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</div><h2>HL Paper 2</h2><div class="specification">
<p class="p1"><span class="s1">A particle can move along a straight line from a point \(O\)</span>. The velocity \(v\)<span class="s1">, in \({\text{m}}{{\text{s}}^{ - 1}}\), </span>is given by the function \(v(t) = 1 - {{\text{e}}^{ - \sin {t^2}}}\) where time \(t \ge 0\) is measured in seconds.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down the first two times \({t_1},{\text{ }}{t_2} > 0\), when the particle changes direction.</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">(i) <span class="Apple-converted-space"> </span>Find the time \(t < {t_2}\) when the particle has a maximum velocity.</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Find the time \(t < {t_2}\) when the particle has a minimum velocity.</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">Find the distance travelled by the particle between times \(t = {t_1}\) and \(t = {t_2}\).</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>\({t_1} = 1.77{\text{ (s)}}\;\;\;\left( { = \sqrt \pi {\text{ (s)}}} \right)\;\;\;{\text{and}}\;\;\;{t_2} = 2.51{\text{ (s)}}\;\;\;\left( { = \sqrt {2\pi } {\text{ (s)}}} \right)\) <strong><em>A1A1</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">(i) <span class="Apple-converted-space"> </span>attempting to find (graphically or analytically) the first \({t_{\max }}\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">\(t = 1.25{\text{ (s)}}\;\;\;\left( { = \sqrt {\frac{\pi }{2}} {\text{ (s)}}} \right)\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>attempting to find (graphically or analytically) the first \({t_{\min }}\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">\(t = 2.17{\text{ (s)}}\;\;\;\left( { = \sqrt {\frac{{3\pi }}{2}} {\text{ (s)}}} \right)\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">distance travelled \( = \left| {\int_{1.772 \ldots }^{2.506 \ldots } {1 - {{\text{e}}^{ - \sin {t^2}}}{\text{d}}t} } \right|\;\;\;\)(or equivalent) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">\( = 0.711{\text{ (m)}}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>M1 </em></strong><span class="s1">for attempting to form a definite integral involving </span>\(1 - {{\text{e}}^{ - \sin {t^2}}}\). To award the <strong><em>A1</em></strong><span class="s1">, correct limits leading to \(0.711\) </span>must include the use of absolute value or a statement such as “distance must be positive”.</p>
<p class="p1">In part (c), award <strong><em>A1FT </em></strong>for a candidate working in degree mode \(\left( {5.39{\text{ (m)}}} \right)\).</p>
<p class="p1"><em><strong>[2 marks]</strong></em></p>
<p class="p1"><em><strong>Total [8 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the function \(f(x) = {x^3} - 3{x^2} - 9x + 10\) , \(x \in \mathbb{R}\).</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 equation of the straight line passing through the maximum and minimum points of the graph \(y = f (x)\) .</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;">Show that the point of inflexion of the graph \(y = f (x)\) lies on this straight line.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">\(f'(x) = 3{x^2} - 6x - 9\) (\(= 0\)) <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\left( {x + 1} \right)\left( {x - 3} \right) = 0\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(x = - 1\); \(x = 3\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(max) (−1, 15); (min) (3, −17) <em><strong>A1A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> The coordinates need not be explicitly stated but the values need to be seen.</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;">\(y = - 8x + 7\) <em><strong>A1 N2</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em><strong>[4 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;">\(f''(x) = 6x - 6 = 0 \Rightarrow \) inflexion (1, −1) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">which lies on \(y = - 8x + 7\) <em><strong>R1AG</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;">There were a significant number of completely correct answers to this question. Many candidates demonstrated a good understanding of basic differential calculus in the context of coordinate geometry whilst other used technology to find the turning points.<br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">There were a significant number of completely correct answers to this question. Many candidates demonstrated a good understanding of basic differential calculus in the context of coordinate geometry whilst other used technology to find the turning points. There were many correct demonstrations of the “show that” in (b).</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Let \(f(x) = {x^4} + 0.2{x^3} - 5.8{x^2} - x + 4,{\text{ }}x \in \mathbb{R}\).</p>
</div>
<div class="specification">
<p class="p1"><span class="s1">The domain of \(f\) </span>is now restricted to \([0,{\text{ }}a]\)<span class="s1">.</span></p>
</div>
<div class="specification">
<p class="p1">Let \(g(x) = 2\sin (x - 1) - 3,{\text{ }} - \frac{\pi }{2} + 1 \leqslant x \leqslant \frac{\pi }{2} + 1\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the solutions of \(f(x) > 0\).</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>For the curve \(y = f(x)\).</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>Find the coordinates of both local minimum points.</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Find the \(x\)-coordinates of the points of inflexion.</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 class="p1">Write down the largest value of \(a\) for which \(f\) <span class="s1">has an inverse. Give your answer correct to 3 </span>significant figures.</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 class="p1">For this value of <span class="s1"><em>a </em></span>sketch the graphs of \(y = f(x)\) and \(y = {f^{ - 1}}(x)\) on the same set of axes, showing clearly the coordinates of the end points of each curve.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Solve \({f^{ - 1}}(x) = 1\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find an expression for \({g^{ - 1}}(x)\), stating the domain.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Solve \(({f^{ - 1}} \circ g)(x) < 1\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">valid method <em>eg</em>, sketch of curve or critical values found <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2">\(x < - 2.24,{\text{ }}x > 2.24,\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p3">\( - 1 < x < 0.8\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p4"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>M1A1A0 </em></strong>for correct intervals but with inclusive inequalities.</p>
<p class="p4"> </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">(i) <span class="Apple-converted-space"> </span>\((1.67,{\text{ }} - 5.14),{\text{ }}( - 1.74,{\text{ }} - 3.71)\) <span class="Apple-converted-space"> </span><strong><em>A1A1</em></strong></p>
<p class="p3"><span class="s1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>A1A0 </em></strong></span>for any two correct terms.</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\(f'(x) = 4{x^3} + 0.6{x^2} - 11.6x - 1\)</p>
<p class="p1">\(f''(x) = 12{x^2} + 1.2x - 11.6 = 0\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p5">\( - 1.03,{\text{ }}0.934\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1A1</em></strong></span></p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span><em>M1 </em></strong>should be awarded if graphical method to find zeros of \(f''(x)\) or turning points of \(f'(x)\) is shown.</p>
<p class="p1"><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">1.67 <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2017-01-26_om_12.42.21.png" alt="M16/5/MATHL/HP2/ENG/TZ1/11.c.ii/M"> <strong><em>M1A1A1</em></strong></p>
<p> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>M1 </em></strong>for reflection of their \(y = f(x)\) in the line \(y = x\) provided their \(f\) is one-one.</p>
<p class="p1"><strong><em>A1 </em></strong><span class="s1">for \((0,{\text{ }}4)\), \((4,{\text{ }}0)\) </span>(Accept axis intercept values) <strong><em>A1 </em></strong>for the other two sets of coordinates of other end points</p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(x = f(1)\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p2">\( = - 1.6\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(y = 2\sin (x - 1) - 3\)</p>
<p class="p1">\(x = 2\sin (y - 1) - 3\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2">\(\left( {{g^{ - 1}}(x) = } \right){\text{ }}\arcsin \left( {\frac{{x + 3}}{2}} \right) + 1\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p3">\( - 5 \leqslant x \leqslant - 1\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1A1</em></strong></span></p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>A1 </em></strong><span class="s2">for −5 and −1</span>, and <strong><em>A1 </em></strong>for correct inequalities if numbers are reasonable.</p>
<p class="p1"><strong><em>[8 marks]</em></strong></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\({f^{ - 1}}\left( {g(x)} \right) < 1\)</p>
<p class="p1">\(g(x) > - 1.6\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">\(x > {g^{ - 1}}( - 1.6) = 1.78\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p3"><span class="s1"><strong>Note: <span class="Apple-converted-space"> </span></strong></span>Accept = in the above.</p>
<p class="p3">\(1.78 < x \leqslant \frac{\pi }{2} + 1\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1A1</em></strong></span></p>
<p class="p3"><span class="s1"><strong>Note: <span class="Apple-converted-space"> </span><em>A1 </em></strong>for \(x > 1.78\) </span>(allow ≥<span class="s1">) and <strong><em>A1 </em></strong></span>for \(x \leqslant \frac{\pi }{2} + 1\).</p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Parts (a) and (b) were well answered, with considerably less success in part (c). Surprisingly few students were able to reflect the curve in \(y = x\) satisfactorily, and many were not making their sketch using the correct domain.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Parts (a) and (b) were well answered, with considerably less success in part (c). Surprisingly few students were able to reflect the curve in \(y = x\) satisfactorily, and many were not making their sketch using the correct domain.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Parts (a) and (b) were well answered, with considerably less success in part (c). Surprisingly few students were able to reflect the curve in \(y = x\) satisfactorily, and many were not making their sketch using the correct domain.</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Parts (a) and (b) were well answered, with considerably less success in part (c). Surprisingly few students were able to reflect the curve in \(y = x\) satisfactorily, and many were not making their sketch using the correct domain.</p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Parts (a) and (b) were well answered, with considerably less success in part (c). Surprisingly few students were able to reflect the curve in \(y = x\) satisfactorily, and many were not making their sketch using the correct domain.</p>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Part d(i) was generally well done, but there were few correct answers for d(ii).</p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Part d(i) was generally well done, but there were few correct answers for d(ii).</p>
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that \(2{x^3} - 3x + 1\) can be expressed in the form \(Ax\left( {{x^2} + 1} \right) + Bx + C\), find the values of the constants \(A\), \(B\) and \(C\).</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>Hence find \(\int {\frac{{2{x^3} - 3x + 1}}{{{x^2} + 1}}} {\text{d}}x\).</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>\(2{x^3} - 3x + 1 = Ax\left( {{x^2} + 1} \right) + Bx + C\)</p>
<p>\(A = 2,\,\,C = 1,\)<em><strong> A1</strong></em></p>
<p>\(A + B = - 3 \Rightarrow B = - 5\)<em><strong> A1</strong></em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\int {\frac{{2{x^3} - 3x + 1}}{{{x^2} + 1}}} {\text{d}}x = \int {\left( {2x - \frac{{5x}}{{{x^2} + 1}} + \frac{1}{{{x^2} + 1}}} \right)} {\text{d}}x\) <em><strong>M1M1</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>M1</strong></em> for dividing by \(\left( {{x^2} + 1} \right)\) to get \(2x\),<em><strong> M1</strong></em> for separating the \(5x\) and 1.</p>
<p>\( = {x^2} - \frac{5}{2}{\text{ln}}\left( {{x^2} + 1} \right) + {\text{arctan}}\,x\left( { + c} \right)\) <em><strong>(M1)A1A1</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)A1</strong></em> for integrating \({\frac{{5x}}{{{x^2} + 1}}}\), <em><strong>A1</strong></em> for the other two terms.</p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p 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 graphs of \(y = {x^2}{{\text{e}}^{ - x}}\) and \(y = 1 - 2\sin x\) for \(2 \leqslant x \leqslant 7\) intersect at points A and B.</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 <em>x</em>-coordinates of A and B are \({x_{\text{A}}}\) and \({x_{\text{B}}}\).</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 the value of \({x_{\text{A}}}\) and the value of \({x_{\text{B}}}\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p 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 area enclosed between the two graphs for \({x_{\mathbf{A}}} \leqslant x \leqslant {x_{\text{B}}}\).</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 Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x_{\text{A}}} = 2.87\) <strong><em>A1</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;">\({x_{{\text{B}}}} = 6.78\) <strong><em>A1</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>[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: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int_{2.87172{\text{K}}}^{6.77681K} {1 - 2\sin x - {x^2}{{\text{e}}^{ - x}}{\text{d}}x} \) <strong><em>(M1)(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;">\( = 6.76\) <strong><em>A1</em></strong></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> Award <strong><em>(M1) </em></strong>for definite integral and <strong><em>(A1</em></strong>) for a correct definite integral.</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 Helvetica;"><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 class="p1">A particle moves in a straight line, its velocity \(v{\text{ m}}{{\text{s}}^{ - 1}}\) at time \(t\) seconds is given by \(v = 9t - 3{t^2},{\text{ }}0 \le t \le 5\).</p>
<p class="p1">At time \(t = 0\), the displacement \(s\) of the particle from an origin \(O\) is 3 m.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the displacement of the particle when \(t = 4\).</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">Sketch a displacement/time graph for the particle, \(0 \le t \le 5\), showing clearly where the curve meets the axes and the coordinates of the points where the displacement takes greatest and least values.</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 class="p1"><span class="s1">For \(t > 5\)</span>, the displacement of the particle is given by \(s = a + b\cos \frac{{2\pi t}}{5}\) <span class="s1">such that \(s\) is continuous for all \(t \ge 0\).</span></p>
<p class="p2">Given further that \(s = 16.5\) when \(t = 7.5\), find the values of \(a\) and \(b\).</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 class="p1"><span class="s1">For \(t > 5\)</span>, the displacement of the particle is given by \(s = a + b\cos \frac{{2\pi t}}{5}\) <span class="s1">such that \(s\) is continuous for all \(t \ge 0\).</span></p>
<p class="p1">Find the times \({t_1}\) and \({t_2}(0 < {t_1} < {t_2} < 8)\) when the particle returns to its starting point.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>METHOD 1</strong></p>
<p class="p2">\(s = \int {(9t - 3{t^2}){\text{d}}t = \frac{9}{2}{t^2} - {t^3}( + c)} \) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p2">\(t = 0,{\text{ }}s = 3 \Rightarrow c = 3\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p2">\(t = 4 \Rightarrow s = 11\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong>METHOD 2</strong></p>
<p class="p2">\(s = 3 + \int_0^4 {(9t - 3{t^2}){\text{d}}t} \) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)(A1)</em></strong></span></p>
<p class="p2">\(s = 11\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2"><span class="s1"><strong><em>[3 marks]</em></strong></span></p>
<p class="p2"><span class="s1"> </span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><img src="images/Schermafbeelding_2016-01-07_om_07.29.21.png" alt></p>
<p class="p2">correct shape over correct domain <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2">maximum at \((3,{\text{ }}16.5)\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2">\(t\) intercept at \(4.64\), \(s\) intercept at \(3\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2">minimum at \((5,{\text{ }} - 9.5)\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\( - 9.5 = a + b\cos 2\pi \)</p>
<p>\(16.5 = a + b\cos 3\pi \) <strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Only award <strong><em>M1</em></strong> if two simultaneous equations are formed over the correct domain.</p>
<p> \(a = \frac{7}{2}\) <strong><em>A1</em></strong></p>
<p>\(b = - 13\) <strong><em>A1</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">at \({t_1}\):</p>
<p class="p1">\(3 + \frac{9}{2}{t^2} - {t^3} = 3\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1">\({t^2}\left( {\frac{9}{2} - t} \right) = 0\)</p>
<p class="p1">\({t_1} = \frac{9}{2}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1">solving \(\frac{7}{2} - 13\cos \frac{{2\pi t}}{5} = 3\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1">\({\text{GDC}} \Rightarrow {t_2} = 6.22\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note:</strong> <span class="Apple-converted-space"> </span>Accept graphical approaches.</p>
<p class="p3"><em><strong>[4 marks]</strong></em></p>
<p class="p3"><em><strong>Total [15 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The following graph shows the two parts of the curve defined by the equation \({x^2}y = 5 - {y^4}\), and the normal to the curve at the point P(2 , 1).</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p> </p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that there are exactly two points on the curve where the gradient is zero.</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>Find the equation of the normal to the curve at the point 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>The normal at P cuts the curve again at the point Q. Find the \(x\)-coordinate of Q.</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>The shaded region is rotated by 2\(\pi \) about the \(y\)-axis. Find the volume of the solid formed.</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>differentiating implicitly: <em><strong>M1</strong></em></p>
