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</div><h2>SL Paper 1</h2><div class="specification">
<p class="p1">Let \(f(x) = {(x - 5)^3}\), for \(x \in \mathbb{R}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find \({f^{ - 1}}(x)\).</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"><span class="s1">Let \(g\) </span>be a function so that \((f \circ g)(x) = 8{x^6}\)<span class="s1">. Find \(g(x)\).</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">interchanging \(x\) and \(y\) (seen anywhere) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><em>eg</em>\(\;\;\;x = {(y - 5)^3}\)</p>
<p class="p1">evidence of correct manipulation <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1"><em>eg</em>\(\;\;\;y - 5 = \sqrt[3]{x}\)</p>
<p class="p1">\({f^{ - 1}}(x) = \sqrt[3]{x} + 5\;\;\;({\text{accept }}5 + {x^{\frac{1}{3}}},{\text{ }}y = 5 + \sqrt[3]{x})\) <span class="Apple-converted-space"> </span><strong><em>A1 <span class="Apple-converted-space"> </span>N2</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: <span class="Apple-converted-space"> </span></strong>If working shown, and they do not interchange \(x\) and \(y\), award <strong><em>A1A1M0 </em></strong>for \(\sqrt[3]{y} + 5\).</p>
<p class="p1">If no working shown, award <strong><em>N1 </em></strong>for \(\sqrt[3]{y} + 5\).</p>
<table class="t1" cellspacing="0" cellpadding="0">
<tbody>
<tr>
<td class="td1" valign="top">
<p class="p3"> </p>
</td>
</tr>
</tbody>
</table>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>METHOD 1</strong></p>
<p class="p1">attempt to form composite (in any order) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><em>eg</em>\(\;\;\;g\left( {{{(x - 5)}^3}} \right),{\text{ }}{\left( {g(x) - 5} \right)^3} = 8{x^6},{\text{ }}f(2{x^2} + 5)\)</p>
<p class="p1">correct working <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1"><em>eg</em>\(\;\;\;g - 5 = 2{x^2},{\text{ }}{\left( {(2{x^2} + 5) - 5} \right)^3}\)</p>
<p class="p1">\(g(x) = 2{x^2} + 5\) <span class="Apple-converted-space"> </span><strong><em>A1 <span class="Apple-converted-space"> </span>N2</em></strong></p>
<p class="p1"><strong>METHOD 2</strong></p>
<p class="p1">recognising inverse relationship <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><em>eg</em>\(\;\;\;{f^{ - 1}}(8{x^6}) = g(x),{\text{ }}{f^{ - 1}}(f \circ g)(x) = {f^{ - 1}}(8{x^6})\)</p>
<p class="p1">correct working</p>
<p class="p1"><em>eg</em>\(\;\;\;g(x) = \sqrt[3]{{(8{x^6})}} + 5\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1">\(g(x) = 2{x^2} + 5\) <span class="Apple-converted-space"> </span><strong><em>A1 <span class="Apple-converted-space"> </span>N2</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-family: times new roman,times; font-size: medium;">Let \(f(x) = {\log _p}(x + 3)\) for \(x > - 3\) . Part of the graph of <em>f</em> is shown below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/folly.png" alt></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The graph passes through A(6, 2) , has an <em>x</em>-intercept at (−2, 0) and has an asymptote </span><span style="font-family: times new roman,times; font-size: medium;">at \(x = - 3\) .</span></p>
<p> </p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find <em>p</em> .</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The graph of <em>f</em> is reflected in the line \(y = x\) to give the graph of <em>g</em> .</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Write down the <em>y</em>-intercept of the graph of <em>g</em> .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Sketch the graph of <em>g</em> , noting clearly any asymptotes and the image of A.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The graph of \(f\) is reflected in the line \(y = x\) to give the graph of \(g\) .<br></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find \(g(x)\) .</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 style="font-family: times new roman,times; font-size: medium;">evidence of substituting the point A <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(2 = {\log _p}(6 + 3)\) </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">manipulating logs <em><strong>A1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \({p^2} = 9\) </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(p = 3\) <em><strong>A2 N2</strong> </em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[4 marks] </span></strong></em></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;">(i) \(y = - 2\) (accept \((0{\text{, }} - 2))\) <em><strong>A1 N1 </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/frank.png" alt></span><em><strong><span style="font-family: times new roman,times; font-size: medium;"> A1A1A1A1 N4</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note</strong>: Award <em><strong>A1</strong></em> for asymptote at \(y = - 3\) , </span><span style="font-family: times new roman,times; font-size: medium;"><em><strong>A1</strong></em> for an increasing function that is concave up, <em><strong>A1 </strong></em></span><span style="font-family: times new roman,times; font-size: medium;">for a positive <em>x</em>-intercept and a negative <em>y</em>-intercept, </span><span style="font-family: times new roman,times; font-size: medium;"><em><strong>A1</strong></em> for passing through the point \((2{\text{, }}6)\) .<br></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em><strong>[5 marks]</strong></em> </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;"><strong>METHOD 1</strong> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">recognizing that \(g = {f^{ - 1}}\) <em><strong>(R1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">evidence of valid approach <em><strong>(M1) </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. switching <em>x</em> and <em>y</em> (seen anywhere), solving for <em>x</em> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct manipulation <em><strong>(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \({3^x} = y + 3\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(g(x) = {3^x} - 3\) <em><strong>A1 N3</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>METHOD 2</strong> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">recognizing that \(g(x) = {a^x} + b\) <em><strong>(R1)</strong></em> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">identifying vertical translation <em><strong>(A1) </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. graph shifted down 3 units, \(f(x) - 3\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">evidence of valid approach <em><strong>(M1) </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. substituting point to identify the base </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(g(x) = {3^x} - 3\) <em><strong>A1 N3</strong> </em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[4 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;">In part (a), many candidates successfully substituted the point A to find the base of the logarithm, although some candidates lost a mark for not showing their manipulation of the logarithm equation into the exponential equation. </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 number of candidates who correctly stated the <em>y</em>-intercept was \( - 2\) had difficulty sketching the graph of the reflection in the line \(y = x\) . A number of candidates graphed directly on the question paper rather than sketching their own graph; candidates should be reminded to show all working for Section B on separate paper. Some correct sketches did not have the position of A indicated. Many candidates had difficulty reflecting the asymptote. </span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Part (c) was often well done, with candidates showing clear and correct working. </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The most successful candidates clearly appreciated the linkage between the question parts. </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;">Let \(f(x) = 6 + 6\sin x\) . Part of the graph of <em>f</em> is shown below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/abba.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The shaded region is enclosed by the curve of <em>f</em> , the <em>x</em>-axis, and the <em>y</em>-axis.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Solve for \(0 \le x < 2\pi \)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) \(6 + 6\sin x = 6\) ;</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) \(6 + 6\sin x = 0\) .</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">a(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Write down the exact value of the <em>x</em>-intercept of <em>f</em> , for \(0 \le x < 2\pi \) .</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The area of the shaded region is <em>k</em> . Find the value of <em>k</em> , giving your answer in </span><span style="font-family: times new roman,times; font-size: medium;">terms of \(\pi \) .</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Let \(g(x) = 6 + 6\sin \left( {x - \frac{\pi }{2}} \right)\) . </span><span style="font-family: times new roman,times; font-size: medium;">The graph of <em>f</em> is transformed to the graph of <em>g</em>.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Give a full geometric description of this transformation.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Let \(g(x) = 6 + 6\sin \left( {x - \frac{\pi }{2}} \right)\) . </span><span style="font-family: times new roman,times; font-size: medium;">The graph of <em>f</em> is transformed to the graph of <em>g</em>.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Given that \(\int_p^{p + \frac{{3\pi }}{2}} {g(x){\rm{d}}x} = k\) and \(0 \le p < 2\pi \) , write down the two values of <em>p</em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) \(\sin x = 0\) <em><strong>A1</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(x = 0\) , \(x = \pi \) <em><strong>A1A1 N2</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(ii) \(\sin x = - 1\) <em><strong>A1</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(x = \frac{{3\pi }}{2}\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1 N1</span></strong></em></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[5 marks]</span></strong></em></p>
<div class="question_part_label">a(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(\frac{{3\pi }}{2}\) <em><strong>A1 N1</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[1 mark]</span></strong></em></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;">evidence of using anti-differentiation <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(\int_0^{\frac{{3\pi }}{2}} {(6 + 6\sin x){\rm{d}}x} \)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct integral \(6x - 6\cos x\) (seen anywhere) <em><strong>A1A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct substitution <em><strong>(A1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(6\left( {\frac{{3\pi }}{2}} \right) - 6\cos \left( {\frac{{3\pi }}{2}} \right) - ( - 6\cos 0)\) , \(9\pi - 0 + 6\)</span></p>
<p><span style="font-family: Times New Roman; font-size: medium;">\(k = 9\pi + 6\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1A1 N3</span></strong></em></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;"> [6 marks]</span></strong></em></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;">translation of \(\left( {\begin{array}{*{20}{c}}<br>{\frac{\pi }{2}}\\<br>0<br>\end{array}} \right)\) <em><strong>A1A1 N2</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;"> [2 marks]</span></strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">recognizing that the area under <em>g</em> is the same as the shaded region in <em>f</em> <em><strong>(M1)</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(p = \frac{\pi }{2}\) , \(p = 0\) <em><strong>A1A1 N3</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[3 marks]</span></strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Many candidates again had difficulty finding the common angles in the trigonometric </span><span style="font-family: times new roman,times; font-size: medium;">equations. In part (a), some did not show sufficient working in solving the equations. Others </span><span style="font-family: times new roman,times; font-size: medium;">obtained a single solution in (a)(i) and did not find another. Some candidates worked in </span><span style="font-family: times new roman,times; font-size: medium;">degrees; the majority worked in radians.</span></p>
<div class="question_part_label">a(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">While some candidates appeared to use their understanding of the graph of the original </span><span style="font-family: times new roman,times; font-size: medium;">function to find the <em>x</em>-intercept in part (b), most used their working from part (a)(ii) sometimes </span><span style="font-family: times new roman,times; font-size: medium;">with follow-through on an incorrect answer.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Most candidates recognized the need for integration in part (c) but far fewer were able to see </span><span style="font-family: times new roman,times; font-size: medium;">the solution through correctly to the end. Some did not show the full substitution of the limits, </span><span style="font-family: times new roman,times; font-size: medium;">having incorrectly assumed that evaluating the integral at 0 would be 0; without this working, </span><span style="font-family: times new roman,times; font-size: medium;">the mark for evaluating at the limits could not be earned. Again, many candidates had trouble </span><span style="font-family: times new roman,times; font-size: medium;">working with the common trigonometric values.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">While there was an issue in the wording of the question with the given domains, this did not </span><span style="font-family: times new roman,times; font-size: medium;">appear to bother candidates in part (d). This part was often well completed with candidates </span><span style="font-family: times new roman,times; font-size: medium;">using a variety of language to describe the horizontal translation to the right by \(\frac{\pi }{2}\) .</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates who attempted part (e) realized that the integral was equal to the value that they had found in part (c), but a majority tried to integrate the function <em>g</em> without success. Some candidates used sketches to find one or both values for <em>p</em>. The problem in the wording of the question did not appear to have been noticed by candidates in this part either.</span></p>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = {x^2}\) and \(g(x) = 2{(x - 1)^2}\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The graph of <em>g</em> can be obtained from the graph of <em>f</em> using two transformations.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Give a full geometric description of each of the two transformations.</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 style="font-family: times new roman,times; font-size: medium;">The graph of <em>g</em> is translated by the vector \(\left( {\begin{array}{*{20}{c}}<br>3\\<br>{ - 2}<br>\end{array}} \right)\) to give the graph of <em>h</em>.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The point \(( - 1{\text{, }}1)\) on the graph of <em>f</em> is translated to the point P on the graph of <em>h</em>.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> Find the coordinates of P.</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 style="font-family: times new roman,times; font-size: medium;">in any order </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">translated 1 unit to the right <em><strong>A1 N1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">stretched vertically by factor 2 <em><strong>A1 N1</strong> </em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[2 marks]</span></strong></em></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;"><strong>METHOD 1</strong> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">finding coordinates of image on <em>g</em> <em><strong>(A1)(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \( - 1 + 1 = 0\) , \(1 \times 2 = 2\) , \(( - 1{\text{, }}1) \to ( - 1 + 1{\text{, }}2 \times 1)\) , \((0{\text{, }}2)\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">P is (3, 0) <em><strong>A1A1 N4</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>METHOD 2</strong> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(h(x) = 2{(x - 4)^2} - 2\) <em><strong>(A1)(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">P is \((3{\text{, }}0)\) <em><strong>A1A1 N4</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;">The translation was often described well as horizontal (or shift) one unit right. There was considerable difficulty describing the vertical stretch as it was often referred to as "stretch by 2" or "amplitude of 2". A full description should include the name (e.g. vertical stretch) and value for full marks. Candidates also had difficulty applying two consecutive transformations to a single point. Often the translations were applied directly to \(( - 1{\text{, }}1)\) instead of first mapping from <em>f</em> to <em>g</em> . A good number of candidates correctly found \(h(x)\), but most could not find P from this 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;">The translation was often described well as horizontal (or shift) one unit right. There was considerable difficulty describing the vertical stretch as it was often referred to as "stretch by 2" or "amplitude of 2". A full description should include the name (e.g. vertical stretch) and value for full marks. Candidates also had difficulty applying two consecutive transformations to a single point. Often the translations were applied directly to \(( - 1{\text{, }}1)\) instead of first mapping from <em>f</em> to <em>g</em> . A good number of candidates correctly found \(h(x)\), but most could not find P from this function. </span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider \(f(x) = {x^2} + qx + r\). The graph of \(f\) has a minimum value when \(x = - 1.5\).</p>
<p class="p1">The distance between the two zeros of \(f\) <span class="s1">is 9</span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that the two zeros are 3 and \( - 6\)<span class="s1">.</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 \(q\) and of \(r\).</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">recognition that the \(x\)<span class="s1">-coordinate of the vertex is \( - 1.5\) </span>(seen anywhere) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)axis of symmetry is \( - 1.5\), sketch, \(f'( - 1.5) = 0\)</p>
<p class="p1">correct working to find the zeroes <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\( - 1.5 \pm 4.5\)</p>
<p class="p1">\(x = - 6\) and \(x = 3\) <span class="Apple-converted-space"> </span><strong><em>AG <span class="Apple-converted-space"> </span>N0</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"><strong>METHOD 1 (using factors)</strong></p>
<p class="p1">attempt to write factors <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\((x - 6)(x + 3)\)</p>
<p class="p1">correct factors <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\((x - 3)(x + 6)\)</p>
<p class="p1"><span class="Apple-converted-space">\(q = 3,{\text{ }}r = - 18\) </span><strong><em>A1A1 <span class="Apple-converted-space"> </span>N3</em></strong></p>
<p class="p1"><strong>METHOD 2 (using derivative or vertex)</strong></p>
<p class="p1">valid approach to find \(q\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\(f'( - 1.5) = 0,{\text{ }} - \frac{q}{{2a}} = - 1.5\)</p>
<p class="p1"><span class="Apple-converted-space">\(q = 3\) </span><strong><em>A1</em></strong></p>
<p class="p1">correct substitution <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\({3^2} + 3(3) + r = 0,{\text{ }}{( - 6)^2} + 3( - 6) + r = 0\)</p>
<p class="p1"><span class="Apple-converted-space">\(r = - 18\) </span><strong><em>A1</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\(q = 3,{\text{ }}r = - 18\) </span><span class="s1"><strong><em>N3</em></strong></span></p>
<p class="p1"><strong>METHOD 3 (solving simultaneously)</strong></p>
<p class="p1">valid approach setting up system of two equations <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\(9 + 3q + r = 0,{\text{ }}36 - 6q + r = 0\)</p>
<p class="p1">one correct value</p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\(q = 3,{\text{ }}r = - 18\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">correct substitution <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\({3^2} + 3(3) + r = 0,{\text{ }}{( - 6)^2} + 3( - 6) + r = 0,{\text{ }}{3^2} + 3q - 18 = 0,{\text{ }}36 - 6q - 18 = 0\)</p>
<p class="p1">second correct value <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\(q = 3,{\text{ }}r = - 18\)</p>
<p class="p1"><span class="Apple-converted-space">\(q = 3,{\text{ }}r = - 18\) </span><strong><em>N3</em></strong></p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">As a ‘show that’ question, part a) required a candidate to independently find the answers. Again, too many candidates used the given answers (of 3 and \( - 6\)) to show that the two zeros were 3 and \( - 6\) (a circular argument). Those who were able to recognize that the \(x\)-coordinate of the vertex is \( - 1.5\) tended to then use the given answers and work backwards thus scoring no further marks in part a).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Answers to part b) were more successful with a good variety of methods used and correct solutions seen.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Consider the functions \(f(x)\) , \(g(x)\) and \(h(x)\) . The following table gives some values </span><span style="font-family: times new roman,times; font-size: medium;">associated with these functions.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><br><img style="display: block; margin-left: auto; margin-right: auto;" src="images/omt.png" alt></span></p>
</div>
<div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The following diagram shows parts of the graphs of \(h\) and \(h''\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img style="display: block; margin-left: auto; margin-right: auto;" src="images/jls.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">There is a point of inflexion on the graph of \(h\) at P, when \(x = 3\) .</span></p>
</div>
<div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Given that \(h(x) = f(x) \times g(x)\) ,<br></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Write down the value of \(g(3)\) , of \(f'(3)\) , and of \(h''(2)\) .</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 style="font-family: times new roman,times; font-size: medium;">Explain why P is a point of inflexion.</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 style="font-family: times new roman,times; font-size: medium;">find the \(y\)-coordinate of P.</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 style="font-family: times new roman,times; font-size: medium;">find the equation of the normal to the graph of \(h\) at P.</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">\(g(3) = - 18\) , \(f'(3) = 1\) , \(h''(2) = - 6\) <em><strong>A1A1A1 N3 </strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[3 marks] </span></strong></em></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;">\(h''(3) = 0\) <em><strong>(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">valid reasoning <em><strong>R1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg </em> \({h''}\) changes sign at \(x = 3\) , change in concavity of \(h\) at \(x = 3\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">so P is a point of inflexion <strong><em>AG N0 </em></strong></span></p>
<p><strong><em><span style="font-family: times new roman,times; font-size: medium;">[2 marks] </span></em></strong></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;">writing \(h(3)\) as a product of \(f(3)\) and \(g(3)\) <em><strong>A1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg </em> \(f(3) \times g(3)\) , \(3 \times ( - 18)\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(h(3) = - 54\) <em><strong>A1 N1 </strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[2 marks] </span></strong></em></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;">recognizing need to find derivative of \(h\) <em><strong>(R1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg </em> \({h'}\) , \(h'(3)\) </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to use the product rule (do <strong>not</strong> accept \(h' = f' \times g'\) ) <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg </em> \(h' = fg' + gf'\) , \(h'(3) = f(3) \times g'(3) + g(3) \times f'(3)\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct substitution <em><strong>(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg </em> \(h'(3) = 3( - 3) + ( - 18) \times 1\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(h'(3) = - 27\) <em><strong>A1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to find the gradient of the normal <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg </em> \( - \frac{1}{m}\) , \( - \frac{1}{{27}}x\) </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to substitute <strong>their</strong> coordinates and <strong>their</strong> normal gradient into the equation of a line <strong><em>(M1)</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg </em> \( - 54 = \frac{1}{{27}}(3) + b\) , \(0 = \frac{1}{{27}}(3) + b\) , \(y + 54 = 27(x - 3)\) , \(y - 54 = \frac{1}{{27}}(x + 3)\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct equation in any form <em><strong>A1 N4</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg </em> \(y + 54 = \frac{1}{{27}}(x - 3)\) , \(y = \frac{1}{{27}}x - 54\frac{1}{9}\)</span></p>
<p><em><span style="font-family: times new roman,times; font-size: medium;"><strong>[7 marks]</strong> </span></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;">Nearly all candidates who attempted to answer parts (a) and (c) did so correctly, as these questions simply required them to understand the notation being used and to read the values from the given table.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">In part (b), the majority of candidates earned one mark for stating that \(h''(x) = 0\) at point P. As this is not enough to determine a point of inflexion, very few candidates earned full marks on this 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;">Nearly all candidates who attempted to answer parts (a) and (c) did so correctly, as these questions simply required them to understand the notation being used and to read the values from the given table.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Part (d) proved to be quite challenging for even the strongest candidates, as almost none of them used the product rule to find \(h'(3)\). The most common error was to say \(h'(3) = f'(3) \times g'(3)\). Despite this error, many candidates were able to earn further method marks for their work in finding the equation of the normal. There were also a small number of candidates who were able to find the equation for \(h'(x)\) , and from that \(h''(x)\). These candidates were often successful in earning full marks, although this method was quite time-consuming.</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;">Let \(f(x) = 2x - 1\) and \(g(x) = 3{x^2} + 2\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find \({f^{ - 1}}(x)\) . </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 style="font-family: times new roman,times; font-size: medium;">Find \((f \circ g)(1)\) . </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 style="font-family: times new roman,times; font-size: medium;">interchanging <em>x</em> and <em>y</em> (seen anywhere) <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(x = 2y - 1\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct manipulation <em><strong>(A1) </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(x + 1 = 2y\) </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({f^{ - 1}}(x) = \frac{{x + 1}}{2}\) <strong><em>A1 N2</em> </strong></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[3 marks] </span></strong></em></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;"><strong>METHOD 1</strong> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to find or \(g(1)\) or \(f(1)\) <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(g(1) = 5\) <em><strong>(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(f(5) = 9\) <em><strong>A1 N2 </strong></em></span></p>
<p><em><span style="font-family: times new roman,times; font-size: medium;"><strong>[3 marks]</strong> </span></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>METHOD 2</strong> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to form composite (in any order) <em><strong>(M1) </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(2(3{x^2} + 2) - 1\) , \(3{(2x - 1)^2} + 2\) </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\((f \circ g)(1) = 2(3 \times {1^2} + 2) - 1\) \(( = 6 \times {1^2} + 3)\) <em><strong>(A1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\((f \circ g)(1) = 9\) <em><strong>A1 N2</strong> </em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[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 answered correctly by nearly all 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;">This question was answered correctly by nearly all candidates. In part (b), there were a few who seemed unfamiliar with the notation for composition of functions, and attempted to multiply the functions rather than finding the composite, and there were a few who found the correct composite function but failed to substitute in \(x = 1\) to find the value.<br></span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagram below shows the graph of a function \(f\) , for \( - 1 \le x \le 2\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img style="display: block; margin-left: auto; margin-right: auto;" src="images/rachel.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Write down the value of \(f(2)\).<br></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 style="font-family: times new roman,times; font-size: medium;">Write down the value of </span><span style="font-family: times new roman,times; font-size: medium;">\({f^{ - 1}}( - 1)\) .</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 style="font-family: times new roman,times; font-size: medium;">Sketch the graph of \({f^{ - 1}}\) on the grid below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/milly.png" alt></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">\(f(2) = 3\) <strong><em>A1 N1</em> </strong></span></p>
<p><strong><em><span style="font-family: times new roman,times; font-size: medium;">[1 mark] </span></em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">\({f^{ - 1}}( - 1) = 0\) <strong><em>A2 N2 </em></strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong><em>[2 marks]<br></em></strong></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;"><strong>EITHER</strong> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to draw \(y = x\) on grid <em><strong>(M1)</strong> </em></span></p>
<p><strong><span style="font-family: times new roman,times; font-size: medium;">OR </span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to reverse <em><strong>x</strong></em> and <em><strong>y</strong></em> coordinates <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg </em> writing or plotting <strong>at least two</strong> of the points </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(( - 2, - 1)\) , \(( - 1,0)\) , \((0,1)\) , \((3,2)\)</span></p>
<p><strong><span style="font-family: times new roman,times; font-size: medium;">THEN </span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct graph <em><strong>A2 N3</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/eggs.png" alt></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[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;">In part (a) of this question, most candidates were able to find the value of \(f(2)\) correctly, while some had trouble finding \({f^{ - 1}}( - 1)\). Many candidates tried to find an equation for the function, or to make tables of values to help them find their answers. The intent of this question was to read the answers from the given graph. Candidates should be reminded that when the command term is "write down", there is no need for them to do large amounts of working.</span></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<div style="font-size: 13.28px; font-family: sans-serif; left: 96.032px; top: 207.867px; transform: scale(1.02607, 1); transform-origin: 0% 0% 0px;" dir="ltr" data-font-name="Helvetica" data-canvas-width="337.5776100605965"><span style="font-size: medium; font-family: times new roman,times;">In part (a) of this question, most candidates were able to find the value of \(f(2)\) correctly, while some had trouble finding \({f^{ - 1}}( - 1)\). Many candidates tried to find an equation for the function, or to make tables of values to help them find their answers. The intent of this question was to read the answers from the given graph. Candidates should be reminded that when the command term is "write down", there is no need for them to do large amounts of working.</span></div>
<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;">In part (b) of this question, candidates were generally successful in reversing the \(x\) and \(y\) coordinates of key points or reflecting in the \(y = x\) line to correctly sketch the graph of the inverse function. Common errors included not sketching the graph for the appropriate domain, or sketching the graph of \(f(-x)\) or the graph of \(-f(x)\).</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;">Let \(f(x) = \sqrt x \) . Line <em>L</em> is the normal to the graph of <em>f</em> at the point (4, 2) .</span></p>
</div>
<div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">In the diagram below, the shaded region <em>R</em> is bounded by the <em>x</em>-axis, the graph of <em>f</em> and </span><span style="font-family: times new roman,times; font-size: medium;">the line <em>L</em> .</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/ring.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Show that the equation of <em>L</em> is \(y = - 4x + 18\) .</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 style="font-family: times new roman,times; font-size: medium;">Point A is the <em>x</em>-intercept of <em>L</em> . Find the <em>x</em>-coordinate 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 style="font-family: times new roman,times;"><span style="font-size: medium;">Find an expression for the area of <em>R</em></span> .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The region <em>R</em> is rotated \(360^\circ \) about the <em>x</em>-axis. Find the volume of the solid formed, </span><span style="font-family: times new roman,times; font-size: medium;">giving your answer in terms of \(\pi \) .</span></p>
<div class="marks">[8]</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 style="font-family: times new roman,times; font-size: medium;">finding derivative <em><strong>(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(f'(x) = \frac{1}{2}{x^{\frac{1}{2}}},\frac{{1}}{{2\sqrt x }}\) </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct value of derivative or its negative reciprocal (seen anywhere) <em><strong>A1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(\frac{1}{{2\sqrt 4 }}\) , \(\frac{1}{4}\) </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">gradient of normal = \(\frac{1}{{{\text{gradient of tangent}}}}\) (seen anywhere) <em><strong>A1 </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \( - \frac{1}{{f'(4)}} = - 4\) , \( - 2\sqrt x \) </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">substituting into equation of line (for normal) <em><strong> M1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(y - 2 = - 4(x - 4)\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(y = - 4x + 18\) <em><strong>AG N0</strong> </em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[4 marks] </span></strong></em></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;">recognition that \(y = 0\) at A <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \( - 4x + 18 = 0\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(x = \frac{{18}}{4}\) \(\left( { = \frac{9}{2}} \right)\) <em><strong>A1 N2</strong> </em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[2 marks] </span></strong></em></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;">splitting into two appropriate parts (areas and/or integrals) <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct expression for area of <em>R</em> <em><strong>A2 N3</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. area of <em>R</em> = \(\int_0^4 {\sqrt x } {\rm{d}}x + \int_4^{4.5} {( - 4x + 18){\rm{d}}x} \) , \(\int_0^4 {\sqrt x } {\rm{d}}x + \frac{1}{2} \times 0.5 \times 2\) (triangle) </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note</strong>: Award <em><strong>A1</strong></em> if d<em>x</em> is missing. </span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[3 marks] </span></strong></em></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;">correct expression for the volume from \(x = 0\) to \(x = 4\) <em><strong>(A1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(V = \int_0^4 {\pi \left[ {f{{(x)}^2}} \right]} {\rm{d}}x\) , \({\int_0^4 {\pi \sqrt x } ^2}{\rm{d}}x\) , \(\int_0^4 {\pi x{\rm{d}}x} \)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(V = \left[ {\frac{1}{2}\pi {x^2}} \right]_0^4\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(V = \pi \left( {\frac{1}{2} \times 16 - \frac{1}{2} \times 0} \right)\) <em><strong>(A1)</strong></em></span></p>
<p><span style="font-family: Times New Roman; font-size: medium;">\(V = 8\pi \) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;">finding the volume from \(x = 4\) to \(x = 4.5\)</span></p>
<p><strong> <span style="font-family: times new roman,times; font-size: medium;">EITHER</span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">recognizing a cone <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(V = \frac{1}{3}\pi {r^2}h\)</span></p>
<p><span style="font-family: Times New Roman; font-size: medium;">\(V = \frac{1}{3}\pi {(2)^2} \times \frac{1}{2}\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">(A1)</span></strong></em></p>
<p><span style="font-family: Times New Roman; font-size: medium;">\( = \frac{{2\pi }}{3}\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;">total volume is \(8\pi + \frac{2}{3}\pi \) \(\left( { = \frac{{26}}{3}\pi } \right)\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1 N4</span></strong></em></p>
<p><strong> <span style="font-family: times new roman,times; font-size: medium;">OR</span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> \(V = \pi \int_4^{4.5} {{{( - 4x + 18)}^2}{\rm{d}}x} \) <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: Times New Roman; font-size: medium;">\( = \int_4^{4.5} {\pi (16{x^2} - 144x + 324){\rm{d}}x} \)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\( = \pi \left[ {\frac{{16}}{3}{x^3} - 72{x^2} + 324x} \right]_4^{4.5}\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: Times New Roman; font-size: medium;">\( = \frac{{2\pi }}{3}\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;">total volume is \(8\pi + \frac{2}{3}\pi \) \(\left( { = \frac{{26}}{3}\pi } \right)\) <em><strong>A1 N4</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;"> [8 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-family: times new roman,times; font-size: medium;">Parts (a) and (b) were well done by most candidates. </span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Parts (a) and (b) were well done by most candidates. </span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">While quite a few candidates understood that both functions must be used to find the area in part (c), very few were actually able to write a correct expression for this area and this was due to candidates not knowing that they needed to integrate from \(0\) to \(4\) and then from \(4\) to \(4.5\). </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;">On part (d), some candidates were able to earn follow through marks by setting up a volume expression, but most of these expressions were incorrect. If they did not get the expression for the area correct, there was little chance for them to get part (d) correct. </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">For those candidates who used their expression in part (c) for (d), there was a surprising amount of them who incorrectly applied distributive law of the exponent with respect to the addition or subtraction. </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;">Let \(f(x) = 3{(x + 1)^2} - 12\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Show that \(f(x) = 3{x^2} + 6x - 9\) .</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">For the graph of <em>f</em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) write down the coordinates of the vertex;</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(ii) write down the <em>y</em>-intercept;</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(iii) find both <em>x</em>-intercepts.</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">b(i), (ii) and (iii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Hence</strong> sketch the graph of <em>f</em> .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(g(x) = {x^2}\) . The graph of <em>f</em> may be obtained from the graph of <em>g</em> by the following two transformations</span></p>
<p style="margin-left: 60px;"><span style="font-family: times new roman,times; font-size: medium;">a stretch of scale factor <em>t</em> in the <em>y</em>-direction,</span></p>
<p style="margin-left: 60px;"><span style="font-family: times new roman,times; font-size: medium;">followed by a translation of </span><span style="font-family: times new roman,times; font-size: medium;">\(\left( \begin{array}{l}<br>p\\<br>q<br>\end{array} \right)\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Write down \(\left( \begin{array}{l}<br>p\\<br>q<br>\end{array} \right)\) </span><span style="font-family: times new roman,times; font-size: medium;">and the value of <em>t</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(f(x) = 3({x^2} + 2x + 1) - 12\) <em><strong>A1</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"> \( = 3{x^2} + 6x + 3 - 12\) <em><strong>A1</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"> \( = 3{x^2} + 6x - 9\) <em><strong>AG N0</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[2 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) vertex is \(( - 1, - 12)\) <em><strong>A1A1 N2</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(ii) \(y = - 9\) , or \((0, - 9)\) <em><strong>A1 N1</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(iii) evidence of solving \(f(x) = 0\) <em><strong>M1</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. factorizing, formula</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">correct working <em><strong>A1</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \(3(x + 3)(x - 1) = 0\) , \(x = \frac{{ - 6 \pm \sqrt {36 + 108} }}{6}\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(x = - 3\) , \(x = 1\) , or \(( - 3{\text{, }}0){\text{, }}(1{\text{, }}0)\) <em><strong>A1A1 N2</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[7 marks]</span></strong></em></p>
<div class="question_part_label">b(i), (ii) and (iii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/ava.png" alt></span><em><strong><span style="font-family: times new roman,times; font-size: medium;"> A1A1A1 N3</span></strong></em></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><strong>Note</strong>: Award <em><strong>A1</strong></em> for a parabola opening upward, </span><span style="font-family: times new roman,times; font-size: medium;"><em><strong>A1</strong></em> for vertex in approximately correct position, </span><span style="font-family: times new roman,times; font-size: medium;"><em><strong>A1</strong></em> for intercepts in approximately correct positions. Scale and labelling not required.</span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[3 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(\left( \begin{array}{l}<br>p\\<br>q<br>\end{array} \right) = \left( \begin{array}{l}<br>- 1\\<br>- 12<br>\end{array} \right)\) , \(t = 3\) <em><strong>A1A1A1 N3</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[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;">
[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), (ii) and (iii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = 7 - 2x\) and \(g(x) = x + 3\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find \((g \circ f)(x)\) .</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 style="font-family: times new roman,times; font-size: medium;">Write down \({g^{ - 1}}(x)\) .</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 style="font-family: times new roman,times; font-size: medium;">Find \((f \circ {g^{ - 1}})(5)\) .</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">attempt to form composite <em><strong>(M1)</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \(g(7 - 2x)\) , \(7 - 2x + 3\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\((g \circ f)(x) = 10 - 2x\) <em><strong>A1 N2</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[2 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\({g^{ - 1}}(x) = x - 3\) <em><strong>A1 N1</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[1 mark]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><strong><span style="font-family: times new roman,times; font-size: medium;">METHOD 1</span></strong></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">valid approach <em><strong>(M1)</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \({g^{ - 1}}(5)\) , \(2\) , \(f(5)\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(f(2) = 3\) <em><strong>A1 N2</strong></em></span></p>
