
<mo>=</mo>
<mn>2</mn>
</math></span> the tangent to the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f(x)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span> is horizontal.</p>
</div>
<div class="specification">
<p>There are two other points on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f(x)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span> at which the tangent is horizontal.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-intercept of the graph.</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 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'(x)">
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 8">
<mi>a</mi>
<mo>=</mo>
<mn>8</mn>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(2)">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>-coordinates of these two points;</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the intervals where the gradient of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f(x)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span> is positive.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the range of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x)">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of possible solutions to the equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = 5">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>5</mn>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = m">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>m</mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m \in \mathbb{R}">
<mi>m</mi>
<mo>∈</mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>, has four solutions. Find the possible values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>5 <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept an answer of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(0,{\text{ }}5)">
<mo stretchy="false">(</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>5</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<p> </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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {f'(x) = } \right) - 4{x^3} + 2ax">
<mrow>
<mo>(</mo>
<mrow>
<msup>
<mi>f</mi>
<mo>′</mo>
</msup>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
</mrow>
<mo>)</mo>
</mrow>
<mo>−</mo>
<mn>4</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mi>a</mi>
<mi>x</mi>
</math></span> <strong><em>(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 4{x^3}">
<mo>−</mo>
<mn>4</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
</math></span> and <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" + 2ax">
<mo>+</mo>
<mn>2</mn>
<mi>a</mi>
<mi>x</mi>
</math></span>. Award at most <strong><em>(A1)(A0) </em></strong>if extra terms are seen.</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 4 \times {2^3} + 2a \times 2 = 0">
<mo>−</mo>
<mn>4</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>2</mn>
<mn>3</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mi>a</mi>
<mo>×</mo>
<mn>2</mn>
<mo>=</mo>
<mn>0</mn>
</math></span> <strong><em>(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for substitution of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 2">
<mi>x</mi>
<mo>=</mo>
<mn>2</mn>
</math></span> into their derivative, <strong><em>(M1) </em></strong>for equating their derivative, written in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span>, to 0 leading to a correct answer (note, the 8 does not need to be seen).</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 8">
<mi>a</mi>
<mo>=</mo>
<mn>8</mn>
</math></span> <strong><em>(AG)</em></strong></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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {f(2) = } \right) - {2^4} + 8 \times {2^2} + 5">
<mrow>
<mo>(</mo>
<mrow>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mn>2</mn>
<mo stretchy="false">)</mo>
<mo>=</mo>
</mrow>
<mo>)</mo>
</mrow>
<mo>−</mo>
<mrow>
<msup>
<mn>2</mn>
<mn>4</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>8</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>2</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>5</mn>
</math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 2">
<mi>x</mi>
<mo>=</mo>
<mn>2</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 8">
<mi>a</mi>
<mo>=</mo>
<mn>8</mn>
</math></span> into the formula of the function.</p>
<p> </p>
<p>21 <strong><em>(A1)(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(x = ){\text{ }} - 2,{\text{ }}(x = ){\text{ 0}}">
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo>−</mo>
<mn>2</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>=</mo>
<mo stretchy="false">)</mo>
<mrow>
<mtext> 0</mtext>
</mrow>
</math></span> <strong><em>(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for each correct solution. Award at most <strong><em>(A0)(A1)</em>(ft) </strong>if answers are given as <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="( - 2{\text{ }},21)">
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>2</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mo>,</mo>
<mn>21</mn>
<mo stretchy="false">)</mo>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(0,{\text{ }}5)">
<mo stretchy="false">(</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>5</mn>
<mo stretchy="false">)</mo>
</math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="( - 2,{\text{ }}0)">
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>2</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0</mn>
<mo stretchy="false">)</mo>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(0,{\text{ }}0)">
<mo stretchy="false">(</mo>
<mn>0</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x < - 2,{\text{ }}0 < x < 2">
<mi>x</mi>
<mo><</mo>
<mo>−</mo>
<mn>2</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0</mn>
<mo><</mo>
<mi>x</mi>
<mo><</mo>
<mn>2</mn>
</math></span> <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em>(ft) </strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x < - 2">
<mi>x</mi>
<mo><</mo>
<mo>−</mo>
<mn>2</mn>
</math></span>, follow through from part (d)(i) provided their value is negative.</p>
<p>Award <strong><em>(A1)</em>(ft) </strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 < x < 2">
<mn>0</mn>
<mo><</mo>
<mi>x</mi>
<mo><</mo>
<mn>2</mn>
</math></span>, follow through only from their 0 from part (d)(i); 2 must be the upper limit.</p>
<p>Accept interval notation.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y \leqslant 21">
<mi>y</mi>
<mo>⩽</mo>
<mn>21</mn>
</math></span> <strong><em>(A1)</em>(ft)<em>(A1)</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Award <strong><em>(A1)</em>(ft) </strong>for 21 seen in an interval or an inequality, <strong><em>(A1) </em></strong>for “<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y \leqslant ">
<mi>y</mi>
<mo>⩽</mo>
</math></span>”.</p>
<p>Accept interval notation.</p>
<p>Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - \infty < y \leqslant 21">
<mo>−</mo>
<mi mathvariant="normal">∞</mi>
<mo><</mo>
<mi>y</mi>
<mo>⩽</mo>
<mn>21</mn>
</math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) \leqslant 21">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>⩽</mo>
<mn>21</mn>
</math></span>.</p>
<p>Follow through from their answer to part (c)(ii). Award at most <strong><em>(A1)</em>(ft)<em>(A0) </em></strong>if <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> is seen instead of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>. Do not award the second <strong><em>(A1) </em></strong>if a (finite) lower limit is seen.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>3 (solutions) <strong><em>(A1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="5 < m < 21">
<mn>5</mn>
<mo><</mo>
<mi>m</mi>
<mo><</mo>
<mn>21</mn>
</math></span> or equivalent <strong><em>(A1)</em>(ft)<em>(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em>(ft) </strong>for 5 and 21 seen in an interval or an inequality, <strong><em>(A1) </em></strong>for correct strict inequalities. Follow through from their answers to parts (a) and (c)(ii).</p>
<p>Accept interval notation.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>All living plants contain an isotope of carbon called carbon-14. When a plant dies, the isotope decays so that the amount of carbon-14 present in the remains of the plant decreases. The time since the death of a plant can be determined by measuring the amount of carbon-14 still present in the remains.</p>
<p>The amount, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math>, of carbon-14 present in a plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> years after its death can be modelled by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><msub><mi>A</mi><mn>0</mn></msub><msup><mtext>e</mtext><mrow><mo>-</mo><mi>k</mi><mi>t</mi></mrow></msup></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>≥</mo><mn>0</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>A</mi><mn>0</mn></msub><mo>,</mo><mo> </mo><mi>k</mi></math> are positive constants.</p>
<p>At the time of death, a plant is defined to have <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn></math> units of carbon-14.</p>
</div>
<div class="specification">
<p>The time taken for half the original amount of carbon-14 to decay is known to be <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5730</mn></math> years.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>A</mi><mn>0</mn></msub><mo>=</mo><mn>100</mn></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mfrac><mrow><mi>ln</mi><mo> </mo><mn>2</mn></mrow><mn>5730</mn></mfrac></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find, correct to the nearest <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> years, the time taken after the plant’s death for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo>%</mo></math> of the carbon-14 to decay.</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><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo>=</mo><msub><mi>A</mi><mn>0</mn></msub><msup><mtext>e</mtext><mn>0</mn></msup></math> <em><strong> A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>A</mi><mn>0</mn></msub><mo>=</mo><mn>100</mn></math> <em><strong> AG</strong></em></p>
<p> </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>correct substitution of values into exponential equation <em><strong> (M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn><mo>=</mo><mn>100</mn><msup><mtext>e</mtext><mrow><mo>-</mo><mn>5730</mn><mi>k</mi></mrow></msup></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>e</mtext><mrow><mo>-</mo><mn>5730</mn><mi>k</mi></mrow></msup><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math></p>
<p><br><strong>EITHER</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5730</mn><mi>k</mi><mo>=</mo><mi>ln</mi><mfrac><mn>1</mn><mn>2</mn></mfrac></math> <em><strong> A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ln</mi><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>=</mo><mo>-</mo><mi>ln</mi><mo> </mo><mn>2</mn></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>ln</mi><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>=</mo><mi>ln</mi><mo> </mo><mn>2</mn></math> <em><strong> A1</strong></em></p>
<p><strong><br>OR</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>e</mtext><mrow><mn>5730</mn><mi>k</mi></mrow></msup><mo>=</mo><mn>2</mn></math> <em><strong> A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5730</mn><mi>k</mi><mo>=</mo><mi>ln</mi><mo> </mo><mn>2</mn></math> <em><strong> A1</strong></em></p>
<p><br><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mfrac><mrow><mi>ln</mi><mo> </mo><mn>2</mn></mrow><mn>5730</mn></mfrac></math> <em><strong> AG</strong></em></p>
<p><strong><br>Note:</strong> There are many different ways of showing that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mfrac><mrow><mi>ln</mi><mo> </mo><mn>2</mn></mrow><mn>5730</mn></mfrac></math> which involve showing different steps. Award full marks for at least two correct algebraic steps seen.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>if <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo>%</mo></math> of the carbon-14 has decayed, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>75</mn><mo>%</mo></math> remains ie, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>75</mn></math> units remain <em><strong> (A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>75</mn><mo>=</mo><mn>100</mn><msup><mtext>e</mtext><mrow><mo>-</mo><mfrac><mrow><mi>ln</mi><mo> </mo><mn>2</mn></mrow><mn>5730</mn></mfrac><mi>t</mi></mrow></msup></math></p>
<p><br><strong>EITHER</strong></p>
<p>using an appropriate graph to attempt to solve for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> <em><strong> (M1)</strong></em></p>
<p><br><strong>OR</strong></p>
<p>manipulating logs to attempt to solve for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ln</mi><mo> </mo><mn>0</mn><mo>.</mo><mn>75</mn><mo>=</mo><mo>-</mo><mfrac><mrow><mi>ln</mi><mo> </mo><mn>2</mn></mrow><mn>5730</mn></mfrac><mi>t</mi></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2378</mn><mo>.</mo><mn>164</mn><mo>…</mo></math></p>
<p><br><strong>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>2380</mn></math> (years) (correct to the nearest 10 years) <em><strong>A1</strong></em></p>
<p> </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>Consider the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>+</mo><mfrac><mn>50</mn><mi>x</mi></mfrac><mo>,</mo><mo> </mo><mo> </mo><mi>x</mi><mo>≠</mo><mn>0</mn><mo>.</mo></math></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mn>1</mn></mfenced></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Solve <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>0</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> has a local minimum at point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>.</p>
<p>Find the coordinates of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>attempt to substitute <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>1</mn></math> <em><strong>(M1)</strong></em></p>
<p>eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mn>1</mn></mfenced><mo>,</mo><mo> </mo><msup><mn>1</mn><mn>2</mn></msup><mo>+</mo><mn>1</mn><mo>+</mo><mfrac><mn>50</mn><mn>1</mn></mfrac></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>52</mn></math> (exact) <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>.</mo><mn>04932</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>.</mo><mn>05</mn></math> <em><strong>A2 N2</strong></em></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><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo>.</mo><mn>76649</mn><mo>,</mo><mo> </mo><mn>28</mn><mo>.</mo><mn>4934</mn></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mfenced><mrow><mn>2</mn><mo>.</mo><mn>77</mn><mo>,</mo><mo> </mo><mn>28</mn><mo>.</mo><mn>5</mn></mrow></mfenced></math> <em><strong>A1A1 N2</strong></em></p>
<p><em><strong>[2 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>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{{48}}{x} + k{x^2} - 58">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>48</mn>
</mrow>
<mi>x</mi>
</mfrac>
<mo>+</mo>
<mi>k</mi>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mn>58</mn>
</math></span>, where <em>x</em> > 0 and <em>k</em> is a constant.</p>
<p>The graph of the function passes through the point with coordinates (4 , 2).</p>
</div>
<div class="specification">
<p>P is the minimum point of the graph of <em>f </em>(<em>x</em>).</p>
</div>
<div class="question">
<p>Sketch the graph of <em>y</em> = <em>f</em> (<em>x</em>) for 0 < <em>x</em> ≤ 6 and −30 ≤ <em>y</em> ≤ 60.<br>Clearly indicate the minimum point P and the <em>x</em>-intercepts on your graph.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><img src="data:image/png;base64,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"><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></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct window. Axes must be labelled.<br><em><strong>(A1)</strong></em><strong>(ft)</strong> for a smooth curve with correct shape and zeros in approximately correct positions relative to each other.<br><em><strong>(A1)</strong></em><strong>(ft)</strong> for point P indicated in approximately the correct position. Follow through from their <em>x</em>-coordinate in part (c). <em><strong>(A1)</strong></em><strong>(ft)</strong> for two <em>x</em>-intercepts identified on the graph and curve reflecting asymptotic properties.</p>
<p><em><strong>[4 marks]</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>A water container is made in the shape of a cylinder with internal height <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span> cm and internal base radius <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span> cm.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-07_om_08.31.01.png" alt="N16/5/MATSD/SP2/ENG/TZ0/06"></p>
<p>The water container has no top. The inner surfaces of the container are to be coated with a water-resistant material.</p>
</div>
<div class="specification">
<p>The volume of the water container is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.5{\text{ }}{{\text{m}}^3}">
<mn>0.5</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</math></span>.</p>
</div>
<div class="specification">
<p>The water container is designed so that the area to be coated is minimized.</p>
</div>
<div class="specification">
<p>One can of water-resistant material coats a surface area of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2000{\text{ c}}{{\text{m}}^2}">
<mn>2000</mn>
<mrow>
<mtext> c</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down a formula for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A"> <mi>A</mi> </math></span>, the surface area to be coated.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Express this volume in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{c}}{{\text{m}}^3}"> <mrow> <mtext>c</mtext> </mrow> <mrow> <msup> <mrow> <mtext>m</mtext> </mrow> <mn>3</mn> </msup> </mrow> </math></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>Write down, in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span>, an equation for the volume of this water container.</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>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \pi {r^2} + \frac{{1\,000\,000}}{r}"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mi>r</mi> </mfrac> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{d}}A}}{{{\text{d}}r}}"> <mfrac> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>A</mi> </mrow> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>r</mi> </mrow> </mfrac> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using your answer to part (e), find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span> which minimizes <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A"> <mi>A</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of this minimum area.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the least number of cans of water-resistant material that will coat the area in part (g).</p>
<div class="marks">[3]</div>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(A = ){\text{ }}\pi {r^2} + 2\pi rh"> <mo stretchy="false">(</mo> <mi>A</mi> <mo>=</mo> <mo stretchy="false">)</mo> <mrow> <mtext> </mtext> </mrow> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mi>h</mi> </math></span> <strong><em>(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for either <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi {r^2}"> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </math></span> <strong>OR</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi rh"> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mi>h</mi> </math></span> seen. Award <strong><em>(A1) </em></strong>for two correct terms added together.</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="500\,000"> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </math></span> <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Units <strong>not </strong>required.</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="500\,000 = \pi {r^2}h"> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mi>h</mi> </math></span> <strong><em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>(A1)</em>(ft) </strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi {r^2}h"> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mi>h</mi> </math></span> equating to their part (b).</p>
<p>Do not accept unless <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="V = \pi {r^2}h"> <mi>V</mi> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mi>h</mi> </math></span> is explicitly defined as their part (b).</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \pi {r^2} + 2\pi r\left( {\frac{{500\,000}}{{\pi {r^2}}}} \right)"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </math></span> <strong><em>(A1)</em>(ft)<em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1)</em>(ft) </strong>for their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{{500\,000}}{{\pi {r^2}}}}"> <mrow> <mfrac> <mrow> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> </mrow> </math></span> seen.</p>
<p>Award <strong><em>(M1) </em></strong>for correctly substituting <strong>only</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{{500\,000}}{{\pi {r^2}}}}"> <mrow> <mfrac> <mrow> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> </mrow> </math></span> into a <strong>correct </strong>part (a).</p>
<p>Award <strong><em>(A1)</em>(ft)<em>(M1) </em></strong>for rearranging part (c) to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi rh = \frac{{500\,000}}{r}"> <mi>π</mi> <mi>r</mi> <mi>h</mi> <mo>=</mo> <mfrac> <mrow> <mn>500</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mi>r</mi> </mfrac> </math></span> and substituting for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi rh"> <mi>π</mi> <mi>r</mi> <mi>h</mi> </math></span> in expression for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A"> <mi>A</mi> </math></span>.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \pi {r^2} + \frac{{1\,000\,000}}{r}"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mi>r</mi> </mfrac> </math></span> <strong><em>(AG)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>The conclusion, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \pi {r^2} + \frac{{1\,000\,000}}{r}"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mi>r</mi> </mfrac> </math></span>, must be consistent with their working seen for the <strong><em>(A1) </em></strong>to be awarded.</p>