<p>\(2xy + {x^2}\frac{{{\text{d}}y}}{{{\text{d}}x}} = - 4{y^3}\frac{{{\text{d}}y}}{{{\text{d}}x}}\) <em><strong>A1A1</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>A1</strong></em> for each side.</p>
<p>if \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\) then either \(x = 0\) or \(y = 0\) <em><strong> M1A1</strong></em></p>
<p>\(x = 0 \Rightarrow \) two solutions for \(y\left( {y = \pm \sqrt[4]{5}} \right)\) <em><strong> R1</strong></em></p>
<p>\(y = 0\) not possible (as 0 ≠ 5) <em><strong>R1</strong></em></p>
<p>hence exactly two points <strong><em>AG</em></strong></p>
<p><strong>Note:</strong> For a solution that only refers to the graph giving two solutions at \(x = 0\) and no solutions for \(y = 0\) award <strong><em>R1</em></strong> only.</p>
<p><em><strong>[7 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>at (2, 1) \(4 + 4\frac{{{\text{d}}y}}{{{\text{d}}x}} = - 4\frac{{{\text{d}}y}}{{{\text{d}}x}}\) <em><strong> M1</strong></em></p>
<p>\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = - \frac{1}{2}\) <em><strong>(A1)</strong></em></p>
<p>gradient of normal is 2 <em><strong>M1</strong></em></p>
<p>1 = 4 + <em>c</em> <em><strong> (M1)</strong></em></p>
<p>equation of normal is \(y = 2x - 3\) <em><strong>A1</strong></em></p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>substituting <em><strong>(M1)</strong></em></p>
<p>\({x^2}\left( {2x - 3} \right) = 5 - {\left( {2x - 3} \right)^4}\) or \({\left( {\frac{{y + 3}}{2}} \right)^2}\,y = 5 - {y^4}\) <em><strong>(A1)</strong></em></p>
<p>\(x = 0.724\) <em><strong> A1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognition of two volumes <em><strong>(M1)</strong></em></p>
<p>volume \(1 = \pi \int_1^{\sqrt[4]{5}} {\frac{{5 - {y^4}}}{y}} {\text{d}}y\left( { = 101\pi = 3.178 \ldots } \right)\) <em><strong> M1A1A1</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>M1</strong></em> for attempt to use \(\pi \int {{x^2}} {\text{d}}y\), <em><strong>A1</strong></em> for limits, <em><strong>A1</strong></em> for \({\frac{{5 - {y^4}}}{y}}\) Condone omission of \(\pi \) at this stage.</p>
<p>volume 2</p>
<p><strong>EITHER</strong></p>
<p>\( = \frac{1}{3}\pi \times {2^2} \times 4\left( { = 16.75 \ldots } \right)\) <strong> <em>(M1)(A1)</em></strong></p>
<p><strong>OR</strong></p>
<p>\( = \pi \int_{ - 3}^1 {{{\left( {\frac{{y + 3}}{2}} \right)}^2}} {\text{d}}y\left( { = \frac{{16\pi }}{3} = 16.75 \ldots } \right)\) <em><strong>(M1)(A1)</strong></em></p>
<p><strong>THEN</strong></p>
<p>total volume = 19.9 <em><strong>A1</strong></em></p>
<p><em><strong>[7 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find \(\int {x{{\sec }^2}x{\text{d}}x} \).</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Determine the value of <em>m</em> if \(\int_0^m {x{{\sec }^2}x{\text{d}}x = 0.5} \), where <em>m</em> > 0.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 35.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {x{{\sec }^2}x{\text{d}}x} = x\tan x - \int {1 \times \tan x{\text{d}}x} \) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 35.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = x\tan x + \ln \left| {\cos x} \right|( + c){\text{ }}\left( { = x\tan x - \ln \left| {\sec x} \right|( + c)} \right)\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 35.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">attempting to solve an appropriate equation <em>eg</em> \(m\tan m + \ln (\cos m) = 0.5\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>m</em> = 0.822 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Award </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> if </span><em style="font-family: 'times new roman', times; font-size: medium;">m</em><span style="font-family: 'times new roman', times; font-size: medium;"> = 0.822 is specified with other positive solutions.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (a), a large number of candidates were able to use integration by parts correctly but were unable to use integration by substitution to then find the indefinite integral of tan <em>x</em>. In part (b), a large number of candidates attempted to solve the equation without direct use of a GDC’s numerical solve command. Some candidates stated more than one solution for <em>m </em>and some specified <em>m </em>correct to two significant figures only.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (a), a large number of candidates were able to use integration by parts correctly but were unable to use integration by substitution to then find the indefinite integral of tan <em>x</em>. In part (b), a large number of candidates attempted to solve the equation without direct use of a GDC’s numerical solve command. Some candidates stated more than one solution for <em>m </em>and some specified <em>m </em>correct to two significant figures only.</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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The curve \(y = {{\text{e}}^{ - x}} - x + 1\) intersects the <em>x</em>-axis at P.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Find the <em>x</em>-coordinate of P.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Find the area of the region completely enclosed by the curve and the coordinate axes.</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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Either solving \({{\text{e}}^{ - x}} - x + 1 = 0\) for <em>x</em>, stating \({{\text{e}}^{ - x}} - x + 1 = 0\), stating P(<em>x</em>, 0) or using an appropriate sketch graph. <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>x</em> = 1.28 <strong><em>A1</em></strong> <strong><em>N1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Accept P(1.28, 0) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Area \( = \int_0^{1.278...} {({{\text{e}}^{ - x}} - x + 1){\text{d}}x} \) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">= 1.18 <strong><em>A1 N1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>M1A0A1</em></strong> if the d<em>x</em> is absent.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This was generally well done. In part (a), most candidates were able to find <em>x</em> = 1.28 successfully. A significant number of candidates were awarded an accuracy penalty for expressing answers to an incorrect number of significant figures.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (b) was generally well done. A number of candidates unfortunately omitted the d<em>x</em> in the integral while some candidates omitted to write down the definite integral and instead offered detailed instructions on how they obtained the answer using their GDC.</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">The functions \(f\) and \(g\) are defined by</p>
<p class="p1">\[f(x) = \frac{{{{\text{e}}^x} + {{\text{e}}^{ - x}}}}{2},{\text{ }}x \in \mathbb{R}\]</p>
<p class="p1">\[g(x) = \frac{{{{\text{e}}^x} - {{\text{e}}^{ - x}}}}{2},{\text{ }}x \in \mathbb{R}\]</p>
</div>
<div class="specification">
<p class="p1">Let \(h(x) = nf(x) + g(x)\) where \(n \in \mathbb{R},{\text{ }}n > 1\).</p>
</div>
<div class="specification">
<p class="p1">Let \(t(x) = \frac{{g(x)}}{{f(x)}}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Show that \(\frac{1}{{4f(x) - 2g(x)}} = \frac{{{{\text{e}}^x}}}{{{{\text{e}}^{2x}} + 3}}\).</p>
<p class="p2">(ii) <span class="Apple-converted-space"> </span>Use the substitution \(u = {{\text{e}}^x}\) to find \(\int_0^{\ln 3} {\frac{1}{{4f(x) - 2g(x)}}} {\text{d}}x\). Give your answer in the form \(\frac{{\pi \sqrt a }}{b}\) where \(a,{\text{ }}b \in {\mathbb{Z}^ + }\).</p>
<div class="marks">[9]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>By forming a quadratic equation in \({{\text{e}}^x}\)<span class="s1">, solve the equation \(h(x) = k\), where \(k \in {\mathbb{R}^ + }\).</span></p>
<p class="p2">(ii) <span class="Apple-converted-space"> </span>Hence or otherwise show that the equation \(h(x) = k\) has two real solutions provided that \(k > \sqrt {{n^2} - 1} \) and \(k \in {\mathbb{R}^ + }\).</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">(i) <span class="Apple-converted-space"> </span>Show that \(t'(x) = \frac{{{{[f(x)]}^2} - {{[g(x)]}^2}}}{{{{[f(x)]}^2}}}\) <span class="s1">for \(x \in \mathbb{R}\).</span></p>
<p class="p2">(ii) <span class="Apple-converted-space"> </span>Hence show that \(t'(x) > 0\) for \(x \in \mathbb{R}\).</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 class="p1">(i) \(\frac{1}{{4\left( {\frac{{{{\text{e}}^x} + {{\text{e}}^{ - x}}}}{2}} \right) - 2\left( {\frac{{{{\text{e}}^x} - {{\text{e}}^{ - x}}}}{2}} \right)}}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\( = \frac{1}{{2({{\text{e}}^x} + {{\text{e}}^{ - x}}) - ({{\text{e}}^x} - {{\text{e}}^{ - x}})}}\) </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\( = \frac{1}{{{{\text{e}}^x} + 3{{\text{e}}^{ - x}}}}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\( = \frac{{{{\text{e}}^x}}}{{{{\text{e}}^{2x}} + 3}}\) </span><span class="s1"><strong><em>AG</em></strong></span></p>
<p class="p2">(ii) <span class="Apple-converted-space"> \(u = {{\text{e}}^x} \Rightarrow {\text{d}}u = {{\text{e}}^x}{\text{d}}x\)</span> <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(\int {\frac{{{{\text{e}}^x}}}{{{{\text{e}}^{2x}} + 3}}{\text{d}}x = \int {\frac{1}{{{u^2} + 3}}{\text{d}}u} } \) </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p2">(when \(x = 0,{\text{ }}u = 1\) and when \(x = \ln 3,{\text{ }}u = 3\))</p>
<p class="p1"><span class="Apple-converted-space">\(\int_1^3 {\frac{1}{{{u^2} + 3}}{\text{d}}u\left[ {\frac{1}{{\sqrt 3 }}\arctan \left( {\frac{u}{{\sqrt 3 }}} \right)} \right]_1^3} \) </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p1">\(\left( { = \left[ {\frac{1}{{\sqrt 3 }}\arctan \left( {\frac{{{{\text{e}}^x}}}{{\sqrt 3 }}} \right)} \right]_0^{\ln 3}} \right)\)</p>
<p class="p1"><span class="Apple-converted-space">\( = \frac{{\pi \sqrt 3 }}{9} - \frac{{\pi \sqrt 3 }}{{18}}\) </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\( = \frac{{\pi \sqrt 3 }}{{18}}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2"><strong><em>[9 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"> \((n + 1){{\text{e}}^{2x}} - 2k{{\text{e}}^x} + (n - 1) = 0\)</span> <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\({{\text{e}}^x} = \frac{{2k \pm \sqrt {4{k^2} - 4({n^2} - 1)} }}{{2(n + 1)}}\) </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\(x = \ln \left( {\frac{{k \pm \sqrt {{k^2} - {n^2} + 1} }}{{n + 1}}} \right)\) </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p2">(ii) <span class="Apple-converted-space"> </span>for two real solutions, we require \(k > \sqrt {{k^2} - {n^2} + 1} \) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p2">and we also require \({k^2} - {n^2} + 1 > 0\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\({k^2} > {n^2} - 1\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\( \Rightarrow k > \sqrt {{n^2} - 1} {\text{ }}({\text{ }}k \in {\mathbb{R}^ + })\) </span><span class="s1"><strong><em>AG</em></strong></span></p>
<p class="p2"><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"><strong>METHOD 1</strong></p>
<p class="p2">\(t(x) = \frac{{{{\text{e}}^x} - {{\text{e}}^{ - x}}}}{{{{\text{e}}^x} + {{\text{e}}^{ - x}}}}\)</p>
<p class="p2"><span class="Apple-converted-space">\(t'(x) = \frac{{{{({{\text{e}}^x} + {{\text{e}}^{ - x}})}^2} - {{({{\text{e}}^x} - {{\text{e}}^{ - x}})}^2}}}{{{{({{\text{e}}^x} + {{\text{e}}^{ - x}})}^2}}}\) </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p2"><span class="Apple-converted-space">\(t'(x) = \frac{{{{\left( {\frac{{{{\text{e}}^x} + {{\text{e}}^{ - x}}}}{2}} \right)}^2} - {{\left( {\frac{{{{\text{e}}^x} - {{\text{e}}^{ - x}}}}{2}} \right)}^2}}}{{{{\left( {\frac{{{{\text{e}}^x} + {{\text{e}}^{ - x}}}}{2}} \right)}^2}}}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2"><span class="Apple-converted-space">\( = \frac{{{{\left[ {f(x)} \right]}^2} - {{\left[ {g(x)} \right]}^2}}}{{{{\left[ {f(x)} \right]}^2}}}\) </span><span class="s1"><strong><em>AG</em></strong></span></p>
<p class="p1"><strong>METHOD 2</strong></p>
<p class="p2"><span class="Apple-converted-space">\(t'(x) = \frac{{f(x)g'(x) = g(x)f'(x)}}{{{{\left[ {f(x)} \right]}^2}}}\) </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p1">\(g'(x) = f(x)\) and \(f'(x) = g(x)\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\( = \frac{{{{\left[ {f(x)} \right]}^2} - {{\left[ {g(x)} \right]}^2}}}{{{{\left[ {f(x)} \right]}^2}}}\) </span><span class="s1"><strong><em>AG</em></strong></span></p>
<p class="p3"><strong>METHOD 3</strong></p>
<p class="p4">\(t(x) = ({{\text{e}}^x} - {{\text{e}}^{ - x}}){({{\text{e}}^x} + {{\text{e}}^{ - x}})^{ - 1}}\)</p>
<p class="p4"><span class="Apple-converted-space">\(t'(x) = 1 - \frac{{{{({{\text{e}}^x} - {{\text{e}}^{ - x}})}^2}}}{{{{({{\text{e}}^x} + {{\text{e}}^{ - x}})}^2}}}\) </span><span class="s2"><strong><em>M1A1</em></strong></span></p>
<p class="p4"><span class="Apple-converted-space">\( = 1 - \frac{{{{\left[ {g(x)} \right]}^2}}}{{{{\left[ {f(x)} \right]}^2}}}\) </span><span class="s2"><strong><em>A1</em></strong></span></p>
<p class="p4"><span class="Apple-converted-space">\( = \frac{{{{\left[ {f(x)} \right]}^2} - {{\left[ {g(x)} \right]}^2}}}{{{{\left[ {f(x)} \right]}^2}}}\) </span><span class="s2"><strong><em>AG</em></strong></span></p>
<p class="p3"><strong>METHOD 4</strong></p>
<p class="p4"><span class="Apple-converted-space">\(t'(x) = \frac{{g'(x)}}{{f(x)}} - \frac{{g(x)f'(x)}}{{{{\left[ {f(x)} \right]}^2}}}\) </span><span class="s2"><strong><em>M1A1</em></strong></span></p>
<p class="p3">\(g'(x) = f(x)\) and \(f'(x) = g(x)\) gives \(t'(x) = 1 - \frac{{{{\left[ {g(x)} \right]}^2}}}{{{{\left[ {f(x)} \right]}^2}}}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p4"><span class="Apple-converted-space">\( = \frac{{{{\left[ {f(x)} \right]}^2} - {{\left[ {g(x)} \right]}^2}}}{{{{\left[ {f(x)} \right]}^2}}}\) </span><span class="s2"><strong><em>AG</em></strong></span></p>
<p class="p3">(ii) <span class="Apple-converted-space"> </span><strong>METHOD 1</strong></p>
<p class="p3">\({\left[ {f(x)} \right]^2} > {\left[ {g(x)} \right]^2}\) (or equivalent) <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p3"><span class="Apple-converted-space">\({\left[ {f(x)} \right]^2} > 0\) </span><strong><em>R1</em></strong></p>
<p class="p3">hence \(t'(x) > 0,{\text{ }}x \in \mathbb{R}\) <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p4"><span class="s2"><strong>Note: <span class="Apple-converted-space"> </span></strong></span>Award as above for use of either \(f(x) = \frac{{{{\text{e}}^x} + {{\text{e}}^{ - x}}}}{2}\) and \(g(x) = \frac{{{{\text{e}}^x} - {{\text{e}}^{ - x}}}}{2}\) or \({{\text{e}}^x} + {{\text{e}}^{ - x}}\) and \({{\text{e}}^x} - {{\text{e}}^{ - x}}\).</p>
<p class="p3"><strong>METHOD 2</strong></p>
<p class="p3">\({\left[ {f(x)} \right]^2} - {\left[ {g(x)} \right]^2} = 1\) (or equivalent) <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p4"><span class="Apple-converted-space">\({\left[ {f(x)} \right]^2} > 0\) </span><span class="s2"><strong><em>R1</em></strong></span></p>
<p class="p3">hence \(t'(x) > 0,{\text{ }}x \in \mathbb{R}\) <strong><em>AG</em></strong></p>
<p class="p4"><span class="s2"><strong>Note: <span class="Apple-converted-space"> </span></strong></span>Award as above for use of either \(f(x) = \frac{{{{\text{e}}^x} + {{\text{e}}^{ - x}}}}{2}\) and \(g(x) = \frac{{{{\text{e}}^x} - {{\text{e}}^{ - x}}}}{2}\) or \({{\text{e}}^x} + {{\text{e}}^{ - x}}\) and \({{\text{e}}^x} - {{\text{e}}^{ - x}}\).</p>
<p class="p3"><strong>METHOD 3</strong></p>
<p class="p4">\(t'(x) = \frac{4}{{{{({{\text{e}}^x} + {{\text{e}}^{ - x}})}^2}}}\)</p>
<p class="p4"><span class="Apple-converted-space">\({\left( {{{\text{e}}^x} + {{\text{e}}^{ - x}}} \right)^2} > 0\) </span><span class="s2"><strong><em>M1A1</em></strong></span></p>
<p class="p4"><span class="Apple-converted-space">\(\frac{4}{{{{\left( {{{\text{e}}^x} + {{\text{e}}^{ - x}}} \right)}^2}}} > 0\) </span><span class="s2"><strong><em>R1</em></strong></span></p>
<p class="p3">hence \(t'(x) > 0,{\text{ }}x \in \mathbb{R}\) <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p3"><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;">
<p class="p1">Parts (a) and (c) were accessible to the large majority of candidates. Candidates found part (b) considerably more challenging.</p>
<p class="p1">Part (a)(i) was reasonably well done with most candidates able to show that \(\frac{1}{{4f(x) - 2g(x)}} = \frac{{{{\text{e}}^x}}}{{{{\text{e}}^{2x}} + 3}}\). In part (a)(ii), a number of candidates correctly used the required substitution to obtain \(\int {\frac{{{{\text{e}}^x}}}{{{{\text{e}}^{2x}} + 3}}{\text{d}}x = \int {\frac{1}{{{u^2} + 3}}{\text{d}}u} } \) but then thought that the antiderivative involved natural log rather than arctan.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Parts (a) and (c) were accessible to the large majority of candidates. Candidates found part (b) considerably more challenging.</p>
<p class="p1">In part (b)(i), a reasonable number of candidates were able to form a quadratic in \({{\text{e}}^x}\) (involving parameters \(n\) and \(k\)) and then make some progress towards solving for \({{\text{e}}^x}\) in terms of \(n\) and \(k\). Having got that far, a small number of candidates recognised to then take the natural logarithm of both sides and hence solve \(h(x) = k\) for \(\chi \). In part (b)(ii), a small number of candidates were able to show from their solutions to part (b)(i) or through the use of the discriminant that the equation \(h(x) = k\) has two real solutions provided that \(k > \sqrt {{k^2} - {n^2} + 1} \) and \(k > \sqrt {{n^2} - 1} \).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Parts (a) and (c) were accessible to the large majority of candidates. Candidates found part (b) considerably more challenging.</p>