<p align="LEFT"><strong><span style="font-family: times new roman,times; font-size: medium;">METHOD 2</span></strong></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">attempt to form composite of <em>f</em> and \({g^{ - 1}}\) <em><strong>(M1)</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \((f \circ {g^{ - 1}})(x) = 7 - 2(x - 3)\) , \(13 - 2x\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\((f \circ {g^{ - 1}})(5) = 3\) <em><strong>A1 N2</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[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;">A majority of candidates found success in the opening question. Common errors in (a) were to give \(f \circ g\) or to multiply <em>f</em> by <em>g</em>. </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;">For (b) some gave the inverse as the reciprocal function \(\frac{1}{{x + 3}}\) , or wrote \(x = y + 3\) . </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;">Most candidates chose to find a composite in (c), sometimes making simple errors when working with brackets and a negative sign. Only a handful used the more efficient \(f(2) = 3\) . Additionally, it was not uncommon for candidates to give a correct substitution but not complete the result. Simple expressions such as \((7 - 2x) + 3\) should be finished as \(10 - 2x\) . </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 following diagram shows the graph of \(y = f(x)\), for </span><span style="font-family: 'times new roman', times; font-size: medium; background-color: #f7f7f7;"><span style="font-family: 'times new roman', times; font-size: medium;"><span style="line-height: normal;">\( - 4 \le x \le 5\).</span></span></span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><br><img src="images/maths_3.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<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 value of \(f( - 3)\).</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;">Write down the value of </span>\({f^{ - 1}}(1)\).</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 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;">Find the domain of \({f^{ - 1}}\).</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 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;">On the grid above, sketch the graph of \({f^{ - 1}}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f( - 3) = - 1\) <strong><em>A1 N1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[1 mark]</em></strong></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 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({f^{ - 1}}(1) = 0\) (accept \(y = 0\)) <strong><em>A1 N1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><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 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;">domain of \({f^{ - 1}}\) is range of \(<span style="font: 20.5px 'Times New Roman';">f\)<em> </em></span><strong><em>(R1)</em></strong></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>eg</em> \({\text{R}}f = {\text{D}}{f^{ - 1}}\)</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;">correct answer <strong><em>A1 N2</em></strong></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>eg</em> \( - 3 \leqslant x \leqslant 3,{\text{ }}x \in [ - 3,{\text{ }}3]{\text{ (accept }} - 3 < x < 3,{\text{ }} - 3 \leqslant y \leqslant 3)\)</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;"><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 style="font-family: arial, helvetica, sans-serif;"><br><img src="images/maths_3c_markscheme.png" alt> <span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>A1A1 N2</em></strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </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;"><strong>Note: </strong>Graph must be approximately correct reflection in \(y = x\).</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;"> <strong>Only</strong> if the shape is approximately correct, award the following:</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;"><strong><em> A1</em></strong> for <em>x</em>-intercept at \(1\), and <strong><em>A1</em></strong> for endpoints within circles.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </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;"><strong><em>[2 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"> </p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagram below shows part of the graph of \(f(x) = (x - 1)(x + 3)\) .</span></p>
<p><span style="font-family: TimesNewRomanPSMT;"><br><img style="display: block; margin-left: auto; margin-right: auto;" src="images/wash.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(a) Write down the \(x\)-intercepts of the graph of \(f\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(b) Find the coordinates of the vertex of the graph of \(f\) .</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Write down the \(x\)-intercepts of the graph of \(f\) .</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 style="font-family: times new roman,times; font-size: medium;">Find the coordinates of the vertex of the graph of \(f\) .</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 style="font-family: times new roman,times; font-size: medium;">(a) \(x = 1\) , \(x = - 3\) (accept (\(1\), \(0\)), (\( - 3\), \(0\)) ) <strong><em>A1A1 N2 </em></strong></span></p>
<p><strong><em><span style="font-family: times new roman,times; font-size: medium;">[2 marks]</span></em></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(b) <strong>METHOD 1</strong> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to find \(x\)-coordinate <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> \(\frac{{1 + - 3}}{2}\) , \(x = \frac{{ - b}}{{2a}}\) , \(f'(x) = 0\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct value, \(x = - 1\) (may be seen as a coordinate in the answer) <strong><em>A1</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to find <strong>their</strong> \(y\)-coordinate <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> \(f( - 1)\) , \( - 2 \times 2\) , \(y = \frac{{ - D}}{{4a}}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(y = - 4\) <strong><em>A1</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">vertex (\( - 1\), \( - 4\)) <em><strong>N3 </strong></em></span><em><strong><span style="font-family: times new roman,times; font-size: medium;"> </span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>METHOD 2</strong> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to complete the square <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> \({x^2} + 2x + 1 - 1 - 3\) </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to put into vertex form <strong><em>(M1)</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> \({(x + 1)^2} - 4\) , \({(x - 1)^2} + 4\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">vertex (\( - 1\), \( - 4\)) <em><strong>A1A1 N3 </strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[4 marks] </span></strong></em></p>
<div class="question_part_label">.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">\(x = 1\) , \(x = - 3\) (accept (\(1\), \(0\)), (\( - 3\), \(0\)) ) <strong><em>A1A1 N2 </em></strong></span></p>
<p><strong><em><span style="font-family: times new roman,times; font-size: medium;">[2 marks]</span></em></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </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;"><strong>METHOD 1</strong> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to find \(x\)-coordinate <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> \(\frac{{1 + - 3}}{2}\) , \(x = \frac{{ - b}}{{2a}}\) , \(f'(x) = 0\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct value, \(x = - 1\) (may be seen as a coordinate in the answer) <strong><em>A1</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to find <strong>their</strong> \(y\)-coordinate <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> \(f( - 1)\) , \( - 2 \times 2\) , \(y = \frac{{ - D}}{{4a}}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(y = - 4\) <strong><em>A1</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">vertex (\( - 1\), \( - 4\)) <em><strong>N3 </strong></em></span><em><strong><span style="font-family: times new roman,times; font-size: medium;"> </span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>METHOD 2</strong> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to complete the square <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> \({x^2} + 2x + 1 - 1 - 3\) </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to put into vertex form <strong><em>(M1)</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> \({(x + 1)^2} - 4\) , \({(x - 1)^2} + 4\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">vertex (\( - 1\), \( - 4\)) <em><strong>A1A1 N3 </strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[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;">Most candidates recognized the values of the x-intercepts from the factorized form of the function. Candidates also showed little difficulty finding the vertex of the graph, and employed a variety of techniques: averaging \(x\)-intercepts, using \(x = \frac{{ - b}}{{2a}}\) , completing the square.</span></p>
<div class="question_part_label">.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates recognized the values of the x-intercepts from the factorized form of the function. Candidates also showed little difficulty finding the vertex of the graph, and employed a variety of techniques: averaging \(x\)-intercepts, using \(x = \frac{{ - b}}{{2a}}\) , completing the square.</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 recognized the values of the x-intercepts from the factorized form of the function. Candidates also showed little difficulty finding the vertex of the graph, and employed a variety of techniques: averaging \(x\)-intercepts, using \(x = \frac{{ - b}}{{2a}}\) , completing the square.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let \(f\left( x \right) = \sqrt {x + 2} \) for <em>x</em> ≥ 2 and <em>g</em>(<em>x</em>) = 3<em>x</em> − 7 for \(x \in \mathbb{R}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down <em>f </em>(14).</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 \(\left( {g \circ f} \right)\) (14).</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 g<sup>−1</sup>(<em>x</em>).</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em>f </em>(14) = 4   <em><strong>A1 N1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to substitute   <em><strong>(M1)</strong></em></p>
<p>eg  <em>g</em> (4), 3 × 4 − 7</p>
<p>5Â Â Â <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>interchanging <em>x</em> and <em>y</em> (seen anywhere)Â Â Â <em><strong>(M1)</strong></em></p>
<p>eg  <em>x</em> = 3<em>y</em> − 7</p>
<p>evidence of correct manipulation   <em><strong>(A1)</strong></em></p>
<p>eg  <em>x</em> + 7 = 3<em>y</em></p>
<p>\({g^{ - 1}}\left( x \right) = \frac{{x + 7}}{3}\)Â Â Â <strong><em>A1 N3</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<p>Â </p>
<p>Â </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 \(f(x) = 8x + 3\) and \(g(x) = 4x\), for \(x \in \mathbb{R}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down \(g(2)\).</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">Find \((f \circ g)(x)\).</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 \({f^{ - 1}}(x)\).</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 class="p1"><span class="Apple-converted-space">\(g(2) = 8\) </span><strong><em>A1 <span class="Apple-converted-space"> </span>N1</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">attempt to form composite (in any order) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"><span class="s1"><em>eg</em>\(\,\,\,\,\,\)\(f(4x),{\text{ }}4 \times (8x + 3)\)</span></p>
<p class="p1"><span class="s2">\((f \circ g)(x) = 32x + 3\) </span><strong><em>A1 <span class="Apple-converted-space"> </span>N2</em></strong></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">interchanging \(x\) and \(y\) (may be seen at any time) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"><span class="s1"><em>eg</em></span>\(\,\,\,\,\,\)\(x = 8y + 3\)</p>
<p class="p1"><span class="s2">\({f^{ - 1}}(x) = \frac{{x - 3}}{8}\,\,\,\,\,\left( {{\text{accept }}\frac{{x - 3}}{8},{\text{ }}y = \frac{{x - 3}}{8}} \right)\) <span class="Apple-converted-space"> </span></span><strong><em>A1 <span class="Apple-converted-space"> </span>N2</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;">
<p class="p1">This question was successfully answered by most candidates. The inverse notation was sometimes mistakenly interpreted as derivative or reciprocal.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">This question was successfully answered by most candidates. The inverse notation was sometimes mistakenly interpreted as derivative or reciprocal.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">This question was successfully answered by most candidates. The inverse notation was sometimes mistakenly interpreted as derivative or reciprocal.</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;">Let \(f(x) = 4x - 2\) and \(g(x) = - 2{x^2} + 8\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find \({f^{ - 1}}(x)\) .</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 style="font-family: times new roman,times; font-size: medium;">Find \((f \circ g)(1)\) .</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 style="font-family: times new roman,times; font-size: medium;">interchanging \(x\) and \(y\) (seen anywhere) <strong><em>(M1)</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> \(x = 4y - 2\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">evidence of correct manipulation <strong><em>(A1) </em></strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> \(x + 2 = 4y\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({f^{ - 1}}(x) = \frac{{x + 2}}{4}\) (accept \(y = \frac{{x + 2}}{4}\) , \(\frac{{x + 2}}{4}\) , \({f^{ - 1}}(x) = \frac{1}{4}x + \frac{1}{2}\) <em><strong>A1 N2 </strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[3 marks] </span></strong></em></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;"><strong>METHOD 1</strong> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to substitute \(1\) into \(g(x)\) <strong><em>(M1)</em></strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> \(g(1) = - 2 \times {1^2} + 8\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(g(1) = 6\) <em><strong>(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(f(6) = 22\) <strong><em>A1 N3</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>METHOD 2</strong> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to form composite function (in any order) <strong><em> (M1)</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> \((f \circ g)(x) = 4( - 2{x^2} + 8) - 2\) \(( = - 8{x^2} + 30)\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct substitution </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> \((f \circ g)(1) = 4( - 2 \times {1^2} + 8) - 2\) , \( - 8 + 30\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(f(6) = 22\) <em><strong>A1 N3 </strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[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;">
<div style="font-size: 13.28px; font-family: sans-serif; left: 96.032px; top: 687.933px; transform: scale(1.03628, 1); transform-origin: 0% 0% 0px;" dir="ltr" data-font-name="Helvetica" data-canvas-width="186.53088555905344"><span style="font-family: times new roman,times; font-size: medium;">The overwhelming majority of candidates answered both parts of this question correctly. There were a few who seemed unfamiliar with the inverse notation and answered part (a) with the derivative or the reciprocal of the function.</span></div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<div style="font-size: 13.28px; font-family: sans-serif; left: 96.032px; top: 687.933px; transform: scale(1.03628, 1); transform-origin: 0% 0% 0px;" dir="ltr" data-font-name="Helvetica" data-canvas-width="186.53088555905344"><span style="font-family: times new roman,times; font-size: medium;">The overwhelming majority of candidates answered both parts of this question correctly. A few candidates made arithmetic errors in part (b) which kept them from finding the correct answer.</span></div>
<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;">Let \(f(x) = 3{x^2} - 6x + p\). The equation \(f(x) = 0\) has two equal roots.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<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 <strong>value </strong>of the discriminant.</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 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;">Hence, show that \(p = 3\).</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 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 \(f\)has its vertex on the \(x\)-axis.</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;">Find the coordinates of the vertex of the graph of \(f\).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p 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 \(f\) has its vertex on the \(x\)-axis.</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 solution of \(f(x) = 0\).</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 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 \(f\) has its vertex on the \(x\)-axis.</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 function can be written in the form \(f(x) = a{(x - h)^2} + k\). Write down the value of \(a\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p 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 \(f\) has its vertex on the \(x\)-axis.</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 function can be written in the form \(f(x) = a{(x - h)^2} + k\). Write down the value of \(h\).<em><br></em></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<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 \(f\) has its vertex on the \(x\)-axis.</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 function can be written in the form \(f(x) = a{(x - h)^2} + k\). Write down the value of \(k\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d(iii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<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 \(f\) has its vertex on the \(x\)-axis.</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 graph of a function \(g\) is obtained from the graph of \(f\) by a reflection of \(f\) in the \(x\)-axis, followed by a translation by the vector \(\left( \begin{array}{c}0\\6\end{array} \right)\). Find \(g\), giving your answer in the form \(g(x) = A{x^2} + Bx + C\).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="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;">correct value \(0\), or \(36 - 12p\) <strong><em>A2 N2</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"><br></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></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 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">correct equation which clearly leads to \(p = 3\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \(36 - 12p = 0,{\text{ }}36 = 12p\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(p = 3\) <strong><em>AG N0</em></strong></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;"><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 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>METHOD 1</strong></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;">valid approach <strong><em>(M1)</em></strong></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>eg</em> \(x = - \frac{b}{{2a}}\)</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;">correct working <strong><em>A1</em></strong></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>eg</em> \( - \frac{{( - 6)}}{{2(3)}},{\text{ }}x = \frac{6}{6}\)</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;">correct answers <strong><em>A1A1 N2</em></strong></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>eg</em> \(x = 1,{\text{ }}y = 0;{\text{ }}(1,{\text{ }}0)\)</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;"><strong>METHOD 2</strong></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;">valid approach <strong><em>(M1)</em></strong></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>eg</em> \(f(x) = 0\), factorisation, completing the square</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;">correct working <strong><em>A1</em></strong></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>eg</em> \({x^2} - 2x + 1 = 0,{\text{ }}(3x - 3)(x - 1),{\text{ }}f(x) = 3{(x - 1)^2}\)</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;">correct answers <strong><em>A1A1 N2</em></strong></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>eg</em> \(x = 1,{\text{ }}y = 0;{\text{ }}(1,{\text{ }}0)\)</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;"><strong>METHOD 3</strong></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;">valid approach using derivative <strong><em>(M1)</em></strong></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>eg</em> \(f'(x) = 0,{\text{ }}6x - 6\)</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;">correct equation <strong><em>A1</em></strong></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>eg</em> \(6x - 6 = 0\)</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;">correct answers <strong><em>A1A1 N2</em></strong></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>eg</em> \(x = 1,{\text{ }}y = 0;{\text{ }}(1,{\text{ }}0)\)</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;"><strong><em>[4 marks]</em></strong></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: 21.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 1\) <strong><em>A1 N1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<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;">\(a = 3\) <strong><em>A1 N1</em></strong></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;"><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">d(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<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;">\(h = 1\) <strong><em>A1 N1</em></strong></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;"><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">d(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<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;">\(k = 0\) <strong><em>A1 N1</em></strong></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;"><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">d(iii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">attempt to apply vertical reflection <em><strong>(M1)</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \( - f(x),{\text{ }} - 3{(x - 1)^2}\), sketch</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;">attempt to apply vertical shift 6 units up <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \( - f(x) + 6\), vertex \((1, 6)\)</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;">transformations performed correctly (in correct order) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \( - 3{(x - 1)^2} + 6,{\text{ }} - 3{x^2} + 6x - 3 + 6\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(g(x) = - 3{x^2} + 6x + 3\) <strong><em>A1 N3</em></strong></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;"><strong><em>[4 marks]</em></strong></span></p>
<p> </p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d(iii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider a function \(f\). The line <em>L</em><sub>1</sub> with equation \(y = 3x + 1\) is a tangent to the graph of \(f\) when \(x = 2\)</p>
</div>
<div class="specification">
<p>Let \(g\left( x \right) = f\left( {{x^2} + 1} \right)\) and P be the point on the graph of \(g\) where \(x = 1\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down \(f'\left( 2 \right)\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find \(f\left( 2 \right)\).</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>Show that the graph of <em>g</em> has a gradient of 6 at P.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <em>L</em><sub>2</sub> be the tangent to the graph of <em>g</em> at P. <em>L</em><sub>1</sub>Â intersects <em>L</em><sub>2</sub> at the point Q.</p>
<p>Find the y-coordinate of Q.</p>
<div class="marks">[7]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>recognize that \(f'\left( x \right)\)Â is the gradient of the tangent at \(x\)Â Â Â <strong><em>(M1)</em></strong></p>
<p><em>eg </em>  \(f'\left( x \right) = m\)</p>
<p>\(f'\left( 2 \right) = 3\)Â (accept <em>m</em> = 3)Â Â Â <em><strong>A1 N2</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>recognize that \(f\left( 2 \right) = y\left( 2 \right)\)   <em><strong>(M1)</strong></em></p>
<p><em>eg</em>Â \(f\left( 2 \right) = 3 \times 2 + 1\)</p>
<p>\(f\left( 2 \right) = 7\)Â Â Â <em><strong>A1 N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognize that the gradient of the graph of <em>g</em> is \(g'\left( x \right)\)   <em><strong>(M1)</strong></em></p>
<p>choosing chain rule to find \(g'\left( x \right)\)Â Â Â <em><strong>(M1)</strong></em></p>
<p><em>eg</em>Â Â \(\frac{{{\text{d}}y}}{{{\text{d}}u}} \times \frac{{{\text{d}}u}}{{{\text{d}}x}},\,\,u = {x^2} + 1,\,\,u' = 2x\)</p>
<p>\(g'\left( x \right) = f'\left( {{x^2} + 1} \right) \times 2x\)Â Â Â <em><strong>A2</strong></em></p>
<p>\(g'\left( 1 \right) = 3 \times 2\)Â Â Â <em><strong>A1</strong></em></p>
<p>\(g'\left( 1 \right) = 6\)Â Â Â <em><strong>AG N0 </strong></em></p>
<p><em><strong>[5 marks]</strong></em></p>
<p>Â </p>
<p>Â </p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Â at Q, <em>L</em><sub>1</sub> =Â <em>L</em><sub>2</sub>Â (seen anywhere)Â Â Â <em><strong> (M1)</strong></em></p>
<p>recognize that the gradient of <em>L</em><sub>2</sub>Â is <em>g'</em>(1)Â Â (seen anywhere)Â Â <em><strong> Â (M1)</strong></em><br><em>eg</em>Â <em>m</em> = 6</p>
<p>finding <em>g </em>(1)  (seen anywhere)   <em><strong>(A1)</strong></em><br><em>eg  </em>\(g\left( 1 \right) = f\left( 2 \right),\,\,g\left( 1 \right) = 7\)</p>
<p>attempt to substitute gradient and/or coordinates into equation of a straight line   <em><strong>M1</strong></em><br><em>eg  </em>\(y - g\left( 1 \right) = 6\left( {x - 1} \right),\,\,y - 1 = g'\left( 1 \right)\left( {x - 7} \right),\,\,7 = 6\left( 1 \right) + {\text{b}}\)</p>
<p>correct equation for <em>L</em><sub>2</sub> </p>
<p><em>eg  </em>\(y - 7 = 6\left( {x - 1} \right),\,\,y = 6x + 1\)   <em><strong>A1</strong></em></p>
<p>correct working to find Q    <em><strong>(A1)</strong></em><br><em>eg  </em>same <em>y</em>-intercept, \(3x = 0\)</p>
<p>\(y = 1\)Â Â Â <em><strong>A1 N2</strong></em></p>
<p><em><strong>[7 marks]</strong></em></p>
<p>Â </p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(f(t) = a\cos b(t - c) + d\) , \(t \ge 0\) . Part of the graph of \(y = f(t)\) is given below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/evening.png" alt></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">When \(t = 3\) , there is a maximum value of 29, at M.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> When \(t = 9\) , there is a minimum value of 15.</span></p>
<p> </p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Find the value of <em>a</em>.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(ii) Show that \(b = \frac{\pi }{6}\) </span><span style="font-family: times new roman,times; font-size: medium;">.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(iii) Find the value of <em>d</em>.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(iv) Write down a value for <em>c</em>.</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">a(i), (ii), (iii) and (iv).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The transformation <em>P</em> is given by a horizontal stretch of a scale factor of \(\frac{1}{2}\) </span><span style="font-family: times new roman,times; font-size: medium;">, followed </span><span style="font-family: times new roman,times; font-size: medium;">by a translation of \(\left( {\begin{array}{*{20}{c}}<br>3\\<br>{ - 10}<br>\end{array}} \right)\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Let \({M'}\) be the image of M under <em>P</em>. Find the coordinates of \({M'}\) .</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 style="font-family: times new roman,times; font-size: medium;">The graph of <em>g</em> is the image of the graph of <em>f</em> under <em>P</em>.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find \(g(t)\) in the form \(g(t) = 7\cos B(t - c) + D\) .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">The graph of <em>g</em> is the image of the graph of <em>f</em> under <em>P</em>.</span></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Give a full geometric description of the transformation that maps the graph of <em>g </em></span><span style="font-family: times new roman,times; font-size: medium;">to the graph of <em>f</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 style="font-family: times new roman,times; font-size: medium;">(i) attempt to substitute <em><strong>(M1) </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(a = \frac{{29 - 15}}{2}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(a = 7\) (accept \(a = - 7\) ) <em><strong>A1 N2</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) \({\text{period}} = 12\) <em><strong>(A1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(b = \frac{{2\pi }}{{12}}\) <em><strong>A1 </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(b = \frac{\pi }{6}\) <em><strong>AG N0</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(iii) attempt to substitute <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(d = \frac{{29 + 15}}{2}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(d = 22\) <em><strong>A1 N2</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(iv) \(c = 3\) (accept \(c = 9\) from \(a = - 7\) ) <em><strong>A1 N1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note</strong>: Other correct values for <em>c</em> can be found, \(c = 3 \pm 12k\) , \(k \in \mathbb{Z}\) . </span></p>
<p><strong><em> <span style="font-family: times new roman,times; font-size: medium;">[7 marks] </span></em></strong></p>
<div class="question_part_label">a(i), (ii), (iii) and (iv).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">stretch takes 3 to 1.5 <em><strong>(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">translation maps \((1.5{\text{, }}29)\) to \((4.5{\text{, }}19)\) (so \({M'}\) is \((4.5{\text{, }}19)\)) </span><em><span style="font-family: times new roman,times; font-size: medium;"><strong>A1 N2</strong> </span></em></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[2 marks] </span></strong></em></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;">\(g(t) = 7\cos \frac{\pi }{3}\left( {t - 4.5} \right) + 12\) <strong><em>A1A2A1 N4</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note</strong>: Award <em><strong>A1</strong></em> for \(\frac{\pi }{3}\) , <em><strong>A2</strong></em> for 4.5, <em><strong>A1</strong></em> for 12.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Other correct values for <em>c</em> can be found, \(c = 4.5 \pm 6k\) , \(k \in \mathbb{Z}\) . </span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[4 marks] </span></strong></em></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;">translation \(\left( {\begin{array}{*{20}{c}}<br>{ - 3}\\<br>{10}<br>\end{array}} \right)\) <em><strong> (A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">horizontal stretch of a scale factor of 2 <strong><em>(A1) </em></strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">completely correct description, in correct order <strong><em>A1 N3</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. translation \(\left( {\begin{array}{*{20}{c}}<br>{ - 3}\\<br>{10}<br>\end{array}} \right)\) then horizontal stretch of a scale factor of 2</span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[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-family: times new roman,times; font-size: medium;">This question was the most difficult on the paper. Where candidates attempted this question, part (a) was answered satisfactorily. </span></p>
<div class="question_part_label">a(i), (ii), (iii) and (iv).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Few answered part (b) correctly as most could not interpret the horizontal stretch. </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;">Few answered part (b) correctly as most could not interpret the horizontal stretch. As a result, there were many who were unable to answer part (c) although follow through marks were often obtained from incorrect answers in both parts (a) and (b). The link between the answer in (b) and the value of <em>C</em> in part (c) was lost on all but the most attentive. </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 part (d), some candidates could name the transformations required, although only a handful provided the correct order of the transformations to return the graph to its original state. </span></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: 12.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(f(x) = a{(x - h)^2} + k\). The vertex of the graph of \(f\) is at \((2, 3)\) and the graph passes through \((1, 7)\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><span>Write down the value of </span></span><span style="font-family: 'times new roman', times; font-size: medium;"><span>\(h\)</span></span><em style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 21px; background-color: #f7f7f7;"><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-style: normal; line-height: normal;"> </span></span></em><span style="font-family: 'times new roman', times; font-size: medium;"><span>and of </span></span><span style="font-family: 'times new roman', times; font-size: medium;"><span>\(k\).</span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px 'Times New Roman';"> </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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find the value of \(a\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px 'Times New Roman';"><em style="font-family: 'times new roman', times; font-size: medium; background-color: #f7f7f7;">\(h = 2,{\text{ }}k = 3\) </em><strong style="font-family: 'times new roman', times; font-size: medium; background-color: #f7f7f7;"><em>A1A1 N2</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px 'Times New Roman';"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px 'Times New Roman';"> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f;"><span><span style="font-family: 'times new roman', times; font-size: medium;"><span style="line-height: normal;">attempt to substitute \((1,7)\) in any order into </span></span><strong style="color: #3f3f3f; font-family: 'times new roman', times; font-size: medium; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">their </strong><span style="font-family: 'times new roman', times; font-size: medium;"><span style="line-height: normal;">\(f(x)\) </span></span><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>(M1)</em></strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \(7 = a{(1 - 2)^2} + 3{\text{, }}7 = a{(1 - 3)^2} + 2{\text{, }}1 = a{(7 - 2)^2} + 3\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium; background-color: #f7f7f7;">correct equation </span><strong style="font-family: 'times new roman', times; font-size: medium; background-color: #f7f7f7;"><em>(A1)</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \(7 = a + 3\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>a </em>= 4 <strong><em>A1 N2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagram below shows the graph of a function \(f(x)\) , for \( - 2 \le x \le 3\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/M12P1TZ2Q5.jpg" alt> </span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Sketch the graph of \(f( - x)\) on the grid below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/M12P1TZ2Q5a.jpg" alt></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The graph of <em>f</em> is transformed to obtain the graph of <em>g</em> . The graph of <em>g</em> is </span><span style="font-family: times new roman,times; font-size: medium;">shown below.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/M12P1TZ2Q5b.jpg" alt></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The function <em>g</em> can be written in the form \(g(x) = af(x + b)\) . Write down the </span><span style="font-family: times new roman,times; font-size: medium;">value of <em>a</em> and of <em>b</em> .</span></p>
<p align="LEFT"> </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><br><img src="images/M12P1TZ2Q5ams.jpg" alt> <span style="font-family: times new roman,times; font-size: medium;"><em><strong>A2 N2</strong> </em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[2 marks] </span></strong></em></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;">\(a = - 2,b = - 1\) <strong><em>A2A2 N4</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note</strong>: Award <em><strong>A1</strong></em> for \(a = 2\) , <em><strong>A1</strong></em> for \(b = 1\) . </span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[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;">In part (a) of this question, a large number of candidates correctly sketched the graph of \(f( - x)\) , as asked. A fairly common error, however, was to graph \( - f(x)\) .</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 (b), many candidates seemed to recognize that the value of <em>a</em> was related to a vertical stretch, though some omitted the negative required for the vertical reflection. Similarly, some candidates gave a positive value for <em>b</em>. </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;">Let \(f(x) = {x^2} + 4\) and \(g(x) = x - 1\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find \((f \circ g)(x)\) .</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 style="font-family: times new roman,times; font-size: medium;">The vector \(\left( {\begin{array}{*{20}{c}}<br>3\\<br>{ - 1}<br>\end{array}} \right)\) translates the graph of \((f \circ g)\) to the graph of <em>h</em> .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find the coordinates of the vertex of the graph of <em>h</em> .</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 style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">The vector \(\left( {\begin{array}{*{20}{c}}<br>3\\<br>{ - 1}<br>\end{array}} \right)\) translates the graph of \((f \circ g)\) to the graph of <em>h</em> .</span></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Show that \(h(x) = {x^2} - 8x + 19\) .</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">The vector \(\left( {\begin{array}{*{20}{c}}<br>3\\<br>{ - 1}<br>\end{array}} \right)\) translates the graph of \((f \circ g)\) to the graph of <em>h</em> .</span></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The line \(y = 2x - 6\) is a tangent to the graph of <em>h</em> at the point P. Find the </span><span style="font-family: times new roman,times; font-size: medium;"><em>x</em>-coordinate of P.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">attempt to form composition (in any order) <em><strong>(M1)</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\((f \circ g)(x) = {(x - 1)^2} + 4\) \(({x^2} - 2x + 5)\) <em><strong>A1 N2</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[2 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><span style="font-family: times new roman,times; font-size: medium;">METHOD 1</span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">vertex of \(f \circ g\) at (1, 4) <em><strong>(A1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">evidence of appropriate approach <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. adding \(\left( {\begin{array}{*{20}{c}}<br>3\\<br>{ - 1}<br>\end{array}} \right)\) </span><span style="font-family: times new roman,times; font-size: medium;">to the coordinates of the vertex of \(f \circ g\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">vertex of <em>h</em> at (4, 3) <em><strong>A1 N3</strong></em></span></p>
<p><strong> <span style="font-family: times new roman,times; font-size: medium;">METHOD 2</span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to find \(h(x)\) <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \({((x - 3) - 1)^2} + 4 - 1\) , \(h(x) = (f \circ g)(x - 3) - 1\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(h(x) = {(x - 4)^2} + 3\) <em><strong>(A1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">vertex of <em>h</em> at (4, 3) <em><strong>A1 N3</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;"> [3 marks]</span></strong></em></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;">evidence of appropriate approach <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \({(x - 4)^2} + 3\) ,\({(x - 3)^2} - 2(x - 3) + 5 - 1\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">simplifying <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(h(x) = {x^2} - 8x + 16 + 3\) , \({x^2} - 6x + 9 - 2x + 6 + 4\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(h(x) = {x^2} - 8x + 19\) <em><strong>AG N0</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;"> [2 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><span style="font-family: times new roman,times; font-size: medium;">METHOD 1</span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">equating functions to find intersection point <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \({x^2} - 8x + 19 = 2x - 6\) , \(y = h(x)\)</span></p>
<p><span style="font-family: Times New Roman; font-size: medium;">\({x^2} - 10x + 25 + 0\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;">evidence of appropriate approach to solve <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. factorizing, quadratic formula</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">appropriate working <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \({(x - 5)^2} = 0\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> \(x = 5\) \((p = 5)\) <em><strong>A1 N3</strong></em></span></p>
<p><strong> <span style="font-family: times new roman,times; font-size: medium;">METHOD 2</span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to find \(h'(x)\) <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: Times New Roman; font-size: medium;">\(h(x) = 2x - 8\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;">recognizing that the gradient of the tangent is the derivative <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. gradient at \(p = 2\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(2x - 8 = 2\) \((2x = 10)\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(x = 5\) <em><strong>A1 N3</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;"> [5 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-family: times new roman,times; font-size: medium;">Candidates showed good understanding of finding the composite function in part (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;">There were some who did not seem to understand what the vector translation meant in part (b). </span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Candidates showed good understanding of manipulating the quadratic in part (c).</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;">There was more than one method to solve for <em>h</em> in part (d), and a pleasing number of candidates were successful in this part of the question. </span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<p class="p1">Let \(f(x) = m - \frac{1}{x}\), for \(x \ne 0\). The line \(y = x - m\) intersects the graph of \(f\) in two distinct points. Find the possible values of \(m\).</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p class="p1">valid approach <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p2"><em>eg</em>\(\,\,\,\,\,\)\(f = y,{\text{ }}m - \frac{1}{x} = x - m\)</p>
<p class="p1">correct working to eliminate denominator <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p2"><em>eg</em>\(\,\,\,\,\,\)\(mx - 1 = x(x - m),{\text{ }}mx - 1 = {x^2} - mx\)</p>
<p class="p1">correct quadratic equal to zero <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2"><em>eg</em>\(\,\,\,\,\,\)\({x^2} - 2mx + 1 = 0\)</p>
<p class="p1">correct reasoning <span class="Apple-converted-space"> </span><span class="s1"><strong><em>R1</em></strong></span></p>
<p class="p1"><span class="s2"><em>eg</em>\(\,\,\,\,\,\)</span>for two solutions, \({b^2} - 4ac > 0\)</p>
<p class="p1">correct substitution into the discriminant formula <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p2"><em>eg</em>\(\,\,\,\,\,\)\({( - 2m)^2} - 4\)</p>
<p class="p1">correct working <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p1"><span class="s2"><em>eg</em>\(\,\,\,\,\,\)\(4{m^2} > 4,{\text{ }}{m^2} = 1\)</span>, sketch of positive parabola on the \(x\)-axis</p>
<p class="p1">correct interval <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1 <span class="Apple-converted-space"> </span>N4</em></strong></span></p>
<p class="p2"><em>eg</em>\(\,\,\,\,\,\)\(\left| m \right| > 1,{\text{ }}m < - 1\) <span class="s3">or \(m > 1\)</span></p>
<p class="p3"><strong><em>[7 marks]</em></strong></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-family: times new roman,times; font-size: medium;">Let \(f(x) = 2{x^3} + 3\) and \(g(x) = {{\rm{e}}^{3x}} - 2\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Find \(g(0)\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Find \((f \circ g)(0)\) .</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find \({f^{ - 1}}(x)\) .</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 style="font-family: times new roman,times; font-size: medium;">(i) \(g(0) = {{\rm{e}}^0} - 2\) <em><strong>(A1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\( = - 1\) <em><strong> A1 N2</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) <strong>METHOD 1</strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">substituting answer from (i) <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \((f \circ g)(0) = f( - 1)\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct substitution \(f( - 1) = 2{( - 1)^3} + 3\) <em><strong>(A1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(f( - 1) = 1\) <em><strong>A1 N3</strong></em></span></p>
<p><strong> <span style="font-family: times new roman,times; font-size: medium;">METHOD 2</span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to find \((f \circ g)(x)\) <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \((f \circ g)(x) = f({{\rm{e}}^{3x}} - 2)\) \( = 2{({{\rm{e}}^{3x}} - 2)^3} + 3\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct expression for \((f \circ g)(x)\) <em><strong>(A1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(2{({{\rm{e}}^{3x}} - 2)^3} + 3\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\((f \circ g)(0) = 1\) <em><strong>A1 N3</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;"> [5 marks]</span></strong></em></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;">interchanging <em>x</em> and <em>y</em> (seen anywhere) <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(x = 2{y^3} + 3\) </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to solve <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \({y^3} = \frac{{x - 3}}{2}\) </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({f^{ - 1}}(x) = \sqrt[3]{{\frac{{x - 3}}{2}}}\) <em><strong>A1 N3</strong> </em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;"> [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 generally done well, although some students consider \({{\rm{e}}^0}\) to be 0, losing them a 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;">A few candidates composed in the wrong order. Most found the formula of the inverse correctly, even if in some cases there were errors when trying to isolate <em>x</em> (or <em>y</em>). A </span><span style="font-family: times new roman,times; font-size: medium;">common incorrect solution found was to find \(y = \sqrt[3]{{\frac{{x - 3}}{2}}}\) .</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let \(f(x) = {x^2}\). The following diagram shows part of the graph of \(f\).</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-11_om_17.08.23.png" alt="M17/5/MATME/SP1/ENG/TZ2/10"></p>
<p>The line \(L\) is the tangent to the graph of \(f\) at the point \({\text{A}}( - k,{\text{ }}{k^2})\), and intersects the \(x\)-axis at point B. The point C is \(( - k,{\text{ }}0)\).</p>
</div>
<div class="specification">