<p>Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{10^6}"> <mrow> <msup> <mn>10</mn> <mn>6</mn> </msup> </mrow> </math></span> as equivalent to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{1\,000\,000}"> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> </math></span>.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi r - \frac{{{\text{1}}\,{\text{000}}\,{\text{000}}}}{{{r^2}}}"> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mo>−</mo> <mfrac> <mrow> <mrow> <mtext>1</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>000</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>000</mtext> </mrow> </mrow> <mrow> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> </math></span> <strong><em>(A1)(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi r"> <mn>2</mn> <mi>π</mi> <mi>r</mi> </math></span>, <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{{{r^2}}}"> <mfrac> <mn>1</mn> <mrow> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> </math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{r^{ - 2}}"> <mrow> <msup> <mi>r</mi> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </math></span>, <strong><em>(A1) </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - {\text{1}}\,{\text{000}}\,{\text{000}}"> <mo>−</mo> <mrow> <mtext>1</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>000</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>000</mtext> </mrow> </math></span>.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi r - \frac{{1\,000\,000}}{{{r^2}}} = 0"> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mo>−</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfrac> <mo>=</mo> <mn>0</mn> </math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for equating their part (e) to zero.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{r^3} = \frac{{1\,000\,000}}{{2\pi }}"> <mrow> <msup> <mi>r</mi> <mn>3</mn> </msup> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </math></span> <strong>OR</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = \sqrt[3]{{\frac{{1\,000\,000}}{{2\pi }}}}"> <mi>r</mi> <mo>=</mo> <mroot> <mrow> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mfrac> </mrow> <mn>3</mn> </mroot> </math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for isolating <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span>.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>sketch of derivative function <strong><em>(M1)</em></strong></p>
<p>with its zero indicated <strong><em>(M1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(r = ){\text{ }}54.2{\text{ }}({\text{cm}}){\text{ }}(54.1926 \ldots )"> <mo stretchy="false">(</mo> <mi>r</mi> <mo>=</mo> <mo stretchy="false">)</mo> <mrow> <mtext> </mtext> </mrow> <mn>54.2</mn> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mrow> <mtext>cm</mtext> </mrow> <mo stretchy="false">)</mo> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mn>54.1926</mn> <mo>…</mo> <mo stretchy="false">)</mo> </math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi {(54.1926 \ldots )^2} + \frac{{1\,000\,000}}{{(54.1926 \ldots )}}"> <mi>π</mi> <mrow> <mo stretchy="false">(</mo> <mn>54.1926</mn> <mo>…</mo> <msup> <mo stretchy="false">)</mo> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mrow> <mo stretchy="false">(</mo> <mn>54.1926</mn> <mo>…</mo> <mo stretchy="false">)</mo> </mrow> </mfrac> </math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution of their part (f) into the given equation.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 27\,700{\text{ }}({\text{c}}{{\text{m}}^2}){\text{ }}(27\,679.0 \ldots )"> <mo>=</mo> <mn>27</mn> <mspace width="thinmathspace"></mspace> <mn>700</mn> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mrow> <mtext>c</mtext> </mrow> <mrow> <msup> <mrow> <mtext>m</mtext> </mrow> <mn>2</mn> </msup> </mrow> <mo stretchy="false">)</mo> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mn>27</mn> <mspace width="thinmathspace"></mspace> <mn>679.0</mn> <mo>…</mo> <mo stretchy="false">)</mo> </math></span> <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{27\,679.0 \ldots }}{{2000}}"> <mfrac> <mrow> <mn>27</mn> <mspace width="thinmathspace"></mspace> <mn>679.0</mn> <mo>…</mo> </mrow> <mrow> <mn>2000</mn> </mrow> </mfrac> </math></span> <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for dividing their part (g) by 2000.</p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 13.8395 \ldots "> <mo>=</mo> <mn>13.8395</mn> <mo>…</mo> </math></span> <strong><em>(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Notes: </strong>Follow through from part (g).</p>
<p> </p>
<p>14 (cans) <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Final <strong><em>(A1) </em></strong>awarded for rounding up their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="13.8395 \ldots "> <mn>13.8395</mn> <mo>…</mo> </math></span> to the next integer.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the lines <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_1}">
<mrow>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_2}">
<mrow>
<msub>
<mi>L</mi>
<mn>2</mn>
</msub>
</mrow>
</math></span> with respective equations</p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_1}\,{\text{:}}\,y = - \frac{2}{3}x + 9">
<mrow>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>:</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>y</mi>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
<mi>x</mi>
<mo>+</mo>
<mn>9</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_2}{\text{:}}\,y = \frac{2}{5}x - \frac{{19}}{5}">
<mrow>
<msub>
<mi>L</mi>
<mn>2</mn>
</msub>
</mrow>
<mrow>
<mtext>:</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>y</mi>
<mo>=</mo>
<mfrac>
<mn>2</mn>
<mn>5</mn>
</mfrac>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mfrac>
<mrow>
<mn>19</mn>
</mrow>
<mn>5</mn>
</mfrac>
</math></span>.</p>
</div>
<div class="specification">
<p>A third line, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_3}">
<mrow>
<msub>
<mi>L</mi>
<mn>3</mn>
</msub>
</mrow>
</math></span>, has gradient <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - \frac{3}{4}">
<mo>−<!-- − --></mo>
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the point of intersection of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_1}"> <mrow> <msub> <mi>L</mi> <mn>1</mn> </msub> </mrow> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_2}"> <mrow> <msub> <mi>L</mi> <mn>2</mn> </msub> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down a direction vector for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_3}"> <mrow> <msub> <mi>L</mi> <mn>3</mn> </msub> </mrow> </math></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 class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_3}"> <mrow> <msub> <mi>L</mi> <mn>3</mn> </msub> </mrow> </math></span> passes through the intersection of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_1}"> <mrow> <msub> <mi>L</mi> <mn>1</mn> </msub> </mrow> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_2}"> <mrow> <msub> <mi>L</mi> <mn>2</mn> </msub> </mrow> </math></span>.</p>
<p>Write down a vector equation for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_3}"> <mrow> <msub> <mi>L</mi> <mn>3</mn> </msub> </mrow> </math></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>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_1} = {L_2}"> <mrow> <msub> <mi>L</mi> <mn>1</mn> </msub> </mrow> <mo>=</mo> <mrow> <msub> <mi>L</mi> <mn>2</mn> </msub> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 12"> <mi>x</mi> <mo>=</mo> <mn>12</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 1"> <mi>y</mi> <mo>=</mo> <mn>1</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {12{\text{, }}1} \right)"> <mrow> <mo>(</mo> <mrow> <mn>12</mn> <mrow> <mtext>, </mtext> </mrow> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </math></span> (exact) <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} { - 4} \\ 3 \end{array}} \right)"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span> (or any multiple of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} { - 4} \\ 3 \end{array}} \right)"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span>) <em><strong>A1 N1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>any correct equation in the form <em><strong>r</strong></em> = <em><strong>a</strong></em> + <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span><em><strong>b</strong></em> (accept any parameter for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span>) where <br><em><strong>a</strong></em> is a position vector for a point on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_1}"> <mrow> <msub> <mi>L</mi> <mn>1</mn> </msub> </mrow> </math></span>, and <em><strong>b</strong></em> is a scalar multiple of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} { - 4} \\ 3 \end{array}} \right)"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span> <em><strong>A2 N2</strong></em></p>
<p><em>eg</em> <em><strong>r</strong></em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \left( {\begin{array}{*{20}{c}} {12} \\ 1 \end{array}} \right) + t\left( {\begin{array}{*{20}{c}} { - 4} \\ 3 \end{array}} \right)"> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mn>12</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mi>t</mi> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p><strong>Note:</strong> Award <em><strong>A1</strong></em> for the form <em><strong>a</strong></em> + <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span><em><strong>b</strong></em>, <em><strong>A1</strong></em> for the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L"> <mi>L</mi> </math></span> = <em><strong>a</strong></em> + <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span><em><strong>b</strong></em>, <em><strong>A0</strong></em> for the form <em><strong>r</strong></em> = <em><strong>b</strong></em> + <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span><em><strong>a</strong></em>.</p>
<p><em><strong>[2 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>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>3</mn><mi>x</mi><mo>-</mo><msup><mn>4</mn><mrow><mn>0</mn><mo>.</mo><mn>15</mn><msup><mi>x</mi><mn>2</mn></msup></mrow></msup></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mn>3</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> on the grid below.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAskAAAHACAYAAABQ0vW4AAAgAElEQVR4Ae29T6tuSXbeqe/ReC6SHLRpjFXksKsQlW0oQeNSZWnWRq4ENy65wXkNMtYoc2bNKtvQhrasTOQuDfM27YEbN5VQMw0qqZFm1wKNb6EPcJp1qtY9++6z9np2vM8bd0XEfjYcxbtjxVrriV/8zVfnnvqtBz0iIAIiIAIiIAIiIAIiIAJvEfitt970IgIiIAIiIAIiIAIiIAIi8KBLsiaBCIiACIiACIiACIiACOwIvHVJ/nt/77970I8YaA5oDmgOaA5oDmgOaA5oDlxhDuzuxW+9Prskv2XViwiIgAiIgAiIgAiIgAgsSMD+IyB7dEnO6MgmAiIgAiIgAiIgAiKwJAFdkpccVnVKBERABERABERABESAIaBLMkNPviIgAiIgAiIgAiIgAksS0CV5yWFVp0RABERABERABERABBgCuiQz9OQrAiIgAiIgAiIgAiKwJAFdkpccVnVKBERABERABERABESAIaBLMkNPviIgAiIgAiIgAiIgAksS0CV5yWFVp0RABERABERABERABBgCuiQz9OQrAiIgAiIgAiIgAiKwJAFdkpccVnVKBERABERABERABESAIaBLMkNPviIgAiIgAiIgAiIgAksS0CV5yWFVp0RABERABERABERABBgCuiQz9OQrAiIgAiIgAiIgAiKwJAFdkpccVnVKBERABERABERABESAIaBLMkNPviIgAiIgAiIgAiIgAksS0CV5yWFVp0RABERABERABERABBgCuiQz9OQrAiIgAiIgAiIgAiKwJAFdkpccVnVKBERABERABERABESAIaBLMkNPviIgAiIgAiIgAiIgAksS0CV5yWFVp0RABERABERABERABBgCuiQz9OQrAiIgAiIgAiIgAiKwJAFdkpccVnVKBERABERABERABESAIaBLMkNPviIgAiIgAiIgAiIgAksS0CV5yWFVp0RABERABERABERABBgCuiQz9OQrAiIgAiIgAiIgAiKwJAFdkpccVnVKBERABERABERABESAIaBLMkNPviIgAiIgAiIgAiIgAksS0CV5yWFVp0RABERABERABERABBgCuiQz9OQrAiIgAiIgAiIgAiKwJAFdkpccVnVKBERABERABERABESAIaBLMkNPviJQQODVq1cPtnDt5+OPf/RGwWefffrW+xuDPoiACIiACIiACDQT0CW5GZkcRGAMAnZBfv/9996I+frrn+mS/IaGPoiACIiACIgAR0CXZI6fvIsI/Ke/+IuH6MfkbOvv/b6N3fr53lp+/M//+eO3yf/hP/yfj31+8cknD/bTqsva31vbLRqOfEbSdm8t+3hHDM7U72Ox72dynm3Datn7n817pt0+Nvt+JudRGzY38j/Ke0u95dIjAqsT0CV59RFetH+2qWfP//tf/ktmfuhpf1favvzyi8dLsv36xevXrx9evPjksc9Z396VtiP40haTybhkNotWOabSFo+n1WZsMtvsY3pMRBYRmI+ALsnzjZkUnyCADqGe9nd1aXn58qvHS7L9moX9PrJdlu3J+vautB0NkbTFZDIumc2iVY6ptMXjabUZm8w2+5geE5FFBOYjoEvyfGMmxcUXAxuA7JB7V5eWb775xeMl2b5BtguzP5m2/+1f/IuHn//85970WZn5WuOe9nfF7Vmnf1OR9a1SW6bLpEtbPKLiFnOx2oxNZjsz346zyiIC8xHQJXm+MZNisMkbILTR97T3jL3tm/+VC/sWefsc5bfLsS343/mdf/jwq1/9auvy5vORrzfoae8Z2/Qz8RnfmXMj7ZVcpM0IxA8zLoxvrEa1IjAvAV2S5x27SytnN/Ke/j1j26B7fLsk++8hbyeD27d19tkux7bgf/d3v/PwJ3/yb/bmx/cjX2/c094ztuln4jO+M+dG2iu5SJsRiB9mXBjfWI1qRWBeArokzzt2l1aONvJKOD212T/W+/3vf//Byu3fSEb9/dM//bdvLsm//OUvHy/L2a9doHg97D25sXql7TaC4iZutxGQlwiMQUCX5DHGQSoaCaDDt9LeM/fnn//k8YJr5dGzz7+9FPuCt0uzfaO8f/a+79Jemdv6meXPbMiXtVfmRtqlzQjFT8Yms1m0SjubO6ahWhGYk4CfmUfqf2trQI23bfVZBHoSsH+sZJs5+jEN2zbs+zbW0ecjbWxu5H+k5x/9o//p4X/9Z//skYOtYWv3f798+fAP/sH/8PDJv/yXj+8odqv9SEtW79xac7W2zzQc2aQNr7WI3YjcfL700hZxOFs3kjbX4tr93bjpEYGrEED3Xl2SrzITJusn2qhtY8+envaRtNmvVLz33m+/+Yd62wXv/5Dvb/7mv71B1ZOLJcnij8TtDZDffKjUljEzedK2H61fv4tbzMVqMzaZzXzRfDvOKosIzEdge2ZG6nVJjqiorpwA2sgrBY6kzf6KxfYSvF/w9qsYozwjcdszkbY9kXPv4naO076VuO2J6F0Eagjsz8y9Cl2S90T0PgQBdIhU2itz2+Bk+dGCz3xRbNZemRtpr9RWmXtkLtJmBOKHmTOMb6xGtSIwLwF0ZuqSPO/YLq2c3ch7+veMbYPKxEcLnonNaqvMjbRXaqvMPTIXaTMC8cPMGcY3VqNaEZiXADozdUmed2yXVs5u5D39e8a2QWXiowXPxGa1VeZG2iu1VeYemYu0GYH4YeYM4xurUa0IzEsAnZm6JM87tlJeRGDkf9iCFnwRsse0I3OTtttmhritx+22HslLBOYkgM5MXZLnHNflVbPfdvT07xnbBpaJjxY8E5vVVpkbaa/UVpl7ZC7SZgTih5kzjG+sRrUiMC8BdGbqkjzv2C6t3DbyMz8GYduOfd/Gav3M5kb+Z/TYgo/aodit9ijH2brWXK3tz+qI2rXmam0f5Txb15qrtf1ZHVG71lyt7aOcR3WtsVvbH+U9U9+aq7X9GQ3eJottNj0icAUCuiRfYZQX7KNt5NlTaa/MbUyy/GjBZ74oNmuvzI20V2qrzD0yF2kzAvHDzBnGN1ajWhGYlwA6M/VN8rxju7RytJFXdn5kbWjBi1tMYOQxlbZ4zFCtuCFCsX1kbrFi1YrA7QTQmalL8u1s5dmRAPoHQWgj72kfWRta8D252HTI4o/MrVJbxsyYSlu80YhbzAWtQ5bbcVZZRGA+AujM1CV5vjG9hOLKi4EBzg6SkbWhBZ/1C/WbtY/MrVIbGhNpi7c8cYu5oHXKcjvOKosIzEcAnZm6JM83ppdQjDbySntlbhv8LD9a8Jkvis3aK3Mj7ZXaKnOPzEXajED8MHOG8Y3VqFYE5iWAzkxdkucd26WVsxt5T/+esW1QmfhowTOxWW2VuZH2Sm2VuUfmIm1GIH6YOcP4xmpUKwLzEkBnpi7J847t0srZjbynf8/YNqhMfLTgmdistsrcSHultsrcI3ORNiMQP8ycYXxjNaoVgXkJoDNTl+R5x3Zp5baRn/kxCNt27Ps2VutnNjfyP6PHFnzUDsVutUc5zta15mptf1ZH1K41V2v7KOfZutZcre3P6ojateZqbR/lPKprjd3a/ijvmfrWXK3tz2jwNllss+kRgSsQ0CX5CqO8YB8r/7GS4bSD5OgZWRta8Fm/UL9Z+8jcKrWhMZG2eCWKW8wFrVOW23FWWURgPgLozNQ3yfON6SUUV14MDHB2kIysDS34rF+o36x9ZG6V2tCYSFu85YlbzAWtU5bbcVZZRGA+AujM1CV5vjG9hGK0kVfaK3Pb4Gf50YLPfFFs1l6ZG2mv1FaZe2Qu0mYE4oeZM4xvrEa1IjAvAXRm6pI879gurZzdyHv694xtg8rERwueic1qq8yNtFdqq8w9MhdpMwLxw8wZxjdWo1oRmJcAOjN1SZ53bJdWzm7kPf17xrZBZeKjBc/EZrVV5kbaK7VV5h6Zi7QZgfhh5gzjG6tRrQjMSwCdmbokzzu2Syuv/D1MA5sdJCNrQws+6xfqN2sfmVulNjQm0hZvdeIWc0HrlOV2nFUWEZiPADozdUmeb0wvodguBraZox+DsW3Dvm9jHX0+0sbmRv5Herb1tuC37/4ZxW61e9yW0rm15mpt36LJ20obXmvOaluOyM3nSy9t2/63fh5Jm2vxPvi7cdMjAlchoEvyVUZ6sX7axp09lfbK3MYky48WfOaLYrP2ytxIe6W2ytwjc5E2IxA/zJxhfGM1qhWBeQmgM1PfJM87tksrRxt5ZedH1oYWvLjFBEYeU2mLxwzVihsiFNtH5hYrVq0I3E4AnZm6JN/OVp4dCaCNutLeM/c33/ziwRat/3z88Y+eUc7yowWf+VqinvaesVntldoqcyNu0vZs+b2pyNhkNsS8t53V9gaAPojAAgTQmalL8gKDvGIX2I28p3/P2HYp/o9/9mfpkGb50YLPfC1pT3vP2Kz2Sm2VuRE3aTteihmbzIaY97az2o6JyCIC8xFAZ6YuyfON6SUUo388wm70jH8vbfYtsl2SGW1owTOxbeIx/r24+YKYVRvSXclN2nx2PS8zNpnNIs08ps9JqEYE5iWAzkxdkucdWylfjIBdkG3B2s9HH/3g4bPPPm3uIVrwzQHlIAIiIAIiIAKLEkBnpi7Jiw787N1C38RU2nvn/qMf//jhxYtPHi/Ln3/+k2dDmeVHCz7ztUQ97T1js9ortVXmRtyk7dnye1ORsclsiHlvO6vtDQB9EIEFCKAzU5fkBQZ5xS7YRu4/3j9/327y2zpU36ut6dvGjvQeacva/v73v//we9/73rPYtqizH9cSxY7qbtFmcTyPl0d1Z+tH0uZ98lLa8vVonM6Os7fdtx+J8dW1+VioFIHVCeiSvPoIL9q/7UEadbHS/q5y27fIH3743Wfdz/KjBZ/5WqKe9p6xWe2V2ipzI27S9mz5vanI2GQ2xLy3ndX2BoA+iMACBNCZqW+SFxjkFbvAbuQ9/XvGtrH0+C9ffqVL8mZyO5dN1VsfGTvjux2ztwRtXrL4mY2NzfpL22YQdx8zNpmNHRPWn9W2w6BXEZiagC7JUw+fxB8RYDd61v9Il9Wzsd3fvkle6XeSM2b35HaUx7ke2bN65MvYkW+my2zIn7EjX2mLCazMLe6xakVgTgK6JM85bpdXjQ6ZSnuP3K9fv35zIbb4X375Rfgtsk2MLD9a8Jkvis3aK3Mj7ZXaKnOPzEXajED8MHOG8Y3VqFYE5iWAzkz9usW8Y7u0cnYj7+nfI/arV68ePvjgW2/+QV7259+y/GjBZ742oXrae8ZmtVdqq8yNuEnb8TabsclsiHlvO6vtmIgsIjAfAXRm6pI835heQjHayCshjKwNLXhxiwmMPKbSFo8ZqhU3RCi2j8wtVqxaEbidADozdUm+na08OxJAG3WlvTK3Ic/yowWf+aLYrL0yN9Jeqa0y98hcpM0IxA8zZxjfWI1qRWBeAujM1CV53rFdXrlt5ujHIGzbsO/bWEef9zm83b7+3u+eJyttwUf2Ci17Ha7BS7ff+93jtpSuwUv3vfe7x20pXYOX7nvvd4/bUroGL9333u8e90zpufel+3r9re/ud0vpufelx/L6W9/d70x5lMvq9YjAVQjoknyVkb5YP+0QyJ7e9srcWd/Qgs98rU+97aNyy3T15oKYS1tMQNxiLmi+styOs8oiAvMRQGemvkmeb0wvoXjkjXxkbWjBV06ekblJ220zQ9zE7TYC8hKBMQigM1OX5DHGSSp2BNDhW2mvzG2YsvxowWe+KDZrr8yNtFdqq8w9MhdpMwLxw8wZxjdWo1oRmJcAOjN1SZ53bJdWzm7kPf17xrZBZeKjBc/EZrVV5kbaK7VV5h6Zi7QZgfhh5gzjG6tRrQjMSwCdmbokzzu2SytnN/Ke/j1j26Ay8dGCZ2Kz2ipzI+2V2ipzj8xF2oxA/DBzhvGN1ahWBOYlgM5MXZLnHVspF4FnBNCCf+agChEQAREQARG4KAF0ZuqSfNGJMXq32W87evr3jG3jwsRHC56JzWqrzI20V2qrzD0yF2kzAvHDzBnGN1ajWhGYlwA6M3VJnndsl1ZuG/mZH4Owbce+b2O1fmZzI/8zemzBR+1Q7FZ7lONsXWuu1vZndUTtWnO1to9ynq1rzdXa/qyOqF1rrtb2Uc6jutbYre2P8p6pb83V2v6MBm+TxTabHhG4AgFdkq8wygv20Tby7Km0V+Y2Jll+tOAzXxSbtVfmRtortVXmHpmLtBmB+GHmDOMbq1GtCMxLAJ2Z+iZ53rFdWjm7kff07xnbBpWJjxY8E5vVVpkbaa/UVpl7ZC7SZgTih5kzjG+sRrUiMC8BdGbqkjzv2F5aObvRs/4ZfDY2448WPBPb+sz6j8ot03WPfmfcMhvSJW1nCMVtEHfGjnxjRU+1yJ+xI98nFfokAusTQGemLsnrz4Ele4g2+t72DGrv3Fl8tOAzX+tTb/uo3DJdvbkg5tIWExC3mAuaryy346yyiMB8BNCZqUvyfGN6CcVoI6+0V+a2wc/yowWf+aLYrL0yN9Jeqa0y98hcpM0IxA8zZxjfWI1qRWBeAujM1CV53rFdWjm7kff07xnbBpWJjxY8E5vVVpkbaa/UVpl7ZC7SZgTih5kzjG+sRrUiMC8BdGbqkjzv2C6tnN3Ie/r3jG2DysRHC56JzWqrzI20V2qrzD0yF2kzAvHDzBnGN1ajWhGYlwA6M3VJnndsl1ZuG/mZH4Owbce+b2O1fmZzI/8zemzBR+1Q7FZ7lONsXWuu1vZndUTtWnO1to9ynq1rzdXa/qyOqF1rrtb2Uc6jutbYre2P8p6pb83V2v6MBm+TxTabHhG4AgFdkq8wyhfso2302dPbXpk76xta8Jmv9am3fVRuma7eXBBzaYsJiFvMBc1XlttxVllEYD4C6MzUN8nzjakUv4PLHHOQIN+edrTge+a2iYniZ5MX+fa2V2lD/cp0nWGO4mf2zIZ0SdsZQnEbxJ2xI99YkWpFYE0C6MzUJXnNcZ++V2gjr7RX5raBzfKjBZ/5otisvTI30l6prTL3yFykzQjEDzNnGN9YjWpFYF4C6MzUJXnesV1aObuR9/TvGdsGlYmPFjwTm9VWmRtpr9RWmXtkLtJmBOKHmTOMb6xGtSIwLwF0ZuqSPO/YLq2c3ch7+veMbYPKxEcLnonNaqvMjbRXaqvMPTIXaTMC8cPMGcY3VqNaEZiXADozdUmed2wvrZzd6Fn/DD4bm/FHC56JbX1m/Ufllum6R78zbpkN6ZK2M4TiNog7Y0e+saKnWuTP2JHvkwp9EoH1CaAzU5fk9efAtD20zRz9WOe2bdj3bayjz/sc3m5ff+93z5OVtuAje4WWvQ7X4KXb7/3ucVtK1+Cl+9773eO2lK7BS/e997vHbSldg5fue+93j3um9Nz70n29/tZ397ul9Nz70mN5/a3v7nemPMpl9XpE4CoEdEm+ykgv1k/b5LOn0l6Z25hk+dGCz3xRbNZemRtpr9RWmXtkLtJmBOKHmTOMb6xGtSIwLwF0Zuqb5HnHdmnlaCOv7PzI2tCCF7eYwMhjKm3xmKFacUOEYvvI3GLFqhWB2wmgM1OX5NvZyrMjAbRRV9rfRe6XL796sMX7+vXrZ5Sz/GjBZ76WqKe9Z2xWe6W2ytyIm7Q9W35vKjI2mQ0x721ntb0BoA8isAABdGbqkrzAIK/YBXYj7+nfM7aN5cuvvnr44INv6ZK8m9g9ufeMbd3I4mc25NvbLm27Sbh5zdhktt5jhuKz2jYI9FEEpiegS/L0Q6gORATYjZ71jzR5HRv7n/7hHz68ePHJcpdk53NUstxY/yNdVs/GzvwzW6bJbcifsSNf13BUIn/GjnyPNHk98mfsyNc1HJXIn7Ej3yNNqheBFQnokrziqKpPyxKwX7P44os/f/j8858cXpKzzqMFn/nKJgIiIAIiIAJXIoDOTP26xZVmw0R9Rd92VNp75bbfP/744x89fmuZXZKz/GjBZ742PXrae8ZmtVdqq8yNuEnb8aaZsclsiHlvO6vtmIgsIjAfAXRm6pI835heQrFt5P7jHfb37Sa/rUP1vdqavm3sSO+Rtm1b+zWLv/zpTx9j2bfJtnjt95P3sa0++/H229hZ3Rlt7n/U1uu37bxuz+eoPtJ7j7Yew8rtT5Zv2879e/TDY7fka2m715z1ed92ZG29+7Fn0ZKvpe0tjN+FNu+DShFYnYAuyauP8KL988PjqHuV9h65v/zyi8dfsbD+Wnx9k/x85Htw9yw9Y/uYeq59WZlb2vaj8fTOjAvji8aEtbPangjpkwjMT0CX5PnH8JI9YDfynv49Yn/44XcPvx22X8HYPll+tOAzX8vR094zNqu9UltlbsRN2rYr7+3PGZvMhpj3trPa3qagNxGYmwA6M/XrFnOP72XVsxs965+BZ2Ob/4rfJGfMzHYPblkOFJ/xRbEze2bLNLkN+TN25Osajkrkz9iR75Emr0f+jB35uoajEvkzduR7pEn1IrAiAV2SVxzVC/QJbeSV9neRe8VL8rvgli2NLH9ms5g97T1js9ql7XhGZWwyGzsmrD+r7ZiILCIwHwFdkucbMynufCkxwMxBwfieza1L8vNl0JN7z9hozCtzS9vzeeY1zLgwvmhMWDurzfmoFIEVCOiSvMIoXrAPaCOvRDKyNrTgxS0mMPKYSls8ZqhW3BCh2D4yt1ixakXgdgLozNTvJN/OVp4dCaCNutJemduQZ/nRgs98UWzWXpkbaa/UVpl7ZC7SZgTih5kzjG+sRrUiMC8BdGbqkjzv2C6v3DZz9GMQtm3Y922so8/7HN5uX3/vd8+TlbbgI3uFlr0O1+Cl2+/97nFbStfgpfve+93jtpSuwUv3vfe7x20pXYOX7nvvd497pvTc+9J9vf7Wd/e7pfTc+9Jjef2t7+53pjzKZfV6ROAqBHRJvspIX6yfdghkT297Ze6sb2jBZ77Wp972UbllunpzQcylLSYgbjEXNF9ZbsdZZRGB+QigM1PfJM83ppdQPPJGPrI2tOArJ8/I3KTttpkhbuJ2GwF5icAYBNCZqUvyGOMkFTsC6PCttFfmNkxZfrTgM18Um7VX5kbaK7VV5h6Zi7QZgfhh5gzjG6tRrQjMSwCdmbokzzu2SytnN/Ke/j1j26Ay8dGCZ2Kz2ipzI+2V2ipzj8xF2oxA/DBzhvGN1ahWBOYlgM5MXZLnHdullbMbeU//nrFtUJn4aMEzsVltlbmR9kptlblH5iJtRiB+mDnD+MZqVCsC8xJAZ6YuyfOOrZSLwDMCaME/c1CFCIiACIiACFyUADozdUm+6MQYvdvstx09/XvGtnFh4qMFz8RmtVXmRtortVXmHpmLtBmB+GHmDOMbq1GtCMxLAJ2ZuiTPO7ZLK7eN/MyPQdi2Y9+3sVo/s7mR/xk9tuCjdih2qz3KcbauNVdr+7M6onatuVrbRznP1rXmam1/VkfUrjVXa/so51Fda+zW9kd5z9S35mptf0aDt8lim02PCFyBgC7JVxjlBftoG3n2VNorcxuTLD9a8Jkvis3aK3Mj7ZXaKnOPzEXajED8MHOG8Y3VqFYE5iWAzkx9kzzv2C6tnN3Ie/r3jG2DysRHC56JzWqrzI20V2qrzD0yF2kzAvHDzBnGN1ajWhGYlwA6M3VJnndsL62c3ehZ/ww+G5vxRwueiW19Zv1H5Zbpuke/M26ZDemStjOE4jaIO2NHvrGip1rkz9iR75MKfRKB9QmgM1OX5PXnwJI9RBt9b3sGtXfuLD5a8Jmv9am3fVRuma7eXBBzaYsJiFvMBc1XlttxVllEYD4C6MzUJXm+Mb2EYrSRV9orc9vgZ/nRgs98UWzWXpkbaa/UVpl7ZC7SZgTih5kzjG+sRrUiMC8BdGbqkjzv2C6tnN3Ie/r3jG2DysRHC56JzWqrzI20V2qrzD0yF2kzAvHDzBnGN1ajWhGYlwA6M3VJnndsl1bObuQ9/XvGtkFl4qMFz8RmtVXmRtortVXmHpmLtBmB+GHmDOMbq1GtCMxLAJ2ZuiTPO7ZLK7eN/MyPQdi2Y9+3sVo/s7mR/xk9tuCjdih2qz3KcbauNVdr+7M6onatuVrbRznP1rXmam1/VkfUrjVXa/so51Fda+zW9kd5z9S35mptf0aDt8lim02PCFyBgC7JVxjlC/bRNvrs6W2vzJ31DS34zNf61Ns+KrdMV28uiLm0xQTELeaC5ivL7TirLCIwHwF0Zuqb5PnGVIrfwWWOOUiQb087WvA9c9vERPGzyYt8e9urtKF+ZbrOMEfxM3tmQ7qk7QyhuA3iztiRb6xItSKwJgF0ZuqSvOa4T98rtJFX2itz28Bm+dGCz3xRbNZemRtpr9RWmXtkLtJmBOKHmTOMb6xGtSIwLwF0ZuqSPO/YLq2c3ch7+veMbYPKxEcLnonNaqvMjbRXaqvMPTIXaTMC8cPMGcY3VqNaEZiXADozdUmed2yXVs5u5D39e8a2QWXiowXPxGa1VeZG2iu1VeYemYu0GYH4YeYM4xurUa0IzEsAnZm6JM87tpdWzm70rH8Gn43N+KMFz8S2PrP+o3LLdN2j3xm3zIZ0SdsZQnEbxJ2xI99Y0VMt8mfsyPdJhT6JwPoE0JmpS/L6c2DaHtpmjn6sc9s27Ps21tHnfQ5vt6+/97vnyUpb8JG9Qsteh2vw0u33fve4LaVr8NJ97/3ucVtK1+Cl+9773eO2lK7BS/e997vHPVN67n3pvl5/67v73VJ67n3psbz+1nf3O1Me5bJ6PSJwFQK6JF9lpBfrp23y2VNpr8xtTLL8aMFnvig2a6/MjbRXaqvMPTIXaTMC8cPMGcY3VqNaEZiXADoz9U3yvGO7tHK0kVd2fmRtaMGLW0xg5DGVtnjMUK24IUKxfWRusWLVisDtBNCZqUvy7Wzl2ZEA2qgr7b1yf/PNLx4+/PC7D7Zo33//vYcvv/wiJJzlRws+87VkPe09Y7PaK7VV5kbcpBcveSgAACAASURBVC1cgo+VGZvMhpj3trPajonIIgLzEUBnpi7J843pJRSzG3lP/x6xX79+/fDixSePY2vx7bMt3levXj0b7yw/WvCZryXqae8Zm9Veqa0yN+Imbc+W35uKjE1mQ8x721ltbwDogwgsQACdmbokLzDIV+wCu9Gz/hlzNrb52+XYFq99u7x/svhowWe+lqe3fd+X7Xvv3Cj+Vsv+M/Jl7Mh3r2X/jvwZO/Lda9m/I3/Gjnz3WvbvyJ+xI9+9lv078mfsyHevRe8isDIBdGbqkrzy6Ktv0xL4+uufPXz00Q+a9aMF3xxQDiIgAiIgAiKwKAF0ZuqSvOjAz94t9G1Hpb137s8+/fThgw++Ff6qhY1rlh8t+MwXxWbtlbmR9kptlblH5iJtRiB+mDnD+MZqVCsC8xJAZ6YuyfOO7dLKbSP3H++ov283+W0dqu/V1vRtY0d6j7Tt2/7Rj3/8+GsWtnC/851vP/zlT3/6LLbZsh/Xso99pOGoPvI/auv1Vm5/WmL0anuLtm0f3N/0nalv6YfHPhP3lrZ7zato690PhtsK2rwPKkVgdQK6JK8+wov2zy8ER92rtL+L3J999unjX7jwf8y35ZDlRws+87UcPe09Y7PaK7VV5kbcpG278t7+nLHJbIh5bzur7W0KehOBuQmgM1PfJM89vpdVz270rH8Gno3t/vbn4D7++EfPUrn9meHh4fEb5qje6zJfa9Pb7jqisnduFD/S5HXIl7EjX9dwVCJ/xo58jzR5PfJn7MjXNRyVyJ+xI98jTV6P/Bk78nUNKkXgCgR0Sb7CKF+wj2ij723PkN8rt12QP//8J89SZfHRgs98LVFv+7PObCp650bxN1KefUS+jB35PhOzq0D+jB357qQ8e0X+jB35PhOzq0D+jB357qQ8e0X+jB35PhOjChFYmAA6M/VN8sKDP3PX0EZeaX8XuV++/OrxH+/Z30/eP1l+tOAzX8vT094zNqu9UltlbsRN2var7+k9Y5PZEPPedlbbEwF9EoH5CaAzU5fk+cd4yR6wG3lP/x6x7U++2WL1H/td5OiCbIOd5UcLPvNFsVl7ZW6kvVJbZe6RuUibEYgfZs4wvrEa1YrAvATQmalL8rxju7RytJFXdn5kbWjBi1tMYOQxlbZ4zFCtuCFCsX1kbrFi1YrA7QTQmalL8u1s5dmRANqoK+2VuQ15lh8t+MwXxWbtlbmR9kptlblH5iJtRiB+mDnD+MZqVCsC8xJAZ6YuyfOO7fLKbTNHPwZh24Z938Y6+rzP4e329fd+9zxZaQs+sldo2etwDV66/d7vHreldA1euu+93z1uS+kavHTfe7973JbSNXjpvvd+97hnSs+9L93X6299d79bSs+9Lz2W19/67n5nyqNcVq9HBK5CQJfkq4z0xfpph0D29LZX5s76hhZ85mt96m0flVumqzcXxFzaYgLiFnNB85XldpxVFhGYjwA6M/VN8nxjegnFI2/kI2tDC75y8ozMTdpumxniJm63EZCXCIxBAJ2ZuiSPMU5SsSOADt9Ke2Vuw5TlRws+80WxWXtlbqS9Ultl7pG5SJsRiB9mzjC+sRrVisC8BNCZqUvyvGO7tHJ2I+/p3zO2DSoTHy14JjarrTI30l6prTL3yFykzQjEDzNnGN9YjWpFYF4C6MzUJXnesV1aObuR9/TvGdsGlYmPFjwTm9VWmRtpr9RWmXtkLtJmBOKHmTOMb6xGtSIwLwF0ZuqSPO/YSrkIPCOAFvwzB1WIgAiIgAiIwEUJoDNTl+SLTozRu81+29HTv2dsGxcmPlrwTGxWW2VupL1SW2XukblImxGIH2bOML6xGtWKwLwE0JmpS/K8Y7u0ctvIz/wYhG079n0bq/Uzmxv5n9FjCz5qh2K32qMcZ+tac7W2P6sjateaq7V9lPNsXWuu1vZndUTtWnO1to9yHtW1xm5tf5T3TH1rrtb2ZzR4myy22fSIwBUI6JJ8hVFesI+2kWdPpb0ytzHJ8qMFn/mi2Ky9MjfSXqmtMvfIXKTNCMQPM2cY31iNakVgXgLozNQ3yfOO7dLK2Y28p3/P2DaoTHy04JnYrLbK3Eh7pbbK3CNzkTYjED/MnGF8YzWqFYF5CaAzU5fkecf20srZjZ71z+CzsRl/tOCZ2NZn1n9Ubpmue/Q745bZkC5pO0MoboO4M3bkGyt6qkX+jB35PqnQJxFYnwA6M3VJXn8OLNlDtNH3tmdQe+fO4qMFn/lan3rbR+WW6erNBTGXtpiAuMVc0HxluR1nlUUE5iOAzkxdkucb00soRht5pb0ytw1+lh8t+MwXxWbtlbmR9kptlblH5iJtRiB+mDnD+MZqVCsC8xJAZ6YuyfOO7dLK2Y28p3/P2DaoTHy04JnYrLbK3Eh7pbbK3CNzkTYjED/MnGF8YzWqFYF5CaAzU5fkecd2aeW2kZ/5MQjbduz7NlbrZzY38j+jxxZ81A7FbrVHOc7WteZqbX9WR9SuNVdr+yjn2brWXK3tz+qI2rXmam0f5Tyqa43d2v4o75n61lyt7c9o8DZZbLPpEYErENAl+QqjvGAfbSPPnkp7ZW5jkuVHCz7zRbFZe2VupL1SW2XukblImxGIH2bOML6xGtWKwLwE0Jmpb5LnHdtLK2c3etY/g8/GZvzRgmdiW59Z/1G5Zbru0e+MW2ZDuqTtDKG4DeLO2JFvrOipFvkzduT7pEKfRGB9AujM1CV5/TmwZA/RRt/bnkHtnTuLjxZ85mt96m0flVumqzcXxFzaYgLiFnNB85XldpxVFhGYjwA6M3VJnm9ML6EYbeSV9srcNvhZfrTgM18Um7VX5kbaK7VV5h6Zi7QZgfhh5gzjG6tRrQjMSwCdmbokzzu2SytnN/Ke/j1j26Ay8dGCZ2Kz2ipzI+2V2ipzj8xF2oxA/DBzhvGN1ahWBOYlgM5MXZLnHdullbMbeU//nrFtUJn4aMEzsVltlbmR9kptlblH5iJtRiB+mDnD+MZqVCsC8xJAZ6YuyfOO7aWVsxs965/BZ2Mz/mjBM7Gtz6z/qNwyXffod8YtsyFd0naGUNwGcWfsyDdW9FSL/Bk78n1SoU8isD4BdGbqkrz+HJi2h7aZox/r3LYN+76NdfR5n8Pb7evv/e55stIWfGSv0LLX4Rq8dPu93z1uS+kavHTfe7973JbSNXjpvvd+97gtpWvw0n3v/e5xz5See1+6r9ff+u5+t5See196LK+/9d39zpRHuaxejwhchYAuyVcZ6cX6aZt89lTaK3Mbkyw/WvCZL4rN2itzI+2V2ipzj8xF2oxA/DBzhvGN1ahWBOYlgM5MfZM879gurRxt5JWdH1kbWvDiFhMYeUylLR4zVCtuiFBsH5lbrFi1InA7AXRm6pJ8O1t5diSANupKe2VuQ57lRws+80WxWXtlbqS9Ultl7pG5SJsRiB9mzjC+sRrVisC8BNCZqUvyvGO7tHJ2I+/p3yv2N9/84uHDD7/7YIvWfj7//CfhGGf50YLPfC1ZT3vP2Kz2Sm2VuRE3aQuX4GNlxiazIea97ay2YyKyiMB8BNCZqUvyfGMqxZ0vcwYYHSTZICDfI/tHH/3g4dWrV4+5X7z45PGi/OWXXzxLdeRvDdGCz3zP9Jv1f9aZTQUbm/XfSHn2kY2d+We2Z0KCCuTP2JFvIOetKuTP2JHvW0KCF+TP2JFvIOetKuTP2JHvW0L0IgKLE0Bnpi7Ji08AdW8OAnYZtm+St88HH3zrwS7OLQ9a8C2x1FYEREAEREAEViaAzkxdklce/Yn7hr7tqLS/q9wff/yj8JKc5UcLPvO16dLT3jM2q71SW2VuxE3ajjfRjE1mQ8x721ltx0RkEYH5CKAzU5fk+cb0EoptI/cf77C/bzf5bR2q79XW9G1jR3qPtGVtv/Odbz/86z/+42exbVFnP64lih3V3aLN4ngeL4/qztaPpM375KW05evROJ0dZ2+7bz8S46tr87FQKQKrE9AlefURXrR/24M06mKl/V3k9n/E19p3tODfhfZIs9VV5kb5K7VV5h6Zi7QZgfhh5gzjG6tRrQjMSwCdmfomed6xvbRydqNn/TP4bGzzt1+12P+OsufM4qMFn/la/N5270NU9s6N4keavA75Mnbk6xqOSuTP2JHvkSavR/6MHfm6hqMS+TN25HukyeuRP2NHvq5BpQhcgQA6M3VJvsIsWLCPaKPvbc+QsrntVyxevvzqMEUWHy34zNcS9rYfduod5EZ9q9LG6Oo9ZtJ2PCsyNpntOOKTBfkzduT7pEKfRGB9AujM1CV5/TkwZQ/RRl5p75nb/jbyZ59+mo5Zlh8t+MzXkva094zNaq/UVpkbcZO246WYsclsiHlvO6vtmIgsIjAfAXRm6pI835heQjG7kff07xXbvj22S/I2vtV9/fXP3hrzrf0tw+B/JznTbf2otF81N+JeyUXa9qv76Z0ZF8b3SYE+icAaBHRJXmMcL9cLtJFXAumhzS7Htlj3P/a3klsetOBbYt27bQ9u99IobbeRFDdxu42AvERgDALozNQ3yWOMk1TsCKDDt9JemdswZfnRgs98UWzWXpkbaa/UVpl7ZC7SZgTih5kzjG+sRrUiMC8BdGbqkjzv2C6v3DZz9GMQtm3Y922so8/7HN5uX3/vd8+TlbbgI3uFlr0O1+Cl2+/97nFbStfgpfve+93jtpSuwUv3vfe7x20pXYOX7nvvd497pvTc+9J9vf7Wd/e7pfTc+9Jjef2t7+53pjzKZfV6ROAqBHRJvspIX6yfdghkT297Ze6sb2jBZ77Wp972UbllunpzQcylLSYgbjEXNF9ZbsdZZRGB+QigM1PfJM83ppdQPPJGPrI2tOArJ8/I3KTttpkhbuJ2GwF5icAYBNCZqUvyGOMkFTsC6PCttFfmNkxZfrTgM18Um7VX5kbaK7VV5h6Zi7QZgfhh5gzjG6tRrQjMSwCdmbokzzu2SytnN/Ke/j1j26Ay8dGCZ2Kz2ipzI+2V2ipzj8xF2oxA/DBzhvGN1ahWBOYlgM5MXZLnHdullbMbeU//nrFtUJn4aMEzsVltlbmR9kptlblH5iJtRiB+mDnD+MZqVCsC8xJAZ6YuyfOOrZSLwDMCaME/c1CFCIiACIiACFyUADozdUm+6MQYvdvstx09/XvGtnFh4qMFz8RmtVXmRtortVXmHpmLtBmB+GHmDOMbq1GtCMxLAJ2ZuiTPO7ZLK7eN/MyPQdi2Y9+3sVo/s7mR/xk9tuCjdih2qz3KcbauNVdr+7M6onatuVrbRznP1rXmam1/VkfUrjVXa/so51Fda+zW9kd5z9S35mptf0aDt8lim02PCFyBgC7JVxjlBftoG3n2VNorcxuTLD9a8Jkvis3aK3Mj7ZXaKnOPzEXajED8MHOG8Y3VqFYE5iWAzkx9kzzv2C6tnN3Ie/r3jG2DysRHC56JzWqrzI20V2qrzD0yF2kzAvHDzBnGN1ajWhGYlwA6M3VJnndsL62c3ehZ/ww+G5vxRwueiW19Zv1H5Zbpuke/M26ZDemStjOE4jaIO2NHvrGip1rkz9iR75MKfRKB9QmgM1OX5PXnwJI9RBt9b3sGtXfuLD5a8Jmv9am3fVRuma7eXBBzaYsJiFvMBc1XlttxVllEYD4C6MzUJXm+Mb2EYrSRV9orc9vgZ/nRgs98UWzWXpkbaa/UVpl7ZC7SZgTih5kzjG+sRrUiMC8BdGbqkjzv2C6tnN3Ie/r3jG2DysRHC56JzWqrzI20V2qrzD0yF2kzAvHDzBnGN1ajWhGYlwA6M3VJnndsl1ZuG/mZH4Owbce+b2O1fmZzI/8zemzBR+1Q7FZ7lONsXWuu1vZndUTtWnO1to9ynq1rzdXa/qyOqF1rrtb2Uc6jutbYre2P8p6pb83V2v6MBm+TxTabHhG4AgFdkq8wygv20Tby7Km0V+Y2Jll+tOAzXxSbtVfmRtortVXmHpmLtBmB+GHmDOMbq1GtCMxLAJ2Z+iZ53rG9tHJ2o2f9M/hsbMYfLXgmtvWZ9R+VW6brHv3OuGU2pEvazhCK2yDujB35xoqeapE/Y0e+Tyr0SQTWJ4DOTF2S158DS/YQbfS97RnU3rmz+GjBZ77Wp972UbllunpzQcylLSYgbjEXNF9ZbsdZZRGB+QigM1OX5PnG9BKK0UZeaa/MbYOf5UcLPvNFsVl7ZW6kvVJbZe6RuUibEYgfZs4wvrEa1YrAvATQmalL8rxju7RydiPv6d8ztg0qEx8teCY2q60yN9Jeqa0y98hcpM0IxA8zZxjfWI1qRWBeAujM1CV53rFdWjm7kff07xnbBpWJjxY8E5vVVpkbaa/UVpl7ZC7SZgTih5kzjG+sRrUiMC8BdGbqkjzv2F5aObvRs/4ZfDY2448WPBPb+sz6j8ot03WPfmfcMhvSJW1nCMVtEHfGjnxjRU+1yJ+xI98nFfokAusTQGemLsnrz4Fpe2ibOfqxzm3bsO/bWEef9zm83b7+3u+eJyttwUf2Ci17Ha7BS7ff+93jtpSuwUv3vfe7x20pXYOX7nvvd4/bUroGL9333u8e90zpufel+3r9re/ud0vpufelx/L6W9/d70x5lMvq9YjAVQjoknyVkV6sn7bJZ0+lvTK3McnyowWf+aLYrL0yN9Jeqa0y98hcpM0IxA8zZxjfWI1qRWBeAujM1DfJ847t0srRRl7Z+ZG1oQUvbjGBkcdU2uIxQ7XihgjF9pG5xYpVKwK3E0Bnpi7Jt7OVZ0cCaKOutPfM/fLlVw9/8MMfPnz44XcP6Wb50YLPfC1hT3vP2Kz2Sm2VuRE3aTtchulaWZnbMRFZRGA+AujM1CV5vjG9hOKVD5mjvr169erBFqz96JL8fJofcfOWjJ3xtfyMP+PL5kb+0uaz63mZsclsiHlvO6vtOQnViMC8BHRJnnfspDwhwG70rH8ijbowWdxVv0nOmJmNHRPWP9PHxs78M1umyW3In7EjX9dwVCJ/xo58jzR5PfJn7MjXNRyVyJ+xI98jTaoXgRUJ6JK84qiqT0sT+FcvXqTfJGedRws+85VNBERABERABK5EAJ2Z+nWLK82GifqKvu2otPfOveo3yb25MfEZX1tWjD/jy+ZG/tJ2vGlmbDIbYt7bzmo7JiKLCMxHQJfk+cZMin9z6bDNfLuh+/tRHarf+t+zrQ3YNrYP4LbuKF/U1i7Jv//97z+aohi2qLMf94liR3Ut2o7aer3n9rJXvpa4t2hz/V625GtpK21Pfwu9hVtL21sYW3wfe/ff1x3Vr6DN+6BSBFYnoEvy6iO8aP+2B1DUxUp779z6Jjkace7bWouYjVtmQ76svTI30i5tRih+MjaZzaJV2tncMQ3VisCcBHRJnnPcpBoQYDd61j+Tx8Ze9ZKcMTMby431z/SxsTP/zJZpchvyZ+zI1zUclcifsSPfI01ej/wZO/J1DUcl8mfsyPdIk+pFYEUCuiSvOKrq09IXKl2S4wmODnfWHmf9dS0bO/PPbJkmtyF/xo58XcNRifwZO/I90uT1yJ+xI1/XcFQif8aOfI80qV4EViSgS/KKo3qBPqGNvNLeO/fvfe97Dx988K3DUc7yowWf+VrCnvaesVntldoqcyNu0na4DNO1sjK3YyKyiMB8BNCZqb9uMd+YXkLxyodM1rf333/vrX+U9/r162fjnfmjBZ/5WqKe9p6xWe2V2ipzI27S9mz5vanI2GQ2xLy3ndX2BoA+iMACBNCZqUvyAoO8YhfQRl7Z55G1oQUvbjGBkcdU2uIxQ7XihgjF9pG5xYpVKwK3E0Bnpi7Jt7OVZ0cCaKOutFfmNuRZfrTgM18Um7VX5kbaK7VV5h6Zi7QZgfhh5gzjG6tRrQjMSwCdmbokzzu2yyu3zRz9GIRtG/Z9G+vo8z6Ht9vX3/vd82SlLfjIXqFlr8M1eOn2e7973JbSNXjpvvd+97gtpWvw0n3v/e5xW0rX4KX73vvd454pPfe+dF+vv/Xd/W4pPfe+9Fhef+u7+50pj3JZvR4RuAoBXZKvMtIX66cdAtnT216ZO+sbWvCZr/Wpt31Ubpmu3lwQc2mLCYhbzAXNV5bbcVZZRGA+AujM1DfJ843pJRSPvJGPrA0t+MrJMzI3abttZoibuN1GQF4iMAYBdGbqkjzGOEnFjgA6fCvtlbkNU5YfLfjMF8Vm7ZW5kfZKbZW5R+YibUYgfpg5w/jGalQrAvMSQGemLsnzju3SytmNvKd/z9g2qEx8tOCZ2Ky2ytxIe6W2ytwjc5E2IxA/zJxhfGM1qhWBeQmgM1OX5HnHdmnl7Ebe079nbBtUJj5a8ExsVltlbqS9Ultl7pG5SJsRiB9mzjC+sRrVisC8BNCZqUvyvGN7aeXsRs/6Z/DZ2Iw/WvBMbOsz6z8qt0zXPfqdcctsSJe0nSEUt0HcGTvyjRU91SJ/xo58n1TokwisTwCdmbokrz8Hpuwh2sgr7ZW5bTCz/GjBZ74oNmuvzI20V2qrzD0yF2kzAvHDzBnGN1ajWhGYlwA6M3VJnndsl1ZuG/mZH4Owbce+b2O1fmZzI/8zemzBR+1Q7FZ7lONsXWuu1vZndUTtWnO1to9ynq1rzdXa/qyOqF1rrtb2Uc6jutbYre2P8p6pb83V2v6MBm+TxTabHhG4AgFdkq8wygv20Tby7Km0V+Y2Jll+tOAzXxSbtVfmRtortVXmHpmLtBmB+GHmDOMbq1GtCMxLAJ2Z+iZ53rFdWjm7kff07xnbBpWJjxY8E5vVVpkbaa/UVpl7ZC7SZgTih5kzjG+sRrUiMC8BdGbqkjzv2F5aObvRs/4ZfDY2448WPBPb+sz6j8ot03WPfmfcMhvSJW1nCMVtEHfGjnxjRU+1yJ+xI98nFfokAusTQGemLsnrz4Ele4g2+t72DGrv3Fl8tOAzX+tTb/uo3DJdvbkg5tIWExC3mAuaryy346yyiMB8BNCZqUvyfGN6CcVoI6+0V+a2wc/yowWf+aLYrL0yN9Jeqa0y98hcpM0IxA8zZxjfWI1qRWBeAujM1CV53rFdWjm7kff07xnbBpWJjxY8E5vVVpkbaa/UVpl7ZC7SZgTih5kzjG+sRrUiMC8BdGbqkjzv2C6t3DbyMz8GYduOfd/Gav3M5kb+Z/TYgo/aodit9ijH2brWXK3tz+qI2rXmam0f5Txb15qrtf1ZHVG71lyt7aOcR3WtsVvbH+U9U9+aq7X9GQ3eJottNj0icAUCuiRfYZQX7KNt5NlTaa/MbUyy/GjBZ74oNmuvzI20V2qrzD0yF2kzAvHDzBnGN1ajWhGYlwA6M/VN8rxje2nl7EbP+mfw2diMP1rwTGzrM+s/KrdM1z36nXHLbEiXtJ0hFLdB3Bk78o0VPdUif8aOfJ9U6JMIrE8AnZm6JK8/B6bsIdrIK+2VuW0ws/xowWe+KDZrr8yNtFdqq8w9MhdpMwLxw8wZxjdWo1oRmJcAOjN1SZ53bJdWzm7kPf17xrZBZeKjBc/EZrVV5kbaK7VV5h6Zi7QZgfhh5gzjG6tRrQjMSwCdmbokzzu2SytnN/Ke/j1j26Ay8dGCZ2Kz2ipzI+2V2ipzj8xF2oxA/DBzhvGN1ahWBOYlgM5MXZLnHdullaONvLLzI2tDC17cYgIjj6m0xWOGasUNEYrtI3OLFatWBG4ngM5MXZJvZyvPQgJoI+9tz7reO3cWHy34zNf61Ns+KrdMV28uiLm0xQTELeaC5ivL7TirLCIwHwF0ZuqSPN+YXkaxbebox2Bs27Dv21hHn/c5vN2+/t7vnicrbcFH9gotex2uwUu33/vd47aUrsFL9733u8dtKV2Dl+5773eP21K6Bi/d997vHvdM6bn3pft6/a3v7ndL6bn3pcfy+lvf3e9MeZTL6vWIwFUI6JJ8lZFerJ+2yWdPpb0ytzHJ8qMFn/mi2Ky9MjfSXqmtMvfIXKTNCMQPM2cY31iNakVgXgLozNQ3yfOO7dLK0UZe2fmRtaEFL24xgZHHVNriMUO14oYIxfaRucWKVSsCtxNAZ6YuybezlWdHAmijrrRX5jbkWX604DNfFJu1V+ZG2iu1VeYemYu0GYH4YeYM4xurUa0IzEsAnZm6JM87tksrZzfynv49Y9ugMvHRgmdis9oqcyPtldoqc4/MRdqMQPwwc4bxjdU8PPzn//z/PPzpn/7bI7PqRWBYAujM1CV52KGTsIwAu9Gz/qNqQwue7TfrPyq3TJfZ2H5n/pkN6ZK2M4TiNog7Y0e+saKnWuTP2JHvk4rzn375y18+/M7v/MPHn5///OfnHdVSBIoJoDNTl+TiAVJ6EbgnAbTg75lLsURABERgS8C+TbY96E/+5N88/OpXv9qa9FkEhiSAzkxdkoccNolC33ZU2itz28zI8qMFn/mi2Ky9MjfSXqmtMvfIXKTNCMQPM2cY31jN27X2rfI//sf/88N77/32469hvG3VmwiMRQCdmbokjzVeU6uxyaYfMdAc0BzQHNAc8DmgX7+Y+lhfXrzN0+zRJTmjI1sZATRx2W9DGH9pO54WGVdxi7llzMyjkpu0xWNmtRmbzDb7mB4T+bXlb/7mv735Jvnf//v/AzWXXQRKCaD9VZfk0uFR8iMCaOKiQ6inXdqORi2/OIhbzA3N1Upu0haPmdVmbDKb+c48psdEHh7sUmy/ZvFP/sn/ot9JzkDJNgwBtBZ1SR5mqCRkSwBNXHQI9bRL23ak3v6ccRe3t1n5W8bM2lRykzYfpedlxiazzT6mz0k8PNjvIf/u737n8a9b2J+D0yMCsxBA+6suybOM5MV0oomLDqGedmk7nowZd3GLuWXMzKOSm7TFY2a1GZvMNvuYRkR++tP/6/RftPjoox88zukPP/zuY6ivv/7Zw/vvv/fwwQffikKrTgS6EkD7qy7JXfEr+K0E0MRFh1BPe8/YxouJL27HMy7jWskt08XOB9YfaRO3eL6tzC3u0P72bAAAIABJREFUcVvtN9/84vGi/PnnP3l48eKTNme1FoE7EkB7mC7Jd4StUPcjgCbu/TK1R0IHYHvE+3mI220sxU3cbiNwm5fm28ODfZPs3ybfRlFeIsATQGtRl2SesSJ0IIAmLrqo9rT3jG0omfjidjwZM66V3DJd7Hxg/ZE2cYvn28rc4h6319q3yLokt3OTx30JoD1Ml+T78la0OxGwiWsHDfqxdNs27Ps21tHnfQ5vt6+/97vnycojbhVa9jpdg5duv/e7x20pndu9tezjtWjyth7Dy339vd49Tks5IjfntC+9X15/67v73VJ67l7cWjS5Fvfxdyt7P69evXq8IBuH169f906n+CJwSMDmYPbokpzRkW1YAraxZ09ve6/c9u2KLVr7sc/Rk/UNLfjM13L1tkf98breuVF81xGVyJexI99Iz7YO+TN25LvVEX1G/owd+UZ6tnXIn7Ej362O6DPyZ+zIN9Jz7zr7x3t2UbZ/sPfy5VePP/Z7ynpE4F0TQGemLsnvekSU7xSBETbyI6G9tH355ReP/8L7b//2bx+/XbF/7W11LQ9a8C2x7t22F7d76JS22yiKm7i1ELDLsV2M7S9a2GP/aC/7QqAlttqKwC0E0JmpS/ItVOXTnQA6fCvtvXLbpdi+Pfb49jn6s0hujwYBLfjM1+L1tPeMzWqv1FaZG3GTtmiV/bouY5PZEPPedlbbMRFZRGA+AujM1CV5vjG9hGJ2I+/p3yO2fbNii9VKj+9/Jsm/dfGBd7u/b0u04DNfi9PT3jM2q71SW2VuxE3atqvr7c8Zm8yGmPe2s9repqA3EZibADozdUmee3yXVc9u5D39e8S2X6uwxWq/p+fx7R+0WN3+Vy7cHg0+WvCZr8Xrae8Zm9Veqa0yN+ImbdEq+3VdxiazIea97ay2YyKyiMB8BNCZqUvyfGMqxZ0vcwYYHSTZICDfyO7/YM8uxm73S/L+H/C5PdKAFnzme6bfrH+k2evY2Lf6G9+Pf/Sjh88++9SlPCtvje2BMv/M5v5ZifwZ+5Gv/Yeb/W6pzTf7lSD7x1fRc+TvbRk78vUcRyXyZ+xHvjbHjJn92O/nHv1lhyN/7wtjR76eQ6UIXIEAOjN1Sb7CLJiwj2gjr7T3yO3fJG8vyfatsi1gfZP86wnck7txHvWS3KPf2y0hix/Z7NeA7IJnz8uvvnr8bBdmm6/7J/LftmHsjK9p6Okfxbb/GPP/mPiPf/Znj/9xcfS/Nhf5j8Jtq0OfRWB2Arokzz6CF9Vvh8SZH8Ozbce+b2O1fmZy/7t/978/Xoit9Lx/9Vd/9azObUelLfjIxmizeHv/KMfZun2se7+f1bFt9957v/3wRz/+8bN+jqDNdd5byz6e50Hlv/7jP35rjtmFz+bdtn4fm31HmrZ2Nhfy3+Zq/byN/U//8A8f/tWLF2+x3Notdut7i54s9mNi/R8RuAABXZIvMMgrdtEPiKO+Vdp75dZft6j729d2SdY3yc9X29m5bt8k738tyKKd9X+e+dc1mX9m650bxT+jzb6N3/+jXOdwxt/bRmXmn9lQv6JcqhOBmQnokjzz6F1YO7uR9/TvFdsuGY+/3/nVV4//r2v7vP9VC5sSWX604DNfFJu1V+ZG2nVJNkLPnzNj5r8WFP2PQZzxf571qSbzz2wWodKe5bZfqfqDH/7w8W8EP/X07U+ZP9s3NvbbSvUmAnMTQGemfid57vG9rHp2o2f9M/BMbLso26K1n+ibOcubxUcLPvNFse9h78WN1fb3//5/P+w3yRkztt/IH80X87d5OuLv1o7Izf8xrq/xo//vBeLO2JEv4ia7CKxEAJ2ZuiSvNNoX6gva6HvbM9S9c2fx0YLPfK1Pve2jctMlOR4ZNB/+7u/+btq/0oD6xtiR7//3X//rIzdbr6P9g8d4JqhWBNYkgM5MXZLXHPfpe4UOmUp7ZW4b2Cw/WvCZL4rN2itzI+36dQsj9PxBY2b/+Cy65Hkk5M/YGV/T19P/TGz7Sxe2Xmf7NRUfW5UisAIBdGbqkrzCKC/YhzOHTNbtnv49Y1ufmPhowTOxWW2VuZF2XZLj1ZSNmf2KxV/+9Kex429qM380JsjeMzbKjexntNnl2P7BY/Sc8Y/8vC7zz2zmj+yeQ6UIrEAAnZm6JK8wygv2wTbqMz/W9W079n0bq/Uzmxv5n9FjCz5qh2K32qMcZ+tac7W2P6tj284uyfataGuu1vbbnK2fW3O1tm/RY3/uzf70m/tYLv0JOLxnbcfk9773vYcvvvjzNwyN5dZ+y7uPx5kyy/UoRP9HBC5AQJfkCwzyil30A+Kob5X2ytzGI8uPFnzmi2Kz9srcR9rt2zxj5j8ffvhda/rs6am9Z2zrCBM/8v344x+94eXcrIz+8V7kv4XL2Blflgvyj7TZn3xzXt/+9v8Y/uUaZxP5uw3lRnY29laHPovA7ARsTWaPvknO6Mg2LAF2o2f9MzBsbMYfLXgmtvWZ9R+VW6brHv3OuGU2pEvazhCK2yDujB35xoqeapE/Y0e+Tyr0SQTWJ4DOTF2S158DU/YQbeSV9srcNphZfrTgM18Um7VX5kbaK7VV5h6Zi7QZgfhh5gzjG6tRrQjMSwCdmbokzzu2SytnN/Ke/j1j26Ay8dGCZ2Kz2ipzI+2V2ipzj8xF2oxA/DBzhvGN1ahWBOYlgM5MXZLnHdullbMbeU//nrFtUJn4aMEzsVltlbmR9kptlblH5iJtRiB+mDnD+MZqVCsC8xJAZ6YuyfOO7dLK0UZe2fmRtaEFL24xgZHHVNriMUO14oYIxfaRucWKVSsCtxNAZ6YuybezlWchAbSR97ZnXe+dO4uPFnzma33qbR+VW6arNxfEXNpiAuIWc0HzleV2nFUWEZiPADozdUmeb0wvo9g2c/RjMLZt2PdtrKPP+xzebl9/73fPk5W24CN7hZa9Dtfgpdvv/e5xW0rX4KX73vvd47aUrsFL9733u8dtKV2Dl+5773ePe6b03PvSfb3+1nf3u6X03PvSY3n9re/ud6Y8ymX1ekTgKgR0Sb7KSC/WT9vks6fSXpnbmGT50YLPfFFs1l6ZG2mv1FaZe2Qu0mYE4oeZM4xvrEa1IjAvAXRm6pvkecd2aeVoI6/s/Mja0IIXt5jAyGMqbfGYoVpxQ4Ri+8jcYsWqFYHbCaAzU5fk29nKsyMBtFFX2nvmfvnyq4c/+OEPH47+l98MeZYfLfjMF8Vm7ZW5kfZKbZW5R+YibUYgfpg5w/jGalQrAvMSQGemLsnzju3SytmNvKd/r9ivXr168z9bq0vy8+ndi7tl6hkbxa/MLW3P55nXMOPC+KIxYe2sNuejUgRWIKBL8gqjqD48I8Bu9Kz/M0GbCjb2qt8kbxCFH1lurH8o6jeVbOzMP7NlmtyG/Bk78nUNRyXyZ+zI90iT1yN/xo58XcNRifwZO/I90qR6EViRgC7JK46q+lT6zR/Cjw4hZNclOSaMuLH2OOuva9nYmX9myzS5DfkzduTrGo5K5M/Yke+RJq9H/owd+bqGoxL5M3bke6RJ9SKwIgFdklcc1Qv0CW3klfbeuVe9JPfmxsRnfG05Mv6ML5sb+Uvb8WabsclsiHlvO6vtmIgsIjAfAV2S5xszKf7NpcM28+2G7u9Hdah+63/PtjZg29g+gNu6o3xRW7sk//73v/9oimLYos5+3CeKHdW1aDtq6/We28te+Vri3qLN9XvZkq+lrbQ9/S30Fm4tbW9hbPF97N1/X3dUv4I274NKEVidgC7Jq4/wov3bHkBRFyvtrbk/+OBb6aX2xYtP3uqivkl+C8ebl1bubxx/8yHzz2zm3tPeMzarXdr2s+jpPWOT2dgxYf1ZbU8E9EkE5iegS/L8Y6geBATYjZ71DyS9qWJjr3pJfgPo4APLjfU/kPVYzcbO/DNbpsltyJ+xI1/XcFQif8aOfI80eT3yZ+zI1zUclcifsSPfI02qF4EVCeiSvOKoqk9dv9kzvMxBgnyRXZfkeIIjbqw9zvrrWjZ25p/ZMk1uQ/6MHfm6hqMS+TN25HukyeuRP2NHvq7hqET+jB35HmlSvQisSECX5BVH9QJ9Qht5pb137t/73vce7Fc0jp4sP1rwma/l62nvGZvVXqmtMjfiJm1HqzBfKytzOyYiiwjMRwCdmfofE5lvTC+heOVDJuvb+++/99bvL79+/frZeGf+aMFnvpaop71nbFZ7pbbK3IibtD1bfm8qMjaZDTHvbWe1vQGgDyKwAAF0ZuqSvMAgr9gFtJFX9nlkbWjBi1tMYOQxlbZ4zFCtuCFCsX1kbrFi1YrA7QTQmalL8u1s5dmRANqoK+2VuQ15lh8t+MwXxWbtlbmR9kptlblH5iJtRiB+mDnD+MZqVCsC8xJAZ6YuyfOO7fLKbTNHPwZh24Z938Y6+rzP4e329fd+9zxZaQs+sldo2etwDV66/d7vHreldA1euu+93z1uS+kavHTfe7973JbSNXjpvvd+97hnSs+9L93X6299d79bSs+9Lz2W19/67n5nyqNcVq9HBK5CQJfkq4z0xfpph0D29LZX5s76hhZ85mt96m0flVumqzcXxFzaYgLiFnNB85XldpxVFhGYjwA6M/VN8nxjegnFI2/kI2tDC75y8ozMTdpumxniJm63EZCXCIxBAJ2ZuiSPMU5SsSOADt9Ke2Vuw5TlRws+80WxWXtlbqS9Ultl7pG5SJsRiB9mzjC+sRrVisC8BNCZqUvyvGO7tHJ2I+/p3zO2DSoTHy14JjarrTI30l6prTL3yFykzQjEDzNnGN9YjWpFYF4C6MzUJXnesV1aObuR9/TvGdsGlYmPFjwTm9VWmRtpr9RWmXtkLtJmBOKHmTOMb6xGtSIwLwF0ZuqSPO/YXlo5u9Gz/hl8NjbjjxY8E9v6zPqPyi3TdY9+Z9wyG9IlbWcIxW0Qd8aOfGNFT7XIn7Ej3ycV+iQC6xNAZ6YuyevPgSl7iDbySntlbhvMLD9a8Jkvis3aK3Mj7ZXaKnOPzEXajED8MHOG8Y3VqFYE5iWAzkxdkucd26WV20Z+5scgbNux79tYrZ/Z3Mj/jB5b8FE7FLvVHuU4W9eaq7X9WR1Ru9Zcre2jnGfrWnO1tj+rI2rXmqu1fZTzqK41dmv7o7xn6ltztbY/o8HbZLHNpkcErkBAl+QrjPKCfbSNPHsq7ZW5jUmWHy34zBfFZu2VuZH2Sm2VuUfmIm1GIH6YOcP4xmpUKwLzEkBnpr5Jnndsl1bObuQ9/XvGtkFl4qMFz8RmtVXmRtortVXmHpmLtBmB+GHmDOMbq1GtCMxLAJ2ZuiTPO7aXVs5u9Kx/Bp+NzfijBc/Etj6z/qNyy3Tdo98Zt8yGdEnbGUJxG8SdsSPfWNFTLfJn7Mj3SYU+icD6BNCZqUvy+nNgyR6ijb63PYPaO3cWHy34zNf61Ns+KrdMV28uiLm0xQTELeaC5ivL7TirLCIwHwF0ZuqSPN+YXkIx2sgr7ZW5bfCz/GjBZ74oNmuvzI20V2qrzD0yF2kzAvHDzBnGN1ajWhGYlwA6M3VJnndsl1bObuQ9/XvGtkFl4qMFz8RmtVXmRtortVXmHpmLtBmB+GHmDOMbq1GtCMxLAJ2ZuiTPO7ZLK7eN/MyPQdi2Y9+3sVo/s7mR/xk9tuCjdih2qz3KcbauNVdr+7M6onatuVrbRznP1rXmam1/VkfUrjVXa/so51Fda+zW9kd5z9S35mptf0aDt8lim02PCFyBgC7JVxjlBftoG3n2VNorcxuTLD9a8Jkvis3aK3Mj7ZXaKnOPzEXajED8MHOG8Y3VqFYE5iWAzkx9kzzv2F5aObvRs/4ZfDY2448WPBPb+sz6j8ot03WPfmfcMhvSJW1nCMVtEHfGjnxjRU+1yJ+xI98nFfokAusTQGemLsnrz4Epe4g28kp7ZW4bzCw/WvCZL4rN2itzI+2V2ipzj8xF2oxA/DBzhvGN1ahWBOYlgM5MXZLnHdullbMbeU//nrFtUJn4aMEzsVltlbmR9kptlblH5iJtRiB+mDnD+MZqVCsC8xJAZ6YuyfOO7dLK2Y28p3/P2DaoTHy04JnYrLbK3Eh7pbbK3CNzkTYjED/MnGF8YzWqFYF5CaAzU5fkecd2aeVoI6/s/Mja0IIXt5jAyGMqbfGYoVpxQ4Ri+8jcYsWqFYHbCaAzU5fk29nKs5AA2sh727Ou986dxUcLPvO1PvW2j8ot09WbC2IubTEBcYu5oPnKcjvOKosIzEcAnZm6JM83ppdRbJs5+jEY2zbs+zbW0ed9Dm+3r7/3u+fJSlvwkb1Cy16Ha/DS7fd+97gtpWvw0n3v/e5xW0rX4KX73vvd47aUrsFL9733u8c9U3rufem+Xn/ru/vdUnrufemxvP7Wd/c7Ux7lsno9InAVArokX2WkF+unbfLZU2mvzG1MsvxowWe+KDZrr8yNtFdqq8w9MhdpMwLxw8wZxjdWo1oRmJcAOjP1TfK8Y7u0crSRV3Z+ZG1owYtbTGDkMZW2eMxQrbghQrF9ZG6xYtWKwO0E0JmpS/LtbOXZkQDaqCvtvXJ/880vHj788LsPtmjt5/PPfxISzvKjBZ/5WrKe9p6xWe2V2ipzI27SFi7Bx8qMTWZDzHvbWW3HRGQRgfkIoDNTl+T5xvQSitmNvKd/r9gfffSDh1evXj1eVF+8+OTxovzll188G+8sP1rwma8l6mnvGZvVXqmtMjfiJm3Plt+bioxNZkPMe9tZbW8A6IMILEAAnZm6JC8wyFfsArvRs/4Z81ti22XYvkm2x/0/+OBbD3Zx3j9u39fbO1rwma/597ZHmr2ud24U33VEJfJl7Mg30rOtQ/6MHfludUSfkT9jR76Rnm0d8mfsyHerI/qM/Bk78o30qE4EViWAzkxdklcd+cX7hTb63vYM771yf/zxj3RJ3oC+F9dNyNMfe+ZGsZFI5M/Yka+0xQRW5hb3WLUiMCcBXZLnHLfLq0aHTKX9XeW2b5Kj30vO8qMFn/napOtp7xmb1V6prTI34iZtx1txxiazIea97ay2YyKyiMB8BNCZqW+S5xvTSyi2jdx/vMP+vt3kt3Wovldb07eNHek90nbU9q//+q8ffv/7338rrsewRZ39uJYodlTncc3mvkd1qH7rj9oy+Vr64TpatLW0Zfohbfk6dz7vmjGTr/fcfBfavA8qRWB1Arokrz7Ci/ZvezhGXay0t+a2b4SzS639I73tY/HtVy38d5S3Nvuc5UcLPvNFsVl7ZW6kvVJbZe6RuUibEYgfZs4wvrEa1YrAvATQmalvkucdWylflMAXX/z5w8uXX93UO7TgbwoqJxEQAREQARFYkAA6M3VJXnDQr9Al9tsQ1j9jzMS230H+7NNPs/DTfpOcdgp8Q26+DNcz/pm+nrlR7EzXmX6h+Jk9syFd0naGUNwGcWfsyDdWpFoRWJOALslrjuvyvUIbeaW9V2779tguydv4Vvf11z97a7y39rcMg/8JuEy39aPSftXciHslF2nbr+6nd2ZcGN8nBfokAmsQ0CV5jXG8XC/Yjbynf4/Ydjm2xbr/sd9n3j9ZfrTgM1/L09PeMzarvVJbZW7ETdr2q+/pPWOT2RDz3nZW2xMBfRKB+QmgM1O/bjH/GC/ZA7SRV3Z6ZG1owYtbTGDkMZW2eMxQrbghQrF9ZG6xYtWKwO0E0JmpS/LtbOXZkQDaqCvtlbkNeZYfLfjMF8Vm7ZW5kfZKbZW5R+YibUYgfpg5w/jGalQrAvMSQGemLsnzju3yym0zRz8GYduGfd/GOvq8z+Ht9vX3fvc8WWkLPrJXaNnrcA1euv3e7x63pXQNXrrvvd89bkvpGrx033u/e9yW0jV46b73fve4Z0rPvS/d1+tvfXe/W0rPvS89ltff+u5+Z8qjXFavRwSuQkCX5KuM9MX6aYdA9vS2V+bO+oYWfOZrfeptH5Vbpqs3F8Rc2mIC4hZzQfOV5XacVRYRmI8AOjP1TfJ8Y3oJxSNv5CNrQwu+cvKMzE3abpsZ4iZutxGQlwiMQQCdmbokjzFOUrEjgA7fSntlbsOU5UcLPvNFsVl7ZW6kvVJbZe6RuUibEYgfZs4wvrEa1YrAvATQmalL8rxju7RydiPv6d8ztg0qEx8teCY2q60yN9Jeqa0y98hcpM0IxA8zZxjfWI1qRWBeAujM1CV53rFdWjm7kff07xnbBpWJjxY8E5vVVpkbaa/UVpl7ZC7SZgTih5kzjG+sRrUiMC8BdGbqkjzv2F5aObvRs/4ZfDY2448WPBPb+sz6j8ot03WPfmfcMhvSJW1nCMVtEHfGjnxjRU+1yJ+xI98nFfokAusTQGemLsnrz4Epe4g28kp7ZW4bzCw/WvCZL4rN2itzI+2V2ipzj8xF2oxA/DBzhvGN1ahWBOYlgM5MXZLnHdulldtGfubHIGzbse/bWK2f2dzI/4weW/BROxS71R7lOFvXmqu1/VkdUbvWXK3to5xn61pztbY/qyNq15qrtX2U86iuNXZr+6O8Z+pbc7W2P6PB22SxzaZHBK5AQJfkK4zygn20jTx7Ku2VuY1Jlh8t+MwXxWbtlbmR9kptlblH5iJtRiB+mDnD+MZqVCsC8xJAZ6a+SZ53bJdWzm7kPf17xrZBZeKjBc/EZrVV5kbaK7VV5h6Zi7QZgfhh5gzjG6tRrQjMSwCdmbokzzu2l1bObvSsfwafjc34owXPxLY+s/6jcst03aPfGbfMhnRJ2xlCcRvEnbEj31jRUy3yZ+zI90mFPonA+gTQmalL8vpzYMkeoo2+tz2D2jt3Fh8t+MzX+tTbPiq3TFdvLoi5tMUExC3mguYry+04qywiMB8BdGbqkjzfmF5CMdrIK+2VuW3ws/xowWe+KDZrr8yNtFdqq8w9MhdpMwLxw8wZxjdWo1oRmJcAOjN1SZ53bJdWzm7kPf17xrZBZeKjBc/EZrVV5kbaK7VV5h6Zi7QZgfhh5gzjG6tRrQjMSwCdmbokzzu2Syu3jfzMj0HYtmPft7FaP7O5kf8ZPbbgo3Yodqs9ynG2rjVXa/uzOqJ2rbla20c5z9a15mptf1ZH1K41V2v7KOdRXWvs1vZHec/Ut+ZqbX9Gg7fJYptNjwhcgYAuyVcY5QX7aBt59lTaK3Mbkyw/WvCZL4rN2itzI+2V2ipzj8xF2oxA/DBzhvGN1ahWBOYlgM5MfZM879heWjm70bP+GXw2NuOPFjwT2/rM+o/KLdN1j35n3DIb0iVtZwjFbRB3xo58Y0VPtcifsSPfJxX6JALrE0Bnpi7J68+BKXuINvJKe2VuG8wsP1rwmS+KzdorcyPtldoqc4/MRdqMQPwwc4bxjdWoVgTmJYDOTF2S5x3bpZWzG3lP/56xbVCZ+GjBM7FZbZW5kfZKbZW5R+YibUYgfpg5w/jGalQrAvMSQGemLsnzju3SytmNvKd/z9g2qEx8tOCZ2Ky2ytxIe6W2ytwjc5E2IxA/zJxhfGM1qhWBeQmgM1OX5HnHdmnlaCOv7PzI2tCCF7eYwMhjKm3xmKFacUOEYvvI3GLFqhWB2wmgM1OX5NvZyrOQANrIe9uzrvfOncVHCz7ztT71to/KLdPVmwtiLm0xAXGLuaD5ynI7ziqLCMxHAJ2ZuiTPN6aXUWybOfoxGNs27Ps21tHnfQ5vt6+/97vnyUpb8JG9Qsteh2vw0u33fve4LaVr8NJ97/3ucVtK1+Cl+9773eO2lK7BS/e997vHPVN67n3pvl5/67v73VJ67n3psbz+1nf3O1Me5bJ6PSJwFQK6JF9lpBfrp23y2VNpr8xtTLL8aMFnvig2a6/MjbRXaqvMPTIXaTMC8cPMGcY3VqNaEZiXADoz9U3yvGO7tHK0kVd2fmRtaMGLW0xg5DGVtnjMUK24IUKxfWRusWLVisDtBNCZqUvy7Wzl2ZEA2qgr7b1yf/PNLx4+/PC7D7Zo33//vYcvv/wiJJzlRws+87VkPe09Y7PaK7VV5kbcpC1cgo+VGZvMhpj3trPajonIIgLzEUBnpi7J843pJRSzG3lP/x6xX79+/fDixSePY2vx7bMt3levXj0b7yw/WvCZryXqae8Zm9Veqa0yN+Imbc+W35uKjE1mQ8x721ltbwDogwgsQACdmbokLzDIV+wCu9Gz/hlzNrb52+XYFq99u7x/svhowWe+lqe3fd+X7Xvv3Cj+Vsv+M/Jl7Mh3r2X/jvwZO/Lda9m/I3/Gjnz3WvbvyJ+xI9+9lv078mfsyHevRe8isDIBdGbqkrzy6C/cN7TR97ZnaO+R++uvf/bw0Uc/CNNk8dGCz3wtWW972KHfVPbOjeJXaWN09R4zaTueFRmbzHYc8cmC/Bk78n1SoU8isD4BdGbqkrz+HJiyh2gjr7T3zv3Zp58+fPDBt8JftbDBzPKjBZ/5otisvTI30l6prTL3yFykzQjEDzNnGN9YjWpFYF4C6MzUJXnesV1auW3k/uMd9fftJr+tQ/W92pq+bexI75G2fds/+vGPH3/Nwhbud77z7Ye//OlPn8U2W/bjWvaxjzQc1Uf+R2293srtT0uMXm1v0bbtg/ubvjP1Lf3w2Gfi3tJ2r3kVbb37wXBbQdt/+ou/8G6oFIGlCeiSvPTwqnMzELBvhbNLrf+DvW1fPvvs08e/cBHZtu32n9GC37fXuwiIgAiIgAhclQA6M/VN8lVnhvo9PAH7c3Aff/yjJp1owTcFU2MREAEREAERWJgAOjN1SV548NW1uQnYBfnzz3/S1Am04JuCqbEIiIAIiIAILEwAnZm6JC88+OravARevvzq8R/v2d9PbnnQgm+JpbYiIAIiIAIisDIBdGbqkrzy6Ktv0xCwP/lmi9V/7HeRWy/I1lm04KcBIqEiIAIiIAIi0JkAOjN1Se48AAovAu+SAFrw71KLcomACIiACIjAyATQmalL8sijJ20i0EgALfjGcGouAiLaAYPBAAAEp0lEQVQgAiIgAssSQGemLsnLDr06dkUCaMFfkYn6LAIiIAIiIAIRAXRm6pIcUVOdCExKAC34Sbsl2SIgAiIgAiJwdwLozNQl+e7IFVAE6gigBV+nTJlFQAREQAREYCwC6MzUJXms8ZIaEaAIoAVPBZezCIiACIiACCxEAJ2ZuiQvNNjqigigBS9CIiACIiACIiACvyaAzkxdkjVTRGAhAmjBL9RVdUUEREAEREAEKALozNQlmcIrZxEYiwBa8GOplRoREAEREAERqCOAzkxdkuvGRplF4O4E0IK/e0IFFAEREAEREIFJCaAzU5fkSQdWskUgIoAWfOSjOhEQAREQARG4IgF0ZuqSfMVZoT4vSwAt+GU7ro6JgAiIgAiIQCMBdGbqktwIVM1FYGQCaMGPrF3aREAEREAEROBdEkBnpi7J73I0lEsEOhNAC75zeoUXAREQAREQgWkIoDNTl+RphlJCRUAEREAEREAEREAE7kVAl+R7kVQcERABERABERABERCBZQjokrzMUKojIiACIiACIiACIiAC9yKgS/K9SCqOCIiACIiACIiACIjAMgR0SV5mKNURERABERABERABERCBexHQJfleJBVHBERABERABERABERgGQK6JC8zlOqICIiACIiACIiACIjAvQjoknwvkoojAiIgAiIgAiIgAiKwDAFdkpcZSnVEBERABERABERABETgXgR0Sb4XScURAREQAREQAREQARFYhoAuycsMpToiAiIgAiIgAiIgAiJwLwK6JN+LpOKIgAiIgAiIgAiIgAgsQ0CX5GWGUh0RAREQAREQAREQARG4FwFdku9FUnFEQAREQAREQAREQASWIaBL8jJDqY6IgAiIgAiIgAiIgAjci4AuyfciqTgiIAIiIAIiIAIiIALLENAleZmhVEdEQAREQAREQAREQATuRUCX5HuRVBwREAEREAEREAEREIFlCOiSvMxQqiMiIAIiIAIiIAIiIAL3IqBL8r1IKo4IiIAIiIAIiIAIiMAyBHRJXmYo1REREAEREAEREAEREIF7EdAl+V4kFUcEREAEREAEREAERGAZArokLzOU6ogIiIAIiIAIiIAIiMC9COiSfC+SiiMCIiACIiACIiACIrAMAV2SlxlKdUQEREAEREAEREAEROBeBHRJvhdJxREBERABERABERABEViGgC7JywylOiICIiACIiACIiACInAvArok34uk4oiACIiACIiACIiACCxDQJfkZYZSHREBERABERABERABEbgXAV2S70VScURABERABERABERABJYhoEvyMkOpjoiACIiACIiACIiACNyLgC7J9yKpOCIgAiIgAiIgAiIgAssQ0CV5maFUR0RABERABERABERABO5FoPmSbA76EQPNAc0BzQHNAc0BzQHNAc2B1edAduH+rcwomwiIgAiIgAiIgAiIgAhckYAuyVccdfVZBERABERABERABEQgJaBLcopHRhEQAREQAREQAREQgSsS0CX5iqOuPouACIiACIiACIiACKQEdElO8cgoAiIgAiIgAiIgAiJwRQK6JF9x1NVnERABERABERABERCBlMD/D9TLUIOOtIpDAAAAAElFTkSuQmCC"></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 <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> for which <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>′</mo><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>0</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="padding-left:60px;"><img src="data:image/png;base64,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"> <em><strong>A1A1A1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>A1</strong></em> for a smooth concave down curve with generally correct shape. If first mark is awarded, award <em><strong>A1</strong></em> for local maximum and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-intercept in approximately correct position, award <em><strong>A1</strong></em> for endpoints at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>0</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>3</mn></math> with approximately correct <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-coordinates.</p>
<p> </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>recognizing that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>′</mo><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>0</mn></math> at local maximum <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>33084</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>33</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>The quadratic equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></mfenced><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>x</mi><mo>+</mo><mfenced><mrow><mn>2</mn><mi>k</mi><mo>-</mo><mn>3</mn></mrow></mfenced><mo>=</mo><mn>0</mn></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math>, has real distinct roots.</p>
<p>Find the range of possible values for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="color:#999;font-size:90%;font-style:italic;">* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.</p>
<p style="color:#999;font-size:90%;font-style:italic;"> </p>
<p>attempts to find an expression for the discriminant, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Δ</mi></math>, in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math> <strong>(M1)</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Δ</mi><mo>=</mo><mn>4</mn><mo>-</mo><mn>4</mn><mfenced><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mn>2</mn><mi>k</mi><mo>-</mo><mn>3</mn></mrow></mfenced><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mo>-</mo><mn>8</mn><msup><mi>k</mi><mn>2</mn></msup><mo>+</mo><mn>20</mn><mi>k</mi><mo>-</mo><mn>8</mn></mrow></mfenced></math> <strong>(A1)</strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong>M1A1</strong> for finding <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mfrac><mrow><mo>-</mo><mn>2</mn><mo>±</mo><msqrt><mn>4</mn><mo>-</mo><mn>4</mn><mfenced><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mn>2</mn><mi>k</mi><mo>-</mo><mn>3</mn></mrow></mfenced></msqrt></mrow><mrow><mn>2</mn><mfenced><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></math>.</p>
<p> </p>
<p>attempts to solve <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Δ</mi><mo>></mo><mn>0</mn></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math> <strong>(M1)</strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong>M1</strong> for attempting to solve <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Δ</mi><mo>=</mo><mn>0</mn></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>.</p>
