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<h2>HL Paper 3</h2><div class="specification">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math> is a simple, connected, planar graph with <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math> vertices and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math> edges.</p>
</div>

<div class="specification">
<p>The complement of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math> has <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>'</mo></math>&nbsp;edges.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the maximum possible value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</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>Find an expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>'</mo></math> in terms of&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</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>Given that the complement of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math> is also planar and connected, find the possible&nbsp;values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</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><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi></math> is a simple graph with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math>&nbsp;vertices and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math> edges.</p>
<p>Given that both <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi></math> and its complement are planar and connected, find the maximum&nbsp;possible value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>substitutes&nbsp;&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>9</mn></math>&nbsp; into either&nbsp;&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mn>3</mn><mi>v</mi><mo>-</mo><mn>6</mn></math>&nbsp; or&nbsp;&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>≤</mo><mn>3</mn><mi>v</mi><mo>-</mo><mn>6</mn></math>&nbsp; &nbsp; &nbsp; &nbsp;<em><strong> (M1)</strong></em></p>
<p>the maximum number of edges is&nbsp; <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>21</mn><mo>&nbsp;</mo><mo>&nbsp;</mo><mfenced><mrow><mi>e</mi><mo>≤</mo><mn>21</mn></mrow></mfenced></math>&nbsp; &nbsp; &nbsp; &nbsp;<em><strong>&nbsp;A1</strong></em></p>
<p><em><strong><br>[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"><msub><mi>κ</mi><mn>9</mn></msub></math>&nbsp;has&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfenced><mtable><mtr><mtd><mn>9</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd></mtr></mtable></mfenced><mo>=</mo></mrow></mfenced><mo>&nbsp;</mo><mn>36</mn><mo>&nbsp;</mo><mtext>edges</mtext></math>&nbsp; &nbsp; &nbsp; &nbsp;<em><strong>&nbsp;(A1)</strong></em></p>
<p>so&nbsp;&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>'</mo><mo>=</mo><mn>36</mn><mo>-</mo><mi>e</mi><mo> </mo><mfenced><mrow><mo>=</mo><mfenced><mtable><mtr><mtd><mn>9</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd></mtr></mtable></mfenced><mo>-</mo><mi>e</mi></mrow></mfenced></math>&nbsp; &nbsp; &nbsp; &nbsp;<em><strong>&nbsp;A1</strong></em></p>
<p><em><strong><br>[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>e</mi><mo>'</mo><mo>≤</mo><mn>21</mn><mo>⇒</mo><mn>36</mn><mo>-</mo><mi>e</mi><mo>≤</mo><mn>21</mn></math>&nbsp; &nbsp; &nbsp; &nbsp;<em><strong>&nbsp;(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>≤</mo><mi>e</mi><mo>≤</mo><mn>21</mn></math>&nbsp; (the possible values are&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>,</mo><mo>&nbsp;</mo><mn>16</mn><mo>,</mo><mo>&nbsp;</mo><mn>17</mn><mo>,</mo><mo>&nbsp;</mo><mn>18</mn><mo>,</mo><mo>&nbsp;</mo><mn>19</mn><mo>,</mo><mo>&nbsp;</mo><mn>20</mn></math>&nbsp;and&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>21</mn></math>)&nbsp; &nbsp; &nbsp; &nbsp;<em><strong>&nbsp;A1</strong></em></p>
<p><em><strong><br>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognises that&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>+</mo><mi>e</mi><mo>'</mo><mo>=</mo><mfrac><mrow><mi>v</mi><mfenced><mrow><mi>v</mi><mo>-</mo><mn>1</mn></mrow></mfenced></mrow><mn>2</mn></mfrac></math>&nbsp;(or equivalent)&nbsp; &nbsp; &nbsp; &nbsp;<em><strong>&nbsp;(A1)</strong></em></p>
<p>uses&nbsp;&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>≤</mo><mn>3</mn><mi>v</mi><mo>-</mo><mn>6</mn></math>&nbsp; and&nbsp;&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>'</mo><mo>≤</mo><mn>3</mn><mi>v</mi><mo>-</mo><mn>6</mn></math>&nbsp; &nbsp; &nbsp; &nbsp;<em><strong>&nbsp;M1</strong></em></p>
<p>to form&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>v</mi><mfenced><mrow><mi>v</mi><mo>-</mo><mn>1</mn></mrow></mfenced></mrow><mn>2</mn></mfrac><mo>-</mo><mfenced><mrow><mn>3</mn><mi>v</mi><mo>-</mo><mn>6</mn></mrow></mfenced><mo>≤</mo><mn>3</mn><mi>v</mi><mo>-</mo><mn>6</mn></math>&nbsp; &nbsp; &nbsp; &nbsp;<em><strong>&nbsp;A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A1</strong></em> for&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>v</mi><mfenced><mrow><mi>v</mi><mo>-</mo><mn>1</mn></mrow></mfenced></mrow><mn>2</mn></mfrac><mo>-</mo><mfenced><mrow><mn>3</mn><mi>v</mi><mo>-</mo><mn>6</mn></mrow></mfenced><mo>=</mo><mn>3</mn><mi>v</mi><mo>-</mo><mn>6</mn></math>.</p>
<p><br>attempts to solve their quadratic inequality (equality)&nbsp; &nbsp; &nbsp; &nbsp;<em><strong>&nbsp;(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>v</mi><mn>2</mn></msup><mo>-</mo><mn>13</mn><mi>v</mi><mo>+</mo><mn>24</mn><mo>≤</mo><mn>0</mn><mo>⇒</mo><mn>2</mn><mo>.</mo><mn>228</mn><mo>…</mo><mo>≤</mo><mi>v</mi><mo>≤</mo><mn>10</mn><mo>.</mo><mn>77</mn><mo>…</mo></math></p>
<p>the maximum possible value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math> is&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>&nbsp;</mo><mo>&nbsp;</mo><mfenced><mrow><mi>v</mi><mo>≤</mo><mn>10</mn></mrow></mfenced></math>&nbsp; &nbsp; &nbsp; &nbsp;<em><strong>&nbsp;A1</strong></em></p>
<p><em><strong><br>[5 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Christine and her friends live in Winnipeg, Canada. The weighted graph shows the location of their houses and the time, in minutes, to travel between each house.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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KfefE3u91/ksBjLeW9PNigschgts2vGN9kBXv4uPx4AwhXjenwINsVFtrBQEhcy7P9CjnY2p5bDmwfSn1jjdD+/lyVAYbEswQ7P10WnXJtWWoRE3SHoVBmmBNCwQmDoQE98Q2C097SJcRQ9Odr5vrzdOysYIT/t+F65d5yyZLA07RB4Lr39A+lN3FOJGGHFePVQBiWNRGgXXJsRksjNwk9b4qJYWOilL2TY+7HcyhyPocfxuyoBCouqxBw5XqeVogNqr/Oxk3mkHaZdVweV2cll/VggKFRgtDOTJDn9bl1u7RwX+J5x/FaBVaN+/qM/c/x/ZfBV2jwPM/7rlaZF4h7zzeVoQ1yUFxaoaWnXX/S1zwoACgsrGNuNBE/66HDw8XUQJDpOukPy6w0Ehs4kQVnDtN2olWc8lP4HO3Jr5ZpsZFojxjLqvyvbHLiZX3i2906mUv5QTubGw2RfRMV7p2617OTl7llWXFQTFtUFW27iuXNCgMLCs4qQvOm6GOxnCxeepPBE1WhHaSuxHceDclaBAWYQGM0JyoKBmaOncrDzoZzSJ91qrUBn+Z3LAbXFl1Y3qa9tRLKdqyqOqgmL59Lb+wkHIRdXqUpHUFhUwtX9wdrBVL3Zuk/5fAp8fqKaz0l7/yDCICogLvBBXWii45g0zKaBmeOv5ZMHH1FUtFfksytB7H2/0toLOiOk9aRavGBdcZEpLGCRe/Sp9HXsymT9lj15p3BMkcVMRRIVhYVHBa2dChqNEALM+z7NZnGFOQQGLD7gpwLDntDMGJg5PpPeg/fnBxSOnsnDwyezaamu0AkwHRM3yDuVnqpxX8Hd6HuoJi6SY4VmK2tuJga7og7vzWaCrFyX7f2PpMeppo1UEQqLRrDaj1SfQCAuQgkqlNB4MFQnAG6oFyow0JFUExgXcnb8lmzc3JGH/eFkJsh4+Lm8vfl9OTpNDB4cncqJTs27nPaIhrv8mgrVc8czlEBVNwjOQ12ARSuEUE1chJBj//NAYeFBGaKzwJNpaIMd1Q9crTP0oMA6SCIYojNBPYHQgOAoFmxjGZ0+lO3L9ybgKe74ylSMfIy/lpN7upT37CnwUlyUX1OhAySBXLK6GwQZRz0IxbKJ/FBc+FWdKSwcLy8di+DbWhVlsdIdUpZUueMgMFBXVGDAZcIBsuXYOXlUDTcIxt2g/EMT7BQXTtZQY6IoLIxY3NgIUYGOF59QOwe4Q5A/BrsETDNJQq1Ddsm5Fdt48FDerDi1F4ICwqK5mUPdMaK46I59lStTWFSh1eKxuIFg2kanG2IDoSi1EYRbhME+AdQdHcuCzgaD+pqYSWI/5YyxLgEdj1X3fNfPo7hwvYREKCzKltFoIL3jn8n9u5vmaV8WXhqkSYnpxkFe0eGh82NojgCsFWodAm8M7KOYa453lzGjbEMbj5XmGVMbmc67D/8pLMqU0sTPeUe2X8cgtvlXSk9Pt/PSIE2KPmGG5iPV/KW/8RRNd0iaSjP/0SAvN5OkmXQxVnsEcC/FMI2b4sJenbEdE4VFBaKZC69gvXkLLw1CUlRUxPQEr+6QkF0+FapZK4eiUQZ3nUmC73IzSVpJHi9SkwDKFRapkGaE5KGguMij090+CosK7DOFhaWXBmkHG8PTRhK7Noa+vTApmQeffycFBp520SlxoKefJaozQmJyc1FcuFdXKSwqlEmmsDDFUfGlQbqmQ6jTSk2IktuQbzw1m8O5DHqP5Of7W/JK1vsSEi/QWl3bkoOn0wWfzPFxq4kAZ5KYqPi1DW8MhsUiNmFIceFWPaWwqFAeVYQFji370iC4APCkiI4VN0iMQRvERXcIFgi6J2/cfU028NZNo7B4If391+TW3ucyHItMVo+8+Rpf612zIkFgqEtOB9ZyJklNmC2fpi/3a/myTlyO4sKJYpgkgsKiQlmUFxblV8vDkwVEBT6LnWqFxHl+KDjk+oZhAdpcNwqLSbnMvTRrNpg2+Z4Az/l0kXyUSVJgNPXSsy7yFuo1UUb4xBooLtwoeQqLCuVQWliUXC0veRPwiVAmU+Qyp8llCguIuDuymhYRk+m/XHK6QvXOPBT1lDNJMvE4tQMPKDEN/DbBT7arGD/E0D4BCosKzMsKCxxXxg2CJws8pbPyTwtBzbhG/3CWsMjaPhEWfElWhepdeKgKjORMEriwsJ2hewKFVr/uk9haCiguWkNtvBCFhRGLeWM5YVHODaIm5limhZmJzm+FKwhCC53VQqgqICgsFhDa3GCaSUKBYZNw9bhg9cT9Q+vnlB3FRfU6ZOsMCosKJEsJC3SAr74jvfNxZswQE2gAYjdZmgDhadjoDqGwMOHqfBtmM6nlTeu00eLUeUrDT4C2K+R/VdYUF1cs2vxFYVGK9nPp7dyYiAE0npNP2qc/i6fopUF40sP5xs6zVFrCPkjdIQtPv1nCIms7LRatVhQ8JWP9Fb0/IJpjHozcKvzZxcAcYywY5glQXMzzaOMfhUUblGfXUFM/RMVCx9liOly+lJpzF8adZAkImQ7eTE9DnVqXOHiz7bLG0zI6OBUYsGbQNN9OKYA1PgyLBCguFpk0uYXCokm6ibghKnRaKU2VCTCGn+C0sPpoprAQmYgITjc1kOxuE+p4ciYJxPSCWOwueUFeGWKOq9dmFy3FRTYb23soLGwTNcSHCo2xA+gwaR42AEpt0ifeOatOjrAQ4QJZKYTO/EUZJgUG7gMIjLmydSa1/iZEraHGgc/+Zst6ylHvIHIhwih0reO9jJDC4hJFMz9Ykatz1eXNp+87ML051uDiGA/lywdbk9U5V2/uyMM+l/SuTr7ZM9CQ61RViGwIDgoMO8z1nqHbqZgn2+RiRsseQWGxLMGC8/Xpm+q4AFRqNzoesGMIjwDuBZ1JgnKG+Z7uweXKWWeEUKiV40hxUY5T3aMoLOqSK3Geigp2kCVgpQ7BGAt0OgzhEsDTtQoMmKZxn1Bg1Ctv3C+wBjGUJ0BxUZ5V1SMpLKoSK3k8nsrQWC4MQix5fuyHKb+pOyR2GmHnH2JCRTjuGYgNmvSrlTnGDXBGSDVmOJriojqzMmdQWJShVPEY9XdyWmlFcInDccPrU2xiM38GTAACA24RWKpUYNCFWK7AwQvuEIbqBCguqjMrOoPCoohQxf06rRRmSVRYhvoEaN6tz87nM3HfmGaS+JynJtOuM0IowupTprioz850JoWFiUrNbXjiwtMWPpxWWhNi4jRMncOTGFkmoET0E409OkvOJMkvdHUb0n2Uz6loL8VFEaHy+yksyrPKPTJZKXmD56IqvRNCDcKCi/6URhbsgeg8df0BCHdYNFA/GGTCAvcJw/IEku04LUD1eVJY1Gc3d6aObmdlnMOy9B90JhztvjTGYCLgTJLFokTbg/uEwQ4BiovlOVJYLM/wckQ7B09ZgJmKgu6QFBD+nRCAeyw5kwTjcWK1FEJ4c/aZ3RuD4mI5nhQWy/G7NEOikWOwT0DdIVyq2D7bEGJE/UgKDDy9xzZFmTNCmqnJFBf1uVJY1Gc3GViGm5pmyCUgljgVT2RkXAJUxIegE4hxJgmsNGiDYhNTbVV1iot6pCks6nGbzFRQUYHKx9AcAQzeBGsO1muOcSgx416EdUtnkuAbgiPUe5SuwuZrLsVFdcYUFtWZTUSFTitlZ1cDYMVTdJ4+3SEVwUV+OAZSq8DQmSShCQwV3ZEXdePZp7iohpjCohqvyZMPGiuuVVER3JKHgzkHqC0JMdLTQ55Jwhkh7VVqiovyrCksyrPiuvIVWNk+VJ/MQnvitM2J8WUTgMBIDvTEb99nkuABhwPHs8vc9h6Ki3JEKSzKcZocpY0S16qoAM3Sofr+FbK3BDTiaEwzSXwUGOjkMPaI09zbrcwUF8W8KSyKGU2OUFHBp4OSwBo4DE9ndIc0ADbSKCEwfJ5JAjEEYeGjKPK9ylFc5JcghUU+n8lePCXjBmanVgJWg4eouGvwEow6QgLoJCAwdKAnvnHPY7vLAWnmbKnuSojiIps9hUU2m8keNcFjHQXXG5qCrHi/W8uCc/a9L0pnMwBBoQLD9ZkkFNrdVyOKC3MZUFiYuUy2YpojGhc0NBQVOaBa2oUywBMa3VEtAY/4MhCv+v4fHSDp2tRypA8fhm4JUFws8qewWGQy2YJGBA0KPnxtdwakDjbDHYUyYSCBNghg/ALqHAStilpX2gOkh2/+baMWFF+D4mKeEYXFPI/Jv2Ql4cAoA6AON+l4F7pDOiyECC/t2kwSpAfCgovGuVMZk/0G2qmYA4WFofTVBBp75TCg6XwTbl4+qXVeDNEmAB06rASwmqEeYuxVF+2E1zNCRgP55f6WbEysQOtya+dD6Q8vDHXqufR2bkw4g/XqyrrcPjyVseFIVzZRXExLgsIiVSN1QBTnhqfAOPQXwg/jXhhIoCsC6EC6nKqqM0KQDq/C+Gv55MH78svB+STZ4+ETObh7XVZvHkh/NC8ZxmfH8uba1AU1FRZ35Gjw0vnsUlyIUFgkqqnerBwcmIDi4E++eMnBQok4SbBYtD2TxNexRuOvnsjjs3nrxHhwKLdXbshu73miFr2Q/v5Waltit+M/YxcXFBazCorGQU2bjtfZ6JOn/mUOXIu+KjgFAG2IulHhKkH9RF1tIsAFE8yMkPOe7K6lhMVk2zVZvbkjR8ePZZCyZjTB1HacMYsLCgsRvgLd9h3VQnxoWPFhIAHXCGD8gwoMPKzAAmpbYCDeYIQ1RMQ33pKTS0vGSxkc3kmMrYDA2JOTmfvEtfLOS0+s4iJ6YaFrVeAJw/bNn1fhuG85AuoOYZktx5FnN0cAbYuO2YIQgNiwMcsM8SK+LgaN2qc1lvPeO3J7/6mMFiK/kGH/F3K0szkVGYZxGAunOLghRnERtbBAgcM3ClHhytx0B+8LJ5OkjSun2zlZPExUggDELwSGziSBwFhGFOgKtDZESiKZ3fwcPZX7d99dGLg5n5gLGfZ+LLcWxmHMH+Xyv9jERbTCIraCdvmmq5s2iEK6Q+rS43ltE0CbY2MmiQ4ybzv99q/3QvoPfixHp9MZIvnxT6eebuz0pMzR+XF1szemPidaYaEmymWeHLqpnryqEoCPGSZhukOUCL99IIAOBu2OziTBN8QCtpcJsHjgHL/DhZw9el8elhIVyCnGXbzu/DoWRWUSi7iIUlioqMA3g78E1B1CcehvGcaectRdWN0gkOEqgcAoEsoQFRAX/ga4Nt6Xg95ZYrGrczn94EN5fD6/lsVVHp9Lb+8n0svcf3Wk679iEBfRCQvcyLiJ+Qp012+/culDY8yyLMcq/6ixjAafyX0sVjRZ5XBTdj94KsOFdh7HPZaTj/dl+xt7QTT0+Vza2Vt2JomKaQgQP8O5DI735Nbs3SvTujZbBGvzUAaob+Oh9B99erUa53goXz7Yk3fmhIifuddUhy4uohIWOugJTwhlzY5aEfjtJgG1PrE8lyuf8dmncvDgs9l6ARcyfPqebK+ty63UaH0sZvSd17fkDayIuEZhsRz1xbMhMLRO6wMQtkFQqOsE27/5735L/HtfzoWcHb81W8o7uaJmarnu8Zn09mYzQVauy/b+R9LzcKrpYunObwlZXEQjLHBj4ukWNyc7ofkK7vM/FYt0hyxTii/lq8dfyNmcdWK2loBRPOTtWyYdPFcJ6EwSfaL/jbW1mSVpvkMucptofPx2k4A9cZF+r8p8PZnWo/aWRI9CWODmg6jABwKDISwCdIc0UZ5YX2BPNigsmoBbOk50PMnXtqvQ0G9YN2DRoMAojdS5A+2JCxGZrVi6MHtmYgV6vbUl0oMXFslCww3IEB4BNK4QFww2CUyFxSv3jlOWDFyDFgubpDUuPPSgjcLaLBhDgQGaOrBThUTZbx3giTjwwT2COPUDCx+upR8KEy2Fbr6T/dRS1tcsYYGhK4OP5GDufSzN5TV4YYGbCjfjUoXVHH/GbIEAyhZl7J/P2ULmG4sCptUtud9/YbgChYUBSqlN2pGjg8d0abRPybETSeEAUYH9//2nP0IxACcAACAASURBVDW6QXDs/zg6mogDFQz6DSsHztUPhHcy7qLfaWGC+DRufEP8aF7wTUtwqeLPPciKuDAKi5fyVf9/t7r+R9DCQgdB4UZgCJcAbkg0lChvBhsExjLqvyvbqYGbVzFTWFyxmP+FuoiOFiIX7Q7qJDr3rI4d+7TT1s7aZD3AcWkxsMwgdLWOqDhQK4mKh2WFCfKroiaZR41f86rXxzeDTMb/qZWq1sOwSViMnsrB/mMKCxsVDBWYnY0Nkn7EgYaQ7hBLZYWGaOdDOc18o2TcwgIdPzpC7Yy1E053/PivHSwEBtokdBY4FwKkasD5v/+tb00+sHbUiaPqNbOOVwYqDJAvFQ34VkGl4iLLKmNiptv0XP1Oxo/fem39zkqrb9tRrrXFxUxYKEP9Xhhz0TCUIC0WahpH4TDEQUDLnCbZJct7/LV88uCjHFGB+MMXFvpEr50ZOjdt7LWx1m91G6Czx/GwVqCzayJoJ9tE3G3GWSRM1E2k+c1ir2Vg+tZz9VvLR8tUy0mFSZdCLc0+LS7AC20c0pybTqPF4pk8PHxCi0UacpX/aBBQyVARcwugSqQ81nkCuPFQ7mg8GGoSwMjxB+9Lb3hxFcHI1CiFISzQoajLQjuyrCdrtCfooLRTwrldiFjtJK8KKM5faNtVECTLUctHy1N51REmWuYaR5EwQRtkMyTFRVI4wQqGPBuDSVgIx1gYWZXdiBsd0PGxXchl08DjuiOAhgAdA0MNAqNTOdHXU8+tirhueD+DH8JCOx8106t5Hu1DsqHW3+hAyox3qEHX2inayVmLMOKIksIEv1WU6Ley1m+tJ2W/1ZKl56s7TONHvUymwdRn/d3f/Z2xrqIOGx+cjcKi/UIOxhUCyChIAO/iSaL9ouMV0wTg88ZNby5/0wIyumDMbM2Gwg41fcVA/o+/lpN7upR3emEdZTTL64IP1yQ82uOCxhiNc53xDmoKNzbQ7WWh0pW0kzKfdC6D3keJZdmvyerNHTl61Jfhiy/k5PFz82ncWotAUhSYhImOvdEyyxK0WUIF/dnNb3/bKCxwDq65ECgsFpDU3oCGQU1dUIEMcRJAJ4MbDk8EmWFy42V1hjPxoe8syIyEO9okAKGYbLjRUOv9nm6U9SlRzdba+LeZ3iavpZ3UwjVGz+QI73mBkOgNZKQHjAbSO9yRWys3WlscSS/N73wCWq+1jqo4VosGhAmFRT7DRvfCxIQGJk5RgaeUR/Lz/S15ZadnGKBT9uVSjRZRa5Gjw8EnM1BYZKLpcgca1zrjHdAY41yzlarLHDVzbaOwUIvTzQPpG2fy4B0dP5TvHJ4m3ibaTPoYq10CaoVNC2j8n3edmCyy3YlJ710hKirwHV+Ar/uevHH3tcmLfUxTisq+XCoUdnhSXbzpErmjsEjAaO8nrIoQAHXGO6gver4hbS/tLl1pUVioG6+gExkP5JNHAwoLlwqzRFq0f0sLC7RzLgevhQUaHACHySjqMD6Vo811WRQWVV8u5T9FPLmiTkDpGwOFhRGLjY3p8Q7aCaYbRfyHvxn70XDC9OvjeAcbzKrGoUyvzps9qRrf6XJ1FH/5R0BFBb7RnqGfw28IdNeDt8ICDREaKJi9fRp81UiFyBQWpqvlvVzKdLx/29TPbkz5RFikByim/nOMhREdNqpfGGIAT03o6GId75AJqcEdC8JC67NRWMxm78wNSk4Nxm0wrYy6PoGkqKgfS3dneiks0LjhiQcdSPSiAnWnhrAwv1yqu4po88rqDjHWDVosClEnxzuggUNnhnvNZHmAqMB+CI3YxjsUgmzggGrCYpaA0VO5f9Nk0WwggYxyaQK+iwoA8E5YwNwKUYFPLAO2CmtqJWEB02nWy6UKr+TFAegY0QkaB/NSWEzEeHK8g06Lwz1lEg/ozHAMxAPHO3R7CywIi9m9v7qSY4mo1D50m7/Yrx6CqEAZeiUs8ASqZlcf/Eyt3SSlG46il0u1luLGL4RO0jj2JhJhYWO8Q+OFxAtUJrAgLHR59ZV1uZX10rjS7UPl5PAEiwRCERVA4pWwwE2V+SRqsYC9i6psw1H4cinvcp6ZYL1JF9whAQmLZcc70OKXWX2c3bEoLERk5upYXXnV/Jr7su2Ds7kOP2HaXuE7hOCNsFDwMMcypAiUaThKvVwqFa/Hf3VwL77ngmfCYtnxDpyiOVf63v8xCgsMsxp+Lm/fXJfVlU3ZPezJ4HI9C6xzcyi7HGPhbNlr3xaKqABoL4QFxAQsFSGBt1rLi4RF6ZdLWU1V55HN1xnTAjLql9a1AJKzQ7JW57SbLVhUTOMdTGMdsA0dS3q8w4JVxm4SGZtDBLKExSSJ46H0H/1sfknvlWuycXdffo5lvccOZYRJmRAIUVQgY84LC12rAmMrGDII5AmLSi+Xyojf083ogDHWoutgGu+gY4XSAgLpReeBBgeCWtd36DoPvL4bBHKFhRtJZCpKEghVVCD7TgsL+IDR8KIR5lOZqbaanrT1KRz20QovlzJF7/k2FaUL7pAG8mUa75A1RVPX2cC0WIgHWCw43qGBQgkwSgqLMAo1ZFGBEnJKWODJDnPh0dj+9V//9eW0UvqJw7iZ2s4FxCiEKW5iG8E03iFriibEMDoB1GVd34H12EYpxB0HhYX/5R+6qEAJOSMs9OkyaRr+jbU1Psn5fx91moPdnR35/d/71qRzL+rYq4x3UJcFxzt0WrzRXZzCwu8ij0FUoIScEBZo0LOe/PC0x0ACdQjoTZwUq3/zN38zcT2oZQwNddZ4B3VZIB6Od6hTAjzHNgEKC9tE24tP2yN8hx6cEBYwMScbf/5Ozk7o5rd2qtqQ+fb9n15/o1SdUpcFxzuE3tSFkT+9D8PITTy5iElUoFSdFxb/8Q/+YPK0iCdGftpjABO/NmI+fm/+4R9mCotPHj2SIrdIPE0ec+oTAb0XfUpz7GmNTVSgvJ0QFkhIlisE1gvcTOwIYr89q+Vfb2aT9QvWDNanajx5tBsEKCzcKIeyqdB2CN8xBWeEBaYEpsXFj/7kTyZWCu0cYLHgtNOYqmf9vJoGA2s90m/UJwYS8IkAhYU/pRWrqEAJOSMskBg8ReqguuTaA9iOGwodAnz/yX3+VDOmtG0CemOrkMA3BAfWjEjWJ4zxYSABHwhQWPhQSjKZ4o72JjZLhZaOU8JCE5X1DUEBYYECww1Gc3YWKW5XAhASsEz88Q9+MKk3yTqDfWolw5iS5D49n98k4BIBCguXSsOcFn2giVVUgIolYXEhw/6n8vP9LdlYmc1iuLkjR1if/v8N5JNHA7G1TD1cIego9CmU7hFz5ebWeQK6imt6+jLqE2aEoD5BZKT3z8fCfyTQLQEKi275F12domJKaHlhMR7Klw+2ZGNtS+4fJ150gxfiHO/L9lozL3Oie6SoinN/mgCsXbBMmALcIbqeBb7pHjFR4rauCVBYdF0C2denqLhis6SwuJCz47dkY+VVud9/cRXr5a+xjPoHcnunJ+eX2+z+oHvELs+QY9MbP28AMCwW6h6BJSPv2JBZMW9uEqCwcLNctG3BN8OyrpDznuyuXZONXOHwXB4ff9GYsEAh0j3CqlyGAEQoXB4YW5EXUJ9g2VD3SNHxeXFxHwnYJEBhYZOmnbgoKhY5LmGxeCmDwzuyutKMq2MxqcVb6B4pZhT7EbBGZLlD0mzgDkkOFuYbSNOE+L9tAhQWbRPPvx5FhZnPEsLiufR2bsjqyg3Z7T03x97RVrpHOgLvwWW1IaiSVAwQVvcIBwtXIcdjbROgsLBNtH582pbgm2GeQJDCAlmke2S+oPlvSkDdIfiuEmgNq0KLxzZFgMKiKbLV4qWoyOe1hLBQV4h7FotkltkhJGnwNwQnxk7UfcqgNYx1qEsCOjW6yzTEfm2KiuIasISwEBkPDuX2StHgzeJEtHFEcjEkqH4IDoY4CWCMBVwbdQPEiTbwiAfuEQYSaIMA6hqEMUM3BCgqynFfSliI6DiLrOmmIoL1LB4PZFQuPY0elewQcHPSX94obmcjh8hE+S+7VgWXBne2iINNGIVFd0VLUVGe/ZLCQkRGz+To7nVZXdmU3cOeDEa6xuZYRoOePDz8hZxebiufsCaPZIfQJF3341Z3CKwONkLSGgZrCOJnIIEmCFBYNEG1OE6KimJGySOWFxaIDVaJRz+V3ZvrkydBPA2u6pLeqjOSV3Xkd7pDoHvEkYJpIRlwh2Eqqa0AMaGND9wjXBrcFlnGkyRAYZGk0c5vva/xzVCOgB1hUe5aTh6VdI/QX+5kETWSKHT8EMC216ZILw1uO/5GYDBSbwhQWLRbVBQV9XhHLywUG90jSiKOb1inICxsuUPS1Lg0eJoI/9sgQGFhg2K5OCgqynEyHUVhkaJC90gKSMB/8bIxfJoKEC9cGrwpunHGS2HRTrlTVCzHmcLCwI/uEQOUADdpI9302Jr00uBNXy/AomKWZgS0zhJIcwQoKpZnS2GRw5DukRw4AexC+cId0tZAS+0UcE385uyRACpRy1nQOtTyZaO5HEWFnaKmsCjBke6REpA8PQQzQ5p0h6SxwFqBGSkQF7h21aXF0/Hxf1wEKCyaK2+KCntsKSxKsqR7pCQozw7TFTTbdk9AUGAWEgQGxmG0fX3PionJnRGgsGimKlBU2OVKYVGRJ90jFYE5fri6Q2CVajtQrLZN3P/rUVjYL0OKCvtMKSxqMqV7pCY4B0+D5QBWg64CxWpX5P27LoWF3TKjqLDLU2OjsFASNb75xFkDmoOnaOPS9WDK5NoXSFPX6XGwqKJPEoWFvSqg9z2+GewSoLCwwJNPnBYgdhgFxjtgrEMX7pB0tiEmtMHj0uBpOvxPYWGnDug9RlFhh2c6FgqLNJEl/tM9sgS8jk9FJ+5SI5NcGhyzSCBeGUiAwmL5OkBRsTzDohgoLIoIVdxP90hFYI4cjsYG4sK1gI4E6YJFBTNY6B5xrYTaTQ+FxXK8KSqW41f2bAqLsqQqHkf3SEVgHR8OaxM6bxfXlcBU1OTS4C6msePii+byFBb1i5qioj67qmdSWFQlVvF4ukcqAuvocFgCICzQ+LgauDS4qyVTkK7RQHrHP5P7dzdlt/fcePB4+EQO7l6f1MHVm3tyMjg3HkdhYcRSuJGiohCR1QMoLKziNEdG94iZi2tbYRVw0R2S5IS6pJ0LhBB+0z2SJOTY7/GpHL16R7Zfh2i4YRYWo/8lJx98IcOxiIyH8uWDLdlY25PeOTbMBy37+a38l0eAoiKPTjP7KCya4WqMle4RIxZnNqo7xIeBkumlwWHNYHCXwHhwKLeNwuKlfPX4CzlLaojznuyumUUIhUW1MqaoqMbL1tEUFrZIVoiH7pEKsFo8FJ21DpJs8bJLXYp1aSl8rZ2cLSwWkzA59uaB9EdJtTE9jsJikVfWFoqKLDLNb6ewaJ6x8Qp0jxixdL4RLyTDy8F8CqxL7pdWOWFxLoPeoeze/XPpDS+MmaKwMGJZ2EhRsYCk1Q0UFq3iXrwY3SOLTLrcgtUvYbXwwR2S5oQ0Qxgh/fimeyRNqLv/hcJi4v64Nh28ubIpu8enMjIkl8LCACW1iaIiBaSDvxQWHUA3XZImbROV9repOwQNuK/BmaXBdSDiCjrMjM5yNJBf7m/JxuSYdbm186H0M57WfS0PpLtQWMwyNx4+lYc7m7K6cl3ePP5a0s4QCov8WkBRkc+nrb0UFm2RLnEdmrRLQGrhEDzt4+NzQF3SRhYzXSBc2w0v5FfHH8uXE5FwIcOn78l2ekDi+Gv55MH78svZ1MrLKZcZ4wvaTb/dq5UVFpOrYibJ5rps7PQkPemUwiK7XLS+45uhWwIUFt3yN149adKGv58mbSOmxjZihUu4E2C98D2k175oy8Uz/uqJPD5LjhN4Lr2dG3Od5eIx5Z/sfSuXSsJCXsrg8M4cK80vhYWSmP+mqJjn0fU/CouuSyDn+kmTNtZYCKGjy8muM7vQ+UJYgH8oAR1Sp0uDT57CX5P7/Rf5SHOmWuaf6PbeasICImyTrpCSRUpRURJUi4dRWLQIu86l0iZtdBAMzROApQgv/wopQJjq0uDIXztLg49lNOjJ0c735e3e2cKYgQW+EBbfeEtO5qwdC0d5tyFTWIy/lpN7NxJjSy5k2Pux3L77UE453bSwnCkqChF1cgCFRSfYq18UJm0d8U/3SHV+Vc9QdwiEXWgBggJ1CFYZiKfmLGFT9weus7qCgZnHMjB0lld8x3Lee0du7z81zoi4Os6nX0kGs1kfm4cyuByVeS6nh/dmg1evyeraltw/7k9X4TRkk66QKygUFVcsXPtFYeFaiRSkJ+kewY0VYsdXgKCV3RBy6BDbH/TYSvYm9UY7KeSzUUvYeCj9D3bk1so12bh3PL/KZDK7o6dy/+67xoWhkofF/FvLLGYGyDtFhds1gMLC7fIxpi7tHglpLIAxwx1txJgEuA5CDhhPAqsFxEWzlrDpgMTVjHdgiLyQ/oMfy9Fpeh5EyPSr543CgqKieq1p/wwKi/aZW7ti0j3CBZGsYb2MSJ+KYrAKtbGOymScgVFYXMjZo/flIUXFZd3L+hG7sNB7Et8M7hKgsHC3bEqnjO6R0qgqHYixCHiSb2eQY6WkNXIwBJSOLYG1xq4lDOMn9uSVBVcIBiu+LwdzAzvP5fSDD+Wx4e2ejWTco0hjFhYUFf5UVAoLf8oqN6V0j+Tiqb0TwiK2p6PlLWEXcnb8lmzc3JGH/eFkJsh4+Lm8vfn9lKvjXAbHe5OxF+A895kb4Fi7+II7MVZhQVHhV1WmsPCrvApTu3ynUHiJqA7AGAs8vccYkpYwWDLKu4TGMjp9KNtrKhauy/b+cWqp7pn4SAuK2QyS24enxVNTIyyUGIUFRYV/FZ3Cwr8yK5XiZKeAG7N8p1Aq+mgOwtiDmNwh6YJFvdG1LyCwQp0lk863q/9jExaZoqL0O2bwxthH8vP9LXnFsES6q+Xse7ooLHwvwZz00z2SA6fkLjCM0R2SxgNLWHLti7aWBk+nI/b/MQmLTFFR+h0zmIl0T964+9pknRDTu1dir09N5Z/CoimyDsVL98hyhYEndnSq+QErTD6Wk4/3Zfsbe9IrGng4W3HRN5M/OjZYLiC28JuWsPxaYXtvLMIiU1TgTbEL76EpeMdMzkvdbJcP45sSoLCIqCbQPVKvsMENHWneUzqmUn7n9S15A+MKjFMqk9fW8QXr4puwQC6wUmdy7YtYZs0kS7Cr3zEIizxRkck97x0zFBaZ2JraQWHRFFlH46V7pHrBoCOFsMAAxvxQtAgUzh7LqP+ubP/oR7K95qewUAbtLQ2uV+R36MKilqhAtch7xwyFRes3DoVF68jduCDdI9XKAQuQFbtDSggLXbb67HPZ9VxYgCCEqnZ2cJHgN0NzBJR1c1foLubaokIK3jFDYdF6oVJYtI7crQvSPVKuPNQdkv/CriJh8UL6+z+cvjp8Yrr122KRJNfe0uDJq8b3O1RhUV9UiIiK9awX3FFYtH6jUFi0jty9C9I9Ulwm6g6BwMgOecJi5gLRN3cGJiyUSXppcA7uVDJ2vkMUFkuJijLvmKGwsFP5KsRCYVEBVuiH0j2SX8JwhcAlkh1yhMXoqRzsPbp6s2egwgJsKFSza8iye0ITFsuJipLvmKGwWLbaVT6fwqIysvBPoHvEXMb6Ho1sd0iWsMCbO38iJ2cXVxEHLCw0k2mhmjerRs/hdz6BkITFsqKi9DtmKCzyK1UDeyksGoAaQpR86lwsRXSMmB2S7Q7JEBYTEaHLW5u+78jR4OXiBQPZkhSq1ZYGDwSAxWyEIiyWExUV3zFDYWGxBpaLisKiHKdoj0o/deJ/zAHuECyYZQ4ZwsJ0cAQWi2S2YeXh0uBJIvV+hyAslhMVugaMSaCnB0NP36i7Mfc+mrBFfL1aZf8sCgv7TFuM8VwGnx9cvewp8TbJhUQsPDVXu8GST51oGGIdlKeNojn/FBYL9S61AcIU4gyWHyyyle1WSp3IvxMCvgsLvX/wzRAuAQoLb8sWA5fek4PPBzJCHsZD+fLBlmysvDqdzjiXL4PKr/FaarpHRLAoFDrFhZdxLQi39NPTXIFMF/QJYB2LVK5K/9UOEizx2yzUSkcXzYHKzccMU1T4WGr10kxhUY9b92eN/488fvz386+WzvIlYp735jvF768omavY3SNYCCrbHVISIg/j0uA16oCvwoKiokZhe3wKhYXHhbeY9OfS27kh82/xUz/jutza+amc9GYWjsWTK2+J1T2CRhLigsEOgeTS4BBsdI9kc/VRWFBUZJdnqHsoLIIqWQiLTXnz+OsrS8bMigGT8/QDgXEsg6xV6iryiNE9ou4QfDPYIYB6pNN5uTR4NlPfhAVFRXZZhryHwiKk0oWff/NA+ibRMB5K/9FPZffmuqyurMstXQHSUv5jco+gE4RIQ6PJYJcAlwbP5+mTsKCoyC/LkPdSWARTuon3UOTlaXwmvb3NEq/2zoskex8aPjxxascb6qA8mOzpDsmuB8vuidXNVsTNF2FBUVFUkmHvp7AIonzxHor3Zffw2XSGSFGeJjMYbshu73nRkbX2p9csQCcRWsCsEIin2Nf1aLJcY3SzFfH0QVhQVBSVYvj7KSwCKOPx2ady8EFJUYH8TsZdvN74ao/JNQvwjo2QlnRWdwjGBTA0SyDpZsPaFyHVo6rkXBcWFBVVSzTM4yksPC/X8bAnBw96MhxrRsYyOv1Yjh7nWCPOe/L2Xk/O9ZSGv5PukZCWdIZYwmJPDO0QCLUeVaHnsrCgqKhSkmEfS2HhbfmOZTQ4ng3G1Bkf+n21quZ42JdPHvUvhcd4+EQOdvalN0y8EKsFBmn3yMICUy2kwfYl4OKBOyTmJ2jbTIviS9ej2GbmuCosKCqKam5c+yksPC3v8dmxvLmmQiL1nVhVczz8XN6ezAS5JqtrW3L/48fWpprWQZd0j/hu1kYnB2FBd0idmrDcOel6hLKIIbgoLCgqYqh51fJIYVGNF4+2RCAUszbcIfgwtE8A41y0o4XAw+9QZyEpXc2v/u/6m6Ki6xJw8/oUFm6WSxSpSpu1fXSPaEMfyxOzixUT7GH9grjAmBdYM0INWt9cyB9FhQul4GYaKCzcLJeoUpU2a/s0ZgFpRYcW4pRa3yohxlvoGiqhLg3uirCgqPDt7mg3vRQW7fLm1XIIoNHUjsGn2SN4SqY7JKdgW9wFVwjqDsQe6hLqVEjBBWFBURFSjWomLxQWzXBlrDUJ+Oge0Y4sdP9+zSLt5DRYkiD2IDDwHYp7pGthQVHRSXX27qIUFt4VWRwJ9sk9ou4QH8eIhF6bQlsavEthQVER+t1iL38UFvZYMqYGCKAh9cE9gjTCr8/gHgFYkrRTRDn5PB6mK2Gh/PDNQAJFBCgsighxf+cEfHCPaMNLd0jn1SUzAT5ZwbIy0YWw0LpNUZFVKtyeJkBhkSbC/84ScLljwIwE+PPpDnG2+lwmzBcr2GWCEz/aFhYUFQn4/FmaAIVFaVQ80BUCrnYMMLPzqc6VWpKfjqQVDLN6fFkavE1hQVGRX4e4N5sAhUU2G+5xmECyY0CH7oKlAGMskBYGfwhAUEBYwNqERbZQr1wObQkLigqXa4H7aaOwcL+MmMIcAi65RyBu0EH58vSbgzWqXRgXox02yg+/XQ2azibTR1HRJN044qawiKOcg88lGlxYC9AxdLW4FjooXB8NM4N/BGCtcH1p8KaFBUWFf/XWxRRTWLhYKkxTLQIuuEfoDqlVdE6dBMuTilTXlgZvUlhQVDhVDb1ODIWF18XHxJsIdOkeUXeIT+87MTGMfRusT7qiKkSGK2tfNCUsKCpir/F2809hYZcnY3OIQBfuEVhN1B3jEAompSYBiFSXlgZvQlhQVNSsHDwtkwCFRSYa7giBQBfuEXREmGnAEA4BV5YGty0sKCrCqaMu5YTCwqXSYFoaI9CmewSdEKwWdIc0VpydRAz3CMZcoGzhHuliirNNYUFR0Uk1iuKiFBZRFDMzqQTacI+oO8QVv7zmnd92CLQpUtMptiUsKCrSZPnfJgEKC5s0GZcXBNpwj8Adgg9DuASSIhW/YdFoOtgQFhQVTZcS46ewYB2IlkCTT546owAihiFcAijf5NoXTS+OtqywoKgIty66lDMKC5dKg2lpnQCeMrWx1tkcNp48Mb4C8dEd0nqRdnLBtpYG17paJ5MUFXWo8Zw6BCgs6lDjOcERSD552hqYh5kheJpliINAUqSiDkEE2A51hQVFhe2SYHx5BCgs8uhwX3QEbD55qjvEhgUkuoLwOMOwViXdI3C52Qp1hAVFhS36jKcsAQqLsqR4XDQEkk+ecGegMa8jDiBScH4X0xKjKSyHM5peGrxOHUpnr6qwoKhIE+T/NghQWLRBmdfwkkDSPQK3Rp2BeTCJY+0DhjgJQExo5466sOyYmyrCQq+LbwYSaJMAhUWbtHktLwks4x7Rxt3G06qX8JjoCQG4Q2wsDV5WWGi9o6hgBeyCAIVFF9R5Te8IQBhoo17FPaLukDrWDu8gMcGFBGCxgOUCdQhjcKoKTq2DeReiqMijw31tEKCwaIMyrxEMgTruEXQifHIMpgosnRHUobpLgxcJC4qKpYuHEVggQGFhASKjiI9AFfcIOhE8pTKQQJJAeoE2CI6ikCcsKCqK6HF/WwQoLNoizesER6CsewSzA2C1oDskuCpgJUMqFsq42PTY9IUpKtJE+L9LAhQWXdLntYMgUOQegQBRn3oQGWYmrBMoqkN6QZOwoKhQOvx2hQCFhSslwXR4TyDPPQJ3CKasMpBAHoFkHUKdSbtH0sKCoiKPJvd1RYDCoivyvG6QBLLcIwcHBxOrxX/9oz+qveBWkMCYqQUCqEO6aivG5kBMIGBGyWvf/d6kHmHbwYNpnYK4YCABlwhQWLhUGkxLMASSpu3f+eY3J50B3CH6wZoG6EAY+61FEwAABM9JREFUSCCLQHJpcFMdQl2iqMiix+1dEqCw6JI+rx08gc8+++xSTKio0O9lV2EMHh4zOCHws7/6q8w6xOXiWUlcJEBh4WKpME3BEFCfuIoJfl9ZbchieRbqJgnmhmFGgiBAYRFEMTITrhLAYLysDvSPf/CDif8cnQM/ZJBVB3QxLVM9orBw9c6PO10UFnGXP3PfMAGMo9AlnNMdg83XaTecDUbfIYG8OpSeNdJhMnlpErgkQGFxiYI/SKAZAhiEh6mmKiwgNOgbb4Z1qLGiDiUFKutQqCUdRr4oLMIoR+bCAwKwUODD2SAeFJajSWQdcrRgmKw5AhQWczj4hwRIgARIgARIYBkCFBbL0OO5JEACJEACJEACcwQoLOZw8A8JkED7BMYyGjyWk4/3Zfsbe9I7Hy8mYTSQ3vHP5P7dTdntPV/czy0kQALOEKCwcKYomJDgCJz3ZHcte62Cjbv78vPeQEbBZbxahsaDQ/nO61vyBlitGYTF+FSOXr0j269fl9WVG5EJiws5O35LNjYPZWDQW9VI82gSaIcAhUU7nHmVaAmM5by3Jxsrd+Ro8PKSwnj4VB7ubMrqynXZPnwWvbgQeSmDwztmYTGjBgFyOzZhAVG1uS6rqfpzWZH4gwQcJEBh4WChMEkhETALi0kOtdMwPaWHhKBUXigsFjGNZdR/V978y5/In66ty+3DU6HRYpESt7hHgMLCvTJhioIiQGFRrjgpLBY5PZfezvflaPD30tu5kWvNWTyXW0igOwIUFt2x55WjIJAhLMZD6X+wI7foCpnVAgqL9O0wGXuy05Nz0ToU2/iSNBH+94UAhYUvJcV0ekpAOwXzIM6NScfhadasJpvCYh4neOzI/f6L6eaZ24z1ZZ4S/7lJgMLCzXJhqoIhoMIiPXizLyf7W7Kxck027j6U01Hs3nMKi7kqjxlFryZngiift+Tk7GLuUP4hAdcIUFi4ViJMT2AEzMJimslZZ7HCgXmcFZKs9lpnTFYu1pUkKf52kwCFhZvlwlQFQ0A7iXmLxTR7uu+a0MStT+SGdSxmdSGa6aaTdTveWVwobPy1nNy7Lqtc0yKY1iHUjFBYhFqyzJcjBFQ8mITFbPEjWiyEFgutrrMppsappXl1Sc/nNwl0T4DCovsyYAqCJpDRGWBWyPG+bGO1yZs/lt4wYr/5wgqlaXM/pl3euHzt/OT184E+tY+Hn8vbN/9D5uqiU6sN60zQTUYAmaOwCKAQmQVHCSx0mGmf+absHv5C+jGLCkeLrotkXYqGFdSTtLgSmd+PYzj9tIty4jWLCVBYFDPiESRAAiRAAiRAAiUJUFiUBMXDSIAESIAESIAEiglQWBQz4hEkQAIkQAIkQAIlCVBYlATFw0iABEiABEiABIoJUFgUM+IRJEACJEACJEACJQlQWJQExcNIgARIgARIgASKCVBYFDPiESRAAiRAAiRAAiUJUFiUBMXDSIAESIAESIAEiglQWBQz4hEkQAIkQAIkQAIlCVBYlATFw0iABEiABEiABIoJUFgUM+IRJEACJEACJEACJQlQWJQExcNIgARIgARIgASKCVBYFDPiESRAAiRAAiRAAiUJUFiUBMXDSIAESIAESIAEiglQWBQz4hEkQAIkQAIkQAIlCfx/3dNdfQ3atEMAAAAASUVORK5CYII="></p>
<p>Christine’s house is located at vertex <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use Dijkstra’s algorithm to find the shortest time to travel from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F</mtext></math>, clearly showing how the algorithm has been applied.</p>
<div class="marks">[6]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence write down the shortest path from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F</mtext></math>.</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>A new road is constructed that allows Christine to travel from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>H</mtext></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> minutes.&nbsp;If Christine starts from home and uses this new road her minimum travel time to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> is reduced, but her minimum travel time to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F</mtext></math> remains the same.</p>
<p>Find the possible values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>.</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>attempts to construct a graph or table to represent Dijkstra’s algorithm &nbsp; &nbsp; &nbsp;&nbsp;<em><strong>M1</strong></em></p>
<p><strong>EITHER</strong></p>
<p><img style="display: block;margin-left:auto;margin-right:auto;" 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"></p>
<p><strong>OR</strong></p>
<p><img style="display: block;margin-left:auto;margin-right:auto;" 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"></p>
<p>a clear attempt at Step 1 (<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C, D, H</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math> considered)&nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<em><strong>M1</strong></em></p>
<p>Steps 2 and 3 correctly completed&nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<em><strong>A1</strong></em></p>
<p>Step 4 (<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A </mtext><mo>:</mo><mo> </mo><mn>44</mn><mo>→</mo><mn>36</mn></math>) correctly completed&nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<em><strong>A1</strong></em></p>
<p>Steps 5 and 6 (<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E </mtext><mo>:</mo><mo> </mo><mn>41</mn><mo>→</mo><mn>40</mn></math>&nbsp; and&nbsp;&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F </mtext><mo>:</mo><mo> </mo><mn>58</mn><mo>→</mo><mn>57</mn></math>&nbsp; or&nbsp;&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>57</mn><mo>→</mo><mn>55</mn></math>&nbsp; or&nbsp;&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>58</mn><mo>→</mo><mn>55</mn></math>)&nbsp;correctly completed&nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<em><strong>A1</strong></em></p>
<p>shortest time&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>55</mn></math>&nbsp; (mins)&nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<em><strong>A1</strong></em></p>
<p><em><strong><br>[6 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>CHGEF</mtext></math>&nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>A1</strong></em> only if it is clear that Dijkstra’s algorithm has been attempted in part&nbsp;(a) (i). This <em><strong>A1</strong></em> can be awarded if the candidate attempts to use Dijkstra’s&nbsp;algorithm but neglects to state <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>55</mn></math> (mins).</p>
<p><em><strong><br>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>minimum travel time from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> is reduced</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>CHA</mtext></math>&nbsp;is now&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>+</mo><mi>t</mi></math>&nbsp; (mins)&nbsp; &nbsp; &nbsp; &nbsp; <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>CBA</mtext></math>&nbsp;is still&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo>+</mo><mn>11</mn></math>&nbsp; (mins)</p>
<p>so&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>+</mo><mi>t</mi><mo>&lt;</mo><mn>36</mn><mo>&nbsp;</mo><mo>&nbsp;</mo><mfenced><mrow><mi>t</mi><mo>&lt;</mo><mn>24</mn></mrow></mfenced></math>&nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<em><strong>(A1)</strong></em></p>
<p><br><strong>Note:</strong> Condone&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>≤</mo><mn>24</mn></math>.</p>
<p><br>travel time from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>C</mtext></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F</mtext></math> remains the same (<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>55</mn></math> mins)</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>CHAF</mtext></math>&nbsp;is now&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>+</mo><mi>t</mi><mo>+</mo><mn>21</mn></math>&nbsp; (mins)&nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>+</mo><mi>t</mi><mo>+</mo><mn>21</mn><mo>≥</mo><mn>55</mn><mo>&nbsp;</mo><mo>&nbsp;</mo><mfenced><mrow><mi>t</mi><mo>≥</mo><mn>22</mn></mrow></mfenced></math>&nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<em><strong>(A1)</strong></em></p>
<p>so&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>22</mn><mo>≤</mo><mi>t</mi><mo>&lt;</mo><mn>24</mn></math>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>22</mn><mo>,</mo><mo>&nbsp;</mo><mn>23</mn></math>.</p>
<p><em><strong><br>[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.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>
<br><hr><br><div class="specification">
<p><strong>This question explores how graph algorithms can be applied to a graph with an&nbsp;unknown edge weight.</strong></p>
<p><br>Graph <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math> is shown in the following diagram. The vertices of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math> represent tourist attractions&nbsp;in a city. The weight of each edge represents the travel time, to the nearest minute, between&nbsp;two attractions. The route between <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F</mtext></math> is currently being resurfaced and this has led to a&nbsp;variable travel time. For this reason, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AF</mtext></math> has an unknown travel time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> minutes, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&#8712;</mo><msup><mi mathvariant="normal">&#8484;</mi><mo>+</mo></msup></math>.</p>
<p style="text-align: center;"><img 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"></p>
</div>

