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Number & Algebra">1. Number & Algebra</a></li><ul class="level-1 "><li class=" parent" style="padding-left: 14px"><i class="expander fa fa-caret-right "></i><a class="std-disabled" href="#" title="Sequences & series">Sequences & series</a></li><ul class="level-2 "><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a class="" href="../34029/partial-sums-race.html" title="Partial sums race">Partial sums race</a></li></ul><li class="" style="padding-left: 14px"><i class="expander fa fa-caret-right "></i><a class="" href="../34833/1a-sequences-series-intro-sn.html" title="1A. Sequences & series intro (SN)">1A. Sequences & series intro (SN)</a></li><li class="" style="padding-left: 14px"><i class="expander fa fa-caret-right "></i><a class="" href="../34896/1b-arithmetic-sequences-series-sn.html" title="1B. Arithmetic sequences & series (SN)">1B. 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<div id="main-column" class="span9"> <article id="problem-of-the-week" style="margin-top: 16px;">
<h1 class="section-title">Problem of the Week</h1>
<ul class="breadcrumb"><li><a title="Home" href="../../../index.html"><i class="fa fa-home"></i></a><span class="divider">/</span></li><li><span class="gray">Assessment</span><span class="divider">/</span></li><li><span class="active">Problem of the Week</span></li></ul>
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<p>skip to the <a class="scroll-to" data-target="PotW"><u>Problem of the Week</u></a> list below</p><div class="yellowBg"><p><img alt="" src="../../../ib/mathanalysis/analysis/prob-of-week/potw_img0-1.jpg" style="float: right; width: 300px; height: 171px;">To me, a <strong>'problem'</strong> is a question where it is not immediately clear how to begin writing a solution. The vast majority of questions that students are asked to answer during a maths course are <strong>exercises </strong>where they are simply practicing (<em>exercising) </em>a certain skill and/or some type of mathematical knowledge - and it is clear from the start how to set up a successful solution. Although most of the 'problems' that appear in the <strong>Problem of the Week</strong> set will not fully meet my idea of a true problem; each is closer to a 'problem' than to an 'exercise'.</p><p>The level of problem solving will vary between questions but when writing these original questions, I am focusing on making some degree of <strong>resourceful thinking / problem solving</strong> necessary to successfully solve the 'problem'. Some problems - or part(s) of some problems - are more suitable for HL students than SL students. This will be clearly indicated in the problem. For example, <strong>problem of the week #1</strong> asks for the volume of a solid of revolution in part (c). Solids of revolution are <u>not</u> in the SL syllabus for Analysis & Approaches - so, part (c) of Problem #1 has been marked as HL only.</p><p>I strive to write problems that involve the application of mathematics contained within the <strong>Analysis & Approaches syllabus</strong> - so, most of these problems can assist students in preparing for external exams - Paper 1 (no GDC), Paper 2 (GDC allowed) and HL Paper 3 (GDC allowed). Whether a GDC is allowed or not is indicated for each problem.</p></div><div class="pinkBg"><p><strong>Problems of the Week </strong>on the Math HL/SL site</p><p>The 'old' collection (over 400 total) of <strong>Problems of the Day</strong> can still be found on the 'old' Math HL/SL site (click on large blue button on left of homepage). You may need to re-enter your password to gain entry to the Math HL/SL site. The large collection of <strong>Problems of the Day</strong> are in the <strong>Assessment </strong>section. I will soon be moving these to an appropriate location here on the Analysis & Approaches site.</p></div><h2><a class="anchor" id="PotW" name="PotW"> </a>Problem of the Week (P.o.t.W.)</h2><p>Clicking on a problem in the list below will open a new P.o.t.W. page with the problem displayed. All of the P.o.t.W. pages are student accessible so they can be shared with (or assigned to) your students. Each P.o.t.W. page will have a link to a downloable PDF file containing the problem. The worked solution / notes for each problem is accessed by clicking on the 'solution' link. Solutions are not student accessible. <span style="color:#008000;"></span></p><p><span style="color:#008000;"><strong>Green</strong> </span>indicates that a <strong><span style="color:#008000;">GDC is allowed</span></strong>; <strong><span style="color:#FF0000;">red</span></strong> indicates <strong><span style="color:#FF0000;">no GDC</span></strong>.