<p> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mo><</mo><mi>k</mi><mo><</mo><mn>2</mn></math> <strong>A1</strong><strong>A1</strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong>A1</strong> for obtaining critical values <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>,</mo><mo> </mo><mn>2</mn></math> and <strong>A1</strong> for correct inequality signs.</p>
<p> </p>
<p><strong>[5</strong><strong> marks]</strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>A scientist conducted a nine-week experiment on two plants, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math>, of the same species. He wanted to determine the effect of using a new plant fertilizer. Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> was given fertilizer regularly, while Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> was not.</p>
<p>The scientist found that the height of Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>,</mo><mo> </mo><msub><mi>h</mi><mi>A</mi></msub><mo> </mo><mtext>cm</mtext></math>, at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> weeks can be modelled by the function <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>h</mi><mi>A</mi></msub><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>sin</mi><mo>(</mo><mn>2</mn><mi>t</mi><mo>+</mo><mn>6</mn><mo>)</mo><mo>+</mo><mn>9</mn><mi>t</mi><mo>+</mo><mn>27</mn></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mn>9</mn></math>.</p>
<p>The scientist found that the height of Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>,</mo><mo> </mo><msub><mi>h</mi><mi>B</mi></msub><mo> </mo><mtext>cm</mtext></math>, at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> weeks can be modelled by the function <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>h</mi><mi>B</mi></msub><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mn>8</mn><mi>t</mi><mo>+</mo><mn>32</mn></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mn>9</mn></math>.</p>
</div>
<div class="specification">
<p>Use the scientist’s models to find the initial height of</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> correct to three significant figures.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>h</mi><mi>A</mi></msub><mfenced><mi>t</mi></mfenced><mo>=</mo><msub><mi>h</mi><mi>B</mi></msub><mfenced><mi>t</mi></mfenced></math>.</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>For <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mn>9</mn></math>, find the total amount of time when the rate of growth of Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> was greater than the rate of growth of Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>32</mn></math> (cm) <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>h</mi><mi>A</mi></msub><mfenced><mn>0</mn></mfenced><mo>=</mo><mi>sin</mi><mfenced><mn>6</mn></mfenced><mo>+</mo><mn>27</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>26</mn><mo>.</mo><mn>7205</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>26</mn><mo>.</mo><mn>7</mn></math> (cm) <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempts to solve <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>h</mi><mi>A</mi></msub><mfenced><mi>t</mi></mfenced><mo>=</mo><msub><mi>h</mi><mi>B</mi></msub><mfenced><mi>t</mi></mfenced></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>4</mn><mo>.</mo><mn>00746</mn><mo>…</mo><mo>,</mo><mn>4</mn><mo>.</mo><mn>70343</mn><mo>…</mo><mo>,</mo><mn>5</mn><mo>.</mo><mn>88332</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>4</mn><mo>.</mo><mn>01</mn><mo>,</mo><mn>4</mn><mo>.</mo><mn>70</mn><mo>,</mo><mn>5</mn><mo>.</mo><mn>88</mn></math> (weeks) <em><strong>A2</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognises that <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>h</mi><mi>A</mi></msub><mo>'</mo><mfenced><mi>t</mi></mfenced></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>h</mi><mi>B</mi></msub><mo>'</mo><mfenced><mi>t</mi></mfenced></math> are required <em><strong>(M1)</strong></em></p>
<p>attempts to solve <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>h</mi><mi>A</mi></msub><mo>'</mo><mfenced><mi>t</mi></mfenced><mo>=</mo><msub><mi>h</mi><mi>B</mi></msub><mo>'</mo><mfenced><mi>t</mi></mfenced></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>18879</mn><mo>…</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>23598</mn><mo>…</mo></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>33038</mn><mo>…</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>.</mo><mn>37758</mn><mo>…</mo></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>47197</mn><mo>…</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>.</mo><mn>51917</mn><mo>…</mo></math> <em><strong>(A1)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award full marks for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfrac><mrow><mn>4</mn><mi mathvariant="normal">π</mi></mrow><mn>3</mn></mfrac><mo>-</mo><mn>3</mn><mo>,</mo><mo> </mo><mfrac><mrow><mn>5</mn><mi mathvariant="normal">π</mi></mrow><mn>3</mn></mfrac><mo>-</mo><mn>3</mn><mo>,</mo><mo> </mo><mfenced><mrow><mfrac><mrow><mn>7</mn><mi mathvariant="normal">π</mi></mrow><mn>3</mn></mfrac><mo>-</mo><mn>3</mn><mo>,</mo><mo> </mo><mfrac><mrow><mn>8</mn><mi mathvariant="normal">π</mi></mrow><mn>3</mn></mfrac><mo>-</mo><mn>3</mn><mo> </mo><mfrac><mrow><mn>10</mn><mi mathvariant="normal">π</mi></mrow><mn>3</mn></mfrac><mo>-</mo><mn>3</mn><mo>,</mo><mo> </mo><mfrac><mrow><mn>11</mn><mi mathvariant="normal">π</mi></mrow><mn>3</mn></mfrac><mo>-</mo><mn>3</mn></mrow></mfenced></math>.</p>
<p><em>Award</em> subsequent marks for correct use of these exact values.</p>
<p> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>18879</mn><mo>…</mo><mo><</mo><mi>t</mi><mo><</mo><mn>2</mn><mo>.</mo><mn>23598</mn><mo>…</mo></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>33038</mn><mo>…</mo><mo><</mo><mi>t</mi><mo><</mo><mn>5</mn><mo>.</mo><mn>37758</mn><mo>…</mo></math> OR</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>47197</mn><mo>…</mo><mo><</mo><mi>t</mi><mo><</mo><mn>8</mn><mo>.</mo><mn>51917</mn><mo>…</mo></math> <em><strong>(A1)</strong></em></p>
<p>attempts to calculate the total amount of time <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mfenced><mrow><mn>2</mn><mo>.</mo><mn>2359</mn><mo>…</mo><mo>-</mo><mn>1</mn><mo>.</mo><mn>1887</mn><mo>…</mo></mrow></mfenced><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mn>3</mn><mfenced><mrow><mfenced><mrow><mfrac><mrow><mn>5</mn><mi mathvariant="normal">π</mi></mrow><mn>3</mn></mfrac><mo>-</mo><mn>3</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mfrac><mrow><mn>4</mn><mi mathvariant="normal">π</mi></mrow><mn>3</mn></mfrac><mo>-</mo><mn>3</mn></mrow></mfenced></mrow></mfenced></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>3</mn><mo>.</mo><mn>14</mn><mo> </mo><mfenced><mrow><mo>=</mo><mi mathvariant="normal">π</mi></mrow></mfenced></math> (weeks) <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[6 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;">
<p>Many students did not change their calculators back to radian mode. This meant they had no chance of correctly answering parts (c) and (d), since even if follow through was given, there were not enough intersections on the graphs.</p>
<p>Most managed part (a) and some attempted to equate the functions in part b) but few recognised that 'rate of growth' was the derivatives of the given functions, and of those who did, most were unable to find them.</p>
<p>Almost all the candidates who did solve part (c) gave the answer <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>05</mn><mo>=</mo><mn>3</mn><mo>.</mo><mn>15</mn></math>, when working with more significant figures would have given them 3.14. They lost the last mark.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The functions <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math> are defined for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math> by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>6</mn><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>12</mn><mi>x</mi><mo>+</mo><mn>1</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>-</mo><mi>x</mi><mo>+</mo><mi>c</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the range of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>g</mi><mo>∘</mo><mi>f</mi></mrow></mfenced><mfenced><mi>x</mi></mfenced><mo>≤</mo><mn>0</mn></math> for all <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math>, determine the set of possible values for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>.</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>attempting to find the vertex <em><strong>(M1)</strong></em></p>
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>1</mn></math> </strong>OR<strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>5</mn></math> </strong>OR <strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>6</mn><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mo>-</mo><mn>5</mn></math></strong></p>
<p>range is<strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>≥</mo><mo>-</mo><mn>5</mn></math></strong> <strong> <em>A1</em></strong></p>
<p> </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><strong>METHOD 1</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>g</mi><mo>∘</mo><mi>f</mi></mrow></mfenced><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>-</mo><mfenced><mrow><mn>6</mn><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>12</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mi>c</mi><mo> </mo><mo> </mo><mfenced><mrow><mo>=</mo><mo>-</mo><mfenced><mrow><mn>6</mn><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mo>-</mo><mn>5</mn></mrow></mfenced><mo>+</mo><mi>c</mi></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><strong><br>EITHER</strong></p>
<p>relating to the range of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> OR attempting to find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mfenced><mrow><mo>-</mo><mn>5</mn></mrow></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>+</mo><mi>c</mi><mo>≤</mo><mn>0</mn></math> <em><strong>(A1)</strong></em></p>
<p><br><strong>OR</strong></p>
<p>attempting to find the discriminant of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>g</mi><mo>∘</mo><mi>f</mi></mrow></mfenced><mfenced><mi>x</mi></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>144</mn><mo>+</mo><mn>24</mn><mfenced><mrow><mi>c</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>≤</mo><mn>0</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>120</mn><mo>+</mo><mn>24</mn><mi>c</mi><mo>≤</mo><mn>0</mn></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><strong><br>THEN</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>≤</mo><mo>-</mo><mn>5</mn></math> <em><strong> A1</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>vertical reflection followed by vertical shift <em><strong>(M1)</strong></em></p>
<p>new vertex is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>1</mn><mo>,</mo><mo> </mo><mn>5</mn><mo>+</mo><mi>c</mi></mrow></mfenced></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>+</mo><mi>c</mi><mo>≤</mo><mn>0</mn></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>≤</mo><mo>-</mo><mn>5</mn></math> <em><strong> A1</strong></em></p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi mathvariant="normal">e</mi><mrow><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup></mrow></msup><mo>-</mo><mn>0</mn><mo>.</mo><mn>5</mn></math>, for <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mn>2</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> for which <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>0</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> on the following grid.</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>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>832554</mn><mo>…</mo><mo>,</mo><mo> </mo><mi>x</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>832554</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>833</mn><mo>,</mo><mo> </mo><mi>x</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>833</mn></math> <em><strong>A1A1</strong></em></p>
<p><br><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,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"> <em><strong>A1A1A1</strong></em></p>
<p><em><strong><br></strong></em><strong>Note: </strong>Award <em><strong>A1</strong></em> for approximately correct shape. Only if this mark is awarded, award <em><strong>A1</strong></em> for approximately correct roots and maximum point and <em><strong>A1</strong></em> for approximately correct endpoints. <br>Allow <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo><</mo><mi>x</mi><mo>≤</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>8</mn><mo>,</mo><mo> </mo><mo> </mo><mn>0</mn><mo>.</mo><mn>8</mn><mo>≤</mo><mi>x</mi><mo><</mo><mn>1</mn></math> for roots, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>4</mn><mo>≤</mo><mi>y</mi><mo>≤</mo><mn>0</mn><mo>.</mo><mn>6</mn></math> for maximum and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>±</mo><mn>2</mn><mo>,</mo><mo> </mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>6</mn><mo>≤</mo><mi>y</mi><mo>≤</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>4</mn></math> for endpoints.</p>
<p><br><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>SpeedWay airline flies from city <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}">
<mrow>
<mtext>A</mtext>
</mrow>
</math></span> to city <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}">
<mrow>
<mtext>B</mtext>
</mrow>
</math></span>. The flight time is normally distributed with a mean of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="260">
<mn>260</mn>
</math></span> minutes and a standard deviation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="15">
<mn>15</mn>
</math></span> minutes.</p>
<p>A flight is considered late if it takes longer than <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="275">
<mn>275</mn>
</math></span> minutes.</p>
</div>
<div class="specification">
<p>The flight is considered to be <strong>on time</strong> if it takes between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
<mi>m</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="275">
<mn>275</mn>
</math></span> minutes. The probability that a flight is on time is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.830">
<mn>0.830</mn>
</math></span>.</p>
</div>
<div class="specification">
<p>During a week, SpeedWay has <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="12">
<mn>12</mn>
</math></span> flights from city <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}">
<mrow>
<mtext>A</mtext>
</mrow>
</math></span> to city <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}">
<mrow>
<mtext>B</mtext>
</mrow>
</math></span>. The time taken for any flight is independent of the time taken by any other flight.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the probability a flight is <strong>not</strong> late.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m"> <mi>m</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the probability that at least <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="7"> <mn>7</mn> </math></span> of these flights are <strong>on time</strong>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that at least <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="7"> <mn>7</mn> </math></span> of these flights are on time, find the probability that exactly <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="10"> <mn>10</mn> </math></span> flights are on time.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>SpeedWay increases the number of flights from city <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}"> <mrow> <mtext>A</mtext> </mrow> </math></span> to city <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}"> <mrow> <mtext>B</mtext> </mrow> </math></span> to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="20"> <mn>20</mn> </math></span> flights each week, and improves their efficiency so that more flights are on time. The probability that at least <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="19"> <mn>19</mn> </math></span> flights are on time is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.788"> <mn>0.788</mn> </math></span>.</p>
<p>A flight is chosen at random. Calculate the probability that it is on time.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {X < 275} \right)"> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo><</mo> <mn>275</mn> </mrow> <mo>)</mo> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1 - 0.158655"> <mn>1</mn> <mo>−</mo> <mn>0.158655</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.841344"> <mn>0.841344</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.841"> <mn>0.841</mn> </math></span> <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {X < 275} \right) - {\text{P}}\left( {X < m} \right) = 0.830"> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo><</mo> <mn>275</mn> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo><</mo> <mi>m</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0.830</mn> </math></span></p>
<p>correct working <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {X < m} \right) = 0.0113447"> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo><</mo> <mi>m</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0.0113447</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="225.820"> <mn>225.820</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="226"> <mn>226</mn> </math></span> (minutes) <em><strong>A1 N3</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>evidence of recognizing binomial distribution (seen anywhere) <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_n{C_a} \times {p^a} \times {q^{n - a}}"> <msub> <mrow> </mrow> <mi>n</mi> </msub> <mrow> <msub> <mi>C</mi> <mi>a</mi> </msub> </mrow> <mo>×</mo> <mrow> <msup> <mi>p</mi> <mi>a</mi> </msup> </mrow> <mo>×</mo> <mrow> <msup> <mi>q</mi> <mrow> <mi>n</mi> <mo>−</mo> <mi>a</mi> </mrow> </msup> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}\left( {n{\text{, }}p} \right)"> <mrow> <mtext>B</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>n</mi> <mrow> <mtext>, </mtext> </mrow> <mi>p</mi> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p>evidence of summing probabilities from <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="7"> <mn>7</mn> </math></span> to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="12"> <mn>12</mn> </math></span> <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {X = 7} \right) + {\text{P}}\left( {X = 8} \right) + \ldots + {\text{P}}\left( {X = 12} \right)"> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo>=</mo> <mn>7</mn> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo>=</mo> <mn>8</mn> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mo>…</mo> <mo>+</mo> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo>=</mo> <mn>12</mn> </mrow> <mo>)</mo> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1 - {\text{P}}\left( {X \leqslant 6} \right)"> <mn>1</mn> <mo>−</mo> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo>⩽</mo> <mn>6</mn> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.991248"> <mn>0.991248</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.991"> <mn>0.991</mn> </math></span> <em><strong>A1 N2</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>finding <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {X = 10} \right)"> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo>=</mo> <mn>10</mn> </mrow> <mo>)</mo> </mrow> </math></span> (seen anywhere) <em><strong>A1</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} {12} \\ {10} \end{array}} \right) \times {0.83^{10}} \times {0.17^2}\,\,\left( { = 0.295952} \right)"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mn>12</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>10</mn> </mrow> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mo>×</mo> <mrow> <msup> <mn>0.83</mn> <mrow> <mn>10</mn> </mrow> </msup> </mrow> <mo>×</mo> <mrow> <msup> <mn>0.17</mn> <mn>2</mn> </msup> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mrow> <mo>(</mo> <mrow> <mo>=</mo> <mn>0.295952</mn> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p>recognizing conditional probability <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {A\left| B \right.} \right)"> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>A</mi> <mrow> <mo>|</mo> <mi>B</mi> <mo stretchy="true" symmetric="true" fence="true"></mo> </mrow> </mrow> <mo>)</mo> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {X = 10\left| {X \geqslant 7} \right.} \right)"> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo>=</mo> <mn>10</mn> <mrow> <mo>|</mo> <mrow> <mi>X</mi> <mo>⩾</mo> <mn>7</mn> </mrow> <mo stretchy="true" symmetric="true" fence="true"></mo> </mrow> </mrow> <mo>)</mo> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{P}}\left( {X = 10 \cap X \geqslant 7} \right)}}{{{\text{P}}\left( {X \geqslant 7} \right)}}"> <mfrac> <mrow> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo>=</mo> <mn>10</mn> <mo>∩</mo> <mi>X</mi> <mo>⩾</mo> <mn>7</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mrow> <mtext>P</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mi>X</mi> <mo>⩾</mo> <mn>7</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> </math></span></p>
<p>correct working <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.295952}}{{0.991248}}"> <mfrac> <mrow> <mn>0.295952</mn> </mrow> <mrow> <mn>0.991248</mn> </mrow> </mfrac> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.298565"> <mn>0.298565</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.299"> <mn>0.299</mn> </math></span> <em><strong>A1 N1</strong></em></p>
<p><strong>Note: Exception to the <em>FT</em> rule:</strong> if the candidate uses an incorrect value for the probability that a flight is on time in (i) and working shown, award full <em><strong>FT</strong></em> in (ii) as appropriate.</p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct equation <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}} {20} \\ {19} \end{array}} \right){p^{19}}\left( {1 - p} \right) + {p^{20}} = 0.788"> <mrow> <mo>(</mo> <mrow> <mtable columnspacing="1em" rowspacing="4pt"> <mtr> <mtd> <mrow> <mn>20</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>19</mn> </mrow> </mtd> </mtr> </mtable> </mrow> <mo>)</mo> </mrow> <mrow> <msup> <mi>p</mi> <mrow> <mn>19</mn> </mrow> </msup> </mrow> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mi>p</mi> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <msup> <mi>p</mi> <mrow> <mn>20</mn> </mrow> </msup> </mrow> <mo>=</mo> <mn>0.788</mn> </math></span></p>
<p>valid attempt to solve <em><strong>(M1)</strong></em></p>