<div class="specification">
<p>Daniel plans to visit all the attractions, starting and finishing at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>. He wants to minimize his&nbsp;travel time.</p>
<p>To find a lower bound for Daniel&rsquo;s travel time, vertex <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and its adjacent edges are first deleted.</p>
</div>

<div class="specification">
<p>Daniel makes a table to show the minimum travel time between each pair of attractions.</p>
<p><img 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"></p>
</div>

<div class="specification">
<p>Write down the value of</p>
</div>

<div class="specification">
<p>To find an upper bound for Daniel&rsquo;s travel time, the nearest neighbour algorithm is used,&nbsp;starting at vertex <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>.</p>
</div>

<div class="specification">
<p>Consider the case where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>3</mn></math>.</p>
</div>

<div class="specification">
<p>Consider the case where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&#62;</mo><mn>3</mn></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down a Hamiltonian cycle in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></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>Use Prim’s algorithm, starting at vertex <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>, to find the weight of the minimum spanning tree of the remaining graph. You should indicate clearly the order in which the algorithm selects each edge.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, for the case where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&lt;</mo><mn>9</mn></math>, find a lower bound for Daniel’s travel time, in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>.</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><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the nearest neighbour algorithm to find two possible cycles.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the best upper bound for Daniel’s travel time.</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>Find the least value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> for which the edge <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AF</mtext></math> will definitely not be used by Daniel.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence state the value of the upper bound for Daniel’s travel time for the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> found in part (e)(i).</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The tourist office in the city has received complaints about the lack of cleanliness of some routes between the attractions. Corinne, the office manager, decides to inspect all the routes between all the attractions, starting and finishing at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>H</mtext></math>. The sum of the weights of all the edges in graph <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>92</mn><mo>+</mo><mi>x</mi><mo>)</mo></math>.</p>
<p>Corinne inspects all the routes as quickly as possible and takes <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> hours.</p>
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> during Corinne’s inspection.</p>
<div class="marks">[5]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>e.g. <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ABCDEGHFA</mtext></math>            <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Accept any other correct answers starting at any vertex.</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"><mn>7</mn></math> vertices, so <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math> edges required for MST                       <em><strong>(M1)</strong></em></p>
<p><br><strong>Note:</strong> To award <em><strong>(M1)</strong></em>, their <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math> edges should not form a cycle.</p>
<p style="padding-left:90px;"><br><img src="data:image/png;base64,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">            <em><strong>M1A1A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1</strong></em> for the first three edges in correct order, <strong><em>A1</em></strong> for <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BH</mtext></math> in correct order and <em><strong>A1</strong></em> for all of the edges correct.</p>
<p><br>weight of MST <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>33</mn></math>            <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> The final <em><strong>A1</strong></em> can be awarded independently of previous marks.</p>
<p> </p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>lower bound <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>33</mn><mo>+</mo><mn>3</mn><mo>+</mo><mi>x</mi></math>                      <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>36</mn><mo>+</mo><mi>x</mi></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>p</mi><mo>=</mo><mn>13</mn></math>           <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</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>q</mi><mo>=</mo><mn>17</mn></math>           <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mn>14</mn></math>           <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to use nearest neighbour algorithm                      <em><strong>(M1)</strong></em></p>
<p>any two correct cycles from<br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ABCDEGHFA,  AFGHBCDE(F)A,  AB(A)FGHCDE(F)A</mtext></math>           <em><strong>A1A1</strong></em></p>
<p><br><strong>Note:</strong> Bracketed vertices may be omitted in candidate’s answer. <br>Award <em><strong>M1A0A1</strong></em> for candidates who list two correct sequences of vertices, but omit the final vertex <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ABCDEGHFA</mtext></math>  <strong>OR</strong>  their shortest cycle from (d)(i)                   <em><strong>(M1)</strong></em></p>
<p>upper bound <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>43</mn></math>           <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>cycle starts: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ABCDEGHF</mtext></math></p>
<p>return to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> has two options, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>FA</mtext><mo>=</mo><mn>18</mn></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>                   <em><strong>(M1)</strong></em></p>
<p>hence least value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>19</mn></math>           <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>upper bound <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>58</mn></math>           <em><strong>A2</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognition that edges will be repeated / there are odd vertices           <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BH</mtext><mo>+</mo><mtext>DG</mtext><mo>=</mo><mn>21</mn><mo>,</mo><mo> </mo><mo> </mo><mtext>BD</mtext><mo>+</mo><mtext>GH</mtext><mo>=</mo><mn>15</mn><mo>,</mo><mo> </mo><mo> </mo><mtext>BG</mtext><mo>+</mo><mtext>DH</mtext><mo>=</mo><mn>21</mn></math>  <strong>OR </strong> <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo>+</mo><mi>x</mi></math>           <em><strong>A1</strong></em></p>
<p>recognizing <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BD</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>GH</mtext></math> is lowest weight and is repeated           <em><strong>(M1)</strong></em></p>
<p>solution to CPP <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>107</mn><mo>+</mo><mi>x</mi></math>           <em><strong>A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>13</mn></math>           <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>M1A0M0A1A1</strong></em> if only pairing <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BD</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>GH</mtext></math> is considered, leading to a correct answer.</p>
<p> </p>
<p><em><strong>[5 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;">
<p>Mostly well done, although some candidates wrote down a path instead of a cycle and some candidates wrote a cycle that did not include all the vertices.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates could apply the algorithm correctly to find the weight of the minimum spanning tree. A common misconception was selecting the shortest edge adjacent to the previous vertex, instead of selecting the shortest edge adjacent to the existing tree. This approach will not necessarily find the minimum spanning tree. A small number of candidates found the correct minimum spanning tree, but did not show evidence of using Prim’s algorithm, which only received partial credit; where a method/algorithm is explicit in the question, working must be seen to demonstrate that approach. Part (b)(ii) was also answered reasonably well, however several candidates did not read the instruction to give their answer in terms of <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">x</mi></math>, instead choosing a specific value.</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates could apply the algorithm correctly to find the weight of the minimum spanning tree. A common misconception was selecting the shortest edge adjacent to the previous vertex, instead of selecting the shortest edge adjacent to the existing tree. This approach will not necessarily find the minimum spanning tree. A small number of candidates found the correct minimum spanning tree, but did not show evidence of using Prim’s algorithm, which only received partial credit; where a method/algorithm is explicit in the question, working must be seen to demonstrate that approach. Part (b)(ii) was also answered reasonably well, however several candidates did not read the instruction to give their answer in terms of <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">x</mi></math>, instead choosing a specific value.</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Mostly well-answered.</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Mostly well-answered.</p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Mostly well-answered.</p>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates could successfully apply the nearest neighbour algorithm to find a correct cycle, but some made errors finding a second one. Part (ii) was done reasonably well, with many candidates either giving the correct answer or gaining follow-through marks for selecting their shortest cycle from part (d)(i). A small number of candidates incorrectly chose their longest cycle.</p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates could successfully apply the nearest neighbour algorithm to find a correct cycle, but some made errors finding a second one. Part (ii) was done reasonably well, with many candidates either giving the correct answer or gaining follow-through marks for selecting their shortest cycle from part (d)(i). A small number of candidates incorrectly chose their longest cycle.</p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question had a mixed response. Some candidates used the table or the graph to realize that the two choices to get from <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">A</mi></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">F</mi></math> are either <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">x</mi></math>. Some incorrectly stated <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">x</mi><mo>=</mo><mn>18</mn></math>. These candidates often achieved success in part (e)(ii), making the connection to their previous answer in part (d).</p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question had a mixed response. Some candidates used the table or the graph to realize that the two choices to get from <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">A</mi></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">F</mi></math> are either <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">x</mi></math>. Some incorrectly stated <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi mathvariant="normal">x</mi><mo>=</mo><mn>18</mn></math>. These candidates often achieved success in part (e)(ii), making the connection to their previous answer in part (d).</p>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>A surprising number of candidates did not seem to realize this was an application of the Chinese Postman Problem and simply equated the given total weight to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>120</mn></math> minutes. Not only does this show a lack of understanding of the problem, but it also showed a lack of appreciation of the amount of work required to answer a 5 mark question. Out of the many candidates who recognized the need to repeat edges connecting the odd vertices, some did not show complete working to explain why they chose to connect <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi>BD</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi>GH</mi></math>, only gaining partial credit.</p>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>A graphic designer, Ben, wants to create an animation in which a sequence of squares is created by a composition of successive enlargements and translations and then rotated about the origin and reduced in size.</p>
<p>Ben outlines his plan with the following storyboards.</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 four frames of the animation are shown below in greater detail.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAxwAAACsCAYAAADxJargAAAgAElEQVR4Ae2de3cU17nm8xXmg8yav2fOmslaM5NzVjI5KyeOg3Nyzoyds06WY5IYGwcHm9icGDtgDDEYHINtnPiCLYTBmJttBBJIGBBIIGwhLpIA3ZC6WwJdW91dl2fWW63qi7rV6u5d3XV7Cvaq3dVVe7/72W+p96/fvau/A25UgApQASpABagAFaACVIAKUIEaKfCdGpXLYqkAFaACVIAKUAEqQAWoABWgAiBw0AmoABWgAlSAClABKkAFqAAVqJkCBI6aScuCqQAVoAJUgApQASpABagAFSBw0AeoABWgAlSAClABKkAFqAAVqJkCBI6aScuCqQAVoAJUgApQASpABagAFSBw0AeoABWgAlSAClABKkAFqAAVqJkCBI6aScuCqQAVoAJUgApQASpABagAFagaOOLxONWjAnkKJJNJzMzM5B0Lw4uOjo4wNJNtpAJlK2CaJm7cuIHBwcGyr+GJVCDsCnR3d2Pv3r1hl4HtD6gCBI6AdqwbzSJwuKE666QC3lOAwOG9PqFF3legqakJGzZsQEtLi/eNpYVUoEIFqgaO6enpCqvi6WFQIJVKQXzDThIJy81PTEwETgZGOALXpWyQogIEDkUBeXloFdi0aVNo286GB1sBAkew+5etq4MCBI46iMwqfKUAgcNX3UVjPaQAgcNDnUFTHFWAwOGonCwsDAqMjIzg4MGDsNcxETjC0OtsYyUKEDgqUYvnUoGsAgSOrBbMBUuBsoHj5s2buHTpUqb1nFKVkYKZECpw/vx5q9WyyO/w4cMhVIBNpgJLK0DgWFobvkMFSilA4CilDt/zswJlA4c08sCBA5m2EjgyUjATQgUaGxszrW5ra8vkmaECVAAgcNALqEB1ChA4qtONV3lfgbKBQxYDyxMUZJPHHco3u9yoQFgVsKdTSfs5pSqsXsB2L6UAgWMpZXicCpRWgMBRWh++618FygYOmbcu0GFvjHDYSnAfdgUIHGH3ALZ/sQIEjsWK8DUVKE8BAkd5OvEs/ylQNnAsblruN7yL3+NrKhAmBQgcYepttnWxArquW1OoNE2z3jIMw9r39PRgYGBg8el87TEF5GtE66tEUwPMeSQt+5LQTcCUrpRklme0nJZOOpLQMS+XGQnoehxIzgOaARhlFlZelYE7i8ARuC5lgxYUqBo4GOGgD1GBtAL2AnLqQQXCpoANF/IFVHt7O7766iuMjY1BjsvUWwKH9z1Cgw5dqMJIAUbcgg9dIMEENF2HoWswDB2GaS6bTN1EOunQDB0pgRU9BQMaoGkwNB26SeDI9YpIJJL7EgSOPDn4IkAKEDgC1JlsijsKMMLhju6s1X0FBCzsJNOo5F4YHh62Ih6nTp0icLjfRctaYJoSoTIge5gpJCQoYaSgp5Iw41PoPvkZhi6dxNDF5dPIhWYMX2jBcLvsT2P4QhsGL5xC74VTuHe+GbHudqvsZY0KyQnHjx+3wFz29kbgsJXgPmgKEDiC1qNsT90VYISj7pKzQo8oIJBhp/n5eev3aeS1TLOSx0Xfvn3bI5bSjCUVMAyYhpmePmXCmlIlEQ0zlQBig9j30m/Qf+Jj9J/8dNl0++Q+9J3aj95Tn+LOic9w98Rh9J7aj1vNn+Hbv25F63tbASM9aWtJe0L0RktLC9atWwfZyyZRQQJHiBwgZE0lcISsw9lc5xXgE9uc15Ql+kMBe0qVvX6joaEhY7gMnu7cuZN5zYxHFTA0QDcAPb1eQ3bplRgGzIkBHN/9ErRYHxKRoWVTMtqHeKwf8dhtaKN3YdwbQmL8DhLRu5hqO44zDe8sLArxqBZ1Nkue/CmAYQOHVE/gqHMnsLq6KUDgqJvUrCioCjDCEdSeZbuqVUCiHAIcg4OD1RbB6+qkgL1oPL3Uf2F9uKyzEPKIDePUrk1IRgYxGxtbNs1H5ZwIpmMxxKNRJCJRTE6MIB4dQ/L0UbTvfXdhJXqdGufDaggcPuw0mlyWAgSOsmTiSVRgaQW4hmNpbfhOOBUgcPio3+XhYnayqENIQ9ZzABgfxKndG5GMDGMuFlk2JSP3kIiMYjYWxUwsgtnxEUw8GMTMxDASrY043/AGIE/D4rakAgSOJaXhGz5XgMDh8w6k+e4rwF8ad78PaIG3FCBweKs/SlmTgvyTZ1UtbGYSJkyLQfT7w/h8z+uYiQ1jZnxk2TQfHYE+OorU6DjikSjmo6OYid2zoh3J1v04/8lfGOGwdV5iT+BYQhge9r0CBA7fdyEb4LYCjHC43QOs32sKEDi81iNL26Ob8qhaw/p5DOuBtaY8xta0HotrTAzgy3c2IR4dwmzs3rJpZnwQicgwEmNRzEXHEI+OYDYqU6qimG9txLkGAsfSPZF+h8CxnEJ8368KEDj82nO02zMKEDg80xU0xCMKEDg80hHlmCGUIT/yJ7+zYWWM9G/9WVOq7qJ518tIRAYwF723bJqeGMJcbMg6TyIbc7ERKz8fjWDm7D58bQFHJpZSjnWhO4fAEbouD02DCRyh6Wo2tFYKEDhqpSzL9asCBA7/9ZxMoxLksJjDNn98ECd3b0IiOoA5CyAEIkqlUev92diINZVKzp2NjkEWk0+dkwjHm4D83ge3JRUgcCwpDd/wuQIEDp93IM13XwE+pcr9PqAF3lKAwOGt/ijHGgJHOSrV/hwCR+01dqOG+7c68KDvyrJp8s63bphXlzoJHHWRmZUEWQFGOILcu2xbNQoQOKpRzd1rCBzu6m/XTuCwlQjWvv/YbiQmY8umwZZPgtXwnNYQOHLEYJYKVKMAIxzVqMZrgqwAgcN/vUvg8EafETi80Q9OW0HgAAgcTnsVywudAoxwhK7L2eBlFCBwLCOQB98mcHijUwgc3ugHp60gcBA4nPYplhcSBbq7uzMtJXBkpGCGClgKEDj85wgEDm/0GYHDG/3gtBUEDgKH0z7F8kKgwK5du3Dw4EGkUin09/db+RA0u6ZNnL53F9827MDNYx94Nn3b8AamhvpqqkNQCidw+K8nCRze6DMChzf6wWkrCBwVAMelS5fwxRdfZPpgeno6k2eGCoRJAflAGBkZgR3lYIRDvfdHu87i1MuPY/zmFc+ms2+tx/DFZvXGhqAEAof/OpnA4Y0+I3B4ox+ctoLAUQFwnD17Ftu2bbP6IB6PIxKJON0fLI8K+EIBiWoIfMt9IBuBQ73botcu4evXnsRMbMx6jv/UeNTa269z97l5ec6//dq+xt7bx3P3uflyr7Wv6fpgM8aunlNvbAhKIHD4r5MJHPXvs4GBAbS1tUH29kbgsJUI1p7AUQFwHD58GOvWrct4ACMcGSmYCbkCfEqVugMIcJzZuHKZHxUr9YNjtX+PwFHYz4ZhQNd1KwlkyGtJku/p6cHg4GDhRSE9Ij93lwKgSfsNHUno1i97J00TCUMDdMM6wZC365jEHPlRcbHLsk3qNpMwjHmYsT6cePtPiEfvYi4qvxpeOs2PxTAfuYfp8WE8uD+AmYk+3B8fhRYbRPzCPrR+tB0wpXXcbAW6urrQ0tJivwSBIyNFoDIEjgqAY3HPEzgWK8LXYVXAnloV1vY70e5oTzrCUfpXjGsPFaXqJ3AU9rSmpYeosp5pfHwc3//+9619MplEb28v7t69W3hRSI9YEQTTzI7uRQdDBveS5gF9CkjGAYGPeibpQ0n6Qr3SpXoS0BNApA+n3nwZ2tgdpCKDyyZtbAz66BCSkUHr18n1yG1o4xPQRoYx234Ebfv/mm5/SH2gWLP3vPtu5rB8lmzYsCHzmhnvKNC++VFcfXtN1an1uX9A9wfrl0384b8ifU7gKCIKD4VSAUY41LvdnlJVasDv9nsEjsJ+tiMaiUQCjz/+ODo7OzEmg05dR0NDg/VQhcKrwnnElHiGaViAIV/yS7RDt2ADMObG8c3xBgy2ncDtM0fqmgZOH8GdM0fR15pOt09/gf4zn6Pv9CEMHXkHB555BNePvY+e4x8tn459guvH5LwP0XPsQ9w6+jf0HD+AG0f3oWP382h590+AkQynAyzR6sWfH4xwLCGUy4cjV5qX/dG+Uj/sd+vA6y63wP3q+Tsc7vcBLfC5AlzDod6BkWsXrUXjbkNFqfoJHIX9LFOnBC4EOJ5++mkrqtHa2mpNqzp37hwjHLmSmTnAYQIy7E6ZJqygx+Qw9r34BIa/asCdM5/XNd09fRh3Th9BX6skyR9H35nD6G87isFjf8Px9Y9jrPMkxrrOLJtGu1ox1tWMsa4WRK6cRqyzGWOd53Cvow2Ri0dx/9YFaKagFrelFCBwLKWMu8cJHOr6EzjUNWQJIVdg8TdUIZejquYzwlGVbK5fZEc4ZD83N2et85O9bNevX89bDOu6sW4bIGENKy1MpbLtkTlVU8M4suV3wPAVzIyP1jXNR8YQj4xZD1+YGR/DXDS2kI9ipvcbtOzZnp7iJQs9lktyggCFKdOz9PQ0LVm8Iik5g4SpIWG3m/uiChA4isri+kECh3oXEDjUNWQJIVeAEQ51B+CicXUNvVQCn1K1RG/YA3Z7Vbj9enoMh/78PDB2EzPjw3VNyegQEtEhxGNDiI/L2ot7mIsOYnZ8GPG+y2jZsxUwBBNso5fb6zCRTrIM3W4izHnopmaxxxLq8DDAReMe9QICh3rHEDjUNWQJIVeAwKHuAFw0rq6hl0ogcBT2hgy85Yt++2lQ6deGNTQ3JqM4tnk9cO8u5qNjdU0CGPMCGbERzMWGkYyMIh4dwuz4PcT7utCyZ9vCugs7VFFiLwEOM9tOu73Wc6ms6I60mlspBRjhKKWOe+8RONS1J3Coa8gSQq4AgUPdATilSl1DL5VA4CjWGwujcRlzywhcyMNMA4c+HcH+bS8gcb8f0+NjdU1z0SgkzcZGMRu7h4RMsYoOWY+ojvdeXQCO9NPIirUq75i0beFBXLlYYsdEBEaskEfeRXyRqwCBI1cN7+QJHOp9QeBQ15AlhFwBruFQdwBOqVLX0EslEDiK9UZ6DYcs2ZCnU0m4wzANa9KRPjWGz7c+Dy12s+6/RTNrwUYUM7FRzMRGkLAiHINWxCPeKxGO1wFD1mWUsYbD1C2Ikv43JFlsJROs0nxltVvK4bakAgSOJaVx9Q0Ch7r8BA51DVlCyBVghEPdAeQpVfJL46WeEuX2e3xKVfn9TOAo1Cr3sbgyAJcBvAF7StUYjm55HojcRDw6UteUjmxIdCMd4Zi3ftxPIhyjiPdeRst7soZDKw84LLQQsFqI5lgypMFD2mxNrSqUhkdyFCBw5IjhoSyBQ70zCBzqGrKEkCvACIe6AzDCoa6hl0ogcBT2hoH0t/75o245asKciuDzrX8Aon11h+7ZcVm7IWkUc7ExxGPD1tSquVjUAo7m97YAErngVhcFCBx1kbniSggcFUtWcAGBo0ASHqAClSnAXxqvTK9iZ3PReDFV/HuMwFHYdwSOQk14pFABAkehJl44QuBQ7wUCh7qGLCHkCjDCoe4AXDSurqGXSiBwFPYGgaNQEx4pVIDAUaiJF44QONR7gcChriFLCLkCXMOh7gCcUqWuoZdKIHAU9gaBo1ATHilUgMBRqIkXjhA41HuBwKGuIUsIuQJtbW0hV0C9+Vw0rq6hl0ogcBT2BoGjUBMeKVSAwFGoiReOEDjUe4HAoa4hSwi5AoxwqDsAIxzqGnqpBAJHYW8QOAo14ZFCBQgchZp44QiBQ70XCBzqGrKEkCtA4FB3AC4aV9fQSyUQOAp7g8BRqAmPFCpA4CjUxAtHCBzqvUDgUNeQJYRMAZlCtXPnzkyrCRwZKarOcNF41dJ58kICR2G3EDgKNQn7kaamJmzcuBF9fX0ZKQgcGSk8lSFwqHcHgUNdQ5YQMgUOHz6M3bt34/79+5BH4jY2NoZMAeebyylVzmvqZokEjkL1CRyFmoT9yPr1663PkpaWFkuKxn37sGHDhrDLkmn//MQoevZuWDJdb9i05HulrqvmvfbNj+KbPc9Vndr+8MNMu8KaKRs4du3alfet7vT0dFg1Y7tDrkB/f38eZDDCoe4QXDSurqFbJRiGAQGMVCoFyWuaBl3XcePGDQwODrpllufqJXB4rktcN0gAQ76wkkiHvTHCYSsBPOi7guTMJBLT94unyVjx40udr3BcbOGmpkDZwCHTSFavXm3VJjSee4OomcCrqYC/FeDvcKj3HyMc6hq6UYLAhWwCGvIZcfr0aczMzFgAcvPmTYyMjLhhlifrJHB4sls8ZxSBI9slMshPCFR4IBE4sv1Sba5s4JCpIxLlsDdGOGwluA+7AoxwqHsA13Coa+hGCRLZENiQ9Itf/AJbt26FfDbI63feeQd37txxwyxP1kng8GS3eM4oAke2SwgcWS2CkCsbOBY3lsCxWBG+DqsCBA71nudTqtQ1dKMEmTplT6X65JNPIFGNs2fPWsdkStXAwIAbZnmyTgKHJ7vFc0YROLJdQuDIahGEHIEjCL3INriqAIFDXX5OqVLX0I0SJMIh0CERDZk+dfv2bczPz1um9PT0YGhoyA2zPFkngcOT3eI5owgc2S4hcGS1CEKOwBGEXmQbXFWAvzSuLj8Xjatr6JUSBEJk46Lx/B4hcOTrwVfFFSBwZHUhcGS1CEKOwBGEXmQbXFWAEQ51+RnhUNfQKyUQOIr3BIGjuC48mq8AgSOrB4Ejq0UQcgSOIPQi2+CqAnxKlbr8XDSurqFXSiBwFO8JAkdxXXg0XwECR1YPAkdWiyDkCBxB6EW2wVUF5Alu3NQU4KJxNf28dDWBo3hvEDiK68Kj+QoQOLJ6EDiyWgQhR+AIQi+yDa4qwAiHuvycUqWuoVdKEOCQxDUc+T1C4MjXg6+KK0DgyOpC4MhqEYQcgSMIvcg2uKoA13Coy89F4+oaeqkEAkdhbxA4CjXhkUIFCBxZTQgcWS2CkCNwBKEX2QZXFWCEQ11+RjjUNfRSCQSOwt4gcBRqwiOFChA4spoQOLJaBCFH4AhCL7INrirACIe6/Fw0rq6hl0ogcBT2BoGjUBMeKVSAwJHVhMCR1SIIOQJHEHqRbXBVAQKHuvxcNK6uoZdKIHAU9gaBo1ATHilUgMCR1YTAkdUiCDkCRxB6kW1wVQECh7r8nFKlrqGXSiBwFPYGgaNQk7AfSaVSkJS7ETiyahA4sloEIUfgCEIvsg2uKsBfGleXn4vG1TX0UgkEjsLeIHAUahL2I3v27MHx48fzZCBwZOUgcGS1CEKOwBGEXmQbXFWAEQ51+RnhUNfQSyUQOAp7g8BRqEnYj3R1dWH9+vWZKIc8SnrDhg1hlyXTfgJHRopAZAgcgehGNsJNBfiUKnX1uWhcXUMvlUDgKOwNAkehJmE/0tLSkgccogcjHFmvIHBktQhCjsARhF5kG+quwO7duzN1MsKRkaLqDBeNVy2dJy8kcBR2C4GjUBMeKVSAwJHVhMCR1SIIOQJHEHqRbairAv39/Vi3bp1VZ3d3Nw4+swLtO5+30vk31uLiWy9A9nLsws7n8/Jfb382c9zOy17Ok/OXykt59jm5deTmVetbXEc96/vq+X9B44r/jAvSTo+l9h3PWTZ9teYhjF09V1df83plZsqAZphIwURKT+DB/Ri0ZAowgOs9NzB8dwAwdSZLA0NksZIOzepazUzBgAbjwSCOvP4H6JF+zMTG6prmoqNIRoYRj97DdCyGRGQEU9FJzMcmoN88j5b3NqX7z+vOGBD7CBzZjiRwZLUIQq4i4Ni3b1+mzdPT05k8M1QgTAqcOHECL774IkZGRqxmn3r5cUyNR61BwlzsHpgq12Dg7HFcfDMNcWHyJd+31ZhDKjVnwQagY9265xGdeAAdQPf1axgevgFTN5l0E4YhyYBm6kiZSSsv4KGZGszJERzcsg7JsT7MRwbqmuaiw5iP3sVs7A4mxwcxH+vF9PgYpkYGoN1oR+ueHYAhqMStHgoQOLIqEziyWgQhVzZwyJN49u7da7VZ5h2efWs9rh/+G24efd/aM1+dDpc/3IrUHOHNzzfTyT+txP379wkaCrBF4PDpHWACugnEDR2vbHkNB48eRSw6Dkzcx6P/7b/grZ//T3z2zMNMlgYrcPCZR3DgmRU48LuHcfCZf8aHv/kR9q/5GY6v/Hvs/Lv/hKbVP8L+VT+pa/pw9c/x8dM/xb6nfox9Tz2Ez3/7f9Cw6hF8+OQK7F/9Exx66d8BY96nDuo/swkc2T4jcGS1CEKubOAQ2Hj22WczT1P47JffxcilZiZFDVo3rkRyZjIIvhTaNpx85VdWhIORjcojG7ZmAhwylYqbzxQwdBiGjngijvMXL+CjhkYMj4zBTCRxu/0UWv78DEbOHGTK0WCo9QCG2vZj+MznGGw7hIG2Q4h++Vd8sfZnmO44gomu1rqmyDfnMH61DRNdZzBxtRVTV5ow0fU17l08jVhnMyZvXYRmpKeA+cw7fWkugSPbbQSOrBZByJUNHNLYeDyeafOxp/6R3+gqfKNrD7Q63v4jElMTGV2Z8Z8CMqXK7k/uq4MORjj85/disWYa0I0UYMqPl+lIpFLQDMA0gVsXW9G5bzvmoiNM0RHEo7JOYhBzsQHMjd9FXI7dH8VUbASJO9/g2LYXAG0S1uJymPXbm9JfJgzpS9OEaU33MtOLTTQNuqFbU+T86aH+s5rAke0zAkdWiyDkKgKO3AYTOKobWC0ekBI4cr3Kn3lGONTvBUY4/On7MtEmZQ1HBTi0hYFremV0/8VzuPzxDsSjo0yWBiOYF+iIDSEuayWiY5iNjVrrJeZvd+PYtv8ANHem15owocO0lrJLzlqxYQpD6jANeYdbvRQgcGSVJnBktQhCrmrgOLLqh/xWlxGOINwDym0gcKgDx52vv+SicWVPdKEAWR0uSUaopnw3L9+USx64fbENlz/eibnxYabxYczGRjC78JkxOy7RjihmYxFMjUcwf/sajm7/I6DN1L8TDR2wUrrfrP60+1SmzEGepMVF4/XqGAJHVmkCR1aLIOSqBg5GONQHWRLtYITD/7cRF42r3wucUuXP+0BDEtaEG4EMCzrS06mkNTcvn8fX+9/FfHSUSSIcAhsWfA0hHhtAMnIPcQtCRpC8fRXHt/0B0B644AiaBRQSrZpbSMkF9rBCG7rBp1TVsVcIHFmxCRxZLYKQI3A4EKVYPE2qktcEDv/fRoxwOAMcXDTuw3tB13MiHOlRqinrOYxZ3Ll4Elc+3gb5Np9pGNPj9zA1MYbp8VHMWBGOyMKUqlHM3/4WR7e/AOguPEBEHnkrYamFyJQFjguRKzksy8U5pap+9yaBI6s1gSOrRRByVQMHp1SpD7IY4QjCLQRw0bj6vSARjvPb1gTDIULbCpl4I+sAJNSho6/jDDoadnDq7cKXWvLDepLk774AmER+ZD3HXGwIydtdOLZtPaC7s4YjtC7rwYYTOLKdQuDIahGEXNXAwSlV6oMsAkcQbiGAEQ71e4GLxoNwLxA4SkW3CRxB8PHat4HAkdWYwJHVIgg5AgenVAXBj11tA4GDwOGqA3qmcgIHgcMzzuhbQwgc2a4jcGS1CEKuauDglCr1QRYjHEG4hQAuGle/F7hoPAj3AoGDwBEEP65vGyKRSF6FBI6sHASOrBZByFUNHJxSpT7IInAE4RbilKpSg6xy3+OUqiDcCwSOUv7OKVVB8HHn2/BP//RPeYUSOLJyEDiyWgQhR+DglKog+LGrbeCUKnX4JnC46sIOVU7gIHA45EohKWb9+vV4//33M61tampC4/e+w+RBDQR+uKkpUDVwcEqV+iBLPpz4WFw1B/bC1XxKlfq9IMDBp1R5wZtVbCBwEDhU/Cd817a0tOC73/0uZC9bKpXClXefQ2J2OvQpOTOJ8WvnwucUAW5x1cDBKVXqgywCRzDuLEY41O8FRjiCcC8QOAgcQfDj+rYhHo/nVdi5+1kkJmNMkzFErjTnacMX/laAwMEpVf72YA9Yz0XjzgDHxTfXeaA3aUL1ChA4CBzVew+vTCtA4MjCFoEjWHdF1cDBKVXqgyxGOIJxMzHCoX4vMMIRhHuBwEHgCIIfu9uGK7vXMLqxEOEhcLjri07XXjVwcEqV+iCLwOG0O9envLa2Nhw+fDhTGYFD/V4gcGTcyVcZwzCg6wZM04SmJSHIkTI0mKaGvsutuPjJG/ylcf7SuK982m1jCRyMcLjtg7Wqn8DBKVW18q1Al/vYY49B13V89NFH2PXY/+agSvE+4qJxf94uAhyGYULmob/313fR0LgPN/t6EZ+bwo2Lzeho2MF7g8DhT+d2yWpOqSJwuOR6Na+2auDglCr1b3UZ4ai5f9ekAoluNDY2WsAhFTDCoX4vMMJRE1eteaES2ZAIh6ZpmJ2dxpm2M+i+0QNdS+DrIw24xAhHBrj4Oxw1d8dAVMAIB4EjEI5cpBFlA0dzczNefvnlTBGcUqU+yCJwZNzJd5n+/v6MzVw0rn4vCHBw0XjGpXyTkQiHPMpzcnISz69bi8tXr+BCx0UAOm62n0LXgV2ZAXep9Q1heI/A4Ru3dtVQAgeBw1UHrGHlZQOH2PDGG29YpsgHzNEnv88PEsVpJASOGnp2HYtmhMMZ4Ljwxto69hqrckIBmVZoLKzhiM/PovPKZWimYUU4uIYj/74gcDjhccEvg1OqCBxB9fKygUPmqj/99NMZHTilKv/DpNpv6PjDfxmX8m2GwKF+L3BKlW/dP8dwPqWq1OcAgSPHVZhdUgFGOAgcSzqHz98oGzgWt5NTqtQHWYxwLPYqf77mL42r3wtcNO5P38+3msBB4Mj3CL6qXAECB4Gjcq/xxxUEDgemRZX6kFnuPUY4/HGjlLKSEQ5ngINTqkp5mR/eI3CU+nvPCIcffNh9GzmlisDhvhfWxoKqgYNTqtQHWfLhROCojWPXs1QuGle/F7hovJ4eW6u6CBwEjlr5VnjKZYSDwBFUb68aODilSn2QReAIxm3FCIf6vcA1HEG4FwgcBI4g+LG7bSBwENRO3X4AABlbSURBVDjc9cDa1U7g4JSq2nlXSEomcBA4QuLqyzSTwEHgWMZF+PayCnBKFYFjWSfx6QlVAwenVKkPshjh8Olds8hsLhpXvxe4aHyRU/nyJYGDwOFLx3XN6OvXr6OpqSmvfkY4CBx5DhGgF1UDB6dUqQ+yCBzBuJMY4VC/FzilKgj3AoGDwBEEP65fG+Q3zXbv3m39eKbU2rhvH66+vQaJyeygO8z5yJXm+nUGa6q5AgQOTqmquZMFvQICB4Ej6D5eXvsIHASO8jyFZ2UV6O3tRX9fX+YAp1RlYYvAkXGLQGSqBg5OqVIfZDHCEYh7CHxKlfq9wKdUBeFeIHAQOILgx/VrQ0tLC7Zt25ZXIadUETjyHCJAL6oGDk6pUh9kETiCcScxwqF+L3BKVRDuBQIHgSMIfuxuGwgcBA53PbB2tRM4OKWqdt4VkpK5aNwZ4Di/bU1IPCaozSRwEDiC6tv1axenVBE46udt9a2pauDglCr1QRYjHPV19lrVxgiH+r3ACEetvLOe5RI4CBz19Ldg1sUIB4EjmJ4NVA0cnFKlPsgicATjtiJwqN8LBA5/3guGYcA0zAXjDeimAc00AOjou9yGSw07UGoQHqb34tF7kCRtnh0fxnx0FPHYEOZiQ0je7sKxbesBfdqfjkCrHVOAwEHgcMyZPFYQgYNTqjzmkv4zh4vGnQGOi2+u81/nh9xiTdMgScDj/v1xfH70MHSkgeNW+ym0f/IGgWPhM4bAEfKbpczmc0oVgaNMV/HdaVUDB6dUqQ+yGOHw3f1iGazrOgYGBjLGM8Khfi8wwpFxJ19lTNOEJPk9gf2f7sPV7m/Q1f0NdC2BtsOfoLPxTQIHgcNXPu22sYxwEDjc9sFa1V81cHBKlfogi8BRK7eubbmbNm3C+++/j3g8blXERePq94IABxeN19Zva1G6wIam6RAIn52dRuOB/Zidn4Npamg++AGnVOVE0BnhqIUHBq9MAgeBI3henW4RgSPnA8GN+cQdb/8RiamJoPpXINsloHHs2DFrGklHRwcan3kEU+NRfpOrcC8xwuHPW0VAQ9ZwSIRj5cpf4c233kT/3dtIzM+i/9JpXOYajszfBQKHP3283lZzShWBo94+V6/6ygaO7u5uHDlyJGMXp1Spf6vLCEfGnXyVaWpqwrlz5zA/P2/ZzSlV6vcCgcNXt0CBsempVbJ6w4C2sIajr/MMOhp2Zgbcbnyh46U6CRwFbsMDRRRghIPAUcQtAnGobODo7e2FTCWR7e7duzj4xN/zg0ThG137g5ARDv/fR1w07gxwcNG43+8FPhbX/rtebE/g8Lt/18d+AgeBoz6eVv9aygYOmTpy/vz5jIWMcKgPsuRDicCRcSnfZhjhUL8XGOHwrfvnGE7gKAYa9jECR46rMLukApxSReBY0jl8/kbZwLFv375MhEPazEXj6oMsAofP754F87loXP1e4KLxINwLBA4bLortCRxB8PHat4ERDgJH7b3MnRrKBo7F5hE41AdZBI7FXuXP14xwqN8LjHD40/fzrSZwFAMN+xiBI99b+Kq4AgQOAkdxz/D/UQKHA+sw7A+UavacUuX/m4jAQeDwvxc70QICR6nPAAKHEz4WrDKmp6exf//+zCPWpXWcUkXgCJaXZ1tD4CBwZL2BuaoU4KJxZ4CDi8arcj8PXUTgIHB4yB19Ykrjvn1IJpOWtZ2dnWCEg8DhE9et2EwCB4GjYqfhBfkKMMLhDHBceGNtvrB85TMFCBwEDp+5rMvmtrS0oK2tLc8KAgeBI88hAvSCwEHgCJA7u9MUAgeBwx3P81qtBA4Ch9d80tv2jI+P43pPTybCIdYSOAgc3vba6q0jcBA4qvceXmkpwKdUOQMc57etoUf5WgECB4HD1w7sCeO5hoPA4QlHrIERBA4CRw3cKlxFMsLhDHBwSpXf7xsCB4HD7z7svv2McBA43PfC2lhA4CBw1MazQlQqF407AxxcNO73m4bAQeDwuw+7bz+Bg8DhvhfWxgICB4GjNp4VolIZ4XAGOBjh8PtNQ+AgcPjdh923n1OqCBzue2FtLCBwEDhq41khKpXAQeAIkbuXaCqBg8BRwj34VlkKMMJB4CjLUXx4EoGDwOFDt/WWyVw07gxwcNG4t/y6HGtM04RhmNappqnDgImUqQPQ0d9xGh0NO1BqEB6m9/jDf+V4FM8hcBA4gnoXEDgIHEH17bq1ixEOZ4CDU6rq5rKOVSTAoesGZH/5cgeaTzcjaWiAqaG/s5XAkfP5QuBwzO0CXRCnVBE4gurgBI6cDwQ3vm3rePuPSExNBNW/QtEuLhp3Bji4aNx/t4v8QrKuS0QDmJ6exMHPP4NmGjCNJHovt+LSvp2McCx8xhA4/OffbljMCAeBww2/q0edBA4CRz38LNB1MMLhDHAwwuG/28Qw0tGNNHQYOHDoIJJ6CrqWwGd73sClT94gcBA4/OfYLlpM4CBwuOh+Na2awEHgqKmDBbHw+/fvo7W11WqaDLS+eulxTI1HObBSuJcGzh4HgcN/d4sFHAtrOFJaAu0dF6FZazg09F9uQ/vH23lfEDj859guWswpVQQOF92vplUTOBQGSU5MweKUqpr6d80Kb29vt8ru7+/HZ2v/lYMqxftIgIOLxmvmrnUqmE+pKvWZwClVdXJDn1fDCAeBw+cuvKT5BA7FgVKpD5hy3iNwLOmbnn6js7MzYx+nVHFKVcYZQp0hcJT6m0/gCPXNUXbjCRwEjrKdxWcnlg0c8k1uR0dHpnnHnvpHfqvrAKwQODIu5dsMgYPA4VvnddRwAgeBw1GHCmVhnFJF4Aiq45cNHCLA7t27LR1aWlqw97H/TuAgcAT1vqioXXxKlTPAwadUVeR2HjyZwEHg8KBbetikRCKBQ4cO5VnICAeBI88hAvSiKuCQ9h9Z9UMCB4EjQLdC9U1hhMMZ4OCi8ep90BtXEjgIHN7wRL9YYWgpfPvNNxlzBwYGQOAgcGQcImCZioAjt+2cUqU+yJIPJ06pyvUqf+b5S+Pq9wIXjfvT9/OtJnAQOPI9gq+WV6CrqytzUnx2BpxSReDIOETAMgQOB6IUpT5klnuPwOH/O4oRDmeAgxEOv98LBI5Sf++5aNzv/u28/dPT0zh+/DhGRkYyhTPCQeDIOEPAMgQOAkfAXLr+zSFwEDjq73VerJHAQeDwol/6yyZGOAgc/vLY8q0lcBA4yvcWnllUAS4adwY4uGi8qHv56CCBg8DhI3f1qKmMcBA4POqaymYROAgcyk4U9gIY4XAGODilyu93EoGDwOF3H3bffgIHgcN9L6yNBQQOAkdtPCtEpXLRuDPAwV8a9/tNQ+AgcPjdh923n1OqCBzue2FtLCBwEDhq41khKpURDmeAgxEOv980BA4Ch9992H37GeEgcLjvhbWxgMBB4KiNZ4WoVAIHgSNE7l6iqQQOAkcJ9+BbZSlA4CBwlOUoPjyJwEHg8KHbestkLhp3Bji4aNxbfl25NQQOAkflXsMr8hXglCoCR75HBOcVgYPAERxvdqkljHA4AxycUuWSA6tUawAwrf+AacI0TRhWSqD/cgs6P9mGuehIVWk2Mox47B5kPzM2ZO1lQB8fv4fZ2Ahmo8OYk3x02Hot+blY8bqscnLskDKrtUtsmZ8Yw/z4KKbHhiwbyylLbJ6LjiEeiWA2NoxUZBDx8WHExweRut2Fo9v/AzAeVN0bor2u61YfVF3IwoVSlr0ZhnRy9ZuUtThVX1rwr2SEg8ARVC8ncBA4gurbdWsXF407AxxcNF43l3WuIh0wTECXEgU8DEBPGTCNOG5dOomrDTugjfWVmXqhjeWn5OgtGON3YMRuQxu9heRYL5KRPiQj/UiO9VkpYR3vQ2q0F6nRW0gtKkPK1Md6MT96yyrDfDBonVetXcZYLxIjN5Aau4XEvZvQI+W1T+xOjd2Ffm8IqUgvzNEepGJi93VovRfx1fYXAXOs6r6xwUDTNEjKhYZKC80tS/L260rLkfMFgsQe2VTLqqZ+v11D4CBw+M1ny7WXwEHgKNdXeN4SCjDC4QxwMMKxhIN5+PBzzz6HZ577vZXWPvsc1q5ZhxeeX481z/wWLz7xf7Hh4f+FV1c+UkZagVdX/rQgbXriYWx8/CHIfvOvV2Dz4yuw+VcrsGXlz6z9n/79IWz85U+w9df/jNeeeMQ69ppVX35ZUsbmlT/Fnx5/yEqv/aYcm+ScQru2/PZnGTtff+rneHXlw2W07xFs/PUKbHrin7Hl8X/FppUr8OdfPYQ//uon2PzUz7Ht336IDSv+Bzas+Rf8/ve/ryqtXbvWuu53v/sdJNmvqylvzZo1kPTss89aZT333HNV2SR1r1u3zipj9erVVpnyupRNHnb3upjGKVUEjro4mguVEDgIHC64XbCqJHAQOILl0RW0xgTku2s7wgEDMHQDpqnjZuc5tH70Nq6daCgjNeLaif15qafpU3Sf2I/rpz7DF7texZVD76PnZCN6mhqt/bWvPsE3xz7C5c//iu6mfbh2cj+uNe1DT1N+OVKuVVbTAWv/4R9X49tjH5dhk9hdxK4vpa4DuHbiU7zwLz9Ez1dyzvJttGw88Sl6vjyI7qZPreu+bf4cV08fxrUvPkXTri1AKlaB+PmnSvRAogmS/va3v+W/WeErKSOZTFoRiTNnzihFS2ybpqam0NTUpFRWhc3w5emMcBA4fOm4ZRhN4CBwlOEmPKWUAlw07gxwcNF4KS/z6Hu6LN2QOfpCGqaVNMNAyjRx69Z1DPffSC/wkCUBJZO8KWsFcpJpwNQ1mIYGQ09ZyV5aIPtiSdft6T855UiZpm6Vo2vJhfK0Zeyx7S1iFwwYYpepwy6vdNvsskSsFGAKoqVTEgaSMC1ISxkmZsTOImseyjkmA3uZupQ7bamc65Y6x/Y4e3rWUueVc9yekpVKpTLrTJa6zq43DHsBsJdeeglXr17NNJfAQeDIOEPAMgQOAkfAXLr+zWGEwxng4JSq+vuuao0ydjYNE7qm497AEN7a8SZm5+IWcHzT04ORkeF8iMgFity8RQ/2wHxhb3GCQAwwcGcQHRc7qi7L0EzLzmQiiQvn2vGXHX+BtgAfAiNWJcbCfjm7JKqT0jE9OY2/7PwLjh4+Vp1d0j4AKV0HNBO3++9g+84dGWiQvpGBugzMy9kEOGQbHR3FE088gebm5rzL7AF+3sESLwQOpH6JlkxMTJQ4s/RbUm8ikcCvf/1rPProo+jr6yt9QYjeXb9+vdVaey8vOKWKwBHUW4DAQeAIqm8rtau7uxvlpsZVD+H0n3+HM689hTOvrVrIr0Lbq79By9ZnrGN2XvZyjhzP5LeszlzbsmU1Dr34y6LltLz6JJpf/H/WuXKe1GeXk7vPtSFt1yoc/sMvkLmmzGut8u1z7f2C3V++8ptMO0udt5xdYp/ocPSFx3DkhV+UrXk5fXPo0CFPlydt2L59e1EblZy3jhfrAhuGgbnZOWzc8Aru9t/G+fMXIMevXb+OwaFBGPIN/nLJNGAUSTKIluNSjjUdB+by/4qUIxEY3dAxOzuLaz3XcKLpBCYmxq2ydDNdh5RcYGeRsuQbf03XrIH9Vye+wuvbXi+8rmhZ8gSvTCDIitDIg4Q1Q4Oe0rDrL29h3QvrMr1XKSDYEY729nYcOHAAAwMDebBSSXnSRimvp6cH7733HiKRSKYsKaeSzY5qyDUCQTJVi1tagb179+Lw4cOWb9uaMMJB4LB9wQ/7tra2ss0kcBA4ynYWnlhcgdxwePEzKjv6wQcfVHZBGWfv2rWrjLPKP+XWrVvln1zGmTK/u6NDvsF2bnNaR6c1lJZ+73vfc67BLpSUknUDhmF9g711y1Zc+7YbX7edtb66v95jA4cMq5f5V2RgbwGIoSOlJTE9M4WW083W1C2Bh+XSYnjRZEqWqSOZSuBU8ykcOPgpEol5pI+nYUTeL7CyiF0CKJKGhgZx7Xo3Ptr7YeF1xY7IY2sXnugl4CHjdtuuG9dv4sD+A/j3f3sM8Xg8M60qd3rUct1rA8fNmzdx4cIFfPjhh5lylrt28ftS79zcHLq6unDp0iV88cUXVrRDzqsEXOR8KUtsk/JOnjyZAZfFdfrl9c6dO2Gnbdu2WXnZV5ukrB07dlhJvoA4uervINAhkY6wp/bNj1pfylSrLa+r3i/L1e7hhx/G+++/X9btS+AgcJTlKDxpaQWcHigvXVP178iHvpOb0+U5aZtdlh9slMGlnzdrMJnSkJxPYnBwCJcvX4ZMW5LRdM+NHtwdHiz2XX/hMWvdQv66DClbBrf2QDoWixWNgiyGi/SAOL8s+U5eyhG9xUaJLs3OzljgYtUjMQoBmcWxiiJ22fY8mHyAzsudVhSg4LrF5Vjlp9e6GEg/sjYNHRp0I2VFhOLz87jT35sZkEs7bA3K8RGxS7aZmRkLOGQalJRhb2ldsq/t48X2EuGQTfYSMZmcnMyUlVtmsWsXH5M2SJqfn8+LlCw+Lwivxa9Ut1dffVW1CHR2diqXcfHiReUyVB9e8ODBAytSp2rI8ePHVYtAS0uLUhn9/f3W3x+lQgDs2bNHtQjr759KIefPn89cvmnTpkx+uUzVwHF81Q8wNdxflzQ5cLMu9dSrPbn1XNz1H0hMVT8/drkO5vvOKyBTO3784x9nCj537lwm70Rm48aNyn8Qcu2QgdoPfvAD3L9/P/ewUv6VV16xHpmpVMiii3fv3o3GxsZFR6t7KQNLiR7IH3mnNvn2UR4T6tQm/SFtzp2/7VTZdStH1wDNgKkZ0GWdxMJ4NpGI4/qtG+gdulPeeupFyzekmNykWVOrTOtpWDKsLpUErXOvLZaXqIwctwb9so5C2lDGdbnnJFMp65pESpZ9L1+nVR806EhY8Q9pg4EUdKSQNE3MG+nnfeWCQSWDewEOOV8G97LZAGL7Qm659rGl9na9UoZd3lLnlnPctqUSG8opN4jnOAEcQdSFbfK/At+5du0aqkmH16zA6S2rHUvvPfGjJcv6Yu3PlnyvlA2lyix1Xan3vtzwq6psWarMHY/8V3RfvlRVHyzVb2+++aaj5R08eNDR8vx+2wjRy1QDmdcsmxPfBOVqInOcnfimzC5TBt8yLcLJwXdvby/eeecduwrlvbRX5jI7BRzT09PWN0FORp8ENMVGmbLi1CZ9I74UtE0Gljdu3MDg4GDQmsb2UIGSCvTduoljx+RBAtVtmzdvti6Uv9kfffRRxX8f5HNJ9W+zfBkiZah8qy9/0+X3VlS3J598UqkIsUPWyoyMjFRdjvztl8iCrEeqdpOogPwGjfzNr3aTMsQOlX6RNReVRCUW2yprw+woy4YNGyqypeoIh4poixsgr50cYNnlOznYsMuUcLWTm4rjLGWH02XKwIFbVgGZYvDpp59m/vg4Eb7Olg5rUaWTcCDTIeRDzMm1JvKBKoNvpzaZ3y0fcqdOnXKkSPn7JPZJXzm1yR97+eBxEjgkwuH031Kn2qtSDoFDRT1e60cF5G/N0NCQZbp8SVftZg8G7cinDOoq3bZu3VrpJQXnywJ/lS/TZHD+29/+tqDcSg6IjuWuD1iqXAEN+SyQL6Gq3WSdTdOJE0rQInU70Zaf/vSnmS87q2mPfKknbVEZH2/ZsgUdly5ZY6C21tayzSgbOKSz7t69mylYpfMyheRkxDnlcX5ObmKvk9NIxMZagJH9TblTbZdBkdP9c+XKFafMC1w5Kjdu4MRgg6iATC9ihIN+EFIF5PPc/ga4GgnsCIcMTuVLooaGhoqKkc9++WV4lalwAk+yaFglKiA6yEBfZXwj169cuVJpPCN6yJdFlTxNabHg0hcSiVaJRksZquMygU+JMMi062o3sUEiPtVGa+R6gWH5okzKkSfilbuVDRzyzaM4oL2pCmeXY+8FDIQindzEwU6cOOFYkTKwlJu/2o4qZoiETWUKlFObRCOkTCc3IWKVG81JW7xYlsq3QF5sD21yTwEn/7a41woCh5vas25/K2BHOKQV9toXP7ZI/pY5PU6sVgcn7PBKJFq1LXK9U58zldpSNnDI4F3C//ZWaUX2daX2TgOHUK0kpzZpszwe0EnHW7t2LVatWuWYA8gCZrHPqbnwop1Mn5FpWrXoc6f6xs1ynJy242Y7WLd7Cjj5N8W9VmRrZoQjqwVzVKASBXKBo5LreC4V8LoCZQOHDNxzHy1Wi8Gnk3AgwsuCKyefICTQpToHr5hDqIQtF5cnkSKx0ckBjER2JHTGrbgCjHAU14VHy1PAyXu1vBprfxaBo/Yas4ZgKkDgCGa/slVA2cCxWKxaAMfiOviaCvhBAQKHH3rJmzYWW2MWBAAhcHjT32iV9xUgcHi/j2hhdQoQOKrTjVdRgYwCXDSekYKZChQoBhbiS0EYcBA4KnAEnkoFchQIwv2f0xxmqUBGgaqBQx61yY0KFFNAFrrZSX5TIugbIxxB7+HatG8xcMhrmbYpye8bgcPvPUj73VKAwOGW8qy31gpUDRyLPyxrbSjL94cCS/nFUsf90arSVnLReGl9+G5xBXLvCcnLQznksdtO/pp58Zprf5TAUXuNWUMwFSBwBLNf2SqFNRwUjwpQASpABagAFaACVIAKUAEqsJwCVUc4liuY71MBKkAFqAAVoAJUgApQASpABQgc9AEqQAWoABWgAlSAClABKkAFaqbA/wcrcSwzfPWddgAAAABJRU5ErkJggg=="></p>
<p>The sides of each successive square are one half the size of the adjacent larger square. Let the sequence of squares be&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>U</mi><mn>0</mn></msub><mo>,</mo><mo>&nbsp;</mo><msub><mi>U</mi><mn>1</mn></msub><mo>,</mo><mo>&nbsp;</mo><msub><mi>U</mi><mn>2</mn></msub><mo>,</mo><mo>&nbsp;</mo><mo>…</mo></math></p>
<p>The first square,&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>U</mi><mn>0</mn></msub></math>,&nbsp;has sides of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo> </mo><mtext>cm</mtext></math>.</p>
</div>