<p class="p1">It was pleasing to see the number of candidates who attempted part (c). In part (c)(i), a large number of candidates were able to correctly apply either the quotient rule or the product rule to find \(t'(x)\). A smaller number of candidates were then able to show equivalence between the form of \(t'(x)\) they had obtained and the form of \(t'(x)\) required in the question. A pleasing number of candidates were able to exploit the property that \(f'(x) = g(x)\) and \(g'(x) = f(x)\). As with part (c)(i), part (c)(ii) could be successfully tackled in a number of ways. The best candidates offered concise logical reasoning to show that \(t'(x) > 0\) for \(x \in \mathbb{R}\).</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the gradient of the tangent to the curve \({x^3}{y^2} = \cos (\pi y)\) at the point (−1, 1) .</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: 28.0px Helvetica;"><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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(3{x^2}{y^2} + 2{x^3}y\frac{{{\text{d}}y}}{{{\text{d}}x}} = - \pi \sin (\pi y)\frac{{{\text{d}}y}}{{{\text{d}}x}}\) <strong><em>A1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">At \(( - 1,{\text{ }}1),{\text{ }}3 - 2\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{3}{2}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(3{x^2}{y^2} + 2{x^3}y\frac{{{\text{d}}y}}{{{\text{d}}x}} = - \pi \sin (\pi y)\frac{{{\text{d}}y}}{{{\text{d}}x}}\) <strong><em>A1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{3{x^2}{y^2}}}{{ - \pi \sin (\pi y) - 2{x^3}y}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">At \(( - 1,{\text{ }}1),{\text{ }}\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{3{{( - 1)}^2}{{(1)}^2}}}{{ - \pi \sin (\pi ) - 2{{( - 1)}^3}(1)}} = \frac{3}{2}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A large number of candidates obtained full marks on this question. Some candidates missed \(\pi \) and/or \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) when differentiating the trigonometric function. Some candidates attempted to rearrange before differentiating, and some made algebraic errors in rearranging.</span></p>
</div>
<br><hr><br><div class="specification">
<p>Consider the function \(f(x) = 2{\sin ^2}x + 7\sin 2x + \tan x - 9,{\text{ }}0 \leqslant x < \frac{\pi }{2}\).</p>
</div>
<div class="specification">
<p>Let \(u = \tan x\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine an expression for \(f’(x)\) in terms of \(x\).</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>Sketch a graph of \(y = f’(x)\) for \(0 \leqslant x < \frac{\pi }{2}\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the \(x\)-coordinate(s) of the point(s) of inflexion of the graph of \(y = f(x)\), labelling these clearly on the graph of \(y = f’(x)\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Express \(\sin x\) in terms of \(\mu \).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Express \(\sin 2x\) in terms of \(u\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence show that \(f(x) = 0\) can be expressed as \({u^3} - 7{u^2} + 15u - 9 = 0\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Solve the equation \(f(x) = 0\), giving your answers in the form \(\arctan k\) where \(k \in \mathbb{Z}\).</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>\(f’(x) = 4\sin x\cos x + 14\cos 2x + {\sec ^2}x\) (or equivalent) <strong><em>(M1)A1</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2018-02-08_om_16.47.49.png" alt="N17/5/MATHL/HP2/ENG/TZ0/11.a.ii/M"> <strong><em>A1A1A1A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>A1 </em></strong>for correct behaviour at \(x = 0\), <strong><em>A1 </em></strong>for correct domain and correct behaviour for \(x \to \frac{\pi }{2}\), <strong><em>A1 </em></strong>for two clear intersections with \(x\)-axis and minimum point, <strong><em>A1 </em></strong>for clear maximum point.</p>
<p> </p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(x = 0.0736\) <strong><em>A1</em></strong></p>
<p>\(x = 1.13\) <strong><em>A1</em></strong></p>
<p><em style="font-size: 14px;"><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to write \(\sin x\) in terms of \(u\) only <strong><em>(M1)</em></strong></p>
<p>\(\sin x = \frac{u}{{\sqrt {1 + {u^2}} }}\) <strong><em>A1</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\cos x = \frac{1}{{\sqrt {1 + {u^2}} }}\) <strong><em>(A1)</em></strong></p>
<p>attempt to use \(\sin 2x = 2\sin x\cos x{\text{ }}\left( { = 2\frac{u}{{\sqrt {1 + {u^2}} }}\frac{1}{{\sqrt {1 + {u^2}} }}} \right)\) <strong><em>(M1)</em></strong></p>
<p>\(\sin 2x = \frac{{2u}}{{1 + {u^2}}}\) <strong><em>A1</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(2{\sin ^2}x + 7\sin 2x + \tan x - 9 = 0\)</p>
<p>\(\frac{{2{u^2}}}{{1 + {u^2}}} + \frac{{14u}}{{1 + {u^2}}} + u - 9{\text{ }}( = 0)\) <strong><em>M1</em></strong></p>
<p>\(\frac{{2{u^2} + 14u + u(1 + {u^2}) - 9(1 + {u^2})}}{{1 + {u^2}}} = 0\) (or equivalent) <strong><em>A1</em></strong></p>
<p>\({u^3} - 7{u^2} + 15u - 9 = 0\) <strong><em>AG</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(u = 1\) or \(u = 3\) <strong><em>(M1)</em></strong></p>
<p>\(x = \arctan (1)\) <strong><em>A1</em></strong></p>
<p>\(x = \arctan (3)\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Only accept answers given the required form.</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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">A function \(f\) is defined by \(f(x) = \frac{1}{2}\left( {{{\text{e}}^x} + {{\text{e}}^{ - x}}} \right),{\text{ }}x \in \mathbb{R}\).</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 Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Explain why the inverse function \({f^{ - 1}}\) does not exist.</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;">(ii) Show that the equation of the normal to the curve at the point P where \(x = \ln 3\) is given by \(9x + 12y - 9\ln 3 - 20 = 0\).</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;">(iii) Find the <em>x</em>-coordinates of the points Q and R on the curve such that the tangents at Q and R pass through \({\text{(0, 0)}}\).</span></p>
<div class="marks">[14]</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;">The domain of \(f\) is now restricted to \(x \geqslant 0\).</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;">(i) Find an expression for \({f^{ - 1}}(x)\)<em>.</em></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;">(ii) Find the volume generated when the region bounded by the curve \(y = f(x)\) and the lines \(x = 0\) and \(y = 5\) is rotated through an angle of \(2\pi \) radians about the <em>y</em>-axis.</span></p>
<div class="marks">[8]</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: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(i) either counterexample or sketch or</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;">recognising that \(y = k{\text{ }}(k > 1)\) intersects the graph of \(y = f(x)\) twice <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;">function is not \(1 - 1\) (does not obey horizontal line test) <strong><em>R1</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;">so \({f^{ - 1}}\) does not exist <strong><em>AG</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;">(ii) \(f'(x) = \frac{1}{2}\left( {{{\text{e}}^x} - {{\text{e}}^{ - x}}} \right)\) <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;">\(f'(\ln 3) = \frac{4}{3}{\text{ }}( = 1.33)\) <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;">\(m = - \frac{3}{4}\) <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;">\(f(\ln 3) = \frac{5}{3}{\text{ }}( = 1.67)\) <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;"><strong>EITHER</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;">\(\frac{{y - \frac{5}{3}}}{{x - \ln 3}} = - \frac{3}{4}\) <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;">\(4y - \frac{{20}}{3} = - 3x + 3\ln 3\) <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;"><strong>OR</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;">\(\frac{5}{3} = - \frac{3}{4}\ln 3 + c\) <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;">\(c = \frac{5}{3} + \frac{3}{4}\ln 3\)</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;">\(y = - \frac{3}{4}x + \frac{5}{3} + \frac{3}{4}\ln 3\) <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;">\(12y = - 9x + 20 + 9\ln 3\)</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;"><strong>THEN</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;">\(9x + 12y - 9\ln 3 - 20 = 0\) <strong><em>AG</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;">(iii) The tangent at \(\left( {a,{\text{ }}f(a)} \right)\) has equation \(y - f(a) = f'(a)(x - a)\). <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;">\(f'(a) = \frac{{f(a)}}{a}\) (or equivalent) <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;">\({{\text{e}}^a} - {{\text{e}}^{ - a}} = \frac{{{{\text{e}}^a} + {{\text{e}}^{ - a}}}}{a}\) (or equivalent) <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;">attempting to solve for <em>a</em> <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;">\(a = \pm 1.20\) <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;"><strong><em>[14 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;">(i) \(2y = {{\text{e}}^x} + {{\text{e}}^{ - x}}\)</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;">\({{\text{e}}^{2x}} - 2y{{\text{e}}^x} + 1 = 0\) <strong><em>M1A1</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>Note:</strong> Award <strong><em>M1 </em></strong>for either attempting to rearrange or interchanging <em>x </em>and <em>y</em>.</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;">\({{\text{e}}^x} = \frac{{2y \pm \sqrt {4{y^2} - 4} }}{2}\) <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;">\({{\text{e}}^x} = y \pm \sqrt {{y^2} - 1} \)</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;">\(x = \ln \left( {y \pm \sqrt {{y^2} - 1} } \right)\) <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;">\({f^{ - 1}}(x) = \ln \left( {x + \sqrt {{x^2} - 1} } \right)\) <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>Note:</strong> Award <strong><em>A1 </em></strong>for correct notation and for stating the positive “branch”.</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;">(ii) \(V = \pi \int_1^5 {{{\left( {\ln \left( {y + \sqrt {{y^2} - 1} } \right)} \right)}^2}{\text{d}}y} \) <strong><em>(M1)(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>Note:</strong> Award <strong><em>M1 </em></strong>for attempting to use \(V = \pi \int_c^d {{x^2}{\text{d}}y} \).</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;">\( = 37.1{\text{ }}\left( {{\text{unit}}{{\text{s}}^3}} \right)\) <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;"><strong><em>[8 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (a) (i), successful candidates typically sketched the graph of \(y = f(x)\), applied the horizontal line test to the graph and concluded that the function was not \(1 - 1\) (it did not obey the horizontal line test).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (a) (ii), a large number of candidates were able to show that the equation of the normal at point P was \(9x + 12y - 9\ln 3 - 20 = 0\). A few candidates used the gradient of the tangent rather than using it to find the gradient of the normal.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) (iii) challenged most candidates. Most successful candidates graphed \(y = f(x)\) and \(y = xf'(x)\) on the same set of axes and found the <em>x</em>-coordinates of the intersection points.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (b) (i) challenged most candidates. While a large number of candidates seemed to understand how to find an inverse function, poor algebra skills (e.g. erroneously taking the natural logarithm of both sides) meant that very few candidates were able to form a quadratic in either \({{\text{e}}^x}\) or \({{\text{e}}^y}\).</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;">Engineers need to lay pipes to connect two cities A and B that are separated by a river of width 450 metres as shown in the following diagram. They plan to lay the pipes under the river from A to X and then under the ground from X to B. The cost of laying the pipes under the river is five times the cost of laying the pipes under the ground.</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 \({\text{EX}} = x\).</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><br><span style="font-family: 'times new roman', times; font-size: medium;"><img src="images/Schermafbeelding_2014-09-15_om_15.01.31.png" alt></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;"> </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 <em>k </em>be the cost, in dollars per metre, of laying the pipes under the ground.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Show that the total cost <em>C</em>, in dollars, of laying the pipes from A to B is given by \(C = 5k\sqrt {202\,500 + {x^2}} + (1000 - x)k\).</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;">(b) (i) Find \(\frac{{{\text{d}}C}}{{{\text{d}}x}}\).</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;"> (ii) Hence find the value of <em>x </em>for which the total cost is a minimum, justifying that this value is a minimum.</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;">(c) Find the minimum total cost in terms of <em>k</em>.</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 angle at which the pipes are joined is \({\rm{A\hat XB}} = \theta \).</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;">(d) Find \(\theta \) for the value of <em>x </em>calculated in (b).</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;">For safety reasons \(\theta \) must be at least 120°.</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;">Given this new requirement,</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;">(e) (i) find the new value of <em>x </em>which minimises the total cost;</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;"> (ii) find the percentage increase in the minimum total cost.</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: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \(C = {\text{AX}} \times 5k + {\text{XB}} \times k\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; 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> Award <strong>(<em>M1) </em></strong>for attempting to express the cost in terms of AX<em>, </em>XB and <em>k.</em></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: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 5k\sqrt {{{450}^2} + {x^2}} + (1000 - x)k\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 5k\sqrt {202\,500 + {x^2}} + (1000 - x)k\) <strong><em>AG</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>[2 marks]</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> </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;">(b) (i) \(\frac{{{\text{d}}C}}{{{\text{d}}x}} = k\left[ {\frac{{5 \times 2x}}{{2\sqrt {202\,500 + {x^2}} }} - 1} \right] = k\left( {\frac{{5x}}{{\sqrt {202\,500 + {x^2}} }} - 1} \right)\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; 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> Award <strong><em>M1 </em></strong>for an attempt to differentiate and <strong><em>A1 </em></strong>for the correct derivative.</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 Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> (ii) attempting to solve \(\frac{{{\text{d}}C}}{{{\text{d}}x}} = 0\) <strong><em>M1</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;"> \(\frac{5}{{\sqrt {202\,500 + {x^2}} }} = 1\) <strong><em>(A1)</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;"> \(x = 91.9{\text{ (m) }}\left( { = \frac{{75\sqrt 6 }}{2}{\text{ (m)}}} \right)\) <strong><em>A1</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> METHOD 1</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;"> for example,</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;"> at \(x = 91\frac{{{\text{d}}C}}{{{\text{d}}x}} = - 0.00895k < 0\) <strong><em>M1</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;"> at </span><span style="font-family: 'times new roman', times; font-size: medium; background-color: #f7f7f7;"><span style="background-color: #ffffff;">\(x = 92\frac{{{\text{d}}C}}{{{\text{d}}x}} = 0.001506k > 0\)</span> </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 Helvetica; 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> Award <strong><em>M1 </em></strong>for attempting to find the gradient either side of \(x = 91.9\) and <strong><em>A1 </em></strong>for two correct values.</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;"> thus \(x = 91.9\) gives a minimum <strong><em>AG</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> 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;"> \(\frac{{{{\text{d}}^2}C}}{{{\text{d}}{x^2}}} = \frac{{1\,012\,500k}}{{{{\left( {{x^2} + 202\,500} \right)}^{\frac{3}{2}}}}}\)</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;"> at \(x = 91.9\frac{{{{\text{d}}^2}C}}{{{\text{d}}{x^2}}} = 0.010451k > 0\) <strong><em>(M1)A1</em></strong></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>Award <strong><em>M1 </em></strong>for attempting to find the second derivative and <strong><em>A1 </em></strong>for the correct value.</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> If \(\frac{{{{\text{d}}^2}C}}{{{\text{d}}{x^2}}}\) is obtained and its value at \(x = 91.9\) is not calculated, award <strong><em>(M1)A1 </em></strong>for correct reasoning <em>eg</em>, both numerator and denominator are positive at \(x = 91.9\).</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: 20.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> thus \(x = 91.9\) gives a minimum <strong><em>AG</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> 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;"> Sketching the graph of either <em>C </em>versus <em>x </em>or \(\frac{{{\text{d}}C}}{{{\text{d}}x}}\) versus <em>x</em>. <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;"> Clearly indicating that \(x = 91.9\) gives the minimum on their graph. <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;"><strong><em>[7 marks]</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> </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;">(c) \({C_{\min }} = 3205k\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; 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> Accept 3200<em>k</em>.</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;"> Accept 3204<em>k</em>.</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 Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[1 mark]</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> </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;">(d) \(\arctan \left( {\frac{{450}}{{91.855865{\text{K}}}}} \right) = 78.463{\text{K}}^\circ \) <strong><em>M1</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;">\(180 - 78.463{\text{K = 101.537K}}\)</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;">\( = 102^\circ \) <strong><em>A1</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>[2 marks]</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> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(e) (i) when \(\theta = 120^\circ ,{\text{ }}x = 260{\text{ (m) }}\left( {\frac{{450}}{{\sqrt 3 }}{\text{ (m)}}} \right)\) <strong><em>A1</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;"> (ii) \(\frac{{133.728{\text{K}}}}{{3204.5407685{\text{K}}}} \times 100\% \) <strong><em>M1</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;"> \( = 4.17{\text{ (% )}}\) <strong><em>A1</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>[3 marks]</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> </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>Total [15 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="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The line \(y = m(x - m)\) is a tangent to the curve \((1 - x)y = 1\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Determine <em>m</em> and the coordinates of the point where the tangent meets the curve.</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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(y = \frac{1}{{1 - x}} \Rightarrow y' = \frac{1}{{{{(1 - x)}^2}}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">solve simultaneously <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{1}{{1 - x}} = m(x - m){\text{ and }}\frac{1}{{{{(1 - x)}^2}}} = m\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{1}{{1 - x}} = \frac{1}{{{{(1 - x)}^2}}}\left( {x - \frac{1}{{{{(1 - x)}^2}}}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Accept equivalent forms.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({(1 - x)^3} - x{(1 - x)^2} + 1 = 0,{\text{ }}x \ne 1\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 1.65729 \ldots \Rightarrow y = \frac{1}{{1 - 1.65729 \ldots }} = - 1.521379 \ldots \)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">tangency point (1.66, –1.52) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(m = {( - 1.52137 \ldots )^2} = 2.31\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\((1 - x)y = 1\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(m(1 - x)(x - m) = 1\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(m(x - {x^2} - m + mx) = 1\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(m{x^2} - x(m + {m^2}) + ({m^2} + 1) = 0\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({b^2} - 4ac = 0\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({(m + {m^2})^2} - 4m({m^2} + 1) = 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(m = 2.31\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">substituting \(m = 2.31 \ldots {\text{ into }}m{x^2} - x(m + {m^2}) + ({m^2} + 1) = 0\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 1.66\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(y = \frac{1}{{1 - 1.65729}} = - 1.52\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">tangency point (1.66, –1.52)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Very few candidates answered this question well but among those a variety of nice approaches were seen. This question required some organized thinking and good understanding of the concepts involved and therefore just strong candidates were able to go beyond the first steps. Sadly a few good answers were spoiled due to early rounding.</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 a circle with centre at the origin O and radius \(r > 0\) .</span></p>