<p>The region \(R\) is enclosed by \(L\), the graph of \(f\), and the \(x\)-axis. This is shown in the following diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-11_om_17.07.29.png" alt="M17/5/MATME/SP1/ENG/TZ2/10.d"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down \(f'(x)\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the gradient of \(L\).</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>Show that the \(x\)-coordinate of B is \( - \frac{k}{2}\).</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of triangle ABC, giving your answer in terms of \(k\).</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>Given that the area of triangle ABC is \(p\) times the area of \(R\), find the value of \(p\).</p>
<div class="marks">[7]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(f'(x) = 2x\) <em><strong>A1</strong></em> <em><strong>N1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to substitute \(x = - k\) into their derivative <strong><em>(M1)</em></strong></p>
<p>gradient of \(L\) is \( - 2k\) <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1 </strong></p>
<p>attempt to substitute coordinates of A and their gradient into equation of a line <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\({k^2} = - 2k( - k) + b\)</p>
<p>correct equation of \(L\) in any form <strong><em>(A1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(y - {k^2} = - 2k(x + k),{\text{ }}y = - 2kx - {k^2}\)</p>
<p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(y = 0\)</p>
<p>correct substitution into \(L\) equation <strong><em>A1</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\( - {k^2} = - 2kx - 2{k^2},{\text{ }}0 = - 2kx - {k^2}\)</p>
<p>correct working <strong><em>A1</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(2kx = - {k^2}\)</p>
<p>\(x = - \frac{k}{2}\) <strong><em>AG</em></strong> <strong><em>N0</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\({\text{gradient}} = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}},{\text{ }} - 2k = \frac{{{\text{rise}}}}{{{\text{run}}}}\)</p>
<p>recognizing \(y = 0\) at B <strong><em>(A1)</em></strong></p>
<p>attempt to substitute coordinates of A and B into slope formula <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(\frac{{{k^2} - 0}}{{ - k - x}},{\text{ }}\frac{{ - {k^2}}}{{x + k}}\)</p>
<p>correct equation <strong><em>A1</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(\frac{{{k^2} - 0}}{{ - k - x}} = - 2k,{\text{ }}\frac{{ - {k^2}}}{{x + k}} = - 2k,{\text{ }} - {k^2} = - 2k(x + k)\)</p>
<p>correct working <strong><em>A1</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(2kx = - {k^2}\)</p>
<p>\(x = - \frac{k}{2}\) <strong><em>AG</em></strong> <strong><em>N0</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach to find area of triangle <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(\frac{1}{2}({k^2})\left( {\frac{k}{2}} \right)\)</p>
<p>area of \({\text{ABC}} = \frac{{{k^3}}}{4}\) <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1 (</strong>\(\int {f - {\text{triangle}}} \)<strong>)</strong></p>
<p>valid approach to find area from \( - k\) to 0 <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(\int_{ - k}^0 {{x^2}{\text{d}}x,{\text{ }}\int_0^{ - k} f } \)</p>
<p>correct integration (seen anywhere, even if <strong><em>M0 </em></strong>awarded) <strong><em>A1</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(\frac{{{x^3}}}{3},{\text{ }}\left[ {\frac{1}{3}{x^3}} \right]_{ - k}^0\)</p>
<p>substituting <strong>their </strong>limits into <strong>their </strong>integrated function and subtracting <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(0 - \frac{{{{( - k)}^3}}}{3}\), area from \( - k\) to 0 is \(\frac{{{k^3}}}{3}\)</p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>M0 </em></strong>for substituting into original or differentiated function.</p>
<p> </p>
<p>attempt to find area of \(R\) <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(\int_{ - k}^0 {f(x){\text{d}}x - {\text{ triangle}}} \)</p>
<p>correct working for \(R\) <strong><em>(A1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(\frac{{{k^3}}}{3} - \frac{{{k^3}}}{4},{\text{ }}R = \frac{{{k^3}}}{{12}}\)</p>
<p>correct substitution into \({\text{triangle}} = pR\) <strong><em>(A1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(\frac{{{k^3}}}{4} = p\left( {\frac{{{k^3}}}{3} - \frac{{{k^3}}}{4}} \right),{\text{ }}\frac{{{k^3}}}{4} = p\left( {\frac{{{k^3}}}{{12}}} \right)\)</p>
<p>\(p = 3\) <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong>METHOD 2 (</strong>\(\int {(f - L)} \)<strong>)</strong></p>
<p>valid approach to find area of \(R\) <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(\int_{ - k}^{ - \frac{k}{2}} {{x^2} - ( - 2kx - {k^2}){\text{d}}x + \int_{ - \frac{k}{2}}^0 {{x^2}{\text{d}}x,{\text{ }}\int_{ - k}^{ - \frac{k}{2}} {(f - L) + \int_{ - \frac{k}{2}}^0 f } } } \)</p>
<p>correct integration (seen anywhere, even if <strong><em>M0 </em></strong>awarded) <strong><em>A2</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(\frac{{{x^3}}}{3} + k{x^2} + {k^2}x,{\text{ }}\left[ {\frac{{{x^3}}}{3} + k{x^2} + {k^2}x} \right]_{ - k}^{ - \frac{k}{2}} + \left[ {\frac{{{x^3}}}{3}} \right]_{ - \frac{k}{2}}^0\)</p>
<p>substituting <strong>their </strong>limits into <strong>their </strong>integrated function and subtracting <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(\left( {\frac{{{{\left( { - \frac{k}{2}} \right)}^3}}}{3} + k{{\left( { - \frac{k}{2}} \right)}^2} + {k^2}\left( { - \frac{k}{2}} \right)} \right) - \left( {\frac{{{{( - k)}^3}}}{3} + k{{( - k)}^2} + {k^2}( - k)} \right) + (0) - \left( {\frac{{{{\left( { - \frac{k}{2}} \right)}^3}}}{3}} \right)\)</p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>M0 </em></strong>for substituting into original or differentiated function.</p>
<p> </p>
<p>correct working for \(R\) <strong><em>(A1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(\frac{{{k^3}}}{{24}} + \frac{{{k^3}}}{{24}},{\text{ }} - \frac{{{k^3}}}{{24}} + \frac{{{k^3}}}{4} - \frac{{{k^3}}}{2} + \frac{{{k^3}}}{3} - {k^3} + {k^3} + \frac{{{k^3}}}{{24}},{\text{ }}R = \frac{{{k^3}}}{{12}}\)</p>
<p>correct substitution into \({\text{triangle}} = pR\) <strong><em>(A1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(\frac{{{k^3}}}{4} = p\left( {\frac{{{k^3}}}{{24}} + \frac{{{k^3}}}{{24}}} \right),{\text{ }}\frac{{{k^3}}}{4} = p\left( {\frac{{{k^3}}}{{12}}} \right)\)</p>
<p>\(p = 3\) <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[7 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</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;">The following diagram shows the graph of a quadratic function <em>f</em> , for \(0 \le x \le 4\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/M12P1TZ2Q8.jpg" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The graph passes through the point P(0, 13) , and its vertex is the point V(2, 1) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The function can be written in the form \(f(x) = a{(x - h)^2} + k\) .</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Write down the value of <em>h</em> and of <em>k</em> .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Show that \(a = 3\) .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find \(f(x)\) , giving your answer in the form \(A{x^2} + Bx + C\) .</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Calculate the area enclosed by the graph of <em>f</em> , the <em>x</em>-axis, and the lines \(x = 2\) and \(x = 4\) .</span></p>
<div class="marks">[8]</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 style="font-family: times new roman,times; font-size: medium;">(i) \(h = 2\) , \(k = 1\) <em><strong>A1A1 N2</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) attempt to substitute coordinates of any point (except the vertex) </span><span style="font-family: times new roman,times; font-size: medium;">on the graph into <em>f</em> <strong><em>M1</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(13 = a{(0 - 2)^2} + 1\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">working towards solution <em><strong> A1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(13 = 4a + 1\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(a = 3\) <em><strong>AG N0</strong></em> </span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[4 marks] </span></strong></em></p>
<div class="question_part_label">a(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">attempting to expand <strong>their</strong> binomial <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(f(x) = 3({x^2} - 2 \times 2x + 4) + 1\) , \({(x - 2)^2} = {x^2} - 4x + 4\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct working <em><strong>(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(f(x) = 3{x^2} - 12x + 12 + 1\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(f(x) = 3{x^2} - 12x + 13\) (accept \(A = 3\) , \(B = - 12\) , \(C = 13\) ) <em><strong>A1 N2</strong> </em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[3 marks] </span></strong></em></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;"><strong>METHOD 1 </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">integral expression <em><strong>(A1) </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(\int_2^4 {(3{x^2}} - 12x + 13)\) , \(\int {f{\rm{d}}x} \)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({\rm{Area}} = [{x^3} - 6{x^2} + 13x]_2^4\) <em><strong>A1A1A1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Award <em><strong>A1</strong></em> for \({x^3}\) , <em><strong>A1</strong></em> for \( - 6{x^2}\) , <em><strong>A1</strong></em> for \(13x\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct substitution of <strong>correct</strong> limits into <strong>their</strong> expression <em><strong>A1A1 </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(({4^3} - 6 \times {4^2} + 13 \times 4) - ({2^3} - 6 \times {2^2} + 13 \times 2)\) , \(64 - 96 + 52 - (8 - 24 + 26)\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note</strong>: Award <em><strong>A1</strong></em> for substituting 4, <em><strong>A1</strong></em> for substituting 2. </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct working <em><strong>(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(64 - 96 + 52 - 8 + 24 - 26,20 - 10\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({\rm{Area}} = 10\) <em><strong> A1 N3</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em><strong>[8 marks] </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>METHOD 2</strong> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">integral expression <em><strong>(A1) </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(\int_2^4 {(3{{(x - 2)}^2}} + 1)\) , \(\int {f{\rm{d}}x} \)<br></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({\rm{Area}} = [{(x - 2)^3} + x]_2^4\) <em><strong>A2A1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note</strong>: Award <em><strong>A2</strong></em> for \({(x - 2)^3}\) , <em><strong>A1</strong></em> for \(x\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span> </p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct substitution of <strong>correct</strong> limits into <strong>their</strong> expression <em><strong>A1A1 </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \({(4 - 2)^3} + 4 - [{(2 - 2)^3} + 2]\) , \({2^3} + 4 - ({0^3} + 2)\) , \({2^3} + 4 - 2\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note</strong>: Award <em><strong>A1</strong></em> for substituting 4, <em><strong>A1</strong></em> for substituting 2. </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct working <em><strong>(A1) </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(8 + 4 - 2\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({\rm{Area}} = 10\) <em><strong>A1 N3</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em> <strong>[8 marks]</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong> METHOD 3 </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">recognizing area from 0 to 2 is same as area from 2 to 4 <em><strong>(R1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. sketch, \(\int_2^4 {f = \int_0^2 f } \)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">integral expression <em><strong>(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(\int_0^2 {(3{x^2}} - 12x + 13)\) , \(\int {f{\rm{d}}x} \)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({\rm{Area}} = [{x^3} - 6{x^2} + 13x]_0^2\) <em><strong>A1A1A1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note</strong>: Award <em><strong>A1</strong></em> for \({x^3}\) , <strong><em>A1</em></strong> for \( - 6{x^2}\) , <em><strong>A1</strong></em> for \(13x\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct substitution of <strong>correct</strong> limits into <strong>their</strong> expression <em><strong>A1(A1) </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(({2^3} - 6 \times {2^2} + 13 \times 2) - ({0^3} - 6 \times {0^2} + 13 \times 0)\) , \(8 - 24 + 26\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note</strong>: Award <em><strong>A1</strong></em> for substituting 2, <em><strong>(A1)</strong></em> for substituting 0. </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({\rm{Area}} = 10\) <em><strong>A1 N3</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em> <strong>[8 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;">In part (a), nearly all the candidates recognized that <em>h</em> and <em>k</em> were the coordinates of the vertex of the parabola, and most were able to successfully show that \(a = 3\) . Unfortunately, a few candidates did not understand the "show that" command, and simply verified that \(a = 3\) would work, rather than showing how to find \(a = 3\) . </span></p>
<div class="question_part_label">a(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">In part (b), most candidates were able to find \(f(x)\) in the required form. For a few candidates, algebraic errors kept them from finding the correct function, even though they started with correct values for <em>a</em>, <em>h</em> and <em>k</em>. </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 (c), nearly all candidates knew that they needed to integrate to find the area, but errors in integration, and algebraic and arithmetic errors prevented many from finding the correct area. </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 following diagram shows part of the graph of a quadratic function <em>f</em> .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/tent.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The <em>x</em>-intercepts are at \(( - 4{\text{, }}0)\) and \((6{\text{, }}0)\) , and the <em>y</em>-intercept is at \((0{\text{, }}240)\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Write down \(f(x)\) in the form \(f(x) = - 10(x - p)(x - q)\) .</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 style="font-family: times new roman,times; font-size: medium;">Find another expression for \(f(x)\) in the form \(f(x) = - 10{(x - h)^2} + k\) .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Show that \(f(x)\) can also be written in the form \(f(x) = 240 + 20x - 10{x^2}\) .</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">A particle moves along a straight line so that its velocity, \(v{\text{ m}}{{\text{s}}^{ - 1}}\) , at time <em>t</em> seconds is </span><span style="font-family: times new roman,times; font-size: medium;">given by \(v = 240 + 20t - 10{t^2}\) , for \(0 \le t \le 6\) .</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Find the value of<em> t</em> when the speed of the particle is greatest.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Find the acceleration of the particle when its speed is zero.</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">d(i) and (ii).</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: TimesNewRomanPS-ItalicMT; font-size: medium;"><span style="font-family: TimesNewRomanPS-ItalicMT; font-size: medium;">\(f(x) = - 10(x + 4)(x - 6)\)</span></span><span style="font-family: times new roman,times; font-size: medium;"> <em><strong>A1A1 N2</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[2 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><strong><span style="font-family: times new roman,times; font-size: medium;">METHOD 1</span></strong></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">attempting to find the <em>x</em>-coordinate of maximum point <strong><em>(M1)</em></strong></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. averaging the <em>x</em>-intercepts, sketch, \(y' = 0\) , axis of symmetry</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">attempting to find the <em>y</em>-coordinate of maximum point <strong><em> (M1)</em></strong></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \(k = - 10(1 + 4)(1 - 6)\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(f(x) = - 10{(x - 1)^2} + 250\) <em><strong>A1A1 N4</strong></em></span></p>
<p align="LEFT"><strong><span style="font-family: times new roman,times; font-size: medium;">METHOD 2</span></strong></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">attempt to expand \(f(x)\) <strong><em>(M1)</em></strong></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \( - 10({x^2} - 2x - 24)\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">attempt to complete the square <strong><em>(M1)</em></strong></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \( - 10({(x - 1)^2} - 1 - 24)\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(f(x) = - 10{(x - 1)^2} + 250\) <em><strong>A1A1 N4</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[4 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">attempt to simplify <strong><em>(M1)</em></strong></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. distributive property, \( - 10(x - 1)(x - 1) + 250\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">correct simplification <strong><em>A1</em></strong></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \( - 10({x^2} - 6x + 4x - 24)\) , \( - 10({x^2} - 2x + 1) + 250\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(f(x) = 240 + 20x - 10{x^2}\) <em><strong>AG N0</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[2 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) valid approach <strong><em>(M1)</em></strong></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. vertex of parabola, \(v'(t) = 0\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(t = 1\) <strong><em>A1 N2</em></strong></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(ii) recognizing \(a(t) = v'(t)\) <strong><em>(M1)</em></strong></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(a(t) = 20 - 20t\) <strong><em>A1A1</em></strong></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">speed is zero \( \Rightarrow t = 6\) <strong><em>(A1)</em></strong></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(a(6) = - 100\) (\({\text{m}}{{\text{s}}^{ - 2}}\)) <em><strong>A1 N3</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[7 marks]</span></strong></em></p>
<div class="question_part_label">d(i) and (ii).</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Parts (a) and (c) of this question were very well done by most 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 part (b), many candidates attempted to use the method of completing the square, but were unsuccessful dealing with the coefficient of \( - 10\). Candidates who recognized that the <em>x</em>-coordinate of the vertex was 1, then substituted this value into the function from part (a), were generally able to earn full marks here. </span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Parts (a) and (c) of this question were very well done by most 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 part (d), it was clear that many candidates were not familiar with the relationship between velocity and acceleration, and did not understand how those concepts were related to the graph which was given. A large number of candidates used time \(t = 1\) in part b(ii), rather than \(t = 6\) . To find the acceleration, some candidates tried to integrate the velocity function, rather than taking the derivative of velocity. Still others found the derivative in part b(i), but did not realize they needed to use it in part b(ii), as well.</span></p>
<div class="question_part_label">d(i) and (ii).</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Let \(f(x) = {x^2} - 4x + 5\).</p>
</div>
<div class="specification">
<p class="p1">The function can also be expressed in the form \(f(x) = {(x - h)^2} + k\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the equation of the axis of symmetry of the graph of \(f\).</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">(i) <span class="Apple-converted-space"> </span></span>Write down the value of \(h\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Find the value of \(k\).</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">correct approach <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p2"><span class="s1"><em>eg</em></span> \(\frac{{ - ( - 4)}}{2},{\text{ }}f'(x) = 2x - 4 = 0,{\text{ (}}{x^2} - 4x + 4) + 5 - 4\)</p>
<p class="p2"><span class="s2">\(x = 2\) </span>(must be an equation) <span class="s1"><strong><em>A1 N2</em></strong></span></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"> \(h = 2\)</span> <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1 <span class="Apple-converted-space"> </span>N1</em></strong></span></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span><strong>METHOD 1</strong></p>
<p class="p1">valid attempt to find \(k\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1"><span class="s2"><em>eg</em></span>\(\,\,\,\,\,\)\(f(2)\)</p>
<p class="p1">correct substitution into <strong>their </strong>function <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p1"><span class="s1"><em>eg</em>\(\,\,\,\,\,\)\({(2)^2} - 4(2) + 5\)</span></p>
<p class="p2"><span class="s3">\(k = 1\) <span class="Apple-converted-space"> </span></span><strong><em>A1 <span class="Apple-converted-space"> </span>N2</em></strong></p>
<p class="p1"><strong>METHOD 2</strong></p>
<p class="p1">valid attempt to complete the square <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1"><span class="s2"><em>eg</em>\(\,\,\,\,\,\)\({x^2} - 4x + 4\)</span></p>
<p class="p1">correct working <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p1"><span class="s1"><em>eg</em>\(\,\,\,\,\,\)\(({x^2} - 4x + 4) - 4 + 5,{\text{ }}{(x - 2)^2} + 1\)</span></p>
<p class="p2"><span class="s3">\(k = 1\) <span class="Apple-converted-space"> </span></span><strong><em>A1 <span class="Apple-converted-space"> </span>N2</em></strong></p>
<p class="p2"><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><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = \cos 2x\) and \(g(x) = 2{x^2} - 1\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find \(f\left( {\frac{\pi }{2}} \right)\) .</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 style="font-family: times new roman,times; font-size: medium;">Find \((g \circ f)\left( {\frac{\pi }{2}} \right)\) .</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 style="font-family: times new roman,times; font-size: medium;">Given that \((g \circ f)(x)\) can be written as \(\cos (kx)\) , find the value of <em>k</em>, \(k \in \mathbb{Z}\) .</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(f\left( {\frac{\pi }{2}} \right) = \cos \pi \) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">(A1)</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\( = - 1\) <em><strong>A1 N2</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[2 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\((g \circ f)\left( {\frac{\pi }{2}} \right) = g( - 1)\) \(( = 2{( - 1)^2} - 1)\) <em><strong>(A1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(= 1\) <em><strong>A1 N2</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\((g \circ f)(x) = 2{(\cos (2x))^2} - 1\) \(( = 2{\cos ^2}(2x) - 1)\) <em><strong>A1</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">evidence of \(2{\cos ^2}\theta - 1 = \cos 2\theta \) (seen anywhere) <em><strong>(M1)</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\((g \circ f)(x) = \cos 4x\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(k = 4\) <em><strong>A1 N2</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">In part (a), a number of candidates were not able to evaluate \(\cos \pi \) , either leaving it or </span><span style="font-family: times new roman,times; font-size: medium;">evaluating it incorrectly.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Almost all candidates evaluated the composite function in part (b) in the given order, many </span><span style="font-family: times new roman,times; font-size: medium;">earning follow-through marks for incorrect answers from part (a). On both parts (a) and (b), </span><span style="font-family: times new roman,times; font-size: medium;">there were candidates who correctly used double-angle formulas to come up with correct </span><span style="font-family: times new roman,times; font-size: medium;">answers; while this is a valid method, it required unnecessary additional work.</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 were not as successful in part (c). Many tried to use double-angle formulas, but either used the formula incorrectly or used it to write the expression in terms of \(\cos x\) and went no further. There were a number of cases in which the candidates "accidentally" came up with the correct answer based on errors or lucky guesses and did not earn credit for their final answer. Only a few candidates recognized the correct method of solution.</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;">Let \(f(x) = \ln (x + 5) + \ln 2\) , for \(x > - 5\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find \({f^{ - 1}}(x)\) .</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 style="font-family: times new roman,times; font-size: medium;">Let \(g(x) = {{\rm{e}}^x}\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find \((g \circ f)(x)\) , giving your answer in the form \(ax + b\) , where \(a,b \in \mathbb{Z}\) .</span></p>
<p> </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 align="LEFT"><strong><span style="font-family: times new roman,times; font-size: medium;">METHOD 1</span></strong></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(\ln (x + 5) + \ln 2 = \ln (2(x + 5))\) \(( = \ln (2x + 10))\) <em><strong>(A1)</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">interchanging <em>x</em> and <em>y</em> (seen anywhere) <strong><em>(M1)</em></strong></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \(x = \ln (2y + 10)\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">evidence of correct manipulation <em><strong>(A1)</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \({{\rm{e}}^x} = 2y + 10\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\({f^{ - 1}}(x) = \frac{{{{\rm{e}}^x} - 10}}{2}\) <strong><em>A1 N2</em></strong></span></p>
<p align="LEFT"><strong><span style="font-family: times new roman,times; font-size: medium;">METHOD 2</span></strong></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(y = \ln (x + 5) + \ln 2\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(y - \ln 2 = ln(x + 5)\) <em><strong>(A1)</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">evidence of correct manipulation <em><strong> (A1)</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \({{\rm{e}}^{y - \ln 2}} = x + 5\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">interchanging <em>x</em> and <em>y</em> (seen anywhere) <strong><em>(M1)</em></strong></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \({{\rm{e}}^{x - \ln 2}} = y + 5\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({f^{ - 1}}(x) = {{\rm{e}}^{x - \ln 2}} - 5\) <strong><em>A1 N2</em></strong></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[4 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><strong><span style="font-family: times new roman,times; font-size: medium;">METHOD 1</span></strong></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">evidence of composition in correct order <em><strong>(M1)</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \((g \circ f)(x) = g(\ln (x + 5) + \ln 2)\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\( = {{\rm{e}}^{\ln (2(x + 5))}} = 2(x + 5)\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\((g \circ f)(x) = 2x + 10\) <em><strong>A1A1 N2</strong></em></span></p>
<p align="LEFT"><strong><span style="font-family: times new roman,times; font-size: medium;">METHOD 2</span></strong></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">evidence of composition in correct order <em><strong>(M1)</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \((g \circ f)(x) = {{\rm{e}}^{\ln (x + 5) + \ln 2}}\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\( = {{\rm{e}}^{\ln (x + 5)}} \times {{\rm{e}}^{\ln 2}} = (x + 5)2\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\((g \circ f)(x) = 2x + 10\) <em><strong>A1A1 N2</strong></em></span></p>
<p><strong><em><span style="font-family: times new roman,times; font-size: medium;">[3 marks]</span></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;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">This was one of the more difficult problems for the candidates. Knowledge of the laws of </span><span style="font-family: times new roman,times; font-size: medium;">logarithms appeared weak as did the inverse nature of the exponential and logarithmic </span><span style="font-family: times new roman,times; font-size: medium;">functions. There were a number of candidates who mistook the notation for the inverse to </span><span style="font-family: times new roman,times; font-size: medium;">mean either the derivative or the reciprocal. The order of composition seemed well </span><span style="font-family: times new roman,times; font-size: medium;">understood by most candidates but they were unable to simplify by the rules of indices to </span><span style="font-family: times new roman,times; font-size: medium;">obtain the correct final answer.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">This was one of the more difficult problems for the candidates. Knowledge of the laws of </span><span style="font-family: times new roman,times; font-size: medium;">logarithms appeared weak as did the inverse nature of the exponential and logarithmic </span><span style="font-family: times new roman,times; font-size: medium;">functions. There were a number of candidates who mistook the notation for the inverse to </span><span style="font-family: times new roman,times; font-size: medium;">mean either the derivative or the reciprocal. The order of composition seemed well </span><span style="font-family: times new roman,times; font-size: medium;">understood by most candidates but they were unable to simplify by the rules of indices to </span><span style="font-family: times new roman,times; font-size: medium;">obtain the correct final answer.</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;">Let \(f(x) = k{\log _2}x\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Given that \({f^{ - 1}}(1) = 8\) , find the value of \(k\) .</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 style="font-family: times new roman,times; font-size: medium;">Find \({f^{ - 1}}\left( {\frac{2}{3}} \right)\) .</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 style="font-family: times new roman,times; font-size: medium;"><strong>METHOD 1</strong> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">recognizing that \(f(8) = 1\) <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(1 = k{\log _2}8\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">recognizing that \({\log _2}8 = 3\) <em><strong> (A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(1 = 3k\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(k = \frac{1}{3}\) <em><strong>A1 N2</strong> </em></span></p>
<p><strong><span style="font-family: times new roman,times; font-size: medium;">METHOD 2 </span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to find the inverse of \(f(x) = k{\log _2}x\) <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(x = k{\log _2}y\) , \(y = {2^{\frac{x}{k}}}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">substituting 1 and 8 <em><strong>(M1) </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(1 = k{\log _2}8\) , \({2^{\frac{1}{k}}} = 8\) </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(k = \frac{1}{{{{\log }_2}8}}\) \(\left( {k = \frac{1}{3}} \right)\) <em><strong>A1 N2</strong> </em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[3 marks]</span></strong></em></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;"><strong><span style="font-size: medium;">METHOD 1</span></strong></span></p>
<p><span style="font-family: times new roman,times;"><span style="font-size: medium;">recognizing that </span><span style="font-size: medium;">\(f(x) = \frac{2}{3}\) <em><strong>(M1)</strong></em></span></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(\frac{2}{3} = \frac{1}{3}{\log _2}x\)</span></p>
<p><span style="font-family: times new roman,times;"><span style="font-size: medium;">\({\log _2}x = 2\) </span><em><strong><span style="font-size: medium;">(A1)</span></strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({f^{ - 1}}\left( {\frac{2}{3}} \right) = 4\) (accept \(x = 4\)) <em><strong>A2 N3</strong></em></span></p>
<p><span style="font-family: times new roman,times;"><strong> <span style="font-size: medium;">METHOD 2</span></strong></span></p>
<p><span style="font-family: times new roman,times;"><span style="font-size: medium;">attempt to find inverse of \(f(x) = \frac{1}{3}{\log _2}x\) </span><em><strong><span style="font-size: medium;">(M1)</span></strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. interchanging <em>x</em> and <em>y</em> , substituting \(k = \frac{1}{3}\) into \(y = {2^{\frac{x}{k}}}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct inverse <em><strong>(A1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \({f^{ - 1}}(x) = {2^{3x}}\) , \({2^{3x}}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({f^{ - 1}}\left( {\frac{2}{3}} \right) = 4\) <em><strong>A2 N3</strong></em></span></p>
<p><span style="font-family: times new roman,times;"><em><strong><span style="font-size: medium;"> [4 marks]</span></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;">A very poorly done question. Most candidates attempted to find the inverse function for \(f\) and used that to answer parts (a) and (b). Few recognized that the explicit inverse function was not necessary to answer the question. </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> Although many candidates seem to know that they can find an inverse function by interchanging <em>x</em> and <em>y</em>, very few were able to actually get the correct inverse. Almost none recognized that if \({f^{ - 1}}(1) = 8\) , then \(f(8) = 1\) . Many thought that the letters "log" could be simply "cancelled out", leaving the \(2\) and the \(8\). </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 very poorly done question. Most candidates attempted to find the inverse function for \(f\) and used that to answer parts (a) and (b). Few recognized that the explicit inverse function was not necessary to answer the question. </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> Although many candidates seem to know that they can find an inverse function by interchanging <em>x</em> and <em>y</em>, very few were able to actually get the correct inverse. Almost none recognized that if \({f^{ - 1}}(1) = 8\) , then \(f(8) = 1\) . Many thought that the letters "log" could be simply "cancelled out", leaving the \(2\) and the \(8\). </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;">Let \(f(x) = \frac{{{{(\ln x)}^2}}}{2}\), for \(x > 0\).</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;">Let \(g(x) = \frac{1}{x}\). The following diagram shows parts of the graphs of \(f'\) and <em>g</em>.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; min-height: 25px; text-align: center; margin: 0px;"><img src="images/maths_10b.png" alt></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 graph of \(f'\) has an <em>x</em>-intercept at \(x = p\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<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;">Show that \(f'(x) = \frac{{\ln x}}{x}\).</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">There is a minimum on the graph of \(f\). Find the \(x\)-coordinate of this minimum.</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 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 value of \(p\).</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 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 \(g\) intersects the graph of \(f'\) when \(x = q\).</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;">Find the value of \(q\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p 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 \(g\) intersects the graph of \(f'\) when \(x = q\).</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;">Let \(R\) be the region enclosed by the graph of \(f'\), the graph of \(g\) and the line \(x = p\).</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;">Show that the area of \(R\) is \(\frac{1}{2}\).</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">correct use of chain rule <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \(\frac{{2\ln x}}{2} \times \frac{1}{x},{\text{ }}\frac{{2\ln x}}{{2x}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>A1 </em></strong>for \(\frac{{2\ln x}}{{2x}}\), <strong><em>A1 </em></strong>for \( \times \frac{1}{x}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(x) = \frac{{\ln x}}{x}\) <strong><em>AG N0</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">correct substitution into quotient rule, with derivatives seen <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \(\frac{{2 \times 2\ln x \times \frac{1}{x} - 0 \times {{(\ln x)}^2}}}{4}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">correct working <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \(\frac{{4\ln x \times \frac{1}{x}}}{4}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(x) = \frac{{\ln x}}{x}\) <strong><em>AG N0</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></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: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">setting derivative \( = 0\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \(f'(x) = 0,{\text{ }}\frac{{\ln x}}{x} = 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">correct working <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \(\ln x = 0,{\text{ }}x = {{\text{e}}^0}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 1\) <strong><em>A1 N2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks] </em></strong></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: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">intercept when \(f'(x) = 0\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(p = 1\) <strong><em>A1 N2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">equating functions <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \(f' = g,{\text{ }}\frac{{\ln x}}{x} = \frac{1}{x}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">correct working <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \(\ln x = 1\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(q = {\text{e (accept }}x = {\text{e)}}\) <strong><em>A1 N2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[3 marks]</span><br></em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">evidence of integrating and subtracting functions (in any order, seen anywhere) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \(\int_q^e {\left( {\frac{1}{x} - \frac{{\ln x}}{x}} \right){\text{d}}x{\text{, }}\int {f' - g} } \)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">correct integration \(\ln x - \frac{{{{(\ln x)}^2}}}{2}\) <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">substituting limits into <strong>their </strong>integrated function and subtracting (in any order) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \((\ln {\text{e}} - \ln 1) - \left( {\frac{{{{(\ln {\text{e}})}^2}}}{2} - \frac{{{{(\ln 1)}^2}}}{2}} \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Do not award <strong><em>M1 </em></strong>if the integrated function has only one term.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">correct working <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \((1 - 0) - \left( {\frac{1}{2} - 0} \right),{\text{ }}1 - \frac{1}{2}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{area}} = \frac{1}{2}\) <strong><em>AG N0</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Notes: </strong>Candidates may work with two separate integrals, and only combine them at the end. Award marks in line with the markscheme.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Let \(f(x) = 1 + {{\text{e}}^{ - x}}\) and \(g(x) = 2x + b\), for \(x \in \mathbb{R}\), where \(b\) is a constant.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find \((g \circ f)(x)\).</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>Given that \(\mathop {\lim }\limits_{x \to + \infty } (g \circ f)(x) = - 3\), find the value of \(b\).</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>attempt to form composite <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(g(1 + {{\text{e}}^{ - x}})\)</p>
<p>correct function <strong><em>A1 N2</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\((g \circ f)(x) = 2 + b + 2{{\text{e}}^{ - x}},{\text{ }}2(1 + {{\text{e}}^{ - x}}) + b\)</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>evidence of \(\mathop {\lim }\limits_{x \to \infty } (2 + b + 2{{\text{e}}^{ - x}}) = 2 + b + \mathop {\lim }\limits_{x \to \infty } (2{{\text{e}}^{ - x}})\) <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(2 + b + 2{{\text{e}}^{ - \infty }}\), graph with horizontal asymptote when \(x \to \infty \)</p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>M0 </em></strong>if candidate clearly has incorrect limit, such as \(x \to 0,{\text{ }}{{\text{e}}^\infty },{\text{ }}2{{\text{e}}^0}\).</p>
<p> </p>
<p>evidence that \({{\text{e}}^{ - x}} \to 0\) (seen anywhere) <strong><em>(A1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(\mathop {\lim }\limits_{x \to \infty } ({{\text{e}}^{ - x}}) = 0,{\text{ }}1 + {{\text{e}}^{ - x}} \to 1,{\text{ }}2(1) + b = - 3,{\text{ }}{{\text{e}}^{{\text{large negative number}}}} \to 0\), graph of \(y = {{\text{e}}^{ - x}}\) or</p>
<p>\(y = 2{{\text{e}}^{ - x}}\) with asymptote \(y = 0\), graph of composite function with asymptote \(y = - 3\)</p>
<p>correct working <strong><em>(A1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(2 + b = - 3\)</p>
<p>\(b = - 5\) <strong><em>A1 N2</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><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = lo{g_3}\sqrt x \) , for \(x > 0\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Show that \({f^{ - 1}}(x) = {3^{2x}}\) .</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 style="font-family: times new roman,times; font-size: medium;">Write down the range of \({f^{ - 1}}\) .</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 style="font-family: times new roman,times; font-size: medium;">Let \(g(x) = {\log _3}x\) , for \(x > 0\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find the value of \(({f^{ - 1}} \circ g)(2)\) , giving your answer as an integer.</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 style="font-family: times new roman,times; font-size: medium;">interchanging <em>x</em> and <em>y</em> (seen anywhere) <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(x = \log \sqrt y \) (accept any base)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">evidence of correct manipulation <em><strong>A1 </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(3^x = \sqrt y \) , \({3^y} = {x^{\frac{1}{2}}}\) , \(x = \frac{1}{2}{\log _3}y\) , \(2y = {\log _3}x\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({f^{ - 1}}(x) = {3^{2x}}\) <em><strong>AG N0</strong></em> </span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[2 marks]</span></strong></em></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;">\(y > 0\) , \({f^{ - 1}}(x) > 0\) <em><strong>A1 N1 </strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[1 mark]</span></strong></em></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;"><strong>METHOD 1</strong> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">finding \(g(2) = lo{g_3}2\) (seen anywhere) <em><strong>A1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to substitute <em><strong>(M1) </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(({f^{ - 1}} \circ g)(2) = {3^{2\log {_3}2}}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">evidence of using log or index rule <em><strong>(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(({f^{ - 1}} \circ g)(2) = {3^{\log {_3}4}}\) , \({3^{{{\log }_3}2^2}}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(({f^{ - 1}} \circ g)(2) = 4\) <em><strong>A1 N1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>METHOD 2</strong> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to form composite (in any order) <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(({f^{ - 1}} \circ g)(x) = {3^{2{{\log }_3}x}}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">evidence of using log or index rule <em><strong>(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(({f^{ - 1}} \circ g)(x) = {3^{{{\log }_3}{x^2}}}\) , \({3^{{{\log }_3}{x^{}}}}^2\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(({f^{ - 1}} \circ g)(x) = {x^2}\) <em><strong>A1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(({f^{ - 1}} \circ g)(2) = 4\) <em><strong>A1 N1</strong> </em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[4 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 were generally skilled at finding the inverse of a logarithmic 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;">Few correctly gave the range of this function, often stating “all real numbers” or “ \(y \ge 0\) ”, missing the idea that the range of an inverse is the domain of the original function.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Some candidates </span><span style="font-family: times new roman,times; font-size: medium;">answered part (c) correctly, although many did not get beyond \({3^{2{{\log }_3}2}}\) . Some attempted to form </span><span style="font-family: times new roman,times; font-size: medium;">the composite in the incorrect order. Others interpreted \(({f^{ - 1}} \circ g)(2)\) as multiplication by 2.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Let \(f(x) = 3\sin \left( {\frac{\pi }{2}x} \right)\), for \(0 \leqslant x \leqslant 4\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Write down the amplitude of \(f\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Find the period of \(f\).</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">On the following grid sketch the graph of \(f\).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2017-02-01_om_05.59.27.png" alt="M16/5/MATME/SP1/ENG/TZ1/03.b"></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">(i) <span class="Apple-converted-space"> </span>3 <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1 <span class="Apple-converted-space"> </span>N1</em></strong></span></p>
<p class="p2">(ii) <span class="Apple-converted-space"> </span>valid attempt to find the period <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"><em>eg</em>\(\,\,\,\,\,\)\(\frac{{2\pi }}{b},{\text{ }}\frac{{2\pi }}{{\frac{\pi }{2}}}\)</p>