<div class="specification">
<p>Ben decides the animation will continue as long as the width of the square is greater than the width of one pixel.</p>
</div>

<div class="specification">
<p>Ben decides to generate the squares using the transformation</p>
<p style="padding-left: 60px;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><msub><mi>x</mi><mi>n</mi></msub></mtd></mtr><mtr><mtd><msub><mi>y</mi><mi>n</mi></msub></mtd></mtr></mtable></mfenced><mo>=</mo><msub><mi mathvariant="bold-italic">A</mi><mi>n</mi></msub><mfenced><mtable><mtr><mtd><msub><mi>x</mi><mn>0</mn></msub></mtd></mtr><mtr><mtd><msub><mi>y</mi><mn>0</mn></msub></mtd></mtr></mtable></mfenced><mo>+</mo><msub><mi mathvariant="bold-italic">b</mi><mi>n</mi></msub></math></p>
<p>where <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="bold-italic">A</mi><mi>n</mi></msub></math> is a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>×</mo><mn>2</mn></math> matrix that represents an enlargement, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="bold-italic">b</mi><mi>n</mi></msub></math> is a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>×</mo><mn>1</mn></math> column vector that represents a translation, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msub><mi>x</mi><mn>0</mn></msub><mo>,</mo><mo> </mo><msub><mi>y</mi><mn>0</mn></msub></mrow></mfenced></math> is a point in <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="bold-italic">U</mi><mn>0</mn></msub></math>&nbsp;and <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msub><mi>x</mi><mi>n</mi></msub><mo>,</mo><mo> </mo><msub><mi>y</mi><mi>n</mi></msub></mrow></mfenced></math> is its image in <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="bold-italic">U</mi><mi>n</mi></msub></math>.</p>
</div>

<div class="specification">
<p>By considering the case where&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msub><mi>x</mi><mn>0</mn></msub><mo>,</mo><mo> </mo><msub><mi>y</mi><mn>0</mn></msub></mrow></mfenced></math>&nbsp;is&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>,</mo><mo> </mo><mn>0</mn></mrow></mfenced></math>,</p>
</div>

<div class="specification">
<p>Once the image of squares has been produced, Ben wants to continue the animation by rotating the image counter clockwise about the origin and having it reduce in size during the rotation.</p>
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi>θ</mi></msub></math> be the enlargement matrix used when the original sequence of squares has been rotated through <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math> degrees.</p>
<p>Ben decides the enlargement scale factor, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math>, should be a linear function of the angle, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math>, and after a rotation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>360</mn><mo>°</mo></math> the sequence of squares should be half of its original length.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for the width of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>U</mi><mi>n</mi></msub></math> in centimetres.</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 the width of a pixel is approximately <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>025</mn><mo> </mo><mtext>cm</mtext></math>, find the number of squares in the final image.</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>Write down <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="bold-italic">A</mi><mn>1</mn></msub></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="bold-italic">A</mi><mi>n</mi></msub></math>, in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>state the coordinates, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msub><mi>x</mi><mn>1</mn></msub><mo>,</mo><mo> </mo><msub><mi>y</mi><mn>1</mn></msub></mrow></mfenced></math>, of its image in <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>U</mi><mn>1</mn></msub></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 <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="bold-italic">b</mi><mn>1</mn></msub></math>.</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>show that <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="bold-italic">b</mi><mi>n</mi></msub><mo>=</mo><mfenced><mtable><mtr><mtd><mn>8</mn><mfenced><mrow><mn>1</mn><mo>-</mo><msup><mn>2</mn><mrow><mo>-</mo><mi>n</mi></mrow></msup></mrow></mfenced></mtd></mtr><mtr><mtd><mn>8</mn><mfenced><mrow><mn>1</mn><mo>-</mo><msup><mn>2</mn><mrow><mo>-</mo><mi>n</mi></mrow></msup></mrow></mfenced></mtd></mtr></mtable></mfenced></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence or otherwise, find the coordinates of the top left-hand corner in <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>U</mi><mn>7</mn></msub></math>.</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>Find, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math>, in the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mfenced><mi>θ</mi></mfenced><mo>=</mo><mi>m</mi><mi>θ</mi><mo>+</mo><mi>c</mi></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi>θ</mi></msub></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find the image of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>1</mn><mo>,</mo><mo> </mo><mn>1</mn><mo>)</mo></math> after it is rotated <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>135</mn><mo>°</mo></math> and enlarged.</p>
<div class="marks">[4]</div>
<div class="question_part_label">f.iii.</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>θ</mi></math> at which the enlargement scale factor equals zero.</p>
<div class="marks">[1]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>After the enlargement scale factor equals zero, Ben continues to rotate the image for another two revolutions.</p>
<p>Describe the animation for these two revolutions, stating the final position of the sequence of squares.</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 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><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mfenced><mfrac><mn>1</mn><msup><mn>2</mn><mi>n</mi></msup></mfrac></mfenced></math>       <strong><em>M</em></strong><em><strong>1A</strong></em><em><strong>1</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"><mfrac><mn>4</mn><msup><mn>2</mn><mi>n</mi></msup></mfrac><mo>&gt;</mo><mn>0</mn><mo>.</mo><mn>025</mn></math>        <em><strong>(A</strong></em><em><strong>1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>2</mn><mi>n</mi></msup><mo>&lt;</mo><mn>160</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>≤</mo><mn>7</mn></math>        <em><strong>(A</strong></em><em><strong>1)</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Accept equations in place of inequalities.  </p>
<p> </p>
<p>Hence there are <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math> squares        <em><strong>A</strong></em><em><strong>1</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><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mfrac><mn>1</mn><mn>2</mn></mfrac></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mfrac><mn>1</mn><mn>2</mn></mfrac></mtd></mtr></mtable></mfenced></math>        <em><strong>A</strong></em><em><strong>1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</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"><msub><mi>A</mi><mi>n</mi></msub><mo>=</mo><mfenced><mtable><mtr><mtd><mfrac><mn>1</mn><msup><mn>2</mn><mi>n</mi></msup></mfrac></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mfrac><mn>1</mn><msup><mn>2</mn><mi>n</mi></msup></mfrac></mtd></mtr></mtable></mfenced></math>        <em><strong>A</strong></em><em><strong>1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>4</mn><mo>,</mo><mo> </mo><mn>4</mn></mrow></mfenced></math>        <em><strong>A</strong></em><em><strong>1</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><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="bold-italic">A</mi><mn>1</mn></msub><mfenced><mtable><mtr><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd></mtr></mtable></mfenced><mo>+</mo><msub><mi mathvariant="bold-italic">b</mi><mn>1</mn></msub><mo>=</mo><mfenced><mtable><mtr><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mn>4</mn></mtd></mtr></mtable></mfenced></math>        <em><strong>(M</strong></em><em><strong>1)</strong></em></p>
<p> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="bold-italic">b</mi><mn>1</mn></msub><mo>=</mo><mfenced><mtable><mtr><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mn>4</mn></mtd></mtr></mtable></mfenced></math>        <em><strong>A</strong></em><em><strong>1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Recognise the geometric series <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="bold-italic">b</mi><mi>n</mi></msub><mo>=</mo><mfenced><mtable><mtr><mtd><mn>4</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>+</mo><mo>…</mo></mtd></mtr><mtr><mtd><mn>4</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>+</mo><mo>…</mo></mtd></mtr></mtable></mfenced></math>        <em><strong>M</strong></em><em><strong>1</strong></em></p>
<p>Each component is equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>4</mn><mfenced><mrow><mn>1</mn><mo>-</mo><mstyle displaystyle="true"><mfrac><mn>1</mn><msup><mn>2</mn><mi>n</mi></msup></mfrac></mstyle></mrow></mfenced></mrow><mstyle displaystyle="true"><mfrac><mn>1</mn><mn>2</mn></mfrac></mstyle></mfrac><mo> </mo><mfenced><mrow><mo>=</mo><mn>8</mn><mfenced><mrow><mn>1</mn><mo>-</mo><mfrac><mstyle displaystyle="true"><mn>1</mn></mstyle><mstyle displaystyle="true"><msup><mn>2</mn><mi>n</mi></msup></mstyle></mfrac></mrow></mfenced></mrow></mfenced></math>        <em><strong>M</strong></em><em><strong>1A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>8</mn><mfenced><mrow><mn>1</mn><mo>-</mo><mfrac><mn>1</mn><msup><mn>2</mn><mi>n</mi></msup></mfrac></mrow></mfenced></mtd></mtr><mtr><mtd><mn>8</mn><mfenced><mrow><mn>1</mn><mo>-</mo><mfrac><mn>1</mn><msup><mn>2</mn><mi>n</mi></msup></mfrac></mrow></mfenced></mtd></mtr></mtable></mfenced></math>        <em><strong>AG</strong></em></p>
<p>  </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mfrac><mn>1</mn><msup><mn>2</mn><mn>7</mn></msup></mfrac></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mfrac><mn>1</mn><msup><mn>2</mn><mn>7</mn></msup></mfrac></mtd></mtr></mtable></mfenced><mfenced><mtable><mtr><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>4</mn></mtd></mtr></mtable></mfenced><mo>+</mo><mfenced><mtable><mtr><mtd><mn>8</mn><mfenced><mrow><mn>1</mn><mo>-</mo><mfrac><mn>1</mn><msup><mn>2</mn><mn>7</mn></msup></mfrac></mrow></mfenced></mtd></mtr><mtr><mtd><mn>8</mn><mfenced><mrow><mn>1</mn><mo>-</mo><mfrac><mn>1</mn><msup><mn>2</mn><mn>7</mn></msup></mfrac></mrow></mfenced></mtd></mtr></mtable></mfenced></math>        <em><strong>M</strong></em><em><strong>1A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>7</mn><mo>.</mo><mn>9375</mn><mo>,</mo><mo> </mo><mn>7</mn><mo>.</mo><mn>96875</mn></mrow></mfenced></math>        <em><strong>A1</strong></em></p>
<p>  </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mfenced><mi>θ</mi></mfenced><mo>=</mo><mi>m</mi><mi>θ</mi><mo>+</mo><mi>c</mi></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mfenced><mn>0</mn></mfenced><mo>=</mo><mn>1</mn><mo>,</mo><mo> </mo><mi>c</mi><mo>=</mo><mn>1</mn></math>        <em><strong>M</strong></em><em><strong>1A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mfenced><mn>360</mn></mfenced><mo>=</mo><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"><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>=</mo><mn>360</mn><mi>m</mi><mo>+</mo><mn>1</mn><mo>⇒</mo><mi>m</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>720</mn></mfrac></math>        <em><strong>A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mfenced><mi>θ</mi></mfenced><mo>=</mo><mo>-</mo><mfrac><mi>θ</mi><mn>720</mn></mfrac><mo>+</mo><mn>1</mn></math></p>
<p>  </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi>θ</mi></msub><mo>=</mo><mfenced><mtable><mtr><mtd><mo>-</mo><mfrac><mi>θ</mi><mn>720</mn></mfrac><mo>+</mo><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mfrac><mi>θ</mi><mn>720</mn></mfrac><mo>+</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math>        <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">f.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mfrac><mn>135</mn><mn>720</mn></mfrac><mo>+</mo><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mfrac><mn>135</mn><mn>720</mn></mfrac><mo>+</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mfenced><mtable><mtr><mtd><mi>cos</mi><mo> </mo><mn>135</mn><mo>°</mo></mtd><mtd><mo>-</mo><mi>sin</mi><mo> </mo><mn>135</mn><mo>°</mo></mtd></mtr><mtr><mtd><mi>sin</mi><mo> </mo><mn>135</mn><mo>°</mo></mtd><mtd><mi>cos</mi><mo> </mo><mn>135</mn><mo>°</mo></mtd></mtr></mtable></mfenced><mfenced><mtable><mtr><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math>        <em><strong>M1A1A1</strong></em></p>
<p> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>1</mn><mo>.</mo><mn>15</mn><mo>,</mo><mo> </mo><mn>0</mn></mrow></mfenced></math>        <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">f.iii.</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>720</mn><mo>°</mo></math>      <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The image will expand from zero (accept equivalent answers)</p>
<p>It will rotate counter clockwise</p>
<p>The design will (re)appear in the opposite (third) quadrant         <em><strong>A1A1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Accept any two of the above</p>
<p> </p>
<p>Its final position will be in the opposite (third) quadrant or <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>180</mn><mo>˚</mo></math> from its original position or equivalent statement.         <em><strong>A1</strong></em></p>
<p> </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">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">d.iii.</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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.iii.</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><strong>This question is about a metropolitan area council planning a new town and the location of a new toxic waste dump.</strong></p>
<p><br>A metropolitan area in a country is modelled as a square. The area has four towns, located at the corners of the square. All units are in kilometres with the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-coordinate representing the distance east and the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-coordinate representing the distance north from the origin at <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>,</mo><mo>&#160;</mo><mn>0</mn><mo>)</mo></math>.</p>
<ul>
<li>Edison is modelled as being positioned at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mo>(</mo><mn>0</mn><mo>,</mo><mo>&#160;</mo><mn>40</mn><mo>)</mo></math>.</li>
<li>Fermitown is modelled as being positioned at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F</mtext><mo>(</mo><mn>40</mn><mo>,</mo><mo>&#160;</mo><mn>40</mn><mo>)</mo></math>.</li>
<li>Gaussville is modelled as being positioned at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>G</mtext><mo>(</mo><mn>40</mn><mo>,</mo><mo>&#160;</mo><mn>0</mn><mo>)</mo></math>.</li>
<li>Hamilton is modelled as being positioned at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>H</mtext><mo>(</mo><mn>0</mn><mo>,</mo><mo>&#160;</mo><mn>0</mn><mo>)</mo></math>.</li>
</ul>
</div>

<div class="specification">
<p>The metropolitan area council decides to build a new town called Isaacopolis located&nbsp;at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>I</mtext><mo>(</mo><mn>30</mn><mo>,</mo><mo>&#160;</mo><mn>20</mn><mo>)</mo></math>.</p>
<p>A new Voronoi diagram is to be created to include Isaacopolis. The equation of the perpendicular bisector of&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="[" close="]"><mtext>IE</mtext></mfenced></math>&nbsp;is&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mi>x</mi><mo>+</mo><mfrac><mn>15</mn><mn>2</mn></mfrac></math>.</p>
</div>

<div class="specification">
<p>The metropolitan area is divided into districts based on the Voronoi regions found&nbsp;in part (c).</p>
</div>

<div class="specification">
<p>A toxic waste dump needs to be located within the metropolitan area. The council wants to locate it as far as possible from the nearest town.</p>
</div>