<p style="text-align: center;"><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;"> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">A point P(\(x\) , \(y\)) , (\(x > 0\), \(y > 0\)) is moving round the circumference of the circle.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(m = \tan \left( {\arcsin \frac{y}{r}} \right)\)</span><span style="font-family: times new roman,times; font-size: medium;"> .</span></p>
</div>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">(a) Given that \(\frac{{{\text{d}}y}}{{{\text{d}}t}} = 0.001r\)</span><span style="font-family: times new roman,times; font-size: medium;"> , show that \(\frac{{{\text{d}}m}}{{{\text{d}}t}} = {\left( {\frac{r}{{10\sqrt {{r^2} - {y^2}} }}} \right)^3}\)</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;">(b) State the geometrical meaning of \(\frac{{{\text{d}}m}}{{{\text{d}}t}}\) </span><span style="font-family: times new roman,times; font-size: medium;">.</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;">(a) \(\frac{{{\text{d}}m}}{{{\text{d}}t}} = \frac{{{\text{d}}m}}{{{\text{d}}y}}\frac{{{\text{d}}y}}{{{\text{d}}t}}\) </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,times; font-size: medium;">\({ = {{\sec }^2}\left( {\arcsin \frac{y}{r}} \right) \times \left( {\arcsin \frac{y}{r}} \right)' \times \frac{r}{{1000}}}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\( = \frac{1}{{{{\cos }^2}\left( {\arcsin \frac{y}{r}} \right)}} \times \frac{{\frac{1}{r}}}{{\sqrt {1 - {{\left( {\frac{y}{r}} \right)}^2}} }} \times \frac{r}{{1000}}\) (or equivalent) <em><strong>A1A1A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\( = \frac{{\frac{1}{{\sqrt {{r^2} - {y^2}} }}}}{{\frac{{{r^2} - {y^2}}}{{{r^2}}}}}\frac{r}{{1000}}\) </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;">\( = \frac{{{r^3}}}{{{{10}^3}\sqrt {{{\left( {{r^2} - {y^2}} \right)}^3}} }}\) </span><span style="font-family: times new roman,times; font-size: medium;">(or equivalent) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\( = {\left( {\frac{r}{{10\sqrt {{r^2} - {y^2}} }}} \right)^3}\) </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;"> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(b) </span><span style="font-family: times new roman,times; font-size: medium;">\(\frac{{{\text{d}}m}}{{{\text{d}}t}}\) </span><span style="font-family: times new roman,times; font-size: medium;">represents the rate of change of the gradient of the line OP <em><strong>A1</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;">[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;">Few students were able to complete this question successfully, although many did obtain partial marks. Many students failed to recognise the difference between differentiating with respect to \(t\) or with respect to \(y\) . Very few were able to give a satisfactory geometrical meaning in part (b).</span></p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The cubic curve \(y = 8{x^3} + b{x^2} + cx + d\) has two distinct points P and Q, where the gradient is zero.</span></p>
</div>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">(a) Show that \({b^2} > 24c\) .<br></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(b) Given that the coordinates of P and Q are \(\left( {\frac{1}{2},{\text{ }} - 12} \right)\) </span><span style="font-family: times new roman,times; font-size: medium;">and \(\left( { - \frac{3}{2},{\text{ }}20} \right)\)</span><span style="font-family: times new roman,times; font-size: medium;"> respectively,</span> <span style="font-family: times new roman,times; font-size: medium;">find the values of \(b\) , \(c\) and \(d\) .</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;">(a) \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 24{x^2} + 2bx + c\) </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;">\(24{x^2} + 2bx + c = 0\) <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\Delta = {\left( {2b} \right)^2} - 96\left( c \right)\) <em><strong>(A1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(4{b^2} - 96c > 0\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({b^2} > 24c\) <em><strong>AG</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;">(b) \(1 + \frac{1}{4}b + \frac{1}{2}c + d = - 12\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(6 + b + c = 0\)<br></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\( - 27 + \frac{9}{4}b - \frac{3}{2}c + d = 20\)<br></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(54 - 3b + c = 0\) <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 each correct equation, up to \(3\), not necessarily simplified.</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;">\(b = 12\), \(c = - 18\), \(d = - 7\) <em><strong>A1</strong></em></span></p>
<p><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;">[8 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;">Many candidates throughout almost the whole mark range were able to score well on this question. It was pleasing that most candidates were aware of the discriminant condition for distinct real roots of a quadratic. Some who dropped marks on part (b) either didn't write down a sufficient number of linear equations to determine the three unknowns or made arithmetic errors in their manual solution – few GDC solutions were seen.</span></p>
</div>
<br><hr><br><div class="specification">
<p>Richard, a marine soldier, steps out of a stationary helicopter, 1000 m above the ground, at time \(t = 0\). Let his height, in metres, above the ground be given by \(s(t)\). For the first 10 seconds his velocity, \(v(t){\text{m}}{{\text{s}}^{ - 1}}\), is given by \(v(t) = - 10t\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Find his acceleration \(a(t)\) for \(t < 10\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Calculate \(v(10)\).</p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>Show that \(s(10) = 500\).</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>At \(t = 10\) his parachute opens and his acceleration \(a(t)\) is subsequently given by \(a(t) = - 10 - 5v,{\text{ }}t \ge 10\).</p>
<p>Given that \(\frac{{{\text{d}}t}}{{{\text{d}}v}} = \frac{1}{{\frac{{{\text{d}}v}}{{{\text{d}}t}}}}\), write down \(\frac{{{\text{d}}t}}{{{\text{d}}v}}\) in terms of \(v\).</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>You are told that Richard’s acceleration, \(a(t) = - 10 - 5v\), is always positive, for \(t \ge 10\).</p>
<p>Hence show that \(t = 10 + \frac{1}{5}\ln \left( {\frac{{98}}{{ - 2 - v}}} \right)\).</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>You are told that Richard’s acceleration, \(a(t) = - 10 - 5v\), is always positive, for \(t \ge 10\).</p>
<p>Hence find an expression for the velocity, \(v\), for \(t \ge 10\).</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>You are told that Richard’s acceleration, \(a(t) = - 10 - 5v\), is always positive, for \(t \ge 10\).</p>
<p>Find an expression for his height, \(s\), above the ground for \(t \ge 10\).</p>
<div class="marks">[5]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>You are told that Richard’s acceleration, \(a(t) = - 10 - 5v\), is always positive, for \(t \ge 10\).</p>
<p>Find the value of \(t\) when Richard lands on the ground.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>(i) \(a(t) = \frac{{{\text{d}}v}}{{{\text{d}}t}} = - 10{\text{ (m}}{{\text{s}}^{ - 2}}{\text{)}}\) <strong><em>A1</em></strong></p>
<p>(ii) \(t = 10 \Rightarrow v = - 100{\text{ (m}}{{\text{s}}^{ - 1}}{\text{)}}\) <strong><em>A1</em></strong></p>
<p>(iii) \(s = \int { - 10t{\text{d}}t = - 5{t^2}( + c)} \) <strong><em>M1A1</em></strong></p>
<p>\(s = 1000{\text{ for }}t = 0 \Rightarrow c = 1000\) <strong><em>(M1)</em></strong></p>
<p>\(s = - 5{t^2} + 1000\) <strong><em>A1</em></strong></p>
<p>at \(t = 10,{\text{ }}s = 500{\text{ (m)}}\) <strong><em>AG</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept use of definite integrals.</p>
<p><em><strong>[6 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{{\text{d}}t}}{{{\text{d}}v}} = \frac{1}{{( - 10 - 5v)}}\) <strong><em>A1</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>\(t = \int {\frac{1}{{ - 10 - 5v}}{\text{d}}v = - \frac{1}{5}\ln ( - 10 - 5v)( + c)} \) <strong><em>M1A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept equivalent forms using modulus signs.</p>
<p> </p>
<p>\(t = 10,{\text{ }}v = - 100\)</p>
<p>\(10 = - \frac{1}{5}\ln (490) + c\) <strong><em>M1</em></strong></p>
<p>\(c = 10 + \frac{1}{5}\ln (490)\) <strong><em>A1</em></strong></p>
<p>\(t = 10 + \frac{1}{5}\ln 490 - \frac{1}{5}\ln ( - 10 - 5v)\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept equivalent forms using modulus signs.</p>
<p> </p>
<p>\(t = 10 + \frac{1}{5}\ln \left( {\frac{{98}}{{ - 2 - v}}} \right)\) <strong><em>AG</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept use of definite integrals.</p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>\(t = \int {\frac{1}{{ - 10 - 5v}}{\text{d}}v = - \frac{1}{5}\int {\frac{1}{{2 + v}}{\text{d}}v = - \frac{1}{5}\ln \left| {2 + v} \right|( + c)} } \) <strong><em>M1A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept equivalent forms.</p>
<p> </p>
<p>\(t = 10,{\text{ }}v = - 100\)</p>
<p>\(10 = - \frac{1}{5}\ln \left| { - 98} \right| + c\) <strong><em>M1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> If \(\ln ( - 98)\) is seen do not award further A marks.</p>
<p> </p>
<p>\(c = 10 + \frac{1}{5}\ln 98\) <strong><em>A1</em></strong></p>
<p>\(t = 10 + \frac{1}{5}\ln 98 - \frac{1}{5}\ln \left| {2 + v} \right|\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept equivalent forms.</p>
<p> </p>
<p>\(t = 10 + \frac{1}{5}\ln \left( {\frac{{98}}{{ - 2 - v}}} \right)\) <strong><em>AG</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept use of definite integrals.</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>\(5(t - 10) = \ln \frac{{98}}{{( - 2 - v)}}\)</p>
<p>\(\frac{{2 + v}}{{98}} = - {{\text{e}}^{ - 5(t - 10)}}\) <strong><em>(M1)</em></strong></p>
<p>\(v = - 2 - 98{{\text{e}}^{ - 5(t - 10)}}\) <strong><em>A1</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{{\text{d}}s}}{{{\text{d}}t}} = - 2 - 98{{\text{e}}^{ - 5(t - 10)}}\)</p>
<p>\(s = - 2t + \frac{{98}}{5}{{\text{e}}^{ - 5(t - 10)}}( + k)\) <strong><em>M1A1</em></strong></p>
<p>at \(t = 10,{\text{ }}s = 500 \Rightarrow 500 = - 20 + \frac{{98}}{5} + k \Rightarrow k = 500.4\) <strong><em>M1A1</em></strong></p>
<p>\(s = - 2t + \frac{{98}}{5}{{\text{e}}^{ - 5(t - 10)}} + 500.4\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept use of definite integrals.</p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(t = 250{\text{ for }}s = 0\) <strong><em>(M1)A1</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<p><strong><em>Total [21 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Parts (i) and (ii) were well answered by most candidates.</p>
<p class="p1">In (iii) the constant of integration was often forgotten. Most candidates calculated the displacement and then used different strategies, mostly incorrect, to remove the negative sign from \( - 500\).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Surprisingly part (b) was not well done as the question stated the method. Many candidates simply wrote down \(\frac{{{\text{d}}v}}{{{\text{d}}t}}\) while others seemed unaware that \(\frac{{{\text{d}}v}}{{{\text{d}}t}}\) was the acceleration.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Part (c) was not always well done as it followed from (b) and at times there was very little to allow follow through. Once again some candidates started with what they were trying to prove. Among the candidates that attempted to integrate many did not consider the constant of integration properly.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">In part (d) many candidates ignored the answer given in (c) and attempted to manipulate different expressions.</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Part (e) was poorly answered: the constant of integration was often again forgotten and some inappropriate uses of Physics formulas assuming that the acceleration was constant were used. There was unclear thinking with the two sides of an equation being integrated with respect to different variables.</p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Although part (e) was often incorrect, some follow through marks were gained in part (f).</p>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>The curve \(C\) is defined by equation \(xy - \ln y = 1,{\text{ }}y > 0\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) in terms of \(x\) and \(y\).</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>Determine the equation of the tangent to \(C\) at the point \(\left( {\frac{2}{{\text{e}}},{\text{ e}}} \right)\)</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>\(y + x\frac{{{\text{d}}y}}{{{\text{d}}x}} - \frac{1}{y}\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\) <strong><em>M1A1A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>A1 </em></strong>for the first two terms, <strong><em>A1 </em></strong>for the third term and the 0.</p>
<p> </p>
<p>\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{{y^2}}}{{1 - xy}}\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept \(\frac{{ - {y^2}}}{{\ln y}}\).</p>
<p> </p>
<p><strong>Note:</strong> Accept \(\frac{{ - y}}{{x - \frac{1}{y}}}\).</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\({m_T} = \frac{{{{\text{e}}^2}}}{{1 - {\text{e}} \times \frac{2}{{\text{e}}}}}\) <strong><em>(M1)</em></strong></p>
<p>\({m_T} = - {{\text{e}}^2}\) <strong><em>(A1)</em></strong></p>
<p>\(y - {\text{e}} = - {{\text{e}}^2}x + 2{\text{e}}\)</p>
<p>\( - {{\text{e}}^2}x - y + 3{\text{e}} = 0\) or equivalent <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept \(y = - 7.39x + 8.15\).</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A skydiver jumps from a stationary balloon at a height of 2000 m above the ground.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Her velocity, \(v{\text{ m}}{{\text{s}}^{ - 1}}\) , <em>t</em> seconds after jumping, is given by \(v = 50(1 - {{\text{e}}^{ - 0.2t}})\) .</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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find her acceleration 10 seconds after jumping.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">How far above the ground is she 10 seconds after jumping?</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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(a = 10{{\text{e}}^{ - 0.2t}}\) <strong><em>(M1)(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">at \(t = 10\) , \(a = 1.35{\text{ }}({\text{m}}{{\text{s}}^{ - 2}})\,\,\,\,\,{\text{(accept }}10{e^{ - 2}})\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 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: 27.0px Helvetica;"><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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(d = \int_0^{10} {50(1 - {{\text{e}}^{ - 0.2t}}){\text{d}}t} \) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 283.83…\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so distance above ground \( = 1720{\text{ (m) (3 sf) }}\left( {{\text{accept 1716 (m)}}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{s}} = \int {50(1 - {{\text{e}}^{ - 0.2t}}){\text{d}}t = 50t + 250{{\text{e}}^{ - 0.2t}}( + c)} \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Taking <em>s</em> = 0 when <em>t</em> = 0 gives <em>c</em> = −250 <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">So when <em>t</em> = 10, <em>s</em> = 283.3...</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so distance above ground \( = 1720{\text{ (m) (3 sf) }}\left( {{\text{accept 1716 (m)}}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><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;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was generally correctly answered. A few candidates suffered the Arithmetic Penalty for giving their answer to more than 3sf. A smaller number were unable to differentiate the exponential function correctly. Part (b) was less well answered, many candidates not thinking clearly about the position and direction associated with the initial conditions.</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: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was generally correctly answered. A few candidates suffered the Arithmetic Penalty for giving their answer to more than 3sf. A smaller number were unable to differentiate the exponential function correctly. Part (b) was less well answered, many candidates not thinking clearly about the position and direction associated with the initial conditions.</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 \(f\) be a function defined by \(f(x) = x + 2\cos x\) , \(x \in \left[ {0,{\text{ }}2\pi } \right]\) . The diagram below </span><span style="font-family: times new roman,times; font-size: medium;">shows a region \(S\) bound by the graph of \(f\) and the line \(y = x\) .</span></p>
