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</div><h2>SL Paper 1</h2><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The first term of a geometric sequence is 2 and the third term is 2.205.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the common ratio of the sequence;</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the eleventh term of the sequence;</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the sum of the first 23 terms of the sequence.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>2<em>r</em><sup>2</sup> = 2.205 <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in geometric sequence formula.</span></p>
<p> </p>
<p><span><em>r</em> = 1.05 <em><strong>(A1) </strong> <strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>2(1.05)<sup>10</sup> <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for the correct substitution, using their answer to part (a), in geometric sequence formula.</span></p>
<p> </p>
<p><span>= 3.26 (3.25778…) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their part (a).</span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{2({{1.05}^{23}} - 1)}}{{(1.05 - 1)}}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their correct substitution in geometric sum formula.</span></p>
<p> </p>
<p><span>= 82.9 (82.8609…) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Accept an answer of 3.97221...if <em>r</em> = −1.05 is found in part (a) and used again in part (c). Follow through from their part (a).</span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">In part (a), 1.1025 proved to be a popular, but erroneous, answer. Similarly to question 4, such candidates failed to find a square root. Whilst this accuracy mark was lost for such candidates, much good work was seen in this question reflecting how well drilled the majority of candidates were in both arithmetic and geometric sequence techniques.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">In part (a), 1.1025 proved to be a popular, but erroneous, answer. Similarly to question 4, such candidates failed to find a square root. Whilst this accuracy mark was lost for such candidates, much good work was seen in this question reflecting how well drilled the majority of candidates were in both arithmetic and geometric sequence techniques.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">In part (a), 1.1025 proved to be a popular, but erroneous, answer. Similarly to question 4, such candidates failed to find a square root. Whilst this accuracy mark was lost for such candidates, much good work was seen in this question reflecting how well drilled the majority of candidates were in both arithmetic and geometric sequence techniques.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><strong>In this question give all answers correct to two decimal places.</strong></p>
<p>Diogo deposited \(8000\) Argentine pesos, \({\text{ARS}}\), in a bank account which pays a nominal annual interest rate of \(15\% \), <strong>compounded monthly</strong>.</p>
<p>Find how much <strong>interest</strong> Diogo has earned after \(2\) years.</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>Carmen also deposited \({\text{ARS}}\) in a bank account. Her account pays a nominal annual interest rate of \(17\% \), <strong>compounded yearly</strong>. After three years, the total amount in Carmen’s account is \({\text{10}}\,{\text{000}}\,{\text{ARS}}\).</p>
<p>Find the amount that Carmen deposited in the bank account.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>The first time an answer is not given to two decimal places the final <em>(A1)</em> is not awarded.</strong></p>
<p>\(FV = 8000 \times {\left( {1 + \frac{{15}}{{100 \times 12}}} \right)^{2 \times 12}}\,\,\,\left( {FV = 8000 \times {{(1.0125)}^{2 \times 12}}} \right)\) <em><strong>(M1)(A1)</strong></em></p>
<p><strong>OR</strong></p>
<p>\(I = 8000 \times {\left( {1 + \frac{{15}}{{100 \times 12}}} \right)^{2 \times 12}} - 8000\) <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution into compound interest formula, <em><strong>(A1)</strong></em> for correct substitutions.</p>
<p><strong>OR</strong></p>
<p>\(N = 24\)</p>
<p>\(I\% = 15\)</p>
<p>\(PV = - 8000\)</p>
<p>\(PMT = 0\)</p>
<p>\((FV = 10778.8084)\)</p>
<p>\(P/Y = 12\)</p>
<p>\(C/Y = 12\) <em><strong>(A1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(C/Y = 12\) seen, <em><strong>(M1)</strong></em> for <strong>all</strong> other correct entries. \(FV = 10778.8084\) need not be seen.</p>
<p><strong>OR</strong></p>
<p>\(N = 2\)</p>
<p>\(I\% = 15\)</p>
<p>\(PV = - 8000\)</p>
<p>\(PMT = 0\)</p>
<p>\((FV = 10778.8084)\)</p>
<p>\(P/Y = 1\)</p>
<p>\(C/Y = 12\) <em><strong>(A1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(C/Y = 12\) seen, <em><strong>(M1)</strong></em> for <strong>all</strong> other correct entries. \(FV = 10778.8084\) need not be seen.</p>
<p>interest \( = 2778.81\) <em><strong>(A1) (C3)</strong></em></p>
<p><strong>Note:</strong> Final answer must be to two decimal places for the <em><strong>(A1)</strong></em> to be awarded.</p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(N = 3\)</p>
<p>\(I\% = 17\)</p>
<p>\((PV = \pm 6243.705564)\)</p>
<p>\(PMT = 0\)</p>
<p>\((FV = \mp 10\,000)\)</p>
<p>\(P/Y = 1\)</p>
<p>\(C/Y = 1\) <em><strong>(A1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(FV = \mp 10\,000\), <em><strong>(M1)</strong></em> for <strong>all</strong> other correct entries. \(PV = \pm 6243.705564\) need not be seen.</p>
<p><strong>OR</strong></p>
<p>\(10\,000 = PV \times {\left( {1 + \frac{{17}}{{100}}} \right)^3}\) <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting into compound interest formula, <em><strong>(A1)</strong></em> for equating \(10\,000\) to the correctly substituted compounded interest formula.</p>
<p>\((PV = )\,\,6243.71\) <em><strong>(A1) (C3)</strong></em></p>
<p><strong>Note:</strong> Answer must be to two decimal places.</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>Question 12: Compound Interest</strong><br>The use of the TVM solver, with lack of working, remains a source of concern, though many more are writing down the calculator display; candidates are advised still to write down substituted formulas prior to using the TVM solver. Compounding periods remain a source of confusion<br>The use of the 0.15 and 0.17 was a common error, as was the computation of the amount in part (a).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 12: Compound Interest<br>The use of the TVM solver, with lack of working, remains a source of concern, though many more are writing down the calculator display; candidates are advised still to write down substituted formulas prior to using the TVM solver. Compounding periods remain a source of confusion<br>The use of the 0.15 and 0.17 was a common error, as was the computation of the amount in part (a).</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The exchange rate between Indian rupees (INR) and Singapore dollars (S$) is \(100{\text{ INR}} = {\text{S\$ }}3.684\) <br></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Kwai Fan changes \({\text{S\$ }}500\) to Indian rupees.</span></p>
<p><span>Calculate the number of Indian rupees she will receive using this exchange rate. <strong>Give your answer correct to the nearest rupee.</strong></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>On her return to Singapore, Kwai Fan has \(2500\) Indian rupees left from her trip. She wishes to exchange these rupees back to Singapore dollars. There is a \(3\% \) commission charge for this transaction and the exchange rate is \(100{\text{ INR}} = {\text{S\$}}3.672\).</span></p>
<p><span>Calculate the commission in Indian rupees that she is charged for this exchange.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>On her return to Singapore, Kwai Fan has \(2500\) Indian rupees left from her trip. She wishes to exchange these rupees back to Singapore dollars. There is a \(3\% \) commission charge for this transaction and the exchange rate is \(100{\text{ INR}} = {\text{S\$}}3.672\).</span></p>
<p><span>Calculate the amount of money she receives in Singapore dollars, <strong>correct to two decimal places</strong>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><em>Financial penalty<strong> (FP) </strong>applies in this question.</em></span></p>
<p><span>\(500 \times \frac{{100}}{{3.684}}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>FP</strong> \( = 13572\) <em><strong>(A1) (C2)</strong></em></span></p>
<p><span><strong>Note: <em>(M1)</em></strong> for multiplication by \(\frac{{100}}{{3.684}}\) <br></span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(2500 \times 0.03\) <em><strong>(M1)</strong></em></span></p>
<p><span>\( = 75{\text{ }}(75.0{\text{, }}75.00)\) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span>If \(2500 \times 0.03 \times \frac{{3.672}}{{100}}\)</span></p>
<p><span>\( = 2.75\)<br></span></p>
<p><span><em>Award <strong>(M1)(A0)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>Financial penalty<strong> (FP) </strong>applies in this question.</em></span></p>
<p><span>\(2425 \times \frac{{3.672}}{{100}}\) </span><span><em><strong>(M1)</strong></em></span><span><strong>(ft)</strong></span></p>
<p><span><strong>FP</strong> \( = 89.05\) </span><span><em><strong>(A1)</strong></em></span><span><strong>(ft)</strong></span></p>
<p><em><span><strong>OR</strong></span></em></p>
<p><span>\(\frac{{3.672}}{{100}} \times 0.97 \times 2500\) </span><span><em><strong>(M1)</strong></em></span><span><strong>(ft)</strong></span></p>
<p><span><strong>FP</strong> \( = 89.05\) </span><span><em><strong>(A1)</strong></em></span><span><strong>(ft)</strong></span></p>
<p><em><span><strong>OR</strong></span></em></p>
<p><span>\(3\% {\text{ of }}91.8 = 2.754\)</span></p>
<p><span>\(91.8 - 2.754\) </span><span><em><strong>(M1)</strong></em></span><span><strong>(ft)</strong></span></p>
<p><span><strong>FP</strong> \( = 89.05\) </span><span><em><strong>(A1)</strong></em></span><span><strong>(ft) <em>(C2)</em></strong></span></p>
<p><span><strong>Note:</strong> <strong>(ft)</strong> in<strong> (c)</strong> if the conversion process is reversed consistently through the question, i.e. multiplication in <strong>(a)</strong> followed by division in <strong>(c)</strong>.<em><strong> <br></strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This caused problems for many candidates. The form of the exchange rate proved difficult.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates managed to answer this correctly.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This part also proved problematic for many candidates.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A store sells bread and milk. On Tuesday, 8 loaves of bread and 5 litres of milk were sold for $21.40. On Thursday, 6 loaves of bread and 9 litres of milk were sold for $23.40. </span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">If \(b =\) the price of a loaf of bread and \(m =\) the price of one litre of milk, Tuesday’s sales can be written</span> <span style="font-size: medium; font-family: times new roman,times;">as \(8b + 5m = 21.40\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using simplest terms, write an equation in <em>b</em> and <em>m</em> for Thursday’s sales.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find <em>b</em> and <em>m</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a sketch, in the space provided, to show how the prices can be found graphically.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>Thursday's sales, \(6b + 9m = 23.40\) <em><strong>(A1)</strong></em></span></p>
<p><span>\(2b + 3m = 7.80\) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(m = 1.40\) <em> (accept 1.4)</em></span><span><em> <strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>\(b = 1.80\) <em> (accept 1.8) <strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><em><span>Award <strong>(A1)</strong>(d) for a reasonable attempt to solve by hand and answer incorrect. <strong>(C2)</strong></span></em></p>
<p><em><span><strong>[2 marks]<br></strong></span></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><span><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQkAAACsCAIAAADnrM7aAAALHUlEQVR4nO3dz2vj6B3H8efev0BnnxYMQwlhYU6CXXzotMxcfJmDBkxgellKF2Iwe/Ghabcr8CUDhXa1zBzKnB52LoUkIDoHD8SLIIUpYwRlGeKsShvcVCtqbzaIbw+yHTmR5R+RHkmPPq9TdidETxK/o1/PIzMCgCgs6wEA5BTaAIiGNgCiCW/DNZsKm6po/FT0AABWI7oN3zZqSst0fcHbBViX4DZ812wpNcNGGpB7gtsY20Z9ekClqE1ue6gEckpwG+dmc0tp8DOfiC4s/ZGq9zyxIwBYUYbXqa4c/pTFHl+1AVIW8wLNYxtsXhZjg1LIUxv+e97Yqhl9n4jowtIfN/j7mBOOdruNNiA9eWqDyHe6Ha3KGGOsqnW6TuypONqAVOWrjbWgDUgV2gCIhjYAoqENgGhoAyAa2gCIhjYAoqENgGhoAyAa2gCIhjYAoqENgGhoAyBagdv49NM2Yz/LehQgrQK38dFHbcbanB9nPRCQU4Hb+OyzNmOfMNbe3z/IeiwgoQK3EZxv7O8fIA9IQ+HbICLkAWmQoQ2a5rG7+3I0usx2VCANSdogIs6PGWvv7HyFPCAR8rRBRN3uO+QBSZGqDQrlMRx+n8moQBqytUHTPLa3vxgMzsWPCqQhYRtEZNvfbW9/gTzgLuRsg4gGg3PkAXchbRsUyuPk5FthowJpyNwGTfNgrN3tvhMzKpCG5G0Q0Wh0ubPzFfKAdcnfBiEP2Egp2qBQHi9evE51VCCNsrRBRKPR5e7uS8xKhBWVqI0AJu3CikrXBk3z2Nt7lfiQQCZlbIOIOp2/YFYixCtpG0R0eHiCPCBGedsgzGmHWKVugzCnHRYrexuEOe2wANogwqRdiII2JpAH3IA2rs3ywLQrILRxw2Bw/vDhM8xKBEIbt2HSLgTQRgTkAYQ2FpnlgVmJpYU2FhqNLvf2vkYepYU2lsCc9tJCG8vN8sC0q1JBGysJ8sCsxFJBG6vCpN2yQRtrQB6lIrgN37MPdK3KGGOsqukHtufP/btrNhU2VdH4aczXyuQ9lIM8njz5EtOupCe2Db9v1Cqq3vOIfOeopVZqRj8ch28bNaVluv7CrxCS1fuLv37993v3PsesROlt1obvmi3l8e+MVo0xpjT+eHTQ0RTGWK1lnq30uiYi8ixdZRp3bnzZmmGv9iVefvLyDXtD9qrbSxAm7ZbBZm14lq4yRev0HN/hGmOK9qznuLZRn3+txzs3m/fn9xtj26hPD6gUtclvHnHNO2gcECNiRA+JDolGq244EchDepu1ccq1avCy9m2jxuqGPZ68sldt49Ix26raNp3wSe252dxSGvzMJ6ILS38UHH3FDP1D9iEdEj2kSSR7RCcrbT4RmNMut43acM2mEvTgu2ZLqejWFQWv7MmHS/he/7lWaRh9d/HnXDn8KYs6vmLzJv93QLRPtD3djXCi4fJx3N1gcI5ZibLapI3QGfPYNupK03QpOM++3zSXHmC49lFHq2idnhN7WrGwjfDQb56Lj4i6RDuh3Uh32XDuDJN2ZbVBG+Ez5uuDK3K4Njm4iuH2jYaiLNhj+O95Y2t6BnJh6Y8b/H1MP3HXqQZEL6a7kW2iF+nuRpCHlDZoY2wb9cmx05WlV1Td8iYfLj2imrt9wRhjTONO6IKV73Q7s7sfnW78nmWla7hdot3pbmSXqJvWKTvmtMunHPfFh0Qvpqfs20T7RIPkx4M57ZIpRxszJ0R7093Ik1R2I5jTLo2StREYEv2Z6OfTSPYp2RuImNMuh1K2MWMT7dPcDcSETtkxp10C5W4jMCI6nL/ym8QNRDynvejQRsiNG4h3vvKLOe2FhjZuGUVd+d0UntNeXGhjseH8DcRNr/ziOe0FhTZWEL7yu7PJlV9M2i0itLGyIRGf3kD8eO0rv8ijcNDG+myi389f+V1tNxLkce/e58fHWSzIgjWhjU0FV37XXDoyGJzX63/ArMRCQBt3Zq+3dASTdosCbSTk9tKRxbsR5FEIaCNpq91AnOXB+bHwIcJK0EY6VriBiCUfOYc2UjZcsgIRc9pzC22IMtuNfHDzBiLyyCe0IdaQyIhYgRjksbf3NWYl5gfayEh4HspDokP6U8fEpN1cQRuZmr+B+O9f//e37BXyyAm0kQ+hFYhD5v3147fjsx+zHlPZoY08GRF16X+/+CGIZNy8FPkIU7gBbeTR377+9g3rj39yKebZcxAJbeRUMGn3yw/MH375o4Bnz8FtaCO/Zks+/vn2P9fPnvtpWs+egxvQRq7N8rDt74iIvrnrCkRYHdrIuyCPuUm74RWIKTx7DgJoowAWzmm//ew57EaSgzaKYZbHq1ff3Pq3TVYgwlJoozCWL/nI6M2rZIU2imSlJR9ZvHmVlNBG8aw6p13sm1fJB20U0npLPmZLRw5THpZc0EZRrf02BkNcxVoP2igwzo+x5CM9aKPY8DYG6UEbhTfLA0/aTRbakEG3+w4Pok4c2pAEntOeOLQhD+SRLLQhlYhJu7AptCGb4fB7PIg6EWhDQnhOeyLQhpzwnPa7QxvSGo0ud3df4km7G0MbksODqDeGNuSHPDaDNkph9pz2rAdSJGijLA4PT3BPcC35asN3uh2tyhhjTFGb3Pb8mE9GG5CqXLUxto26oj3ve77vHLXUqsZPYz4bbUCqctXGKde2pj14lq5WdOtq8WejDUhVntq4svRKZdrGlcOfMo07iz8dbUCq8taGqlte8B9oA7KVtzbW3m+0AVIT82rN+HxDaZru7TEBCLToxZrtdar7TXPJ9fiYoactq03jW87JpsXf3zhqqUrQaxBJ/Ofn86cm5XYz3HQ+v+W8n+nm86cm5XYz3HQ+v2W0kbtN41vOyabz3gZAVtAGQDS0ARANbQBEQxsA0dAGQDS0ARAtn21cOr1n2uTuea3J+57oAVxY+oP4tSVJ8z37QJ+siKxq+kH8ishEhX7aaovbtye4pe3C0h/EzzpNmu+aLeV6RtVT7kT8qnPZht83alua8dajS8dsqwuGntrWnV5HUxgT2obfN2oVVe95k2k1lZrRFxSHazaVWss888ntGw2lZtjCqiQi8j2rozImto2xbdQj57mG5bINh2uzHuaWfAhwyrWq2vxNU1XE7jfCPEtXxb5WJq4svSL4L5HX09X7qloR+/2em837S//65LGN+d9QeFq7AO4/7H/5dMq1SnZtrPSbS55/ZrZqSoOfidvwhaU/UvUjU/DfAr9v1GaHVAsP2vPaxvULU3Abs41m1calY7ZVtW06Yt/dz+Ga6LM737M6qtqxPFf0ftI1m0q1wd/7FOy4HunWxe3Pymsbme03aLrRTNrwvf5zrdIw+uJPiImI/DPeULaWLqpJxvWLMrNjSCIKjqIj99J5bOPW+Yao39a1TNpw7aOOVtE6PUf00dQ1cd/4laVXbizAyyaPYrVx4zqV0jJdwa8W8W24faOhKBnsMfwz3lAeBAcV4Y8FEr3f8M94Q6kb9piIyOvptV/xs4gj2Fy2Mbl0yyYX+423wu9vCG/DNZtKVn9EQ/c3FE0/soX/tMUfU819y4t21PlsAyB7aAMgGtoAiIY2AKKhDYBoaAMgGtoAiIY2AKKhDYBoaAMgGtoAiIY2AKKhDSmIXjlcCmhDCg7XMpjJLzm0IQHfNVuK8kh7XGVMUVtHGa6NkgnakMDYNupMaRh9V+iiVtmhDQmEn0uycIUnrAttFN+VpVemKzz9vlGrCn/0hJzQRvGFTsTnVkLD3aCNogse7fpAty6yePiazNBG0Y1t43HwkFLGFLXJBT5kWnJoAyDa/wHsujjis8maWQAAAABJRU5ErkJggg==" alt><strong><span> (A1)(A1)</span></strong></span></em><span><strong><span>(ft)</span></strong></span></p>
<p><em><span><strong>(A1)</strong> each for two reasonable straight lines. The intersection point must be approximately correct to earn both marks, otherwise penalise at least one line. </span></em></p>
<p><em><span>Note: The follow through mark is for candidate’s line from (a). <strong>(C2)</strong></span></em></p>
<p><em><span><strong>[2 marks]<br></strong></span></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">a) Nearly all the candidates were able to write the equation but very few simplified it.</span></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">b) A majority of candidates were able to find the values of <em>b</em> and <em>m</em>. Some used the right method but made arithmetical errors, many of which were due to them using the method of substitution which involved fractions. GDC use was expected.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"> </span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">c) A majority of candidates did not attempt this part. For those who did, very few were able to sketch the graph correctly. Common errors were to plot the point (1.4, 1.8) or draw a straight line through that point and the origin.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The annual fees paid to a school for the school years 2000, 2001 and 2002 increase as a geometric progression. The table below shows the fee structure.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the common ratio for the increasing sequence of fees.</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><strong><span>Give your answer correct to 2 decimal places.</span></strong></p>
<p><span>The fees continue to increase in the same ratio.</span></p>
<p><span>Find the fees paid for 2006.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><strong>Give your answer correct to 2 decimal places.</strong></span></p>
<p><span>The fees continue to increase in the same ratio.</span></p>
<p><span>A student attends the school for eight years, starting in 2000.</span></p>
<p><span>Find the <strong>total</strong> fees paid for these eight years.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(r = \frac{{8320}}{{8000}}\) (or equivalent) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for dividing correct terms.</span></p>
<p><br><span><em>r </em>= 1.04 <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> In (b) and (c) <strong>(ft)</strong> from candidate’s <em>r</em>.</span></p>
<p><span> Allow lists, graphs <em>etc.</em> as working in (b) and (c).</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em><strong>Financial penalty (FP) applies in this part</strong></em><br></span></p>
<p><span> </span></p>
<p><span>Fees = 8000 (1.04)<sup>6</sup> <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into correct formula.</span></p>
<p><br><span><em><strong>(FP)</strong></em> Fees = 10122.55 USD (USD not required) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Special exception to the note above.</span></p>
<p><span>Award maximum of <em><strong>(M1)(A0)</strong></em> if 5 is used as the power.</span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em><strong>Financial penalty (FP) applies in this part</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span>\({\text{Total}} = \frac{{8000({{1.04}^8} - 1)}}{{1.04 - 1}}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into correct formula.</span></p>
<p><span> </span></p>
<p><span>Give full credit for solution by lists.</span></p>
<p><span><em><strong>(FP) </strong></em> Total = 73713.81 USD (USD not required) <em><strong>(A1)</strong></em><strong>(ft) <em>(C2)</em></strong></span></p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Many marks were lost through incorrect rounding or premature rounding (if a year by year</span> <span style="font-size: medium; font-family: times new roman,times;">approach was used).</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">This part was well attempted, errors being the use of 4% as the common ratio.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Many marks were lost through incorrect rounding or premature rounding (if a year by year</span> <span style="font-size: medium; font-family: times new roman,times;">approach was used).</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The common error here was the use of the incorrect index in the formula.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Many marks were lost through incorrect rounding or premature rounding (if a year by year</span> <span style="font-size: medium; font-family: times new roman,times;">approach was used).</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Attempts at calculation without use of the formula were largely unsuccessful.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">An amount, <em>C</em>, of Australian Dollars (AUD) is invested for 5 years at 2.5 % yearly simple interest. The interest earned on this investment is 446.25 AUD.</span></p>
</div>
<div class="question">
<p><span>5000 AUD is invested at a nominal annual interest rate of 2.5 % <strong>compounded half yearly</strong>.</span></p>
<p><span>Calculate the length of time in years for the interest on this investment to exceed 446.25 AUD.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span>\(446.25 = 5000{\left( {1 + \frac{{2.5}}{{2(100)}}} \right)^{2n}} - 5000\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span><br><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for substitution into compound interest formula. Award <em><strong>(A1)</strong></em> for correct values.</span></p>
<p><span> </span></p>
<p><span>\(5446.25 = 5000{\left( {1 + \frac{{2.5}}{{2(100)}}} \right)^{2n}}\) <em><strong>(A1)</strong></em><br></span></p>
<p><span><em>n</em> = 3.44<br></span></p>
<p><span><em>n</em> = 3.5 <em><strong>(A1)</strong></em><br></span></p>
<p><span><strong>OR</strong><br></span></p>
<p><span>5446.25 = 5000(1.0125)<sup>2<em>n</em></sup> <em><strong>(A1)(M1)(A1)</strong></em></span></p>
<p><span><br><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for 5446.25 seen.</span></p>
<p><span>Award <em><strong>(M1)</strong></em> for substitution into compound interest formula.</span></p>
<p><span>Award <em><strong>(A1)</strong></em> for correct values.</span></p>
<p><span> </span></p>
<p><span><em>n</em> = 3.44 years<br></span></p>
<p><span>3.5 years required <em><strong>(A1)</strong></em> <em><strong>(C4)</strong></em></span></p>
<p><span><br><strong>Notes:</strong> For incorrect substitution into compound interest formula award at most <em><strong>(M1)(A0)(A1)(A0)</strong></em>.</span></p>
<p><span>Award <em><strong>(A3)</strong></em> for 3.44 seen without working.</span></p>
<p><span>Allow solution by lists. In this case</span></p>
<p><span>Award <em><strong>(A1)</strong></em> for half year rate 1.25 % seen.</span></p>
<p><span><em><strong>(A1)</strong></em> for 5446.25 seen.</span></p>
<p><span><em><strong>(M1)</strong></em> for at least 2 correct uses of multiplication by 1.0125</span></p>
<p><span>5000 × 1.0125 = 5062.5 and 5062.5 </span><span><span>× </span>1.0125 = 5125.78125</span></p>
<p><span> <em><strong>(A1)</strong></em> <em>n</em> = 3.5</span></p>
<p><span>If yearly rate used then award <em><strong>(A0)(A1)(M1)(A0)</strong></em></span><span class="Apple-style-span"><br></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span><em><strong>[4 marks]</strong></em></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was poorly answered by many of the candidates. Candidates confuse interest with principal in the formulas.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The idea of compounding periods and the implication for determining the level of interest is poorly understood. The correct answer is 3.5 years. Interpretation of compounding periods is expected.</span></p>
</div>
<br><hr><br><div class="specification">
<p><em><span style="font-size: medium; font-family: times new roman,times;"><strong>In this question give all answers correct to two decimal places.</strong> </span></em></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Chiara is an Italian tourist visiting Sweden. The exchange rate for changing euros (€) into Swedish Krona (SEK) is 1€ = 10.275 SEK. She converts 350 euros into Swedish Krona at a bank which charges 2 % commission.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the amount of commission charged in <strong>SEK</strong>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the amount of money she receives from the bank after commission.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Chiara returns to Italy with 296 SEK. She changes this money back into euros at a bank and receives 32€. The bank does not charge commission.</span></p>
<p><span>Calculate the value in SEK of 1€.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>350 × 10.275 </span><span><span>× </span>0.02 <em><strong>(M1)(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for </span><span><span>×</span>10.275, <em><strong>(M1)</strong></em> for </span><span><span>×</span>0.02.</span></p>
<p><br><span>71.93 (SEK) <em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>3524.33(SEK) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C1)</strong></em></span></p>
<p><span><strong>Note:</strong> Accept 3524.32. Follow through from their answer to part (a).</span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{296}}{{32}}\)</span><span> </span><em><strong><span>(M1)</span></strong></em></p>
<p><span>9.25 <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">A common error in Question 9 was finding the amount of money received for part (a) rather than just the commission. Some candidates had difficulties giving the appropriate number of decimal places.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">A common error in Question 9 was finding the amount of money received for part (a) rather than just the commission. Some candidates had difficulties giving the appropriate number of decimal places.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">A common error in Question 9 was finding the amount of money received for part (a) rather than just the commission. Some candidates had difficulties giving the appropriate number of decimal places.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Consider the function \(f (x) = ax^3 − 3x + 5\), where \(a \ne 0\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \(f ' (x) \). </span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of \(f ′(0)\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The function has a local maximum at <em>x</em> = −2.</span></p>
<p><span>Calculate the value of <em>a</em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\( f '(x) = 3ax^2 - 3\) <em><strong>(A1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award a maximum of <em><strong>(A1)(A0)</strong></em> if any extra terms are seen.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>−3 <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from their part (a).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(f '(x) = 0\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> This may be implied from line below.</span></p>
<p><br><span>\(3a(-2)^2 - 3 = 0\) <em><strong>(M1)</strong></em></span></p>
<p><span>\((a =) \frac{1}{4}\) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C3)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from their part (a).</span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates could find the derivative of the cubic function and find the value of the derivative at \(x = 0\). For part (c) many candidates calculated the value of the function rather than the derivative at \(x = - 2\).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates could find the derivative of the cubic function and find the value of the derivative at \(x = 0\).<br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates could find the derivative of the cubic function and find the value of the derivative at \(x = 0\). For part (c) many candidates calculated the value of the function rather than the derivative at \(x = - 2\). However only the best realized that the derivative is zero at the maximum and so calculated the value of \(a\).</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Given that \(z = \frac{{12\cos (A)}}{{4q + r}}\) and that \(A = {60^ \circ }\), \(q = 8\) and \(r = 32\);</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the <strong>exact </strong>value of \(z\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write your answer to part (a) correct to 2 decimal places.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write your answer to part (a) correct to three significant figures.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>Write your answer to part (a) in the form \(a \times {10^k}\), where </span><span><span><span>1 ≤ <em>a</em> < 10, \(k \in {\mathbb{Z}}\) .</span></span></span></span></p>
<div class="marks">[2]</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><span>\(z = \frac{{12\cos ({{60}^ \circ })}}{{(4(8) + 32)}}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> <span><span>Award </span></span><span><span><em>(</em></span></span><strong><em><span><span>M1) </span></span></em></strong><span><span>for correct substituted formula seen.</span></span></span></p>
<p><span> </span></p>
<p><span><span><span>\( = 0.09375\left( {\frac{3}{{32}}} \right)\) <em><strong>(A1)(C2)</strong></em></span></span></span></p>
<p><span><span><span><em><strong>[2 marks]</strong></em></span></span></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span>\(0.09\) </span><span><em><strong>(A1)</strong></em></span><span><strong>(ft) <em>(C1)</em></strong></span></span></p>
<p><span><span><strong><em>[1 mark]</em></strong></span></span></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(0.0938\) <strong><em>(A1)</em>(ft) <em>(C1)</em></strong></span></p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<p> </p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(9.375 \times {10^{ - 2}}\) (\(9.38 \times {10^{ - 2}}\)) <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft) <em>(C2)</em></strong></span></p>
<p><span><span><span><strong>Note: </strong>Award <strong><em>(A1)</em>(ft) </strong>for \(9.375\), <strong><em>(A1)</em>(ft) </strong>for \( \times {10^{ - 2}}\). Follow through from their part (a).</span></span></span></p>
<p><em><strong><span><span><span>[2 marks]</span></span></span></strong></em></p>
<p> </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;">
<p><span style="font-family: times new roman,times; font-size: medium;">Although the use of radians leading to an incorrect answer of \( - 0.1785774388\) was seen on a minority of scripts, many candidates produced correct answers for parts (a) and (b)(i). The requirement for an answer to 3 significant figures led many to count the first zero after the decimal point and as a consequence gave an incorrect answer of \(0.094\). Despite any previous incorrect working, it was pleasing to see that most candidates were able to express their answer to part (a) in standard form. </span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Although the use of radians leading to an incorrect answer of \( - 0.1785774388\) was seen on a minority of scripts, many candidates produced correct answers for parts (a) and (b)(i). The requirement for an answer to 3 significant figures led many to count the first zero after the decimal point and as a consequence gave an incorrect answer of \(0.094\). Despite any previous incorrect working, it was pleasing to see that most candidates were able to express their answer to part (a) in standard form </span></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Although the use of radians leading to an incorrect answer of \( - 0.1785774388\) was seen on a minority of scripts, many candidates produced correct answers for parts (a) and (b)(i). The requirement for an answer to 3 significant figures led many to count the first zero after the decimal point and as a consequence gave an incorrect answer of \(0.094\). Despite any previous incorrect working, it was pleasing to see that most candidates were able to express their answer to part (a) in standard form. </span></p>
<p><span style="font-size: medium;"> </span></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: small;"><span style="font-size: medium;">Although the use of radians leading to an incorrect answer of \( - 0.1785774388\) was seen on a minority of scripts, many candidates produced correct answers for parts (a) and (b)(i). The requirement for an answer to 3 significant figures led many to count the first zero after the decimal point and as a consequence gave an incorrect answer of \(0.094\). Despite any previous incorrect working, it was pleasing to see that most candidates were able to express their answer to part (a) in standard form.</span> </span></p>
<div class="question_part_label">b.iii.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>When Bermuda \({\text{(B)}}\), Puerto Rico \({\text{(P)}}\), and Miami \({\text{(M)}}\) are joined on a map using straight lines, a triangle is formed. This triangle is known as the Bermuda triangle.</p>
<p>According to the map, the distance \({\text{MB}}\) is \(1650\,{\text{km}}\), the distance \({\text{MP}}\) is \(1500\,{\text{km}}\) and angle \({\text{BMP}}\) is \(57^\circ \).</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAdMAAAE/CAYAAAAdeClUAAAgAElEQVR4Ae2dCVgV5ffHv6CZEi6AKSoKKKDgjqIi/tMMNbTS1NzQpFJzqdxKKzU19WduqW1WUmFuaS64koqK5pJSJJqQgAGKgSVuEbnC/3kHBi5wL9wLd5/vPI8xd+Zdzvmc6Z77LueMTW5ubi54kAAJkAAJkAAJlJuAbblrsiIJkAAJkAAJkIBEgM6UDwIJkAAJkAAJVJAAnWkFAbI6CZAACZAACdCZ8hkgARIgARIggQoSoDOtIEBWJwESIAESIAE6Uz4DJEACJEACJFBBAnSmFQTI6iRAAiRAAiRAZ8pngARIgARIgAQqSIDOtIIAWZ0ESIAESIAE6Ez5DJAACZAACZBABQnQmVYQIKuTAAmQAAmQAJ0pnwESIAESIAESqCABOtMKAmR1EjA/AtcQNbMrPNzc1f/zGY0V244iMSvH/EQvU6IsxCzvLenVfnkMHojyGeEYI+n6BnZkSFfKbIUFihHISkTUtuWY+FE+02K3Cz/eRmLU91jx+ueIsUjUadgxyhcebr4YE55WqJYezuhM9QCRTZCAeRGojW7zjyDp7DcYameHlnN+QEJKMpLEvz9OYvM7dXFgykgMmLQBFyzSoZoXbcuXJgsxqydi1JSPcPxh6do8iPkKQ0Om4ZNj/5VeUIF3KytQZ6pMAsolYOsM3xEzseJhCoLmrMa6n5/GvG61LZuHcz98mdLPsnWg9BZPgCNTizchFSABayWQg6zEA1gxyj9vulpMTx9MwO3i6qqd5i1WV0wDi/rhMchQnd3OSsSh5aPRSpom7otZa6ORFr0c7cXntsvzpzLlqcHeWBq+DXOCmsPDrTmeD7sAqakibYipdX+MWR6OmIx7eZI+iMGKtuJ6b6yIiinaX/gFZOE2Eg9+jDE+okxz9Jm5obBucV3xABnhb+TxGLUJMTHhRfh8HJ2RJ1NBvfxpWZmh1H4YohJlikK3JzBoZbxU4+bKAWgm5IzJKmgh7ySv32b9P8JNceHGRxjk4Y6CqXYI3kexvYClOzyCZmJNVCKKt1S0YVEvCmtm9lVZkuiLWWFRJZYhcjJisEO1fel5KNZ+WbYo2nnhJzHNHTYTfaTnQFvZC6uLM45Mi/LgJxKwcgL3kBGzDd9u+hV2ge9geHtHs9U358+dmNZ3MvZn54uYHYlPXonUSt4SdUUtUX/Sb0jAJnzSrxFscy5hx1svYmpERn6bZ7Fx1hu4EuiGfDdYrK94fD5pav61Rmjh5qSmDXE7A4dWTsZPCcAPn/ZD/YJW4vFJyICCT8BZbJw0DQ9+dsSedVHIUzMbF9bNQAjq49j8bqihUrrEaeTbGKSKIzsSK1/4DzUOhGKkZ1UAt3EhbDpemPNDftuiBdH+XIxatwuvbfsKk3xLtFqOCznIurABU56fhUOyrUQr8esxL2Q7Nk8Mw6bJfrBX13LWLwh9YwI+iVeteBYb50xAzA2VelnR+OilkKLlpOfhNySs0GRP0WExW6gbPpZ4DmTZD+L4nFB8GNJcvezF9FHXdLEi/EgCJGC5BLJxbs7T8JJ/cbs1RZf+M7AxdSA++nAYmtqb61fANRz9bHmeI/UehdCfLiAp5QKOfT8d3e3KssYdXNy/Bfuz7dB04mackdaKj2BZkLP05Xo6+Zo0esu5eAhhkiNtheFhx6V15YSf5qPRlbMqzqdYX95TsPm3i0j6IwLTOziioA35esoFHF3RD0LE7J+Si46CAdgFzsMeUf+3zXjNW5Q6i++3VcXUfbFISvkVmyfmebfsPb8iqcwNPq0wdMUPkn4JJ5ajp8QlDsfPX5OEzknchrclR+qM7nN253M4jtCRrQDE4JMZaxGTVR99Q49i80RvqU6tiVvxe8peTPIt7voqw7nfR/h92xuoJUo6vIHNScn4ebIvKuckYuu0hZIjLdBP2CpsFJoK573yA4TGSOPZYjCBBwnHsE44UrsXEXr2IpJSLuLMtin59VZia+IdAHeQuGVlniNVfRak9jOw/92vcPR2js62yBMmB7ePfoVZERmFthEy7JuH7nYZOLR4M36+rTqVUUKFggvm+n9SgYA8IQESqAgBNRuQVryB7vgWozpNwJoL8nRfRfowQN2cTKSeE07BAd1fHYluzlUAVIGz30AM69+ojA6rwjNkneScvuqaiYPh27DmvdcLRqD3Mm8jG3dw8XgkzomWWj+P4CfqQ3wZ2jo/iSnTB0rOsGQndmg5uCfaiB8gtnawt7OFrWcItqckI+GbAPwZuRM7wt7H6Enhec747k3czlb9Im6EvsOfzvsBY++NJ3q6Sl3Y9R+M55uKMWgttOraJc9Zley85JXWz+PF55pKoybb+u3Rq7ODShlV/V7FWy/mj65s66Pb1MkYKhxvfASOJqiOCFWq63Cac/EkwmNFOwGYOn1g/g+0KnDu9ireGi5sFYN1R/7I23ldrF1bZ3d0kH55iOfxVazYthMHL3linvTjaV3+CPsa4o7FlXwWus3AHvFDKW4uutXQ1RayINlI+jVasld25Cz0adEEHm5N0KZX/ig7OwoHY67LhUv9y2neUvHwJglYGQGxAanfZHze3AEDeszFvGkd0Xl7CDzN7Wd1zr+4cUl8QddG3VpiylI+qqKG02PyBw1/NUw75peu4lQDdniAf27kfUnatXRD3QL9bWFXoxaE6y7pZmrnTe2q9pp1HmsmjcK8SHmqWOXmo7VQw66gYQCPwamGqi55ZfPkUamn7enjtVC9oPlaaNjcGSiQo1C/Wt1awb2gnBge14DTo0LBDMRdugn4SmNNbXstUS7nnxu4LK46tENLd1X9Cm118/wlXIMvxNyA6mFbvzfeW5cNpxkLsDE+Ep9Mkeet7dB0+AKsePs5eFb9C8m/3JCcqWrdEuc62UKufROXz6uxnXwb/+DqTTE6LvtQRVx2aZYgARKwCgK2dd3QQowIEpNxxRzDY2wfg0MjIeA1/JaSqbKp5g5uZ/5bug0Kph3FF/IsLPt4K479ca5gKjOvcmVUd8hbL84+l4KrBQPIHGTfvqlhzbS4MxTTjwvzHKl3MGatWIXNP10onAotXUoD3y3U72bUWSQX6Cec6G1k3hXdO8OnUcUcqWjFtroDGoqTG7/gXLKq4ym0Va3mjaB+z3gVOPsOw7yI80j6bT9CVyzHsg/fQHe7vLXjaVsSkVO5DtzbiVH3Xfx981+VZ0EVYXltURU1natLDeVNceeHkMmhZCkx+LKfi2pHGs/pTDWi4Q0SsF4COVk3kSnU83RHA3NcN7V1Refn20rjw3ObtuCotDP2HjKit2DDtkulGyYrHUmJYlxZA67tA/Hss76o89cp7NyfqlKvKpoEBKKluBK7HeuP/pm3jppxGB8u2qJmVKpSteA0C1eSpDEZ7Nzao8dzT8O3zjUc2xGVt+O1oJwpTlT1+wJLvj2ft6s2509ELVuOjQKPdxCe8BI/WCp22DbxR7/Wop3jWLZoS37s8j1kRH2BJeuErXwxvGtjNbtd7+HP8Ml5O6mDFiAqyxXd+vVD334D0Ker6hi2Nny6+BR7FsTsw7r8HdDDsSbxWjlt4QjfwG7StP7N1auxXlr2ELIvyNvZ6zMbUVwzrdgDwtokYJ0ExG7ecHz03iLsz26F4ZN7oolZ/qSuiiY9B+ZtqokPxahOTeEhNk+9sKjojlF1RrJvjPbSl3EG9k/qKm2+8ur0Bk6ivvSlmbdmCtg26Y4QaVPSWawLCcgvNxOXGrTSsGZavLMa8GrvK5XNjpiMJxq7w6NxAEaduI+mwreUWDMtXt+wn209+2GWtKEpA4fmPIM2YhOakG/NWcnBvbZgBHylH1Iqo1iNoTF5shaOQlVCY2w9MWD2WDQV7q5g3bEpuoSE4gLEJrC3MUrtVHIV1A8chpfFRqwCGwsZu+atb9v1REhPd9iiKjwHTszbsFVQTl7XtEPTkS+hV5M65bSFLWq0H4Spgc5A9g+Y16t13nMmye6M7tMGoX0N7f4H0a6UYW3O1kmABPRKID+dYKuXsDFb/W7eA84ipeAXeK9b3sYbvXavp8Zs6z+HxTu+xGvii04cdoF47autCM3feaqxG9tGeHb2R5gzXOxaFUcrDJ0XhjVfTUAn8YW/7TBixGjDthH6LvkWX04MzHOeUvvfYvn4DtKaaX7lUv5UQf3npiNsXrDkSCAcx/AF2Lz2E4wRm4F02LxSSicVuFULvpO/QUTY4kKGkoyzEXrgG0wqcHBV0eTpCZgoc0Y1QO12IfED5GnMmJLPC3aoi4e4A1vY+07ApgNrsERmKaQWU99h4ZrDYkQZez9M+j4coXNkhuKi4DgboTvmom99sXqdV+6Nb9ZimWr7wl4r1uKr2U/B2bYCtrBvjpErvi0qQ/6zoG1YjBDRJjc3NzdPWv6XBEiABJRD4EHMcnSSkhA4o6ccq4ibiFn+CgatjAECl+NYaL8Sm2aUQ4ia6kKAzlQXWixLAiRgPQSyorHihWKJAAq0U3WwBRd5QgIaCdCZakTDGyRAAtZOQKSo27VxFWatjCzcdCSmJ6ePxIBunlplvrF2RtRPOwJ0ptpxYikSsEgCn6/6HIMGD4Kjo/mmDbRIsBSaBIoR4AakYkD4kQSshYBwpEsXLUJmphQEYy1qUQ8SMEsCdKZmaRYKRQLlJ/Dff/9hwvjx2LzpO/h17IC48+fL3xhrkgAJaEWAzlQrTCxEApZBQDjSN6dORXxcHNauX48mHh7Iyir9JViWoRmlJAHzJkBnat72oXQkoDWBK1eu4OWQEKm8cKQNGjSAn58f4uPz3lWpdUMsSAIkoDMBOlOdkbECCZgfAeFIRwQHw9HJCUuXLZMcqZDyMXt7XExKMj+BKREJWBkBOlMrMyjVUR6B2NhYyZF2DgiQHGm1aiKDTd7h6uqK6FOn5Y/8SwIkYCACdKYGAstmScAYBE6ePIkBffth0OAhmL9gAVQdqejfxSXvjReJiYnGEId9kIBiCdCZKtb0VNzSCQhHOmLoMLw5fTrGjhurVh3ZuWZnl3w7p9oKvEgCJFAuAnSm5cLGSiRgWgIihlQ40rUbN2h0pLKEQ4KHISU5Wf7IvyRAAgYgQGdqAKhskgQMSUBOxiAcqb+/f5ld1axZEwkJCWWWYwESIIHyE6AzLT871iQBoxIQMaQzZ8yQkjFs3RGulSMVAnp5eeHWrVtGlZWdkYDSCNCZKs3i1NciCcjJGE4cPy4lY2jdurXWeri5u+O79Ru0Ls+CJEACuhOgM9WdGWuQgFEJiBhSkdXoemam5EhFMgZdDjs7O6m4cMg8SIAEDEOAztQwXNkqCeiFgJyMQTT2dVhYQTIGXRr39PSUiqelpelSjWVJgAR0IEBnqgMsFiUBYxIQsaEiq5G3j0+JZAy6ytHIzRWpqam6VmN5EiABLQnQmWoJisVIwJgERAxpUI+eUjKGTz/7rEQyBl1lEdmR/mXCe12xsTwJaE2AzlRrVCxIAsYhoE0yBl0l8fb2RnR0tK7VWJ4ESEBLAnSmWoJiMRIwBoH169ZJyRiWrVheZjIGXeSxt7fHjRs3dKnCsiRAAjoQsMnNzc3VoTyLkgAJGIiArskYdBFDrL+KaeOkFGZC0oUby5KAtgQ4MtWWFMuRgIEIiJCVJYsXS8kYtM1qpKsocniM2B3MgwRIQP8EKuu/SbZIAiSgLQE5GUN8XFy5Yki17UeOTWXCe22JsRwJ6EaAI1PdeLE0CeiNwPXr16VkDIZ2pLLAvXoHIe78efkj/5IACeiRAJ2pHmGyKRLQloCYbh3Yv79UfE9ERLmSMWjbl1zOwcEBWQyPkXHwLwnolQCdqV5xsjESKJuAnNVIH8kYyu6tsISfnx/i4+MLL/CMBEhAbwToTPWGkg2RQNkEpBjS4GApGcPSZcsqnIyh7B4LSzxmbw+RKJ8HCZCA/gnQmeqfKVskAbUE5GQMgwYPkWJIq1WrpracoS66urriUgpTChqKL9tVNgE6U2Xbn9obicCO8HApGcPc+fP0moxBF/FdXFyk4iLmlAcJkIB+CdCZ6pcnWyOBEgREMoapkyZDxJAGDx9e4r6xLsgj4WvXrhmrS/ZDAoohwDhTxZiaihqbgIghXRO2BksXLZIcqb+/v7FFKNHfkOBh+Ovq1RLXeYEESKBiBOhMK8aPtUlALQHVZAxHjh8zSuiLWkGKXXRxaYiEhIRiV/mRBEigogQ4zVtRgqxPAsUIqDrStevXm40jFWLWq+eMW7duFZOYH0mABCpKgM60ogRZnwRUCIgY0pdDQqQrW7ZtMytHKoRyc3fHd+s3qEjMUxIgAX0QoDPVB0W2QQIA5GQMjk5OEDGkjo6OZsdFTngvUhnyIAES0B8BOlP9sWRLCiYQGxuLEcHB6BwQIDlSeeesuSHx9PSURMrMzDQ30SgPCVg0ATpTizYfhTcHAiIZw4C+/aSsRvMXLDBqVqPy6O/XsQNSU5m8oTzsWIcENBGgM9VEhtdJQAsCkZGRUjKGN6dPN1kyBi3ELFKkiYcH/mXC+yJM+IEEKkqAzrSiBFlfsQREMoaxo0ZLMaRjx421GA7e3t6Ijo62GHkpKAlYAgE6U0uwEmU0OwLCkZpTMgZdANnb2+NiUpIuVViWBEigDAJM2lAGIN4mAVUCqjGkEQf2Q97Qo1rG3M99mjdH9KnT5i4m5SMBiyLAkalFmYvCmpKAqiMVyRgs0ZEKfk5OThJGEcrDgwRIQD8E6Ez1w5GtWDkB4XjenDpV0tLcshrpil6Of83Ozta1KsuTAAloIEBnqgEML5OATEBOxiA+i2QMDRo0kG9Z7N9evYMQd/68xcpPwUnA3AjQmZqbRSiPWREQ7/4UyRi8fXzMOhmDrtAcHByQnp6hazWWJwES0ECAzlQDGF4mAZGMIahHTykZw6effWb2yRh0sZifnx/S0i7rUoVlSYAESiFAZ1oKHN5SLgHhSEcMHQZLSsagi7Xq1K2LE8eP61KFZUmABEohwNCYUuDwljIJyDGkn4euRmBgoFVCqF27Ni6lMKWgVRqXSpmEAEemJsHOTs2VgOxI127cYLWOVLB3cXGRTCDWhHmQAAlUnACdacUZsgUrICBiSJcsXozNm77D1h3h8Pf3twKtNKsg3mrTyM0V165d01yId0iABLQmwGlerVGxoLUSKJ6MwRpCX7SxlXhd3F9Xr2pTlGVIgATKIMCRaRmAeNu6CYiXZItkDPFxcbD0ZAy6WsrFpSESEhJ0rcbyJEACagjQmaqBwkvKICCSMQzs319Sdk9EhFUkY9DFcvXqOSMlJUWXKixLAiSggQCdqQYwvGzdBOSsRtaWjEEXq7m5u2Pf3ghdqrAsCZCABgJ0phrA8LL1EhAxpF0DukjJGER6QLEZR4mHCI8Rh5jq5kECJFAxAnSmFePH2hZGoHgyBqU6UmE2eaNVZmamhVmR4pKA+RGgMzU/m1AiAxHYER4uZTVatmI5xo4ba6BeLKtZv44dkJrK5A2WZTVKa44EGBpjjlahTHonoJqMwdpjSHWB18TDA1czmPBeF2YsSwLqCNCZqqPCa1ZDQMSQrglbg6WLFkFkNaIjLWpab29vxMfHF73ITyRAAjoToDPVGRkrWAoB1WQMR44fK1gjtBT5jSFnXWdn7N61yxhdsQ8SsGoCXDO1avMqVzlVR6q0ZAy6WN3V1RXRp07rUoVlSYAE1BCgM1UDhZcsm4CIIe0TFCQpsWXbNo5ISzGnk5OTdFcw40ECJFB+AnSm5WfHmmZIoHgyBkdHRzOU0nxEkvkw4b352ISSWCYBOlPLtBulVkNAiiENDkZQ795QcjIGNWhKvdSrdxBSkpNLLcObJEACpROgMy2dD+9aCAE5GcOgwUPw1rRpis1qVB5zubm5IT2d4THlYcc6JCAToDOVSfCvxRKIjIyUkjHMnT+PyRjKYUUvLy+kpV0uR01WIQESkAkwNEYmwb8WSYDJGCputjp16+LE8eMVb4gtkICCCXBkqmDjW7rqdKT6saBIeH8pJRUinIgHCZBA+QhwZFo+bqxlQgKqMaQRB/bD09PThNJYftcyv7S0NLK0fHNSAxMR4MjURODZbfkIqDpSkYxBdgTla421ZAKN3FzB8BiZBv+SgO4E6Ex1Z8YaJiIgYkhfDgmRemdWI/0aoXNAAP66elW/jbI1ElAQATpTBRnbklWVkzE4OjlJMaTyuzgtWSdzkt3FpSGio6PNSSTKQgIWRYDO1KLMZe7C5uDOzb+QcS0LD/QoamJiIkYEB0OMnpiMQY9gVZqqV88ZN27cULnCUxIgAV0I0JnqQotlSyFwF+mHF+OFdh3RpX13BC8+jPQHuaWU1+6WSMYQ1KMnRDKG+QsWMBmDdth0LuXTvDn27Y3QuR4rkAAJ5BGgM+WToBcCuekReH/ar2jz9vuY/oIzznz2BsYsPFQhhypnNXpz+nQmY9CLlTQ3YmdnJ928fv265kK8QwIkoJEAQ2M0ouEN7Qnk4t6lZPw3YQ7eC/HGIw+6w7PG63j1qzmY26gOlr7YEvY22rcmSsoxpJ+HrkZgYKBulVlaZwLyGnRmZibk5Pc6N8IKJKBgAhyZKtj4FVU9N+sCdi4ehz5P9MXoxT+jTauGeEQ0WrkBur2zAisGVUHk7PF4a0sS7uvQmexI127cQEeqA7eKFvXr2AFx589XtBnWJwFFEqAzVaTZ9aH0bZxbMwfTd/+JqriIE7+cxcE9pwqndSs3wtPvrcB7vYADb0/BjC/DsHLlfqSXsowqYkhnzpiBzZu+w9Yd4fD399eHoGxDSwJNPDyQlZWlZWkWIwESUCVAZ6pKg+daEMjFg6vJSL15EceO+GHNnm3Yemg/Ql/xRIKY1l3/G7LyHaaNfUuMmD8LAx1/R9QvNnjyxSdRT8N0r5yMQeSIFTGkrVu31kIWFtEnAT8/P8THx+uzSbZFAoohQGeqGFPrSdHcy9gzezheWrgVfwU9jXbVK+VP636ET0ZUl6Z139wYjztSd7l4+CAXTr0XYs2y4WjlIE0ClxBEbHp5c+pUXM/MlBypvH5XoiAvGJTAY/b2uJiUZNA+2DgJWCsBOlNrtaze9crFgwcP8N+v2/HJD3/i0qbNOJqcgevytG1lFwROXyRN60bOmoGl++NxOe4n/JLZCmNm9Ye3fSW1EolkDAP795fufR0WBjpStZiMctHV1RXRp04bpS92QgLWRoDO1NosWm59cnEn+QSOJKlbM7uL9KjVWLE/Bf9UeRKhcT8i9JUWuPLtbMz69lzRad2lH+L15okIGzMGC05XhVczZ9SsrH5uV85q5O3jw2QM5bab/io6OTlJjYkkGTxIgAR0I0Bnqhsv6y2dexn7Fk3CmImfICr9bqGeuf8gee8SjFlRBX2f9kCdFq3gaueislv3NczckVyQ8cimuje6P/0UBiz5AktHtoWDBkcqYki7BnSRkjEwq1EhblOeySEx2dnZphSDfZOARRKgM7VIs+lb6FzcTzyKH/6uh3q/f4FXX/0SMf88lDrJvRqPn8+l4G9/bzRSfVoKduvmYPfUqfjg8BU8yP0PmemX8J/fNCx4wUdjbGnxZAzVqlXTt0Jsr5wEhgQPQ0pycjlrsxoJKJeA6tejcikoXvMcZNu2w7vrN2Fj6KvwOr8SY9/ciLish7Bx7oDne7SAo301FM/wIe3W/WARXm2WiLBRwzB09BIcuNEAfn71S5SVEa9ftw4jhg7DshXLmdVIhmJGf2vWrIn09AwzkoiikIBlEKAztQw7GVjKSqjp4Y2GVauiXrdxWCSCQ/e9j9cWHUT6gwe4dukKXBo4Qt0WIhsHf0x4dzBqeHXB4KkTMdinJtSvkOZlNZo9cxZEMoa+/foZWCc2Xx4CXl5eSEu7XJ6qrEMCiiZgk5ubK+/HVDQIKq9CIPcmzq56DS8sjoXXqA8x12sbxnzzAEHd2sCjsTtcG7mgQQNn1KlVFdkJP+HAyQw06j8Y3eo9qtJI4amIIf3k448RsXcvFixcyGQMhWjM7kyegk9K4VSv2RmHApk1ATpTszaPoYR7gKxrmch6UBn2tR1hr26T0IMriFoo8usmorqTE+o+noULv2cWE8gFgXM+wsLhbTRuNJKTMcTHxTGGtBg9c/wodvKKt/Sci4/jG3rM0UCUyWwJ0JmarWkMI1huVhy2vj8P35xLQ1J8Gh46dMDQiePxysAucCseC3o/CVtefwlv/2CLZ1Z8g/nd7HAt/U9cuRyDHYv2wGbsAswaqHmjER2pYWxo6FY93NwRcWA/PD09Dd0V2ycBqyHANVOrMaU2ioh8uh8huttS7Ig4gtiTm/B+j/+weU4Ieg2ehx0Jt1Fkzv8RDwxY+hne6yV27L6JFb8+hEuzZmjRtisGfvBpqTt2RQxpn6AgSag9ERFMxqCNecykTCM3V6SmppqJNBSDBCyDAJ2pZdhJP1I+TMOpHbfh4e6IyrBF1XodMOx/3+D7Ob1R8/waTB06ExsTiiZtsLFvgWFz5iCkYMfuUkT8XafUHbtMxqAfc5mqlc4BAfiXCe9NhZ/9WigBOlMLNVz5xH6A+9m/49CplMJXolV2QquR/0PY3N5wzNyFuZO/xKkbeTGmeX3YoHK97pii5Y5daQNLcDCCevdmVqPyGcnktby9vREdHW1yOSgACVgSATpTS7KWzrI+RFbqJWTKc7eVnOHpXw3Rn25A1N8PCluzqQmfF9/Dh6PaAuc/xzufnMANuY4olXsNZ87WxYdfv4eB3ppDX+SdoIMGD8Fb06ZxA0shYYs6s7e3x40bNyxKZgpLAqYmQGdqagsYrP+7SD+8BEO7v4vdSXnvcAGc0L5PL9T+eyNmLdlf+O5RIYNNXQRMmoVJHexwKWwNIlJUUgraPI7O40ZrDH0R1XeEh0vJGObOn8dkDAazqXEa9mneHPv2RhinM/ZCAlZCgM7USgxZRI3c20gMX4gxo75AQrNmqFdVvlsJDgFD8Ua3Wri2+T28E1aYpF6UsLFvg5fmvI52OO0b3TEAACAASURBVIVdJ9OKbkaSm1Dz9/NVn2PqpMlSMobg4cPVlOAlSyJgZ2cniSvWvnmQAAloR4DOVDtOFlTqAf6OXIzgSeuQ3u41fBH6Fno2LPCmwCMeeGH2dPRwuolj8ydjXsSlgiT1gA2qej+DUQNqIfHqLaiunGoCIBzp0kWLJEfq7++vqRivWxAB+TV4THhvQUajqCYnQGdqchPoW4BKeKxGTTzSfCK+/HqSmqlZGzzi3h9L1s5BoFMqto4Pxmthv+LGg/xFUhtHePu1QkOHx1DawyFiSCeMH4/Nm77DkePHmNVI32Y0cXu9egch7vx5E0vB7knAcgiU9n1pOVpQUhUCNrDz9kP3nEqofC8Vx7//FO9NGIRuTTzQPmg03lt9EMlZgL3PUCxdtxADvG8ics5wDJj8JQ6cTUb65RhEHKyNMb0aa3SmTMaggttKTx0cHJDF8BgrtS7VMgQBZkAyBFWjtvkQWWfDsftBDwzxrZHf81848NZQvBN5GTdv3C8mTSU49pqDsGVD4WNfCbl3/sSv+3cgfOdu7I1MgX2XoXh9xuvor2HXrlhHe3PKFDg6OeHdGTOYjKEYXWv5KDaUifCY+QsWWItK1IMEDEqg+Fu1DNoZG9c3gVzcTw7H7K018PYc2ZGKPhzRIqAF/vn+DrqMn4px/TqiWSNnPPbgbyTHRiJ0/oeYuNobOye3Q7Wq9eH73Djp3/tliMdkDGUAsqLbj9nb48Tx41akEVUhAcMS4DSvYfkatvXcDESt2o8mA/zxeJH3nlVG3bb9MW/TFoRO64+OXg1Qs2olVLZ3hmdAMBZ8MQNNtv+I+LuqwaSlixobG4sRwcEQ2XGWLlvGGNLScVn8XVdXV1xKYUpBizckFTAaATpTo6E2QEc3f8OBAw3R2uOxEo3bunbFoI711Lyk2waVG7ZHoPtlXC6S6ahEEwUXRDKGAX37QSRjENN+1apVK7jHE+sk4OLiIikm3iLDgwRIoGwCdKZlMzLbEg+Sf8MhPIZqVeRhqXi12lVkZIjXq5Uy6sy9g3/v1Ec9B3Wv+y6qrpzV6M3p05mMoSgaq/4k/2BieIxVm5nK6ZEAnakeYRq3qYf4J/Mv/Hs7DVfFCFO8f3TxSHRr3wldOnVEt8FzsTX+lprEC3eRfnAzwpt3hPejshNWL7mIIR0xdJgUQzp23Fj1hXjVagkMCR6GlGS+JNxqDUzF9EqAG5D0itOYjVVCdac6eOzhAZz74woa/Pw+Vt1+Am8veQoX923E15FrMH34ddzd+D8M87KXnO3xsNXYGHEYBy49gU/2dkL1UsRlMoZS4CjkVs2aNZGQkKAQbakmCVSMAJ1pxfiZtHYlh7rwRDzWrXwXvzUaiVULe8BRDDYHDsGwyJUYP/ZLzPuwO55c1Q91Lx/BpwvXIaHdS1iy/nUEPq7e9CKGdMH8+dJOzq07wtG6dWuT6sjOTUfAy8uLb48xHX72bGEEOM1r7gbLisaq9zYj8U7JNVAb1w54tlNNZJ9IgMMTLfIcqdDHxg4Ne0zBlx8PQ80DP+LMtYewdR+Cr3+JRtSGd/GcVw2om+CVkzGIkIi169fTkZr7s2Fg+dzc3fHd+g0G7oXNk4B1EKAzNWs7PsDfRzfjo2/nYcqSQ0Xf8iLktnVDj1eeRW38jR/CduJslmo23UdRL3AQXmycguR08QYYW1St5QD7yurcKCAlY5g6FdczMyVHKudnNWs8FM6gBOSE9+JHFg8SIIHSCdCZls7HtHdzUnDwwH08H+iMhK8mYewnP+OfIgPUynj8ydGYPagxHp5ehknvhyNR1aE+Yo9addrCx00l0b0ajeRkDOLW12FhzGqkhpESL3l6ekpqp6WlKVF96kwCOhGoNGfOnDk61WBh4xH4NxP3fPpi+PAgtPz3FMJWbUeiox+6ta6LgmgY25rw8G+Hx9NOY9e2jdhwOB1VHWugRtV7uHJ4J35s/ByGtq+jJt40Tw0RR/hySAi8fXyYjMF4lrWYnkRoVOMmTdC4cWOLkZmCkoApCNCZmoK6tn1WcUI9xyqAbQ24dWwFp8Rd+Cr0KG636Ir/a1KjIBG9TZU6aNmjD55q5oDci/uwetVX2HAwFY92GImpL/jATv3MLuRkDKNfHYvZc2bjkUce0VYyllMIgTNnzuDxxx9Hs2bNFKIx1SSB8hFgovvycTNJrdyss/hqwsv44FgjvLRmFd7tUlftRiJthGMyBm0oscz6desQHx/PhPd8FEigDAJcMy0DkDndtrFviZAPFiGkWSK+mfg+1sapS8pQtsTiC1IkY/g8dDWzGpWNS9El7O3tcTEpSdEMqDwJaEOAzlQbSmZTxgaV63XH25/PwzPYh/dHzMfOy3d0kk4kY5g9c5aU1SgwMFCnuiysPAI+zZsj+tRp5SlOjUlARwLqI/d1bITFjUlAJKp/FvPXZuHOiDmYNvZR3BjVFP9l+WDI8HZw0LA+KsIbPvn4Y0Ts3Ss5Un9/f2MKzb4slICTk5MkudjxzXApCzUixTYKAY5MjYJZ351Ugr3PEMxbFoIG53dg62/10W+ob6mO9M2pU/Mc6fr1oCPVtz2stz1HR0dJOSa8t14bUzP9EKAz1Q9HE7Rig6rVaqPjnG/x7TvdUU9DMobr169DONL4uDgmYzCBlayhy169gxB3/rw1qEIdSMBgBOhMDYbWwA3n3sYV2x6YMbItHDQ4UjE1N7B/f0mQPRERnKYzsEmstXkHBwekp2dYq3rUiwT0QoDOVC8YTdCIjQOa+TWBvYY1UjmrEZMxmMA2Vtaln58f0tIuW5lWVIcE9EuAzlS/PM2iNSmGNDgYgwYPYVYjs7CIZQtRp25d6S1Clq0FpScBwxKgMzUsX6O3LidjEI5UvNC7WrVqRpeBHVoXgdq1a+NSSqp1KUVtSEDPBOhM9QzUlM3tCA+XkjHMnT+PyRhMaQgr69vFxUXSSORx5kECJKCeAJ2pei4Wd1UkY5g6abIUQxo8fLjFyU+BzZeAPLtx7do18xWSkpGAiQkwaYOJDVDR7kUyhjVha7B00SImY6goTNbXSGBI8DD8dfWqxvu8QQJKJ0BnasFPgHCkcgzpkePHGPpiwbY0d9FdXBoiISHB3MWkfCRgMgKc5jUZ+op1rOpI165fT0daMZysXQaBevWccevWrTJK8TYJKJcAnakF2l7EkIoXeotjy7ZtdKQWaENLE9nN3R3frd9gaWJTXhIwGgE6U6Oh1k9HcjIGRycnKYZUzp2qn9bZCgmoJyDCY8Qh0lPyIAESKEmAzrQkE7O9EhsbixHBwegcEMBkDGZrJesUTH5jTGZmpnUqSK1IoIIE6EwrCNBY1UUyhgF9+0lZjeYvWMBkDMYCz34KCPh17IDUVCZvKADCExJQIUBnqgLDXE8jIyOlZAxvTp/OZAzmaiQFyNXEwwNXM5jwXgGmporlIMDQmHJAM2YVkYyBMaTGJM6+NBHw9vZGfHy8ptu8TgKKJsCRqRmbn47UjI2jQNHqOjvjYlKSAjWnyiRQNgGOTMtmZPQSqjGkEQf2w9PT0+gysEMSKE7A1dUV0adOF7/MzyRAAgA4MjWzx0DVkYpkDHSkZmYgBYvj5OQkaS/Cs3iQAAkUJUBnWpSHST+JLymRHlAczGpkUlOwczUE5JhmJrxXA4eXFE+AztRMHgE5GYMQZ+myZcxqZCZ2oRhFCfTqHYSU5OSiF/mJBEiA07zm8AyI90SKZAzePj5MxmAOBqEMGgm4ubkhPZ3hMRoB8YZiCXBkamLTi2QMQT16SskYPv3sMyZjMLE92H3pBLy8vJCWdrn0QrxLAgokQGdqQqMLRzpi6DAwGYMJjcCudSJQp25dnDh+XKc6LEwCSiBAZ2oiK4sYUuFIPw9dzaxGJrIBu9WdgEh4fyklFWLXOQ8SIIFCAnSmhSyMdqaajCEwMNBo/bIjEqgoARcXF6mJtLS0ijbF+iRgVQToTI1oTvFrfsnixdi86Tts3REOf39/I/bOrkig4gSqVauGRm6uYHhMxVmyBesiwAxIRrJn8WQM8iutjNQ9uyEBvREQrwD86+pVvbXHhkjAGghwZGoEK4oXKotkDPFxcUzGYATe7MKwBFxcGiIhIcGwnbB1ErAwAnSmBjaYSMYwsH9/qZc9ERFMxmBg3mze8ATq1XNGSkqK4TtiDyRgQQToTA1oLDmrEZMxGBAymzY6ATd3d+zbG2H0ftkhCZgzATpTA1lHxJB2DegiJWMQ6QHFxg0eJGANBER4jDjE8gUPEiCBPAJ0pgZ4EoonY6AjNQBkNmkyAvLmuczMTJPJwI5JwNwI0Jnq2SI7wsOlZAzLVixnMgY9s2Vz5kPAr2MHpKammo9AlIQETEyAoTF6NIBqMgbGkOoRLJsyOwJNPDxwNYMJ783OMBTIZAQ4MtUDehFDSkeqB5BswmII+Pn5IT4+3mLkpaAkYGgCHJlWkLBqMoYjx48x9KWCPFndMgg8Zm+Pi0lJliEspSQBIxDgyLQCkFUd6dr16+lIK8CSVS2LgKurK6JPnbYsoSktCRiQAJ1pOeGKGNI+QUFS7S3bttGRlpMjq1kmAScnJ0lw8WJ7HiRAAgCnecvxFDAZQzmgsYpVEXB0dJT0yc7Otiq9qAwJlJcAR6Y6kpNiSIODEdS7N5iMQUd4LG5VBIYED0NKcrJV6URlSKC8BOhMdSAnJ2MYNHgI3po2jVmNdGDHotZHoGbNmkhPZ3iM9VmWGpWHAJ2pltQiIyOlZAxz589jMgYtmbGYdRPw8vJCWtpl61aS2pGAlgToTLUAJWJIx44ajbUbNyB4+HAtarAICVg/gTp16+K79RusX1FqSAJaEKAzLQMSkzGUAYi3FUtATngvQsR4kIDSCXA3r4YnQDWGNOLAfnh6emooycskoEwC8v8TaWlp/P9DmY8AtVYhwJGpCgz5VNWRimQM8peGfJ9/SYAE8gg0cnPFtWvXiIMEFE+AzrTYIyBiSF8OCZGuMqtRMTj8SALFCHQOCMBfV68Wu8qPJKA8AnSmKjaXkzE4OjlJMaTyextVivCUBEhAhYCLS0NER0erXOEpCSiTAJ1pvt1FWrQRwcEQv7SZjEGZ/zNQa90J1KvnjBs3buhekTVIwMoI0JkCEMkYgnr0hEjGMH/BAiZjsLKHnOoYjoBP8+bYtzfCcB2wZRKwEAKKd6bfb94sJWOYOGUykzFYyENLMc2HgJ2dnSTM9evXzUcoSkICJiCg6NCYt6dPx5ZNm9HYowkeeaSKCfCzSxKwbALyvoLMzEzIye8tWyNKTwLlI6DYkansSBcuXoQdu3bh3LmzWL9uXfkoshYJKJhAr95BiDt/XsEEqDoJKPAVbCKGdETwcJyNPYPPV3+JwB49pOfg3RkzpA1ILVq2ROvWrflskAAJaEnAwcEBWVlZWpZmMRKwTgKKGpkKR9r32WcRf/48Nm7eXOBIhWnFdNXylSsxeeJEcP3HOh92amUYAn5+foiPjzdM42yVBCyEgGKc6Z9//oneTwfh77/+xs69e9CuXbsSJhIj0ldGjcKsmTNL3OMFEiAB9QQes7fHiePH1d/kVRJQCAFFONOLFy+ix5Pdcf/+PRw6EoUmTZpoNK/8Vpgd4eEay/AGCZBAIQFXV1dcSkktvMAzElAgAat3pufPn8dzvfugQUMXHDh4EGJ9p6xDrJ9OnTQZIiMSDxIggdIJuLi4SAVE4hMeJKBUAlbtTHfu3Im+fZ5BOz8/acdutWrVtLKzWD9dtmI5Vn32mVblWYgElExA/v8qOztbyRiou8IJWK0zFY50yhsT8dzz/fDturU6ZzXq2asXLiYlSdmRFP6MUH0SKJPAkOBhSElOLrMcC5CAtRKwSmf6/ty5kiN9dfw4fLh8eblsJ35tv/3uu/hoxYpy1WclElASgZo1ayIhIUFJKlNXEihCwOqcqUjG8O03YZg97328NW1aEWV1/SB29zbx8AA3I+lKjuWVRsDLywu3bt1SmtrUlwQKCFiNMxUxpK+89BK2bdmCDz9aiREjRhQoWZGTkSEhWLliBUT7PEiABNQTcHN3x3frN6i/yaskoAACVuFM5WQMJ44dl5IxPPfcc3oznaenp/RatuOMo9MbUzZkfQTkhPf80Wl9tqVG2hGweGcq3qUoshpduZyG3T9EqE3GoB0KzaXE6PSr1as1F+AdElA4AfGjUxxpaWkKJ0H1lUrAop2pSMbQpZM/bt28hWM/nSw1GUNFDCx/UcTGxlakGdYlAasm0MjNFampTN5g1UamchoJWKwzFY5UTsYQ9eNRrZIxaKSgxY1XRo/G/n37tCjJIiSgTAKdAwLwLxPeK9P41BoW6UxFDGlQz55o0aqVTskYKmLvgIAAfPHZKibBrwhE1rVqAt7e3oiOjrZqHakcCWgiYHHOVE7GIJIqbPp+s87JGDSBKOu6iDsVcasxMTFlFeV9ElAkAXt7e4g9DDxIQIkELMqZrly5UkrG8OJLIfjEBKn+hAPfvm2bEp8T6kwCZRLwad4c+/ZGlFmOBUjAGglUthSlRDKGLZs24+0Z72LU6NEmEVskcRBfFuJ9p46OjiaRgZ2SgLkSkMNjxAsiRH5rHiSgJAIWMTKdMnmy5EhFMgZTOVL5oRBTvRcuXJA/8i8JkEA+AdmBMuE9HwklEjBrZyoCwHsGBmL3zp3YtHUL9JmMQb2x7yEjagH6uDVHn9kHkZFTslRbX18c+/HHkjd4hQRIAL16ByHu/HmSIAHFETBbZypnNRLJGCL279ciGUMObkfNRis3d3jI//qGIVF2iLejMMtH5Z5cxq05ng+7AKlYTjL2bXXFij9+wQr3E9h38U6JB0LsWIzYu7fEdV4gARKAFKKWnp5BFCSgOAJm6UxFDGnnjp2kZAw79+7RLhlDThoOb9qPwjcq2qHl8/5oImmYg9sxh7Gj8KaKoduiX4BrXoyQrTt6DUjFpMbtMCm5M3o1qapSLu9UnsoS66Y8SIAEihLw8/NDWtrlohf5iQQUQMDsNiDJyRjqODtjW/h2LZMx5CDrzA6EOS1ETEo31ChhuOuI+bU2PvrpAro5Vym8K0arL6Wgc4HTrALnbjOwJ2VGYRk1ZyI4/fLly9yEpIYNLymbQJ26dXGCeayV/RAoVHuzGplGHjiAZ54OgoeXJ/b+EKGlIxWWu46ft23BuXXLsSQsHFGJt4uaMycHDfqOLOpIcQeJ29bgt2fl0WvRKqV9Er+++SLk0gjxnlIJ1K5dG5dSmFJQqfZXst5m40xFMoaxo8egS9cndM5qlJO4GyvXXQJwFhvnTMaoHiMwK/wCsmTL2taBZ+Ni49WcVJzYVRshPd11TgMlfn3zRcgyXP4lgUICLi4u0ofExMTCizwjAQUQMAtn+v3mzVIyhoGDB2F1aKjO2G09Q7A9JRkJP23FijnBaCqc6qR3ERpzU2NbORdPYrd3HzxZX2XaV2PpojfEr2++CLkoE34iAUFAZAoTx7Vr1wiEBBRFwOTOVCRjeGfadCkZwweLFlUIvq2zL54JmY9dP4ViuPfv+HrbGRSb8M1v/w4uHo9Bs8AWatZXyxZB/Prmi5DL5sQSyiQwJHgY/rp6VZnKU2vFEjCpM5WzGuk7GYOt85OYMn0gsO0wYm7LsTEqNpameB/HU77ly2Ik//pWaZGnJEAC+QRcXBpyGYRPg+IIaHCm1xA1s6v6eE11iHIuYE3f5vnlVeI21ZUFIMeQbtuyBZ+v/tIAyRhsYd/AHU083dHAvqSKeVO8/wffGiXvaRC5xGW/jh0g0qbxIAESKEqgXj1nLoMURcJPCiCgwZvURrf5R5BwYjl62gGI3YU9ZzStP+bg9tENWBabDbSejYg/zmN7SFONm3pkR5qUkIjtO3cisEcPA2DOQdaVa2g9+Rl4ltCwYlO8srBNPDzAtGkyDf4lgUICbu7uXAYpxMEzhRAo4WpU9ba1rwUnz27oLtYfV0fhTzUzphDJErb+iU5POqtWVXsuYkh7PPUU/v7rb4hkDM2bN1dbTreL95AR8wN2x2TkZTHCPWREf4UlR9ti7BO1SzZVwSnekg3yCgmQgCoBOeE9E5uoUuG5tRMo1ZlKylfuiCGjewIRW3CgRHo9kSxhF/Y0fg59GpS+K1ZOxiDaPHQkSrusRtrSv/0LVvX3h5ebO1qN+hQn/+2G6e89BWc12uVcjMapLk+jfQWmeLUVi+VIQIkEPD09JbUzMzOVqD51VigBNe6mOImqaNi9L/raHceyNT8V3R2bk4aD36Sjz+B2qFm8mspnMbU7fOgw3L17Fw8fPMS899+HSNAgrlf8kLMWJSMpJRlnQyfj+W6esNfQsK3ncHw22U/jfQ3VeJkESEAHAmJPQWoqkzfogIxFLZyAFs4UQI1OeHFaALLXhWJ7YmHy95yLR7GvcV88VUasptj9evL0KezYsxv9Bw5AfFyclKChpbeP9FaY9+fOxc8//2zhKCk+CZCATEDsKfg3qyBtinyZf0nAaglo50xRFZ79R2Go3a/YvPtcfmahazi65jQ6PtNS61GeWCN9a9o0ROzbJ40ixU5evw4dsH/fPgwZ+IK0G3hg/wH48ssvIaaFeZAACVgmAfF2pejoaMsUnlKTQDkIaJ/ovkYbPD+6GTau3o2fX2mHJ67uxqfoj688xZtVyvcLVOzklXfziinf3bt2Yf/+/Vj1yadY/L+FqGZXDR06dsTTQUF4KjCQieXLYWBWIQFTELC3t8fFpCRTdM0+ScAkBLQcmQrZaqHN4BHoiS1Yue0YotbE4JmRncqVQUidpmIq+IVBeekEfz0bi6MnjuP1SZOQlfUv3psxEx1828G/Q0dMmTxZj+ut6iTR7pp4M4a8a1G7GixFAsoh4NO8OaJPnVaOwtRU8QS0H5kCsK3fBYP618aoOSMxafg3OCaNSg3DsH79+hgzZoz0T/Rw/vx57N2zB4cOHsTO7eFSp409mqDL//0fevfpg/bt2xtGEA2tijdjyO821VCEl0lAsQScnJwk3UViE/5/otjHQFGKl+pMc7Juoujm9tp4YuRLaLluF7r2b6O3Uak2xMV6q7zmKsqL3cCHDx+W1lu//SZMaqKNry96Pt0LTz31lH5Db4oJqJ9dyMUa5UcSsCICjo55qTqZ2MSKjEpVSiVgk5ubm1uyhEgnOACjpNeaibuNMDRsK+Z1qw3kXMLuVXHwHfc06tvm4HbUXHQJ+RbZBY3YoeWcbdhaShakgqJ6OlFdb/35dDT+uX3boOut4vVSa8LCMH/BAj1pwGZIwPoITBg/Hj179kTffv2sTzlqRALFCGhwpsVKWdjHP//8E7t378bBA5E4e+YM7t+/j8fr1IF/QGf07t0bAV26FLwqqjyqnTx5Esd+/FHamVye+qxDAkogsGTxYlSvXgNjx41VgrrUUeEErNKZFrepvN4qHOD5c79Jtyuy3rp+3TqI3Yr8xV2cND+TQCGBHeHhUngMZ3AKmfDMegmUumZqLWprWm89fOgwyrPeGh8fL+08thY+1IMEDEGgTt26ELveeZCAEggoYmRamiHl9dYjUVE4fuy4VuutHm7uOB3zC+NeSwPLe4onIPYWBPXoiXPxcRVaVlE8SAKwCAKKd6bFrSSvt/545AjEZqbi663ujRtj5rvvYuOmTcWr8jMJkIAKAfFDVaQMjTiwH3Lye5XbPCUBqyJAZ1qGOTWtt44MCZGyM/FLogyAvK1oAt27dcOChQvh7++vaA5U3voJ0JnqaGMR3/rHH38gNjYW+/ZGSLWHBA9DtyefhMhHygB1HYGyuFUTmDljBvz8/LhZz6qtTOUEAUVsQNKnqeVcwqJNMY115swZxJ6JxVerV0vp0xq5uSKod2+09fWFr68v11X1CZ9tWRwBF5eGSEhIsDi5KTAJ6EqAI1NdiZVS/vr164iJicGvMTGI2LsXIuWgeK9j125PonWb1mjTpg03YpTCj7esj4AIjxEvr/j0s8+sTzlqRAIqBOhMVWDo+1TkJf05OlqKtftu/Qap+V69g9C5c2e0aNkSrVu31neXbI8EzIqAWA4Z0Lef9MpFsxKMwpCAngnQmeoZaGnNiVCB06dO4cSJE0XWW8WaUns/P663lgaP9yySgPhB2TWgC0PJLNJ6FFoXAnSmutDSY1mx3irWkk6eOIkjUYe53qpHtmzKvAiIuGyGx5iXTSiN/gnQmeqfablaFOutFy5ckHL+cr21XAhZyUwJDB08GK+MHo3AwEAzlZBikUDFCdCZVpyhQVoQ02MibWHU4cPgeqtBELNRIxEQ4TEibCx4+HAj9chuSMD4BOhMjc+8XD1yvbVc2FjJDAiIF0OIH4ZMeG8GxqAIBiNAZ2owtIZrmOuthmPLlvVPIDIyUorDZgpO/bNli+ZDgM7UfGxRbkm43lpudKxoBAJywvuklGQj9MYuSMA0BOhMTcPdoL1yvdWgeNm4jgTEj70Ovu1w5Pgxhn/pyI7FLYcAnanl2KrcknK9tdzoWFFPBER4zNYd4UxUoieebMb8CNCZmp9NDCoR11sNipeNayDAhPcawPCy1RCgM7UaU5ZPEa63lo8ba+lGYMnixahevQbGjhurW0WWJgELIUBnaiGGMpaYXG81Fmll9SMS3kdHRzM8RllmV5S2dKaKMrfuynK9VXdmrFGSwMmTJzFi6DAmvC+JhleshACdqZUY0hhqcL3VGJStsw85POZcfBxfQ2idJla8VnSmin8Eyg+A663lZ6fEmkx4r0SrK0dnOlPl2BrAA2SlJSIu6SKSEhPxBzphwmh/OOiJAddb9QTSSpvp3q0bFixcCH9/fyvVkGopmQCdqZKsn3sbSadP49fdH+OdtfHwmBGOPaN9UMlADLjeaiCwFtosw2Ms1HAUWysCdKZaYbKmQneRsmEcAt/NwJhNGzCtY62Syj24hIiFi3CwSnv8X8fW8GnmBXdne1QuWVLrK2Wtt4q3ijRo0EDr9ljQ8gh8vupzpKVdKB/QmAAADxdJREFU5o5eyzMdJdaCQEW+H7VonkXMj8AtJP56AbALRAfvGiXFy72BmE/exextp3H9xl6ErxJF7OE9/gt8+1ZnONiUrKLNlWrVqknZb1q3bi3FGqqut/5v/nxcSkmFX8cO6NrtSbRu0xpNmzaFo6OjNk2zjIUQqFfPGefOnbUQaSkmCehGgCNT3XhZfuns45jXcTg2PPkpjq7sjceLOMcsJG54D++lDcRnb/kCly4i/nwMTv/yEJ1fG4EODoaaEAbKWm/18vLiLlALf/rkHb1MeG/hhqT4agnQmarFYq0Xc3Hv7Co8+9wqOP4vHBuGNUGhL72L9MPLMWZUKNLbvYRZc8ahj4+j2qnd3Kw/cHTLOnz19SacQke88uZ0jH+2KewLG6swwNLWW32aN4enp2eF+2ADxiUgfjB1DeiC0zG/cNbBuOjZmxEIcJrXCJDNp4u7SI05gYvwwcC29VUcKYDcu8h6WA9dnnTH15GhmPrsLzgX+jHefrJBEYeam3UOa6eOx4Ibg/Dt1hh863AFWyZMxfxqn2Fhj3pF26yA4sJZin/Bw4dDXm/97dw5fLdxI6JPnUYjN1cE9e6Ntr6+4HprBUAbsaq8Jp6ZmUlnakTu7Mo4BGyN0w17MQsCuX8j7uTvQAN/tGtctahINjXgGTgS01fvQGToBLSrcRZhY+Zh8x//FZbL/Rsnlr+N9/fVxri3R6Lj448ClRuiU2BdbFm8Hb/dyy0oK0avR8Lex4tPNEfTJ17G4p0XkFV4u6CcNifyeqtwrOIF02JkI0IsRK5Xsd4qRjtDBw+G2OAiMu2I9Vge5klArIvHnT9vnsJRKhKoAAE60wrAs7iqN3/H8UOZsHuyDTwe1TAna2OHhoGvY8WCwah9PxKffn8W2ZKiubgXvwNLw+JQqdswDGgrb16yQeVHqgCJP+PclXt5JaXR60iM2euACVtjcOHQTDTe8zbmR6ajnP60CGqxMUnEKoqk6YeioqT3ZL4yejT++ee2lLJOvDtzwvjxWL9uHWJjY6WRbZEG+MFkBJp4eCArK8tk/bNjEjAUATpTQ5E1u3ZzkR13CvvvO6N7Zy9UL1W+R1EvcBBe9LTF1cR03JbK3sKZXdtw7qEzggYFwKXAFz/EnWzx5ZiBv27cB3QYvYqy537Yjg2rP8byRV/hSMb9UqXSdFNMHwYGBuKtadOk3K8RB/ajZ8+eOHHiBAb07YeW3j4QMY4i2bpYi+VhOgJ+fn6Ij483nQDsmQQMRIBrpgYCa37NZuH306eRBW908HYqe22zihMauNqjUrUqeUkd7l7EiZ0JwCPPo5dfHZX6/yAl7iIAR1SpbKMyel2scfTa0v3RPDw2DnBvWRWb3/oQGx++iNBx+tktLK+39u3Xj+utZvYgPmZvj4tJSWYmFcUhgYoToDOtOEMzbyEX/8WH45Pvj+L09jig5hh41K+iIvNdXEtMwZ16HnCxV3Fm9zJxJbUauk9ogdpif9KfF3DqykOgY1t411Z5bO5dQdypdKBSe7jXu4MzX+eNXp8pbfQqO1NUhn31asBD4JHAjmheXf8TJfJ6q4hvFWuucnxr7JlYab2V8a0qj4IRTl1dXaUNZEboil2QgFEJqHwrGrVfdmY0Ajao5v083nr3KaQNHIS42BjsX7AGmJwfN5r9M1b1H4ldnWch9INhaOXwCJB7C3Ebv8L2JpPwZZ+G0ij0wY2rEBOktTo1U5niBXJSf8WBxPtA65bwsE/BnjJHr6oOMxd3k84gKtsebTo1Re2CqWPDwZHXW+U1Vzm+9deYGGm9VfTcq3cQOnfujBYtW4Lxrfq1hZOTk9SgmG5neJN+2bI10xKgMzUtf+P1XrkGXHz8pX89VXu1a40h817E2bnz8ELfH/DsE41w+9cE2PaeiK9XPIGGj6h6OAf4utdRCZXJxoWo/TiHmugwuAsaZ5zWYvSaP8UryXAXl87+jHT44MXioTqqMhrwXKy3qq65ii95sdt0//79mD1zltTzkOBhEGt9jG+tuCHkrFbZ2Xnb2ireIlsgAfMgQGdqHnYwoRT28Oz3HjY//RouJV/CdTjA5e0GeNy+6KNRuWFTBFQCVAJlgP/ise+7n4HHh2NMkDtyk3eVPXp1UplKzk1HbFQc0ODFvFCd3HSc2PQjstzboFXzxnAuJoMxIHG91fCUxY+TlORkKb2k4XtjDyRgHAJFvzGN0yd7MUMCNlUd4ertCFdNstVuge49HkPYzX+RA8AWd3B59xp8cbEenlkxAl1EqsFkUbn00WsT1Vnem0k4ffwG7AaLUB3gwc3buJWwEZM+24MX+rRCTXtXdGpTEzf+voabj7bHoCBPFIuO1SStXq5zvVUvGEs0UrNmTaSnZ5S4zgskYMkE6Ewt2XrGlN2mIXpNGY+IN9djm/ezcE6PQujiBPT636eY39c9b+pXi9FroS/Nwe3YY/jhfn30bF8dSVsXYMnXf6Lj6FmImtYG9araIjfrMmK2LMWEOXtQ/aVF8Lj7A3ZEnMWtmq3Qd9RIPO1VQ2VXseFhcL1VP4zFOnR0dLR+GmMrJGAmBJib10wMYRli5OBOeiwO7/8JybkN0Drg/9DR06FwDTX3EnaMC0ZYp1BsDWmaN3r9fhp6vhWLXivCsLRfvtOVlP0HMcuDMWjluTzVPadg844J8LUrdLdim+/fe6ehy/j98HjhdbzWry3q5l7AppnvY2ulCdgcPgLVzx7DibhbqOXTBU91dtdrfmBdbaK63rpvb4RUneutJSmKRBoi/pcJ70uy4RXLJUBnarm2M0PJc3En4TtMejMegTPyR68LDqLW5KWYP7RFUUeXcwFrnu+PeRiDD4JO4e0PgOkRoRjtbaei1w0cf38gRq71xccnFiLocTGRkoWY5YMwaOU/aNvLH62aOuPR9J+w+ft0+C35Bh+94IFHVFow1alqPuHdu3Yxn7CKIcSPjqAePXEuPo5vAlLhwlPLJsBpXsu2n5lJb4OqXoOx4ou80evZ3KYYvWFU0dFrvsS5qb/gh9i7qDexC57pUx97lryDsJ3nEOzdEQXu9N4lxP54GfB9pTC2NfcGLv/+F9BgON75aCJ8RVrEnAuom9Af89YdQ8oAD3iqDm5NRIjrrZrByyExaWlpDI/RjIl3LIwAnamFGcz8xbVF1XptETSyrXpRc68j8edEJB/bgxg0wKC2rqjq4oJhA+phXOgWHHm5Xf4IVI5hBTxmtEFDOUJHzi8sbVrKv3j/Jq6mZAN+tWCAvA/q9dDxKtdbiwITb/1JTU2lMy2KhZ8smIAZ/Ia3YHoUXXcCNo/BoWYOHjq2x6BAJyQcPIyz16qjY++esL9/AN/uSUReht57uHLmFOLQDE+3a5iX0hByfmEndG7fpCC/cM6leJy8ZYeWXbxRR3eJTFJDNbZVrB0qLZ9w54AA/MuE9yZ59tipYQhwZGoYrmxVI4FHUdvLH0Hi38hJeJB1DTdxC79ffIAO3pVx6OMv8X3LUWiJSzj4/Uk8tOuLNh6P5bf2Ly6e+RVZaIUnWsv5ge/iUvRRnEMTvNaqPiz116HS4lvFO2jFjl6RP5kHCVgDATpTa7Cixepgg8r2j0u5f2u/MhcdXpmFrIw/EBcTh0uPVIKj/zPo/m8SDu07i+ZBzVCjSip+2vc74DUJbRvJmZRuIfHXC4BdoIrTtVggkuBKWG+1t7fHjRs3LNtQlJ4EVAhwN68KDJ6aI4EHyLp6A3f+jcX332zC7t2HcaH+a/g2bCz8H68Km9tRmNXpJWzp8yVOLOkBB3NUQc8yqeYT/uKzVVLr4qXbzzz7rMXkE5Z39DI8Rs8PB5szGQE6U5OhZ8flIvAgCxl/xOG3v2uhCU5g7TfrsT4yCY+N+w4np3eEPF4tV9sWWkldfKtI1i/e6Wqu+YTFD4KuAV2kF7uL9WMeJGDpBOhMLd2CipY/Fw+yriI54XfEnb2A++2GYmDLGoomoi6+VQB5dfw4tPX1hVirNBfn5eHmLm28kkNlFG04Km/xBOhMLd6EVIAENBNQfX/rkajDBckjBg0egtZtWqNp06aQ3+SiuRXD3Jkwfrw0euYmJMPwZavGJUBnalze7I0ETEpAdb01Yu9eyC9HN8V668wZM6SRsnhpOw8SsHQCdKaWbkHKTwIVICCvt4owle/Wb5BaMtZ6647wcCk8Zv6CBRXQgFVJwDwI0Jmahx0oBQmYnIDqeuuJEycgJ+s31HprZGQk/jd/Pg5FRZlcdwpAAhUlQGdaUYKsTwJWSsDQ660Mj7HSB0ehatGZKtTwVJsEdCWg7/VWMRJu6e3DHb26GoLlzZIAnalZmoVCkYD5E9DHeqsIj9m6IxytW7c2f4UpIQmUQoDOtBQ4vEUCJKAdgfKut4odvX5+fszRqx1mljJjAnSmZmwcikYClkpA2/XWz1d9jn/+uY23pk2zVFUpNwlIBOhM+SCQAAkYnICm9VZHJyc4ODiA4TEGNwE7MDABOlMDA2bzJEACJQkUX29lwvuSjHjFsgjQmVqWvSgtCVg9gZzEMAzoMRfnSmjqjO4Tp2DYM73QzVPZOZhLoOEFkxOw1HcpmxwcBSABEjAMAVvPEGxPiUfEnACg9WxE/JGMpJSLOHNgOurun4NRfadjzYXbhumcrZJAOQnQmZYTHKuRAAkYk4At7D37Ye5Hb6Fl9g9YtjYGdKfG5M++yiJAZ1oWId4nARIwGwK2dd3Qwg7IPpeCqzlmIxYFIQHQmfIhIAESsBgCOVdT8Fs2YNfSDXX57WUxdlOCoHwclWBl6kgClkog8RROJOZN6OZknMSni77AOfji5f5twC1IlmpU65S7snWqRa1IgASsgkD2D5jX6wfMy1fGLvANLNs2FM/61rIK9aiE9RCgM7UeW1ITErA+AmI37/YQeHIOzfpsa2Ua8RG1MoNSHRIgARIgAeMToDM1PnP2SAIkQAIkYGUE6EytzKBUhwSsg8Ad/HPjP+DeP/gnmzEw1mFT69aC6QSt277UjgQsjkDJdIJ2aDlnG7aGNGUsn8VZUzkC05kqx9bUlARIgARIwEAEOM1rILBslgRIgARIQDkE6EyVY2tqSgIkQAIkYCACdKYGAstmSYAESIAElEOAzlQ5tqamJEACJEACBiJAZ2ogsGyWBEiABEhAOQToTJVja2pKAiRAAiRgIAL/D/7Mer2WyIH7AAAAAElFTkSuQmCC" alt></p>
<p>Calculate the distance from Bermuda to Puerto Rico, \({\text{BP}}\).</p>
<p> </p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the area of the Bermuda triangle.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\({\text{B}}{{\text{P}}^2} = {1650^2} + {1500^2} - 2 \times 1650 \times 1500\,\cos \,(57^\circ )\) <em><strong>(M1)(A1)</strong></em></p>
<p>\(1510\,({\text{km}})\,\,\,\left( {1508.81...\,({\text{km}})} \right)\) <em><strong>(A1) (C3)</strong></em></p>
<p><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for substitution in the cosine rule formula, <em><strong>(A1)</strong></em> for correct substitution.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{1}{2} \times 1650 \times 1500 \times \sin \,57^\circ \) <em><strong>(M1)(A1)</strong></em></p>
<p>\( = 1\,040\,000\,({\text{k}}{{\text{m}}^2})\,\,\,\left( {1\,037\,854.82...\,({\text{k}}{{\text{m}}^2})} \right)\) <em><strong>(A1) (C3)</strong></em></p>
<p>Note: Award <em><strong>(M1)</strong></em> for substitution in the area of triangle formula, <em><strong>(A1)</strong></em> for correct substitution.</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Question 6: Non-right angle trigonometry.<br>Instead of using the law of cosines weaker candidates substituted into Pythagoras’ theorem and likewise used \(A = \frac{1}{2}bh\) instead of \(A = \frac{1}{2}ab\sin C\). Those that did select the correct formula almost always made correct substitutions but were not always able to calculate the correct answer.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 6: Non-right angle trigonometry. Instead of using the law of cosines weaker candidates substituted into Pythagoras’ theorem and likewise used \(A = \frac{1}{2}bh\) instead of \(A = \frac{1}{2}ab\sin C\). Those that did select the correct formula almost always made correct substitutions but were not always able to calculate the correct answer.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The fifth term of an arithmetic sequence is 20 and the twelfth term is 41.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Find the common difference. </span></p>
<p><span>(ii) Find the first term of the sequence.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the eighty-fourth term.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the sum of the first 200 terms.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(u_5 = u_1 + 4d = 20\)</span></p>
<p><span>\(u_{12} = u_1 + 11d = 41\) <em><strong>(M1)</strong></em><br></span></p>
<p><em><span><strong>(M1)</strong> for both equations correct</span></em> <span>(or <em><strong>(M1)</strong></em> for \(20 + 7d = 41\))</span></p>
<p><span>\(7d = 21\)</span></p>
<p><span>\(d = 3\) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span>(ii) \(u_1 + 12 = 20\)</span></p>
<p><span>\(u_1 = 8\) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span><em><strong>[3 marks]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(u_{84} = 8 + (84 - 1)3\)</span></p>
<p><span>\(= 257\) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(S_{200} = 100(16 + 199 \times 3)\) <em><strong>(M1)</strong></em></span></p>
<p><span>\( = 61300\) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was generally answered well. Most of the candidates had a good understanding of how to use the formulae for an arithmetic sequence.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was generally answered well. Most of the candidates had a good understanding of how to use the formulae for an arithmetic sequence.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was generally answered well. Most of the candidates had a good understanding of how to use the formulae for an arithmetic sequence.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The second term of an arithmetic sequence is <span class="s1">30</span>. The fifth term is <span class="s1">90</span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>the common difference of the sequence;</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>the first term of the sequence.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The first, second and fifth terms of this arithmetic sequence are the first three terms of a geometric sequence.</p>
<p class="p1">Calculate the seventh term of the <strong>geometric </strong>sequence.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>\({u_1} + d = 30,{\text{ }}{u_1} + 4d = 90,{\text{ }}3d = 90 - 30\;\;\;\)(or equivalent) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for <strong>one </strong>correct equation. Accept a list of at least <span class="s1">5 </span>correct terms.</p>
<p class="p2"> </p>
<p class="p1">\((d = ){\text{ }}20\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1"> </p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\(({u_1} = ){\text{ }}10\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C3)</em></strong></p>
<p class="p1"><strong>Note: </strong>Follow through from (a)(i), irrespective of working shown if \({u_1} = 30 - {\text{ (their }}d)\;\;\;\)<strong>OR</strong>\(\;\;\;{u_1} = 90 - 4 \times {\text{ (their }}d{\text{)}}\)</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(({u_7} = ){\text{ }}10({3^{(7 - 1)}}\;\;\;\)<strong>OR</strong>\(\;\;\;({u_7} = ){\text{ 10}} \times {3^6}\) <strong><em>(M1)(A1)</em>(ft)</strong></p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substituted geometric sequence formula, <strong><em>(A1)</em>(ft) </strong>for their correct substitutions.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>\(10;{\text{ }}30;{\text{ }}90;{\text{ }}270;{\text{ }}810;{\text{ }}2430;{\text{ }}7290\) <strong><em>(M1)(A1)</em>(ft)</strong></p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for a list of at least 5 consecutive terms of a geometric sequence, <strong><em>(A1)</em>(ft) </strong>for terms corresponding to their answers in part (a).</p>
<p> </p>
<p>\( = 7290\) <strong><em>(A1)</em>(ft) <em>(C3)</em></strong></p>
<p><strong>Note: </strong>Follow through from part (a).</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Part (a) was answered correctly by many candidates, but working using equations was rarely seen. A “trial and error” method, based upon a list of terms was the most seen method.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>In part (b) many found the correct answer, but many others did not. Some gave the seventh term of the arithmetic sequence, some gave a term of an incorrect order and some a completely incorrect answer. Finding the correct ratio was the most common problem. Often repeated multiplication was used to find the answer, but also the formula for the nth term of a geometric sequence was used. Several did not use the correct three terms from the question.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The length of a square garden is (<em>x</em> + 1) m. In one of the corners a square of 1 m length is used only for grass. The rest of the garden is only for planting roses and is shaded in the diagram below.</span></p>
<p> </p>
<p style="text-align: center;"><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The area of the shaded region is <em>A</em> .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down an expression for <em>A</em> in terms of <em>x</em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of <em>x</em> given that <em>A</em> = 109.25 m<sup>2</sup>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The owner of the garden puts a fence around the shaded region. Find the length of this fence.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>(<em>x</em> + 1)<sup>2</sup> – 1 <strong><em>or</em></strong> <em>x</em><sup>2</sup> + 2<em>x</em> <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(<em>x</em> + 1)<sup>2</sup> – 1 = 109.25 <em><strong>(M1)</strong></em></span></p>
<p><span><em>x</em><sup>2</sup> + 2<em>x </em></span><span><span>– </span>109.25 = 0 <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for writing an equation consistent with their </span><span>expression in (a) (accept equivalent forms), <em><strong>(M1)</strong></em> for correctly </span><span>removing the brackets.</span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span>(<em>x</em> + 1)<sup>2 </sup></span><span><span>– </span>1 = 109.25 <em><strong>(M1)</strong></em></span></p>