<p class="p1">period \( = 4\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1 <span class="Apple-converted-space"> </span>N2</em></strong></span></p>
<p class="p2"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2017-02-01_om_06.02.18.png" alt="M16/5/MATME/SP1/ENG/TZ1/03.b/M"> <strong><em>A1A1A1A1 N4</em></strong></p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Almost all candidates correctly stated the amplitude but then had difficulty finding the correct period. Few students faced problems in sketching the graph of the given function, even if they had found the wrong period, thus indicating a lack of understanding of the term ‘period’ in part a(ii). Most sketches were good although care should be taken to observe the given domain and to draw a neat curve.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Almost all candidates correctly stated the amplitude but then had difficulty finding the correct period. Few students faced problems in sketching the graph of the given function, even if they had found the wrong period, thus indicating a lack of understanding of the term ‘period’ in part a(ii). Most sketches were good although care should be taken to observe the given domain and to draw a neat curve.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Let <em>f</em> be the function given by \(f(x) = {{\rm{e}}^{0.5x}}\) , \(0 \le x \le 3.5\) . The diagram shows the </span><span style="font-family: times new roman,times; font-size: medium;">graph of <em>f</em> .</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/infinity.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">On the same diagram, sketch the graph of \({f^{ - 1}}\) .</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 style="font-family: times new roman,times; font-size: medium;">Write down the range of \({f^{ - 1}}\) .</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 style="font-family: times new roman,times; font-size: medium;">Find \({f^{ - 1}}(x)\) .</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 style="font-family: times new roman,times; font-size: medium;"><br><img src="images/infinity2.png" alt></span><em><strong><span style="font-family: times new roman,times; font-size: medium;"> A1A1A1 N3</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note</strong>: Award <em><strong>A1</strong></em> for approximately correct (reflected) shape, </span><span style="font-family: times new roman,times; font-size: medium;"><em><strong>A1</strong></em> for right end point in circle, <em><strong>A1</strong></em> for through \((1{\text{, }}0)\) . </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;">\(0 \le y \le 3.5\) <em><strong>A1 N1</strong> </em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[1 mark]</span></strong></em></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;">interchanging <em>x</em> and <em>y</em> (seen anywhere) <strong><em>M1 </em></strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(x = {e^{0.5y}}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">evidence of changing to log form <strong><em>A1</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(\ln x = 0.5y\) , \(\ln x = \ln {{\rm{e}}^{0.5y}}\) (any base), \(\ln x = 0.5y\ln {\rm{e}}\) (any base) </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({f^{ - 1}}(x) = 2\ln x\) <em><strong>A1 N1 </strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[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;">There were a large number of candidates who were unaware of the geometric relationship between a function and its inverse. Those that had some idea of the shape of the graph often did not consider the specified domain. Many more students were able to use an analytical approach to finding the inverse of a function and had little problem using logarithms to solve for <em>y</em>. Candidates were clearly more comfortable with algebraic procedures than graphical interpretations. </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 were a large number of candidates who were unaware of the geometric relationship between a function and its inverse. Those that had some idea of the shape of the graph often did not consider the specified domain. Many more students were able to use an analytical approach to finding the inverse of a function and had little problem using logarithms to solve for <em>y</em>. Candidates were clearly more comfortable with algebraic procedures than graphical interpretations. </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 large number of candidates who were unaware of the geometric relationship between a function and its inverse. Those that had some idea of the shape of the graph often did not consider the specified domain. Many more students were able to use an analytical approach to finding the inverse of a function and had little problem using logarithms to solve for <em>y</em>. Candidates were clearly more comfortable with algebraic procedures than graphical interpretations.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Let \(f(x) = 5x\) and \(g(x) = {x^2} + 1\), for \(x \in \mathbb{R}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find \({f^{ - 1}}(x)\).</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>Find \((f \circ g)(7)\).</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>interchanging \(x\) and \(x\) <em><strong>(M1)</strong></em></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(x = 5y\)</p>
<p>\({f^{ - 1}}\left( x \right) = \frac{x}{5}\) <em><strong>A1</strong></em> <em><strong>N2</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>attempt to substitute 7 into \(g(x)\) or \(f(x)\) <em><strong>(M1)</strong></em></p>
<p><em>eg</em>\(\,\,\,\,\,\)\({7^2} + 1,{\text{ }}5 \times 7\)</p>
<p>\(g(7) = 50\) <em><strong>(A1)</strong></em></p>
<p>\(f\left( {50} \right) = 250\) <em><strong>A1</strong></em> <em><strong>N2</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>attempt to form composite function (in any order) <em><strong>(M1)</strong></em></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(5({x^2} + 1),{\text{ }}{(5x)^2} + 1\)</p>
<p>correct substitution <em><strong>(A1)</strong></em></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(5 \times ({7^2} + 1)\)</p>
<p>\((f \circ g)(7) = 250\) <em><strong>A1</strong></em> <em><strong>N2</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="specification">
<p>The following diagram shows the graph of a function \(f\), with domain \( - 2 \leqslant x \leqslant 4\).</p>
<p><img src="images/Schermafbeelding_2018-02-11_om_09.13.25.png" alt="N17/5/MATME/SP1/ENG/TZ0/03"></p>
<p>The points \(( - 2,{\text{ }}0)\) and \((4,{\text{ }}7)\) lie on the graph of \(f\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the range of \(f\).</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 \(f(2)\);</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 \({f^{ - 1}}(2)\).</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>On the grid, sketch the graph of \({f^{ - 1}}\).</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>correct range (do not accept \(0 \leqslant x \leqslant 7\)) <strong> <em>A1 N1</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\([0,{\text{ }}7],{\text{ }}0 \leqslant y \leqslant 7\)</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>\(f(2) = 3\) <em><strong>A1 N1</strong></em></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>\({f^{ - 1}}(2) = 0\) <strong><em>A1 N1</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2018-02-11_om_10.32.42.png" alt="N17/5/MATME/SP1/ENG/TZ0/03.c/M"> <strong><em>A1A1A1 N3</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Award <strong><em>A1 </em></strong>for both end points within circles,</p>
<p><strong><em>A1 </em></strong>for images of \((2,{\text{ }}3)\) and \((0,{\text{ }}2)\) within circles,</p>
<p><strong><em>A1 </em></strong>for approximately correct reflection in \(y = x\), concave up then concave down shape (do not accept line segments).</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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = \frac{1}{2}{x^2} + kx + 8\) , where \(k \in \mathbb{Z}\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the values of <em>k</em> such that \(f(x) = 0\) has two equal roots.</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Each value of <em>k</em> is equally likely for \( - 5 \le k \le 5\) . Find the probability that </span><span style="font-family: times new roman,times; font-size: medium;">\(f(x) = 0\) has no roots.</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><strong><span style="font-family: times new roman,times; font-size: medium;">METHOD 1</span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">evidence of discriminant <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \({b^2} - 4ac\) , discriminant = 0</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct substitution into discriminant <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \({k^2} - 4 \times \frac{1}{2} \times 8\) , \({k^2} - 16 = 0\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(k = \pm 4\) <em><strong>A1A1 N3</strong></em></span></p>
<p><strong> <span style="font-family: times new roman,times; font-size: medium;">METHOD 2</span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">recognizing that equal roots means perfect square <em><strong>(R1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. attempt to complete the square, \(\frac{1}{2}({x^2} + 2kx + 16)\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct working</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(\frac{1}{2}{(x + k)^2}\) , \(\frac{1}{2}{k^2} = 8\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\(k = \pm 4\) <em><strong>A1A1 N3</strong></em></span></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;"> [4 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">evidence of appropriate approach <em><strong>(M1)</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \({b^2} - 4ac < 0\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">correct working for <em>k</em> <em><strong>A1</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \( - 4 < k < 4\) , \({k^2} < 16\) , list all correct values of <em>k</em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(p = \frac{7}{{11}}\) <em><strong>A2 N3</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[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;">A good number of candidates were successful in using the discriminant to find the correct values of <em>k</em> in part (a), however, there were many who tried to use the quadratic formula without recognizing the significance of the discriminant. </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 very poorly done by nearly all candidates. Common errors included finding the wrong values for <em>k</em>, and not realizing that there were 11 possible values for <em>k</em>. </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;">Let \(f(x) = 3x - 2\) and \(g(x) = \frac{5}{{3x}}\), for \(x \ne 0\).</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;">Let \(h(x) = \frac{5}{{x + 2}}\), for \(x \geqslant 0\). The graph of <em>h </em>has a horizontal asymptote at \(y = 0\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<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;">Find \({f^{ - 1}}(x)\).</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 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;">Show that \(\left( {g \circ {f^{ - 1}}} \right)(x) = \frac{5}{{x + 2}}\).</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 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;">Find the \(y\)-intercept of the graph of \(h\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p 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;">Hence, sketch the graph of \(h\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p 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;">For the graph of \({h^{ - 1}}\), write down the \(x\)-intercept;</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p 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;">For the graph of \({h^{ - 1}}\), write down the equation of the vertical asymptote.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<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;">Given that \({h^{ - 1}}(a) = 3\), find the value of \(a\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">interchanging \(x\) and \(y\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \(x = 3y - 2\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\({f^{ - 1}}(x) = \frac{{x + 2}}{3}{\text{ }}\left( {{\text{accept }}y = \frac{{x + 2}}{3},{\text{ }}\frac{{x + 2}}{3}} \right)\) <strong><em>A1 N2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></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: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">attempt to form composite (in any order) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \(g\left( {\frac{{x + 2}}{3}} \right),{\text{ }}\frac{{\frac{5}{{3x}} + 2}}{3}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">correct substitution <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \(\frac{5}{{3\left( {\frac{{x + 2}}{3}} \right)}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(\left( {g \circ {f^{ - 1}}} \right)(x) = \frac{5}{{x + 2}}\) <strong><em>AG N0</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></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: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">valid approach <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \(h(0),{\text{ }}\frac{5}{{0 + 2}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(y = \frac{5}{2}{\text{ }}\left( {{\text{accept (0, 2.5)}}} \right)\) <strong><em>A1 N2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times;"><img src="images/maths_8cii_markscheme.png" alt> <span style="font-size: medium;"><strong><em>A1A2 N3</em></strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Notes: </strong>Award <strong><em>A1 </em></strong>for approximately correct shape (reciprocal, decreasing, concave up).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong> Only </strong>if this <strong><em>A1 </em></strong>is awarded, award <strong><em>A2 </em></strong>for all the following approximately correct features: <em>y</em>-intercept at \((0, 2.5)\), asymptotic to <em>x</em>-axis, correct domain \(x \geqslant 0\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> If only two of these features are correct, award <strong><em>A1</em></strong>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">c(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = \frac{5}{2}{\text{ }}\left( {{\text{accept (2.5, 0)}}} \right)\) <strong><em>A1 N1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">d(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 0\) (must be an equation) <strong><em>A1 N1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">d(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">attempt to substitute \(3\) into \(h\) (seen anywhere) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \(h(3),{\text{ }}\frac{5}{{3 + 2}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">correct equation <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \(a = \frac{5}{{3 + 2}},{\text{ }}h(3) = a\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(a = 1\) <strong><em>A1 N2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">attempt to find inverse (may be seen in (d)) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \(x = \frac{5}{{y + 2}},{\text{ }}{h^{ - 1}} = \frac{5}{x} - 2,{\text{ }}\frac{5}{x} + 2\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">correct equation, \(\frac{5}{x} - 2 = 3\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(a = 1\) <strong><em>A1 N2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Let \(f(x) = p + \frac{9}{{x - q}}\), for \(x \ne q\). The line \(x = 3\) is a vertical asymptote to the graph of \(f\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down the value of \(q\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The graph of \(f\) has a \(y\)-intercept at \((0,{\text{ }}4)\).</p>
<p class="p1">Find the value of \(p\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The graph of \(f\) has a <em>\(y\)</em>-intercept at \((0,{\text{ }}4)\).</p>
<p class="p1">Write down the equation of the horizontal asymptote of the graph of \(f\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(q = 3\) <span class="Apple-converted-space"> </span><strong><em>A1 <span class="Apple-converted-space"> </span>N1</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">correct expression for \(f(0)\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1"><em>eg</em>\(\;\;\;p + \frac{9}{{0 - 3}},{\text{ }}4 = p + \frac{9}{{ - q}}\)</p>
<p class="p1">recognizing that \(f(0) = 4\;\;\;\)(may be seen in equation) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">correct working <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1"><em>eg</em>\(\;\;\;4 = p - 3\)</p>
<p class="p1">\(p = 7\) <span class="Apple-converted-space"> </span><strong><em>A1 <span class="Apple-converted-space"> </span>N3</em></strong></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(y = 7\;\;\;\)(must be an equation, do not accept \(p = 7\) <span class="Apple-converted-space"> </span><strong><em>A1 <span class="Apple-converted-space"> </span>N1</em></strong></p>
<p class="p1"><strong><em>[1 mark]</em></strong></p>
<p class="p1"><strong><em>Total [6 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;">
<p>Parts (a) and (b) were generally well done. Some candidates incorrectly answered \(q = - 3\), rather than \(q = 3\), in part (a), but then were able to earn follow-through marks in part (b).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Parts (a) and (b) were generally well done. Some candidates incorrectly answered \(q = - 3\), rather than \(q = 3\), in part (a), but then were able to earn follow-through marks in part (b).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Many candidates did not recognize the connection between parts (b) and (c) of this question, and many did a good deal of unnecessary work in part (c) before giving the correct answer. In part (c), many candidates did not write the equation of the asymptote, but just wrote the number.</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: 12.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(f(x) = p{x^3} + p{x^2} + qx\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Given that \(f'(x) \geqslant 0\), show that \({p^2} \leqslant 3pq\).</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(x) = 3p{x^2} + 2px + q\) <strong><em>A2 N2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 17.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Note:</em></strong> Award <strong><em>A1</em></strong> if only 1 error.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 17.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f; background-color: #f7f7f7;"><span style="font-family: 'times new roman', times; font-size: medium;">evidence of discriminant (must be seen explicitly, not in quadratic formula) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f; background-color: #f7f7f7;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \({b^2} - 4ac\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f; background-color: #f7f7f7;"><span style="font-family: 'times new roman', times; font-size: medium;">correct substitution into discriminant (may be seen in inequality) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f; background-color: #f7f7f7;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \({(2p)^2} - 4 \times 3p \times q,{\text{ }}4{p^2} - 12pq\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f; background-color: #f7f7f7;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(x) \geqslant 0\) then \(f'\) has two equal roots or no roots <strong><em>(R1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f; background-color: #f7f7f7;"><span style="font-family: 'times new roman', times; font-size: medium;">recognizing discriminant less or equal than zero <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f; background-color: #f7f7f7;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \(\Delta \leqslant 0,{\text{ }}4{p^2} - 12pq \leqslant 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f; background-color: #f7f7f7;"><span style="font-family: 'times new roman', times; font-size: medium;">correct working that clearly leads to the required answer <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f; background-color: #f7f7f7;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \({p^2} - 3pq \leqslant 0,{\text{ }}4{p^2} \leqslant 12pq\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f; background-color: #f7f7f7;"><span style="font-family: 'times new roman', times; font-size: medium;">\({p^2} \leqslant 3pq\) <strong><em>AG N0</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f; background-color: #f7f7f7;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 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;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> </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;">Let \(f(x) = 8x - 2{x^2}\) . Part of the graph of <em>f</em> is shown below.</span></p>
<p><span style="font-family: TimesNewRomanPSMT;"><br><img src="images/spin.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the <em>x</em>-intercepts of the graph.</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Write down the equation of the axis of symmetry.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Find the <em>y</em>-coordinate of the vertex.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b(i) and (ii).</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">evidence of setting function to zero <em><strong> (M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(f(x) = 0\) , \(8x = 2{x^2}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">evidence of correct working <em><strong>A1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(0 = 2x(4 - x)\) , \(\frac{{ - 8 \pm \sqrt {64} }}{{ - 4}}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>x</em>-intercepts are at 4 and 0 (accept (4, 0) and (0, 0) , or \(x = 4\) , \(x = 0\) ) <em><strong>A1A1 N1N1</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;"> [4 marks]</span></strong></em></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;">(i) \(x = 2\) (must be equation) <em><strong>A1 N1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) substituting \(x = 2\) into \(f(x)\) <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(y = 8\) <em><strong>A1 N2</strong> </em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[3 marks]</span></strong></em></p>
<div class="question_part_label">b(i) and (ii).</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was answered well by most candidates.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">This question was answered well by most candidates. Some did not give an equation for their </span><span style="font-family: times new roman,times; font-size: medium;">axis of symmetry.</span></p>
<div class="question_part_label">b(i) and (ii).</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The velocity <em>v</em> ms<sup>−1</sup> of a particle at time <em>t</em> seconds, is given by \(v = 2t + \cos 2t\) , </span><span style="font-family: times new roman,times; font-size: medium;">for \(0 \le t \le 2\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Write down the velocity of the particle when \(t = 0\) .</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">When \(t = k\) , the acceleration is zero.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Show that \(k = \frac{\pi }{4}\)</span><span style="font-family: times new roman,times; font-size: medium;"> .</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(ii) Find the exact velocity when \(t = \frac{\pi }{4}\)</span><span style="font-family: times new roman,times; font-size: medium;"> .</span></p>
<div class="marks">[8]</div>
<div class="question_part_label">b(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">When \(t < \frac{\pi }{4}\) , \(\frac{{{\rm{d}}v}}{{{\rm{d}}t}} > 0\)</span><span style="font-family: times new roman,times; font-size: medium;"> and when \(t > \frac{\pi }{4}\) , \(\frac{{{\rm{d}}v}}{{{\rm{d}}t}} > 0\) </span><span style="font-family: times new roman,times; font-size: medium;"> .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Sketch a graph of <em>v</em> against <em>t</em> .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Let <em>d</em> be the distance travelled by the particle for \(0 \le t \le 1\) .</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Write down an expression for <em>d</em> .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Represent <em>d</em> on your sketch.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d(i) and (ii).</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(v = 1\) <em><strong>A1 N1</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[1 mark]</span></strong></em></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;">(i) \(\frac{{\rm{d}}}{{{\rm{d}}t}}(2t) = 2\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1</span></strong></em></p>
<p><span style="font-family: Times New Roman; font-size: medium;">\(\frac{{\rm{d}}}{{{\rm{d}}t}}(\cos 2t) = - 2\sin 2t\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1A1</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note</strong>: Award <em><strong>A1</strong></em> for coefficient 2 and <em><strong>A1</strong></em> for <span lang="EN-US">\( - \sin 2t\)</span> .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">evidence of considering acceleration = 0 <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(\frac{{{\rm{d}}v}}{{{\rm{d}}t}} = 0\) , \(2 - 2\sin 2t = 0\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct manipulation <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(\sin 2k = 1\) , \(\sin 2t = 1\)</span></p>
<p><span style="font-family: Times New Roman; font-size: medium;">\(2k = \frac{\pi }{2}\) (accept \(2t = \frac{\pi }{2}\) ) </span><strong><em><span style="font-family: times new roman,times; font-size: medium;">A1</span></em></strong></p>
<p><span style="font-family: Times New Roman; font-size: medium;">\(k = \frac{\pi }{4}\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">AG N0</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) attempt to substitute \(t = \frac{\pi }{4}\) into <em>v<strong> </strong></em></span><strong><em><span style="font-family: times new roman,times; font-size: medium;">(M1)</span></em></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(2\left( {\frac{\pi }{4}} \right) + \cos \left( {\frac{{2\pi }}{4}} \right)\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(v = \frac{\pi }{2}\) <em><strong>A1 N2</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;"> [8 marks]</span></strong></em></p>
<div class="question_part_label">b(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/ray.png" alt></span><em><strong><span style="font-family: times new roman,times; font-size: medium;"> A1A1A2 N4</span></strong></em></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><strong>Notes</strong>: Award <em><strong>A1</strong></em> for <em>y</em>-intercept at \((0{\text{, }}1)\) , <strong><em>A1</em></strong> for curve having zero gradient at \(t = \frac{\pi }{4}\)</span><span style="font-family: times new roman,times; font-size: medium;"> , </span><span style="font-family: times new roman,times; font-size: medium;"><em><strong>A2</strong></em> for shape that is concave down to the left of \(\frac{\pi }{4}\) </span><span style="font-family: times new roman,times; font-size: medium;">and concave up to the right </span><span style="font-family: times new roman,times; font-size: medium;">of \(\frac{\pi }{4}\) </span><span style="font-family: times new roman,times; font-size: medium;">. If a correct curve is drawn without indicating \(t = \frac{\pi }{4}\)</span><span style="font-family: times new roman,times; font-size: medium;"> , do not award the </span><span style="font-family: times new roman,times; font-size: medium;">second <em><strong>A1</strong></em> for the zero gradient, but award the final <em><strong>A2</strong></em> if appropriate. Sketch need not be drawn to scale. Only essential features need to be clear.</span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[4 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) correct expression <em><strong>A2</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \(\int_0^1 {(2t + \cos 2t){\rm{d}}t} \) , \(\left[ {{t^2} + \frac{{\sin 2t}}{2}} \right]_0^1\) , \(1 + \frac{{\sin 2}}{2}\) , \(\int_0^1 {v{\rm{d}}t} \)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(ii)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/deb.png" alt></span><em><strong><span style="font-family: times new roman,times; font-size: medium;"> A1</span></strong></em></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><strong>Note</strong>: The line at \(t = 1\) needs to be clearly after \(t = \frac{\pi }{4}\)</span><span style="font-family: times new roman,times; font-size: medium;"> .</span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[3 marks]</span></strong></em></p>
<div class="question_part_label">d(i) and (ii).</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates gave a correct initial velocity, although a substantial number of candidates answered that \(0 + \cos 0 = 0\) .</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;">For (b), students commonly applied the chain rule correctly to achieve the derivative, and many recognized that the acceleration must be zero. Occasionally a student would use a double-angle identity on the velocity function before differentiating. This is not incorrect, but it usually caused problems when trying to show \(k = \frac{\pi }{4}\) . At times students would reach the equation \(\sin 2k = 1\) and then substitute the \(\frac{\pi }{4}\) , which does not satisfy the “show that” instruction. </span></p>
<div class="question_part_label">b(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The challenge in this question is sketching the graph using the information achieved and provided. This requires students to make graphical interpretations, and as typical in section B, to link the early parts of the question with later parts. Part (a) provides the <em>y</em>-intercept, and part (b) gives a point with a horizontal tangent. Plotting these points first was a helpful strategy. Few understood either the notation or the concept that the function had to be increasing on either side of the \(\frac{\pi }{4}\) , with most thinking that the point was either a max or min. It was the astute student who recognized that the derivatives being positive on either side of \(\frac{\pi }{4}\) creates a point of inflexion. </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Additionally, important points should be labelled in a sketch. Indicating the \(\frac{\pi }{4}\) on the <em>x</em>-axis is a requirement of a clear graph. Although students were not penalized for not labelling the \(\frac{\pi }{2}\) on the <em>y</em>-axis, there should be a recognition that the point is higher than the <em>y</em>-intercept. </span></p>
<p> </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;">While some candidates recognized that the distance is the area under the velocity graph, surprisingly few included neither the limits of integration in their expression, nor the “d<em>t</em>”. Most unnecessarily attempted to integrate the function, often giving an answer with “+C”, and only earned marks if the limits were included with their result. Few recognized that a shaded area is an adequate representation of distance on the sketch, with most fruitlessly attempting to graph a new curve.</span></p>
<div class="question_part_label">d(i) and (ii).</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Let \(f(x) = p{x^2} + (10 - p)x + \frac{5}{4}p - 5\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that the discriminant of \(f(x)\) is \(100 - 4{p^2}\).</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 values of \(p\) so that \(f(x) = 0\) has two <strong>equal</strong> roots.</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">correct substitution into \({b^2} - 4ac\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><em>eg</em>\(\;\;\;{(10 - p)^2} - 4(p)\left( {\frac{5}{4}p - 5} \right)\)</p>
<p class="p1">correct expansion of each term <span class="Apple-converted-space"> </span><strong><em>A1A1</em></strong></p>
<p class="p1"><em>eg</em>\(\;\;\;100 - 20p + {p^2} - 5{p^2} + 20p,{\text{ }}100 - 20p + {p^2} - (5{p^2} - 20p)\)</p>
<p class="p1">\(100 - 4{p^2}\) <span class="Apple-converted-space"> </span><strong><em>AG <span class="Apple-converted-space"> </span>N0</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>recognizing discriminant is zero for equal roots <strong><em>(R1)</em></strong></p>
<p><em>eg</em>\(\;\;\;D = 0,{\text{ }}4{p^2} = 100\)</p>
<p>correct working <strong><em>(A1)</em></strong></p>
<p><em>eg</em>\(\;\;\;{p^2} = 25\), \(1\) correct value of \(p\)</p>
<p><strong>both </strong>correct values \(p = \pm 5\) <strong><em>A1 N2</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<p><strong><em>Total [6 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;">
<p>Many candidates were able to identify the discriminant correctly and continued with good algebraic manipulation. A commonly seen mistake was identifying the constant as \(\frac{5}{4}p\) instead of \(\frac{5}{4}p - 5\). Mostly a correct approach to part b) was seen \((\Delta = 0)\), with the common error being only one answer given for \(p\), even though the question said values (plural).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates were able to identify the discriminant correctly and continued with good algebraic manipulation. A commonly seen mistake was identifying the constant as \(\frac{5}{4}p\) instead of \(\frac{5}{4}p - 5\). Mostly a correct approach to part b) was seen \((\Delta = 0)\), with the common error being only one answer given for \(p\), even though the question said values (plural).</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;">Let \(f\) be a quadratic function. Part of the graph of \(f\) is shown below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img style="display: block; margin-left: auto; margin-right: auto;" src="images/ally.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The vertex is at P(\(4\), \(2\)) and the <em>y</em>-intercept is at Q(\(0\), \(6\)) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Write down the equation of the axis of symmetry.</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The function <em>f</em> can be written in the form \(f(x) = a{(x - h)^2} + k\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Write down the value of <em>h</em> and of <em>k</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 style="font-family: times new roman,times; font-size: medium;">The function <em>f</em> can be written in the form \(f(x) = a{(x - h)^2} + k\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find <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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(x = 4\) (must be an equation) <em><strong>A1 N1</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[1 mark]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(h = 4\) , \(k = 2\) <em><strong>A1A1 N2</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">attempt to substitute coordinates of any point on the graph into <em>f</em> <em><strong>(M1)</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \(f(0) = 6\) , \(6 = a{(0 - 4)^2} + 2\) , \(f(4) = 2\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">correct equation (do <strong>not</strong> accept an equation that results from \(f(4) = 2\) ) <em><strong>(A1)</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \(6 = a{( - 4)^2} + 2\) , \(6 = 16a + 2\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(a = \frac{4}{{16}}\left( { = \frac{1}{4}} \right)\) <em><strong>A1 N2</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[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;">A surprising number of candidates missed part (a) of this question, which required them to write the equation of the axis of symmetry. Some candidates did not write their answer as an equation, while others simply wrote the formula \(x = - \frac{b}{{2a}}\) . </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 answered correctly by the large majority of candidates. </span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The rest of this question was answered correctly by the large majority of candidates. The mistakes seen in part (c) were generally due to either incorrect substitution of a point into the equation, or substitution of the vertex coordinates, which got the candidates nowhere. </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 following diagram shows part of the graph of <em>f</em> , where \(f(x) = {x^2} - x - 2\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/gary.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find both <em>x</em>-intercepts.</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 style="font-family: times new roman,times; font-size: medium;">Find the <em>x</em>-coordinate of the vertex.</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">evidence of attempting to solve \(f(x) = 0\) <em><strong>(M1)</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">evidence of correct working <em><strong>A1</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \((x + 1)(x - 2)\) , \(\frac{{1 \pm \sqrt 9 }}{2}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">intercepts are \(( - 1{\text{, }}0)\) and \((2{\text{, }}0)\) (accept \(x = - 1\) , \(x = 2\) ) <em><strong>A1A1 N1N1</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[4 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">evidence of appropriate method <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \({x_v} = \frac{{{x_1} + {x_2}}}{2}\) , \({x_v} = - \frac{b}{{2a}}\) ,</span><span style="font-family: times new roman,times; font-size: medium;"> reference to symmetry </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({x_v} = 0.5\) <em><strong>A1 N2</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[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-family: times new roman,times; font-size: medium;">This question was consistently the best handled one on the entire paper.</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 consistently the best handled one on the entire paper.</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 \(f(x) = \ln ({x^4} + 1)\) .</span></p>
</div>
<div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The second derivative is given by \(f''(x) = \frac{{4{x^2}(3 - {x^4})}}{{{{({x^4} + 1)}^2}}}\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The equation \(f''(x) = 0\) has only three solutions, when \(x = 0\) , \( \pm \sqrt[4]{3}\) \(( \pm 1.316 \ldots )\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the value of \(f(0)\) .</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 style="font-family: times new roman,times; font-size: medium;">Find the set of values of \(x\) for which \(f\) is increasing.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Find \(f''(1)\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) <strong>Hence</strong>, show that there is no point of inflexion on the graph of \(f\) at \(x = 0\) .</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">There is a point of inflexion on the graph of \(f\) at \(x = \sqrt[4]{3}\) \((x = 1.316 \ldots )\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Sketch the graph of \(f\) , for \(x \ge 0\) .</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 style="font-family: times new roman,times; font-size: medium;">substitute \(0\) into \(f\)<em><strong> </strong></em> <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> \(\ln (0 + 1)\) , \(\ln 1\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(f(0) = 0\) <em><strong>A1 N2 </strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[2 marks] </span></strong></em></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;">\(f'(x) = \frac{1}{{{x^4} + 1}} \times 4{x^3}\) (seen anywhere) <strong><em>A1A1</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note</strong>: Award <em><strong>A1</strong></em> for \(\frac{1}{{{x^4} + 1}}\) and <strong><em>A1</em></strong> for \(4{x^3}\) . </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">recognizing \(f\) increasing where \(f'(x) > 0\) (seen anywhere) <strong><em>R1</em></strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> \(f'(x) > 0\) , diagram of signs </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to solve \(f'(x) > 0\) <strong><em>(M1)</em></strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> \(4{x^3} = 0\) , \({x^3} > 0\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(f\) increasing for \(x > 0\) (accept \(x \ge 0\) ) <strong><em>A1 N1 </em></strong></span></p>
<p><strong><em><span style="font-family: times new roman,times; font-size: medium;">[5 marks] </span></em></strong></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;">(i) substituting \(x = 1\) into \(f''\) <strong><em>(A1)</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> \(\frac{{4(3 - 1)}}{{{{(1 + 1)}^2}}}\) , \(\frac{{4 \times 2}}{4}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(f''(1) = 2\) <strong><em> A1 N2</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) valid interpretation of point of inflexion (seen anywhere) <strong><em>R1</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> no change of sign in \(f''(x)\) , no change in concavity, </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(f'\) increasing both sides of zero </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to find \(f''(x)\) for \(x < 0\) <strong><em>(M1)</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> \(f''( - 1)\) , \(\frac{{4{{( - 1)}^2}(3 - {{( - 1)}^4})}}{{{{({{( - 1)}^4} + 1)}^2}}}\) , diagram of signs </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct working leading to positive value <strong><em>A1</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> \(f''( - 1) = 2\) , discussing signs of numerator <strong>and</strong> denominator </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">there is no point of inflexion at \(x = 0\) <em><strong>AG N0 </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em><strong> </strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[5 marks] </span></strong></em></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;"><img src="images/jcp.png" alt></span><em><span style="font-family: times new roman,times; font-size: medium;"><strong> A1A1A1 N3</strong> </span></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Notes</strong>: Award <em><strong>A1</strong></em> for shape concave up left of POI and concave down right of POI. </span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> Only if this <em><strong>A1</strong></em> is awarded, then award the following: </span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"><em><strong> A1</strong></em> for curve through (\(0\), \(0\)) , <strong><em>A1</em></strong> for increasing throughout. </span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> Sketch need not be drawn to scale. Only essential features need to be clear. </span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[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-family: times new roman,times; font-size: medium;">Many candidates left their answer to part (a) as \(\ln 1\). While this shows an understanding for substituting a value into a function, it leaves an unfinished answer that should be expressed as an integer.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Candidates who attempted to consider where \(f\) is increasing generally understood the derivative is needed. However, a number of candidates did not apply the chain rule, which commonly led to answers such as “increasing for all \(x\)”. Many set their derivative equal to zero, while neglecting to indicate in their working that \(f'(x) > 0\) for an increasing function. Some created a diagram of signs, which provides appropriate evidence as long as it is clear that the signs represent \(f’\).</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;">Finding \(f''(1)\) proved no challenge, however, using this value to <strong>show that</strong> no point of inflexion exists proved elusive for many. Some candidates recognized the signs must not change in the second derivative. Few candidates presented evidence in the form of a calculation, which follows from the “hence” command of the question. In this case, a sign diagram without numerical evidence was not sufficient.</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;">Few candidates created a correct graph from the information given or found in the question. This included the point (\(0\), \(0\)), the fact that the function is always increasing for \(x > 0\) , the concavity at \(x = 1\) and the change in concavity at the given point of inflexion. Many incorrect attempts showed a graph concave down to the right of \(x = 0\) , changing to concave up.</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;">Let \(f(x) = \frac{x}{{ - 2{x^2} + 5x - 2}}\) for \( - 2 \le x \le 4\) , \(x \ne \frac{1}{2}\) , \(x \ne 2\) . The graph of \(f\) is given below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/M12P1TZ2Q10.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The graph of \(f\) has a local minimum at A(\(1\), \(1\)) and a local maximum at B.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Use the quotient rule to show that \(f'(x) = \frac{{2{x^2} - 2}}{{{{( - 2{x^2} + 5x - 2)}^2}}}\) .</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Hence find the coordinates of B.</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Given that the line \(y = k\) does not meet the graph of <em>f</em> , find the possible values </span><span style="font-family: times new roman,times; font-size: medium;">of <em>k</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 style="font-family: times new roman,times; font-size: medium;">correct derivatives <strong>applied</strong> in quotient rule <em><strong>(A1)A1A1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(1\), \( - 4x + 5\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for 1, <em><strong>A1</strong></em> for \( - 4x\) and <em><strong>A1</strong></em> for \(5\), <strong>only</strong> if it is clear candidates are using the quotient rule. </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct substitution into quotient rule <em><strong>A1 </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>e.g.</em> \(\frac{{1 \times ( - 2{x^2} + 5x - 2) - x( - 4x + 5)}}{{{{( - 2{x^2} + 5x - 2)}^2}}}\) , \(\frac{{ - 2{x^2} + 5x - 2 - x( - 4x + 5)}}{{{{( - 2{x^2} + 5x - 2)}^2}}}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct working <em><strong>(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>e.g.</em> \(\frac{{ - 2{x^2} + 5x - 2 - ( - 4{x^2} + 5x)}}{{{{( - 2{x^2} + 5x - 2)}^2}}}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">expression clearly leading to the answer <em><strong>A1 </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>e.g.</em> \(\frac{{ - 2{x^2} + 5x - 2 + 4{x^2} - 5x}}{{{{( - 2{x^2} + 5x - 2)}^2}}}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(f'(x) = \frac{{2{x^2} - 2}}{{{{( - 2{x^2} + 5x - 2)}^2}}}\) <em><strong>AG N0</strong> </em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[6 marks] </span></strong></em></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;">evidence of attempting to solve \(f'(x) = 0\) <strong><em>(M1) </em></strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(2{x^2} - 2 = 0\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">evidence of correct working <em><strong>A1 </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \({x^2} = 1,\frac{{ \pm \sqrt {16} }}{4}{\text{, }}2(x - 1)(x + 1)\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct solution to quadratic <em><strong>(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(x = \pm 1\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct <em>x</em>-coordinate \(x = - 1\) (may be seen in coordinate form \(\left( { - 1,\frac{1}{9}} \right)\) ) <em><strong>A1 N2</strong></em> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to substitute \( - 1\) into <em>f</em> (do not accept any other value) <em><strong>(M1) </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(f( - 1) = \frac{{ - 1}}{{ - 2 \times {{( - 1)}^2} + 5 \times ( - 1) - 2}}\) </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct working </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(\frac{{ - 1}}{{ - 2 - 5 - 2}}\) <strong><em>A1 </em></strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct <em>y</em>-coordinate \(y = \frac{1}{9}\) (may be seen in coordinate form \(\left( { - 1,\frac{1}{9}} \right)\) ) <strong><em>A1 N2</em></strong> </span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[7 marks] </span></strong></em></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;">recognizing values between max and min <em><strong>(R1) </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\frac{1}{9} < k < 1\) <em><strong>A2 N3</strong> </em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[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;">While most candidates answered part (a) correctly, there were some who did not show quite enough work for a "show that" question. A very small number of candidates did not follow the instruction to use the quotient rule. </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 (b), most candidates knew that they needed to solve the equation \(f'(x) = 0\) , and many were successful in answering this question correctly. However, some candidates failed to find both values of <em>x</em>, or made other algebraic errors in their solutions. One common error was to find only one solution for \({x^2} = 1\) ; another was to work with the denominator equal to zero, rather than the numerator.</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 (c), a significant number of candidates seemed to think that the line \(y = k\) was a vertical line, and attempted to find the vertical asymptotes. Others tried looking for a horizontal asymptote. Fortunately, there were still a good number of intuitive candidates who recognized the link with the graph and with part (b), and realized that the horizontal line must pass through the space between the given local minimum and the local maximum they had found in part (b). </span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Given that \({2^m} = 8\) and \({2^n} = 16\), write down the value of \(m\) and of \(n\).</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">Hence or otherwise solve \({8^{2x + 1}} = {16^{2x - 3}}\).</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">\(m = 3,{\text{ }}n = 4\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1A1 <span class="Apple-converted-space"> </span>N2</em></strong></span></p>