<div class="specification">
<p>The toxic waste dump, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>T</mtext></math>, is connected to the towns via a system of sewers.</p>
<p>The connections are represented in the following matrix, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">M</mi></math>, where the order of rows and columns is (<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E,&#160;F,&#160;G,&#160;H,&#160;I,&#160;T</mtext></math>).</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">M</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mn>1</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>0</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>1</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>1</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>0</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>1</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>0</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>0</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>0</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>0</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>1</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>0</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>1</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>1</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>0</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>0</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>1</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>0</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>0</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>0</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>1</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>0</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>1</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>1</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>0</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>1</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>0</mn><mo>&#160;</mo><mo>&#160;</mo></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></p>
<p>A leak occurs from the toxic waste dump and travels through the sewers. The pollution takes one day to travel between locations that are directly connected.</p>
<p>The digit <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">M</mi></math> represents a direct connection. The values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> in the leading diagonal of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">M</mi></math> mean that once a location is polluted it will stay polluted.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The model assumes that each town is positioned at a single point. Describe possible circumstances in which this modelling assumption is reasonable.</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>Sketch a Voronoi diagram showing the regions within the metropolitan area that are closest to each town.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of the perpendicular bisector of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="[" close="]"><mtext>IF</mtext></mfenced></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that the coordinates of one vertex of the new Voronoi diagram are <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>20</mn><mo>,</mo><mo> </mo><mn>37</mn><mo>.</mo><mn>5</mn><mo>)</mo></math>, find the coordinates of the other two vertices within the metropolitan area.</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>Sketch this new Voronoi diagram showing the regions within the metropolitan area which are closest to each town.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A car departs from a point due north of Hamilton. It travels due east at constant speed to a destination point due North of Gaussville. It passes through the Edison, Isaacopolis and Fermitown districts. The car spends <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo>%</mo></math> of the travel time in the Isaacopolis district.</p>
<p>Find the distance between Gaussville and the car’s destination point.</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 location of the toxic waste dump, given that this location is not on the edge of the metropolitan area.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Make one possible criticism of the council’s choice of location.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find which town is last to be polluted. Justify your answer.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of days it takes for the pollution to reach the last town.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A sewer inspector needs to plan the shortest possible route through each of the connections between different locations. Determine an appropriate start point and an appropriate end point of the inspection route.</p>
<p><strong>Note</strong> that the fact that each location is connected to itself does not correspond to a sewer that needs to be inspected.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the size of each town is small (in comparison with the distance between the towns)<br><strong>OR</strong><br>if towns have an identifiable centre<br><strong>OR</strong><br>the centre of the town is at that point       <em><strong>R1</strong></em></p>
<p><strong><br>Note:</strong> Accept a geographical landmark in place of “centre”, e.g. “town hall” or “capitol”.</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 style="padding-left:30px;"><img src="data:image/png;base64,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">       <em><strong>A1</strong></em></p>
<p><strong><br>Note:</strong> There is no need for a scale / coordinates here. Condone boundaries extending beyond the metropolitan area.</p>
<p> </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>the gradient of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>IF</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>40</mn><mo>-</mo><mn>20</mn></mrow><mrow><mn>40</mn><mo>-</mo><mn>30</mn></mrow></mfrac><mo>=</mo><mn>2</mn></math>          <em><strong>(A1)</strong></em></p>
<p>negative reciprocal of any gradient          <em><strong>(M1)</strong></em></p>
<p>gradient of perpendicular bisector <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math></p>
<p><strong><br>Note:</strong> Seeing <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></math> (for example) used clearly as a gradient anywhere is evidence of the “negative reciprocal” method despite being applied to an inappropriate gradient.</p>
<p> </p>
<p>midpoint is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mrow><mn>40</mn><mo>+</mo><mn>30</mn></mrow><mn>2</mn></mfrac><mo>,</mo><mo> </mo><mfrac><mrow><mn>40</mn><mo>+</mo><mn>20</mn></mrow><mn>2</mn></mfrac></mrow></mfenced><mo>=</mo><mfenced><mrow><mn>35</mn><mo>,</mo><mo> </mo><mn>30</mn></mrow></mfenced></math>          <em><strong>(A1)</strong></em></p>
<p>equation of perpendicular bisector is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>-</mo><mn>30</mn><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mfenced><mrow><mi>x</mi><mo>-</mo><mn>35</mn></mrow></mfenced></math>         <em><strong>A1</strong></em></p>
<p><strong><br>Note:</strong> Accept equivalent forms <em>e.g.</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>x</mi><mo>+</mo><mfrac><mn>95</mn><mn>2</mn></mfrac></math>  or  <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>y</mi><mo>+</mo><mi>x</mi><mo>-</mo><mn>95</mn><mo>=</mo><mn>0</mn></math>.<br>Allow <em><strong>FT</strong> </em>for the final <em><strong>A1</strong> </em>from their midpoint and gradient of perpendicular bisector, as long as the <em><strong>M1</strong> </em>has been awarded</p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the perpendicular bisector of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>EH</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>20</mn></math>          <em><strong>(A1)</strong></em></p>
<p><strong><br>Note:</strong> Award this <em><strong>A1</strong> </em>if seen in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-coordinate of any final answer or if <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math> is used as the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-value in the equation of any other perpendicular bisector.</p>
<p><br>attempt to use symmetry <strong>OR</strong> intersecting two perpendicular bisectors         <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mn>25</mn><mn>3</mn></mfrac><mo>,</mo><mo> </mo><mn>20</mn></mrow></mfenced></math>         <em><strong>A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>20</mn><mo>,</mo><mo> </mo><mn>2</mn><mo>.</mo><mn>5</mn></mrow></mfenced></math>         <em><strong>A1</strong></em></p>
<p> </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 style="padding-left:30px;"><img 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">         <em><strong>M1A1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Award <em><strong>M1</strong> </em>for exactly four perpendicular bisectors around <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>I</mtext></math> (<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>IE</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>IF</mtext></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>IG</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>IH</mtext></math>) seen, even if not in exactly the right place.</p>
<p>Award <em><strong>A1</strong> </em>for a completely correct diagram. Scale / coordinates are NOT necessary. Vertices should be in approximately the correct positions but only penalized if clearly wrong (condone northern and southern vertices appearing to be very close to the boundary).</p>
<p>Condone the Voronoi diagram extending outside of the square.</p>
<p>Do not award follow-though marks in this part.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo>%</mo></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math>         <em><strong>(A1)</strong></em></p>
<p>recognizing line intersects bisectors at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>c</mi></math> (or equivalent) but different <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-values          <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><msub><mi>x</mi><mn>1</mn></msub><mo>+</mo><mfrac><mn>15</mn><mn>2</mn></mfrac></math>  and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msub><mi>x</mi><mn>2</mn></msub><mo>+</mo><mfrac><mn>95</mn><mn>2</mn></mfrac></math></p>
<p>finding an expression for the distance in Isaacopolis in terms of one variable         <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mn>2</mn></msub><mo>-</mo><msub><mi>x</mi><mn>1</mn></msub><mo>=</mo><mfenced><mrow><mn>95</mn><mo>-</mo><mn>2</mn><mi>c</mi></mrow></mfenced><mo>-</mo><mfrac><mrow><mn>2</mn><mi>c</mi><mo>-</mo><mn>15</mn></mrow><mn>3</mn></mfrac><mo>=</mo><mn>100</mn><mo>-</mo><mfrac><mrow><mn>8</mn><mi>c</mi></mrow><mn>3</mn></mfrac></math></p>
<p>equating their expression to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo>-</mo><mfrac><mrow><mn>8</mn><mi>c</mi></mrow><mn>3</mn></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>3</mn><mo>×</mo><mn>40</mn><mo>=</mo><mn>12</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>33</mn></math></p>
<p>distance <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>33</mn><mo> </mo><mfenced><mtext>km</mtext></mfenced></math>        <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>must be a vertex (award if vertex given as a final answer)         <em><strong>(R1)</strong></em></p>
<p>attempt to calculate the distance of at least one town from a vertex         <em><strong>(M1)</strong></em></p>
<p><br><strong>Note:</strong> This must be seen as a calculation or a value.</p>
<p><br>correct calculation of distances        <em><strong>A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>65</mn><mn>3</mn></mfrac></math>  <strong>OR  </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>21</mn><mo>.</mo><mn>7</mn></math>  <strong>AND  </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>406</mn><mo>.</mo><mn>25</mn></msqrt></math>  OR  <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>.</mo><mn>2</mn></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mn>25</mn><mn>3</mn></mfrac><mo>,</mo><mo> </mo><mn>20</mn></mrow></mfenced></math>        <em><strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>R1M0A0A0</strong></em> for a vertex written with no other supporting calculations.<br>Award <em><strong>R1M0A0A1</strong></em> for correct vertex with no other supporting calculations. <br>The final <em><strong>A1</strong></em> is not dependent on the previous <em><strong>A1</strong></em>. There is no follow-through for the final <em><strong>A1</strong></em>.</p>
<p>Do not accept an answer based on “uniqueness” in the question.</p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>For example, any one of the following:</em></p>
<p>decision does not take into account the different population densities</p>
<p>closer to a city will reduce travel time/help employees</p>
<p>it is closer to some cites than others        <em><strong>R1</strong></em></p>
<p> </p>
<p><strong>Note:</strong> Accept any correct reason that engages with the scenario.<br>Do not accept any answer to do with ethical issues about whether toxic waste should ever be dumped, or dumped in a metropolitan area.</p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>attempting <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="bold-italic">M</mi><mn>3</mn></msup></math>         <em><strong>M1</strong></em></p>
<p>attempting <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="bold-italic">M</mi><mn>4</mn></msup></math>         <em><strong>M1</strong></em></p>
<p>e.g.</p>
<p>last row/column of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="bold-italic">M</mi><mn>3</mn></msup><mo>=</mo><mfenced><mrow><mn>3</mn><mo> </mo><mo> </mo><mo> </mo><mn>5</mn><mo> </mo><mo> </mo><mo> </mo><mn>1</mn><mo> </mo><mo> </mo><mo> </mo><mn>6</mn><mo> </mo><mo> </mo><mo> </mo><mn>0</mn><mo> </mo><mo> </mo><mo> </mo><mn>7</mn></mrow></mfenced></math></p>
<p>last row/column of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="bold-italic">M</mi><mn>4</mn></msup><mo>=</mo><mfenced><mrow><mn>10</mn><mo> </mo><mo> </mo><mn>12</mn><mo> </mo><mo> </mo><mo> </mo><mn>4</mn><mo> </mo><mo> </mo><mo> </mo><mn>16</mn><mo> </mo><mo> </mo><mo> </mo><mn>1</mn><mo> </mo><mo> </mo><mo> </mo><mn>18</mn></mrow></mfenced></math></p>
<p>hence Isaacopolis is the last city to be polluted          <em><strong>A1</strong></em></p>
<p><strong><br>Note:</strong> Do not award the <em><strong>A1</strong></em> unless both <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="bold-italic">M</mi><mn>3</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="bold-italic">M</mi><mn>4</mn></msup></math> are considered. <br>Award <em><strong>M1M0A0</strong></em> for a claim that the shortest distance is from <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math> and that it is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math>, without any support.</p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>attempting to translate <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">M</mi></math> to a graph or a list of cities polluted on each day        <em><strong> (M1)</strong></em></p>
<p>correct graph or list         <em><strong>A1</strong></em></p>
<p><em><strong><img style="display:block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></strong></em></p>
<p>hence Isaacopolis is the last city to be polluted          <em><strong>A1</strong></em></p>
<p><strong><br>Note:</strong> Award <em><strong>M1A1A1</strong></em> for a clear description of the graph in words leading to the correct answer.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>it takes <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math> days        <em><strong>A1</strong></em></p>
<p><strong> </strong></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">f.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p>the orders of the different vertices are:</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E     2</mtext></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F     1</mtext></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>G     2</mtext></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>H     2</mtext></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>I        1</mtext></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>T     2</mtext></math>           <em><strong>(A1)</strong></em></p>
<p><br><strong>Note:</strong> Accept a list where each order is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> greater than listed above.</p>
<p><br><strong>OR</strong></p>
<p>a correct diagram/graph showing the connections between the locations           <em><strong>(A1)</strong></em></p>
<p><br><strong>Note:</strong> Accept a diagram with loops at each vertex.<br>This mark should be awarded if candidate is clearly using their correct diagram from the previous part.</p>
<p><br><strong>THEN</strong></p>
<p><em>“Start at F and end at I” </em> <strong>OR </strong> <em>“Start at I and end at F”            <strong>A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A1A0</strong></em> for “<em>it could start at either F or I”</em>.<br>Award <em><strong>A1A1</strong></em> for <em>“IGEHTF”</em> <strong>OR</strong> <em>“FTHEGI”</em>.<br>Award <em><strong>A1A1</strong></em> for <em>“F and I”</em> <strong>OR</strong> <em>“I and F”</em>.</p>
<p><strong> </strong></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">f.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Question 2 was based on Voronoi diagrams, but a substantial number of candidates appeared to have not met this topic.</p>
<p>2(a) was generally well answered, although a strangely common answer was to claim that the towns must be 1km by 1km! Perhaps this came from thinking of coordinates as representing pixels rather than points.</p>
<p>2(b) was done well by most candidates who knew what a Voronoi diagram was.</p>
<p>2(c)(i) showed some poor planning skills by many candidates who found a line perpendicular to the given Voronoi edge rather than finding the gradient of IF.</p>
<p>In 2(c)(ii) candidates would have benefited from taking a step back and thinking about the symmetry of the situation before unthinkingly intersecting a lot of lines.</p>
<p>2(c)(iii) was done well by some, but many did not seem to have any intuition for the effect of adding a point to a Voronoi diagram.</p>
<p>2(d) was probably the worst answered question. Candidates did not seem to have the problem-solving tools to deal with this slightly unfamiliar situation.</p>
<p>In 2(e) many candidates clearly did not know that the solution to the toxic waste problem (as described in the syllabus) occurs at a vertex of the Voronoi diagram.</p>
<p>A pleasing number of candidates were able to approach 2(f) even if they were unable to do earlier parts of the question, and in these very long questions candidates should be advised that sometimes later parts are not necessarily harder or impossible to access. Very few who attempted the matrix power approach could interpret what zeroes meant in the matrices produced, but a good number successfully turned the matrix into a graph and proceeded well from there.</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.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">c.iii.</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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.iii.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>This question compares possible designs for a new computer network between&nbsp;multiple school buildings, and whether they meet specific requirements.</strong></p>
<p><br>A school&rsquo;s administration team decides to install new fibre-optic internet cables underground.&nbsp;The school has eight buildings that need to be connected by these cables. A map of the&nbsp;school is shown below, with the internet access point of each building labelled <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A&#8211;H</mtext></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
<p>Jonas is planning where to install the underground cables. He begins by determining the&nbsp;distances, in metres, between the underground access points in each of the buildings.</p>
<p>He finds&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AD</mtext><mo>=</mo><mn>89</mn><mo>.</mo><mn>2</mn><mo>&#8202;</mo><mtext>m</mtext></math>,&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>DF</mtext><mo>=</mo><mn>104</mn><mo>.</mo><mn>9</mn><mo>&#8202;</mo><mtext>m</mtext></math>&nbsp;and&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mtext>D</mtext><mo>^</mo></mover><mtext>F</mtext><mo>=</mo><mn>83</mn><mo>&#176;</mo></math>.</p>
</div>

<div class="specification">
<p>The cost for installing the cable directly between <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F</mtext></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>21</mn><mo>&#8202;</mo><mn>310</mn></math>.</p>
</div>

<div class="specification">
<p>Jonas estimates that it will cost <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>110</mn></math> per metre to install the cables between all the&nbsp;other buildings.</p>
</div>

<div class="specification">
<p>Jonas creates the following graph, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math>, using the cost of installing the cables between two&nbsp;buildings as the weight of each edge.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>The computer network could be designed such that each building is directly connected to at&nbsp;least one other building and hence all buildings are indirectly connected.</p>
</div>

<div class="specification">
<p>The computer network fails if any part of it becomes unreachable from any other part.&nbsp;To help protect the network from failing, every building could be connected to at least&nbsp;two other buildings. In this way if one connection breaks, the building is still part of the&nbsp;computer network. Jonas can achieve this by finding a Hamiltonian cycle within the graph.</p>
</div>