<p><span><em>x</em> + 1 = \(\sqrt {110.25} \) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for writing an equation consistent with their</span> <span>expression in (a) (accept equivalent forms), <em><strong>(M1)</strong></em> for taking the </span><span>square root of both sides.</span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span>(<em>x</em> + 1)<sup>2</sup> – 10.5<sup>2</sup> = 0 <em><strong>(M1)</strong></em></span></p>
<p><span>(<em>x</em> </span><span><span>–</span> 9.5) (<em>x</em> + 11.5) = 0 <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for writing an equation consistent with their </span><span>expression in (a) (accept equivalent forms), <em><strong>(M1)</strong></em> for factorised left </span><span>side of the equation.</span></p>
<p><br><span><em>x</em> = 9.5 <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C3)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from their expression in part (a)</span>.</p>
<p><span>The last mark is lost if<em> x</em> is non positive.</span></p>
<p><span>If the follow through equation is not quadratic award at most</span> <em><strong><span>(M1)(M0)(A1)</span></strong></em><strong><span>(ft)</span></strong><span>.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>4 × (9.5 + 1) = 42 m <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for correct method for finding the length of the fence. Accept equivalent methods.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Some candidates were able to answer this question correctly, but the majority experienced difficulty in finding the correct expression for the area of the shaded region. Those who showed working could then be awarded follow through marks for correctly equating their expressions to the given area and for their found value of <em>x</em>. Many candidates also could not find the perimeter of the shaded region in part c) even though they had found the value of <em>x</em> correctly.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Some candidates were able to answer this question correctly, but the majority experienced difficulty in finding the correct expression for the area of the shaded region. Those who showed working could then be awarded follow through marks for correctly equating their expressions to the given area and for their found value of <em>x</em>. Many candidates also could not find the perimeter of the shaded region in part c) even though they had found the value of <em>x</em> correctly.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Some candidates were able to answer this question correctly, but the majority experienced difficulty in finding the correct expression for the area of the shaded region. Those who showed working could then be awarded follow through marks for correctly equating their expressions to the given area and for their found value of <em>x</em>. Many candidates also could not find the perimeter of the shaded region in part c) even though they had found the value of <em>x</em> correctly.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Factorise the expression \({x^2} - kx\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Hence solve the equation \({x^2} - kx = 0\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The diagram below shows the graph of the function \(f(x) = {x^2} - kx\) for a particular value of \(k\).<br></span></p>
<p><br><span><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAa8AAAESCAIAAADFXc39AAAWlElEQVR4nO3d32tbV4LAcf0bfpJATwkNtOSlzMPYeTFtBkJZiDAtGNZpSJVOl2VZPBup2y6lMCMbFFKKBQURU7mwzKKV2JdlqxqzMGhIxwYt28H2ZRna6U38EEQxAhljLmcfTqw6tiwd6f4659zvhzwUSq1rVfnq3HvOPTclAABCpOI+AADQAjUEACGoIQBI1BAAhKCGACBRQwAQghoCgEQNAUAIaggAEjUEACGoIQBI1BAAhKCGACBRQwAQghpe7sfmndey6Uw2/TcPd34SQgjxfKv4y2vvNZ56MR8ZgDBQw1E85/Fb6atvPd7zhBDi+GDr05u3HjvUELARNRzpZOfhq5nr5Z0TIYQQnlPLl7/txXxMAEJBDUfy9tZvXc3eaRwIIbwfmr8uNp8ex31MAEJBDUf7sXnnteydxoHwejtffNz4gbNkwFbUcLTnW8VfZl8t/+nHbz756D+YPwEsRg1H6+2U38xeWbj7m/LWAefIgM2o4WhHzuN3slfeW987jPtIAISLGo525Dz+zcdbnCID9qOGI3i9nS8+fPwdS2qAJKCGF3m9nc9uXvnH9a8rHz76eXVhv9+P86AAhIwaXuQdbn10LX3rwy+/PThzhlxZq7iuG99RAQgXNVSVTWc2arW4jwJAWKihkk6nk01nFnK5uA8EQFiooZKVUimbzmTTmU6nE/exAAgFNRyv3+/LFN7P5ytrlbgPB0AoqOF47Xb7xuxsNp2R/8DkMmAlajieHBJm0xk5SGy323EfEYDgUcMxut2uvFyYTWeEECul0kqpFPdBAQgeNRyj2WjIqWRZQ5nFbrcb93EBCBg1HGMhl5PLDGUNhRA3ZmdbrVasBwUgeNRwFNd1s+mMvAVlUMPKWuV+Ph/rcQEIHjUcpd1uD8I3qKHrugu5HCfLgB/esz+UF19JpVIzi+u7PS12iaKGqgY1BELV6XRuzM7GfRRhO9pf/21191D0nqzOZeeruzrkkBqqooaIRsIuxRztV2/PLG/qsJ0yNVRFDRENv9N03rPt9eW5VCqV+tXq9k8X/tWnq5vPR/3nh1urD+r70Z26Hu1Xl5bq3/t4vd726lwqlUql7tWfnfg5FGqoihoiAn6XcHnf15demVlc3z38c3X+5TNQz918cG+5vjtu9+LjZ08+X5z/l81nkTwIqPdkdfHRtt/49rZX51Lz1X1/P4YaqqKGiIC/0+Rjt/7+zMyDzcOLVfhpe/Vt5SGY19tdX1oKf3LDczfLlQCy6+1W52eyq9u+RobUUB01RAR8nSb3nqzOZedWn1wc/Xn71fnJhk5H+9W3Q57cONxdrzTdYyGOn23/0de5+bP6Yur68ugrAAqooSpqiLD5O03+aXv1V6nU7er+0YV/9Xxz+ReTps3br84PH2YGwXv2pLw4kzrl6yTXO9x8MDP8F58MNVRFDRG2ylplyrvgDzeXf07L3Op278K/PReLk2f1e6lUKpV6Zan+vSevFc6kUmfPNr3d6vwv/A24FF4lAKcXDd36YurnvsqJlZmluusN1jZeeGdeRg1VUUOE7cbsrI8dkv5aX8wOG2R5h5sPhl9M9L6vL72Smlmuf/35cvV/z3fC2z0/DyOEONlezaYuNTRzo1/FP2+3Oj8zs7x5KA53q/fmlwcT4sdu/f2Z1PXlerO8/KXKNdAga2j3vtDUEKFqt9ty17gp//vDzeWZmWGnw0f71dup4ee88hzzxQDqgueby9eDWAk4+lV8kxcNv+48Kb+/dK62csg8837dVZqoCayGg52vgvqBuqGGCJXPzeJOtlezw2cSRtRwREOFrKH/ZSvjXmWowRLCoc6e8MrUZufmrqdS2cX6X/38CkGODYuFgsV7/1FDhMf3RsJH+9Xblyw/HlvDyyYxho0NpzhTHvMqPvW2V+dSM0vVP//x9Hz5/K9wyczSEEHWUA71bd3OgBoiPPIhEz5+wGUXDcXI64bu5j8vL//D/CWtnGYmeogxr+Lzhw8uGva2V+dezvHxs83V5eX355QX3wQ8i3JjdrbZaAT7MzVBDREevw8gG30qOmROWQhx7NaX79W/P9mvzqeuL2/+3+nqv1MBzCkrvIo/3n51/sUJ8uk6m92/PHlUXt899Nz6vXt190Tm8mt391/LzTGLzwOu4WCnaPtQQ4REXnN3HGfqn3CyvZoddT54bpQnT6vnX9yl13uyOjeTmntQ33/pLNP3ekOlV/Hn5ZWG8nx87sG//dfn86mZuReTy3IZ5rzCLYlB19DiuRRqiJD4HkMc7Vdvj74qp+W9KNoJfr3hSqlULBQC/7Gxo4YIyeBpE1Pydqvzb53frua8n7ZX315UXu7nufWl+bLvzRQME3wNbX2OEjVEGOTTJqb4++K59aWZ29XdvzwpL80/+PrZ2HB57uaD2wpB9Hr79eXFTyPaw0YnodyL4ve7TkvUEGGYftMaeSUu9cpi+Q/jU/jC4X79twr7G365nbwUipBq2Gq1bszOTr+qXkvUEGHwdzceghRKDX0vJdURNUTg/N6Nh0CFtWuDfc92oIYI3Eqp5GuZIQIVVg3ltWE/S6h0Qw0RLIuXoxkqxB29/C6v1ww1RLAsvlXBUCHW0LLblqkhgmXl0gujhbvbq023LVNDBMhxHJvGCnYIt4Y2nQtQQwSoslax8pYto4VbQ3md2I6lNtQQQbFyCZoFQn8uijXfgdQQQbHy9gQLhF5DeX3Edd2wXyhs1BBBWcjlbFpuYY0onplnx1IbaohAyKW4FowP7BNFDe1YakMNEQj7btOyRkTPU7ZgqQ01hH/9fp9tGrQVUQ2bjYa/h+DEjxrCP/k0KOZP9BRRDS1YUkAN4R/zJzqLqIZCiMpaxeiV2NQQPlmzvsJW0dXQ/4PB4kUN4RPzJ5qLroZCiGKhYO5KbGoIPyy4WGS9SGto9AOkqCH8sGAi0XqR1lCYfBWZGsIP9u/SX9Q1NPdBENQQUzP6rCg5oq6hMHYlNjXE1IqFwkqpFPdRYIwYamjoBRRqiOnw/BNTxFBDQyfXqCGms1GrGb3SNjliqKEwcyU2NcQU5I3JrVYr7gPBePHU0MQ9sakhpsCNyQaJp4ZCiJVSyayV2NQQUzB3SVkCxVZDec+mQTfqUUNMigfjmSW2GgrTlh1QQ0zK6FtREyjOGpq1JJUaYiIsrDFOnDUURl1VoYaYiIkLJxIu5hoa9MgUagh1hi6qTbiYayjMuZudGkKdvOGKhTVmib+GpizIooZQZ+jN+AkXfw3lYn39PzrUEIoMuv6Ds+KvoTDktIIaQpFBc4M4S4saGjE8pIZQwYprc2lRQ2HCNl/UECpYcW0uXWooh4c6r0ighhjLdV2z7jfFWbrUUGi/WpUaYiyeEWo0jWqo+TZf1BCjaf4Bxlga1VDoPTykhhhN508vVOhVQ52/XakhRuBWPAvoVUOh8RcsNcQIRqyZxWja1VDb4SE1xGWMWDCLsbSrodB1eEgNcRkGhnbQsYZ6Dg+pIYZiYGgNHWsotBweUkMMZcomTBhL0xpqODykhhiKPRqsoWkNhX7DQ2qIi9i8yyb61lC34SE1xEUMDG2ibw2FZsNDaohzGBhaRusaajU8pIY4h4GhZbSuodBpeEgNcRYDQ/voXkN9FnNRQ5zFwNA+utdQaLPQnxpigIGhlQyooSbDQ2qIAQaGVjKghkKP4SE1hMTA0FZm1FCH4SE1hMTA0FZm1FAI0Wq14v1CpoYQDAytZkwNRdzfydQQ/X6fgaHFTKphvF/L1BDy+jUDQ1uZVEMhxEIut1IqxfLS1DDhdLh4jVAZVkPHceJ6ejc1TDgdFjYgVIbVUAhRLBSKhUL0r0sNk4yBYRKYV0M5POx0OhG/LjVMso1ajYGh9cyroYhpKwdqmFhyL6VWqxX3gSBcRtYwlk8nNUwsfTZSQqiMrKGI45I2NUwmeWVGk002ESpTayivam/UapG9IjVMprhm7RA9U2soIl+MTQ0TKMYVXYiewTUU0S7GpoYJtJDLMTBMDrNrGOVXNzVMGjZoSBqzayiEKBYK0cz3UcNEkRem2aAhUYyvYWSrbahhonAfXgIZX0MR1QeXGiaH/IrlPryksaGG0ay2oYbJsVIqsdw6gWyooTi94O26bngvQQ0TIq4b4RE7S2oowl8lSw0T4n4+z6qaZLKnhq7rhnoHFTVMAvn4nVBPMqAte2ooQt52iRpaL/rbPaEVq2oY6qeZGlqPTQwTzqoaijCnU6ih3cK+0gL92VZDIUSxULifzwf+Y6mh3dirBhbWUH7JB353CjW0GJMnEFbWUIRzdwo1tBWTJ5DsrGG/3w98sy9qaKvKWoXJEwhbayhCuKOAGlqJO08wYG0NxendpkF951NDK7GfKwZsrmGw14OooX3k9WX2c4Vkcw3F6VxhIJtjU0PLsG0XzrG8hiK45YfU0DIhrUuFueyvYbfbvTE7638IQA1twgJDXGR/DUVAH31qaA35BckCQ5yTiBqKIE6LqKE15JPFWGCIc5JSQ//ny9TQDgFOrMEySamh8H2+TA0twDkyRkhQDcXp+fJ0p0jU0AKcI2OEZNXQz9CAGpqOc2SMlqwaCh9/Jaih0ThHxliJq6GY9v5lamg0zpExVhJrKO9fnnS/L2pormajwVprjJXEGgohOp3OpA/BoIaGknuhcz8yxkpoDcXpA9LU9y+hhibq9/v383nuR4aK5NZw0r8n1NBEk37nIcmSW0MhhOu66vOM1NA4U1wPQZIluoZikgU31NAscklNZa0S94HAGEmvoRBipVRSeUgQNTTL/XyeJTWYCDV88YC9sQ/HoIYG2ajVWFKDSVFDIU4XYYy+gEgNTSEvF7ZarbgPBIahhi+02+3RT5KkhkaQlwuDfZQ2EoIa/kw+Zfyy1RjU0Ahy1RSXCzEFavizwQrEoX+XqKH+5PcZlwsxHWr4khHLMqih5uS1DlYXYmrU8LzLrsFTQ52pzIMBo1HDIeSWJ+eWZFNDbclNicaukQJGo4bDXbwCRQ21xUJrBIIaDndxRoUa6omZEwTFmBpm05mIe3Tu/EuHGkb/JmhO3mY+YpVoSIL6H9Hv9+m4PqjhKHKTGznFrEOGdKihPscgJ5FjueckqDdBTtkt5HKtVkth27Efm3dey6Yz2St/33x6LLyDPz1691o6c728c+L/UEANxxr8lYs9AUKnEulwDDFuURPgm+C6rtyEMZvOFAuFdrs9+gKo97SRv5K5Vvz95qNP1/cOAzkGSNRwPJnC2BMgdCqRDscQ447WYbwJnU6nslaRP7myVrn89P/5VvGX2fTr+cYPXrBHkHjUUIn8mMZ+iUefEsV4AP1+Xx5DjJPI4b0J/X6/3W4XCwU5+N2o1S586rzDrY+upd9Zd47COIAkC7iG8lPCH/7wJ6g/F7YiljW8+tbjPcaGwWJsOMEB3M/n413MEfubEPsxyPU0sb8PYRyA4ziD326lVLrsFkPv4JtPisV/euPqteIWVw2DRQ0nOIDR2zpEcwxJruFgaWHs70OAB9DtdjdqtYVcTn7dtlqtUZ8u74fmr4vNp4fO43eyVz7aevo/tUf/+ZQhYkCo4QQHIMbtcxPBMSS2hvLSrRwxxf4+BHUAgxU2G7XamBU23t76ravZNz5qOodCeL2dz26mr94sNpweLQwMNZzgAOQ/yH1uYgli7G9CXMdwNoVxHcNZQR0Aq6+1YkwNY3f20y9XZSdzV9HoS3Rxq67YawgrUUNV5/76JTmIUWLXQkSGGqq6OBghiGEjhYiSKTX0es5//3v53WuvxnZP5tBTs0iD2HO26uW7V958uNML/bUu8g52vizeTGey6as3i1/tHByH/YLDU3h6c2423jmE3rcP33j9buPHeF4d4TCkhic7D1/NZNOZrGY1FNEFsbdTfjObzmTTsdTQO9z6Xf5R+8Dzenu1u1cy195rhLqw49y0yanjp43ffdzY6wl5GDGtQPZ+aL73ejb9GjW0jCE1FOJFDvSroYhwhHiyU74eTw2fbz36vfMiPEfO43ey6Q+aB2H9n7gkhS/z9tZvvRZHDY+fNop/V/70b6mhdaihqtGTmN1uV+7AHOqCifhq+NJRHDQ+yN567ITTIaUU9pzN8rvX79T2oj5T9no7n98tf9s7aNylhtahhqrGLumQC7NDvXVPjxo+3yreCmMDlX6/v1Iq3ZidHbN760HjbkzXDb2Dbz4pfrXX8wQ1tBE1VKWywG0QxJB2Y9aghl5v57O3QrhoOOF3yaHzzWcRXL58yYu74o6FENTQSvrUcDBLcO7P4DNnQA0lpXO9qcRfw963D+98vhP0iMx13cmvMxw5j9+J8vNwslO+fvHzeadxENHrI3T61HAsY2oohNio1bLpTOA7M8dcw95368XyVtBraxzHmWoOyjvc+uhaaJcvx2BsaCNqqGrSW8HkcrlioRDgRHOcNfSebj364jSFXm/vq4+/DGA+V75LlbXKpO+Sd9D+7M6bse3/TA1tZEoNT5+Pk86EurZjhClujB2svAliXuXkoPHBhasHUel9t37n9ZdPEgPYe1leUmg2Gsr/hdwEP5NNZ7JvFNe3nNguGVBDG5lSw/hNt03AYHKA28vOkguSwptuAqZADVX52TRFDoI2arUAj8dcnU4nuCEzEBhqqMrnFlLtdlsmQOGxuTYbzC+x1QV0Qw1V+d9QT64juTE7G8sD0WM3+PW5aAA9UUNVQW0vKgdHK6VSogZHrVaLoTE0Rw1VBbjZsuM4C7lcQuYQut2ufDrwJHPHQAyooapgt57v9/tykFgsFCweLjUbDSZMYApqqCqMB3EMBon2jZss/tVgK2qoKrzHEskB1EIuZ8eJc7fbXSmV5LVRi4e9sA81VBXqQ9q63a5ck1gsFBzHCe+FQtXv95uNhnxAsLm/BRKLGqqK4JGVjuPICQfjmig7KEe4LKCBoaihqsge4GtWEwcdlJcIE7VsCJahhqoifpz52SbqOdoanN0v5HJ0EBaghqoirqHkOM7Z4mgyKdFut2Wp7+fzepYamAI1VBVLDaVut9tsNBZyucFQMZaBWKfTqaxVbszOyhuN9T+LByZCDVXFWMOBsz0qFgqtVivsVc39fv/si66USnG1GAgbNVSlQw0HZKHkaHEhl6usVQIsY7fb7XQ6G7Xa/Xxebq1KBJEE1FCVVjUccF231WrJB2/Kct3P51dKpWaj0W63HccZnchut+s4juM4zUZjo1YrFgqDn1MsFJqNBqfDSA5qqErPGp4l09ZsNCprlbNdU/lzP5+X+Wu329xTjGSihqr0r+FQg9HfUIQPGKCGqgytIQBF1FAVNQTsRg1VUUPAbtRQFTUE7EYNVVFDwG7UUBU1BOxGDVVRQ8Bu1FAVNQTsRg1VUUPAbtRQFTUE7EYNVVFDwG7UUBU1BOxGDVVRQ8Bu1FAVNQTsRg1VUUPAbtRQFTUE7EYNVVFDwG7UUBU1BOxGDVVRQ8Bu1FAVNQTsRg1VUUPAbtRQFTUE7EYNVVFDwG7UUBU1BOxGDVVRQ8Bu1FAVNQTsRg1VUUPAbtRQFTUE7EYNVVFDwG7UUBU1BOxGDVVRQ8Bu1FAVNQTsRg1VUUPAbtRQFTUE7EYNVVFDwG7UUBU1BOxGDVVRQ8Bu1FAVNQTsRg1VUUPAbtRQFTUE7EYNVVFDwG7UUBU1BOxGDVVRQ8Bu1BAAhKCGACBRQwAQghoCgEQNAUAIaggAEjUEACGoIQBI1BAAhKCGACBRQwAQghoCgPT/hGsH2fGJteIAAAAASUVORK5CYII=" alt></span></p>
<p><span>Write down the value of \(k\) for this function.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The diagram below shows the graph of the function \(f(x) = {x^2} - kx\) for a particular value of \(k\).<br></span></p>
<p><br><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Find the minimum value of the function \(y = f(x)\) .</span></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><span>\(x(x - k)\) <em><strong>(A1) (C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(x = 0\) <strong>or</strong> \(x = k\) <em><strong>(A1) (C1)</strong></em></span></p>
<p><span><strong>Note:</strong> Both correct answers only.</span></p>
<p><span><em><strong>[1 mark]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(k = 3\) <em><strong>(A1) (C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{Vertex at }}x = \frac{{ - ( - 3)}}{{2(1)}}\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note: <em>(M1)</em></strong> for correct substitution in formula.</span></p>
<p><br><span>\(x = 1.5\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>\(y = - 2.25\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>\(f'(x) = 2x - 3\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note: <em>(M1)</em></strong> for correct differentiation.</span></p>
<p><br><span>\(x = 1.5\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span><br><span>\(y = - 2.25\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>OR</strong></span></p>
<p><span><em>for finding the midpoint of their 0 and 3</em> <em><strong>(M1)</strong></em></span><br><span>\(x = 1.5\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span><br><span>\(y = - 2.25\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Note: </strong>If final answer is given as \((1.5{\text{, }}{- 2.25})\) award a maximum of <em><strong>(M1)(A1)(A0)</strong></em></span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was poorly answered by all but the best candidates. The links between the parts were not made. The idea of the line of symmetry for the graph was seldom investigated. The “minimum value of the function” was often incorrectly given as a coordinate pair.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was poorly answered by all but the best candidates. The links between the parts were not made. The idea of the line of symmetry for the graph was seldom investigated. The “minimum value of the function” was often incorrectly given as a coordinate pair.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was poorly answered by all but the best candidates. The links between the parts were not made. The idea of the line of symmetry for the graph was seldom investigated. The “minimum value of the function” was often incorrectly given as a coordinate pair.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was poorly answered by all but the best candidates. The links between the parts were not made. The idea of the line of symmetry for the graph was seldom investigated. The “minimum value of the function” was often incorrectly given as a coordinate pair.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Minta deposits <span class="s1">1000 </span>euros in a bank account. The bank pays a nominal annual interest rate of <span class="s1">5</span>%, <strong>compounded quarterly</strong>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the amount of money that Minta will have in the bank after <span class="s1">3 </span>years. Give your answer correct to two decimal places.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Minta will withdraw the money from her bank account when the interest earned is <span class="s1">300 </span>euros.</p>
<p class="p1">Find the time, in years, until Minta withdraws the money from her bank account.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(1000{\left( {1 + \frac{5}{{4 \times 100}}} \right)^{4 \times 3}}\) <strong><em>(M1)(A1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substitution into compound interest formula, <strong><em>(A1) </em></strong>for correct substitution.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>\({\text{N}} = 3\)</p>
<p>\({\text{I}}\% = 5\)</p>
<p>\({\text{PV}} = - 1000\)</p>
<p>\({\text{P/Y}} = 1\)</p>
<p>\({\text{C/Y}} = 4\) <strong><em>(A1)(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for \({\text{C/Y}} = 4\) seen, <strong><em>(M1) </em></strong>for other correct entries.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>\({\text{N}} = 12\)</p>
<p>\({\text{I}}\% = 5\)</p>
<p>\({\text{PV}} = - 1000\)</p>
<p>\({\text{P/Y}} = 4\)</p>
<p>\({\text{C/Y}} = 4\) <strong><em>(A1)(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for \({\text{C/Y}} = 4\) seen, <strong><em>(M1) </em></strong>for other correct entries.</p>
<p> </p>
<p>\( = 1160.75\) (€) <strong><em>(A1) (C3)</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(1000{\left( {1 + \frac{5}{{4 \times 100}}} \right)^{4 \times t}} = 1300\) <strong><em>(M1)(A1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for using the compound interest formula with a variable for time, <strong><em>(A1) </em></strong>for substituting correct values and equating to \(1300\).</p>
<p> </p>
<p><strong>OR</strong></p>
<p>\({\text{I}}\% = 5\)</p>
<p>\({\text{PV}} = \pm 1000\)</p>
<p>\({\text{FV}} = \mp 1300\)</p>
<p>\({\text{P/Y}} = 1\)</p>
<p>\({\text{C/Y}} = 4\) <strong><em>(A1)(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for 1300 seen, <strong><em>(M1) </em></strong>for the other correct entries.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>\({\text{I}}\% = 5\)</p>
<p>\({\text{PV}} = \pm 1000\)</p>
<p>\({\text{FV}} = \mp 1300\)</p>
<p>\({\text{P/Y}} = 4\)</p>
<p>\({\text{C/Y}} = 4\) <strong><em>(A1)(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for 1300 seen, <strong><em>(M1) </em></strong>for the other correct entries.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>Sketch drawn of two appropriate lines which intersect at a point</p>
<p><img src="data:image/png;base64,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" alt></p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for a sketch with a straight line intercepted by appropriate curve, <strong><em>(A1) </em></strong>for a numerical answer in the range \(5.2-5.6\).</p>
<p> </p>
<p>\(t = 5.28{\text{ (years)}}\;\;\;(5.28001 \ldots )\) <strong><em>(A1) (C3)</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><span style="font-size: medium; font-family: times new roman,times;">The tenth term of an arithmetic sequence is 32 and the common difference is –6.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the first term of the sequence.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the 21<sup>st</sup> term of the sequence.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the sum of the first 30 terms of the sequence.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>32 = <em>u</em><sub>1</sub> + (10 − 1) × (−6) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in correct formula. Accept correct alternative methods.</span></p>
<p><br><span><em>u</em><sub>1 </sub>= 86 <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>u</em><sub>21</sub> = 86 + (21 − 1) × (</span><span><span>−</span>6) <em><strong>(M1)</strong></em></span></p>
<p><span><span><em>u</em><sub>21</sub> =</span> </span><span><span>−</span>34 <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in correct formula.</span> <span>Accept correct alternative methods.</span> <span>Award <em><strong>(M1)</strong></em> for a list of at least 5 correct terms seen. </span><span>Follow through from their answer to part (a).</span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span><span><em>u</em><sub>21</sub></span> = 32 + 11 </span><span><span>× </span>(</span><span><span>−</span>6) <em><strong>(M1)</strong></em></span></p>
<p><span><em><span>u</span></em><span><sub>21</sub></span> = </span><span><span>−</span>34 <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({S_{30}} = \frac{{30}}{2}(2 \times 86 + (30 - 1) \times ( - 6))\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for their correct substitution in correct formula. Accept correct alternative methods. For a list award <em><strong>(M1)</strong></em> for the</span> <span>correct addition of at least 10 terms. </span></p>
<p><br><span>\({S_{30}} = -30\) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Follow through from their answer to part (a).</span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was very well answered by most candidates. Correct working was clearly shown. Many candidates used 32 as their first term and many others subtracted 6 rather than multiplied by -6, indicating a lack of attention in their algebraic notation and manipulation.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was very well answered by most candidates. Correct working was clearly shown. Many candidates used 32 as their first term and many others subtracted 6 rather than multiplied by -6, indicating a lack of attention in their algebraic notation and manipulation.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was very well answered by most candidates. Correct working was clearly shown. Many candidates used 32 as their first term and many others subtracted 6 rather than multiplied by -6, indicating a lack of attention in their algebraic notation and manipulation.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The first three terms of a geometric sequence are \({u_1} = 486,{\text{ }}{u_2} = 162,{\text{ }}{u_3} = 54\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(r\), the common ratio of the sequence.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(n\) for which \({u_n} = 2\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the sum of the first 30 terms of the sequence.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{162}}{{486}}\)\(\,\,\,\)<strong>OR</strong>\(\,\,\,\)\(\frac{{54}}{{162}}\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for dividing any \({u_{n + 1}}\) by \({u_n}\).</p>
<p> </p>
<p>\( = \frac{1}{3}{\text{ }}(0.333,{\text{ }}0.333333 \ldots )\) <strong><em>(A1)</em></strong> <strong><em>(C2)</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>\(486{\left( {\frac{1}{3}} \right)^{n - 1}} = 2\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for their correct substitution into geometric sequence formula.</p>
<p> </p>
<p>\(n = 6\) <strong><em>(A1)</em>(ft)</strong> <strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (a).</p>
<p>Award <strong><em>(A1)(A0) </em></strong>for \({u_6} = 2\) or \({u_6}\) with or without working.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\({S_{30}} = \frac{{486\left( {1 - {{\frac{1}{3}}^{30}}} \right)}}{{1 - \frac{1}{3}}}\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution into geometric series formula.</p>
<p> </p>
<p>\( = 729\) <strong><em>(A1)</em>(ft)</strong> <strong><em>(C2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Javier starts training for a running race.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">On the first day he runs 1.5 km. Every day he runs 10 % more than the day before.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the distance he runs on the second day of training.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the <strong>total</strong> distance Javier runs in the first seven days of training.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Javier stops training on the day his total distance exceeds 100 km.</span></p>
<p><span>Calculate the number of days Javier has trained for the running race.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>1.65 (km) or 1650 (m) <em><strong>(A1) </strong> <strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{1.5({{1.1}^7} - 1)}}{{1.1 - 1}}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of candidate’s 10 % into the correct </span><span>formula.</span> <span>Accept a list.</span></p>
<p><br><span>14.2 (km) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{1.5({{1.1}^n} - 1)}}{{1.1 - 1}} > 100\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for setting up their inequality/equation. Accept a list.</span></p>
<p><br><span><em>n</em> = 21.371... <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><em>n</em> = 22 <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C3)</strong></em></span></p>
<p><span><strong>Notes:</strong> Follow through from their values of 1.1 and 1.5 in part (b). The final <em><strong>(A1)</strong></em><strong>(ft)</strong> is for rounding up their answer for <em>n</em> to a whole number of days.</span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Most candidates could answer the first part of this question, although a number found it difficult to find the total distance run after 7 days. Many gave the correct answer of 1.65 km or 1650 m for part (a). <br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">In part (b), stronger candidates answered correctly, however many used a list or the incorrect arithmetic formula. <br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">In part (c), the most common mistake was to use the arithmetic formula. Many candidates rounded their answer down rather than up.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Claudia travels from Buenos Aires to Barcelona. She exchanges 8000 Argentine Pesos (ARS) into Euros (EUR).</p>
<p>The exchange rate is 1 ARS = 0.09819 EUR. The bank charges a 2% commission on the exchange.</p>
</div>
<div class="specification">
<p>When Claudia returns to Buenos Aires she has 85 EUR left and exchanges this money back into ARS. The exchange rate is 1 ARS = 0.08753 EUR. The bank charges \(r\)% commission. The commission charged on this exchange is 14.57 ARS.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the amount of Euros that Claudia receives. Give your answer correct to two decimal places.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(r\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(8000 \times 0.09819 \times 0.98\) <strong><em>(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for multiplying 8000 by 0.09819, <strong><em>(M1) </em></strong>for multiplying by 0.98 (or equivalent).</p>
<p> </p>
<p>769.81 (EUR) <strong><em>(A1)</em></strong> <strong><em>(C3)</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(r\% \times \frac{{85}}{{0.08753}} = 14.57\) <strong><em>(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for dividing 85 by 0.08753, and <strong><em>(M1) </em></strong>for multiplying their \(\frac{{85}}{{0.08753}}\) by \(r\% \) and equating to 14.57.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>\(\frac{{85}}{{0.08753}} = {\text{971.095}} \ldots \) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for dividing 85 by 0.08753.</p>
<p> </p>
<p>\(\frac{{14.57}}{{9.71095 \ldots }}\)\(\,\,\,\)<strong>OR</strong>\(\,\,\,\)\(\frac{{14.57}}{{971.095 \ldots }} \times 100\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for dividing 14.57 by 9.71095… or equivalent.</p>
<p> </p>
<p>\(r = 1.50{\text{ }}(1.50036 \ldots )\) <strong><em>(A1)</em></strong> <strong><em>(C3)</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The first term of an arithmetic sequence is 3 and the sum of the first two terms is 11.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the second term of this sequence.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the common difference of this sequence.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the fourth term of this sequence.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The <em>n</em><sup>th</sup> term is the first term in this sequence which is greater than 1000. Find the value of <em>n</em>.</span></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><span>8 <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>5 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>1</span><span>8</span><em><strong><span> (A1)</span></strong></em><strong><span>(ft)</span></strong><em><strong><span> (C1)</span></strong></em></p>
<p><em><strong><span>[1 mark]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>3 + 5 × (<em>n</em> – 1) > 1000 <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Allow equality sign and equal to 1001</span></p>
<p><br><span><em>n</em> > 200.4 <em><strong>(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Accept <em>n</em> = 200.4 or 5<em>n</em> =1002</span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span><em><strong>(M1)</strong></em> for attempt at listing, <em><strong>(A1)</strong></em> for 998 and 1003 seen. <em><strong>(M1)(A1)</strong></em></span></p>
<p><span><em>n</em> = 201 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from their answer to (b).</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Most candidates achieved at least the first three marks on this question and a significant number gained full marks. Up to five marks could be awarded even to students who did not find correctly the value of the <em>n</em>th term, but showed correct method and attempted to find the value of <em>n</em>. Some candidates lost the last mark for giving a non integer value.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Most candidates achieved at least the first three marks on this question and a significant number gained full marks. Up to five marks could be awarded even to students who did not find correctly the value of the <em>n</em>th term, but showed correct method and attempted to find the value of <em>n</em>. Some candidates lost the last mark for giving a non integer value.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Most candidates achieved at least the first three marks on this question and a significant number gained full marks. Up to five marks could be awarded even to students who did not find correctly the value of the <em>n</em>th term, but showed correct method and attempted to find the value of <em>n</em>. Some candidates lost the last mark for giving a non integer value.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Most candidates achieved at least the first three marks on this question and a significant number gained full marks. Up to five marks could be awarded even to students who did not find correctly the value of the <em>n</em>th term, but showed correct method and attempted to find the value of <em>n</em>. Some candidates lost the last mark for giving a non integer value.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">In a television show there is a transparent box completely filled with identical cubes. Participants have to estimate the number of cubes in the box. The box is 50 cm wide, 100 cm long and 40 cm tall.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the volume of the box.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Joaquin estimates the volume of one cube to be 500 cm<sup>3</sup>. He uses this value to estimate the number of cubes in the box.</span></p>
<p><span>Find Joaquin’s estimated number of cubes in the box.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The actual number of cubes in the box is 350.</span></p>
<p><span>Find the percentage error in Joaquin’s estimated number of cubes in the box.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(50 \times 100 \times 40 = 200\,000{\text{ c}}{{\text{m}}^3}\) <em><strong>(M1)(A1) (C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in the volume formula.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{200\,000}}{{500}} = 400\) <em><strong> (M1)(A1)</strong></em><strong>(ft) </strong><em><strong> (C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for dividing their answer to part (a) by 500.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{400 - 350}}{{350}} \times 100 = 14.3{\text{ }}\% \) <em><strong> (M1)(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span></p>
<p><span><br><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in the percentage error formula.</span></p>
<p><span>Award <em><strong>(A1)</strong></em> for answer, follow through from part (b).</span></p>
<p><span>Accept –14.3 %.</span></p>
<p><span>% sign not necessary.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question proved to be the one that most candidates answered correctly. Many received full marks and the only error seen was incorrect substitution in the percentage error formula.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question proved to be the one that most candidates answered correctly. Many received full marks and the only error seen was incorrect substitution in the percentage error formula.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question proved to be the one that most candidates answered correctly. Many received full marks and the only error seen was incorrect substitution in the percentage error formula.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Pietro arrives in Singapore and, at the airport, changes 800 euros (EUR) to Singapore dollars (SGD).</p>
<p class="p1">The bank rates quoted at the airport for exchanging EUR with SGD are given in the following table. Also given are the rates for exchanging SGD with British pounds (GBP) and US dollars (USD<span class="s1">). There is no commission charged on exchanges.</span></p>
<p class="p1" style="text-align: center;"><span class="s1"><img src="images/Schermafbeelding_2015-12-19_om_17.06.44.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the number of <span class="s1">SGD </span>Pietro receives.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Pietro also has <span class="s1">100 GBP </span>that he wishes to change to <span class="s1">USD </span>for a trip to Cambodia.</p>
<p class="p1">To perform this transaction, the <span class="s1">GBP </span>must first be converted to <span class="s1">SGD </span>and then to <span class="s1">USD</span>.</p>
<p class="p1">Calculate the number of <span class="s1">USD </span>Pietro receives.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(800 \times 1.55\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for multiplication by \(1.55\).</p>
<p class="p2"> </p>
<p class="p1">\( = 1240\) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C2)</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\frac{{100 \times 1.92}}{{1.28}}\) <span class="Apple-converted-space"> </span><strong><em>(A1)(M1)(M1)</em></strong></p>
<p class="p1"><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for multiplication by a GBP rate (\(1.92\)<span class="s1"> </span>or \(2.05\)), <strong><em>(M1) </em></strong>for division by a USD rate (\(1.28\)<span class="s1"> </span>or \(1.15\)), <strong><em>(A1) </em></strong>for two correct rates used.</p>
<p class="p2"> </p>
<p class="p1">\( = 150\) <span class="Apple-converted-space"> </span><strong><em>(A1) (C4)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award a maximum of <strong><em>(A1)</em>(ft)<em>(M1)(M1)(A1)</em>(ft) </strong>for \(\frac{{100 \times 2.05}}{{1.15}}\), if in part (a) a rate of \(1.75\)<span class="s1"> </span>is used.</p>
<p class="p1">Award a maximum of <strong><em>(A1)</em>(ft)<em>(M1)(M1)(A1)</em>(ft) </strong>if division by an EUR rate is seen in part (a) and multiplication by \(1.28\)<span class="s1"> </span>and division by \(1.92\)<span class="s1"> </span>is seen in (b).</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Many candidates lost at least two marks on this question for using an incorrect rate. The difference between “Bank buys” and “Bank sells” was not understood by many candidates. Their use of the table was often not consistent, leading to the candidates losing 4 marks, 2 in part (a) and 2 in part (b). Only very few candidates were confused on when to multiply and when to divide by a conversion rate. It was disappointing to see that so many candidates were not able to apply their knowledge of currency conversion in the real world context where both rates are given and the candidate had to decide which one to use. Methods marks were given out frequently, showing candidates were confident to calculate currency conversion with given rates.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates lost at least two marks on this question for using an incorrect rate. The difference between “Bank buys” and “Bank sells” was not understood by many candidates. Their use of the table was often not consistent, leading to the candidates losing 4 marks, 2 in part (a) and 2 in part (b). Only very few candidates were confused on when to multiply and when to divide by a conversion rate. It was disappointing to see that so many candidates were not able to apply their knowledge of currency conversion in the real world context where both rates are given and the candidate had to decide which one to use. Methods marks were given out frequently, showing candidates were confident to calculate currency conversion with given rates.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The number of apartments in a housing development has been increasing by a constant amount every year.</p>
<p class="p1">At the end of the first year the number of apartments was 150, and at the end of the sixth year the number of apartments was 600.</p>
<p class="p1">The number of apartments, \(y\), can be determined by the equation \(y = mt + n\), where \(t\)<em> </em>is the time, in years.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of \(m\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">State what \(m\) represents <strong>in this context</strong>.</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 class="p1">Find the value of \(n\).</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 class="p1">State what \(n\) represents <strong>in this context</strong>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\frac{{600 - 150}}{{6 - 1}}\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p2"><strong>OR</strong></p>
<p class="p2">\(600 = 150 + (6 - 1)m\) <strong><em>(M1)</em></strong></p>
<p class="p2"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into gradient formula or arithmetic sequence formula.</p>
<p class="p2"> </p>
<p class="p2">\( = 90\) <strong><em>(A1) (C2)</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">the annual rate of growth of the number of apartments <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C1)</em></strong></p>
<p class="p2"><strong>Note: </strong>Do not accept common difference.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(150 = 90 \times (1) + n\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution of their gradient and one of the given points into the equation of a straight line.</p>
<p class="p2"> </p>
<p class="p1">\(n = 60\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C2)</em></strong></p>
<p class="p2"><strong>Note: </strong>Follow through from part (a).</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">the initial number of apartments <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C1)</em></strong></p>
<p class="p2"><strong>Note: </strong>Do not accept “first number in the sequence”.</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><span>Calculate exactly \(\frac{{{{(3 \times 2.1)}^3}}}{{7 \times 1.2}}\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write the answer to part (a) correct to 2 significant figures.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the percentage error when the answer to part (a) is written correct to 2 significant figures.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write your answer to <strong>part (c)</strong> in the form \(a \times {10^k}\) where \(1 \leqslant a < 10{\text{ and }}k \in \mathbb{Z}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(29.7675\) <em><strong>(A1) (C1)</strong></em></span></p>
<p><span><strong>Note: </strong>Accept exact answer only.</span></p>
<p><em><strong><span>[1 mark]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(30\) <em><strong>(A1)</strong></em><strong>(ft) <em>(C1)</em></strong></span></p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{30 - 29.7675}}{{29.7675}} \times 100\% \) <em><strong>(M1)</strong></em></span></p>
<p><span>For correct formula with correct substitution.</span></p>
<p><span>\( = 0.781\% \) <em>accept</em> \(0.78\% \)<em> only if formula seen with </em>\(29.7675\)<em> as denominator</em> <em><strong>(A1)</strong></em><strong>(ft) <em>(C2)</em></strong></span></p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(7.81 \times {10^{ - 1}}\% \) (\(7.81 \times {10^{ - 3}}\) with no percentage sign) <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates gained maximum marks. The common errors were in the initial calculation due to forgetting to use brackets when entering the denominator into the GDC; using 2 decimal places instead of 2 significant figures in part (b); and using the wrong value as the denominator in part (c). Some candidates were still using the old Information booklet with the wrong formula for percentage error. Because examiners believed that the wording was ambiguous the correct answer given to 2 significant figures was awarded full marks for this part.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates gained maximum marks. The common errors were in the initial calculation due to forgetting to use brackets when entering the denominator into the GDC; using 2 decimal places instead of 2 significant figures in part (b); and using the wrong value as the denominator in part (c). Some candidates were still using the old Information booklet with the wrong formula for percentage error. Because examiners believed that the wording was ambiguous the correct answer given to 2 significant figures was awarded full marks for this part.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates gained maximum marks. The common errors were in the initial calculation due to forgetting to use brackets when entering the denominator into the GDC; using 2 decimal places instead of 2 significant figures in part (b); and using the wrong value as the denominator in part (c). Some candidates were still using the old Information booklet with the wrong formula for percentage error. Because examiners believed that the wording was ambiguous the correct answer given to 2 significant figures was awarded full marks for this part.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates gained maximum marks. The common errors were in the initial calculation due to forgetting to use brackets when entering the denominator into the GDC; using 2 decimal places instead of 2 significant figures in part (b); and using the wrong value as the denominator in part (c). Some candidates were still using the old Information booklet with the wrong formula for percentage error. Because examiners believed that the wording was ambiguous the correct answer given to 2 significant figures was awarded full marks for this part.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>For a study, a researcher collected 200 leaves from oak trees. After measuring the lengths of the leaves, in cm, she produced the following cumulative frequency graph.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_17.29.13.png" alt="M17/5/MATSD/SP1/ENG/TZ2/06"></p>
</div>
<div class="specification">
<p>The researcher finds that 10% of the leaves have a length greater than \(k\) cm.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the median length of these leaves.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of leaves with a length less than or equal to 8 cm.</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>Use the graph to find the value of \(k\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Before measuring, the researcher estimated \(k\) to be approximately 9.5 cm. Find the percentage error in her estimate.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>9 (cm) <strong><em>(A1)</em></strong> <strong><em>(C1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>40 (leaves) <strong><em>(A1)</em></strong> <strong><em>(C1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\((200 \times 0.90 = ){\text{ }}180\) or equivalent <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for a horizontal line drawn through the cumulative frequency value of 180 and meeting the curve (or the corresponding vertical line from 10.5 cm).</p>
<p> </p>
<p>\((k = ){\text{ }}10.5{\text{ (cm)}}\) <strong><em>(A1)</em></strong> <strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept an error of ±0.1.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\left| {\frac{{9.5 - 10.5}}{{10.5}}} \right| \times 100\% \) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Award <strong><em>(M1) </em></strong>for their correct substitution into the percentage error formula.</p>
<p> </p>
<p>\({\text{9.52 (% ) }}\left( {{\text{9.52380}} \ldots {\text{ (% )}}} \right)\) <strong><em>(A1)</em>(ft)</strong> <strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Follow through from their answer to part (c)(i).</p>
<p>Award <strong><em>(A1)(A0) </em></strong>for an answer of \( - 9.52\) with or without working.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Shiyun bought a car in 1999. The value of the car \(V\) , in USD, is depreciating according to the exponential model</span><br><span style="font-family: times new roman,times; font-size: medium;">\[V = 25000 \times {1.5^{ - 0.2t}}{\text{, }}t \geqslant 0\]</span><br><span style="font-family: times new roman,times; font-size: medium;">where \(t\) is the time, in years, that Shiyun has owned the car.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of the car when Shiyun bought it.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the value of the car three years after Shiyun bought it. Give your answer correct to <strong>two decimal places</strong>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the time for the car to depreciate to half of its value since Shiyun bought it.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(25000{\text{ USD}}\) <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(25000 \times {1.5^{ - 0.6}}\) <em><strong>(M1)</strong></em></span><br><span>\(19601.32{\text{ USD}}\) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(12500 = 25000 \times {1.5^{ - 0.2t}}\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(M1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <strong><em>(A1)</em>(ft)</strong> for \(12 500\) seen. Follow through from their answer to part (a). Award <em><strong>(M1)</strong></em> for equating their half value to \(25000 \times {1.5^{ - 0.2t}}\) . Allow the use of an inequality.</span></p>
<p><span><strong>OR</strong></span></p>
<p><span>Graphical method (sketch):</span></p>
<p><span><strong><em>(A1)</em>(ft)</strong> for \(y =12 500\) seen on the sketch. Follow through from their answer to part (a). <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span><em><strong>(M1)</strong></em> for the exponent model and an indication of their intersection with their horizontal line. <em><strong>(M1)</strong></em></span></p>
<p><span><span>\(8.55\) </span> <span><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></span></span></p>
<p><span><span><em><strong>[3 marks]<br></strong></em></span></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">A substituted value of \(t = 1\) in part (a) saw many incorrect answers of \(23052.70\) for this part of the question. Part (b) was better attempted with many correct answers seen. Many candidates picked up the first two marks of part (c) equating a correct expression to half their answer found in part (a). Many though did not seem to know the correct process of using their GDC to find the required answer. Much <em>trial and improvement</em> was seen here with varying degrees of success.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">A substituted value of \(t = 1\) in part (a) saw many incorrect answers of \(23052.70\) for this part of the question. Part (b) was better attempted with many correct answers seen. Many candidates picked up the first two marks of part (c) equating a correct expression to half their answer found in part (a). Many though did not seem to know the correct process of using their GDC to find the required answer. Much <em>trial and improvement</em> was seen here with varying degrees of success.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">A substituted value of \(t = 1\) in part (a) saw many incorrect answers of \(23052.70\) for this part of the question. Part (b) was better attempted with many correct answers seen. Many candidates picked up the first two marks of part (c) equating a correct expression to half their answer found in part (a). Many though did not seem to know the correct process of using their GDC to find the required answer. Much <em>trial and improvement</em> was seen here with varying degrees of success.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The fourth term, <em>u</em><sub>4</sub>, of a geometric sequence is 135. The fifth term, <em>u</em><sub>5</sub>, is 101.25 .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the common ratio of the sequence.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find <em>u</em><sub>1</sub>, the first term of the sequence.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the sum of the first 10 terms of the sequence.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{101.25}}{{135}}\) <em><strong>(M1)</strong></em></span></p>
<p><span>\( = \frac{3}{4}(0.75)\) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({u_1}{\left( {\frac{3}{4}} \right)^4} = 101.25\) <em><strong>(M1)</strong></em></span></p>
<p><strong><span>OR</span></strong></p>
<p><span>\({u_1}{\left( {\frac{3}{4}} \right)^3} = 135\) <em><strong>(M1)</strong></em></span></p>
<p><strong><span>OR</span></strong></p>
<p><span>(by list)</span></p>
<p><span><span>\({u_3} = 180,{\text{ }}{u_2} = 240\)</span></span><span> <em><strong>(M1)<br><br></strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for their correct substitution in geometric sequence</span> <span>formula, or stating explicitly </span><span><span>\({u_3}\)</span> and </span><span><span>\({u_2}\)</span>.</span></p>
<p><span><br></span><span><span>\(({u_1} = )320\)</span> <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span><br><br></p>
<p><span><strong>Note:</strong> Follow through from their answer to part (a).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({S_{10}} = \frac{{320\left( {1 - {{\left( {\frac{3}{4}} \right)}^{10}}} \right)}}{{1 - \left( {\frac{3}{4}} \right)}}\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for their correct substitution in geometric series formula. </span></p>
<p><span> Accept a list of all their ten geometric terms.</span></p>
<p><br><span>= 1210 (1207.918...) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from their parts (a) and (b).</span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The weakest candidates erroneously used an arithmetic sequence rather than a geometric sequence as specified in the question.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The weakest candidates erroneously used an arithmetic sequence rather than a geometric sequence as specified in the question.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The weakest candidates erroneously used an arithmetic sequence rather than a geometric sequence as specified in the question.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">A quadratic function \(f:x \mapsto a{x^2} + b\), where \(a\) and \(b \in \mathbb{R}\) and \(x \geqslant 0\), is represented by the mapping diagram.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><br><span style="font-family: 'times new roman', times; font-size: medium;"><img src="images/Schermafbeelding_2014-09-03_om_08.19.32.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using the mapping diagram, write down two equations in terms of \(a\) and \(b\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Solve the equations to find the value of</span></p>
<p><span>(i) \(a\);</span></p>
<p><span>(ii) \(b\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of \(c\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(a{(1)^2} + b = - 9\) <strong><em>(A1)</em></strong></span></p>
<p><span>\(a{(3)^2} + b = 119\) <strong><em>(A1) (C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Accept equivalent forms of the equations.</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(a = 16\) <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span>(ii) \(b = - 25\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Follow through from part (a) irrespective of whether working is seen.</span></p>
<p><span> If working is seen follow through from part (i) to part (ii).</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(16{c^2} - 25 = 171\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct quadratic with their \(a\) and \(b\) substituted.</span></p>
<p> </p>
<p><span>\(c = 3.5\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Accept \(x\) instead of \(c\).</span></p>
<p><span> Follow through from part (b).</span></p>
<p><span> Award <strong><em>(A1) </em></strong>only, for an answer of \( \pm 3.5\) with or without working.</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was answered reasonably well with many candidates able to write down the two equations and solve them for a and b. Errors such as mistaking the equation given for \(3{a^2} + b = 119\) meant that marks were lost even though the candidates appeared to know what they needed to do. Most candidates who were able to set up the equation in part (c) solved it correctly. Follow through marks were awarded to many candidates for correct working with their substituted values from part (b).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was answered reasonably well with many candidates able to write down the two equations and solve them for a and b. Errors such as mistaking the equation given for \(3{a^2} + b = 119\) meant that marks were lost even though the candidates appeared to know what they needed to do. Most candidates who were able to set up the equation in part (c) solved it correctly. Follow through marks were awarded to many candidates for correct working with their substituted values from part (b).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was answered reasonably well with many candidates able to write down the two equations and solve them for a and b. Errors such as mistaking the equation given for \(3{a^2} + b = 119\) meant that marks were lost even though the candidates appeared to know what they needed to do. Most candidates who were able to set up the equation in part (c) solved it correctly. Follow through marks were awarded to many candidates for correct working with their substituted values from part (b).</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The planet Earth takes one year to revolve around the Sun. Assume that a year is 365 days and the path of the Earth around the Sun is the circumference of a circle of radius \(150000000{\text{ km}}\).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img 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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the distance travelled by the Earth in <strong>one day</strong>.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Give your answer to part (a) in the form \(a \times {10^k}\) where \(1 \leqslant a \leqslant 10\) and \(k \in \mathbb{Z}\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(2\pi \frac{{150000000}}{{365}}\) <em><strong>(M1)(A1)(M1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for substitution in correct formula for circumference of circle.</span></p>
<p><span>Award <em><strong>(A1)</strong></em> for correct substitution.</span></p>
<p><span>Award <em><strong>(M1)</strong></em> for dividing their perimeter by \(365\).</span></p>
<p><span>Award <em><strong>(M0)(A0)(M1)</strong></em> for \(\frac{{150000000}}{{365}}\) .</span></p>
<p><span> </span></p>
<p><span>\(2580000{\text{ km}}\) <em><strong>(A1)</strong></em> <em><strong>(C4)</strong></em></span></p>
<p><span><em><strong>[4 marks]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(2.58 \times {10^6}\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <strong><em>(A1)</em>(ft)</strong> for \(2.58\), <strong><em>(A1)</em>(ft)</strong> for \({10^6}\) . </span><span>Follow through from their answer to part (a).</span> <span>The follow through for the index should be dependent not only on the answer to part (a), but also on the value of their mantissa.</span> <span>No <em><strong>(AP)</strong></em> penalty for first <em><strong>(A1)</strong></em> provided their value is to 3 sf or is all their digits from part (a).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">A significant number of candidates simply divided \(150 000 000\) by \(365\) and consequently lost all but one method mark in part (a). Presumably these candidates assumed that the given value was the circumference rather than the radius. <br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">A significant number of candidates simply divided \(150 000 000\) by \(365\) and consequently lost all but one method mark in part (a). Presumably these candidates assumed that the given value was the circumference rather than the radius. Recovery in part (b) did, however, result in many getting both marks here. It was noted on some answers to part (b) that the index power was negative rather than positive suggesting a misunderstanding by candidates of standard form.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Albena travels to Bulgaria on a business trip. She is paid 3550 Bulgarian levs (BGN) at the end of her trip. She converts all her BGN into euros (EUR), at an exchange bureau that sells 1 EUR for 1.95 BGN and charges 3 % commission.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the amount that Albena receives in EUR.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">At the airport shop, Albena buys chocolates that cost 34.50 BGN. She uses 20 EUR to pay for the chocolates but receives her change in BGN. The shop’s exchange rate is 1 EUR = 1.90 BGN.</p>
<p class="p1">Find how many BGN she receives as change.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\frac{{0.97 \times 3550}}{{1.95}}\) <span class="Apple-converted-space"> </span><strong><em>(M1)(M1)(M1)</em></strong></p>
<p class="p2"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for \(0.97\) seen, <strong><em>(M1) </em></strong>for \(0.97 \times 3550\), <strong><em>(M1) </em></strong>for division by \(1.95\).</p>
<p class="p2"> </p>
<p class="p1"><strong>OR</strong></p>
<p class="p2">\((3550 - 0.03 \times 3550) \times \frac{1}{{1.95}}\) <strong><em>(M1)(M1)(M1)</em></strong></p>
<p class="p2"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for \(0.03 \times 3550\) seen, <strong><em>(M1) </em></strong>for subtracting \(0.03 \times 3550\) from \(3550\), <strong><em>(M1) </em></strong>for division by \(1.95\).</p>
<p class="p2"> </p>
<p class="p2">\( = 1765.90{\text{ (EUR)}}\) <strong><em>(A1) (C4)</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(20 \times 1.90 - 34.50\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for subtraction of \(34.50\) from their product of \(20 \times 1.90\).</p>
<p class="p2"> </p>
<p class="p1">\( = 3.50\,\,\,{\text{(BGN)}}\) <strong><em>(A1) (C2)</em></strong></p>
<p class="p2"><strong>Notes: </strong>Award at most <strong><em>(M1)(A0) </em></strong>for an answer of \(4\), but only if working seen.</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A concert choir is arranged, per row, according to an arithmetic sequence. There are 20 singers in the fourth row and 32 singers in the eighth row.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the common difference of this arithmetic sequence.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>There are 10 rows in the choir and 11 singers in the first row.</span></p>
<p><span>Find the <strong>total</strong> number of singers in the choir.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>20 = <em>u</em><sub>1</sub> + 3<em>d</em> <em><strong> (A1)</strong></em></span></p>
<p><span>32 = <em>u</em><sub>1</sub> + 7<em>d</em> <em><strong> (A1)</strong></em></span></p>
<p><span> </span></p>
<p><span><strong>Note:</strong> Award<em><strong> (A1)</strong> </em>for each equation, <em><strong>(A1)</strong></em> for correct answer.</span></p>
<p><span> </span></p>
<p><strong><span>OR</span></strong></p>
<p><span>\(d = \frac{{32 - 20}}{4}\) </span><em><strong><span> (A1)(A1)</span></strong></em></p>
<p><span> </span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong> </em>for numerator,<em><strong> (A1)</strong></em> for denominator.<br></span></p>
<p><span> </span></p>
<p><span><em>d</em> = 3 <em><strong>(A1) (C3)</strong></em></span><em><strong><span><br></span></strong></em></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{10}}{2}(2 \times 11 + 9 \times 3)\) <em><strong>or</strong></em> \(\frac{{10}}{2}(11 + 38)\)</span><span> <em><strong> </strong></em></span><em><strong><span>(M1)(A1)</span></strong></em><strong><span>(ft)</span></strong></p>
<p><span> </span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong> </em>for correct substituted formula,<em><strong> (A1)</strong></em> for correct</span> <span>substitution, follow through from their answer to part (a).</span></p>
<p><span> </span></p>
<p><strong><span>OR</span></strong></p>
<p><span>11 + 14 + ... + 38 <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong> </strong></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for attempt at the sum of a list,<strong><em> (A1)</em>(ft)</strong> for all</span> <span>correct numbers, follow through from their answer to part (a).</span></p>
<p><span> </span></p>
<p><span>= 245 <em><strong>(A1)</strong></em><strong>(ft) </strong><em><strong> (C3)</strong></em></span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was very well answered with most candidates finding the common difference and the total number of singers. Most candidates used the given formulae, rather than making lists. A common mistake was to find the number of singers in the back row, rather than find the total number of singers in the choir.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was very well answered with most candidates finding the common difference and the total number of singers. Most candidates used the given formulae, rather than making lists. A common mistake was to find the number of singers in the back row, rather than find the total number of singers in the choir.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A building company has many rectangular construction sites, of varying widths, along a road.</p>
<p class="p1">The area, \(A\), of each site is given by the function</p>
<p class="p1">\[A(x) = x(200 - x)\]</p>
<p class="p1">where \(x\) is the <strong>width </strong>of the site in metres and \(20 \leqslant x \leqslant 180\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Site <span class="s1">S </span>has a width of \(20\)<span class="s1"> m</span>. Write down the area of <span class="s1">S</span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Site <span class="s1">T </span>has the same area as site <span class="s1">S</span>, but a different width. Find the width of <span class="s1">T</span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">When the width of the construction site is \(b\) metres, the site has a maximum area.</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>Write down the value of \(b\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Write down the maximum area.</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 class="p1">The range of \(A(x)\) is \(m \leqslant A(x) \leqslant n\).</p>
<p class="p1">Hence write down the value of \(m\) and of \(n\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(3600{\text{ (}}{{\text{m}}^2})\) <span class="Apple-converted-space"> </span><strong><em>(A1)(C1)</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(x(200 - x) = 3600\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for setting up an equation, equating to their \(3600\).</p>
<p class="p2"> </p>
<p class="p1">\(180{\text{ (m)}}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C2)</em></strong></p>
<p class="p1"><strong>Note: </strong>Follow through from their answer to part (a).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>\(100{\text{ (m)}}\) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C1)</em></strong></p>
<p class="p1"> </p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\(10\,000{\text{ (}}{{\text{m}}^2})\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(C1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Follow through from their answer to part (c)(i).</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(m = 3600\;\;\;\)<strong>and</strong>\(\;\;\;n = 10\,000\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C1)</em></strong></p>
<p class="p1"><strong>Notes:<span class="Apple-converted-space"> </span></strong>Follow through from part (a) and part (c)(ii), but only if their \(m\) is less than their \(n\). Accept the answer \(3600 \leqslant A \leqslant 10\,000\).</p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The exchange rates between the British pound (GBP) and the United States dollar (USD) and between the USD and the Euro (EUR) are given below.</span></p>
<p style="text-align: center;"><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the exchange rate between GBP and EUR in the form 1 GBP = <em>k</em> EUR,</span> <span>where <em>k</em> is a constant. Give your answer correct to <strong>two decimal places</strong>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Isabella changes 400 USD into Euros and is charged 2 % commission.</span></p>
<p><span>Calculate how many Euros she receives. Give your answer correct to <strong>two decimal places</strong>.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><em>k</em> = 2.034 × 0.632 <em><strong>(M1)</strong></em></span></p>
<p><span>= 1.29 (1 GBP = 1.29 EUR) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Accept 1.29 only</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong><span>Financial penalty (FP) applies in part (b).</span></strong></em></p>
<p><span> </span></p>
<p><span>400 × 0.632 <em><strong>(M1)</strong></em></span></p>
<p><span>= 252.80 EUR</span><span><span> </span><em><strong>(A1)</strong></em></span></p>
<p><span>2 % of 252.80 = 5.06 EUR</span><span><span> </span><em><strong>(A1)</strong></em></span></p>
<p><span><em><strong>(FP)</strong></em> She receives 247.74 EUR</span><span><span> </span><em><strong>(A1)</strong></em></span></p>
<p><strong><span>OR</span></strong></p>
<p><span><em><strong>(FP)</strong></em> 0.98 </span><span><span>×</span> 252.80 = 247.74 EUR</span><span><span> </span><em><strong>(A1)(A1)</strong></em></span><span><span> </span><em><strong>(C4)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Accept <em><strong>(A1)</strong></em> for 0.98 seen.</span></p>
<p><span> </span></p>
<p><em><strong><span>[4 marks]</span></strong></em></p>
<p><span> </span></p>
<p> </p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Most students gained full marks on this question. However, some students found the required format of the answer in part (a) confusing.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Most students gained full marks on this question. However, some students found the required format of the answer in part (a) confusing.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider <em>c</em> = 5200 and <em>d</em> = 0.0000037.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of <em>r</em> = <em>c </em></span><span><span>× </span><em>d</em>.</span></p>
<p><span> </span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down your value of <em>r</em> in the form </span><span><span><em>a</em> × </span>10<em><sup>k</sup></em>, where 1 </span><span><span>≤ </span></span><span><span><span><em>a</em> < </span></span>10 and \(k \in \mathbb{Z}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Consider the following statements about <em>c</em>, <em>d</em> and <em>r</em>. Only <strong>three</strong> of these statements are true.</span></p>
<p><span>Circle the true statements.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><em>r</em> = 0.01924 <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><span><strong>Note:</strong> Accept 0.0192 and 0.019</span></p>
<p><span><em><strong>[1 mark]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>r</em> = 1.924 × 10<sup>−2</sup> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for 1.924, <em><strong>(A1)</strong></em> for 10<sup>−2</sup></span>. <span>Accept 1.92 and 1.9</span>. <span>Follow through from their part (a).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span> <em><strong>(A1)(A1)(A1) </strong> <strong>(C3)</strong></em></span></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for each true statement circled.</span> <span>Do not follow through from part (a).</span> <span>Award <em><strong>(A1)(A1)(A0)</strong></em> if 1 extra term seen. </span><span>Award <em><strong>(A1)(A0)(A0)</strong></em> if 2 extra terms seen.</span> <span>Award <em><strong>(A0)(A0)(A0)</strong></em> if all terms circled.</span> <span>Accept other indications of the correct statements i.e. highlighted or ticks.</span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates could find the value of <em>r</em> and give it in standard form, although some did not give it to the correct degree of accuracy. Some candidates gave a positive index and others used calculator notation rather than standard form. <br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates could find the value of <em>r</em> and give it in standard form, although some did not give it to the correct degree of accuracy. Some candidates gave a positive index and others used calculator notation rather than standard form. <br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">There were a number of candidates who were unable to find the three true statements about set notation.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The average radius of the orbit of the Earth around the Sun is 150 million kilometres.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><br><img src="images/Schermafbeelding_2014-09-02_om_14.06.16.png" alt></span></p>