</p><table class="table table-bordered"><tbody><tr><td><a href="../31711/potw-1.html" target="_blank"><span style="color:#000000;">Problem of the Week</span></a></td><td><a href="../31747/potw-1-solution.html" target="_blank"><span style="color:#008000;"></span><span style="color:#000000;"> Solution</span></a></td><td><a href="../31776/potw-2.html" target="_blank"><span style="color:#008000;"></span><span style="color:#000000;">Brief description of P.o.t.W.</span><span style="color:#000000;"></span></a></td></tr><tr><td><a href="../31711/potw-1.html" target="_blank"><span style="color:#008000;">PotW_1_16-11-19 <img alt="" height="16" src="../../../img/tib-icons/standard-level-24.png" title="" width="16"> <img alt="" height="16" src="../../../img/tib-icons/higher-level-24.png" title="" width="16"></span></a></td><td><a href="../31747/potw-1-solution.html" target="_blank"><span style="color:#008000;">solution_1</span></a></td><td>integral calculus; areas (SL) and volume (HL); GDC allowed</td></tr><tr><td><a href="../31776/potw-2.html" target="_blank"><span style="color:#008000;">PotW_2_26-11-19 <img alt="" height="16" src="../../../img/tib-icons/standard-level-24.png" title="" width="16"> <img alt="" height="16" src="../../../img/tib-icons/higher-level-24.png" title="" width="16"></span></a></td><td><a href="../31787/potw-2-solution.html" target="_blank"><span style="color:#008000;">solution_2</span></a></td><td>expected value for lottery and 'fair' game; GDC allowed</td></tr><tr><td><a href="../31800/potw-3.html" target="_blank"><span style="color:#FF0000;">PotW_3_02-12-19 <img alt="" height="16" src="../../../img/tib-icons/standard-level-24.png" title="" width="16"> <img alt="" height="16" src="../../../img/tib-icons/higher-level-24.png" title="" width="16"></span></a></td><td><a href="../31802/potw-3-solution.html" target="_blank"><span style="color:#FF0000;">solution_3</span></a></td><td>domain, range and equation of tangent in terms of a constant; No GDC</td></tr><tr><td><a href="../31931/potw-4.html" target="_blank"><span style="color:#FF0000;">PotW_4_13-12-19 <img alt="" height="16" src="../../../img/tib-icons/higher-level-24.png" title="" width="16"></span></a></td><td><a href="../31955/potw-4-solution.html" target="_blank"><span style="color:#FF0000;">solution_4</span></a></td><td>challenging problem requiring geometry & trigonometry; No GDC</td></tr><tr><td><a href="../32074/potw-5.html" target="_blank"><span style="color:#008000;">PotW_5_02-01-20</span> </a><a href="../31800/potw-3.html" target="_blank"><span style="color:#FF0000;"><img alt="" height="16" src="../../../img/tib-icons/standard-level-24.png" title="" width="16"> </span><span style="color:#FF0000;"><img alt="" height="16" src="../../../img/tib-icons/higher-level-24.png" title="" width="16"></span><span style="color:#FF0000;"> </span></a></td><td><a href="../32075/potw-5-solution.html" target="_blank"><span style="color:#008000;">solution_5</span></a></td><td>integral calculus; bisecting shape modelling a piece of toast. GDC allowed</td></tr><tr><td><a href="../32326/potw-6.html" target="_blank"><span style="color:#008000;">PotW_6_22-01-20 </span></a><a href="../31800/potw-3.html" target="_blank"><span style="color:#FF0000;"><img alt="" height="16" src="../../../img/tib-icons/standard-level-24.png" title="" width="16"> </span><span style="color:#FF0000;"><img alt="" height="16" src="../../../img/tib-icons/higher-level-24.png" title="" width="16"></span><span style="color:#FF0000;"></span></a><a href="../32326/potw-6.html" target="_blank"><span style="color:#008000;"></span></a></td><td><a href="../32356/potw-6-solution.html" target="_blank"><span style="color:#008000;">solution_6</span></a></td><td>area of overlap of 2 circles; sectors & segments; calculus. GDC allowed</td></tr><tr><td><a href="../32548/potw-7.html" target="_blank"><span style="color:#008000;">PotW_7_10-02-20 </span></a><a href="../31800/potw-3.html" target="_blank"><span style="color:#FF0000;"><img alt="" height="16" src="../../../img/tib-icons/standard-level-24.png" title="" width="16"> </span><span style="color:#FF0000;"><img alt="" height="16" src="../../../img/tib-icons/higher-level-24.png" title="" width="16"></span><span style="color:#FF0000;"></span></a><a href="/media/ib/mathanalysis/analysis/prob-of-week/problems/potw_7_10-02-20.pdf" target="_blank"><span