<p><em>eg</em> graph</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.956961"> <mn>0.956961</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.957"> <mn>0.957</mn> </math></span> <em><strong>A1 N1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.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>A particle moves in a straight line such that its velocity, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo> </mo><mtext>m s</mtext><msup><mrow></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>, at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> seconds is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfrac><mrow><mfenced><mrow><msup><mi>t</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></mfenced><mi>cos</mi><mo> </mo><mi>t</mi></mrow><mn>4</mn></mfrac><mo>,</mo><mo> </mo><mn>0</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mn>3</mn></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine when the particle changes its direction of motion.</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 times when the particle’s acceleration is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>.</mo><mn>9</mn><mo> </mo><msup><mtext>m s</mtext><mrow><mo>-</mo><mn>2</mn></mrow></msup></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the particle’s acceleration when its speed is at its greatest.</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>recognises the need to find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>0</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>57079</mn><mo>…</mo><mo> </mo><mfenced><mrow><mo>=</mo><mfrac><mi mathvariant="normal">π</mi><mn>2</mn></mfrac></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>57</mn><mo> </mo><mfenced><mrow><mo>=</mo><mfrac><mi mathvariant="normal">π</mi><mn>2</mn></mfrac></mrow></mfenced></math> (s) <em><strong>A1</strong></em></p>
<p> </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>recognises that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mi>v</mi><mo>'</mo><mfenced><mi>t</mi></mfenced></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>t</mi><mn>1</mn></msub><mo>=</mo><mn>2</mn><mo>.</mo><mn>26277</mn><mo>…</mo><mo>,</mo><mo> </mo><msub><mi>t</mi><mn>2</mn></msub><mo>=</mo><mn>2</mn><mo>.</mo><mn>95736</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>t</mi><mn>1</mn></msub><mo>=</mo><mn>2</mn><mo>.</mo><mn>26</mn><mo>,</mo><mo> </mo><msub><mi>t</mi><mn>2</mn></msub><mo>=</mo><mn>2</mn><mo>.</mo><mn>96</mn></math> (s) <em><strong>A1A1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>M1A1A0</strong></em> if the two correct answers are given with additional values outside <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mn>3</mn></math>.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>speed is greatest at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>3</mn></math> <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>.</mo><mn>83778</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>.</mo><mn>84</mn><mo> </mo><mfenced><msup><mtext>m s</mtext><mrow><mo>-</mo><mn>2</mn></mrow></msup></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 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;">
<p>In part (a) many did not realize the change of motion occurred when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>0</mn></math>. A common error was finding <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>(</mo><mn>0</mn><mo>)</mo></math> or thinking that it was at the maximum of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math>. </p>
<p>In part (b), most candidates knew to differentiate but some tried to substitute in <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>.</mo><mn>9</mn></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>, while others struggled to differentiate the function by hand rather than using the GDC. Many candidates tried to solve the equation analytically and did not use their technology. Of those who did, many had their calculators in degree mode.</p>
<p>Almost all candidates who attempted part (c) thought the greatest speed was the same as the maximum of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math>.</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>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {x^3} - 5{x^2} + 6x - 3 + \frac{1}{x}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mn>5</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>6</mn>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mn>3</mn>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mi>x</mi>
</mfrac>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x > 0">
<mi>x</mi>
<mo>></mo>
<mn>0</mn>
</math></span></p>
</div>
<div class="specification">
<p>The function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {x^3} - 5{x^2} + 6x - 3 + \frac{1}{x}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mn>5</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>6</mn>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mn>3</mn>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mi>x</mi>
</mfrac>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x > 0">
<mi>x</mi>
<mo>></mo>
<mn>0</mn>
</math></span>, models the path of a river, as shown on the following map, where both axes represent distance and are measured in kilometres. On the same map, the location of a highway is defined by the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right) = 0.5{\left( 3 \right)^{ - x}} + 1">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0.5</mn>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
<mrow>
<mo>−<!-- − --></mo>
<mi>x</mi>
</mrow>
</msup>
</mrow>
<mo>+</mo>
<mn>1</mn>
</math></span>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The origin, O(0, 0) , is the location of the centre of a town called Orangeton.</p>
<p>A straight footpath, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P">
<mi>P</mi>
</math></span>, is built to connect the centre of Orangeton to the river at the point where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = \frac{1}{2}">
<mi>x</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span>.</p>
</div>
<div class="specification">
<p>Bridges are located where the highway crosses the river.</p>
</div>
<div class="specification">
<p>A straight road is built from the centre of Orangeton, due north, to connect the town to the highway.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right)">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = \frac{1}{2}">
<mi>x</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the function, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P\left( x \right)">
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> , that would define this footpath on the map.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the domain of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P">
<mi>P</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of the bridges relative to the centre of Orangeton.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the distance from the centre of Orangeton to the point at which the road meets the highway.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>This straight road crosses the highway and then carries on due north.</p>
<p>State whether the straight road will ever cross the river. Justify your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( {\frac{1}{2}} \right) = {\left( {\frac{1}{2}} \right)^3} - 5{\left( {\frac{1}{2}} \right)^2} + 6\left( {\frac{1}{2}} \right) - 3\frac{1}{{\left( {\frac{1}{2}} \right)}}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<mo>−</mo>
<mn>5</mn>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>6</mn>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>−</mo>
<mn>3</mn>
<mfrac>
<mn>1</mn>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
</math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into given function.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{7}{8}\,\,\left( {0.875} \right)">
<mfrac>
<mn>7</mn>
<mn>8</mn>
</mfrac>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.875</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)</strong></em><em><strong>(G2)</strong></em></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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0 - \frac{7}{8}}}{{0 - \frac{1}{2}}}">
<mfrac>
<mrow>
<mn>0</mn>
<mo>−</mo>
<mfrac>
<mn>7</mn>
<mn>8</mn>
</mfrac>
</mrow>
<mrow>
<mn>0</mn>
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</mrow>
</mfrac>
</math></span> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into gradient formula. Accept equivalent forms such as <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{7}{8} = \frac{1}{2}m">
<mfrac>
<mn>7</mn>
<mn>8</mn>
</mfrac>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>m</mi>
</math></span>.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{7}{4}">
<mfrac>
<mn>7</mn>
<mn>4</mn>
</mfrac>
</math></span> (1.75) <em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P\left( x \right) = \frac{7}{4}x\,\,\left( {1.75x} \right)">
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>7</mn>
<mn>4</mn>
</mfrac>
<mi>x</mi>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mrow>
<mo>(</mo>
<mrow>
<mn>1.75</mn>
<mi>x</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>(A1)</strong></em><strong>(ft)<em>(G3)</em></strong></p>
<p><strong>Note:</strong> Follow through from part (a).</p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0 < <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> < <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span> <em><strong>(A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for both endpoints correct, <em><strong>(A1)</strong></em> for correct mathematical notation indicating an interval with two endpoints. Accept weak inequalities. Award at most <em><strong>(A1)</strong></em><em><strong>(A0)</strong></em> for incorrect notation such as 0 − 0.5 or a written description of the domain with correct endpoints. Award at most <em><strong>(A1)</strong></em><em><strong>(A0)</strong></em> for 0 < <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> < <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span>.</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>(0.360, 1.34) ((0.359947…, 1.33669)) <em><strong>(A1)(A1)</strong></em></p>
<p>(3.63, 1.01) ((3.63066…, 1.00926…)) <em><strong>(A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)(A1)</strong></em> for each correct coordinate pair. Accept correct answers in the form of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0.360"> <mi>x</mi> <mo>=</mo> <mn>0.360</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 1.34"> <mi>y</mi> <mo>=</mo> <mn>1.34</mn> </math></span> <em>etc</em>. Award at most <strong><em>(A0)(A1)(A1)(A1)</em>ft</strong> if one or both parentheses are omitted.</p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( 0 \right) = 0.5{\left( 3 \right)^0} + 1">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0.5</mn>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
<mn>0</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>1</mn>
</math></span> <em><strong>(M1)</strong></em></p>
<p>1.5 (km) <em><strong>(A1)(G2)</strong></em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>domain given as <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x > 0">
<mi>x</mi>
<mo>></mo>
<mn>0</mn>
</math></span> (but equation of road is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0">
<mi>x</mi>
<mo>=</mo>
<mn>0</mn>
</math></span>) <em><strong> (R1)</strong></em></p>
<p><strong>OR</strong></p>
<p>(equation of road is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0">
<mi>x</mi>
<mo>=</mo>
<mn>0</mn>
</math></span>) the function of the river is asymptotic to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0">
<mi>x</mi>
<mo>=</mo>
<mn>0</mn>
</math></span> <em><strong> (R1)</strong></em></p>
<p>so it does not meet the river <em><strong> (A1)</strong></em></p>
<p><strong>Note:</strong> Award the <em><strong>(R1)</strong></em> for a correct mathematical statement about the equation of the river (and the equation of the road). Justification must be based on <strong>mathematical reasoning</strong>. Do not award <em><strong>(R0)</strong></em><em><strong>(A1)</strong></em>.</p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[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>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {{\text{e}}^{2\,{\text{sin}}\left( {\frac{{\pi x}}{2}} \right)}}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mn>2</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>sin</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mi>π<!-- π --></mi>
<mi>x</mi>
</mrow>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</msup>
</mrow>
</math></span>, for <em>x</em> > 0.</p>
<p>The <em>k </em>th maximum point on the graph of <em>f</em> has <em>x</em>-coordinate <em>x<sub>k</sub></em> where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k \in {\mathbb{Z}^ + }">
<mi>k</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<msup>
<mrow>
<mi mathvariant="double-struck">Z</mi>
</mrow>
<mo>+</mo>
</msup>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <em>x<sub>k</sub></em><sub> + 1</sub> = <em>x<sub>k</sub></em> + <em>a</em>, find <em>a</em>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find the value of <em>n</em> such that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sum\limits_{k = 1}^n {{x_k} = 861} "> <munderover> <mo movablelimits="false">∑</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mrow> <mrow> <msub> <mi>x</mi> <mi>k</mi> </msub> </mrow> <mo>=</mo> <mn>861</mn> </mrow> </math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>valid approach to find maxima <em><strong>(M1)</strong></em></p>
<p><em>eg</em> one correct value of <em>x<sub>k</sub></em>, sketch of <em>f</em></p>
<p>any two correct consecutive values of <em>x<sub>k</sub></em> <em><strong>(A1)(A1)</strong></em></p>
<p><em>eg x</em><sub>1</sub> = 1, <em>x</em><sub>2</sub> = 5</p>
<p><em>a</em> = 4 <em><strong>A1 N3</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing the sequence <em>x</em><sub>1,<sup> </sup></sub> <em>x</em><sub>2</sub><sub>,<sup> </sup></sub> <em>x</em><sub>3, …,</sub> <em>x</em><sub>n</sub> is arithmetic <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <em>d</em> = 4</p>
<p>correct expression for sum<em> <strong>(A1)</strong><br></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{n}{2}\left( {2\left( 1 \right) + 4\left( {n - 1} \right)} \right)"> <mfrac> <mi>n</mi> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>+</mo> <mn>4</mn> <mrow> <mo>(</mo> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </math></span></p>
<p>valid attempt to solve for <em>n</em> <em><strong>(M1)</strong></em></p>
<p><em>eg</em> graph, 2<em>n</em><sup>2</sup> − <em>n</em> − 861 = 0</p>
<p><em>n</em> = 21 <em><strong>A1 N2</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</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>OAB is a sector of the circle with centre O and radius <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
<mi>r</mi>
</math></span>, as shown in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAiQAAAEiCAYAAADJQsnwAAAgAElEQVR4Ae2dDXQV5bX3/0m9LqGIGGDVEwPlIjeht9hAE9Qr8XJAG6rWwkoKLtsaXICtH0l84wsB/Fjc3GupJVlwm2Cl1ZNCsKhg8mKlKhEwtsEqJECEW00upVhjTllAFEiptSTnXXuSSYbk5OR8zJz5+s9arDOZeeZ59v7tIfmf/XwlBAKBAHiQAAmQAAmQAAmQgIkEEk1sm02TAAmQAAmQAAmQgEKAgoQvAgmQAAmQAAmQgOkEKEhMDwENIAESIAESIAESoCDhO0ACJEACbiJwoRFlkxKQkDALZY0dAC7AX3MfEhISkLCwBn43sdDN1y50tNThpbLlWKcwDVFxRwv2vFSG+9Y14kKIYta8Zey7QkFizajTKhIgARIgAbsQuHAQG26bhfnL9qEzpM0daNzwQ9w8fxl2hS4Yshan3rzEqY7RLxIgARIggXAIXAJPzgYEAhvCKcwyJGAYAWZIDEPLikmABEjAbAJn0fLGOixMli6aBCQvXIc3Wtr7GTVYGv7iZ7ufL0NNox9dvTVIV8VOlC28trvLZ9ZybGpswb6yWcrPk8p6uiX8NVgoXUKTSlCzswSz5DxhASpbPgPQrw65l7wQZTWN8Pc0dKGxDJOU55/Enj9o23sENS1ngY4WvFG2EMlKvXOwfNO+3md7Te09+Qg1CychIWESFr70DhpryjR8nsI+/+e9JZWTni4WlWFCwhwsr9yDlo4e48S3f8rEsj9K6Tosy7wcCZPK0DigP0banYrMZXVKtX9clol/6u02k0tn0bLnxT6WCcmYtbwSe8S/UIfYV7m8h6lwHeS5Lv9FviYkXIuFZTv7/FDaCCfmwYyRGO5B5fI53e/BYDYEe1R7TdYh4UECJEACJOA0An8PtFY/GPAAstZUkH/eQGnDuUAg8I9AW/UPu+/nVQfaFAwhnvU8GKhu/btSqrO1OrDI069uz7xA3nenKPVdU9oQ+IeUbKsO5PW3wbMysPtMZyBoHUrZKYFF1ccDnWJhQ2ngmv7Pqz97HwwU53W31+dnRqB498lBAvrnQHXeNUF49PiR7Qs0S6NynDsc8A2ou6ecd22g4VxncN+uKQ00KI731KN8BGtXjcGZwPu+RYPE6vZAacMn2oo0558EGkpvD+6Lap9SevBynkXVgVbF33BiHuxdCQweQ8+igO/9Mxp7Q58yQ6JVZzwnARIgAacQOFuP8vyn4IcH3pW1aOsMINDZhnfX5sEzlI9dx7Dz5zLA9XaUNnwCWT+zs7Uai+RB///g2F8ki/AZju58AZUyCtb7H9jd9ncEAn9H23NT8ectRwZpwQNv6bs4J/W1PIIbRn7eU0ff9UDncVQvmgLgCN46dkqTjZEqpyDPdxjnAp0417AWXrlU9xQ2YyneP9eJwLl3UeoVIxtRfeDDoQeNeleiuvmMYndr9YPdXGr34cgJSW98hpat/4nFVUcAzyL43pdyAXS21WKltFFXiqUbGtDhycGmfzSg9BoxxovShnMIHF2KjAEDIsYhZ9MhNJQqVuOa0gb8I/AmlmaMQFfLS3hocSX8vf5JrFqxe2U2gN9g2dJfolHNyGjJXvgj3tzwGwAZKN59UrGvl0FdKR7Z2qLw62qpwSPLpFw2Vu5uRafGD3/lapTXnQLCirm2cfX8FOrKV6PSr8YmgEDgDN73LYLHX4nHftmAIXI8akWgIOlFwRMSIAEScA6Brr8cxyFlysy3UVAwCx75bZ/owXWLF+LuoRRJ4mQs2tmGQOczmNW6BzU1z2Dl9/O7xQfO4eSZz4Cu46h/sR6AB9l33wmv51IAl8Iz+0E8XpwxCMgs3P3tr2GEmDJiBIbjMqQu2opA4Di2zDqF2pqXULnyB8it7BY050+ewXltTZ47sPA7/4oRSMSI9H/H7YoIyMDdC2/H5BGJwIh/xazb07RPhDgXu/MwL3WkYvfV/zYb39CW1vr3xDLcM1nKCcKbseLxe+CBH3UbfovmAV0z2krCOf8MR+tfR60UzS7Co/dMUfgg8WrMXrEcxRKrul/jzeaLSHRXnDgGE2eKeGvEmptnYWHZFtTUtuJfyhrRGWjDzkWTkYgLOHFkX3f9eT9EweyrlT/8iZ5vYPWbbQgEGvCT2WOAcGIezJ0LH+JAdaMiIKsWX4vLlW6zK/AVRWAB/s270HC2r5MvWBXqtQEaTr3BTxIgARIgAfsS6DrXDmVYgycJo76o+e45/AqMHT6UX2fxQWURZvf8Ubm49OUYe8VlQNdf0f5HUTwZmDphjObb7WW4YuzlFz+i/uSZhAlXiXBRjy50fLAZD86+B1VB5hsPH3sFLjJ1eBKuGK7xRammxx61yrA/h+OqUV/ss3vsl3GtCBwFmgxtUf3z4hvpKX3lkIjhVyR12/XHo/jw5AVkjA270SAFL+Bc+0nl+jXfSMdErXu9sfoIhz/8BMgQKac5Er+MeU/4sHHM47hnTS2qln0PVeptyf78fAVyUhPRdqxZvRriM4yYB3v65Ic4rDILdt/fjk//2gWM1DoWrCA0jIPf51USIAESIAEbEki8PAlKAsF/FMeVLpYeJ86fwckgX7a1LvZ1IWSj2LcN2xva0NnbLdFTMvGLSLpGvr634dBxbdfKZzhz8py2ur7z/oKiqwVbH1qJKr8H3uJfoHp7A9o6z/V2a/Q9aMJZr3/NeKOpVdN11IXzZ9q7MzfXTMKXx8b6vf4SXJ7UrWj++EYTjmmTCb2xGodrv3xlUAiJnuuw8Cc7lW6S5t3bUV39K5TmTQHqfozcgpfQ0nUZkif2ZI3+8inOaevX1BhWzDXle0+/OApXKRm3nu6qgHTZaP9tQI4nPEZDS5beVnlCAiRAAiRgFwKJk27Endnyl6Iemzf+rnvWSZcf+3ybsDlINqLPry50tB7FYbng+RdcP+fbmJsxGid+uwO/0X4TTpyArDuzZFAJaje/iDpldsrn8O95Cv+1RlL4YRwdbWg+LMaMxsTrszFvbga+dOL3qP5NON/ow6g/liJa/x4rxcYPukdCdPl348n/2tg9Nue+f0daeH9rQ1hyGSZlfRMyWgS16/CjjUcgy9Wh62PsefInWCN4vN/GrLSLckVKfV0f12CxMoNqDh7Zcw6TZs9FTs53cNfcmZpxQpfgS1Ou66n/RWys+7hbXHUcQaUyOyoZcyr/gDPhxDyYFyO/hjl3SxddHdaWV+MDGesitj/SPeMmefmesMeQiJLhQQIkQAIk4DgCIWZNKDNU1BkeA2dOBJ/5khHwemV2St8MlqDlQs2y6T/7pPN4oHpR/xkynsCN3huVGSee4t0BmaPRO8tG+/w/GgKl18iMF9UPCeC5QEOp9+IZPgPiqs52uSaQV/3nvru99f0wUN3WM0Xm3LuBUq9n6Fksne8HfNmaclo7+1oIBAJ/CzT75mvqU20ffBYMEOUsG/TNUgoEQtTv/Y/A7ra/DzJTpn/MB74rgUBn4Nz7GwN5/WdbyTvGWTbBJByvkQAJkIDbCFyKq3NWo652LfKUlDrgyVuL2v+p7ZkRMjiPxKu/hSdeqUKxMmNFvqEXY2PD/8NzBbcoAyg373xP+dabePU8/LTu9e4uAkmoSP1161E4bczglWvvqGMgipX8gDILpHjjdrz03P9VBphGMiBSW61u5yOuw9JX6rB7W2kvQ5mpUuzbjeZXHkKGDKSVI3Eibv2vR/vKjPsC8FmwvpHLMOnWh7BWulSU44vK0v3AKGQs3YLm3S/0spTBwt5iH3Y3b8HSjFE95ft/qM/5+mIlRbzF8O2uxk9zvtwzLmMUMh5+Bg3VWj+mIK+0Gg1bVmK251KEG/P+FsjIjxGT78ZTdbvh642j+i6sw6KewcADnxt4JUHE28DLvEICJEACJEACoQh0oLHsju6FvjwPonr/WuRcfSnQsQ9ld8zDsrrhyKt+E5tyxoWqhPdIoJcABUkvCp6QAAmQAAmET6ALHY0/xR2ZD6N77dF+T2pFSr9b/JEEghHgoNZgVHiNBEiABEhgCAKJGJHxILY0VGu6GeSRnq6GutXdGZMhauFtElAJMEOikuAnCZAACZAACZCAaQSYITENPRsmARIgARIgARJQCVCQqCT4SQIkQAIkQAIkYBoBChLT0LNhEogzgbN7sLxnG3rZSr7/v+SFZXhpT0v3okxxNo3NkQAJkAAFCd8BEnALgZGz8ZO2TpzZvRIezIev+W+9Szx3tr2LH1/1BubfnIsHK3tWinQLF/pJAiRgCQIUJJYIA40gAXMJKPth/Pin8GWfRtVjW7AvzN05zbWarZMACTiJAAWJk6JJX0iABEiABEjApgRi3hbIpn7TbBIgAS2BLj8aN/8Sm2tHI8/3XVwXxlbh2sd5TgIkQAKxEqAgiZUgnycBWxLYhsVp27C4n+2e4t14edEUjOh3nT+SAAmQgNEE2GVjNGHWTwKWJNB/UGsDqkvzgDU3Y/LCTd1biFvSbhpFAiTgVAIUJE6NLP0igQgIJHoykLP056jzzYe/aiUe2tqCYHuVRlAli5IACZBARAQoSCLCxcIk4GQCl+KqCZPggR+Hm9u4HomTQ03fSMCCBChILBgUmkQC5hC4gHOfnlU2R7s2LZnjSMwJAlslAdcS4KBW14aejpOAhoDMstn+K5TnPwW/9z/w3K0TwW8rGj48JQESMJwAd/s1HDEbIAGLEJCl4yffjDX+wezJRrGvAAtuzUaG59LBCvE6CZAACRhCgILEEKyslARIgARIgARIIBICzMpGQotlSYAESIAESIAEDCFAQWIIVlZKAiRAAiRAAiQQCQEKkkhosSwJOIjA3/72N6xfv95BHtEVEiABOxPgLBs7R4+2k0CUBESMFBYW4tlnn1VqyM/Pj7ImPkYCJEAC+hBghkQfjqyFBGxDQBUjTU1Nis1VVVXMlNgmejSUBJxLgILEubGlZyQQlIDP54OIkZqaGuW+fFKUBEXFiyRAAnEkwC6bOMJmUyRgNgEZMyLiQ0RISkqKYo58ys85OTnKz+y+MTtKbJ8E3EmAgsSdcafXLiQgYqSgoADNzc29YkTFoIqScePGKZcoSlQy/CQBEogXAQqSeJFmOyRgIgFVjNTX1yM1NTWoJSJK5H5WVpZyn6IkKCZeJAESMIgABYlBYFktCViFgHTHSGZExMaMGTNCmiX3KUpCIuJNEiABgwhQkBgEltWSgBUI7N27F7m5uWGJEdVerSgZOXIk8vLy1Fv8JAESIAHDCHAvG8PQsmISMJeAiBHpfgmVGUlISEAgEAhqaDjPB32QF0mABEggCgKc9hsFND5CAlYnoIqJioqKIbtpBvNFmymR+niQAAmQgJEEKEiMpMu6ScAEAloxEuvAVBElmzZtUjItFCUmBJNNkoCLCHAMiYuCTVedT6C1tRVFRUWQzEisYkSlJWNIzp49q4iSgwcPYurUqeotfpIACZCAbgQ4hkQ3lKyIBMwlIGJEFjcTARGuGAk1hqS/N8EWVetfhj+TAAmQQLQE2GUTLTk+RwIWIqCKEa/XG7YYidR8ETnz5s1TRI+0x4MESIAE9CRAQaInTdZFAiYQUMVIeno6SkpKDLVAuoOkHcnEUJQYipqVk4DrCLDLxnUhp8NOIiA7986cOVMRCeXl5Rg2bFhE7kXSZaNWrO4WLD9H06ZaDz9JgARIQEuAgkRLg+ckYCMCegiDaASJIJK277rrLowdO5aixEbvDE0lASsTYJeNlaND20hgEAJ6iJFBqg7rsmRiZJBrU1MTVq1aFdYzLEQCJEACoQhQkISiw3skYEECqhhRxUCk3TR6uaTuEFxXV6eIE73qZT0kQALuJMB1SNwZd3ptUwJaMSKb5okoMPOQ9n/xi19g2rRpihnhTjc202a2TQIkYE0CzJBYMy60igSCEvD5fEo3iRXEiGqgLJQm++XIjsJczVWlwk8SIIFICVCQREqM5UnAJAJWXphMlpivrq7mEvMmvRtslgScQICzbJwQRfrgeAIiRiQD0dzcjNTUVN38jXaWzWAGWFk0DWYzr5MACViDADMk1ogDrSCBQQmoYkS6RfQUI4M2GMMNGUMiq8XKwmnt7e0x1MRHSYAE3EaAGRK3RZz+2oqAjBXJzc1VxmhIt4jeh94ZErFPHXgr51w4Te+IsT4ScC4BChLnxpae2ZyADBDNysoyTIwIHiMEidQr2ZFvfvObygqyzzzzjM0jQfNJgATiQYBdNvGgzDZIIEIC8RAjEZoUUfGkpCRIdkfWSpEuJx4kQAIkMBQBrkMyFCHeJ4E4E1DFSEVFBYzopomXO7JGybp165Qsj4x9yc7OjlfTbIcESMCGBNhlY8Og0WTnEtCKkXgsMmZUl402QrW1tZgzZw4OHjwIWbOEBwmQAAkEI0BBEowKr5GACQRaW1uV2Sl5eXmIhxgRF+MhSKQdTgc24YVikyRgMwIUJDYLGM11JgEzxIiQjJcgkbbuvfdenDx5Es8//zzM2n/HmW8PvSIBZxDgoFZnxJFe2JiAKkZk/Y54ZUbMwCVTgOUoLCw0o3m2SQIkYHECFCQWDxDNczYBVYykp6ejpKTE0c5KVkS6bjjzxtFhpnMkEDUBdtlEjY4PkkBsBGQBsZkzZyprdZi1gFg8u2xUWurAXVl51s6ziFR/+EkCJKAPAQoSfTiyFhKIiIBVVjM1Q5AIKHUFWr335okoCCxMAiRgKQIUJJYKB41xAwGriBFhbZYgkbZXr16N7du34/XXX4cspMaDBEjA3QQoSNwdf3ofZwKqGJFxFJIlkMXDzDzMFCQqC/Gfy8ub+RawbRKwBgEOarVGHGiFCwiof4CtIkbMRi6DXFetWsVBrmYHgu2TgEUIMENikUDQDOcTsOLiYGZmSNSIHzp0CNOmTTN0E0G1LX6SAAlYlwAzJNaNDS1zEAErihGr4JXl5Ddt2qTseSPToHmQAAm4kwAzJO6MO72OIwERIwUFBbDijBIrZEjUUBQXF6OlpYUruapA+EkCLiPADInLAk5340tAFSOy5obseMtjcAKyMFxbW5uyQ/DgpXiHBEjAqQSYIXFqZOmX6QTUtTasvACYlTIkEjDJkKSlpWHnzp3Izs42PYY0gARIIH4EKEjix5otuYiAXVYjtZogkVdEFXIfffSR6dOiXfTK0lUSMJ0ABYnpIaABTiNgFzEi3K0oSMQujidx2v8K+kMCQxPgGJKhGbEECYRNQBUjFRUV3KclbGoDC3I8yUAmvEICTifADInTI0z/4kZAK0by8/Pj1m4sDVk1QyI+cTxJLJHlsyRgPwIUJPaLGS22IAFZPyMnJwd5eXmwixgRjFYWJGIfx5NY8GWnSSRgEAEKEoPAslr3ELCrGJEIWV2QiI0ynuSTTz5BeXk5ZLl5HiRAAs4kwDEkzowrvYoTAVWMeL1eW2VG4oRHl2ZWrFih7Hfj8/l0qY+VkAAJWJMAMyTWjAutsgEBVYykp6fb9tu7HTIk8iqo+90cPHgQstQ8DxIgAecRoCBxXkzpURwIyM69M2fOhJ3FiGCyiyARW9X9gN566y123cThHWcTJBBvAhQk8SbO9mxPQMRIYWGh4ofdxzXYSZAI97vuuktZgn/NmjW2f4/oAAmQwMUEKEgu5sGfSCAkASeJEXHUToJE7OVU4JCvJ2+SgK0JcFCrrcNH4+NJQBUjTU1NWLVqFbsN4gm/py3ZoLC6uhqPPfYY2tvbTbCATZIACRhFgBkSo8iyXkcR0IoRWRsjJSXFEf7ZLUOiQr/33nuV02eeeUa9xE8SIAGbE6AgsXkAaX58CKgDKp0kRoScXQWJzHAaN26cki2RBel4kAAJ2J8Au2zsH0N6YDABp4oRg7EZWr1kqKTrJjc3FyJOeJAACdifADMk9o8hPTCQgIiRgoICNDc3K7M7DGzKlKrtmiFRYbHrRiXBTxKwPwEKEvvHkB4YREAVI/X19Y7dudfugoRdNwa9/KyWBEwgQEFiAnQ2aX0C6qZuThYjEgW7CxLxQY3V6dOnkZSUZP2XixaSAAkEJUBBEhQLL7qZwN69e5GVlQWnixGJsRMEifghXTdXXnkluGCam//n0ne7E6AgsXsEab+uBNwkRgScUwSJ2nWzc+dOZGdn6/pOsDISIIH4EOAsm/hwZis2IKCKkYqKCseOGbFBGKIyUZ11wwXTosLHh0jAEgQoSCwRBhphNgGtGMnPzzfbHLYfBYFbb70VycnJ2LBhQxRP8xESIAGzCbDLxuwIsH3TCUi6XxbXysvLg9vEiFO6bNSXSN3r5uDBg5g6dap6mZ8kQAI2IEBBYoMg0UTjCLhZjAhVpwkS8Wn16tXYt28fnn/+ee43ZNx/HdZMAroTYJeN7khZoV0IqGLE6/W6LjNilxhFY2dRURHa2trw2muvRfM4nyEBEjCJADMkJoFns+YSUMVIeno6ysvLXftN2okZEnmzamtrMWfOHHBtEnP/n7F1EoiEAAVJJLRY1hEEZOfemTNnwu1iRILpVEEivnFtEkf8d6UTLiJAQeKiYNNVQMRIYWGhgsLNmRH1XXCyIOEAVzXK/CQBexCgILFHnGilDgQoRgZCdLIgEW9lP6Jdu3ZxgOvA0PMKCViOAAe1Wi4kNMgIAqoYaWpqwqpVq1w7ZsQItlauc/HixRzgauUA0TYS0BCgINHA4KkzCWjFiGzEJqt68nAHgWHDhmHFihV48skn0d7e7g6n6SUJ2JQABYlNA0ezwyfg8/kgmRGKkfCZOamkLHrHFVydFFH64lQCHEPi1MjSL4WAjCGoqqqiGBnkfXD6GBLV7UOHDmHatGlobm5GamqqepmfJEACFiJAQWKhYNAUfQmIGCkoKOAfoRBY3SJIBEFxcbFCYs2aNSGI8BYJkIBZBChIzCLPdg0loIqR+vp67twbgrSbBIkshjdu3DjwnQjxQvAWCZhIgILERPhs2hgCMlYkNzeXf3jCwOsmQSI41GnA27dvD4MOi5AACcSTAAe1xpM22zKcwN69eylGDKds3wa++93vKtOARbTyIAESsBYBChJrxYPWxEBAxEhWVhYzIzEwdPqjSUlJvdOAZTo4DxIgAesQoCCxTixoSQwEVDFSUVHBMSMxcHTDo7feeqviJncDdkO06aOdCFCQ2ClatDUoAa0Yyc/PD1qGF0lAJaBdLI1ZEpUKP0nAfAIUJObHgBbEQEBmThQVFUEyIxQjMYB02aOSJZHF0rZt2+Yyz+kuCViXAGfZWDc2tGwIAiJGZBXOvLw8ipEhWA12222zbLQc1Mza6dOnIWNLeJAACZhLgBkSc/mz9SgJqGLE6/VSjETJ0O2PzZgxA3PnzsWWLVvcjoL+k4AlCDBDYokw0IhICKhiJD09HeXl5dy5NxJ4/cq6OUMiKJgl6fdC8EcSMJEAMyQmwmfTkROQQYjSTUMxEjk7PjGQALMkA5nwCgmYRYAZErPIs92ICYgYKSwsVJ5jZiRifEEfcHuGRKAwSxL01eBFEog7AWZI4o6cDUZDgGIkGmp8JhwCzJKEQ4llSMB4AsyQGM+YLcRIQBUjTU1NkCW/U1JSYqyRj6sEmCHpJsEsifpG8JMEzCPADIl57NlyGAQoRsKAxCIxE1CzJDt27Ii5LlZAAiQQHQEKkui48ak4EfD5fGBmJE6wXd7MAw88oOwGLCKYBwmQQPwJUJDEnzlbDJOAbBVfVVXFbpowebFYbARuuukmpQLucRMbRz5NAtES4BiSaMnxOUMJiBgpKChAc3MzUlNTDW3LzZVzDMnF0ZcxSk8++STeeustrm9zMRr+RAKGE2CGxHDEbCBSAqoYqa+vpxiJFB7Lx0RA3Qn4wIEDMdXDh0mABCInQEESOTM+YSAB+YYqmRERIzLQkAcJxJOA7AQseyOVlpbGs1m2RQIkAIBdNnwNLENAnXpJMRK/kLDLZiDr9vZ2jB49mqJ4IBpeIQFDCTBDYiheh1fur8HChATIH7Xk5XtwtsuPxk3LMSshE8v3nIrIeYqRiHCxsIEEZOffiooKvPzyywa2wqpJgAT6E7ik/wX+TAJhE/DkYNOZ3bhqcjEwJwX/u3EH2ieMx6WeG3B92siwq1HFiPwRYDdN2NhY0EAC2dnZSEtLw5IlSziOyUDOrJoEtAQoSLQ0eB4hgS6cbdiFzf7RuGvnRvx2QTGKMkbhG23hV6MVI/n5+eE/yJIkYCABmdklYqS2tpaCxEDOrJoEtATYZaOlwfMICXyOvxw/Cj8O48DYebg3Y1REz7e2tqKoqEhJj1OMRISOheNA4J577lEGWMuYEh4kQALGE6AgMZ6xc1voOo76F+sBzz14/AeZGBGBpyJGcnJylBkNFCMRgGPRuBGQ7sPp06ejrq4ubm2yIRJwMwEKEjdHP1bfO9rQfBjIfiIP3pHhv0qqGPF6vaAYiTUIfN5IAitWrFBWCzayDdZNAiTQTSD8vyIkRgIXEVDHj2ThzqwJCPdFUsVIeno6SkpKLqqRP5CA1QiIaJbZNjLWiQcJkICxBML9O2KsFazdhgR6xo94JmHCVZeGZb9sWibdNCJGysvLuTR3WNRYyEwCMgX4Rz/6EacAmxkEtu0aAlwYzTWhNtdRESOFhYWKERQj5sZC2zoXRtPSCH7e0tKiTAE+ffo0RKDwIAESMIYAMyTGcGWtGgIUIxoYPLUdAZkCPHfuXOzYscN2ttNgErATAQoSO0XLhraqYqSpqQmrVq1iN40NY0iTgQceeACy6SMPEiAB4wiwy8Y4tq6vWStGZNO8lJQU1zOxGgB22YQXEXmXhw8fzv1twsPFUiQQFQFmSKLCxofCIeDz+SCZEYqRcGixjJUJyC7AMrj1rbfesrKZtI0EbE2AGRJbh8+6xkt6u6qqimLEuiFSLGOGJPwAHTp0CNOmTQMHt4bPjCVJIBICzJBEQotlwyIgYqSgoADPPfccu2nCIsZCdiAwdepUZXArV261Q7Roox0JUJDYMWoWtlkVI/X19dyUzMJxomnREZB1dCTzx4MESEB/AtDfXBUAABjoSURBVOyy0Z+pa2uUsSK5ubkc+GejN4BdNpEFS1YaHjduHD766CNm/yJDx9IkMCQBZkiGRMQC4RCQpbUpRsIhxTJ2JiAzxZYsWYLt27fb2Q3aTgKWJEBBYsmw2MsoESNZWVnMjNgrbLQ2SgLz589nt02U7PgYCYQiQEESig7vDUlAFSMVFRWQ7dp5kIDTCWRmZmL//v2QWTc8SIAE9CNAQaIfS9fVpBUj+fn5rvOfDruTgLrhngzc5kECJKAfAQ5q1Y+lq2qSwX0y4yAvLw8UI/YNPQe1Rhc7VYyfP3+e2yFEh5BPkcAAAsyQDEDCC0MRoBgZihDvO53A17/+dcXFAwcOON1V+kcCcSNAQRI31M5oSBUjXq+XmRFnhJReREGAS8lHAY2PkMAQBNhlMwQg3u4joIqR9PR0lJeXM1Xdh8a2Z+yyiT507LaJnh2fJIFgBJghCUaF1wYQkN1OZcwIxcgANLzgUgLstnFp4Om2YQQoSAxD65yKRYwUFhZSjDgnpPREBwLsttEBIqsgAQ0BdtloYPB0IAFVjMgddtMM5GP3K+yyiS2CardNIBCIrSI+TQIkAAoSvgSDElDFSFNTE2SfGlk2m4ezCFCQxBZP+T8yfPhwHDx4ELIbMA8SIIHoCbDLJnp2jn6SYsTR4aVzOhGQbptly5Yp2yboVCWrIQHXEqAgcW3oQzvu8/nAzEhoRrxLAkLglltu4d42fBVIQAcC7LLRAaLTqli/fr3yC5bdNE6L7EB/2GUzkEmkV9rb2zF69Gg0NzcjNTU10sdZngRIoIfAJSRBAloCIkYKCgqUX64cM6Ilw3MSCE5A9rZZsmQJ3nnnHQqS4Ih4lQTCIsAum7AwuaOQKkZk0zB+03NHzOmlPgRuuukmZeC3PrWxFhJwJwF22bgz7gO8lu6Z3NxcZXDejBkzBtznBWcSYJeNPnGVVYzHjRuH06dPQzImPEiABCInwAxJ5Mwc94SspUAx4riw0qE4EpDuzenTp6OhoSGOrbIpEnAWAQoSZ8UzYm/UhZ2km4aZkYjx8QES6CWQl5dHQdJLgyckEDkBCpLImTnmCVWMVFRUUIw4Jqp0xCwC06ZNw6OPPmpW82yXBGxPgILE9iGMzgGtGMnPz4+uEj5FAiTQS0DdbK+lpaX3Gk9IgATCJ0BBEj4rx5SUAXhFRUWQzAjFiGPCSkdMJiCrtqrTf002hc2TgC0JUJDYMmzRGy1iJCcnB9LfTTESPUc+SQLBCMj039/97nfBbvEaCZDAEAQ47XcIQE66rYoRr9eLNWvWOMk1+hIlAU77jRLcII9Jd01aWhrOnz8PyZjwIAESCJ8AMyThs7J1SVWMpKeno6SkxNa+0HgSsCoBdUHBAwcOWNVE2kUCliVAQWLZ0OhnmOzcK900IkbKy8v5zU0/tKyJBAYQkN1/Dx48OOA6L5AACYQmQEESmo/t74oYKSwspBixfSTpgF0I3HDDDdi1a5ddzKWdJGAZAhxDYplQ6G+IKkakZmZG9OfrhBo5hkT/KKrjSLiMvP5sWaOzCTBD4tD4qmKkqakJq1atYjeNQ+NMt6xHQB1H8v7771vPOFpEAhYmQEFi4eBEa5pWjMimebLPBg8SIIH4EeA4kvixZkvOIUBB4pxY9nri8/kgmRGKkV4kPCGBuBLgOJK44mZjDiHAMSQOCaTqxvr161FVVUUxogLhZ0gCHEMSEk/UN9VxJFyPJGqEfNCFBChIHBR0ESMFBQVobm6G2o/tIPfoigEEKEgMgNpTpbCV6b9Tp041rhHWTAIOIsAuG4cEUxUj9fX1FCMOiSndsDcBGUfy3nvv2dsJWk8CcSRAQRJH2EY1JWNFJDMiYmTGjBlGNcN6SYAEIiAwZcoUHDlyJIInWJQE3E2AXTY2j//evXuRlZVFMWLzOJplPrtsjCN/6NAhTJs2DYFAwLhGWDMJOIgAMyQ2DibFiI2DR9MdT2D8+PGKjzLAlQcJkMDQBChIhmZkyRKqGKmoqGA3jSUjRKPcTiApKQlz587F8ePH3Y6C/pNAWAQoSMLCZK1CWjGSn59vLeNoDQmQQC+B6667Dg0NDb0/84QESGBwAhQkg7Ox5J3W1lYUFRVBMiMUI5YMEY0igV4CmZmZ2LdvX+/PPCEBEhicAAe1Ds7GcndEjOTk5CAvL49ixHLRsadBHNRqbNy4QJqxfFm7swgwQ2KTeKpixOv1UozYJGY0kwTUBQplsUIeJEACoQlQkITmY4m7qhhJT09HSUmJJWyiESRAAuERWLJkCY4dOxZeYZYiARcToCCxePBl517pphExUl5ejmHDhlncYppHAiSgJSD/d9955x3tJZ6TAAkEIUBBEgSKVS6JGCksLKQYsUpAaAcJREFAum3q6uqieJKPkIC7CFCQWDTeqhgR85gZsWiQaBYJhEFgwoQJ2L9/P+T/NA8SIIHBCXCWzeBsTLujipGmpibIPjUpKSmm2cKGnU2As2ziE1/hzF2448OardiXADMkFosdxYjFAkJzSEAHAjKwlRvt6QCSVTiaAAWJxcLr8/nAzIjFgkJzSCBGAv/8z/+MDz74IMZa+DgJOJsABYmF4rt+/XpUVVWxm8ZCMaEpJKAHgcmTJ+NPf/qTHlWxDhJwLAGOIbFIaEWMFBQUsJ/ZIvFwixkcQxKfSKsrtgYCgfg0yFZIwIYEmCGxQNBUMVJfXw91ZUcLmEUTSIAEdCIwZswYpSYRJjxIgASCE6AgCc4lbldlFo1kRkSMzJgxI27tsiESIIH4EUhKSsL06dNx8uTJ+DXKlkjAZgQoSEwM2N69e5Gbm0sxYmIM2DQJxIuA7EN14sSJeDXHdkjAdgQoSEwKmYiRrKwsihGT+LNZEog3gSlTpnAJ+XhDZ3u2IkBBYkK4VDFSUVHBbhoT+LNJEjCDwFVXXQWOITGDPNu0CwHOsolzpLRiJD8/P86tszkSuJgAZ9lczMPInzjTxki6rNsJBChI4hjF1tZWZefevLw8UIzEETybGpQABcmgaHS/IaswDx8+nFP7dSfLCp1CgF02cYokxUicQLMZErAogWHDhnGmjUVjQ7OsQYCCJA5xUMWIjLJnZiQOwNkECViUAGfaWDQwNMsSBChIDA6DKkbS09NRUlJicGusngRIwMoExo8fz5k2Vg4QbTOVAAWJgfilzzgnJwciRsrLyyEpWx4kQALuJZCcnIxPPvnEvQDoOQmEIMBBrSHgxHJLxEhhYaFSBcVILCT5rJEEOKjVSLoD6+ZMm4FMeIUEVALMkKgkdPykGNERJqsiAQcRkFk2crS3tzvIK7pCAvoQuESfaliLSkAVI01NTZB9athNo5LhJwmQQEpKigLh1KlTkP1teJAACfQRYIakj0XMZ/3FiPrLJ+aKWQEJkIBjCMydOxfHjx93jD90hAT0IsAMiV4kATz66KM4ePAgtm/fDooRHcGyKhJwEIHU1FR0dHQ4yCO6QgL6EGCGRB+OWLBgAdatWwf5ZTN69GidamU1JEACTiPATfacFlH6oxcBChIdSIoY2bZtG3w+H44eParMrpHuGx4kQAIk0J/AiBEjOPW3PxT+TAIAKEhifA1UMfL0009j0aJFykBWGdAq2RIeJEACJNCfwMSJE/Hss8/2v8yfScD1BChIYngFiouLlcyIiJH77rtPqUnGjsjsGhlHsn79+hhq56MkQAJOJKBO/WUW1YnRpU+xEODCaFHS27BhA+6//35oxYi2qkOHDmHatGnYtGkTZHdfHiRgRQJcGC3+UREhwl1/48+dLVqfADMkUcRoKDEiVU6dOhX19fVYuHAh9u7dG0UrfIQESMCJBNS1ic6fP+9E9+gTCURNgIIkQnSqGJk/f35vN81gVcyYMUPJkGRlZUE22eNBAiRAAkJgyZIlOHbsGGGQAAloCFCQaGAMdaoVI1u3bh2quHJfumuWLVuG/Px8sM84LGQsRAKOJ3DllVdyLRLHR5kORkqAgiRMYvv378fSpUshmZFwxYhadUlJCdra2jjzRgXCTxJwOQFZi+TIkSMup0D3SeBiAlyp9WIeQX8SMTJr1izcdtttEYsRqVD6jJ977jmkpaUhMzMT2dnZQdvhRRIgAXcQkLVIeJAACVxMgLNsLuYx4CdVjHz1q1/Fu+++O+B+JBeqqqqUqcCvv/46N9aKBBzLGkaAs2wMQxuyYnUWXiAQCFmON0nATQTYZRMi2qoYkbVFXnvttRAlw7sl40nS09Px5JNPhvcAS5EACTiSgLoWiSOdo1MkECUBZkgGAdfe3o7x48crm+S9/fbbumU0WlpalK4bmRIss3B4kICZBJghMYe+/H6RPa8++ugjbsRpTgjYqgUJMEMSJCjyy+LGG2/UXYxIU7L5niyWVlRUxFk3QdjzEgm4gUBSUpLiJtcicUO06WO4BChI+pFSxYhc1jMzom1GZurIIRvy8SABEnAvgZMnT7rXeXpOAv0IUJBogKhiRBYx27x5s27dNJomlFOZdSOb78kqrtImDxIgAfcRkPWJTpw44T7H6TEJDEKAgqQHjFaMvPnmm5g+ffogyPS5LONH5s6diy1btuhTIWshARIgARIgARsToCDpCZ7s1iuZkXiIEfV9kW9IBQUFzJKoQPhJAi4iIIujvfPOOy7ymK6SQGgCFCQAFixYgFdffTWuYkTCwixJ6JeTd0nAyQS4OJqTo0vfoiHgekEiYkQGl9bU1BjeTRMsQMySBKPCayTgDgKyDAAPEiCBbgKuFiSqGHn66adNW85dzZLs2LGD7yQJkICLCEiXzcsvv+wij+kqCYQm4FpBUlxcrGRGRIzI+BEzjwceeEBZUp67AZsZBbZNAiRAAiRgJgFXCpINGzagtLQU0YmRLnS07ETZwmshq1wmJC/Eun1+dMUQxZtuugmyTP2BAwdiqIWPkgAJ2InAmDFjFHNlMD0PEiABwHWCRMTI/fffH70Y+WAzHvQuxeGpG9DW+QkaHj6Nh5e/gIMd0UsSWZekoqICGzdu5DtJAiTgEgJcrdUlgaabYRNwlSBRxYislBpVN01HAzbcvxJv3FqC1Q/NgCdxFNJneXFN3e/R1PZ52NCDFczOzsazzz7LKcDB4PAaCZAACZCA4wm4RpBoxcjWrVujCOynaNzwn1hWl4Unlt+GqxVyXTh/ph3ncRLt5y5EUWffI7LHjSyU1tDQ0HeRZyRAAo4mIP/njxw54mgf6RwJhEvAFYJExmcsXboUkhmJTowAXR/vwc/W/gae4vvwndTLevh+jr8cPwo/xiLp8kvCZT5ouZycHO5vMygd3lAJKGOXZPySDv/UOvlpDgH5IsKDBEigm4DjBYmIkVmzZuG2226LWowAn+HozhdQ6c/A3XO+hpG9b08HWpuPAZ5JmHDVpb1Xoz254YYb2G0TLTyXPRcIBKDHP5dho7skQAIWJuBoQaKKka9+9asxiBEAXcdR/2I9gEasuXms5pvpWNy8phGeu29B5sjYUcq3JdlDh902Fv4fQ9NIQEcC48ePxwcffKBjjayKBOxLIPa/ohb1XRUjKSkpeO2112KzsqMNzYf9QLYPzZ1930w7m33IRv+sSWxNzZs3j4IkNoR8mgRsQyA5ORmffvqpbeyloSRgJAFHChLZuVe6aUSMvP3221Cn10UL8sL/HkC134PsO2/EpF5ip1Dn+xlqPdmYk5kUbdUDnps5cya2b98+4DovkAAJkAAJkICTCfT+eXWKkyJGbrzxRt3ECKDOpEnDN9JTehdu6fr4t/jV5jZ4H56H63TorlH5f+UrX1EWSeNiSSoRfpKAcwnIBnvcz8a58aVnkRFwlCBRxYgg0CMz0o0yEcOvSMLwi2bSfIqDz1eiMm0Zyu7LxIjImIcsLdkcGUfyhz/8IWQ53iQBErA/gQkTJnA/G/uHkR7oRMAxgkQVI5JZ2Lx5c8zdNFq+l/zL15HrqcfmX7+HDpxFS80aLF37JfieXoyMEfoj9Hq9/NakDQDPSYAESIAEHE9A/7+mJiDTipE333xTyTDoasZILx7f82OMX3s9Lk+4At6Xx+KRunVYNLlvArCe7cn03z//+c96Vsm6SIAESIAESMDSBBICspiBzY8FCxbg1VdfhSFixAQ2hw4dwrRp05R1Jkxonk1anIAsiKbXf1s967I4NkuaJzt8Dx8+HM3NzeAiaZYMEY2KIwHbZ0icJkYk9vILSg7J/PAgARJwLgHZWJMHCZBANwFbCxIRI9u2bUNNTY3+3TQmviHqN6VTp06ZaAWbJgESIAESIIH4EbCtIFHFyNNPPw3ZKddph8y0OXnypNPcoj8kQAJBCJw/fz7IVV4iAXcRsKUgKS4uVjIjIkbuu+8+R0ZMZtqcOHHCkb7RKRIggT4CS5YswbFjx/ou8IwEXErAdoJkw4YNKC0thZPFiEvfRbpNAq4kcOWVV7rSbzpNAv0J2EqQiBi5//77XSFGuOlW/1eVP5MACZAACTiZgG0EiSpG5s+f79huGu2Lxk23tDR4TgIkQAIk4HQCthAkWjGydetWp8eE/pEACbiIALOhLgo2XQ1JwPKCZP/+/Vi6dCkkM0IxEjKWvEkCJGBDAsyG2jBoNNkQApcYUqtOlYoYmTVrFv7617/iww8/xPXXX69TzdavRhZFk432ZEYRDxLoT0DP90LPuvrbyZ+HJiC7/aprDw1dmiVIwLkELL10vHTVuHk63KhRozB58mTnvn30jARIQCEwceJETJ06lTRIwNUE4iJIuvyNeOW1rfjvxWtQp+CegrzSEhR+71vI8Fzq6gDQeRIgARIYikDXxzW4d/oLmFFXhUWplw1VnPdJwJYEDB5D8jn8e0pwc/IjePsLudjSGVA2BQucq8bCpHexNPkOPLLnY3TZEh2NJgESIIF4EPgMR3e+gEp/PV6sP87fl/FAzjZMIWBghqQLHY0/xR2ZlZhYvQPP5HwZF6ufT9FY9n1kLgNKG57D0oxRpgBgoyRAAiRgaQId+1D20GvAqFew7MgDaH5tEVIv/mVqafNpHAmES8C417qrBVsfKUWd5w5875Zx/cSImDcKGT94GMWe32Dtz/bgY6ZJwo0Zy5EACbiGQBfO7tuBuhnzseT2bHhqfwZfHTfddE34XeaoYYKk6+jbeLHWD8/dtyBz5CDNjEhG2rUe+CtfwM6jn7kMPd0lARIggSEIdLXgpbXAw9+ZjFGZt+BuTyM273wPZ4d4jLdJwI4EBlEKsbrShY7Wozg8VDWJYzBhajKAY2hu7RiqNO+TAAnoQuBz+BtfxUtlC5GckIAE+TdrOSpfboT/QgtefrmF4xR04Rx7JV1H38Ve77dwnXypG3kjFj8xH/7Nu9Bwlinl2OmyBqsRMEiQWM1N2kMCJKAQ6PJj37p7kXHHizg+sRCN6kDz3f8H6Z1vYsV4L352mn/srPG2nEKd7/eY8e2vYYRi0GWYlPVNZPtfwa92fUTRaI0g0QodCRgkSBIxImUSrh3K0K5TOH6oDfBkY05m0lCleZ8ESCAmAp/j4+0/wryHT+PhV36KpTkZ8Ki/ARI9yMh5GE+9sgxobgPzlTGB1ufhs+9h5+afY3HasO4sVkICvpC2GLU4gsqf78ZR6kZ9OLMWyxBQfx3pblDipBtxZ7YndHqxow3Nh4cYZ6K7ZayQBFxK4Gw9yvOfAoofxg+CzmpLxIiMu7Hy+uEuBWQltz9Dy0tbgedOdi+VEOhZMiHwd7RWPwhP7euo57g7KwWMtuhAwDBBgsRULFi9DN5B04uf4+NdNdiMB7G+MAsjdXCGVZAACQxGQP7AbcAavwfXpiX3dAEEKzsG3pwb+P8xGJp4Xut4D7/e+29Y7B3Tr9VLcfUtObjbwzVJ+oHhjw4gYJwggXzbWoyfV9+BY7k/wMpN++BXU4wdLXij7F5Mzz+HZdsfxbyruVqrA94lumBpAh1obT4GIBlTJ4wJMg3f0sa7y7iuj7Fn9eNYO2Ycrgr2G1qZnQjULn4Ij3FhSXe9Gw73NtjrrqPLI5Ga8wReaV6J6SefQsYXekb0X16AXUnz8UrjMyi6zsNfjjoSZ1UkQAI2JtD1ASpvnY6bf1wL/5qbccWcSrSoX+TELeX+bCyu9QOoxY9vTkHK8j2cBmzjkNP0PgIGrtTa1wjPSIAEzCbwGVoq85C2+BiKd7+On8zu3xVgtn1snwRIwO0EDM6QuB0v/ScBqxDomTIKLqxllYjQDhIggYsJUJBczIM/kYBjCSSmfhvLizPgX7MWv2j8NLifXX401rVw2m9wOrxKAiRgIAEKEgPhsmoSsBaBMZj9+Eb48j7Essw7sbxyD1o61AEKXeho2YNNGxvxxcxJIWbhWMsjWkMCJOAcAhQkzoklPSGBoQmMmIJFv6xFw/bvAJu/j7TLv9CzdPxKbH3/CmTf8y1MHsFfC0ODZAkSIAG9CXBQq95EWR8JkAAJkAAJkEDEBPhVKGJkfIAESIAESIAESEBvAhQkehNlfSRAAiRAAiRAAhEToCCJGBkfIAESIAESIAES0JsABYneRFkfCZAACZAACZBAxAT+Py3Axv2/tF4lAAAAAElFTkSuQmCC"></p>
<p>The angle AOB is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\theta ">
<mi>θ<!-- θ --></mi>
</math></span> radians, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 < \theta < \frac{\pi }{2}">
<mn>0</mn>
<mo><</mo>
<mi>θ<!-- θ --></mi>
<mo><</mo>
<mfrac>
<mi>π<!-- π --></mi>
<mn>2</mn>
</mfrac>
</math></span>.</p>
<p>The point C lies on OA and OA is perpendicular to BC.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{OC}} = r\,{\text{cos}}\,\theta "> <mrow> <mtext>OC</mtext> </mrow> <mo>=</mo> <mi>r</mi> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of triangle OBC in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span> and <em>θ</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>Given that the area of triangle OBC is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{5}"> <mfrac> <mn>3</mn> <mn>5</mn> </mfrac> </math></span> of the area of sector OAB, find <em>θ</em>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{cos}}\,\theta = \frac{{{\text{OC}}}}{r}"> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mtext>OC</mtext> </mrow> </mrow> <mi>r</mi> </mfrac> </math></span> <em><strong>A1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{OC}} = r\,{\text{cos}}\,\theta "> <mrow> <mtext>OC</mtext> </mrow> <mo>=</mo> <mi>r</mi> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> </math></span> <em><strong>AG N0</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>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}{\text{OC}} \times {\text{OB}}\,{\text{sin}}\,\theta "> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <mtext>OC</mtext> </mrow> <mo>×</mo> <mrow> <mtext>OB</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>sin</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> </math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{BC}} = r\,{\text{sin}}\,\theta "> <mrow> <mtext>BC</mtext> </mrow> <mo>=</mo> <mi>r</mi> <mspace width="thinmathspace"></mspace> <mrow> <mtext>sin</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}r\,{\text{cos}}\,\theta \times {\text{BC}}"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mi>r</mi> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> <mo>×</mo> <mrow> <mtext>BC</mtext> </mrow> </math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}r\,{\text{sin}}\,\theta \times {\text{OC}}"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mi>r</mi> <mspace width="thinmathspace"></mspace> <mrow> <mtext>sin</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> <mo>×</mo> <mrow> <mtext>OC</mtext> </mrow> </math></span></p>
<p>area <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{1}{2}{r^2}\,{\text{sin}}\,\theta \,{\text{cos}}\,\theta "> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>sin</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> </math></span> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( { = \frac{1}{4}{r^2}\,{\text{sin}}\left( {2\theta } \right)} \right)"> <mrow> <mo>(</mo> <mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>sin</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mi>θ</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </math></span> (must be in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span> and <em>θ) </em> <em><strong>A1 N2</strong></em></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>valid attempt to express the relationship between the areas (seen anywhere) <em><strong>(M1)</strong></em></p>
<p><em>eg</em> OCB = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{5}"> <mfrac> <mn>3</mn> <mn>5</mn> </mfrac> </math></span>OBA , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}{r^2}\,{\text{sin}}\,\theta \,{\text{cos}}\,\theta = \frac{3}{5} \times \frac{1}{2}{r^2}\theta "> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>sin</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> <mo>=</mo> <mfrac> <mn>3</mn> <mn>5</mn> </mfrac> <mo>×</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mi>θ</mi> </math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{4}{r^2}\,{\text{sin}}\,2\theta = \frac{3}{{10}}{r^2}\theta "> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>sin</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mn>2</mn> <mi>θ</mi> <mo>=</mo> <mfrac> <mn>3</mn> <mrow> <mn>10</mn> </mrow> </mfrac> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mi>θ</mi> </math></span></p>
<p>correct equation in terms of <em>θ</em> only<em> </em> <em><strong>A1</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{sin}}\,\theta \,{\text{cos}}\,\theta = \frac{3}{5}\theta "> <mrow> <mtext>sin</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mi>θ</mi> <mo>=</mo> <mfrac> <mn>3</mn> <mn>5</mn> </mfrac> <mi>θ</mi> </math></span> , <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{4}{\text{sin}}\,2\theta = \frac{3}{{10}}\theta "> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> <mrow> <mtext>sin</mtext> </mrow> <mspace width="thinmathspace"></mspace> <mn>2</mn> <mi>θ</mi> <mo>=</mo> <mfrac> <mn>3</mn> <mrow> <mn>10</mn> </mrow> </mfrac> <mi>θ</mi> </math></span></p>
<p>valid attempt to solve <strong>their</strong> equation <em><strong>(M1)</strong></em></p>
<p><em>eg </em>sketch, −0.830017, 0</p>
<p>0.830017</p>
<p><em>θ </em>= 0.830<em> </em> <em><strong>A1 N2</strong></em></p>
<p><strong>Note:</strong> Do not award final <em><strong>A1</strong></em> if additional answers given.</p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</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>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = x{{\text{e}}^{ - x}}">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>x</mi>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mo>−<!-- − --></mo>
<mi>x</mi>
</mrow>
</msup>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x) = - 3f(x) + 1">
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mn>3</mn>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mn>1</mn>
</math></span>.</p>
<p>The graphs of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> intersect at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = p">
<mi>x</mi>
<mo>=</mo>
<mi>p</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = q">
<mi>x</mi>
<mo>=</mo>
<mi>q</mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p < q">
<mi>p</mi>
<mo><</mo>
<mi>q</mi>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
<mi>p</mi>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
<mi>q</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the area of the region enclosed by the graphs of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>valid attempt to find the intersection <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f = g">
<mi>f</mi>
<mo>=</mo>
<mi>g</mi>
</math></span>, sketch, one correct answer</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = 0.357402,{\text{ }}q = 2.15329">
<mi>p</mi>
<mo>=</mo>
<mn>0.357402</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>q</mi>
<mo>=</mo>
<mn>2.15329</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p = 0.357,{\text{ }}q = 2.15">
<mi>p</mi>
<mo>=</mo>
<mn>0.357</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mi>q</mi>
<mo>=</mo>
<mn>2.15</mn>
</math></span> <strong><em>A1A1 N3</em></strong></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>attempt to set up an integral involving subtraction (in any order) <strong><em>(M1)</em></strong></p>
<p><em>eg</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,">
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_p^q {\left[ {f(x) - g(x)} \right]{\text{d}}x,{\text{ }}} \int_p^q {f(x){\text{d}}x - } \int_p^q {g(x){\text{d}}x} ">
<msubsup>
<mo>∫</mo>
<mi>p</mi>
<mi>q</mi>
</msubsup>
<mrow>
<mrow>
<mo>[</mo>
<mrow>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>−</mo>
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</mrow>
<mo>]</mo>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
</mrow>
<msubsup>
<mo>∫</mo>
<mi>p</mi>
<mi>q</mi>
</msubsup>
<mrow>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
<mo>−</mo>
</mrow>
<msubsup>
<mo>∫</mo>
<mi>p</mi>
<mi>q</mi>
</msubsup>
<mrow>
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mrow>
<mtext>d</mtext>
</mrow>
<mi>x</mi>
</mrow>
</math></span></p>
<p>0.537667</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{area}} = 0.538">
<mrow>
<mtext>area</mtext>
</mrow>
<mo>=</mo>
<mn>0.538</mn>
</math></span> <strong><em>A2 N3</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = x - 8">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mn>8</mn>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right) = {x^4} - 3">
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>4</mn>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mn>3</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h\left( x \right) = f\left( {g\left( x \right)} \right)">
<mi>h</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h\left( x \right)"> <mi>h</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{C}}"> <mrow> <mtext>C</mtext> </mrow> </math></span> be a point on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span>. The tangent to the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{C}}"> <mrow> <mtext>C</mtext> </mrow> </math></span> is parallel to the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span>.</p>
<p>Find the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-coordinate of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{C}}"> <mrow> <mtext>C</mtext> </mrow> </math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>attempt to form composite (in any order) <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( {{x^4} - 3} \right)"> <mi>f</mi> <mrow> <mo>(</mo> <mrow> <mrow> <msup> <mi>x</mi> <mn>4</mn> </msup> </mrow> <mo>−</mo> <mn>3</mn> </mrow> <mo>)</mo> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\left( {x - 8} \right)^4} - 3"> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mi>x</mi> <mo>−</mo> <mn>8</mn> </mrow> <mo>)</mo> </mrow> <mn>4</mn> </msup> </mrow> <mo>−</mo> <mn>3</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h\left( x \right) = {x^4} - 11"> <mi>h</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <msup> <mi>x</mi> <mn>4</mn> </msup> </mrow> <mo>−</mo> <mn>11</mn> </math></span> <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing that the gradient of the tangent is the derivative <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{h'}"> <mrow> <msup> <mi>h</mi> <mo>′</mo> </msup> </mrow> </math></span></p>
<p>correct derivative (seen anywhere) <em><strong>(A1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h'\left( x \right) = 4{x^3}"> <msup> <mi>h</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>4</mn> <mrow> <msup> <mi>x</mi> <mn>3</mn> </msup> </mrow> </math></span></p>
<p>correct value for gradient of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> (seen anywhere) <em><strong>(A1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'\left( x \right) = 1"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>1</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m = 1"> <mi>m</mi> <mo>=</mo> <mn>1</mn> </math></span></p>
<p>setting <strong>their</strong> derivative equal to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1"> <mn>1</mn> </math></span> <em><strong>(M1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="4{x^3} = 1"> <mn>4</mn> <mrow> <msup> <mi>x</mi> <mn>3</mn> </msup> </mrow> <mo>=</mo> <mn>1</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.629960"> <mn>0.629960</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = \sqrt[3]{{\frac{1}{4}}}"> <mi>x</mi> <mo>=</mo> <mroot> <mrow> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> <mn>3</mn> </mroot> </math></span> (exact), <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.630"> <mn>0.630</mn> </math></span> <em><strong>A1 N3</strong></em></p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> defined by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>90</mn><msup><mtext>e</mtext><mrow><mo>-</mo><mn>0</mn><mo>.</mo><mn>5</mn><mi>x</mi></mrow></msup></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>∈</mo><msup><mi mathvariant="normal">ℝ</mi><mo>+</mo></msup></math>.</p>
<p>The graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>x</mi></math> intersect at point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math>.</p>
</div>
<div class="specification">
<p>The line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> has a gradient of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math> and is a tangent to the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> at the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Q</mtext></math>.</p>
</div>
<div class="specification">
<p>The shaded region <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> is enclosed by the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and the lines <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>x</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-coordinate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the exact coordinates of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Q</mtext></math>.</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>Show that the equation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo> </mo><mi>ln</mi><mo> </mo><mn>45</mn><mo>+</mo><mn>2</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-coordinate of the point where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> intersects the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>x</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the area of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> is tangent to the graphs of both <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and the inverse function <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>.</p>