</div>
<div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The average radius of the orbit of the Earth around the Sun is 150 million kilometres.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><br><img src="images/Schermafbeelding_2014-09-02_om_14.06.16_1.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down this radius, in kilometres, in the form \(a \times {10^k}\), where \(1 \leqslant a < 10,{\text{ }}k \in \mathbb{Z}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The Earth travels around the Sun in one orbit. It takes one year for the Earth to complete one orbit.</span></p>
<p><span>Calculate the distance, in kilometres, the Earth travels around the Sun in one orbit, assuming that the orbit is a circle.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Today is Anna’s 17th birthday.</span></p>
<p><span>Calculate the total distance that Anna has travelled around the Sun, since she was born.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(1.5 \times {10^8}{\text{ (km)}}\) <strong><em>(A2) (C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(A2) </em></strong>for the correct answer.</span></p>
<p><span> Award <strong><em>(A1)(A0) </em></strong>for 1.5 and an incorrect index.</span></p>
<p><span> Award <strong><em>(A0)(A0) </em></strong>for answers of the form \(15 \times {10^7}\).</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(2\pi 1.5 \times {10^8}\) <strong><em>(M1)</em></strong></span></p>
<p><span>\( = 942\,000\,000{\text{ (km) (942}}\,{\text{477}}\,{\text{796.1}} \ldots {\text{, }}3 \times {10^8}\pi ,{\text{ }}9.42 \times {10^8})\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into correct formula. Follow through from part (a).</span></p>
<p><span> Do not accept calculator notation \(9.42{\text{E}}8\).</span></p>
<p><span> Do not accept use of \(\frac{{22}}{7}\) or\( 3.14\) for \(\pi\).</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(17 \times 942\,000\,000\) <strong><em>(M1)</em></strong></span></p>
<p><span>\( = 1.60 \times {10^{10}}{\text{ (km) }}\left( {{\text{1.60221}} \ldots \times {{10}^{10}}{\text{, 1.6014}} \times {{10}^{10}},{\text{ 16}}\,{\text{022}}\,{\text{122}}\,{\text{530, }}(5.1 \times {{10}^9})\pi } \right)\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Follow through from part (b).</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A function <em>f</em> (<em>x</em>) = <em>p</em>×2<em><sup>x</sup></em> + <em>q</em> is defined by the mapping diagram below.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of</span></p>
<p><span>(i) <em>p</em> ;</span></p>
<p><span>(ii) <em>q</em> .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of <em>r </em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of <em>s </em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>(i) 2<em>p</em> + <em>q</em> = 11 and 4<em>p</em> + <em>q</em> = 17 <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for either two correct equations or a correct equation in one unknown equivalent to 2<em>p</em> = 6 .</span></p>
<p> </p>
<p><span><em>p</em> = 3 <em><strong>(A1)</strong></em></span></p>
<p> </p>
<p><span>(ii) <em>q</em> = 5 <em><strong>(A1)</strong> <strong>(C3)</strong></em></span></p>
<p><span><strong>Notes:</strong> If only one value of <em>p</em> and <em>q</em> is correct and no working shown, award <em><strong>(M0)(A1)(A0)</strong></em>.</span></p>
<p><span> </span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>r</em> = 8 <strong><em>(A1)</em>(ft)</strong> <em><strong>(C1)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their answers for <em>p</em> and <em>q</em> irrespective of whether working is seen.</span></p>
<p><span><em><strong>[1 mark]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>3 × 2<em><sup>s</sup></em> + 5 = 197 <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for setting the correct equation.</span></p>
<p> </p>
<p><span><em>s</em> = 6 <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their values of <em>p</em> and <em>q</em>.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Candidates both understood how to interpret a mapping diagram correctly and did very well on this question or the question was very poorly answered or not answered at all. Writing down two simultaneous equations in part (a) proved to be elusive to many and this prevented further work on this question. Candidates who were able to find values of <em>p</em> and <em>q</em> (correct or otherwise) invariably made a good attempt at finding the value of <em>s</em> in part (c).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Candidates both understood how to interpret a mapping diagram correctly and did very well on this question or the question was very poorly answered or not answered at all. Writing down two simultaneous equations in part (a) proved to be elusive to many and this prevented further work on this question. Candidates who were able to find values of <em>p</em> and <em>q</em> (correct or otherwise) invariably made a good attempt at finding the value of <em>s</em> in part (c).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Candidates both understood how to interpret a mapping diagram correctly and did very well on this question or the question was very poorly answered or not answered at all. Writing down two simultaneous equations in part (a) proved to be elusive to many and this prevented further work on this question. Candidates who were able to find values of <em>p</em> and <em>q</em> (correct or otherwise) invariably made a good attempt at finding the value of <em>s</em> in part (c).</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Given the arithmetic sequence: \({u_1} = 124{\text{, }}{u_2} = 117{\text{, }}{u_3} = 110{\text{, }}{u_4} = 103, \ldots \)</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the common difference of the sequence.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the sum of the first \(50\) terms of the sequence.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>\({u_k}\) is the first term in the sequence which is negative. </span></p>
<p><span>Find the value of \(k\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(d = - 7\) <em><strong>(A1) (C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({S_{50}} = \frac{{50}}{2}(2(124) + 49( - 7))\) <em><strong>(M1)<br></strong></em><strong> <br></strong></span></p>
<p><span><strong>Note:</strong> <em><strong>(M1)</strong></em> for correct substitution.</span></p>
<p><span><br>\( = - 2375\) <em><strong>(A1)</strong></em><strong>(ft) <em>(C2)</em></strong></span></p>
<p><span><strong><em>[2 marks]<br></em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(124 - 7(k - 1) < 0\) <em><strong>(</strong><strong>M1)</strong></em></span></p>
<p><span>\(k > 18.7\) <em>or \(18.7\) seen</em> <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span>\(k = 19\) <em><strong>(A1)</strong></em><strong>(ft) <em>(C3)</em><br></strong></span></p>
<p><span><strong>Note: <em>(M1)</em></strong> for correct inequality or equation seen or for list of values seen or for use of trial and error.</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(a) Again, the omission of the negative sign was a too common fault.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This was generally well attempted.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The common misconception was confusion between \(k\) and the value of the \(k\)<sup>th</sup> term. Close reading of this part was required from the candidates.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A ladder is standing on horizontal ground and leaning against a vertical wall. The length of the ladder is \(4.5\) metres. The distance between the bottom of the ladder and the base of the wall is \(2.2\) metres.</p>
<p>Use the above information to sketch a labelled diagram showing the ground, the ladder and the wall.</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>Calculate the distance between the top of the ladder and the base of the wall.</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>Calculate the <strong>obtuse</strong> angle made by the ladder with the ground.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><img 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" alt></p>
<p><em><strong>(A1) (C1)</strong></em></p>
<p><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for drawing an approximately right angled triangle, with correct labelling of the distances \(4.5\,({\text{m}})\) and \(2.2\,({\text{m}})\).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\sqrt {\,{{4.5}^2} - {{2.2}^2}} \,\,\,({\text{accept eqivalent }}eg\,\,{d^2} + {2.2^2} = {4.5^2})\) <em><strong>(M1)</strong></em></p>
<p>\( = 3.93\,({\text{m}})\,\,\,\left( {\sqrt {\,15.41} \,({\text{m}}),\,\,3.92555...\,({\text{m}})} \right)\) <em><strong>(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> Award<em><strong> (M1)</strong></em> for a correct substitution in the Pythagoras formula.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(180^\circ - {\cos ^{ - 1}}\left( {\frac{{2.2}}{{4.5}}} \right)\)<em> <strong>(M1)(M1)</strong></em></p>
<p><strong>OR</strong></p>
<p>\(180^\circ - {\tan ^{ - 1}}\left( {\frac{{3.92555...}}{{2.2}}} \right)\)<em> <strong>(M1)(M1)</strong></em></p>
<p><strong>OR</strong></p>
<p>\(180^\circ - {\sin ^{ - 1}}\left( {\frac{{3.92555...}}{{4.5}}} \right)\)<em> <strong>(M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for a correct substitution in the correct trigonometric ratio.<br>Award <em><strong>(M1)</strong></em> for subtraction from \(180^\circ \) (this may be implied if the sum of their inverse of the trigonometric ratio and their final answer equals \(180\)).</p>
<p>\( = 119^\circ \,\,\,(119.267...^\circ )\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></p>
<p><strong>Note:</strong> Follow through from their part (b) if cosine is not used. Accept \(119.239...\) or \(119.151...\) from use of \(3\) sf values.</p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Question 3: Right angle trigonometry.<br>Candidates sketched the ladder leaning against the wall and recognized that Pythagoras’ theorem was needed to find the distance between the top of the ladder and the base of the wall (but not always correctly). Although it was a right triangle a number of the candidates used the law of sines (instead of Pythagoras’ theorem) and law of cosines (instead of a trigonometry ratio). Many candidates failed to find the obtuse angle made by the ladder with the ground even though the word obtuse was in bold type in the question.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 3: Right angle trigonometry.<br>Candidates sketched the ladder leaning against the wall and recognized that Pythagoras’ theorem was needed to find the distance between the top of the ladder and the base of the wall (but not always correctly). Although it was a right triangle a number of the candidates used the law of sines (instead of Pythagoras’ theorem) and law of cosines (instead of a trigonometry ratio). Many candidates failed to find the obtuse angle made by the ladder with the ground even though the word obtuse was in bold type in the question.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 3: Right angle trigonometry.<br>Candidates sketched the ladder leaning against the wall and recognized that Pythagoras’ theorem was needed to find the distance between the top of the ladder and the base of the wall (but not always correctly). Although it was a right triangle a number of the candidates used the law of sines (instead of Pythagoras’ theorem) and law of cosines (instead of a trigonometry ratio). Many candidates failed to find the obtuse angle made by the ladder with the ground even though the word obtuse was in bold type in the question.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Gabriella purchases a new car.</p>
<p class="p1">The car’s value in dollars, \(V\), is modelled by the function</p>
<p class="p1">\[V(t) = 12870 - k{(1.1)^t},{\text{ }}t \geqslant 0\]</p>
<p class="p1">where \(t\) is the number of years since the car was purchased and \(k\) is a constant.</p>
</div>
<div class="specification">
<p class="p1">After two years, the car’s value is <span class="s1">$9143.20</span>.</p>
</div>
<div class="specification">
<p class="p1">This model is defined for \(0 \leqslant t \leqslant n\). At \(n\) years the car’s value will be zero dollars.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down, and simplify, an expression for the car’s value when Gabriella <span class="s1">purchased it.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of \(k\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of \(n\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(12870 - k{(1.1)^0}\) </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for correct substitution into \(V(t)\).</p>
<p class="p2"> </p>
<p class="p3"><span class="Apple-converted-space">\( = 12870 - k\) </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C2)</em></strong></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Accept \(12870 - 3080\) <strong>OR</strong> 9790 for a final answer.</p>
<p class="p2"> </p>
<p class="p4"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(9143.20 = 12870 - k{(1.1)^2}\) </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for correct substitution into \(V(t)\).</p>
<p class="p2"> </p>
<p class="p3"><span class="Apple-converted-space">\((k = ){\text{ }}3080\) </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C2)</em></strong></p>
<p class="p4"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(12870 - 3080{(1.1)^n} = 0\) </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for correct substitution into \(V(t)\).</p>
<p class="p2"> </p>
<p class="p3"><strong>OR</strong></p>
<p class="p3"><img src="images/Schermafbeelding_2017-03-07_om_07.33.35.png" alt="N16/5/MATSD/SP1/ENG/TZ0/15.c/M"> <strong><em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for a correctly shaped curve with some indication of scale on the vertical axis.</p>
<p class="p2"> </p>
<p class="p3"><span class="Apple-converted-space">\((n = ){\text{ }}15.0{\text{ }}(15.0033 \ldots )\) </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C2)</em></strong></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Follow through from part (b).</p>
<p class="p2"> </p>
<p class="p3"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The following Venn diagram shows the relationship between the sets of numbers</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\[\mathbb{N},{\text{ }}\mathbb{Z}{\text{, }}\mathbb{Q}{\text{ and }}\mathbb{R}{\text{.}}\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The number –3 belongs to the set of \(\mathbb{Z}{\text{, }}\mathbb{Q}\) and \(\mathbb{R}\), but not \(\mathbb{N}\), and is placed in the appropriate position on the Venn diagram as an example.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><br><img src="images/Schermafbeelding_2014-09-02_om_14.14.57.png" alt><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Write down the following numbers in the appropriate place in the Venn diagram.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>4</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>\(\frac{1}{3}\)</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>\(\pi \)</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>\(0.38\)</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>\(\sqrt 5 \)</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>\(-0.25\)</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><span><br><img src="images/Schermafbeelding_2014-09-02_om_14.19.00.png" alt> <strong><em>(A1)(A1)(A1)(A1)(A1)(A1) (C6)</em></strong></span></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for each number correctly placed.</span></p>
<p><span> Award <strong><em>(A0) </em></strong>for any entry in more than one region.</span></p>
<p> </p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span><br><img src="images/Schermafbeelding_2014-09-02_om_14.19.00_2.png" alt> <strong><em>(A1)(A1)(A1)(A1)(A1)(A1) (C6)</em></strong></span></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for each number correctly placed.</span></p>
<p><span> Award <strong><em>(A0) </em></strong>for any entry in more than one region.</span></p>
<p> </p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span><br><img src="images/Schermafbeelding_2014-09-02_om_14.19.00_1.png" alt> <strong><em>(A1)(A1)(A1)(A1)(A1)(A1) (C6)</em></strong></span></span></p>
<p><span> </span></p>
<p><span><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for each number correctly placed.</span></p>
<p><span> Award <strong><em>(A0) </em></strong>for any entry in more than one region.</span></p>
<p><span> </span></p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span><br><img src="images/Schermafbeelding_2014-09-02_om_14.19.00_3.png" alt> <strong><em>(A1)(A1)(A1)(A1)(A1)(A1) (C6)</em></strong></span></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for each number correctly placed.</span></p>
<p><span> Award <strong><em>(A0) </em></strong>for any entry in more than one region.</span></p>
<p> </p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span><br><img src="images/Schermafbeelding_2014-09-02_om_14.19.00_4.png" alt> <strong><em>(A1)(A1)(A1)(A1)(A1)(A1) (C6)</em></strong></span></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for each number correctly placed.</span></p>
<p><span> Award <strong><em>(A0) </em></strong>for any entry in more than one region.</span></p>
<p> </p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span><br><img src="images/Schermafbeelding_2014-09-02_om_14.19.00_5.png" alt> <strong><em>(A1)(A1)(A1)(A1)(A1)(A1) (C6)</em></strong></span></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for each number correctly placed.</span></p>
<p><span> Award <strong><em>(A0) </em></strong>for any entry in more than one region.</span></p>
<p> </p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A satellite travels around the Earth in a circular orbit \(500\) kilometres above the Earth’s surface. The radius of the Earth is taken as \(6400\) kilometres.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the radius of the satellite’s orbit.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the distance travelled by the satellite in one orbit of the Earth. Give your answer correct to the nearest km.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down your answer to (b) in the form \(a \times {10^k}\) , where \(1 \leqslant a < 10{\text{, }}k \in \mathbb{Z}\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><span>\(6900\) km </span><span> <em><strong>(A1) (C1)</strong></em></span></span></p>
<p><span><span><em><strong>[1 mark]</strong></em></span></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(2\pi (6900)\) <strong><em>(M1)(A1)</em>(ft)</strong></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for substitution into circumference formula, <strong><em>(A1)</em>(ft) </strong>for correct substitution. Follow through from part (a).</span></p>
<p> </p>
<p><span>\( = 43354\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></span></p>
<p><span><strong>Notes:</strong> Follow through from part (a). The final <em><strong>(A1)</strong></em> is awarded for rounding their answer correct to the nearest km. Award <em><strong>(A2)</strong></em> for \(43 400\) shown with no working.</span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(4.3354 \times {10^4}\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <strong><em>(A1)</em>(ft)</strong> for \(4.3354\), <strong><em>(A1)</em>(ft)</strong> for \( \times {10^4}\) . Follow through from part (b). Accept \(4.34 \times {10^4}\) .</span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Candidates appeared to be confused by the context in this question. They had difficulty identifying the radius and many used the formula for the area of a circle, rather than the circumference. </span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Candidates appeared to be confused by the context in this question. They had difficulty identifying the radius and many used the formula for the area of a circle, rather than the circumference. A large number of candidates misread the final sentence in part b and did not write their answer to the nearest kilometre.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Candidates appeared to be confused by the context in this question. They had difficulty identifying the radius and many used the formula for the area of a circle, rather than the circumference.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(U\) is the set of <strong>positive </strong>integers less than or equal to \(10\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(A\), \(B\) and \(C\) are subsets of \(U\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em> </em>\(A = \left\{ {{\text{even integers}}} \right\}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em> </em>\(B = \left\{ {{\text{multiples of }}3} \right\}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em> </em>\(C = \left\{ {6,{\text{ }}7,{\text{ }}8,{\text{ }}9} \right\}\)</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>List the elements of \(A\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>List the elements of \(B\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the Venn diagram with <strong>all </strong>the elements of \(U\).</span></p>
<p><br><span><img src="images/Schermafbeelding_2014-09-02_om_17.36.22.png" alt></span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(2, 4, 6, 8, 10\) <strong><em>(A1) (C1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Do not penalize the use of \(\left\{ {{\text{ }}} \right\}\).</span></p>
<p><span> </span></p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(3, 6, 9\) <strong><em>(A1) (C1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Do not penalize the use of \(\left\{ {{\text{ }}} \right\}\).</span></p>
<p><span> Follow through from part (a) only if their \({\text{U}}\) is listed.</span></p>
<p> </p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span> <br><img src="images/venny.jpg" alt width="500" height="316"> <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)<em>(A1)</em>(ft)<em>(A1)</em>(ft) <em>(C4)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(A1)</em>(ft) </strong>for the correct placement of \(6\).</span></p>
<p><span> Award <strong><em>(A1)</em>(ft) </strong>for the correct placement of \(8\) and \(9\) and the empty region.</span></p>
<p><span> Award <strong><em>(A1)</em>(ft) </strong>for the correct placement of \(2\), \(4\), \(3\), \(7\), and \(10\).</span></p>
<p><span> Award <strong><em>(A1)</em>(ft) </strong>for the correct placement of \(1\) and \(5\).</span></p>
<p><span> If an element is in more than one region, award <strong><em>(A0) </em></strong>for that element.</span></p>
<p><span> Follow through from their answers to parts (a) and (b).</span></p>
<p> </p>
<p><span><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was done well by most candidates. The most frequent error was to omit the placement of 1 and 5 or to include 0 in the set of even integers.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was done well by most candidates. The most frequent error was to omit the placement of 1 and 5 or to include 0 in the set of even integers.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was done well by most candidates. The most frequent error was to omit the placement of 1 and 5 or to include 0 in the set of even integers.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the universal set \(U = \{ x \in \mathbb{N}|3 < x < 13\} \), and the subsets \(A = \{ {\text{multiples of 3}}\} \) and \(B = \{ 4,{\text{ }}6,{\text{ }}12\} \).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>List the elements of the following set.</span></p>
<p><span><em>A</em></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>List the elements of the following set.</span></p>
<p><span>\(A \cap B'\)</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down one element of \((A \cup B)'\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>One of the statements in the table below is false. Indicate with an <strong>X</strong> which statement is false. Give a reason for your answer.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>6, 9, 12 <em><strong> (A1) (C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>9 <strong><em> (A1)</em>(ft)<em> (C1)</em></strong></p>
<p><span><br> </span><strong>Note:</strong> Follow through from their part (a)(i).</p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>any element from {5, 7, 8, 10, 11} <em><strong> (A1)(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for finding </span><span>\((A \cup B)\), follow through from their <em>A</em>.</span></p>
<p><span>Award full marks if all correct elements of </span><span><span>\((A \cup B)'\)</span> are listed.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>\(15 \notin U\) <em><strong> (R1)(A1) (C2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Accept correct reason in words.</span></p>
<p><span>If the reason is incorrect, both marks are lost.</span></p>
<p><span>Do not award <em><strong>(R0)(A1)</strong></em>.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The question was not well answered by the majority of the candidates. Many did not identify the universal set correctly and so took 3 to be a member of this set. This affected their answers in a)(i) and a)(ii).</span></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">The question was not well answered by the majority of the candidates. Many did not identify the universal set correctly and so took 3 to be a member of this set. This affected their answers in a)(i) and a)(ii).</span></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Not many students answered (b) correctly. Some listed all correct elements of the given set instead of just one, which shows that they did not read the question carefully.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Although many candidates could indicate which statement in the table in c) was false, often they were unable either to identify or articulate a correct reason for it.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A manufacturer in England makes \(16 000\) garden statues. \(12\% \) are defective and cannot be sold.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number of statues that are non-defective.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The manufacturer sells each non-defective statue for \(5.25\) British pounds (GBP) to an American company. The exchange rate from GBP to US dollars (USD) is \(1{\text{ GBP}} = 1.6407{\text{ USD}}\).</span></p>
<p><span>Calculate the amount in USD paid by the American company for all the non-defective statues. Give your answer correct to <strong>two decimal places</strong>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The American company sells one of the statues to an Australian customer for \(12{\text{ USD}}\). The exchange rate from Australian dollars (AUD) to USD is \(1{\text{ AUD}} = 0.8739{\text{ USD}}\) .</span></p>
<p><span>Calculate the amount that the Australian customer pays, in AUD, for this statue. Give your answer correct to <strong>two decimal places</strong>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(0.88 \times 16000\) <strong>OR</strong> \(16000 - 0.12 \times 16000\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(14080\) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(1.6407 \times 5.25 \times 14080\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(121 280.54{\text{ USD}}\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their answer to part (a).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(12 \times \frac{1}{{0.8739}}\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(13.73{\text{ AUD}}\) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Note:</strong> If division used in part (b) and multiplication used in part (c), award <em><strong>(M0)(A0)</strong></em> for part (b) and <strong><em>(M1)(A1)</em>(ft)</strong> for part (c).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was generally well answered with much correct working seen in parts (a) and (b). The most popular incorrect answer in part (a) was \(1920\) – candidates simply stating the number of defective items rather than the number of non-defective items. Unfortunately in part (c) many candidates multiplied by \(0.8739\) rather than divided and \(10.49\) proved a popular, but erroneous, answer.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was generally well answered with much correct working seen in parts (a) and (b). The most popular incorrect answer in part (a) was \(1920\) – candidates simply stating the number of defective items rather than the number of non-defective items. Unfortunately in part (c) many candidates multiplied by \(0.8739\) rather than divided and \(10.49\) proved a popular, but erroneous, answer.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was generally well answered with much correct working seen in parts (a) and (b). The most popular incorrect answer in part (a) was \(1920\) – candidates simply stating the number of defective items rather than the number of non-defective items. Unfortunately in part (c) many candidates multiplied by \(0.8739\) rather than divided and \(10.49\) proved a popular, but erroneous, answer.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The diagram shows triangle ABC in which angle BAC \( = 30^\circ \), BC \( = 6.7\) cm and AC \( = 13.4\) cm.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"> </span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAe8AAACbCAIAAADEL4T5AAAU+UlEQVR4nO3d72vb9qLH8fwbfSSDHtkcw0qf5FHcwCieByaE3VAIlN055sS9t9AHo7u1fNN7Rx/cLmDTMGK4kNkspzAGqUzLGDQpInAxXVrRDMrmCnpYT+OIQzA+RhwHE77oPvhKsmTLP5LYsX58XuRJZklRnO7tr7+SpSkVwEUaQiYYYJnOr3Ai+1iQlEnvHcAETU16BwBOizSElTCzWJSOte/lvU0uzjLTycIbBB18CzUH1+msuaqqKqkU4yE2uCI0yOR2DGCSUHNwHdQcwAZqDq7TVXMii99zMcy0gL+h5uA6tOZdB0I5oTHpPQOYINQcXKf7KKhYyi6FmUA4sVlRMNMCPoWag+vYzZurx1JhkWVCc4UKcg7+hJqD69jWXJt+wXwL+BZqDq5jW/NWlb8dxtgcfAw1B9exO6eFzyaDATZ6X5BbE903gIlBzcFVenyyn2XimcJPIlIOPoaaAwB4AWoOAOAFqDm4UrPZfPnyZbPZnPSOADgFag4u02w2Szw/G4n8+81/u5lKIegAFGoOrmF0nEuna7Waqqr59TyCDkCh5uAC5o5LkmR+CEEHoFBzcLQ+HTcg6AAqag6ONUzHDQg6AGoOjnOqjhsQ9BEhirRb2somg7dK8omqqqTKp4KhWHYP146fqJYs/vw4uxRO8HKPJVBzcJCzddyAoI+AzCfpx2vjBYmoqnoi87dYJsB+lBVPJr1v/qX/FfpeiQg1B6col8vXFxbO1nEDDTo94wXOpPP6ZX4amxOl8kPuyYcejzYqhfxTeVKvaYqY/YTtvNicBWoOkzeSjhvy6/nZSOTg4OD8m/KlD6XEZZb5JCf6oN4WDYlfifXKpVIpcXH9/cpEfCglLvd/h4SawySNtuMGBP20iLy3ycVZJhT76qtkMKDfL7sliz+XClzMFBF9yenURv4/ggFT4FqyyOcS09pF0PhK+9VAkYStbPKjFaFRrxSWw+2bcbdk8VEmGmKDt77b+NL0hoAo0m6pwM1xQkOLLH2IKBKfiYbY6Jpof5MpbYfnOKFhbNy6MJHFpwUuxgRYJhTjeEkhqkqUymayfTU37YCBrlEpLLfvXKhPW9ttpxvd+QDLTCezPzz+lt9vP43G6tPJh2W5/RzaPiHa9easl+9vyeJPRS7OMgE2uFysNFBzmAza8esLC6PtuAFBHx6Rd+5FQ2z0viA3pMKifpPV9v1XjYjoS66Jyt8FboZlAle0zrdk4X5Mz0r7UpfBFaHxRylxmWUCYW6nKq7FmIA+XUBXCcWye4q2vP6GQJu7v5zk31X523QfrmTFVpVPBW2DqzkRs1e0yeVfq3R/LAtr1Q4v81VCfzsjl/TeVcav0/EEVYrxkOn9Sp/tWNeTCnPaQy1ZuB/TXgno6vQ14FgW7se0Pez9hGh/i5mMcKRvuiqsxNnofUH+p8zfovPpqDlcNKPj5XJ5rD/oL5ubCPpg5H1peZrVSnFipIGoqv6tHhHLknQa13iI9k5fkebYGIPLfJIJzW38+F08xDI0gnQ6Xl/mRMx9ZFpe2/j1XCGbKeyJhUWWmcnwT9a4R5XqTsbyhqDjd6G7sfjdzg/3/ntHrgvmhfWfeLtUbbWPK9LCaiuacmneqlSYM/06/bZjRV9d9NvV1vbF98RYnb5jIJViPDTEE3IkcDOmSfO6mJ1nmfmcWNf/KItF6Rg1h4tzYR03/0QEvS99AK5NR3RUg35LR45EoSNrbUk6va4Pey2jV32bWozot9dXs1yq8EaffqE90g+u0vq3g/ihlLjMBj9JZgX5hG75ciyxJsgtrY897heoZZeZmVv5qWvUTH+XHt/SsXC7njZPkf5D+26nc1WaWvN9VOjy3S8bfZ+QhvllSftDhDnhH9qsV/yeUCWYN4eLcfEdN/9oBL03u6gZs+SWiByZp1a0gaRp0rzK3w7T0aKyl4uG2mGikxjBj+e4J1UjeJaZhK67AJrbqi05nxPr+nyI/Qja9CpCR83Wbmrb0V+oLN/qK9oP+e2eIvvt2FHeFBPT7dmqXi8b/Z4Q25clm5u0oOYwXhPsuHkfEHR79B29ljw6PAyEuZ0Pr1+/6xjbaqPvy0n+g7HklWz5/W75HU2OvLeZ5ZLREMsE2OBSjhe1I3t0Ra2wGn0Qfaskn+j1/yS399vu7l+JJV7WcbG2KdsRtDpguE1Hu9oLFX1VMF5v+o6vO3rdbzsWRHr2lK5Cf0G6imV1+ry92ZdbfZ8Q62tY96SQ8ttT4a8Ym8MYOaHj5p1B0G20a16VxWdF7mOWCYQ///rx67ppbPtO2n2tz3jMZIS/K9Izeu6KviR97x/PFLZK/G7H2R20Ux1zI6aZ6Lq0s5YMBlhm+l+5H/c7Z3sss/PaWvENsfLC5q6B+qQ5za52RDSxJUkvRLllivuJ6SAkMa34SU6sSruvZWvRtR/6UVasS7uiTPpsx7peQ1i5ksi/lFt0vkV7BrRSTycLbxSVKNLuU1Em/Z+Q9mvYsSw+E6R39LWHvoQQWXz6RHvhRM1h9CRJ4tJph3TcgKDb0d7Ux7hHovx3MTtvOrmQVnU6mX0mKcS0ZEEPirFkxxl+ATa6UpJovem4ko7oTbQJ5XimIEj0wKaxinlMbQ20fvzQ2Lh1kx3HKum37YVb8l5e28koVxQkpXNnjN/Uulnt4ORSboeu0ns7FsfvdsuVCn3ZM29ZP8mSCYQT2ZL+BqbfE6JPvocTa8+lhnkLlvdAqDmMljM7bkDQx4HIYim7co9/IQpPHmeXwpYLA8DFQc1hNBzecQOCPmpHAjdjabd5mhguEGoO50U7PhuJbG9vT3pfhoKgjxSdS2l/+JPIO/eil/1xXRdnQc3h7IyOl3jeXVcuRNBHicgin23Pm/ebTYYxQs3hLNzbcQMNusPnhQCGh5rD6Xig44ZyucwyAQQdvAE1h2F5qeMGBB08AzWHwTzZcQOCDt6AmkM/tVqNXlrWkx037O/vYw4d3A41B3s+6bjh4OAAQQdXQ82hk986bkDQwdVQc2ijHWeZgN86bkDQwb1Qc1BVU8fz63mf3/AeQQeXQs39Dh3vhqCDG6Hm/oWO94Ggg+ug5n6Ejg8DQQd3Qc39BR0/FQQdXAQ194tms1nieXT8tBB0cAvU3Ptox2cjEXT8bGjQ8+v5Se8IQD+ouZeh46OCoIPzoebeZHT8mwcP0PGRQNDB4VBzrzE6zqXTkiRNenc8BUEHJ0PNvQMdvwDNZvNmKoWggwOh5l6Ajl8kBB2cCTV3N3R8IhB0cCDU3K3Q8clC0MFpUHNXovebR8cnC0EHR0HNXaZcLl9fWEDHHQJBB+dAzV0DHXem0QW9JYs/P84uhZlAmBMaNgscCdwMywQsX/GCRM79k8ETUHMXoB2/mUqh4840gqAT+eXDpXBwKbe1Kyk98twQMkFrypnQXKGCmAOFmjsa7fj1hQVc9cnhzhf0upidDyfyL+VW72VIQ/j2a6FqaveRwN0qSsdn+ongQai5Q6HjrmME/ZS3VCWKuBYL3i5V+6RcVdWWLL1XzKtJhTlMs4AJau446Lh70aDfTKVOEXRSKcYvx7gNOmPOBpdyO5IyeLVjqbCc4t/3iDlRpGe5xDTLBNjg0tqeTFRVVRuS8GMuEc8IVXkvnwwGWCZ+T6gSIovfczEmwAaXixW76XpwCdTcQdBxDzht0IlUmGPime9pcRuVwnKYmc+J9UGrVYrzXwsN25gTRVyLRe8LcktVW1X+dphZLEr/bAgrYSbAMtPJLC/KLTq9wxoz9aQqrMRxTNXVUHNHQMe95DRBJw1hJRxcaXeZVIrx0MCqEqnwmf15L6qqHgncfEY40paUy2uJz+nLA5EKc8yM/hBpCCthZlGfeT+WCouseU/AbVDzCZMk6WYqhY57TLPZ5NLpIYLe3dBhqnosFW4Zve7UEDLBGdtHUXNvQ80nRpIkLp1Gxz0sv54fFPSOpKpaVfuPzftNs9Cah2LZve7Jd9Tc21DzCUDH/WNw0BtCJjhtOp55JHAf9z+LvO80iz5Xw8QzfEUPen1f+LWBmnsdan6h0HEfGhT0VpW/HdbOJ2nJe/lkfE3UPkDUqvK3w1HjW6rvNIuqakdBLR8ymse8uR+g5heEdnw2Einx/CnPRwbXGxT0hrSzlgwGWCYU4x6J7c8Q2dWcVIrL34q9Pi+qryiLjzLREMsE2ChXFCSFxrr9CdLXlfa3MxnhN9M1A+zn3MH5UPOxQ8dBHWoOHeBcUPMxQsfBDEGHsULNxwIdB1sIOowPaj5i6Dj0h6DDmKDmI1Or1dBxGAaCDuOAmo9ArVbLr+fRcRhefj1/fWHh4OBg0jsC3oGanws6DmdG/+Ug6DAqqPkZoeNwfgg6jBBqfmq04ywTyK/na7XapHcH3A1Bh1FBzU8BHYdx2N7eRtDh/FDzoaDjMFblchlBh3NCzQdAx+FiIOhwTqh5T+g4XDAEHc4DNbfRbDb/srmJjsPFQ9DhzFBzi2azWeL52UgEHYdJQdDhbFBzDToOzoGgwxmg5ug4OBGCDqfl65obHefSaUmSJr07ABYIOpyKT2uOjoMrIOgwPN/VHB0HdymXyywTwG3BYSAf1RwdB5dC0GEYvqg5Og5uh6DDQN6vOb2kEToOboegQ39ernm5XL6+sICOg2ccHBzMRiIIOtjyZs3RcfAqBB168VrN0XHwPAQdbHmn5rTj1xcW9vf3uXT6ZiqFe7yBVyHo0M0LNTc6bv7Hvb+//82DB7gtOngVgg4d3F1z2453LICP0oFXIehg5taaD+y4ecnZSARTLuBJCDoY3Ffz4Ttu+ObBg28ePBjrXgFMCoIOlJtqvr+/f9qOU81mczYSwVku4FUIOqhuqbkkSVw6fYaOG7a3t7l0erR7BeAcNOglnp/0jsDEOL3m5++4AcNz8DYa9Px6ftI7ApPh3JqPsONUiefxDx28DUH3MyfWnHZ85G8ba7UaywRwcgt4G4LuW86qubnj48juzVQKR4rA8w4ODm6mUgi63zil5uPuOLW9vY1TFcEPms0mgu43k6/5aDtODp/dvXppaura3ecHpOvRWq02G4mc80cAuAKC7jeTrPkYxuPHbzfurL6qq8ovq18U33bnXFVx5RbwDwTdVyZT84ODg2E7Tg5/yd64NDU1NTV16Ub22duG3UPX7hR/OSTqMDXPr+e3t7dH++sAOBaC7h8XXfNarZZfzw89Hq+/yv5n9pdDYkyhXNvQG11/tfrp1NX/en7YIofP7l698sXWH2TQTIuqqtvb2/iXDb6CoPvExdX8lB3vdnK49eepS3efN4iqquTtxrWpK3eeH6mqqqrHbzf+xXioPzq9c/qfDuBiCLofXETNz91x6uj5nWt0AK7le+rPW4cn9DFr3PtpNpssEzjrPgC4FYLueeOtOe04ywTy6/lzHedU3j5bvcHeea7Pmh89v3Nlil19daIvcLh1Y+rStY3fBw/OVXU2EqnVamffGQB3QtC9bVw1N3f8nOk8ebXKTmkufbF1QFRV/dvWDbar5pb/0AfuGgq+haB72OhrPsKOm7QOX22t3vjTlDadYlvzYcfmXDq9v78/oh0DcBkadC6dHuLtcksWf36cXQozAZYJsFGu+ESUT6SnT6Rh/keDCzbKmo+n423k7ca1KfbG1t+6D3uevFplh5s3V1W1xPO4cCj4GQ36zVSqX9CJ/PLhUji4lONFmWj/ReSzyWBorlBBzR3IWnPyvrQ8c4Y/1bg7rmk8v3Pp09VXdfUc57SoqDnA4KC3qvztMDOfE+vW/04UcW2OExp268BkWWpOpMIcE2DjheHfRzWbzYvouKqq5OD53U+v3n12qA0T/tj64k+XbhR/V06Ut1t39PPNh4GaA6j9g94QMsFA2L7aR7v8C9Tcgcw1r4vZr1azt8PMYlE6Hrhms9ks8Ty99ua4Oq78snr1knYA9OqdjdKrQ3Owld+37lybop8F3fpdGXqr+AARAEVHY11BP5YKiyyDGRWXMdW8IWTmC1K9z2uy5iI6Pk74ABGAWVfQjwRuhmVmMsJQB6LAIYyaH0uFWxnhSPtDBlcEuzlot3ecQs0BOliDjpq7kl5zUikufysqRNVmz23+kNvb27ORCJdOu7fjVLPZxGUUATrQoKuqqs+0oOYuQ2tOGsLXnxlzZKRSjIfCy3zVOjpn6Tmn+MIXvjz9peonRPSfcQWnoTWnb6w6/qhDHQsFAC+iTeg+Q1FViSzuSsOfdAAXZkpVVSIVPrO+CJMqn8JnBAD8THlTTEyzTDxTECRFOy9YkYTNwk8VBWFwoilVrYtZrmsYfiRwM6c68RwAvIbI4pONTDSkvV+nn+xHE5xqShbux2zOYNFOOI2t7OCPBwDgfFN2s+Q05foEeo+zFQEAwDkmeZdnAAAYFdQcAMALUHMAAC9AzQEAvAA1BwDwAtQcAMALUHMAAC9AzQEAvAA19xlFEvgfcol498VOiVxeS0yzTICNrpSkYa6d16ryt8O4/AOAM6DmfkIqxfnF5OfTNpeuVn4tff9CJsad2gd/AJhU+VTwdHeRBYDxQc19x+5uJMfvdl+0L2ffEDLBQXcqUPZyiS8ziWnUHMAhUHPf6XVvKcsC0TWx31VP62L2y5wo4UKbAM6BmvtO35o3JKGQSfyPILf6bEARv01m95SBl01WpOfZpTATYJnp5MOydjFORRK2ssmPVoR69eXDpTATYKP3BblF5L1NLs4ygXBiE5fPBjgD1Nx3eta8IWSC9MKZ8Qxf6XlzGWUvl6C3kO1bc2UvF52/J1SJ5eYn+l2ugks5XpQJXSwUTmQfC5KiqkTeuRe9jNukAJwBau47/Wda9DHydIp/b5fUuvhwtVSlI/c+NScNYeWKcUMrIr98uDyX3VNUVbvecvsoq3Uj9J60uB0lwOmh5r4zcN68d1KJIv7vvXbl+9T8SOBmekQZNQcYC9TcdwbXXD2WCot2SbW9G3iAZbpvIXskcDOs/aFU1BxgLFBz3xmi5kcCF+8x09KxWK+xuX4nQo5v3yD49f+JDYKaA4wJau47NjUn70vLMzHukSi3VLUlC/fnTCeWkCqfCs7nxHrXlgYeBQ2Zx+8xzJsDjBNq7ivWqZJ2iBuVwnJYuw2sfraJ7ow1bx9QDbBMPFMQJIXQWLdvRVt53f42uCJ82NFPqsHdaAFODTUHAPAC1BwAwAtQcwAAL/h/AcDHBlS23JIAAAAASUVORK5CYII=" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the size of angle ACB.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Nadia makes an accurate drawing of triangle ABC. She measures angle BAC and finds it to be 29°.</span></p>
<p><span>Calculate the percentage error in Nadia’s measurement of angle BAC.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{\sin {\text{A}}{\operatorname{\hat B}}{\text{C}}}}{{13.4}} = \frac{{\sin 30^\circ }}{{6.7}}\)</span><span> <em><strong>(M1)(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substituted formula, <em><strong>(A1)</strong></em> for correct substitution.</span></p>
<p><br><span>\({\text{A}}{\operatorname{\hat B}}{\text{C}}\)</span><span> = 90° </span><span> <em><strong>(A1)</strong></em></span></p>
<p><span>\({\text{A}}{\operatorname{\hat C}}{\text{B}}\)</span><span><span> =</span> 60° <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C4)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span><strong>Note:</strong> Radians give no solution, award maximum <em><strong>(M1)(A1)(A0)</strong></em>.</span></p>
<p><span> </span></p>
<p><em><strong><span>[4 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{29 - 30}}{{30}} \times 100\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into correct formula.</span></p>
<p><br><span>% error = −33.3 % <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Percentage symbol not required. Accept positive answer.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Use of cosine rule was common. The assumption of a right angle in the given diagram was minimal.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;"><span style="font-size: medium; font-family: times new roman,times;">The incorrect denominator was often seen in the error formula.</span></span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Passengers of Flyaway Airlines can purchase tickets for either Business Class or Economy Class.</p>
<p class="p2">On one particular flight there were <span class="s1">154 </span><span class="s2">passengers.</span></p>
<p class="p2">Let \(x\) be the number of Business Class passengers and \(y\) be the number of Economy Class passengers on this flight.</p>
</div>
<div class="specification">
<p class="p1">On this flight, the cost of a ticket for each Business Class passenger was <span class="s1">320 </span>euros and the cost of a ticket for each Economy Class passenger was <span class="s1">85 </span>euros. The total amount that Flyaway Airlines received for these tickets was \({\text{14}}\,{\text{970 euros}}\).</p>
</div>
<div class="specification">
<p class="p1">The airline’s finance officer wrote down the total amount received by the airline for these tickets as \({\text{14}}\,{\text{270 euros}}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Use the above information to write down an equation in \(x\) <span class="s1">and \(y\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Use the information about the cost of tickets to write down a second equation <span class="s1">in \(x\) and \(y\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of \(x\) <span class="s1">and the value of \(y\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the percentage error.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(x + y = 154\) </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C1)</em></strong></p>
<p class="p1"><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(320x + 85y = 14\,970\) </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C1)</em></strong></p>
<p class="p1"><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(x = 8,{\text{ }}y = 146\) </span><strong><em>(A1)</em>(ft)<em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C2)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Follow through from parts (a) and (b) irrespective of working seen, <strong>but only </strong>if both values are positive integers.</p>
<p class="p1">Award <strong><em>(M1)(A0) </em></strong>for a reasonable attempt to solve simultaneous equations algebraically, leading to at least one incorrect or missing value.</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(\left| {\frac{{14270 - 14970}}{{14970}}} \right| \times {\text{ }}100\) </span><strong><em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for correct substitution into percentage error formula.</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\( = 4.68(\% ){\text{ }}(4.67601 \ldots ){\text{ }}\) </span><strong><em>(A1) (C2)</em></strong></p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Let \(f (x) = x^2 - 6x + 8\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Factorise \(x^2 - 6x + 8\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Hence, or otherwise, solve the equation \(x^2 - 6x + 8 = 0\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Let \(g(x) = x + 3\).</span></p>
<p><span>Write down the solutions to the equation \(f (x) = g(x)\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\( (x - 2)(x - 4)\) <em><strong>(A1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>x</em> = 2, <em>x</em> = 4 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>x</em> = 0.807, <em>x</em> = 6.19 <em><strong>(A1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award maximum of <em><strong>(A0)(A1)</strong></em> if coordinate pairs given.</span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span><em><strong>(M1)</strong></em> for an attempt to solve \(x^2 - 7x + 5 = 0\) via formula with correct values substituted. <em><strong>(M1)</strong></em></span></p>
<p><span>\(x = \frac{{7 \pm \sqrt {29} }}{2}\) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em><br></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This was generally well answered, but a number seemed not to know the term “factorise”.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;"><span style="font-size: medium; font-family: times new roman,times;">This was generally well answered.</span></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;"><span style="font-size: medium; font-family: times new roman,times;"><span style="font-size: medium; font-family: times new roman,times;">This part proved problematic for many candidates. It was expected that the GDC was used, though many attempted an algebraic solution.</span></span></span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Given that \(h = \sqrt {{\ell ^2} - \frac{{{d^2}}}{4}} \) ,</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the <strong>exact</strong> value of \(h\) when \(\ell = 0.03625\) and \(d = 0.05\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the answer to part (a) correct to three decimal places.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the answer to part (a) correct to three significant figures.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the answer to part (a) in the form \(a \times {10^k}\) , where \(1 \leqslant a < 10{\text{, }}k \in \mathbb{Z}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(h = \sqrt {{{0.03625}^2} - \frac{{{{0.05}^2}}}{4}} \) <em><strong>(M1)</strong></em></span><br><span>\( = 0.02625\) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Note: </strong>Award <em><strong>(A1)</strong></em> only for \(0.0263\) seen without working</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(0.026\) <em><strong>(A1)</strong></em><strong>(ft) <em>(C1)</em></strong></span></p>
<p><span><strong><em>[1 mark]<br></em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(0.0263\) <em><strong>(A1)</strong></em><strong>(ft) <em>(C1)</em></strong></span></p>
<p><span><strong><em>[1 mark]<br></em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(2.625 \times {10^{ - 2}}\)</span></p>
<p><span>for \(2.625\) <strong>(ft)</strong> from unrounded (a) only <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>for \( \times {10^{ - 2}}\) <em><strong>(A1)</strong></em><strong>(ft) <em>(C2)</em></strong></span></p>
<p><span><strong><em>[2 marks]<br></em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This was answered correctly by the majority of the candidates however some candidates entered the numbers incorrectly and arrived at the wrong answer.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Correction to decimal places was less well attempted than to significant figures.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Correction to decimal places was less well attempted than to significant figures.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most made a successful attempt to change their answer to part (a) into scientific notation. Some were penalised for not using their answer to (a).</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The following table gives the exchange rate from US dollars to euros and from US dollars to Japanese Yen.<strong> Give all answers in this question correct to two decimal places</strong>.</span></p>
<p style="text-align: center;"><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Enrico has 475 USD.</span></p>
<p><span>How many euros is this worth?<br></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a, i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Enrico has 475 USD.</span></p>
<p><span>Enrico goes to a bank to exchange his dollars. The bank charges 3 % commission.</span></p>
<p><span>How many euros does Enrico receive?</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><span>Find the exchange rate from euros to yen.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><strong><em>Note: Financial penalty (FP) applies in this part</em></strong></span></p>
<p><span><strong><em> </em></strong></span></p>
<p><span><em><strong>(FP)</strong></em> \(475 \times 0.6337 = 301.01\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span> </span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for multiplication by 0.6337.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">a, i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><strong><em>Note: Financial penalty (FP) applies in this part</em></strong>\(\frac{3}{{100}} \times 301.01 = 9.03\) <strong><em>(M1)</em></strong></span></p>
<p><span><span><br> </span><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for multiplication by 3/100.</span></p>
<p><span><strong><em> </em></strong></span></p>
<p><span><strong><em>(FP) </em></strong> \(301.01 - 9.03 = 291.98\) <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>\(0.97 \times 301.01\) <strong><em>(M1)</em></strong></span></p>
<p><span><strong><em>(FP)</em></strong> \(= 291.98\) <strong><em>(A1)</em>(ft)</strong> <strong><em>(C4)</em></strong></span></p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a, ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p> </p>
<p><em><strong><span>Note: Financial penalty (FP) applies in this part</span></strong></em></p>
<p><span> </span></p>
<p><span><em><strong>(FP)</strong></em> \(\frac{{{\rm{99}}{\rm{.7469}}}}{{{\rm{0}}{\rm{.6337}}}}{\rm{ = 157}}{\rm{.40}}\) <em><strong>(M1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for dividing by 0.6337.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was well answered by many candidates, particularly part (a), however a significant number lost the financial penalty mark for not giving an answer correct to two decimal places, as stated in the question.</span></p>
<div class="question_part_label">a, i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was well answered by many candidates, particularly part (a), however a significant number lost the financial penalty mark for not giving an answer correct to two decimal places, as stated in the question.</span></p>
<div class="question_part_label">a, ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was well answered by many candidates, particularly part (a), however a significant number lost the financial penalty mark for not giving an answer correct to two decimal places, as stated in the question.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Astrid invests 1200 Euros for five years at a nominal annual interest rate of 7.2 %, <strong>compounded monthly</strong>.</span></p>
</div>
<div class="question">
<p><span>Find the interest Astrid has earned during the five years of her investment. <strong>Give your answer correct to two decimal places.</strong></span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span>\(I = 1200{\left( {1 + \frac{{7.2}}{{600}}} \right)^{5 \times 12}} - 1200\) <em><strong> (M1)(A1)</strong></em></span><br><span><em>I</em> = 518.15 Euros <em><strong>(A1) (C3)</strong></em></span></p>
<p> </p>
<p><span><strong>Notes:</strong> Award<em><strong> (M1)</strong></em> for substitution in the compound interest formula, <em><strong>(A1)</strong></em> for correct substitutions,<em><strong> (A1)</strong> </em>for correct answer.</span></p>
<p><span>If final amount found is 1718.15 and working shown award <em><strong>(M1) (A1)(A0)</strong></em>.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-size: medium; font-family: times new roman,times;">Part (a) of this question was incorrectly answered by many candidates not noticing that the rate of interest was compounded monthly rather than annually. A number of candidates gave the final amount as the answer, rather than the interest. </span></p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Neung is going home to Vietnam after working in Singapore.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">She has 5000 Singapore dollars (SGD) and changes these into American dollars (USD)</span><br><span style="font-size: medium; font-family: times new roman,times;">to take home.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The exchange rate between Singapore dollars (SGD) and American dollars (USD) is</span></p>
<p style="text-align: left; margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">1 USD = 1.2945 SGD.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">There is also a 2.4 % commission on the exchange.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the amount of commission on the exchange <strong>in SGD</strong>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the number of American dollars (USD) Neung takes home. <strong>Give your answer correct to 2 decimal places.</strong></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>At the airport in Vietnam, Neung changes 150 USD into Vietnamese dong (VND) to pay for her transport home.</span></p>
<p><span>The exchange rate between American dollars (USD) and Vietnamese dong (VND) is</span></p>
<p><span>1 USD = 19 495 VND.</span></p>
<p><span><span><span>There is no commission.</span></span></span></p>
<p><span><span>Calculate the number of Vietnamese dong that Neung receives.</span><strong> Give your answer correct to the nearest thousand dong.</strong></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>5000 × 0.024 <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for multiplication by 0.024.</span></p>
<p><br><span>=120 <em><strong>(A1) </strong> <strong>(C2)</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(4880 \times \frac{1}{{1.2945}}\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for multiplication by \(\frac{1}{{1.2945}}\).</span></p>
<p><br><span>= 3769.80 <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Correct answer to 2 dp only. Follow through from their part (a).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(150 \times 19495\) <em><strong>(M1)<br><br></strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for \( \times 19495\)</span><span>.</span><br><br></p>
<p><span>\(= 2924000\) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Correct answer to nearest 1000 only.</span> <span>Do not penalize incorrect accuracy in (c) if this has already been</span> <span>penalized in part (b).</span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Marks were awarded in part (a) for multiplication by 0.024 in part (b) for division by 1.2945 and in part (c) for multiplication by 19495. Candidates did not follow specified levels of accuracy. Candidates were able to answer later parts of the question even if they did not answer the first parts correctly.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Marks were awarded in part (a) for multiplication by 0.024 in part (b) for division by 1.2945 and in part (c) for multiplication by 19495. Candidates did not follow specified levels of accuracy. Candidates were able to answer later parts of the question even if they did not answer the first parts correctly.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Marks were awarded in part (a) for multiplication by 0.024 in part (b) for division by 1.2945 and in part (c) for multiplication by 19495. Candidates did not follow specified levels of accuracy. Candidates were able to answer later parts of the question even if they did not answer the first parts correctly.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Consider the sequence</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">\[{\text{512, 128, 32, 8, }} \ldots \]</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the exact value of the ninth term of the sequence.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the least number of terms required for the sum of the sequence to be greater than 682.6</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\({u_9} = 512{\left( {\frac{1}{4}} \right)^8}\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for substituted geometric sequence formula, <em><strong>(A1)</strong></em> for correct substitution.</span></p>
<p><strong><span> </span></strong></p>
<p><strong><span>OR</span></strong></p>
<p><span>If a list is used, award <em><strong>(M1)</strong></em> for a list of 9 terms, <em><strong>(A1)</strong></em> for all 9 terms correct. <em><strong>(M1)(A1)</strong></em></span></p>
<p><span>\( = \frac{1}{{128}}\) (\(0.0078125\)) <em><strong>(A1) (C3)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for exact answer only.</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{512\left( {1 - {{\left( {\frac{1}{4}} \right)}^n}} \right)}}{{1 - \left( {\frac{1}{4}} \right)}} > 682.6\) <strong><em>(M1)(A1)</em>(ft)</strong></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for setting substituted geometric sum formula \( > 682.6\) <strong><em>(A1)</em>(ft)</strong> for correct substitution into geometric sum formula. Follow through from their common ratio.</span></p>
<p><span><strong> </strong></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>If list is used, award <em><strong>(M1)</strong></em> for S(6) and S(7) seen, values don’t have to be correct.</span></p>
<p><span><em><strong>(A1)</strong></em> for correct S(6) and S(7). (S(6) \( = 682.5\) and S(7) \( = 682.625\)). <em><strong>(M1)(A1)</strong></em></span></p>
<p><span>\(n = 7\) <strong><em>(A1)</em>(ft) <em>(C3)</em></strong></span></p>
<p><span><strong>Notes:</strong> Follow through from their common ratio. Do not award the final <strong><em>(A1)</em>(ft)</strong> if \(n\) is less than \(5\) or if \(n\) is not an integer.</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The upper quartile of candidates scored well on this question with the vast majority scoring more than 4 marks. However, the lower quartile did very badly with the majority scoring less than 2 marks. A fundamental error in part (a) resulted in many less able candidates using a common ratio of \(4\) instead of \({\raise0.5ex\hbox{$\scriptstyle 1$}<br>\kern-0.1em/\kern-0.15em<br>\lower0.25ex\hbox{$\scriptstyle 4$}}\)</span><span style="font-size: medium; font-family: times new roman,times;">. Where lists were used in either part of the question, they were either invariably incomplete or contained numerical errors. Indeed, using lists seem to be as problematic in this question as they were in Q6 on arithmetic sequences. Correctly quoted and substituted formula in a correct inequality (= sign was allowed) did earn many candidates two marks here. The required answer of \(7\) however did not always follow.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The upper quartile of candidates scored well on this question with the vast majority scoring more than 4 marks. However, the lower quartile did very badly with the majority scoring less than 2 marks. A fundamental error in part (a) resulted in many less able candidates using a common ratio of \(4\) instead of \({\raise0.5ex\hbox{$\scriptstyle 1$}<br>\kern-0.1em/\kern-0.15em<br>\lower0.25ex\hbox{$\scriptstyle 4$}}\)</span><span style="font-size: medium; font-family: times new roman,times;">. Where lists were used in either part of the question, they were either invariably incomplete or contained numerical errors. Indeed, using lists seem to be as problematic in this question as they were in Q6 on arithmetic sequences. Correctly quoted and substituted formula in a correct inequality (= sign was allowed) did earn many candidates two marks here. The required answer of \(7\) however did not always follow.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A tree begins losing its leaves in October. The number of leaves that the tree loses each day increases by the same number on each successive day.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the number of leaves that the tree loses on the 21st October.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the total number of leaves that the tree loses in the 31 days of the month of October.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(u_{21} = 24 + (21 - 1)(16)\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substituted formula, <em><strong>(A1)</strong></em> for correct substitutions.</span></p>
<p><br><span>\(u_{21} = 344\) <em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({S_{31}} = \frac{{31}}{2}\left[ {2(24) + (31 - 1)(16)} \right]\) <strong><em>(M1)(A1)</em>(ft)</strong><span><br> </span></span></p>
<p><span><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for correct substituted formula, <strong><em>(A1)</em>(ft)</strong> for correct substitutions. <strong>(ft)</strong> from their value for <em>d</em>.</span></p>
<p><span><span><br> </span>\(S_{31} = 8184\) <strong><em>(A1)</em>(ft)</strong> <strong><em>(C3)</em></strong></span></p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This was generally well attempted, often by listing.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;"><span style="font-size: medium; font-family: times new roman,times;">The common misconception was the use of the “term by term” formula. Listing the values in this part was usually not a successful strategy. The incorrect substitution of the answer to (a) also led to errors.</span></span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A cuboid has the following dimensions: length = 8.7 cm, width = 5.6 cm and height = 3.4 cm.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the <strong>exact</strong> value of the volume of the cuboid, in cm<sup>3</sup>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write your answer to part (a) correct to</span></p>
<p><span>(i) one decimal place;</span></p>
<p><span>(ii) three significant figures.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write your answer to <strong>part (b)(ii)</strong> in the form \(a \times 10^k\), where \(1 \leqslant a < 10 , k \in \mathbb{Z}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{V}} = 8.7 \times 5.6 \times 3.4\) <em><strong>(M1)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for multiplication of the 3 given values.</span></p>
<p><span><br>\(=165.648\) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) 165.6 <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Note:</strong> Follow through from their answer to part (a).</span><br><br></p>
<p><span>(ii) 166 <em><strong>(A1)</strong></em><strong>(ft) <em>(C2)</em><br></strong></span></p>
<p><br><span><strong>Note:</strong> Follow through from their answer to part (a).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(1.66 \times 10^2\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for 1.66, <em><strong>(A1)</strong></em><strong>(ft)</strong> for \(10^2\). Follow through from their answer to part (b)(ii) only. The follow through for the index should be dependent on the value of the mantissa in part (c) and their answer to part (b)(ii).</span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The first term of an arithmetic sequence is \(0\) and the common difference is \(12\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of the \({96^{{\text{th}}}}\) term of the sequence.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The first term of a geometric sequence is \(6\). The \({6^{{\text{th}}}}\) term of the geometric sequence is equal to the </span><span><span>\({17^{{\text{th}}}}\)</span> term of the arithmetic sequence given above.</span></p>
<p><span>Write down an equation using this information.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The first term of a geometric sequence is \(6\). The \</span><span><span>\({6^{{\text{th}}}}\)</span> term of the geometric sequence is equal to the </span><span><span>\({17^{{\text{th}}}}\)</span> term of the arithmetic sequence given above.</span></p>
<p><span>Calculate the common ratio of the geometric sequence.<br></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\({u_{96}} = {u_1} + 95d\) <em><strong>(M1)</strong></em></span></p>
<p><span>\( = 0 + 95 \times 12\)</span></p>
<p><span>\( = 1140\) <em><strong>(A1) (C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(6{r^5} = 16d\) <em><strong>(A1)</strong></em></span></p>
<p><span>\(6{r^5} = 16 \times 12\) (\(192\)) <em><strong>(A1) (C2)</strong></em></span></p>
<p><span><strong>Note: <em>(A1)</em></strong> only, if both terms seen without an equation.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({r^5} = 32\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Note: (ft)</strong> from their (b).</span></p>
<p><br><span>\(r = 2\) <em><strong>(A1)</strong></em><strong>(ft) <em>(C2)</em></strong></span></p>
<p><span><strong><em><br></em></strong><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Part (a) was done well. There was some confusion in answering part (b) with many candidates unsure what they needed to write down. Often the two terms were seen somewhere in the working without the equation being written down in the answer box, or the equation was seen in the working for part (c). Part (c) was answered well, often with follow-through marks being awarded from an incorrect part (b) provided the working was seen.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Part (a) was done well. There was some confusion in answering part (b) with many candidates unsure what they needed to write down. Often the two terms were seen somewhere in the working without the equation being written down in the answer box, or the equation was seen in the working for part (c). Part (c) was answered well, often with follow-through marks being awarded from an incorrect part (b) provided the working was seen.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Part (a) was done well. There was some confusion in answering part (b) with many candidates unsure what they needed to write down. Often the two terms were seen somewhere in the working without the equation being written down in the answer box, or the equation was seen in the working for part (c). Part (c) was answered well, often with follow-through marks being awarded from an incorrect part (b) provided the working was seen.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(512\) competitors enter round 1 of a tennis tournament, in which each competitor plays a match against one other competitor.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The winning competitor progresses to the next round (round 2); the losing competitor leaves the tournament.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The tournament continues in this manner until there is a winner.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number of competitors who play in round 6 of the tournament.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the total number of matches played in the tournament.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(512{\left( {\frac{1}{2}} \right)^5}\) <strong><em>(M1)(A1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substituted geometric progression formula, <strong><em>(A1) </em></strong>for correct substitution.</span></p>
<p><span> If a list is used, award <strong><em>(M1) </em></strong>for a list of at least six terms, beginning with \(512\) and <strong><em>(A1) </em></strong>for first six terms correct.</span></p>
<p> </p>
<p><span>\(16\) <strong><em>(A1) (C3)</em></strong></span></p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({S_9} = 256\left( {\frac{{1 - {{\left( {\frac{1}{2}} \right)}^9}}}{{1 - \frac{1}{2}}}} \right)\) <strong>OR</strong> \(\frac{{({2^9} - 1)}}{{2 - 1}}\) <strong><em>(M1)(A1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substituted sum of a GP formula, <strong><em>(A1) </em></strong>for correct substitution.</span></p>
<p><span> If a list is used, award <strong><em>(A1) </em></strong>for at least 9 correct terms, including \(1\), and <strong><em>(M1) </em></strong>for their 9 terms, including \(1\), added together.</span></p>
<p> </p>
<p><span>\(511\) <strong><em>(A1) (C3)</em></strong></span></p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">The first part of this question was answered quite well, especially by candidates who used a list. Part (b) was poorly answered. Common errors in part (b) were to find the number of rounds rather than the total number of matches played or to take the first term as 512 rather than 256.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">The first part of this question was answered quite well, especially by candidates who used a list. Part (b) was poorly answered. Common errors in part (b) were to find the number of rounds rather than the total number of matches played or to take the first term as 512 rather than 256.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Only one of the following four sequences is arithmetic and only one of them is geometric.</p>
<p class="p1"><span class="Apple-converted-space"> </span>\({a_n} = 1,{\text{ }}2,{\text{ }}3,{\text{ }}5,{\text{ }} \ldots \)</p>
<p class="p1"><span class="Apple-converted-space"> </span>\({b_n} = 1,{\text{ }}\frac{3}{2},{\text{ }}\frac{9}{4},{\text{ }}\frac{{27}}{8},{\text{ }} \ldots \)</p>
<p class="p1"><span class="Apple-converted-space"> </span>\({c_n} = 1,{\text{ }}\frac{1}{2},{\text{ }}\frac{1}{3},{\text{ }}\frac{1}{4},{\text{ }} \ldots \)</p>
<p class="p1"><span class="Apple-converted-space"> </span>\({d_n} = 1,{\text{ }}0.95,{\text{ }}0.90,{\text{ }}0.85,{\text{ }} \ldots \)</p>
<p class="p1">State which sequence is</p>
<p class="p1">(i) arithmetic;</p>
<p class="p1">(ii) geometric.</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>For <strong>another </strong>geometric sequence \({e_n} = - 6,{\text{ }} - 3,{\text{ }} - \frac{3}{2},{\text{ }} - \frac{3}{4},{\text{ }} \ldots \)</p>
<p>write down the common ratio;</p>
<div class="marks">[1]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For <strong>another </strong>geometric sequence \({e_n} = - 6,{\text{ }} - 3,{\text{ }} - \frac{3}{2},{\text{ }} - \frac{3}{4},{\text{ }} \ldots \)</p>