<p class="p1"><span class="s1"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">attempt to apply \({({2^a})^b} = {2^{ab}}\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><em>eg</em>\(\;\;\;6x + 3,{\text{ }}4(2x - 3)\)</p>
<p class="p1">equating <strong>their </strong>powers of \(2\) (seen anywhere) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1"><em>eg</em>\(\;\;\;3(2x + 1) = 8x - 12\)</p>
<p class="p1">correct working <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><em>eg</em>\(\;\;\;8x - 12 = 6x + 3,{\text{ }}2x = 15\)</p>
<p class="p1">\(x = \frac{{15}}{2}\;\;\;(7.5)\) <span class="Apple-converted-space"> </span><strong><em>A1 <span class="Apple-converted-space"> </span>N2</em></strong></p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<p class="p1"><strong><em>Total [6 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;">
<p class="p1">Indices laws were well understood with many candidates solving the equation correctly. Some candidates used logs, which took longer, and errors crept in.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Indices laws were well understood with many candidates solving the equation correctly. Some candidates used logs, which took longer, and errors crept in.</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;">Let \(f(x) = p(x - q)(x - r)\) . Part of the graph of <em>f</em> is shown below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/glee.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The graph passes through the points (−2, 0), (0, − 4) and (4, 0) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Write down the value of <em>q</em> and of <em>r</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 style="font-family: times new roman,times; font-size: medium;">Write down the <strong>equation</strong> of the axis of symmetry.</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 style="font-family: times new roman,times; font-size: medium;">Find the value of <em>p</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 style="font-family: times new roman,times; font-size: medium;">\(q = - 2\) , \(r = 4\) or \(q = 4\) , \(r = - 2\) <em><strong>A1A1 N2</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[2 marks]</span></strong></em></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;">\(x = 1\) (must be an equation) <em><strong>A1 N1</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[1 mark]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">substituting \((0{\text{, }} - 4)\) into the equation <em><strong>(M1)</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \( - 4 = p(0 - ( - 2))(0 - 4)\) , \( - 4 = p( - 4)(2)\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">correct working towards solution <em><strong>(A1)</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \( - 4 = - 8p\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(p = \frac{4}{8}\) \(\left( { = \frac{1}{2}} \right)\) <em><strong>A1 N2</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The majority of candidates were successful on some or all parts of this question, with some </span><span style="font-family: times new roman,times; font-size: medium;">candidates using a mix of algebra and graphical reasoning and others ignoring the graph and </span><span style="font-family: times new roman,times; font-size: medium;">working only algebraically. Some did not recognize that <em>p</em> and <em>q</em> are the roots of the quadratic </span><span style="font-family: times new roman,times; font-size: medium;">function and hence gave the answers as 2 and \( - 4\).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">A common error in part (b) was the absence </span><span style="font-family: times new roman,times; font-size: medium;">of an equation. Some candidates wrote down the equation \(x = \frac{{ - b}}{{2a}}\) but were not able to </span><span style="font-family: times new roman,times; font-size: medium;">substitute correctly. Those students did not realize that the axis of symmetry is always </span><span style="font-family: times new roman,times; font-size: medium;">halfway between the <em>x</em>-intercepts.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">More candidates had trouble with part (c) with erroneous </span><span style="font-family: times new roman,times; font-size: medium;">substitutions and simplification mistakes commonplace.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1"><span class="s1">Let \(f(x) = 6x\sqrt {1 - {x^2}} \)</span>, for \( - 1 \leqslant x \leqslant 1\)<span class="s1">, and \(g(x) = \cos (x)\)</span>, for \(0 \leqslant x \leqslant \pi \)<span class="s1">.</span></p>
<p class="p2">Let \(h(x) = (f \circ g)(x)\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write \(h(x)\) in the form \(a\sin (bx)\), where \(a,{\text{ }}b \in \mathbb{Z}\).</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Hence find the range of \(h\).</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">attempt to form composite in any order <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"><em>eg</em>\(\,\,\,\,\,\)\(f\left( {g(x)} \right),{\text{ }}\cos \left( {6x\sqrt {1 - {x^2}} } \right)\)</p>
<p class="p1">correct working <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\(6\cos x\sqrt {1 - {{\cos }^2}x} \)</p>
<p class="p1">correct application of Pythagorean identity (do not accept \({\sin ^2}x + {\cos ^2}x = 1\)) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\({\sin ^2}x = 1 - {\cos ^2}x,{\text{ }}6\cos x\sin x,{\text{ }}6\cos x \left| \sin x\right|\)</p>
<p class="p2">valid approach (do not accept \(2\sin x\cos x = \sin 2x\)<span class="s1">) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></span></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\(3(2\cos x\sin x)\)</p>
<p class="p1"><span class="Apple-converted-space">\(h(x) = 3\sin 2x\) </span><strong><em>A1 <span class="Apple-converted-space"> </span>N3</em></strong></p>
<p class="p1"><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">valid approach <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)amplitude \( = 3\), sketch with max and min \(y\)-values labelled, \( - 3 < y < 3\)</p>
<p class="p1">correct range <span class="Apple-converted-space"> </span><strong><em>A1 <span class="Apple-converted-space"> </span>N2</em></strong></p>
<p class="p2"><span class="s1"><em>eg</em>\(\,\,\,\,\,\)\( - 3 \leqslant y \leqslant 3\)</span>, \([ - 3,{\text{ }}3]\) from \( - 3\) to 3</p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Do not award <strong><em>A1 </em></strong>for \( - 3 < y < 3\) <span class="s2">or for “between \( - 3\)</span> and <span class="s2">3”.</span></p>
<p class="p1"><strong><em>[2 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;">
<p class="p1">In part (a), nearly all candidates found the correct composite function in terms of \(\cos x\), though many did not get any further than this first step in their solution to the question. While some candidates seemed to recognize the need to use trigonometric identities, most were unsuccessful in finding the correct expression in the required form.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">In part (b), very few candidates were able to provide the correct range of the function.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A quadratic function \(f\) can be written in the form \(f(x) = a(x - p)(x - 3)\). The graph of \(f\) has axis of symmetry \(x = 2.5\) and \(y\)-intercept at \((0,{\text{ }} - 6)\)</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(p\).</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>Find the value of \(a\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The line \(y = kx - 5\) is a tangent to the curve of \(f\). Find the values of \(k\).</p>
<div class="marks">[8]</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>METHOD 1 (using <em>x</em>-intercept)</strong></p>
<p>determining that 3 is an \(x\)-intercept <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(x - 3 = 0\), <img src="images/Schermafbeelding_2017-08-11_om_13.55.43.png" alt="M17/5/MATME/SP1/ENG/TZ1/09.a/M"></p>
<p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(3 - 2.5,{\text{ }}\frac{{p + 3}}{2} = 2.5\)</p>
<p>\(p = 2\) <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong>METHOD 2 (expanding <em>f </em>(<em>x</em>)) </strong></p>
<p>correct expansion (accept absence of \(a\)) <strong><em>(A1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(a{x^2} - a(3 + p)x + 3ap,{\text{ }}{x^2} - (3 + p)x + 3p\)</p>
<p>valid approach involving equation of axis of symmetry <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(\frac{{ - b}}{{2a}} = 2.5,{\text{ }}\frac{{a(3 + p)}}{{2a}} = \frac{5}{2},{\text{ }}\frac{{3 + p}}{2} = \frac{5}{2}\)</p>
<p>\(p = 2\) <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong>METHOD 3 (using derivative)</strong></p>
<p>correct derivative (accept absence of \(a\)) <strong><em>(A1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(a(2x - 3 - p),{\text{ }}2x - 3 - p\)</p>
<p>valid approach <strong>(<em>M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(f’(2.5) = 0\)</p>
<p>\(p = 2\) <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to substitute \((0,{\text{ }} - 6)\) <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\( - 6 = a(0 - 2)(0 - 3),{\text{ }}0 = a( - 8)( - 9),{\text{ }}a{(0)^2} - 5a(0) + 6a = - 6\)</p>
<p>correct working <strong><em>(A1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\( - 6 = 6a\)</p>
<p>\(a = - 1\) <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1 (using discriminant)</strong></p>
<p>recognizing tangent intersects curve once <strong><em>(M1)</em></strong></p>
<p>recognizing one solution when discriminant = 0 <strong><em>M1</em></strong></p>
<p>attempt to set up equation <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(g = f,{\text{ }}kx - 5 = - {x^2} + 5x - 6\)</p>
<p>rearranging their equation to equal zero <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\({x^2} - 5x + kx + 1 = 0\)</p>
<p>correct discriminant (if seen explicitly, not just in quadratic formula) <strong><em>A1</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\({(k - 5)^2} - 4,{\text{ }}25 - 10k + {k^2} - 4\)</p>
<p>correct working <strong><em>(A1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(k - 5 = \pm 2,{\text{ }}(k - 3)(k - 7) = 0,{\text{ }}\frac{{10 \pm \sqrt {100 - 4 \times 21} }}{2}\)</p>
<p>\(k = 3,{\text{ }}7\) <strong><em>A1A1</em></strong> <strong><em>N0</em></strong></p>
<p><strong>METHOD 2 (using derivatives)</strong></p>
<p>attempt to set up equation <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(g = f,{\text{ }}kx - 5 = - {x^2} + 5x - 6\)</p>
<p>recognizing derivative/slope are equal <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(f’ = {m_T},{\text{ }}f' = k\)</p>
<p>correct derivative of \(f\) <strong><em>(A1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\( - 2x + 5\)</p>
<p>attempt to set up equation in terms of either \(x\) or \(k\) <strong><em>M1</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(( - 2x + 5)x - 5 = - {x^2} + 5x - 6,{\text{ }}k\left( {\frac{{5 - k}}{2}} \right) - 5 = - {\left( {\frac{{5 - k}}{2}} \right)^2} + 5\left( {\frac{{5 - k}}{2}} \right) - 6\)</p>
<p>rearranging their equation to equal zero <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\({x^2} - 1 = 0,{\text{ }}{k^2} - 10k + 21 = 0\)</p>
<p>correct working <strong><em>(A1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(x = \pm 1,{\text{ }}(k - 3)(k - 7) = 0,{\text{ }}\frac{{10 \pm \sqrt {100 - 4 \times 21} }}{2}\)</p>
<p>\(k = 3,{\text{ }}7\) <strong><em>A1A1</em></strong> <strong><em>N0</em></strong></p>
<p><strong><em>[8 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">The following diagram shows part of the graph of a quadratic function \(f\).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2017-02-02_om_09.12.00.png" alt="M16/5/MATME/SP1/ENG/TZ2/01"></p>
<p class="p1">The vertex is at \((3,{\text{ }} - 1)\) <span class="s1">and the \(x\)</span>-intercepts at 2 and 4<span class="s1">.</span></p>
<p class="p2">The function \(f\) can be written in the form \(f(x) = {(x - h)^2} + k\).</p>
</div>
<div class="specification">
<p class="p1">The function can also be written in the form \(f(x) = (x - a)(x - b)\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down the value of \(h\) and of \(k\).</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 down the value of \(a\) and of \(b\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the \(y\)-intercept.</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">\(h = 3,{\text{ }}k = - 1\) </span><strong><em>A1A1 <span class="Apple-converted-space"> </span>N2</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">\(a = 2,{\text{ }}b = 4{\text{ }}({\text{or }}a = 4,{\text{ }}b = 2)\) </span><strong><em>A1A1 <span class="Apple-converted-space"> </span>N2</em></strong></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">attempt to substitute \(x = 0\) into their \(f\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\({(0 - 3)^2} - 1,{\text{ }}(0 - 2)(0 - 4)\)</p>
<p class="p1"><span class="Apple-converted-space">\(y = 8\) </span><strong><em>A1 <span class="Apple-converted-space"> </span>N2</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;">
<p class="p1">Nearly all candidates performed well on this question, earning full marks on all three question parts.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Nearly all candidates performed well on this question, earning full marks on all three question parts. In part (b), there were some candidates who factored the quadratic expression correctly, but went on to give negative values for \(a\) and \(b\).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Nearly all candidates performed well on this question, earning full marks on all three question parts.</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;">Let \(f(x) = \frac{{ax}}{{{x^2} + 1}}\) , \( - 8 \le x \le 8\) , \(a \in \mathbb{R}\) .The graph of <em>f</em> is shown below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/bernie.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The region between \(x = 3\) and \(x = 7\) is shaded.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Show that \(f( - x) = - f(x)\) .</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 style="font-family: times new roman,times; font-size: medium;">Given that \(f''(x) = \frac{{2ax({x^2} - 3)}}{{{{({x^2} + 1)}^3}}}\) , find the coordinates of all points of inflexion.</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">It is given that \(\int {f(x){\rm{d}}x = \frac{a}{2}} \ln ({x^2} + 1) + C\) </span><span style="font-family: times new roman,times; font-size: medium;">.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Find the area of the shaded region, giving your answer in the form \(p\ln q\) .</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(ii) Find the value of \(\int_4^8 {2f(x - 1){\rm{d}}x} \)</span><span style="font-family: times new roman,times; font-size: medium;"> .</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><strong><span style="font-family: times new roman,times; font-size: medium;">METHOD 1</span></strong></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">evidence of substituting \( - x\) for \(x\) <em><strong>(M1)</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(f( - x) = \frac{{a( - x)}}{{{{( - x)}^2} + 1}}\) <em><strong>A1</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(f( - x) = \frac{{ - ax}}{{{x^2} + 1}}\) \(( = - f(x))\) <em><strong>AG N0</strong></em></span></p>
<p align="LEFT"><strong><span style="font-family: times new roman,times; font-size: medium;">METHOD 2</span></strong></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(y = - f(x)\) is reflection of \(y = f(x)\) in <em>x</em> axis</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">and \(y = f( - x)\) is reflection of \(y = f(x)\) in <em>y</em> axis <em><strong>(M1)</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">sketch showing these are the same <em><strong>A1</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(f( - x) = \frac{{ - ax}}{{{x^2} + 1}}\) \(( = - f(x))\) <em><strong>AG N0</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[2 marks]</span></strong></em></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;">evidence of appropriate approach <em><strong>(M1) </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(f''(x) = 0\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">to set the numerator equal to 0 <em><strong>(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(2ax({x^2} - 3) = 0\) ; \(({x^2} - 3) = 0\) </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(0, 0) ,</span> <span style="font-family: Times New Roman; font-size: medium;">\(\left( {\sqrt 3 ,\frac{{a\sqrt 3 }}{4}} \right)\) , \(\left( { - \sqrt 3 , - \frac{{a\sqrt 3 }}{4}} \right)\) (accept \(x = 0\) , \(y = 0\) etc) </span><em><span style="font-family: times new roman,times; font-size: medium;"><strong>A1A1A1A1A1 N5</strong> </span></em></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;"> [7 marks]</span></strong></em></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;">(i) correct expression <em><strong>A2</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(\left[ {\frac{a}{2}\ln ({x^2} + 1)} \right]_3^7\) , \(\frac{a}{2}\ln 50 - \frac{a}{2}\ln 10\) , \(\frac{a}{2}(\ln 50 - \ln 10)\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">area = \(\frac{a}{2}\ln 5\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1A1 N2</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) <strong>METHOD 1</strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">recognizing the shift that does not change the area <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(\int_4^8 {f(x - 1){\rm{d}}x} = \int_3^7 {f(x){\rm{d}}x} \) , \(\frac{a}{2}\ln 5\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">recognizing that the factor of 2 doubles the area <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(\int_4^8 {2f(x - 1){\rm{d}}x = } 2\int_4^8 {f(x - 1){\rm{d}}x} \) \(\left( { = 2\int_3^7 {f(x){\rm{d}}x} } \right)\)</span></p>
<p><span style="font-family: Times New Roman; font-size: medium;">\(\int_4^8 {2f(x - 1){\rm{d}}x = a\ln 5} \) (i.e. \(2 \times \) <strong>their</strong> answer to (c)(i)) <em><strong> </strong></em></span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1 N3</span></strong></em></p>
<p><strong> <span style="font-family: times new roman,times; font-size: medium;">METHOD 2</span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">changing variable</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">let \(w = x - 1\) , so \(\frac{{{\rm{d}}w}}{{{\rm{d}}x}} = 1\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(2\int {f(w){\rm{d}}w = } \frac{{2a}}{2}\ln ({w^2} + 1) + c\) <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">substituting correct limits</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(\left[ {a\ln \left[ {{{(x - 1)}^2} + 1} \right]} \right]_4^8\) , \(\left[ {a\ln ({w^2} + 1)} \right]_3^7\) , \(a\ln 50 - a\ln 10\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">(M1)</span></strong></em></p>
<p><span style="font-family: Times New Roman; font-size: medium;">\(\int_4^8 {2f(x - 1){\rm{d}}x = a\ln 5} \) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1 N3</span></strong></em></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;"> [7 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;">Part (a) was achieved by some candidates, although brackets around the \( - x\) were commonly neglected. Some attempted to show the relationship by substituting a specific value for <em>x</em> . This earned no marks as a general argument is required. </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 many recognized the requirement to set the second derivative to zero in (b), a majority neglected to give their answers as ordered pairs, only writing the <em>x</em>-coordinates. Some did not consider the negative root. </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;">For those who found a correct expression in (c)(i), many finished by calculating \(\ln 50 - \ln 10 = \ln 40\) . Few recognized that the translation did not change the area, although some factored the 2 from the integrand, appreciating that the area is double that in (c)(i).</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = 3 + \frac{{20}}{{{x^2} - 4}}\) , for \(x \ne \pm 2\) . The graph of <em>f</em> is given below.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/fajita.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The <em>y</em>-intercept is at the point A.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Find the coordinates of A.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Show that \(f'(x) = 0\) at A.</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The second derivative \(f''(x) = \frac{{40(3{x^2} + 4)}}{{{{({x^2} - 4)}^3}}}\)</span><span style="font-family: times new roman,times; font-size: medium;"> . Use this to</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) justify that the graph of <em>f</em> has a local maximum at A;</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) explain why the graph of <em>f</em> does <strong>not</strong> have a point of inflexion.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Describe the behaviour of the graph of \(f\) for large \(|x|\) .</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 style="font-family: times new roman,times; font-size: medium;">Write down the range of \(f\) .</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 style="font-family: times new roman,times; font-size: medium;">(i) coordinates of A are \((0{\text{, }} - 2)\) <em><strong>A1A1 N2</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) derivative of \({x^2} - 4 = 2x\) (seen anywhere) <em><strong>(A1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">evidence of correct approach <em><strong> (M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. quotient rule, chain rule</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">finding \(f'(x)\) <em><strong>A2</strong></em></span></p>
<p><span style="font-family: Times New Roman; font-size: medium;">e.g. \(f'(x) = 20 \times ( - 1) \times {({x^2} - 4)^{ - 2}} \times (2x)\) , \(\frac{{({x^2} - 4)(0) - (20)(2x)}}{{{{({x^2} - 4)}^2}}}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">substituting \(x = 0\) into \(f'(x)\) (do not accept solving \(f'(x) = 0\) ) <em><strong>M1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">at A \(f'(x) = 0\) <em><strong>AG N0</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;"> [7 marks]</span></strong></em></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;">(i) reference to \(f'(x) = 0\) (seen anywhere) <em><strong> (R1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">reference to \(f''(0)\) is negative (seen anywhere) <em><strong>R1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">evidence of substituting \(x = 0\) into \(f''(x)\) <em><strong> M1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">finding \(f''(0) = \frac{{40 \times 4}}{{{{( - 4)}^3}}}\) \(\left( { = - \frac{5}{2}} \right)\) <em><strong>A1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">then the graph must have a local maximum <em><strong>AG</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) reference to \(f''(x) = 0\) at point of inflexion <em><strong>(R1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">recognizing that the second derivative is never 0 <em><strong>A1 N2</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(40(3{x^2} + 4) \ne 0\) , \(3{x^2} + 4 \ne 0\) , \({x^2} \ne - \frac{4}{3}\) , the numerator </span><span style="font-family: times new roman,times; font-size: medium;">is always positive </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note</strong>: Do not accept the use of the first derivative in part (b). </span></p>
<p><strong><span style="font-family: times new roman,times; font-size: medium;"><em>[6 marks]</em> </span></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">correct (informal) statement, including reference to approaching \(y = 3\) <em><strong>A1 N1</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. getting closer to the line \(y = 3\) , horizontal asymptote at \(y = 3\)</span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[1 mark]</span></strong></em></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;"><strong>correct</strong> inequalities, \(y \le - 2\) , \(y > 3\) , <em><strong>FT</strong></em> from (a)(i) and (c) <em><strong>A1A1 N2</strong> </em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[2 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-family: times new roman,times; font-size: medium;">Almost all candidates earned the first two marks in part (a) (i), although fewer were able to apply the quotient rule 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;">Many candidates were able to state how the second derivative can be used to identify maximum and inflection points, but fewer were actually able to demonstrate this with the given function. For example, in (b)(ii) candidates often simply said "the second derivative cannot equal 0" but did not justify or explain why this was true. </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;">Not too many candidates could do part (c) correctly.</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 (d) even those who knew what the range was had difficulty expressing the inequalities correctly. </span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">Solve \({\log _2}x + {\log _2}(x - 2) = 3\) , for \(x > 2\) .</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">recognizing \(\log a + \log b = \log ab\) (seen anywhere) <em><strong>(A1)</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \({\log _2}(x(x - 2))\) , \({x^2} - 2x\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">recognizing \({\log _a}b = x \Leftrightarrow {a^x} = b\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">(A1)</span></strong></em></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \({2^3} = 8\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">correct simplification <em><strong>A1</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \(x(x - 2) = {2^3}\) , \({x^2} - 2x - 8\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">evidence of correct approach to solve <em><strong>(M1)</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. factorizing, quadratic formula</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">correct working <em><strong>A1</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \((x - 4)(x + 2)\) , \(\frac{{2 \pm \sqrt {36} }}{2}\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(x = 4\) <em><strong>A2 N3</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[7 marks]</span></strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Candidates secure in their understanding of logarithm properties usually had success with this </span><span style="font-family: times new roman,times; font-size: medium;">problem, solving the resulting quadratic either by factoring or using the quadratic formula. </span><span style="font-family: times new roman,times; font-size: medium;">The majority of successful candidates correctly rejected the solution that was not in the </span><span style="font-family: times new roman,times; font-size: medium;">domain. A number of candidates, however, were unclear on logarithm properties. Some </span><span style="font-family: times new roman,times; font-size: medium;">unsuccessful candidates were able to demonstrate understanding of one property but without </span><span style="font-family: times new roman,times; font-size: medium;">both were not able to make much progress. A few candidates employed a “guess and check” </span><span style="font-family: times new roman,times; font-size: medium;">strategy, but this did not earn full marks.</span></p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagram below shows the graph of a function \(f(x)\) , for \( - 2 \le x \le 4\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/999.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(h(x) = f( - x)\) . Sketch the graph of \(h\) on the grid below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/chubby.png" alt></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times;"><span style="font-size: medium;">Let \(g(x) = \frac{1}{2}f(x - 1)\) </span><span style="font-size: medium;">. The point \({\text{A}}(3{\text{, }}2)\) on the graph of \(f\) is transformed to the </span><span style="font-size: medium;">point P on the graph of \(g\) . Find the coordinates of P.</span></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 style="font-family: times new roman,times;"><span style="font-size: medium;"><br><img src="images/penny.png" alt></span><span style="font-size: medium;"> <em><strong>A2 N2</strong></em></span></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><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 style="font-family: times new roman,times; font-size: medium;">evidence of appropriate approach <em><strong> (M1) </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. reference to any horizontal shift and/or stretch factor, \(x = 3 + 1\) , \(y = \frac{1}{2} \times 2\) </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">P is \((4{\text{, }}1)\) (accept \(x = 4\) , \(y = 1\)) <em><strong>A1A1 N3</strong> </em></span></p>
<p><span style="font-family: times new roman,times;"><em><strong><span style="font-size: medium;">[3 marks]</span></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;">Part (a) was generally solved correctly. Students had no trouble in deciding what transformation had to be done to the graph, although some confused \(f( - x)\) with \( - f(x)\) . </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 generally poorly done. They could not "read" that the transformation shifted the curve 1 unit to the right and stretched it in the \(y\)-direction with a scale factor of \(\frac{1}{2}\) . It was often seen that the shift was interpreted, but in the opposite direction. Also, the stretch was applied to both coordinates of the point. Those candidates who answered part (a) incorrectly often had trouble on (b) as well, indicating a difficulty with transformations in general. However, there were also candidates who solved part (a) correctly but could not interpret part (b). This would indicate that it is simpler for them to plot the transformation of an entire function than to find how a particular point is transformed. </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;">Let \(f(x) = 3{(x + 1)^2} - 12\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Show that \(f(x) = 3{x^2} + 6x - 9\) .</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 style="font-family: times new roman,times; font-size: medium;">For the graph of <em>f </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(i) write down the coordinates of the vertex; </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) write down the <strong>equation</strong> of the axis of symmetry; </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(iii) write down the <em>y</em>-intercept; </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> (iv) find both <em>x</em>-intercepts. </span></p>
<div class="marks">[8]</div>
<div class="question_part_label">b(i), (ii), (iii) and (iv).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Hence</strong> sketch 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 style="font-family: times new roman,times; font-size: medium;">Let \(g(x) = {x^2}\) . The graph of <em>f</em> may be obtained from the graph of <em>g</em> by the two transformations: </span></p>
<p style="margin-left: 60px;"><span style="font-family: times new roman,times; font-size: medium;">a stretch of scale factor <em>t</em> in the <em>y</em>-direction</span></p>
<p style="margin-left: 60px;"><span style="font-family: times new roman,times; font-size: medium;">followed by </span><span style="font-family: times new roman,times; font-size: medium;">a translation of \(\left( {\begin{array}{*{20}{c}}<br>p\\<br>q<br>\end{array}} \right)\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> Find \(\left( {\begin{array}{*{20}{c}}<br>p\\<br>q<br>\end{array}} \right)\) and the value of <em>t</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(f(x) = 3({x^2} + 2x + 1) - 12\) <strong><em>A1</em></strong></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\( = 3{x^2} + 6x + 3 - 12\) <em><strong>A1</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\( = 3{x^2} + 6x - 9\) <em><strong>AG N0</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[2 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) vertex is \(( - 1{\text{, }} - 12)\) <em><strong> A1A1 N2</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(ii) \(x = - 1\) (<strong>must</strong> be an equation) <em><strong>A1 N1</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(iii) \((0{\text{, }} - 9)\) <em><strong>A1 N1</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(iv) evidence of solving \(f(x) = 0\) <em><strong>(M1)</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. factorizing, formula,</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">correct working <em><strong>A1</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \(3(x + 3)(x - 1) = 0\) , \(x = \frac{{ - 6 \pm \sqrt {36 + 108} }}{6}\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(( - 3{\text{, }}0)\), \((1{\text{, }}0)\) </span><span style="font-family: times new roman,times; font-size: medium;"><em><strong>A1A1 N1N1</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[8 marks]</span></strong></em></p>
<div class="question_part_label">b(i), (ii), (iii) and (iv).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="images/lamb.png" alt></span><em><strong><span style="font-family: times new roman,times; font-size: medium;"> A1A1 N2</span></strong></em></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><strong>Note</strong>: Award <em><strong>A1</strong></em> for a parabola opening upward, <em><strong>A1</strong></em> for vertex and intercepts in approximately correct positions.</span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[2 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(\left( {\begin{array}{*{20}{c}}<br>p\\<br>q<br>\end{array}} \right) = \left( {\begin{array}{*{20}{c}}<br>{ - 1}\\<br>{ - 12}<br>\end{array}} \right)\)</span><span style="font-family: times new roman,times; font-size: medium;"> , \(t = 3\) </span><span style="font-family: times new roman,times; font-size: medium;">(accept \(p = - 1\) , \(q = - 12\) , \(t = 3\) ) <em><strong>A1A1A1 N3</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">This problem was generally well done. The “show that” question in part (a) was done correctly </span><span style="font-family: times new roman,times; font-size: medium;">by most candidates, with a few attempting to show it by working backwards, which earned no </span><span style="font-family: times new roman,times; font-size: medium;">marks.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Most candidates were able to identify the vertex but were unable to write the equation </span><span style="font-family: times new roman,times; font-size: medium;">for the axis of symmetry. There was a great deal of success with the <em>x</em> and <em>y</em> intercepts.</span></p>
<div class="question_part_label">b(i), (ii), (iii) and (iv).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Some of the sketches of the graph left much to be desired even if they were technically </span><span style="font-family: times new roman,times; font-size: medium;">correct; many were v-shaped.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The final part was poorly done, indicating that defining a </span><span style="font-family: times new roman,times; font-size: medium;">graph in terms of stretch and translation was unfamiliar to many candidates.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: TimesNewRomanPSMT;">The equation </span><span style="font-family: TimesNewRomanPS-ItalicMT;">\({x^2} - 3x + {k^2} = 4\)</span><span style="font-family: TimesNewRomanPSMT;"> has two distinct real roots. Find the possible values of </span><em><span style="font-family: TimesNewRomanPS-ItalicMT;">k </span></em><span style="font-family: TimesNewRomanPSMT;">.</span></span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">evidence of rearranged quadratic equation (may be seen in working) <em><strong>A1 </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>e.g.</em> \({x^2} - 3x + {k^2} - 4 = 0\) , \({k^2} - 4\) </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">evidence of discriminant (must be seen explicitly, not in quadratic formula) <em><strong>(M1) </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>e.g</em>. \({b^2} - 4ac\) , \(\Delta = {( - 3)^2} - 4(1)({k^2} - 4)\) </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">recognizing that discriminant is greater than zero (seen anywhere, including answer) <strong><em> R1</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>e.g</em>. \({b^2} - 4ac > 0\) , \(9 + 16 - 4{k^2} > 0\) </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct working (accept equality) <em><strong>A1 </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>e.g</em>. \(25 - 4{k^2} > 0\) , \(4{k^2} < 25\) , \({k^2} = \frac{{25}}{4}\) </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">both correct values (even if inequality never seen) <em><strong>(A1) </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>e.g</em>. \(\pm \sqrt{{\frac{{25}}{4}}}\) , \( \pm 2.5\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct interval <em><strong>A1</strong> <strong>N3 </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>e.g</em>. \( - \frac{5}{2} < k < \frac{5}{2}\) , \( - 2.5 < k < 2.5\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Do not award the final mark for unfinished values, or for incorrect or reversed </span><span style="font-family: times new roman,times; font-size: medium;">inequalities, including \( \le \) , \(k > - 2.5\) , \(k < 2.5\) . </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Special cases:</strong> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">If working shown, and candidates attempt to rearrange the quadratic equation to equal zero, but find an incorrect value of <em>c</em>, award <em><strong>A1M1R1A0A0A0</strong></em>. </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">If working shown, and candidates do not rearrange the quadratic equation to equal zero, but find \(c = {k^2}\) or \(c = \pm 4\) , award <em><strong>A0M1R1A0A0A0</strong></em>. </span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[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;">The majority of candidates who attempted to answer this question recognized the need to use the discriminant, however very few were able to answer the question successfully. The majority of candidates did not recognize that the quadratic equation must first be set equal to zero. In addition, many candidates simply set their discriminant equal to zero, instead of setting it greater than zero. Even many of the strongest candidates, who obtained the correct numerical values for <em>k</em>, were unable to write their final answers as a correct interval. </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">This question is a good example of candidates who reach for familiar methods, without really thinking about what the question is asking them to find. There were many candidates who attempted to solve for <em>x</em> using the quadratic formula or factoring, even though the question did not ask them to solve for <em>x</em>. </span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">Let \(f(x) = {x^2} + x - 6\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down the \(y\)-intercept of the graph of \(f\).</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">Solve \(f(x) = 0\).</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 class="p1">On the following grid, sketch the graph of \(f\), for \( - 4 \le x \le 3\).</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-13_om_16.03.12.png" alt></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>\(y\)-intercept is \( - 6,{\text{ }}(0,{\text{ }} - 6),{\text{ }}y = - 6\) <strong><em>A1</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>valid attempt to solve <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\;\;\;(x - 2)(x + 3) = 0,{\text{ }}x = \frac{{ - 1 \pm \sqrt {1 + 24} }}{2}\), one correct answer</p>
<p>\(x = 2,{\text{ }}x = - 3\) <strong><em>A1A1 N3</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p> <strong><em>A1A1A1</em></strong></p>
<p><img src="image.html" alt> </p>
<p><strong>Note:</strong> The shape must be an approximately correct concave up parabola. Only if the shape is correct, award the following:</p>
<p><strong><em>A1</em></strong> for the \(y\)-intercept in circle <strong>and</strong> the vertex approximately on \(x = - \frac{1}{2}\), below \(y = - 6\),</p>
<p><strong><em>A1</em></strong> for <strong>both</strong> the \(x\)-intercepts in circles,</p>
<p><strong><em>A1</em></strong> for <strong>both</strong> end points in ovals.</p>
<p><em><strong>[3 marks]</strong></em></p>
<p><em><strong>Total [7 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 class="p1">Parts (a) and (b) of this question were answered quite well by nearly all candidates, with only a few factoring errors in part (b).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Parts (a) and (b) of this question were answered quite well by nearly all candidates, with only a few factoring errors in part (b).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">In part (c), although most candidates were familiar with the general parabolic shape of the graph, many placed the vertex at the \(y\)-intercept \((0,{\text{ }} - 6)\), and very few candidates considered the endpoints of the function with the given domain.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Let \(f(x) = {x^2} - x\), for \(x \in \mathbb{R}\). The following diagram shows part of the graph of \(f\).</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-11_om_09.25.10.png" alt="N17/5/MATME/SP1/ENG/TZ0/08"></p>
<p>The graph of \(f\) crosses the \(x\)-axis at the origin and at the point \({\text{P}}(1,{\text{ }}0)\).</p>
</div>
<div class="specification">
<p>The line <em>L</em> is the normal to the graph of <em>f</em> at P.</p>
</div>
<div class="specification">
<p>The line \(L\) intersects the graph of \(f\) at another point Q, as shown in the following diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-11_om_09.27.48.png" alt="N17/5/MATME/SP1/ENG/TZ0/08.c.d"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that \(f’(1) = 1\).</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 equation of \(L\) in the form \(y = ax + b\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the \(x\)-coordinate of Q.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of the region enclosed by the graph of \(f\) and the line \(L\).</p>
<div class="marks">[6]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(f’(x) = 2x - 1\) <strong><em>A1A1</em></strong></p>
<p>correct substitution <strong><em>A1</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(2(1) - 1,{\text{ }}2 - 1\)</p>
<p>\(f’(1) = 1\) <strong><em>AG N0</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>correct approach to find the gradient of the normal <strong><em>(A1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(\frac{{ - 1}}{{f'(1)}},{\text{ }}{m_1}{m_2} = - 1,{\text{ slope}} = - 1\)</p>