<div class="specification">
<p>After more research, Jonas decides to install the cables as shown in the diagram below.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>Each individual cable is installed such that each end of the cable is connected to a building&rsquo;s access point. The connection between each end of a cable and an access point has a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>4</mn><mo>%</mo></math> probability of failing after a power surge.</p>
<p>For the network to be successful, each building in the network must be able to communicate with every other building in the network. In other words, there must be a path that connects any two buildings in the network. Jonas would like the network to have less than a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>%</mo></math> probability of failing to operate after a power surge.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AF</mtext></math>.</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 cost per metre of installing this cable.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State why the cost for installing the cable between <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F</mtext></math> would be higher than between the other buildings.</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>By using Kruskal’s algorithm, find the minimum spanning tree for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math>, showing clearly the order in which edges are added.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find the minimum installation cost for the cables that would allow all the buildings to be part of the computer network.</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>State why a path that forms a Hamiltonian cycle does not always form an Eulerian circuit.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Starting at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math>, use the nearest neighbour algorithm to find the upper bound for the installation cost of a computer network in the form of a Hamiltonian cycle.</p>
<p><strong>Note:</strong> Although the graph is not complete, in this instance it is not necessary to form a table of least distances.</p>
<div class="marks">[5]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>By deleting <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math>, use the deleted vertex algorithm to find the lower bound for the installation cost of the cycle.</p>
<div class="marks">[6]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that Jonas’s network satisfies the requirement of there being less than a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>%</mo></math> probability of the network failing after a power surge.</p>
<div class="marks">[5]</div>
<div class="question_part_label">h.</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"><msup><mtext>AF</mtext><mn>2</mn></msup><mo>=</mo><mn>89</mn><mo>.</mo><msup><mn>2</mn><mn>2</mn></msup><mo>+</mo><mn>104</mn><mo>.</mo><msup><mn>9</mn><mn>2</mn></msup><mo>-</mo><mn>2</mn><mfenced><mrow><mn>89</mn><mo>.</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mn>104</mn><mo>.</mo><mn>9</mn></mrow></mfenced><mi>cos</mi><mo> </mo><mn>83</mn></math>         <em><strong>(M1)(A1)</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution into the cosine rule and <em><strong>(A1)</strong></em> for correct substitution.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AF</mtext><mo>=</mo><mn>129</mn><mo> </mo><mo> </mo><mtext>m</mtext><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>129</mn><mo>.</mo><mn>150</mn><mo>…</mo></mrow></mfenced></math>          <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><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>21310</mn><mo>÷</mo><mn>129</mn><mo>.</mo><mn>150</mn><mo>…</mo></math>         <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>165</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>
<div class="question" style="padding-left: 20px;">
<p>any reasonable statement referring to the lake         <em><strong>R1</strong></em></p>
<p>(eg. there is a lake between <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>F</mtext></math>, the cables would need to be installed under/over/around the lake, special waterproof cables are needed for lake, etc.)</p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>edges (or weights) are chosen in the order</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>CE</mtext><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mfenced><mn>8239</mn></mfenced></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>DG</mtext><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mfenced><mn>8668</mn></mfenced></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BD </mtext><mo> </mo><mo> </mo><mo> </mo><mfenced><mn>8778</mn></mfenced></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mfenced><mn>8811</mn></mfenced></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>DE </mtext><mo> </mo><mo> </mo><mo> </mo><mfenced><mn>8833</mn></mfenced></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>EH</mtext><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mfenced><mn>9251</mn></mfenced></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>DF</mtext><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>11</mn><mo> </mo><mn>539</mn></mrow></mfenced></math>               <em><strong>A1A1A1</strong></em></p>
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"></p>
<p><strong>Note:</strong> Award <em><strong>A1</strong> </em>for the first two edges chosen in the correct order. Award <em><strong>A1A1 </strong></em>for the first six edges chosen in the correct order. Award <em><strong>A1A1A1</strong> </em>for all seven edges chosen in the correct order. Accept a diagram as an answer, provided the order of edges is communicated.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Finding the sum of the weights of their edges               <em><strong>(M1)<br></strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8239</mn><mo>+</mo><mn>8668</mn><mo>+</mo><mn>8778</mn><mo>+</mo><mn>8811</mn><mo>+</mo><mn>8833</mn><mo>+</mo><mn>9251</mn><mo>+</mo><mn>11539</mn></math></p>
<p>total cost <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>$</mo><mn>64119</mn></math>               <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>a Hamiltonian cycle is not always an Eulerian circuit as it does not have to include all edges of the graph (only all vertices)             <em><strong>R1</strong></em></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>edges (or weights) are chosen in the order</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>DG</mtext><mo> </mo><mo> </mo><mo> </mo><mfenced><mn>8668</mn></mfenced></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>GH</mtext><mo> </mo><mo> </mo><mo> </mo><mfenced><mn>9603</mn></mfenced></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>HE</mtext><mo> </mo><mo> </mo><mo> </mo><mfenced><mn>9251</mn></mfenced></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>EC</mtext><mo> </mo><mo> </mo><mo> </mo><mfenced><mn>8239</mn></mfenced></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>CB</mtext><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>13</mn><mo> </mo><mn>156</mn></mrow></mfenced></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BA</mtext><mo> </mo><mo> </mo><mo> </mo><mfenced><mn>8811</mn></mfenced></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AF</mtext><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>21</mn><mo> </mo><mn>310</mn></mrow></mfenced></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>FD</mtext><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>11</mn><mo> </mo><mn>539</mn></mrow></mfenced></math>              <em><strong>A1A1A1</strong></em></p>
<p><img style="display:block;margin-left:auto;margin-right:auto;" 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"></p>
<p><strong><br>Note:</strong> Award <em><strong>A1</strong> </em>for the first two edges chosen in the correct order. Award <em><strong>A1A1</strong> </em>for the first five edges chosen in the correct order. Award <em><strong>A1A1A1</strong> </em>for all eight edges chosen in the correct order. Accept a diagram as an answer, provided the order of edges is communicated.</p>
<p> </p>
<p>finding the sum of the weights of their edges                <em><strong>(M1)</strong></em><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8668</mn><mo>+</mo><mn>9603</mn><mo>+</mo><mn>9251</mn><mo>+</mo><mn>8239</mn><mo>+</mo><mn>13156</mn><mo>+</mo><mn>8811</mn><mo>+</mo><mn>21310</mn><mo>+</mo><mn>11539</mn></math></p>
<p>upper bound <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>$</mo><mn>90</mn><mo> </mo><mn>577</mn></math>              <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to find MST after deleting vertex D         <em><strong>(M1)</strong></em><br>these edges (or weights) (in any order)</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>CE</mtext><mo> </mo><mo> </mo><mo> </mo><mfenced><mn>8239</mn></mfenced></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext><mo> </mo><mo> </mo><mo> </mo><mfenced><mn>8811</mn></mfenced></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>EH</mtext><mo> </mo><mo> </mo><mo> </mo><mfenced><mn>9251</mn></mfenced></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>GH</mtext><mo> </mo><mo> </mo><mo> </mo><mfenced><mn>9603</mn></mfenced></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BE</mtext><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>10</mn><mo> </mo><mn>153</mn></mrow></mfenced></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>FG</mtext><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>12</mn><mo> </mo><mn>606</mn></mrow></mfenced></math>              <em><strong>A1</strong></em></p>
<p style="text-align:left;"><br><strong>Note:</strong> Prim’s or Kruskal’s algorithm could be used at this stage.</p>
<p style="text-align:left;"><br>reconnect <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math> to MST with two different edges         <em><strong>(M1)</strong></em></p>
<p style="text-align:left;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>DG</mtext><mo> </mo><mo> </mo><mo> </mo><mfenced><mn>8668</mn></mfenced></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BD</mtext><mo> </mo><mo> </mo><mo> </mo><mfenced><mn>8778</mn></mfenced></math>              <em><strong>A1</strong></em></p>
<p style="text-align:left;"><br><strong>Note:</strong> This <strong><em>A1</em> </strong>is independent of the first <em><strong>A</strong></em> mark and can be awarded if both <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>DG</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>BD</mtext></math> are chosen to reconnect <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math> to the MST, even if the MST is incorrect.<br><br></p>
<p><img style="display:block;margin-left:auto;margin-right:auto;" 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"></p>
<p><strong><br></strong>finding the sum of the weights of their edges              <em><strong>(M1)</strong></em><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8239</mn><mo>+</mo><mn>8811</mn><mo>+</mo><mn>9251</mn><mo>+</mo><mn>9603</mn><mo>+</mo><mn>10153</mn><mo>+</mo><mn>12606</mn><mo>+</mo><mn>8668</mn><mo>+</mo><mn>8778</mn></math></p>
<p><br><strong>Note:</strong> For candidates with an incorrect MST or no MST, the weights of at least seven of the edges being summed (two of which must connect to <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>D</mtext></math>) must be shown to award this <em><strong>(M1)</strong></em>.</p>
<p><br>lower bound <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>$</mo><mn>76</mn><mo> </mo><mn>109</mn></math>              <em><strong>A1</strong></em></p>
<p> </p>
<p><em><strong>[6 marks]</strong></em></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>recognition of a binomial distribution         <em><strong>(M1)<br></strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>~</mo><mtext>B</mtext><mfenced><mrow><mn>2</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>014</mn></mrow></mfenced></math></p>
<p>finding the probability that a cable fails (at least one of its connections fails)<br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>&gt;</mo><mn>0</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>027804</mn></math>  <strong>OR  </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>-</mo><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>=</mo><mn>0</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>027804</mn></math>             <em><strong>A1</strong></em></p>
<p>recognition that <strong>two</strong> cables must fail for the network to go offline         <em><strong>M1</strong></em></p>
<p>recognition of binomial distribution for network, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi><mo>~</mo><mtext>B</mtext><mfenced><mrow><mn>8</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>027804</mn></mrow></mfenced></math>         <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>Y</mi><mo>≥</mo><mn>2</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>0194</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>0193602</mn><mo>…</mo></mrow></mfenced></math>  <strong>OR  </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>-</mo><mtext>P</mtext><mfenced><mrow><mi>Y</mi><mo>&lt;</mo><mn>2</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>0194</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>0193602</mn><mo>…</mo></mrow></mfenced></math>             <em><strong>A1</strong></em></p>
<p>therefore, the diagram satisfies the requirement since <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>94</mn><mo>%</mo><mo>&lt;</mo><mn>2</mn><mo>%</mo></math>             <em><strong>AG</strong></em></p>
<p><br><strong>Note:</strong> Evidence of binomial distribution may be seen as combinations.</p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>recognition of a binomial distribution          <em><strong>(M1)<br></strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>~</mo><mtext>B</mtext><mfenced><mrow><mn>16</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>014</mn></mrow></mfenced></math></p>
<p>finding the probability that at least <strong>two</strong> connections fail<br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>≥</mo><mn>2</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>0206473</mn><mo>…</mo></math>  <strong>OR  <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>-</mo><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>&lt;</mo><mn>2</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>0206473</mn><mo>…</mo></math></strong>             <em><strong>A1</strong></em></p>
<p>recognition that the previous answer is an overestimate          <em><strong>M1</strong></em></p>
<p>finding probability of two ends of the same cable failing, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>~</mo><mtext>B</mtext><mfenced><mrow><mn>2</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>014</mn></mrow></mfenced></math>,<br>and the ends of the other <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn></math> cables not failing, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>~</mo><mtext>B</mtext><mfenced><mrow><mn>14</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>014</mn></mrow></mfenced></math><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>F</mi><mo>=</mo><mn>2</mn></mrow></mfenced><mo>×</mo><mtext>P</mtext><mfenced><mrow><mi>S</mi><mo>=</mo><mn>0</mn></mrow></mfenced><mo>=</mo><mn>0</mn><mo>.</mo><mn>0000160891</mn><mo>…</mo></math>             <em><strong>(A1)</strong></em></p>
<p> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>0000160891</mn><mo>…</mo><mo>×</mo><mn>8</mn><mo>=</mo><mn>0</mn><mo>.</mo><mn>00128713</mn><mo>.</mo><mo>.</mo><mo>.</mo></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>0206473</mn><mo>…</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>00128713</mn><mo>…</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>0194</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>0193602</mn><mo>…</mo></mrow></mfenced></math>             <em><strong>A1</strong></em></p>
<p>therefore, the diagram satisfies the requirement since <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>94</mn><mo>%</mo><mo>&lt;</mo><mn>2</mn><mo>%</mo></math>             <em><strong>AG</strong></em></p>
<p> </p>
<p><strong>METHOD 3</strong></p>
<p>recognition of a binomial distribution          <em><strong>M1<br></strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>~</mo><mtext>B</mtext><mfenced><mrow><mn>16</mn><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>014</mn></mrow></mfenced></math></p>
<p>finding the probability that the network remains secure if <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> connections fail or if <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> connections fail provided that the second failed connection occurs at the other end of the cable with the first failure         <em><strong>(M1)</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math>(remains secure) <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>≤</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mfrac><mn>1</mn><mn>15</mn></mfrac><mo>×</mo><mtext>P</mtext><mfenced><mrow><mi>X</mi><mo>=</mo><mn>2</mn></mrow></mfenced></math>             <em><strong>A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>9806397625</mn></math>             <em><strong>A1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math>(network fails) <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>9806397625</mn><mo>=</mo><mn>0</mn><mo>.</mo><mn>0194</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>0193602</mn><mo>…</mo></mrow></mfenced></math>              <em><strong>A1</strong></em></p>
<p>therefore, the diagram satisfies the requirement since <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>94</mn><mo>%</mo><mo>&lt;</mo><mn>2</mn><mo>%</mo></math>             <em><strong>AG</strong></em></p>
<p> </p>
<p><strong>METHOD 4</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math>(network failing)</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1</mn><mo>-</mo><mtext>P</mtext><mfenced><mrow><mn>0</mn><mo> </mo><mtext>connections failing</mtext></mrow></mfenced><mo>-</mo><mtext>P</mtext><mfenced><mrow><mn>1</mn><mo> </mo><mtext>connection failing</mtext></mrow></mfenced><mo>-</mo><mtext>P</mtext><mfenced><mrow><mn>2</mn><mo> </mo><mtext>connections on the same cable failing</mtext></mrow></mfenced></math>          <em><strong>M1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1</mn><mo>-</mo><mn>0</mn><mo>.</mo><msup><mn>986</mn><mn>16</mn></msup><mo>-</mo><mmultiscripts><mi>C</mi><mn>1</mn><mprescripts></mprescripts><mn>16</mn></mmultiscripts><mo>×</mo><mn>0</mn><mo>.</mo><mn>014</mn><mo>×</mo><mn>0</mn><mo>.</mo><msup><mn>986</mn><mn>15</mn></msup><mo>-</mo><mmultiscripts><mi>C</mi><mn>1</mn><mprescripts></mprescripts><mn>8</mn></mmultiscripts><mo>×</mo><mn>0</mn><mo>.</mo><msup><mn>014</mn><mn>2</mn></msup><mo>×</mo><mn>0</mn><mo>.</mo><msup><mn>986</mn><mn>14</mn></msup></math>              <em><strong>A1A1A1</strong></em></p>
<p><br><strong>Note:</strong> Award <em><strong>A1</strong></em> for each of 2<sup>nd</sup>, 3<sup>rd</sup> and last terms.</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>0194</mn><mo> </mo><mo> </mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>0193602</mn><mo>…</mo></mrow></mfenced></math>              <em><strong>A1</strong></em></p>
<p>therefore, the diagram satisfies the requirement since <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>94</mn><mo>%</mo><mo>&lt;</mo><mn>2</mn><mo>%</mo></math>             <em><strong>AG</strong></em></p>
<p> </p>
<p><em><strong>[5 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;">
<p>This question part was intended to be an easy introduction to help candidates begin working with the larger story and most candidates handled it well. However, it was surprisingly common for a candidate to correctly choose the cosine rule and to make the correct substitutions into the formula but then arrive at an incorrect answer. The frequency of this mistake suggests that candidates were either making simple entry mistakes into their GDC or forgetting to ensure that their GDC was set to degrees rather than radians.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(b) and (c) Most candidates were able to gain the three marks available.</p>
<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;">
<p>(d), (f) and (g) These three question parts required candidates to demonstrate their ability to carry out graph theory algorithms. Kruskal’s algorithm was split into two different question parts to guide candidates to show their work. As a result, many were able to score well in part (d)(ii) either from having the correct MST or from “follow through” marks from an incorrect MST. However, without this guidance in 2(f) and 2(g), many candidates did a poor job of showing the process they were using to apply the algorithms. The candidates that scored well were detailed in showing the order of how edges were selected and how they were being summed to arrive at the final answers. Although “follow through” within the problem was not available for the final answer in parts 2(f) and 2(g), many candidates missed the opportunity to gain the final method mark in both parts by not fully showing the process they used.</p>
<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;">
<p>Many candidates were able to state the definitions of Hamiltonian cycles and Eulerian circuits. However, the question was not asking for definitions but rather a distinct conclusion of why a Hamiltonian cycle is not always an Eulerian circuit. Disappointingly, many incorrect answers contained five or more lines or writing that may have used up exam time that could have been devoted to other question parts. Another common mistake seen here was candidates incorrectly trying to state a reason based on the number of odd vertices.</p>
<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;">
<p>This question was very challenging for almost all the candidates. Although there were several different methods that candidates could have used to answer this question, most candidates were only able to gain one or two marks here. Many candidates did recognize that something binomial was needed, but few knew how to setup the correct parameters for the distribution.</p>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>The weights of the edges in the complete graph <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="G">
  <mi>G</mi>
</math></span> are given in the following table.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-10_om_09.18.27.png" alt="M17/5/MATHL/HP3/ENG/TZ0/DM/02"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Starting at A , use the nearest neighbour algorithm to find an upper bound for the travelling salesman problem for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="G">
  <mi>G</mi>
</math></span>.</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>By first deleting vertex A , use the deleted vertex algorithm together with Kruskal’s algorithm to find a lower bound for the travelling salesman problem for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="G">
  <mi>G</mi>
</math></span>.</p>
<div class="marks">[7]</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>the edges are traversed in the following order</p>
<p>AB&nbsp;&nbsp;&nbsp;&nbsp; <strong><em>A1</em></strong></p>
<p>BC</p>
<p>CF&nbsp;&nbsp;&nbsp;&nbsp; <strong><em>A1</em></strong></p>
<p>FE</p>
<p>ED&nbsp;&nbsp;&nbsp;&nbsp; <strong><em>A1</em></strong></p>
<p>DA&nbsp;&nbsp; <strong><em>A1</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{upper bound}} = {\text{weight of this cycle}} = 4 + 1 + 2 + 7 + 11 + 8 = 33">
  <mrow>
    <mtext>upper bound</mtext>
  </mrow>
  <mo>=</mo>
  <mrow>
    <mtext>weight of this cycle</mtext>
  </mrow>
  <mo>=</mo>
  <mn>4</mn>
  <mo>+</mo>
  <mn>1</mn>
  <mo>+</mo>
  <mn>2</mn>
  <mo>+</mo>
  <mn>7</mn>
  <mo>+</mo>
  <mn>11</mn>
  <mo>+</mo>
  <mn>8</mn>
  <mo>=</mo>
  <mn>33</mn>
</math></span>&nbsp;&nbsp;&nbsp;&nbsp; <strong><em>A1</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>having deleted A, the order in which the edges are added is</p>
<p>BC&nbsp;&nbsp;&nbsp;&nbsp; <strong><em>A1</em></strong></p>
<p>CF&nbsp;&nbsp;&nbsp;&nbsp; <strong><em>A1</em></strong></p>
<p>CD&nbsp;&nbsp;&nbsp;&nbsp; <strong><em>A1</em></strong></p>
<p>EF&nbsp;&nbsp;&nbsp;&nbsp; <strong><em>A1</em></strong></p>