<p>find the <strong>exact </strong>value of the tenth term. Give your answer as a fraction.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b(ii).</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>\({d_n}\;\;\;\;\;\)<strong>OR</strong>\(\;\;\;1,{\text{ }}0.95,{\text{ }}0.90,{\text{ }}0.85,{\text{ }} \ldots \) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C1)</em></strong></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\({b_n}\;\;\;\)<strong>OR</strong>\(\;\;\;1,{\text{ }}\frac{3}{2},{\text{ }}\frac{9}{4},{\text{ }}\frac{{27}}{8},{\text{ }} \ldots \) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C1)</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\frac{1}{2}\;\;\;\)<strong>OR</strong>\(\;\;\;0.5\) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Accept ‘divide by <span class="s1">2</span>’ for <strong><em>(A1)</em></strong><em>.</em></p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\( - 6{\left( {\frac{1}{2}} \right)^{10 - 1}}\) <span class="Apple-converted-space"> </span><strong><em>(M1)(A1)</em>(ft)</strong></p>
<p class="p1"><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for substitution in the GP \({n^{{\text{th}}}}\) term formula, <strong><em>(A1)</em>(ft) </strong>for their correct substitution.</p>
<p class="p1">Follow through from their common ratio in part (b)(i).</p>
<p class="p2"> </p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">\(\left( { - 6,{\text{ }} - 3,{\text{ }} - \frac{3}{2},{\text{ }} - \frac{3}{4},} \right) - \frac{3}{8},{\text{ }} - \frac{3}{{16}},{\text{ }} - \frac{3}{{32}},{\text{ }} - \frac{3}{{64}},{\text{ }} - \frac{3}{{128}}\) <span class="Apple-converted-space"> </span><strong><em>(M1)(A1)</em>(ft)</strong></p>
<p class="p1"><strong>Notes:<span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for terms <span class="s1">5 </span>and <span class="s1">6 </span>correct (using their ratio).</p>
<p class="p1">Award <strong><em>(A1)</em>(ft) </strong>for terms <span class="s1">7</span>, <span class="s1">8 </span>and <span class="s1">9 </span>correct (using their ratio).</p>
<p class="p2"> </p>
<p class="p1">\( - \frac{3}{{256}}\;\;\;\left( { - \frac{6}{{512}}} \right)\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C3)</em></strong></p>
<div class="question_part_label">b(ii).</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(ii).</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">\(80\) matches were played in a football tournament. The following table shows the number of goals scored in all matches.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the mean number of goals scored per match.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the median number of goals scored per match.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A local newspaper claims that the mean number of goals scored per match is two. Calculate the percentage error in the local newspaper’s claim.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{0 \times 16 + 1 \times 22 + 2 \times 19 \ldots }}{{80}}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting correct values into mean formula.</span></p>
<p> </p>
<p><span>1.75 <em><strong>(A1) (C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>An attempt to enumerate the number of goals scored. <em><strong>(M1)</strong></em></span></p>
<p><span><span>\(2\) </span> <span><em><strong>(A1) (C2)</strong></em></span></span></p>
<p><span><span><em><strong>[2 marks]<br></strong></em></span></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{2 - 1.75}}{{1.75}} \times 100\) <em><strong>(M1)</strong></em></span><br><span>\(14.3 \% \) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted \(\% \) error formula. \(\% \) sign not required. Follow through from their answer to part (a). If \(100\) is missing and answer incorrect award <em><strong>(M0)(A0)</strong></em>. If \(100\) is missing and answer incorrectly rounded award <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong><em><strong>(AP)</strong></em>.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">In parts (a) and (b), \(2.5\) was a common incorrect error for both parts as some candidates were confused as to the concept of both the mean and the median from tabular data and simply looked at the mean and median of the <em>Number of goals</em>, ignoring the weighting of the number of matches. Candidates faired a little better with part (c) and many correct answers (many as follow through answers) were seen in this part of the question.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">In parts (a) and (b), \(2.5\) was a common incorrect error for both parts as some candidates were confused as to the concept of both the mean and the median from tabular data and simply looked at the mean and median of the <em>Number of goals</em>, ignoring the weighting of the number of matches. Candidates faired a little better with part (c) and many correct answers (many as follow through answers) were seen in this part of the question.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">In parts (a) and (b), \(2.5\) was a common incorrect error for both parts as some candidates were confused as to the concept of both the mean and the median from tabular data and simply looked at the mean and median of the <em>Number of goals</em>, ignoring the weighting of the number of matches. Candidates faired a little better with part (c) and many correct answers (many as follow through answers) were seen in this part of the question.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate \(\frac{{77.2 \times {3^3}}}{{3.60 \times {2^2}}}\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Express your answer to part (a) in the form \(a \times 10^k\), where \(1 \leqslant a < 10\) and \(k \in {\mathbb{Z}}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Juan estimates the length of a carpet to be 12 metres and the width to be 8 metres. He then estimates the area of the carpet.</span></p>
<p><span>(i) Write down his estimated area of the carpet.</span></p>
<p><span>When the carpet is accurately measured it is found to have an area of 90 square metres.</span></p>
<p><span>(ii) Calculate the percentage error made by Juan.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(144.75\left( { = \frac{{579}}{4}} \right)\) <em><strong>(A1)</strong></em></span></p>
<p><span><em>accept</em> 145 <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(1.4475 \times 10^2\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><em>accept</em> \(1.45 \times 10^2\) <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>Unit penalty <strong>(UP)</strong> is applicable in question part (c)(i) <strong>only</strong>.</em><br></span></p>
<p><span> </span></p>
<p><span><em><strong>(UP)</strong></em> (i) Area = 96 m<sup>2</sup> <em><strong>(A1)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span>(ii) \(\% {\text{ error}} = \frac{{(96 - 90)}}{{90}} \times 100\) <em><strong>(M1)</strong></em></span></p>
<p><span>\( = \frac{{6 \times 100}}{{90}}\)</span></p>
<p><span>\(\frac{{20}}{3}\% \) or 6.67 % <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C3)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span><em><strong>[3 marks]<br></strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(a) This was answered correctly by the majority of the candidates however some candidates entered the numbers without using brackets and arrived at the wrong answer.</span></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(b) Most made a successful attempt to change their answer to part (a) into scientific notation.</span></p>
<p> </p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(c) (i) Many candidates managed to find the answer but then lost the mark by not adding the units.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Several candidates are still having a problem finding the percentage error. The formula is given in their information booklet and they should have had practice using all the formulae that they are given. There are some schools that are still using the incorrect formula sheet for percentage error.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The following diagram shows a rectangle with sides of length 9.5 ×10<sup>2</sup> m and 1.6 ×10<sup>3</sup> m.</span></p>
<p style="text-align: center;"> <span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the area of the rectangle in the form <em>a</em> × 10<sup><em>k</em></sup>, where 1 ≤ <em>a</em> < 10, <em>k</em> ∈ \(\mathbb{Z}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Helen’s estimate of the area of the rectangle is \(1\,600\,000{\text{ }}{{\text{m}}^2}\).</span></p>
<p><span>Find the percentage error in Helen’s estimate.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em><strong><span>UP applies in part (a).</span></strong></em></p>
<p><span> </span></p>
<p><span>\(9.5 \times 10^2 \times 1.6 \times 10^3\) <em><strong>(M1)</strong></em></span><br><span><em><strong>(UP)</strong></em> \( = 1.52 \times {10^6}{\text{ }}{{\text{m}}^2}\) <em><strong>(A1)(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for multiplication of the two numbers.</span></p>
<p><span>Award <em><strong>(A1)</strong></em> for \(1.52\), <em><strong>(A1)</strong></em> for \(10^6\).</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{1600000 - 1520000}}{{1520000}} \times 100\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution in formula, <em><strong>(A1)</strong></em><strong>(ft)</strong> for their correct substitution.</span></p>
<p><br><span>= 5.26 % (percent sign not required). <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C3)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Accept positive or negative answer.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This was generally well done except for missing or incorrect units. Most candidates could give their answer in standard form and find the percentage error.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This was generally well done except for missing or incorrect units. Most candidates could give their answer in standard form and find the percentage error.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">\(z = \frac{{17{x^2}}}{{a - b}}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of <em>z </em>when <em>x</em> = 12.5, <em>a</em> = 0.572 and <em>b</em> = 0.447. Write down your full calculator display.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down your answer to part (a)</span></p>
<p><span>(i) correct to the nearest 1000 ;</span></p>
<p><span>(ii) correct to three significant figures.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write your answer to <strong>part (b)(ii)</strong> in the form <em>a</em> × 10<sup><em>k</em></sup>, where 1 ≤ <em>a</em> < 10, \(k \in \mathbb{Z}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(z = \frac{{17{{(12.5)}^2}}}{{(0.572 - 0.447)}}\) <em><strong>(M1)</strong></em></span></p>
<p><span><br><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into formula.</span></p>
<p><br><span>= 21250 <em><strong>(A1) </strong> <strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) 21000 <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>(ii) 21300 <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from part (a).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(2.13 \times 10^4\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for 2.13, <em><strong>(A1)</strong></em><strong>(ft)</strong> for \(\times 10^4\). Follow through from part (b)(ii).</span></p>
<p><span><em><strong>[ 2 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates calculated \(\frac{{17{x^2}}}{a} - b\) instead of \(\frac{{17{x^2}}}{{a - b}}\) on their calculators; however they were able to get follow through points. It is important that candidates learn how to correctly input expressions into their calculators.<br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates calculated \(\frac{{17{x^2}}}{a} - b\) instead of \(\frac{{17{x^2}}}{{a - b}}\) on their calculators; however they were able to get follow through points. It is important that candidates learn how to correctly input expressions into their calculators.<br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Although the question explicitly stated in bold to use the answer to <strong>part(b)(ii)</strong> many candidates used their answer to part (a) for part (c). The general notes about rounding in the mark scheme are over-ruled if the question has explicit directions such as in this question.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Water has a lower boiling point at higher altitudes. The relationship between the boiling point of water (<em>T</em>) and the height above sea level (<em>h</em>) can be described by the model \(T = -0.0034h +100\) where <em>T</em> is measured in degrees Celsius (</span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">°</span>C) and <em>h</em> is measured in metres from sea level.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the boiling point of water at sea level.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use the model to calculate the boiling point of water at a height of 1.37 km above sea level.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Water boils at the top of Mt. Everest at 70 </span><span><span>°</span>C.</span></p>
<p><span>Use the model to calculate the height above sea level of Mt. Everest.<br></span></p>
<p><span> </span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>100 °C <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(<em>T</em> = -0.0034 \times 1370 + 100\) <em><strong>(A1)(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <strong><em>(A1)</em></strong> for 1370 seen, <em><strong>(M1)</strong></em> for substitution of their <em>h</em> into</span> <span>the equation.</span></p>
<p><br><span>95.3 °C (95.342) <em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><span><strong>Notes:</strong> If their <em>h</em> is incorrect award at most <em><strong>(A0)(M1)(A0)</strong></em>. If their <em>h</em> = 1.37</span> <span>award at most <em><strong>(A0)(M1)(A1)</strong></em><strong>(ft)</strong>.</span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(70 = -0.0034h + 100\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted equation.</span></p>
<p><br><span><em>h</em> = 8820 m (8823.52...) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Note:</strong> The answer is 8820 m (or 8.82 km.) units are required.</span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The majority of the candidates showed they were able to substitute values into the model. The most common mistake was to neglect converting 1.37 km into metres. Some candidates did not appreciate the practical considerations of this question; Mount Everest will never be less than one metre high. It is important to remind students to check their answers in terms of the context of the information given.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The majority of the candidates showed they were able to substitute values into the model. The most common mistake was to neglect converting 1.37 km into metres. Some candidates did not appreciate the practical considerations of this question; Mount Everest will never be less than one metre high. It is important to remind students to check their answers in terms of the context of the information given.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The majority of the candidates showed they were able to substitute values into the model. The most common mistake was to neglect converting 1.37 km into metres. Some candidates did not appreciate the practical considerations of this question; Mount Everest will never be less than one metre high. It is important to remind students to check their answers in terms of the context of the information given.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: 'times new roman', times;">The length, in cm, of six baseball bats was measured. The lengths are given below.</span></p>
<p style="text-align: center;"><span style="font-size: medium; font-family: 'times new roman', times;">104.5, 105.1, 104.8, 105.2, 104.9, 104.9</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the <strong>exact value</strong> of the mean length.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write your answer to part (a) in the form <em>a</em> × 10<sup><em>k</em></sup> where 1 ≤ <em>a</em> < 10 and \(k \in \mathbb{Z}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Marian calculates the mean length and finds it to be 105 cm.</span></p>
<p><span>Calculate the percentage error made by Marian.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\left( {\frac{{104.5 + 105.1 + ...}}{6}} \right)\) <em><strong>(M1)</strong></em> </span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for use of mean formula.</span><br><br></p>
<p><span>= 104.9 (cm) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>1.049 × 10<sup>2 </sup><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for 1.049, <em><strong>(A1)</strong></em><strong>(ft)</strong> for 10<sup>2</sup>. Follow through from their part (a).</span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{105 - 104.9}}{{104.9}} \times 100\) (%) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for their correctly substituted % error formula.</span></p>
<p><br><span>% error = 0.0953 (%) (0.0953288...) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> A 2sf answer of 0.095 following </span><span><span>\(\frac{{105 - 104.9}}{{105}} \times 100\)</span> working is awarded no marks.</span> <span>Follow through from their part (a), provided it is not 105.</span> <span>Do not accept a negative answer.</span> <span>% sign not required.</span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Another well answered question with candidates showing a good understanding of standard form and many correct answers were seen in parts (a) and (b). Whilst the formula is given for percentage error, there were still a minority of candidates who divided by 105 rather than the required value of 104.9.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Another well answered question with candidates showing a good understanding of standard form and many correct answers were seen in parts (a) and (b). Whilst the formula is given for percentage error, there were still a minority of candidates who divided by 105 rather than the required value of 104.9.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Another well answered question with candidates showing a good understanding of standard form and many correct answers were seen in parts (a) and (b). Whilst the formula is given for percentage error, there were still a minority of candidates who divided by 105 rather than the required value of 104.9.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>In the Canadian city of Ottawa:</p>
<p>\[\begin{array}{*{20}{l}} {{\text{97% of the population speak English,}}} \\ {{\text{38% of the population speak French,}}} \\ {{\text{36% of the population speak both English and French.}}} \end{array}\]</p>
</div>
<div class="specification">
<p>The total population of Ottawa is \(985\,000\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the percentage of the population of Ottawa that speak English but not French.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the number of people in Ottawa that speak both English and French.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down your answer to part (b) in the form \(a \times {10^k}\) where \(1 \leqslant a < 10\) and <em>k </em>\( \in \mathbb{Z}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(97 - 36\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for subtracting 36 from 97.</p>
<p> </p>
<p><strong>OR</strong></p>
<p><img src="images/Schermafbeelding_2017-08-15_om_12.54.01.png" alt="M17/5/MATSD/SP1/ENG/TZ1/02.a/M"></p>
<p><strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for 61 <strong>and </strong>36 seen in the correct places in the Venn diagram.</p>
<p> </p>
<p>\( = 61{\text{ }}(\% )\) <strong><em>(A1)</em></strong> <strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept 61.0 (%).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{36}}{{100}} \times 985\,000\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for multiplying 0.36 (or equivalent) by \(985\,000\).</p>
<p> </p>
<p>\( = 355\,000{\text{ }}(354\,600)\) <strong><em>(A1)</em></strong> <strong><em>(C2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(3.55 \times {10^5}{\text{ }}(3.546 \times {10^5})\) <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong><em> </em><strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1)(ft) </em></strong>for 3.55 (3.546) <strong>must </strong>match part (b), and <strong><em>(A1)(ft)</em></strong> \( \times {10^5}\).</p>
<p>Award <strong><em>(A0)(A0) </em></strong>for answers of the type: \(35.5 \times {10^4}\). Follow through from part (b).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>In this question, give all answers correct to 2 decimal places.</strong></p>
<p>Jose travelled from Buenos Aires to Sydney. He used Argentine pesos, ARS, to buy 350 Australian dollars, AUD, at a bank. The exchange rate was 1 ARS = 0.1559 AUD.</p>
</div>
<div class="specification">
<p>The bank charged Jose a commission of 2%.</p>
</div>
<div class="specification">
<p>Jose used his credit card to pay his hotel bill in Sydney. The bill was 585 AUD. The value the credit card company charged for this payment was 4228.38 ARS. The exchange rate used by the credit card company was 1 AUD = \(x\) ARS. No commission was charged.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use this exchange rate to calculate the amount of ARS that is equal to 350 AUD.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the <strong>total </strong>amount of ARS Jose paid to get 350 AUD.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(x\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>Note: </strong>In this question, the first time an answer is not to 2 dp the final <strong><em>(A1) </em></strong>is not awarded.</p>
<p> </p>
<p>\(\frac{{350}}{{0.1559}}\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for dividing 350 by 0.1559.</p>
<p> </p>
<p>\( = 2245.03{\text{ (ARS)}}\) <strong><em>(A1) (C2)</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>\(2245.03 \times 1.02\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for multiplying their answer to part (a) by 1.02.</p>
<p> </p>
<p>\( = 2289.93{\text{ (ARS)}}\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></p>
<p><strong>OR</strong></p>
<p>\(2245.03 \times 0.02\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for multiplying their answer to part (a) by 0.02.</p>
<p> </p>
<p>\( = 44.9006\)</p>
<p>\(2245.03 + 44.90\)</p>
<p>\( = 2289.93{\text{ (ARS)}}\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from part (a).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{4228.38}}{{585}}\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for dividing 4228.38 by 585.</p>
<p> </p>
<p>\( = 7.23\) <strong><em>(A1) (C2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">\(U\) is the set of all the <strong>positive</strong> integers less than or equal to \(12\).</span><br><span style="font-size: medium; font-family: times new roman,times;">\(A\) , \(B\) and \(C\) are subsets of \(U\) .</span><br><span style="font-size: medium; font-family: times new roman,times;">\[A = \{ 1{\text{, }}2{\text{, }}3{\text{, }}4{\text{, }}6{\text{, }}12\} \]</span><span style="font-size: medium; font-family: times new roman,times;">\[B = \{ {\text{odd integers}}\} \]</span><span style="font-size: medium; font-family: times new roman,times;">\[C = \{ 5{\text{, }}6{\text{, }}8\} \]</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of elements in \(A \cap C\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>List the elements of \(B\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the following Venn diagram with <strong>all</strong> the elements of \(U\) .</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(1\) (one) <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><span><strong>Note:</strong> \(6\), \(\{6\} \) or \(\{1\} \) earns no marks.</span></p>
<p><span><em><strong>[1 mark]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(1\), \(3\), \(5\), \(7\), \(9\), \(11\) <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><span><strong>Note:</strong> Do not penalise if braces, parentheses or brackets are seen.</span></p>
<p><span><em><strong>[1 mark]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><img 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" alt><span> <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C4)</strong></em></span></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for the empty set \(A \cap B \cap C\) .</span></p>
<p><span>Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for the correct placement of \(6\), \(5\), \(1\) and \(3\).</span></p>
<p><span>Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for the correct placement of \(2\), \(4\), \(12\), \(7\), \(9\), \(11\), \(8\).</span></p>
<p><span>Award <strong><em>(A1)</em>(ft)</strong> for the correct placement of \(10\).</span></p>
<p><span>Follow through from part (b).</span></p>
<p><span><em><strong>[4 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">There was much confusion amongst candidates as to the understanding of the words <em>number of elements</em>. Many candidates simply wrote down \(6\) or \(\{ 6\} \) and consequently lost the first mark.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">There was much confusion amongst candidates as to the understanding of the words <em>number of elements</em>. Many candidates simply wrote down \(6\) or \(\{ 6\} \) and consequently lost the first mark. Part (b) was done well and many successful attempts were made at completing the Venn diagram in part (c). The most common error in the last part of the question was the omission of the element \(10\).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Part (b) was done well and many successful attempts were made at completing the Venn diagram in part (c). The most common error in the last part of the question was the omission of the element \(10\).</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The diagram below represents a rectangular flag with dimensions 150 cm by 92 cm. The flag is divided into three regions A, B and C.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the total area of the flag.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of <em>y</em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The areas of regions A, B, and C are equal.</span></p>
<p><span>Write down the area of region A.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using your answers to <strong>parts (b) and (c)</strong>, find the value of <em>x</em>.</span></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><span><em><strong>Units are required in this question for full marks to be awarded.</strong></em><br></span></p>
<p><span>13800 cm<sup>2</sup> <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>75 <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><strong><em>Units are required in this question for full marks to be awarded.</em></strong><br></span></p>
<p><span>4600 cm<sup>2</sup> <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C1)</strong></em></span></p>
<p><span><br><strong>Notes:</strong> Units are required unless already penalized in part (a). Follow through from their part (a).<br></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(0.5(x + 92) \times 75 = 4600\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><strong><span>OR</span></strong></p>
<p><span>\(0.5 \times 150 \times (92 - x) = 4600\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution into area formula, <em><strong>(A1)</strong></em><strong>(ft)</strong> for their correct</span> <span>substitution.</span></p>
<p><br><span>(= 30.7 (cm)(30.6666...(cm)) </span><span><em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C3)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from their parts (b) and (c).</span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A snack container has a cylindrical shape. The diameter of the base is \(7.84\,{\text{cm}}\). The height of the container is \(23.4\,{\text{cm}}\). This is shown in the following diagram.</p>
<p><img 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" alt></p>
<p>Write down the radius, in \({\text{cm}}\), of the base of the container.</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>Calculate the area of the base of the container.</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>Dan is going to paint the curved surface and the base of the snack container.</p>
<p>Calculate the area to be painted.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(3.92\,({\text{cm}})\) <em><strong>(A1) (C1)</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\pi \times {3.92^2}\) <em><strong>(M1)</strong></em></p>
<p>\( = 48.3\,{\text{c}}{{\text{m}}^2}\,\,\,(15.3664\,\pi \,{\text{c}}{{\text{m}}^2},\,\,48.2749...\,{\text{c}}{{\text{m}}^2})\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in area of circle formula. Follow through from their part (a). The answer is<strong> \(48.3\,{\text{c}}{{\text{m}}^2}\)</strong>, units are required.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(2 \times \pi \times 3.92 \times 23.4 + 48.3\) <em><strong> (M1)(M1)</strong></em></p>
<p>\(625\,{\text{c}}{{\text{m}}^2}\,\,\,(624.618...\,{\text{c}}{{\text{m}}^2})\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></p>
<p><strong>Note: </strong>Award <em><strong>(M1)</strong></em> for correct substitution in curved surface area formula, <em><strong>(M1)</strong></em> for adding their answer to part (b). Follow through from their parts (a) and (b). The answer is <strong>\(625\,{\text{c}}{{\text{m}}^2}\)</strong>, units are required.</p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Question 11: Cylinder base area and curved surface area.</p>
<p>In responses to this question, units were sometimes missing or the wrong units were given. The question explicitly asked for the base and curved surface area but many gave both the top and bottom as well as the curved surface area, or omitted the ends.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 11: Cylinder base area and curved surface area.</p>
<p>In responses to this question, units were sometimes missing or the wrong units were given. The question explicitly asked for the base and curved surface area but many gave both the top and bottom as well as the curved surface area, or omitted the ends.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 11: Cylinder base area and curved surface area.</p>
<p>In responses to this question, units were sometimes missing or the wrong units were given. The question explicitly asked for the base and curved surface area but many gave both the top and bottom as well as the curved surface area, or omitted the ends.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The first term of an arithmetic sequence is 7 and the sixth term is 22.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find </span><span>the common difference.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find </span><span>the twelfth term.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find </span><span>the sum of the first 100 terms.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(7 + 5d = 22\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in the AP formula. Accept list of numbers as solution.</span></p>
<p><br><span>\(d = 3\) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(u_{12} = 7 + 11 \times 3\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(= 40\) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Accept list of numbers.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(S_{100} = \frac{{100}}{{2}} (2 \times 7 + 99 \times 3)\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in the AP formula.</span></p>
<p><br><span>= 15550 <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Accept 15600</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Most candidates recognized the arithmetic sequence and used the correct formula, although some used a list to find the answers. A significant number of candidates were unable to find the sum of the first 100 terms and attempted to find the 100<sup>th</sup> term instead.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Most candidates recognized the arithmetic sequence and used the correct formula, although some used a list to find the answers. A significant number of candidates were unable to find the sum of the first 100 terms and attempted to find the 100<sup>th</sup> term instead.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Most candidates recognized the arithmetic sequence and used the correct formula, although some used a list to find the answers. A significant number of candidates were unable to find the sum of the first 100 terms and attempted to find the 100<sup>th</sup> term instead.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Consider the arithmetic sequence</span><br><span style="font-size: medium; font-family: times new roman,times;">\[{\text{326, 321, 316, 311, }} \ldots {\text{, 191.}}\]</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of the common difference of this sequence.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the sum of the first 10 terms of this sequence.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number of terms in this sequence.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(d = 321 - 326\) (or equivalent)</span></p>
<p><span>\( = - 5\) <em><strong>(A1)(A1) (C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for negative sign. <em><strong>(A1)</strong></em> for 5.</span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({S_{10}} = \frac{{10}}{2}(2(326) + 9( - 5))\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted formula. Follow through from part (a).</span></p>
<p><span><strong> </strong></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>\({u_{10}} = 281\)</span></p>
<p><span>\({S_{10}} = \frac{{10}}{2}(326 + 281)\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted formula, not for finding 281.</span></p>
<p><span> </span></p>
<p><span><strong>OR</strong></span></p>
<p><span>If a list is seen award <em><strong>(M1)</strong></em> for the correct list of 10 terms consistent with their \(d\). <em><strong>(M1)</strong></em></span></p>
<p><span>\( = 3035\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></span></p>
<p><span><span><strong>Note:</strong> If \(d = 5\) final answer is 3485. Follow through from part (a).</span> <span>No follow through if list used.</span></span></p>
<p><span><span><em><strong>[2 marks]</strong></em><br></span></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(191 = 326 + (n - 1)( - 5)\) (or equivalent) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award (M1) for correctly substituted formula. Follow through from part (a).</span></p>
<p><span><strong> </strong></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>If a list is seen award <em><strong>(M1)</strong></em> for the complete and correct list of terms or complete list of terms consistent with their \(d\). <em><strong>(M1)</strong></em></span></p>
<p><span>\(n = 28\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span></p>
<p><span><strong>Note:</strong> \(n\) must be a positive integer. Follow through from part (a). No follow through if list used.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">At whatever ability, there were good attempts by all candidates on this question with an overwhelming majority scoring half marks or more. The most common error was in part (a) where \(5\), rather than \( - 5\) resulted in a lost mark. Recovery was, of course, possible in the remainder of the question. Further errors occurred where lists, rather than formulae, were used in parts (b) and (c). Using properly constructed and accurate lists were not in themselves penalized; arithmetical errors seen in a significant number of lists given by candidates, however, were penalized.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">At whatever ability, there were good attempts by all candidates on this question with an overwhelming majority scoring half marks or more. The most common error was in part (a) where \(5\), rather than \( - 5\) resulted in a lost mark. Recovery was, of course, possible in the remainder of the question. Further errors occurred where lists, rather than formulae, were used in parts (b) and (c). Using properly constructed and accurate lists were not in themselves penalized; arithmetical errors seen in a significant number of lists given by candidates, however, were penalized.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">At whatever ability, there were good attempts by all candidates on this question with an overwhelming majority scoring half marks or more. The most common error was in part (a) where \(5\), rather than \( - 5\) resulted in a lost mark. Recovery was, of course, possible in the remainder of the question. Further errors occurred where lists, rather than formulae, were used in parts (b) and (c). Using properly constructed and accurate lists were not in themselves penalized; arithmetical errors seen in a significant number of lists given by candidates, however, were penalized.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Factorise the expression \({x^2} - 3x - 10\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A function is defined as \(f(x) = 1 + {x^3}\) for \(x \in \mathbb{Z}{\text{, }} {- 3} \leqslant x \leqslant 3\).</span></p>
<p><span>(i) List the elements of the domain of \(f(x)\).</span></p>
<p><span>(ii) Write down the range of \(f(x)\).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\((x - 5)(x + 2)\) <em><strong>(A1)(A1) (C2)</strong></em></span></p>
<p><span><strong>Note: </strong>Award <em><strong>(A1)</strong></em> for \((x + 5)(x - 2)\), <em><strong>(A0)</strong></em> otherwise. If equation is equated to zero and solved by factorizing award <em><strong>(A1)</strong></em> for both correct factors, followed by <em><strong>(A0)</strong></em>.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \( - 3\), \( - 2\), \( - 1\), \(0\), \(1\), \(2\), \(3\) <em><strong>(A1)(A1) (C2)</strong></em></span></p>
<p><span><strong><br>Note: </strong>Award <em><strong>(A2)</strong></em> for all correct answers seen and no others. Award <em><strong>(A1)</strong></em> for 3 correct answers seen.</span></p>
<p><br><span>(ii) \( - 26\), \( - 7\), 0,1, 2, 9, 28 <em><strong>(A1)(A1) (C2)</strong></em></span></p>
<p><span><strong><br>Note: </strong>Award <em><strong>(A2)</strong></em> for all correct answers seen and no others. Award <em><strong>(A1)</strong></em> for 3 correct answers seen. If domain and range are interchanged award <em><strong>(A0)</strong></em> for (b)(i) and <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong> for (b)(ii).</span></p>
<p><span><em><strong>[4 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">It was surprising how many candidates could not factorise this expression. Of those that could some went on to find the zeros of a quadratic equation which was not what the question was asking. Some confused domain and range and many did not write down all the values when they did know domain and range.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">It was surprising how many candidates could not factorise this expression. Of those that could some went on to find the zeros of a quadratic equation which was not what the question was asking. Some confused domain and range and many did not write down all the values when they did know domain and range.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Daniela is going for a holiday to South America. She flies from the US to Argentina stopping in Peru on the way.</p>
<p>In Peru she exchanges 85 United States dollars (USD) for Peruvian nuevo sol (PEN). The exchange rate is 1 USD = 3.25 PEN and a flat fee of 5 USD commission is charged.</p>
</div>
<div class="specification">
<p>At the end of Daniela’s holiday she has 370 Argentinean peso (ARS). She converts this back to USD at a bank that charges a 4% commission on the exchange. The exchange rate is 1 USD = 9.60 ARS.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the amount of PEN she receives.</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>Calculate the amount of USD she receives.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\((85 - 5) \times 3.25\) <strong><em>(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for subtracting 5 from 85, <strong><em>(M1) </em></strong>for multiplying by 3.25.</p>
<p>Award <strong><em>(M1) </em></strong>for \(85 \times 3.25\), <strong><em>(M1) </em></strong>for subtracting \(5 \times 3.25\).</p>
<p> </p>
<p>\( = 260{\text{ (PEN)}}\) <strong><em>(A1)</em></strong> <strong><em>(C3)</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{(370 \times 0.96)}}{{9.6}}\) <strong><em>(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for multiplying by 0.96 (or equivalent), <strong><em>(M1) </em></strong>for dividing by 9.6. If division by 3.25 seen in part (a), condone multiplication by 9.6 in part (b).</p>
<p> </p>
<p>\( = 37{\text{ (USD)}}\) <strong><em>(A1)</em></strong> <strong><em>(C3)</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Assume the Earth is a perfect sphere with radius <span class="s1">6371 km</span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the volume of the Earth in \({\text{k}}{{\text{m}}^3}\)<span class="s1">. Give your answer in the form \(a \times {10^k}\)</span>, where \(1 \leqslant a < 10\) <span class="s1">and \(k \in \mathbb{Z}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The volume of the Moon is \(2.1958 \times {10^{10}}\;{\text{k}}{{\text{m}}^3}\)<span class="s1">.</span></p>
<p class="p2">Calculate how many times greater in volume the Earth is compared to the Moon.</p>
<p class="p2">Give your answer correct to the nearest <strong>integer</strong>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{4}{3}\pi {(6371)^3}\) <strong><em>(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into volume formula.</p>
<p> </p>
<p>\( = 1.08 \times {10^{12}}\;\;\;(1.08320 \ldots \times {10^{12}})\) <strong><em>(A2) (C3)</em></strong></p>
<p><strong>Notes: </strong>Award <strong><em>(A1)(A0) </em></strong>for correct mantissa between 1 and 10, with incorrect index.</p>
<p>Award <strong><em>(A1)(A0) </em></strong>for \(1.08\rm{E}12\)</p>
<p>Award <strong><em>(A0)(A0) </em></strong>for answers of the type: \(108 \times {10^{10}}\).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{1.08320 \ldots \times {{10}^{12}}}}{{2.1958 \times {{10}^{10}}}}\) <strong><em>(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for dividing their answer to part (a) by \(2.1958 \times {10^{10}}\).</p>
<p> </p>
<p>\( = 49.3308 \ldots \) <strong><em>(A1)</em>(ft)</strong></p>
<p><strong>Note: </strong>Accept \(49.1848...\) from use of 3 sf answer to part (a).</p>
<p> </p>
<p>\( = 49\) <strong><em>(A1) (C3)</em></strong></p>
<p><strong>Notes: </strong>Follow through from part (a).</p>
<p>The final <strong><em>(A1) </em></strong>is awarded for their unrounded non-integer answer seen and given correct to the nearest integer.</p>
<p>Do not award the final <strong><em>(A1) </em></strong>for a rounded answer of 0 or if it is incorrect by a large order of magnitude.</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>In part (a) many candidates correctly substituted the volume formula and wrote correctly their answer using scientific notation. The calculator notation E12 was very rarely used. A minority converted to metres, resulting in an incorrect exponent. Some candidates used an incorrect equation or used their calculator incorrectly.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>In part (b) many candidates subtracted the values, where they should be divided, resulting in an answer of an unrealistic magnitude. Some reversed the numerator and denominator, leading to an answer of 0.02, which would have rounded to the unrealistic answer of 0. When a reasonable answer was found, the final mark for rounding was lost by some candidates when there was no rounding or when rounding was incorrect. There seemed to be little understanding of whether or not an answer was reasonable.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>In this question, give all answers to two decimal places.</strong></p>
<p>Karl invests 1000 US dollars (USD) in an account that pays a nominal annual interest of 3.5%, <strong>compounded quarterly</strong>. He leaves the money in the account for 5 years.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the amount of money he has in the account after 5 years.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the amount of <strong>interest</strong> he earned after 5 years.</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>Karl decides to donate this <strong>interest</strong> to a charity in France. The charity receives 170 euros (EUR). The exchange rate is 1 USD = <em>t</em> EUR.</p>
<p>Calculate the value of <em>t</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(1000{\left( {1 + \frac{{3.5}}{{4 \times 100}}} \right)^{4 \times 5}}\) <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution in compound interest formula, <em><strong>(A1)</strong></em> for correct substitution.</p>
<p><strong>OR </strong></p>
<p><em>N</em> = 5</p>
<p><em>I</em> = 3.5</p>
<p><em>PV</em> = 1000</p>
<p><em>P</em>/<em>Y</em> = 1</p>
<p><em>C</em>/<em>Y</em> = 4</p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <em>C</em>/<em>Y</em> = 4 seen, <em><strong>(M1)</strong></em> for other correct entries.</p>
<p><strong>OR</strong></p>
<p><em>N</em> = 5 × 4</p>
<p><em>I</em> = 3.5</p>
<p><em>PV</em> = 1000</p>
<p><em>P</em>/<em>Y</em> = 1</p>
<p><em>C</em>/<em>Y</em> = 4</p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <em>C</em>/<em>Y</em> = 4 seen, <em><strong>(M1)</strong></em> for other correct entries.</p>
<p>= 1190.34 (USD) <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution in compound interest formula, <em><strong>(A1)</strong></em> for correct substitution.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>190.34 (USD) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C4)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for subtraction of 1000 from their part (a)(i). Follow through from (a)(i).</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>\(\frac{{170}}{{190.34}}\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for division of 170 by their part (a)(ii).</p>
<p>= 0.89 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note:</strong> Follow through from their part (a)(ii).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">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><span style="font-family: times new roman,times; font-size: medium;">Consider the following four numbers.</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;">\(p = 0.00314{\text{ ; }}q = 0.00314 \times {10^2}{\text{ ; }}r = \frac{\pi }{{1000}}{\text{ ; }}s = 3.14 \times {10^{ - 2}}\)</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>One of these numbers is written in the form \(a \times {10^k}\) where \(1 \leqslant a < 10\) and \(k \in \mathbb{Z}\). Write down this number.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the smallest of these numbers.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of <strong><em>q</em> + <em>s</em></strong>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Give your answer to part (c) in the form \(a \times {10^k}\) where \(1 \leqslant a < 10\) and \(k \in \mathbb{Z}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>3.14 × 10<sup>–2</sup> <em><strong>or</strong> s</em> <em><strong>(A1) (C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>0.00314 <strong><em>or</em></strong> 3.14 × 10<sup>–3</sup> <strong><em>or</em></strong> <em>p</em> <em><strong> (M1)(A1) (C2)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for indication of comparing numbers where at least one of them is converted. The converted number does not have to be correct. A single converted number is sufficient for <em><strong>(M1)</strong></em> to be awarded.<em><strong><br></strong></em></span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>0.3454 (0.345) <em><strong> (A1) (C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>3.454 × 10<sup>–1</sup> (3.45 × 10<sup>–1</sup>) <em><strong> (A1)(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span></p>
<p><span> </span></p>
<p><span><span><strong>Notes:</strong> Follow through from their (c).</span></span></p>
<p><span><span>Award <em><strong>(A1)</strong></em> for 3.454 (3.45) <em><strong>(A1)</strong></em> for 10<sup>–1</sup>.</span></span></p>
<p><span><span> </span></span></p>
<p><em><strong><span><span>[2 marks]</span></span></strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">In general this question was answered correctly by the majority of the candidates.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">In general this question was answered correctly by the majority of the candidates. Part b presented difficulty for some students by asking them to compare the given numbers. A common error found in this part was that the value of π was given as 3.14. A method mark was awarded when a comparison was attempted.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">In general this question was answered correctly by the majority of the candidates.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">In general this question was answered correctly by the majority of the candidates.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Susi travels from Singapore to Thailand and changes 1500 Singapore dollars (SGD) to Thai baht (THB). The exchange rate is 1 SGD buys 21.03464 THB.</span></p>
</div>
<div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Susi leaves Thailand and travels to Indonesia. She has \(20\,000\) THB and uses these to </span><span style="font-family: 'times new roman', times; font-size: medium;">buy Indonesian rupiah (IDR). The exchange rate is 3.28352 THB buys 1000 IDR.</span></p>
</div>
<div class="specification">
<p><span style="font-family: 'times new roman', times; font-size: medium;">Susi wants to find the approximate exchange rate between Singapore dollars and Indonesian rupiah and uses the exchange rates for Thai baht to do this.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the number of Thai baht Susi buys. Give your answer <strong>correct to the</strong></span> <span><strong>nearest baht</strong>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>Calculate the <strong>total</strong> number of Indonesian rupiah Susi receives, <strong>correct to the</strong></span> <span><strong>nearest thousand rupiah</strong>.</span></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>Calculate Susi’s exchange rate between Singapore dollars and Indonesian rupiah.</span> <span>Give your answer in the form 1 SGD buys <em>x</em> IDR, where <em>x</em> is given correct to the </span><span>nearest rupiah.</span></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>1500 \( \times \) 21.03464 <em><strong>(M1)</strong></em></span></p>
<p><span><span>\( = 31\,552\) </span><span> <em><strong>(A1) (C2)</strong></em></span></span></p>
<p><span><span><em><strong>[2 marks]</strong></em></span></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{20 000}} \times \frac{{1000}}{{3.28352}}\) <strong><em>(M1)</em></strong></span></p>
<p><span>\( = {\text{6}}\,{\text{091}}\,{\text{000}}\) <em><strong>(A1) (C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{21.03464}}{{3.28352}} \times 1000\) <em><strong> (M1)</strong></em></span></p>
<p><span>1 SGD = 6406 IDR <em><strong>(A1) (C2)</strong></em></span></p>
<p><span><strong> </strong></span></p>
<p><span><strong>Note:</strong> Accept 6406.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The vast majority of candidates answered at least part of this question with a significant </span><span style="font-family: times new roman,times; font-size: medium;">number achieving full marks. A number did have a financial penalty applied for not giving </span><span style="font-family: times new roman,times; font-size: medium;">their answers according to the specified accuracy level for the question. The most difficult </span><span style="font-family: times new roman,times; font-size: medium;">part turned out to be (c) and a number of students didn’t attempt it at all. There were very few</span> <span style="font-family: times new roman,times; font-size: medium;">candidates who used the incorrect conversion.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The vast majority of candidates answered at least part of this question with a significant</span> <span style="font-family: times new roman,times; font-size: medium;">number achieving full marks. A number did have a financial penalty applied for not giving </span><span style="font-family: times new roman,times; font-size: medium;">their answers according to the specified accuracy level for the question. The most difficult </span><span style="font-family: times new roman,times; font-size: medium;">part turned out to be (c) and a number of students didn’t attempt it at all. There were very few</span> <span style="font-family: times new roman,times; font-size: medium;">candidates who used the incorrect conversion.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The vast majority of candidates answered at least part of this question with a significant</span> <span style="font-family: times new roman,times; font-size: medium;">number achieving full marks. A number did have a financial penalty applied for not giving </span><span style="font-family: times new roman,times; font-size: medium;">their answers according to the specified accuracy level for the question. The most difficult </span><span style="font-family: times new roman,times; font-size: medium;">part turned out to be (c) and a number of students didn’t attempt it at all. There were very few</span> <span style="font-family: times new roman,times; font-size: medium;">candidates who used the incorrect conversion.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">\(T = \frac{{\left( {\tan (2z) + 1} \right)\left( {2\cos (z) - 1} \right)}}{{{y^2} - {x^2}}}\), where \(x = 9\), \(y = 41\) and \(z = 30^\circ \).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the <strong>exact </strong>value of \(T\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Give your answer to \(T\) correct to</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>two significant figures;</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>three decimal places.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Pyotr estimates the value of \(T\) <span class="s1">to be \(0.002\)</span>.</p>
<p class="p1">Calculate the percentage error in Pyotr’s estimate.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\frac{{\left( {\tan (2 \times 30) + 1} \right)\left( {2\cos (30) - 1} \right)}}{{{{41}^2} - {9^2}}}\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Note:<span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for correct substitution into formula<span class="s1">.</span></p>
<p class="p3"> </p>
<p class="p1">\( = 0.00125\;\;\;\left( {\frac{1}{{800}}} \right)\) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C2)</em></strong></p>
<p class="p1"><strong>Note:<span class="Apple-converted-space"> </span></strong>Using radians the answer is \( - 0.000570502\), award at most <strong><em>(M1)(A0)</em></strong>.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> \(0.0013\)</span><span class="s1"><span class="Apple-converted-space"> </span></span><strong><em>(A1)</em>(ft)</strong></p>
<p class="p1"><strong>Note: </strong>Follow through from part (a).</p>
<p class="p2"> </p>
<p class="p1">(ii) <span class="Apple-converted-space"> \(0.001\)</span><span class="s1"> <span class="Apple-converted-space"> </span></span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C2)</em></strong></p>
<p class="p1"><strong>Note:<span class="Apple-converted-space"> </span></strong>Follow through from part (a).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\left| {\frac{{0.002 - 0.00125}}{{0.00125}}} \right| \times 100\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for their correct substitution into the percentage error formula. Absolute value signs are not required.</p>
<p class="p1">Their <strong>unrounded </strong>answer from part (a) must be used.</p>
<p class="p1">Do <strong>not </strong>accept use of answers from part (b).</p>
<p class="p2"> </p>
<p class="p1">\( = 60{\text{ (%)}}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C2)</em></strong></p>
<p class="p1"><strong>Notes: </strong>The \({\text{%}}\)<span class="s1"> </span>sign is not required.</p>
<p class="p1">The answer from radians is \(450.568{\text{%}}\), award <strong><em>(M1)(A1)</em>(ft)</strong>.</p>
<p class="p1">Follow through from part (a).</p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Despite a significant number of candidates scoring well on this question, many candidates failed to use their calculator correctly. Common errors identified were: the use of radians; incorrect use of the double parentheses, calculating tan(61) instead of tan(60) + 1 ; or premature rounding. Such candidates earned, at most, method in part (a).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Despite errors in part (a), part (b)(i) tended to be often a correct follow through answer but some candidates struggled to give a 2 sf answer correctly, using truncation instead of rounding or dropping the leading zeros. Part (b)(ii) was more often answered correctly.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>In part (c) many candidates used the percentage error formula incorrectly, reversing the estimated and the exact value, or using one of the rounded answers from part (b) as the exact value.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">56 students were given a test out of 40 marks. The teacher used the following box and whisker plot to represent the marks of the students.</span></p>
<p style="text-align: center;"><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down </span><span>the median mark</span><span>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down</span><span> the 75<sup><span>th</span></sup> percentile mark</span><span>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the range of marks.</span></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><span>Estimate the number of students who achieved a mark greater than 32.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>30 <em><strong> (A1) (C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>32 <strong><em> (A1) (C1)</em></strong></span></p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>38 – 10 = 28 <strong><em> (A1)(A1) (C2)</em></strong></span></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em></strong> for 10 and 38 seen, <strong><em>(A1)</em></strong> for correct answer only.</p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>0.25 × 56 = 14 <em><strong> (M1)(A1) (C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for multiplying 0.25 by 56.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Many students had difficulty with reading the box and whisker plot and interpreting this question. Some candidates had difficulty with finding the range in part (a)(iii). Many wrote down the end points for the required range of data instead of writing the difference between the largest and smallest values. A number of candidates had problems estimating the number of students who achieved a mark greater than 32. Many students used the number 40 instead of the total number of student 56 for the estimation in part b).</span></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Many students had difficulty with reading the box and whisker plot and interpreting this question. Some candidates had difficulty with finding the range in part (a)(iii). Many wrote down the end points for the required range of data instead of writing the difference between the largest and smallest values. A number of candidates had problems estimating the number of students who achieved a mark greater than 32. Many students used the number 40 instead of the total number of student 56 for the estimation in part b).</span></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Many students had difficulty with reading the box and whisker plot and interpreting this question. Some candidates had difficulty with finding the range in part (a)(iii). Many wrote down the end points for the required range of data instead of writing the difference between the largest and smallest values. A number of candidates had problems estimating the number of students who achieved a mark greater than 32. Many students used the number 40 instead of the total number of student 56 for the estimation in part b).</span></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Many students had difficulty with reading the box and whisker plot and interpreting this question. Some candidates had difficulty with finding the range in part (a)(iii). Many wrote down the end points for the required range of data instead of writing the difference between the largest and smallest values. A number of candidates had problems estimating the number of students who achieved a mark greater than 32. Many students used the number 40 instead of the total number of student 56 for the estimation in part b).</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A comet orbits the Sun and is seen from Earth every <span class="s1">37 </span>years. The comet was first seen from Earth in the year <span class="s1">1064</span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the year in which the comet was seen from Earth for the fifth time.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Determine how many times the comet has been seen from Earth up to the year <span class="s1">2014</span><span class="s2">.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(1064 + (5 - 1) \times 37\) </span><strong><em>(M1)(A1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for substituted arithmetic sequence formula, <strong><em>(A1) </em></strong>for correct substitution.</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\( = 1212\) </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C3)</em></strong></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(2014 > 1064 + (n - 1) \times 37\) </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for a correct substitution into arithmetic sequence formula.</p>
<p class="p3">Accept an equation.</p>
<p class="p3"> </p>
<p class="p3"><span class="Apple-converted-space">\((n < ){\text{ }}26.6756 \ldots \) </span><strong><em>(A1)</em></strong></p>
<p class="p3"><span class="s2">26 </span>(times) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C3)</em></strong></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award the final <strong><em>(A1) </em></strong>for the correct rounding <strong>down </strong>of their unrounded answer.</p>
<p class="p2"> </p>
<p class="p3"><strong>OR</strong></p>
<p class="p3"><span class="Apple-converted-space">\(2014 > 1064 + 37t\) </span><strong><em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for a correct substitution into a linear model (where \(t = n - 1\)).</p>
<p class="p3">Accept an equation or weak inequality.</p>
<p class="p3">Accept \(\frac{{2014 - 1064}}{{37}}\) for <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong>.</p>
<p class="p2"> </p>
<p class="p3"><span class="Apple-converted-space">\((t < ){\text{ }}25.6756 \ldots \) </span><strong><em>(A1)</em></strong></p>
<p class="p2"> </p>
<p class="p3"><span class="s2">26 </span>(times) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C3)</em></strong></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award the final <strong><em>(A1) </em></strong>for adding <span class="s2">1 </span>to the correct rounding down of their unrounded answer.</p>
<p class="p2"> </p>
<p class="p3"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p><span>Kunal borrows 200 000 Indian rupees (INR) from a money lender for 18 months at a nominal annual interest rate of \(15\% \), <strong>compounded monthly</strong>.</span></p>
<p><span>Calculate the <strong>total amount</strong> that Kunal must repay at the end of the 18 months. Give your answer to the nearest rupee.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span>\(A = 200000{\left( {1 + \frac{{15}}{{100 \times 12}}} \right)^{1.5 \times 12}}\) <em><strong>(M1)(A1)</strong></em><strong> <br></strong></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituted compound interest formula, <em><strong>(A1)</strong></em> for correct substitutions.</span></p>
<p><br><span>\( = 250115.4788\) INR <em><strong>(A1)</strong></em></span></p>
<p><span>\( = 250115\) INR <em><strong>(A1) (C4)</strong></em></span></p>
<p><span><strong>Note:</strong> Award final <em><strong>(A1)</strong></em> for their answer correct to the nearest rupee.</span></p>
<p><span><em><strong>[4 marks]</strong></em><br></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-size: medium; font-family: times new roman,times;">In part (b), some candidates simply worked out the interest earned. If a correct substitution into the correct formula was seen leading to \(50115\) then only one mark was lost. Whilst many correctly quoted formula were seen in part (b), an incorrect substitution (particularly poor or missing use of the factor \(12\)) lost the next two marks and, whilst the final mark could be earned irrespective of incorrect working, many candidates either ignored the final demand or did not know how to give their answer to the nearest rupee.</span></p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Sasha travelled from the USA to Mexico and converted 650 US dollars (USD) to Mexican pesos (MXN). Her bank offered an exchange rate of 1 USD = 12.50 MXN.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number of MXN that Sasha received.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Before her return to the USA, Sasha exchanged 2300 MXN back into USD. The bank charged a commission of 1 %. The exchange rate was still 1 USD = 12.50 MXN. </span></p>
<p><span>Write down the commission charged by the bank in MXN.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>Before her return to the USA, Sasha exchanged 2300 MXN back into USD. The bank charged a commission of 1 %. The exchange rate was still 1 USD = 12.50 MXN. </span></span></p>
<p><span>Calculate the amount of USD that Sasha received after commission. Give your answer correct to the nearest USD.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>650×12.50 <em><strong>(M1)</strong></em></span></p>
<p><span>8125 (MXN) <em><strong>(A1) </strong></em><em><strong>(C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Accept 8130.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>23 (MXN) <em><strong>(A1) </strong></em><em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{2300 - their{\text{ }}23}}{{12.50}}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for setting up the expression.</span></p>
<p><span> </span></p>
<p><span>182.16 (USD) <em><strong>(A1)</strong></em><strong>(ft)</strong><br></span></p>
<p> </p>
<p><span><strong>Note:</strong> Follow through from their answer to part (b).<br></span></p>
<p><span> </span></p>
<p><span>182 (USD) <em><strong>(A1)</strong></em><strong>(ft) </strong><em><strong>(C3)</strong></em><br></span></p>
<p> </p>
<p><span><strong>Notes:</strong> Award final <em><strong>(A1)</strong></em> for their answer correct to the nearest USD.<br></span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">A lot of good work was seen in this question with many completely correct solutions. The two marks which were seen to be lost more often than others were the answer to part (b) where $1.84 was seen rather than the required answer of 23 MXN, and the final mark in part (c) where, in many cases, the answer was left as $ 182.16.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">A lot of good work was seen in this question with many completely correct solutions. The two marks which were seen to be lost more often than others were the answer to part (b) where $1.84 was seen rather than the required answer of 23 MXN, and the final mark in part (c) where, in many cases, the answer was left as $ 182.16.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">A lot of good work was seen in this question with many completely correct solutions. The two marks which were seen to be lost more often than others were the answer to part (b) where $1.84 was seen rather than the required answer of 23 MXN, and the final mark in part (c) where, in many cases, the answer was left as $ 182.16.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Julio is making a wooden pencil case in the shape of a large pencil. The pencil case consists of a cylinder attached to a cone, as shown.</p>