<p><br><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" alt></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;">A and C are the points of intersection of the line \(y = x\) and the graph of \(f\) , and B is </span><span style="font-family: times new roman,times; font-size: medium;">the minimum point of \(f\) .</span></p>
</div>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">(a) If A, B and C have <em>x</em>-coordinates \(a\frac{\pi }{2}\)</span><span style="font-family: times new roman,times; font-size: medium;">, \(b\frac{\pi }{6}\) and \(c\frac{\pi }{2}\)</span><span style="font-family: times new roman,times; font-size: medium;">, where \(a\) , \(b\), \(c \in \mathbb{N}\) ,</span> <span style="font-family: times new roman,times; font-size: medium;">find the values of \(a\) , \(b\) and \(c\) .<br></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(b) Find the range of \(f\) .<br></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(c) Find the equation of the normal to the graph of f at the point C, giving your </span><span style="font-family: times new roman,times; font-size: medium;">answer in the form \(y = px + q\) .<br></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(d) The region \(S\) is rotated through \({2\pi }\) about the <em>x</em>-axis to generate a solid.</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> (i) Write down an integral that represents the volume \(V\) of this solid.</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> (ii) Show that \(V = 6{\pi ^2}\)</span><span style="font-family: times new roman,times; font-size: medium;"> .</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;">(a) <strong>METHOD 1</strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">using GDC</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;">\(a = 1\)</span>, \(b = 5\), \(c = 3\) <em><strong>A1A2A1</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;">\(x = x + 2\cos x \Rightarrow \cos x = 0\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\( \Rightarrow x = \frac{\pi }{2}\), \(\frac{{3\pi }}{2}\) ... <em><strong>M1</strong></em></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;">\(a = 1\)</span>, \(c = 3\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(1 - 2\sin x = 0\) <em><strong>M1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\( \Rightarrow \sin x = \frac{1}{2} \Rightarrow x = \frac{\pi }{6}\) or \(\frac{{5\pi }}{6}\)</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;">\(b = 5\)</span> <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Final <em><strong>M1A1</strong></em> is independent of previous work.</span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[4 marks]</span></strong></em></p>
<p><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;">(b) </span><span style="font-family: times new roman,times; font-size: medium;">\(f\left( {\frac{{5\pi }}{6}} \right) = \frac{{5\pi }}{6} - \sqrt 3 \) </span><span style="font-family: times new roman,times; font-size: medium;"> (or \(0.886\)) <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(f(2\pi ) = 2\pi + 2\) (or \(8.28\)) <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">the range is </span><span style="font-family: times new roman,times; font-size: medium;">\(\left[ {\frac{{5\pi }}{6} - \sqrt 3 ,{\text{ }}2\pi + 2} \right]\) (</span><span style="font-family: times new roman,times; font-size: medium;">or [\(0.886\), \(8.28\)]) <em><strong>A1</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[3 marks]</span></strong></em></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;">(c) \(f'(x) = 1 - 2\sin x\) <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(f'\left( {\frac{{3\pi }}{6}} \right) = 3\) </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;">gradient of normal \( = - \frac{1}{3}\)</span><span style="font-family: times new roman,times; font-size: medium;"> </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,times; font-size: medium;">equation of the normal is </span><span style="font-family: times new roman,times; font-size: medium;">\(y - \frac{{3\pi }}{2} = - \frac{1}{3}\left( {x - \frac{{3\pi }}{2}} \right)\)</span><span style="font-family: times new roman,times; font-size: medium;"> </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,times; font-size: medium;">\(y = - \frac{1}{3}x + 2\pi \) </span><span style="font-family: times new roman,times; font-size: medium;"> (or equivalent decimal values) <em><strong>A1 N4</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[5 marks]</span></strong></em></p>
<p><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;">(d) (i) \(V = \pi \int_{\frac{\pi }{2}}^{\frac{{3\pi }}{2}} {\left( {{x^2} - {{\left( {x + 2\cos x} \right)}^2}} \right)} {\text{d}}x\) </span><span style="font-family: times new roman,times; font-size: medium;">(or equivalent) <em><strong>A1A1</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 limits and <em><strong>A1</strong></em> for \(\pi \) and integrand.</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) \(V = \pi \int_{\frac{\pi }{2}}^{\frac{{3\pi }}{2}} {\left( {{x^2} - {{\left( {x + 2\cos x} \right)}^2}} \right)} {\text{d}}x\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\( = - \pi \int_{\frac{\pi }{2}}^{\frac{{3\pi }}{2}} {\left( {4x\cos x + 4{{\cos }^2}x} \right)} {\text{d}}x\)<br></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">using integration by parts <em><strong>M1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">and the identity \(4{\cos ^2}x = 2\cos 2x + 2\) , <em><strong>M1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(V = - \pi \left[ {\left( {4x\sin x + 4\cos x} \right) + \left( {\sin 2x + 2x} \right)} \right]_{\frac{\pi }{2}}^{\frac{{3\pi }}{2}}\) </span><strong><em><span style="font-family: times new roman,times; font-size: medium;">A1A1</span></em></strong></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Award <em><strong>A1</strong></em> for \({4x\sin x + 4\cos x}\) and <em><strong>A1</strong></em> for sin \({2x + 2x}\) .</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;">\( = - \pi \left[ {\left( {6\pi \sin \frac{{3\pi }}{2} + 4\cos \frac{{3\pi }}{2} + \sin 3\pi + 3\pi } \right) - \left( {2\pi sin\frac{\pi }{2} + 4\cos \frac{\pi }{2} + \sin \pi + \pi } \right)} \right]\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\( = - \pi \left( { - 6\pi + 3\pi - \pi } \right)\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\( = 6{\pi ^2}\) <em><strong>AG N0</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Do not accept numerical answers.</span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[7 marks]</span></strong></em></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;">Total [19 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;">Generally there were many good attempts to this, more difficult, question. A number of </span><span style="font-family: times new roman,times; font-size: medium;">students found \(b\) to be equal to 1, rather than 5. In the final part few students could </span><span style="font-family: times new roman,times; font-size: medium;">successfully work through the entire integral successfully.</span></p>
</div>
<br><hr><br><div class="specification">
<p>A curve <em>C</em> is given by the implicit equation \(x + y - {\text{cos}}\left( {xy} \right) = 0\).</p>
</div>
<div class="specification">
<p>The curve \(xy = - \frac{\pi }{2}\) intersects <em>C</em> at P and Q.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = - \left( {\frac{{1 + y\,{\text{sin}}\left( {xy} \right)}}{{1 + x\,{\text{sin}}\left( {xy} \right)}}} \right)\).</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>Find the coordinates of P and Q.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that the gradients of the tangents to <em>C</em> at P and Q are <em>m</em><sub>1</sub> and <em>m</em><sub>2</sub> respectively, show that <em>m</em><sub>1</sub> × <em>m</em><sub>2</sub> = 1.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of the three points on <em>C</em>, nearest the origin, where the tangent is parallel to the line \(y = - x\).</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>attempt at implicit differentiation <em><strong>M1</strong></em></p>
<p>\(1 + \frac{{{\text{d}}y}}{{{\text{d}}x}} + \left( {y + x\frac{{{\text{d}}y}}{{{\text{d}}x}}} \right){\text{sin}}\left( {xy} \right) = 0\) <em><strong>A1M1A1</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>A1</strong> </em>for first two terms. Award <em><strong>M1</strong> </em>for an attempt at chain rule <em><strong>A1</strong> </em>for last term.</p>
<p>\(\left( {1 + x\,{\text{sin}}\left( {xy} \right)} \right)\frac{{{\text{d}}y}}{{{\text{d}}x}} = - 1 - y\,{\text{sin}}\left( {xy} \right)\) <em><strong>A1</strong></em></p>
<p>\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = - \left( {\frac{{1 + y\,{\text{sin}}\left( {xy} \right)}}{{1 + x\,{\text{sin}}\left( {xy} \right)}}} \right)\) <em><strong>AG</strong></em></p>
<p><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p>when \(xy = - \frac{\pi }{2},\,\,{\text{cos}}\,xy = 0\) <em><strong>M1</strong></em></p>
<p>\( \Rightarrow x + y = 0\) <em><strong>(A1)</strong></em></p>
<p><strong>OR</strong></p>
<p>\(x - \frac{\pi }{{2x}} - {\text{cos}}\left( {\frac{{ - \pi }}{2}} \right) = 0\) or equivalent <em><strong>M1</strong></em></p>
<p>\(x - \frac{\pi }{{2x}} = 0\) <em><strong>(A1)</strong></em></p>
<p><strong>THEN</strong></p>
<p>therefore \({x^2} = \frac{\pi }{2}\left( {x = \pm \sqrt {\frac{\pi }{2}} } \right)\left( {x = \pm 1.25} \right)\) <em><strong>A1</strong></em></p>
<p>\({\text{P}}\left( {\sqrt {\frac{\pi }{2}} ,\, - \sqrt {\frac{\pi }{2}} } \right),\,\,{\text{Q}}\left( { - \sqrt {\frac{\pi }{2}} ,\,\sqrt {\frac{\pi }{2}} } \right)\) <strong>or</strong> \(P\left( {1.25,\, - 1.25} \right),\,Q\left( { - 1.25,\,1.25} \right)\) <em><strong>A1</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>m</em><sub>1 </sub>= \( - \left( {\frac{{1 - \sqrt {\frac{\pi }{2}} \times - 1}}{{1 + \sqrt {\frac{\pi }{2}} \times - 1}}} \right)\) <em><strong>M1A1</strong></em></p>
<p><em>m</em><sub>2 </sub>= \( - \left( {\frac{{1 + \sqrt {\frac{\pi }{2}} \times - 1}}{{1 - \sqrt {\frac{\pi }{2}} \times - 1}}} \right)\) <em><strong>A1</strong></em></p>
<p><em>m</em><sub>1 </sub><em>m</em><sub>2 </sub>= 1 <em><strong>AG</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>M1A0A0</strong> </em>if decimal approximations are used.<br><strong>Note:</strong> No <strong>FT</strong> applies.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>equate derivative to −1 <em><strong>M1</strong></em></p>
<p>\(\left( {y - x} \right){\text{sin}}\left( {xy} \right) = 0\) <em><strong>(A1)</strong></em></p>
<p>\(y = x,\,{\text{sin}}\left( {xy} \right) = 0\) <em><strong>R1</strong></em></p>
<p>in the first case, attempt to solve \(2x = {\text{cos}}\left( {{x^2}} \right)\) <em><strong>M1</strong></em></p>
<p>(0.486,0.486) <strong>A1</strong></p>
<p>in the second case, \({\text{sin}}\left( {xy} \right) = 0 \Rightarrow xy = 0\) and \(x + y = 1\) <em><strong>(M1)</strong></em></p>
<p>(0,1), (1,0) <em><strong> A1</strong></em></p>
<p><em><strong>[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;">
[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 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;">Consider the curve with equation \({\left( {{x^2} + {y^2}} \right)^2} = 4x{y^2}\).</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;">Use implicit differentiation to find an expression for \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\).</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 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 equation of the normal to the curve at the point (1, 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 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>METHOD 1</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;">expanding the brackets first:</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;">\({x^4} + 2{x^2}{y^2} + {y^4} = 4x{y^2}\) <strong><em>M1</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;">\(4{x^3} + 4x{y^2} + 4{x^2}y\frac{{{\text{d}}y}}{{{\text{d}}x}} + 4{y^3}\frac{{{\text{d}}y}}{{{\text{d}}x}} = 4{y^2} + 8xy\frac{{{\text{d}}y}}{{{\text{d}}x}}\) <strong><em>M1A1A1</em></strong></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> Award <strong><em>M1 </em></strong>for an attempt at implicit differentiation.</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;"> Award <strong><em>A1 </em></strong>for each side correct.</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;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{ - {x^3} - x{y^2} + {y^2}}}{{x{y^2} - 2xy + {y^3}}}\) or equivalent <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;"><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;">\(2\left( {{x^2} + {y^2}} \right)\left( {2x + 2y\frac{{{\text{d}}y}}{{{\text{d}}x}}} \right) = 4{y^2} + 8xy\frac{{{\text{d}}y}}{{{\text{d}}x}}\) <strong><em>M1A1A1</em></strong></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> Award <strong><em>M1 </em></strong>for an attempt at implicit differentiation.</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;"> Award <strong><em>A1 </em></strong>for each side correct.</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;">\(\left( {{x^2} + {y^2}} \right)\left( {x + y\frac{{{\text{d}}y}}{{{\text{d}}x}}} \right) = {y^2} + 2xy\frac{{{\text{d}}y}}{{{\text{d}}x}}\)</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;">\({x^3} + {x^2}y\frac{{{\text{d}}y}}{{{\text{d}}x}} + {y^2}x + {y^3}\frac{{{\text{d}}y}}{{{\text{d}}x}} = {y^2} + 2xy\frac{{{\text{d}}y}}{{{\text{d}}x}}\) <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;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{ - {x^3} - x{y^2} + {y^2}}}{{y{x^2} - 2xy + {y^3}}}\) or equivalent <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;"><strong><em>[5 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: 21.0px Helvetica;"><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 Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">at (1, 1), \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) is undefined <strong><em>M1A1</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;">\(y = 1\) <strong><em>A1</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>METHOD 2</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;">gradient of normal \( = - \frac{1}{{\frac{{{\text{d}}y}}{{{\text{d}}x}}}} = - \frac{{\left( {y{x^2} - 2xy + {y^3}} \right)}}{{\left( { - {x^3} - x{y^2} + {y^2}} \right)}}\) <strong><em>M1</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;">at (1, 1) gradient \( = 0\) <strong><em>A1</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;">\(y = 1\) <strong><em>A1</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>[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;">An open glass is created by rotating the curve \(y = {x^2}\) , defined in the domain \(x \in [0,10]\), \(2\pi \) radians about the <em>y</em>-axis. Units on the coordinate axes are defined to be in centimetres.</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;">When the glass contains water to a height \(h\) cm, find the volume \(V\) of water in terms of \(h\) .</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;">If the water in the glass evaporates at the rate of 3 cm<sup>3</sup> per hour for each cm<sup>2</sup> of exposed surface area of the water, show that,</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\(\frac{{{\text{d}}V}}{{{\text{d}}t}} = - 3\sqrt {2\pi V} \)</span><span style="font-family: times new roman,times; font-size: medium;"> , where \(t\) is measured in hours.</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;">If the glass is filled completely, how long will it take for all the water to evaporate?</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">volume \( = \pi \int_0^h {{x^2}{\text{d}}y} \) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">(M1)</span></strong></em></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\(\pi \int_0^h {y{\text{d}}y} \) </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,times; font-size: medium;">\(\pi \left[ {\frac{{{y^2}}}{2}} \right]_0^h = \frac{{\pi {h^2}}}{2}\) <em><strong>A1</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;">\(\frac{{{\text{d}}V}}{{{\text{d}}t}} = - 3 \times \)</span><span style="font-family: times new roman,times; font-size: medium;"> surface area </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;">surface area \( = \pi {x^2}\) <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\( = \pi h\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(V = \frac{{\pi {h^2}}}{2} \Rightarrow h\sqrt {\frac{{2V}}{\pi }} \) <em><strong>M1A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\frac{{{\text{d}}V}}{{{\text{d}}t}} = - 3\pi \sqrt {\frac{{2V}}{\pi }} \) </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;">\(\frac{{{\text{d}}V}}{{{\text{d}}t}} = - 3\sqrt {2\pi V} \) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;"> AG</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Assuming that </span><span style="font-family: times new roman,times; font-size: medium;">\(\frac{{{\text{d}}h}}{{{\text{d}}t}} = - 3\)</span><span style="font-family: times new roman,times; font-size: medium;"> without justification gains no marks.</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.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">\({V_0} = 5000\pi \) (\( = 15700\) cm<sup>3</sup>) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\frac{{{\text{d}}V}}{{{\text{d}}t}} = - 3\sqrt {2\pi V} \)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">attempting to separate variables <em><strong>M1</strong></em></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;">\(\int {\frac{{{\text{d}}V}}{{\sqrt V }}} = - 3\sqrt {2\pi } \int {{\text{d}}t} \) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(2\sqrt V = - 3\sqrt {2\pi t} + c\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(c = 2\sqrt {5000\pi } \) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(V = 0\) <em><strong>M1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\( \Rightarrow t = \frac{2}{3}\sqrt {\frac{{5000\pi }}{{2\pi }}} = 33\frac{1}{3}\) hours </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1</span></strong></em></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;"> </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;">\(\int_{5000\pi }^0 {\frac{{{\text{d}}V}}{{\sqrt V }}} = - 3\sqrt {2\pi } \int_0^T {{\text{d}}t} \) <em><strong>M1A1A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Award <em><strong>M1</strong></em> for attempt to use definite integrals, <em><strong>A1</strong></em> for correct limits </span><span style="font-family: times new roman,times; font-size: medium;">and <em><strong>A1</strong></em> for correct integrands.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\left[ {2\sqrt V } \right]_{5000\pi }^0 = 3\sqrt {2\pi } T\) </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;">\(T = \frac{2}{3}\sqrt {\frac{{5000\pi }}{{2\pi }}} = 33\frac{1}{3}\) hours</span> <em><strong><span style="font-family: times new roman,times; font-size: medium;">A1</span></strong></em></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;">[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;">This question was found to be challenging by many candidates and there were very few completely correct solutions. Many candidates did not seem able to find the volume of revolution when taken about the <em>y</em>-axis in (a). Candidates did not always recognize that part (b) did not involve related rates. Those candidates who attempted the question made some progress by separating the variables and integrating in (c) but very few were able to identify successfully the values necessary to find the correct answer.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was found to be challenging by many candidates and there were very few completely correct solutions. Many candidates did not seem able to find the volume of revolution when taken about the <em>y</em>-axis in (a). Candidates did not always recognize that part (b) did not involve related rates. Those candidates who attempted the question made some progress by separating the variables and integrating in (c) but very few were able to identify successfully the values necessary to find the correct answer.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was found to be challenging by many candidates and there were very few completely correct solutions. Many candidates did not seem able to find the volume of revolution when taken about the <em>y</em>-axis in (a). Candidates did not always recognize that part (b) did not involve related rates. Those candidates who attempted the question made some progress by separating the variables and integrating in (c) but very few were able to identify successfully the values necessary to find the correct answer.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Xavier, the parachutist, jumps out of a plane at a height of \(h\) metres above the ground. After free falling for 10 seconds his parachute opens. His velocity, \(v\,{\text{m}}{{\text{s}}^{ - 1}}\), \(t\) seconds after jumping from the plane, can be modelled by the function</p>