<p>&nbsp;</p>
<p><strong>Note:</strong>&nbsp;&nbsp;&nbsp;&nbsp; Accept indication of the correct order on a diagram.</p>
<p>&nbsp;</p>
<p>to find the lower bound, we now reconnect A using the two edges with the lowest weights, that is AB and AF&nbsp;&nbsp;&nbsp;&nbsp; <strong><em>(M1)(A1)</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{lower bound}} = 1 + 2 + 5 + 7 + 4 + 6 = 25">
  <mrow>
    <mtext>lower bound</mtext>
  </mrow>
  <mo>=</mo>
  <mn>1</mn>
  <mo>+</mo>
  <mn>2</mn>
  <mo>+</mo>
  <mn>5</mn>
  <mo>+</mo>
  <mn>7</mn>
  <mo>+</mo>
  <mn>4</mn>
  <mo>+</mo>
  <mn>6</mn>
  <mo>=</mo>
  <mn>25</mn>
</math></span>&nbsp;&nbsp;&nbsp;&nbsp; <strong><em>A1</em></strong></p>
<p>&nbsp;</p>
<p><strong>Note:</strong>&nbsp;&nbsp;&nbsp;&nbsp; Award <strong><em>(M1)(A1)A1 </em></strong>for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{LB}} = 15 + 4 + 6 = 25">
  <mrow>
    <mtext>LB</mtext>
  </mrow>
  <mo>=</mo>
  <mn>15</mn>
  <mo>+</mo>
  <mn>4</mn>
  <mo>+</mo>
  <mn>6</mn>
  <mo>=</mo>
  <mn>25</mn>
</math></span> obtained either from an incorrect order of correct edges or where order is not indicated.</p>
<p>&nbsp;</p>
<p><strong><em>[7 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 graph <em>G</em> represented in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAT4AAAF/CAYAAADQPKX5AAAgAElEQVR4Ae19D3QV5Zn3L7GH2jZmLXV3vRG+Rc2XWAsKhrB+EkqK7g1dbHGxyNrFxCVB+1WhC8eEgrjq1uCGuPHbhu63VS5L0EoRw4HttstNmxQ+g1sgGKuseHOyShu80UXUQIpAT+77nWeSCZPJ3Htn5s7MnT/Pe849996Zd94/v2fmmffP83ueHCGEACdGgBFgBAKEQG6A+spdZQQYAUZAQoAVH98IjAAjEDgEWPEFTuRZ7HDiN9hVPRMVW95CIovN4KoZAVZ8fA84hkCitx0/3HIEbTteQS9rPsdw54rGI8CKbzwmfMQWBD5G97/+J77S+ABCbXvR2XvOllq4UEZADwKs+PSgxHkyR+D0q3hx35ewqGYR7gntxPrIKzidealcAiNgCgFWfKZg44uMIXAOPS+9CKz+OoouvwEV95Sg/7lfoOs0z3eN4ci5rUKAFZ9VSHI5yRFIHEfngetx16yJAK5AefW3Ee5vQ7Trw+TX8BlGwEYEWPHZCC4XTQgkcHrfC9g1O4wZecO3W27hLVgSjuO5H/0/vMuDPr5NsoBADjM3soB6oKr8AB1r5uPWjUc0er0Ykdg2LCu6VOMcH2IE7EOAR3z2Ycsl03iv51/RhI0YEALEjpQ/QydasSzUiR2dx9mmj+8UxxFgxec45EGqkExYYlhUfQvyVd3OverL+Kt7CtimT4UL/3UGAVZ8zuAcwFouoL/jH/FQ0yWYcuUEjf7nYVLxNUDbety//ufo57U+DYz4kF0I8BqfXcgGutxz6NlSieLqnSMoqNfy1OcBhNai/a0nMC+f38WBvnUc6jwrPoeA5moYAUbAPQjw69U9suCWMAKMgEMIsOJzCGiuhhFgBNyDACs+98iCW8IIMAIOIcCKzyGguZphBD788EP09PTgk08+YUgYgawhwIova9AHp2JSdps2bcKsWbPwhS98AcXFxfjsZz+LO+64A7t27WIlGJxbwTU95V1d14jCnw05cOAAVq1ahcOHDyft4MKFCyXFOGnSpKR5+AQjYCUCrPisRJPLGoMATWlpdKcnlZaWYv/+/fjMZz6jJzvnYQQyQoCnuhnBxxenQqCuri7V6THnaEQYiUTGHOM/jIBdCPCIzy5kA14uTXHLysoMo3Dq1ClMnEh++zgxAvYhwCM++7ANdMnd3d2m+n/s2DFT1/FFjIARBFjxGUGL8+pG4Le//a3uvMqM77//vvIv/2YEbEGAFZ8tsHKhjAAj4GYEWPG5WToebRsZJ589e9ZU60+f5thrpoDjiwwhwJsbhuDizKkQeO211/Czn/0MDz/8cKpsac+RaUtlZaVk4My2fWnh4gwmEOARnwnQ+JKLCJw4cQLbtm2TWBkzZszA7t270dzcjFgsBjJMNpLous7OTknhrVixApMnT5Z+t7W1gdgfnBgByxCgYEOcGAEjCJw6dUpEo1GxcOFCAUD61NfXi87OTnH27NnRovr6+kRpaeloHjmv1ndNTc2Ya/XWMVoZ/2AEDCBAwV84MQK6ECDFRgpOVlyk+EgBkpJKlvQoP7XSU5dFZbS0tIwqUVKmzc3NIhaLqbPyf0ZAFwKs+HTBZDTTeRHv+qnY2VgpQoAI1bWLAaNFuCQ/KR1SMvLITVY6dFxvolFga2vrmBEiKU9SeKRMjaTu7u5xypfKTqV8jZRvT17/3A/24ON8qaz4rMZ8KC4ONlWKUKhSNO78pYidGbK6BtvLIyWiVlTyVDbTyuXRYqblkDKl0SYpT7nM2tracdPtTOvJ+Hof3A8ZY+DCAljxWSqUj0RX4wIRqtwkDsbPW1qy3YWRIqHRFykPWZGQUiHloly3y7QdctmZlqO8Xp4KK9ccaZRKo8PsJu/eD9nFzf7aWfFZhvGQONPVJMpDD4jWE95RerROpp7K0nqakamsEQjtUHzK+knZUX/kekgZUn+cnwp7835QYunn36z4rJLu0DERCV8ryuueGV3bA01322LijFV1WFQOKQFSBtkYIckKyaKuJC1GHsEqp8LymqKVI9ikDfDQ/ZC0Dz4+wYrPIuEOxSIijLCo23pQxKVlvQFxLLJMhLBANHZ9ZFEt5ovJuiIYabpTik+JlJaipzVLO6fCbr8flPgE8TcrPkukPiQG2teKUGitaB9QbGZIb/2QQDgiYorDllSpsxD3TP2GG5wNxaeEypmpvXvvByUWQf79KcssoQNd0AW8d7wX/Sgci0LuFJQtKQPW9+LEYAJF+c4QZYhN0dHRIcWz2LNnD4gCRqwI8o83ffr0sW0M2L+ioiLQp7q6Gq+++ioIn6qqKgmFmpoaLF68GHPmzMnQE7S77oeAiVhXd515EnU1xcuZJuDKKYUI9ffi+HsXxndkWiEm5dkLNTkGIGrX8uXLJaoXPcz0gBMFjFy6P/jgg4FXekrBkIv72bNnY+PGjSDnp9FoFCdPnkRFRYUUCGnDhg0gZ6rmUvbvB3PtDs5V9j6NgcExF/kzb8M9oWM4cPR9JEb7PYgTsXcRXnILCm1CmhwD0ENKUcvooaWHt7W1VXqY6aGmh5vjWIwKRPMHeXwOh8MSz7ivr08aHRPnmEbIFBmOIsTRKFp/yt79oL+NAc8Z5Hm+tX0/L060PiBCoWUicox4GudF/OAmURluEl0WGzEnY1N4gcKV7TU+IzI3Q9G7WL5z98PFOvmXXgR4c0MvUrryDYhYW5OoDBFxPyTK67aJLosMmWlnMpljAF1Nc0kmLyk+GTIZe6VpjMxkSW0aY9/9ILeNv80hwP74XD7ip3UmWqOTfdyRq6dvf/vbmDlzpieD8uTk5EiIC0E2xt5L8sYRTX8pMpzsO5CmyrSmyskbCLDic6GcKB4tbVSQnzvlw3XHHXfA6445va74lLeL2vEqvZTIgWp5ebknX0rKvvn9Nys+l0iYHG3u27dPUnZkYkGpvr4ef/7nf+6r3Vg/KT751qEd9Zdffhk7d+7E5s2bpcNkGnPvvffipptu4s0lGSgXfbPiy6Iw6IGRbckaGxtHHxhrbMmy2LEUVftR8Sm7Sy+wf/u3fxu1oaRzbEOpRMgdv1nxZUEONEUi+zrlVJbs7ObNm+f5qWw6OP2u+JT9l+VMbvQp0VR40aJFuP3223kqrAQqC79Z8TkEOo8EhoEOkuKTby15ZL9169YxU2E/j+zlvrv1mxWfjZJJdsMHee0niIpPeYsFZS1X2Wc3/mbFZ4NUeIqTHNSgKz4lMlq790FZ8lDikI3frPgsQj2ZfRc7BhgLMCu+sXjQP3lmQLv56k0ur9prju+lu46w4stAHnTDqs0YamtrpUVsNmPQBpYVnzYu8lGaCnd1deGf/umfJM8xdJzMmubOnSvxruV8/J0ZAqz4TODHhqsmQBu5hBWffuxoFkHOEpS7/2Qg7QdDdv0o2JOTFZ9OXPkm1AlUmmys+NIAlOS036iLSbrp2GFWfCmg5mlHCnBMnmLFZxK4kcvke1LJEuHlFeOYsuLTwIzfrhqgWHSIFZ9FQAKSj0DytM0OE4xjyopvBDM2LTB+85i5ghWfGdTSX8PrzukxUuYItOJjY1LlreDMb1Z89uIsm8aoWSJBNprXQjxwik++MbRspjIPMqMFMR9TIsCKT4mGvb/pxc4OE7QxDoziS8amCIJjAG3RZ+coK77s4M73/1jcfa34+I03Vthu+MeKL7tS4BnPMP6+U3yyYHmNI7sPWLLaWfElQ8b540Fe486q4pOV1Pvvvz8q9WuuucaUx2GtXS32fTYKq2t+sOJzjSjGNMRKqwYrn+sxjbTyj7kYRZlf1draKkpLSynizLgPHe/u7k5bCYVZbGlpGS2HrmtubhZeCLOYtnM+zSDL26fd83y3KGpcJmE16bmWZaz+Xrhwoa7n2gkQDYSXPCna60qSdmq4k4tFJPZJ2nbX1tamKWdYGRKI6kSCoTCLylB/VB4JK3WoP3VJ/D8bCMgPQzbq5jqNISCH1SSFJctNDqupLomePeUzKefX+qZnNXkaEgPta0VIY0A0XNZUUdn4Y9Eeo9jV5pMBxTdSyUC7qAtBhOraxZiqh06I9rXfFHXtJ1O2hkZoWmAkOyaP/LTeQqQYSTicvIOALGfvtJhbSggkC2JPxykZfa7Tz8pGBlrhiIgNyTI4L+Jd20RdeUggtExEjo3RQHImXd/WKT4hxFDsx6IpheIjJSXf+Hq/b7jhhnFTWRlsXT3kTK5CQJa7qxrFjTGEgHoQ8tWvftXwc02jyNRJS/ENXzEUi4gwNAZfqQscczbXmvXCc/ivI29isGgJVs27ImmR5GfMaHr99ddBzjwpOM+hQ4dAHmq9HlvWKAacnxFwEwKzZ8/GunXrcPbsWUSjUfz+97833DwiEJDHo2wlaxTf4Ov411/+d9o+/OIXv0ibRysDKT4CmxMjwAi4B4HPfOYzCIfDmDFjhqlGvfnmm4avS/QfwnORHWgLLcMTfz0T+YZLGL7gUyavQ//GW/EHGy9eHaprR/XFv/yLEWAEGIGUCAwODqY8L51sq0bxJWrNUoK69h9h2XVm1R5gesRHim5ACFojhDjzBp4s/nT6TnAORoARYARGEMjLy0uPRTiC2NCInhHnEe9qRWPleWy89Suo2nIUOlSnZh2mFd+Y0vIKUXbj58cc0vpz8803ax1Oe2zq1Klp83AGRoARyA4CZp/P66+/3mCDJyBUsggP/ctORMKnsK367/BizzmDZQxnt0bx4VJcW3J92vl2eXm54UZS9PmioiLD1/EFjAAj4AwCt99+u+GK6Lk2vUmZewWmTC8A8DZiJ8yN+SxSfPr6PXHiRLS0tOjLPJJr8uTJUvg9QxdxZkaAEXAMAXquly9fbqi+xx57zFD+MZkTv8PHH5wHcA2KJ+mYLo+5ePiPo4qPqly8eDFqamo0mjL+0D333CO51V65cmVWt77Ht4yPMAKMACFAvFxSes8++ywoBrCeRIOf6dOn68k6Lk+i/wh2Nf0tHtxyCuVrl+OrhZeOy6PrwBirvpR/tChrJWmZGsmKTGXpTZxbmdZC3/RfeSxZmXzc/QiwAbP7ZaS3hcS+oOeSZEo0UqKtpXuuZSZW8jrSUdYgUF4nIru7RHyU0ZG8tGRnjDM3kpVk4rjMBWxoaJDAIwcDpOjUnFtiasg8QAKWk3cRYMXnXdkpW06KjmRJik9NP5Of6xUrVkh5iFqq9Vwry3P6d1YVn9xZAo5AVAMon6dvUoZEkKZ85JRArRyVefm3exFgxede2ehpGT13NEAhOdJgJNVzSAqP8rkxOb7Gp2v+rZGJrMSJJtPa2orGxkbMnTuX1/00cPL0odMdWFOQA/LZN/ZTgIotbyHh6c55v/FEMaP19hUrVqC5uVla16Pn0ovJM4pPBpeci8ZiMekv7fhSDFxOfkAggdNdv8Bz/Vp9KcOSsinmre21iuRjhhAgR7/07P3617+WePPEmfdy8pziI7DJrm/v3r3S7jDxeCmgMu0ucfIyAh+i69U/xPPx88NsIJkVNNCOugXzUWZ2987LkLik7du2bZP4uAUFBdi1a5cvePOeVHx0P5Dt0Pe//31pyE1DbxqCUwwBTh5FIJHApL+oxrzQBEUHzqHnpQheW3QLCj17pyq647GfNJioq6tDVVUV6uvrsX37dvNGxy7ru2knBW7oB60v0JCbvEPQyI+G4c8//zwzPdwgHKNtyP0jFF2ruihxHJ27/hD3//AanuaqoLH7L63n0bNF7qNoXZ2muX5KvniPksuqvr4+SS7FxcXScNxPQgpqXxK9r2DXl76O265SjgKDioZz/aZ1c1o/j8fj6O7u9p3SIyR9ofioI8T7279/P2pra3HnnXdiw4YNvO7n3LNiQ03n0Nt5CF+quCEtB9yGygNZJE1tab2cZk/ErqJ1dLMMC7cD6Omprhpcmvpu3LgR5C2C1iXeeecdPProo75Zl1D319f/pWnuH6HihYm+7qZbOkfr42vWrMHmzZuldfPq6mp41VRFD6a+GfEpO1tZWSltudOaH61NsMmLEh1v/B6e5pZjZr4vb1FXCYFi6s6fP19SehTigdb2/Kz0CHzf3lW07kdb7zfeeKM0dKcteU5eQYCnuU5Jip4RWhenROvkQQnx4FvFR4KkdT8yeaGteJr60tY82/s59UhlUI88zZ3J09wMUEx5KT0HtA5O6+G0Lk7r46b946WsyZ0nfbXGpwUxDdmJ6nbddddJQt63b580EgySkLVwcfOxRO9BHCi/HXfxNNcWMSlNVchFFC0NBS35esSnFKaa6tbW1qY8zb9dhEBuURUiD82COReTLuqIC5tC6930LMimKkFUeiSWwCg+6qyS6lZRUcFUNxc+mNwk+xCQTVVo3ZvW9vxqqqIHQd9PddUgENWNvMWS8InqRju/DQ0NEgVOnZf/MwJ+QIDW84jSGRRTFT0yC5zik0FRU92eeeaZQL8BZVz4218IkKnK0qVLcfjwYUSjUSkAuL96aK43gZrqqiGSqW7kdYL4vjT858QI+AUBWseWTVXIlVs4HPZL1zLuR6AVH6FHu7vkdYKpbhnfS1yASxCQTVVoHZuoZ2SqwiFaxwonsFNdJQxqqtuhQ4ekjQ82eVGixL+9gACZqjz++OPSel5QTVX0yCnwIz4lSLS1T94oaKufqW5KZPi3FxBQe0kOqqmKHlmx4lOhRFv8THVTgcJ/XY+AH70k2wk6Kz4NdGmKq6S6UcBkprppAMWHso4A3Zd+9ZJsJ7i8xpcEXZnqRtHhaZGY7P1oJMjrfkkA48OOI0DrebQkQ6YqfvSSbCegPOJLgy6ZACijujHVLQ1gfNoRBGQvyVQZ3Z+kADnpR4AVnw6smOqmAyTO4ggCNLWVqWeyl2Q2VTEOPU91dWLGVDedQHE22xAImpdk24AEwIrPILpMdTMIGGe3BAEyVbnvvvuk9TzykhwUh6GWgKdRCE91NUBJd4ipbukQ4vNWIkCbakSpJGplkLwkW4mhuixWfGpEdP5nqptOoDibaQRk6pnsJdlPAb1Ng2LRhTzVzQBIprplAB5fmhIB9pKcEp6MT/KIL2MIIbnuZqqbBUByERIC7CXZ/huBFZ9FGDPVzSIgA16MbKrCXpLtvRF4qmshvjLV7eqrr5aiur388ssS9Y2mxJwYgVQIsKlKKnSsP8eKz2JMtahuzz//PPtDsxhnPxXHXpKdlyZPdW3CXEl1Iy+4THWzCWiPF6v0kkymKuwl2RmBsuKzEWeiEpH3W6IWcVQ3G4H2YNGyqYrSSzI7wHBOkDzVtRlrmvqqo7o9+uij7OXFZtzdXDx7Sc6+dHjE55AMiOpGVCNyb0WeNIiCxCl4CMimKnQf0P3AXpKzcw+w4nMQd6K6Ef2Io7o5CLqLqiIvyWVlZVJMZ7oPmG+bPeGw4nMYezXVjbzn0noPJ/8iQPJVekkm7968npddebPisxL/wR78/KkqFOTkICcnBwVVT+PnPafH1SBT3chrbmNjI+6++27Qug8n/yFAcp07d64kZ5L3unXrMM6u83QH1hQM3zN03+Tk3IUtPef8B4aLesSKzyphJH6DXd+5E1VvzEPHmSEIcR5Hqk5jQ/nfo+N0QrMWWutjqpsmNL44SKYqkydPlvqS3EvyBbz7i114rl/R5fB8lBVeqjjAP61GgBWfRYgmetvxwy2fxj1VC3BdHsE6AaHyJbhn2n5Euz5MWoua6kaUJU7eRoCmtiRH2VRl7969yQ3YB1/D9h9OxPMD9LIUw5/oMhTxk2nrTcDwWgRv7pVTMD0Ux6FX38agXOZgHLH/mouKmRPlI5rfMtWtubkZK1asAEd104TJEweJerZy5UpJjiRPMmUi793aKYHTh3ajqW0zvlcfwa6Onov3jvYFfNQqBIQLUiwWEwAEfXs3fSS6GhcIYKqojLwhzgydEO2PrBVNB+NiyECnotGohEVpaanH8dDuNMmZPn5M3d3dguRG/evs7EzfxaFjIhIOSfmHcQmJ8rpWETtj5I5JX022crS2trpW1jzis+oNgstRsvpZHGy6CT+vnobLLlmF40v/FqtmhWAEZKa6WSYQRwsy5SU59zosi8YhhuLo2v0M6sqBfRsfxP3/3MUjP5ulZ+SZtLkpPig+93O4/E9KsLpxNcqxE9X3N6Cj/4LhjjHVzTBkWbtANlXJyEtybgglC5ejof0w2tdOw76m3TiUZEMsax31W8XZGgYr6/XHVHdAHIt8R9zfelya2g7F28Ta8pBAeZPoymDq0tzcLE0XampqRF9fnxI2T/7201SX5LFw4UJJPjStsyQNtIu6UImoaz9pSXHZLISnun57W2j0J9HzEr5THcesqX8sTW1zQ3+GDT/ZjUb8AOte7IG2QYtGQapDTHVTAeKSvzL1LB6PSyZJlgX0zitA8bRiFE/Kc0lP/dkMnupaItcEBk/04g11WXnX4KZZf6w+avg/U90MQ2brBbZ6SR6Mo7ekGt8oYjs+O4XIis8SdHORP+sOrC7vxPr6HXhrkMZ3CQy+9VO0tM7A/RXXGNrg0GoSU920UHH2GJmqkKkRmRyRqUqm1LNE/xHs2XME/SPTgUT/ATxd/ypuW1GGfGe7FrzasrkGINftjzU+IYbiB8XWuvCoeUKoskm0xQbkblr2La+d0PqS19b9vLrGR/eobKpCJkdWpNF1YDLxCVWKxp2/9I0pC+Ej36dWYGV1Ga4wqPKL4rNaOKnKk23G6GHUZTOWqjAHz3lR8SltK732onFQtOOqcrPi46muRwf5THWzX3BkqrJhw4ZR6hl502avKvbj7kQN7IHZCZRtqkOmulEoQlp3IueWDQ0NKShSNjXEh8Wyl2QfClXRJVZ8CjC8+JNcHJHJCxk9EymelB9HdctMkmSqsmrVKqkQ8pLMDkMzw9ONV/NU141SMdEmorpRlC5KHNXNBIAjl7CXZPPYeelKVnxeklaattLUVxnVjdanaJ2KU3oECCcyVamqqkJ9fX3Gpirpa+Qc2USAp7rZRN+GuuWobnPmzJEe4nfeeQcc1S010LSeR8yLw4cPIxqNcmzb1HD54iyP+HwhxvGdoOhdHNVtPC7qI2ovyRzQW42QP/+z4vOnXKVeqalutH7FaRgBmtrq9pLMoPkOAVZ8vhPp2A7JVDdat6L1K47qBimwk34vyWPx5H/+QIAVnz/kmLIXtO5H0b1cGdVtXIQxe6OMUSB3Ws+TA3qTKRCn4CHAii9AMldGdaPoX2SvlvWUPw8NcYGhWARhhBCOHMOQeBHLbPBOovSSzAG9sy75rDaAFV9W4Xe+cqK6UdSvmpoalJWVSetczrfC2RppPY+m+Bl5SXa2yVybzQiwOYvNALuxeIr6RS6VgkB1I1MVms7u2bNHmupb5jDUjYLlNulGgEd8uqHyV0aZ6kZ2a5s3b8b8+fPR09Pjq07SVJ6m9JZ7SfYVSsHsDCu+YMp9tNd+pbrJXpJpSk9Te5ric2IEZARY8clIBPjbT1Q3LS/JyQN6B1joAe86r/EF/AaQu+8HqhtN1ZcuXcrUM1mo/J0UAR7xJYUmmCe8SnUj8xTySkOJvNQw9SyY96/eXrPi04tUgPJ5iepGpirkhUY2VWEvyQG6UTPoKiu+DMDz86VeoLqRqQpRzx5++GG0tLRg48aNoCk7J0YgHQKs+NIhFODzaqrb3LlzJZ6rpZCMUNYuKa5GG/rRVv1FXJJzF7b0nEtZjRzQW6ae0RSdEyOgFwFWfHqRCnA+mepGEFhOdRuhrAkhKOLfyCc1ZY29JAf4ZrSo66z4LALS78VoUd1ofc3JRPWxl2QnEfdvXTYrvgROd6xDQQ553FB/0k9n/Au7N3smU92am5ulqG60vkZ2c04kMlWhqTaxTIhtQt5meD3PCeSdqOM0ejr24KWnqlC4pgOnNau8gP4jz2HNVwqQkzMNVU8fQH9CM6OugzYrvg/RFaWVG40Uno+ywks1TvAhNyNAyoa4r+Td2SmqG3lJlk1VYrEYm6q4+QYx3LZz6NmyCo+3bMXK2m04q3l9AoNHfoBvPvQ2Kl44DjG0F1Unn8Q3mw5hUDN/+oP2Kr7TR/Hqp59EfEheu6HvIQy0P4IFS25Bob21p+895zCNAJm8KKO6kR2d1YmmtkovyWSqQmE0OfkJgUtRtCyCH/3Lk3giHNLuWKIHL657CbMeeQDzQhOA3Ksw77urMavpKbyYZhNMu0DAVtWT+N1k/EXdrQgpa0n04KWG/8Kisin2Vp6sx3zcMgRkqlttba1kR2dlVDfZVIUCpdPU+tlnn+WprWWS81ZBid5XsKPtKhRPyrvY8PwbUHHPu9jReRxmZry2UtZyQ9fi2otNlX5RJ3ZNuhM/5GmuChlv/qWpL9nPTZ061bKobuQl+b777pMA4YDe3rwvrGv1OfR27kVbqBBrrpygKvY82na8gt57r0ORcnClyqX112B2rSKMHKNOHMKX/urLuMrhmo20kvMaR0BNdVN7d6b/NCKUEzkGpWms2hUWmarMmDEDBQUFYC/JMlpB/h7EidjbwLRCTMqzTmlYV5Ie2SSOo3PXH6Fi5kQ9uTmPxxCQqW7k4JS8O5MSk72l0H9iWMipsbFR2hmmTQs5HylDOaD39u3bQVNpToyAHQjYOtVVN1ia5n6pHC/kO6tv1e3g//YhQMqKvDtfffXVkhK78sor8d5776WskJRdYWEhent72UtySqSCeDIPk4qvAZ7rxYnBBIos0h0OaqCRaW7FDcgPovwC1GeZ6nbHHXekVXoyLKT0/uEf/kGKgCYf429GALgUhWXzEVZDkfgAx1/7GGGT1iHOKT6e5qpF5+v/tHa3e/duQ3388Y9/bCg/Zw4GArmFt2DJtP2IdimM5QfjiL1xE5aYtA5xTPHJ09yZFg1VgyFy7/byV7/6leHGHz58GLSjy4kRGINAbhHu2vANHPreD9DRfwFIvIuOv2/CodUP4S6TYUgdUnw0zY2h/K6beJo7RqL+/XP06FFTnXv77bdNXccXeRWBEblYRPQAACAASURBVFrrJV9EdVs/+jfeij8Y550nF3klD+CFhivQUvJp5FyyDNHiv8ULq2dBYdlnCACHNjfIOrsBDxlqGmdmBBgB/yOQi/x5GxAXF02dtPs8AaFZD6Al/gBatDMYOurQiM9QmzizDxC4/PLLTfUiL8/sO9xUdXxRQBFgxRdQwdvd7ZkzZ5qqwux1pirjiwKLACu+wIre3o7PmTMHX/ziFw1V8q1vfQscCtIQZJzZJAKs+EwCx5elRmDnzp04duxY6kyKs5/73OfwH//xH1BT3RRZ+CcjYBkCrPgsg5ILIgTIlZSSekZeVdKl0tJSibFB3zLVLd01fJ4RyAQBh3Z1M2kiX+sVBMiVFMXnIHu81tbWURbGl7/8ZRA3lxyXqlN9fT3kKS7lk6luL7/8skR9Yy/LasT4vyUICBekWCwmAAj65uRNBKLRqCTD0tLSpHI8deqUlEeW9dmzZzU7qyyrr69PMw8fdD8Cra2tkrzd2FKe6lry+ghuIWovyXv37k3qJVm5cUGelJON5sLhMMjFPCWK6kau5zkxAlYiwIrPSjQDVha5nKKAQ0ovyUrllgkcpBhJidbU1KCiokLy3UdKlhMjYAUCvMZnBYoBLEP2kkzreXZ5SSYlSpsj5N+PlCsFD29oaGCTlwDeb1Z3mUd8ViMagPLIM7LsJZkCDpEDUjuTOqobOzKwE+1glM2KLxhytqSXNNUk9/F33nknKMCQk16S5ahu5JKelK4dUd0sAYkL8QQCrPg8IabsN5JMVe6++27JfXxLS4sUYCjZ5oRdrSXvzqRs7YjqZlebuVx3IsBrfO6Ui6taRWyKVatWSW3q7u7G9OnTs9Y+UrbKqG6HDh2SNj44PkfWROLJinnE50mxOddoCgREbAraYKDpZTaVnrLXFNWNlHA8HpcMpZnqpkSHf6dDgBVfOoQCep7W85YvXz4a9YwCCLltVEVKmJSxMqpbQMXF3TaIAE91DQIWhOxK6lk0GgUZFLs1qaO6MdXNrZJyV7t4xOcueWS9NcSSILYEJWJPuFnpyWDRut+6detASpr4wHPnzgUpb06MQDIEWPElQyZgx41Qz9wKDVPd3CoZ97WLFZ/7ZOJ4i+yknjndGaa6OY24N+vjNT5vys2yVjtBPbOssToLYqqbTqACnI1HfAEWvtPUM6ehZqqb04h7pz5WfN6RlWUtzSb1zLJO6CyIqW46gQpYNlZ8ARO4G6hnTkPOVDenEXd/fbzG534ZWdZCN1HPLOuUzoKY6qYTqIBk4xFfQAS9adMmV1LPnIafqW5OI+7O+ljxuVMulrVKpp7JXpLdSD2zrLM6C1JT3eilwClYCPBU18fy7unpwdKlS6WoZ26nnjktBpnqpvTuTC8Fp11tOd1vrm8YAR7x+fROIOpZcXGx1DuvUM+cFgUpOTJ5UVLd6GXByf8IsOLzmYzV1LP9+/cnjXrms66b7o6S6kYvC47qZhpKz1zIis8zokrfUDJVUUc946lbetwoB1Hd6CXBUd304eX1XKz4rJDgYA86dr2Ap6oqsKbjA40ST6OnYw9eeqoKhWs6cFojR6aHiHq2aNEiKRIZRT2jKRwnYwjQS4KiujU3N0tR3eglYp+XlwvoP/Iz6Z4oyMlBgU33hTEEgpObFV+msk68hS1/uR4trU+idtspjdLOoWfLKjzeshUra7fhrEaOTA8pqWf02+6oZ5m21+3Xy1Q3CmdJLxPLo7ol+nHo6eUo+doOHJ/y19h3ZgjxhnnIdzswfmqfcEGKxWICgKBvr6ahWESEUSLq2k9qd2HomIiEQyJU1y4GtHMYPnr27FlRW1srYUff9N/tieRMHy+kvr4+sXDhQqm9ra2tFjX5I9HVuECEKjeJg/HzFpXpzmIIM7fKmkd8Hn2LydSzxsZGtLa2ZiXqmUeh091sNdWtrq4OtHlkPiUweORf8FDTFGzasByzQhPMF8VXZoQAK76M4MvOxUQ9oykYBdqhgDv0m5M9CNC6H0V1o5cLvWQoxKbpdb9ED15c9wPgnhuR2L4ctLaXU1CFp37eg0F7ms+lJkGAFV8SYNx6mKln2ZEMvVwyjeqW6H0FO9quxazrb8Ts1S2IiwEce+JTaAqvxj8f+Tg7HQtoraz4PCJ4pp5lX1CZUd0SGDzRizdCJaj4i5kISU9ePq67txZPhF9F7bpd6Elkv49BaQFT1jwgaaaeuUdI5qluF/De8V70o3BsZ3KnoGxJGbC+FycGEyjK57HIWIDs+cco24OrZaUy9cwyKC0ryBzVbQKunFKIUH8vjr93YXxbphViUh4/juOBsecII20PrhmXytSzjCG0vQBjVLdc5M+8DfeEjuHA0fdxcVY7iBOxdxFecgsK+Wm0XWZyBQy1jISLvgNJPUv040jLGnyFdjpzpqHqqSh6Bi+qBxeJZ0xTDFHd8suwctNc/PuDf4etbxF/5wL6D+1Ay2vfwIa7isAP4xho7f3jBtNHbxswnxTtdSWSoaZsnItwRMSGZGSHxED7WhEaMdwdzrNYRGKfyBnGfHd3d4vS0lLp09nZOeacH/7IGI3tCxn1flNUNnWKOOF25g0RqZwqQstaxYlRHMde4cZ/zc3N0n1QU1MjyPhZOw2IWFuTqAyRIXdIlNdtE10+NWR2swGzK0zova34tG9vM0flG4XYAskfHDMlu+caLcUnsV5Ca0X7wEUtN3SiVSwLpWDCuKdLY1pCLyv5xUUvsSAn+X52IwY8urZ3QK2rdFrPI1bAnXfeidraWmzfvh20exiMdA69nXvRplrczw1dj9nT4ngu+rotTh3swpZ40sSXLigowIwZM7Bt2za7quJyM0CAFV8G4FlxKVPPaHH/7fFQ5l6BKdML0P/acbzn/qW+Me1XUt2qqqqkl1pmVLcxxfMfCxBgxWcBiGaLIOrZ5MmTA049y8Ok4muAtr3o7D03DsrQ9Cm40oN3qaVUt3Go8IFMEfDgLZVpl91xvUw9I8eXe/fuBbECgpkuRdE3voW60E6sr9+Bt6SdXPJV9++IHvoY04oLkOdhYJRUN3rJ0cuOU/YRYMXnsAw+/PBDLF++XHJ0SQ4vKcDNxIkTHW6Fy6rLL8cj+/ZiNZ7CFy+7BAVV38eBXx/FoX03YUnZFM+bedBLjV5u9JIrKysDR3Vzwf3nhh2XoOzqUj9px492NqPRqBugd7wNWru64xvxiYhFFlvqu3B8Hc4fIX+JSpOXU6dOOd8IB2vkXV0XKPhsN0FJPevr6wNZ/XPSQuAC+jsacP9z/ws/eaTcV16J1VS3+fPng6O6ad0D9h/jqa7NGNNu3oYNG1BRUSFNdSigTXBMVYyAm8Bgzz689NRyzGm5Ag0vPIASn3JX6aVHLz9KHNXNyD1iXV5WfNZhOa4kmXr28MMPo6WlRQpkQ299TkoEEjjdsQ4FOZfgsvv/HadvehivtTzge+/E9PJTRnWjlyObvCjvC3t/s1sqm/ClADX33XefVDpFPeMAQMmAzkX+vA2Iiw3JMvj2OL0EKarbnDlzQPZ+77zzDh599FGeETggcR7x2QAyWeuT1T5Z73PUMxsA9lmRlZWVoJejbVHdfIaXFd1hxWcFiiNlyNQzenvX19cHjHpmIZABLIqpbs4Knae6FuFN63kUj3XPnj1SYBoOAGQRsAEqRqa6Pf3009LU9+jRo3j88cfB68LW3wQ84rMAU6aeWQAiFyEhQEpu3bp11kR1Y0yTIsCKLyk0+k4w9UwfTpzLGAJMdTOGl9HcrPiMIjaSn6lnJoHjy3QjwFQ33VAZzshrfIYhg2Rtv3TpUhw+fBjRaJRZGCYw5Ev0IUA8buJz33jjjRK/m3Z+GxoamN+tD76kuXjElxQa7RNMPdPGhY/ahwCt+9HGGb1kN2/eDKa6ZY41Kz6dGDL1TCdQnM02BJjqZh20rPh0YMnUMx0gcRZHEGCqmzUw8xpfGhyZepYGID7tOAJMdcscch7xpcCQqWcpwOFTWUdATXVj7876RcKKTwMrpp5pgMKHXImATHWjXV/y7sxR3fSJiae6KpxoPY+MR8lUpbW1VfqtysJ/GQFXIUDrfmTycvXVVzPVTadkeMSnAEqmntGhWCzGSk+BDf90NwJqqtvcuXNBL3FO2giw4gMkB5Bq6llRUZE2YnyUEXAxAjRboZc2JY7qllxQgVd8RD1buXIlRz1Lfo/wGY8hQC9tdVQ39u48VoiBXuOjQC8y9Yy9JI+9MfiftxFgqltq+QV2xEeekSnQCyUK/MKu4VPfKHzWewjIVDd6qTPVbaz8Aqf4ZOrZnXfeidraWingC+2KcWIE/IoAvdSVUd3opR/0FCjFp6aebdy4kb3buuIJkCOt5SAnR/4UoGLLW0hQ+053YE2BfHzku2ILeqSTruiA6xshU93oZU8v/cBHdXMwsHrSqmKxmAAg6Nuu1NnZKUpLS6UP/eaUHQRIzvTRTidFe12JQDgiYkPqHENioH2tCGGxiMQ+UZ/k/wYQaGlpkWRQU1Mj+vr6DFxpLGtra2sKWRsry+rcgRjxkTU7WbWTdTtHPXP94IQbaDMCTHUDfK341NQzsm7n9Tybnyou3hMIBJ3q5ltzFqaeeeL540ZmEYEgU918OeJj6lkWnyYrqm6rRvElqs2MnEvwB7c+iX4ryucyRhEIKtXNV4qPprZMPRu9p737IxxBbEjQDojiM4SB9rUIebdXrm550KhuvlF8TD1z9XPFjfMAAkGiuvlijY+pZx54qriJnkAgKFQ3z4/4mHrmieeJG+khBIJAdfOs4mPqmYeeJG6qJxHwNdXNaotoM+UZZW6QtfnChQslq3CyQufkHQS0mRsyK2OY1TGcJyTCkWNCInAMtIu6kPIckrA7vIODl1p69uxZUVtbKz1v9fX1gv7rSW5mbnhujY9MVVatWiW9QdmVlCcHEhqNzkX+vA2Iiw0a5wDkz0NDXKBB+ywftRkBmvoSr33q1KmSa/tDhw5J1hNeJgN4aqrL1DOb73AunhFIgQBR3bq7uxGPx6WwDF6O6pZ1xUdxa9va2iS46VsrTgCt5y1fvlx629TX10uBVbz8tklxb/n6FMlaTrQppSVr+Tx/uxOB6dOnS3z3dFHdSNa/+tWvpE4ke66z2kM9c3U78kSjUclTirzmo/ym9TvZUwut55FXFTpP13DyHgJ6Ze29ngW3xbTOR+t99FySlxd53c8rsk7mH8hWiTY3N0uAKZWd1u+mpiYpHyk+WRHa2jAu3HIE9MqaXYVZDr0jBZKio2eXntHvfe97up5rN8jagOL7RMQii9N2LFTXLgZSQC7v9GgpOq1jixcvFqdOnUpRIp9yKwJGZc0vN7dKMnW7SG6FhYVpdYPy+dYt66G46Nr9I9FYOXWk/JAor3tG7O6Ki9/H9ordJn0zGljjuxRFy16EGDqGSDiEUF07BlRcyjPHtuKrlySfuROtjLy/GkkXLlwAWZNz8hYCZmRdV1fnrU5yayUErrjiCvT29hpCg2KApEuJ/gN4+q/D+NquOK5Z2YYhSd/E0f43N2Hol9/F/yiO4FS6QpKcN6D4kpQwejgXedctwD0zPzt6RP2jq6tLfSjt/z179vAieFqU3JeBZe0+mdjVIjOybmxsTP1cJ36D3eu/hdW/XYaf/GA1FpWERp2H5oZKsOihf8RPGj+D2IlBU92yzo4v0YM9PwG+tujm0QaqW2QGICqDdoXIgzIn7yCwc+dOU41lWZuCLasXmZX1m2++mcQxcAKn9/0QD275NOra70FJntb47HKU3Pe/8ZtXzXXdMsWX6D+GIx8X42sp2vHxxx+nOJv8VHV1dfKTfMZXCLCsfSXOlJ0ZHEwyWkv04KWGrehHGYon5SUvI/9mLCpPfjrVGdOKr3/jrfiDjcqiQwhHOpQHLPvd3NyMcDhsWXlckP0I0FRGzzqOuiUsazUi7v9vVtZJezYYR+yNfiBUiClXTkiaLZMTphUfbW681TAP+VLtCQy+9SNsOJi6KTfffHPqDEnOktIjX2GcvIPAnDlzTCk+lrV3ZCy31KysiQKXraQ1eTbRllzkFf0p/vTy1MXNmjXLcNkzZsxgpWcYtexfMG/ePMONWLhwIcvaMGrZv8ByWecVoHiavb62U2sqI5jmFmHhwqKkGxtUFNHMiHJmJP3ud7+Dkupk5FrOmz0EzMiagl1z8h4C5LTAaEop69wpKFtSBvS3Idr1odGi9eVPbZqocXbomIiEQyKpofKZN0R7V3KDY6K2EMVFacyY7DdZgsvup4gBINNiNFrl4UND4kzsl6J1Z6OovHataB8YF0lb6ttQ/KDYWheWcAtVbhIH4+dd32cjsib5ejsNiFhbk6iU3WeFKkVjW0yc8XanUrae6KTys7xq1Spx77336nqudcladkVW3iS6ziR7Jl4Vv4ylokskb74B5sZIISkU31C8UzQteyLpwys3gx4ImeeXTOmR1T8lyivTnpQcXrksr38PxSJiwTcrxTfpgQklUXxnDorG8gVibfsJMSTOi3j7Y6I8xQ3hJkzSyZqoTrKs3dRuY205L060PiBCoWUicmz4QRyKt4m15beIuvaTxorySG6Zk0vyo9+UrJX1kDhzbOvwi6S8TkTalS+RARFr/5GItP6n6ReLAcVnDWVNKVd6Y9BNT04O6UPKkEDUoqh1d3ePOivw/oOiRIF+j2CrqfiGz40dYZ8U7XW3XHTUqS7Ohf9lWcsvOlnW9LB4PmkOBrTk5vmejlFuNNojuaqTLGv1c21G1kPxLrE7UifKITuivUhZ0x4Hqluj/d+A4tMuwMmjBJzsCZZA11KQTrbHurpSKD7pobpWpeRGPBaHIyKWifSt64DukmTFp/sCT2SkF1GJwJhROB1b4KsRn3Lw4XXP59ZtbuhbUswol+wJNhqNSqYS8+fPH/Xll1HBLr440fsKdrRdjulTrhi/cdS2F52951zc+qA0bSJm3fVXKN+3Gl974Dm8NXgO/R1bEb1yLf6m/ArPg0D+MMkJMFlYFBQUIBaLgZySejl5SvHJQJOtV19fH8gZYkVFBTZs2AASjv9SAoMnevEGrkltwe6/jnusR7nIK3kALxzchD/7+b344mXX4N7jt+PJVbMR8uQTdhF+cha7cuXKUSfA27dv94XJkWfFQuYSzz77LFpaWvDwww9j7ty5oPi6nBiB7CDwKVx2+SRMW/0k6sqBturvYH3Hu0hkpzGW1EpesidPnoxf//rXoPg269atA826/JA8q/hk8GnITUNvSsXFxdKQ3D+jv1zkTSrENLxt2guFjBN/24kAMZeew3eahnD36u+iof0w2tcCT956P5qOmOOn29nadGWTSzFyEUYu5Mjebu/evaBQk35Knld8JAyis+3fv18yjq6qqpKG5n6J55BbeAuWhD+tuucu4L3jvegPz0dZ4aWqc/zXcQQSPXjxO9/DiVnXD09tc6/CvA070NUI1K7bhR4PDfsogBCtnRP/trW1VYqu5kd/mL5QfHSj0xCchuI0JKehOQ3Raaju+SRZsV+F56Kv4/RoZwZxIvYuwktuQaFvJDjaOe/9kEj1Z1Xtzsf/vOkG2Eu8UlWZwV+aJdFaObl/ow0MWkNftGhRBiW6/FJPWAsYbCSZucgW5WT+4n6zlxTmLNR3Dxswq0XnT3OWj0RX4wIBhQGzOPOGiFSWi2Wtx4eDoquBcNF/cgMvM6TITMWMvZ2LuqOrKZ6y49PVI0UmMnSmB42sy8kGyZVJpuYoDDTDkWPjHhaJFSPFHSADzm2iywOUNS28/an4hBAUG2KrwtDWI5Q1UnSuf0a0bqQMj/la8RE2ZEUuv82ILRCEt1mG94Stl/tW8dmKmvWF03Mhz4qC+FzkEKQun41n3DxavyD32LTxQa6PNm7c6AtbpIyByUIBOTk5Uq0BuO2ygK6+Ksm9//r166XMTzzxRCCd/AZiaZw2Psjspbu7G/F4XDJ78cXGh777nHMxAhICNAAgMxUy+ifjf3oGAuvZ3PpBtLtLVPN9tUjW7u6Bt1vHU93syE/Js/Wfkw/jmAZixKd84Sv5vmT2Qlv2NPTnxAj4EQEa5al5tr42U9EpxMApPhkXGuLTUN//fF+5x/wdNATIiP/uu+/2Hc/WCjkGYnMjHVD0RqSNj9LSUjzzzDOYPn16ukv4vEkEeHPDJHAGL6OXOlHO+J7WBi6wIz4lHDLflyzWyfUOKUKaInBiBLyGgBbPll/kGlI0vizo3yto44NsmmgBPpl3Wf/23pme8eaGfTh3dnb62Eu5tbjxiE/xMvAt31fRR/7pPwRodiLzbGnN2vc8WytEaK0e9U9pxO+V3dx7g+/rDex5xGetnILIs7UCQd7cSPP24EXiNAAZPM2bGwYBS5GdN+VSgJPmFE910wBENk80dZA3Pvzr5j4NEHzaNQiQmcry5ctHzVTIFyVvYBgTD4/4dOJF6yjM99UJVopsPOJLAY6OU8yz1QGSjiw84tMBEmVhvq9OoDibLQjQi5d5thZCa8VCYdDKYL6veYmn39wYiRk86p8QAh6MH2weofFXMs92PCaZHuERn4mXCPN9TYCm95JEH37xo5+gfzR/KLAu9mmUxzzb0RvB2h+Zas6gXx90h45G5Z96xDckznQ1iXBduxgwWrDP8rMDXXsF6nsPzPbCd7H0oLrwvoiAvl+pFd9J0V5XIoCwqIu0ivZYMNWfJ0Im6BO3a3Ox4rNQNGxMmh7MVIpvKBYRYeXaHinA1mPiTPpifZGDjeadEyMrPouxZr5vakBTKT75yqF4l9gdkQP3LBCNXR/Jp3z7zTxbZ0XLmxvWLpn6N76vxTilKi43VIKFyxrQHm/D2vJX0fTiq4qYwqmu9N455tlmSWbO6tlg1cZTl/Hy1jPiu3jViGlLaK1oHxi6eNgnv2hphEKfEiZBiWfrFtHxiM/GF87EiROliG6tra1obGzE/PnzceDAARtr9FvRucibVIhp0woxKc9ftyqZqRQXF0sCi8ViUjAsMpPi5AwC/rqbnMHMcC0y35dcBpWVlUkuhGiKwykdAgkMnvhvlKz5Oop8cqdq8WyLiorSAcHnrUbALUPPILSDNj5ksxcKck5TnaCl5FPd8yLe9VOxuysuhie150X84P8VdY+0ibhPZrnRaFSa1tL0ln5zyh4CPnmPWv06sKc8Lb4vTXk4jSAwcBj/Z2YBLsnJQUHV93FgcB4e+bs/Q8jjd6mSZ1tTU4O9e/cGN56tW2727OncYNccVLOX5CM+f94PzLN1p1w9/i51y+vDeDto9Ldu3TpEo1FwfF/j+Ln9Chrlbdq0SQpeRb4caQOD49m6R2qs+LIsC3V8X3I9xBsfWRZKhtXL8WxXrFiB5uZmbN++Hek3MD5Ax5qZIH+F4z4VW9CTyLBRfPkYBFjxjYEjO38mTZqEZ599FrLZy9y5c/Haa69lpzFca0YIUKiCyZMnIx6Po7u7Gw8++KBk1J620NOvI/rcEY1swfVOowGGZYdY8VkGZeYF0VSIpkSym3va+ODRX+a4OlECxbMld/AUxLu2tlbawNDvDj6B011H8ennT2BICKKRjnxOor3u61hSNgX8oFosRXcuPQa7VcqNDzJ7IRdFfkl+3NxQ8mzNmamcF/HY8XHOGCSnDQF3wmrXfc8vEotfJFYUJ2980FSJpkw0daIpFCd3IUCjcXU8W1qzNZ4mIFT0J8gbc+E59HYewKT7b0UhP6VjkLHkj10alcu1BgG/8X39MuKznWc7dExEFjziS46yNU9GZqXwu8SS14dWIafR07EHLz1VhcI1HdreRQZ70LHrBTxVVYE1HR9oFQLm+2rCktWDTvBsE72vYNeXyjEznx9RO4TNqNqBKs6hZ8sqPN6yFStrt+GsVh2Jt7DlL9ejpfVJ1G47pZVjzDHm+46BIyt/nOPZ0jT3EL5UcQPys9LTAFSa2YCRr06JAE1XwiERShFDYtjrcImoaz+Zsij5pNf5vl6d6jrKs+Vprny72/bNIz6PvdyY7+uswGgDQ45n6xTPlqe59suYFZ/9GNtSA9mI7d+/H/X19aiqqpJsyGgqxsk6BMiInIzJyZciGZeTkTmtudqbeJprL77DpbPicwJlm+qQzV6Y72stwDTKyxrPNnEcnQeux12z7Faw1mLmtdJY8XlNYhrtZb6vBigmD5nj2ZqsTOuy3OuwLLISJT7zOK3V1WweY8WXTfQtrJv5vpmDaZpnm3nVXILDCLDicxhwu6tjvq9xhDPj2Rqvj6/IPgKs+LIvA8tbQC6QyBWSvPFx9913gzc+tGFua2uTgkBt3rxZ8o24ceNGBzYwtNvCR51DgBWfc1g7WpO88cF8X23YZZ5tRUUFKAhUX18fu4PXhsqfR22zEAx0wSPxYAEpuMyw0e5iEYl9okDlpGivK1Gch4BNnjiUfN+amhpB/7OV3GDArObZZgsLrjd7CORQ1f5U6dwrNQI0raMRTmlpKZ5++mnMnj1bncX2/+RdmFI2bjsa5e3cuVOyeyQMnn/+eR2ekW2HhCvIAgI81c0C6NmqksxeaEoXxPi+tMa5cuVKSenR2icZf6d3B58tSXG9diPAIz67EXZh+dkc+WRjxOeGka4Lb4NAN4lHfAEUv8z3JTf3lIqLi+HH+L5kpqLm2WZjeh/AW8z9Xc7e8iLX7AYElG7uaePDbjf3Tm1ucDxbN9xd7m0Dj/jc/26ytYWy2YvM9yU39zQ19GpS82xpTZPj2XpVmja22706mVvmNAJk5kKjPhqV1dbWChoNWp3sHPGRmQoFZ6I6mpubbWm/1XhwedlBgDc3bHypeLVo4qxSmEQy+XjmmWegP0xi+h7btblhZ5vT94pzeA0Bnup6TWIOtFfN9yUXTTSFdGNS82zJTMVKRe3GPnObMkeAR3yZY+jbEkjZRSIRrFixAgsXLpR81JEXmEySlSM+Wotcv349Dh8+LPFszYV2zKQ3fK1XEeARn1cl50C7aePjwQcfhNv4vqSQhJkyawAABJNJREFUKZ4t82wduAn8WkV2lha5Vq8hYBXfN9PNDebZeu3OcWd7ecTn1zeaxf2S4/uS2Qu5cJo/fz4OHDhgcS3Ji6NRnlY82+RX8BlGIDkCrPiSY8NnNBDIBt+XebYaguBDGSHAmxsZwRfci2kEZsbTidHNDebZBvces7PnPOKzE10fl20335d5tj6+eVzQtUsee+yxx1zQDm6CRxH4whe+gKVLl+Kzn/2sZPby7rvv4qabbkJ+fv6YHtF0dffu3dKHTkyYMEGyDfz85z8PUqLKRPFslyxZIo0oKZ7tmjVrxuVR5uffjIBhBNy558Kt8iIC0WhUlJaWSpQx+k1J6QRB3tFVf7e2to7mJaoZnSfqmd0OE7yIMbfZGgR4jc/wq4IvSIUATVFphEY7v6tWrcJHH32ErVu3prpEOvfII4/g9ddfx549e9Dc3Izq6moe5aVFjTOYRYAVn1nk+LqUCMjc2ZSZVCfJI/KOHTuYcqbChf9ajwBvbliPKZcIYNasWYZxuOyyy1jpGUaNLzCDACs+M6jxNWkR6OjoSJtHneHIkSPo6elRH+b/jIDlCLDisxxSLpAQOHr0qCkgzF5nqjK+KLAIsOILrOi544xAcBFgxRdc2buy53l5ea5sFzfKXwiw4vOXPF3Tm9tuu81UW66//npT1/FFjIARBFjxGUGL8+pGYObMmbrzyhlra2uRqaNTuSz+ZgRSIcCKLxU6fM40AuTGiuhmRlJNTY2R7JyXETCNACs+09DxhekQoNgdxMLQkzo7O0EGzJwYAScQYMXnBMoBroNc15PzUorYppUolkcsFsPs2bO1TvMxRsAWBJiyZgusXKgWAmScLNvp0e4tbWTwmp4WUnzMbgRY8dmNMJfPCDACrkOAp7quEwk3iBFgBOxGgBWf3Qhz+YwAI+A6BFjxuU4k3CBGgBGwGwFWfHYjzOUzAoyA6xBgxec6kXCDGAFGwG4EWPHZjXCgy/8AHWtmgkJKan8qsGbLLnT0nA40Stx55xFgxec85gGq8QrMa+iCGGhHXSiEcOQYhoSAkD4DiLUvAZ57ELcWz0bVlqMYDBAy3NXsIsCKL7v4B7j2fBTNW4aGn7QhUglsq/4u/vnIxwHGg7vuJAKs+JxEm+saj0DeVNy74XEsC/0Utet2oScxPgsfYQSsRoAVn9WIcnmGEcgNXY/Z00JA21509p4zfD1fwAgYRYAVn1HEOL/1CORegSnTCwC8jdgJXumzHmAuUY0AKz41IvyfEWAEfI8AKz7fi9gDHUx8gOOvxQFcg+JJHHPDAxLzfBNZ8XlehN7vQKL/TRx4ox+hZX+JisJLvd8h7oHrEWDF53oR+byBg0exdd2j2NK/AKu/PQ9X8R3pc4G7o3t8m7lDDgFsxWn0dGzBmq+FUb2tAGvbf4jVJZcHEAfucjYQYEek2UA9MHUSZW0+bt14RLvHoUo0fn8JvjL7NpSEJmjn4aOMgA0IsOKzAVQukhFgBNyNAE913S0fbh0jwAjYgAArPhtA5SIZAUbA3Qiw4nO3fLh1jAAjYAMCrPhsAJWLZAQYAXcj8P8BDEGz9Uh8irUAAAAASUVORK5CYII="></p>
</div>