<p>The cylinder has a radius of <em>r</em> cm and a height of 12 cm.</p>
<p>The cone has a base radius of <em>r</em> cm and a height of 10 cm.</p>
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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for the slant height of the cone <strong>in terms of <em>r</em></strong>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The total external surface area of the pencil case rounded to 3 significant figures is 570 cm<sup>2</sup>.</p>
<p>Using your graphic display calculator, calculate the value of <em>r</em>.</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>(slant height<sup>2</sup> =) 10<sup>2</sup> + <em>r </em><sup>2</sup> <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> For correct substitution of 10 and <em>r</em> into Pythagoras’ Theorem.</p>
<p>\(\sqrt {{{10}^2} + {r^2}} \) <em><strong>(A1) (C2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\pi {r^2} + 2\pi r \times 12 + \pi r\sqrt {100 + {r^2}} = 570\) <em><strong>(M1)(M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in curved surface area of cylinder and area of the base, <em><strong>(M1)</strong></em> for their correct substitution in curved surface area of cone, <em><strong>(M1)</strong></em> for adding their 3 surface areas and equating to 570. Follow through their part (a).</p>
<p>= 4.58 (4.58358...) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C4)</strong></em></p>
<p><strong>Note:</strong> Last line must be seen to award final <em><strong>(A1)</strong></em>. Follow through from part (a).</p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Matryoshka dolls, or Russian dolls, are similarly designed dolls which open up and fit inside each other.</p>
<p>The largest set of these type of dolls is a 51 piece set which was completed in 2003. The height of the largest piece in this set is 54 cm. The heights of successive smaller dolls are 94 % of the preceding larger doll, as shown.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the height of the smallest doll in this set.</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 <strong>total</strong> height if all 51 dolls were placed one on top of another.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>54 × (0.94)<sup>50</sup> <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution into geometric sequence formula, <em><strong>(A1)</strong></em> for correct substitution.</p>
<p>2.45 (cm) (2.44785… cm) <em><strong>(A1) (C3)</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{54 \times \left( {1 - {{\left( {0.94} \right)}^{51}}} \right)}}{{1 - 0.94}}\) (or equivalent) <strong><em>(M1)(A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution into geometric series formula, <em><strong>(A1)</strong></em><strong>(ft)</strong> for correct substitution using their common ratio from part (a).</p>
<p>= 862 (cm) (861.650…(cm)) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the following numbers in increasing order.</span></p>
<p><span>\(3.5\), \(1.6 \times 10^{−19}\), \(60730\), \(6.073 \times 10^{5}\), \(0.006073 \times 10^6\), \(\pi\), \(9.8 \times 10^{−18}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the median of the numbers in part (a).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State which of the numbers in part (a) is irrational.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><span>\(1.6 \times 10^{−19}\)</span>, </span><span><span>\(9.8 \times 10^{−18}\)</span>,</span><span><span> \(\pi\)</span>, </span><span><span>\(3.5\)</span>, </span><span><span>\(0.006073 \times 10^6\)</span>, \(60730\), </span><span>\(6.073 \times 10^{5}\) <em><strong>(A4)</strong></em></span></p>
<p><em><span>Award <strong>(A1)</strong> for </span></em><em><span><span><span> \(\pi\) </span></span>before 3.5</span></em></p>
<p><em><span>Award <strong>(A1)</strong> for </span></em><em><span><span><span>\(1.6 \times 10^{−19}\)</span></span> before </span></em><span><span>\(9.8 \times 10^{−18}\)</span></span></p>
<p><em><span>Award <strong>(A1)</strong> for the three numbers containing 6073 in the correct</span> <span>order.</span></em></p>
<p><em><span>Award <strong>(A1)</strong> for the pair with negative indices placed before 3.5 and</span></em> <span><span>\(\pi\) </span></span><em><span>and the remaining three numbers placed after (independently of</span></em> <em><span>the other three marks).</span></em></p>
<p><em><span>Award <strong>(A3)</strong> for numbers given in correct decreasing order.</span></em></p>
<p><em><span>Award <strong>(A2)</strong> for decreasing order with at most 1 error <strong>(C4)</strong></span></em></p>
<p><em><span><strong>[3 marks]</strong></span></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>The median is 3.5. <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><em><span>Follow through from candidate’s list. <strong>(C1)</strong></span></em></p>
<p><em><span><strong>[1 mark]</strong></span></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\pi\) is irrational. <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This was the best-answered question on the paper with most candidates achieving 5 or 6 marks. The main errors were finding the mean instead of the median in part (b) and giving numbers with negative indices as irrational numbers for part (c). Some candidates gave the list in reverse order (which lost them one mark).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This was the best-answered question on the paper with most candidates achieving 5 or 6 marks. The main errors were finding the mean instead of the median in part (b) and giving numbers with negative indices as irrational numbers for part (c). Some candidates gave the list in reverse order (which lost them one mark).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This was the best-answered question on the paper with most candidates achieving 5 or 6 marks. The main errors were finding the mean instead of the median in part (b) and giving numbers with negative indices as irrational numbers for part (c). Some candidates gave the list in reverse order (which lost them one mark).</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the function \(f(x) = 1.25 - {a^{ - x}}\) , where a is a positive constant and \(x \geqslant 0\). The diagram shows a sketch of the graph of \(f\) . The graph intersects the \(y\)-axis at point A and the line \(L\) is its horizontal asymptote.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the \(y\)-coordinate of A .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The point \((2{\text{, }}1)\) lies on the graph of \(y = f(x)\) . Calculate the value of \(a\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The point \((2{\text{, }}1)\) lies on the graph of \(y = f(x)\) . Write down the equation of \(L\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(y = 1.25 - {a^0}\) \(1.25 - 1\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(= 0.25\) <em><strong>(A1) (C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)(A1)</strong></em> for \((0{\text{, }}0.25)\) .</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(1 = 1.25 - {a^{ - 2}}\) <em><strong>(M1)</strong></em></span><br><span>\(a = 2\) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(y = 1.25\) <em><strong>(A1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(y =\) “a constant”, <em><strong>(A1)</strong></em> for \(1.25\).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Very few candidates showed working and subsequently lost marks due to this. Many candidates seemed to forget that \({a^0} = 1\) and not \(0\).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Very few candidates showed working and subsequently lost marks due to this. Many candidates seemed to forget that \({a^0} = 1\) and not \(0\).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Very few candidates showed working and subsequently lost marks due to this. Many candidates seemed to forget that \({a^0} = 1\) and not \(0\).</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><strong>In this question give all answers correct to the nearest whole number.</strong></p>
<p>Loic travelled from China to Brazil. At the airport he exchanged 3100 Chinese Yuan, \({\text{CNY}}\), to Brazilian Real, \({\text{BRL}}\), at an exchange rate of \({\text{1}}\,{\text{ CNY = 0}}{\text{.3871 BRL}}\).</p>
<p>No commission was charged.</p>
<p>Calculate the amount of \({\text{BRL}}\) he received.</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>When he returned to China, Loic changed his remaining \({\text{BRL}}\) at a bank. The exchange rate at the bank was \({\text{1}}\,{\text{ CNY = 0}}{\text{.3756 BRL}}\) and a commission of \(5\% \) was charged. He received \(285\,\,{\text{CNY}}\).</p>
<p>i) Calculate the amount of \({\text{CNY}}\) Loic would have received if no commission was charged.</p>
<p>ii) Calculate the amount of \({\text{BRL}}\) Loic exchanged when he returned to China.</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>\(3100\, \times \,0.3871\) <em><strong>(M1)</strong></em></p>
<p>\( = 1200\) <em><strong>(A1) (C2)</strong></em></p>
<p>Note: Award <em><strong>(M1)</strong></em> for multiplication by \(0.3871\). Answer must be an integer for the <em><strong>(A1)</strong></em> to be awarded.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>i) \(\frac{{285}}{{0.95}}\) <em><strong>(M1)</strong></em></p>
<p>\( = 300\) <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for division by \(0.95\). Answer must be an integer for the <em><strong>(A1)</strong></em> to be awarded.</p>
<p> </p>
<p>ii) \({\text{their }}300 \times 0.3756\) <em><strong>(M1)</strong></em></p>
<p>\( = 113\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C4)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for multiplying their answer to part (b)(i) by \(0.3756\). Follow through from part (b)(i). Answer must be an integer.</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Question 9: Currency exchange<br>In this question, incorrect rounding was once again the cause of many lost marks. It was surprising how many candidates have little idea about currency exchange and even less about the notion of commission. This part of the course is tested every year.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>In this question, incorrect rounding was once again the cause of many lost marks. It was surprising how many candidates have little idea about currency exchange and even less about the notion of commission. This part of the course is tested every year.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Consider the geometric sequence 16, 8, <em>a</em>, 2, <em>b</em>, …</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the common ratio.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of</span><span> <em>a</em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of <em>b</em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The sum of the first <em>n</em> terms is 31.9375. Find the value of <em>n</em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>0.5 \(\left( {\frac{1}{2}} \right)\)</span> <em><strong><span> (A1)</span></strong></em><span> </span><em><strong><span>(C1)</span></strong></em></p>
<p><em><strong><span>[1 mark]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>4 <em><strong>(A1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>1 <strong><em> (A1) (C2)</em></strong></span></p>
<div><span><strong><em>[1 mark]</em></strong></span></div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{16(1 - {{0.5}^n})}}{{(1 - 0.5)}} = 31.9375\) <em><strong>(M1)(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in the GP formula, <em><strong>(M1)</strong></em> for</span> <span>equating their sum to 31.9375.</span></p>
<p><span> </span></p>
<p><strong><span>OR</span></strong></p>
<p><span>sketch of the function </span><span>\(y = \frac{{16(1 - {{0.5}^n})}}{{(1 - 0.5)}} \) </span><em><strong><span>(M1)</span></strong></em></p>
<p><span>indication of point where <em>y</em> = 31.9375 <em><strong>(M1)</strong></em></span></p>
<p><strong><span>OR</span></strong></p>
<p><span>16 + 8 + 4 + 2 + 1 + 0.5 + 0.25 + 0.125 + 0.0625 = 31.9375 <em><strong>(M1)(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for a list of at least 7 correct terms, <em><strong>(A1)</strong></em> for the sum</span> <span>of the terms equated to 31.9375.</span></p>
<p><br><span><em>n</em> = 9 <em><strong> (A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from their answer to part (a) but answer mark is</span> <span>lost if <em>n</em> is not a whole number.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Parts a) and b) of this question were well answered by many of the candidates, although in</span> <span style="font-family: times new roman,times; font-size: medium;">some cases students wrote ½ instead of 2 for the common ratio in a).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Parts a) and b) of this question were well answered by many of the candidates, although in</span> <span style="font-family: times new roman,times; font-size: medium;">some cases students wrote ½ instead of 2 for the common ratio in a).</span></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Parts a) and b) of this question were well answered by many of the candidates, although insome cases students wrote ½ instead of 2 for the common ratio in a).</span></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates were </span><span style="font-family: times new roman,times; font-size: medium;">also able to set an equation in c) with a correct expression of the sum of the first n terms </span><span style="font-family: times new roman,times; font-size: medium;">equated to 31.9375, for which they gained two more marks. The last mark in many cases was</span> <span style="font-family: times new roman,times; font-size: medium;">not awarded either because the candidates didn’t know how to solve the equation or/and </span><span style="font-family: times new roman,times; font-size: medium;">gave an incorrect answer.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Mr Tan invested 5000 Swiss Francs (CHF) in Bank A at an annual simple interest rate of <em>r</em> %, for four years. The total interest he received was 568 CHF.</span></p>
</div>
<div class="question">
<p><span>Mr Black invested 5000 CHF in Bank B at a nominal annual interest rate of 3.6 %, </span><span><strong>compounded quarterly</strong> for four years.</span></p>
<p><span>Calculate the total interest he received at the end of the four years. Give your answer correct to <strong>two decimal places</strong>.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><em><strong><span>Financial penalty (FP) applies in part (b).</span></strong></em></p>
<p><span> </span></p>
<p><span>\(I = 5000(1.009)^{16} - 5000\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution into the compound interest formula, <em><strong>(A1)</strong></em> for correct values.</span></p>
<p><br><span><em><strong>(FP)</strong></em> <em>I</em> = 770.70 CHF <em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was answered well by many candidates, with a majority of them gaining maximum marks. Some candidates used the proper formula but had done incorrect substitution.</span></p>
</div>
<br><hr><br><div class="specification">
<p>Each year the soccer team, Peterson United, plays 25 games at their home stadium. The owner of Peterson United claimed that last year the mean attendance per game at their home stadium was 24500.</p>
</div>
<div class="specification">
<p>The actual total attendance last year was 617700.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Based on the owner’s claim, calculate the total attendance for the games at Peterson United’s home stadium last year.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the percentage error in the owner’s claim.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down your answer to <strong>part (b)</strong> in the form <em>a</em> × 10<em><sup>k</sup></em> where 1 ≤ a < 10, \(k \in \mathbb{Z}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>24500 × 25 <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for multiplying 24500 by 25.</p>
<p>= 613000 (612500) <em><strong>(A1) (C2)</strong></em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\left| {\frac{{612500 - 617700}}{{617700}}} \right| \times 100\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into the percentage error formula.</p>
<p>= 0.842 (0.841832) <strong>(A1)<em>(ft) </em> (C2)</strong></p>
<p><strong>Note:</strong> Follow through from part (a).</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>8.42 × 10<sup>−1</sup> <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft) <em>(C2)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(A0)(A0)</em></strong> for answers of the type 84.2 × 10<sup>−2</sup>. Follow through from part (b). Ignore ‘%’ sign.</p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The population of big cats in Africa is increasing at a rate of 5 % per year. At the beginning of 2004 the population was \(10\,000\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the population of big cats at the beginning of 2005.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the population of big cats at the beginning of 2010.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number of years, from the beginning of 2004, it will take the population of big cats to exceed \(50\,000\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(10\,000 \times 1.05\)</span></p>
<p><span>\( = 10\,500\) <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(10\,000 \times {1.05^6}\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into correct formula.</span></p>
<p><br><span>\( = 13\,400\) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(50\,000 = 10\,000 \times 1.05''\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for \(10\,000 \times 1.05''\) or equivalent, <em><strong>(A1)</strong></em> for \(50\,000\)</span></p>
<p><br><span>\(n = 33.0\) (Accept 33) <em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was well answered by many candidates, particularly part (a).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was well answered by many candidates, particularly part (a). However, a significant number of students lost a mark for rounding up rather than down in part (b).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was well answered by many candidates, particularly part (a). However, a significant number of students lost a mark for rounding up rather than down in part (b). Part (c) proved to be the most difficult both for generating the equation and for solving it.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the numbers \(p = 2.78 \times {10^{11}}\) and \(q = 3.12 \times {10^{ - 3}}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate \(\sqrt[3]{{\frac{p}{q}}}\). Give your full calculator display.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down your answer to part (a) correct to two decimal places;</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down your answer to part (a) correct to three significant figures.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write your answer to <strong>part (b)(ii) </strong>in the form \(a \times {10^k}\), where \(1 \leqslant a < 10,{\text{ }}k \in \mathbb{Z}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(\sqrt[3]{{\frac{{2.78 \times {{10}^{11}}}}{{3.12 \times {{10}^{ - 3}}}}}}\)\(\,\,\,\)<strong>OR</strong>\(\,\,\,\)\(\sqrt[3]{{8.91025 \ldots \times {{10}^{13}}}}\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution into given expression.</p>
<p> </p>
<p>44664.59503 <strong><em>(A1)</em></strong> <strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for a correct answer with at least 8 digits.</p>
<p>Accept 44664.5950301.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>44664.60 <strong><em>(A1)</em>(ft)</strong><em> </em><strong><em>(C1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> For a follow through mark, the answer to part (a) must be to at least 3 decimal places.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>44700 <strong><em>(A1)</em>(ft)</strong><em> </em><strong><em>(C1)</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Answer to part (a) must be to at least 4 significant figures.</p>
<p>Accept any equivalent notation which is correct to 3 significant figures.</p>
<p>For example \(447 \times {10^2}\) or \(44.7 \times {10^3}\).</p>
<p>Follow through from part (a).</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(4.47 \times {10^4}\) <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong> <strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Award <strong><em>(A1)</em>(ft) </strong>for 4.47 and <strong><em>(A1)</em>(ft) </strong>for \({10^4}\).</p>
<p>Award <strong><em>(A0)(A0) </em></strong>for answers such as \(44.7 \times {10^3}\).</p>
<p>Follow through from part (b)(ii) <strong>only</strong>.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Veronica wants to make an investment and accumulate 25 000 EUR over a period of 18 years. She finds two investment options.</span></p>
</div>
<div class="question">
<p><span>Option 2 offers a nominal annual interest rate of 4 %, <strong>compounded monthly</strong>.</span></p>
<p><span>Find the amount that Veronica has to invest with option 2 to have 25 000 EUR in her account after 18 years. Give your answer correct to <strong>two decimal places</strong>.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span>\({\text{C}} = {\left( {1 + \frac{{0.04}}{{12}}} \right)^{12 \times 18}} = 25000\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution into a compound interest formula.</span> <span>Award <em><strong>(A1)</strong></em> for correct substitution and equation.</span></p>
<p> </p>
<p><span>C =12183.39 (EUR) <em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><span><strong>Note:</strong> The final <em><strong>(A1)</strong></em> can only be given for seeing the correct figures.</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-size: medium; font-family: times new roman,times;">In part (b) a mark was awarded for substitution of <strong>any</strong> values into a compound interest formula. This seemed to be as far as the majority of candidates were able to go and few scripts gave the required answer of 12183.39 EUR.</span></p>
</div>
<br><hr><br><div class="specification">
<p>Consider the geometric sequence \({u_1} = 18,{\text{ }}{u_2} = 9,{\text{ }}{u_3} = 4.5,{\text{ }} \ldots \).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the common ratio of the sequence.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \({u_5}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the smallest value of \(n\) for which \({u_n}\) is less than \({10^{ - 3}}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{1}{2}{\text{ }}(0.5)\) <strong><em>(A1)</em></strong> <strong><em>(C1)</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(18 \times {\left( {\frac{1}{2}} \right)^4}\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for their correct substitution into the geometric sequence formula. Accept a list of their five correct terms.</p>
<p> </p>
<p>\(1.125{\text{ }}\left( {1.13,{\text{ }}\frac{9}{8}} \right)\) <strong><em>(A1)</em>(ft)</strong> <strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from their common ratio from part (a).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(18 \times {\left( {\frac{1}{2}} \right)^{n - 1}} < {10^{ - 3}}\) <strong><em>(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Award <strong><em>(M1) </em></strong>for their correct substitution into the geometric sequence formula with a variable in the exponent, <strong><em>(M1) </em></strong>for comparing their expression with \({10^{ - 3}}{\text{ }}\left( {\frac{1}{{1000}}} \right)\).</p>
<p>Accept an equation.</p>
<p> </p>
<p>\(n = 16\) <strong><em>(A1)</em>(ft)</strong> <strong><em>(C3)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from their common ratio from part (a). “\(n\)” must be a positive integer for the <strong><em>(A1) </em></strong>to be awarded.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Let \(p = \frac{{\cos x + \sin y}}{{\sqrt {{w^2} - z} }}\),</p>
<p class="p1">where \(x = 36^\circ ,{\text{ }}y = 18^\circ ,{\text{ }}w = 29\) and \(z = 21.8\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">Calculate the value of \(p\)</span>. Write down your full calculator display.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write your answer to part (a)</p>
<p class="p2">(i) <span class="Apple-converted-space"> </span>correct to two decimal places;</p>
<p class="p2">(ii) <span class="Apple-converted-space"> </span>correct to three significant figures.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">Write your answer to </span><strong>part (b)(ii) </strong>in the form \(a \times {10^k}\), where \(1 \leqslant a < 10,{\text{ }}k \in \mathbb{Z}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(\frac{{\cos 36^\circ + \sin 18^\circ }}{{\sqrt {{{29}^2} - 21.8} }}\) </span><strong><em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for correct substitution into formula.</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\( = 0.0390625\) </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C2)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Accept \(\frac{5}{{128}}\).</p>
<p class="p2"> </p>
<p class="p3"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span><span class="s1">0.04 <span class="Apple-converted-space"> </span></span><strong><em>(A1)</em>(ft) </strong></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span><span class="s1">0.0391 <span class="Apple-converted-space"> </span></span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C2)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Follow through from part (a).</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(3.91 \times {10^{ - 2}}\) </span><strong><em>(A1)</em>(ft)<em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C2)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note</strong><span class="s1"><strong>: <span class="Apple-converted-space"> </span></strong></span>Answer should be consistent with their answer to part (b)(ii). Award <strong><em>(A1)</em>(ft) </strong>for 3.91, and <strong><em>(A1)</em>(ft) </strong>for \({10^{ - 2}}\). Follow through from part (b)(ii).</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: 'times new roman', times;">The first term of an arithmetic sequence is 3 and the seventh term is 33.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the common difference;</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the 95<sup>th</sup> term of the sequence;</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the sum of the first 250 terms.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>33 = 3 + <em>d</em>(6) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted formula or a correct numerical expression to find the common difference.</span></p>
<p><span> </span></p>
<p><span>(<em>d</em> =)5 <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>u</em><sub>95</sub> = 3 + 94(5) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their correctly substituted formula.</span></p>
<p><span> </span></p>
<p><span>= 473 <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em> <br></span></p>
<p><span><strong>Note:</strong> Follow through from their part (a).</span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>S<sub>250</sub> = 125[2(3) + 249(5)] <em><strong>(M1)</strong></em> <br></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted formula.<br></span></p>
<p><span> </span></p>
<p><span>S<sub>250</sub> = 156375 <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their part (a).</span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Much good work was seen in parts (a) and (b) showing that many centres had well prepared their students for questions on arithmetic sequences. In part (c) however there was poor use of \({S_n} = \frac{n}{2}\){first term + last term} with the incorrect calculation \(\frac{{250}}{2}\{ 3 + 250\} \) seen on a significant number of scripts.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Much good work was seen in parts (a) and (b) showing that many centres had well prepared their students for questions on arithmetic sequences. In part (c) however there was poor use of \({S_n} = \frac{n}{2}\){first term + last term} with the incorrect calculation \(\frac{{250}}{2}\{ 3 + 250\} \) seen on a significant number of scripts.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Much good work was seen in parts (a) and (b) showing that many centres had well prepared their students for questions on arithmetic sequences. In part (c) however there was poor use of \({S_n} = \frac{n}{2}\){first term + last term} with the incorrect calculation \(\frac{{250}}{2}\{ 3 + 250\} \) seen on a significant number of scripts.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Yun Bin invests \(5000{\text{ euros}}\) in an account which pays a nominal annual interest rate of \(6.25\% \) , <strong>compounded monthly</strong>.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Give all answers correct to two decimal places.</strong></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of the investment after 3 years.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the difference in the final value of the investment if the interest was compounded quarterly at the same nominal rate.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(FV = 5000{\left( {1 + \frac{{6.25}}{{1200}}} \right)^{3 \times 12}}\) <em><strong>(M1)(A1)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituted compound interest formula, <em><strong>(A1)</strong></em> for correct substitutions.</span></p>
<p> </p>
<p><span><strong>OR</strong></span></p>
<p> </p>
<p><span>\(N = 3\)</span><br><span>\(I\% = 6.25\)</span><br><span>\(PV = - 5000\)</span><br><span>\(P/Y = 1\)</span><br><span>\(C/Y = 12\) <em><strong>(M1)(A1)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(C/Y = 12\) seen, <em><strong>(M1)</strong></em> for other correct entries.</span></p>
<p> </p>
<p><span><strong>OR</strong></span></p>
<p> </p>
<p><span>\(N = 36\)</span><br><span>\(I\% = 6.25\)</span><br><span>\(PV = - 5000\)</span><br><span>\(P/Y = 12\)</span><br><span>\(C/Y = 12\) <em><strong>(M1)(A1)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(C/Y = 12\) seen, <em><strong>(M1)</strong></em> for other correct entries.</span></p>
<p> </p>
<p><span>\( = 6028.22\) <em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> The answer should be given correct to two decimal places or the final <em><strong>(A1)</strong></em> is not awarded.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(FV = 5000{\left( {1 + \frac{{6.25}}{{400}}} \right)^{3 \times 4}}\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted compound interest formula.</span></p>
<p> </p>
<p><span><strong>OR</strong></span></p>
<p> </p>
<p><span>\(N = 3\)</span><br><span>\(I\% = 6.25\)</span><br><span>\(PV = - 5000\)</span><br><span>\(P/Y = 1\)</span><br><span>\(C/Y = 4\) <em><strong>(M1)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for all correct entries seen.</span></p>
<p> </p>
<p><span><strong>OR</strong></span></p>
<p> </p>
<p><span>\(N = 12\)</span><br><span>\(I\% = 6.25\)</span><br><span>\(PV = - 5000\)</span><br><span>\(P/Y = 4\)</span><br><span>\(C/Y = 4\) <em><strong>(M1)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for all correct entries seen.</span></p>
<p> </p>
<p><span>\(FV = 6022.41\) <em><strong>(A1)</strong></em></span><br><span>\({\text{Difference}} = 5.80\) <strong><em>(A1)</em>(ft)</strong> <em><strong>(C3)</strong></em></span></p>
<p> </p>
<p><span><span><strong>Notes:</strong> Accept \(5.81\). This answer should be given correct to two decimal places or the final</span><span> <em><strong>(A1)</strong></em> is not awarded unless this has already been penalized in part (a). Follow through from part (a).</span></span><br><span><strong>Notes:</strong> Illustrating use of GDC notation acceptable in this case only. However on P2 an answer given with no working would receive G2.</span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">In the diagram, triangle ABC is isosceles. AB = AC and angle ACB is 32°. The length of side AC is <em>x</em> cm.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the size of angle CBA.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the size of angle CAB.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The area of triangle ABC is 360 cm<sup>2</sup>. Calculate the length of side AC. Express your answer in <strong>millimetres</strong>.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>32° <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>116° <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(360 = \frac{1}{2} \times {x^2} \times \sin 116^\circ \) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for substitution into correct formula with 360 seen, </span><span><em><strong>(A1)</strong></em><strong>(ft)</strong> for correct substitution, follow through from their answer to </span><span>part (b).</span></p>
<p><br><span><em>x</em> = 28.3 (cm) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><em>x</em> = 283 (mm) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C4)</strong></em></span></p>
<p><span><strong>Notes:</strong> The final <em><strong>(A1)</strong></em><strong>(ft)</strong> is for their cm answer converted to mm. If their </span><span>incorrect cm answer is seen the final <em><strong>(A1)</strong></em><strong>(ft)</strong> can be awarded for </span><span>correct conversion to mm.</span></p>
<p><span><em><strong>[4 marks]</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Candidates had difficulties finding the length of the side of the isosceles triangle and chose an incorrect angle in their substitution into the area formula. Many candidates thought this question related to right angle triangle trigonometry.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Candidates had difficulties finding the length of the side of the isosceles triangle and chose an incorrect angle in their substitution into the area formula. Many candidates thought this question related to right angle triangle trigonometry.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Candidates had difficulties finding the length of the side of the isosceles triangle and chose an incorrect angle in their substitution into the area formula. Many candidates thought this question related to right angle triangle trigonometry.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The first term, \({u_1}\), of an arithmetic sequence is \(145\). The fifth term, \({u_5}\), of the sequence is \(113\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the common difference of the sequence.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The \({n^{{\text{th}}}}\) term, \({u_n}\), of the sequence is \(–7\).</span></p>
<p><span>Find the value of \(n\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The \({n^{{\text{th}}}}\) term, \({u_n}\), of the sequence is \(–7\).</span></p>
<p><span>Find \({S_{20}}\), the sum of the first twenty terms of the sequence.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(145 + (5 - 1)d = 113\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correctly substituted AP formula.</span></p>
<p> </p>
<p><span><strong>OR</strong></span></p>
<p><span>\(\frac{{113 - 145}}{4}\) <strong><em>(M1)</em></strong></span></p>
<p><span>\( = - 8\) <strong><em>(A1) (C2)</em></strong></span></p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(145 + (n - 1) \times - 8 = - 7\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for their correctly substituted AP formula.</span></p>
<p><span> If a list is used award <strong><em>(M1) </em></strong>for their correct values down to \(−7\).</span></p>
<p> </p>
<p><span>\(n = 20\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Follow through from their part (a).</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({S_{20}} = \frac{{20}}{2}\left( {2 \times 145 + (20 - 1) \times - 8} \right)\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for their correctly substituted sum of an AP formula.</span></p>
<p><span> If a list is used award <strong><em>(M1) </em></strong>for their correct terms up to \(1380\)</span></p>
<p> </p>
<p><span>\( = 1380\) <strong><em>(A1)</em>(ft)</strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Follow through from their part (a).</span></p>
<p> </p>
<p><span><strong>OR</strong></span></p>
<p><span>\({S_{20}} = \frac{{20}}{2}\left( {145 + ( - 7)} \right)\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correctly substituted sum of an AP formula.</span></p>
<p> </p>
<p><span>\( = 1380\) <strong><em>(A1) (C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>If candidates have listed the terms correctly and given the common difference as \(8\), award <strong><em>(M1)(A0) </em></strong>for part (a), <strong><em>(M1)(A0) </em></strong>for an answer of \(−18\) or \(18\) for part (b) and <strong><em>(M1)(A1)</em>(ft) </strong>for an answer of \(4420\) in part (c) with working seen.</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates gave an answer of 8 rather than –8 but were awarded follow through marks in parts (b) and (c) where working was shown. Some candidates appeared unaware that the common difference in both the AP formula for a term and for a sum is multiplied rather than added or subtracted. Candidates who used a list to answer this question were able to gain full marks.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates gave an answer of 8 rather than –8 but were awarded follow through marks in parts (b) and (c) where working was shown. Some candidates appeared unaware that the common difference in both the AP formula for a term and for a sum is multiplied rather than added or subtracted. Candidates who used a list to answer this question were able to gain full marks.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates gave an answer of 8 rather than –8 but were awarded follow through marks in parts (b) and (c) where working was shown. Some candidates appeared unaware that the common difference in both the AP formula for a term and for a sum is multiplied rather than added or subtracted. Candidates who used a list to answer this question were able to gain full marks.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A rumour spreads through a group of teenagers according to the exponential model</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;">\(N = 2 \times {(1.81)^{0.7t}}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">where <em>N</em> is the number of teenagers who have heard the rumour <em>t</em> hours after it is first started.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number of teenagers who started the rumour.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of teenagers who have heard the rumour five hours after it is first started.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Determine the length of time it would take for 150 teenagers to have heard the rumour. <strong>Give your answer correct to the nearest minute.</strong></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><em>N</em> = 2 × (1.81)<sup>0.7×0</sup> <em><strong>(M1)</strong></em></span><br><span><em>N</em> = 2 <em><strong>(A1) (C2)</strong></em></span></p>
<p> </p>
<p><span><strong>Notes:</strong> Award<em><strong> (M1)</strong></em> for correct substitution of<em> t</em> = 0.</span><br><span>Award<em><strong> (A1)</strong></em> for correct answer.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>16.0 (3 s.f) <em><strong>(A1) (C1)</strong></em></span></p>
<p><span> </span></p>
<p><span><strong>Note:</strong> Accept 16 and 15.</span></p>
<p><span> </span></p>
<p><em><strong><span>[1 mark]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>150 = 2 × (1.81)<sup>0.7<em>t</em></sup> <em><strong>(M1)</strong></em></span></p>
<p><span><em>t</em> = 10.39... h <em><strong>(A1)</strong></em></span></p>
<p><span><em>t</em> = 624 minutes <em><strong> (A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></span></p>
<p><span> </span></p>
<p><span><strong>Notes:</strong> Accept 10 hours 24 minutes. Accept alternative methods.</span></p>
<p><span>Award last <strong><em>(A1)</em>(ft)</strong> for correct rounding to the nearest minute of their </span><span>answer.</span></p>
<p><span>Unrounded answer must be seen so that the follow through can be</span> <span>awarded.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Parts (a) and (b) were confidently answered with many candidates correctly finding the number who started the rumour and also the number involved after 5 hours. A common mistake was to let <em>t</em> = 0 but not evaluate the expression correctly.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Parts (a) and (b) were confidently answered with many candidates correctly finding the number who started the rumour and also the number involved after 5 hours. A common mistake was to let <em>t</em> = 0 but not evaluate the expression correctly.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Very few candidates could answer part (c). With the working shown, it was obvious candidates could correctly state the equation, but could not use their calculators to find the value of<em> t</em>.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The golden ratio, \(r\) , was considered by the Ancient Greeks to be the perfect ratio between the lengths of two adjacent sides of a rectangle. The exact value of \(r\) is \(\frac{{1 + \sqrt 5 }}{2}\).</p>
<p>Write down the value of \(r\)</p>
<p>i) correct to \(5\) significant figures;</p>
<p>ii) correct to \(2\) decimal places.</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>Phidias is designing rectangular windows with adjacent sides of length \(x\) metres and \(y\) metres. The area of each window is \(1\,{{\text{m}}^2}\).</p>
<p>Write down an equation to describe this information.</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>Phidias designs the windows so that the ratio between the longer side, \(y\) , and the shorter side, \(x\) , is the golden ratio, \(r\).</p>
<p>Write down an equation in \(y\) , \(x\) and \(r\) to describe this information.</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>Find the value of \(x\) .</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>i) \(1.6180\) <em><strong>(A1)</strong></em></p>
<p>ii) \(1.62\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (a)(i).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(xy = 1\) <em><strong>(A1) (C1)</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{y}{x} = r\) <strong>OR</strong> \(\frac{y}{x} = \frac{{1 + \sqrt 5 }}{2}\) <strong>OR</strong> equivalent <em><strong>(A1) (C1)</strong></em></p>
<p><strong>Note:</strong> Accept \(\frac{y}{x} = \) their part (a)(i) or (a)(ii).</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\({x^2}r = 1\) or eqivalent <em><strong>(M1)</strong></em></p>
<p>\(x = 0.786\,\,\,(0.78615...)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting their part (c) into their equation from part (b). Follow through from parts (a), (b) and (c). Use of \(r = 1.62\) gives \(0.785674...\)</p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Question 13: Golden ratio<br>This question was partially answered by all but the best candidates. Parts (a) and (b) yielded the most success. Only the best candidates were successful in part (d).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 13: Golden ratio<br>This question was partially answered by all but the best candidates. Parts (a) and (b) yielded the most success. Only the best candidates were successful in part (d).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 13: Golden ratio<br>This question was partially answered by all but the best candidates. Parts (a) and (b) yielded the most success. Only the best candidates were successful in part (d).</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 13: Golden ratio<br>This question was partially answered by all but the best candidates. Parts (a) and (b) yielded the most success. Only the best candidates were successful in part (d).</p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The surface of a red carpet is shown below. The dimensions of the carpet are in metres.</span></p>
<div style="text-align: center;"><img src="images/Schermafbeelding_2014-09-02_om_14.31.51.png" alt></div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down an expression for the area, \(A\), in \({{\text{m}}^2}\), of the carpet.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The area of the carpet is \({\text{10 }}{{\text{m}}^2}\).</span></p>
<p><span>Calculate the value of \(x\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The area of the carpet is \({\text{10 }}{{\text{m}}^2}\).</span></p>
<p><span>Hence, write down the value of the length and of the width of the carpet, in metres.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(2x(x - 4)\) <strong>or</strong> \(2{x^2} - 8x\) <strong><em>(A1) (C1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A0) </em></strong>for \(x - 4 \times 2x\).</span></p>
<p> </p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(2x(x - 4) = 10\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for equating their answer in part (a) to \(10\).</span></p>
<p> </p>
<p><span>\({x^2} - 4x - 5 = 0\) <strong><em>(M1)</em></strong></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>Sketch of \(y = 2{x^2} - 8x\) and \(y = 10\) <strong><em>(M1)</em></strong></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>Using GDC solver \(x = 5\) and \(x = - 1\) <strong><em>(M1)</em></strong></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>\(2(x + 1)(x - 5)\) <strong><em>(M1)</em></strong></span></p>
<p><span>\(x = 5{\text{ (m)}}\) <strong><em>(A1)</em>(ft) <em>(C3)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Follow through from their answer to part (a).</span></p>
<p><span> Award at most <strong><em>(M1)(M1)(A0) </em></strong>if both \(5\) and \(-1\) are given as final answer.</span></p>
<p><span> Final <strong><em>(A1)</em>(ft) </strong>is awarded for choosing only the positive solution(s).</span></p>
<p> </p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(2 \times 5 = 10{\text{ (m)}}\) <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span>\(5 - 4 = 1{\text{ (m)}}\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Follow through from their answer to part (b).</span></p>
<p><span> Do not accept negative answers.</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Solve the following equation for <em>x</em></span></p>
<p><span>\(3(2x +1) − 2(3 − x)=13\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Factorize the expression \(x^2 + 2x − 3\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the <strong>positive</strong> solution of the equation</span></p>
<p><span>\(x^2 + 2x − 6 = 0\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(6x+ 3 - 6 + 2x = 13\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(8x = 16\)</span></p>
<p><span>\(x = 2\) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\((x + 3) (x - 1)\) <em><strong>(A1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(x = 1.64575...\)</span></p>
<p><span>\(x = 1.65\) <em><strong>(A2)</strong></em></span></p>
<p><em><span>If formula is used award <strong>(M1)(A1)</strong> for correct solution. If graph is sketched award <strong>(M1)(A1)</strong> for correct solution. <strong>(C2)</strong></span></em></p>
<p><em><span><strong>[2 marks]</strong></span></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">(a) Many candidates forgot that a minus times a minus gives a plus and so did not solve the equation correctly.</span></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">(b) A good attempt was made at factorising the function although \(x(x + 2) – 3\) was seen frequently too.</span></p>
<p> </p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">(a) Many candidates forgot that a minus times a minus gives a plus and so did not solve the equation correctly.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">(b) A good attempt was made at factorising the function although \(x(x + 2) – 3\) was seen frequently too.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">(c) Few candidates realised that they had to use their GDC to find this answer and hence there were few correct answers. Some did not read the question correctly and solved part (b) to find the positive solution of the expression they had factorised.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Yoshi is spending a year travelling from Japan to Italy and then to the United States of America.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Before Yoshi leaves Japan he changes 100 000 Japanese Yen (JPY) into euro (EUR). The exchange rate is 1 JPY = 0.006 EUR.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the amount Yoshi receives, in EUR.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Yoshi spends 426.70 EUR in Italy. In an American bank he changes the remaining</span> <span>amount, into US dollars (USD), at an exchange rate of 1 USD = 0.673 EUR.</span></p>
<p><span>The bank charges 1.5 % commission.</span></p>
<p><span>Calculate the amount, in USD, Yoshi receives after commission.</span> <strong><span>Give your answer correct to the nearest USD.</span></strong></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(0.006 \times 100000\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for multiplication by 0.006.</span></p>
<p><br><span>\( = 600\) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{(600 - 426.70)}}{{0.673}} \times 0.985\) <em><strong>(M1)(M1)(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for subtracting 426.70 from their answer to part (a), <em><strong>(M1)</strong></em> for division by 0.673, <em><strong>(M1)</strong></em> for multiplication by 0.985 (or equivalent).</span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span>\(\frac{{173.30 - (600 - 426.70) \times 0.015}}{{0.673}}\) <em><strong>(M1)(M1)(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for subtracting 426.70 from their answer to part (a), <em><strong>(M1)</strong></em> for</span> <span>division by 0.673, <em><strong>(M1)</strong></em> for multiplication by 0.015 (or equivalent) and</span> <span>subtraction from their 173.30.</span></p>
<p><br><span>254 <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C4)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Follow through from their part (a). In order to award the final <em><strong>(A1)</strong></em><strong>(ft) </strong></span><span>the answer must be given correct to the nearest dollar. </span><span>If division used in part (a) and multiplication in part (b) award at most</span> <em><strong><span>(M1)(M1)(M1)(A0)</span></strong></em><span>.</span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Consider the following statements</p>
<p>\(z\,:\,x\) is an integer<br>\(q\,:\,x\) is a rational number<br>\(r\,:\,x\) is a real number.</p>
<p>i) Write down, in words, \(\neg q\).</p>
<p>ii) Write down a value for \(x\) such that the statement \(\neg q\) is true.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write the following argument in symbolic form:<br>“If \(x\) is a real number and \(x\) is not a rational number, then \(x\) is not an integer”.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Phoebe states that the argument in part (b) can be shown to be valid, without the need of a truth table.</p>
<p>Justify Phoebe’s statement.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>i) \(x\) is not a rational number <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Accept “\(x\) is an irrational number”.</p>
<p> </p>
<p>ii) any non-rational number (for example: \(\pi ,\,\sqrt 2 \), …) <em><strong>(A1) (C2)</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\((r \wedge \neg q) \Rightarrow \neg z\) <em><strong>(A1)(A1)(A1) (C3)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for “\( \Rightarrow \)” seen, <em><strong>(A1)</strong></em> for “\(\neg z\)” as the consequent and <em><strong>(A1)</strong></em> for “\((r \wedge \neg q)\)” or “\((\neg q \wedge r)\)” as the antecedent (the parentheses are required).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>all integers are rational numbers (and therefore \(x\) cannot be an integer if it is not a rational number) <em><strong>(R1)</strong></em></p>
<p><strong>Note:</strong> Accept equivalent expressions.</p>
<p><strong>OR</strong></p>
<p>if \(x\) is an integer, then \(x\) is a rational number, therefore if \(x\) is not a rational number, then \(x\) is not an integer (contrapositive) <strong><em>(R1) (C1)</em></strong></p>
<p><strong>Note: </strong>Accept “If \(x\) is not in \(\mathbb{Q}\), then \(x\) is not in \(\mathbb{Z}\)” with a Venn diagram showing \(\mathbb{R}\), \(\mathbb{Q}\) and \(\mathbb{Z}\) correctly.</p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Question 5 Logic<br>In part (a), the majority of candidates were able to state the negation, but surprisingly many were unable to give an example of a non-rational number.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>In part (b), a common error was the lack of parentheses in the antecedent. A further error was the use of the “intersection” symbol rather than that for conjunction; care must be taken in this regard.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Part (c) proved problematic for all but the best candidates.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The volume of a sphere is \(V{\text{ = }}\sqrt {\frac{{{S^3}}}{{36\pi }}} \), where \(S\) is its surface area.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The surface area of a sphere is 500 cm<sup>2</sup> .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>Calculate the volume of the sphere. Give your answer correct to <strong>two decimal</strong></span> <span><strong>places</strong>.</span></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down your answer to (a) correct to the nearest integer.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down your answer to (b) in the form \(a \times {10^n}\), where \(1 \leqslant a < 10\) and \(n \in \mathbb{Z}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(V{\text{ = }}\sqrt {\frac{{{500^3}}}{{36\pi }}} \) <em><strong>(M1)</strong></em></span><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong> </em>correct substitution into formula.</span></p>
<p><br><span><em>V</em> = 1051.305 … <em><strong>(A1)</strong></em></span><br><span><em>V</em> = 1051.31 cm<sup>3</sup> <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C3)</strong></em></span></p>
<p><span><span><strong>Note:</strong> Award last <strong><em>(A1)</em>(ft)</strong> for correct rounding to 2 decimal places of</span> <span>their answer. Unrounded answer must be seen so that the follow</span> <span>through can be awarded.</span></span></p>
<p><span><span> </span></span></p>
<p><em><strong><span><span>[3 marks]</span></span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>1051 <strong><em>(A1)</em>(ft)</strong></span></p>
<p><em><span><strong>[1 mark]</strong></span></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><span> \(1.051 \times {10^3}\)</span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span><br><br><span><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for 1.051 (accept 1.05)<em><strong> (A1)</strong></em> for </span><span> \( \times {10^3}\).</span></span></p>
<p><span><span> </span></span></p>
<p><em><strong><span><span>[2 marks]</span></span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well answered by many of the candidates. A significant number of candidates lost two marks in part (a) for not using the calculator correctly and omitting brackets in the denominator when entering the volume expression in their GDC. Also, those students who did not show the unrounded answer in the working box could not be awarded the last mark in part a). Follow through marks were awarded for parts (b) and (c) which most candidates gained.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well answered by many of the candidates. A significant number of candidates lost two marks in part (a) for not using the calculator correctly and omitting brackets in the denominator when entering the volume expression in their GDC. Also, those students who did not show the unrounded answer in the working box could not be awarded the last mark in part (a). Follow through marks were awarded for parts (b) and (c) which most candidates gained.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well answered by many of the candidates. A significant number of candidates lost two marks in part (a) for not using the calculator correctly and omitting brackets in the denominator when entering the volume expression in their GDC. Also, those students who did not show the unrounded answer in the working box could not be awarded the last mark in part a). Follow through marks were awarded for parts (b) and (c) which most candidates gained.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Five pipes labelled, “6 metres in length”, were delivered to a building site. The contractor measured each pipe to check its length (in metres) and recorded the following;</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">5.96, 5.95, 6.02, 5.95, 5.99.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Find the mean of the contractor’s measurements.</span></p>
<p><span>(ii) Calculate the percentage error between the mean and the stated, <strong>approximate</strong> length of 6 metres.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate \(\sqrt {{{3.87}^5} - {{8.73}^{ - 0.5}}} \), giving your answer</span></p>
<p><span>(i) correct to the nearest integer,</span></p>
<p><span>(ii) in the form \(a \times 10^k\), where 1 ≤ <em>a</em> < 10, \(k \in {\mathbb{Z}}\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>(i) Mean = (5.96 + 5.95 + 6.02 + 5.95 + 5.99) / 5 = 5.974 (5.97) <em><strong>(A1)</strong></em></span></p>
<p> </p>
<p><span>(ii) \({\text{% error}} = \frac{{error}}{{actualvalue}} \times 100\% \)</span></p>
<p><span>\( = \frac{{6 - 5.974}}{{5.974}} \times 100\% = 0.435\% \)</span><em><strong><span> (M1)(A1)</span></strong></em><strong><span>(ft)</span></strong></p>
<p><em><span><strong>(M1)</strong> for correctly substituted formula.</span> </em></p>
<p><span><em>Allow 0.503% as follow through from 5.97</em></span></p>
<p><em><span>Note: An answer of 0.433% is incorrect. <strong>(C3)</strong></span></em></p>
<p> </p>
<p><em><span><strong>[3 marks]</strong></span></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>number is 29.45728613</span></p>
<p><span>(i) Nearest integer = 29 <em><strong>(A1)</strong></em></span></p>
<p> </p>
<p><span>(ii) Standard form = 2.95 × 10<sup>1</sup> (<em>accept</em> 2.9</span><span><span> × 10<sup>1</sup></span>) <strong><em>(A1)</em>(ft)<em>(A1)</em></strong></span></p>
<p><em><span>Award <strong>(A1)</strong> for each correct term</span></em></p>
<p><em><span>Award <strong>(A1)(A0)</strong> for 2.95</span><span> × 10 <strong>(C3)</strong></span></em></p>
<p> </p>
<p><em><span><strong>[3 marks]</strong></span></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">a) Almost all candidates calculated the mean correctly but less than half were able to find the % error, many dividing by 6. This was despite the boldening of 'approximate' in the question.</span></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">b) Main errors were giving the answer correct to 1 significant figure (30) or 1 decimal place. Some candidates just counted the number of figures on the calculator to determine the index for the standard form, giving 10<sup>9</sup> instead of 10<sup>1</sup>.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A rectangle is 2680 cm long and 1970 cm wide.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the perimeter of the rectangle, giving your answer in the form \(a \times {10^k}\), where \(1 \leqslant a \leqslant 10\) and \(k \in \mathbb{Z}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the area of the rectangle, giving your answer correct to the nearest thousand square centimetres.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><strong><em>Note: Unit penalty (UP) applies in this part</em></strong></span></p>
<p><span> </span></p>
<p><span>(2680 + 1970) × 2 <em><strong>(M1)</strong></em></span></p>
<p><span><em><strong>(UP)</strong></em> = 9.30 </span><span><span>× </span>10<sup>3</sup> cm <em><strong>(A1)(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for correct formula.</span></p>
<p><span><em><strong>(A1)</strong></em> for 9.30 (Accept 9.3)</span>.</p>
<p><span><em><strong>(A1)</strong></em> for 10<sup>3</sup>.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>2680 × 1970 <em><strong>(M1)</strong></em></span></p>
<p><span>= 5279600 <em><strong>(A1)</strong></em></span></p>
<p><span>= 5,280,000 (5280 thousand) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C3)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted formula.</span></p>
<p><span>Accept 5.280 </span><span><span>× </span>10<sup>6</sup>.</span></p>
<p><br><span><strong>Note:</strong> The last <em><strong>(A1)</strong></em> is for specified accuracy, <strong>(ft)</strong> from their answer.</span></p>
<p><span>The <em><strong>(AP)</strong></em> for the paper is not applied here.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was well answered by many candidates although the majority lost a mark as a unit penalty in part (a). Some candidates used the wrong formula for the perimeter. Most could give their answer in standard form.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was well answered by many candidates although the majority lost a mark as a unit penalty in part (a). Some candidates used the wrong formula for the perimeter. Most could give their answer in standard form.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">Give all answers in this question correct to two decimal places.</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Isabel is travelling from Geneva to Toronto via Amsterdam.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">She changes 1240 Swiss francs (CHF) to Euros (EUR).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The exchange rate is 1 CHF = 0.7681 EUR.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the amount of Euros Isabel receives.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Isabel then changes 750 EUR into Canadian dollars (CAD) and is charged 3.12 % commission.</span></p>
<p><span>The exchange rate is 1 CAD = 0.7470 EUR .</span></p>
<p><span>Calculate the amount of Canadian dollars she receives.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>1240 × 0.7681 <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for multiplying by 0.7681</span></p>
<p><span> </span></p>
<p><span>= 952.44 <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{750}}{{0.7470}} \times (1 - 0.0312)\) <em><strong>(M1)(M1)(M1)</strong></em></span></p>
<p><span> <strong>Note:</strong> Award <em><strong>(M1)</strong></em> for dividing by 0.7470, <em><strong>(M1)</strong></em> for subtracting 0.0312 from 1, <em><strong>(M1)</strong></em> for multiplying by the (1 – 0.0312).</span></p>
<p><span> </span></p>
<p><strong><span>OR</span></strong></p>
<p><span>\(\frac{{750}}{{0.7470}} (= 1004.016...)\) <em><strong>(M1)</strong></em></span></p>
<p><span>1004.016... × 0.0312 (= 31.325...) <em><strong>(M1)</strong></em> </span></p>
<p><span>1004.016... − 31.325... <em><strong>(M1)</strong></em></span></p>
<p><span> <strong>Note:</strong> Award <em><strong>(M1)</strong></em> for dividing by 0.7470, <em><strong>(M1)</strong></em> for multiplication by 0.0312, <em><strong>(M1)</strong></em> for subtraction of their 31.325 from their 1004.016.<br></span></p>
<p><span> </span></p>
<p><span><strong>OR</strong><br></span></p>
<p><span>750 </span><span><span>× </span>3.12 % = 23.4 <em><strong>(M1)</strong></em><br></span></p>
<p><span>750 </span><span><span>−</span> 23.4 = 726.60 <em><strong>(M1)</strong></em><br></span></p>
<p><span>\(\frac{{726.60}}{{0.7470}} \) <em><strong>(M1)</strong></em><br></span></p>
<p><span> <strong>Note:</strong> Award <em><strong>(M1)</strong></em> for multiplication by 3.12 %, <em><strong>(M1)</strong></em> for subtraction of their 23.4 from 750, <em><strong>(M1)</strong></em> for division by 0.7470.<br></span></p>
<p><span> </span></p>
<p><span>= 972.69 <em><strong>(A1)</strong></em> <em><strong>(C4)</strong></em><br></span></p>
<p><span><strong>Note:</strong> If division by 0.7681 is used in part (a) then award <em><strong>(M1)</strong></em> for multiplying by 0.7470 in part (b).<br></span></p>
<p><span><em><strong>[4 marks]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was generally well done with the majority of candidates correctly using the currency conversions (multiplying in part (a) and dividing in part (b)) and, in most cases, working out the commission correctly in part (b). On a few scripts, candidates failed to round either one or both of their answers correctly to two decimal places and, as a consequence, lost a mark.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was generally well done with the majority of candidates correctly using the currency conversions (multiplying in part (a) and dividing in part (b)) and, in most cases, working out the commission correctly in part (b). On a few scripts, candidates failed to round either one or both of their answers correctly to two decimal places and, as a consequence, lost a mark.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A type of candy is packaged in a right circular cone that has volume \({\text{100 c}}{{\text{m}}^{\text{3}}}\) and vertical height 8 cm.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_11.14.55.png" alt="M17/5/MATSD/SP1/ENG/TZ1/09"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the radius, \(r\), of the circular base of the cone.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the slant height, \(l\), of the cone.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the curved surface area of the cone.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(100 = \frac{1}{3}\pi {r^2}(8)\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution into volume of cone formula.</p>
<p> </p>
<p>\(r = 3.45{\text{ (cm) }}\left( {3.45494 \ldots {\text{ (cm)}}} \right)\) <strong><em>(A1)</em></strong> <strong><em>(C2)</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>\({l^2} = {8^2} + {(3.45494 \ldots )^2}\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for correct substitution into Pythagoras’ theorem.</p>
<p> </p>
<p>\(l = 8.71{\text{ (cm) }}\left( {8.71416 \ldots {\text{ (cm)}}} \right)\) <strong><em>(A1)</em>(ft)</strong><em> </em><strong><em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (a).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\pi \times 3.45494 \ldots \times 8.71416 \ldots \) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for their correct substitutions into curved surface area of a cone formula.</p>
<p> </p>
<p>\( = 94.6{\text{ c}}{{\text{m}}^2}{\text{ }}(94.5836 \ldots {\text{ c}}{{\text{m}}^2})\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from parts (a) and (b). Accept \(94.4{\text{ c}}{{\text{m}}^2}\) from use of 3 sf values.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Sergei is training to be a weightlifter. Each day he trains at the local gym by lifting a metal bar that has heavy weights attached. He carries out successive lifts. After each lift, the same amount of weight is <strong>added</strong> to the bar to increase the weight to be lifted.</p>
<p>The weights of each of Sergei’s lifts form an arithmetic sequence.</p>
<p>Sergei’s friend, Yuri, records the weight of each lift. Unfortunately, last Monday, Yuri misplaced all but two of the recordings of Sergei’s lifts.</p>