<p>attempt to substitute correct normal gradient and coordinates into equation of a line <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(y - 0 = - 1(x - 1),{\text{ }}0 = - 1 + b,{\text{ }}b = 1,{\text{ }}L = - x + 1\)</p>
<p>\(y = - x + 1\) <strong><em>A1 N2</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>equating expressions <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(f(x) = L,{\text{ }} - x + 1 = {x^2} - x\)</p>
<p>correct working (must involve combining terms) <strong><em>(A1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\({x^2} - 1 = 0,{\text{ }}{x^2} = 1,{\text{ }}x = 1\)</p>
<p>\(x = - 1\,\,\,\,\,\left( {{\text{accept }}Q( - 1,{\text{ }}2)} \right)\) <strong><em>A2 N3</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(\int {L - f,{\text{ }}\int_{ - 1}^1 {(1 - {x^2}){\text{d}}x} } \), splitting area into triangles and integrals</p>
<p>correct integration <strong><em>(A1)(A1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(\left[ {x - \frac{{{x^3}}}{3}} \right]_{ - 1}^1,{\text{ }} - \frac{{{x^3}}}{3} - \frac{{{x^2}}}{2} + \frac{{{x^2}}}{2} + x\)</p>
<p>substituting <strong>their</strong> limits into <strong>their</strong> integrated function and subtracting (in any order) <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(1 - \frac{1}{3} - \left( { - 1 - \frac{{ - 1}}{3}} \right)\)</p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>M0 </em></strong>for substituting into original or differentiated function.</p>
<p> </p>
<p>area \( = \frac{4}{3}\) <strong><em>A2 N3</em></strong></p>
<p><strong><em>[6 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 class="p1">The following diagram shows the graph of a function \(f\).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-01-13_om_05.56.49.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find \({f^{ - 1}}( - 1)\).</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 \((f \circ f)( - 1)\).</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 class="p1">On the same diagram, sketch the graph of \(y = f( - x)\).</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>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\;\;\;\)horizontal line on graph at \( - 1,{\text{ }}f(a) = - 1,{\text{ }}( - 1,5)\)</p>
<p>\({f^{ - 1}}( - 1) = 5\) <strong><em>A1 N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">attempt to find \(f( - 1)\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><em>eg</em>\(\;\;\;\)line on graph</p>
<p class="p1">\(f( - 1) = 2\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1">\((f \circ f)( - 1) = 1\) <span class="Apple-converted-space"> </span><strong><em>A1 <span class="Apple-converted-space"> </span>N3</em></strong></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="s1"><img src="images/Schermafbeelding_2016-01-13_om_06.13.13.png" alt> <span class="Apple-converted-space"> </span></span><strong><em>A1A1 <span class="Apple-converted-space"> </span>N2</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>The shape <strong>must </strong>be an approximately correct shape (concave down and increasing). <strong>Only </strong>if the shape is approximately correct, award the following for points in circles:</p>
<p class="p1"><strong><em>A1 </em></strong>for the \(y\)-intercept,</p>
<p class="p1"><strong><em>A1 </em></strong>for any <strong>two </strong>of these points \(( - 5,{\text{ }} - 1),{\text{ }}( - 2,{\text{ }}1),{\text{ }}(1,{\text{ }}2)\).</p>
<p class="p1"><em><strong>[2 marks]</strong></em></p>
<p class="p1"><em><strong>Total [7 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 class="p1">Typically candidates were more successful in finding the composite function than the inverse. Some students tried to find the function, rather than read values from the given graph. The sketch of \(f( - x)\) was often well done, with the most common error being a reflection in the <em>x</em>-axis.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Typically candidates were more successful in finding the composite function than the inverse. Some students tried to find the function, rather than read values from the given graph. The sketch of \(f( - x)\) was often well done, with the most common error being a reflection in the <em>x</em>-axis.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Typically candidates were more successful in finding the composite function than the inverse. Some students tried to find the function, rather than read values from the given graph. The sketch of \(f( - x)\) was often well done, with the most common error being a reflection in the <em>x</em>-axis.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the value of \({\log _2}40 - {\log _2}5\) .</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 style="font-family: times new roman,times; font-size: medium;">Find the value of \({8^{{{\log }_2}5}}\) .</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 style="font-family: times new roman,times; font-size: medium;">evidence of correct formula <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> \(\log a - \log b = \log \frac{a}{b}\) , \(\log \left( {\frac{{40}}{5}} \right)\) , \(\log 8 + \log 5 - \log 5\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Ignore missing or incorrect base. </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct working <em><strong>(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg </em> \({\log _2}8\) , \({2^3} = 8\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({\log _2}40 - {\log _2}5 = 3\) <em><strong>A1 N2 </strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[3 marks] </span></strong></em></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;">attempt to write \(8\) as a power of \(2\) (seen anywhere) <em><strong> (M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> \({({2^3})^{{{\log }_2}5}}\) , \({2^3} = 8\) , \({2^a}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">multiplying powers <em><strong> (M1) </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> \({2^{3{{\log }_2}5}}\) , \(a{\log _2}5\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct working <em><strong> (A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> \({2^{{{\log }_2}125}}\) , \({\log _2}{5^3}\) , \({\left( {{2^{{{\log }_2}5}}} \right)^3}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({8^{{{\log }_2}5}} = 125\) <em><strong>A1 N3 </strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[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;">Many candidates readily earned marks in part (a). Some interpreted \({\log _2}40 - {\log _2}5\) to mean \(\frac{{{{\log }_2}40}}{{{{\log }_2}5}}\) , an error which led to no further marks. Others left the answer as \({\log _2}5\) where an integer answer is expected.</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) proved challenging for most candidates, with few recognizing that changing \(8\) to base \(2\) is a helpful move. Some made it as far as \({2^{3{{\log }_2}5}}\) yet could not make that final leap to an integer.</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;">Let \(f(x) = \sqrt {x - 5} \) , for \(x \ge 5\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find \({f^{ - 1}}(2)\) .</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Let \(g\) be a function such that \({g^{ - 1}}\) exists for all real numbers. Given that </span><span style="font-family: times new roman,times; font-size: medium;">\(g(30) = 3\) , find \((f \circ {g^{ - 1}})(3)\) .</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><strong><span style="font-family: times new roman,times; font-size: medium;">METHOD 1</span></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to set up equation <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> \(2 = \sqrt {y - 5} \) , \(2 = \sqrt {x - 5} \)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct working <em><strong>(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> \(4 = y - 5\) , \(x = {2^2} + 5\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({f^{ - 1}}(2) = 9\) <strong><em>A1 N2</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>METHOD 2</strong> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">interchanging \(x\) and \(y\) (seen anywhere) <strong><em>(M1)</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg </em> \(x = \sqrt {y - 5} \)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct working <strong><em>(A1)</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> \({x^2} = y - 5\) , \(y = {x^2} + 5\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\({f^{ - 1}}(2) = 9\) <strong><em>A1 N2</em> </strong></span></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[3 marks] </span></strong></em></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;">recognizing \({g^{ - 1}}(3) = 30\) <strong><em>(M1)</em> </strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> \(f(30)\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct working <em><strong>(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> \((f \circ {g^{ - 1}})(3) = \sqrt {30 - 5} \) , \(\sqrt {25} \)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\((f \circ {g^{ - 1}})(3) = 5\) <em><strong>A1 N2</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note</strong>: Award <em><strong>A0</strong></em> for multiple values,<em> eg</em> \( \pm 5\) . </span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[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;">Candidates often found an inverse function in which to substitute the value of \(2\). Some astute candidates set the function equal to \(2\) and solved for \(x\). Occasionally a candidate misunderstood the notation as asking for a derivative, or used \(\frac{1}{{f(x)}}\) .</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;">For part (b), many candidates recognized that if \(g(30) = 3\) then \({g^{ - 1}}(3) = 30\) , and typically completed the question successfully. Occasionally, however, a candidate incorrectly answered \(\sqrt {25} = \pm 5\).</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<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 equation \({x^2} + (k + 2)x + 2k = 0\) has two distinct real roots.</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;">Find the possible values of \(k\).</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">evidence of discriminant <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \({b^2} - 4ac,{\text{ }}\Delta = 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">correct substitution into discriminant <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \({(k + 2)^2} - 4(2k),{\text{ }}{k^2} + 4k + 4 - 8k\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">correct discriminant <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \({k^2} - 4k + 4,{\text{ }}{(k - 2)^2}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">recognizing discriminant is positive <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \(\Delta > 0,{\text{ }}{(k + 2)^2} - 4(2k) > 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">attempt to solve <strong>their </strong>quadratic in \(k\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> factorizing, \(k = \frac{{4 \pm \sqrt {16 - 16} }}{2}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">correct working <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \({(k - 2)^2} > 0,{\text{ }}k = 2\), sketch of positive parabola on the <em>x</em>-axis</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">correct values <strong><em>A2 N4</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \(k \in \mathbb{R}{\text{ and }}k \ne 2,{\text{ }}\mathbb{R}\backslash 2,{\text{ }}\left] { - \infty ,{\text{ }}2} \right[ \cup \left] {2,{\text{ }}\infty } \right[\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[8 marks]</em></strong></span></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-family: times new roman,times; font-size: medium;">Let \(f(x) = 3\ln x\) and \(g(x) = \ln 5{x^3}\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Express \(g(x)\) in the form \(f(x) + \ln a\) , where \(a \in {{\mathbb{Z}}^ + }\) .</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The graph of <em>g</em> is a transformation of the graph of <em>f</em> . Give a full geometric </span><span style="font-family: times new roman,times; font-size: medium;">description of this transformation.</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">attempt to apply rules of logarithms <em><strong>(M1)</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \(\ln {a^b} = b\ln a\) , \(\ln ab = \ln a + \ln b\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">correct application of \(\ln {a^b} = b\ln a\) (seen anywhere) <strong><em>A1</em></strong></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \(3\ln x = \ln {x^3}\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">correct application of \(\ln ab = \ln a + \ln b\) (seen anywhere) <strong><em>A1</em></strong></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \(\ln 5{x^3} = \ln 5 + \ln {x^3}\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">so \(\ln 5{x^3} = \ln 5 + 3\ln x\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(g(x) = f(x) + \ln 5\) (accept \(g(x) = 3\ln x + \ln 5\) ) <em><strong>A1 N1</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[4 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">transformation with correct name, direction, and value <strong><em>A3</em></strong></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. translation by \(\left( {\begin{array}{*{20}{c}}<br>0\\<br>{\ln 5}<br>\end{array}} \right)\) </span><span style="font-family: times new roman,times; font-size: medium;">, shift up by \(\ln 5\) , vertical translation of \(\ln 5\)</span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[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 very poorly done by the majority of candidates. While candidates seemed to have a vague idea of how to apply the rules of logarithms in part (a), very few did so successfully. The most common error in part (a) was to begin incorrectly with \(\ln 5{x^3} = 3\ln 5x\) . This error was often followed by other errors. </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 (b), very few candidates were able to describe the transformation as a vertical translation (or shift). Many candidates attempted to describe numerous incorrect transformations, and some left part (b) entirely blank. </span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider a function <em>f </em>(<em>x</em>) , for −2 ≤ <em>x</em> ≤ 2 . The following diagram shows the graph of <em>f</em>.</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <em>f</em> (0).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <em>f </em><sup>−1</sup> (1).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the range of <em>f </em><sup>−1</sup>.</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>On the grid above, sketch the graph of <em>f </em><sup>−1</sup>.</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>\(f\left( 0 \right) =Â - \frac{1}{2}\)Â Â Â <em><strong>A1 N1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>f </em><sup>−1</sup> (1) = 2   <em><strong>A1 N1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>−2 ≤ <em>y</em> ≤ 2, y∈ [−2, 2] (accept −2 ≤ <em>x</em> ≤ 2)   <em><strong>A1 N1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img 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"><strong>A1</strong><strong>A1A1A1Â N4</strong></p>
<p><strong>Note:</strong> Award <em><strong>A1</strong></em> for evidence of approximately correct reflection in <em>y</em> = <em>x</em> with correct curvature.</p>
<p>(<em>y</em>Â =Â <em>x</em> does not need to be explicitly seen)</p>
<p>Only if this mark is awarded, award marks as follows:</p>
<p><em><strong>A1</strong></em> for both correct invariant points in circles,</p>
<p><em><strong>A1</strong></em> for the three other points in circles,</p>
<p><em><strong>A1</strong></em> for correct domain.</p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = \frac{1}{2}{x^3} - {x^2} - 3x\) . Part of the graph of <em>f</em> is shown below.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/sheldon.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">There is a maximum point at A and a minimum point at B(3, − 9) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the coordinates of A.</span></p>
<div class="marks">[8]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Write down the coordinates of</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(i) the image of B after reflection in the <em>y</em>-axis;</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) the image of B after translation by the vector \(\left( {\begin{array}{*{20}{c}}<br>{ - 2}\\<br>5<br>\end{array}} \right)\) ;</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(iii) the image of B after reflection in the <em>x</em>-axis followed by </span><span style="font-family: times new roman,times; font-size: medium;">a horizontal stretch with scale factor \(\frac{1}{2}\) .</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">b(i), (ii) and (iii).</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">\(f(x) = {x^2} - 2x - 3\) <em><strong>A1A1A1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">evidence of solving \(f'(x) = 0\) <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \({x^2} - 2x - 3 = 0\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">evidence of correct working <em><strong>A1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \((x + 1)(x - 3)\) , \(\frac{{2 \pm \sqrt {16} }}{2}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(x = - 1\) (ignore \(x = 3\) ) <em><strong>(A1) </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">evidence of substituting <strong>their</strong> negative <em>x</em>-value into \(f(x)\) <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(\frac{1}{3}{( - 1)^3} - {( - 1)^2} - 3( - 1)\) , \( - \frac{1}{3} - 1 + 3\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(y = \frac{5}{3}\) <em><strong>A1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">coordinates are \(\left( { - 1,\frac{5}{3}} \right)\) <em><strong>N3</strong> </em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[8 marks] </span></strong></em></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;">(i) \(( - 3{\text{, }} - 9)\) <em><strong>A1 N1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) \((1{\text{, }} - 4)\) <em><strong>A1A1 N2</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(iii) reflection gives \((3{\text{, }}9)\) <em><strong>(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">stretch gives \(\left( {\frac{3}{2}{\text{, }}9} \right)\) <em><strong>A1A1 N3</strong> </em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[6 marks] </span></strong></em></p>
<div class="question_part_label">b(i), (ii) and (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;">A majority of candidates answered part (a) completely.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Candidates were generally successful in </span><span style="font-family: times new roman,times; font-size: medium;">finding images after single transformations in part (b). Common incorrect answers for (biii) </span><span style="font-family: times new roman,times; font-size: medium;">included \(\left( {\frac{3}{2},\frac{9}{2}} \right)\) </span><span style="font-family: times new roman,times; font-size: medium;">, (6, 9) and (6, 18) , demonstrating difficulty with images from horizontal </span><span style="font-family: times new roman,times; font-size: medium;">stretches.</span></p>
<div class="question_part_label">b(i), (ii) and (iii).</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Let \(f'(x) = \frac{{6 - 2x}}{{6x - {x^2}}}\), for \(0 < x < 6\).</p>
<p class="p1"><span class="s1">The graph of \(f\) </span>has a maximum point at P<span class="s1">.</span></p>
</div>
<div class="specification">
<p class="p1"><span class="s1">The \(y\)</span>-coordinate of P is \(\ln 27\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the \(x\)-coordinate of <span class="s1">P</span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find \(f(x)\), expressing your answer as a single logarithm.</p>
<div class="marks">[8]</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">The graph of \(f\) </span>is transformed by a vertical stretch with scale factor \(\frac{1}{{\ln 3}}\). The image of P under this transformation has coordinates \((a,{\text{ }}b)\).</p>
<p class="p1">Find the value of \(a\) and of \(b\), where \(a,{\text{ }}b \in \mathbb{N}\).</p>
<div class="marks">[[N/A]]</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">recognizing \(f'(x) = 0\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">correct working <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\(6 - 2x = 0\)</p>
<p class="p1"><span class="Apple-converted-space">\(x = 3\) </span><strong><em>A1 <span class="Apple-converted-space"> </span>N2</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">evidence of integration <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\(\int {f',{\text{ }}\int {\frac{{6 - 2x}}{{6x - {x^2}}}{\text{d}}x} } \)</p>
<p class="p1">using substitution <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\(\int {\frac{1}{u}{\text{d}}u} \) where \(u = 6x - {x^2}\)</p>
<p class="p1">correct integral <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\(\ln (u) + c,{\text{ }}\ln (6x - {x^2})\)</p>
<p class="p1">substituting \((3,{\text{ }}\ln 27)\) into <strong>their </strong>integrated expression (must have \(c\)) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\(\ln (6 \times 3 - {3^2}) + c = \ln 27,{\text{ }}\ln (18 - 9) + \ln k = \ln 27\)</p>
<p class="p1">correct working <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1"><span class="s1"><em>eg</em></span>\(\,\,\,\,\,\)\(c = \ln 27 - \ln 9\)</p>
<p class="p1"><strong>EITHER</strong></p>
<p class="p2"><span class="Apple-converted-space">\(c = \ln 3\) </span><span class="s2"><strong><em>(A1)</em></strong></span></p>
<p class="p1">attempt to substitute <strong>their </strong>value of \(c\) into \(f(x)\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\(f(x) = \ln (6x - {x^2}) + \ln 3\) <span class="Apple-converted-space"> </span><strong><em>A1 <span class="Apple-converted-space"> </span>N4</em></strong></p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">attempt to substitute <strong>their </strong>value of \(c\) into \(f(x)\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\(f(x) = \ln (6x - {x^2}) + \ln 27 - \ln 9\)</p>
<p class="p1">correct use of a log law <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\(f(x) = \ln (6x - {x^2}) + \ln \left( {\frac{{27}}{9}} \right),{\text{ }}f(x) = \ln \left( {27(6x - {x^2})} \right) - \ln 9\)</p>
<p class="p1"><span class="Apple-converted-space">\(f(x) = \ln \left( {3(6x - {x^2})} \right)\) </span><strong><em>A1 <span class="Apple-converted-space"> </span>N4</em></strong></p>
<p class="p1"><strong><em>[8 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">\(a = 3\) </span><strong><em>A1 <span class="Apple-converted-space"> </span>N1</em></strong></p>
<p class="p1">correct working <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\(\frac{{\ln 27}}{{\ln 3}}\)</p>
<p class="p1">correct use of log law <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\(\frac{{3\ln 3}}{{\ln 3}},{\text{ }}{\log _3}27\)</p>
<p class="p1"><span class="Apple-converted-space">\(b = 3\) </span><strong><em>A1 <span class="Apple-converted-space"> </span>N2</em></strong></p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Part a) was well answered.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">In part b) most candidates realised that integration was required but fewer recognised the need to use integration by substitution. Quite a number of candidates who integrated correctly omitted finding the constant of integration.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">In part c) many candidates showed good understanding of transformations and could apply them correctly, however, correct use of the laws of logarithms was challenging for many. In particular, a common error was \(\frac{{\ln 27}}{{\ln 3}} = \ln 9\).</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 \(f(x) = 2k{x^2} - 4kx + 1\) , for \(k \ne 0\) . The equation \(f(x) = 0\) has two equal roots.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the value of <em>k</em> .</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The line \(y = p\) intersects the graph of <em>f</em> . Find all possible values of <em>p</em> .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">valid approach <em><strong>(M1)</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \({b^2} - 4ac\) , \(\Delta = 0\) , \({( - 4k)^2} - 4(2k)(1)\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">correct equation <em><strong>A1</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \({( - 4k)^2} - 4(2k)(1) = 0\) , \(16{k^2} = 8k\) , \(2{k^2} - k = 0\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">correct manipulation <em><strong>A1</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. \(8k(2k - 1)\) , \(\frac{{8 \pm \sqrt {64} }}{{32}}\)</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(k = \frac{1}{2}\) <em><strong>A2 N3</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[5 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">recognizing vertex is on the <em>x</em>-axis <em><strong>M1</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">e.g. (1, 0) , sketch of parabola opening upward from the <em>x</em>-axis</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(p \ge 0\) <em><strong>A1 N1</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[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-family: times new roman,times; font-size: medium;">Those who knew to set the discriminant to zero had little trouble completing part (a). Some knew that having two equal roots means the factors must be the same, and thus surmised that \(k = \frac{1}{2}\) will achieve \((x - 1)(x - 1)\) . This is a valid approach, provided the reasoning is completely communicated. Many candidates set \(f = 0\) and used the quadratic formula, which misses the approach entirely. </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) proved challenging for most, and was often left blank. Those who considered a graphical interpretation and sketched the parabola found greater success. </span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following diagram shows part of the graph of a quadratic function \(f\)<span class="s1">.</span></p>
<p class="p2" style="text-align: center;"><img src="images/Schermafbeelding_2016-01-22_om_09.59.14.png" alt></p>
<p class="p2">The vertex is at \((1,{\text{ }} - 9)\)<span class="s2">, and the graph crosses the <em>y</em>-</span>axis at the point \((0,{\text{ }}c)\).</p>
<p class="p1">The function can be written in the form \(f(x) = {(x - h)^2} + k\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down the value of \(h\) and of \(k\).</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 \(c\).</p>
<p class="p1"> </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>Let \(g(x) = - {(x - 3)^2} + 1\). The graph of \(g\) is obtained by a reflection of the graph of \(f\) in the \(x\)-axis, followed by a translation of \(\left( {\begin{array}{*{20}{c}} p \\ q \end{array}} \right)\).</p>
<p><br>Find the value of \(p\) and of \(q\).</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <em>x</em>-coordinates of the points of intersection of the graphs of \(f\) and \(g\).</p>
<div class="marks">[7]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(h = 1,{\text{ }}k = - 9\;\;\;\left( {{\text{accept }}{{(x - 1)}^2} - 9} \right)\) <strong><em>A1A1 N2</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>attempt to substitute \(x = 0\) into <strong>their </strong>quadratic function <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\;\;\;f(0),{\text{ }}{(0 - 1)^2} - 9\)</p>
<p>\(c = - 8\) <strong><em>A1 N2</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>attempt to expand <strong>their </strong>quadratic function <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\;\;\;{x^2} - 2x + 1 - 9,{\text{ }}{x^2} - 2x - 8\)</p>
<p>\(c = - 8\) <strong><em>A1 N2</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>evidence of correct reflection <strong><em>A1</em></strong></p>
<p><em>eg</em>\(\;\;\; - \left( {{{(x - 1)}^2} - 9} \right)\), vertex at \((1,{\text{ }}9)\), <em>y</em>-intercept at \((0,{\text{ }}8)\)</p>
<p>valid attempt to find horizontal shift <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\;\;\;1 + p = 3,{\text{ }}1 \to 3\)</p>
<p>\(p = 2\) <strong><em>A1 N2</em></strong></p>
<p>valid attempt to find vertical shift <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\;\;\;9 + q = 1,{\text{ }}9 \to 1,{\text{ }} - 9 + q = 1\)</p>
<p>\(q = - 8\) <strong><em>A1 N2</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>An error in finding the reflection may still allow the correct values of \(p\) and \(q\) to be found, as the error may not affect subsequent working. In this case, award <strong><em>A0 </em></strong>for the reflection, <strong><em>M1A1 </em></strong>for \(p = 2\), and <strong><em>M1A1 </em></strong>for \(q = - 8\).</p>
<p>If no working shown, award <strong><em>N0 </em></strong>for \(q = 10\).</p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach (check <strong><em>FT </em></strong>from (a)) <strong><em>M1</em></strong></p>
<p><em>eg</em>\(\;\;\;f(x) = g(x),{\text{ }}{(x - 1)^2} - 9 = - {(x - 3)^2} + 1\)</p>
<p>correct expansion of both binomials <strong><em>(A1)</em></strong></p>
<p><em>eg</em>\(\;\;\;{x^2} - 2x + 1,{\text{ }}{x^2} - 6x + 9\)</p>
<p>correct working <strong><em>(A1)</em></strong></p>
<p><em>eg</em>\(\;\;\;{x^2} - 2x - 8 = - {x^2} + 6x - 8\)</p>
<p>correct equation <strong><em>(A1)</em></strong></p>
<p><em>eg</em>\(\;\;\;2{x^2} - 8x = 0,{\text{ }}2{x^2} = 8x\)</p>
<p>correct working <strong><em>(A1)</em></strong></p>
<p><em>eg</em>\(\;\;\;2x(x - 4) = 0\)</p>
<p>\(x = 0,{\text{ }}x = 4\) <strong><em>A1A1 N3</em></strong></p>
<p><strong><em>[7 marks]</em></strong></p>
<p><strong><em>Total [16 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>The following table shows the probability distribution of a discrete random variable \(A\), in terms of an angle \(\theta \).</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-11_om_09.10.36.png" alt="M17/5/MATME/SP1/ENG/TZ1/10"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that \(\cos \theta = \frac{3}{4}\).</p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that \(\tan \theta > 0\), find \(\tan \theta \).</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>Let \(y = \frac{1}{{\cos x}}\), for \(0 < x < \frac{\pi }{2}\). The graph of \(y\)between \(x = \theta \) and \(x = \frac{\pi }{4}\) is rotated 360° about the \(x\)-axis. Find the volume of the solid formed.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>evidence of summing to 1 <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(\sum {p = 1} \)</p>
<p>correct equation <strong><em>A1</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(\cos \theta + 2\cos 2\theta = 1\)</p>
<p>correct equation in \(\cos \theta \) <strong><em>A1</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(\cos \theta + 2(2{\cos ^2}\theta - 1) = 1,{\text{ }}4{\cos ^2}\theta + \cos \theta - 3 = 0\)</p>
<p>evidence of valid approach to solve quadratic <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)factorizing equation set equal to \(0,{\text{ }}\frac{{ - 1 \pm \sqrt {1 - 4 \times 4 \times ( - 3)} }}{8}\)</p>
<p>correct working, clearly leading to required answer <strong><em>A1</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\((4\cos \theta - 3)(\cos \theta + 1),{\text{ }}\frac{{ - 1 \pm 7}}{8}\)</p>
<p>correct reason for rejecting \(\cos \theta \ne - 1\) <strong><em>R1</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(\cos \theta \) is a probability (value must lie between 0 and 1), \(\cos \theta > 0\)</p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>R0 </em></strong>for \(\cos \theta \ne - 1\) without a reason.</p>
<p> </p>
<p>\(\cos \theta = \frac{3}{4}\) <em><strong>AG N0</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)sketch of right triangle with sides 3 and 4, \({\sin ^2}x + {\cos ^2}x = 1\)</p>
<p>correct working </p>
<p><strong><em>(A1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)missing side \( = \sqrt 7 ,{\text{ }}\frac{{\frac{{\sqrt 7 }}{4}}}{{\frac{3}{4}}}\)</p>
<p>\(\tan \theta = \frac{{\sqrt 7 }}{3}\) <strong><em>A1</em></strong> <strong><em>N2</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to substitute either limits or the function into formula involving \({f^2}\) <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(\pi \int_\theta ^{\frac{\pi }{4}} {{f^2},{\text{ }}\int {{{\left( {\frac{1}{{\cos x}}} \right)}^2}} } \)</p>
<p>correct substitution of both limits and function <strong><em>(A1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(\pi \int_\theta ^{\frac{\pi }{4}} {{{\left( {\frac{1}{{\cos x}}} \right)}^2}{\text{d}}x} \)</p>
<p>correct integration <strong><em>(A1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(\tan x\)</p>
<p>substituting <strong>their </strong>limits into <strong>their </strong>integrated function and subtracting <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(\tan \frac{\pi }{4} - \tan \theta \)</p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>M0 </em></strong>if they substitute into original or differentiated function.</p>
<p> </p>
<p>\(\tan \frac{\pi }{4} = 1\) <strong><em>(A1)</em></strong></p>
<p><em>eg</em>\(\,\,\,\,\,\)\(1 - \tan \theta \)</p>
<p>\(V = \pi - \frac{{\pi \sqrt 7 }}{3}\) <strong><em>A1</em></strong> <strong><em>N3</em></strong></p>
<p> </p>
<p><strong><em>[6 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-family: times new roman,times; font-size: medium;">Let \(f(x) = {x^2}\) and \(g(x) = 2x - 3\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find \({g^{ - 1}}(x)\) .</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 style="font-family: times new roman,times; font-size: medium;">Find \((f \circ g)(4)\) .</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 style="font-family: times new roman,times; font-size: medium;">for interchanging <em>x</em> and <em>y</em> (may be done later) <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(x = 2y - 3\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({g^{ - 1}}(x) = \frac{{x + 3}}{2}\) (accept \(y = \frac{{x + 3}}{2},\frac{{x + 3}}{2}\) ) <em><strong>A1 N2</strong> </em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[2 marks]</span></strong></em></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;"><strong>METHOD 1</strong> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(g(4) = 5\) <em><strong>(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">evidence of composition of functions <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(f(5) = 25\) <em><strong> A1 N3</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>METHOD 2</strong> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(f \circ g(x) = {(2x - 3)^2}\) <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(f \circ g(4) = {(2 \times 4 - 3)^2}\) <em><strong> (A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">= 25 <em><strong>A1 N3</strong></em> </span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[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;">Many candidates performed successfully in finding the inverse function, as well as the composite at a specified value of <em>x</em>. </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 performed successfully in finding the inverse function, as well as the composite at a specified value of <em>x</em>. Some candidates made arithmetical errors especially if they expanded the binomial before substituting \(x = 4\) . </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;">Part of the graph of a function <em>f</em> is shown in the diagram below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/rugby.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">On the same diagram sketch the graph of \(y = - f(x)\) .</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Let \(g(x) = f(x + 3)\) .</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Find \(g( - 3)\) .</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(ii) Describe fully the transformation that maps the graph of <em>f</em> to the graph </span><span style="font-family: times new roman,times; font-size: medium;">of <em>g</em>.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b(i) and (ii).</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="images/game.png" alt></span><em><strong><span style="font-family: times new roman,times; font-size: medium;"> M1A1 N2</span></strong></em></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><strong>Note</strong>: Award <em><strong>M1</strong></em> for evidence of reflection in <em>x</em>-axis, </span><span style="font-family: times new roman,times; font-size: medium;"><em><strong>A1</strong></em> for correct vertex <strong>and</strong> all intercepts approximately correct.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) \(g( - 3) = f(0)\) <em><strong> (A1)</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">\(f(0) = - 1.5\) <em><strong>A1 N2</strong></em></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(ii) translation (accept shift, slide, etc.) of \(\left( {\begin{array}{*{20}{c}}<br>{ - 3}\\<br>0<br>\end{array}} \right)\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1A1 N2</span></strong></em></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[4 marks]</span></strong></em></p>
<div class="question_part_label">b(i) and (ii).</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">This question was reasonably well done. Many recognized the graph of \( - f(x)\) as a reflection </span><span style="font-family: times new roman,times; font-size: medium;">in a horizontal line, but fewer recognized the <em>x</em>-axis as the mirror line.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">A fair number gave </span><span style="font-family: times new roman,times; font-size: medium;">\(g( - 3) = f(0)\) , but did not carry through to \(f(0) = - 1.5\) . The majority of candidates </span><span style="font-family: times new roman,times; font-size: medium;">recognized that moving the graph of \(f(x)\) by 3 units to the left results in the graph of \(g(x)\) , </span><span style="font-family: times new roman,times; font-size: medium;">but the language used to describe the transformation was often far from precise </span><span style="font-family: times new roman,times; font-size: medium;">mathematically.</span></p>
<div class="question_part_label">b(i) and (ii).</div>
</div>
<br><hr><br><div class="question">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Consider the equation \({x^2} + (k - 1)x + 1 = 0\) , where <em>k</em> is a real number.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find the values of <em>k</em> for which the equation has two <strong>equal</strong> real solutions.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>METHOD 1</strong> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">evidence of valid approach <strong><em>(M1) </em></strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \({b^2} - 4ac\) , quadratic formula </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct substitution into \({b^2} - 4ac\) (may be seen in formula) <em><strong>(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \({(k - 1)^2} - 4 \times 1 \times 1\) , \({(k - 1)^2} - 4\) , \({k^2} - 2k - 3\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">setting <strong>their</strong> discriminant equal to zero <em><strong>M1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(\Delta = 0,{(k - 1)^2} - 4 = 0\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempt to solve the quadratic <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \({(k - 1)^2} = 4\) , factorizing </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct working <em><strong>A1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \((k - 1) = \pm 2\) , \((k - 3)(k + 1)\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(k = - 1\) , \(k = 3\) (do not accept inequalities) <em><strong>A1A1 N2</strong> </em></span></p>
<p><em><span style="font-family: times new roman,times; font-size: medium;"><strong>[7 marks]</strong> </span></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>METHOD 2</strong> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">recognizing perfect square <em><strong>(M1) </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \({(x + 1)^2} = 0\) , \({(x - 1)^2}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct expansion <em><strong>(A1)(A1) </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \({x^2} + 2x + 1 = 0\) , \({x^2} - 2x + 1\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">equating coefficients of <em>x</em> <em><strong>A1A1 </strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(k - 1 = - 2\) , \(k - 1 = 2\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(k = - 1\) , \(k = 3\) <em><strong>A1A1 N2</strong> </em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[7 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;">Most candidates approached this question correctly by using the discriminant, and many were successful in finding both of the required values of <em>k</em>. There did seem to be some confusion about the expression "two <strong>equal</strong> real solutions", as some candidates approached the question as though the equation had two distinct real roots, using \({b^2} - 4ac > 0\) , rather than \({b^2} - 4ac = 0\) . </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">There were also a good number who recognized that the quadratic must be a perfect square, although many who used this method found only one of the two possible values of <em>k</em>. In addition, there were many unsuccessful candidates who tried to use the entire quadratic formula as though they were solving for <em>x</em>, without ever seeming to realize the significance of the discriminant. </span></p>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write the expression \(3\ln 2 - \ln 4\) in the form \(\ln k\), where \(k \in \mathbb{Z}\).</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>Hence or otherwise, solve \(3\ln 2 - \ln 4 = - \ln x\).</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">correct application of \(\ln {a^b} = b\ln a\) (seen anywhere) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1"><em>eg</em>\(\;\;\;\ln 4 = 2\ln 2,{\text{ }}3\ln 2 = \ln {2^3},{\text{ }}3\log 2 = \log 8\)</p>
<p class="p1">correct working <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1"><em>eg</em>\(\;\;\;3\ln 2 - 2\ln 2,{\text{ }}\ln 8 - \ln 4\)</p>
<p class="p1">\(\ln 2\;\;\;{\text{(accept }}k = 2{\text{)}}\) <span class="Apple-converted-space"> </span><strong><em>A1 <span class="Apple-converted-space"> </span>N2</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><strong>METHOD 1</strong></p>
<p>attempt to substitute <strong>their </strong>answer into the equation <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\;\;\;\ln 2 = - \ln x\)</p>
<p>correct application of a log rule <strong><em>(A1)</em></strong></p>
<p><em>eg</em>\(\;\;\;\ln \frac{1}{x},{\text{ }}\ln \frac{1}{2} = \ln x,{\text{ }}\ln 2 + \ln x = \ln 2x\;\;\;( = 0)\)</p>
<p>\(x = \frac{1}{2}\) <strong><em>A1 N2</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>attempt to rearrange equation, with \(3\ln 2\) written as \(\ln {2^3}\) or \(\ln 8\) <strong><em>(M1)</em></strong></p>
<p><em>eg</em>\(\;\;\;\ln x = \ln 4 - \ln {2^3},{\text{ }}\ln 8 + \ln x = \ln 4,{\text{ }}\ln {2^3} = \ln 4 - \ln x\)</p>
<p>correct working applying \(\ln a \pm \ln b\) <strong><em>(A1)</em></strong></p>
<p><em>eg</em>\(\;\;\;\frac{4}{8},{\text{ }}8x = 4,{\text{ }}\ln {2^3} = \ln \frac{4}{x}\)</p>
<p>\(x = \frac{1}{2}\) <strong><em>A1 N2</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<p><strong><em>Total [6 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;">
<p class="p1">Part (a) was answered correctly by a large number of candidates, though there were quite a few who applied the rules of logarithms in the wrong order.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>In part (b), many candidates knew to set their answer from part (a) equal to \( - \ln x\), but then a good number incorrectly said that \(\ln 2 = - \ln x\) led to \(2 = - x\).</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>Let \(f\left( x \right) = p{x^2} + qx - 4p\), where <em>p</em> ≠0. Find Find the number of roots for the equation \(f\left( x \right) = 0\).</p>
<p>Justify your answer.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><strong>METHOD 1</strong></p>
<p>evidence of discriminant   <em><strong>(M1)</strong></em><br><em>eg  </em>\({b^2} - 4ac,\,\,\Delta \)</p>
<p>correct substitution into discriminant   <em><strong>(A1)</strong></em><br><em>eg  </em>\({q^2} - 4p\left( { - 4p} \right)\)</p>
<p>correct discriminant    <em><strong>A1</strong></em><br><em>eg</em>  \({q^2} + 16{p^2}\)</p>
<p>\(16{p^2} > 0\,\,\,\,\left( {{\text{accept}}\,\,{p^2} > 0} \right)\)Â Â <em><strong>Â A1</strong></em></p>
<p>\({q^2} \geqslant 0\,\,\,\,\left( {{\text{do not accept}}\,\,{q^2} > 0} \right)\)Â Â <em><strong>Â A1</strong></em></p>
<p>\({q^2} + 16{p^2} > 0\)Â <em><strong> Â Â A1</strong></em></p>
<p>\(f\) has 2 roots   <em><strong>A1 N0</strong></em></p>
<p>Â </p>
<p><strong>METHOD 2</strong></p>
<p><em>y</em>-intercept = −4<em>p</em> (seen anywhere)   <em><strong>A1</strong></em></p>
<p>if <em>p</em> is positive, then the <em>y</em>-intercept will be negative   <em><strong>A1</strong></em></p>
<p>an upward-opening parabola with a negative <em>y</em>-intercept   <em><strong> R1</strong></em><br><em>eg</em> sketch that must indicate<em> p</em> > 0.</p>
<p>if <em>p</em> is negative, then the y-intercept will be positive   <em><strong>A1</strong></em></p>
<p>a downward-opening parabola with a positive y-intercept   <em><strong> R1</strong></em><br><em>eg</em> sketch that must indicate <em>p</em> > 0.</p>
<p>\(f\) has 2 roots   <em><strong>A2 N0</strong></em></p>
<p><em><strong>[7 marks]</strong></em></p>
<p>Â </p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>Let <em>f</em>(<em>x</em>) = <em>ax</em><sup>2</sup> − 4<em>x</em> − <em>c</em>. A horizontal line, <em>L</em> , intersects the graph of<em> f</em> at <em>x</em> = −1 and <em>x</em> = 3.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The equation of the axis of symmetry is <em>x</em> = <em>p</em>. Find <em>p</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, show that <em>a</em> = 2.</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>The equation of <em>L</em> is <em>y</em> = 5 . Find the value of <em>c.</em></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong> (using symmetry to find <em>p</em>)</p>
<p>valid approach   <em><strong>(M1)</strong></em></p>
<p><em>eg</em>  \(\frac{{ - 1 + 3}}{2}\), <img src="data:image/png;base64,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"></p>
<p><em>p</em> = 1Â Â Â <em><strong>A1 N2</strong></em></p>
<p><em><strong>Note:</strong></em> Award no marks if they work backwards by substituting <em>a</em> = 2 into \( - \frac{b}{{2a}}\) to find <em>p</em>.</p>
<p>Do not accept \(p = \frac{2}{a}\).</p>
<p>Â </p>
<p><strong>METHOD 2</strong> (calculating <em>a</em> first)<br>(i) & (ii) valid approach to calculate <em>a</em>Â Â Â <em><strong> M1</strong></em></p>