<div class="specification">
<p>The graph <em>G</em> is a plan of a holiday resort where each vertex represents a villa and the edges represent the roads between villas. The weights of the edges are the times, in minutes,&nbsp;Mr José, the security guard, takes to walk along each of the roads. Mr José is based at villa A.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State, with a reason, whether or not <em>G</em> has an Eulerian circuit.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use Kruskal’s algorithm to find a minimum spanning tree for <em>G</em>, stating its total weight. Indicate clearly the order in which the edges are added.</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>Use a suitable algorithm to show that the minimum time in which Mr José can get from A to E is 13 minutes.</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 minimum time it takes Mr José to patrol the resort if he has to walk along every road at least once, starting and ending at A. State clearly which roads need to be repeated.</p>
<div class="marks">[7]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>no because the graph has vertices (A, B, D, F) of odd degree&nbsp; &nbsp; &nbsp; &nbsp; <em><strong>R1</strong></em></p>
<p>&nbsp;</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>the edges are added in the order</p>
<p>BI&nbsp; &nbsp;5 &nbsp;</p>
<p>DH&nbsp; &nbsp;5&nbsp; &nbsp; &nbsp; &nbsp;<em><strong>A1</strong></em></p>
<p>AB&nbsp; &nbsp;6 &nbsp;</p>
<p>AF&nbsp; &nbsp;6 &nbsp;</p>
<p>CI&nbsp; &nbsp;6&nbsp; &nbsp; &nbsp; &nbsp;<em><strong>A1</strong></em></p>
<p>CD&nbsp; &nbsp;7 &nbsp;</p>
<p>EF&nbsp; &nbsp;7&nbsp; &nbsp; &nbsp; &nbsp;<em><strong>A1</strong></em></p>
<p>total weight&nbsp;= 42&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<em><strong>A1</strong></em></p>
<p><strong>Note:</strong> The orders of the edges with the same weight are interchangeable.<br>Accept indication of correct edge order on a diagram.</p>
<p>&nbsp;</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>clear indication of using Dijkstra for example&nbsp; &nbsp; &nbsp; &nbsp;<em><strong>M1</strong></em></p>
<p><img 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"></p>
<p>&nbsp;</p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>there are 4 vertices of odd degree (A, F, B and D)&nbsp; &nbsp; &nbsp; &nbsp;<em><strong>(A1)</strong></em></p>
<p>attempting to list at least 2 possible pairings of odd vertices&nbsp; &nbsp; &nbsp; <em><strong>&nbsp;M1</strong></em></p>
<p>A → F and B → D has minimum weight 6 + 17&nbsp;= 23</p>
<p>A → B and F → D has minimum weight 6 + 18&nbsp;= 24</p>
<p>A → D and F → B has minimum weight 20 + 12&nbsp;= 32&nbsp; &nbsp; &nbsp; &nbsp;<em><strong>A1A1</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>A1A0</strong></em> for 2 pairs.</p>
<p>&nbsp;</p>
<p>minimum time is (116&nbsp;+ 23 =) 139 (mins)&nbsp; &nbsp; &nbsp; &nbsp;<em><strong>(M1)A1</strong></em></p>
<p>roads repeated are AF, BC and CD&nbsp; &nbsp; &nbsp; &nbsp;<em><strong>A1</strong></em></p>
<p>&nbsp;</p>
<p><em><strong>[7 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In the context of graph theory, explain briefly what is meant by a circuit;</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>In the context of graph theory, explain briefly what is meant by an Eulerian circuit.</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>The graph <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="G">
  <mi>G</mi>
</math></span> has six vertices and an Eulerian circuit. Determine whether or not its complement <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="G'">
  <msup>
    <mi>G</mi>
    <mo>′</mo>
  </msup>
</math></span> can have an Eulerian circuit.</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 an example of a graph <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="H">
  <mi>H</mi>
</math></span>, with five vertices, such that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="H">
  <mi>H</mi>
</math></span> and its complement <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="H'">
  <msup>
    <mi>H</mi>
    <mo>′</mo>
  </msup>
</math></span> both have an Eulerian trail but neither has an Eulerian circuit. Draw <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'">
  <msup>
    <mi>H</mi>
    <mo>′</mo>
  </msup>
</math></span> as your solution.</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>a circuit is a walk that begins and ends at the same vertex and has no repeated edges&nbsp;&nbsp;&nbsp;&nbsp; <strong><em>A1</em></strong></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>an Eulerian circuit is a circuit that contains every edge of a graph&nbsp;&nbsp;&nbsp;&nbsp; <strong><em>A1</em></strong></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>if <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="G">
  <mi>G</mi>
</math></span> has an Eulerian circuit all vertices are even (are of degree 2 or 4)&nbsp;&nbsp;&nbsp;&nbsp; <strong><em>A1</em></strong></p>
<p>hence, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="G'">
  <msup>
    <mi>G</mi>
    <mo>′</mo>
  </msup>
</math></span> must have all vertices odd (of degree 1 or 3)&nbsp;&nbsp;&nbsp;&nbsp; <strong><em>R1</em></strong></p>
<p>hence, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="G'">
  <msup>
    <mi>G</mi>
    <mo>′</mo>
  </msup>
</math></span> cannot have an Eulerian circuit&nbsp;&nbsp;&nbsp;&nbsp; <strong><em>R1</em></strong></p>
<p>&nbsp;</p>
<p><strong>Note:</strong>&nbsp;&nbsp;&nbsp;&nbsp; Award <strong><em>A1 </em></strong>to candidates who begin by considering a specific <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="G">
  <mi>G</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="G'">
  <msup>
    <mi>G</mi>
    <mo>′</mo>
  </msup>
</math></span> (diagram). Award <strong><em>R1R1 </em></strong>to candidates who then consider a general <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="G">
  <mi>G</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="G'">
  <msup>
    <mi>G</mi>
    <mo>′</mo>
  </msup>
</math></span>.</p>
<p>&nbsp;</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>for example</p>
<p><img src="images/Schermafbeelding_2017-08-10_om_10.15.08.png" alt="M17/5/MATHL/HP3/ENG/TZ0/DM/M/03.c"></p>
<p><strong><em>A2</em></strong></p>
<p><strong><em>A2</em></strong></p>
<p>&nbsp;</p>
<p><strong>Notes:</strong>&nbsp;&nbsp;&nbsp;&nbsp; Each graph must have 3 vertices of order 2 and 2 odd vertices. Award <strong><em>A2</em></strong> if one of the graphs satisfies that and the final <strong><em>A2 </em></strong>if the other graph is its complement.</p>
<p>&nbsp;</p>
<p><strong><em>[4 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">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 following weighted graph <em>G</em>.</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>State what feature of <em>G</em> ensures that <em>G</em> has an Eulerian trail.</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>State what feature of <em>G</em> ensures that <em>G</em> does not have an Eulerian circuit.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an Eulerian trail in <em>G</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>Starting and finishing at B, find a solution to the Chinese postman problem for<em> G</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the total weight of the solution.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em>G</em> has an Eulerian trail because it has (exactly) two vertices (B and F) of odd degree      <em><strong>R1</strong></em></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><em>G</em> does not have an Eulerian circuit because not all vertices are of even degree      <em><strong>R1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>for example BAEBCEFCDF      <em><strong>A1A1</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>A1</strong> </em>for start/finish at B/F, <em><strong>A1</strong> </em>for the middle vertices.</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>we require the Eulerian trail in (b), (weight = 65)     <em><strong>(M1)</strong></em></p>
<p>and the minimum walk FEB (15)     <em><strong>A1</strong></em></p>
<p>for example BAEBCEFCDFEB    <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Accept EB added to the end or FE added to the start of their answer in (b) in particular for follow through.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>total weight is (65 + 15=)80     <em><strong> A1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.iii.</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.</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">c.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>Mathilde delivers books to five libraries, A, B, C, D and E. She starts her deliveries at library D and travels to each of the other libraries once, before returning to library D. Mathilde wishes to keep her travelling distance to a minimum.</p>
<p>The weighted graph <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="H">
  <mi>H</mi>
</math></span>, representing the distances, measured in kilometres, between the five libraries, has the following table.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-09_om_05.58.38.png" alt="N17/5/MATHL/HP3/ENG/TZ0/DM/01"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the weighted graph <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="H">
  <mi>H</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>Starting at library D use the nearest-neighbour algorithm, to find an upper bound for Mathilde’s minimum travelling distance. Indicate clearly the order in which the edges are selected.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>By first removing library C, use the deleted vertex algorithm, to find a lower bound for Mathilde’s minimum travelling distance.</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><img src="images/Schermafbeelding_2018-02-09_om_06.16.03.png" alt="N17/5/MATHL/HP3/ENG/TZ0/DM/M/01.a"></p>
<p>complete graph on 5 vertices     <strong><em>A1</em></strong></p>
<p>weights correctly marked on graph     <strong><em>A1</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>clear indication that the nearest-neighbour algorithm has been applied     <strong><em>M1</em></strong></p>
<p>DA (or 16)     <strong><em>A1</em></strong></p>
<p>AB (or 18) then BC (or 15)     <strong><em>A1</em></strong></p>
<p>CE (or 17) then ED (or 19)     <strong><em>A1</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{UB}} = 85">
  <mrow>
    <mtext>UB</mtext>
  </mrow>
  <mo>=</mo>
  <mn>85</mn>
</math></span>     <strong><em>A1</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>an attempt to find the minimum spanning tree     <strong><em>(M1)</em></strong></p>
<p>DA (16) then BE (17) then AB (18) (total 51)     <strong><em>A1</em></strong></p>
<p>reconnect C with the two edges of least weight, namely CB (15) and CE (17)     <strong><em>M1</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{LB}} = 83">
  <mrow>
    <mtext>LB</mtext>
  </mrow>
  <mo>=</mo>
  <mn>83</mn>
</math></span>     <strong><em>A1</em></strong></p>
<p><strong><em>[4 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>The simple, complete graph <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\kappa _n}(n > 2)">
  <mrow>
    <msub>
      <mi>κ<!-- κ --></mi>
      <mi>n</mi>
    </msub>
  </mrow>
  <mo stretchy="false">(</mo>
  <mi>n</mi>
  <mo>&gt;</mo>
  <mn>2</mn>
  <mo stretchy="false">)</mo>
</math></span> has vertices <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_1},{\text{ }}{{\text{A}}_2},{\text{ }}{{\text{A}}_3},{\text{ }} \ldots ,{\text{ }}{{\text{A}}_n}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>1</mn>
    </msub>
  </mrow>
  <mo>,</mo>
  <mrow>
    <mtext>&nbsp;</mtext>
  </mrow>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>2</mn>
    </msub>
  </mrow>
  <mo>,</mo>
  <mrow>
    <mtext>&nbsp;</mtext>
  </mrow>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>3</mn>
    </msub>
  </mrow>
  <mo>,</mo>
  <mrow>
    <mtext>&nbsp;</mtext>
  </mrow>
  <mo>…<!-- … --></mo>
  <mo>,</mo>
  <mrow>
    <mtext>&nbsp;</mtext>
  </mrow>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mi>n</mi>
    </msub>
  </mrow>
</math></span>. The weight of the edge from <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_i}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mi>i</mi>
    </msub>
  </mrow>
</math></span> to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_j}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mi>j</mi>
    </msub>
  </mrow>
</math></span> is given by the number <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="i + j">
  <mi>i</mi>
  <mo>+</mo>
  <mi>j</mi>
</math></span>.</p>
</div>