<p>On that day, Sergei lifted 21 kg on the third lift and 46 kg on the eighth lift.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For that day find how much weight was added after each lift.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For that day find the weight of Sergei’s first lift.</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>On that day, Sergei made 12 successive lifts. Find the total combined weight of these lifts.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>5<em>d</em> = 46 − 21 <strong>OR</strong> <em>u</em><sub>1</sub> + 2<em>d</em> = 21 and <em>u</em><sub>1</sub> + 7<em>d</em> = 46 <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for a correct equation in <em>d</em> or for two correct equations in <em>u</em><sub>1</sub> and <em>d</em>.</p>
<p>(<em>d =</em>) 5 (kg) <em><strong>(A1) (C2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>u</em><sub>1</sub> + 2 × 5 = 21 <em><strong>(M1)</strong></em></p>
<p><em><strong>OR</strong></em></p>
<p><em>u</em><sub>1</sub> + 7 × 5 = 46 <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution of their <em>d</em> into either of the two equations.</p>
<p>(<em>u</em><sub>1 </sub>=) 11 (kg) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (a)(i).</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>\(\frac{{12}}{2}\left( {2 \times 11 + \left( {12 - 1} \right) \times 5} \right)\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into arithmetic series formula.</p>
<p>= 462 (kg) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note:</strong> Follow through from parts (a) and (b).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">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><span style="font-family: times new roman,times; font-size: medium;">The table below shows the frequency distribution of the number of dental fillings for a group of \(25\) children.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of \(q\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to find</span><br><span>(i) the mean number of fillings;</span><br><span>(ii) the median number of fillings;</span><br><span>(iii) the standard deviation of the number of fillings.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(q = 25 - (4 + 3 + 8 + 4 +1)\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for subtraction from \(25\) of all values from the table.</span></p>
<p> </p>
<p><span>\( = 5\) <em><strong>(A1) (C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(2.2\) <strong><em>(A2)</em>(ft) <em>(C2)</em></strong></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for use of mean formula with correct substitution. Follow through from part (a), irrespective of whether working is shown.</span></p>
<p> </p>
<p><span>(ii) \(2\) <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p> </p>
<p><span>(iii) \(1.39\) <strong><em>(A1)</em>(ft)</strong> <em><strong>(C1)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from part (a), irrespective of whether working is shown. Award <em><strong>(A1)</strong></em> for \(1.38\).</span></p>
<p> </p>
<p><em><strong><span>[4 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Part b was not well answered by the majority of candidates, indicating that the use of the GDC is not a natural tool for answering this type of question. Many students ignored the frequencies when finding the mean, median, and standard deviation.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Part b was not well answered by the majority of candidates, indicating that the use of the GDC is not a natural tool for answering this type of question. Many students ignored the frequencies when finding the mean, median, and standard deviation.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Jane plans to travel from Amsterdam to Chicago. She changes \(1500\) Euros (\({\text{EUR}}\)) to US Dollars </span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">(\({\text{USD}}\))</span> at an exchange rate of \(1{\text{ EUR}}\) to \(1.33{\text{ USD}}\). Give all answers in this question <strong>correct to two decimal places</strong>.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the number of </span><span><span>\({\text{USD}}\) </span>Jane receives.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Jane spends \(1350{\text{ USD}}\) and then decides to convert the remainder back to \({\text{EUR}}\) </span><span>at a rate of \(1{\text{ EUR}}\) to \(1.38{\text{ USD}}\).</span></p>
<p><span>Calculate the amount of </span><span><span>\({\text{EUR}}\) </span>Jane receives.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>If Jane had waited until she returned to Amsterdam she could have changed her \({\text{USD}}\) at a rate of \(1{\text{ EUR}}\) to \(1.36{\text{ USD}}\) but the bank would have charged \(0.8\% \) commission.</span></p>
<p><span>Calculate the amount of \({\text{EUR}}\) Jane gained or lost by changing her money in Chicago.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><em>Financial penalty <strong>(FP)</strong> may apply in this question.</em></span></p>
<p><span>\(1500 \times 1.33\)</span></p>
<p><span><em><strong>(FP)</strong></em> \( = 1995.00\) <em>(accept</em> \(1995\)<em>)</em> <em><strong>(A1) (C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>Financial penalty <strong>(FP)</strong> may apply in this question.</em></span></p>
<p><span>\({\text{USD left}} = 1995 - 1350 = 645\) <em><strong>(A1)</strong></em></span></p>
<p><span>\( = \frac{{645}}{{1.38}}{\text{ Euros}}\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><em><strong>(FP)</strong></em> \( = 467.39{\text{ Euros}}\) <em><strong>(A1)</strong></em><strong>(ft) <em>(C3)</em></strong></span></p>
<p><span><strong><em>[3 marks]<br></em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>Financial penalty <strong>(FP)</strong> may apply in this question.</em></span></p>
<p><span>\(\frac{{645}}{{1.36}} \times 0.992 = 470.47\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><em><strong>(FP)</strong></em> She lost \(3.08{\text{ Euros}}\) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Notes: </strong>The word ‘lost’ is not required.<strong><br></strong>If candidate has divided in (a) and multiplied in (b) and (c) consistently award <strong><em>(A0)(A1)</em>(ft)<em>(A1)</em>(ft)</strong> for answers of \( - 222.18\) for \({\text{USD}}\) left and \(306.61{\text{ Euros}}\) in (b) and <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong> for \(299.75\) and \(6.86\) in (c).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well answered by a number of the candidates although a significant number lost a mark due to a financial penalty through not giving an answer correct to 2 decimal places. A very common mistake was to use \(8\% \) (\(0.08\)) for \(0.8\% \) (\(0.008\)) as the multiplier in part (c).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well answered by a number of the candidates although a significant number lost a mark due to a financial penalty through not giving an answer correct to 2 decimal places. A very common mistake was to use \(8\% \) (\(0.08\)) for \(0.8\% \) (\(0.008\)) as the multiplier in part (c).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well answered by a number of the candidates although a significant number lost a mark due to a financial penalty through not giving an answer correct to 2 decimal places. A very common mistake was to use \(8\% \) (\(0.08\)) for \(0.8\% \) (\(0.008\)) as the multiplier in part (c).</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>One of the locations in the \(2016\) Olympic Games is an amphitheatre. The number of seats in the first row of the amphitheatre, \({u_1}\) , is \(240\). The number of seats in each subsequent row forms an arithmetic sequence. The number of seats in the sixth row, \({u_6}\) , is \(270\).</p>
<p>Calculate the value of the common difference, \(d\).</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>There are \(20\) rows in the amphitheatre.</p>
<p>Find the <strong>total</strong> number of seats in the amphitheatre.</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>Anisha visits the amphitheatre. She estimates that the amphitheatre has \(6500\) seats.</p>
<p>Calculate the percentage error in Anisha’s estimate.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\({\text{270}}\,{\text{ = }}\,{\text{240}}\,{\text{ + }}\,d\,(6 - 1)\) <em><strong>(M1)</strong></em></p>
<p><strong>OR</strong></p>
<p>\(d = \,\,\frac{{270 - 240}}{5}\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into the arithmetic sequence formula.</p>
<p>\((d = )\,6\) <em><strong>(A1) (C2)</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{20}}{2}[2 \times 240 + 19 \times {\text{their }}d]\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into sum of an arithmetic sequence.</p>
<p><strong>OR</strong></p>
<p>\({u_{20}} = 354\)</p>
<p>\({S_{20}} = \frac{{20}}{2}[240 + 354]\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into sum of an arithmetic sequence.</p>
<p><strong>OR</strong><br>adding \(20\) terms consistent with their \(d\) <em><strong>(M1) </strong></em></p>
<p> \( = 5940\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note: </strong>Follow through from (a).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\left| {\frac{{6500 - 5940}}{{5940}}} \right| \times 100\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into percentage error formula.</p>
<p>\( = 9.43\,(\% )\,\,\,(9.42760...)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note: </strong>Follow through from (b).</p>
<p> </p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Question 6: Arithmetic sequence and series<br>This question was well attempted by the majority.<br>In part (a), a common error was calculating the difference as 5.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Part (b) was well attempted by the majority; with full follow-through being obtained.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>In part (c) The incorrect denominator was the major error here.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The table below shows some exchange rates for the Japanese Yen (\({\text{JPY}}\)).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Minbin has \(1250\) Japanese Yen which she wishes to exchange for Chinese Yuan.</span></p>
<p><span>Calculate how many Yuan she will receive. Give your answer to the nearest Yuan.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Rupert has \(855\) Canadian Dollars which he wishes to exchange for Japanese Yen. </span></p>
<p><span>Calculate how many Yen he will receive. Give your answer to the nearest Yen.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find how many Norwegian Kroner there are to the Euro. Give your answer correct to 2 decimal places.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><em>Financial accuracy penalty <strong>(FP)</strong> is applicable where indicated in the left hand column.</em></span></p>
<p><span>Multiplying \(1250\) by \(0.07127\) or \(0.7127\) <em><strong>(M1)</strong></em></span></p>
<p><span><em><strong>(FP)</strong></em> \(89\) <em><strong>(A1) (C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>Financial accuracy penalty <strong>(FP)</strong> is applicable where indicated in the left hand column.</em></span></p>
<p><span>Dividing by \(0.010406\) or \(0.10406\) <em><strong>(M1)</strong></em><br></span></p>
<p><span><em><strong>(FP)</strong></em> \(82164\) <em><strong>(A1) (C2)</strong></em><br></span></p>
<p><span><strong>Note: </strong>If candidate has divided in (a) and multiplied in (b) award <strong><em>(M1)(A1)</em>(ft)</strong> for \(9\) in (b).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>Financial accuracy penalty <strong>(FP)</strong> is applicable where indicated in the left hand column.</em></span></p>
<p><span><em><strong>(FP)</strong></em> \(\frac{{0.057319}}{{0.0072591}}\) <em>allow</em> \(0.57319\)<em> and/or</em> \(0.072591\)<em> <strong>(M1)</strong></em><br></span></p>
<p><span>\(7.90\) <em><strong>(A1) (C2)</strong></em><br></span></p>
<p><span><strong>Note:</strong> The <em><strong>(M1)</strong></em> is being allowed for misreading values from the table but do not <strong>(ft)</strong> to candidate’s answers.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well answered by a number of candidates with few confusing the conversions. Some found the last part difficult with many leaving it out.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well answered by a number of candidates with few confusing the conversions. Some found the last part difficult with many leaving it out.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well answered by a number of candidates with few confusing the conversions. Some found the last part difficult with many leaving it out.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Pierre invests <span class="s1">5000 </span>euros in a fixed deposit that pays a nominal annual interest rate of <span class="s1">4.5%</span>, compounded <strong>monthly</strong>, for seven years.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the value of Pierre’s investment at the end of this time. Give your answer correct to two decimal places.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Carla has <span class="s1">7000 </span>dollars to invest in a fixed deposit which is compounded <strong>annually</strong>.</p>
<p class="p1">She aims to double her money after 10 years.</p>
<p class="p1">Calculate the minimum annual interest rate needed for Carla to achieve her aim.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(5000{\left( {1 + \frac{{4.5}}{{12 \times 100}}} \right)^{12 \times 7}}\) <strong><em>(M1)(A1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substitution into compound interest formula, <strong><em>(A1) </em></strong>for correct substitutions.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>\(N = 7\)</p>
<p>\(I\% = 4.5\)</p>
<p>\(PV = ( \pm )5000\)</p>
<p>\(P/Y = 1\)</p>
<p>\(C/Y = 12\) <strong><em>(A1)(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for \(C/Y = 12\) seen, <strong><em>(M1) </em></strong>for all other correct entries.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>\(N = 84\)</p>
<p>\(I\% = 4.5\)</p>
<p>\(PV = ( \pm )5000\)</p>
<p>\(P/Y = 12\)</p>
<p>\(C/Y = 12\) <strong><em>(A1)(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for \(C/Y = 12\) seen, <strong><em>(M1) </em></strong>for all other correct entries.</p>
<p> </p>
<p>\( = 6847.26{\text{ (euros)}}\) <strong><em>(A1) (C3)</em></strong></p>
<p><strong>Note: </strong>Answer must be correct to 2 decimal places for the final <strong><em>(A1) </em></strong>to be awarded.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(14000 = 7000{\left( {1 + \frac{r}{{100}}} \right)^{10}}\) <strong><em>(M1)(A1)</em></strong></p>
<p><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for substitution into compound interest formula equated to 14000 or equivalent.</p>
<p>Award <strong><em>(A1) </em></strong>for correct substitutions.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>\(N = 10\)</p>
<p>\(PV = \pm 7000\)</p>
<p>\(FV \mp 14000\)</p>
<p>\(P/Y = 1\)</p>
<p>\(C/Y = 1\) <strong><em>(A1)(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for \(C/Y = 1\) seen, <strong><em>(M1) </em></strong>for other correct entries. \(PV\) and \(FV\)<em> </em>must have opposite signs.</p>
<p> </p>
<p>\(r = 7.18\% \;\;\;(7.17734 \ldots \% ,{\text{ }}0.0718)\) <strong><em>(A1) (C3)</em></strong></p>
<p><strong>Note: </strong>Do not penalize if \(\%\) sign is missing. Do not accept \(0.0718\%\).</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Many correct answers were given for part (a). Incorrect answers were in most cases the result of incorrect substitution into the compound interest formula, or incorrect use of the calculator, both in using the formula or when using the finance application. A common mistake was the use of 0.045 instead of 4.5 for r in the formula.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>In part (b) a correct equation was often given, but an analytical or graphical solution was rarely found. When the finance application of the GDC was used candidates often found the correct answer.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Juan buys a bicycle in a sale. He gets a discount of 30% off the original price and pays 560 US dollars (USD).</p>
</div>
<div class="specification">
<p>To buy the bicycle, Juan takes a loan of 560 USD for 6 months at a nominal annual interest rate of 75%, <strong>compounded monthly</strong>. Juan believes that the total amount he will pay will be less than the original price of the bicycle.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the original price of the bicycle.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the difference between the original price of the bicycle and the total amount Juan will pay.</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>\(\frac{{560}}{{70}} \times 100\) (or equivalent) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for dividing 560 by 0.7 or equivalent.</p>
<p> </p>
<p>\( = 800{\text{ (USD)}}\) <strong><em>(A1) (C2)</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>\(560{\left( {1 + \frac{{75}}{{12 \times 100}}} \right)^{12 \times \frac{1}{2}}}\) <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substitution into interest formula, <strong><em>(A1) </em></strong>for their correct substitution.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>\({\text{N}} = \frac{1}{2}\)</p>
<p>\({\text{I% }} = 75\)</p>
<p>\({\text{PV}} = ( \pm )560\)</p>
<p>\({\text{P/Y}} = 1\)</p>
<p>\({\text{C/Y}} = 12\) <strong><em>(A1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for \({\text{C/Y}} = 12\) seen, <strong><em>(M1) </em></strong>for all other entries correct.</p>
<p><strong>OR</strong></p>
<p>\({\text{N}} = 6\)</p>
<p>\({\text{I% }} = 75\)</p>
<p>\({\text{PV}} = ( \pm )560\)</p>
<p>\({\text{P/Y}} = 12\)</p>
<p>\({\text{C/Y}} = 12\) <strong><em>(A1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for \({\text{C/Y}} = 12\) seen, <strong><em>(M1) </em></strong>for all other entries correct.</p>
<p> </p>
<p>\( = 805.678 \ldots {\text{ (USD)}}\) <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A3) </em></strong>for 805.678… (806) seen without working.</p>
<p> </p>
<p>(Juan spends) 5.68 (USD) (5.67828… USD) (more than the original price) <strong><em>(A1)</em>(ft)<em> (C4)</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1"><span class="s1">The distance \(d\) </span>from a point \({\text{P}}(x,{\text{ }}y)\) to the point \({\text{A}}(1,{\text{ }} - 2)\) <span class="s1">is given by \(d = \sqrt {{{(x - 1)}^2} + {{(y + 2)}^2}} \)</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the distance from \({\text{P}}(100,{\text{ }}200)\) to \({\text{A}}\)<span class="s1">. Give your answer correct to two decimal places.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down your answer to <strong>part (a) </strong>correct to three significant figures.</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 class="p1">Write down your answer to <strong>part (b) </strong>in the form \(a \times {10^k}\), where \(1 \leqslant a < 10\) and \(k \in \mathbb{Z}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\sqrt {{{(100 - 1)}^2} + {{(200 + 2)}^2}} \) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">\(\sqrt {50605} \;\;\;( = 224.955 \ldots )\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(M1)(A1) </em></strong>if \(\sqrt {50605} \) seen.</p>
<p class="p2"> </p>
<p class="p1">\({\text{224.96}}\) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C3)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for their answer given correct to <span class="s1">2 </span>decimal places.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="s1">\(225\) <span class="Apple-converted-space"> </span></span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Follow through from their part (a).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(2.25 \times {10^2}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C2)</em></strong></p>
<p class="p1"><strong>Notes: </strong>Award <strong><em>(A1)(A0) </em></strong>for \(2.25\) and an incorrect index value.</p>
<p class="p1">Award <strong><em>(A0)(A0) </em></strong>for answers such as \(22.5 \times {10^1}\).</p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Expand the expression \(x(2{x^3} - 1)\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Differentiate \(f(x) = x(2{x^3} - 1)\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the \(x\)-coordinate of the local minimum of the curve \(y = f(x)\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(2{x^4} - x\) <strong><em>(A1)(A1) (C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for \(2{x^4}\), <em><strong>(A1)</strong></em> for \( - x\).</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(8{x^3} - 1\) <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft) <em>(C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A1)</em>(ft) </strong>for \(8{x^3}\), <strong><em>(A1)</em>(ft) </strong>for \(–1\). Follow through from their part (a).</span></p>
<p><span> Award at most <strong><em>(A1)(A0) </em></strong>if extra terms are seen.</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(8{x^3} - 1 = 0\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for equating their part (b) to zero.</span></p>
<p> </p>
<p><span>\((x = )\frac{1}{2}{\text{ (0.5)}}\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Follow through from part (b).</span></p>
<p><span> \(0.499\) is the answer from the use of trace on the GDC; award <strong><em>(A0)(A0)</em></strong>.</span></p>
<p><span> For an answer of \((0.5, –0.375)\), award <strong><em>(M1)(A0)</em></strong>.</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">A surprising number of candidates were unable to correctly expand the expression given in part (a). Most candidates were able to differentiate their function but a considerable number were unable to find the x-coordinate of the minimum point. Candidates must read the questions correctly as answers giving ordered pairs were not awarded the final mark. A number of candidates did not use calculus to determine the local minimum but graphed the function, often achieving full marks for part (c), even when parts (b) or (a) were incorrect or left blank.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">A surprising number of candidates were unable to correctly expand the expression given in part (a). Most candidates were able to differentiate their function but a considerable number were unable to find the x-coordinate of the minimum point. Candidates must read the questions correctly as answers giving ordered pairs were not awarded the final mark. A number of candidates did not use calculus to determine the local minimum but graphed the function, often achieving full marks for part (c), even when parts (b) or (a) were incorrect or left blank.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">A surprising number of candidates were unable to correctly expand the expression given in part (a). Most candidates were able to differentiate their function but a considerable number were unable to find the x-coordinate of the minimum point. Candidates must read the questions correctly as answers giving ordered pairs were not awarded the final mark. A number of candidates did not use calculus to determine the local minimum but graphed the function, often achieving full marks for part (c), even when parts (b) or (a) were incorrect or left blank.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Marcus has been given 500 Australian dollars (AUD) by his grandmother for his 18th birthday.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">He plans to deposit it in a bank which offers a nominal annual interest rate of 6.0 %, <strong>compounded quarterly</strong>, for three years.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the total amount of interest Marcus would earn, in AUD, over the three years. <strong>Give your answer correct to two decimal places.</strong></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Marcus would earn the same amount of interest, <strong>compounded annually</strong>, for three years if he deposits the 500 AUD in a second bank.</span></p>
<p><span>Calculate the interest rate the second bank offers.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(500{\left( {1 + \frac{6}{{100 \times 4}}} \right)^{4 \times 3}} - 500\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution in correct formula <em><strong>(A1)</strong></em> for correct substitutions.</span></p>
<p><br><span>\(= 97.81\) <em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><br><span><strong>Note:</strong> The answer must be given to 2 dp or the final <em><strong>(A1)</strong></em> is not awarded.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(97.8090... = 500{\left( {1 + \frac{r}{{100}}} \right)^3} - 500\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution in correct formula, <em><strong>(A1)</strong></em><strong>(ft)</strong> for their correct substitutions.</span></p>
<p><br><span>\(= 6.14\) (6.13635...) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C3)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from their answer to part (a).</span></p>
<p> </p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p><span>Charles invests \(3000{\text{ USD}}\) in a bank that offers compound interest at a rate of \(3.5\% \) per annum, compounded half-yearly.</span></p>
<p><span>Calculate the number of years that it takes for Charles’s money to double.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span>\(6000 = 3000{\left( {1 + \frac{{3.5}}{{200}}} \right)^{2n}}\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><br><span><strong>Note: <em>(M1)</em></strong> for substituting values into a compound interest formula, <em><strong>(A1)</strong></em> for correct values with a variable for the power.</span></p>
<p><br><span>\(n = 20{\text{ years}}\) <em><strong>(A1) (C3)</strong></em><br></span></p>
<p><br><span><strong>Note: </strong>If \(n\) used in formula instead of \(2n\), can allow as long as final answer is halved to get \(20\).</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">Part (a) on simple interest was answered well - common errors being \(0.04\) in the numerator as well as \(100\) in denominator, and using \(6000\) as the interest. Part (b) was not well done. Candidates struggled with interest that was not compounded yearly although such questions have been asked on previous papers.</span></p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">In the diagram, \({\text{B}}\hat {\text{A}}{\text{C}} = {90^ \circ }\) . The length of the three sides are \(x{\text{ cm}}\), \((x + 7){\text{ cm}}\) and \((x + 8){\text{ cm}}\).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img 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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down and <strong>simplify</strong> a quadratic equation in \(x\) which links the three sides of the triangle.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Solve the quadratic equation found in part (a).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of the perimeter of the triangle.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\({(x + 8)^2} = {(x + 7)^2} + {x^2}\) <em><strong>(A1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for a correct equation.</span></p>
<p><span> </span></p>
<p><span>\({x^2} + 16x + 64 = {x^2} + 14x + 49 + {x^2}\) <em><strong>(A1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correctly removed parentheses.</span></p>
<p><span> </span></p>
<p><span>\({x^2} - 2x - 15 = 0\) <em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em> <br></span></p>
<p><span><strong>Note:</strong> Accept any equivalent form.</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(x = 5\), \(x = - 3\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span> </p>
<p><span><strong>Notes:</strong> Accept <strong><em>(A1)</em>(ft)</strong> only from the candidate’s <strong>quadratic</strong> equation.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(30{\text{ cm}}\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C1)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from a positive answer found in part (b).</span></p>
<p><span><em><strong>[1 mark]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium;"><span style="font-family: times new roman,times;">This question proved to be difficult for the majority of candidates. Many simply were unable to see that, to relate the three given lengths, a Pythagorean equation needed to be produced. Indeed, many did not seem to appreciate the concept of a quadratic equation and, as a consequence, either wrote down a linear equation linking one length to the sum of the other two lengths or multiplied all three lengths together. For the minority who stated a correct Pythagorean equation, many could not remove brackets successfully and arrived at \({x^2} = 15\) . Consequently, very few candidates earned more than one mark for part (a). Where the</span> <span style="font-family: times new roman,times;">correct quadratic equation was seen in part (a), many were able to solve this quadratic correctly in part (b) and arrive at the required value of \(x = 5\) for the answer for part (c).</span></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium;"><span style="font-family: times new roman,times;">This question proved to be difficult for the majority of candidates. Many simply were unable to see that, to relate the three given lengths, a Pythagorean equation needed to be produced. Indeed, many did not seem to appreciate the concept of a quadratic equation and, as a consequence, either wrote down a linear equation linking one length to the sum of the other two lengths or multiplied all three lengths together. For the minority who stated a correct Pythagorean equation, many could not remove brackets successfully and arrived at \({x^2} = 15\) . Consequently, very few candidates earned more than one mark for part (a). Where the</span> <span style="font-family: times new roman,times;">correct quadratic equation was seen in part (a), many were able to solve this quadratic correctly in part (b) and arrive at the required value of \(x = 5\) for the answer for part (c).</span></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium;"><span style="font-family: times new roman,times;">This question proved to be difficult for the majority of candidates. Many simply were unable to see that, to relate the three given lengths, a Pythagorean equation needed to be produced. Indeed, many did not seem to appreciate the concept of a quadratic equation and, as a consequence, either wrote down a linear equation linking one length to the sum of the other two lengths or multiplied all three lengths together. For the minority who stated a correct Pythagorean equation, many could not remove brackets successfully and arrived at \({x^2} = 15\) . Consequently, very few candidates earned more than one mark for part (a). Where the</span> <span style="font-family: times new roman,times;">correct quadratic equation was seen in part (a), many were able to solve this quadratic correctly in part (b) and arrive at the required value of \(x = 5\) for the answer for part (c).</span></span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A teacher earns an annual salary of \(45 000\) USD for the first year of her employment. Her annual salary increases by \(1750\) USD each year.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the annual salary for the fifth year of her employment.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>She remains in this employment for 10 years. Calculate the <strong>total</strong> salary she earns in this employment during these 10 years.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(45000 + (5 - 1)1750\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituted AP formula, <em><strong>(A1)</strong></em> for correct substitutions.</span></p>
<p><span> </span></p>
<p><span>\( = 52000\) USD <em><strong>(A1) (C3)</strong></em></span></p>
<p><span><strong>Notes:</strong> If a list is used, award <em><strong>(M1)</strong></em> for recognizing AP, award <em><strong>(A1)</strong></em> for seeing 52000 in their list, <em><strong>(A1)</strong></em> for final answer.</span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{10}}{2}(2(45000) + (10 - 1)(1750))\) <em><strong>(M1)(A1)</strong></em></span> </p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for substituted AP formula, <em><strong>(A1)</strong></em><strong>(ft)</strong> for correct substitutions. Follow through from their common difference used</span> <span>in part (a).</span></p>
<p> </p>
<p><span>\( = 528750\) USD <em><strong>(A1)</strong></em><strong>(ft) </strong><em><strong> (C3)</strong></em></span></p>
<p><span><span><strong>Notes:</strong> Accept \(529 000\). If a list is used, award</span> <span><em><strong>(M1)</strong></em> for recognizing sum of AP, <em><strong>(A1)</strong></em> for seeing \(60 750\) included in the sum or \(528 750\) in a cumulative list.</span></span></p>
<p><em><strong><span><span>[3 marks]</span></span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Although part a was very well done, a large number of candidates multiplied the difference by \(n\) rather than \(n - 1\). </span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Although part a was very well done, a large number of candidates multiplied the difference by \(n\) rather than \(n - 1\). Many candidates misread, or misinterpreted, part b and found the \({10^{{\text{th}}}}\) term rather than the sum of the first \(10\) terms.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;"><em><strong>In this question give all answers correct to 2 decimal places.</strong></em></span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">George travelled from the USA to Europe and changed \(1200\) dollars (USD) into</span> <span style="font-size: medium; font-family: times new roman,times;">Euros (EUR). The exchange rate was \(1{\text{ USD}} = 0.8154{\text{ EUR}}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the number of EUR George received.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>On his return, George had \(160\) EUR to change back into USD. There was \(4.5\% \) commission charged on the exchange. The exchange rate was \(1\) USD = \(0.8202\) EUR. </span></p>
<p><span>Calculate the value, in EUR, of the commission that George paid.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>On his return, George had \(160\) EUR to change back into USD. There was \(4.5\% \) commission charged on the exchange. The exchange rate was \(1\) USD = \(0.8202\) EUR.</span></p>
<p><span>Calculate the number of dollars George received.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><em><strong>The first time the answer is not given to 2 decimal places the final (A1) in that part is not awarded, incorrect rounding, following correct method, can be ignored in subsequent parts.</strong></em></span></p>
<p><span>\</span><span>(1200 \times 0.8154\) <em><strong>(M1)</strong></em></span></p>
<p><span>\( = 978.48{\text{ EUR}}\) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em><strong>The first time the answer is not given to 2 decimal places the final (A1) in that part is not awarded, incorrect rounding, following correct method, can be ignored in subsequent parts.</strong></em></span></p>
<p><span><span>\(160 \times 0.045\) </span> <span><em><strong>(M1)</strong></em></span></span></p>
<p><span>\( = 7.20{\text{ EUR}}\) <em><strong>(A1) (C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em><strong>The first time the answer is not given to 2 decimal places the final (A1) in that part is not awarded, incorrect rounding, following correct method, can be ignored in subsequent parts.</strong></em></span></p>
<p><span>\(152.80 \times \frac{1}{{0.8202}}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their answer to part (b).</span></p>
<p> </p>
<p><span>\( = 186.30{\text{ USD}}\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></span></p>
<p><span><strong>Note:</strong> Follow through from part (b).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">At whatever ability, there were good attempts by all candidates on this question with an overwhelming majority scoring half marks or more. Indeed, three out of the first four marks were invariably earned with only answers of \(7.2\) EUR losing the final mark in part (b). In part (c), errors were invariably caused by candidates ignoring the commission charge or multiplying by \(0.8202\) rather than dividing by this value. Another common, but incorrect, method seen was multiply \(152.80\) by \((1 + 1 - 0.8202)\), giving the wrong answer of \(180.27\) USD. Both marks were lost in all the cases listed.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">At whatever ability, there were good attempts by all candidates on this question with an overwhelming majority scoring half marks or more. Indeed, three out of the first four marks were invariably earned with only answers of \(7.2\) EUR losing the final mark in part (b). In part (c), errors were invariably caused by candidates ignoring the commission charge or multiplying by \(0.8202\) rather than dividing by this value. Another common, but incorrect, method seen was multiply \(152.80\) by \((1 + 1 - 0.8202)\), giving the wrong answer of \(180.27\) USD. Both marks were lost in all the cases listed.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">At whatever ability, there were good attempts by all candidates on this question with an overwhelming majority scoring half marks or more. Indeed, three out of the first four marks were invariably earned with only answers of \(7.2\) EUR losing the final mark in part (b). In part (c), errors were invariably caused by candidates ignoring the commission charge or multiplying by \(0.8202\) rather than dividing by this value. Another common, but incorrect, method seen was multiply \(152.80\) by \((1 + 1 - 0.8202)\), giving the wrong answer of \(180.27\) USD. Both marks were lost in all the cases listed.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Ludmila takes a loan of 320 000 Brazilian Real (BRL) from a bank for two years at a nominal annual interest rate of 10%, <strong>compounded half yearly</strong>.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of times interest is added to the loan in the two years.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the <strong>exact </strong>amount of money that Ludmila must repay at the end of the two years.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Ludmila estimates that she will have to repay \({\text{360}}\,{\text{000}}\) BRL at the end of the two years.</span></p>
<p><span>Calculate the percentage error in her estimate.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>4 <strong><em>(A1) (C1)</em></strong></span></p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(320\,000{\left( {1 + \frac{{10}}{{2 \times 100}}} \right)^{2 \times 2}}\) <strong><em>(M1)(A1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substituted compound interest formula, <strong><em>(A1) </em></strong>for correct substitutions.</span></p>
<p> </p>
<p><span><strong>OR</strong></span></p>
<p><span>\({\text{N}} = 2\)</span></p>
<p><span>\({\text{I}}\% = 10\)</span></p>
<p><span><span>\({\text{PV}} = - 320000\)</span></span></p>
<p><span>\({\text{P }}/{\text{ Y}} = 1\)</span></p>
<p><span>\({\text{C }}/{\text{ Y}} = 2\) <strong><em>(A1)(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for </span><span>\({\text{C }}/{\text{ Y}} = 2\) seen, <strong><em>(M1) </em></strong>for correctly substituted values from the question into the finance application.</span></p>
<p> </p>
<p><span><strong>OR</strong></span></p>
<p><span>\({\text{N}} = 4\)</span></p>
<p><span>\({\text{I}}\% = 10\)</span></p>
<p><span><span>\({\text{PV}} = - 320000\)</span></span></p>
<p><span>\({\text{P }}/{\text{ Y}} = 2\)</span></p>
<p><span>\({\text{C }}/{\text{ Y}} = 2\)</span><span> <strong><em>(A1)(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for </span><span>\({\text{C }}/{\text{ Y}} = 2\)</span><span> seen, <strong><em>(M1) </em></strong>for correctly substituted values from the question into the finance application.</span></p>
<p> </p>
<p><span>amount to repay </span><span>\( = 388962\) <em><strong>(A1) (C3)</strong></em></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(C2) </em></strong>for final answer \(389000\) if \(388962\) not seen previously.</span></p>
<p> </p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\left| {\frac{{360\,000 - 388\,962}}{{388\,962}}} \right| \times 100\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correctly substituted percentage error formula.</span></p>
<p> </p>
<p><span>\( = 7.45{\text{ (% ) }}(7.44597 \ldots )\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Follow through from their answer to part (b).</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A cuboid has a rectangular base of width \(x\)<span class="s1"><em> </em>cm </span>and length <span class="s1">2\(x\) cm </span>. The height of the cuboid is \(h\) <span class="s1">cm </span>. The total length of the edges of the cuboid is \(72\)<span class="s1"> cm</span>.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-20_om_08.27.58.png" alt></p>
<p class="p1">The volume, \(V\), of the cuboid can be expressed as \(V = a{x^2} - 6{x^3}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of \(a\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of \(x\) that makes the volume a maximum.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(72 = 12x + 4h\;\;\;\)(or equivalent) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for a correct equation obtained from the total length of the edges.</p>
<p class="p2"> </p>
<p class="p1">\(V = 2{x^2}(18 - 3x)\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1">\((a = ){\text{ }}36\) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C3)</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\frac{{{\text{d}}V}}{{{\text{d}}x}} = 72x - 18{x^2}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1">\(72x - 18{x^2} = 0\;\;\;\)<strong>OR</strong>\(\;\;\;\frac{{{\text{d}}V}}{{{\text{d}}x}} = 0\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Notes:<span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1) </em></strong>for<span class="Apple-converted-space"> </span>\( - 18{x^2}\)<span class="Apple-converted-space"> </span>seen. Award <strong><em>(M1) </em></strong>for equating derivative to zero.</p>
<p class="p2"> </p>
<p class="p1">\((x = ){\text{ 4}}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C3)</em></strong></p>
<p class="p1"><strong>Note: </strong>Follow through from part (a).</p>
<p class="p2"> </p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">Sketch of \(V\) with visible maximum <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">Sketch with \(x \geqslant 0,{\text{ }}V \geqslant 0\) and indication of maximum (e.g. coordinates) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)</strong></p>
<p class="p1">\((x = ){\text{ 4}}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C3)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: </strong>Follow through from part (a).</p>
<p class="p1">Award <strong><em>(M1)(A1)(A0) </em></strong>for \((4,{\text{ }}192)\).</p>
<p class="p1">Award <strong><em>(C3) </em></strong>for \(x = 4,{\text{ }}y = 192\).</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>The model in this question seemed to be too difficult for the vast majority of the candidates, and therefore was a strong discriminator between grade 6 and grade 7 candidates. An attempt to find an equation for the volume of the cube often started with <em>V</em> = <em>x</em> x 2<em>x</em> x <em>h</em> . Many struggled to translate the total length of the edges into a correct equation, and consequently were unable to substitute <em>h</em>. Some tried to write <em>x</em> in terms of <em>h</em> and got lost, others tried to work backwards from the expression given in the question.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>As very few found a value for <em>a</em>, often part (b) was not attempted. When a derivative was calculated this was usually done correctly.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Emma places \({\text{€}}8000\) in a bank account that pays a nominal interest rate of \(5\% \) per annum, compounded quarterly.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the amount of money that Emma would have in her account after 15 years. Give your answer correct to the nearest Euro.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>After a period of time she decides to withdraw the money from this bank. There is \({\text{€}}9058.17\) in her account. Find the number of months that Emma had left her money in the account.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(FV = 8000{(1.0125)^{60}}\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span><strong>Note: <em>(M1)</em></strong> for substituting in compound interest formula, <em><strong>(A1)</strong></em> for correct substitution.</span></p>
<p><span>\({\text{€}}16857\) only <em><strong>(A1) (C3)</strong></em></span></p>
<p><span><em><strong>[3 marks]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(8000{(1.0125)^n} = 9058.17\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note: <em>(M1)</em></strong> for equating compound interest formula to \(9058.17\)</span></p>
<p><br><span>\(n = 10\) <em>correct answer only <strong>(A1)</strong><br></em></span></p>
<p><br><span>So 30 months, <strong>(ft)</strong> on their \(n\) <em><strong>(A1)</strong></em><strong>(ft)<em> (C3)</em></strong></span></p>
<p><br><span><strong>Note: </strong>Award <em><strong>(C2)</strong></em> for \(2.5\) seen with no working.</span></p>
<p><span><strong><em>[3 marks]</em></strong><br></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Again this is a question that has been tested before but few candidates managed to gain full marks. Many, in part (b), believed they had to subtract \(8000\) from the value to get the interest first. This could possibly be a result of the way the formula is given in the formula booklet so teachers need to be aware of this.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Again this is a question that has been tested before but few candidates managed to gain full marks. Many, in part (b), believed they had to subtract \(8000\) from the value to get the interest first. This could possibly be a result of the way the formula is given in the formula booklet so teachers need to be aware of this.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A liquid is heated so that after \(20\) seconds of heating its temperature, \(T\) , is \({25^ \circ }{\text{C}}\) and after \(50\) seconds of heating its temperature is \({37^ \circ }{\text{C}}\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The temperature of the liquid at time \(t\) can be modelled by \(T = at + b\) , where \(t\) is the time in seconds after the start of heating.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Using this model one equation that can be formed is \(20a + b = 25\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using the model, write down a second equation in \(a\) and \(b\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using your graphic display calculator or otherwise, find the value of \(a\) and of \(b\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use the model to predict the temperature of the liquid \(60{\text{ seconds}}\) after the start of heating.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(50a + b = 37\) <em><strong>(A1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(50a + b\) , <em><strong>(A1)</strong></em> for \(= 37\) .</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(a = 0.4\), \(b = 17\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span></p>
<p> </p>
<p><span>Notes: Award <em><strong>(M1)</strong></em> for attempt to solve their equations if this is done analytically. If the GDC is used, award <strong>(ft)</strong> even if no working seen.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(T = 0.4(60) + 17\) <em><strong>(M1)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of their values and \(60\) into equation for \(T\).</span></p>
<p> </p>
<p><span>\(T = 41{\text{ }}{{\text{(}}^ \circ }{\text{C}})\) <em><strong>(A1)</strong></em><strong>(ft) </strong><em><strong> (C2)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Follow through from their part (b).</span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The seventh term, \({u_7}\) , of a geometric sequence is \(108\). The eighth term, \({u_8}\) , of the sequence is \(36\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the common ratio of the sequence.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \({u_1}\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The sum of the first \(k\) terms in the sequence is \(118 096\) . Find the value of \(k\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(r = \frac{{36}}{{108}}\left( {\frac{1}{3}} \right)\) <em><strong>(A1) (C1)</strong></em></span></p>
<p><span><strong>Note:</strong> Accept \(0.333\).</span></p>
<p><em><strong><span>[1 mark]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({u_1}{\left( {\frac{1}{3}} \right)^7} = 36\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in formula for nth term of a GP. Accept equivalent forms.</span></p>
<p> </p>
<p><span>\({u_1} = 78732\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Accept \(78 700\). Follow through from their common ratio found in part (a). If \(0.333\) used from part (a) award <strong><em>(M1)(A1)</em>(ft)</strong> for an answer of \(79 285\) or \(79 300\) irrespective of whether working is shown.</span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(118096 = \frac{{78732\left( {1 - {{\left( {\frac{1}{3}} \right)}^k}} \right)}}{{\left( {1 - \frac{1}{3}} \right)}}\) <em><strong>(M1)(M1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in the sum of a GP formula, <em><strong>(M1)</strong></em> for equating their sum to \(118 096\). Follow through from parts (a) and (b).</span></p>
<p><span><strong>OR</strong></span></p>
<p><span>Sketch of the function \(y = 78732\frac{{\left( {1 - {{\left( {\frac{1}{3}} \right)}^k}} \right)}}{{\left( {1 - \frac{1}{3}} \right)}}\) <em><strong>(M1)</strong></em></span><br><span>Indication of point where \(y = 118 096\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>\(78 732 + 26 244 + 8748 + 2916 + 972 + 324 + 108 + 36 + 12 + 4 = 118 096\) <em><strong>(M1)(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for a list of at least 8 correct terms, <em><strong>(M1)</strong></em> for the sum of the terms equated to \(118 096\).</span></p>
<p> </p>
<p><span>\(k =10\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></span></p>
<p><span><span><strong>Notes:</strong> Follow through from parts (a) and (b). If k is not an integer, do not award final</span><span> <em><strong>(A1)</strong></em>. Accept alternative methods. If \(0.333\) and \(79 285\) used award <strong><em>(M1)(M1)(A1)</em>(ft)</strong> for \(k = 5\). If \(0.333\) and \(79 300\) used award <em><strong>(M1)(M1)(A0)</strong></em>.</span></span></p>
<p><em><strong><span><span>[3 marks]</span></span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">In part a, many candidates gave the common ratio as 3. </span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">In part a, many candidates gave the common ratio as 3. While they could set up the equation for part c, relatively few succeeded in solving it. Those who arrived at an answer did not always realize that the answer must be an integer.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">In part a, many candidates gave the common ratio as 3. While they could set up the equation for part c, relatively few succeeded in solving it. Those who arrived at an answer did not always realize that the answer must be an integer.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A shipping container is a cuboid with dimensions \({\text{16 m}}\), \({\text{1}}\frac{{\text{3}}}{{\text{4}}}{\text{ m}}\) and \({\text{2}}\frac{{\text{2}}}{{\text{3}}}{\text{ m}}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the <strong>exact</strong> volume of the container. Give your answer as a fraction.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Jim estimates the dimensions of the container as 15 m, 2 m and 3 m and uses these to estimate the volume of the container.</span></p>
<p><span>Calculate the percentage error in Jim’s estimated volume of the container.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(V = 16 \times 1\frac{3}{4} \times 2\frac{2}{3}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in volume formula. Accept decimal substitution of \(2.66\) or better.</span></p>
<p><span> </span></p>
<p><span>\( = 74.6666{\text{ }} \ldots \) <em><strong>(A1)</strong></em></span><br><span>\( = {\text{74}}\frac{{\text{2}}}{{\text{3}}}{\text{ }}{{\text{m}}^{\text{3}}}{\text{ }}\left( {\frac{{{\text{224}}}}{{\text{3}}}{\text{ }}{{\text{m}}^{\text{3}}}} \right)\) <em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><span><strong>Note:</strong> Correct answer only.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{% error}} = \frac{{\left( {90 - 74\frac{2}{3}} \right) \times 100}}{{74\frac{2}{3}}}\) <em><strong>(A1)(M1)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(90\) seen, or inferred in numerator, <em><strong>(M1)</strong></em> for correct substitution into percentage error formula.</span></p>
<p><span> </span></p>
<p><span>\( = 20.5\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span><strong>Note:</strong> Accept \( - 20.5\).</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well answered by the majority of candidates. Candidates encountered difficulty in part (a) with using fractions finding the exact volume. Nearly all candidates could use the formula for volume and most could achieve at least 2 marks in this first part. Most candidates could find the percentage error correctly using the formula once they found the estimate for the volume. Very few candidates substituted the formula incorrectly, or had an incorrect denominator.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well answered by the majority of candidates. Candidates encountered difficulty in part (a) with using fractions finding the exact volume. Nearly all candidates could use the formula for volume and most could achieve at least 2 marks in this first part. Most candidates could find the percentage error correctly using the formula once they found the estimate for the volume. Very few candidates substituted the formula incorrectly, or had an incorrect denominator.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">\(10 000\) people attended a sports match. Let \(x\) be the number of adults attending the sports match and \(y\) be the number of children attending the sports match.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down an equation in \(x\) and \(y\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The cost of an adult ticket was \(12\) Australian dollars (AUD). The cost of a child ticket was \(5\) Australian dollars (AUD).</span></p>
<p><span> Find the total cost for a family of 2 adults and 3 children.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The total cost of tickets sold for the sports match was \(108800{\text{ AUD}}\).</span></p>
<p><span>Write down a second equation in \(x\) and \(y\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of \(x\) and the value of \(y\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><span>\(x + y = 10000\) </span><span> <em><strong>(A1) (C1)</strong></em></span></span></p>
<p><span><span><em><strong>[1 mark]<br></strong></em></span></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(2 \times 12 + 3 \times 5\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(39{\text{ }}(39.0{\text{, }}39.00)\) (AUD) <em><strong>(A1) (C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(12x + 5y = 108800\) <em><strong>(A1) (C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(x = 8400\), \(y = 1600\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Follow through from their equations. If \(x\) and \(y\) are both incorrect then award <em><strong>(M1)</strong></em> for attempting to solve simultaneous equations.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The first three marks were obtained by a significant majority of candidates. The second equation in \(x\) and \(y\) proved to be a little more elusive and a popular, but incorrect, answer seen was \(12x + 5y = 10000\) . Where working was seen in part (d), much of it was wrong. Indeed, a popular, but erroneous method, was to make either \(x\) (or \(y\)) the subject using one equation and then back substituting the value found into the same equation. Answers, involving decimals, should have flagged to the candidate that something was going wrong somewhere and another look at the question was required. Algebra is always a discriminator on these papers and centres would be well advised to reinforce concepts in such topics.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The first three marks were obtained by a significant majority of candidates. The second equation in \(x\) and \(y\) proved to be a little more elusive and a popular, but incorrect, answer seen was \(12x + 5y = 10000\) . Where working was seen in part (d), much of it was wrong. Indeed, a popular, but erroneous method, was to make either \(x\) (or \(y\)) the subject using one equation and then back substituting the value found into the same equation. Answers, involving decimals, should have flagged to the candidate that something was going wrong somewhere and another look at the question was required. Algebra is always a discriminator on these papers and centres would be well advised to reinforce concepts in such topics.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The first three marks were obtained by a significant majority of candidates. The second equation in \(x\) and \(y\) proved to be a little more elusive and a popular, but incorrect, answer seen was \(12x + 5y = 10000\) . Where working was seen in part (d), much of it was wrong. Indeed, a popular, but erroneous method, was to make either \(x\) (or \(y\)) the subject using one equation and then back substituting the value found into the same equation. Answers, involving decimals, should have flagged to the candidate that something was going wrong somewhere and another look at the question was required. Algebra is always a discriminator on these papers and centres would be well advised to reinforce concepts in such topics.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The first three marks were obtained by a significant majority of candidates. The second equation in \(x\) and \(y\) proved to be a little more elusive and a popular, but incorrect, answer seen was \(12x + 5y = 10000\) . Where working was seen in part (d), much of it was wrong. Indeed, a popular, but erroneous method, was to make either \(x\) (or \(y\)) the subject using one equation and then back substituting the value found into the same equation. Answers, involving decimals, should have flagged to the candidate that something was going wrong somewhere and another look at the question was required. Algebra is always a discriminator on these papers and centres would be well advised to reinforce concepts in such topics.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;"><em>f</em> (<em>x</em>) = 5<em>x</em><sup>3</sup> − 4<em>x</em><sup>2</sup> + <em>x</em></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find <em>f</em>'(<em>x</em>). </span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find using your answer to part (a) the <em>x</em>-coordinate of</span></p>
<p><span>(i) the local maximum point;</span></p>
<p><span>(ii) the local minimum point.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>15<em>x</em><sup>2</sup> – 8<em>x</em> + 1 <em><strong>(A1)(A1)(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for each correct term.</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>15<em>x</em><sup>2</sup> – 8<em>x</em> +1 = 0 <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for setting their derivative to zero.</span></p>
<p> </p>
<p><span>(i) \((x =)\frac{1}{5}(0.2)\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong> </strong></span></p>
<p><span>(ii) \((x =)\frac{1}{3}(0.333)\) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C3)</strong></em></span></p>
<p><span><strong>Notes:</strong> Follow through from their answer to part (a).</span></p>
<p><br><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Many candidates lost 1 mark in part (a) through not realizing that the derivative of<em> x</em> is 1. As a consequence, 15<em>x</em><sup>2</sup> – 8<em>x</em> proved to be a popular answer. <br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Very few candidates gained the marks in part (b) to find the maximum and minimum point. Although the question indicated to use their answer to part (a), very few candidates set the derivative to zero which would have given them 1 mark. It seemed as if many candidates were trying to use their calculators to find the coordinates but could not find which was the maximum and which was the minimum.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">José stands 1.38 kilometres from a vertical cliff.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Express this distance in metres.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>José estimates the angle between the horizontal and the top of the cliff as 28.3° and uses it to find the height of the cliff.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span><span>Find the height of the cliff according to José’s calculation.<strong> Express your answer in metres, to the nearest whole metre.</strong></span></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>José estimates the angle between the horizontal and the top of the cliff as 28.3° and uses it to find the height of the cliff.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>The actual height of the cliff is 718 metres. Calculate the percentage error made by José when calculating the height of the cliff.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>1380 (m) <em><strong>(A1) (C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(1380\tan 28.3\) <em><strong> (M1)</strong></em></span></p>
<p><span>\( = 743.05 \ldots \) .<em><strong> (A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>\( = 743\) (m) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <strong><em>(M1)</em> </strong>for correct substitution in tan formula or equivalent,</span> <span><em><strong>(A1)</strong></em><strong>(ft)</strong> for their 743.05 seen, <em><strong>(A1)</strong></em><strong>(ft)</strong> for their answer correct to </span><span>the nearest m.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{percentage error}} = \frac{{743.05 \ldots - 718}}{{718}} \times 100\) <em><strong> (M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in formula.</span></p>
<p><br><span>= 3.49 % (% <em>symbol not required</em>) <em><strong> (A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Accept 3.48 % for use of 743.</span></p>
<p><span>Accept negative answer.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was well answered by the majority of candidates although it was surprising to find some who could not express the given distance in metres. Where working was present, follow through marks could be awarded in the remainder of the question. Most candidates could give their answer correct to the nearest metre and find the percentage error correctly, using the formula. A common error was to use the calculated value in the denominator.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was well answered by the majority of candidates although it was surprising to find some who could not express the given distance in metres. Where working was present, follow through marks could be awarded in the remainder of the question. Most candidates could give their answer correct to the nearest metre and find the percentage error correctly, using the formula. A common error was to use the calculated value in the denominator.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was well answered by the majority of candidates although it was surprising to find some who could not express the given distance in metres. Where working was present, follow through marks could be awarded in the remainder of the question. Most candidates could give their answer correct to the nearest metre and find the percentage error correctly, using the formula. A common error was to use the calculated value in the denominator.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Ross is a star that is 82 414 080 000 000 km away from Earth. A spacecraft,</span> <span style="font-size: medium; font-family: times new roman,times;">launched from Earth, travels at 48 000 kmh<sup>–1</sup> towards Ross.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the <strong>exact</strong> time, in hours, for the spacecraft to reach the star Ross.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Give your answer to part (a) in years. (Assume 1 year = 365 days)</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Give your answer to part (b) in the form <em>a</em>×10<em><sup>k</sup></em>, where 1 ≤ <em>a</em> < 10 and \(k \in \mathbb{Z}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{{\text{82 414 080 000 000}}}}{{48\;000}}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in correct formula.</span></p>
<p> </p>
<p><span>1 716 960 000 (hours) <em><strong>(A1) </strong></em><em><strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{{\text{their (a)}}}}{{24 \times 365}}\) <em><strong>(M1)</strong></em></span></p>
<p><span>196 000 (years) <em><strong>(A1)</strong></em><strong>(ft) </strong><em><strong>(C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> from their part (a).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>1.96×10<sup>5</sup> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft) </strong><em><strong>(C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for 1.96 (accept 1.96000), <em><strong>(A1)</strong></em><strong>(ft)</strong> for 10<sup>5</sup> .</span> <span>Follow through from their answer to part (b).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">(a) The large numbers given in the stem of this question led to some candidates being a factor of 10 out in their answer to part (a) and therefore losing at least the A mark. Errors were compounded in this first part of the question with some candidates dividing by 48000<sup>–1</sup> which effectively meant multiplying by 48000. Much good work, however, was seen in the remaining two parts of the question with candidates well able to show a correct standard form from their figures.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">(a) The large numbers given in the stem of this question led to some candidates being a factor of 10 out in their answer to part (a) and therefore losing at least the A mark. Errors were compounded in this first part of the question with some candidates dividing by 48000<sup>–1</sup> which effectively meant multiplying by 48000. Much good work, however, was seen in the remaining two parts of the question with candidates well able to show a correct standard form from their figures.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">(a) The large numbers given in the stem of this question led to some candidates being a factor of 10 out in their answer to part (a) and therefore losing at least the A mark. Errors were compounded in this first part of the question with some candidates dividing by 48000<sup>–1</sup> which effectively meant multiplying by 48000. Much good work, however, was seen in the remaining two parts of the question with candidates well able to show a correct standard form from their figures.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Dumisani has received a scholarship of 5000 US dollars (USD) to study in Singapore.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">He has to travel from South Africa and must change USD for his air fare of 6600 South African rand (ZAR).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The exchange rate is 1USD = 8.2421 ZAR.</span></p>
<p><em><strong><span style="font-family: 'times new roman', times; font-size: medium;">In this question give all answers correct to two decimal places.</span></strong></em></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the number of USD that Dumisani must change to pay for his air fare.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>On arrival in Singapore, Dumisani changes 3000 USD to Singapore dollars (SGD) to pay for his school fees. There is a 2.8% commission charged on the exchange.</span></p>