<p>\(v(t) = \left\{ {\begin{array}{*{20}{l}} {9.8t{\text{,}}}&{0 \leqslant t \leqslant 10} \\ {\frac{{98}}{{\sqrt {1 + {{(t - 10)}^2}} }},}&{t > 10} \end{array}} \right.\)</p>
</div>
<div class="specification">
<p>His velocity when he reaches the ground is \(2.8{\text{ m}}{{\text{s}}^{ - 1}}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find his velocity when \(t = 15\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the vertical distance Xavier travelled in the first 10 seconds.</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>Determine the value of \(h\).</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(v(15) = \frac{{98}}{{\sqrt {1 + {{(15 - 10)}^2}} }}\) <strong><em>(M1)</em></strong></p>
<p>\(v(15) = 19.2{\text{ }}({\text{m}}{{\text{s}}^{ - 1}})\) <strong><em>A1</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\int\limits_0^{10} {9.8t\,{\text{d}}t} \) <strong><em>(M1)</em></strong></p>
<p>\( = 490{\text{ }}({\text{m}})\) <strong><em>A1</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>\(\frac{{98}}{{\sqrt {1 + {{(t - 10)}^2}} }} = 2.8\) <strong><em>(M1)</em></strong></p>
<p>\(t = 44.985 \ldots {\text{ }}({\text{s}})\) <strong><em>A1</em></strong></p>
<p>\(h = 490 + \int\limits_{10}^{44.9...} {\frac{{98}}{{\sqrt {1 + {{(t - 10)}^2}} }}{\text{d}}t} \) <strong><em>(M1)(A1)</em></strong></p>
<p>\(h = 906{\text{ (m}})\) <strong><em>A1</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The function \(f(x) = 3\sin x + 4\cos x\) is defined for \(0 < x < 2\pi \) .</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 Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Write down the coordinates of the minimum point on the graph of <em>f </em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">The points \({\text{P}}(p,{\text{ }}3)\) and \({\text{Q}}(q,{\text{ }}3){\text{, }}q > p\), lie on the graph of \(y = f(x)\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Find <em>p </em>and <em>q </em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the coordinates of the point, on \(y = f(x)\) , where the gradient of the graph is 3.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the coordinates of the point of intersection of the normals to the graph at the points P and Q.</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;">\((3.79, - 5)\) <span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>A1 </em></strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><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.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(p = 1.57{\text{ or }}\frac{\pi }{2},{\text{ }}q = 6.00\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[2 marks]</span><br></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;">\(f'(x) = 3\cos x - 4\sin x\) <strong><em>(M1)(A1)</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(3\cos x - 4\sin x = 3 \Rightarrow x = 4.43...\) <strong><em>(A1)</em></strong></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;">Coordinates are \((4.43, -4)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[4 marks]</span><br></em></strong></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;">\({m_{{\text{normal}}}} = \frac{1}{{{m_{{\text{tangent}}}}}}\) <strong><em>(M1)</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium; line-height: normal;">gradient at P is \( - 4\) so gradient of normal at P is \(\frac{1}{4}\) </span><strong style="font-family: 'times new roman', times; font-size: medium; line-height: normal;"><em>(A1)</em></strong></p>
<p><span style="font-family: 'times new roman', times; font-size: medium; line-height: normal;">gradient at Q is 4 so gradient of normal at Q is \( - \frac{1}{4}\) </span><strong style="font-family: 'times new roman', times; font-size: medium; line-height: normal;"><em>(A1)</em></strong></p>
<p><span style="font-family: 'times new roman', times; font-size: medium; line-height: normal;">equation of normal at P is \(y - 3 = \frac{1}{4}(x - 1.570...){\text{ }}({\text{or }}y = 0.25x + 2.60...)\) </span><strong style="font-family: 'times new roman', times; font-size: medium; line-height: normal;"><em>(M1)</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">equation of normal at Q is \(y - 3 = \frac{1}{4}(x - 5.999...){\text{ }}({\text{or }}y = -0.25x + \underbrace {4.499...}_{})\) <strong><em>(M1)</em></strong></span><span style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 14px; line-height: 20px;"> </span></p>
<p><strong style="font-family: 'times new roman', times; font-size: medium; line-height: normal;">Note: </strong><span style="font-family: 'times new roman', times; font-size: medium; line-height: normal;">Award the previous two </span><strong style="font-family: 'times new roman', times; font-size: medium; line-height: normal;"><em>M1 </em></strong><span style="font-family: 'times new roman', times; font-size: medium; line-height: normal;">even if the gradients are incorrect in \(y - b = m(x - a)\) where \((a,b)\) are coordinates of P and Q (or in \(y = mx + c\) with </span><em style="font-family: 'times new roman', times; font-size: medium; line-height: normal;">c </em><span style="font-family: 'times new roman', times; font-size: medium; line-height: normal;">determined using coordinates of P and Q.</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;">intersect at \((3.79,{\text{ }}3.55)\) <strong><em>A1A1</em></strong></span> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>N2 </em></strong>for 3.79 without other working.</span><span style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 14px; line-height: 20px;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 14px; line-height: 20px;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]<br></em></strong></span></p>
<p> </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="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Candidates answered parts (a) and (b) of this question well and, although many were also successful in part (c), just a few candidates gave answers to the required level of accuracy. Part d) was rather challenging for many candidates. The most common errors among the candidates who attempted this question were the confusion between tangents and normals and incorrect final answers due to premature rounding.</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: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Candidates answered parts (a) and (b) of this question well and, although many were also successful in part (c), just a few candidates gave answers to the required level of accuracy. Part d) was rather challenging for many candidates. The most common errors among the candidates who attempted this question were the confusion between tangents and normals and incorrect final answers due to premature rounding.</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: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Candidates answered parts (a) and (b) of this question well and, although many were also successful in part (c), just a few candidates gave answers to the required level of accuracy. Part d) was rather challenging for many candidates. The most common errors among the candidates who attempted this question were the confusion between tangents and normals and incorrect final answers due to premature rounding.</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: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Candidates answered parts (a) and (b) of this question well and, although many were also successful in part (c), just a few candidates gave answers to the required level of accuracy. Part d) was rather challenging for many candidates. The most common errors among the candidates who attempted this question were the confusion between tangents and normals and incorrect final answers due to premature rounding.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the equation of the normal to the curve \({x^3}{y^3} - xy = 0\) at the point (1, 1).</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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x^3}{y^3} - xy = 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(3{x^2}{y^3} + 3{x^3}{y^2}y' - y - xy' = 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1</em></strong> for correctly differentiating each term.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 1,{\text{ }}y = 1\) \(3 + 3y' - 1 - y' = 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> \(2y' = - 2\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> \(y' = - 1\) <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">gradient of normal = 1 <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">equation of the normal \(y - 1 = x - 1\) <strong><em>A1 N2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(y = x\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A2R5</em></strong> for correct answer and correct justification.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This implicit differentiation question was well answered by most candidates with many achieving full marks. Some candidates made algebraic errors which prevented them from scoring well in this question.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Other candidates realised that the equation of the curve could be simplified although the simplification was seldom justified.</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">A curve is defined \({x^2} - 5xy + {y^2} = 7\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{5y - 2x}}{{2y - 5x}}\).</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 equation of the normal to the curve at the point \((6,{\text{ }}1)\).</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">Find the distance between the two points on the curve where each tangent is parallel to the line \(y = x\).</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 class="p1">attempt at implicit differentiation <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p2">\(2x - 5x\frac{{{\text{d}}y}}{{{\text{d}}x}} - 5y + 2y\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1A1</em></strong></span></p>
<p class="p3"> </p>
<p class="p2"><strong>Note:</strong> <span class="Apple-converted-space"> </span><strong><em>A1</em></strong> for differentiation of \({x^2} - 5xy\), <strong><em>A1</em></strong> for differentiation of \({y^2}\) and \(7\).</p>
<p class="p3"> </p>
<p class="p2">\(2x - 5y + \frac{{{\text{d}}y}}{{{\text{d}}x}}(2y - 5x) = 0\)</p>
<p class="p2">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{5y - 2x}}{{2y - 5x}}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>AG</em></strong></span></p>
<p class="p2"><span class="s1"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{5 \times 1 - 2 \times 6}}{{2 \times 1 - 5 \times 6}} = \frac{1}{4}\) <strong><em>A1</em></strong></p>
<p>gradient of normal \( = - 4\) <strong><em>A1</em></strong></p>
<p>equation of normal \(y = - 4x + c\) <strong><em>M1</em></strong></p>
<p>substitution of \((6,{\text{ }}1)\)</p>
<p>\(y = - 4x + 25\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept \(y - 1 = - 4(x - 6)\)</p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>setting \(\frac{{5y - 2x}}{{2y - 5x}} = 1\) <strong><em>M1</em></strong></p>
<p>\(y = - x\) <strong><em>A1</em></strong></p>
<p>substituting into original equation <strong><em>M1</em></strong></p>
<p>\({x^2} + 5{x^2} + {x^2} = 7\) <strong><em>(A1)</em></strong></p>
<p>\(7{x^2} = 7\)</p>
<p>\(x = \pm 1\) <strong><em>A1</em></strong></p>
<p>points \((1,{\text{ }} - 1)\) and \(( - 1,{\text{ }}1)\) <strong><em>(A1)</em></strong></p>
<p>distance \( = \sqrt 8 \;\;\;\left( { = 2\sqrt 2 } \right)\) <strong><em>(M1)A1</em></strong></p>
<p><strong><em>[8 marks]</em></strong></p>
<p><strong><em>Total [15 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="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The point P, with coordinates \((p,{\text{ }}q)\) , lies on the graph of \({x^{\frac{1}{2}}} + {y^{\frac{1}{2}}} = {a^{\frac{1}{2}}}\) , \(a > 0\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The tangent to the curve at P cuts the axes at (0, <em>m</em>) and (<em>n</em>, 0) . Show that <em>m</em> + <em>n</em> = <em>a</em> .</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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x^{\frac{1}{2}}} + {y^{\frac{1}{2}}} = {a^{\frac{1}{2}}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{1}{2}{x^{ - \frac{1}{2}}} + \frac{1}{2}{y^{ - \frac{1}{2}}}\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = - \frac{{\frac{1}{{2\sqrt x }}}}{{\frac{1}{{2\sqrt y }}}} = - \sqrt {\frac{y}{x}} \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Accept \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 1 - \frac{{{a^{\frac{1}{2}}}}}{{{x^{\frac{1}{2}}}}}\) from making </span><em style="font-family: 'times new roman', times; font-size: medium;">y</em><span style="font-family: 'times new roman', times; font-size: medium;"> the subject of the equation, and all correct subsequent working</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">therefore the gradient at the point P is given by</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = - \sqrt {\frac{q}{p}} \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">equation of tangent is \(y - q = - \sqrt {\frac{q}{p}} (x - p)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\((y = - \sqrt {\frac{q}{p}} x + q + \sqrt q \sqrt p )\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>x</em>-intercept: <em>y</em> = 0, \(n = \frac{{q\sqrt p }}{{\sqrt q }} + p = \sqrt q \sqrt p + p\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>y</em>-intercept: <em>x</em> = 0, \(m = \sqrt q \sqrt p + q\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(n + m = \sqrt q \sqrt p + p + \sqrt q \sqrt p + q\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 2\sqrt q \sqrt p + p + q\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {\left( {\sqrt p + \sqrt q } \right)^2}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = a\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><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">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates were able to perform the implicit differentiation. Few gained any further marks.</span></p>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the differential equation \(y\frac{{{\text{d}}y}}{{{\text{d}}x}} = \cos 2x\).</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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Show that the function \(y = \cos x + \sin x\) satisfies the differential equation.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Find the general solution of the differential equation. Express your solution in the form \(y = f(x)\), involving a constant of integration.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) For which value of the constant of integration does your solution coincide with the function given in part (i)?</span></p>
<div class="marks">[10]</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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A different solution of the differential equation, satisfying <em>y</em> = 2 when \(x = \frac{\pi }{4}\), defines a curve <em>C</em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Determine the equation of <em>C</em> in the form \(y = g(x)\) , and state the range of the function <em>g</em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A region <em>R</em> in the <em>xy</em> plane is bounded by <em>C</em>, the <em>x</em>-axis and the vertical lines <em>x</em> = 0 and \(x = \frac{\pi }{2}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Find the area of <em>R</em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) Find the volume generated when that part of <em>R</em> above the line <em>y</em> = 1 is rotated about the <em>x</em>-axis through \(2\pi \) radians.</span></p>