<p style="text-align:center;"><img src="data:image/png;base64,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"></p>
<p>Find the shaded area enclosed by the graphs of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> and the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>Attempt to find the point of intersection of the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>x</mi></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>5</mn><mo>.</mo><mn>56619</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>5</mn><mo>.</mo><mn>57</mn></math> <em><strong>A1</strong></em></p>
<p> </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><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>-</mo><mn>45</mn><msup><mtext>e</mtext><mrow><mo>-</mo><mn>0</mn><mo>.</mo><mn>5</mn><mi>x</mi></mrow></msup></math> <em><strong>A1</strong></em></p>
<p>attempt to set the gradient of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>45</mn><msup><mtext>e</mtext><mrow><mo>-</mo><mn>0</mn><mo>.</mo><mn>5</mn><mi>x</mi></mrow></msup><mo>=</mo><mo>-1</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Q</mtext></math> has coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo> </mo><mi>ln</mi><mo> </mo><mn>45</mn><mo>,</mo><mo> </mo><mn>2</mn></mrow></mfenced></math> (accept (<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo> </mo><mi>ln</mi><mo> </mo><mfrac><mn>1</mn><mn>45</mn></mfrac><mo>,</mo><mo> </mo><mn>2</mn></math>) <em><strong>A1</strong></em><em><strong>A1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>A1</strong></em> for each value, even if the answer is not given as a coordinate pair.</p>
<p style="padding-left:30px;"> Do not accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>ln</mi><mo> </mo><mfrac><mn>1</mn><mn>45</mn></mfrac></mrow><mrow><mo>-</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></mfrac></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>ln</mi><mo> </mo><mn>45</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>5</mn></mrow></mfrac></math> as a final value for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>. Do not accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>0</mn></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>00</mn></math> as a final value for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>.</p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to substitute coordinates of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Q</mtext></math> (in any order) into an appropriate equation <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>-</mo><mn>2</mn><mo>=</mo><mo>-</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn><mo> </mo><mi>ln</mi><mo> </mo><mn>45</mn></mrow></mfenced></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>=</mo><mo>-</mo><mn>2</mn><mo> </mo><mi>ln</mi><mo> </mo><mn>45</mn><mo>+</mo><mi>c</mi></math> <em><strong>A1</strong></em></p>
<p>equation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo> </mo><mi>ln</mi><mo> </mo><mn>45</mn><mo>+</mo><mn>2</mn></math> <em><strong>AG</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>ln</mi><mo> </mo><mn>45</mn><mo>+</mo><mn>1</mn><mfenced><mrow><mo>=</mo><mn>4</mn><mo>.</mo><mn>81</mn></mrow></mfenced></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>appropriate method to find the sum of two areas using integrals of the difference of two functions <em><strong>(M1)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Allow absence of incorrect limits.</p>
<p> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mo>∫</mo><mrow><mn>4</mn><mo>.</mo><mn>806</mn><mo>…</mo></mrow><mrow><mn>5</mn><mo>.</mo><mn>566</mn><mo>…</mo></mrow></msubsup><mfenced><mrow><mi>x</mi><mo>-</mo><mfenced><mrow><mo>-</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo> </mo><mi>ln</mi><mo> </mo><mn>45</mn><mo>+</mo><mn>2</mn></mrow></mfenced></mrow></mfenced><mo>d</mo><mi>x</mi><mo>+</mo><msubsup><mo>∫</mo><mrow><mn>5</mn><mo>.</mo><mn>566</mn><mo>…</mo></mrow><mrow><mn>7</mn><mo>.</mo><mn>613</mn><mo>…</mo></mrow></msubsup><mfenced><mrow><mn>90</mn><msup><mtext>e</mtext><mrow><mo>-</mo><mn>0</mn><mo>.</mo><mn>5</mn><mi>x</mi></mrow></msup><mo>-</mo><mfenced><mrow><mo>-</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo> </mo><mi>ln</mi><mo> </mo><mn>45</mn><mo>+</mo><mn>2</mn></mrow></mfenced></mrow></mfenced><mo>d</mo><mi>x</mi></math> <em><strong>(A1)(A1)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>A1</strong></em> for one correct integral expression including correct limits and integrand.<br> Award <em><strong>A1</strong></em> for a second correct integral expression including correct limits and integrand.</p>
<p> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1</mn><mo>.</mo><mn>52196</mn><mo>…</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1</mn><mo>.</mo><mn>52</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>by symmetry <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>52</mn><mo>…</mo></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>3</mn><mo>.</mo><mn>04</mn></math> <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Accept any answer that rounds to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>0</mn></math> (but do not accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math>).</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = \ln x">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>ln</mi>
<mo><!-- --></mo>
<mi>x</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x) = 3 + \ln \left( {\frac{x}{2}} \right)">
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>3</mn>
<mo>+</mo>
<mi>ln</mi>
<mo><!-- --></mo>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mi>x</mi>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x > 0">
<mi>x</mi>
<mo>></mo>
<mn>0</mn>
</math></span>.</p>
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
<mi>g</mi>
</math></span> can be obtained from the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span> by two transformations:</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="\begin{array}{*{20}{l}} {{\text{a horizontal stretch of scale factor }}q{\text{ followed by}}} \\ {{\text{a translation of }}\left( {\begin{array}{*{20}{c}} h \\ k \end{array}} \right).} \end{array}">
<mtable columnalign="left" rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mrow>
<mtext>a horizontal stretch of scale factor </mtext>
</mrow>
<mi>q</mi>
<mrow>
<mtext> followed by</mtext>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mrow>
<mtext>a translation of </mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mi>h</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>k</mi>
</mtd>
</mtr>
</mtable>
</mrow>
<mo>)</mo>
</mrow>
<mo>.</mo>
</mrow>
</mtd>
</mtr>
</mtable>
</math></span></p>
</div>
<div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h(x) = g(x) \times \cos (0.1x)">
<mi>h</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>×<!-- × --></mo>
<mi>cos</mi>
<mo><!-- --></mo>
<mo stretchy="false">(</mo>
<mn>0.1</mn>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 < x < 4">
<mn>0</mn>
<mo><</mo>
<mi>x</mi>
<mo><</mo>
<mn>4</mn>
</math></span>. The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span> and the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = x">
<mi>y</mi>
<mo>=</mo>
<mi>x</mi>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-14_om_10.34.27.png" alt="M17/5/MATME/SP2/ENG/TZ1/10.b.c"></p>
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
<mi>h</mi>
</math></span> intersects the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{h^{ - 1}}">
<mrow>
<msup>
<mi>h</mi>
<mrow>
<mo>−<!-- − --></mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</math></span> at two points. These points have <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> coordinates 0.111 and 3.31 correct to three significant figures.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q"> <mi>q</mi> </math></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>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span>;</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_{0.111}^{3.31} {\left( {h(x) - x} \right){\text{d}}x} "> <msubsup> <mo>∫</mo> <mrow> <mn>0.111</mn> </mrow> <mrow> <mn>3.31</mn> </mrow> </msubsup> <mrow> <mrow> <mo>(</mo> <mrow> <mi>h</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <mrow> <mtext>d</mtext> </mrow> <mi>x</mi> </mrow> </math></span>.</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>Hence, find the area of the region enclosed by the graphs of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{h^{ - 1}}"> <mrow> <msup> <mi>h</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d"> <mi>d</mi> </math></span> be the vertical distance from a point on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span> to the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = x"> <mi>y</mi> <mo>=</mo> <mi>x</mi> </math></span>. There is a point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(a,{\text{ }}b)"> <mrow> <mtext>P</mtext> </mrow> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>b</mi> <mo stretchy="false">)</mo> </math></span> on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span> where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d"> <mi>d</mi> </math></span> is a maximum.</p>
<p>Find the coordinates of P, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.111 < a < 3.31"> <mn>0.111</mn> <mo><</mo> <mi>a</mi> <mo><</mo> <mn>3.31</mn> </math></span>.</p>
<div class="marks">[7]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q = 2"> <mi>q</mi> <mo>=</mo> <mn>2</mn> </math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q = 1"> <mi>q</mi> <mo>=</mo> <mn>1</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h = 0"> <mi>h</mi> <mo>=</mo> <mn>0</mn> </math></span>, and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 3 - \ln (2)"> <mi>k</mi> <mo>=</mo> <mn>3</mn> <mo>−</mo> <mi>ln</mi> <mo></mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </math></span>, 2.31 as candidate may have rewritten <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x)"> <mi>g</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </math></span> as equal to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3 + \ln (x) - \ln (2)"> <mn>3</mn> <mo>+</mo> <mi>ln</mi> <mo></mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>ln</mi> <mo></mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </math></span>.</p>
<p> </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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h = 0"> <mi>h</mi> <mo>=</mo> <mn>0</mn> </math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q = 1"> <mi>q</mi> <mo>=</mo> <mn>1</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h = 0"> <mi>h</mi> <mo>=</mo> <mn>0</mn> </math></span>, and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 3 - \ln (2)"> <mi>k</mi> <mo>=</mo> <mn>3</mn> <mo>−</mo> <mi>ln</mi> <mo></mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </math></span>, 2.31 as candidate may have rewritten <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x)"> <mi>g</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </math></span> as equal to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3 + \ln (x) - \ln (2)"> <mn>3</mn> <mo>+</mo> <mi>ln</mi> <mo></mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>ln</mi> <mo></mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </math></span>.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 3"> <mi>k</mi> <mo>=</mo> <mn>3</mn> </math></span> <strong><em>A1</em></strong> <strong><em>N1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q = 1"> <mi>q</mi> <mo>=</mo> <mn>1</mn> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h = 0"> <mi>h</mi> <mo>=</mo> <mn>0</mn> </math></span>, and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 3 - \ln (2)"> <mi>k</mi> <mo>=</mo> <mn>3</mn> <mo>−</mo> <mi>ln</mi> <mo></mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </math></span>, 2.31 as candidate may have rewritten <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x)"> <mi>g</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </math></span> as equal to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3 + \ln (x) - \ln (2)"> <mn>3</mn> <mo>+</mo> <mi>ln</mi> <mo></mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>ln</mi> <mo></mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </math></span>.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>2.72409</p>
<p>2.72 <strong><em>A2</em></strong> <strong><em>N2</em></strong></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>recognizing area between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = x"> <mi>y</mi> <mo>=</mo> <mi>x</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span> equals 2.72 <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><img src="images/Schermafbeelding_2017-08-14_om_17.00.04.png" alt="M17/5/MATME/SP2/ENG/TZ1/10.b.ii/M"></p>
<p>recognizing graphs of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{h^{ - 1}}"> <mrow> <msup> <mi>h</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></span> are reflections of each other in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = x"> <mi>y</mi> <mo>=</mo> <mi>x</mi> </math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math>area between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = x"> <mi>y</mi> <mo>=</mo> <mi>x</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span> equals between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = x"> <mi>y</mi> <mo>=</mo> <mi>x</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{h^{ - 1}}"> <mrow> <msup> <mi>h</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2 \times 2.72\int_{0.111}^{3.31} {\left( {x - {h^{ - 1}}(x)} \right){\text{d}}x = 2.72} "> <mn>2</mn> <mo>×</mo> <mn>2.72</mn> <msubsup> <mo>∫</mo> <mrow> <mn>0.111</mn> </mrow> <mrow> <mn>3.31</mn> </mrow> </msubsup> <mrow> <mrow> <mo>(</mo> <mrow> <mi>x</mi> <mo>−</mo> <mrow> <msup> <mi>h</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> <mrow> <mtext>d</mtext> </mrow> <mi>x</mi> <mo>=</mo> <mn>2.72</mn> </mrow> </math></span></p>
<p>5.44819</p>
<p>5.45 <strong><em>A1</em></strong> <strong><em>N3</em></strong></p>
<p><strong><em>[??? marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid attempt to find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d"> <mi>d</mi> </math></span> <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math>difference in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y"> <mi>y</mi> </math></span>-coordinates, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d = h(x) - x"> <mi>d</mi> <mo>=</mo> <mi>h</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>x</mi> </math></span></p>
<p>correct expression for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d"> <mi>d</mi> </math></span> <strong><em>(A1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\ln \frac{1}{2}x + 3} \right)(\cos 0.1x) - x"> <mrow> <mo>(</mo> <mrow> <mi>ln</mi> <mo></mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mi>x</mi> <mo>+</mo> <mn>3</mn> </mrow> <mo>)</mo> </mrow> <mo stretchy="false">(</mo> <mi>cos</mi> <mo></mo> <mn>0.1</mn> <mi>x</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>x</mi> </math></span></p>
<p>valid approach to find when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d"> <mi>d</mi> </math></span> is a maximum <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math>max on sketch of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d"> <mi>d</mi> </math></span>, attempt to solve <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d’ = 0"> <msup> <mi>d</mi> <mo>′</mo> </msup> <mo>=</mo> <mn>0</mn> </math></span></p>
<p>0.973679</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0.974"> <mi>x</mi> <mo>=</mo> <mn>0.974</mn> </math></span> <strong><em>A2 N4 </em></strong></p>
<p>substituting <strong>their</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span> value into <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h(x)"> <mi>h</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </math></span> <strong><em>(M1)</em></strong></p>
<p>2.26938</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = 2.27"> <mi>y</mi> <mo>=</mo> <mn>2.27</mn> </math></span> <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[7 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[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>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Gemma and Kaia started working for different companies on January 1st 2011.</p>
<p>Gemma’s starting annual salary was <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>45</mn><mo> </mo><mn>000</mn></math>, and her annual salary increases <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>%</mo></math> on January 1st each year after 2011.</p>
</div>
<div class="specification">
<p>Kaia’s annual salary is based on a yearly performance review. Her salary for the years 2011, 2013, 2014, 2018, and 2022 is shown in the following table.</p>
<p style="text-align: left;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find Gemma’s annual salary for the year 2021, to the nearest dollar.</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>Assuming Kaia’s annual salary can be approximately modelled by the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>a</mi><mi>x</mi><mo>+</mo><mi>b</mi></math>, show that Kaia had a higher salary than Gemma in the year 2021, according to the model.</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><strong>METHOD 1</strong></p>
<p>using geometric sequence with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>02</mn></math> <em><strong>(M1)</strong></em></p>
<p>correct expression or listing terms correctly <em><strong>(A1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45000</mn><mo>×</mo><mn>1</mn><mo>.</mo><msup><mn>02</mn><mn>10</mn></msup></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45000</mn><mo>×</mo><mn>1</mn><mo>.</mo><msup><mn>02</mn><mrow><mn>11</mn><mo>-</mo><mn>1</mn></mrow></msup></math> OR listing terms</p>
<p>Gemma’s salary is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>54855</mn></math> (must be to the nearest dollar) <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mn>10</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>PV</mtext><mo>=</mo><mo>∓</mo><mn>45000</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>I</mtext><mo>%</mo><mo>=</mo><mn>2</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P/Y</mtext><mo>=</mo><mn>1</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C/Y</mtext><mo>=</mo><mn>1</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mi>V</mi><mo>=</mo><mo>±</mo><mn>54854</mn><mo>.</mo><mn>7489</mn><mo>…</mo></math> <em><strong>(M1)(A1)</strong></em></p>
<p>Gemma’s salary is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>54855</mn></math> (must be to the nearest dollar) <em><strong>A1</strong></em></p>
<p> </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>finds <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>1096</mn><mo>.</mo><mn>89</mn><mo>…</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>-</mo><mn>2160753</mn><mo>.</mo><mn>8</mn><mo>…</mo></math> (accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>-</mo><mn>2</mn><mo>.</mo><mn>16</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></math>) <em><strong>(A1)(A1)</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>(A1)(A1)</strong></em> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mn>1096</mn><mo>.</mo><mn>89</mn><mo>…</mo><mi>x</mi><mo>+</mo><mn>33028</mn><mo>.</mo><mn>49</mn><mo>…</mo></math>, or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mn>1096</mn><mo>.</mo><mn>89</mn><mo>…</mo><mi>x</mi><mo>+</mo><mn>43997</mn><mo>.</mo><mn>4</mn><mo>…</mo></math>, or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mn>1096</mn><mo>.</mo><mn>89</mn><mo>…</mo><mi>x</mi><mo>+</mo><mn>45094</mn><mo>.</mo><mn>3</mn><mo>…</mo></math></p>
<p><br>Kaia’s salary in 2021 is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>56063</mn><mo>.</mo><mn>21</mn></math> (accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>56817</mn><mo>.</mo><mn>09</mn></math> from <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>-</mo><mn>2</mn><mo>.</mo><mn>16</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></math>) <em><strong>A1</strong></em></p>
<p>Kaia had a higher salary than Gemma in 2021 <em><strong>AG</strong></em></p>
<p> </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>Many errors were seen in part (a). Some candidates used the incorrect formula <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>02</mn></mrow><mn>100</mn></mfrac></mrow></mfenced><mn>10</mn></msup></math> or used an incorrect value for the exponent e.g. 9 was often seen. Others lost the final mark for not answering to the nearest dollar.<br>Very few tried to make a table of values.</p>
<p>In part (b) students often let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> represent the number of years since a given year, rather than the year itself. Despite this, most were able to find the correct amount with their equation and were awarded marks as appropriate. Some students did not realise regression on GDC was expected and tried to work with a few given data points, others had difficulty dealing with the constant in the regression equation if it was reported using scientific notation.</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>A rocket is travelling in a straight line, with an initial velocity of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="140">
<mn>140</mn>
</math></span> m s<sup>−1</sup>. It accelerates to a new velocity of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="500">
<mn>500</mn>
</math></span> m s<sup>−1</sup> in two stages.</p>
<p>During the first stage its acceleration, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
<mi>a</mi>
</math></span> m s<sup>−2</sup>, after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span> seconds is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a\left( t \right) = 240\,{\text{sin}}\left( {2t} \right)">
<mi>a</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>240</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>sin</mtext>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mi>t</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant k">
<mn>0</mn>
<mo>⩽<!-- ⩽ --></mo>
<mi>t</mi>
<mo>⩽<!-- ⩽ --></mo>
<mi>k</mi>
</math></span>.</p>
</div>
<div class="specification">
<p>The first stage continues for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
<mi>k</mi>
</math></span> seconds until the velocity of the rocket reaches <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="375">
<mn>375</mn>