<div class="specification">
<p>Consider the general graph <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\kappa _n}">
  <mrow>
    <msub>
      <mi>κ<!-- κ --></mi>
      <mi>n</mi>
    </msub>
  </mrow>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) &nbsp; &nbsp; Draw the graph <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\kappa _4}">
  <mrow>
    <msub>
      <mi>κ</mi>
      <mn>4</mn>
    </msub>
  </mrow>
</math></span>&nbsp;including the weights of all the edges.</p>
<p>(ii) &nbsp; &nbsp; Use the nearest-neighbour algorithm, starting at vertex <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_1}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>1</mn>
    </msub>
  </mrow>
</math></span>, to find a Hamiltonian cycle.</p>
<p>(iii) &nbsp; &nbsp; Hence, find an upper bound to the travelling salesman problem for this weighted graph.</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>Consider the graph <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\kappa _5}">
  <mrow>
    <msub>
      <mi>κ</mi>
      <mn>5</mn>
    </msub>
  </mrow>
</math></span>. Use the deleted vertex algorithm, with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_5}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>5</mn>
    </msub>
  </mrow>
</math></span> as the deleted vertex, to find a lower bound to the travelling salesman problem for this weighted graph.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) &nbsp; &nbsp; Use the nearest-neighbour algorithm, starting at vertex <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_1}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>1</mn>
    </msub>
  </mrow>
</math></span>, to find a Hamiltonian cycle.</p>
<p>(ii) &nbsp;&nbsp; Hence find and simplify an expression in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n">
  <mi>n</mi>
</math></span>, for an upper bound to the travelling salesman problem for this weighted graph.</p>
<div class="marks">[7]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>By splitting the weight of the edge <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_i}{{\text{A}}_j}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mi>i</mi>
    </msub>
  </mrow>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mi>j</mi>
    </msub>
  </mrow>
</math></span>&nbsp;into two parts or otherwise, show that all Hamiltonian cycles of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\kappa _n}">
  <mrow>
    <msub>
      <mi>κ</mi>
      <mi>n</mi>
    </msub>
  </mrow>
</math></span> have the same total weight, equal to the answer found in (c)(ii).</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color: #999;font-size: 90%;font-style: italic;">* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.</p><p>(i) &nbsp; &nbsp; <img src="images/Schermafbeelding_2017-03-02_om_08.49.36.png" alt="N16/5/MATHL/HP3/ENG/TZ/DM/M/04.a">&nbsp;&nbsp; &nbsp; <strong><em>A1A1</em></strong></p>
<p>&nbsp;</p>
<p><strong>Note: <em>A1 </em></strong>for the graph, <strong><em>A1 </em></strong>for the weights.</p>
<p>&nbsp;</p>
<p>(ii) &nbsp; &nbsp; cycle is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_1}{{\text{A}}_2}{{\text{A}}_3}{{\text{A}}_4}{{\text{A}}_1}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>1</mn>
    </msub>
  </mrow>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>2</mn>
    </msub>
  </mrow>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>3</mn>
    </msub>
  </mrow>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>4</mn>
    </msub>
  </mrow>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>1</mn>
    </msub>
  </mrow>
</math></span>&nbsp;&nbsp; &nbsp; <strong><em>A1</em></strong></p>
<p>(iii) &nbsp; &nbsp; upper bound is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3 + 5 + 7 + 5 = 20">
  <mn>3</mn>
  <mo>+</mo>
  <mn>5</mn>
  <mo>+</mo>
  <mn>7</mn>
  <mo>+</mo>
  <mn>5</mn>
  <mo>=</mo>
  <mn>20</mn>
</math></span>&nbsp;&nbsp; &nbsp; <strong><em>A1</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_5}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>5</mn>
    </msub>
  </mrow>
</math></span>&nbsp;deleted, (applying Kruskal’s Algorithm) the minimum spanning tree will consist of the edges <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_1}{{\text{A}}_2},{\text{ }}{{\text{A}}_1}{{\text{A}}_3}{\text{, }}{{\text{A}}_1}{{\text{A}}_4}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>1</mn>
    </msub>
  </mrow>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>2</mn>
    </msub>
  </mrow>
  <mo>,</mo>
  <mrow>
    <mtext>&nbsp;</mtext>
  </mrow>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>1</mn>
    </msub>
  </mrow>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>3</mn>
    </msub>
  </mrow>
  <mrow>
    <mtext>,&nbsp;</mtext>
  </mrow>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>1</mn>
    </msub>
  </mrow>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>4</mn>
    </msub>
  </mrow>
</math></span>, of weights 3, 4, 5 &nbsp; &nbsp; <strong><em>(M1)A1</em></strong></p>
<p>the two edges of smallest weight from <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_5}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>5</mn>
    </msub>
  </mrow>
</math></span> are <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_5}{{\text{A}}_1}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>5</mn>
    </msub>
  </mrow>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>1</mn>
    </msub>
  </mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_5}{{\text{A}}_2}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>5</mn>
    </msub>
  </mrow>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>2</mn>
    </msub>
  </mrow>
</math></span> of weights 6 and 7 &nbsp; &nbsp; <strong><em>(M1)A1</em></strong></p>
<p>so lower bound is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3 + 4 + 5 + 6 + 7 = 25">
  <mn>3</mn>
  <mo>+</mo>
  <mn>4</mn>
  <mo>+</mo>
  <mn>5</mn>
  <mo>+</mo>
  <mn>6</mn>
  <mo>+</mo>
  <mn>7</mn>
  <mo>=</mo>
  <mn>25</mn>
</math></span>&nbsp;&nbsp; &nbsp; <strong><em>A1</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) &nbsp; &nbsp; starting at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_1}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>1</mn>
    </msub>
  </mrow>
</math></span> we go&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_2},{\text{ }}{{\text{A}}_3}{\text{ }} \ldots {\text{ }}{{\text{A}}_n}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>2</mn>
    </msub>
  </mrow>
  <mo>,</mo>
  <mrow>
    <mtext>&nbsp;</mtext>
  </mrow>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>3</mn>
    </msub>
  </mrow>
  <mrow>
    <mtext>&nbsp;</mtext>
  </mrow>
  <mo>…</mo>
  <mrow>
    <mtext>&nbsp;</mtext>
  </mrow>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mi>n</mi>
    </msub>
  </mrow>
</math></span></p>
<p>we now have to take&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_n}{{\text{A}}_1}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mi>n</mi>
    </msub>
  </mrow>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>1</mn>
    </msub>
  </mrow>
</math></span></p>
<p>thus the cycle is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_1}{{\text{A}}_2}{{\text{A}}_3} \ldots {{\text{A}}_{n - 1}}{{\text{A}}_n}{{\text{A}}_1}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>1</mn>
    </msub>
  </mrow>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>2</mn>
    </msub>
  </mrow>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>3</mn>
    </msub>
  </mrow>
  <mo>…</mo>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mrow>
        <mi>n</mi>
        <mo>−</mo>
        <mn>1</mn>
      </mrow>
    </msub>
  </mrow>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mi>n</mi>
    </msub>
  </mrow>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>1</mn>
    </msub>
  </mrow>
</math></span>&nbsp;&nbsp; &nbsp; <strong><em>A1A1</em></strong></p>
<p>&nbsp;</p>
<p><strong>Note: </strong>Final <strong><em>A1 </em></strong>is for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_n}{{\text{A}}_1}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mi>n</mi>
    </msub>
  </mrow>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>1</mn>
    </msub>
  </mrow>
</math></span>.</p>
<p>(ii) &nbsp; &nbsp; smallest edge from <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_1}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>1</mn>
    </msub>
  </mrow>
</math></span> is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_1}{{\text{A}}_2}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>1</mn>
    </msub>
  </mrow>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>2</mn>
    </msub>
  </mrow>
</math></span> of weight 3, smallest edge from <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_2}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>2</mn>
    </msub>
  </mrow>
</math></span> (to a new vertex) is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_2}{{\text{A}}_3}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>2</mn>
    </msub>
  </mrow>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>3</mn>
    </msub>
  </mrow>
</math></span> of weight 5, smallest edge from <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_{n - 1}}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mrow>
        <mi>n</mi>
        <mo>−</mo>
        <mn>1</mn>
      </mrow>
    </msub>
  </mrow>
</math></span> (to a new vertex) is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_{n - 1}}{{\text{A}}_n}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mrow>
        <mi>n</mi>
        <mo>−</mo>
        <mn>1</mn>
      </mrow>
    </msub>
  </mrow>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mi>n</mi>
    </msub>
  </mrow>
</math></span> of weight <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2n - 1">
  <mn>2</mn>
  <mi>n</mi>
  <mo>−</mo>
  <mn>1</mn>
</math></span>&nbsp;&nbsp; &nbsp; <strong><em>(M1)</em></strong></p>
<p>weight of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_n}{{\text{A}}_1}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mi>n</mi>
    </msub>
  </mrow>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mn>1</mn>
    </msub>
  </mrow>
</math></span> is&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n + 1">
  <mi>n</mi>
  <mo>+</mo>
  <mn>1</mn>
</math></span></p>
<p>weight is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3 + 5 + 7 + &nbsp;\ldots &nbsp;+ (2n - 1) + (n + 1)">
  <mn>3</mn>
  <mo>+</mo>
  <mn>5</mn>
  <mo>+</mo>
  <mn>7</mn>
  <mo>+</mo>
  <mo>…</mo>
  <mo>+</mo>
  <mo stretchy="false">(</mo>
  <mn>2</mn>
  <mi>n</mi>
  <mo>−</mo>
  <mn>1</mn>
  <mo stretchy="false">)</mo>
  <mo>+</mo>
  <mo stretchy="false">(</mo>
  <mi>n</mi>
  <mo>+</mo>
  <mn>1</mn>
  <mo stretchy="false">)</mo>
</math></span>&nbsp;&nbsp; &nbsp; <strong><em>A1</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{(n - 1)}}{2}(2n + 2) + (n + 1)">
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mo stretchy="false">(</mo>
      <mi>n</mi>
      <mo>−</mo>
      <mn>1</mn>
      <mo stretchy="false">)</mo>
    </mrow>
    <mn>2</mn>
  </mfrac>
  <mo stretchy="false">(</mo>
  <mn>2</mn>
  <mi>n</mi>
  <mo>+</mo>
  <mn>2</mn>
  <mo stretchy="false">)</mo>
  <mo>+</mo>
  <mo stretchy="false">(</mo>
  <mi>n</mi>
  <mo>+</mo>
  <mn>1</mn>
  <mo stretchy="false">)</mo>
</math></span> &nbsp; &nbsp;<strong><em>M1A1</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = n(n + 1)">
  <mo>=</mo>
  <mi>n</mi>
  <mo stretchy="false">(</mo>
  <mi>n</mi>
  <mo>+</mo>
  <mn>1</mn>
  <mo stretchy="false">)</mo>
</math></span> (which is an upper bound) &nbsp; &nbsp; <strong><em>A1</em></strong></p>
<p>&nbsp;</p>
<p><strong>Note: </strong>Follow through is not applicable.</p>
<p>&nbsp;</p>
<p><strong><em>[7 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>put a marker on each edge <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_i}{{\text{A}}_j}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mi>i</mi>
    </msub>
  </mrow>
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mi>j</mi>
    </msub>
  </mrow>
</math></span>&nbsp;so that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="i">
  <mi>i</mi>
</math></span> of the weight belongs to vertex <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_i}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mi>i</mi>
    </msub>
  </mrow>
</math></span>&nbsp;and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="j">
  <mi>j</mi>
</math></span> of the weight belongs to vertex <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_j}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mi>j</mi>
    </msub>
  </mrow>
</math></span>&nbsp;&nbsp; &nbsp; <strong><em>M1</em></strong></p>
<p>the Hamiltonian cycle visits each vertex once and only once and for vertex <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_i}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mi>i</mi>
    </msub>
  </mrow>
</math></span>&nbsp;there will be weight <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="i">
  <mi>i</mi>
</math></span> (belonging to vertex <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{A}}_i}">
  <mrow>
    <msub>
      <mrow>
        <mtext>A</mtext>
      </mrow>
      <mi>i</mi>
    </msub>
  </mrow>
</math></span>) both going in and coming out &nbsp; &nbsp; <strong><em>R1</em></strong></p>
<p>so the total weight will be <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sum\limits_{i = 1}^n {2i = 2\frac{n}{2}(n + 1) = n(n + 1)} ">
  <munderover>
    <mo movablelimits="false">∑</mo>
    <mrow>
      <mi>i</mi>
      <mo>=</mo>
      <mn>1</mn>
    </mrow>
    <mi>n</mi>
  </munderover>
  <mrow>
    <mn>2</mn>
    <mi>i</mi>
    <mo>=</mo>
    <mn>2</mn>
    <mfrac>
      <mi>n</mi>
      <mn>2</mn>
    </mfrac>
    <mo stretchy="false">(</mo>
    <mi>n</mi>
    <mo>+</mo>
    <mn>1</mn>
    <mo stretchy="false">)</mo>
    <mo>=</mo>
    <mi>n</mi>
    <mo stretchy="false">(</mo>
    <mi>n</mi>
    <mo>+</mo>
    <mn>1</mn>
    <mo stretchy="false">)</mo>
  </mrow>
</math></span>&nbsp;&nbsp; &nbsp; <strong><em>A1AG</em></strong></p>
<p>&nbsp;</p>
<p><strong>Note: </strong>Accept other methods for example induction.</p>
<p>&nbsp;</p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="G">
  <mi>G</mi>
</math></span> is a simple, connected graph with eight vertices.</p>
</div>

<div class="specification">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="H">
  <mi>H</mi>
</math></span> is a connected, planar graph, with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v">
  <mi>v</mi>
</math></span> vertices, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="e">
  <mi>e</mi>
</math></span> edges and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span> faces. Every face in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="H">
  <mi>H</mi>
</math></span> is bounded by exactly <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
  <mi>k</mi>
</math></span> edges.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the minimum number of edges in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="G"> <mi>G</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>Find the maximum number of edges in <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">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the maximum number of edges in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="G"> <mi>G</mi> </math></span>, given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="G"> <mi>G</mi> </math></span> contains an Eulerian circuit.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2e = kf"> <mn>2</mn> <mi>e</mi> <mo>=</mo> <mi>k</mi> <mi>f</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>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = 9"> <mi>v</mi> <mo>=</mo> <mn>9</mn> </math></span> and <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>.</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>Find the possible values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = 13"> <mi>v</mi> <mo>=</mo> <mn>13</mn> </math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>7 (a tree)        <em><strong>A1</strong></em></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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{8 \times 7}}{2}\left( {7 + 6 + 5 + 4 + 3 + 2 + 1} \right)"> <mfrac> <mrow> <mn>8</mn> <mo>×</mo> <mn>7</mn> </mrow> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <mrow> <mn>7</mn> <mo>+</mo> <mn>6</mn> <mo>+</mo> <mn>5</mn> <mo>+</mo> <mn>4</mn> <mo>+</mo> <mn>3</mn> <mo>+</mo> <mn>2</mn> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </math></span>  (a complete graph)        <em><strong>(M1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" =  28"> <mo>=</mo> <mn>28</mn> </math></span>        <em><strong>A1</strong></em></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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{8 \times 6}}{2}"> <mfrac> <mrow> <mn>8</mn> <mo>×</mo> <mn>6</mn> </mrow> <mn>2</mn> </mfrac> </math></span> (since every vertex must be of degree 6)        <em><strong>(M1)</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" =  24"> <mo>=</mo> <mn>24</mn> </math></span>        <em><strong>A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>counting the edges around every face gives <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="kf"> <mi>k</mi> <mi>f</mi> </math></span> edges       <em><strong>A1</strong></em></p>
<p>but as every edge is counted in 2 faces        <em><strong>R1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" \Rightarrow kf = 2e"> <mo stretchy="false">⇒</mo> <mi>k</mi> <mi>f</mi> <mo>=</mo> <mn>2</mn> <mi>e</mi> </math></span>       <em><strong>AG</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>using <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v - e + f = 2"> <mi>v</mi> <mo>−</mo> <mi>e</mi> <mo>+</mo> <mi>f</mi> <mo>=</mo> <mn>2</mn> </math></span> with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = 9"> <mi>v</mi> <mo>=</mo> <mn>9</mn> </math></span>       <em><strong>M1</strong></em></p>
<p><strong>EITHER</strong></p>
<p>substituting <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2e = 3f"> <mn>2</mn> <mi>e</mi> <mo>=</mo> <mn>3</mn> <mi>f</mi> </math></span>  into  <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\left( 9 \right) - 2e + 2f = 4"> <mn>2</mn> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> <mo>−</mo> <mn>2</mn> <mi>e</mi> <mo>+</mo> <mn>2</mn> <mi>f</mi> <mo>=</mo> <mn>4</mn> </math></span>       <em><strong>(M1)</strong></em></p>
<p><strong>OR</strong></p>
<p>substituting <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="e = \frac{{3f}}{2}"> <mi>e</mi> <mo>=</mo> <mfrac> <mrow> <mn>3</mn> <mi>f</mi> </mrow> <mn>2</mn> </mfrac> </math></span>  into  <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="9 - e + f = 2"> <mn>9</mn> <mo>−</mo> <mi>e</mi> <mo>+</mo> <mi>f</mi> <mo>=</mo> <mn>2</mn> </math></span>       <em><strong>(M1)</strong></em></p>
<p><strong>THEN</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="18 - f = 4"> <mn>18</mn> <mo>−</mo> <mi>f</mi> <mo>=</mo> <mn>4</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f = 14"> <mi>f</mi> <mo>=</mo> <mn>14</mn> </math></span>       <em><strong>A1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2v - kf + 2f = 4"> <mn>2</mn> <mi>v</mi> <mo>−</mo> <mi>k</mi> <mi>f</mi> <mo>+</mo> <mn>2</mn> <mi>f</mi> <mo>=</mo> <mn>4</mn> </math></span>  (or equivalent)       <em><strong>M1</strong></em></p>
<p>when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = 13"> <mi>v</mi> <mo>=</mo> <mn>13</mn> </math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {k - 2} \right)f = 22"> <mrow> <mo>(</mo> <mrow> <mi>k</mi> <mo>−</mo> <mn>2</mn> </mrow> <mo>)</mo> </mrow> <mi>f</mi> <mo>=</mo> <mn>22</mn> </math></span>  or  <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {2 - k} \right)f =  - 22"> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mo>−</mo> <mi>k</mi> </mrow> <mo>)</mo> </mrow> <mi>f</mi> <mo>=</mo> <mo>−</mo> <mn>22</mn> </math></span>       <em><strong>A1</strong></em></p>
<p><strong>EITHER</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {k - 2} \right)f = 1 \times 2 \times 11"> <mrow> <mo>(</mo> <mrow> <mi>k</mi> <mo>−</mo> <mn>2</mn> </mrow> <mo>)</mo> </mrow> <mi>f</mi> <mo>=</mo> <mn>1</mn> <mo>×</mo> <mn>2</mn> <mo>×</mo> <mn>11</mn> </math></span>      <em><strong>M1</strong></em></p>
<p><strong>OR</strong></p>
<p>substituting at least two of  <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = 13{\text{, }}4{\text{, }}3"> <mi>k</mi> <mo>=</mo> <mn>13</mn> <mrow> <mtext>, </mtext> </mrow> <mn>4</mn> <mrow> <mtext>, </mtext> </mrow> <mn>3</mn> </math></span>  into  <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f = \frac{{22}}{{k - 2}}"> <mi>f</mi> <mo>=</mo> <mfrac> <mrow> <mn>22</mn> </mrow> <mrow> <mi>k</mi> <mo>−</mo> <mn>2</mn> </mrow> </mfrac> </math></span>  (or equivalent)      <em><strong>M1</strong></em></p>
<p><strong>THEN</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f = 2{\text{, }}11{\text{, 22}}"> <mi>f</mi> <mo>=</mo> <mn>2</mn> <mrow> <mtext>, </mtext> </mrow> <mn>11</mn> <mrow> <mtext>, 22</mtext> </mrow> </math></span>  (since <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f &gt; 1"> <mi>f</mi> <mo>&gt;</mo> <mn>1</mn> </math></span>)       <em><strong>A1</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.iii.</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">b.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>A driver needs to make deliveries to five shops <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A">
  <mi>A</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="B">
  <mi>B</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
  <mi>C</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="D">
  <mi>D</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="E">
  <mi>E</mi>
</math></span>. The driver starts and finishes his journey at the warehouse <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="W">
  <mi>W</mi>
</math></span>. The driver wants to find the shortest route to visit all the shops and return to the warehouse. The distances, in kilometres, between the locations are given in the following table.</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>By deleting <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="W"> <mi>W</mi> </math></span>, use the deleted vertex algorithm to find a lower bound for the length of a route that visits every shop, starting and finishing at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="W"> <mi>W</mi> </math></span>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Starting from <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="W"> <mi>W</mi> </math></span>, use the nearest-neighbour algorithm to find a route which gives an upper bound for this problem and calculate its length.</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>deleting <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{W}}"> <mrow> <mtext>W</mtext> </mrow> </math></span> and its adjacent edges, the minimal spanning tree is</p>
<p style="padding-left:60px;"><img src="data:image/png;base64,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">    <em><strong>A1A1A1A1</strong></em></p>
<p><strong>Note:</strong> Award the <em><strong>A1’s</strong></em> for either the edges or their weights.</p>
<p>the minimum spanning tree has weight = 54</p>
<p><strong>Note:</strong> Accept a correct drawing of the minimal spanning tree.</p>
<p>adding in the weights of 2 deleted edges of least weight <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{WB}}"> <mrow> <mtext>WB</mtext> </mrow> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{WC}}"> <mrow> <mtext>WC</mtext> </mrow> </math></span>       <em><strong>(M1)</strong></em><br>lower bound = 54 + 36 + 39</p>
<p>= 129         <em><strong>A1</strong></em></p>
<p><em><strong>[6 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt at the nearest-neighbour algorithm      <em><strong>M1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{WB}}"> <mrow> <mtext>WB</mtext> </mrow> </math></span><br><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{BA}}"> <mrow> <mtext>BA</mtext> </mrow> </math></span><br><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{AD}}"> <mrow> <mtext>AD</mtext> </mrow> </math></span><br><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{DE}}"> <mrow> <mtext>DE</mtext> </mrow> </math></span><br><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{EC}}"> <mrow> <mtext>EC</mtext> </mrow> </math></span><br><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{CW}}"> <mrow> <mtext>CW</mtext> </mrow> </math></span>         <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>M1</strong></em> for a route that begins with <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{WB}}"> <mrow> <mtext>WB</mtext> </mrow> </math></span> and then <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{BA}}"> <mrow> <mtext>BA</mtext> </mrow> </math></span>.</p>
<p>upper bound = 36 + 11 + 15 + 12 + 22 + 39 = 135       <em><strong>(M1)A1</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>