<div class="marks">[12]</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: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) <strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = - \sin x + \cos x\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(y\frac{{{\text{d}}y}}{{{\text{d}}x}} = (\cos x + \sin x)( - \sin x + \cos x)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {\cos ^2}x - {\sin ^2}x\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \cos 2x\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><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: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({y^2} = {(\sin x + \cos x)^2}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2y\frac{{{\text{d}}y}}{{{\text{d}}x}} = 2(\cos x + \sin x)(\cos x - \sin x)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(y\frac{{{\text{d}}y}}{{{\text{d}}x}} = {\cos ^2}x - {\sin ^2}x\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \cos 2x\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) attempting to separate variables \(\int {y{\text{ d}}y = \int {\cos 2x{\text{ d}}x} } \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{1}{2}{y^2} = \frac{1}{2}\sin 2x + C\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Award </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for a correct LHS and </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for a correct RHS.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><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: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(y = \pm {(\sin 2x + A)^{\frac{1}{2}}}\) </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) \(\sin 2x + A \equiv {(\cos x + \sin x)^2}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({(\cos x + \sin x)^2} = {\cos ^2}x + 2\sin x\cos x + {\sin ^2}x\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">use of \(\sin 2x \equiv 2\sin x\cos x\). <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>A</em> = 1 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[10 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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) substituting \(x = \frac{\pi }{4}\) and <em>y</em> = 2 into \(y = {(\sin 2x + A)^{\frac{1}{2}}}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so \(g(x) = {(\sin 2x + 3)^{\frac{1}{2}}}\). <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">range <em>g</em> is \(\left[ {\sqrt 2 ,{\text{ }}2} \right]\) <strong><em>A1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Accept [1.41, 2]. Award </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for each correct endpoint and </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for the correct closed interval.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \(\int_0^{\frac{\pi }{2}} {{{(\sin 2x + 3)}^{\frac{1}{2}}}{\text{d}}x} \) </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>(M1)(A1)</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">= 2.99 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) \(\pi \int_0^{\frac{\pi }{2}} {(\sin 2x + 3){\text{d}}x - \pi (1)\left( {\frac{\pi }{2}} \right)} \) (or equivalent) <strong><em>(M1)(A1)(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Award </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>(M1)(A1)(A1)</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for \(\pi \int_0^{\frac{\pi }{2}} {(\sin 2x + 2){\text{d}}x} \)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 17.946 - 4.935{\text{ }}( = \frac{\pi }{2}(3\pi + 2) - \pi \left( {\frac{\pi }{2}} \right))\) </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Award </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for \(\pi (\pi + 1)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[12 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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was not well done and was often difficult to mark. In part (a) (i), a large number of candidates did not know how to verify a solution, \(y(x)\), to the given differential equation. Instead, many candidates attempted to solve the differential equation. In part (a) (ii), a large number of candidates began solving the differential equation by correctly separating the variables but then either neglected to add a constant of integration or added one as an afterthought. Many simple algebraic and basic integral calculus errors were seen. In part (a) (iii), many candidates did not realize that the solution given in part (a) (i) and the general solution found in part (a) (ii) were to be equated. Those that did know to equate these two solutions, were able to square both solution forms and correctly use the trigonometric identity \(\sin 2x = 2\sin x\cos x\). Many of these candidates however started with incorrect solution(s).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (b), a large number of candidates knew how to find a required area and a required volume of solid of revolution using integral calculus. Many candidates, however, used incorrect expressions obtained in part (a). In part (b) (ii), a number of candidates either neglected to state ‘π’ or attempted to calculate the volume of a solid of revolution of ‘radius’ \(f(x) - g(x)\).</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;">By using the substitution \(x = 2\tan u\), show that \(\int {\frac{{{\text{d}}x}}{{{x^2}\sqrt {{x^2} + 4} }} = \frac{{ - \sqrt {{x^2} + 4} }}{{4x}} + C} \).</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: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</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;">\(\frac{{{\text{d}}x}}{{{\text{d}}u}} = 2\,{\text{se}}{{\text{c}}^2}u\) <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;">\(\int {\frac{{2\,{\text{se}}{{\text{c}}^2}u{\text{d}}u}}{{4{{\tan }^2}u\sqrt {4 + 4{{\tan }^2}u} }}} \) <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;">\(\int {\frac{{2\,{\text{se}}{{\text{c}}^2}u{\text{d}}u}}{{4{{\tan }^2}u \times 2\,\sec u}}} \) \(( = \int {\frac{{{\text{d}}u}}{{4{{\sin }^2}u\sqrt {{{\tan }^2}u + 1} }}{\text{ or }} = \int {\frac{{2\,{\text{se}}{{\text{c}}^2}u{\text{d}}u}}{{4{{\tan }^2}u\sqrt {4{{\sec }^2}u} }})} } \) <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;"><strong>OR</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;">\(u = \arctan \frac{x}{2}\)</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;">\(\frac{{{\text{d}}u}}{{{\text{d}}x}} = \frac{2}{{{x^2} + 4}}\) <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;">\(\int {\frac{{\sqrt {4{{\tan }^2}u + 4{\text{d}}u} }}{{2 \times 4{{\tan }^2}u}}} \) <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;">\(\int {\frac{{2\,\sec u{\text{d}}u}}{{2 \times 4{{\tan }^2}u}}} \) <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;"><strong>THEN</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;">\( = \frac{1}{4}\int {\frac{{\sec u{\text{d}}u}}{{{{\tan }^2}u}}} \)</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;">\( = \frac{1}{4}\int {{\text{cosec}}\,u\cot u{\text{d}}u{\text{ }}\left( { = \frac{1}{4}\int {\frac{{\cos u}}{{{{\sin }^2}u}}{\text{d}}u} } \right)} \) <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;">\( = - \frac{1}{4}{\text{cosec}}\,u( + C){\text{ }}\left( { = - \frac{1}{{4\sin u}}( + C)} \right)\) <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;">use of either \(u = \frac{x}{2}\) or an appropriate trigonometric identity <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;">either \(\sin u = \frac{x}{{\sqrt {{x^2} + 4} }}\) or \({\text{cosec}}\,u = \frac{{\sqrt {{x^2} + 4} }}{x}\) (or equivalent) <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;">\( = \frac{{ - \sqrt {{x^2} + 4} }}{{4x}}( + C)\) <strong><em>AG</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>[7 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates found this a challenging question. A large majority of candidates were able to change variable from <em>x</em> to <em>u</em> but were not able to make any further progress.</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The function <em>f</em> is defined by \(f(x) = x\sqrt {9 - {x^2}} + 2\arcsin \left( {\frac{x}{3}} \right)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Write down the largest possible domain, for each of the two terms of the function, <em>f</em> , and hence state the largest possible domain, <em>D</em> , for <em>f</em> .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Find the volume generated when the region bounded by the curve <em>y</em> = <em>f</em>(<em>x</em>) , the <em>x</em>-axis, the <em>y</em>-axis and the line <em>x</em> = 2.8 is rotated through \(2\pi \) radians about the <em>x</em>-axis.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) Find \(f'(x)\) in simplified form.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(d) <strong>Hence</strong> show that \(\int_{ - p}^p {\frac{{11 - 2{x^2}}}{{\sqrt {9 - {x^2}} }}} {\text{d}}x = 2p\sqrt {9 - {p^2}} + 4\arcsin \left( {\frac{p}{3}} \right)\), where \(p \in D\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(e) Find the value of <em>p</em> which maximises the value of the integral in (d).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(f) (i) Show that \(f''(x) = \frac{{x(2{x^2} - 25)}}{{{{(9 - {x^2})}^{\frac{3}{2}}}}}\).</span></p>
<p style="margin: 0px 0px 0px 30px; font: 22px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> (ii) Hence justify that <em>f</em>(<em>x</em>) has a point of inflexion at <em>x</em> = 0 , but not at \(x = \pm \sqrt {\frac{{25}}{2}} \) .</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: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) For \(x\sqrt {9 - {x^2}} \), \( - 3 \leqslant x \leqslant 3\) and for \(2\arcsin \left( {\frac{x}{3}} \right)\), \( - 3 \leqslant x \leqslant 3\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow D{\text{ is }} - 3 \leqslant x \leqslant 3\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><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: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) \(V = \pi \int_0^{2.8} {{{\left( {x\sqrt {9 - {x^2}} = 2\arcsin \frac{x}{3}} \right)}^2}{\text{d}}x} \) <em><strong>M1A1</strong></em><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">= 181<span style="font: 20.0px Helvetica;"> </span><strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><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: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = {(9 - {x^2})^{\frac{1}{2}}} - \frac{{{x^2}}}{{{{(9 - {x^2})}^{\frac{1}{2}}}}} + \frac{{\frac{2}{3}}}{{\sqrt {1 - \frac{{{x^2}}}{9}} }}\) <em><strong>M1A1</strong></em><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {(9 - {x^2})^{\frac{1}{2}}} - \frac{{{x^2}}}{{{{(9 - {x^2})}^{\frac{1}{2}}}}} + \frac{2}{{{{(9 - {x^2})}^{\frac{1}{2}}}}}\)<span style="font: 20.0px Helvetica;"> </span><strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{9 - {x^2} - {x^2} + 2}}{{{{(9 - {x^2})}^{\frac{1}{2}}}}}\)<span style="font: 20.0px Helvetica;"> </span><strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{11 - 2{x^2}}}{{\sqrt {9 - {x^2}} }}\)<span style="font: 20.0px Helvetica;"> </span><strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(d) \(\int_{ - p}^p {\frac{{11 - 2{x^2}}}{{\sqrt {9 - {x^2}} }}{\text{d}}x = \left[ {x\sqrt {9 - {x^2}} + 2\arcsin \frac{x}{3}} \right]_{ - p}^p} \) <em><strong>M1</strong></em><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = p\sqrt {9 - {p^2}} + 2\arcsin \frac{p}{3} + p\sqrt {9 - {p^2}} + 2\arcsin \frac{p}{3}\)<span style="font: 20.0px Helvetica;"> </span><strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 2p\sqrt {9 - {p^2}} + 4\arcsin \left( {\frac{p}{3}} \right)\)<span style="font: 20.0px Helvetica;"> </span><strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><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: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(e) \(11 - 2{p^2} = 0\) <em><strong>M1</strong></em><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(p = 2.35\,\,\,\,\,\left( {\sqrt {\frac{{11}}{2}} } \right)\)<span style="font: 20.0px Helvetica;"> </span><strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A0</em></strong> for \(p = \pm 2.35\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><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: 23.0px Helvetica;"><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: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(f) (i) \(f''(x) = \frac{{{{(9 - {x^2})}^{\frac{1}{2}}}( - 4x) + x(11 - 2{x^2}){{(9 - {x^2})}^{ - \frac{1}{2}}}}}{{9 - {x^2}}}\) <em><strong>M1A1</strong></em><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{ - 4x(9 - {x^2}) + x(11 - 2{x^2})}}{{{{(9 - {x^2})}^{\frac{3}{2}}}}}\)<span style="font: 20.0px Helvetica;"> </span><strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{ - 36x + 4{x^3} + 11x - 2{x^3}}}{{{{(9 - {x^2})}^{\frac{3}{2}}}}}\)<span style="font: 20.0px Helvetica;"> </span><strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{x(2{x^2} - 25)}}{{{{(9 - {x^2})}^{\frac{3}{2}}}}}\)<span style="font: 20.0px Helvetica;"> </span><strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii)<span style="font: 20.0px Helvetica;"> </span><strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">When \(0 < x < 3\), \(f''(x) < 0\). When \( - 3 < x < 0\), \(f''(x) > 0\).<span style="font: 20.0px Helvetica;"> </span><strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f''(0) = 0\)<span style="font: 20.0px Helvetica;"> </span><strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>THEN</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Hence \(f''(x)\) changes sign through <em>x</em> = 0 , giving a point of inflexion.<span style="font: 20.0px Helvetica;"> </span><strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = \pm \sqrt {\frac{{25}}{2}} \) is outside the domain of <em>f</em>.<span style="font: 20.0px Helvetica;"> </span><strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = \pm \sqrt {\frac{{25}}{2}} \) is not a root of \(f''(x) = 0\) .<span style="font: 20.0px Helvetica;"> </span><strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [21 marks]</em></strong></span></p>
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<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">It was disappointing to note that some candidates did not know the domain for arcsin. Most candidates knew what to do in (b) but sometimes the wrong answer was obtained due to the calculator being in the wrong mode. In (c), the differentiation was often disappointing with \(\arcsin \left( {\frac{x}{3}} \right)\) causing problems. In (f)(i), some candidates who failed to do (c) guessed the correct form of \(f'(x)\) (presumably from (d)) and then went on to find \(f''(x)\) correctly. In (f)(ii), the justification of a point of inflexion at <em>x</em> = 0 was sometimes incorrect – for example, some candidates showed simply that \(f'(x)\) is positive on either side of the origin which is not a valid reason.</span></p>
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<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A body is moving through a liquid so that its acceleration can be expressed as</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[\left( { - \frac{{{v^2}}}{{200}} - 32} \right){\text{m}}{{\text{s}}^{ - 2}},\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">where \(v{\text{ m}}{{\text{s}}^{ - 1}}\) is the velocity of the body at time <em>t</em> seconds.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The initial velocity of the body was known to be \(40{\text{ m}}{{\text{s}}^{ - 1}}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Show that the time taken, <em>T</em> seconds, for the body to slow to \(V{\text{ m}}{{\text{s}}^{ - 1}}\) is given by</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[T = 200\int_V^{40} {\frac{1}{{{v^2} + {{80}^2}}}{\text{d}}v.} \]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) (i) Explain why acceleration can be expressed as \(v\frac{{{\text{d}}v}}{{{\text{d}}s}}\), where <em>s</em> is displacement, in metres, of the body at time <em>t</em> seconds.</span></p>
<p style="margin: 0px 0px 0px 30px; font: 26px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> (ii) <strong>Hence</strong> find a similar integral to that shown in part (a) for the distance, <em>S</em> metres, travelled as the body slows to \(V{\text{ m}}{{\text{s}}^{ - 1}}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) <strong>Hence</strong>, using parts (a) and (b), find the distance travelled and the time taken until the body momentarily comes to rest.</span></p>
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<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \(\frac{{{\text{d}}v}}{{{\text{d}}t}} = - \frac{{{v^2}}}{{200}} - 32\left( { = \frac{{ - {v^2} - 6400}}{{200}}} \right)\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int_0^T {{\text{d}}t = \int_{40}^V { - \frac{{200}}{{{v^2} + {{80}^2}}}{\text{d}}v} } \) <strong><em>M1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(T = 200\int_V^{40} {\frac{1}{{{v^2} + {{80}^2}}}{\text{d}}v} \) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) (i) \(a = \frac{{{\text{d}}v}}{{{\text{d}}t}} = \frac{{{\text{d}}v}}{{{\text{d}}s}} \times \frac{{{\text{d}}s}}{{{\text{d}}t}}\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = v\frac{{{\text{d}}v}}{{{\text{d}}s}}\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \(v\frac{{{\text{d}}v}}{{{\text{d}}s}} = \frac{{ - {v^2} - {{80}^2}}}{{200}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int_0^S {{\text{d}}s = \int_{40}^V -{\frac{{200v}}{{{v^2} + {{80}^2}}}{\text{d}}v} } \) <strong><em>M1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int_0^S {{\text{d}}s = \int_V^{40} {\frac{{200v}}{{{v^2} + {{80}^2}}}{\text{d}}v} } \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(S = 200\int_V^{40} {\frac{v}{{{v^2} + {{80}^2}}}{\text{d}}v} \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) letting <em>V</em> = 0 <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">distance \( = 200\int_0^{40} {\frac{v}{{{v^2} + {{80}^2}}}{\text{d}}v = 22.3{\text{ metres}}} \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">time \( = 200\int_0^{40} {\frac{1}{{{v^2} + {{80}^2}}}{\text{d}}v = 1.16{\text{ seconds}}} \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [14 marks]</em></strong></span></p>
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<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Many students failed to understand the problem as one of solving differential equations. In addition there were many problems seen in finding the end points for the definite integrals. Part (b) (i) should have been a simple point having used the chain rule, but it seemed that many students had not seen this, even though it is clearly in the syllabus.</span></p>
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<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A helicopter H is moving vertically upwards with a speed of 10 ms<sup>−1</sup> . The helicopter is \(h\) m directly above the point Q which is situated on level ground. The helicopter is observed from the point P which is also at ground level and PQ \( = 40\) m. This information is represented in the diagram below.</span></p>
<p><br><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" alt></p>
<p><span style="font-family: times new roman,times; font-size: medium;">When \(h = 30\),<br></span></p>