<p><span>Calculate the value, <strong>in USD</strong>, of the commission that Dumisani has to pay.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The exchange rate is \(1{\text{ USD }} = 1.29903{\text{ SGD}}\).</span></p>
<p><span>Calculate the number of SGD Dumisani receives.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(6600 \times \frac{1}{{8.2421}}\) <strong><em>(M1)</em></strong></span></p>
<p><span>\( = 800.77\) <strong><em>(A1) (C2)</em></strong></span></p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(3000 \times 0.028\) <strong><em>(M1)</em></strong></span></p>
<p><span>\( = 84.00\) (accept 84) <strong><em>(A1) (C2)</em></strong></span></p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\((3000 - 84) \times 1.29903\) <strong><em>(M1)</em></strong></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>\(3000 \times 1.29903 \times 0.972\) <strong><em>(M1)</em></strong></span></p>
<p><span>\( = 3787.97\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes:</strong> Follow through from their answer to part (b).</span></p>
<p> </p>
<p><span><strong>Note: </strong>Do not penalize in part (c) if conversion process has been reversed consistently ie, multiplication by \(8.2421\) in part (a) and division by \(1.29903\) in part (c).</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p><span>The sets \(P\), \(Q\) and \(U\) are defined as</span></p>
<p><span><span><em>U</em> = {Real Numbers} , <em>P</em> = {Positive Numbers} and <em>Q</em> = {Rational Numbers}.</span></span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Write down in the correct region on the Venn diagram the numbers</span></p>
<p><span>\(\frac{{22}}{7}\) , \(5 \times {10^{ - 2}}\) , \(\sin (60^\circ )\) , \(0\) , \(\sqrt[3]{{ - 8}}\) , \( - \pi \).</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span><img src="data:image/png;base64,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" alt> </span><span><em><strong>(A1)(A1)(A1)</strong></em></span><span><em><strong>(A1)(A1)(A1) (C6)</strong></em></span></p>
<p><span> </span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for each number placed once in the correct region. Accept equivalent forms for numbers.</span></p>
<p><span> </span></p>
<p><em><strong><span>[6 marks]</span></strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-family: 'times new roman', times; font-size: medium;">Very few candidates gained full marks in this question. A common error turned out to be that \(\frac{{22}}{7}\) and \(5 \times {10^{ - 2}}\) were not considered rational numbers. Also, \(0\) and \(\sin (60^\circ )\) were often placed incorrectly. However, it was encouraging that very few candidates placed values in more than one region.</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1"><strong>In this question give all answers correct to two decimal places.</strong></p>
<p class="p1">Javier takes <span class="s1">5000 </span>US dollars (<span class="s1">USD</span>) on a business trip to Venezuela. He exchanges <span class="s1">3000 USD </span>into Venezuelan bolívars (<span class="s1">VEF</span>).</p>
<p class="p2"><span class="s2">The exchange rate is </span>1 USD \( = \) 6.3021 VEF<span class="s2">.</span></p>
</div>
<div class="specification">
<p class="p1">During his time in Venezuela, Javier spends <span class="s1">1250 USD </span>and <span class="s1">12 000 VEF</span>. On his return home, Javier exchanges his remaining <span class="s1">VEF </span>into <span class="s1">USD</span>.</p>
<p class="p2"><span class="s2">The exchange rate is </span>1 USD \( = \) 8.7268 VEF<span class="s2">.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Calculate the amount of <span class="s1">VEF </span><span class="s2">that Javier receives.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">Calculate the total amount, in </span><span class="s2">USD</span>, that Javier has remaining from his <span class="s2">5000 USD </span>after his trip to Venezuela.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>The first answer not given correct to two decimal places is not awarded the final <em>(A1)</em>.</strong></p>
<p class="p1"><strong>Incorrect rounding is not penalized thereafter. </strong></p>
<p class="p1"><span class="Apple-converted-space">\(3000 \times 6.3021\) </span><strong><em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for multiplying <span class="s1">3000 </span>by <span class="s1">6.3021</span>.</p>
<p class="p2"> </p>
<p class="p1">\( = 18906.30\) <strong><em>(A1) <span class="Apple-converted-space"> </span>(C2)</em></strong></p>
<p class="p3"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(\frac{{18906.30 - 12000}}{{8.7268}}{\text{ + }}(2000 - 1250)\) </span><strong><em>(M1)(M1)(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for subtracting <span class="s1">12 000 </span>from their answer to part (a) OR for <span class="s1">6906.30 </span>seen, <strong><em>(M1) </em></strong>for dividing their amount by <span class="s1">8.7268 </span>(can be implied if <span class="s1">791.389… </span>seen) and <strong><em>(M1) </em></strong>for \(2000 - 1250\) <strong><em>OR</em></strong> 750 seen.</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\( = 1541.39\) </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C4)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Follow through from part (a).</p>
<p class="p2"> </p>
<p class="p3"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The length of one side of a rectangle is 2 cm longer than its width.</span></p>
<p><span>If the smaller side is <em>x</em> cm, find the perimeter of the rectangle in terms of <em>x</em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The length of one side of a rectangle is 2 cm longer than its width.</span></p>
<p><span>The perimeter of a square is equal to the perimeter of the rectangle in part (a).</span></p>
<p><span>Determine the length of each side of the square in terms of <em>x</em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The length of one side of a rectangle is 2 cm longer than its width.</span></p>
<p><span>The perimeter of a square is equal to the perimeter of the rectangle in part (a).</span></p>
<p><span>The sum of the areas of the rectangle and the square is \(2x^2 + 4x +1\) (cm<sup>2</sup>).</span></p>
<p><span>(i) Given that this sum is 49 cm<sup>2</sup>, find <em>x</em>.</span></p>
<p><span>(ii) Find the area of the square.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><span><em><strong>Unit penalty (UP) is applicable where indicated in the left hand column.</strong></em><br></span></span></p>
<p><span><span><em><strong>(UP)</strong></em> \({\text{P (rectangle)}} = 2x + 2(x + 2) = 4x + 4{\text{ cm}}\)</span> <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<p><em><span><strong>(UP)</strong> Simplification not required</span></em></p>
<p><em><span><strong>[1 mark]</strong><br></span></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em><strong>Unit penalty (UP) is applicable where indicated in the left hand column.</strong></em><br></span></p>
<p><span><em><strong>(UP)</strong></em> Side of square = (4<em>x</em> + 4)/4 = <em>x</em> + 1 cm <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(2x^2 + 4x + 1 = 49\) or equivalent <em><strong>(M1)</strong></em></span></p>
<p><span>\((x + 6)(x – 4) = 0\)</span></p>
<p><span>\(x = - 6\) and \(4\) <em><strong>(A1)</strong></em></span></p>
<p><span><em>Note: award <strong>(A1)</strong> for the values or for correct factors </em><br></span></p>
<p><span>Choose \(x = 4\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><em>Award </em><strong><em>(A1)</em>(ft)</strong><em> for choosing positive value. </em> <em><strong>(C3)</strong></em></span></p>
<address><em><span> </span></em></address>
<p><span>(ii) \({\text{Area of square}} = 5 \times 5 = 25{\text{ c}}{{\text{m}}^2}\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><em><span>Note: Follow through from both (b) and (c)(i). <strong>(C1)</strong></span></em></p>
<p><em><span><strong> </strong></span></em></p>
<p><em><span><strong>[4 marks]<br></strong></span></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">a) and b) Two thirds of the candidates found the perimeter of the rectangle and the side of the square correctly, though most of them did not include units (thereby incurring a unit penalty).</span></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">a) and b) Two thirds of the candidates found the perimeter of the rectangle and the side of the square correctly, though most of them did not include units (thereby incurring a unit penalty).</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"> </span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">c) Although a majority of candidates produced the quadratic equation many were unable to solve it correctly. This could easily be done using the GDC so it was disappointing.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"> </span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A hydraulic hammer drives a metal post vertically into the ground by striking the top of the post. The distance that the post is driven into the ground, by the \(n{\text{th}}\) strike of the hammer, is \({d_n}\).</p>
<p class="p2"><span class="s1">The distances \({d_1},{\text{ }}{d_2},{\text{ }}{d_3}{\text{ }} \ldots ,{\text{ }}{d_n}\) </span>form a geometric sequence.</p>
<p class="p1">The distance that the post is driven into the ground by the first strike of the hammer, \({d_1}\), is <span class="s2">64 cm</span>.</p>
<p class="p1">The distance that the post is driven into the ground by the second strike of the hammer, \({d_2}\), is <span class="s2">48 cm</span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of the common ratio for this sequence.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the distance that the post is driven into the ground by the eighth strike of the <span class="s1">hammer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">Find the </span><strong>total depth </strong>that the post has been driven into the ground after <span class="s2">10 </span>strikes of the hammer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(48 = 64r\) </span><strong><em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for correct substitution into geometric sequence formula.</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\( = 0.75\left( {\frac{3}{4},{\text{ }}\frac{{48}}{{64}}} \right)\) </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C2)</em></strong></p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(64 \times {(0.75)^7}\) </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for correct substitution into geometric sequence formula or list of eight values using their \(r\). Follow through from part (a), only if answer is positive.</p>
<p class="p2"> </p>
<p class="p3"><span class="s2">\( = 8.54{\text{ }}({\text{cm}}){\text{ }}(8.54296 \ldots {\text{ cm}})\) <span class="Apple-converted-space"> </span></span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C2)</em></strong></p>
<p class="p2"> </p>
<p class="p3"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\({\text{depth}} = \frac{{64\left( {1 - {{(0.75)}^{10}}} \right)}}{{1 - 0.75}}\) </span><strong><em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for correct substitution into geometric series formula. Follow through from part (a), only if answer is positive.</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\( = 242({\text{cm}}){\text{ }}(241.583 \ldots )\) </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C2)</em></strong></p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">In an arithmetic sequence, the fifth term, <em>u</em><sub>5</sub>, is greater than the first term, <em>u</em><sub>1</sub>. The difference between these terms is 36.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the common difference, <em>d</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The tenth term of the sequence is double the seventh term.</span></p>
<p><span>(i) Write down an equation in <em>u</em><sub>1</sub> and <em>d</em> to show this information.</span></p>
<p><span>(ii) Find <em>u</em><sub>1</sub>.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\({u_1} + 4d - {u_1} = 36\) <em><strong>(M1)<br><br></strong></em></span></p>
<p><span><strong>Note:</strong> Accept equivalent forms including the use of a instead of \({u_1}\).</span></p>
<p><br><span>\((d =) 9\) <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \({u_{10}} = 2{u_7}\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct use of 2 (may be implied).</span></p>
<p><br><span>\({u_1} + 9d = 2[{u_1} + 6d]\) <em><strong>(A1)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Accept equivalent forms.</span> <span>Award <em><strong>(M1)(A0)</strong></em> for \(a + 9d = 2[a + 6d]\).</span></p>
<p><br><span>(ii) \({u_1} + 81 = 2{u_1} + 108\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(({u_1} =) - 27\) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C4)</strong></em></span><br><br></p>
<p><span><strong>Notes:</strong> Follow through from their <em>d</em> found in part (a) and equation in (b)(i).</span> <span>Do not penalize further use of a instead of \({u_1}\).</span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times;">Some candidates confused geometric sequence with arithmetic sequence. Candidates found the algebraic manipulations difficult so scores on this question were weak.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Some candidates confused geometric sequence with arithmetic sequence. Candidates found the algebraic manipulations difficult so scores on this question were weak.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Obi travels from Dubai to Pretoria and changes \(2000\) United Arab Emirates Dirham \(({\text{AED}})\) at a bank. He receives \(6160\) South African Rand \(({\text{ZAR}})\).</p>
<p>The exchange rate is \(1\;{\text{AED}} = x\,{\text{ZAR}}\).</p>
<p>Calculate the value of \(x\) .</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>Obi decides to invest half of the money he receives, \(3080\,\,{\text{ZAR}}\), in an account which pays a nominal interest rate of \(9\,\% \), <strong>compounded monthly</strong>.</p>
<p>The amount of money in the account will have doubled before the end of the \(n{\text{th}}\) year of the investment.</p>
<p>Calculate the minimum value of \(n\) .</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>\(\frac{{6160}}{{2000}}\) <em><strong>(M1)</strong></em></p>
<p>\( = 3.08\) <em><strong>(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct division.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(3080\,{\left( {1 + \frac{9}{{12 \times 100}}} \right)^{n \times 12}} = 6160\) <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution into compound interest formula equated to \(6160\), <em><strong>(A1)</strong></em> for correct substitution.</p>
<p><strong>OR</strong></p>
<p>\(I = 9\)</p>
<p>\(PV = \pm 3080\)</p>
<p>\(FV = \mp 6160\)</p>
<p>\(P/Y = 1\)</p>
<p>\(C/Y = 12\) <em><strong>(A1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(C/Y = 12\) seen, <em><strong>(M1)</strong></em> for other correct entries.<br>\(FV\) and \(PV\) must have opposite sign.</p>
<p>\( = 7.73048...\) <em><strong>(A1)</strong></em></p>
<p>\( = 8\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C4)</strong></em></p>
<p><strong>Note:</strong> Award the final <em><strong>(A1)</strong></em><strong>(ft)</strong> for the correct rounding <strong>up</strong>, of their unrounded answer, to complete years.</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Question 10: Currency conversion and compound interest.</p>
<p>Currency conversion was done well by all but the weakest candidates. Most of the candidates that used the compound interest formula did a correct substitution but some did not equate this to the future value and found solving an equation to be challenging. Candidates that used the financial application on their GDC almost always wrote down a correct unrounded answer.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 10: Currency conversion and compound interest.</p>
<p>Currency conversion was done well by all but the weakest candidates. Most of the candidates that used the compound interest formula did a correct substitution but some did not equate this to the future value and found solving an equation to be challenging. Candidates that used the financial application on their GDC almost always wrote down a correct unrounded answer.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Consider the following sequence:</span></p>
<p style="text-align: center;"><span style="font-size: medium; font-family: times new roman,times;">57, 55, 53 ..., 5, 3</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number of terms of the sequence.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the sum of the sequence.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>3 = 57 + (<em>n</em> − 1) × (−2)</span></p>
<p><em><strong><span>OR</span></strong></em></p>
<p><span>57 = 3 + (<em>n</em> − 1) × (2) <em><strong>(A1)(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for 3 <strong>or</strong> 57 seen as<em> u<sub>n</sub></em>, <em><strong>(M1)</strong></em> for correctly substituted formula or list of values seen.</span></p>
<p><br><span><em>n</em> = 28 <em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({{\text{S}}_{28}} = \frac{{28}}{2}(57 + 3)\)</span></p>
<p><em><strong><span>OR</span></strong></em></p>
<p><span>\({{\rm{S}}_{28}} = \frac{{28}}{2}(2(57) + (28 - 1) \times - 2)\)</span></p>
<p><em><strong><span>OR</span></strong></em></p>
<p><span>\({{\rm{S}}_{28}} = \frac{{28}}{2}(2(3) + (28 - 1) \times 2)\)</span><span> <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Note: <em>(A1)</em>(ft)</strong> for 28 seen.</span></p>
<p><span>Award <em><strong>(M1)</strong></em> for correctly substituted formula or list of values seen.</span></p>
<p><br><span>\({{\rm{S}}_{28}} = 840\)</span><span> <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C3)</strong></em></span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Most candidates recognised the arithmetic sequence and used the correct formula, although some used a list to find the answers. A common error was to use the common difference as 2 rather than −2. Many candidates were awarded follow through marks in part (b), correctly using their incorrect value of <em>n</em> from part (a).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Most candidates recognised the arithmetic sequence and used the correct formula, although some used a list to find the answers. A common error was to use the common difference as 2 rather than −2. Many candidates were awarded follow through marks in part (b), correctly using their incorrect value of n from part (a).</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Given \(p = x - \frac{{\sqrt y }}{z}\) , \(x = 1.775\) , \(y = 1.44\) and \(z = 48\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the value of \(p\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Barry <strong>first</strong> writes \(x\) , \(y\) and \(z\) correct to one significant figure and <strong>then</strong> uses these values to estimate the value of \(p\) .</span><br><span>(i) Write down \(x\) , \(y\) and \(z\) each correct to one significant figure.</span><br><span>(ii) Write down Barry’s estimate of the value of \(p\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the percentage error in Barry’s estimate of the value of \(p\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(p = 1.775 - \frac{{\sqrt {1.44} }}{{48}}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted equation for \(p\).</span></p>
<p> </p>
<p><span><span>\( = 1.75\) \(\left( {1.750{\text{, }}\frac{7}{4}} \right)\) </span><span> <em><strong>(A1)(C2)</strong></em></span></span></p>
<p><span><span><em><strong>[2 marks]</strong></em></span></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(x = 2\), \(y =1\), \(z = 50\) <em><strong>(A1)</strong></em></span></p>
<p><br><span>(ii) \(p =1.98\) \(\left( {\frac{{99}}{{50}}} \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from part (b)(i), irrespective of whether working is shown.</span></p>
<p><span><strong>Note:</strong> If 2 s.f. used throughout part (b)(i) award <strong><em>(A1)</em>(ft)</strong> for \(1.78\) or \(1.8\).</span></p>
<p> </p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{1.98 - 1.75}}{{1.75}} \times 100\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correctly substituted \(\% \) error formula.</span></p>
<p><span><strong>Note:</strong> Follow through from parts (a) and (b).</span></p>
<p> </p>
<p><span>\( = 13.1\% \) <strong><em>(A1)</em>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><span><span><strong>Notes:</strong> \(\% \) sign not required. Do not accept \( - 13.1\% \). If 100 missing and incorrect answer, award</span> <span><em><strong>(M0)(A0)</strong></em>. If 100 missing and answer incorrectly rounded, award <em><strong>(M1)(A1)</strong></em>.</span></span></p>
<p><em><strong><span><span>[2 marks]</span></span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was not well answered by the majority of candidates. Candidates encountered difficulty in part b, not being able to express their answer to one significant figure, or used a mixture of one and two significant figures. Follow through marks in parts bii and c were awarded for candidates who showed their working in calculating \(p\) and the percentage error.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was not well answered by the majority of candidates. Candidates encountered difficulty in part b, not being able to express their answer to one significant figure, or used a mixture of one and two significant figures. Follow through marks in parts bii and c were awarded for candidates who showed their working in calculating \(p\) and the percentage error.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was not well answered by the majority of candidates. Candidates encountered difficulty in part b, not being able to express their answer to one significant figure, or used a mixture of one and two significant figures. Follow through marks in parts bii and c were awarded for candidates who showed their working in calculating \(p\) and the percentage error.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The \(x\)-coordinate of the minimum point of the quadratic function \(f(x) = 2{x^2} + kx + 4\) is \(x =1.25\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Find the value of \(k\) .</span></p>
<p><span>(ii) Calculate the \(y\)-coordinate of this minimum point.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Sketch the graph of \(y = f(x)\) for the domain \( - 1 \leqslant x \leqslant 3\).</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(1.25 = - \frac{k}{{2(2)}}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong> OR</strong></span></p>
<p><span>\(f'(x) = 4x + k = 0\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for setting the gradient function to zero.</span></p>
<p><span> </span></p>
<p><span>\(k = - 5\) <em><strong>(A1) (C2)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span>(ii) \(2{(1.25)^2} - 5(1.25) + 4\) <em><strong>(M1)</strong></em></span></p>
<p><span>\( = 0.875\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></span></p>
<p><span><strong>Note:</strong> Follow through from their \(k\).</span></p>
<p><span> </span></p>
<p><span><em><strong>[4 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZgAAAGyCAIAAABWbkVSAAAbDElEQVR4nO3d329U553H8ecPmBtfcoGEhJB8ESmKqrlIhFZwAaJCYqpICNFWFqlmBWh3RWh1QFnFJep6Um0dtXKmKZsqVndQo3XSHGU3bBZPG9LijEC7dTpeBSuddmEFU7zF3dliGQYHm3P24uBh8M/58Z3zfc4579dVYjueE8Pn42ee8zzPMT4ARJzRvgAA6BZF1rq56bFvD+zaYcxTx87/wfN9f+nz0X3bdhz/YMbTvjQg2Siy9nhzl3PP9qUOj93wfN+/e+2Dl3f/xdnpJe3LApKNImvX/NTIfpM65s4s+r7vz338yncv39O+JiDhKLJ2eV9Mvf6cefrE+B99f6k2/v3vT97RviQg6Siy9t2dGNxqtg1dWXgw/ZPvfHCLCTJAG0XWgVvnj/abQz8tf/TD1xmOARagyDpwvzJ60PQ9s2eweJvhGGABiqwD3t2JM1v7jo7duK99JQB8nyLryFJt/O/+2r2+qH0dAAIUWdu82YvffbU4s8i7SsAWFFmLvMWZT37y5r/99lb57dfevTq/xhLYSqVSLBbDvzIAFFmLHs5NvNJvtqSP/XTNFqvX65lMxhhTrVbDvzgg4SgyGa7rptNpY4zjONrXAiQORSagVqul02nXdY0xxphyuax9RUCyUGQC8vl8JpOp1+vGmOCfta8ISBaKrFvVatUYUyqVfN83xjRGZ9rXBSQIRdYt13Ub82LGmBUfARACikxSUGQAQkbwJFFkgAqCJ4kiA1QQPEkUGaCC4EmiyAAVBE8SRQaoIHiSKDJABcGTRJEBKgieJIoMUEHwJFFkgAqCtz7vTqX02Z+eOAh2YebSG8d27zDGmNRzR0Z+teKcWIoMUEHw1uLNXf949NT+frN9ePLxyfxL/3d5+MCBkyPn3h176zsD6S3GbN0z8mnzY8YpMkAFwVvtwcyVD8cvvz+0e8sTRfbwd+e+Pjh++9G/e7cvnOxPma1nJu4+HpRRZIAKgreem+7A9uYi826+99Lo9IPHX1CbGHzWmKPuzOMxG0UGqCB461lZZKvMTw7vMk8PTy4wIgOUEbz1bFZk3u/PZbY/O/wfzJEB6gjeejYuMu9BZTTTf/L8zIPmj5pVQrlUIOlI2no2LDLv1vjJ5188f2PFJ2kuQAXBW88GRbZw6/zgN/5han7Vs8YpMkAFwVvPekW2ND/15vEzP1+xFDZAkQEqCN561iyypfmrheN/9c61B40Wu3ftw59Pf/HoXykyQAXBW8/qIvMWb51/8akvn3rrXfeR98Z+9M3DTTcuKTJABcFbzbt//RO3MHigz5jUvlNv/ezDqVnP973ZX57ZvXXVbcnnz07fbfyXFBmgguBJosgAFQRPEkUGqCB4kigyQAXBk0SRASoIniSKDFBB8CRRZIAKgieJIgNUEDxJFBmgguBJosgAFQRPEkUGqCB4kigyQAXBk0SRASoIniSKDFAhFrxyuVytVqW+W0RRZIAKseC5rpvP56W+W0RRZIAKseDV6/V0Ol2r1aS+YRRRZIAKyeAxKKPIABWSwWNQRpEBKoSDl/BBGUUGqBAOXsIHZRQZoEI+eEkelFFkgAr54NVqNWNMMgdlFBmgoifBy+fzyRyUUWSAip4EL7GDMooMUNGr4CVzUEaRASp6FbxkDsooMkBFD4OXwEEZRQao6GHwEjgoo8gAFb0NXtIGZRQZoKK3wUvaoIwiA1T0PHj5fL5QKPT6VSxBkQEqeh68arWaTqfr9XqvX8gGFBmgIozgOY7jum4IL6SOIgNUhBG8SqWSyWRCeCF1FBmgIqTgZbPZUqkUzmsposgAFSEFr1QqJWFQRpEBKsILXiaTKZfLob2cCooMUBFe8EqlkuM4ob2cCooMUBFe8IJTsCuVSmivGD6KDFARavBc183lcmG+YsgoMkBFqMGL/aNJKDJARdjBi/c2cooMUBF28OK9jZwiA1QoBC+fz8d1xxJFBqhQCF6Mt5FTZIAKneA5jlMsFlVeuqcoMkCFTvDiuo2cIgNUqAUvk8nEbxs5RQaoUAteLLeRU2SACs3gZTKZmO1YosgAFZrBKxaLMdtGTpEBKpSDF7NBGUUGqFAOXszO9qHIABX6wYvToIwiA1ToBy9OgzKKDFBhRfBiMyijyAAVVgQvNoMyigxQYUvw4jEoo8gAFbYELx6DMooMUGFR8GIwKKPIABUWBS8Guy8pMkCFXcGL+pEYFBmgwq7gRX1QRpEBKqwLXqQHZRQZoMK64EV6UEaRASpsDF50B2UUGaDCxuBFd1BGkQEqLA1eRAdlFBmgwtLgRXRQRpEBKuwNXhQHZRQZoMLe4EVxUEaRASqsDl7kBmUUGaDC6uBFblBGkQEqbA9etAZlFBmgwvbgRWtQRpEBKiIQvAgNyigyQEUEghehQRlFBqiIRvCiMiijyAAV0QheVAZlFBmgIjLBi8SgjCIDVEQmeJEYlFFkgIooBc/+QRlFBqiIUvDsf/YlRQaoiFjwLH/2JUUGqIhY8CwflFFkgIroBc/mQRlFBqiIXvBsHpRRZICKSAbP2kEZRQaoiGTwrF1TRpEBKqIaPDvXlFFkgIqoBq9cLmcymXq9rn0hT6DIABURDp7jOK7ral/FEygyQEWEg1epVNLptFWDMooMUBHt4OXz+UKhoH0Vj1FkgIpoB69WqxljarWa9oU8QpEBKiIfvEKhkM/nta/iEYoMUBH54NXr9XQ6bcn6WIoMUBGH4Lmua8mmJYoMUBGH4NXr9UwmUy6XtS+EIgN0xCR4lmxaosgAFfEJng2bligyIFAsFsN8ufgEz4b1sRQZ4C+HMcxXjFXw1DctUWSAr/H2KFbBU18fS5EBrutms9mQXzRuwSsUCopLMSgyJJzWus64BU93fSxFhoTL5/MqO21iGLxisai1FIMiQ5JVq9V0Oq0ytxPP4GUymZDv/gYoMiSZ4t22eAZPaykGRYbE0l2UHtvg5XK58I8qo8iQTOrbBGMbPJWlGBQZkkn94IY4By/8Hy5FhgRSX7/px7vIwl+KQZEhgVSmcVaIefBCnoCkyJA0Nuxx9mNfZL7vZ7PZ0JZiUGRIGq2lTivEP3hh/sagyJAoxWIx/G2Va0pE8HK5nPi2CW/+xuTFfzl3tjAx86DxQYoMyVGr1Sx6XIb2BYQh+IlXq1WR7+bNf/7+0NfSzx4bOT81u+g1f4oiQ3LYMMffkJTgCS3F8BZnfv7t3dt2HPnHq/NLqz9NkSEhyuWyDXP8DQkKXveHvXmzvzyze2tqzw9+PbdGi/kUGZIhWMevfrJ8swQFr+vfIXcmh/cZ89zpi7e9db6CIkMSqK/jXy1Zwetqd35t/ESfMakDp773twO7dphU+uDLhSszC81fQpEh9qrVqvo6/tWSFbwu9lJ4C1dy24zpOzh8YXp20Zu/MXH2yI7UireZFBliT/3JGGtKXPA6PQt7ccY9asy2Q2P/vfy+8sEt93ifefrE+B8bX2RWkblowA7BVhl75vgbEpe0TjdgLs2e/5uU2T7g3mx8yLt+LmPM9uHJxeWP0FyIMd1z5DeWxOB1tgFzafrsTtO38+xnj99JzrgDJvXMyFTjIxQZYiyfz+dyOe2rWFtCg9fJ+/wvyiPP9aUOj91Yfm/5sDK61+wcnPjfxpdQZIirYKufbXP8DQkNXkd/Kou3x0/3m725KzXP933/XmX0a/0vjF178HgxBkWGuArz8IUOJDd4HY2TF2YuvXFsz56DzneGXnxhYPBn00+u76fIEEsqz9xtS3KDF8xcyp4yTpEhfmS3KvdIooNXLpdl7yVTZIgfx3Hs2Ry+nqQHT/YPiSJDzFi7cGyFpAdP9kwligxxYvPCsRUInuQplxQZ4iSXy1m7cGwFguf7vp/NZkW2j1FkiA1LnirSIoLn+8sb+ru/L0ORIR4sPHFsYwTvEZEjligyxEOnZyuoIXiPdf9gK4oMMVCtVm3ejbQmgvdY97vJKDLEgNSUcZgI3hMKhUI3t2koMkSd/buR1kTwntDlviWKDJEWHKFs+W6kNRG8lbp5RglFhkiLxG6kNRG8NXS8DpAiQ3RF9E1lgOCtIXiD2cEiGooMERXc6Yrim8oAwVtbZ3cwKTJEUbD81eZzEzdF8NZVKBTaHWlTZIiiCO2pXA/B20i7C2ooMkROqVSK0J7K9RC8jQRLnFs/xoQiQ7TIHmOliOBtolgstn6wHEWGaMlmsxFdb7ECwdtc6zMIFBkiJNLrLVYgeJtrfTUGRYaosPw5le0ieC1p8U+dIkMkdLxS0loEr1WtrMagyBAJMVhvsQLBa8OmqzEoMtivrftXUUHw2rDpagyKDJaTOtXdNgSvPRuvHqTIYLMYbEVaD8FrWz6fX+84c4oMNovf1FgDwWtbvV5fb7KMIoO1Yjk11kDwOrHeZBlFBjtF/ZSeTRG8DgWTZStWllFksFD8Vo2tRvA6t3plGUUGCzmOk8/nta+itwheV1bsuaXIYJtgQ2Vcp8YaCF5XglNQGk9doshgldhPjTUQvG4FT10KJssoMtgjCVNjDQRPQGOyjCKDPbLZbOynxhoInozgLw1FBkvk8/nYnDXWCoInIxjGU2SwQTyO4W8LwRNTqVRiuR0X0RLXbeEbo8gkGWOScKsb1krUBH8zikySMSbG+3Jhv0RN8DejyCQZY4It5fF4Mg2iJWkT/M0oMknBZH+wpTyBw3soSuAEfzOKTFLjrmWwSjZpE67QkswJ/mYUmaTm5RfxPv4J9kjsBH8zikzSinVkG5wlC4gI5mSTOcHfjCKTtKLImPhHr3GXPECRSVq9sj84HiPhw370SHCbkukLnyKTteYWpeQcpYIwFYvFJN+mXIEik7TeXksm/iErWGzBb8cGikzSBpvGk7xYEbKChYqN4zzhU2SyNigy7i5BBLOua6LIJG18jA9dhi7xV2g9FJmkTc8j4y8iuuE4Dost1kSRSWrlYEW6DJ1hscUGKDJJLZ4QG+wpocvQOlpsYxSZpNaPug5uPLHoH63I5/Ms39kYRSaprTP7Oe0HrWDJWCsoMkntPnyELsPGaLEWUWSSOniKEl2G9dBiraPIJHX2OLjg8UuVSkX8ehBd5XKZvxWto8gkdfxcS373ohnj9HZRZJK6eUAvXYYALdYBikxSl08ap8sQHPpEi7WLIpPUZZH5dFmylUolYwwt1gGKTFL3Reb7fqFQoMsSKPgdRot1hiKTJFJkPiu5k4eReJcoMklSReazty5JaLHuUWSSBIvMX+4y/n7HGy0mgiKTJFtkvu/n83n+lscYf75SKDJJ4kXmLz8sh7/r8cOIWxBFJqkXRebz7iN2gsM1mQMVRJFJ6lGR+dybj5FqtZrJZDhWUxZFJql3RebTZbEQLNx3XVf7QuKGIpPU0yLzl3fh8cs8oli43zsUmaReF5nP9EpksWGjpygySSEUWYDb9hFSr9dzuRw3KHuKIpMUWpH5vE+JiFqtls1mHcdhBN1TFJmkMIvMZ8rMesHUPs/KCgFFJinkIvObpsxqtVrIL42NBSuZGTKHgyKTFH6RBYKJZM53t0S9Xg/OL2FSLDQUmSStIvOXV5mxQEkdt5VVUGSSFIvM9/1qtZrNZnO5HBHSEkyKMWsZPopMkm6R+ct3+nlTE756vR68wS+Xy9rXkkQUmST1IgsUi0VjDG8zQ1OpVDKZjOM43HLRYkXwYsOSIvOX32ayfCkEruum0+lisah9IYlmS/DiwZ4i85fvnXE3s3eC3xYs2beBRcGLAauKLFAul9PpNHcAxPH+3SrWBS/SLCwyf/kOAIszpTAQs5CNwYsuO4sswIR09+r1uuu6DMQsZG/wosjmIvOblgi4rss7zXbxm8BmVgcvciwvskC1WnUch20ArWv8AuDWpLUiELwIiUSRBSqViuM4mUyGibONBXu/crkcAzGbRSZ4kRChIguUy+VMJkOdralUKgXvJVm/Yr+IBc9ykSuyAIldgR9I5EQyeNaKaJEFSK/PDyGyIhw8C0W6yALBhpukJblWqwXT+Un7H4+NyAfPKjEoMn95tVRCUl0qlYJ7uPl8ngWu0RWH4NkjHkUWiHedNYZg2Wy2VCqxqi7q4hM8G8SpyBqCaaMg8NrX0q16vc4QLJZiGDxFsSyyQFBnwYqqKA5hqtVqcBYIQ7BYim3wVMS4yAK1Wq1YLOZyOWNMNpt1XdfyQU21Wi0Wi0EFFwoFFrXGVcyDF7LYF1lDvV4vl8vBs4KCt2n2DHOC8goO/AiGkBw/HXtJCV44klNkzYLicBynMUwL/+bA6vIqFouWjxYhKInB651kFllDMEwrFArZbNYY4zhOoVAol8s9GqlRXmhIdPDEJbzImgWl5rpuY6TmOE4+n3ddt1gsViqV1kdtwReXSiXXdQuFguM4wW3HTCYTvKVl5gsETxJFtp6gjIrFouu6uVzOcZxg1NYQLFhrlFTzp4ISzOVyruu6rlsulyuVCuWFZgRPEkXWsVqtVlnG20O0i+BJosgAFQRPEkUGqCB4kigyQAXBk0SRASoIniSKDFBB8CRRZIAKgieJIgNUEDxJFBmgguBJosgAFQRPEkUGqCB4kigyQIVY8Miwzw8BWBZyFigySfwQgABFFmH8EIBAx1moVqvpdNp13fZerrMXW+MbkWF+CMCybrIQPFA1k8m0/rAFikwSPwQg0GUWarVa8LAux3FaOURTJngGAHpm0y5jBCHJMCIDhNRqteCBD4VCYdMvJnjtWpqvnM8dPjDw8qtDJ7568PS70/NLjc9RZICIYrEYPBa+xYfUELz2eLcvnOx/6sjYfy36vu/VruT27Tjy08p9L/gsRQZ0qV6vBwOxtm5cEry23Jkc3mf6vjVeezQKW5o+u9P0v+DeCJqMIgO6FEzzt/sAGoLXjrsTg1uNyZy77j3xkdThsaDJKDJAhXTwvDuV0md/8jb/wihamj6705gtpy7ONT708PPRvVsaYzSKDIm3MDv59un9/cYYY/oP5D6aWQyjDuSC581d/3j01P5+s314clHsu9pkqTb+rT6z4v/vpjuw3ZiDo5X7PkWGpPPuX/3x4cOvvnfp3yd//ct/Or0vZbZ95dzvHnb7XW9NvPm9lweeS6W+MjI1581/NvbinlTqUBC6gFTwHsxc+XD88vtDu7fEt8gWZ9yjZu0i2zU8Oe9TZEg47w//+uroVOM+fjAVM+DOiHzvGfdIqm/nGxc+/vvhd8q/mSh+2jzWkw3eTXdge3yL7OHcxZe2rF1kmbPT93yKDGi2cGVom8SILPDw89G9W1LbDwxNzK5+s0qRteFhZXSvMVsHJ+42PuT9/lxmK3NkwCoLt86/lHnxvcbipK7NTQ7vMdtyVxbW+IYUWTvuXR56KmUOjd1s/CQXrgxte3wfkyIDfN9bnJ06P3IsnUrtOPSDSzMLMt918bp77EuN+egVKLK2/PnK0C6z5aWLc48Gyw8ro3tZRwY082anPnTHRr93Yn+/MSa15/Wpe90PyuZ/O3rmtffeGEjtOOLe8Pwv7vz5iW9KkbXHm/ng+I7mlf17UwfevMrKfmC1xZvjp3cZ8+zgxObHV6zDW5z5tPjxp5/94oevvH998eHno3u39B175ze/+NFrxZvNNdNq8I6m1tuXvm9kqjFlFP8i8/2l+co/Dx1+/sjLrw6deH730TcvN42cKTKg2cPK6F6zfcC92ek3WLh27usp88yR0f+c93zfv3dt7PiOx//6GCMySRQZ8IQZd8DsGZ6c2/wru0ORSaLIgCZLtXFna2a08qDni/spMkkUGRLt4e/OfWWb2fHVnFuefTB345PRF48MX5S6a7khqeB5969/4hYGD/QZk9p36q2ffTi1xqK12KPIkGwLM1feHjrxjYGBY6dyZ8cmrs2H1QIETxJFBqggeJIoMkAFwZNEkQEqCJ4kigxQQfAkUWSACoIniSIDVBA8SRQZoILgSaLIABUETxJFBqggeJIoMkAFwZNEkQEqCJ4kigxQQfAkUWSACoIniSIDVBA8SRQZoILgSaLIABUETxJFBqggeJIoMkAFwZNEkQEqCJ4kigxQQfAkUWSACoIniSIDVBA8SRQZoILgSaLIABUETxJFBqggeJIoMkAFwZNEkQEqCJ4kigxQQfAkUWSACoIniSIDVBA8SRQZoILgSaLIABUETxJFBqggeJIoMkAFwZNEkQEqCJ4kigxQQfAkUWSACoIniSIDVBA8SRQZoILgSaLIABUETxJFBqggeJIoMkAFwZNEkQEqCJ4kigxQQfAkUWSACoIniSIDVBA8SRQZoILgSaLIABUETxJFBqggeJIoMkAFwZNEkQEqCJ4kigxQQfAkUWSACoIniSIDVBA8SRQZoILgSaLIABUETxJFBqggeJIoMkAFwZNEkQEqCJ4kigxQQfAkUWSACoIniSIDVBA8SRQZoILgSaLIABUETxJFBqggeJIoMkAFwZNEkQEqCJ4kigxQQfAkUWSACoIniSIDVBA8SRQZoILgSaLIABUETxJFBqggeJIoMkAFwZNEkQEqCJ4kigxQQfAkUWSACoIniSIDVBA8SRQZoILgSaLIABUETxJFBqggeJIoMkAFwZNEkQEqCJ4kigxQQfAkUWSACoIniSIDVBA8SRQZoILgSaLIABUETxJFBqggeJIoMkAFwZNEkQEqCJ4kigxQQfAkUWSACoIniSIDVBA8SRQZoILgSaLIABUETxJFBqggeJIoMkAFwZNEkQEqCJ4kigxQQfAkUWSACoIniSIDVBA8SRQZoILgSaLIABUEr1Pe/M3Jjz849+aPJ255yx+jyAAVBK993p3K+7lD6d1HR85PzS40f4YiA1QQvDYtVj/69pdTO/5y9Oodb9UnKTJABcFrh/c/l858OZXKDP+6trrFfIoMUELwWufdm3ztWZPqP/3R2jVGkQFKCF7r/jh+4mljtu0/NTQ4sHu72fKlgy+PXrm12PQVFBmgguC1bOHK0DZj+g4PX7j6p8Wl+RuXzh55xjz5NpMiA1QQvJbNuAPGmENjN5d7y7vlvtBn+k6M15a/xKyidK1AspC0JrPnj6ZWd1Fg38iFt4+mjBlwZxpf7/3+XGar2T48ufz2kuYCVBC8li19dnZnn9l5dnqp8aGb7sB288zI1NIG/xmAnqPIWjc/NbLfpL4xduOLRx94+Pno3q39g5fmVC8LAEXWBu/2hZP9W57NXZ7zfN/3HlRGM/3Hx67d074uIOkosrZ4izO/ev3Y/l0Hvzk0dHJg4JV3ptdY3w8gZBQZgMijyABEHkUGIPL+H32Ruv1CEu7TAAAAAElFTkSuQmCC" alt><span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></span></span></p>
<p> </p>
<p><span><span><strong>Notes:</strong> Award</span><span> <strong><em>(A1)</em>(ft)</strong> for a curve with correct concavity consistent with their \(k\) passing through (0, 4).</span></span></p>
<p><span><strong><em>(A1)</em>(ft)</strong> for minimum in approximately the correct place. Follow through from their part (a).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was not answered well at all except by the more able. Indeed, of the lower quartile of candidates, the maximum mark achieved was only 1. Of those that did make a successful attempt at the question, very few used the fact that \(1.25 = - \frac{k}{{2(2)}}\) preferring instead to differentiate and equate to zero. But such candidates were in the minority as substituting \(x = 1.25\) into the given quadratic and equating to zero produced the popular, but erroneous, answer of \(- 5.7\). Recovery was possible for the next two marks if this incorrect value had been seen to be substituted into the correct quadratic, along with \(x = 1.25\) to arrive at an answer of \(0\). This would have given (M1)(A1)(ft). However, candidates who had an answer of \(k = - 5.7\) in part (a)(i), invariably showed no working in part (ii) and consequently earned no marks here. Irrespective of incorrect working in part (a), the quadratic function clearly passes through (0, 4) and has a minimum at \(x = 1.25\). Using this information, a minority of candidates picked up at least one of the two marks in part (b).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was not answered well at all except by the more able. Indeed, of the lower quartile of candidates, the maximum mark achieved was only 1. Of those that did make a successful attempt at the question, very few used the fact that \(1.25 = - \frac{k}{{2(2)}}\) preferring instead to differentiate and equate to zero. But such candidates were in the minority as substituting \(x = 1.25\) into the given quadratic and equating to zero produced the popular, but erroneous, answer of \(- 5.7\). Recovery was possible for the next two marks if this incorrect value had been seen to be substituted into the correct quadratic, along with \(x = 1.25\) to arrive at an answer of \(0\). This would have given (M1)(A1)(ft). However, candidates who had an answer of \(k = - 5.7\) in part (a)(i), invariably showed no working in part (ii) and consequently earned no marks here. Irrespective of incorrect working in part (a), the quadratic function clearly passes through (0, 4) and has a minimum at \(x = 1.25\). Using this information, a minority of candidates picked up at least one of the two marks in part (b).</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Tomás is playing with sticks and he forms the first three diagrams of a pattern. These diagrams are shown below.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_17.25.44.png" alt="M17/5/MATSD/SP1/ENG/TZ2/05"></p>
<p>Tomás continues forming diagrams following this pattern.</p>
</div>
<div class="specification">
<p>Tomás forms a total of 24 diagrams.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Diagram \(n\) is formed with 52 sticks. Find the value of \(n\).</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 total number of sticks used by Tomás for all 24 diagrams.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(4 + 3(n - 1) = 52\) <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for substitution into the formula of the \(n\)th term of an arithmetic sequence, <strong><em>(A1) </em></strong>for correct substitution.</p>
<p> </p>
<p>\(n = 17\) <strong><em>(A1)</em></strong> <strong><em>(C3)</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{24}}{2}(2 \times 4 + 23 \times 3)\)\(\,\,\,\)<strong>OR</strong>\(\,\,\,\)\(\frac{{24}}{2}(4 + 73)\) <strong><em>(M1)(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Notes:</strong> Award <strong><em>(M1) </em></strong>for substitution into the sum of the first \(n\) terms of an arithmetic sequence formula, <strong><em>(A1)</em>(ft) </strong>for their correct substitution, consistent with part (a).</p>
<p> </p>
<p>924 <strong><em>(A1)</em>(ft)</strong> <strong><em>(C3)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from part (a).</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The company Snakezen’s Ladders makes ladders of different lengths. All the ladders that the company makes have the same design such that:</p>
<p style="padding-left: 90px;">the first rung is 30 cm from the base of the ladder,</p>
<p style="padding-left: 90px;">the second rung is 57 cm from the base of the ladder,</p>
<p style="padding-left: 90px;">the distance between the first and second rung is equal to the distance between all adjacent rungs on the ladder.</p>
<p>The ladder in the diagram was made by this company and has eleven equally spaced rungs.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_10.59.54.png" alt="M17/5/MATSD/SP1/ENG/TZ1/05"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the distance from the base of this ladder to the top rung.</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>The company also makes a ladder that is 1050 cm long.</p>
<p>Find the maximum number of rungs in this 1050 cm long ladder.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(30 + (11 - 1) \times 27\) <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for substituted arithmetic sequence formula, <strong><em>(A1) </em></strong>for correct substitutions.</p>
<p> </p>
<p>\( = 300{\text{ (cm)}}\) <strong><em>(A1)</em></strong> <strong><em>(C3)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Units are not required.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(1050 \geqslant 30 + (n - 1) \times 27\) <strong><em>(M1)(A1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for substituted arithmetic sequence formula \( \leqslant 1050\), accept an equation, <strong><em>(A1) </em></strong>for correct substitutions.</p>
<p> </p>
<p>\(n = 38\) <strong><em>(A1)</em>(ft)</strong><em> </em><strong><em>(C3)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Follow through from their 27 in part (a). The answer must be an integer and rounded down.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Inge borrows € 4500 for 2 years.</span></p>
</div>
<div class="question">
<p><span>Bank 1 charges compound interest at a rate of 15 % per annum, compounded quarterly.</span></p>
<p><span>Calculate the <strong>total</strong> amount to be repaid at the end of the 2 years.<strong> Give your answer correct to two decimal places</strong>.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span><strong><em>Note: Financial penalty (FP) applies in this part</em></strong></span></p>
<p> </p>
<p><span>\(A = 4500{\left( {1 + \frac{{15}}{{400}}} \right)^{4 \times 2}}\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution into CI formula, <em><strong>(A1)</strong></em> for correct substitution.</span></p>
<p><span> </span></p>
<p><span><em><strong>(FP)</strong></em> <em>A</em> = € 6041.12 <em>(€ not required)</em> <em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-size: medium; font-family: times new roman,times;">This is a question that has been tested before but few candidates managed to gain full marks.</span> <span style="font-size: medium; font-family: times new roman,times;">Compounding the interest quarterly and using the correct compound interest formula </span><span style="font-size: medium; font-family: times new roman,times;">appeared to challenge many candidates.</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">Mandzur, a farmer, takes out a loan to buy a buffalo. He borrows 900 000 Cambodian riels (KHR) for 2 years. The nominal annual interest rate is 15%, compounded <strong>monthly</strong>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the amount of the <strong>interest </strong>that Mandzur must pay. Give your answer correct to the nearest 100 KHR.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down your answer to part (a) in the form \(a \times {10^k},{\text{ where }}1 \leqslant a < 10,{\text{ }}k \in \mathbb{Z}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(FV = 900000{\left( {1 + \frac{{15}}{{12 \times 100}}} \right)^{24}}\) <span class="Apple-converted-space"> </span><strong><em>(M1)(A1)</em></strong></p>
<p class="p2"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for substitution in the compound interest formula (either \(FV\)<em> </em>or interest), do not penalize if \(–PV\) not seen.</p>
<p class="p1">Award <strong><em>(A1) </em></strong>for correct substitution.</p>
<p class="p1"> </p>
<p class="p2"><strong>OR</strong></p>
<p class="p2">\({\text{N}} = 2\)</p>
<p class="p1">\({\text{I% = 15}}\)</p>
<p class="p1">\({\text{PV = 900}}\,{\text{000}}\)</p>
<p class="p1">\({\text{P/Y}} = 1\)</p>
<p class="p1">\({\text{C/Y}} = 12\) <span class="Apple-converted-space"> </span><strong><em>(A1)(M1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for \({\text{C/Y}} = 12\) seen, <strong><em>(M1) </em></strong>for other correct entries.</p>
<p class="p1"> </p>
<p class="p2"><strong>OR</strong></p>
<p class="p2">\({\text{N}} = 24\)</p>
<p class="p1">\({\text{I% = 15}}\)</p>
<p class="p1">\({\text{PV = 900}}\,{\text{000}}\)</p>
<p class="p1">\({\text{P/Y}} = 12\)</p>
<p class="p1">\({\text{C/Y}} = 12\) <strong><em>(A1)(M1)</em></strong></p>
<p class="p1"><strong>Note:<span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1) </em></strong>for \({\text{C/Y}} = 12\) seen, <strong><em>(M1) </em></strong>for other correct entries.</p>
<p class="p1"> </p>
<p class="p1">\({\text{interest = 321615.945}}\) <strong><em>(A1)</em></strong></p>
<p class="p1">\( = 312\,600\;\;\;{\text{(KHR)}}\) <strong><em>(A1)</em>(ft) <em>(C4)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: </strong>Award the final <strong><em>(A1) </em></strong>for the correct rounding of their unrounded answer.</p>
<p class="p1">If final amount is \(1 212 600\) and working is shown award <strong><em>(M1)(A1)(A0)(A1)</em>(ft)</strong><em>.</em></p>
<p class="p1">Award <strong><em>(A2) </em></strong>for \((FV = )\ 1212600\) if no working is seen<span class="s1">.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(3.126 \times {10^5}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C2)</em></strong></p>
<p class="p2"><strong>Notes: </strong>Award <strong><em>(A1)</em>(ft) </strong>for their \(3.126\) \((3.13)\), <strong><em>(A1)</em>(ft) </strong>for \( \times {10^5}\).</p>
<p class="p1">Follow through from part (a).</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p><span>Consider the numbers \(\sqrt 3 \), \(6\), \(2\frac{1}{2}\), \(\pi \), \( - 5\), and the sets \(\mathbb{N}\), \(\mathbb{Z}\), and \(\mathbb{Q}\). Complete the following table by placing a tick in the appropriate box if the number is an element of the set.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span><strong>Note:</strong> Accept any symbol for ticks. Do not penalize if candidate had also indicated, by a different symbol, that the number is not an element of the set.</span></p>
<p><span>Row \(\mathbb{N}\) correct, no extra entries. <em><strong>(A1) (C1)</strong></em></span></p>
<p><span>Row \(\mathbb{Z}\) <em><strong>(A1)(A1) (C2)</strong></em></span></p>
<p><span><strong>Note: </strong>Award <em><strong>(A1)</strong></em> for each correct tick and no extra entries. Award <em><strong>(A1)</strong></em> only for both ticks correct and 1 extra entry, <em><strong>(A0)</strong></em> otherwise.</span></p>
<p><span>Row \(\mathbb{Q}\) <em><strong>(A1)(A1)(A1) (C3)</strong></em></span></p>
<p><span><strong>Note: </strong>Award <em><strong>(A1)</strong></em> for each correct tick and no extra entries. Award <em><strong>(A2)</strong></em> only for all 3 correct and one extra entry. Award <em><strong>(A1)</strong></em> only for 2 correct and one extra entry. <em><strong>(A0)</strong></em> otherwise.</span></p>
<p><span><em><strong>[6 marks]</strong></em><br></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was poorly answered with many thinking </span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\(\mathbb{Q}\)</span> was the set of irrational numbers. Very few candidates were awarded full marks for this question.</span></p>
</div>
<br><hr><br><div class="specification">
<p style="text-align: left;"><span style="font-size: medium; font-family: times new roman,times;">A quadratic function, \(f(x) = a{x^2} + bx\), is represented by the mapping diagram below.</span></p>
<p style="text-align: center;"><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use the mapping diagram to write down <strong>two</strong> equations in terms of <em>a</em> and<em> b</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of</span><span> <em>a</em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of <em>b</em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the <em>x</em>-coordinate of the vertex of the graph of <em>f </em>(<em>x</em>).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>4<em>a</em> + 2<em>b</em> = 20</span></p>
<p><span><em>a </em>+ <em>b</em> = 8 <em><strong> </strong></em><em><strong>(A1)</strong></em></span></p>
<p><span><em>a</em> – b = –4 <em><strong> (A1) (C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award<em><strong> (A1)(A1)</strong> </em>for any two of the given or equivalent equations.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>a</em> = 2 <em><strong> (A1)</strong></em><strong>(ft)</strong></span></p>
<p><em><strong><span>[1 mark]</span></strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>b</em> = 6 <strong><em> (A1)</em>(ft)<em> (C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note:</strong> Follow through from their (a).</span></p>
<p> </p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(x = - \frac{6}{{2(2)}}\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in correct formula.</span></p>
<p> </p>
<p><span>\( = -1.5\) <em><strong>(A1)</strong></em><strong>(ft) </strong><em><strong> (C2)</strong></em></span></p>
<p> <em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates attempted this question but very few of them completed it entirely. A number of students wrote incorrect equations in part (a), which shows that the mapping diagram was poorly understood and read. Part (c) proved to be difficult for many who didn’t know how to find the <em>x</em>-coordinate of the vertex of the graph of the function. Some students gave the two coordinates instead of the <em>x</em>-coordinate only.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates attempted this question but very few of them completed it entirely. A number</span> <span style="font-family: times new roman,times; font-size: medium;">of students wrote incorrect equations in part (a), which shows that the mapping diagram was </span><span style="font-family: times new roman,times; font-size: medium;">poorly understood and read. Part (c) proved to be difficult for many who didn’t know how to </span><span style="font-family: times new roman,times; font-size: medium;">find the <em>x</em>-coordinate of the vertex of the graph of the function. Some students gave the two </span><span style="font-family: times new roman,times; font-size: medium;">coordinates instead of the <em>x</em>-coordinate only.</span></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates attempted this question but very few of them completed it entirely. A numberof students wrote incorrect equations in part (a), which shows that the mapping diagram was poorly understood and read. Part (c) proved to be difficult for many who didn’t know how to find the <em>x</em>-coordinate of the vertex of the graph of the function. Some students gave the two coordinates instead of the <em>x</em>-coordinate only.</span></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates attempted this question but very few of them completed it entirely. A number</span> <span style="font-family: times new roman,times; font-size: medium;">of students wrote incorrect equations in part (a), which shows that the mapping diagram was </span><span style="font-family: times new roman,times; font-size: medium;">poorly understood and read. Part (c) proved to be difficult for many who didn’t know how to </span><span style="font-family: times new roman,times; font-size: medium;">find the <em>x</em>-coordinate of the vertex of the graph of the function. Some students gave the two </span><span style="font-family: times new roman,times; font-size: medium;">coordinates instead of the <em>x</em>-coordinate only.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The number of cells, <em>C</em>, in a culture is given by the equation \(C = p \times 2^{0.5t} + q\), where <em>t</em> is the time in hours measured from 12:00 on Monday and <em>p</em> and <em>q</em> are constants.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The number of cells in the culture at 12:00 on Monday is 47.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The number of cells in the culture at 16:00 on Monday is 53.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use the above information to </span><span>write down two equations in <em>p</em> and <em>q</em> ;</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use the above information to </span><span>calculate the value of <em>p</em> and of <em>q</em> ;</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use the above information to </span><span>find the number of cells in the culture at 22:00 on Monday.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><em>p</em> + <em>q</em> = 47 <em><strong>(A1)</strong></em></span></p>
<p><span>4<em>p</em> + <em>q</em> = 53 <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Reasonable attempt to solve their equations <em><strong>(M1)</strong></em></span></p>
<p><span><em>p</em> = 2, <em>q</em> = 45 <em><strong>(A1) </strong> <strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Accept only the answers </span><span><span><em>p</em> = 2, <em>q</em> = 45</span>.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>C</em> = 2 × 2<sup>0.5(10)</sup> + 45 <em><strong>(M1)</strong></em></span></p>
<p><span><em>C</em> = 109 <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution of 10 into the formula with their values of <em>p</em> and <em>q</em>.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Concern was expressed about the wording of the question; answers were given great leeway by examiners and suggestions for wording are welcome. The 24 hour clock method of describing time is the norm in IB examinations. It should be recognised that the purpose of this question was to discriminate at the grade 6/7 level.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The concept of the zero index was not understood by many.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Concern was expressed about the wording of the question; answers were given great leeway by examiners and suggestions for wording are welcome. The 24 hour clock method of describing time is the norm in IB examinations. It should be recognised that the purpose of this question was to discriminate at the grade 6/7 level.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The use of the GDC was (as always) expected in solving the simultaneous equations.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Concern was expressed about the wording of the question; answers were given great leeway by examiners and suggestions for wording are welcome. The 24 hour clock method of describing time is the norm in IB examinations. It should be recognised that the purpose of this question was to discriminate at the grade 6/7 level.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Working was required for follow through in this part.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The speed of light is \({\text{300}}\,{\text{000}}\) kilometres per second. The average distance from the Sun to the Earth is 149.6 million km.</p>
</div>
<div class="specification">
<p>A light-year is the distance light travels in one year and is equal to \({\text{9}}\,{\text{467}}\,{\text{280}}\) million km. Polaris is a bright star, visible from the Northern Hemisphere. The distance from the Earth to Polaris is 323 light-years.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the time, <strong>in minutes</strong>, it takes for light from the Sun to reach the Earth.</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 distance from the Earth to Polaris in millions of km. Give your answer in the form \(a \times {10^k}\) with \(1 \leqslant a < 10\) and \(k \in \mathbb{Z}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{149600000}}{{300000 \times 60}}\) <strong><em>(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for dividing the <strong>correct </strong>numerator (which can be presented in a different form such as \(149.6 \times {10^6}\) or \(1.496 \times {10^8}\)) by \({\text{300}}\,{\text{000}}\) and <strong><em>(M1) </em></strong>for dividing by 60.</p>
<p> </p>
<p>\( = 8.31{\text{ }}({\text{minutes}}){\text{ }}(8.31111 \ldots {\text{, 8 minutes 19 seconds}})\) <strong><em>(A1) (C3)</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(323 \times 9467\,280\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for multiplying 323 by \(9\,467\,280\), seen with <strong>any </strong>power of 10; therefore only penalizing incorrect power of 10 once.</p>
<p> </p>
<p>\( = 3.06 \times {10^9}{\text{ ( = }}3.05793 \ldots \times {10^9})\) <strong><em>(A1)(A1) (C3)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for 3.06.</p>
<p>Award <strong><em>(A1) </em></strong>for \( \times {10^9}\)</p>
<p>Award <strong><em>(A0)(A0) </em></strong>for answers of the type: \(30.6 \times {10^8}\)</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>In this question give all answers correct to the nearest whole number.</em></strong></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Fumie is going for a holiday to Great Britain. She changes \({\text{100}}\,{\text{000}}\) Japanese Yen (JPY) into British Pounds (GBP) with no commission charged.</span></p>
<p><span>The exchange rate between GBP and JPY is</span></p>
<p><span>1 GBP = 129 JPY.</span></p>
<p><span>Calculate the value of \({\text{100}}\,{\text{000}}\) JPY in GBP.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>At the end of Fumie’s holiday in Great Britain she has 239 GBP. She converts this back to JPY at a bank, which does not charge commission, and receives </span><span><span><span>30 200 JPY</span></span></span></p>
<p><span>(i) Find the exchange rate of this second transaction.</span></p>
<p><span>(ii) Determine, when changing GBP back to JPY, whether the exchange rate found in part (b)(i) is better value for Fumie than the exchange rate in part (a). Justify your answer.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{100\,000}}{{129}}\) <strong><em>(M1)</em></strong></span></p>
<p><span>\( = 775{\text{ (GBP)}}\) <strong><em>(A1) (C2)</em></strong></span></p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(\frac{{30\,200}}{{239}}\) <strong><em>(M1)</em></strong></span></p>
<p><span>\(1 {\text{ GBP}} = 126 {\text{ JPY}}\) <strong><em>(A1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Accept \(126\) (\({\text{JPY}}\)).</span></p>
<p><span> Award <strong><em>(M1) </em></strong>for \(\frac{{239}}{{30\,300}}\).</span></p>
<p><span> Award <strong><em>(A0) </em></strong>for \(1{\text{ JPY}} = 0 {\text{ GBP}}\)</span></p>
<p> </p>
<p><span>(ii) No, the part (b)(i) rate is not better value than the part (a) rate. <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span>\(30\,200 < 30\,831\) <strong><em>(R1)</em></strong></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>No, the part (b)(i) rate is not better value than the part (a) rate. <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span>\(129 > 126\) <strong><em>(R1) (C4)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Accept “part (a) rate is better” for the <strong><em>(A1)</em>(ft)</strong>.</span></p>
<p><span> Follow through from part (b)(i).</span></p>
<p><span> A numerical comparison must be seen to award <strong><em>(R1)</em></strong>.</span></p>
<p><span> </span></p>
<p><span><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Arthur and Jacob dream of owning a speedboat that costs \({\text{35}}\,{\text{300}}\) euros (EUR).</p>
<p>Arthur invested \(x\) EUR in an account that pays a nominal annual interest rate of 3.6%, compounded <strong>monthly</strong>. After 18 years he will have \({\text{35}}\,{\text{300}}\) EUR in the account.</p>
</div>
<div class="specification">
<p>Jacob invested 9000 EUR for \(n\) years. The investment has a nominal annual interest rate of 3.2% and is compounded <strong>quarterly</strong>. After \(n\) years, the investment will be worth \({\text{35}}\,{\text{300}}\) EUR.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the value of Arthur’s initial investment, \(x\). Give your answer to two decimal places.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(n\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(35\,300 = PV{\left( {1 + \frac{{3.6}}{{100 \times 12}}} \right)^{12 \times 18}}\) <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept “\(x\)” instead of \(PV\). Award <strong><em>(M1) </em></strong>for substitution into compound interest formula, <strong><em>(A1) </em></strong>for correct substitution.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>\(N = 18\)</p>
<p>\(I\% = 3.6\)</p>
<p>\(FV = ( \pm )35\,300\)</p>
<p>\(P/Y = 1\)</p>
<p>\(C/Y = 12\) <strong><em>(A1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for \(C/Y = 12\) seen, <strong><em>(M1) </em></strong>for all other correct entries.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>\(N = 216\)</p>
<p>\(I\% = 3.6\)</p>
<p>\(FV = ( \pm )35\,300\)</p>
<p>\(P/Y = 12\)</p>
<p>\(C/Y = 12\) <strong><em>(A1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for \(C/Y = 12\) seen, <strong><em>(M1) </em></strong>for all other correct entries.</p>
<p> </p>
<p>\(PV = 18483.03\) <strong><em>(A1)</em></strong> <strong><em>(C3)</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(35\,300 = 9000{\left( {1 + \frac{{3.2}}{{100 \times 4}}} \right)^{4 \times n}}\) <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1) </em></strong>for substitution into compound interest formula and equating to \(35\,300\), <strong><em>(A1) </em></strong>for correct substitution.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>\(I\% = 3.2\)</p>
<p>\(PV = ( \pm )9000\)</p>
<p>\(FV = ( \mp )35\,300\)</p>
<p>\(P/Y = 1\)</p>
<p>\(C/Y = 4\) <strong><em>(A1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for \(C/Y = 4\) seen, <strong><em>(M1) </em></strong>for all other correct entries.</p>
<p> </p>
<p><strong>OR</strong></p>
<p>\(I\% = 3.2\)</p>
<p>\(PV = ( \pm )9000\)</p>
<p>\(FV = ( \mp )35\,300\)</p>
<p>\(P/Y = 4\)</p>
<p>\(C/Y = 4\) <strong><em>(A1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for \(C/Y = 4\) seen, <strong><em>(M1) </em></strong>for all other correct entries.</p>
<p> </p>
<p>\(n = 43\) <strong><em>(A1)</em></strong> <strong><em>(C3)</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The graph of the quadratic function \(f (x) = c + bx − x^2\) intersects the <em>y</em>-axis at point A(0, 5) and has its vertex at point B(2, 9).</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of <em>c</em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of <em>b</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the <em>x</em>-intercepts of the graph of <em>f</em> .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down \(f (x)\) in the form \(f (x) = −(x − p) (x + q)\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>5 <em><strong>(A1)</strong></em> <em><strong>(C1)</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{ - b}}{{2( - 1)}} = 2\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in axis of symmetry formula.</span></p>
<p><br><strong><span>OR</span></strong></p>
<p><span>\(y = 5 + bx - x^2\)</span></p>
<p><span>\(9 = 5 + b (2) - (2)^2\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of 9 and 2 into their quadratic equation.</span></p>
<p><br><span>\((b =) 4\) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from part (a).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>5, −1 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Follow through from parts (a) and (b), irrespective of working shown.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(f (x) = -(x - 5)(x + 1)\) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C1)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Follow through from part (c).</span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Many candidates did not see the connection between the <em>x</em>-intercepts and the factored form of a quadratic function. The syllabus explicitly sates that the graphs of quadratics should be linked to solutions of quadratic equations by factorizing and vice versa. This was one of the most challenging questions for candidates.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Many candidates did not see the connection between the <em>x</em>-intercepts and the factored form of a quadratic function. The syllabus explicitly sates that the graphs of quadratics should be linked to solutions of quadratic equations by factorizing and vice versa. This was one of the most challenging questions for candidates.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Many candidates did not see the connection between the <em>x</em>-intercepts and the factored form of a quadratic function. The syllabus explicitly sates that the graphs of quadratics should be linked to solutions of quadratic equations by factorizing and vice versa. This was one of the most challenging questions for candidates.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Many candidates did not see the connection between the <em>x</em>-intercepts and the factored form of a quadratic function. The syllabus explicitly sates that the graphs of quadratics should be linked to solutions of quadratic equations by factorizing and vice versa. This was one of the most challenging questions for candidates.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The function \(g(x)\) is defined as \(g(x) = 16 + k({c^{ - x}})\) where \(c > 0\) .</span><br><span style="font-size: medium; font-family: times new roman,times;">The graph of the function \(g\) is drawn below on the domain \(x \geqslant 0\) .</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The graph of \(g\) intersects the <em>y</em>-axis at (0, 80) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of \(k\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The graph passes through the point (2, 48) . </span></p>
<p><span>Find the value of \(c\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The graph passes through the point (2, 48) . </span></p>
<p><span>Write down the equation of the horizontal asymptote to the graph of \(y = g(x)\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><span>\(80 = 16 + k({c^0})\)</span><span> <em><strong>(M1)</strong></em></span></span></p>
<p><span>\(k = 64\) <em><strong>(A1) (C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(48 = 16 + 64({c^{ - 2}})\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substitution of their \(k\) and (2, 48) into the equation for \(g(x)\).</span></p>
<p> </p>
<p><span>\(c = \sqrt 2 \) (\(1.41\)) (\(1.41421 \ldots \)) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></span></p>
<p><span><strong>Notes:</strong> Award <strong><em>(M1)(A1)</em>(ft)</strong> for \(c = \pm \sqrt 2 \) . Follow through from their answer to part (a).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(y = 16\) <em><strong>(A1)(A1) (C2)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(y = \) a constant, <em><strong>(A1)</strong></em> for \(16\).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This was perhaps the most difficult question on the paper. Being the last question some candidates may have felt that they were under pressure to complete and many scripts showed no attempt at an answer to this question. The response by the upper quartile of candidates was quite encouraging with many achieving at least 4 of the 6 marks available. For the rest, many fell at the first hurdle and were unable to obtain a value of \(k\). This, in turn, led to problems in finding \(c\). For a large number of candidates the only mark that they achieved was identifying that the asymptote was a linear equation in \(y\).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This was perhaps the most difficult question on the paper. Being the last question some candidates may have felt that they were under pressure to complete and many scripts showed no attempt at an answer to this question. The response by the upper quartile of candidates was quite encouraging with many achieving at least 4 of the 6 marks available. For the rest, many fell at the first hurdle and were unable to obtain a value of \(k\). This, in turn, led to problems in finding \(c\). For a large number of candidates the only mark that they achieved was identifying that the asymptote was a linear equation in \(y\).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This was perhaps the most difficult question on the paper. Being the last question some candidates may have felt that they were under pressure to complete and many scripts showed no attempt at an answer to this question. The response by the upper quartile of candidates was quite encouraging with many achieving at least 4 of the 6 marks available. For the rest, many fell at the first hurdle and were unable to obtain a value of \(k\). This, in turn, led to problems in finding \(c\). For a large number of candidates the only mark that they achieved was identifying that the asymptote was a linear equation in \(y\).</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(p = \frac{{2\cos x - \tan x}}{{\sqrt y - z}}.\)</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the value of \(p\) when \(x = 45^\circ \), \(y = 8192\) and \(z = 64\). Write down your full calculator display.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down your answer to part (a)</span></p>
<p><span>(i) correct to two decimal places;</span></p>
<p><span>(ii) correct to four significant figures;</span></p>
<p><span>(iii) in the form \(a \times {10^k}\), where \(1 \leqslant a < 10,{\text{ }}k \in \mathbb{Z}\).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{2\cos 45^\circ - \tan 45^\circ }}{{\sqrt {8192} - 64}}\) <strong><em>(M1)</em></strong></span></p>
<p><span>\( = 0.015625\) <strong><em>(A1) (C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes:</strong> Accept \(\frac{1}{{64}}\) and also \(1.5625 \times {10^{ - 2}}\).</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) 0.02 <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span>(ii) 0.01563 <strong><em>(A1)</em>(ft)</strong></span></p>
<p> </p>
<p><span><strong>Notes:</strong> For parts (i) and (ii), accept equivalent standard form representations.</span></p>
<p> </p>
<p><span>(iii) \(1.5625 \times {10^{ - 2}}\) <strong><em>(A2)</em>(ft) <em>(C4)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes:</strong> Award <strong><em>(A1)(A0) </em></strong>for correct mantissa, between 1 and 10, with incorrect index.</span></p>
<p><span> Follow through from their answer to part (a).</span></p>
<p><span> Where the candidate has correctly rounded their mantissa from part (a) and has the correct exponent, award <strong><em>(A0)(A1)</em></strong></span></p>
<p><span> Award <strong><em>(A0)(A0) </em></strong>for answers of the type: \(15.625 \times {10^{ - 3}}\).</span></p>
<p> </p>
<p><span><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Jackson invested 12 000 Australian dollars (AUD) in a bank that offered simple interest at an annual interest rate of <em>r</em> %. The value of Jackson’s investment doubled after 20 years.</span></p>