</math></span> m s<sup>−1</sup>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for the velocity, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v"> <mi>v</mi> </math></span> m s<sup>−1</sup>, of the rocket during the first stage.</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>Find the distance that the rocket travels during the first stage.</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>During the second stage, the rocket accelerates at a constant rate. The distance which the rocket travels during the second stage is the same as the distance it travels during the first stage.</p>
<p>Find the total time taken for the two stages.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>recognizing that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = \int a "> <mi>v</mi> <mo>=</mo> <mo>∫</mo> <mi>a</mi> </math></span> <em><strong>(M1)</strong></em></p>
<p>correct integration <em><strong>A1</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 120\,{\text{cos}}\left( {2t} \right) + c"> <mo>−</mo> <mn>120</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mi>t</mi> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mi>c</mi> </math></span></p>
<p>attempt to find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c"> <mi>c</mi> </math></span> using their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v\left( t \right)"> <mi>v</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </math></span> <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 120\,{\text{cos}}\left( 0 \right) + c = 140"> <mo>−</mo> <mn>120</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>+</mo> <mi>c</mi> <mo>=</mo> <mn>140</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v\left( t \right) = - 120\,{\text{cos}}\left( {2t} \right) + 260"> <mi>v</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>−</mo> <mn>120</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mi>t</mi> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mn>260</mn> </math></span> <em><strong>A1 N3</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>evidence of valid approach to find time taken in first stage <em><strong>(M1)</strong></em></p>
<p><em>eg</em> graph, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 120\,{\text{cos}}\left( {2t} \right) + 260 = 375"> <mo>−</mo> <mn>120</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mi>t</mi> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mn>260</mn> <mo>=</mo> <mn>375</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 1.42595"> <mi>k</mi> <mo>=</mo> <mn>1.42595</mn> </math></span> <em><strong>A1</strong></em></p>
<p>attempt to substitute <strong>their</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v"> <mi>v</mi> </math></span> and/or <strong>their</strong> limits into distance formula <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^{1.42595} {\left| v \right|} "> <msubsup> <mo>∫</mo> <mn>0</mn> <mrow> <mn>1.42595</mn> </mrow> </msubsup> <mrow> <mrow> <mo>|</mo> <mi>v</mi> <mo>|</mo> </mrow> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int {260 - 120} \,{\text{cos}}\left( {2t} \right)"> <mo>∫</mo> <mrow> <mn>260</mn> <mo>−</mo> <mn>120</mn> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mi>t</mi> </mrow> <mo>)</mo> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_0^k {\left( {260 - 120\,{\text{cos}}\left( {2t} \right)} \right)} \,{\text{d}}t"> <msubsup> <mo>∫</mo> <mn>0</mn> <mi>k</mi> </msubsup> <mrow> <mrow> <mo>(</mo> <mrow> <mn>260</mn> <mo>−</mo> <mn>120</mn> <mspace width="thinmathspace"></mspace> <mrow> <mtext>cos</mtext> </mrow> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mi>t</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mspace width="thinmathspace"></mspace> <mrow> <mtext>d</mtext> </mrow> <mi>t</mi> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="353.608"> <mn>353.608</mn> </math></span></p>
<p>distance is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="354"> <mn>354</mn> </math></span> (m) <em><strong>A1 N3</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing velocity of second stage is linear (seen anywhere) <em><strong>R1</strong></em></p>
<p><em>eg</em> graph, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s = \frac{1}{2}h\left( {a + b} \right)"> <mi>s</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mi>h</mi> <mrow> <mo>(</mo> <mrow> <mi>a</mi> <mo>+</mo> <mi>b</mi> </mrow> <mo>)</mo> </mrow> </math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = mt + c"> <mi>v</mi> <mo>=</mo> <mi>m</mi> <mi>t</mi> <mo>+</mo> <mi>c</mi> </math></span></p>
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int {v = 353.608} "> <mo>∫</mo> <mrow> <mi>v</mi> <mo>=</mo> <mn>353.608</mn> </mrow> </math></span></p>
<p>correct equation <em><strong>(A1)</strong></em></p>
<p><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}h\left( {375 + 500} \right) = 353.608"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mi>h</mi> <mrow> <mo>(</mo> <mrow> <mn>375</mn> <mo>+</mo> <mn>500</mn> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>353.608</mn> </math></span></p>
<p>time for stage two <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="=0.808248"> <mo>=</mo> <mn>0.808248</mn> </math></span> (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.809142"> <mn>0.809142</mn> </math></span> from 3 sf) <em><strong>A2</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.23420"> <mn>2.23420</mn> </math></span> (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.23914"> <mn>2.23914</mn> </math></span> from 3 sf)</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.23"> <mn>2.23</mn> </math></span> seconds (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.24"> <mn>2.24</mn> </math></span> from 3 sf) <em><strong>A1 N3</strong></em></p>
<p><em><strong>[6 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>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = {x^2} - 1">
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mn>1</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x) = {x^2} - 2">
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−<!-- − --></mo>
<mn>2</mn>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \in \mathbb{R}">
<mi>x</mi>
<mo>∈<!-- ∈ --></mo>
<mrow>
<mi mathvariant="double-struck">R</mi>
</mrow>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(f \circ g)(x) = {x^4} - 4{x^2} + 3"> <mo stretchy="false">(</mo> <mi>f</mi> <mo>∘</mo> <mi>g</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow> <msup> <mi>x</mi> <mn>4</mn> </msup> </mrow> <mo>−</mo> <mn>4</mn> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mn>3</mn> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the following grid, sketch the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(f \circ g)(x)"> <mo stretchy="false">(</mo> <mi>f</mi> <mo>∘</mo> <mi>g</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant x \leqslant 2.25"> <mn>0</mn> <mo>⩽</mo> <mi>x</mi> <mo>⩽</mo> <mn>2.25</mn> </math></span>.</p>
<p><img src="images/Schermafbeelding_2017-08-15_om_08.00.33.png" alt="M17/5/MATME/SP2/ENG/TZ2/06.b"></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(f \circ g)(x) = k"> <mo stretchy="false">(</mo> <mi>f</mi> <mo>∘</mo> <mi>g</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>k</mi> </math></span> has exactly two solutions, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant x \leqslant 2.25"> <mn>0</mn> <mo>⩽</mo> <mi>x</mi> <mo>⩽</mo> <mn>2.25</mn> </math></span>. Find the possible values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>attempt to form composite in either order <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f({x^2} - 2),{\text{ }}{({x^2} - 1)^2} - 2"> <mi>f</mi> <mo stretchy="false">(</mo> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> <mo>−</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mrow> <mo stretchy="false">(</mo> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> <mo>−</mo> <mn>1</mn> <msup> <mo stretchy="false">)</mo> <mn>2</mn> </msup> </mrow> <mo>−</mo> <mn>2</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="({x^4} - 4{x^2} + 4) - 1"> <mo stretchy="false">(</mo> <mrow> <msup> <mi>x</mi> <mn>4</mn> </msup> </mrow> <mo>−</mo> <mn>4</mn> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mn>4</mn> <mo stretchy="false">)</mo> <mo>−</mo> <mn>1</mn> </math></span> <strong><em>A1</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(f \circ g)(x) = {x^4} - 4{x^2} + 3"> <mo stretchy="false">(</mo> <mi>f</mi> <mo>∘</mo> <mi>g</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow> <msup> <mi>x</mi> <mn>4</mn> </msup> </mrow> <mo>−</mo> <mn>4</mn> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mn>3</mn> </math></span> <strong><em>AG</em></strong> <strong><em>N0</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2017-08-15_om_08.05.50.png" alt="M17/5/MATME/SP2/ENG/TZ2/06.b/M"> <strong><em>A1</em></strong></p>
<p><strong><em>A1A1</em></strong> <strong><em>N3</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>A1 </em></strong>for approximately correct shape which changes from concave down to concave up. Only if this <strong><em>A1 </em></strong>is awarded, award the following:</p>
<p><strong><em>A1 </em></strong>for left hand endpoint in circle <strong>and </strong>right hand endpoint in oval,</p>
<p><strong><em>A1 </em></strong>for minimum in oval.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>evidence of identifying max/min as relevant points <strong><em>(M1)</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0,{\text{ }}1.41421,{\text{ }}y = - 1,{\text{ }}3"> <mi>x</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>1.41421</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mi>y</mi> <mo>=</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>3</mn> </math></span></p>
<p>correct interval (inclusion/exclusion of endpoints must be correct) <strong><em>A2</em></strong> <strong><em>N3</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 1 < k \leqslant 3,{\text{ }}\left] { - 1,{\text{ 3}}} \right],{\text{ }}( - 1,{\text{ }}3]"> <mo>−</mo> <mn>1</mn> <mo><</mo> <mi>k</mi> <mo>⩽</mo> <mn>3</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mrow> <mo>]</mo> <mrow> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mrow> <mtext> 3</mtext> </mrow> </mrow> <mo>]</mo> </mrow> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">(</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>3</mn> <mo stretchy="false">]</mo> </math></span></p>
<p><strong><em>[3 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>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{{6x - 1}}{{2x + 3}}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>6</mn>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mn>1</mn>
</mrow>
<mrow>
<mn>2</mn>
<mi>x</mi>
<mo>+</mo>
<mn>3</mn>
</mrow>
</mfrac>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \ne - \frac{3}{2}">
<mi>x</mi>
<mo>≠<!-- ≠ --></mo>
<mo>−<!-- − --></mo>
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>, find the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-intercept.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence or otherwise, write down <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {{\text{lim}}}\limits_{x \to \infty } \left( {\frac{{6x - 1}}{{2x + 3}}} \right)">
<munder>
<mrow>
<mrow>
<mtext>lim</mtext>
</mrow>
</mrow>
<mrow>
<mi>x</mi>
<mo stretchy="false">→</mo>
<mi mathvariant="normal">∞</mi>
</mrow>
</munder>
<mo></mo>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>6</mn>
<mi>x</mi>
<mo>−</mo>
<mn>1</mn>
</mrow>
<mrow>
<mn>2</mn>
<mi>x</mi>
<mo>+</mo>
<mn>3</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></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>valid method <em><strong>(M1)</strong></em></p>
<p><em>eg </em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>(0), sketch of graph</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span>-intercept is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - \frac{1}{3}">
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
</math></span> (exact), −0.333, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {0,\, - \frac{1}{3}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mn>0</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em> recognizing that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {{\text{lim}}}\limits_{x \to \infty } f\left( x \right)">
<munder>
<mrow>
<mrow>
<mtext>lim</mtext>
</mrow>
</mrow>
<mrow>
<mi>x</mi>
<mo stretchy="false">→</mo>
<mi mathvariant="normal">∞</mi>
</mrow>
</munder>
<mo></mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math></span> is related to the horizontal asymptote, </p>
<p>table with large values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>, their <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
<mi>y</mi>
</math></span> value from (a)(iii), L’Hopital’s rule <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {{\text{lim}}}\limits_{x \to \infty } f\left( x \right) = 3">
<munder>
<mrow>
<mrow>
<mtext>lim</mtext>
</mrow>
</mrow>
<mrow>
<mi>x</mi>
<mo stretchy="false">→</mo>
<mi mathvariant="normal">∞</mi>
</mrow>
</munder>
<mo></mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>3</mn>
</math></span>.</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {{\text{lim}}}\limits_{x \to \infty } \left( {\frac{{6x - 1}}{{2x + 3}}} \right) = 3">
<munder>
<mrow>
<mrow>
<mtext>lim</mtext>
</mrow>
</mrow>
<mrow>
<mi>x</mi>
<mo stretchy="false">→</mo>
<mi mathvariant="normal">∞</mi>
</mrow>
</munder>
<mo></mo>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>6</mn>
<mi>x</mi>
<mo>−</mo>
<mn>1</mn>
</mrow>
<mrow>
<mn>2</mn>
<mi>x</mi>
<mo>+</mo>
<mn>3</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>3</mn>
</math></span> <em><strong>A1 N2</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</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>The following diagram shows the graph of a function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f(x)">
<mi>y</mi>
<mo>=</mo>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 6 \leqslant x \leqslant - 2">
<mo>−<!-- − --></mo>
<mn>6</mn>
<mo>⩽<!-- ⩽ --></mo>
<mi>x</mi>
<mo>⩽<!-- ⩽ --></mo>
<mo>−<!-- − --></mo>
<mn>2</mn>
</math></span>.</p>
<p>The points <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="( - 6,{\text{ }}6)">
<mo stretchy="false">(</mo>
<mo>−<!-- − --></mo>
<mn>6</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>6</mn>
<mo stretchy="false">)</mo>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="( - 2,{\text{ }}6)">
<mo stretchy="false">(</mo>
<mo>−<!-- − --></mo>
<mn>2</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>6</mn>
<mo stretchy="false">)</mo>
</math></span> lie on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
<mi>f</mi>
</math></span>. There is a minimum point at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="( - 4,{\text{ }}0)">
<mo stretchy="false">(</mo>
<mo>−<!-- − --></mo>
<mn>4</mn>
<mo>,</mo>
<mrow>
<mtext> </mtext>
</mrow>
<mn>0</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p style="text-align: left;">Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x) = f(x - 5)">
<mi>g</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mn>5</mn>
<mo stretchy="false">)</mo>
</math></span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the range of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the domain of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g"> <mi>g</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p>
<p>correct interval <strong><em>A2</em></strong> <strong><em>N2</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant y \leqslant 6,{\text{ }}[0,{\text{ }}6]"> <mn>0</mn> <mo>⩽</mo> <mi>y</mi> <mo>⩽</mo> <mn>6</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>6</mn> <mo stretchy="false">]</mo> </math></span>, from 0 to 6</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>correct interval <strong><em>A2</em></strong> <strong><em>N2</em></strong></p>
<p><em>eg</em><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,\,\,\,\,"> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> <mspace width="thinmathspace"></mspace> </math><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 1 \leqslant x \leqslant 3,{\text{ }}[ - 1,{\text{ }}3]"> <mo>−</mo> <mn>1</mn> <mo>⩽</mo> <mi>x</mi> <mo>⩽</mo> <mn>3</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mo stretchy="false">[</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mrow> <mtext> </mtext> </mrow> <mn>3</mn> <mo stretchy="false">]</mo> </math></span>, from <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 1"> <mo>−</mo> <mn>1</mn> </math></span> to 3</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">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A discrete random variable, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math>, has the following probability distribution:</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msup><mi>k</mi><mn>2</mn></msup><mo>-</mo><mi>k</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>12</mn><mo>=</mo><mn>0</mn></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>, giving a reason for your answer.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mo>(</mo><mi>X</mi><mo>)</mo></math>.</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><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>41</mn><mo>+</mo><mi>k</mi><mo>-</mo><mn>0</mn><mo>.</mo><mn>28</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>46</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>29</mn><mo>-</mo><mn>2</mn><msup><mi>k</mi><mn>2</mn></msup><mo>=</mo><mn>1</mn></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>-</mo><mn>2</mn><msup><mi>k</mi><mn>2</mn></msup><mo>+</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>=</mo><mn>0</mn><mo>.</mo><mn>13</mn></math> (or equivalent) <em><strong>A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msup><mi>k</mi><mn>2</mn></msup><mo>-</mo><mi>k</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>12</mn><mo>=</mo><mn>0</mn></math> <em><strong>AG</strong></em></p>
<p> </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>one of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>2</mn></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>3</mn></math> <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>3</mn></math> <em><strong>A1</strong></em></p>
<p>reasoning to reject <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn></math> eg <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mn>1</mn></mfenced><mo>=</mo><mi>k</mi><mo>-</mo><mn>0</mn><mo>.</mo><mn>28</mn><mo>≥</mo><mn>0</mn></math> therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>≠</mo><mn>0</mn><mo>.</mo><mn>2</mn></math> <em><strong>R1</strong></em></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempting to use the expected value formula <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mo>(</mo><mi>X</mi><mo>)</mo><mo>=</mo><mn>0</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>41</mn><mo>+</mo><mn>1</mn><mo>×</mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>3</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>28</mn></mrow></mfenced><mo>+</mo><mn>2</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>46</mn><mo>+</mo><mn>3</mn><mo>×</mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>29</mn><mo>-</mo><mn>2</mn><mo>×</mo><mn>0</mn><mo>.</mo><msup><mn>3</mn><mn>2</mn></msup></mrow></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1</mn><mo>.</mo><mn>27</mn></math> <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1A0</strong></em> if additional values are given.</p>
<p> </p>
<p><em><strong>[2 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;">
<p>Part (a) was well done in this question, with most candidates recognising that the probabilities needed to sum to 1. Many candidates also approached part (b) appropriately. While many did so by graphing the quadratic on the GDC and identifying the zeros, most solved the equation analytically. Those that used the GDC, often assumed there was only one <em>x</em>-intercept and did not investigate the relevant area of the graph in more detail. While some who found the two required values of <em>k</em> recognised that <em>k</em> = 0.2 should be rejected by referring to the original probabilities, most had lost sight of the context of the question, and were unable to give a valid reason using P(<em>X</em> = 1) to reject this solution. Those that obtained one solution in part (b), were generally able to find the expected value successfully in part (c).</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>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{{8x - 5}}{{cx + 6}}">
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>8</mn>
<mi>x</mi>
<mo>−<!-- − --></mo>
<mn>5</mn>
</mrow>
<mrow>
<mi>c</mi>
<mi>x</mi>
<mo>+</mo>
<mn>6</mn>
</mrow>
</mfrac>
</math></span> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \ne - \frac{6}{c},\,\,c \ne 0">
<mi>x</mi>
<mo>≠<!-- ≠ --></mo>
<mo>−<!-- − --></mo>
<mfrac>
<mn>6</mn>
<mi>c</mi>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>c</mi>
<mo>≠<!-- ≠ --></mo>
<mn>0</mn>
</math></span>.</p>
</div>
<div class="question">
<p>Write down the equation of the horizontal asymptote to the graph of <em>f</em>.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>valid approach <em><strong>(M1)</strong></em><br><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mathop {{\text{lim}}\,f}\limits_{x \to \infty } \left( x \right),\,\,y = \frac{8}{c}">
<munder>
<mrow>
<mrow>
<mtext>lim</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>f</mi>
</mrow>
<mrow>
<mi>x</mi>
<mo stretchy="false">→</mo>
<mi mathvariant="normal">∞</mi>
</mrow>
</munder>
<mo></mo>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mi>y</mi>
<mo>=</mo>
<mfrac>
<mn>8</mn>
<mi>c</mi>
</mfrac>
</math></span></p>
<p><em>y</em> = −4 (must be an equation) <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>Let <em>f</em>(<em>x</em>) = ln <em>x</em> − 5<em>x</em> , for <em>x</em> > 0 .</p>
</div>
<div class="question">
<p>Solve<em> f '</em>(<em>x</em>)<em> = f "</em>(<em>x</em>).</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><strong>METHOD 1 (using GDC)</strong></p>
<p>valid approach <em><strong>(M1)</strong></em></p>
<p><em>eg </em><img src="data:image/png;base64,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"></p>
<p>0.558257</p>
<p><em>x</em> = 0.558 <em><strong>A1 N2</strong></em></p>
<p><strong>Note:</strong> Do not award <em><strong>A1</strong></em> if additional answers given.</p>
<p> </p>
<p><strong>METHOD 2 (analytical)</strong></p>
<p>attempt to solve their equation <em>f '(x) = f "</em>(<em>x</em>) (do not accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{x} - 5 = - \frac{1}{{{x^2}}}">
<mfrac>
<mn>1</mn>
<mi>x</mi>
</mfrac>
<mo>−</mo>
<mn>5</mn>
<mo>=</mo>
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span>) <em><strong>(M1)</strong></em></p>
<p><em>eg </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="5{x^2} - x - 1 = 0,\,\,\frac{{1 \pm \sqrt {21} }}{{10}},\,\,\frac{1}{x} = \frac{{ - 1 \pm \sqrt {21} }}{2},\,\, - 0.358">
<mn>5</mn>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mi>x</mi>
<mo>−</mo>
<mn>1</mn>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mrow>
<mn>1</mn>
<mo>±</mo>
<msqrt>
<mn>21</mn>
</msqrt>
</mrow>
<mrow>
<mn>10</mn>
</mrow>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mfrac>
<mn>1</mn>
<mi>x</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mo>−</mo>
<mn>1</mn>
<mo>±</mo>
<msqrt>
<mn>21</mn>
</msqrt>
</mrow>
<mn>2</mn>
</mfrac>
<mo>,</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mo>−</mo>
<mn>0.358</mn>
</math></span></p>
<p>0.558257</p>
<p><em>x</em> = 0.558 <em><strong>A1 N2</strong></em></p>
<p><strong>Note:</strong> Do not award <em><strong>A1</strong></em> if additional answers given.</p>
<p><em><strong>[2 marks]</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br>