style="color:#008000;"></span></a></td><td><a href="../34281/potw-7-solution.html" target="_blank"><span style="color:#008000;">solution_7</span></a></td><td>rigorous application of cosine rule; using GDC to find max of a function</td></tr><tr><td><a href="../34382/potw-8.html" target="_blank"><span style="color:#FF0000;">PotW_8_21-05-20</span> </a><a href="../31800/potw-3.html" target="_blank"><span style="color:#FF0000;"><img alt="" height="16" src="../../../img/tib-icons/higher-level-24.png" title="" width="16"></span></a></td><td><a href="../34429/potw-8-solution.html" target="_blank"><span style="color:#FF0000;">solution_8</span></a></td><td>geometry & trig; area bounded by circle & absolute value graph; No GDC</td></tr><tr><td><a href="../34534/potw-9.html" target="_blank"><span style="color:#FF0000;">PotW_9_31-05-20 </span></a><a href="../31800/potw-3.html" target="_blank"><span style="color:#FF0000;"><img alt="" height="16" src="../../../img/tib-icons/standard-level-24.png" title="" width="16"> </span><span style="color:#FF0000;"><img alt="" height="16" src="../../../img/tib-icons/higher-level-24.png" title="" width="16"></span><span style="color:#FF0000;"></span></a><a href="/media/ib/mathanalysis/analysis/prob-of-week/problems/potw_9_31-05-20.pdf" target="_blank"><span style="color:#FF0000;"></span></a></td><td><a href="../34548/potw-9-solution.html" target="_blank"><span style="color:#FF0000;">solution_9</span></a></td><td>integral calculus; area bounded by parabola & line (parabolic segment); No GDC</td></tr><tr><td><a href="../35146/potw-10.html" target="_blank"><span style="color:#FF0000;">PotW_10_17-07-20</span></a> <a href="../31800/potw-3.html" target="_blank"><span style="color:#FF0000;"><img alt="" height="16" src="../../../img/tib-icons/standard-level-24.png" title="" width="16"> </span><span style="color:#FF0000;"><img alt="" height="16" src="../../../img/tib-icons/higher-level-24.png" title="" width="16"></span><span style="color:#FF0000;"></span></a></td><td><a href="../35154/potw-10-solution.html" target="_blank"><span style="color:#FF0000;">solution_10</span></a></td><td>trigonometry; find 2 different methods for proving result for an isosceles triangle</td></tr><tr><td><a href="../35299/potw-11.html" target="_blank"><span style="color:#FF0000;">PotW_11_02-08-20 </span></a><a href="../31800/potw-3.html" target="_blank"><span style="color:#FF0000;"><img alt="" height="16" src="../../../img/tib-icons/standard-level-24.png" title="" width="16"> </span><span style="color:#FF0000;"><img alt="" height="16" src="../../../img/tib-icons/higher-level-24.png" title="" width="16"></span><span style="color:#FF0000;"></span></a><a href="../35299/potw-11.html" target="_blank"><span style="color:#FF0000;"></span></a></td><td><a href="../35300/potw-11-solution.html" target="_blank"><span style="color:#FF0000;">solution_11</span></a></td><td>sequences; 3 terms belong to both an arithmetic and a geometric sequence</td></tr><tr><td><a href="../35951/potw-12.html" target="_blank"><span style="color:#FF0000;">PotW_12_29-08-20 </span></a><a href="../31800/potw-3.html" target="_blank"><span style="color:#FF0000;"><img alt="" height="16" src="../../../img/tib-icons/standard-level-24.png" title="" width="16"> </span><span style="color:#FF0000;"><img alt="" height="16" src="../../../img/tib-icons/higher-level-24.png" title="" width="16"></span><span style="color:#FF0000;"></span></a><a href="../35951/potw-12.html" target="_blank"><span style="color:#FF0000;"></span></a></td><td><a href="../35963/potw-12-solution.html" target="_blank"><span style="color:#FF0000;">solution_12</span></a></td><td>2 probability problems involving geometry & trigonometry; no GDC</td></tr><tr><td><a href="../37077/potw-13.html" target="_blank"><span style="color:#FF0000;">PotW_13_5-12-20</span></a> <a href="../31800/potw-3.html" target="_blank"><span style="color:#FF0000;"><img alt="" height="16" src="../../../img/tib-icons/standard-level-24.png" title="" width="16"> </span><span style="color:#FF0000;"><img alt="" height="16" src="../../../img/tib-icons/higher-level-24.png" title="" width="16"></span><span style="color:#FF0000;"></span></a></td><td><a href="../37078/potw-13-solution.html" target="_blank"><span style="color:#FF0000;">solution_13</span></a></td><td>angles of a triangle consecutive terms of an arithmetic sequence; GDC allowed</td></tr></tbody></table><script>document.querySelectorAll('.tib-teacher-only').forEach(e => e.remove());</script>
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