</div>
<div class="question">
<p><span>Maddison invests 15 000 AUD in a bank that offers compound interest at a nominal annual interest rate of 4.44 %, <strong>compounded quarterly</strong>.</span></p>
<p><span>Calculate the number of years that it will take for Maddison’s investment to triple in value.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span>\(45000 = 15000{\left( {1 + \frac{{4.44}}{{400}}} \right)^{4n}}\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituted compound interest formula, <em><strong>(A1)</strong></em> for a correctly substituted formula and correctly equated to 45 000.</span></p>
<p><span><br><strong>OR</strong> </span></p>
<p><span><span>\(3= {\left( {1 + \frac{{4.44}}{{400}}} \right)^{4n}}\) </span><em><strong>(M1)(A1)</strong></em><br></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituted compound interest formula, <em><strong>(A1)</strong></em> for a correctly substituted formula and correctly equated to 3.</span></p>
<p><span> </span></p>
<p><span><em> n</em> = 25 years <em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(A1)(M0)(A0)</strong></em> if 24.9 or 24.88 seen as a final answer, with no working seen. Award, at most, <em><strong>(A1)(M1)(A0)</strong></em> if working is seen and a final answer of 24.9 or 24.88 is given.<br></span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-size: medium; font-family: times new roman,times;">In part (b), writing down any substituted form of the compound interest formula led to a significant number of candidates scoring at least 1 mark for method here. Often, however, the formula was incorrectly substituted or was not correctly equated to 45 000 and subsequent marks were then lost.</span></p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The equation of a line <em>L</em><sub>1</sub> is \(2x + 5y = −4\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the gradient of the line <em>L</em><sub>1</sub>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A second line <em>L</em><sub>2</sub> is perpendicular to <em>L</em><sub>1</sub>.</span></p>
<p><span>Write down the gradient of <em>L</em><sub>2</sub>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The point (5, 3) is on <em>L</em><sub>2</sub>.</span></p>
<p><span>Determine the equation of <em>L</em><sub>2</sub>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Lines <em>L</em><sub>1</sub> and <em>L</em><sub>2</sub> intersect at point P.</span></p>
<p><span>Using your graphic display calculator or otherwise, find the coordinates of P.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{-2}{{5}}\) <strong><em>(A1)</em></strong> <em><strong>(C1)</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{5}{{2}}\) <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from their answer to part (a).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(3 = \frac{5}{2} \times 5 + c\) <em><strong>(M1)</strong></em></span><br><br></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of their gradient into equation of line. Follow through from their answer to part (b).</span></p>
<p><br><span>\(y = \frac{5}{2}x - \frac{19}{2}\) <em><strong>(A1)(ft)</strong></em><br></span></p>
<p><strong><span>OR</span></strong></p>
<p><span>\(y - 3 = \frac{5}{2}(x - 5)\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for correct substitution of their gradient into equation of line.</span> <span>Follow through from their answer to part (b).</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(3, −2) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong> <strong><em>(C2)</em></strong></span></p>
<p><br><span><strong>Notes:</strong> If parentheses not seen award at most <em><strong>(A0)(A1)</strong></em><strong>(ft)</strong>. Accept <em>x</em> = 3, <em>y</em> = −2. Follow through from their answer to part (c), even if no working is seen. Award <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong> for a sensible attempt to solve \(2x + 5y = −4\) and their \(y = \frac{5}{2}x - \frac{19}{2}\) or equivalent, simultaneously.</span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the function \(f(x) = p{(0.5)^x} + q\) where <em>p</em> and <em>q</em> are constants. The graph of <em>f</em> (<em>x</em>) passes through the points \((0,\,6)\) and \((1,\,4)\) and is shown below.</span></p>
<p style="text-align: center;"><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down two equations relating <em>p</em> and <em>q</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of <em>p</em> and of <em>q</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the equation of the horizontal asymptote to the graph of <em>f</em> (<em>x</em>).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><em>p</em> + <em>q</em> = 6 <em><strong>(A1)</strong></em><br></span></p>
<p><span>0.5<em>p</em> + <em>q</em> = 4 <em><strong>(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><span><br><strong>Note:</strong> Accept correct equivalent forms of the equations.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>p</em> = 4, <em>q</em> = 2 <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> If both answers are incorrect, award <em><strong>(M1)</strong></em> for attempt at solving</span> <span>simultaneous equations.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>y</em> = 2 <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for “<em>y</em> = a constant”, <em><strong>(A1)</strong></em><strong>(ft)</strong> for 2. Follow through from their value for <em>q</em> as long as their constant is greater than 2 and less than 6.</span></p>
<p><span>An equation must be seen for any marks to be awarded.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">A significant number of candidates found it difficult to identify and write two equations that relate<em> p</em> and <em>q</em>. Many of those who wrote the equations were unable to solve them or use their GDC to find the values of <em>p</em> and <em>q</em> in part b). Although the question in part c) was quite standard, there were many errors in the responses. Many students wrote <em>x</em> = 2 or only 2 instead of <em>y</em> = 2.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">A significant number of candidates found it difficult to identify and write two equations that relate<em> p</em> and <em>q</em>. Many of those who wrote the equations were unable to solve them or use their GDC to find the values of <em>p</em> and <em>q</em> in part b). Although the question in part c) was quite standard, there were many errors in the responses. Many students wrote <em>x</em> = 2 or only 2 instead of <em>y</em> = 2.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">A significant number of candidates found it difficult to identify and write two equations that relate<em> p</em> and <em>q</em>. Many of those who wrote the equations were unable to solve them or use their GDC to find the values of <em>p</em> and <em>q</em> in part b). Although the question in part c) was quite standard, there were many errors in the responses. Many students wrote <em>x</em> = 2 or only 2 instead of <em>y</em> = 2.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Eva invests \({\text{USD}}2000\) at a nominal annual interest rate of \(8\% \) <strong>compounded half-yearly</strong>.</span></p>
<p><span>Calculate the value of her investment after \(5\) years, correct to the nearest dollar.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Toni invests \({\text{USD}}1500\) at an annual interest rate of \(7.8\% \) <strong>compounded yearly</strong>.</span></p>
<p><span>Find the number of <strong>complete</strong> years it will take for his investment to double in value.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>\(2000{(1.04)^{10}}\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span><strong>Note: <em>(M1)</em></strong> for substitution into CI formula. <em><strong>(A1)</strong></em> for correct substitution.</span></p>
<p><span> </span></p>
<p><span>\(2960\) <em><strong>(A1)</strong></em></span></p>
<p><span><strong>Note: </strong>Award the final <em><strong>A1</strong></em> for rounding their answer correctly to the nearest Yuan.</span></p>
<p><span> </span></p>
<p><span><strong>OR</strong></span></p>
<p><span>\(2000{\left( {1 + \frac{8}{{200}}} \right)^{10}} - 2000\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span><strong>Note: <em>(M1)</em></strong> for substitution into CI formula. <em><strong>(A1)</strong></em> for correct substitution.</span></p>
<p><span> </span></p>
<p><span>\(2960\) <em><strong>(A1) (C3)</strong></em></span></p>
<p><span><strong>Note: </strong>Award the final <em><strong>A1</strong></em> for rounding their answer correctly to the nearest Yuan.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(1500{(1.078)^n} = 3000\) <em><strong>(M1)(M1)</strong></em></span></p>
<p><br><span><strong>Note: <em>(M1)</em></strong> for correct substitution in CI formula, <em><strong>(M1)</strong></em> for \(3000\) seen.</span></p>
<p><br><span>\(n = 10{\text{ years}}\) <em>(</em>\(n = 9.23{\text{ years}}\) <em>not accepted)</em> <em><strong>(A1)</strong></em></span></p>
<p><em><span><strong>OR</strong></span></em></p>
<p><span>\(1500{(1.078)^n} - 1500 = 1500\) <em><strong>(M1)(M1)</strong></em></span></p>
<p><br><span><strong>Note: <em>(M1)</em></strong> for correct substitution in CI formula, <em><strong>(M1)</strong></em> for \(1500\) seen.</span></p>
<p><br><span>\(n = 10{\text{ years}}\) <em>(</em>\(n = 9.23{\text{ years}}\) <em>not accepted)</em> <em><strong>(A1)</strong></em></span></p>
<p><em><span><strong>OR</strong></span></em></p>
<p><span><em><strong>(M2)</strong> for list or graph. <strong>(M2)</strong></em></span></p>
<p><span>\(n = 10{\text{ years}}\) <em>(</em>\(n = 9.23{\text{ years}}\) <em>not accepted)</em> <em><strong>(A1)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> If simple interest formula is used in both parts <strong>(a)</strong> and <strong>(b)</strong> then award<em> <strong>(M0)(M0)(A0)</strong> </em>in <strong>(a)</strong> and </span></p>
<p><span><strong>(b)</strong> \(1500 = \frac{{1500(7.8)n}}{{100}}\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span><em><strong>(M1)</strong></em> for substitution in SI formula or lists,<em> <strong>(A1)</strong></em> for correct substitution.</span></p>
<p><span><br>\(n = 13\)<em> <strong>(A1) (C3)</strong></em></span></p>
<p><span><br><strong>Note:</strong> Correct answer only. If \(9.23\) seen without working award <em><strong>(A2)</strong></em>.</span></p>
<p><br><span><strong>Note: </strong>If calculator notation is used in either part with correct unrounded answer award <em><strong>(A1)</strong></em><strong>(d)</strong> only if <em><strong>(FP)</strong></em> is applied in<strong> (a)</strong> or <em><strong>(AP)</strong></em> in<strong> (b)</strong>. Otherwise <strong><em>(A2)</em>(d)</strong> if penalty has already been applied in a previous question.</span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The use of the TVM solver, and consequent lack of working, was a source of concern; candidates are advised still to write down substituted formulas prior to using the TVM solver.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The use of \(8\% \) in the second part was a common error. The compounding period was again a discriminator for the candidature.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The use of the TVM solver, and consequent lack of working, was a source of concern; candidates are advised still to write down substituted formulas prior to using the TVM solver.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The use of \(8\% \) in the second part was a common error. The compounding period was again a discriminator for the candidature.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p><span>1 Brazilian Real (BRL) = 2.607 South African Rand (ZAR). Giving answers <strong>correct to two decimal places</strong>,</span></p>
<p><span>(i) convert 300 BRL to ZAR,</span></p>
<p><span>(ii) find how many Real it costs to purchase 300 Rand.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><em><strong><span>Financial accuracy penalty (FP) is applicable where indicated in the left hand column.</span></strong></em></p>
<p><span>1 BRL = 2.607 </span><span>ZAR</span></p>
<p> </p>
<p><span><em><strong>(FP) </strong></em></span><span>(i) \(300 \times 2.607 = 782.10 {\text{ ZAR}}\) <em><strong>(A1)</strong></em></span></p>
<p><em><span>Note: 782.1 is <strong>(A0)(FP)</strong></span></em></p>
<p><br><span><em><strong>(FP)</strong></em> (ii)</span> <span>\(300 \times \frac{1}{{2.607}} = 115.07{\text{ BRL}}\)</span><span> <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><em><span>Note: Follow through only if processes are reversed.</span></em> <em><strong><span>(C2)</span></strong></em></p>
<p> </p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-size: medium; font-family: times new roman,times;">a) Was well done, though many were awarded financial penalty with an answer of 782.1 for a(i).</span></p>
<p> </p>
</div>
<br><hr><br><div class="question">
<p><span>Consider the numbers 3, −5 , \(\sqrt{7}\), \(2^{−3}\) and 1.75.</span></p>
<p><span>Complete the table below, placing a tick (</span><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAPCAIAAABm5AhFAAAA5ElEQVQokWP4TxZgIFLd+/fv79+/T5q2Y0cmyrNyWbZMJUHb1HpXdR5Vi5IW4h35e1KNgSOLt355O5oEHm2/J9UYuDGZK2S3YMrh1NZVru/PLC8YW/f682cC2vbv3w9h7NuckaHFwulWvObufayGQrVdvjg33oKDQdhbr2bCg7tLcqxYGUyK45eux+UWhG1d5frBogwMxtl+brziDG5S8WW49KA58ktDtIgkAwMDAwOTY+n2l6+J1PZ//6bYTDEGBgYfvbqpuDRg0fb16zkvBRHzqr7379+ToO3////ICY8EbUQCAMRdzWFSum9AAAAAAElFTkSuQmCC" alt><span>) to show which of the number sets, \(\mathbb{N}, \mathbb{Q} {\text{ and }} \mathbb{R}\)</span><span> these numbers belong to. The first row has been completed as an example.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span><img src="data:image/png;base64,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" alt><span> </span></span></p>
<p><span><em><strong>(A1)</strong></em> for \(\mathbb{N}\) column correct.</span></p>
<p><span><em><strong>(A2)</strong></em> for \(\mathbb{R}\) column correct, award <em><strong>(A1)</strong></em> if one <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAPCAIAAABm5AhFAAAA5ElEQVQokWP4TxZgIFLd+/fv79+/T5q2Y0cmyrNyWbZMJUHb1HpXdR5Vi5IW4h35e1KNgSOLt355O5oEHm2/J9UYuDGZK2S3YMrh1NZVru/PLC8YW/f682cC2vbv3w9h7NuckaHFwulWvObufayGQrVdvjg33oKDQdhbr2bCg7tLcqxYGUyK45eux+UWhG1d5frBogwMxtl+brziDG5S8WW49KA58ktDtIgkAwMDAwOTY+n2l6+J1PZ//6bYTDEGBgYfvbqpuDRg0fb16zkvBRHzqr7379+ToO3////ICY8EbUQCAMRdzWFSum9AAAAAAElFTkSuQmCC" alt>is missing, award <em><strong>(A0)</strong></em> if two or more <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAPCAIAAABm5AhFAAAA5ElEQVQokWP4TxZgIFLd+/fv79+/T5q2Y0cmyrNyWbZMJUHb1HpXdR5Vi5IW4h35e1KNgSOLt355O5oEHm2/J9UYuDGZK2S3YMrh1NZVru/PLC8YW/f682cC2vbv3w9h7NuckaHFwulWvObufayGQrVdvjg33oKDQdhbr2bCg7tLcqxYGUyK45eux+UWhG1d5frBogwMxtl+brziDG5S8WW49KA58ktDtIgkAwMDAwOTY+n2l6+J1PZ//6bYTDEGBgYfvbqpuDRg0fb16zkvBRHzqr7379+ToO3////ICY8EbUQCAMRdzWFSum9AAAAAAElFTkSuQmCC" alt>missing.</span></p>
<p><span><em><strong>(A3)</strong></em> for \(\mathbb{Q}\) column correct, award <em><strong>(A2)</strong></em> for two correctly placed <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAPCAIAAABm5AhFAAAA5ElEQVQokWP4TxZgIFLd+/fv79+/T5q2Y0cmyrNyWbZMJUHb1HpXdR5Vi5IW4h35e1KNgSOLt355O5oEHm2/J9UYuDGZK2S3YMrh1NZVru/PLC8YW/f682cC2vbv3w9h7NuckaHFwulWvObufayGQrVdvjg33oKDQdhbr2bCg7tLcqxYGUyK45eux+UWhG1d5frBogwMxtl+brziDG5S8WW49KA58ktDtIgkAwMDAwOTY+n2l6+J1PZ//6bYTDEGBgYfvbqpuDRg0fb16zkvBRHzqr7379+ToO3////ICY8EbUQCAMRdzWFSum9AAAAAAElFTkSuQmCC" alt>and no extra entries, award <em><strong>(A1)</strong></em> for one correctly placed <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAPCAIAAABm5AhFAAAA5ElEQVQokWP4TxZgIFLd+/fv79+/T5q2Y0cmyrNyWbZMJUHb1HpXdR5Vi5IW4h35e1KNgSOLt355O5oEHm2/J9UYuDGZK2S3YMrh1NZVru/PLC8YW/f682cC2vbv3w9h7NuckaHFwulWvObufayGQrVdvjg33oKDQdhbr2bCg7tLcqxYGUyK45eux+UWhG1d5frBogwMxtl+brziDG5S8WW49KA58ktDtIgkAwMDAwOTY+n2l6+J1PZ//6bYTDEGBgYfvbqpuDRg0fb16zkvBRHzqr7379+ToO3////ICY8EbUQCAMRdzWFSum9AAAAAAElFTkSuQmCC" alt>and no extra entries or <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAPCAIAAABm5AhFAAAA5ElEQVQokWP4TxZgIFLd+/fv79+/T5q2Y0cmyrNyWbZMJUHb1HpXdR5Vi5IW4h35e1KNgSOLt355O5oEHm2/J9UYuDGZK2S3YMrh1NZVru/PLC8YW/f682cC2vbv3w9h7NuckaHFwulWvObufayGQrVdvjg33oKDQdhbr2bCg7tLcqxYGUyK45eux+UWhG1d5frBogwMxtl+brziDG5S8WW49KA58ktDtIgkAwMDAwOTY+n2l6+J1PZ//6bYTDEGBgYfvbqpuDRg0fb16zkvBRHzqr7379+ToO3////ICY8EbUQCAMRdzWFSum9AAAAAAElFTkSuQmCC" alt>placed in all entries. <em><strong>(A6)</strong></em> <em><strong>(C6)</strong></em></span></p>
<p> </p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Ben inherits $6500. Ben invests his money in a bank that pays compound interest at a rate of 4.5% per annum.</span></p>
</div>
<div class="question">
<p><span>Calculate the value of <strong>Ben’s</strong> investment at the end of 6 years. Give your answer <strong>correct to 2 decimal places</strong>.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span>\({\text{Ben Amount}} = 6500{\left( {1 + \frac{{4.5}}{{100}}} \right)^6}\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span>\( = $8464.69\) <em><strong>(A1)</strong></em></span></p>
<p><span><em><strong>(M1)(A1)(A0)</strong> if interest only found (=$1964.69) <strong>(C3)</strong></em></span></p>
<p><span><em><strong>[3 marks]<br></strong></em></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was also well done. However many candidates only gave the interest instead of the total investment. Some also lost a mark by failing to give the answer to part (b) to two decimal places.<br></span></p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Jenny invested $20 000 in a bank account that paid 3.5 % annual simple interest. She withdrew her investment from the account when its value was $31 200.</span></p>
</div>
<div class="question">
<p><span>Ramón invests $18 000 in a bank account that pays 3.4 % nominal annual interest, <strong>compounded quarterly</strong>.</span></p>
<p><span>Find the minimum number of years that Ramón must invest the money for his investment to be worth $27 000.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span>\(27000 = 18000{\left[ {1 + \frac{{3.4}}{{100 \times 4}}} \right]^{4n}}\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituted compound interest formula, <em><strong>(A1)</strong></em> for correct substitutions.</span></p>
<p><br><span>\((n =) 12\) <em><strong>(A1)</strong></em> <em><strong>(C3)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Correct answer only. If 11.976… seen award <em><strong>(A2)</strong></em>.</span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">Although this question was late in the paper there were a number of candidates who scored fullmarks. Others were able to do simple interest but not compound interest or vice versa. However there were a large number that scored zero.</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">A hotel has a rectangular swimming pool. Its length is \(x\) metres, its width is \(y\) metres and its perimeter is \(44\) metres.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down an equation for \(x\) and \(y\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The area of the swimming pool is \({\text{112}}{{\text{m}}^2}\).</p>
<p class="p1">Write down a second equation for \(x\) and \(y\).</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 class="p1">Use your graphic display calculator to find the value of \(x\) and the value of \(y\).</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 class="p1">An Olympic sized swimming pool is \(50\) m long and \(25\) m wide.</p>
<p class="p1">Determine the area of the hotel swimming pool as a percentage of the area of an Olympic sized swimming pool.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(2x + 2y = 44\) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Accept equivalent forms.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(xy = 112\) <span class="Apple-converted-space"> </span><strong><em>(A1) (C1)</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(8\), \(14\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C2)</em></strong></p>
<p class="p1"> </p>
<p class="p1"><strong>Notes: </strong>Accept \(x = 8\), \(y = 14\) <span class="Apple-converted-space"> </span><strong>OR</strong> <span class="Apple-converted-space"> </span>\(x = 14\), \(y = 8\)</p>
<p class="p1">Follow through from their answers to parts (a) and (b) only if both values are positive.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\frac{{112}}{{1250}} \times 100\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for \(112\) divided by \(1250\).</p>
<p class="p2"> </p>
<p class="p1">\( = 8.96\) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C2)</em></strong></p>
<p class="p2"><strong>Note: </strong>Do not penalize if percentage sign seen.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The graph of the quadratic function \(f(x) = a{x^2} + bx + c\) intersects the <em>y</em>-axis at point A (0, 5) and has its vertex at point B (4, 13).</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><br><img src="images/Schermafbeelding_2014-09-20_om_14.11.23.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of \(c\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>By using the coordinates of the vertex, B, or otherwise, write down <strong>two </strong>equations in \(a\) and \(b\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of \(a\) and of \(b\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>5 <strong><em>(A1) (C1)</em></strong></span></p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>at least one of the following equations required</em></span></p>
<p><span>\(a{(4)^2} + 4b + 5 = 13\)</span></p>
<p><span>\(4 = - \frac{b}{{2a}}\)</span></p>
<p><span>\(a{(8)^2} + 8b + 5 = 5\) <strong><em>(A2)(A1) (C3)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A2)(A0) </em></strong>for one correct equation, or its equivalent, and <strong><em>(C3) </em></strong>for any two correct equations.</span></p>
<p><span> Follow through from part (a).</span></p>
<p><span> The equation \(a{(0)^2} + b(0) = 5\) earns no marks.</span></p>
<p> </p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(a = - \frac{1}{2},{\text{ }}b = 4\) <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft) <em>(C2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Follow through from their equations in part (b), but only if their equations lead to unique solutions for \(a\) and \(b\).</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A race track is made up of a rectangular shape \(750{\text{ m}}\) by \(500{\text{ m}}\) with semi-circles at each end as shown in the diagram.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Michael drives around the track once at an average speed of \(140{\text{ km}}{{\text{h}}^{ - 1}}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the distance that Michael travels.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>Calculate how long Michael takes in</span> <span><strong>seconds</strong>.</span></span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><em>Unit penalty <strong>(UP)</strong> may apply in this question.</em></span></p>
<p><span>\({\text{Distance}} = \pi \times 500 + 2 \times 750\) <em><strong>(M1)</strong></em></span></p>
<p><span><em><strong>(UP)</strong></em> \( = 3070{\text{ m}}\) <em><strong>(A1) (C2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>Unit penalty <strong>(UP)</strong> may apply in this question.</em></span></p>
<p><span>\({\text{140 km}}{{\text{h}}^{ - 1}} = \frac{{140 \times 1000}}{{60 \times 60}}{\text{ m}}{{\text{s}}^{ - 1}}\) <em><strong>(M1)</strong></em><br></span></p>
<p><span>\( = 38.9{\text{ m}}{{\text{s}}^{ - 1}}\) <em><strong>(A1)</strong></em><br></span></p>
<p><span>\({\text{Time}} = \frac{{3070}}{{38.889}}\) <em><strong>(M1)</strong></em><br></span></p>
<p><span><em><strong>(UP)</strong></em> \( = 78.9{\text{ seconds}}\) <em>(accept</em> \(79.0\)<em> seconds) </em> <strong><em>(A1)</em>(ft) <em> (C4)</em></strong><em><br></em></span></p>
<p><span><strong><em>[4 marks]<br></em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Candidates generally answered part (a) well. A usual mistake was taking \(500\) as the radius. Some candidates worked out the area rather than the circumference. A good number of candidates correctly answered part (b). Others seemed to get lost in the conversion with multiplication by \(3600\) and not multiplying by \(1000\) being common errors. Again follow through marks could be awarded from the candidate’s answer to part (a) provided working was shown.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Candidates generally answered part (a) well. A usual mistake was taking \(500\) as the radius. Some candidates worked out the area rather than the circumference. A good number of candidates correctly answered part (b). Others seemed to get lost in the conversion with multiplication by \(3600\) and not multiplying by \(1000\) being common errors. Again follow through marks could be awarded from the candidate’s answer to part (a) provided working was shown.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Chocolates in the shape of spheres are sold in boxes of 20.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Each chocolate has a radius of 1 cm.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the volume of 1 chocolate.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the volume of 20 chocolates.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The diagram shows the chocolate box from above. The 20 chocolates fit perfectly in the box with each chocolate touching the ones around it or the sides of the box.</span></p>
<p><span><br><img src="images/Schermafbeelding_2014-09-02_om_14.27.38.png" alt><br></span></p>
<p><span>Calculate the volume of the box.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The diagram shows the chocolate box from above. The 20 chocolates fit perfectly in the box with each chocolate touching the ones around it or the sides of the box.</span></p>
<p><span><br><img src="images/Schermafbeelding_2014-09-02_om_14.27.38_1.png" alt><br></span></p>
<p><span>Calculate the volume of empty space in the box.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><strong><em>The first time a correct answer has incorrect or missing units, the final (A1) is not awarded.</em></strong></span></p>
<p><span>\(\frac{4}{3}\pi {(1)^3}\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into correct formula.</span></p>
<p> </p>
<p><span>\( = 4.19{\text{ }}\left( {{\text{4.18879}} \ldots ,{\text{ }}\frac{4}{3}\pi } \right){\text{ c}}{{\text{m}}^3}\) <strong><em>(A1) (C2)</em></strong></span></p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><strong><em>The first time a correct answer has incorrect or missing units, the final (A1) is not awarded.</em></strong></span></p>
<p><span>\(83.8{\text{ }}\left( {{\text{83.7758}} \ldots ,{\text{ }}\frac{{80}}{3}\pi } \right){\text{ c}}{{\text{m}}^3}\) <strong><em>(A1)</em>(ft) <em>(C1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Follow through from their answer to part (a).</span></p>
<p> </p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><strong><em>The first time a correct answer has incorrect or missing units, the final (A1) is not awarded.</em></strong></span></p>
<p><span>\(10 \times 8 \times 2\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for correct substitution into correct formula.</span></p>
<p> </p>
<p><span>\( = 160{\text{ c}}{{\text{m}}^3}\) <strong><em>(A1) (C2)</em></strong></span></p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><strong><em>The first time a correct answer has incorrect or missing units, the final (A1) is not awarded.</em></strong></span></p>
<p><span>\(76.2{\text{ }}\left( {{\text{76.2241}} \ldots ,{\text{ }}\left( {160 - \frac{{80}}{3}\pi } \right)} \right){\text{ c}}{{\text{m}}^3}\) <strong><em>(A1)</em>(ft) <em>(C1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Follow through from their part (b) and their part (c).</span></p>
<p> </p>
<p><span><strong><em>[1 mark] </em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">An iron bar is heated. Its length, \(L\), in millimetres can be modelled by a linear function, \(L = mT + c\), where \(T\) <span class="s1">is the temperature measured in degrees Celsius (°C)</span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">At <span class="s1">150°</span><span class="s1">C </span>the length of the iron bar is <span class="s1">180 mm</span>.</p>
<p class="p1">Write down an equation that shows this information.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">At <span class="s1">210°</span><span class="s1">C </span>the length of the iron bar is <span class="s1">181.5 mm</span>.</p>
<p class="p1">Write down an equation that shows this second piece of information.</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 class="p1">At <span class="s1">210°</span><span class="s1">C </span>the length of the iron bar is <span class="s1">181.5 mm</span>.</p>
<p class="p1">Hence, find the length of the iron bar at <span class="s1">40°</span><span class="s1">C</span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(180 = 150m + c\;\;\;\)(or equivalent) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C1)</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(181.5 = 210m + c\;\;\;\)(or equivalent) <span class="Apple-converted-space"> </span><strong><em>(A1) <span class="Apple-converted-space"> </span>(C1)</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(m = 0.25,{\text{ }}c = 176.25\) <span class="Apple-converted-space"> </span><strong><em>(A1)(A1)</em>(ft)</strong></p>
<p class="p1"><strong>Note: </strong>Follow through from part (a) and part (b), irrespective of working shown.</p>
<p class="p2"> </p>
<p class="p1">\(L = 0.025(4) + 176.25\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Note:<span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for substitution of their \(m\), their \(c\) and <span class="s1">40 </span>into equation.</p>
<p class="p2"> </p>
<p class="p1">\(L = 177\;\;\;(177.25){\text{ (mm)}}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C4)</em></strong></p>
<p class="p1"><strong>Note: </strong>Follow through, within <strong>part (c)</strong>, from their \(m\) and \(c\) only if working shown.</p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>The equations in part (a) and (b) were given correctly by the vast majority of the candidates.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The equations in part (a) and (b) were given correctly by the vast majority of the candidates.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Part (c) was in most cases either completely correct or awarded no marks at all. Only few were able to find the values of <em>m</em> and<em> c</em>, and therefore the length at 40<strong>°</strong>C. Part (c) was often left open or answered incorrectly. A common answer was <em>L = 40m + c</em> . Very few partial correct responses were given. Some candidates managed a correct 3 sf answer by intelligent guessing. As the question was not structured asking for the m and c values explicitly, not many candidates made an attempt to find those values. Very few seemed to realize they could find those values using their GDC. An attempt to use simultaneous equations was the most common approach.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the truth table.</span></p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAYEAAADHCAIAAABwTXi2AAAOm0lEQVR4nO3dz0tc9x7G8fNvzMrArJQKLW5CFzIr6Q8IoZBVwYW5oZZS6EoIiimhi8KAksKlcGFQErqca0h20uGQSymYq7SLXqIDhbRNdSFFDrOQIIfvXZyJjjPjEz+Nme9nyPvFWSRpU8Y3nmfOnNGahBDKI5c4ODg4Bn+EEJJigwLORh+BOAJxhOM4bNDL0UcgjkAcgQ0yoI9AHIE4AhtkQB+BOAJxBDbIgD4CcQTiCGyQAX0E4gjEEdggA/oIxBGII7BBBvQRiCMQR2CDDOgjEEcgjsAGGdBHII5AHMHbBrW2lt4vj1wqj7y//Li5dXf+g5FL5ZHLN+78uJfHfmgu+oQQQsj32mVGv/j3999eHZlcSPdjPyY3cfpobVYrSZIkycRc/T/r1elSkiSlmdqTbGCPIEac44+6Ut3Y2VydqyRJkrw1vfTD7smplLc2lyqVpc1Wz9mVP63PVGbqT3tPu3x3Y3VuKkmS0szd9X9dS0o3G9krnZzeNiiEcLS39nl55P0bs/PfPN7Lw8HW0kflkY9Xm4exH5iPPq1fVq9fLo/Orm5nofV4+b2x8sjn9/eOYj8sH3HOdLRb/yRJJirTX9Z3svxZfaaUlOYaAxuhSHGKj7oyPTO3tLGbh4PN6odJcq2203kqHWxWr1aqG61Tf/H5s/pnpanaTve25K0nq9OlpDS9+qR11NpcqiRJMl3ffbVH6XCD9tP5yfLIR8tbByGEEPIsXRwfeX95q/WSv/f6OehTLPJxnD/uX3+nfGWlyUXiS+w35iaS5MPqZtHt9/p0+dVPnvOLFKfro86zxs1SUqlunjqV8mf1mdLxvxNCCCFrzHX9SaG1Ua2UkuPrpt36dFKaqj15xc8+fxt0tLX89qXx+fTFc9Rhc+VjroNCCCHkra1vPhgZ+2DpcfuTKEsXRi9NLG3FvwoaUJziiV3quyxHm9Vy6eTZPmvMlZJydXNg3V4tzvGrKuGT+m7PR3O0WS13Xu4d7tSu9VwHtf+8NFN/1t6Sg83qhx2/PVZcRr1k0f4GdxuUN1dO3eBoPV5+b2x8du1PnurbN8uO57i4QnRxMyjEjxNCcdL126B8pzZ1cu4VJ0+/5/nX5vXGOdqslvtsUL5Tm0om5hrHp9JGtVLqNy7FP5qYqT/NiztEfXaqvWjJyQu0/cbcxKvfDAr+Nuhob+3z8uhi2v7Asu2V2fHRL+7/+Tzy4wohxO/zx/3r75TffnHZ4+lmUIgfJ4QzN+hwp9Zx67Q4FQd4MyjE2aCj3fonHRuRPanNlEqf1Z/1PZWeP6t/VirdbBz8rzZV7rk9FEIoXnkdXzzmF3UzKPjboP10frJcjE6+9987/xgfuXIr9XANFEL8Pidx8r0f/7m0VL1+2cnNoBA/TghnbtB+Y26iuIuR7/6wNP1WaXr1Se87Qa9TjA0qrlM+qz97HvLdjaXpUjJ1s9HnGqgtf1KbKr9bebd01qVN1pgrJaWZ+rP8+e5GrVr9crp0ATeDgrsNOtpafvv4f6029sH8Stoc5NPVS8Tuk7e2790YvVQeuXxjab158Hj57bGrK9s+Jih6nBDO2qCsMVc6vm8yNVdr7Ax2gEKUDSpeOrWVKnO1xo4+lYpLm7f6vh8fQmhfSSVJUpquru8cbFbLfV+y2fnaoO6bQc5E79PJWytXcTodXdzZ8rcNPk73zaALdvrl7atxtUF5li6On9wMcid2n05dN87i8xSn0+FO7VrS50tdBmrgcfKscfPMV1UX4Pf6dPmi7ql52qD8t/uzl8vX1/ZiPgjFz2mW731/670xV638xDmltVGtlAb5Nnxfg46TP63PvPXavgDq+W7jy0pSnq7/fiH/OS8bdLS1NHH8P9n39PTeycdpVnwN54tWbmbIR5xTTt0SGeBXJPYaZJzTN4Iu+lLo1M21i5khLxs0FOgjEEcgjsAGGdBHII5AHIENMqCPQByBOAIbZEAfgTgCcQQ2yIA+AnEE4ghskAF9BOIIxBHYIAP6CMQRiCOwQQb0EYgjEEdggwzoIxBHII7ABhnQRyCOQByBDTKgj0AcgTgCG2RAH4E4AnEENsiAPgJxBOIIbJABfQTiCMQR2CAD+gjEEYgjsEEG9BGIIxBH6N4gDg4OjsEfgeug86CPQByBOEKZ12LnRx+BOAJxBDbIgD4CcQTiCGyQAX0E4gjEEdggA/oIxBGII7BBBvQRiCMQR3C1QXmWLo6f+e5d/J+tHrlPli6Mnv3u5pWV5pv1o0SHCXEEbxv09acrv7Tav14cP/l56llz7fanb/wG3Zq9t93Ki18vjF4an0+zEELIW821hdl7bJBbxBFcbdBh88H6ixOpa4NCyJsPH8Q9yyL3yZvrD5uH7d+c2qBwOl0csT95XCOO4GqDOvVskAOO+nRvUHyO4vhDHIENMnDUhw0aKsQR2CADR33YoKFCHIENMnDUhw0aKsQR2CADR33YoKFCHIENMnDUhw0aKsQR2CADR33YoKFCHIENMnDUhw0aKsQRXG5Q1zcljC6mWdwvTmzz0Wc/nZ/s+C4NLzPtI45TxBFcbpBX9BGIIxBHYIMM6CMQRyCOwAYZ0EcgjkAcgQ0yoI9AHIE4AhtkQB+BOAJxBDbIgD4CcQTiCGyQAX0E4gjEEdggA/oIxBGII7BBBvQRiCMQR2CDDOgjEEcgjsAGGdBHII5AHIENMqCPQByBOAIbZEAfgTgCcQQ2yIA+AnEE4ghskAF9BOIIxBHYIAP6CMQRiCOwQQb0EYgjEEdggwzoIxBHII7ABhnQRyCOQByBDTKgj0AcgThC9wZxcHBwDP4IXAedB30E4gjEEcq8Fjs/+gjEEYgjsEEG9BGIIxBHYIMM6CMQRyCOwAYZ0EcgjkAcgQ0yoI9AHIE4gqsNyrN0cfzMd+/Grq5sx/2x85H7ZOnC6Blxrqw046aJHsc34gjeNujrT1d+abV/vTg+MrmQ7ocQQsiaa7c/fcM3KISeLCGEkO99f+vK7TSLPEIO4vhFHMHVBh02H6y/eD7vOdny5sMHkZ/sY/cJfTcohMPm3Rob5BlxBFcb1KnvyRaZgz690/zb1k9/RX1IbQ7i+EUcgQ0ycNCnK0ve2qot+0jkII5fxBHYIAMHfXpv23tJ5CCOX8QR2CADB316roO266uPXCRyEMcv4ghskIGDPtwPGkrEEdggAwd9PGYpOIjjF3EENsjAQR+PWQoO4vhFHIENMnDQx2OWgoM4fhFHcLlBXd+UMLoY/QvwCr6+V8NNloKXTx6XiCO43CCv6CMQRyCOwAYZ0EcgjkAcgQ0yoI9AHIE4AhtkQB+BOAJxBDbIgD4CcQTiCGyQAX0E4gjEEdggA/oIxBGII7BBBvQRiCMQR2CDDOgjEEcgjsAGGdBHII5AHIENMqCPQByBOAIbZEAfgTgCcQQ2yIA+AnEE4ghskAF9BOIIxBHYIAP6CMQRiCOwQQb0EYgjEEdggwzoIxBHII7ABhnQRyCOQByBDTKgj0AcgTgCG2RAH4E4AnGE7g3i4ODgGPwRuA46D/oIxBGII5R5LXZ+9BGIIxBHYIMM6CMQRyCOwAYZ0EcgjkAcgQ0yoI9AHIE4AhtkQB+BOAJxBFcblGfp4nj/t+7Grq5sR//h6pH7dP28+a7jykozaqDYnzyuEUdwtUGF/XR+sjy6mGbHp9TzvfSrq/NpFvNRhRC9T5bemr233cqLXy+MXhpvN8lbzbWF2XtskFvEEYZig0LIt+/defSGb1DeXH/YPGz/5tQGhRAOmw/W2SC3iCMMwQblv/70cxb9dVgIXvqEEHo3KD5HcfwhjuB/gw627nybskFd2KChQhzB6wZ13m3tel0Wj48+IQQ2aMgQR/C6QSe7k23f/e4RG9SFDRoqxBH8bxD3g/phg4YKcYQh2CA/fPQJIbBBQ4Y4Ahtk4KNPCIENGjLEEdggAx99Qghs0JAhjuBqg7q/V8PVORbi9yl0vW84uZDux35IIXiJ4xRxBFcb5B19BOIIxBHYIAP6CMQRiCOwQQb0EYgjEEdggwzoIxBHII7ABhnQRyCOQByBDTKgj0AcgTgCG2RAH4E4AnEENsiAPgJxBOIIbJABfQTiCMQR2CAD+gjEEYgjsEEG9BGIIxBHYIMM6CMQRyCOwAYZ0EcgjkAcgQ0yoI9AHIE4AhtkQB+BOAJxBDbIgD4CcQTiCGyQAX0E4gjEEdggA/oIxBGII7BBBvQRiCMQR2CDDOgjEEcgjtC9QRwcHByDPwLXQedBH4E4AnGEMq/Fzo8+AnEE4ghskAF9BOIIxBHYIAP6CMQRiCOwQQb0EYgjEEdggwzoIxBHII7gaoO6f958xzF2dWU7j/rgQvQ+WbowesZbm1dWmrHrxP7kcY04gqsNKuyn85Pl0cU0Oz6rnu+lX12dT7OYjyoEF32KmZ5cSPdP/mjv+1tXbnfkisNBHL+IIwzFBoWQb9+784gN6rtBIRw279bYIM+IIwzBBuW//vRz7BOs4KBPzwblv2399FfUh9TmII5fxBH8b9DB1p1voz/JFxz06dqgvLVVWz51TRSNgzh+EUfwukGdN1y7XpfF46BP7237rtdl0TiI4xdxBK8bdLI72fbd7x6xQW0910Hb9dVHbJB3xBH8bxD3gzpxP2goEUcYgg3yw0Gfvu+LueAgjl/EEdggAwd92KChRByBDTJw0IcNGkrEEVxtUPebPuMOvja6k6/v1XA207E/eVwjjuBqg7yjj0AcgTgCG2RAH4E4AnEENsiAPgJxBOIIbJABfQTiCMQR2CAD+gjEEYgjsEEG9BGIIxBHYIMM6CMQRyCOwAYZ0EcgjkAcgQ0yoI9AHIE4AhtkQB+BOAJxBDbIgD4CcQTiCGyQAX0E4gjEEdggA/oIxBGII7BBBvQRiCMQR2CDDOgjEEcgjsAGGdBHII5AHIENMqCPQByBOAIbZEAfgTgCcQQ2yIA+AnEE4ghskAF9BOIIxBG6N4iDg4Nj8Ed7gwAgFjYIQExsEICY/g95UhvbhRd1AgAAAABJRU5ErkJggg==" alt></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Consider the propositions <em>p</em> and <em>q</em>:</span></p>
<p><em><span>p: x is a number less than 10.</span></em></p>
<p><span><em><span><span>q: x2 is a number greater than 100.</span></span></em></span></p>
<p><span><span>Write in words the compound proposition \(\neg p \vee q\).</span></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Using part (a), determine whether \(\neg p \vee q\) is true or false, for the case where \(x\) is a number less than 10 and \(x^2\) is a number greater than 100.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down a value of \(x\) for which \(\neg p \vee q\) is false.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span> </span></span></p>
<p><span><em><strong>(A1)</strong></em> for third column and <em><strong>(A1)</strong></em><strong>(ft)</strong> for fourth column <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(x\) is greater than or equal to (not less than) 10 or \(x^2\) is greater than 100. <em><strong>(A1)(A1)</strong></em> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for “greater than or equal to (not less than) 10”, <em><strong>(A1)</strong></em> for “or </span><span><span>\(x^2\)</span> is greater than 100”.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>True <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from their answer to part (a).</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Any value of \(x\) such that \( - 10 \leqslant x < 10\). <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from their answer to part (a).</span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This was provocative in the G2 and the comments indicate that candidates found the wording confusing. Candidates were able to write in words the compound proposition \(\neg p \vee q\) and following from their truth table the candidates could state if this was true or false.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This was provocative in the G2 and the comments indicate that candidates found the wording confusing. Candidates were able to write in words the compound proposition \(\neg p \vee q\) and following from their truth table the candidates could state if this was true or false. In part (c) many candidates either stated the correct answer “true” or stated an answer consistent with their truth table and received follow-through marks. Candidates had difficulty writing down a value of \(x\) for which \(\neg p \vee q\) is false.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This was provocative in the G2 and the comments indicate that candidates found the wording confusing. Candidates were able to write in words the compound proposition \(\neg p \vee q\) and following from their truth table the candidates could state if this was true or false. In part (c) many candidates either stated the correct answer “true” or stated an answer consistent with their truth table and received follow-through marks. Candidates had difficulty writing down a value of \(x\) for which \(\neg p \vee q\]) is false.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This was provocative in the G2 and the comments indicate that candidates found the wording confusing. Candidates were able to write in words the compound proposition \(\neg p \vee q\) and following from their truth table the candidates could state if this was true or false.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A solid right circular cone has a base radius of 21 cm and a slant height of 35 cm.<br>A smaller right circular cone has a height of 12 cm and a slant height of 15 cm, and is removed from the top of the larger cone, as shown in the diagram.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the radius of the base of the cone which has been removed.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the curved surface area of the cone which has been removed.</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>Calculate the curved surface area of the remaining solid.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(\sqrt {{{15}^2} - {{12}^2}} \) <em><strong> (M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into Pythagoras theorem.</p>
<p><strong>OR</strong></p>
<p>\(\frac{{{\text{radius}}}}{{21}} = \frac{{15}}{{35}}\) <em><strong> (M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for a correct equation.</p>
<p>= 9 (cm) <em><strong>(A1) (C2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\pi \times 9 \times 15\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their correct substitution into curved surface area of a cone formula.</p>
<p>\( = 424\,\,{\text{c}}{{\text{m}}^2}\,\,\,\,\,\left( {135\pi ,\,\,424.115...{\text{c}}{{\text{m}}^2}} \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note</strong>: Follow through from part (a).</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>\(\pi \times 21 \times 35 - 424.115...\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their correct substitution into curved surface area of a cone formula and for subtracting their part (b).</p>
<p>\( = 1880\,\,{\text{c}}{{\text{m}}^2}\,\,\,\,\,\left( {600\pi ,\,\,1884.95...{\text{c}}{{\text{m}}^2}} \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (b).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Last year a South American candy factory sold 4.8 × 10<sup>8</sup> spherical sweets. Each sweet has a diameter of 2.5 cm.</p>
<p>The factory is producing an advertisement showing all of these sweets placed in a straight line.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>The advertisement claims that the length of this line is <em>x</em> times the length of the Amazon River. The length of the Amazon River is 6400 km.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the length, in cm, of this line. Give your answer in the form <em>a</em> × 10<sup><em>k</em></sup> , where 1 ≤ <em>a</em> < 10 and k ∈ \(\mathbb{Z}\).</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>Write down the length of the Amazon River in cm.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>x</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>4.8 × 10<sup>8</sup> × 2.5 <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for multiplying by 2.5.</p>
<p>1.2 × 10<sup>9</sup> (cm) (<em><strong>A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A0)(A0)</strong></em> for answers of the type 12 × 10<sup>8</sup>.</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>640 000 000 (cm) (6.4 × 10<sup>8</sup> (cm)) <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{1.2 \times {{10}^9}}}{{6.4 \times {{10}^8}}}\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for division by 640 000 000.</p>
<p>= 1.88 (1.875) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C3)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (a) and part (b)(i).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A park in the form of a triangle, ABC, is shown in the following diagram. AB is 79 km and BC is 62 km. Angle A\(\mathop {\text{B}}\limits^ \wedge \)C is 52°.</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>Calculate the length of side AC in km.</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>Calculate the area of the park.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>(AC<sup>2</sup> =) 62<sup>2</sup> + 79<sup>2</sup> − 2 × 62 × 79 × cos(52°) <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting in the cosine rule formula, <em><strong>(A1)</strong></em> for correct substitution.</p>
<p>63.7 (63.6708…) (km) <em><strong> (A1) (C3)</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{1}{2}\) × 62 × 79 × sin(52°) <em><strong>(M1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituting in the area of triangle formula, <em><strong>(A1)</strong></em> for correct substitution.</p>
<p>1930 km<sup>2</sup> (1929.83…km<sup>2</sup>) <em><strong>(A1) (C3)</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Consider the numbers \(2\), \(\sqrt 3 \), \( - \frac{2}{3}\) and the sets \(\mathbb{N}\), \(\mathbb{Z}\), \(\mathbb{Q}\) and \(\mathbb{R}\).</span></p>
<p><span>Complete the table below by placing a tick in the appropriate box if the number is an element of the set, and a cross if it is not.<img src="data:image/png;base64,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" alt></span></p>
<p> </p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A function \(f\) is given by \(f(x) = 2{x^2} - 3x{\text{, }}x \in \{ - 2{\text{, }}2{\text{, }}3\} \).</span></p>
<p><span>Write down the range of function \(f\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span> <em><strong>(A1)(A1)(A1) (C3)</strong></em></span></span></p>
<p><span><strong>Note:</strong> Accept any symbol for ticks. Do not penalise if the other boxes are left blank.<strong><br></strong></span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{Range}} = \{ 2{\text{, }}9{\text{, }}14\} \) <em><strong>(A1)</strong></em><strong>(ft) <em>(C1)</em></strong></span></p>
<p><span><strong>Note: </strong>Brackets not required.<em><strong><br></strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">There was a lack of familiarity with number systems and mappings - it was surprising to see how few knew what a mapping diagram involved. Part (c) (range) was also poorly answered with many giving an interval although they had correctly worked out the values for the function.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">There was a lack of familiarity with number systems and mappings - it was surprising to see how few knew what a mapping diagram involved. Part (b) (range) was also poorly answered with many giving an interval although they had correctly worked out the values for the function.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Fabián stands on top of a building, <span class="s1">T</span>, which is on a horizontal street.</p>
<p class="p1">He observes a car, <span class="s1">C</span>, on the street, at an angle of depression of <span class="s1">30°</span>. The base of the building is at <span class="s1">B</span>. The height of the building is <span class="s1">80 </span>metres.</p>
<p class="p1">The following diagram indicates the positions of <span class="s1">T</span>, <span class="s1">B </span>and <span class="s1">C.</span></p>
<p class="p1" style="text-align: center;"><span class="s1"><img src="images/Schermafbeelding_2015-12-20_om_09.20.36.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show, in the appropriate place on the diagram, <strong>the values </strong>of</p>
<p class="p1">(i) the height of the building;</p>
<p class="p1">(ii) the angle of depression.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the distance, <span class="s1">BC</span>, from the base of the building to the car.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Fabián estimates that the distance from the base of the building to the car is <span class="s1">150 </span>metres. Calculate the percentage error of Fabián’s estimate.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="s1"><img src="data:image/png;base64,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" alt> <span class="Apple-converted-space"> </span></span><strong><em>(A1)(A1) <span class="Apple-converted-space"> </span>(C2)</em></strong></p>
<p class="p3"><strong>Notes:<span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1) </em></strong>for 80 m in the correct position on diagram.</p>
<p class="p3">Award <strong><em>(A1) </em></strong>for 30° in a correct position on diagram.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\tan 30^\circ = \frac{{80}}{{{\text{BC}}}}\;\;\;\)<strong>OR</strong>\(\;\;\;\tan 60^\circ = \frac{{{\text{BC}}}}{{80}}\;\;\;\)<strong>OR</strong>\(\;\;\;\frac{{80}}{{\sin 30^\circ }} = \frac{{{\text{BC}}}}{{\sin 60^\circ }}\) <strong><em>(M1)</em></strong></p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for a correct trigonometric or Pythagorean equation for BC with correctly substituted values.</p>
<p> </p>
<p>\(({\text{BC}} = ){\text{ 139 (m)}}\;\;\;\left( {138.564 \ldots {\text{ (m)}}} \right)\) <strong><em>(A1)</em>(ft) <em>(C2)</em></strong></p>
<p><strong>Notes: </strong>Accept an answer of \(80\sqrt 3 \) which is the exact answer.</p>
<p>Follow through from part (a).</p>
<p>Do not penalize use of radians unless it leads to a negative answer.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\left| {\frac{{150 - 138.564 \ldots }}{{138.564 \ldots }}} \right| \times 100\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Notes:<span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for their correct substitution into the percentage error formula.</p>
<p class="p2"> </p>
<p class="p1">\( = 8.25(\% )\;\;\;(8.25317 \ldots \% )\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft) <span class="Apple-converted-space"> </span><em>(C2)</em></strong></p>
<p class="p1"><strong>Notes: </strong>Accept \(7.91(\%)\)<span class="s1"> (\(7.91366...\) </span>if \(139\)<span class="s1"> </span>is used.</p>
<p class="p3"><span class="s2">Accept \(8.23(\%)\) </span>(\(8.22510...\) <span class="s2">if \(138.6\)</span> <span class="s2">is used.</span></p>
<p class="p1">Follow through from their answer to part (b).</p>
<p class="p1">If answer to part (b) is \(46.2\)<span class="s1">, </span>answer to part (c) is \(225\%\), award <strong><em>(M1)(A1)</em>(ft) </strong>with or without working seen. If answer to part (b) is negative, award at most <strong><em>(M1)(A0)</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="question" style="padding-left: 20px; padding-right: 20px;">
<p>Assume that the Earth is a sphere with a radius, \(r\) , of \(6.38 \times {10^3}\,{\text{km}}\) .</p>
<p><img src="data:image/png;base64,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" alt></p>
<p>i) Calculate the surface area of the Earth in \({\text{k}}{{\text{m}}^2}\).</p>
<p>ii) Write down your answer to part (a)(i) in the form \(a \times {10^k}\) , where \(1 \leqslant a < 10\) and \(k \in \mathbb{Z}\) .</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>The surface area of the Earth that is covered by water is approximately \(3.61 \times {10^8}{\text{k}}{{\text{m}}^2}\) .</p>
<p>Calculate the percentage of the surface area of the Earth that is covered by water.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>i) \(4\pi {(6.38 \times {10^3})^2}\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into the surface area of a sphere formula.</p>
<p>\( = 512\,000\,000\,\,\,(511506576,\,\,162\,817\,600\pi )\) <em><strong>(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> Award at most <em><strong>(M1)(A0)</strong></em> for use of \(3.14\) for \(\pi \), which will give an answer of \(511\,247\,264\).</p>
<p> </p>
<p>ii) \(5.12 \times {10^8}\,\,\,(5.11506... \times {10^8},\,\,1.628176\pi \times {10^8})\) <em><strong>(A1)</strong></em><strong>(ft)<em>(A1)</em><strong>(ft)<em> (C2)</em></strong></strong></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(5.12\) and <em><strong>(A1)</strong></em> for \( \times {10^8}\).<br>Award <em><strong>(A0)(A0)</strong></em> for answers of the type: \(5.12 \times {10^7}\).<br>Follow through from part (a)(i).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{3.61 \times {{10}^8}}}{{5.11506...\,\, \times {{10}^8}}} \times 100\) <strong>OR</strong> \(\frac{{3.61}}{{5.11506...\,}} \times 100\) <strong>OR</strong> \(0.705758... \times 100\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution. Multiplication by \(100\) must be seen.</p>
<p>\( = 70.6\,(\% )\,\,\,\,(70.5758...\,(\% ))\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (C2)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (a). Accept the use of \(3\) sf answers, which gives a final answer of \(70.5\,(\% )\,\,\,\,(70.5758...\,(\% ))\) .</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Question 1: Surface area of a sphere; scientific notation and percentage.<br>The weakest candidates were unable to square a number given in scientific notation or write the answer in scientific notation. Weaker candidates used the area of a circle formula rather than the surface area of a sphere. Premature rounding caused some candidates to obtain an incorrect final answer. Many candidates confused percentage of a quantity with percentage error or found the reciprocal of the correct answer. Overall this question was well attempted.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 1: Surface area of a sphere; scientific notation and percentage.<br>The weakest candidates were unable to square a number given in scientific notation or write the answer in scientific notation. Weaker candidates used the area of a circle formula rather than the surface area of a sphere. Premature rounding caused some candidates to obtain an incorrect final answer. Many candidates confused percentage of a quantity with percentage error or found the reciprocal of the correct answer. Overall this question was well attempted.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>Consider the numbers \( - 1,\,\,4,\,\,\frac{2}{3},\,\,\sqrt 2 ,\,\,0.35\) and \( - {2^2}\).</p>
<p>Complete the following table by placing a tick (<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABUAAAASCAYAAAC0EpUuAAABLElEQVQ4EdWTP2vCQBjGX539AG4pZIogOGbuUFIHFT9BB4Pp5t61s1KhdMwQdwU/QOkaydYh6OQgcZOSKcP5yPkHgpfTHLr04OB4797f+zx39xYAgO48infm7XE3QbfrGY2GU1psz6Rx++ojQeR/4dXxEMZMSCchcjWQIPp+R90aIsgA8nRF6BFo9DBZJdLyCtAjUGtjEGykQAWlDHHowTZM2O4v4ovITPuHR7CNlKLYx8CqoOqMsRLfRSgh2mcRZh8dVLUH6A0Xc7ZB0G9Dv3KPabII5btsiYljQtdM2G891LUKWm6IHCL37Gwo585dtLhaPi98n7TC01raUUX9kV6ey0RUpqduk2ol6dGzdiKSKgUY/n48fPpRbtsnpQW+EEvdFlHwlL/Q/4HuAAoRIMzxYx0jAAAAAElFTkSuQmCC" alt>) to indicate if the number is an element of the number set. The first row has been completed as an example.</p>
<p><img src="data:image/png;base64,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" alt></p>
<p> </p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><img 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" alt></p>
<p><em><strong>(A1)(A1)(A1)(A1)(A2) (C6)</strong></em></p>
<p>Note: <strong>Row 1</strong> has been given in the question.<br><strong>Row 2 to row 5:</strong> Award <em><strong>(A1)</strong></em> for each correct row.<br><strong>Row 6:</strong> Award <em><strong>(A1)</strong></em> for both \(\mathbb{N}\) <strong>not</strong> selected <strong>and</strong> \(\mathbb{Z}\) selected; award <em><strong>(A1)</strong></em> for both \(\mathbb{Q}\) <strong>and</strong> \(\mathbb{R}\) selected. Do not penalize if crosses (or similar) appear in the empty cells.</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p>Question 2: Classification of numbers.<br>Stronger candidates were able to correctly identify if a number was rational, real or natural with the weaker candidates not recognizing that all rational numbers are real or perhaps these candidates lacked familiarity with the mathematical notation. Only the best candidates knew that \(\frac{2}{3} \in \)¤, \(\sqrt 2 \notin \)¤ and that \( - {2^2} \in \)¥ but \( - {2^2} \in \)<strong>¢</strong>.</p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">\(U = \{ x|x{\text{ is an integer, }}2 < x < 10\}\)</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><em>A</em> and <em>B</em> are subsets of <em>U</em> such that <em>A</em> = {multiples of 3}, <em>B</em> = {factors of 24}.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>List the elements of</span></p>
<p><span>(i) <em>U</em> ;</span></p>
<p><span>(ii) <em>B</em> .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the elements of <em>U</em> on the Venn diagram.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down \(n (A \cap B)\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>(i) 3, 4, 5, 6, 7, 8, 9 <em><strong>(A1)</strong></em></span></p>
<p><span>(ii) 3, 4, 6, 8 <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Follow through from part (a)(i).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span><em><strong>(A1)</strong></em><strong>(ft)</strong> for their 3, 6</span><br><span><span><em><strong>(A1)</strong></em><strong>(ft)</strong></span> for their 4, 8, 9</span><br><span><span><em><strong>(A1)</strong></em><strong>(ft)</strong></span> for their 5, 7 </span><span><em><strong><span><em><strong>(A1)</strong></em></span></strong></em></span><span><strong><span><span><span><strong>(ft)</strong></span></span></span></strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C3)</strong></em></span><br><br></p>
<p><span><strong>Note:</strong> Follow through from their universal set and set B in part (a).</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>2 <em><strong>(A1)</strong></em><strong>(ft)</strong> <em><strong>(C1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from their Venn diagram.</span></p>
<p><span><em><strong>[1 mark]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates were unable to write down correctly the universal set which was integers between \(2\) and \(10\). Some candidates did not read the direction “on the Venn diagram” so complained of lack of space for their answer. It is important candidates read the directions carefully. Many candidates listed the elements of the intersection rather than answering the question to specify the number of elements. The empty set for \(\left( {A \cup B} \right)'\) was awarded a maximum of 2 marks as this has simplified the problem.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates were unable to write down correctly the universal set which was integers between \(2\) and \(10\). Some candidates did not read the direction “on the Venn diagram” so complained of lack of space for their answer. It is important candidates read the directions carefully. Many candidates listed the elements of the intersection rather than answering the question to specify the number of elements. The empty set for \(\left( {A \cup B} \right)'\) was awarded a maximum of 2 marks as this has simplified the problem.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates were unable to write down correctly the universal set which was integers between \(2\) and \(10\). Some candidates did not read the direction “on the Venn diagram” so complained of lack of space for their answer. It is important candidates read the directions carefully. Many candidates listed the elements of the intersection rather than answering the question to specify the number of elements. The empty set for \(\left( {A \cup B} \right)'\) was awarded a maximum of 2 marks as this has simplified the problem.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p><span>The Venn diagram shows the number sets \(\mathbb{N}\), \(\mathbb{Z}\), \(\mathbb{Q}\) and \(\mathbb{R}\). Place each of the following</span> <span>numbers in the appropriate region of the Venn diagram.</span></p>
<p><span>\(\frac{{1}}{{4}}\), −3, π, cos 120°, 2.7 × 10<sup>3</sup>, 3.4 × 10<sup>–2</sup></span></p>
<p><span><img 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" alt></span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span><img 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" alt><span> <em><strong>(A1)(A1)(A1)(A1)(A1)(A1) </strong> <strong>(C6)</strong></em></span></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for each number placed once in the correct section. Accept equivalent forms for numbers.</span></p>
<p><span> </span></p>
<p><span><em><strong>[6</strong></em> <em><strong>marks]</strong></em></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">About half of the students answered this question correctly. The placement of cos120 and </span><span style="font-family: times new roman,times; font-size: medium;">π appeared to cause the most problems.</span></p>
</div>
<br><hr><br><div class="specification">
<p>The following table shows four different sets of numbers: \(\mathbb{N}\), \(\mathbb{Z}\), \(\mathbb{Q}\) and \(\mathbb{R}\).</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>Complete the second column of the table by giving <strong>one</strong> example of a number from each set.</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>Josh states: “Every integer is a natural number”.</p>
<p>Write down whether Josh’s statement is correct. Justify your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><img 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"><em><strong>(A1)(A1)(A1)(A1)(C4)</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Incorrect <em><strong>(A1)</strong></em></p>
<p>Natural numbers are positive integers. Integers can also be negative. (or equivalent) <em><strong>(R1) (C2)</strong></em></p>
<p><strong>Note:</strong> Accept a correct justification. Do not award <em><strong>(R0)(A1)</strong></em>.<br>Accept: a statement with an example of an integer which is not natural.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Temi’s sailing boat has a sail in the shape of a right-angled triangle, \({\text{ABC}}{\text{.}}\,\,\,{\text{BC}} = \,\,5.45{\text{m}}\),<br>angle \({\text{CAB}} = {76^{\text{o}}}\) and angle \({\text{ABC}} = {90^{\text{o}}}\).</p>
<p>Calculate \({\text{AC}}\), the height of Temi’s sail.</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><img 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" alt></p>
<p>William also has a sailing boat with a sail in the shape of a right-angled triangle, \({\text{TRS}}\).<br>\({\text{RS}}\,\,{\text{ = }}\,\,{\text{2}}{\text{.80m}}\). The area of William’s sail is \({\text{10}}{\text{.7}}\,{{\text{m}}^2}\).</p>
<p>Calculate \({\text{RT}}\), the height of William’s sail.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>Units are required in parts (a) and (b).</strong></p>
<p>\({\text{sin}}\,\,{76^{\text{o}}} = \,\,\frac{{5.45}}{{{\text{AC}}}}\) <em><strong>(M1)</strong></em></p>
<p><strong>Note: </strong>Award<em> <strong>(M1)</strong></em> for correct substitution into correct trig formula. </p>
<p>\({\text{AC}}\,\, = \,\,5.62{\text{m}}\,\,\,( = 5.61684...{\text{m}})\) <em><strong>(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> The answer is \(5.62{\text{m}}\), <strong>the units are required. </strong></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>\(\frac{1}{2}\,\, \times \,\,2.80\,\, \times \,\,{\text{RT}}\,\,{\text{ = }}\,\,{\text{10}}{\text{.7}}\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into area of a triangle formula or equivalent.</p>
<p>\({\text{RT}}\,\,{\text{ = }}\,\,{\text{7}}{\text{.64}}\,{\text{m (7}}{\text{.64285}}...{\text{m)}}\) <em><strong>(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> The answer is \({\text{7}}{\text{.64}}\,{\text{m}}\), <strong>the units are required.</strong></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Question 2: Trigonometry and area<br>The response to this question was mixed, with many fully correct attempts. Those failing to score 6 marks often either lost a mark due to the use of Pythagoras and premature rounding or due to an incorrect trigonometric ratio used in a right angled triangle. The use of sine and cosine rule often led to errors.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 2: Trigonometry and area<br>The response to this question was mixed, with many fully correct attempts. Those failing to score 6 marks often either lost a mark due to the use of Pythagoras and premature rounding or due to an incorrect trigonometric ratio used in a right angled triangle. The use of sine and cosine rule often led to errors.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Each day a supermarket records the midday temperature and how many cold drinks are sold on that day. The following table shows the supermarket’s data for the last 6 days. This data is also shown on a scatter diagram.</p>
<p><img 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" alt></p>
<p><img 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" alt></p>
<p>Write down</p>
<p>i) the mean temperature, \({\bar x}\) ;</p>
<p>ii) the mean number of cold drinks sold, \({\bar y}\) .</p>
<p> </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>Draw the line of best fit on the scatter diagram.</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>Use the line of best fit to estimate the number of cold drinks that are sold on a day when the midday temperature is \(10\,^\circ {\text{C}}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>i) \(14\) <em><strong>(A1)</strong></em></p>
<p> </p>
<p>ii) \(380\) <em><strong>(A1) (C2)</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img 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" alt></p>
<p><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1) (C2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for a <strong>straight</strong> line going through <strong>their</strong> mean point, <em><strong>(A1)</strong></em> for intercepting the y-axis between \(160\) and \(220\) inclusive. Follow through from part (a).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>an attempt to use their line of best fit to find \(y\) value at \(x = 10\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for an indication of use of their line of best fit (dotted lines or some indication of mark in the correct place on graph).</p>
<p><strong>OR</strong></p>
<p>\(13.4\,(10) + 192\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into the regression equation, \(y = 13.4x + 192\).</p>
<p>\( = 326\) <em><strong>(A1)</strong></em><strong>(ft) <em><strong>(C2)</strong></em></strong></p>
<p><strong>Note:</strong> Follow through from part (b). Accept answers between \(310\) and \(340\), inclusive.</p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Question 9: Linear regression.</p>
<p>The correct means were usually written down. Many candidates drew a line of best fit that did not go through their \((\bar x,\,\,\bar y)\). Almost all candidates were able to use the line of best fit (either the one they had drawn or the regression line found using their GDC) to make a reasonable estimate. Feedback from teachers suggests that many are using line of best fit and line of regression as synonyms. This is not the case; both are explicitly mentioned in the guide and candidates are expected to understand both terms.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin-top: 0cm;"><span style="font-size: 11.0pt; font-family: 'Arial','sans-serif'; color: #3f3f3f;">Question 9: Linear regression.</span></p>
<p style="margin-top: 0cm; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; text-align: start; widows: 2; -webkit-text-stroke-width: 0px; word-spacing: 0px;"><span style="font-size: 11.0pt; font-family: 'Arial','sans-serif'; color: #3f3f3f;">The correct means were usually written down. Many candidates drew a line of best fit that did not go through their \((\bar x,\,\,\bar y)\). Almost all candidates were able to use the line of best fit (either the one they had drawn or the regression line found using their GDC) to make a reasonable estimate. Feedback from teachers suggests that many are using line of best fit and line of regression as synonyms. This is not the case; both are explicitly mentioned in the guide and candidates are expected to understand both terms.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin-top: 0cm;"><span style="font-size: 11.0pt; font-family: 'Arial','sans-serif'; color: #3f3f3f;">Question 9: Linear regression.</span></p>
<p style="margin-top: 0cm; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; text-align: start; widows: 2; -webkit-text-stroke-width: 0px; word-spacing: 0px;"><span style="font-size: 11.0pt; font-family: 'Arial','sans-serif'; color: #3f3f3f;">The correct means were usually written down. Many candidates drew a line of best fit that did not go through their \((\bar x,\,\,\bar y)\). Almost all candidates were able to use the line of best fit (either the one they had drawn or the regression line found using their GDC) to make a reasonable estimate. Feedback from teachers suggests that many are using line of best fit and line of regression as synonyms. This is not the case; both are explicitly mentioned in the guide and candidates are expected to understand both terms.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br>