<p><em>eg </em>  <em>a</em> + 4 − <em>c</em> = <em>a</em>(3<sup>2</sup>) − 4(3) − <em>c</em>,  <em>f</em>(−1) = <em>f</em>(3)</p>
<p>correct working   <em><strong>A1</strong></em></p>
<p>eg  8<em>a</em> = 16</p>
<p><em>a</em> = 2Â Â Â <em><strong>AG N0</strong></em></p>
<p>valid approach to find <em>p    <strong>(M1)</strong></em></p>
<p><em>eg</em>Â Â \( - \frac{b}{{2a}},\,\,\,\frac{4}{{2\left( 2 \right)}}\)</p>
<p><em>p</em> = 1Â Â Â <em><strong>A1 N2</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><strong>METHOD 1</strong></p>
<p>valid approach<strong>Â Â Â Â <em>M1</em></strong></p>
<p><em>eg</em> \( - \frac{b}{{2a}},\,\,\,\frac{4}{{2a}}\) (might be seen in (i)), <em>f' </em>(1) = 0</p>
<p>correct equation   <em><strong>A1</strong></em></p>
<p><em>eg</em> \(\frac{4}{{2a}}\) = 1, 2<em>a</em>(1) − 4 = 0</p>
<p><em>a</em> = 2Â Â Â <em><strong>AG N0</strong></em></p>
<p>Â </p>
<p><strong>METHOD 2</strong> (calculating <em>a</em> first)<br>(i) & (ii) valid approach to calculate <em>a</em>Â Â Â <em><strong> M1</strong></em></p>
<p><em>eg </em>  <em>a</em> + 4 − <em>c</em> = <em>a</em>(3<sup>2</sup>) − 4(3) − <em>c</em>,  <em>f</em>(−1) = <em>f</em>(3)</p>
<p>correct working   <em><strong>A1</strong></em></p>
<p>eg  8<em>a</em> = 16</p>
<p><em>a</em> = 2Â Â Â <em><strong>AG N0</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>valid approach   <em><strong>(M1)</strong></em><br>eg  <em>f</em>(−1) = 5, <em>f</em>(3) =5</p>
<p>correct working    <em><strong>(A1)</strong></em><br>eg  2 + 4 − <em>c</em> = 5, 18 − 12 − <em>c</em> = 5</p>
<p><em>c</em>Â = 1Â Â Â <em><strong>A1 N2</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.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;">Let \(f(x) = {{\rm{e}}^{x + 3}}\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Show that \({f^{ - 1}}(x) = \ln x - 3\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Write down the domain of \({f^{ - 1}}\) .</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 style="font-family: times new roman,times; font-size: medium;">Solve the equation \({f^{ - 1}}(x) = \ln \frac{1}{x}\) .</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 style="font-family: times new roman,times; font-size: medium;">(i) interchanging <em>x</em> and <em>y</em> (seen anywhere) <em><strong>M1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(x = {{\rm{e}}^{y + 3}}\) </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct manipulation <em><strong>A1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(\ln x = y + 3\) , \(\ln y = x + 3\) </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({f^{ - 1}}(x) = \ln x - 3\) <em><strong>AG N0</strong></em> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) \(x > 0\) <em><strong>A1 N1</strong></em> </span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[3 marks]</span></strong></em></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;">collecting like terms; using laws of logs <em><strong>(A1)(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(\ln x - \ln \left( {\frac{1}{x}} \right) = 3\) , \(\ln x + \ln x = 3\) , \(\ln \left( {\frac{x}{{\frac{1}{x}}}} \right) = 3\) , \(\ln {x^2} = 3\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">simplify <em><strong>(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">e.g. \(\ln x = \frac{3}{2}\) , \({x^2} = {{\rm{e}}^3}\)</span></p>
<p><span style="font-family: Times New Roman; font-size: medium;">\(x = {{\rm{e}}^{\frac{3}{2}}}\left( { = \sqrt {{{\rm{e}}^3}} } \right)\) </span><em><span style="font-family: times new roman,times; font-size: medium;"><strong>A1 N2</strong> </span></em></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;"> [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;">Many candidates interchanged the \(x\) and \(y\) to find the inverse function, but very few could write down the correct domain of the inverse, often giving \(x \ge 0\) , \(x > 3\) and "all real numbers" as responses. </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;">Where students attempted to solve the equation in (b), most treated \(\ln x - 3\) as \(\ln (x - 3)\) and created an incorrect equation from the outset. The few who applied laws of logarithms often carried the algebra through to completion. </span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p class="p1">Three consecutive terms of a geometric sequence are \(x - 3\)<span class="s1">, 6 </span>and \(x + 2\).</p>
<p class="p1">Find the possible values of \(x\).</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p class="p1"><strong>METHOD 1</strong></p>
<p class="p1">valid approach <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\(r = \frac{6}{{x - 3}},{\text{ }}(x - 3) \times r = 6,{\text{ }}(x - 3){r^2} = x + 2\)</p>
<p class="p1">correct equation in terms of \(x\) only <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\(\frac{6}{{x - 3}} = \frac{{x + 2}}{6},{\text{ }}(x - 3)(x + 2) = {6^2},{\text{ }}36 = {x^2} - x - 6\)</p>
<p class="p1">correct working <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\({x^2} - x - 42,{\text{ }}{x^2} - x = 42\)</p>
<p class="p1">valid attempt to solve <strong>their </strong>quadratic equation <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)factorizing, formula, completing the square</p>
<p class="p1">evidence of correct working <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\((x - 7)(x + 6),{\text{ }}\frac{{1 \pm \sqrt {169} }}{2}\)</p>
<p class="p1">\(x = 7,{\text{ }}x = - 6\) <strong><em>A1 N4</em></strong></p>
<p class="p1"><strong>METHOD 2 (finding </strong><span class="s1"><strong><em>r </em></strong></span><strong>first)</strong></p>
<p class="p1">valid approach <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\(r = \frac{6}{{x - 3}},{\text{ }}6r = x + 2,{\text{ }}(x - 3){r^2} = x + 2\)</p>
<p class="p1">correct equation in terms of \(r\) only <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\(\frac{6}{r} + 3 = 6r - 2,{\text{ }}6 + 3r = 6{r^2} - 2r,{\text{ }}6{r^2} - 5r - 6 = 0\)</p>
<p class="p1">evidence of correct working <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\((3r + 2)(2r - 3),{\text{ }}\frac{{5 \pm \sqrt {25 + 144} }}{{12}}\)</p>
<p class="p1"><span class="Apple-converted-space">\(r = - \frac{2}{3},{\text{ }}r = \frac{3}{2}\) </span><strong><em>A1</em></strong></p>
<p class="p1">substituting their values of \(r\) to find \(x\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><em>eg</em>\(\,\,\,\,\,\)\((x - 3)\left( {\frac{2}{3}} \right) = 6,{\text{ }}x = 6\left( {\frac{3}{2}} \right) - 2\)</p>
<p class="p1"><span class="Apple-converted-space">\(x = 7,{\text{ }}x = - 6\) </span><strong><em>A1 <span class="Apple-converted-space"> </span>N4</em></strong></p>
<p class="p1"><strong><em>[6 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p class="p1">Nearly all candidates attempted to set up an expression, or pair of expressions, for the common ratio of the geometric sequence. When done correctly, these expressions led to a quadratic equation which was solved correctly by many candidates.</p>
</div>
<br><hr><br><div class="specification">
<p>The following diagram shows the graph of a function \(f\), for −4 ≤ <em>x</em> ≤ 2.</p>
<p><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the same axes, sketch the graph of \(f\left( { - x} \right)\).</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>Another function, \(g\), can be written in the form \(g\left( x \right) = a \times f\left( {x + b} \right)\). The following diagram shows the graph of \(g\).</p>
<p><strong><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbIAAAGACAYAAADIwee6AAAgAElEQVR4Ae2dC3RV1bnv/zswUHoAvaD3NAEuWhiJPVePIoitMGoETGQ4BA4UX5WHYHttRalckwCtm5uIPIIXq8AZKCYCXqkHSxraHhEKEcaF9sIBweoZslNsfSXhHoFCzBWlzV53zA072VnZj7n3XnOvOdf6rzEysh7z8f9+39z729+a6xGwLMsCFxIgARIgARIwlECeobop2zcE/oaWuocRCAQQCBTgtmcOoi1iexitDYtQUDAXdU3nfUODhpIACXQnwEDWnQn3aEWgJ/KnrIPV/j5qSoA9v30PzWEhMA99vnkbZhX9BWf+X2SHVqophgRIIHcEGMhyx5o9ZUMgbxCuv70I+OA0Pr8Yt/L+fjCGfeNmXF/QK5uWWZcESMBwAgxkhjvQP/J7om//K4EPjuOjz/4G4Dya6l/GwTsnYXgfDmP/jANaSgLdCfAboDsT7tGSQE/0vbx/p7K2o9hy6BY8OXkIOIg7sXCNBPxIgN8BfvS6kTbn4e8u7498hPCnT46jofq3GPLIBAzkCDbSmxRNAk4S4NeAkzTZlkICefjaZf3xNZzEkbXrsKd4FiYP5NyYQuBsmgSMIcBAZoyrKDSvb38MBdDz1odQPnYgTylySJAACUQIMJBxIBhEoAcGLVyF5bOuRZ8Uqk+fPo3y8nJ8+umnKUryMAmQgOkEeppuAPX7hEDbQTxXk4eyJ8chX+Ln1/Lly7Fy5Ur85S9/wfr1630CiWaSgD8JBPiIKn863gir2w7imbseR8v0xzEodBLfefIHGCFxqf3Ro0cxfPjwDhO3bt2KKVOmdGxzhQRIwFsEJH7bestgWmMQgXAbPgv9GW+HzuE7P54tFcTOnTuHH/zgBygrK4sY+vTTT0NkZ+JUIxcSIAFvEmBG5k2/+taqNWvW4NFHH8Unn3yCwYMH44svvsCtt96K4uJiVFdX+5YLDScBLxNgIPOyd31mW2NjI4qKihA9lSgeNCxe7rB//36MGTMG+/btw+jRo31GheaSgPcJMJB538e+sFCcUrzvvvsittbX10f+RwOZ2BBXMO7Zswd79+5F7969fcGERpKAXwhwjswvnva4ndu3b8e2bdsSnj5csGBBhMCzzz7rcRI0jwT8R4AZmf987jmLxYUcAwYMwMaNGzFjxowO+2IzMrGzrq4OU6dORSgUQmFhYUc5rpAACZhNgBmZ2f6jeiByqlAEsWnTpiXlIS7BF+W4kAAJeIsAMzJv+ZPWxBCwZ2Qxh7hKAiTgIQLMyDzkTJpCAiRAAn4kwEDmR6/TZhIgARLwEAEGMg85k6aQAAmQgB8JMJD50eu0mQRIgAQ8RICBzEPONN+U82g5uBYzCwIIBApwW0UdGtvC5ptFC0iABJQSYCBTipeNyxMIo+3IduzEFLzcbKG9+XVMPLEYxU/tQat8IyxJAiTgQwIMZD50upYmhz/CobM3Yvqo/Mibn/Pyv405M+8CXtmFQ63MyrT0GUWRgCYEGMg0cYTvZeRdjeLiwZEgdoHFeZz48CMUzZ+MUf04TH0/PgiABJIQ4Buik8DhIZcItDWiYcsGbDw+C5uXjEIfl2SwWxIgATMIMJCZ4SefqAyjteGnuGbcMrQIi4uBScdvxpTCfj6xn2aSAAlkQoDnbDKhxjqKCOSh39ilaLa+QvOhTSjHBkwtXoS6pvOK+mOzJEACXiAg/azFxYsXR+ytrKxEdD0RAHsZ+3a8evYy9m3WiUcAsHOyb8erZS9j39aljnXqCA6sbUbb9Nsw/uqvdciqqqrqWE+1EgwG4xax25xqWzSSqoz9uBfr2GHabbZv28vLMGGdeARSj794tez+sG87UUe06fpiSS7BYFCypPvFTNIqaJmkN6da29+3akpuscp3f5bRoALEC6LNWXLKNkss1JolwATVTeIqTNBFr3RG5nrEpQD/EWhtQMWNdbh57ypMGdgrbfv59Pu0kbECCRhJQHqOLNXpRJ2sN0mr4GaSXlVaw011mFNQioqNB9EibhsLN6Fh+TqcWPQwSjIIYjqNR1ktqtjK9p9OOWpNh5Z8WZO4Cqt00SsdyORdwZIkkD6BvMsKMfr2ZlTPuhkFPQIoePDnODP1Obw8+1pefp8+TtYgAV8R4OX3vnK3xsb2uRazN76L2XyBs8ZOojQS0JMA58j09AtVOUCAc2QOQGQTJGAAAelTi7qcC5VhapJWYY9Jek3SKjNWdCpjEltqVTNyTOKq03eXdCBT4za2SgIkQAIkQALZEWAgy44fa5MACZAACbhMgIHMZQewexIgARIggewIMJBlx4+1SYAESIAEXCbAQOayA9g9CZAACZBAdgQYyLLjx9okQAIkQAIuE2Agc9kB7J4ESIAESCA7AtKBTItH9WdnK2uTAAmQAAl4kIB0IDPtRj0P+oomkQAJkAAJxCEgHcji1OUuEiABEiABEnCdAAOZ6y6gABIgARIggWwISAcyzpFlg5l1SYAESIAEVBGQDmScI1PlArZLAiRAAiSQDQHpQJZNJ6xLAiRAAiRAAqoIMJCpIst2SYAESIAEckKAgSwnmNkJCZAACZCAKgIMZKrIsl0SIAESIIGcEGAgywlmdkICJEACJKCKAAOZKrJslwRIgARIICcEGMhygpmdkAAJkAAJqCIQsCzLUtU42yUBNwkEAgFweLvpAfZNArkhIJ2RmXRDtElahZtN0muS1tx8hJzrxSS21Oqc32NbMomr0K2LXulAFgub6yRAAiRAAiSgCwEGMl08QR0kQAIkQAIZEeAcWUbYWMkEApwjM8FL1EgC2ROQzsh0ORcqY7JJWoU9Juk1SavMWNGpjElsqVXNyDGJq07fXdKBTI3b2CoJkAAJkAAJZEeAgSw7fqxNAiRAAiTgMgEGMpcdwO4FgTDaGnfgmZnXQcxrBQKlqNh4EC1h0iEBEiCB1AQYyFIzYgnFBMJNb2L9vwIT174Dy/oKzQcm4sTCybh/1UG0Ke6bzZMACZhPgIHMfB8absGX+PMf++PueaUo7COGYy/kj5qDnywZgz2r6nGwlWmZ4Q6mfBJQTqCn8h7YAQkkJXAphhZ/y1aiF75+1TDk2/ZykwRIgATiEWBGFo8K92lB4GsTRqIokqVpIYciSIAENCUgHcgqKys1NYGyvEfgNA7taMLDPxqLgdIj1HsUaBEJkIAcAemvCdNu1JMzn6X0IxBG2+HN2HjlI3h4xOX6yaMiEiAB7QhIP6IqGshEZhZdT2SNvYx9O149exn7NuvEIwDYOdm349Wyl7Fvu1qn7E6Uli7DsO9chyt6BbrZF9VWVVUVXU36PxgMxj1ut9m+Ha+SvYx9W+c68bTa96XaFvalKmM/rnsdu8/s+u3b9vIy9nm9jmDk+iLeRyazBINBmWJalDFJqwBmkl6lWts/tOpXvWa9/3m7I+MIEK8jM2dRytZhDNTqMNCLzZnEVUjWRa/0qUUtoq7rYZ8ClBEIN6Hhue3oe+8/4ZroBR5t72Fj7X60KuuUDZMACXiBgHQgS3U60QswaINLBNqOoW7hbIyb/0OMK7jk4tM9Agj0LcFmDEAfl2SxWxIgATMI8D4yM/zkXZXhj1A3bxqm1r4Xx8YxuGfMVZD+tRWnBe4iARLwPgEGMu/7WG8L84ZgSs27sGr0lkl1JEAC+hLgj119fUNlJEACJEACEgQYyCQgsQgJkAAJkIC+BBjI9PUNlZEACZAACUgQYCCTgMQiJEACJEAC+hJgINPXN1RGAiRAAiQgQUD6EVUSbbEICWhFQLxt2rIsrTRRDAmQgPMEpDMyk26INkmrcKlJek3S6vzHRW2LJrGlVjVjwSSuOn13SQcyNW5jqyRAAiRAAiSQHQEGsuz4sTYJkAAJkIDLBDhH5rID2L06ApwjU8eWLZOATgSkMzKTzt2apFUMBpP0mqRVpw+ajBaT2FKrjEfTL2MSV2GdLnqlA1n6LmENEiABEiABElBPgIFMPWP2QAIkQAIkoJAAA5lCuGyaBEiABEhAPQEGMvWM2QMJkAAJkIBCAgxkCuGyaRIgARIgAfUEGMjUM2YPJEACJEACCgkwkCmEy6ZJgARIgATUE5AOZJWVlerVsAcSIAESIAESSJOAdCDT5ca3NO1jcRIgARIgAY8TkA5kHudA80iABEiABAwlwEBmqOMomwRIgARI4AIB6UDGOTIOGRIgARIgAR0JSAcyzpHp6D5qIgESIAESkA5kREUCJEACJEACOhJgINPRK9REAiRAAiQgTYCBTBoVC5IACZAACehIgIFMR69QEwmQAAmQgDQBBjJpVCxIAiRAAiSgIwEGMh29Qk0kQAIkQALSBBjIpFGxoFoCYbQ17kHdL57BzGGL0NAaVtsdWycBEvAMgYBlWZZnrKEhxhIIN9ZiYuVeXPbWJmzGQuw+tgRj+2X3OysQCIDD29ghQeEkIE1A+pvCpBuiTdIqPGWSXlVa8wpn4zevvoDFS6ZJD16vFVTFVgUnalVB1azvAkFAl3EgHcjUuI2tkgAJkAAJkEB2BBjIsuPH2iRAAiRAAi4T4ByZyw5g97EEvkRj7QwU/XQY58hisXCdBEggKQHpjEyXc6FJrbl40CStQrJJek3SKjNWdCpjEltqVTNyTOKq03eXdEaWDmDxypfY8vbteEPAXsa+zTrxCAB2TvbteLXsZezb7tX5G7435I8o+nELpv/oNlx9SaCbfVFtVVVV0dWk/4PBYNzjdpvt2/Eq2cvYt3WuE0+rfV+qbWFfqjL247rXsfvMrt++bS8vY5/X6whGri/i8nuZJRgMyhTTooxJWgUwk/Sq1XrOCtVMs5C/0Np9tj3rsQSIq+/NWdSydZYDtTrLM9qaSVyFZl30Sp9adD3iUgAJkAAJkAAJxCGQ1qlFLVLIOEZwl1cI8GIPr3iSdpBALgl4MiOLnZ/LJcxM+zJJrzKtrQ2oKOiNojmvAy3LMO6yQSitPQY/PahKGdtMB2aSetSaBE4Wh0ziKszURW/PLJizKgk4R6DfWKxotrDCuRbZEgmQgE8IeDIj84nvaCYJkAAJkAAA6UDG+TGOFxIgARIgAR0JSAcyXc6F6giRmkiABEiABNwjIB3I3JPInkmABEiABEggMQEGssRseIQESIAESMAAAtKBjHNkBniTEkmABEjAhwSkAxnnyHw4OmgyCZAACRhAQDqQGWALJZIACZAACfiQAAOZD51Ok0mABEjASwQYyLzkTdpCAiRAAj4kwEDmQ6fTZBIgARLwEgEGMi95k7aQAAmQgA8JMJD50Ok0mQRIgAS8RICBzEvepC0kQAIk4EMC0i/W9CEbmmw4gUAgAMuyDLeC8kmABFIRkM7ITLoh2iStwkEm6TVJa6rBr9txk9hSq5rRYxJXnb67pAOZGrexVRIgARIgARLIjgADWXb8WJsESIAESMBlApwjc9kB7F4dAc6RqWPLlklAJwLSGZlJ525N0ioGg0l6TdKq0wdNRotJbKlVxqPplzGJq7BOF73SgSx9l7AGCZAACZAACagnwECmnjF7IAESIAESUEiAgUwhXDZNAiRAAiSgngADmXrG7IEESIAESEAhAQYyhXDZNAmQAAmQgHoCDGTqGbMHEiABEiABhQQYyBTCZdMkQAIkQALqCUgHssrKSvVq2AMJkAAJkAAJpElAOpDpcuNbmvaxOAmQAAmQgMcJSAcyj3OgeSRAAiRAAoYSYCAz1HGUTQIkQAIkcIGAdCDjHBmHDAmQAAmQgI4EpAMZ58h0dB81kQAJkIA5BHbu3Im6ujrHBUsHMsd7ZoMkQAIkQAK+ItDW1oapU6di8uTJaGxsdMx2BjLHULIhEiABEiCBZASmTJmCUCgUKVJUVIRNmzbh3LlzyapIHZN+saY4tch5MimmLKQJAb5YUxNHUAYJ2AiI4LV9+/ZIdnbTTTfhxRdfxA033GArJb/pyYzMtPk8k/SapFX+Y6BHSZPYUquaMWMSV0EgU729e/eGyM4++eQTXH/99Rg+fDiWLl2K06dPZwTWk4EsIxKsRAIuERC/TsUE+IkTJ1xSwG5JwB0CgwYNwvr167Fjxw7U19fjjjvuwNGjR9MWI31qUZym4UICJEACJEACKgls3bo1kq2l00daGZllWTDhTwAwQafQKJZgMGiUXpPY6qj1iy++gPiwirkB8SfWo8u+ffuMGAtCr45s42miVnXf29myFZ+FjRs3Rob/pEmTIheCiFOO6S5pZWRikJiwmDTJb5JW4XuT9OqmNTrBvXz58sjHaMGCBZgwYQLEfIHQunr1auzatStyikX3z5lubJPxotZkdLI7lg1bcfl9eXk5tm3bFglm06ZNi3wWMlGUVkaWSQesk5pAphOmqVtmCR0IROfAbr31VoggJgLY3r17I6dPRBCLLh9//HHkQ71///7oLv4nAc8REJ8HcWGHuPz+yiuvjFzwMWPGjIyDmADEQOa5YUKDkhM4j5bDr6DitgIEAtdh5rP70RJOXiPTo7IBLNq+CGoiK1u5cmV0F/+TgKcIiAs5xA86cWGHOKUuLvQQF3xkuzCQZUuQ9Q0iEEbb4bW4/4k/oXTzh7Da38TMz5bh/lUH0eagFekGsNiu77//fmZlsUC47ikCb7zxBoqLi/Hmm2+mfUFHUhCW5HJhbleysMvFqFWdA4xm2/6+VVNyi1W++7NOQGd3W+X506ya0LnOfRmuffHFF9bWrVutm266KfIn1sU+mSWW6+rVq61JkybJVHOtTKxe10RIdkytkqAyKOYs24+trTOGigsxLOQ/Ym399CvLam+2DqyaYeUD1tCVh6y/JtAorjySWpwVLNVlxoVM0xoMBjO2NdcVTWMby6c9VGOVwB60PrN2l99ildS8b7XHFk5jPZsAFu1GcI2Og1OnTkU+zPv27Yse1u6/yeNAO5gxgkziKmSr0Nv+6VZrdj6s/PLXrJ2r/odV8/7ZGELxV3lqMWm+yoPeIfAlju97Ezvzh+Gqr/eymfUVdv7L73A8zbmybE4h2gR02ezfvz/nyroQ4YafCOQN/A6+N30EWqqX4LUhszDrmn4pzZcOZOJeJ1MWk7SacktD1PcmsY1qvvC/DZ+G/gRcNwyD+kgP+65NxGyJ11GkugoxpnjKVfs40H2uzKRxQK0ph59mBfpjZGkJ8vFNjL7276WuSOypmQWUQwJaExCXxourCpubmyOX0UfvA3NadGxWNnr0aKebZ3sk4AgBtT8S9uFf9n2IWYXXpAxm2f80dQQHGyEB1QT6YFDRN4B3j+PTtjTPIQIQAUy8Q2nMmDEYP3583PvAnLZA96zMaXvZHgkIAuGW3XhmRzvuKwbeDTVLXVHMQMax4xMCl2LYmDtQYrc2fBIfHj2DkntuwbA4nwZ7ADt16hTmzp2b1c2bdgmJtmOzskRluJ8EPEUg/BHqK3fhhsd+gv82fQxaXtmFQ03vYOOzb6Apye/POB9dT2GhMSTQQSBv2C2457q92HEo5lURbc0IvXsj7hlzVZfTF4kCmAguuVyYleWSNvuSJxBGa8MiPFtVFXm8mnhUVaC0Fo1Jgk3StsPHUFtagMC4F4D5P8GUgX1QcP23UdyyAU89/wG+/f07MDBJtEpyKGm3kYPhpjrMKbgbtY1fpi7sSonzaDm4FjMLAggECnBbRR0aMzitlBvprWj87bMXtQYQuK0CGw+3INNxoV5zGG2Ne1D3i2cwc9giNLTqq7SDRV4h7l76XRx8ai0aWs4D4SY0LF+Fg/OfwN2Fl0aKuRLA2hrRULcZv6t/FRUNJzvkihW9srLOMVolvsB0H6PhFhx8dubFL9tSVNQdkzpN1cUBbm2EP0LdnJEorT2m53dA+BPsevXX+LyDT37CsxodRZKt5F2D2TuaYb21FFMKxVWKeegz4nG8ZTXjrRVTUJjiAi3pQNbt7dAiBQwuRm1LMnVuHguj7ch27MQUvNxsob35dUw8sRjFT+1Bq5uy4vbdjqZtr+BfcSfWNluw2ptxYOIJLBz5faw6fCZuDbd3hhs34N7Kl7H1sTJs+sJtNbL9iw/HI9i84gpsHHEJAj1mY0dREJvnj8I7tjmw6ClE5RmY+CV670+xcesy7PpDfJB6ZGXnu4zR4JPzNR+jZ3Ckfj9w73o8HvwJmg9MxIm5D+Ap2w8F2ZGT23Ln0VS/EnNrm3PbrXRv4ru1Di9c8RwqOt7c0Ywds1NflCHdRZoFpQNZ1wfbnsHhVSux/4p/RH6aHeasePgjHDp7I6aPyo+cMsrL/zbmzLwLEOdcdcserFb88bKJmHd7IfoIQHn5GDVvIZaUvI1VW97WMPACeYWz8ZtXX8DiJdNy5lJnOuqF/FGPYKP4wWDtwMRhf8UPp3RexJGzABY1RvwS/c0WvLz4cQyN7rP91yIrCzd1HaOBPlqP0fAH/46zN0/EqHxxz2AP5I+6BzOnA6/s+IOWn6dOl1toO7wOi/Zfgtu1/XI9jYNbXsXO6hX430eOoaHR/dRAOpB1ghbPq9uE5/EA5pcO6dyt21re1SguHhwz73EeJz78CEXzJ2NUvwzMVmlf4D/ZtIpgdgWuuqFAZa++btuVU4hZEHc9K+v2edJ7jOYNHY3igTE3vkcu6hmM+XffiNS312bhqGyrnm/GuueBx+bfga9n25ai+uHGX2FF9WEAO/G7X2/BuKJprp+2Tf8bve3QBdAPj0RfRaAcb1bMQdRW4enjsyKnkSJZj+OdqGhwACbcPPRClqaieR+2aVoAi7pIi6wsKqbLf93HaBjnT/0ZtQt/huMVazB/xOVd1Ou1cQYth94DHpuBEX176CUtRo04G7PDEtM1h3DPXbegGDtRPfUJrHNxGkQ6kF2YIzuDw+s2XwCdYvItxm4XVy9cWVPQtwjj5izDpt+/hd8fdz8NlgLS+gfsOHoHflQSm1VK1WShOARMDWCxprielcWKEevaj9GTaKgYheVrX8Gc6l/h9zsO4Li2F3tdONN1ANfiYa2DbecgyMsfgaLh47G7eScWFrs7DSIdyBYvDqLt8GvY+o3HNf9V0wlaXPnSb+xSNFtfofnQJpRjA6YWL0Jd0/nYQhqun8HhF3+FK5c+iBFG/GDQEOFFSV4IYFG6emVlXxowRq/A2BWHIC5MObRhOlA9FcXz6pPejxRlnfP/bYewfusQjPv2QOPOwOTlj8OCJ2e5ev1BHqLX74v7ABL+FeDV3x3Guq35eGTykJh5p1y7+0s01t6dROcFG6pePWK7n6EX8kdMx7IXlqCk5f/gQCg3WVm4sRalCZlGed+NI6f+FgNS/DJ7DVv6P5TjX2aZso2RrtGqeIGfWKJP4sj5RRyKWOiRlYVxvuU9F8ZohlADfTBiZiVeqJmGlu2HENIuKzuDw+sbMOSRCegbyNBGV6vloc+gYbjOoeeYZmJKHqLX71viKq5Ef5/iu/mtWLVsMgb1iH4B98Bl45ahBa9jTlHv7G6Gk1Z+KQpnb0mi84L+4PeGozBOrhm5IbbkEunesi0YPZecmKvQuwXDB3Q+8jLc9CbWvzcGT86+Nse/zLJjmy0rp+o3NjaivLwcw4cPjzTplQAW5aNDVibG6Nv/8V9cGKNRCpn8T/Bkl0yacrpO69vYsnIhpg66BJH788SP38vGobqlBTvnfBM9AjrfqytghNH26X9gRMXEuN+7TuOK116cr/v4xS65eiyauwS6dpzdvRD5mIaa0DlYO2a7ZkQ8xXH3iac4fDAcNxfped1SuKUBz225FPdOjwaxMNqO/QK1e7reJBvXNp/vjAawoqIiXH755RABTCzii99ri5tZWXSMXvuP//niDy1Txqj4sj2ODyaMRJFup+v7jcWKyO0gFsRDeCM/fM/uRnl+Pkpq3ke7tQWzL96w7/5YPo+Ww29gW8fDGtrRcvBFPL1nBB4tvsI1eZKBzDV9GXd84akjpajYeBAt4qETkac4rMOJRQ+jJPay3Ix7cLKihbbGOiy8/wHMnz8OBTFZb99vbgEKzLnO0kkqMm3FBjBRPhQKYdGiRZ4MYFEe7mRl4kkunWN01VPRRxP1gH5j9Dya6uai4OKTR8TbH8WDaJevOI1FZeOTPuooypj/kxA4+2/42cgC9AgE8Gz9AexvG4snq25HvovRxMWuk4By4FDeZYUYfXszqmfdHAkMBQ/+HGemPoeXc37KLrUx1uchzCueiuo9cR6TUnIHxgy78Pik1C3lsERrAyoKeqNozutAyzKMu2xQTh+nEy+AVVdXo7CwMIcQnOhKXFk3Ej2K5uADtKB63JVSp+lznZWFm+oNGqM9cdk/3ITbQ9WYNbIAT1Wtw4Ovfo6pG57HbImXNDrhVe+20Qv5YxfjrYtn5x6ffAu+O/bigxzcNDr+i6O7742+hr37Ef32mKRV0DNJr9taQ6GQVVZWFnnFuvgvthMtKl7DnqgvJ/any3b16tXWpEmTnOg67TbS1Zp2Bw5WoFYHYdqa0oWtZzMyN38csG/nCXgnA3OOTa6zMueUsyUScJZAQARYZ5tkayTgHAERwF566aXIW5nLysrw0EMPSZ8+FLeTeH14r1mzBrt27UJ9fb1z0NkSCRhGQDoj6/rQYL2tNEmrIGmS3lxp9WMGlglbt7KyTLS69a1BrerI68JWOpCpQ8GWSaCTgB8DWKf16a+5cwVj+jpZgwRUEmAgU0mXbUsTYACTRtWtoFtZWTch3EECLhHgHJlL4NntBQLZzIGlYuiHObIoA86VRUnwvx8JSGdkupwLlXGSSVqFPSbpdUorM7DuIzkbtrnOyrLR2t1ytXuoVR1fXdhKBzJ1KNiynwicPn0aS5cuhXiUlFjEkzjMvJFZL69xrkwvf1BNbgkwkOWWt297EwFMnP4aMGAAzpw5EyeAiUcg7UHdL57BzGGL0NAqnivGJR0Cuc7K0tHGsiSgkgADmUq6bBuxAUzc77Rv3764GVi4cQPurXwZWx8rw6YvCC4TAszKMqHGOl4gwEDmBS9qaEO8ACZu2h09enRcteKVN1VXEWwAABkBSURBVL959QUsXjIt7nHulCPArEyOE0t5iwADmbf86bo16QYw1wV7TACzMo85lOZIEWAgk8LEQqkIMIClIpS748zKcseaPelBgIFMDz8Yq4IBTD/XMSvTzydUpJaAdCCrrKxUq4StG0WAAUxvdzEr09s/VOcsAelApsuNb86az9bSJXDu3LmOy+ijVyHGvYgjfAy1pQUQT9dI/FeQ05dxpmuryeWZlZnsPWpPl4D0I6rSCWQie4stb9+OJ9Jexr7NOvEIAHZO9u14texl7Nvx6sybNw8PPPAAtm/fHrmZuaamBjt37oxXtGOfvV37dkfBjpW/4XtD/oiiH7dg+o9uw9WXBLrZFy1aVVUVXU36PxgMxj1u12LfjlfJXsa+rVud8vLyyOtvHnzwQdTW1nb5TAqtdv2ptr1Yx+4zGQas05WAYOb6YnvhZ8JNXd4EmlBgzAGTtArZOus9deqUJd5ELN62LN5G/OCDD8aQdnr1nBWqmWYhf6G1+2x71o17/Q3RMoBUvUVa5zFr50KtdiLObevCVvrUohZR1/Ww7x8BiebABg8e7B8IHrCUc2UecCJNSElAOpDFnipM2SoLGEtAeg7MaQtbG1BR0BtFc14HWpZh3GWDOH/mAGPOlTkAkU1oT6Cn9gopMCcERAAT81/Lly9HQUFB5FFSiZ7CoURQv7FY0WxhhZLG/d2oyMoeffRR7N+/P+GTVfxNiNabToCBzHQPZqk/NoCJppYsWYKSkpIsW2V1nQjEZmU5/XGiEwRq8TQBBjJPuzexcfYAtmDBAkyYMAG9e/dOXIlHjCXArMxY11G4BAEGMglIXirCAOYlb8rbwqxMnhVLmkeAgcw8n2WkmAEsI2yeqsSszFPupDExBBjIYmB4cZUBzItezcwmZmWZcWMt/QkwkOnvo4wUMoBlhM3zlZiVed7FvjRQ+hFVvqRjoNEMYJ1OE894tCzxUBIusQTWrFkD8ZxM8YxMLiTgBQKevCHatJu3ndArAlhdXR1uvfXWyL1g4irEvXv3YsqUKY5eieiEVi98cFTYkCu2Iivbtm0bjh49mrEZudKascCYitQaA8PhVV3Y8tSiw47NdXPMwHJN3Pz+onNlmzdvxg033GC+QbTA9wQYyAwdAgxghjpOE9kiKxswYAAeeughFBYWaqKKMkggMwKcI8uMm2u1GMDk0XOOLDkrMVf28ccfo7q6OnlBHiUBzQlwjkwDB8meZxbPyrvvvvuUzoGlwiGrNVU7PN6dQK7Ziqxs5cqVaGxs7C4mxZ5ca00hJ+lhak2KJ6uDurCVDmRZWcvKWREQAWzy5Ml4/PHHMWPGDCUXcWQlkJWNJBCdK3vppZeM1E/RJBAlwEAWJaHh/2gAGzNmDMaPH48333zT8asQNTSbknJIIJusLIcy2RUJJCXAQJYUjzsH7QHs1KlTmDt3LsQvaC4k4CQBZmVO0mRbbhFgIHOLfJx+GcDiQOEu5QSYlSlHzA4UE2AgUwxYpvlPPvkkMgcWPYXIDEyGGss4RYBZmVMk2Y5bBBjI3CIPRN7YKy7iePnllyNzYAxgLjrD512Ll6lmegWjz9HRfA0IMJC54AT7KcSysjLOgbngB3bZSUDcFC3GIa9g7GTCNXMISAeyyspKc6zSVKk9gEUzML6VWVOH+UyWeMoHszKfOd0j5koHMl1ufDORe6IAxqsQTfSmdzUzK/Oub71umXQg8zoIFfYxgKmgyjZVEmBWppIu21ZFgIFMAVkGMAVQ2WROCDArywlmduIwAelAxjmy1OTFM+vEVYi8jD41K5bQlwCzMn19Q2XxCUgHMs6RxQco9ooAVl5ejqKiIl5GnxgTjxhCgFmZIY6izA4C0oGsowZXOgjEBjCxU9zYzEdJdeDhisEEmJUZ7DwfSmcgy8Dp9gAWCoUi73QaNGhQBq2xCgnoR4BZmX4+oaLEBKRfrClOLfp9nkwEMHHDqLjXRtw8Kn61ig88Fz0J8MWa2flFjHdxulz8UOM4z44la6sl4MmMzOn5vEQZmFMfbqf1qhwyJmlVyUFF27qxTZaV6aY1mT+oNRmd7I7pwtaTgSw713TWVh3AOnviGgnoSYBzZXr6haq6EmAg68ojssUAFgcKd/mSQLKszJdAaLSWBBjIYtzCABYDI6erYbQ17sAzM6+DmNcKBEpRsfEgWsI5FcHOEhBgVpYADHdrQ0D6Yg9tFCsQIgIYL+JQAFayyXDTG3huSw/c+f3bUdjnb2g5uB4LJj+Nj+fX49dPjEIfyXbsxXixh51I5tviPkmxVFdXZ94Ia5KAIgLSGZkuk3oyHGS16pKByeqVsV11Gee1fok//7E/7p5XisI+Yjj2Qv6oOfjJkjHYs6oeB1v9k5Y5z9a50WDPynTWareaWu1EnNvWha10IHPOdPdb0iWAuU9CBwWXYmjxtzCwy0jsha9fNQz5OsijhggBzpVxIOhMoMvXh85CndDGAOYExdy18bUJI1EUydJy1yd7SkzAnpUlLskjJJBbAr6YIzt9+jQ2b96MRx99lDcy53Z8ZdjbSTRU/He8ffdzeGLE5Rm2gciFI5ZlZVyfFbsT4FxZdybc4z4B6YxMl3OhMsiiWkUAW7NmDQYMGIB33nkn8oQCMVnt1I3MMlpkykT1ypR1u4x6rWG0Hd6MjVc+goezCGJuc8qkf/VsM1HVtU40KxPPFDVlMYFrlKVJWoVmXfRKZ2TpCBaPsootb9+OOi32v72MfTu2bHTdXiZ2+9y5c5FHSYlH7Nxyyy0YPHhwpFpsGbHDvh1tO/a/vYx9O7ZsdN1exr4dLRf7317Gvh1bNrpuL2PfjpaL/W8vY9+OLRtdt5exb0fLdfy3TmLIgV9izs6Wjl3dV/pi6F3Tcf/wKxC4eLCy7E6Uli7DsO9chyt6BRL6p6qqqntzcfYEg8E4e7v7PaU9ccaKSXXiabXvS7UtQIoyo0ePjjAdP358N//Y24jWSfZ94GYd++Cwa7Fv28vL2Of1OoKR64sluQSDQcmS7heLag2FQu6LkVAQ1StR1PUiSrW2f2jVr3rNev/zdkfsBOBIO7lqRClbB40QnyvBlp8vB6FebMqUMRC1XBe90qcWXY+4GQjQ7RRiBib4p0q4CQ3PbUffe/8J10Qv8Gh7Dxtr96PVPxSMsFR8rsRZDnHvJRcS0IGApwOZDoCpQYJA2zHULZyNcfN/iHEFl1x8ukcAgb4l2IwBGd8QLdEzi2RIYPjw4ZFT9+JKYC4k4DYBBjK3PeD3/sMfoW7eNEyt3hmHxBjcM+YqcJDGQePyLnEBlXiVEbMylx3B7iMEepIDCbhKIG8IptS8C6vGVRXsPAMC4gpGcTGV+M/T+BkAZBXHCPDHrmMo2RAJ+IuACF7Myvzlc12tlQ5kWlxiqStF6iIBnxKI3lfGuTKfDgBNzJYOZLH3gWiinTJIgARcJsCszGUHsPsIAelARl4kQAIkEI8As7J4VLgvlwQYyHJJm32RgAcJMCvzoFMNM0k6kHGOzDDPUi4J5JAAs7IcwmZX3QhIBzLOkXVjxx0kQAIXCTAr41Bwk4B0IHNTJPsmARLQnwCzMv195FWFDGRe9SztIoEcE2BWlmPg7K6DQFqvceE8WQc3rhhAIBAIiMffG6DUOxLF/WTiaR+hUIhP+/COW7W3xJMZmWnzeSbpNUmr9p8+m0CT2CbSqmNWlkirDb8WmyZpFcB00evJQKbFiKQIEvApAc6V+dTxLprNQOYifHZNAl4koGNW5kXOtKmTAANZJwuukQAJOESAWZlDINmMFAHpiz2kWmMhEtCIAC/2cNcZ5eXlEQHV1dXuCmHvnicgnZHpMqkn4xGTtAp7TNJrklaZsaJTGZPYymjVJSuT0arLODBJq07fXdKBTBdHUwcJkIAZBDhXZoafvKCSgcwLXqQNJKApAV2yMk3xUJZDBDhH5hBINqMfAc6R6eETzpXp4Qcvq5DOyEw6d2uSVjG4TNJrklbTPrgmsU1Hq9tZWTpa3R4zJmnV6btLOpC57WD2TwIkYCYBzpWZ6TeTVDOQmeQtaiUBQwm4nZUZio2yJQkwkEmCYjESIIHMCTAry5wda6YmwECWmhFLkAAJOECAWZkDENlEXAIMZHGxcCcJkIDTBJiVOU2U7UUJMJBFSfA/CZCAcgLMypQj9mUHDGS+dDuNJgF3CDArc4e713uVDmR8O7TXhwLtI4HcEGBWlhvOfupFOpCZdqOen5xIW0nAJALMykzylhlapQOZGeZQJQmQgAkEmJWZ4CVzNDKQmeMrbysNt+DgszNREAggEChFRd0xtHnbYl9bx6zM1+533HjpQMY5MsfZs8EOAmdwpH4/cO96NFtfofnARJyY+wCeajjZUYIr3iPArMx7PnXLIulAxjkyt1zk/X7DH/w7zt48EaPyewHohfxR92DmdOCVHX9Aq/fN962FzMp863rHDZcOZI73zAZJ4CKBvKGjUTxQBLGLS/gkPjw6GPPvvhH9ovv435MEmJV50q05N4qBLOfI2WFiAmG0NTagduHPcLxiDeaPuDxxUR7xBAFmZZ5wo+tGSL9YU5xa5DyZ6/7ysICTaKi4A+OqDwPIR3H5Grzw5GQU9sn8txZfrGnGcGlsbERRURFCoRBEYONCAukSyPxbIt2ecljetPk8k/Sq03oFxq44BKu9GYc2TAeqp6J4Xj2awjkcOC53pY6t84Y5qVV1VuakVudJdm3RJK1CuS56PRnIug4NbrlCIHwMtaUFEFlR4r8ClNYeQ5dYlZePETMr8ULNNLRsP4RQW5ejrpjCTtUT4FyZesZe7iGtU4uyIMQpyNhIbd+O1469jH2bdeIRQOR0rxdZW6eOYPOmv+DFT/di7/+s7GZ8VVVVt33xdgSDwXi7Pcstaqz982PfFuXs+1Jtq66za9euiPzx48fnTFuUV/S/DINo2eh/v9cR9ru+WJJLMBiULOl+MZO0Clom6c2N1nbr7O6F1tDZW61P2zMfTwAyr+xCzdywdcYwFVpDoZAlfCb+O7mo0Oqkvti2TNIqdOuiVzojcz3iUoBHCZxHU9183LT677DsmR9j+oh8oOW3+OmsrRj2XDVmX5P5Bfi82MO8IVNeXh4RXV1dbZ54KnaNgPQcWezpK9fUSnZsklZhkkl6ndfaE5f9w024PVSNWSML0CNwHR589XNM3fB8VkFMcqhoVcx5turMU6VVxVyZKq0q6JqkVdivi17pQKbCaWyTBIA89LlmJjY2W+I8ICzrXWx8YgpGRJ7yQT5+I6D6Cka/8fSLvQxkfvE07SQBQwioyMoMMZ0yMyTAObIMwbGa/gQ4R6a/jxIp5FxZIjLcH4+AdEamy7nQeEbY95mkVWg3Sa9JWu3jQvdtk9iq1upkVqZaq5PjyiStOn13SQcyJ53FtkiABEggGQHOlSWjw2N2AgxkdiLcJgES0IKAk1mZFgZRhDICDGTK0LJhEiCBbAgwK8uGnr/qMpD5y9+0lgSMIsCszCh3uSaWgcw19OyYBEggFQFmZakI8bggwEDGcUACJKA1AWZlWrtHC3EMZFq4gSJIgAQSEWBWlogM90cJSAcyLR7VH1XN/yRAAr4iwKzMV+5O21jpQGbajXppk2AFEiABbQkwK9PWNVoIkw5kWqilCBIgAd8SYFbmW9enNJyBLCUiFiABEtCBALMyHbygpwbpQMY5Mj0dSFUk4CcCzMr85G15W6UDGefI5KGyJAmQgBoCzMrUcDW9VelAZrqh1E8CJOANAszKvOFHJ61gIHOSJtsiARJQToBZmXLExnUg/WJNcWqR82TG+dfXgvliTe+6v7GxEUVFRQiFQhCBjYu/CXgyIzNtPs8kvSZpNe2jbRJbt7Wmk5W5rTWdcWiSVmGXLno9GcjSGTgsSwIkYCYBzpWZ6TcVqhnIVFBlmyRAAsoJpJOVKRfDDlwlwEDmKn52TgIkkA0BZmXZ0PNOXemLPbxjMi3xCwFe7OEPT5eXl0cMra6u9ofBtLIbAemMTJdJvW4WxNlhklYh3yS9JmmNMzS03mUSW520psrKdNKaagCapFWn7y7pQJbKATxOAiRAAm4Q4FyZG9T16pOBTC9/UA0JkEAGBFJlZRk0ySoGEeAcmUHOotT0CHCOLD1eppfmXJnpHsxcv3RGZtK5W5O0CteZpNckrZl/LNypaRJbHbUmysp01JpohJmkVafvLulAlgg895MACZCADgQ4V6aDF9zRwEDmDnf2SgIkoIBAoqxMQVdsUiMCDGQaOYNSLhIIf4S6OSNRWnsMYUIhgTQIMCtLA5aHijKQeciZ3jDlPJrqV2JubbM3zKEVOSfArCznyF3vkIHMdRdQQCeBMNoOr8Oi/Zfg9vzOvVwjgXQIMCtLh5Y3yjKQecOP3rCi7RDWPQ88Nv8OfN0bFtEKlwgwK3MJvEvdMpC5BJ7d2gmcweF1m4HHZmBE3x72g9wmgbQIMCtLC5fxhaUDGd8ObbyvNTZAnFLchOdxPx4ecbnGOinNJALRrOzUqVMmyabWDAhIBzLTbtTLgAWruEWg7RDWbx2CpfNHoY9bGtiv5whEs7IjR454zjYa1JWA9COq0glkInuLLW/f7irhwpa9jH2bdeIRAOyc7NvxatnL2LcdqWOdxJADv8ScnS3xmru4ry+G3vVdFH/1MT7/r9/CNX17XLBnwQzs+ud6/N/i6Wj81VpULl7crY2qqqpu++LtCAaD8Xbryw1qfBrPx/Z9qbYFyFRl7MfdrjN37lysXbsWZWVlEK95if1eijcw7Prt26zTnYBg5PpiSS7BYFCypPvFTNIqaJmk13GtZ3db5fmwgER/06ya0LmMBpVo06TFcbYKjTdJa1lZmUISzjZtEldhuS56pU8tahF1XQ/7FOA4gX5jsaLZEhGn8+/sbpTn56Ok5n20W1swu/BSx7tlg/4h0Lt3b/8Y61NLpQNZqpTcp/xoNgmQAAmQgMsEpAOZyzrZPQmQAAmQAAnEJdAz7l7uJAE3CURON/IRVW66gH2TgEkE0rpqkfNkJrmWWvliTY4BEvAHAU+eWjRtPs8kvSZpNe0jbBJbalUzukziKgjooteTgUzNEGOrJEACJEACOhJgINPRK9REAiRAAiQgTYCBTBoVC5IACZAACehIQPpiDx3FUxMJJCPAiz2S0eExEvAOAemMTJdJPRn0JmkV9pik1yStMmNFpzImsaVWNSPHJK46fXdJBzI1bmOrJEACJEACJJAdAQay7PixNgmQAAmQgMsEOEfmsgPYvToCnCNTx5Ytk4BOBKQzMpPO3ZqkVQwGk/SapFWnD5qMFpPYUquMR9MvYxJXYZ0ueqUDWfouYQ0SIAESIAESUE+AgUw9Y/ZAAiRAAiSgkAADmUK4bJoESIAESEA9AQYy9YzZAwmQAAmQgEICDGQK4bJpEiABEiAB9QQYyNQzZg8kQAIkQAIKCTCQKYTLpkmABEiABNQTkA5kfDu0emewBxIgARIggfQJSAcyXW58S99E1iABEiABEvAyAelA5mUItI0ESIAESMBcAgxk5vqOykmABEiABADwocEcBp4lwIcGe9a1NIwEuhCQzshMmiMzSavwhkl6TdLaZaQbsGESW2pVM6BM4qrTd5d0IFPjNrZKAiRAAiRAAtkRYCDLjh9rkwAJkAAJuExAeo5MpLy8l8xlb7H7tAhwjiwtXCxMAsYS8GRGxvPM6sajaWzVkXC+ZZPYUqvz/hctmsRVJ72eDGRqhhhbJQESIAES0JEAA5mOXqEmEiABEiABaQIMZNKoWFA5gdYGVBQEIOa2LvzdjdrGL5V3yw5IgATMJiB9sYfZZlK9/gTOo6luPm6auhYtUbElNQhtn43CDH9u8WKPKEj+JwFvE5D+ijBpEtIkrWJ4maRXmda2o/j5C/3xv862w7KsC387Mg9iJn5slbFVAINaFUA17LtAp++unmrcwVZJIB0CYbQerMeqnRtQ9PRgnCm9FSVjC9EnnSZYlgRIwLcEpDMy3xKi4eoJhBvxixUb0IIW7Kn+AaaOK8ZdFXVobAur75s9kAAJGE+Ac2TGu9BDBoRbcPjXv8GWny1G9R6geGU9fv3EqIwzM86ReWhs0BQSSEJAOiPjOfEkFLM8RLYXAeblY8Sk72PF7n/D7oXXYc+qehxs9U9WxnGQ5QcpQXVyTQDGgd26sJXOyNIRLB5lFVvevh2Pn72MfZt14hFA5LFhWrK2TmLIgV9izs6OaxDjGNAXQ++ajvuHX4HAxaMdfv/qz9j1z7swpv4PuHTv6m51q6qquu2LtyMYDMbbrS83qPFpB9cYGvZ9qbZF1VRl7Md1rxODI7Jq12/ftpeXsc/rdQQjtxfpQOa2UPbvMwLhY6id8BSwugazCy/1mfE0lwRIIB0C0qcW02mUZUkgawJtzTg+Yg6+yyCWNUo2QAJeJ8BA5nUPG2BfuOUwtm07jJaL02Hhlv149um3Mf7RMehngH5KJAEScJcAA5m7/Nl7hMBpHPjZXSjoEUCgYCZW7f8r7nxyPsbm9yIfEiABEkhJgHNkKRGxAAmQAAmQgM4EmJHp7B1qIwESIAESSEng/wN5FG9WsY0KRgAAAABJRU5ErkJggg=="></strong></p>
<p>Write down the value of <em>a</em> and of <em>b</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><img 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YFg8PMt/8c//Skqy8u5ELY0cfCPeKGLUW7Qmg++Xr8X0Zoo2QJvPmWHOu+EOA5cXI7lUfKEc6jpq+WFFwFZrVpVVRNeLkJYepe1GyPjCzdWCSErcxbldg2gvql9znwRkUHQ4M03qyKCFTlMnD9rR//gkJyssvO4+/vxyCMP4ac/+inIk5TX68Vjjz+OwrziBQta2cQjJCMNGPWNjRHCzdxsdLV1cSFoqSZ/6nkfAwPuuSsVATloZdtt7Y4ATuSxUH6kfFGOZ+RRmT2XLGHrcPADaq/bOXuNI+iuZ7SP6UEjiKUZWaEVTXe3dcb7kXaD9KAez2hI2TLq9IiOjsH+p5/C3XfdiS/9/d9ja3EJfvDD74eUTqQXZncGjJcinU/i7/z58zywyXjs7++HZzS0E8RwVZ4M9ugd4yV1dXdNGhkqxbMsAymdcK0VrFIMz0WXrDElifz5RP42l0YjQD+NhfFcdVTivkaUIOhkdRcl2LuGpiCEnteo6Cj86le/uobWYi9MZ/W72DLD+Xw4sA0Xv7zxquFkrCUrZJ6w1el00Cgsxq5PnW243ly1XBWBMCDAk842DNVXi1QR+ItAQNY2cntLG8ZJec9BcjmdGBwc5IBTwN3rRlN9Exe8EpPHqvnR3bc0tTF8uQD34kUu2CQmyYinpuoYKCgDD6murgFe38KDRCxlHUkH2tPDh8qOzut223qWEp5F0WLbyCI7SLqochbzsCxhW9/cCN+gbzF0luxZOiPXNxA4QL5kRBdBKLDlvYgClvBROlzOTSJVwmKiAyxlRZctW0pqi6J1SWJHj7FckjV0LIpWKB7WUCf4QOH9Q5kVkSCRbyAuEjnxaGqio0p8pPqaWkyMKzt+yXpjlN7rnldzXuUtaF7PLnFm0S9h1KdsB5BbZXKA4b/Ix+4G1WnU74OfPFLwkDha2QoS4PH2Y4K83HCQBkZ9uJE8G3CQxi9ehO+ilwNOAyySAxtukkYH0afsTEaWFUlpSSli4vVc4Jqbm8u8sPDALHlqMqUn8cAqc2CQnHatu7RIZT45Po654ItU/q7gi6OVragBbsrIxI3SBwAHE9sVaQm4pJG1priiSZT4ERsdD0HgYweR5EFR4RYlYFoQzS1bixWXYbIMpMjTkSkjY0GVVB9SEVARmB0B1UBqdnzUuyoC1wMCsqZ8ZdXV3NS1rq4WwyMjXPBrtXZh/4EDXPBKTP7fn/6UG17J9V23zcYNvzwx+swz+7lht+JIBTe81tfVw8rJWfb+3n7UNtRzg+0vf/lLDPYqazgrS9jqONqaJ0+NEid6UEkSIfmV1SPIfVuoC0xw4pmL6kTOypkXcrkVVDAfb+dsqd/ykvzcWMmBzKN4gZVF+6Gz97wkn8+nOL6ydLYZWVm8YApTfDK0sXxYH9604kPQFxm4wJZmZbv37OaCV2IyOzsb2jA4tggHALwFjy8pLg4HDGEpc8OmDWEpNxyF8tRnKbxeMgfBXoLtlGPJYSEBg7+V+JQlbEtK+Hm5LLnZSuC4IJpR0TokadIW9KwSD61I4YdXnVavOnQPQyehiUFSEj/9wKjjYzJLTaXX6XHjclmbjWFo2fkVGRsTg9hsDgKoXK7W9p3b51fBMOSW1bIvvXiAGz1oU0sTN/6Gbc7zeLOyPAzNGvoiacPo8MuHQ19wmEo8fvxt2BznwlR6iIvl6OiP6B3HC4efhc/PxzGwssoqDA8rq6uT21s6OjvQUs9HkAfCtLyCj7GL8D/8apnigQhkrWwHxzwBPSgHE5mxMR980WNy+7ei+W5KSkHClhJFeZBLnGZlpdtK5WZXPN/GzRuh1/JxXA0cHf2h0Hpbt26HTrNc8TaWw8C2LcUseLucvErnMWdnQ8PJmWByvjE8yIdnLmrX/gtuxXW2sla2RoMBglZWVqX7K3OOzYsz77MXzuPtSj7C1tHKtqycn5ns8epjOHv+fcX7oywGOFrZekdGUFl+BLzomSuqqjEyyMfk29rZCfrjJWl1fMS2JjwNFERF4XPhss7Z8tL4vPE54R3HgH8MpvhELljn6bw1+Z026o2gSD2Rnng6Z0tC1uV2I91kAg/Tb6fLjdTkOAhC5K/E+4eH2co2Pp4f5zGR/m5FEn+y3pempo5I4nlWXmy2HpCTbB6SZ8wDt4OP+Lu0su1x8BPH1O/zY8zPhzceHvpqkEc6puR2ubgQtMTzmMfDhaAN8iqKfBwF9Hq9cHA0HtTW1SkuF2QJ245OfhxOO5wu8NJh+/ouoKO9PTiORfQnnak7ceJERPM4lTkaCAY4CkgxlfdI/97Zwc/ku8vaFelwTvLH+uwQJ8Hjx/ywOfhxGnPyxAmMejyTWCvxRZaw5ehcOMNQ4sQXquaiAF54Jcfz8jqLEt2Yb5q8ObXgG+3I5p6CsvOQyAGHAFn2tRFTHY3C5+5l6WxFcYKbrRjGK5YBQuR3WtqalXzjEHSRr1ekN8bnG4FOx4FJOvMgNQGBk37Ak86W+oHIUZ/lbeyCZhkL+hExEmoWRnjClo6qabVRik5lZEkksuYjwcBDYoYQHAhawtI7PAyn6wIPsDIeHY7z3PDqdJzHiJcPH9ncgHp5EtP9HidW3gDstvcxwYlL1H73EPr7e7npDjwYnQXB1CksaIkPWcL25fIXMKywE+cgaHN91hyr4caZ94DHg842TvRfooSGhrq54I+Y+11dXTg/NBAx/MzKCEdHf8geoqW1CbSq4SG1nDoFPyc+ve1OO+x2PvSgFIjgueee46ELMB5/+7snFJdhsjbdBfBznkqj1TIn2Tz0ggSjETnrV/HAKiRBg7z8Qi54JSZzc3MQFxfHB78cObUQBC1W5+cFtug5QDdv7Wpoo/hQ02SmZwJ8uHVnLU9jAi+J1LUCnbVVMMlCy2wxQ6vjoxekxqfCaORjckAr27a2Uwo2v3zSZI3c0sSPVXpnJ61s+bDsxMWLuMjJ6nZiXEJbUwP8skYO+f0rXDlbW07DN8HHKpxWtmdt9nBBEdJyBZ0Wt2ZlhrTMcBaWnW2BRnVqEU6I1bJVBCIfAd4MpCIfUZVDFYHIQ0DW/PRYTU3kcT4DR6e7upjV7Ay3I+qyy+VAbW1tRPE0EzNkIFd+hB93jd3WbpAXKTWFHoHa6mOhLzRMJTY1tYSp5NAXS33W6ebDyc3wyAiIX14SjV0jw8r6cpYlbO02fkD19PaDtrp4SENDQ+ix87FtRHh2dPOx5U289vb3wuPhYxuZt3O2PU5+PImdP8dJ5KfLfXbMw4cfZ8knsneMh3GWeOyydcHvFxVlV5aw1UiysilakSBxPyntNXwIW9IhCArrEYK4zfVJOlsNIt+/7BX10PBhZ8CLU/8rsOXkBzlf4Cnxwi/jU1l7o3k2q/JjgSynFvOslZpdRUBFYB4IqDrbeYClZlUR4BQBWUvWjs42eL3KLsHl4uu0OeHm5GA4RU+pq+ZHH17FSThA6it1dXVwOl1yu42y+TixRCaQ/OIEKsvLuQmxV11zDN4xPpybdJ0+ja6uM8r2RZnUvSNeWK3vysytfLbOTuXPhssStvV1J+HnpMN2O3vg4cSZgVbQIjrBoHxPlMEBbcbpDcpvxchglWWJidZxE4OZp+DxF8VLMBgMgHRRblMomi9erwMu8bHfqY2Jhk7Lh6qGomq1nGpVtG3nQ7yu4Q+KxzWWJWwh8DPIakm/zImO2efzob+PDy9HkiTBM8jHCoFeQq93DKKfE30dRyvb5ZcE9I16IGmWzWesUyxv75APN0p89IORES/GRryKYTUfwkxny8dmJ6uWBuOKizFZwnbntm2IidfPpy0Uy5u9KhdpKSmK0Z8PYb1OQKKJD17JYjaRo6DWhti4sKxsJ8RxfOVLX0FiYiJuuOEG3Gq+BU/87jfzafZr83LkQeqDGyaQlJQALR/yCykpRnzASRSwmKgYGOKjr+0fEXglNt6AoqKCCORsepa2btmKqGhlZZjs/RVenE5rJBFRMcbpEY+wq/GJyaA/XtLGQn7cNa7MXRkWWL/z7f+DU6dP4dvf+AbcfX146pmn8Nm//jvodQbse/DBBdOUwMe27HJdNAo5ctu5dvX6BbfJUj9oNvPjkYmw0RsTlhqihdOLgAmXrJVteRU/zgw6rd3wDvOxv2HttmL/iy8uvAMt4ZO0kPnlL3+5hBQXR6qhoQHdIT7DTIZ3kt+Pqqqj+Ma3v40f/ehHqH2rFlqdDk8+++yCGaZdAw2FA+Qk7T9wgBNOgYryCm54ZX22p4cLfikSnLWzkwteicmXXngBw4OjivIrS9hKfkV5nBdxiQ4uC5wwPC5B8vvmVT+lMpPOlrzG8JJEUQToL4RJkDT46te/cUVs5+xbs5FjsUBYRGBq3s7Z+nyjgMjHPrJf5GQsYOELRUic8MvLeeAQvv6LLkrWNnJxScmiCS1VAYmkT4rmIxBBUuYKFEXzofeg1dfuez+xVM24aDoWixk6bWj7QWJyIujf1WnUO4bS27dcffm6/b2lqBjgJOLLmnV8RNWizkJ9VhPiPhuuTqjVCsxuIVzlh7pcC02ItbLWlqEmPVmeLGFrMZsnH4j0L7krw6OrC0e9Y6N10IIPAylayay46ebAioaDgZYEbdQSTLqO1RyDPkqHv/3aFxfcRXhy10ir8KSkFHbOlge+E4wJ3PBq0PNha0IdPSY2FtmxsQvu80v94M6dO5ea5DX0ZIn6/Qeew2Dv4LQBo2kzSfSNs8PuM22H0UF4SZTg84+zz2u4uHxYnu5P+Kff9iE6wftU1nSJAlo3tbXB3mObkY7oFxmvM5VB5Qb5nClANl2n56ne03MCEB2fSNtCM+UA7I5zeKOqerqqsGtUBuFB+M3EC/EaxH+6gug59ucXZyxDDh0KqfbySy+xuLbT0pEkVj7jZ4ajFlQPwmS2NiZeg/hPS0ecCODhF2fGXpLwZtUx2GxnpyuCXWOYXu6302WaituENP129Lh3HP/4zW/jZ7/4GZbP4HaT1cc3AjrW4RvxYmRkhAXK8Hp98Pq97LvPOzJriL1gnyVcZkqT/WAG7OndDPaTmd7TIO6z0hnx4vmXXphxGznY16iNZ+r5wTaeqR9QHYP1men9mTqmzLSlTbiVVVVgpH9mB/Sh6Adz1YdwIOypvjP1JWqT1vZmtHc0z+gwZC46QdwYrjOMO1QGqzONLTP067no0P3+/l6UV1bOWgbRob+ZUvA+lTddXyH+qC5+kguz8BosZzo67DlRwuHXyuFVOBCBrJWtb3QMh8uex8ZNdyAzPR1lFQGjg7w1a5Bxczqeee5lwOeD2WzGltKtqKqqZk6qo3Ra7Lp3N6xtXahrbQQZhJVuLUVmZiaeu2xkkWXOREFeASoq30Cv3QmtUY+HHnwI5E2l7bICPicnB7fcYsETTzwJnSAgIyMTW0tLUVNVDWd/LybpdHXh5DvHodfqkZ6RgdJtpXj5wAFQc2dlZqGgIB9VlZVwOBzMqOWRRx+5gs7evXvZIPLMM78HzdotZguKCotQ31AHm8PJ9HJ79+xBx6kuNDSeBFVoW2kpyDlFTe0xkPfgjIwMFBUW4sirr2DwQh/0CQbcv+d+dL17ZrI+u3fvxMUREVWVFSzGYnX1MWzZUoLaujo47HaG075998N65gzqGk8EcNu+EzpoUFUTiLhSkLceWWYLDr1yGB7PGIwGHfbu3ofT755BV1cX63e7792ODy4KePaFp6HRaLFuzSqsX58XqI/NAUgS7r//fpw6cxrNjSehEYHSnTug12pRWVXF6kdtbLnlFhw68Bw6uzrx8osvYtfuneh+t3uyPju2bYNvzIfD5UdYmRtWbcD6grzJNg7SOd3SjubmVpDL4p3bd0Gr16K8opLxSnSyPpKFF188gjHfKPR6Lfbu+SRs79nQ1N4OQMK2rTsw6vOg8kgZJAHYuHEj1q5dP0kn2Jco7m7vUB+qqyth0O2AMS4JR4g3Ciqfk41bP5qNA4dewtiYH3FxRuzbsxf27m7UtQQixJRu2Yoxvw8VR8oYr2vWbUDe+j/Xx2LJQt7qPJperqoAACAASURBVPzz9/4ZOTm56OnpxrpVm7A8WkL5K+Wsv1GfXXvrSrx44CX8zzNPo+HtGmA6va4gwD86iiyLGR1tp7Bq7Wq8dOBFXIQ02Zfq6uph7Qm06ad2PYDoaA1efCVQH0Zn9Wq8eOAFjPn8SDUmYNe+PWioq0OPwwEyvdq3by9cLhfKy8tZX6I+Tc8dOXgQXlGEyZSB4qIC1Fa/A5vLAdHvw9888hkIuqhJbIN0DpUdxuioD5Wvv4rt9+5GfV0DbA7bZF9yOM6hqrqKYV2wYROrz5FDh+D1+5CemIrirVtw7NgJ2Lut0FKf3fcp2P7QM9mXgnT2P/M0dRskp6SwMaSpqQndZDx0uc+63X2oKC9jfbR4UzGyV2az34MjXiQnJmLr1q2oqKrE6IUBvFx2GA/e/0nY/nQebe2BNqY+S6uzZ556EpJGC0t6FkpKS9DU1hKIZnOZTo/9fdQcC7xzmzdtRmZGxuT4Fxsfj+2lpThWdRx2Zw+0Oj327tkF9x/Po67jz31Jp9Pj+ReeBh30zDJlsDGyjbxF0fh2mY7Tbkd7azMkScdOKNycmYWXDx1iOMbExmDHtu0or3gTva7A2HXfrk/hwoWzqG9qAqDB1uISdjzzmf3Ps2dysi0oKipB2+lT6OrsmqTz7h96cPLt4yxIfVFxCcwZH8KLrxxmZQSxr6p8Cw6XAzqdDnv3fhKnmlrR47BDEOid3INOGv+aT2JszAeDRovirUSH6tNBrykbU4jOiXeOszFl0x23Y+VHb8FzB8kYVGLvzNrVq1Hx6htwD7hYH33woQfQ3zvExlGqQHFRCYwGPZvYaSDBnGFGSelWlB06hBG2IJNw39696DzVgeaTzew93bXzkyBVz3MHnmP12b19Bz6ABk8//zT77fdLUPJglSzfyM8d2I8d2/YgJja0OjDWK0L8X1NLE5ITk5lAD3HRIS+u22ZDR0MD7tu3L+Rlh7xAUYIpMwNFBYV4+umnERUdFXISoSyQQmpZVuXAkpUVymIny6LJ4jm7HV//5jcnr830xeF0otc9c7i/Z596Ch3vvoujR4/OVETEXKfV+f4Xfo+HHv0baCPgOMVMwNBqqa2tHXaHA1uLtyE2UclhdiYur7xOLkYpMEl+Qf6VNyLwFxlLHj/+NnZs3xGB3F3L0nMvPoed92xHtE65rW9ZwpZt03CgpwtCTFsSsvbHgw8o9DnhHceAbxQmTs7aUlzjvXv3oKSkGL9/8kUsj4pclF29LsTp48IyKXjx0CtobW7ED77//cme4/V6MeAZRYYpdfKa3C88BSIgIeZ0XWArPLn1W+p8xGNTWwdGBwaQabEgK2PFFRbkS82PXHr9w8PQiH5uzt7T1jcPenu5+Ic7n6zRsqmNn/NUNrsdJMR4SJ4xD9y8OMsHoBUE1NXUo7rqGD716cCWe6TiLPpEthUcav4OvngQ//wP3wJtbT3++OPs77HHH8eOu++Gf4wP15uLwYSc2wz29y+miPA+K0poamllgnbzbbdR5AQuBC2BMubxMFVUeAEKTelkr+B08hOLm3YNaEKsZJIlbNs76pTkcV60nXYH/CIfZ1f7+i6gvaNjXvVTMvM7J07Akm3G22/XoKm2Dnsf3DejMYeSfBJt0ssPDFwIKRsVlZV44OFPo+uPVvzrv/4bvve977G//+9734PX70dm5odDSi9SC4vUPksrrYa2Jox6PNi4eTOio6PRZQ3ouiMVy6l8UZ/tG+ibeiliv5ONhtPBSVQtACdOnGB2JUoCKkvYahH5utogiH6yWpvBMjSYR/1cAAIseHzguZUrc3H0rTdQd6wWe/fsBc1yIzPJsv+TzToZw02Mj+PSpUvX/JH3n4W6NOVuK24Gi2fZQIYhI9s6bmrAqGcUmzZuQmxMDKNCBmJcpQjEdjr8VKcW06Ey+zVZOlufbwQ6XaDzzl6c8nfppVvooLfU3NPRBApVRlafPCQ6thJzeRAjfk+f7sQddxSDrHf/98knw6IfXSgurB+QC0QObA140tlSe0TaeBDQ0bZjdGCIrWiDgpZ4peNV0drIN44iXqke0CzjQg9KdjESR2MtxTSO0scoOvWSNe2buMgsuhc67i3pcxcnAuc9l5ToAokNj3vR855tgU8v/WM9V/ltpRVuTX0tqmqq8fDDD097Vm7puQxQ7On5E/pHZj5fqRRfvNMVx0W8+25PxKgPaOu4hRlDDYGO5kwVtIR1zx96MDE+3SnOyGsJl+sC3A5n5DE2DUckaMe9fKjriH1xXIOLM5zVnaZ6YbkkS9i+8PyzGO4dDAsDoS70ZPNJ2OwzOzMINb3FlOfzeOA4d24xRSzps9arhC0Rz7Xk4I03j6GuvhZ7tt+ruBFCEBDS3ZPujot08SI+uDjz4f9IqoN4wzisPd0zOrVYSl7ZiraphbXzpk2bEB177e7bufffh9/Ph0/v3l43LgzyMc5SIIKgv4WlbPOF0nqp7CX4FfbtLkvYCpz466SG0Gp13DjzNhqNyM7JXmj/WdrnRAnr108frmztylzU1tah4w+duPvjH8eIwp5aCJjsHAuSkpKWFqOFUlu2DDcuW77Qp5f0OXJsQI5RlNYzk2ehprZWjI16sHHNOuagYjogcnJzl8Rt53S053uNHOKsSJ//0bH50glVfqX7wHzqoRPIq998ngh9XlnCds26XOj0fBhJpcamIi4uLvRIhaHEAY8HjQ3kAYaDJGhQd9l71XTcZmVl4a3jbzEPWLt271Zc4LZ2WHHuQmitkaerd0iuXeQjli3VlewMaqqrFd1GphVtY0M9fB4fNm3ajJjE+Bmbob6phZuQm902B85Os3s0Y+UUvKHRCUjPylCQg/mRzswwQx+vrAyTZSA1v2qpuf+SEaDjC3eWlCDD/FGUHXo5ooymIrVdeDOQUhJHErT1DY2gc9S0dRzpnsyUxEqlHVkIyFrZ0hYhL8naY4V3JFKPolyJosvlQF1D/ZUXI/QXmZhUXfaJPRuLtBX25rFjsP+xGzs/odyWcveZbrh7Z3aROFsd1HuzI1BX1zB7hjDdpa3joKDduGmjLEHb1tEWJm5CX2x3dw/cbj7OrpKDiB5rd+hBCFOJlZVViu+2yRK2Pd38eJByu3ohSnxYyQ0NDYFeMB6SRpTQejkwxFz8ksB966238J7dDqW2lHuHeuEZHZuL1Yi4z5PuiwCzKjAeUBQg2joOrmjJYYWc9L7tfTnZIiKPy+WExzMaEbzMxQQ5tXD3986VLWLud3S0w09HLRVMsoStxJOTCI6cWmgIVz5OJbDQerI6y+XOTAK3pqYGf7TZcM8990Sw4wsF377LpOn4Ck9pqR1FUHg6csEo+iVsvI63joXpokLx1DFUXmdF4PrU2VIsRw6cGczaMtfJTZvDgbtLSpCWmYmjr74ma+vvOqm67GqoOtuZoWI6WhK0o2QMpepoZ0ZKvRPpCMharDS0NMHnVdhuWiaSLocLw14+ztU5nS5UVQZif8qsnmLZaO116HJ8zfkwkXVZh9t37hzu/sRd6F+ic4THao+BYoRykTiyRibvUYcPHWRWyeHGdlJHO+qDXB3t1TxRvORIOIp2NV/T/W47dQodp/jQMZOL1ne7+dHZdnadmjWQ/XTtEeprsoRte2srxseUjZggt+JWmxUX+s7Lza5oPr1OQFxKgqI8yCVOHSU1NVFu9ivy0Zby62+8gaG+Idx958fQ3xv+qDGJujgInBxXw7JlV+AVyT8ECEhINIV95yioo/WPBVa0cnW0V2NnSjKyoOdXX4/E3zFRsdBHydNFK80/6WxbWeB6pTmRR7++vhkTw8ouGGUJW170igx2jRa8qMDGfCKGLvARlo30iu5FeBHLpBXuW2+ySMN33fWxsK9wB30exQ0i5A0DADha2V68tBx9/Q7ZVVtIRlo1NdU3QhIFbN5826JUD+4BHzfjwcj4MMa8fLgY5S0QAYXElAQODKR27tiBmHj9Qt6bJX9mVW4OPrTiQ0tOdyEE9XodTBlpC3l0yZ8hi9mbbzYtim5ycipeP/o6+fnC3XffBXcY46Imx8dBz4vnM45WtsuWXcSHMs1hc9dIgvZE40lAo8XGjesWJWips6alGSEs48MALTE+FobEhe0eLerFXMDDsfEGFJeULOBJZR7ZsrUU0dHKyjBZK1uNIHATSUer0WDZclnVUqbVp1CNj49Hbs7KKVci++u63LxFM0gC94233oDk9+PjtKUcJoGbk7saicl8DFyLBnUJC6CIWnnkrlEb2vCFVAXvsBcnWk9Aq9GioGDxgpbKXLt6PZbr+NiazcjIRFZG1hK25uJIGfXKCq/5cK+LAEtvWVKprOzIfOqlaN7W9laMjyu7XSAXAGu3FS8fOCg3u+L5fvOb34aEh8T4eLzx5luQoMFdYRK4LS1N6ObFQCokqC5dIQfC0Ge9I140tjZCK+mwsSg/ZJP7qsrKpQNmkZRa6pvQbeMjChgFIuiQee5+kbCE5PGnn30ew4PKnmGWJWyhkZctJKgsthCNANGnrCJcbhUk0Y9hpb1jy2SWNuI8vtB11sTERLzxxlFAEnD3XXeGXIfroz4g8jHp4s2phc83JLPXyMtGW8fNHc0QtMDGDeuwPITn+kdH+DDsJKR8kh+Snw+HPKSz5WNzPtAHSWerdJIlRQsLC5XmUzb97CwLN/rllLSbULJu8VuzssFZREbqKHd+7GOLKOHaR9mW8ttvgpwk3HXXnSF1r0iBEdI4ifrDm1OLgo3F1zbmAq+wFW1zMyBqULCuCMujoxZY0vSPrSvg4/0i7i2ZZiSlrZi+IhF21RCvhzmLny3v0tJS6BXe9pYlbLMtnISBo+Mp6akh24IKd/+OjdEjJeOmcJMJWfkWszlkZQULoi1lOhZE6eN33RUyHa7REMdNaLUgFjx80vpgRXpKSFj1esfZ1jEVtqlwA4So0OuBEwzGCFjTyIPLEGdETLSykWnkcQosF6JgMi3OYFIurVDkW7Vq1aKN7RbLhyxhe+DFAxju52M7pr6pAXZOdHVO53kcraxYbBsu2fMvv3Q4LLRoS/no669P6nApctBi01tvvQmb49xii1ma5zk6+uP3jeCFl18GnYNdTGJbx80noYGAwo0FbPBeTHkzPVvGHNDzEZC9ubMdLfWNM1Uloq4P9g7iyGuvRRRPszHz0sGXMcJD8HjPmAeSyIcuQRwT4eNE75GUGodNRfmz9ZGIule8tShs/NCW8ptvvQWdMQ533nknFitwN2xcg7QEPhyGcOXUQhOFrVtKoNMsPNg9eXQ62doKSJqwrWiDHbU4P1/xIx9BXub6zLFYkJ29aq5sEXPfO+aJGF7mYmR8bAQS+c1XMMla2SYnJECgUPccJEGvgY4sLThIfb0e1FTVcMBpIF5CddWxsPJKW8pvvX4USStW4O677kLPIiwzT9Y14PwAHw5DeHJqMYEJlFdULDh4/PDwMBpbW6HTalBYtClsK9pgR62prwNZzvKQurqs6Opu54FVOgaNWCGGC16JSY1Wy2xDlGRYViACSZSg4cWxvyiRrQV4sPCcGJfg948gJjZWyT4gmzZtHcUnx8vOv9CMtMV498c/DrvdhtraGtD5w/mm4ZERaDWC4noaOXxzFYhAlNDfP4z41HjImqlPAWBkxIuTjSdg0BmQl79uSWwrhocHoYuJCamF85QqhfQr8+GsERATw8e54HFJRFQILcdDCubVhUVAcBpZ70vbGX7i2fY47PhgfOJqqCPyt2e0Fz2c6JcnJBFd3V1LgmNUdBRee/UVZGZm4c4771rQlrJnaAhjnKgTlgTUUBERNHC4HfMXtLSibTy5pIKWqnz+/AUuBC3xOuTxwM/JUUCaEPc5+Qh0T9jWNdQrHuZTlrDtOFkfqlc17OW4XS74OXGO3Nd3Ae0dHWHHJBQE6OzjiRMnQlGUrDJotU9GU+lpabjrrrths/XIei6YiXS+A0OhPQ8aLDvUnzzswkytc2tr89Sfc36nrePm1nZojfolW9EGmeq28hOZhvps3wU+gqiMjY0taBIcbJel/qSxi3hWMskStlIYXLOFq9J+SYQk8eHUgjAgL0pcJNqGWeJEK9zy148iISUJd99N28rztFLmpB/wds52PsHjR4ZH0NzczHR8RSvzlmTreGo35cv1wlTO1e/XGwKydLakS+BFrzjuFbFs+QdL/lIvpGNQYOyLXhFRsXzoaEj/FRsbfp3t1VhS/7t3zz3o6bajtrYWFLJvriSSy85lfPQDrnS2AEaGvYiR0WdJb9548gQMhjjk5a1R5J0kHmJj+DDkIRuOG5ddVASnud6nq++TWkkav8iFTQTxTv1AFx2lqEpB1rKKlt8kGPhIF/lgkwatkTG89/78tkeVqhyta9/rWhqd7dV1pIneKwdfhTkzCx/72MdkbV91/fEPGBnm52jC1XWO1N80DnRYO+aM+kMTJFrRGowJiglawrCnp0dxXZ3ctjx73g6X66zc7Irnk27kZweR4jArnWQJ2yNlFdyYzzc2n0SP7U9K4yqLvmd0FG4nHzoa6ijvKWgQQQL3tddfh+XDFuTnF6Kr88ysGLudZ+EZVVZHMyuDU29evIgPLvIxmRVFP5vsiJh5UhvQ0TZDr9Mjb/0qRVdqFxwO8CIUhgf70dc7MrVnROz3sf4RHHmFH4c8L7z0LHz9ymIrS9gqHXR3Pj1O0Oqg4cQcPcFoRMbNfMTepRXN6ls/Op+mCHle0uEerngVBQV5KN5yB7qsMwtcs9kCQ1xcyHmYWiCt3voHQ+CdaNky3Lhs4U4ipvIU7u/CpSjkWnIAzbJpSZGq4eTJE9DR8R6Fto6nMpZlsUC4xMc2ssmUjjQTP2EhuTLsE7TMbmBq31jq77KELUXi0On58NmZkZ6OOKNhqXFcED2ylrW/z4dLQYpjevr0ewuqZygfIqvoZ3//LAqLirG1+E50njo1bfE9Pd0YDZM1stXajc997lHcsnolnnzyd9PSn9dFjtw1Ttw4gY5pLOjJyKufjvecbERSUkpECFpqA+sf32Nn2efVHgpldrqcOO/qV4j6/MiSPLBk8+Mzf8OabAiCsjJMloHU/JpBza0iEH4E6JzfA5/+NMgXdtVrryF39erwE71MwdbTja53e3DPzk/gP3/yE3z1y19eFG3eDKSmq+xgfy873mOMi8P69eu5cCozXT3UayoC4UJA1sr2id+GYPYerhpcVW53TzfGh/kImuByu1DfxMcZZlq5VFdHTiBu2lI+dOggCvPzUXrX3dfocOlcrrvXfVXvCM3PLLMF61bnQisIEP3K+lsNTY3mV0p9fe0VDwz29qO1oxPGBCPy10aWoG1va7mC10j+0d39LtxuPhxFeL3eeZ99VxL7ysrXQFGmlEyyhC2UXX3PCx+3083cNc7rIYUyDw30wWrlwxpZkIDm1shzwHHgwLPILywI6HC7/ryl7HK5w2ogRXaYpLMSQnAGnSvdF23NTumzg8ODIKNEvdGI9WvzCBSF3qbpyTo4UdMQ9+7eIXg8o9NXJMKu+sZ8oHeMl9Te8Qf4x5QNpiPrzeDENwBrdxE+8HKQPSUhDbk5OVz0V0nQYNOmTRHHK+mSSYdbVFyErSV349TpwPEkOotLBmjhShpa1UoSpBB4K+PNqcWa3EBkmuH+QbQ2t8KYkoaC1WsjcuuYDKR4SZkmE+J4iVTFC6iX+dQwqbD0jnmmwqTqbKeioX7nFgFyCPDww/ejprYOVUfDr8N1ORz48Ec+gh/88If4f7/61UXhxqPOlkXvaW6G3mBA4frIW9EuqkHUh1UEwoCArJVtS1sLNwfD7Q47+nv5sOijIPflr5aFoVnDUKQo4blnnglDwaEpcnmUBk8f2M+OBZXcdSd++ZOfo3sRIfrm4koUBLaSC8lcmSNrZK/fi2eeeAbvNJ5AnF7PdOaRtnU8te0OHjoEOo7EQ2poaEATJzYcZKB4+gw/+vD2lnZMiMrqbGW51Whvboa124a8Vbm4KSMTjc2NrO+aszKRbEpD2SvlgOjHiox0FBQWoe3UKVDUFYNWj/UFeew8ZNdpK8uzqaAI6ZnpqKkJxHHNyEhHVkYWqutqMORyQ6vVYsfu3bDZbHC5XBBFEVlZWUg1paDs4GFA0CItNZEd/eg8fRr9AwPQ6XTIz88HHfc4Vn0MGZnpSEhIgsViQWdnFyvDlGqCJduCpqY6XDg3BK1ewNatpVfQKSwMbJNWVb0JQRCQmpqCVavWouv0abgHBqAP0unuBhli0fb6hs0bIAhadHS0QivoEGeMw60rb0VdfQ08Q6PsmaLiEpBgDdaH6IyPi2htb8Hg8Ci6Ok4hZ9VqnDl9BkOeIcZvcXExeqw96LZZGdbrNm6EoBFg7QrUh+pmMplwrLoaPr8PBr0RBYUb4XCcm6SzccNGkDA4fvwtVp/MjCyGATlnJ+MsSkTnD1Yr/njZ0f+6DRug1+rQ3tkJSRQZhkSntqkWnrEx1DXUoWB9AeiYArUR4bRuzTr4fKM42UwBwUWYsyyMTrCNKU9hYSHOWK14n+iIWmzavAZanZ55GaL7tO2bZEpFc30DyNmHQadFUVEJqwtNoKgfrFuzhkXyaW1th+QTkbsmF5mZmairq2N1MZlS2Zby33/p7/G173wTP7g0js8+/Cg789nc3srqQ33JlJyEuoZGjI0F2qe4ZAuj093dzeqzKjc3QKe5GZKogSXnZljMtzA6xEd6hgl6Qce2kW3v/gGVlZW4bfPtEKKAk3WNoGPehHVKugmNdfV44nfPoLX1bUDSMz6v/q+3141kUyrsPT3INJsn6QT77KnOLlxwOSD6NLjt9o2Iitahru4k45XahupUVVkNUfLBYDCiqKgIdDyJjG2C2JOxWGszBRDQIjfHjIzMrEncjEYjVq5ciYamOgz0idBgDFtKSxmbdbUBYyiiQW3UXNuI+LgYCBMarN2Sj+7uHhD/hAv1JZfLiY6OLvZuZOd+CFlZHwUJkTGfD6kJCchZuRItTW240HcOWkGLwuLb0OvuY7GLyeAsWJ+KinJWRlJKAvILCkDGQ729A5N0nG4XOigAvVZAbkY2MiyZaGiohyhK0Op0yFu/nr3rdPzrnRMnsaXkNvT2DgUccogi6N2IWr4cFdVVbK6QFJeGtXmrmdGPw+FkdWf1cTjR3tUJckCUnWlBWloaG/8I1yCdhoYmDAxcgFarQ2HRZgz2D2FqX1q2XIM3qo8jSivgz3T+PL4FcHMwd6SAiPTUDLad3NreyuprMOixfn0e6uqb4Bm6EMCtaBMGB0cn6WTn5MAQHY3KqipGx5S6ArmrVl4xvhEdh82BTmsHi+2ak5MDU3oa60tU4WAb19fVY2hsADqNAQWF62C3n2d9idqYHJUcKTuC3sF+rF2bhxs+0E5Px2FHR2snO9uak70G6RlJ1/TZmoY6jPWNQqsDCotuZx7fKKYvYWuxmKHXGXH8xHE2pqQl3cTah/qSzxfQvVJ9yENYdzfJFi02376BuZMNjjsbNxRCutGLd2qaYXPYcLP5Q1geG3X167dkv2UJW1ESkJebizSTCdRxLFlZIAMReklJZ7Y5P4/9Dp7FTU9ORWp8PMTLxhIfSkuHXk8HyyUkXNZJ0CCp1WigofO7ggZrcnIxmmWerHhSQgJIL0Zh4LUGA6OzobCQ/WbPAGxwToiNZbTpwbS0m5BqSodOb4DoA46/8w4k0Y+LFz9gL0ucy4jU1EzExqZOGnIE6NACXzPp6YaEBfFk1AUswxJMqYhjdALrmLiUFJg1EiAJTDCRsM2mZ6iUy+eRM1IzMZboZ5MHjUaDqXTIIUBUFJCUYMJIrxUJaans2dT0VETHxrA60oWktCQiwVzjGXUGhn16ejqg0TDsKU+W2Qw/VVbQQSMsh3EKbpqoZVgmfQCzJZtFf4+LC5w/jktJgkGvm8QtMSkFN2g0LA8J7eXLNaDzykTHoA8ICKpPB6xIT01n2MQZjcjMymJ8U58ADDCbzYD05zYO9hO6Rik1JQXLKPCCIEEfrceNgjBZBpUXJWgZXT8NmGR4RG1gNCA9I521DwkZgsNszmSYkFEOpcB9MEFDVso//OG/o6+vD//y2L9iXe5a3LZ1CyuX+pvWaIRGF4XMjAxWf7pGiVZprD6SBG1MNIRxLZs0EA8JxoBzjPSMjED/Mxjgv/zCJyQnMgFJgnaZEDX5btD2Kp0JJgF1756tWL9+NTXRnxNJZEkESeaKigq4nb2IS0pi9yfpXO5LqUkGROnMkCh+KGEgLJ/ELaiXzrRkgCqk1dEbA8QlxcE4pY2NWkOgH4gSdHEJLE/WZQyC721mugXxMX2Bd0MK+OglTILvoNvdC88YhYETsSZ/FVvZJyUYGc0AVcCgNyDLnEHRuifPu6enZ0BDdQ3Wx0T9PIreOFYGtT0N9JSC9TGbswGNyCZKdD0lxQStLpr1L5bPEAdzphnQaaFPCPSDzIxM+EQRBiHAjcmUhfZWK25akQlBG404owSJ/GpLEujdoP5tpr6l08OoDwyFRpqkC9rJd8NgNMBMvEmAMSGOvYPBfq+/TIfeyfj4aECjY/Whd2ZqX7pRBG6hM6kSoDcE6ATHt+C7Qe9dDJWBD6A3Ghh/wX4gXXbSk5mRjjFGR8sm+DT+Bt8xg1bH+tstZgskjYS4yw5drqajj6P2MTPs9XFxk30p2MaELYW2TPQlY2LYi2M1J3D4xQOoqX4HtvMOSH4/ttxRjNuK74RR0CEhJeAr/Wo6tOgw55ihEbRISAiM30Hcgm1sSc/CaPwYaw/q04RBMA99p3GFjSmiBH1coE3TTSYWuoXkD40qVE86HaDRSGyxw/ifHJc+ADQxyMo0we6w0S1FkyydLW3LGhJjFXXiLBcl8uij02oRHR3N/Dn39w7gwlA/vP1j6PMNAf4xpMQlITYxDgnGZMQnBzqc3PJDmY/OJlptDhTkrQ9lsWErq7b6GIq2lISt/FAW3NZ2Cv/xH/+G6NjXNwAAIABJREFU8ooqvHH0FebiMZTlUyjHm2++OTQ62x/9CJVvvIGjR4+GksWQlkXvVWvjCSQkpMDjG0NRYRETLCElEobCGhrqsCp3HRcO82m3jCb9Fpq0KpDc/f1oPnkSTQ0NOFF7HNXv1EEnaLFh0yamnqE2v+OOOybHVrd7AOnpJgU4nT9JsrFINqVMLqjmX8LinwhMs+Yoh0Jq0Sydh0QrlajoQBQdmi2lmkzsj/EuSujvH4Zz6Dx63b3ocV6A2OxBUlwKEk3JSEtIYDPg6OipS5Dw1To+MRkFicnhIxDiknkRtFTttWtX47nnnsMXvvB53HXnx/Hm20eRt74gZIj4/AEn7P7xEJzpXja968OQMbvIgmhSeLKxGWlpK7B+7dpFlra0j5MfbV6Sxby0ltNOlwv2zm4ca6hBZXkl3n7nOJLiEmDOsbDJ1Lce+ycUFd42o4BKCLM71FC2m0C7lDO4GA0lndnKkiVBD1e8jEcf+txs5UTMPdI1rsrNmT4UnKBBYmo8+0N2DkTfOLxeCeeHzmHQNYhuq5Vte9D2Ma180xJSkWhKDVvEWSt5Ijp9Grvu3R0x+M3GyG9/9xv8zec+P1uWiLnX0tKExMRk/PznP2PbTXfecTeOHn0DBYX5i+aRdLRPPPUUK+c3v/0NJnwSHnv8uwsuN5LP2dLWcXNHMzLT0pB7WdAePnQQu3bvWXB9l/LB6qpj2LKVj90Y1mfjEye3UkOJEx0vGx8ZwYmTJ1Fe9grq6hth6+7BqH8Ut20uwj27duNHP/lPZGVlIDExoNaajf7I4Bg6u7tQVMjHZObpp5/GZx7+DBKTlfM9LUvYstFqNuQj6Z4oMcMKOSwJuijE6oDYRAtgBtt2HukdwvnRQXj7R3HS0Qy0SkgwxCEm2YiUuGQkJifMONOTQ3NqHsnvwzAnkWlIP9Lfy4dVJ2Hs8/nhlyTWVr/8+c9AC9FP3PNxvPLKqygqWtwAUVpaCvrD/v1Tm3PB3yP1nK3b7UZHezMy0m5CzhR3mMOcOF6gBhkd4yfM4pjPj2h/6BwvuPt7UV9bh7crq9DU0Yr21g6IkogtW7diz977sGljHtat24jY2Nh5913yZSDrKMu8S75+H5AlbAs3FHGDQJbFjJj46a0+56oEbTvHm1IRj1TAElDA97vc6PP0Y7h3FO2Odvj9fiQYkxCTGoc0Qzz0yUZEaxcW/D0l7SYUbojsLcQgZvRiMQETvBDhn2RwEzTuonZ9glblWhH33nsPXnuNIgctTuCGsvqRuLIlC+OO9nakpqzAqimCluq9YePGUFY/rGWtuuyAI6xEQlQ4GWJpLxskLqRIp8OO5o42NNW2o7q2Eo0nTjKD1JxVa1BSsgWPPf44SopvD8liwRCvnzRqWwivS/0MxcHWLwLbUPAry0CKwqvRgPWXnoJbMWcvXMCwy40BmoX6/dDp9TClJiEpLhkxiQELbTkDKOEqXbwR2ihZcx7F4ff5RqDT8RGujHglC9Sr2+HzX/g8nv/983j96FEUFoZOh7uYxok0pxaDbjdOtLcjLSVlWh2td2Qc0THKHaGYD9Z0LpjsTXgYv8gxy403TIB23OZKNHaQgVJnZwcqKypQWVnFjj7qDUbkrspG6dZS7Ni+Ax+9xczNOztXnXm/L2uUP3DoMLaXlCI+OWDmHcmVbmpqQTIdx8jMDDmbNHBTEPMc2naxWNi2s3fYhyHPANy9Lths70PSAEY6SmA0IjnVhNTUmbednc7zaG5qwX17Il9nS9vIB/a/jEc+90jIcQ1HgdWVx2FZlcOORkwtn7aUNYIG99zzCTzxP/+LnbvvnXpbme8R5NSCto6b29uRmZIyqaOdCop3ZATPv/wSHrn/oZD4hZ5adji+HzlUxoROTEzkLxZOttYiGgLoiON0ieInl1VWoqq8HI2tHejp7oLo92PHjh34whe/gI2bNsGSlYnY+PDrJQd7B/FO60nsKN02HasRd+3lV8pwV8ntbPxWijlZwtY/NqYUf/OmSw4e6G8pEs2WYxPpL5YZNdBsc7h/DAOjvSAh3NnZjtZ2cVLnm2BMRFxcAqKjAzNXsuZbs5YP38i0jZy/ecNSwBoSGrmrPjJ5bnVqgdRm//Xz/0J8TCweevhh7P/909hxr8ICN0KskclRRFd7BxO0OTNYHS+P0mLjmo3QhCAAw9R2Cdf3/LVr2HnNcJUfynLprL7ITpIHSnU6XDhWX4uTNTVoaG5Ea2Mz2xYuLC7Gpx+5DwVrCpmApbPlSqSRkWElyC6IptfTr7jPfFnC1hinh6DlQx1OYwCdDVMi0UCemEp/wR2A1cxV3LnzLqbzdTk7mTME2uohL0bjF0W832OD2XyLEuzOiyatbOtOnET2rSu5MIxo73gXOTk3IDZm+m3vH/zg35mnmn0PPIBDBw+idJuCM/QIWNk6nQ60dnQgJysb5uyZz3mKoh+Nze/glpUWaDlQLTW0tWP7inTyfRHRiSbqNfU1sHa+D8+QGxUVlejo7MCKD92EtStXYvu2XfjVL36N9esj4+iVRgvERy3MVkWJhtAaopnXLCVoB2nK09mSVedlTzvBB9XP+SMQ1PkODAS2nfuGRpmHK/LgkxCXgNTUdCQmGqHTLA948Zk/ibA+wZOuzuf1Q1h+aVZdHbXHD77/ffzrv/0bXnnhILbdsz2s+M1UuNI6W6fbySxVLZlZMOdkzzqZoknXOEc6W/Lhu2zZsojb8ibhOtg7hHfqT6LijXIce70a9gtOkCeo9UX52FG6nRkk3px2E5bHRqZQo/dHlQszvdXXXpe1srWe6kTu2kBYrWuLiKwrPXYHMtOV9RQyEyJBnS/pfcktGfmu7e52IiMjGYP9w2jvaGauy8jgKs6YgMT4eCQkmRATrfy0fEIS0dXVibz8vJmqF1HX3QO9SDAaEBM7s66O2uO7jz3GTrbte+B+PPP005Ghw11CJJ3M9287LJlmWHKy56RM+1tWWw/Wr145Z95IyHD2/FkstbOImerd39+PsiNlOFZdheaOLlitncxifvv27fji174Oszkda9Zs4MIrE01i+jweZJjmPpM7Ex5Leb2+oQlrcnMV9SQmS9g2tDZwI2zddjuSjEbExs88yC5lI89Ga2CgDzZ7F4qK8kD2XGuxGiP9I7gw5MLwoAfWbivEzmbo9EbExaUgOVaPuIRkRZT8ZNH59vG3uRG2dAzCbzLNiRUJj8cfewx+3xjT4R549rklX+EqtTpgK9rODpgzLbDkyPde1NHeyo2wtXZaFRG2tHK1vWdD3ckTOFHfgLrj77Bt4awPZWFj0W149JGHcPsdt7OACcExggJqjPnoXHDku0Ck4PF2m5UbYfvO8beZsaRS+m1qY1nClhx285L8ECNyC3Ym/DSk/BClSZ5jEmNAf8E0PuzF2QvnMTzcj46eC5C63oVOq0OqKQlJxkQYE5IhRAlL4k7zYgToFoO4yPqcR2B30uFqtFrc+6k9ePXQoSXV4dJ23FInctXX3toOSxataOULWsYnhbviJJHzhaVIpLawn7fjdMspvHW8GuWvvA7nOQcSUlYgL28tHvr0A7hv355AcItZGJJoLOAgBZxayBMfHFRnSVicW2crShge985oaLIkXM6DCNPRLP9zBJ95PLrkWcVxEeN+75yrr0nGRAne8Qn0DVxAb28vLgwNgbxQGXQ6Fh0nPjEVKekpWC5EhUWXQub+PBz/IrxYP9AsYxORSfzm+EKrkR/84D+YDvfQ8y9g+733zPFEaG7/9Oc/R3lZ2dIEIhAlOPtJ0HaAdLRyto6vriXtvkydEF59P5J+03EZUtuEOvn84xge9qC8rIKFuXyn7h04z7tYNK2dO3eioKgImzffBnNGpuytS57GLlIrSeMXZdct1PjPtzwau8jZkZLnreeemgga+EZHWaQHpba75gMsWUtSzE5h7prNp9iw5B3xjeDceSdy5Q4GgoY5E4iOyQycIxYljHhHMODxgDoTxXakQ+5GgxEG2kqPNSAlKTVkg82fznYhPnn6M4BhAWgRhb5/1oa4pGSkRskP9EAv4mOPPQbqQ/d/+tN44n//B/ft3bsILuQ9upQrW2evC+0dnQsWtOR4weroxNr4/LBM6OQhJj/X+w47bhZuRXT04gcEq9XK4gbX1deio72DbQubs1Zgy8e24Z+++x2s27ARK2/NXvCA3jc0QPE0kZEeeh8B8hGTl/NG6QOM+sdYTGAKQxnpaal2OGbDQVYPPFxWhk/t+iQXqxoKEk7xM5UKUzUb2FffI1+oLsd55OYs0NhECDjZYAZXFKcTAM3kz/cNYGSwHz22P8Ha8x6LG5yUlIb4RDrnG4foKJqMzE+nTZtbf/qTG+vWXV2LyPztcvbBQPFPF3C+/1/+5fswGONw/wMP4L9FEY/cf394K3nxIj64OBFeGgACxlCdsGRkLmhFSwxeusGLszYn1lOXjfwxFvazZ3HzR0h4zW91S7scZ850obmxGWRc80ZZGWznziLnw9lYVbARn//8Z1Fa+glYsue5BT9LK5MB1SVR4kLYUiCCyqpK3B/ud2MWvOZz66Wyl/HAJx+Aks5NZAlbUivykjQagQXZ5oFfOvLDgiOHkFkSvIFts0Aw7okRkRlcURABq7WL+XbWaQUkxCUhMTkZ5FgjGJB8NjY0ooSP3vKR2bJE1L3MzAzoFhEC7Jv/8A9sN+fvPvMZCJKIBx98KHz1W7YMNy6b3+RnvszYum3osnUjJ9OMrFnO0c5VriBo8WFLNvOUxoGsheXmD0PQzO30gU1SXS40nGxEVVUVyioqWRCD9DQTNhduxnce/y527NiOhFRT2OwjUpNpF0acqwki4j6tFP1LpA8PRYUFUQOJ2Rood4xKlrDdvGEz9PFLE+N1scBmpWdAbzQstpgled7v8bDjNFnmgGAMB9HlMQIyYjKQQStfcSXbdvaM+dgZPyZ8RRE6HR01MiA61ogPpWUgOubaDikJGpxuO4PcHE6OgPV0wyJkI1HuFv004H/xbz7Pdsg++5nPwi+KePSRR6fJFYJLYTY8CwjaLuRaLMjMmtlhhZyakJ0BbaHe+tFbAA4c3XRau5BmMmG59toVg63HhpdePIDaxkZ0trXD9icbEpIScP/9D+IXv/gF8vNWY0VWVtiE69V4O51O3Ei2yKbALtXV9yPpNzn1z1+1JpJYmpWXjZs2QCsoK8PmNpCatQrqTd4RoBn9wMAQBgeH0Td0gR2B0eoMTPjGxBqxIsWE6NhYHnYMw9IUtH3+8//8Ob75T9/Ef//613jkkdD7hg6nUwu73Y6Ork7kmnOQZQnfpC4s4IewUNKLt7W1oeb4cTQ3NOBE7QnY3rchJ2cVSm7fiI0FhSjYXIycW0K3LRxC9tWirgMEZK1sn/jt7/Do3/ARPP5YzTGsyVnDhX7Z3euG3eFA/nrlHEUEt50zL4/DpKuiAAn9vb1wO8+juzug801ISsENkoSP5OQsSOe71O+Kw2aHYNTDlCjfQGo6Hmmr9Ktf+zJIxf23f/3XgFYbfh3udIws4JrDYWdGPGty1yEjM30BJUz/SENTA/Lz8qe/GSFXvV4vU5u89XYtzpw+gyNlh+DxjCI7y4wNmzbgO4//E3Zu347U1Mg502qz26HXa5GaHDk8zdSc/b396Oq2chM8/sc//jEefuDTSFbQCYcsYcvDdlGwU5DOVoh0R6iXmR1wXkBXl1VRYRvELfhJhlMUMSkYNWnE64fHM4helxs9jm64+i6wqDkJhiSYTPFISEhBVFR0xLnDc7icSJYSgUUK2yAuX/zilwGNgHDocMNh5c+2jru7sCp3DdIzQjt4d3V2RZywDepcK954A5VVVaivq8fo2CgMegP27NmBX//i1yguKkJ8cty8jQODfSDcny6nE8nJyUhd3Pww3GxOls+Dzn6SWbLnU/iIiixhm5OdO5XnyP5O578UVoTLBSjOlIQ1UmRjS64iY6JTkW5KxYCnD5s2bMbo6BAuDPWjx+5ER5eVxfMln66xyQm4KWVur01y8VlMPpMpFUZD3GKKuObZL37hC9CIIj7713/LDM0efTQ0uz2hPvpjs9vQ2d2OVbnrQIZioU7ZMtw6hprmdOWdamtDeVk5jp84Duu73ej5Yw8s2dnYvu0ufOYzn0H+6pXwjE8gd+UCrf2nIxrGa9RnDQY+7E3CCMN1W7Sqs71um3ZpKkYr39EBN/oGhzE80IehsVFoBC2SEuKQGGOEIS6RBVeY71GjpeF+YVR+Sjrcb30Nv/7f/8GjDy1ehxtKpxZMR9vZgdzsdcgyh27reGFIhe6pkREv2lubcbKxAQ1NzaitOYa+C31Yt3ED8vMLsXHdOpSUFCMjDHGsQ1cLtaS/ZARkrWwbGhqwKncVF95CHE4nyFKOnPhHeiJ9bWdLE7bfG/nB4wnLA/ufw74HrzxzGlj5ZsB0+ZwvrdLcDgd6+4dhc52Hz/ZHaCAhJSkFyYnJMBqTEB2rDXt4tsqKStAKLLgdHsq+wHS4UQK+8rd/B3F0DJ+jFe8iCIgToTlja+9xoN3ajnW5G0Kqo51aNa/fiyMHDmPvvn1hVR0M9vfC7nDi5IkTqKysRFlFBWODdK6bNhfhh//+Q+y67z52PGsqf1d/P/LKQdxRtA2xidda2F+dV+nfTfVN5I8HeQracMjFgLxdnXXYYbkl8sODUp3I2Q/Zm5CPd6WSLMrWni5YsixcCFtbTzdSU1O5ELa0ZZRpnjvSilKd42q6clz7kf4xPTMTQSc4om8c7kEPPL0D/z97XwLfRnH9/2WzlmVJlm87wjHGdY0xIXHuixDcNE1DSrmvhJZy/GmhlJYeP1pKW6Dtr/21tEBDOQuhUI5wJFwhhDSEkMO5fMR2HGOMURzFVmz5tizLsiL9P2+kVeR7ZUvendaTj7Pa3Zl533nzZmbneO+hps4Ml7MSEDVI1BkRm2RgqkaR2PPNzMpkVrQGliFc97SknJicjJvWroXd2Y0f//hnY886DM7ja6urUV1Xi9kR2KMNLlj0qWjkTM8Nq/N4+kBzu7rx+ed1ePfdt/HJ9o9RUnEE9s52ZGRlgbzikM/h+bPnwpiWFFKHeVZ2LrRx4/kUCi59ZH+npKdBoOPvQbbSI0tx7Lk7HA4UlhZzM9gWHizCmYlnIto0Bis3Y2dTv5SyBlunnQ/j2FQyESJbxuxXSpXekOcMa0MDpp9/nkoRnoZFEkBLlHPmzDn9UMYvURuDdBP9pSEPeXB2daPLbkdzqw1tje34pPYY67gTDYnQJ+gw1ZiCJFPauGaKBMta3witVhvRj641ZMrR5cIt3/0u+k4B99z9k4BDCRmsOR1lHHq2NFDV1dSgylyL2XlzkZ4ZWZdn7jN6cKKuDufPnAXtOA6c0MzoQPE+7NyxE4cOFaPk8GE0nTyJxRcsRsHSpfj+T+/GvFnzxu1uruFEA3MfGH3at8dpvqvsV1tbG85wu5ERgX32SBRVo+AsMeTyeNzQJMga7kLOWm4CWdSvvHI1YuN0cvNUNN6M/BkgKzc8BINBh4zMM3mACrIgdfaXzx43Vm2sHvQnHcEnIwkt7TY0NdrQ1dgMi/kEUOFBYnwiUuLi2Z5vQpIx5GXnqaY06CbgsMmaG24AWeP+7k03ITpGjx9973uhD7hjndm6PairrUF1XZ1/RhvZgZZVviBiWlY2tCF+DtGycGlpBUqLDmLnvn3YtWMnnG4XFs6ei3lz54IMhxSsWB72j6OsaVO5cVqWlBDHhQlMkgNDUhxWrigYd38wURlceemViFbYqIWswZYGL14OuNDhnGj96ObZJqqSR6KjETU4cyonh1hEAWdPHf9gO5Af5B4wLcaENJNPPYX0fNts7WhqtcLS2Ax73TEIHjfiDclISIvH1Pg0xMRpodWMXMeZZ52FqOiJWT78zg03sFnejd/6FgQ4cNf3fhz6gDuQMaPcsxktDbQWC/Jn5CHdNDFyRHzPzcgcsXyErYscY9TX4ZPt27Ft64fYdWA/41FWdjaWLluG2169FV+96GuIiY0JcdgehTEDXk8LwevOgKQTfpucmDphMjvewpEjAoOOEx0lZsZ7YvqCkfgqC8GGNzeNlIeq3pWVlaLD1qYqTMOBOXb8c2zavHm416p7vv7F9RHHRB91NOudPn0WCpYtxYoFC5GTmYt2RyfMNUexr3Q3duw/hKqScrTbh6/n0rJSmC0NEccrEbjuuutw85134oc/+Bl2HNwvPZZ1HctybFdLByprq5GRmI70CTbvt2nzu8OWy2Kx4IFf/gQXXPwVzJ87Fz/7+c9RUlGOB+76JT78eDdKSkqw7tFHcekllzIPVrI6oGGpjf5i9yd7R4+kkhiHSGbNx1WCZmQY5IjgQOnOkSOp6C31XYRZySBrZqvhwIWSxERyj8aT4wQJt9qvSu3aa+MTkEN/Odmot9nQaWtCW3sHaptOwHzyBOITjUhJMjGHCvpYDbTaoM25CXZy/tCDD6K8qAh33/5dvP/Bh8hIlzfbdLpDMz7P1GAqS5GYmIy8mV9SVHTI2EmNuRZ79+zD+1vfwScf70ZyfCIysnNw1513YdUlq7Bq1eqIzl5HYoCbE8P+VIZIf3iMxKexvBOhrK3hUDEr7WZP1mAb6v5MqEwIZ3xaRhY4GW0ZVk6amMfdC3EcB2LGXceiwA5Z0UErCnTKuaPDiabOZjTWW1BTWwNyYhyv0SIhLRFOhx3wTMAeZlDByPTle++9h6svuwxf/9rX8O8P/430jNEH3FAsSNFAW3xoH0SdDovmzZ3Q7R3p1HB1dQ1+ec892L6nEOaqKnQ6OzE9dwYuufRS/P43v0fejFwkJU0s74Oqod9PRWW2H5LRb0SmJKfUZ+3o+PrF0HCC0w9a1Moa6voVMdw3k0Ytws3RyfwU4YDT1YOulk40OzrQ1diKpvZmaEQRBr+KUWJ8GtImyFQf+SW99oorYGttxVvvvYfsrJEdAMh1RMAG2uID7PT2ktlLQPvdkQ5kBnH33r3Yvn0HDpeXo6K4GJ1OB5ZfsAQXFnwVCxYtwYz8PKSlqGNwjTQ/JvOf5MBYOSBrsC2rPIxzzs7lQs/W2miFQavz+3QdK1smJl1jiw0NdJKUAyV24gg5eShYxscJxMMHS+DRioiJEtHV1o5mux0etwvJ8cnQJxmYilFsgq7/snMYq72lrQ3fvOIKONtb8cKrGzAjb3j1LjmDLRtoSw9BFLRYtGh2xGa05ByDHKYX7SnCzv2fYO/uXdAadJg7YzaWLF2EeYsWw2CIwYrlK8PIrchlVVi0H/m5+Wx/OHJUwpNzbU0dABeyc9Tveai7242mpjpkjdNlY3g4N3ouNTXVOCs7OyQd7dFzDS2GrE/jooOlOCs1k4vBlpa4yMZo7jj8mIbGwnHEdgF9TlIc4SN4nPwsHbngQqYp/fSMy+2BzWZDU3sjumwOHLJUAG43jGRtzJSGZEM8YpOMoCXdcJy8JwtmH7//Aa6/5npcsupibN/+IXJyhrG2M4qebfDS8VLythPGMxT11kbU1VRj6/Yd2LxlKyrLiqEzGpGTm4eCJYvwh9//L+YsmB1QvaIVhD07d4OWlENZ/lZKwgUX7dqGtieuFFa3xwnAqxT5kOg6HR3Yv/8gN4Ptnj17cGV8KqJTlLMsKGuwFQR+BgQNBG706iDSlj0/A1hIrVHhyLRv73EF8VYU2CnngH6vuxcdLQ602tvRZrOAHInTGKbVaBCflISk5FSkpSRCEKPHvKtOKmgvvfEKvvWttVix4uvDD7gj6Nl2dLQxow+kM7xknAMtccPT48aW7Vuw9YP3UVRUCnNNLVo727Hyqytx683fxvz5jyInOxsJw3hLYh8jghZ9HjdEDs5GuCGQmRuFpVE+eeIrD0EgnsoaPdRRGg/hVXjfVha7lhasAi258RAycrJg1PHjOUOj4QMrm8lw4rqQ5FQQBAia4TtZmr0mpdFfApCdBdLvpcG3yW5Dj82OMmsFW3ZONBigS0lEUnwKUhIMIS876/V6vPjPF3HTjd/FxRdfgo0b30R+/qz+TWmYmW1LWwvKSsugNRqwZM7YZrS0LLxn1y58snsfig7uQXFpBbSiBssKluCKyy/HBYuWYO7C+aPaGJYA9/VFAaILMZwYjmHmbaIl9Oq+0gAWI6rfhjNxUZegVZ2bxZFqd9mSpcwP90hxIv1O1p5tpEFM5j/JAdVxwO1BS1cbmpoa0dViR6e9GS43EG8wIi49GYmaWBjjExGtj5a1nErOzK+/6lpUfl6DDz94t9+S8lB7tl0dXThwaB+0RiOWyhxoez1uNFttKCsuxv6D+7GVTCHu24vkqdMwM+8cXLhoMQpWLcfSpQWyMKuuTiYBTXJgAjlAam3SSlg4yA7/6R+U+6svvx50p+6fhfv3o6ulS90g/eiqq6vw8htvcIHV4/Hg8ccf5wIrgSRPVTV1dOBkjEEUkJSQhLzc87BgyQIUFKzEBRcsRlJ6GnqsnSitrsAn+z7Gnh3bUVl1GLT3SfuZNEMeKtAM980t72B6bh5bUqZlaykM3PukE8AHDh2AIT5+xIGWaFGHsGXLFnz/B3dg/vmz8OVzzsYNN38HBwr3Yc2VV+FoRQVOmD/FRzs+wgN/+D0Kli0f90D78muvSdBVf922ZZvqMUoAmczWVku3qr622dpYG1M1yCBw1He12FqCnoz8s+bTT/Glc76Me371C1B7DEeQtYzsdPExeBFD3C4nPCIf+x4ejxtuFz/74Q4nHeDgI7jJUESIxiJGKpmoERGnSUBcHC07U9a96O5wormzFR0tLSg1H2IOMAwaEbrEZKQlJcGUltzvsBW593rllRdxyy23oGB5QWAPl5bopeDboz0EQ3wiFs2aM+gwFDX8d7dswfat21BWUYbKqiqW9JJVq3DHj+7E3NmzMX16PvQRNFnqdtoluKq/Ot18yayHPP5wEOisiSuM7SvSRXaG2Hdln3sunnrmKdx99910N9vpAAAgAElEQVTY/PZmrHv0YaxYMb4T+LIG20zTyHqCkWZUKPmnpJggRskqVijZRiRu6plnYbmXDysstAd6yerxCVtEmDhMpjmZ2dAaIsdb2vONS6K/OCArCzM9HrQ12tDpcKCjrRHVlSdRVubyLTunJSLemASjwYC4uDisX78e3/rWjWwP95333gnMNGkgJQ84BqMB88i7kiCg3mLFnv2F2L17Nw7uL0RxcTGmTk3FoiVLsebqa3HB0iVYsGRhv0F9GJaE7fGypcvCllekM5qdnx9pEmHLn6ykaTWRk9mwAQWg0WmRZDSGM8uI5pWTkwONRv64QEu+N6y5AcuXFuCeX/4S37j4G7j1ptvw69/eC9MYzaNO7tlGtIpHzpxZ5HH3jmpUf+RcJu4tqaDExvJxgIOWdMOlxjNWDhO/TjTUobvNgXZ7O5wuO3S6eJhMqTAa4nDNDTeg6cQJXHL55aipqsKPfnQXutq6EaXXY/+O7fjXu2+gwXwCqVOnYs6smVi4eDHWXLMGObnK6WHSdkJPdy8XeqtUb2qQA7ny09vjgXcKP/2B3HL9J8Tb/N57+Mndd6PD7sDj69bh8qsuDfkDV9Zgu2njRlxUsBR6vfpPJJeXVzIPMqS2ofZQb6lH0eEqXPbNFWqHyvQqX3ttE25Yc7XqsRLA99/fgfNmnoOsjGnhwSv57iTVDPpN1z4BIM9C0rPhKNF2AQ1SPW60ttpQX38Sdns7hD7g/x75C/bt3YcZs2ej0WpFa1MTyOTs8sUrsPqyr6PgggJMyyQd91FmPBIGulKQMA68DodR5vOebifefPddrLnyWp8FK4mezPQTHe2Nt7Zg9fLl0MeNwr+JBjYEvcKDB6ARDJg3b/oQb9X1qLvbgeLSMixbcgF8Hu/VhW8gmp079mL+4vmhn0iW2j2Ajo5O/PGPf8STTz6OgmWr8Oyzf4cpPSOwMjWQ5sB7WYPtipUr8VnFpyztIHUKN0Bfu32ePkQJUafVLajN+2ftpO8ovadM+uXhj9cvjuhT3WC66EEz/6Hi0PIm0ZdCt8M3oyEsRJ/eB8IArIH3QVgpbjCdUbFSArl0AkBocxnodfeyfQ+9JqY/TygeYRU86HP5+MqSyqHjGaD/NqDM/cozFJ2BNPyYiSdtzi4kkKF/qpMoDYReN8MIkIKFi2Hu9gjQCx5/3ZOdajc8U0Sgx8Wedbt87wmHr978cTwibbgzakPmwepYM3IcotPnw9Hj7gU5t47WRsPNBgQ/RsI6DB1WBqksQfH8LAjUM/EigN8/tlEc2tel4Ha52W+6BgfpvfRMq9cheWoivqiohs3eCZfTCY1Wi/RUn7tBKR5dpbwG5kFlEwUx8J6lEWmrV2Tllq797DowmBLfPb66POUeoJfsr2N6LvHeX8cd7jbEiQkBOWA8hz8/v24zq0NmPzeI78zzr4//A+t4KN4PF4dkigLVw2h0ulzdiNXoA3XHEgb9R3kEwhCyz8pO31XUv2miWNR+fcqA/mJQX0DviX/BouCnQ6o+gfrzuNHj9B2uixGjB+P1t+NgngihtHWiT9+I1FfL6FP60QnuQ4PKSx+QhHW4PkVq64xpA3k7nvL4y0L5Uv0FxpaBNCiCnw7ruww+JyUD64/hC/rP4xEhCp5A3bBs/O2Mftc3WVlbzTorC1/UfRGUcuSfQUPZ0BFpH6mzvR13//xunJvxZfRRAQWR+RgNThFUfvZ4iiDiVNBXr9z3FI8Okkhpg/MJzmMoDET4kccfZVaD1l67Jhge+x2l0aDH5WJjBeVFHlGpPANDMJ2B76T74DjBGOm9hE2KQ020N4hnUvwPtr2PHZ98gof+989StoOuUh70QkoXHEl6T9dwlYfyl8oQTPfyqy/Do089DFNyEuMblYv4F1w+QeiFxxMdwOrrnnz5UZ160AeBpfClk9J7NMAp/1kxKQ6Vl3zZSnFYXWk0gMsVyCcYg4Sb6Nz+s9tw2WVX4ZILV/QrC9EhGy09QfwKxkj0KBAtibd0f0aMCLGHPi5OyyY9d6EPGkSxEjF8VE9+GtI9lceDqED9SPQYIQCvbnkLlcVlePD+ezHFE92/vFQX7IkvdjSiAndSPkRH4hnFknjS77efb1KZpDjBeUjv6Cp5C6a8pTjQaFBUVoKH/vRH/O8Tf0SSzu9hyZ+3VF6pXHRlvKAPF6ozpvTqq2cJL+XNnrvpC8HN6iZYFqQ8WJ7u0/IgYaXnUh7CEHS+e/etuPLyK7GyYHmAbywv/3/B+QzVvijaSHGC24nEt4EyQvmSWtbAzlaSb+oboj1u/OGxvyDJYMAtN98eaD8SVuIjtQ9qXy5PdECWpPfSNRir9GzgNTjOwDJL7UNqx5R2YBx69smBPfjXP57DY0/9I5B9MC/ooVTHA/MIzo/iBLeNgXlQ2mC8A/Oi+HTQNJi3wflTfIe7Bz//yU9w/wP3Iy3RNOTYItGVZF2Se+lK+dDvTwp34vEnnsSZqVPxuz88SI/lB+8ooanhpNcQH+8tLi4eJaY6Xq+98Ubv/fffrw4wo6B4+NGHvfPnLhwllnpeky25Y8ePqwfQCEhy83K9zz6zfoQY6nn1l0cf9a5cuVI9gEZA8vEnn3iTk5O97e2tI8RSz6vs3DzvSy+9pB5AIyC5fu313jtuv32EGOp5teHNDd6s7Cz1ABoBSWtTK9nA9H762acjxBr5VXN7u/e2//ddr0YUvWuvv97b3Bq6/Ad/EMgfoSdjhoUDgudU4Gs/LBlOZtKPA0IYbQj3y/i/+IY2ZWhpeoJdBY+Z4zTp5iZ4PNBwBJjk4L8hvPzyq7j7Jz9EXGwc81O9YsXyMRU7aENzTOnVl4iXXoCdYYlmy2vqY+J/BiLad+EhDDRqoXbMTrcLgsJ2ZtXOo/8GfO5eWuBVfxir/XmzuRYXX3EZbrnpRtx2860oLS7GWAda4tKog+1YgSpXBfx8bbndHmg4MOauXF2Oj7KLDpBwEIKNWgTDtVjqcPOt38aCBYuwYNEivPaGOiw3sRlN0HmMYMxq+82LkYgA3zgycnN6Mz+A/j/mB9kUnzVzDlosVuw7dAB/+L//G7fb1lFHJubd4T+GheoqCB3y48RgjLoYJxPNcIOYzOSKRuvp7sHXvnYxrr/2Wjz/3L9gtVoxa84sJjDXrRl8+G+iwHrYcZWJovZfSEcctUtWD1OGOhGnHnQBJGMZw0RRg2fWP4vLr7gE0aJ0XDCQ5Zh+yP70J8fbfAQ+ljYkXkonNKX7yWv4OKDjqN8aWOpfP/hrWOvr8at7f8VemUwmfOeGm3HPL3+GjjDZah1IU849TWhp2ZuX3Rq3R+ivFiWnkArG8QxQs1EQyqikxWg+GthYVmfJH/V111wTtoGWmCl/sJUfddRKimwEPgSAeMDUF3laNopsxYU9dwcv310DXOyR5amNb2zE7IWzfYYj/JyZP38ujh9rwN59e8POq1AytLuc4GX3g5d9e4n/PNlKJ89U/+2ho6sLjz3+CL6c/WXcfOvNjB0tbW24eOVyfCk9Axarlf3Ri1FHprF8FShZAcsLCpCZyYct5y/n5WL5ilVKsisk2mtvvBGJnNhD/dHtP8ayuXNDKp9ikQc4j29tb8bx48dRUFDQD1JaRga7LyoqwupVq/u9m6ib/Bn5eOLv67iwJkc8IR3bGfnqt8hEWC+/8lrExqnfSh9hnZE7A9/59rcnSuxUSycuRo+77vwxUlPPxPdv/z7a/tyCH/7wB8idOQt9bgEG8bTlslEH26SURDzz90eRnZWt2gIHA1uycCGMcX5l++AXKvw9My8P3l5elueB1QXLx31IYKKqIevLJoicyAEGzGxbbDZm6SclKakfuwxanx6Lpa6+3/OJvNHHapjVM8kwyUTSHgut/BnTkZOTN5akE54mKzODm0McGRnpWHWlMh98oVZMXIIBTzz2BFKTU0NNOnp8v3rhpasvxY2d38JP77sfP7rzR1iwZNGgtKMOtuTdZM0N3xmUUK0P8s4/X63QBuHKTM/A1PQICMAgSuF5cM23rw9PRhOQy/KVX2eWnSaA1PhJDJjZ0il1CqJ26FmOW8HzE1ptLG5Ycz140WG+6pqrQzYYP/4KHVsOc+bkQyBTjRyE2Lg4FCzpv/KiVtg0ht3xgzsiCi9GH4PFFy7GiS8+G3KgJeKy9mz3FO6JKNBwZl5TXQM6yclDsNrqcWh/MQ9QGcYPt33EDVaL+SQa22zc4A0GmmRIYLeOrrbgx2hvb2f3bAbU783E3pQcLJtYguOgVl7OhzN2KqK59jhsjdZxlHbiknZ396CmpnbiCI6T0tZt2yI+LiTFJeFE7XEMp90va7CtqTwtsP94+mmcEXUGzjjD9/elzC+hu7t7nKwIX/J6m5V5WAlfjpHLiTrP2rq6yBEIc86f+R2VhznbiGTXaKtHZ6dvcIoIgTBmOtCoRXLGVEybNg11Jxr6Uam3Wtj9giVL+j2f6JvqWp/D+ommOxZ6DSeOjyWZImlsLbbAB5UiAEIg6nI4YbM1hpBCmahudy+ysrJw8de/Dp1Bx8atRx59OOxgNr+zBcnTzoT5pAVWy9B9uqzBVvRbiyGnBE8+/TTuv+9+3H+/7+/ZfzwDvV49Pk5FD3mTGbwPumvXTpx3/nmgMqglCGRo3/8dZLFYcM011+Ccc85BwfJl2LZtm1pgDonj+eeex4IlC3DueefihjVrUFXt8wo1ZGSlHvqPzNKXpsVixa9+9Rv84I4fKIVmWLoD9YHjYmOxfHkBigr390tTXVaFqampWLxwcb/nE3VDfGyxteDtTe/iujXXTRTZMdHp6ejAD37yQ9x2x/cwb8E8/Pa3D0R8ZjMmoP5ETz/9NG665RZ8c/UV+MlPfqhqrFI5pRkcrSaeN/M8HDl6VHqlmuvDDz+CZcuWYdXqS3DffffiwQcfxO23hWdJmdotDeZkfKaysgy/+tk98LhcKK2oYs+KSkr682Fk88v93z7x93Xel17hw6h3MPLW1lZvXm6uV6MVve3N9uBXyv7uO8XoNzc1e69ce613w0sveV9a/09vdna212gweg8dOqQsvmGoP/HEE94zU6d619641rvq619jRr6TU5O95aWlw6RQ9nFZaan34XUPeTVarXflavUZ/B/KEUFDQ4OXePrPZ59lzGtuPuk9c9pZ3kfXrVOMmUcrKrxPPfUYk828GXmK4RiNsMPu8M5fvNi7eOFC70233OLNOnMak9ErL73S29fnHC35hL9f9/e/ee/79X3e9998x3vnj+9iWK+99toJxzEWgsTrxYvnM8xlZepq/72OPu+qS1Z6CWMkwu/u/19vaupU79XXXu/tbG/3Um+eN326t2DxYu/fH/n7IJIY9GSIB4ePHvG2d3Z6c7+U473/17/2fvTRxxErwBDkQ3rU0HC8n0cGYsDNN93iXXbRhV6tRqMqbyUNDc3efXt3e9985XVWWVJBKyqOMOElXqspfPThRwznyktWeskLhhSeeurvDO9tN90kPVL8eujAAe+JEw39cOTPmOFdvXp1v2dquBlqsCVcn3zysXfh/IXe//fd272LL7zAu07BgVbiU0+vw0t8VPNg+/qbr3v/8qc/Mci79+71NjWf9BZceCGT0U8++lgqiiquxM+X/vkiw/Lpp596P/u0ynv1lZczT2vUgas12O0O76efHfXef/+vvau/vlqVg+1T65/yLl682Lt+/bOsLYX7Q+uLY597n1n/bL8PuNKyYu+bmzYNWW2ylpGL9h/EhudeREtnB/740EP46le/goUXLMbB/Qf7T5NVcFddY0Zra1MAyeaNb+Oc6dNx4dLlPifOKrKXK4jkH1XAVWuu6adS8+UvnwWtRoOCFSsC5VD6B/njpHDs+HE88sdHkBQXF4D0nVu/h+wvZaPDYQ88U/qHawjbvZrR1cqVgT1A9UcCsWxZAfYUfoI///4P+Hjbh7jrrrukV4pdmfUolVu0IFN7P77nHh+PPG7oNEb8/Fe/ZPctbS2K8W4owlpNDNZ8x6ev6unrg0eIQm7OdMyfO7dfnzBUWiWf0Z7tqy+/gU57O65cs1ZJKEPSpuXdfz33KiqqqnDLLf8PX/vq1/CLX94f1uX5rMxs5qCATjtLgewpX3XFFdJtv6uswZac815/81ocP3YMR0pL8dBDD6G6uhoXf+NilJeX98tQ6RsNsy3q02iqNdfg6eeew4/uuAMieQynoCK3a2434HENNnP01ltb8POf34uCZcuUZmeAfrQgwtXXgxkzZrC978ALYqm7D2Twfd7cwbplwfEm8rfg8UDQ9BdvMo3plncAfyKhAgNUf4KJU0NOSElAtFYd5yJon0rtVpmuuOyyQC17qJEJgKfXx9Vly8fmHi24TsL9O1hKe3t6UHxwP1544YVwkwlrfna3A5vefhMP/vp30KjQuxa1mz17duL40U/x0b8/QnZuHv760J9w+/dvDysfQsksuJ6HTVewvAB6TSxIlyjn3HPxs5/9DB/9+0Nmc/TX99w7bDolXmRlZWBqcjIj/Ytf/gZPPf13htvl8asUq8jyv04jwGAwBthENm8fefQxfP/22yFoNZBmk4EICv+IH2BkQYLz6ee16HZ145bbbpEeKX7VauMCHa4Ehr63BAw+PCe9V+w6zMxWMTwjEBY9gMZvXGOEaKp5pdXFIypawOYPN+LHP/gfkM1bNQY6bFReVY0bv7UWjfZOtLSo+6TvA7/4DZ5Y9wSbfQ+eLqiHwwmmNCxfsRxvbXgDa9dejxdffBH79xcqAlB84IEHICnJs69WD+AOGoJFiLjk0tXIycrpB3Dp0mX48U9/ir899je43L3QBE2l+0Wc4BuTyWfS7re/eQBXX345MjIyGQKN4BcJFc1sE5JSQH9SeP31DThSVsIMBtx/331obmjAw+vWMcPvUhwlr4sWDZ650nLNfff+GuvWrVNVRzZrzoxBrKKZraDGpeQRZraDCqHwA1Ebg4SEFNjtDoWRyCO/YMEcdjL0ww8+wf6Du+UlUiBW7dFqlB46BIPRiL179+KiC76Cw+UlyFKh5b7nXngOM+ech6XLljJOCUNs2SjAwhFJ5p6fi6eeeApbt27DJ3v3YNGiiVefE2++9dYRQdLLbdu2DwluacES/OMfT0/YQEt6XY8//uSIeMkV2fLlK1BXb8Fdd/0IbTafYYB2p2+wbSXDAB434uIi+4VLg9CTTz6Dlpbh94gIS6oxEb/67W9YmW677Xugv9/WWbBk+VK88cYb+PMf/wQxNvJLiGazecSlK/ryListxVNPPQXyQCOFbVs/RO70HFx3zcSpgpD61iN/+5tvD14CMuBKckCqVCuC9r1pZqvGZeSBerYDiqK62zoLP8YMtm3ZhlfeeBkvv/oSUpLSVMdLCVDOebm4+tqr8Z3v3YJ33tiEe++9F5s2vYGf/vQXUhRVXKmf2LLpXfz54Uexc8dOkK1su923WmTvtKOjpRtxSZHvr0JlBqlWXb92LfLz82EQlcEnZvqNm48EXisOvVBAOnc33HDDSEnD+k6r0TKdqZEyraqqwrtvb8IrGzZg/fr1g6J+6ayzsHLlSnz44YeD3oX7wfzZ8+FwDT8DqLOY0d7eOYhsemYGvnfzbfjd736HU6f33gfFC+cDY3z8qLxtbW6GQXfahCAtx7z11nt48um/hxPKqHlpYvXMSL+b9uOGCSQHBqOh31sXm9mqbxl5oJ5tP9AqvKH9eV7MNW565zVce9UaLFqwQIWc7A/J5XIhDl7ceccd+NNDD6G7Y3j57p9y4u5eef1lbHr3XfY3kOoFF16IufnTcfDwkUFbOAPjTvS93W6H2+lr+1dee+lEk/fRG/KM8oCHH7z/gXfDSxu8H+/dHXjTcLLBe+O3vtVPZSXwUsEfpAto7x2sS/vgr+/zakSRqTApCK8faVKf+eLzz/o9k26e/eeL3tmzZ3v7evukR4pfg/XoyosPee+45U6mWyYBo6P1za2t0q2i16amk4Nkc/6M2Vyp/ijKwBGIf+XCi1St+iNB//OfHvY+/OjD0i27tre3e/tO+fTb+71QwQ3pVkvqPllnZXlf3/SmClANDYFUf6ivpfDiSy+pTvXni+Ofe5964plAf7ThzTe9jz70kPcZv9760KWK7NNRHRHQkLxy9Sp8c+XXsfWj7Vj5tZX4yoqL0N7ZiaeeeoYdPlLmM2FoqsM5InCqSOVHQp6kj4U+RoP6xnq2UZ6e7luepSXoLRs34X9+/FOIGllVJGUZ0es55/g8P1VVH8WdP/wJHl33MKqrKgI0n3z6Bdx5x22q2LuNS4gf9HVN84Q+jg4jBRirsh9TYmLgaZbsB6kMHMCs+qxb9zgsJ4/hzu/dgSq/jLY0tmHDa6/j709O7ErMSBzq6XbjeEMtzjrzLKSkJLKohXv2INWUiktWqterjl4fg0Bf63eMMcUzZaSiTui76soa/OIX9+C3D/wGa27+DgwisGTZcraqOaFAgojJ6snf2PgG/vnCi2h3trNBgUzGkdcHNYbD5eVISUqBNHANwqii08h11nqUlRzGo3/9Kw4UH8Ilqy9B7vQ8VJSW4abv34bLFPJZOohn/gcbN36AvOlfxsVf/waamk5i7tz5/aLOnjsb6/7y537PlLrZue0TZE3PRU6m74Dcp7U1qKuvg727A5b6epjSktXjDaavj4+PALcHZsvnOFhYyPbLa2o+ZXZng/UMlarvYLp//ssjuO9en5bEY488FvwKv/vjg/3ulb45dGAPLvrqV5CXl4eFsxei09mJ1NQ0vP/BB6qbyATzis5N7Cs9gJUFK+EWfMPIKeFUcBRFf69atQpHPz+KztZ2aLU6lB4pwQUXKKv2JWuwJcVlUhTPycpVlIFyiDvaO2GPoY3O04d4KN2N37keBYuXQB972pmvnPwiGSc+Ph75M2fijXfeQtmhYjh6HUhOSsVvfnWvegaCIAbMm3cePBDx/BNPs6fsdK8LkK5Ts85SjR5zzoxsJBvjGU46LPXF4Sq88M/nQYekKvYXQ7fiIiTFTdCGeBAPh/wZFYXoKPXMCobESHaRuzpQXvIp1q9/HtFaEUfLP4PBENfvwNxwaSfy+azps/D+ux8ALhfTlBB10azeSU4XL7lgIqGMSmvZ8gKUVpShofoYXEIvZixYgOx03wfiqIkVjOB2eUArBRSWLytg/M7KzFIQ0WDSphQT6I/C9u3b4XF3AYjswdjBKE4/kTXYGjQJULnRmECJPBoBZOB/YDg35zzQn5pCe2srikv248qrrsPyleqxFjUcjwp3HcLNt92MvNxzh4uimuflB4/gvDkz2QoMnZ42XaXQoQg5HCHLQYMWveUknNg4pKO64ptfxYZ/vYRvX3HThGkhhFrK1d9cFUjy6muvYXXBV0DOHdQaZp0/E/S3p7AQNrOFi8GWeBktahhLMzMzQH9qDqJWC0FQdqJ1Bm0Jj8okWnpVkX7qSHhpv1NEFBd4ye9ue6cDJlPSSEVSzbs6iwVyTq+rAbC1sRHxBqOql+IkPv31b3/Dti1bJuSEvERzrFdqX9bGZmSkmbhoY/X1VqSlJapypWhgHbS0tbFPrgSVGt4YiJeM7pBlOR5Cr8uFaI3v40ApvEHmK4aHUH5UXSYZh0cKWK1N6On122YbKaIK3tkdnSC/q7yEeovPnyoPeN0uFxwuJw9QucJI+7NMd5yTj2+H3c7FQEtCQFg9HvUePAsWVJooNNXz4eiecBcXFYXVLnIwL+T+ljXYHjpQLDc/xeNZzHUYygi94sCGANDc3ISyitOneYeIoqpH+/btUxWekcCQf2BmwGSkSCp5x5tRi+JifvoDsuHOSyCZpT6Bh+B0OEF2AngJ1Hc5HMPbPJiIcsgabHnZryWGucgoNgfmwwhrsPP4iajs8dDg43t7QAk96jNgMQAhu+XNqIXInH0MVRL1PfOAM8kVZHXJqmC0Kk2fqoIzQ4OQtWfb7eiCXqfeAwbBRaPlDXKYwENw97jRO6UXeo0y5sNC5VFHR1vEzVyGimm4+L3dPZgSLXCxhMjTni3xu7urB/pYPtoYOcjgpX319ngwJaqPC5llTlI8fYgW+ZADUlVSWl1V3mfUKRE8fX3TIQ4eQoerGw1f8LMPevz4CR7YyjA2nDyJji5ll424YVYIQKltmetqmeGIEJIpFpXaF32A8xCa2m2w2fhYRiZ+uvlgK6t6QYxWXGZlDbavbHgRXS0dPMgrikuLUWs+xgVWe3s7aqs+4wIrLcaVl5dwgZVAVh05AnvnYLvTqiwAR1ataPZVXHoAAp345yAcrqzkZqJgrTMzgyscsBWOli68vWUTD1AZxg1v/gs9HcpuK8k6t601KKufFEqN0pbHUHq2oeQxUXGTk5ORNyd/osiNiw59lS1Y4HOpNa6MJihx/qI5MGr7OyIIN2lamnJ6PEgZr6oGRy72ovXRWLRoKcj6qawv9XAzPcT8Fsybg+hoHpACWdlZ8KjQrOxwLNdwdJiH9pc9wzjUGa584X4uSwozM7IhaGWNy+HGF3J+CQkmGA2nPdOEnMEEJmhubkZxET+zxT07d00gd8ZHqnRPEU62to4vk2FSV1fX4NZbb8Y555yDF9f/c5hYITzmaGbrdnRhz55CQEVmT0fidOH+g+jpUZ/3nKEw15gtMNfwcXpa1AjIykofqhiqfJablYvoGGUnjbIOSKmSe5OgJjmgEAeqa2tQ+1ktrrj0m/jzww/jR3fdNS4kvB2QGldhJxNPcuC/lAOyZrZ7CvmZ0dSaa9DT0c1FdVqtFuwvOsgFVtqz3b5jGxdYCaTZXItGW2NE8OZm52D2+dNZ3uE4OMibnu2ewj0R4WskMq04zM/KEZPZRj4MRXR394AcUfAStm/fgY4uso2sXJA12NZW1ymHMETK9ZZ6n65tiOmUiN7e3g5akuQhCG4PSkv5McBhtTais9MeMdYKoghBEMKybxmOATtiBR0i49pafowZmDk6QV9nsTLXpanRM40AACAASURBVEOwXHWPXA4nbLbIbNNEorBlZaUB5/GRyF9OnrIGW4/AkQoFHTDgyKgFLzr3HjE8A4scoeQhjtPtBs1IOTOZEB7WcmJSMDyFnbhcNKyNyeqSJw7UMJS4MxYyTDkm8vHknu1EcnsgLY4cPAyE/t9+32i14uyzz8b//eUv496z/dtjj2HL5s1cOCL4b6/3yfJPcmCsHJD1GXX4cDk3iuHWRitaOvjQCa5vbMSObdvHWncTmo6MGbz1zjsTSnM8xHbu2AXy+BKpIGnshWMJ2N3by4fzeABOZxc2vfUWN7qrW7ZtB6lo8RAOl5ejsoSPPWZXjxvVNVU8sJVhrKyuQq/CVjhk6fMUH9qHEw3HkZ+Xj+TUZJTS+rfbjaysLKSkxKNwzwG43C6kJk/FnHlzmEGBxtYmGDRGzFs0D7Xmz1BTeRwQXZgxezbS00woLCxkeZjSTMjJzcHBwkK02u3QCAKWr1gBMsptNvv2hiQ6e3btg8stID09Hvn58xgdW2srtFotFixYAHNdDXbtKESaKQ2Z06Yh7/zzA3TS0kzIzc1B+eHDsPsNUi9ZsoTRIOfiVJ4lSxayiiksPACy/5qSlMKwkYEEokPPKI3FUgeLpZ6lycvLhSBqUF1VBZfbjbTEREa3pKQIdrsDBoMOM2fOYN6IpPIQnb5eD+NjR4sNNdU1jA5d6WNhKDrTZ8xg2IgOYc3JyWFOuw8ePMjuSedt1rwZsFgaIJVn/tz5LA3VFwXy60q8lOjQs2XLlrHymM2+fXmiQ3VQWlbG0kh0yssrcOJEA6hcM2fNgbW+nvGO9i7n5s+G2+1CcVkZNKIYoLNr1y7Qe4/bzeiQi746s5k9y58+HaKowaHiQ6y8GRkZMKWno/xwCZxOFzRaDWbNnMH2hWpqagJpiMdV1dUsz6zsbGSkp2Pnrl2MbkpKInJyzmWyY6mvgd1pZ2pgRCdYZk2mVJSUlDG+abUaiB4RV954NTxdfazMiImBKHrg7vJbIhOjIEZrcO+9/4PcnFwkpqUgRqNly8jWujomY7PzZyMqWsD+gz4j/VSe9PR0HD5cgrfffhelwcb7mR9QF0SIcMMNS20dtDodrHUWmDIzBsks1Zetxcbka+Hc+YyOJKNSne4v3M/aIMnbnDnzAnUsyRK5b6usqGB8zE7PYHRIdhxOZ0BmK48cQVenneVDMkoefqgOKQ+JTsnBClgbTuBI+RHMmjUzQEeSpRZbCyqrKv11mo6MjEwQHafTCWNiImadf36g3VK7WbRgdqBtBNMhuhSM8fGYNXMmO/BGbS5Ax18eSkMyTfikNieloXZLhiKKDQIWzy5AU3s9zDVmhm3G9OnMfB/1QxTijfE47/zzBtGx2RpRU0MWs9zIyslCstHX/5Ecxht1mDXL1w+1+Q2oLFgwd5DMSvJHWw5JRiPrH4L7N2qDRIfaNsVJzUiHMS4BB/bvZ/Wl02pYnZaUl8Nhb4coapE/fQY67Z0gRwvEg9y8PBhitTh0sJSdI5D6LnIWYLFYA22Q+gZqTxLfqM0UHjzAZFGqY+IblYfa7rw5+TDXHh/UL9FZE9aWPSLru6hvq7cOpkN5ZPvrR2qnEh0qj9PuO1dBfCOLb5KM5uZkw6Azsv6B8pD4JskSPVu0YG5Aduie+hQyySj1O9QvUaC2X1lVgWnJZyFaQW+msgZbNwRMO3MadPEG1tCpE4EgIN5ohKjRIyMzi2m4G3U+/dbkpBTEx8XB43cunGhMQFbeFHagJFHrixOcBzEkPTMLCc5OiPD5HNQZDMjJygLNICQ65KCY8jRofMYK4k1pjA7jKDVMQzKSkpKgFUVo9T5bzukZPqfGRp1Pxyo2IQ6nppwBjf9oS3JiIhMqyoM6FwoJcbEMq9bgw5LopyPNZjRaLfTaWIhRHmi0OmgEEUSHYgt+OnFxcZgiREMTo2H5BpeH6HjQC4NWCxsESEZDjMnxMOi0rMyEQ6MzQK/VQ4gGtBoNooVopGekM+xGo5FhpfK4HQ6IWh2jE1ye6JhoeDx90LPBQ4DWjy0xNREandbPaUAjapFgTACoPIKAGL0WmVlZ7H2ATmwsqNHHxujZIEN1QnEo0CADaJCQFAeh7zQd6b3kRVIriCC8osfDPlAonRSH1bEHiNHHImqKA2KUgZXHoNMF4hAudDsRp4uFJwrQ+eUrN0hOCI8oEM910Gl0rG6JjiQHjI4YzZyJO9wu6DRa5ObmouJQBVpbm1knlJSSyD6GPj/+OQAvzpyaAXKcbrVYWN2QLLlcbt/sTiNAH6v38wCgQRYeDwwGA+NTrCYW2TnZ0OiAKW4tQI4ypgDocwNRInAK2OPqg62lFZp4n1xnZWQE6FB5DDoNHG49dG43BCEaoniab4kBOYiBxxXD6pXSDJIlQUASyYoAaAw+OhkmE0UNyKxOr4fbewqxiAEEn4WozMxM1tYlOjqDlskayQGFgbIkaERGx9UH6Aw+GSU61HakNqjTJyDhFNkA1jA6wbIk0aE2CK8IXayvv4iPp3YqSRKYnFJ5iA61RwoppnSYaC/dH0+r18OjFWGAgdkcjtcZA30KkyUQRh2meL2ITfD1F8bEZOSImkAbJJqx+hjWH5A8SbJESKT+jfqa2FOnqCExHCSzUt+lidVjiucUYmL1TO61sXEsTnB/QA8EjRbRMTHQnPKy31MEbyAPqTwJsbGY4vJC1AsMh86tDcSJ8/MpVhsLIdoDrdHHN4MxERnpAuMX0dGIGiRQ30xyQHwTopCZ4WvHEu+pPHqvE+IZfp4M7Jc0OibfLkEM9F1SvyPVEDlrZ3V4SgzUD30UUZDoJOhjYPd6QedBCAe1RYlvNNASr6lP8fQJMCT4+JZmMrF+ieSJ+lHqe+NY30X3Puq+PsWDmOhouNHn573IJnuAcnboZe3Z0owk3ZTKCse4peL/GhsbodNqFTc6LYdFjS02NNZaMHPBHDnRFY+zZ2chlhYsURyHHAAHi4pAH2dpKWlyooccx2K14hy5e7aj7M3zpGfr6nahcN9+FKxYFjLPlEhAM/5Z8/Kh1ajfYD6tYIgaDbKyMpVgVUg0yd5088kTyMjOCSmdUpGra6qRnXW2omOYrJktmb2TZn1KMUsuXZpRREfLKpbcLCMWLy0pBfTHS+BloCV+Lpg3L6JspaVx2q/t6Zahu8eJo3U5DNPoNdwMtFSeRUsWySmWKuLQdhovQYiJQuLUM3mBi+T4ZMWxyjogxZPB6dLiUm7Ms9HX1ttvbVRcCOQC+MdzT8uNqng82r+rq4uMfviO7dvxi3t+wrYr/vnc83jggd+Oq7y8GbV4e+Or4yrvRCbm5QAi8YRktsbMh949OSIo85/rmMj6HCutf774T3S0RU7vXg4umVNAWWOyHHoRj0N7Uh7mNFy5tXnZhfR40OFwyo6uZEQ6uNFia1MSQki06ZCVK0L6oHSAj/7CFcJxojlcWOTk0+EkaeAj2J382AggmY3lw4wzq3x+pEAdsiprsF2yiJ+lmERaRubEG0VyciqWzJ2rDkkYBQV9bq1cuXKUWOp5TYcx6KAKD4G3me3c2b5TnjzwdsZ03yl+HrCSzEqHvdSOl7pYgzGyXrXCyYMzp02DqJWOb4UzZ/l5yRpsc3Pz5OeocMyZs2YpjEA++bg4Om3sO/EnP5VyMc/LyVWOeIiUjYZ4RMfwsSLD08zW4/Egy396NcQqUSR6YmoyU6fhQRIS49Mw5Qy/upki3JJPNC4uAbPiEuQnUDjmmuuuUxiBTJeUr721EV0tMg6CKF4coOjw4Yjt1YW7eGZrE7ZtfS/c2UYkP1oyem3T6xHJOxKZfrJjK8yWhkhkHf48+/q4MWrR4+rChk0vwsOJi71t27ahq4OP7Y/i0v0oO+zTiQ+/kIU3RzIUsmUrP45J3n3nHcWNm8ia2To67XBzYm/Y0dkOZ4xPXza84hX+3KaSjiQnM3GaGcxZwMeSN9VU7pyZSDUmhr/SIpFjVBSiOHEgHy1qMXf2hWFxwBAJVg7Mc9bM8xGj52M7ISvLZ0dgYBnUeE965h0dLWqENiSmxtaT8AjKrm/Ioq7ViuBkGxRaUQfBbzhjSK6r6GFrZyfKOHIeX7THZx1JRSwcFkr5wfKIOY8fluhYX/DkPL7HjeJDu+HkxAVDUclh9HTwceqo1myBhRMvYOQ8Xq9Rdg80lOZm0CYxoyKhpAl3XFlGLdwuN0S/dZRwAwh3fmTDlxedYFIMdzvtiOVA15adRrY2IsUUGSMR4ZaDjo42aMRYxOhlLd6Em3xI+fFk1IL2lztsHUhK42O/rqWxDYaUWEQL6pcDZsNZFBGrV78mBfUH1Ndq/Fb3QhJ4BSK7VIBV1sz26KdHFGDP2Ehara3cOE1wOB2oa7SNraATnIoEpdYSGb3VSBTF3tkJh4uPcwY8nUYmrJZGSySqLCJ5dtqbuBhoqfCtZJfaJRmFjQg7wpZpb3cPGq1NYcsv0hkdLilTfFyQNdgWH+Bn+bC2rgZuNx+6q01NDSgu5eNABDWGvbt3R7pNhC3/Oks9Wtvbw5ZfJDPi6TQy8aG0lJ/+oKKyOpJVF9a86y11aG0+GdY8I5WZ0+FkDj8ilX+48929ezccfgc04c5bbn6yBltmKFpujgrHEz3/pQ69I8x3Wjbq42hvkbGDGTeJMGPCkD1PM1sqrsLnTMLAcfVmESE7LGEv8KTz+NBZKmvPtqOri3lJCT37iU9B+6BRMdHM48rEUw+NYm+PBy5XFxdOE6hkbbY2JKTwsVfH5CBa4GL/nqc9W5ID2lskV2Y8BJ6w8iSzvR43PD19iNGr38GD1HfpkpTdu5c1s3XZHWwznIfGBUQBHr9fUpUDpoG2qYmffY+TzSdUztHT8E6ePMn8Y55+MvkrHBygQzHkBYyXpe+TVqvie3Vy+d7e2Y6Wlla50RWNR24DPVG03sVHiIkVEaWwwpqswfbdrW+jq40PG6MHSgthNn/BhQS02+2oreHD8Dg1q/Ijn3LBVwJZW1sDOiTFReBoeZ5WYyoqy5hbXh54W/3FF9wMCvXWeljq63lgKxsP3n1rMxdYCeS//vUmuro6FMUr6zy8IPChFE6c1Ag+R9KKclUmcaPBgMwvfUlmbOWjzTz3HOVByESQnZ0Dg9+xuswkykXjxKAFMYhMYM6Yng8P+iBA/cZjss4+GzSn4SGkpfkco/OAlWGUNXqoozQaDU0XlAUsa2Y7Y8Z0aHV8DGJJCQkwGuPVUcOjoGhqbUVlZdUosdTxmgSl8GCROsDIQFFZWcnNaWRwNrM9cGAvPAIfA1h5RQUcHd0yJEb5KOQS0mw2Kw9EBgJBKyIrTf1O7qWiZGXnIVrhb0NZB6QkwDxcyVC6MHlckoeqmsTo5wBvB6QmK26SA9xxgGx5i7LmlhErmizqB4v2RwxAuDOuqzNzcyDCarUwxwnh5kFE8nN7sHX79ohkHYlMzeZatNj4sN3Km+rP/oP89AeVleWREK+I5FlrNqPR1hiRvMOdKZ2cpjbGS9ixZye6u5Vd4ZA12FaUVvLCU6ZozYsVls5OO8rKyvjgrSigkhesAKzWRrR2NnPBW15O9krMrK7ix1BEbe0xCbbqr41WKzrb+TjURwYiqI3xEkqLS0GGOJQMsgZbXpwQECM9AiCIym6Ey65QtwcahZc2ZGPlMiIfcsDbzJZLUeAEtIcT72oCJo0HhSpS/3F7tqEyYDL+JAeU5sDknq3SNTBJf5IDkeeArJntkSNHuNkHtVjq0NLGh7Po+nordmzfEflaDgMFWurc8s47YchpYrLYuWMXiL+TIbwccDq78O5773Fj5Gb7tu2KOw2XWwOHy8tReZiPPWbas60+elRu0RSPd+ToUcXHMFmD7d5D+xRf75ZbW+Y6CzfGvMknZGI8H2pKJCiGJD7c65GsGI0GEH+5CByp/pzh1SM+JhbgRPXHYDRAiOFjO0EfHQttHB8qlrT/WVLByXkTAMUH9sGlsIMaWb2RqLAycCgdpsAsiPHRuNxuwO60h1I8xeKSOpW9hZ8DES6XA24XJ+bkODJq4T2jG3aXAx5OTKI6HC4IPYo1m5AId/d1wd3Fh4s93hwRuNyyhrqQ6ivUyLJGpRXLlyM2gQ8rUnl5edBw4uhepxFg0CWGWmeKxU9MT1GMdqiEtbqEyZltqEyTEf8MTQzi45Oh4cQqE81sPXzYykesPg6CwMdga0jQYdnSAhkSo44oK1cuh16v7Bg2+mDr9iA+MZEL7ylUrTqdDlHRyn/FyBGxhKQU0B8vYdGsRbxAxaxZ07nBCo5mttGCiCVLFnDD2wXz5nCDNTuLH4tMU8DPFhgJgFFnVFwORh+VRAFvbtigOFC5APaVHkJ3h1tudEXjVddWY/OWdxXFIJc4Lcg+96/n5UZXPF5JSRHI/B0PgTfVn7ff2sgDWxnGnRwZYmEyy4m5RnJMU1xWyo0crH9xPTralN2yG32wJWfRvBw0AaAVREDkYykGbg8abXycnBbcHrS3tnPTuJxOF1yceOLmzahFW6eynVYoQtjp4MNbGZWJySwd5OAg0J6trMGDg7JMFMTRl5EBLJq9ZKLwjJtORkY6tHo+TvQlJ6di6dz54y7zRGTgEQVceOGFE0EqLDQySQ4Myi8dySkMbzPb/Nlz5RRLFXHypuepAoccEBkZGdAZDHKiKh6HtusysjIUxyEXwIVf+SrbYpQbPxLxZA22OefngpYRefiSycjgZ98jLiEBer0mEvUa9jyp7mfO5KfjSjNNDTsPIpUhbzPb887hp41lZExjju55+KAxmVIjJWJhzzdGH4MMPT+D7YI5s8LOg1AzlDV+btz4KrpbukLNW5H4RUUl3OzV1dfXY+v7fBi1oCXv117bpEidjoXoti0fwVx/cixJJz5NXx/6ONG1dXZ149U33oTbxcdy5+a3NqOni4++a//BUpQVFU+8/I2BYkdHG7Zs3TaGlMok2fzeO4obN5E1s7W7XHBzYrPT6XKBdCx5CPFGA/JnzuQBKmgZeUE+H0vexNCz83IwNZ6PZWQ6jRwdNYULORBjRMzNX8iNG8sZs2YgJpqP1aOsTH5WDDwuoKOLD69a1LBs7c1QWjdY1sxWJ8SCF2cEWvJEIPKxZ9vU3onSkoNcdLIkKIXF+7jASiCPlR/ByebWsON1u3vx2GOPIj3NhDPOOAMFy5dj+9Zxuh7s6+PmuElvjwf7Dn0CN/rCzttIZFhyuAzdvcp6e5FbLnIPauHEbR2NB3peBgUAoqiDKCg7LvzHOSJwuXqg0fChxd7b3cOs8SQlJMltj4rFoz17m9WKNJNJMQyhEG5rsUGrTUCMXtbijeysf//7P+DF55/DtWuuYy7GXnrlFWgEN17d+A4uWbVadj7BEXlyREAfG222dqSY+DDdabM2IsmUxsV5k5aODmhFDfR69fdf1B943L3c2F8gm95abWxws5vw37JmtuSIgJfQ0tKuuMFpubyyu5zc+IQkQam38mPY3+lyw+EO714d7VOZa2pRXFICGnSfe+45fPjee3C5gKcff1JutQ+Kx8PhHQm0KEajsY2f5UO7w8HFQEv8dTkccLr4mIXTRMFmC//KkSRn4b4ePVqj+Lgga7A9tO9AuMsesfxqaqrBi/P4ppMnUFzKh2I4fcl+9PHHEau3cGdsNpvRGma9YLvdiZ/+z08RGxcXgFuwYgXIRGhvb2/gWag/eDuNXFzMxyEeqoeKyspQq0Ox+CSzzU18HOoj5/GEl5fw8ccfgzArGeStscmLpWQ5TtMmoxY+bwSnn03+GjcHaMlI1pfZuCmFMQM6xRHGkJ5uAv0NDE63CwXLxm4nlqeZLSs7J8ZCfPVEn4mTIRIcmORsaFyVtWfbZutCQoqy691yi9XV0dFv5iE3nRLx6LCJy9GCWE7sI9P+Fy97deRvM0qIAp2ejWQoLzqMi6/6Bj4/+jlI93Asgac9Wyof7YfzYtOblv7j4hLGUi0Tnqa7uxsCosN+ziASBaG9+95eN/R6fSSyD3ueLbYWGJLiQLa9lQqyJiseuLhxFg1RVHxtXm5lOpwdONnEz75HQ7NFbtEUj3f82DF0OMO7ZzuoUG4P7v7VPXjy4cfHPNAOylPlD6iTPVZXzwxFqBwqg3eioZ6b/qC1tRmtnRydi3Dwsb8syekUzynppyJXWcP8ps1vYuHCi5CVbkKMXot6v7EAg9GIpNg41FnrAY8HokaDdJMJ1norXG4XIAjIzMhAR0cH2tt9dnXJWTrteUlG4rU6LdJS0lBfb4Wb0gDIzMxES1sb7J2d7D5Ap97C8hRFkdFptNrg9OvUUhqa1X60eyemTTXBlJ6JdFMa6iwWhk2iQ7Mzh/8QQj86goB0Uyo7XcewCQJYmrgktHQRFp89WEoTXJ7UZJ/Vl6bmJoZVq9EhzZSCRqsVpPPLeGBKR0tXh688fjoUuaq2BrVV1TCmJiItKYXNGJo77dAQ3/zlOdnayu6JDn0ZHW86CY0oItFoZHy0WizMBrAgijClJaOn2wkpTXq6z4pSv/pKSGB0Ou0Oli4nKytQHrIlPC11KvOaZLY0MLpSfVmtVuzfU4bk5HSkpSSio9sJu79Oic6pXg9O+nnA6ishIVDHg+pUAFITUxmdALb4eCTFxYGVh6yVCUKgPK1ERxCQmpjMeMx4LQgw6rRshhWQJYOO8ZHkoORoCbK6sqGbkd+fjtGIhIQENPr5Rvl63C787a+PsbxH+m/tjWuRZkqDVuej8/xrL2NWXh7yF8wNfIwGyuOnQ+UpLitDT1c3y1r0AORaU0QUXOhjPD5ysIi9l2ZhUp1KMkszSVZfALKoToUo1JNcAwjw2i/nJAcZ6elotDWCHHxLbZBm+k2tzawtxMcb2WxPoiNqtKytsDROXxuktiCI0bD4nTlIdMx1x3Hw0D6kpqQgPSN9kMzS7Ky5uZnRleqnvq4OZAJD6h+CsRGdYFmS6Eh1KooatnQf4IHHA5LZ7u4eNJO8CUKgLUh9iJSG2vrBg4eg1WhYe6K2wWQJwNSMdDbLCbR1rYb1Q8H9jtQGpTTUFoL7v2A6rE/xt+0AnQFyTu3aQ+UxpfXr34gO1U9ZZRUEzynEGxMRHS0G+lmpDln5yN6BxwNqc33dTpyg/kGkthHUnqjv8peH2gLhp7ZNfKN71j/4+5Dg8ki8D/SR/vK0tLX7ZMnfN1P/Z7ZYUFpajMtXr2ZtcFi+CUCisX+fP4gO4CtPrwdSP5qcnOzjgfUkyHyhRqeBKcV0uk/xY+vocvj7VV+fQqtLkuwE+j9rE7Zt24Zrr74ScXHRIzXxiL6TNdhSS6muqkBsVDSmnjkVZPmIQpZGA6dei4qSErjdbpxpMrFBsL2tBW2dnazCabBtOmlF5ZFqAG4sXLSEDRJSHiZSIUhJQ11tNZpsLdCIvobhsNsDdDIEAXGxOpQWFUGAgKmmNEantaXxNJ3MTDS3tqLF2oS+Hic8LjcTaqlTSkkyIS0FqKmrRVO9dUg6hJW+3H10gDMzMpG2IIXFp/LQIE8N4+TJelQdqWI8mL9oCRuUpfKkJKWwwbayphrt1kYYExLYB0dweaiD6ek9A3U1tcQSnDRb2CDR3NwOW4uNlZHoUGdSVVkFd08PLlq5AhpBZOo3RFiXk41YxKGyqgqdXd0wxEQjY+UqtHc2BeKQsPX2elh5iK9Z2VlISkhAa6sDjTZfHVIDlMpDwmBYtgQGty6Qh1bUsvqqrKiAqHGjqqIS6StXwNl5MlA/9CHgdNpReriIlSc3N5fRsdTXB/Z5qTxN9fWoriY5AC4qWEbUAnmQLLn1WlRWVcPe1QFDbCwy0lei3dEeiEODLd1T/XjcbuTPm8causR7JktJKWiwWOB0uNkBjtycbAhCUiAPSZaIb/auHhhjY7Bs+UW48647YaGPOQCUpsvpQulBnw50dk4OcrJyUFFVgXpLPUwpKdhZWYntm7fiqquvZvESV30TMdHe/nTi4lBVVYU///7/UGuuZcvafZ4+RGmi0OfqY/dEr8PewWSEDnTRkmethfjmAZOllDTU1p1Eg/kzZjB1auJKxMSgHx2q08qSw+wD1xAbxwbbztbO07KUkYF2qh9/efLnzGF0LFb6wHUzOjClwVxTgyZrIzPNmnHZFazuJN4S34hO9ZGjEAQRdeYaNtiSLNlsvtkY1XFrayerHyqXr34Aq83GDi0mGI2s3ZprzThZX8/aU/rF34Cjs3NQeaiOKSSnpbDBtr2zM3Byn2S2036azux5c5iMNjbWM2P+jE66CTU1VXC7PSgqqUQ68cDhDNBhH8l6MaitZ7DBtrO9NUCHykMfOUzeIGD2rFmYKp7u/8iOMe3h11rq0GA2Q6vVIe0bF4NOQEt8o0Gw1+P28USMxpkpiaxfCu4PpLbe0dgCCG60NjfDlN6fDvVNUh9J/VCaaSU6nc5AO6UBLSpa6y+PwOwW0ySmNYi3xLfm5lZUHi5hvJ07bx5iYjMCWKU6rrXUoMFig5YmNd/8BiRZkvq/pqYm1FRVs3qrrTVjXlIKBpenFWXBdNgkzdfnSHSqzNRH2sAmCumr4HCelgMakKmNV5QcDowtNNja/LJEBSCeNDcdQ+XhwyyPr65YASAGUr+TnpqOXk8fk3v6IKF/igavjHCk7KjX2eeQEVP5KF8cO+Ztbm1VHogMBMeOHfNufHODjJjqiLL+mfXqACIDxXvvvOf97IsvZMQMPcruvbu9d955u7fv1KlA4r4+p7ep6WTgPpQf69Y95F25emUoSRSL29PT6X3m2We8vUFlVwyMDMKvbNjg7WxvlxFT+Sh79+717tu7T3kgMhA47A5vaUWFjJjqiHLgwCFvb59TUTCyDkgp+jUwSXySAyriwMGDhbjl//0A//PTn0Kj9X0pC6KATW9uxr33/Ryzzj8/ZLS8HZAKuYCTCSY5MMkBefPq5/7xD25YZa6r4+ZAhM3WiKIS35IODwzeVVjIA0yG0WKxsH2xcAIuKirCaaY2yAAAFs9JREFU1756MSorSnHTTd/C2uvXsr/rr74eVRVlOP/cnHCSU21ePMmstG2hWmYGAaPzJdQn8BBoj9nMiWlJ4ueuXXtA5wmUDPIWsUV5W7tKFkSibakzw+XkQwOstbWV7blK2NV8JY4e2sePbWQabFtbfYfWwsXXrJwclB89gobjx3FswN/HH380ZtN1vOnZ0v49L4GnwZbOl0iHsdTOXzIQYbXy8WFAvDx06EDgkJdSvJU1igryhmSlytCfLulRiXSiUv36X54ePtyUEYP7OPH61F8YZIl3/yQj3NFpafoLd+DNglS4yz+Z32kOKH6I5zSUEX8RTj6mNCMWY0JfTu7ZTii7J4lNcmAwByb3bAfzZPLJJAf+0zgga85aUlLEzT4o6YOSzhcPod7aiMJdO3mAyjBueecdbrDu2bWT6W5zA5gToOQ9ZfOWLQG9YrXD3r59B7q7etQOk+E7fOQIKg+Xc4GV9mxrPv2UC6wE8sjRo4qPYbIGWzI8zhTkOWAtOSJgyu4cYCXF8wS/oQYO4GJqRgYPMBnGlDQT03/mAnAfH75hiZeiNwZnTk1lhjV44G3y1GSyCcFFoC0KY1L4tykiUXgaDwpL+XFIceDQAbjcylq8kiWGHlIH1kSiyiKQpyAqr7wss1gksNaTfJhrpP0ZyTKLzOIpGo1WDZT28iGbAVFRsqMqHdF9Rg+OWXzGCZTGIod+c0NTwDKdnPhKxqEVuXZOVuWIT2QRi5fgcSu/wyzrBMmVl1yKWE6Mec/Omw5Rq+VCBnRaEcZEHRdYqVmlpfHhMJwYmmyMg0YjS7yV5z9nM9vk2BSfYy0O+lpjohFChJ1RhEuA9NExEDR89F2xCTqsYhabwlX6yOazcsUK6PXK9rWyeiOy0cpBu2K1RQNt9Bi9r0S2ugfnHhtnRF7O9MEvVPpk+vQ8lSIbDCsndzqiopU1PD4Y1TBPOJrZkheluUumgwx58BBm5M1AjGZs3pgmunzTpk1jdrwnmu5Y6JHdbK3WMJakiqRJTkxUhG4wUVkt5vVNbwanUfXv4rJSdHXwcUCqpuYzvPnuJlXzUwJHyzDPPrteulX9tbisEORMgYfAm57t66+9zQNbGcZ/f/RvbrCWlpWi1nyMC7xtthYQXl7CU888g442nzMZpTDLGmzBzbwWzIOLUsz8T6ZLMxnldz3kc1iAyLyjyE+hXEze9GxldhrKMZRnyh5+Whk/SNUhELKWkefPna0OtDJQZGRmQavh40RfauqZyJ/hlVEq5aPQgHDB4sXKA5GJICMjA+SVZTKEnwP5s/npD8gDFS+BJ5nV6XTIzOJHO2Hx4sUgzEoGWYPteefPVBJjSLTPZH4q+fj2jktIQJzCm/ZymUtLnXPmzJAbXfF4ppTkMZtPVBy8ygGce04WQKc7Odi3zcw6i63I8NAjmEw+39gqr34Gj/zGmqL5wbtoyRLF12dlyeDGtzYyp8M8CEHV4SPcqKiQLdS339nMA1sZxpdffp0brFve34oaSx0fePv60MfJiWQyEPHyq68zx/c8MPetjW+jw8bHGY79B4tRtP8QD2xFR1cXtm37mAusBPKtd95SfAyTNbN12B1wu/hYoW+3d0IfG82FEMTHG5E/ax4XWGkmM5+jZeS8WXlIjTfywduoKERHTeEC65RoYP78hRDBh27wnFmzoU9QdvlQbsVmZWaBly1bj9ONDk4OohL/O9vb4VH41ImsmS2tdYsaWVHlylXE4hk0Omg0fDSupvZOVBw5GDFehDtjnrz+VFd+DuIvF6GvD2Q4hovQ68GhA3vhUrjjksurkvIy9HQ75EZXNF5dnRn1dbWKYpBLnIwcxXJiz4DKpNXEQiQnNQqG/zhHBL0eN6IVZqrc+nT3uNHj6kZsBDzJyMUQSrw2WxsSUhJCSaJY3K6ODsTotVzs2/LkiIAOynW1dCMhJVaxug2FMJODWOpo1f8xQ/aGEQ3EiHzoBdNap/q56pMWt7tX8b5AFq+qa6pDkW9F47Y22hQ3OC2XAR3OLjQ0h9fnqlzaY4lXV8/JHigAp92Jjm5lbaGOhcdqT0ODVlM7H/rLxMvm5lYuBlrC2t7ZDkcXHzJLHwaNVqvaxTWA7+jRKsXHBVmDbeHOPQHQav9BjgjcbvJnq/7QdPIE9u/nYxmZvmI/+ugj9TPVj7CmrhatrXzYneZh1hVc8fv3Fwbfqvp3ZWWlqvEFgzObzdw4USG77rVmczB8Vf/+978/UtxWuqzBFrw4IaBlDVHDzSEDgZwm8HIiwk3HC/jxTsNavoePjy7ejFrAI6/bUEPvq/ShmJB5wEl/QHzlRwpCroWIJJC1Z9tia0FSSlJEAIQ707YWG+KSUrgQhJ6ObjidTiSk8cFbq8UCEydu9mivTqOJRXSM+rsEnvZsqb3arC1IMfEhs9QfJCSlhLubiUh+PMks7YH2dDu5OW9CS95JKYmK7tvK6onsTgc3zqI1Wh166aABB8EFN5o6mzlA6oPY1MnHsiyhbWpugt3ZwQ1veQFKnWxTez03/UGD1YreHj7UFu2OTjS1WngRBbjh5garKCq/PCtrsN22bSu62vg4Pl9cWorjDce5EAK7w4m6Gj6O+hNDPzv6BRd8JZB1Fgvsnfyo/vDCWBq4yo9UcuM83txwAi5XFxfstVob0dzIhwEOMuq/det2LvhKIN/e/Da6e5TdVpKneCQvljoY73Fz4zxeo9Ug+ayz1ME3GSiyM/mxhZoWnwwDL7aReXKxFz0FuZnZgKcPENRvPGba1GlQw6xGRvNCUkoaBDc/s0UXJ/vLAd57lOWtrJnt3BlzodXxoVeXkZmJxHjlfRcGKniEH47OTrQe58OlFi3EVdXwc7LT0tAAu11Zl1ojVH3/V5yYaiTQ7j4PqqprAA8fFq+O19TApXAn27+yh7+z1Teisa1l+AgqekOGjubm82MrfV7+XGhj9IpyUNYBKUURThKf5MB/OAd4OyD1H14dk8Wb5EBEOCBrZvv8Cy9EhHgkMt21Zw86WrojkXXY87TZGnG4vDzs+UYqw8JCfvQrLRYLWtr42P/iTc+WJ5mtrubHIA/JLPUJPASyJsdTf/DXv/4VpFWjZJA12MLFh1UTxkhaMhKV3QiXW6HNzU0oq6iQG13ReKQLum/fPkUxhEKcOq7WVj6sc/GmZ1taWhxKVSgal6fBlg718WKIhTv9ZUWl0Edc1tGnvOn5KoAqD4IAWUWSl1mEY8Xr4pGbkxVhKuHJXvQA06fnhSezCcjFlGKCzsiHQ4oJYEdYSeRm8yMHZ03j5wCiKSUdBqPyKiphFZbJzAIcmNyzDbBi8sckB5ThwN8eewxbNm/Ghx9+qAyAEKl6PB4IHBj2D7FYk9EnORBRDshaRi4qKlLciLNcLtBSDC/7Hpb6emzdslVu0RSP99rGjYpjkAtg+7ZtqKvjw3GCgF5unMc7nV14deMb3Bi1ePe9t5ijc7lyo2S8kpIilBYVKQlBNm1yRMDT3n1JufJjmKzBtrKyDGR4modQZ65Fa3s7D1ARbzAgJzeHC6zkPH7meefwgRVAdnYODPHxXOB1eaIQxYmuLems5k+fwY3z+OnZ50Or58NlXZopHVMz0rmQWYfDgSqOnDwUH6iA263sGCZrsHXxtGTkEbgxatFpd6DOzMfsyyMKMH/GjwUpS30dnPbIWD0jk4Xbd2zHC8+/gKojR8bfOfKkZ+t24QvSXZXVc4yfNePNwdxQB1cXL9oJNrRabeMt8sSl50QGiCGCqPyRLlmnia5dfS1iE/j4Opw+Ox86FdjBlCPxOq2IpKmpcqKqIk58Ch8G3YlZSUmJ0GrCf9iE1Imuv24tOlrbUG/9/+1df0wUdxb/dJhddoGKCKKWUo7jkKKlnKvQskWixBBLKCrUEsspIr0mpufRUJt6Tf+5XC5pmp6HyZHWtrTheoZTQcuKlkNdkeuRHuLyyx/noeEsp2LRWloRWGbHy3vLrCuBZA9ZlokzCbDMzvf9+Lz3vt+Z77zv+17G1au9oGUFJSUlk7eRSp5qSUHxrhHh80JBCXNq2O1jTths6I3q6LuCg4OpbMjk/WgaWwaHBGFFWvo0cnwwVlmrMxH4KOHru8OjBCl6T2MwqKOCFD11iNAB4sy/7aIlH5J9QDXYqs0PKKxEcWpLCr799g5sKtyEJ2MXoe/WLTz//PPobG/Hjd7eSe+AoraiFmrygwHJjkCV3HxT3+UNn/XG8EL3WjL1tVMcX96QlWiSz4r6QPhyTbtHI9Keyn3ewmDK6TZ9fQr9A+rY7aWr4yz2VlumHANvEKQbg7Kyj7xB2is0v24+je7L/51S2tQZbttWzAMtEZ4bEoKcrGxAkvAg+8r4sgOYDEB79x6YTDOftDlec8gnfCfDtKnpn1Pus5ORw5M2/deug2JMLcfO0g/w403fjgseDbaqmC9SrE5FLaSpnz5UyE/p36l96JpS0cYSo2nDBxlQxtLz9v8eOvb/JQbdxS9YsOC+NkN3bmNr8TY4pwDv+8rjf9RW1MJjxWbChSqaome4VFLcXxZFNbxFcHmgv84Pvn5r69E726SlS1xCz/QPkVHRMAR7o6udes3DwsKRkKCOgiGUIPVcSsrUg+AlipGRkQjw8q4/Z86cw1ctzaip3O8lLWYm2cREdfgsoRcXFzczQRxHqujoaFCBfzUchgADKMbUcqSkpPgcW49GpUVPPqWap5qoqCj4Qx2PjCEhsxGrkm3ryFHiY9VTOWj2rFkI0hu80hdQklRRQSGSnknCiaPHsTY3Fz/2+3aKyiuKjkOUZjeiIqKgiqdxScb8xx5TzZrgsDlh0HvJZ8cx5QOdCgwMRISKBluz2Qyjj5eAeTTY7j+0FwM31bEBMy0Mv3yl54Ecaboad1/pxdE6dRS1oE72gEU97+pOnDyJb77t9YopQ0NCsLv8Q5w4fgIrli+H9eQJ/Pb3v5uQV9+167yZPRVcoZ9ro3+VzwM3fVsgfULBx/lioL8fByz7nPvZjvP9jDolClyZa6BfHRm+re2tONveOqMgnEiY/v5bqirIU32oxuc3xB5NI0eGRmDfF3/FMynPISoiAl/U1oLeipqWLkXkTyJQWbkPdvsQYqJisWp1BuobrLh15RqCQ4KxOjMLLbYWtLeeBr2OWJWejuiYWHy+Zw/TWBgXgyXLnkVtbS16ui8jYJYBBQVF6Ghrw8ULFzAgSViWmIjohTGo+OxTCIKIqIhIZGRmwtrYgL6eKzAaDMjOzcXZtg7ODDUEBaHrQhdWZazCu+++ywUDFsb9DC9krUHd4cO40tsLg0FEfn4BGhsbcerUKa7gs71kOyA4UFHxF/axuNh4pKaZYak+iDNdF/CoMRDbirehtb0ZthbnBgKrMjJAilVWVnKbpxY9hazsLBw8eJCLilNhhbw169DY9JWLz+uvv4aRYRlN9VaeMWhoasKK5GdxqO4Q/n3hIsuyY8cOtHfa8HVzO0TIyMzIAG3WXFVVxd9nZq7G00//HJV7K3Hn9h0EBAVgfW4OKMlC0ee1rVtZpn1VVVxej6b/TCYT6uvqYGtr4++ID1WtaTndCkEUQPoYRBHlFRXw1+mwcuVKbrN/tHoUVZHKXZOF5ubTjB0VY9iyaQvs0hCO1FpgF/RIWuLkQ9grB/Fpbmlh+9C57MwsCKKIj8s/ZvssX74cJlMiqmtqcfv77xE0axZy12WjxdaJf/z9JOtcVFQEWkx/7NgxJpu8ZBkSTIlsYzqRnGxCenoGbDYb+vr60Ge1Yk5mJgTRgE/+/CkcIyNIS0tDsmkJqmssvN8t2efpuDgUvvoKvrvxHdOdHxYO6PW48Z1zsA4KmoWQR4OREL8YYfPDscxkYpwkScKmwgLYOttha7FxxmNpaRnTYD7JS1F90ILfbH8L3d908/nxfulFEZs3b0HnWRsSFpuwa9cuDA4OQvGlxoYGdF26xE1ffDEH/kYDdu7cxfZJSkpinT7/rIL3bWV/y81FTXUNLv7nIu7evYvt27dzNS0FN7M5BfHxi1BaWgqHw4EnHn8c6/PycKz+GC73ONd9F+S/DOj98f5777n0oaeDWosFEvSwfnkCGS+sRl3dEbS1dbAN33jjDVzqvogG60lusyx5CRITTNi9+wPcutWPhdHRyMnLg7Xeiu6ebugFEevzX4KtpdXlS4o+5eXlTGNBWBgy16xBff1hdHb+yxUb7nxSU82Ii4vH7t1luH17COHh4di4cSP7+Q93foDFUoX1G3LQ0XEeVquVZd308i8wd8E8KHyiI6ORnpGORqsVTc3NzJt8tqu7m8/RCbM5GfPDHscH5bsZ+9lhYSgqKED9oTr0fHsF+oAArF+XhXPnulBfX880CgsKQMtk9uxxJpm6+Lj1Owqf8+fPQ4KA0IgIzJ8zBx9+8gn77Lx5c1FYWIQjNTW4duMG9HoROWtfwqXuC/jb0eN8zYb8fMybO9vFJz4+FmZz2n39G/E5f74TTU1O/VLTUhEV9QRKd+5iWclnycb1h79ET+9V7iNz17+EY3XHcebcGRiNRhQXF6P9bBs6mts5NaahwYoVK9JdfIZHRvD2WD6pZsTE/BR/3PUnljU1LQ2pZvM9fcgPNuTgcs9VWCy1fM263HV4LHw+qO+iQ8GtrKyMK4JR31Rc/Ct0dJzFqdZTECFibfZahM4N5f7AT6fDq69s4ZoLRCMmKgY6o29zeTxa+kPK0pPNRI/Bkl0CvdOjrMpxr5FkXgRP302UeUnTUkq91XFpcKr5aIqOOAGf0Wuo/bAgw18QMWQfZGNRcgvxtkvDkOHH6wRFvchTTMqUmEHvXI/HKfiyHxwimAa3kWVeUsRt6K7BPgxJAKgNtXel7QsCp8MTX+daRB3u4yPoeDAjTSh1fkTwg1EWeKmSS1Y421DVJqItCw6mSXop1xgEf24jS/Taf4Q3876PD5yyKXyIDulPOJCs7jrTNSOyBD/7CESDEwPmI0uudHlpaJD5Kan+7joTBkSDzgn2Ye6kiddEGCi2oDZ2xT6KbHaJ/YB0Yl6SjCHZuSRC4aO00euN7G8KJrTkS8EAgg4OSYL/6Fpblyz6e37A/ui2TMxlQ2U5g0QSjh7iqO8QjqO+RNfTFRs3bIZdtuNgdbXLPq5r7BKGh0cmXj+po8wzAX56IwykjSjwoA1BvGcv8jeZaNxbyuTSeRQ3xUcVvxhrY2rL+kkyBMMY3NxiQxB0EGQqAuCMwrF8hiQaDhy4K/hxbIzlQz5AuPsJd532c/NZxf8GJTsekR339HPzRwU3ha9i47H+Rvq4fF/QMS2SjXBS+NDNqSDJHMc6QeR4Izp0kC/RwZgIOme7cWKDY5DsTH2OwkeJberzRH8MyxIekUYYN4of5uHWPxBHmfpItzgeixvLMjQIh+AHHSUfjcYPC+kWy+T7in4KJtTPuMctyUQHXTeWj6sNdBD0ziQnBWuF7qAsQSc7QDE0Lg1pGILozzrRwwnxG8uHdOY4pf5O8euxsc5KDwPkf/zZGevu+pBfsy6iP8e64ud0jmzIWFMfKDigH9WblvlQ/LhsPNr3MSEf/vJ4sPWhjBprDYEZjcCK9DSU/LoE2WvXzmg5NeE0BDQEfIeA8/bVd/w1zhoCqkHg+s0+bMzLxx/ef483u6Bi7O+88w5SzanaQKsaK2qCagj4BgHtydY3uGtcVYgADa5vvvUmbG0dNEeGuMXx+GVREcypqSrURhNZQ0BDYDoR0Abb6URb46UhoCGgIaAh8FAioE0jP5Rm15TWENAQ0BDQEJhOBLTBdjrR1nhpCGgIaAhoCDyUCGiD7UNpdk1pDQENAQ0BDYHpROB/pGRY4/WwQ8gAAAAASUVORK5CYII="><em><strong>A2 N2</strong></em><br><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognizing horizontal shift/translation of 1 unit   <em><strong>(M1)</strong></em></p>
<p><em>eg</em>  <em>b </em>= 1, moved 1 right</p>
<p>recognizing vertical stretch/dilation with scale factor 2Â Â Â <em><strong>(M1)</strong></em></p>
<p><em>eg  a</em> = 2,  <em>y </em>×(−2)</p>
<p><em>a</em> = −2, <em> b</em> = −1  <em><strong> A1A1 N2N2</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = \sin x + \frac{1}{2}{x^2} - 2x\) , for \(0 \le x \le \pi \) .</span></p>
</div>
<div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Let \(g\) be a quadratic function such that \(g(0) = 5\) . The line \(x = 2\) is the axis of </span><span style="font-family: times new roman,times; font-size: medium;">symmetry of the graph of \(g\) .</span></p>
</div>
<div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The function \(g\) can be expressed in the form \(g(x) = a{(x - h)^2} + 3\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find \(f'(x)\) .</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 style="font-family: times new roman,times; font-size: medium;">Find \(g(4)\) .</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 align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Write down the value of \(h\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Find the value of \(a\) .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Find the value of \(x\) for which the tangent to the graph of \(f\) is parallel to the </span><span style="font-family: times new roman,times; font-size: medium;">tangent to the graph of \(g\) .</span></p>
<div class="marks">[6]</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 style="font-family: times new roman,times; font-size: medium;">\(f'(x) = \cos x + x - 2\) <em><strong>A1A1A1 N3</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note</strong>: Award <em><strong>A1</strong></em> for each term. </span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[3 marks] </span></strong></em></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;">recognizing \(g(0) = 5\) gives the point (\(0\), \(5\)) <em><strong>(R1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">recognize symmetry <em><strong> (M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg</em> vertex, sketch </span></p>
<p><br><img src="data:image/png;base64,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" alt></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(g(4) = 5\) <em><strong>A1 N3 </strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[3 marks] </span></strong></em></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;">(i) \(h = 2\) <em><strong> A1 N1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) substituting into \(g(x) = a{(x - 2)^2} + 3\) (not the vertex) <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg </em> \(5 = a{(0 - 2)^2} + 3\) , \(5 = a{(4 - 2)^2} + 3\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">working towards solution <em><strong>(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg </em> \(5 = 4a + 3\) , \(4a = 2\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(a = \frac{1}{2}\) <em><strong>A1 N2 </strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;"> </span></strong></em></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[4 marks] </span></strong></em></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;">\(g(x) = \frac{1}{2}{(x - 2)^2} + 3 = \frac{1}{2}{x^2} - 2x + 5\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct derivative of \(g\) <em><strong>A1A1</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg </em> \(2 \times \frac{1}{2}(x - 2)\) , \(x - 2\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">evidence of equating both derivatives <em><strong>(M1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg </em> \(f' = g'\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">correct equation <em><strong>(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg </em> \(\cos x + x - 2 = x - 2\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">working towards a solution <em><strong>(A1)</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>eg </em> \(\cos x = 0\) , combining like terms </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(x = \frac{\pi }{2}\) <em><strong>A1 N0</strong> </em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note</strong>: Do not award final <em><strong>A1</strong></em> if additional values are given. </span></p>
<p><strong><em><span style="font-family: times new roman,times; font-size: medium;">[6 marks] </span></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;">
<p style="font-size: 13.28px; font-family: sans-serif; left: 506.013px; top: 127.867px; transform: scale(1.03286, 1); transform-origin: 0% 0% 0px;" dir="ltr" data-font-name="Helvetica" data-canvas-width="91.92416273955348"><span style="font-family: times new roman,times; font-size: medium;">In part (a), most candidates were able to correctly find the derivative of 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;">In part (b), many candidates did not understand the significance of the axis of symmetry and the known point (\(0\), \(5\)), and so were unable to find \(g(4)\) using symmetry. A few used more complicated manipulations of the function, but many algebraic errors were 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;">In part (c), a large number of candidates were able to simply write down the correct value of \(h\), as intended by the command term in this question. A few candidates wrote down the incorrect negative value. Most candidates attempted to substitute the \(x\) and \(y\) values of the known point correctly into the function, but again many arithmetic and algebraic errors kept them from finding the correct value for \(a\).</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Part (d) required the candidates to find the derivative of \(g\), and to equate that to their answer from part (a). Although many candidates were able to simplify their equation to \(\cos x = 0\), many did not know how to solve for \(x\) at this point. Candidates who had made errors in parts (a) and/or (c) were still able to earn follow-through marks in part (d).</span></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: 12.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Write down the value of</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \({\log _3}27\);</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 style="font-family: 'times new roman', times; font-size: medium;">(ii) \({\log _8}\frac{1}{8}\);</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 style="font-family: 'times new roman', times; font-size: medium;">(iii) \({\log _{16}}4\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a(iii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Hence, solve \({\log _3}27 + {\log _8}\frac{1}{8} - {\log _{16}}4 = {\log _4}x\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \({\log _3}27 = 3\) <strong><em>A1 N1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \({\log _8}\frac{1}{8} = - 1\) <em><strong>A1 N1</strong></em></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><em><strong>[1 mark]</strong></em></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;">(iii) \({\log _{16}}4 = \frac{1}{2}\) <em><strong>A1 N1</strong></em></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">a(iii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">correct equation with <strong>their </strong>three values <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \(\frac{3}{2} = {\log _4}x{\text{, }}3 + ( - 1) - \frac{1}{2} = {\log _4}x\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">correct working involving powers <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \(x = {4^{\frac{3}{2}}}{\text{, }}{4^{\frac{3}{2}}} = {4^{{{\log }_4}x}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 8\) <strong><em>A1 N2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a(iii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p class="p1">Let \(f(x) = 3{\tan ^4}x + 2k\) and \(g(x) = - {\tan ^4}x + 8k{\tan ^2}x + k\)<span class="s1">, for \(0 \leqslant x \leqslant 1\), where \(0 < k < 1\)</span>. The graphs of \(f\) and \(g\) intersect at exactly one point. Find the value of \(k\).</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p class="p1"><span class="s1">discriminant \( = 0\) </span>(seen anywhere) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">valid approach <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"><span class="s2"><em>eg</em></span>\(\,\,\,\,\,\)\(f = g,{\text{ }}3{\tan ^4}x + 2k = - {\tan ^4}x + 8k{\tan ^2}x + k\)</p>
<p class="p1">rearranging their equation (to equal zero) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"><span class="s2"><em>eg</em></span>\(\,\,\,\,\,\)\(4{\tan ^4}x - 8k{\tan ^2}x + k = 0,{\text{ }}4{\tan ^4}x - 8k{\tan ^2}x + k\)</p>
<p class="p1">recognizing LHS is quadratic <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"><span class="s2"><em>eg</em></span>\(\,\,\,\,\,\)\(4{({\tan ^2}x)^2} - 8k{\tan ^2}x + k = 0,{\text{ }}4{m^2} - 8km + k\)</p>
<p class="p1">correct substitution into discriminant <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"><span class="s2"><em>eg</em></span>\(\,\,\,\,\,\)\({( - 8k)^2} - 4(4)(k)\)</p>
<p class="p2">correct working to find discriminant or solve discriminant \( = 0\) <span class="Apple-converted-space"> </span><span class="s2"><strong><em>(A1)</em></strong></span></p>
<p class="p2"><span class="s2"><em>eg</em></span>\(\,\,\,\,\,\)\(64{k^2} - 16k,{\text{ }}\frac{{ - ( - 16) \pm \sqrt {{{16}^2}} }}{{2 \times 64}}\)</p>
<p class="p1">correct simplification <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p2"><span class="s2"><em>eg</em></span>x\(\,\,\,\,\,\)\(16k(4k - 1),{\text{ }}\frac{{32}}{{2 \times 64}}\)</p>
<p class="p1"><span class="s1">\(k = \frac{1}{4}\) <span class="Apple-converted-space"> </span></span><strong><em>A1 <span class="Apple-converted-space"> </span>N2</em></strong></p>
<p class="p1"><strong><em>[8 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p class="p1">There was a minor issue with the domain of the function, but this did not affect any candidate. The question was amended for publication.</p>
<p class="p1">Most candidates recognized the need to set the functions equal to each other and many rearranged the equation to equal zero. Few students then recognized the quadratic form and the need to find the discriminant. Those who did use the discriminant generally completed it correctly.</p>
</div>
<br><hr><br>