</div>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">(a) show that the rate of change of \({\rm{H}}\hat {\text{P}}{\text{Q}}\) is \(0.16\) radians per second;</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(b) find the rate of change of PH.</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;">(a) let \({\text{H}}\hat {\text{P}}{\text{Q}} = \theta \)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\tan \theta = \frac{h}{{40}}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({\sec ^2}\theta \frac{{{\text{d}}\theta }}{{{\text{d}}t}} = \frac{1}{{40}}\frac{{{\text{d}}h}}{{{\text{d}}t}}\) </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,times; font-size: medium;">\(\frac{{{\text{d}}\theta }}{{{\text{d}}t}} = \frac{1}{{4{{\sec }^2}\theta }}\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">(A1)</span></strong></em></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\( = \frac{{16}}{{4 \times 25}}\) \(\left( {\sec \theta = \frac{5}{4}{\text{ or }}\theta = 0.6435} \right)\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1</span></strong></em></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\( = 0.16\)</span> radians per second <em><strong>AG</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;">(b) \({x^2} = {h^2} + 1600\), where PH \( = x\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(2x\frac{{{\text{d}}x}}{{{\text{d}}t}} = 2h\frac{{{\text{d}}h}}{{{\text{d}}t}}\) </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,times; font-size: medium;">\(\frac{{{\text{d}}x}}{{{\text{d}}t}} = \frac{h}{x} \times 10\) <em><strong>A1</strong></em></span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\( = \frac{{10h}}{{\sqrt {{h^2} + 1600} }}\) </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;">\(h = 30\) , \(\frac{{{\text{d}}x}}{{{\text{d}}t}} = 6\)</span><span style="font-family: times new roman,times; font-size: medium;"> ms<sup>–1</sup></span><span style="font-family: times new roman,times; font-size: medium;"><sup> </sup></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;"><strong>Note:</strong> Accept solutions that begin\(x = 40\sec \theta \) or use \(h = 10t\) .</span></p>
<p><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;">[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;">For those candidates who realized this was an applied calculus problem involving related rates of change, the main source of error was in differentiating inverse tan in part (a). Some found part (b) easier than part (a), involving a changing length rather than an angle. A number of alternative approaches were reported by examiners.</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following diagram shows a vertical cross section of a building. The cross section of the roof of the building can be modelled by the curve \(f(x) = 30{{\text{e}}^{ - \frac{{{x^2}}}{{400}}}}\), <span class="s1">where \( - 20 \le x \le 20\).</span></p>
<p class="p1">Ground level is represented by the <span class="s1">\(x\)</span>-axis.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-01-29_om_16.39.22.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find \(f''(x)\).</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>Show that the gradient of the roof function is greatest when \(x = - \sqrt {200} \).</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">The cross section of the living space under the roof can be modelled by a rectangle <span class="s1">\(CDEF\)</span> with points \({\text{C}}( - a,{\text{ }}0)\) and \({\text{D}}(a,{\text{ }}0)\), where \(0 < a \le 20\).</p>
<p class="p2">Show that the maximum area \(A\) <span class="s1">of the rectangle \(CDEF\) </span>is \(600\sqrt 2 {{\text{e}}^{ - \frac{1}{2}}}\).</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 class="p1">A function \(I\) <span class="s1">is known as the Insulation Factor of </span>\(CDEF\). The function is defined as \(I(a) = \frac{{P(a)}}{{A(a)}}\) where \({\text{P}} = {\text{Perimeter}}\) and \({\text{A}} = {\text{Area of the rectangle}}\).</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>Find an expression for \(P\) in terms of \(a\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Find the value of <span class="s1">\(a\) </span>which minimizes \(I\).</p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>Using the value of \(a\) found in part (ii) calculate the percentage of the cross sectional area under the whole roof that is not included in the cross section of the living space.</p>
<div class="marks">[9]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(f'(x) = 30{{\text{e}}^{ - \frac{{{x^2}}}{{400}}}} \bullet - \frac{{2x}}{{400}}\;\;\;\left( { = - \frac{{3x}}{{20}}{{\text{e}}^{ - \frac{{{x^2}}}{{400}}}}} \right)\) <strong><em>M1A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>M1 </em></strong>for attempting to use the chain rule.</p>
<p> </p>
<p>\(f''(x) = - \frac{3}{{20}}{{\text{e}}^{ - \frac{{{x^2}}}{{400}}}} + \frac{{3{x^2}}}{{4000}}{{\text{e}}^{ - \frac{{{x^2}}}{{400}}}}\;\;\;\left( { = \frac{3}{{20}}{{\text{e}}^{ - \frac{{{x^2}}}{{400}}}}\left( {\frac{{{x^2}}}{{200}} - 1} \right)} \right)\) <strong><em>M1A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>M1 </em></strong>for attempting to use the product rule.</p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the roof function has maximum gradient when \(f''(x) = 0\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for attempting to find \(f''\left( { - \sqrt {200} } \right)\).</p>
<p> </p>
<p><strong>EITHER</strong></p>
<p>\( = 0\) <strong><em>A1</em></strong></p>
<p><strong>OR</strong></p>
<p>\(f''(x) = 0 \Rightarrow x = \pm \sqrt {200} \) <strong><em>A1</em></strong></p>
<p><strong>THEN</strong></p>
<p>valid argument for maximum such as reference to an appropriate graph or change in the sign of \(f''(x)\) <em>eg</em> \(f''( - 15) = 0.010 \ldots ( > 0)\) and \(f''( - 14) = - 0.001 \ldots ( < 0)\) <strong><em>R1</em></strong></p>
<p>\( \Rightarrow x = - \sqrt {200} \) <strong><em>AG</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>\(A = 2a \bullet 30{{\text{e}}^{ - \frac{{{a^2}}}{{400}}}}\;\;\;\left( { = 60a{{\text{e}}^{ - \frac{{{a^2}}}{{400}}}} = - 400g'(a)} \right)\) <strong><em>(M1)(A1)</em></strong></p>
<p><strong>EITHER</strong></p>
<p>\(\frac{{{\text{d}}A}}{{{\text{d}}a}} = 60a{{\text{e}}^{ - \frac{{{a^2}}}{{400}}}} \bullet - \frac{a}{{200}} + 60{{\text{e}}^{ - \frac{{{a^2}}}{{400}}}} = 0 \Rightarrow a = \sqrt {200} {\text{ }}\left( { - 400f''(a) = 0 \Rightarrow a = \sqrt {200} } \right)\) <strong><em>M1A1</em></strong></p>
<p><strong>OR</strong></p>
<p>by symmetry <em>eg</em> \(a = - \sqrt {200} \) found in (b) or \({A_{{\text{max}}}}\) coincides with \(f''(a) = 0\) <strong><em>R1</em></strong></p>
<p>\( \Rightarrow a = \sqrt {200} \) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>A0(M1)(A1)M0M1 </em></strong>for candidates who start with \(a = \sqrt {200} \) and do not provide any justification for the maximum area. Condone use of \(x\).</p>
<p> </p>
<p><strong>THEN</strong></p>
<p>\({A_{{\text{max}}}} = 60 \bullet \sqrt {200} {{\text{e}}^{ - \frac{{200}}{{400}}}}\) <strong><em>M1</em></strong></p>
<p>\( = 600\sqrt 2 {{\text{e}}^{ - \frac{1}{2}}}\) <strong><em>AG</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) perimeter \( = 4a + 60{{\text{e}}^{ - \frac{{{a^2}}}{{400}}}}\) <strong><em>A1A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Condone use of \(x\).</p>
<p> </p>
<p>(ii) \(I(a) = \frac{{4a + 60{{\text{e}}^{ - \frac{{{a^2}}}{{400}}}}}}{{60a{{\text{e}}^{ - \frac{{{a^2}}}{{400}}}}}}\) <strong><em>(A1)</em></strong></p>
<p>graphing \(I(a)\) or other valid method to find the minimum <strong><em>(M1)</em></strong></p>
<p>\(a = 12.6\) <strong><em>A1</em></strong></p>
<p>(iii) area under roof \( = \int_{ - 20}^{20} {30{{\text{e}}^{ - \frac{{{x^2}}}{{400}}}}} {\text{d}}x\) <strong><em>M1</em></strong></p>
<p>\( = 896.18 \ldots \) <strong><em>(A1)</em></strong></p>
<p>area of living space \( = 60 \cdot (12.6...) \cdot e - {\frac{{(12.6...)}}{{400}}^2} = 508.56...\)</p>
<p>percentage of empty space \( = 43.3\% \) <strong><em>A1</em></strong></p>
<p><strong><em>[9 marks]</em></strong></p>
<p><strong><em>Total [21 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">Consider the curve with equation \({x^3} + {y^3} = 4xy\).</p>
</div>
<div class="specification">
<p class="p1">The tangent to this curve is parallel to the \(x\)-axis at the point where \(x = k,{\text{ }}k > 0\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Use implicit differentiation to show that \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{4y - 3{x^2}}}{{3{y^2} - 4x}}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of \(k\).</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 class="p1"><span class="Apple-converted-space">\(3{x^2} + 3{y^2}\frac{{{\text{d}}y}}{{{\text{d}}x}} = 4\left( {y + x\frac{{{\text{d}}y}}{{{\text{d}}x}}} \right)\) </span><strong><em>M1A1</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\((3{y^2} - 4x)\frac{{{\text{d}}y}}{{{\text{d}}x}} = 4y - 3{x^2}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2"><span class="Apple-converted-space">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{4y - 3{x^2}}}{{3{y^2} - 4x}}\) </span><span class="s1"><strong><em>AG</em></strong></span></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0 \Rightarrow 4y - 3{x^2} = 0\) </span><strong><em>(M1)</em></strong></p>
<p class="p1">substituting \(x = k\) and \(y = \frac{3}{4}{k^2}\) into \({x^3} + {y^3} = 4xy\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\({k^3} + \frac{{27}}{{64}}{k^6} = 3{k^3}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1">attempting to solve \({k^3} + \frac{{27}}{{64}}{k^6} = 3{k^3}\) for \(k\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\(k = 1.68{\text{ }}\left( { = \frac{4}{3}\sqrt[3]{2}} \right)\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Condone substituting \(y = \frac{3}{4}{x^2}\) into \({x^3} + {y^3} = 4xy\) and solving for \(x\).</p>
<p class="p1"><strong><em>[5 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 generally well done. Some use of partial differentiation accompanied by rudimentary partial derivative notation was observed in a few candidate’s solutions.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">In part (b), a large number of candidates knew to use \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\) and seemingly understood the required solution plan but were unable to correctly substitute \(x = k\) and \(y = \frac{{3{k^2}}}{4}\) into the relation and solve for \(k\).</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function \(f(x) = \frac{{\sqrt x }}{{\sin x}},{\text{ }}0 < x < \pi \).</p>
</div>
<div class="specification">
<p>Consider the region bounded by the curve \(y = f(x)\), the \(x\)-axis and the lines \(x = \frac{\pi }{6},{\text{ }}x = \frac{\pi }{3}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the \(x\)-coordinate of the minimum point on the curve \(y = f(x)\) satisfies the equation \(\tan x = 2x\).</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the values of \(x\) for which \(f(x)\) is a decreasing function.</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>Sketch the graph of \(y = f(x)\) showing clearly the minimum point and any asymptotic behaviour.</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 coordinates of the point on the graph of \(f\) where the normal to the graph is parallel to the line \(y = - x\).</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>This region is now rotated through \(2\pi \) radians about the \(x\)-axis. Find the volume of revolution.</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>attempt to use quotient rule or product rule <strong><em>M1</em></strong></p>
<p>\(f’(x) = \frac{{\sin x\left( {\frac{1}{2}{x^{ - \frac{1}{2}}}} \right) - \sqrt x \cos x}}{{{{\sin }^2}x}}{\text{ }}\left( { = \frac{1}{{2\sqrt x \sin x}} - \frac{{\sqrt x \cos x}}{{{{\sin }^2}x}}} \right)\) <strong><em>A1A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>A1 </em></strong>for \(\frac{1}{{2\sqrt x \sin x}}\) or equivalent and <strong><em>A1 </em></strong>for \( - \frac{{\sqrt x \cos x}}{{{{\sin }^2}x}}\) or equivalent.</p>
<p> </p>
<p>setting \(f’(x) = 0\) <strong><em>M1</em></strong></p>
<p>\(\frac{{\sin x}}{{2\sqrt x }} - \sqrt x \cos x = 0\)</p>
<p>\(\frac{{\sin x}}{{2\sqrt x }} = \sqrt x \cos x\) or equivalent <strong><em>A1</em></strong></p>
<p>\(\tan x = 2x\) <strong><em>AG</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(x = 1.17\)</p>
<p>\(0 < x \leqslant 1.17\) <strong><em>A1A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>A1 </em></strong>for \(0 < x\) and <strong><em>A1 </em></strong>for \(x \leqslant 1.17\). Accept \(x < 1.17\).</p>
<p> </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><img src="images/Schermafbeelding_2018-02-08_om_16.19.25.png" alt="N17/5/MATHL/HP2/ENG/TZ0/10.b/M"></p>
<p>concave up curve over correct domain with one minimum point above the \(x\)-axis. <strong><em>A1</em></strong></p>
<p>approaches \(x = 0\) asymptotically <strong><em>A1</em></strong></p>
<p>approaches \(x = \pi \) asymptotically <strong><em>A1</em></strong></p>
<p> </p>
<p>Note: For the final <strong><em>A1 </em></strong>an asymptote must be seen, and \(\pi \) must be seen on the \(x\)-axis or in an equation.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(f’(x){\text{ }}\left( { = \frac{{\sin x\left( {\frac{1}{2}{x^{ - \frac{1}{2}}}} \right) - \sqrt x \cos x}}{{{{\sin }^2}x}}} \right) = 1\) <strong><em>(A1)</em></strong></p>
<p>attempt to solve for \(x\) <strong><em>(M1)</em></strong></p>
<p>\(x = 1.96\) <strong><em>A1</em></strong></p>
<p>\(y = f(1.96 \ldots )\)</p>
<p>\( = 1.51\) <strong><em>A1</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>\(V = \pi \int_{\frac{\pi }{6}}^{\frac{\pi }{3}} {\frac{{x{\text{d}}x}}{{{{\sin }^2}x}}} \) <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> <strong><em>M1 </em></strong>is for an integral of the correct squared function (with or without limits and/or \(\pi \)).</p>
<p> </p>
<p>\( = 2.68{\text{ }}( = 0.852\pi )\) <strong><em>A1</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.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="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The acceleration of a car is \(\frac{1}{{40}}(60 - v){\text{ m}}{{\text{s}}^{ - 2}}\), when its velocity is \(v{\text{ m}}{{\text{s}}^{ - 2}}\). Given the car starts from rest, find the velocity of the car after 30 seconds.</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: 24.0px Helvetica;"><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: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}v}}{{{\text{d}}t}} = \frac{1}{{40}}(60 - v)\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">attempting to separate variables \(\int {\frac{{{\text{d}}v}}{{60 - v}} = \int {\frac{{{\text{d}}t}}{{40}}} } \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( - \ln (60 - v) = \frac{t}{{40}} + c\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(c = - \ln 60\) (or equivalent) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">attempting to solve for <em>v</em> when <em>t</em> = 30 <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(v = 60 - 60{e^{ - \frac{3}{4}}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(v = 31.7{\text{ (m}}{{\text{s}}^{ - 1}})\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><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: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}v}}{{{\text{d}}t}} = \frac{1}{{40}}(60 - v)\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}t}}{{{\text{d}}v}} = \frac{{40}}{{60 - v}}\) (or equivalent) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int_0^{{v_f}} {\frac{{40}}{{60 - v}}{\text{d}}v = 30} \) where \({v_f}\) is the velocity of the car after 30 seconds. <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">attempting to solve \(\int_0^{{v_f}} {\frac{{40}}{{60 - v}}{\text{d}}v = 30} \) for \({v_f}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(v = 31.7{\text{ (m}}{{\text{s}}^{ - 1}})\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates experienced difficulties with this question. A large number of candidates did not attempt to separate the variables and instead either attempted to integrate with respect to <em>v </em>or employed constant acceleration formulae. Candidates that did separate the variables and attempted to integrate both sides either made a sign error, omitted the constant of integration or found an incorrect value for this constant. Almost all candidates were not aware that this question could be solved readily on a GDC.</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">A particle moves along a straight line so that after <em>t</em><em> </em>seconds its displacement <em>s</em> , in metres, satisfies the equation \({s^2} + s - 2t = 0\) . Find, in terms of <em>s</em> , expressions for its velocity and its acceleration.</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: 11.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2s\frac{{{\text{d}}s}}{{{\text{d}}t}} + \frac{{{\text{d}}s}}{{{\text{d}}t}} - 2 = 0\) <strong style="font-weight: bold;"><em style="font-style: italic;">M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(v = \frac{{{\text{d}}s}}{{{\text{d}}t}} = \frac{2}{{2s + 1}}\) <strong style="font-weight: bold;"><em style="font-style: italic;">A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong style="font-weight: bold;">EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(a = \frac{{{\text{d}}v}}{{{\text{d}}t}} = \frac{{{\text{d}}v}}{{{\text{d}}s}}\frac{{{\text{d}}s}}{{{\text{d}}t}}\) <strong style="font-weight: bold;"><em style="font-style: italic;">(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}v}}{{{\text{d}}s}} = \frac{{ - 4}}{{{{(2s + 1)}^2}}}\) <strong style="font-weight: bold;"><em style="font-style: italic;">(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(a = \frac{{ - 4}}{{{{(2s + 1)}^2}}}\frac{{{\text{d}}s}}{{{\text{d}}t}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong style="font-weight: bold;">OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2{\left( {\frac{{{\text{d}}s}}{{{\text{d}}t}}} \right)^2} + 2s\frac{{{{\text{d}}^2}s}}{{{\text{d}}{t^2}}} + \frac{{{{\text{d}}^2}s}}{{{\text{d}}{t^2}}} = 0\) <strong style="font-weight: bold;"><em style="font-style: italic;">(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{{\text{d}}^2}s}}{{\underbrace {{\text{d}}{t^2}}_a}} = \frac{{ - 2{{\left( {\frac{{{\text{d}}s}}{{{\text{d}}t}}} \right)}^2}}}{{2s + 1}}\) <strong style="font-weight: bold;"><em style="font-style: italic;">(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong style="font-weight: bold;">THEN</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(a = \frac{{ - 8}}{{{{(2s + 1)}^3}}}\) <strong style="font-weight: bold;"><em style="font-style: italic;">A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong style="font-weight: bold;"><em style="font-style: italic;">[6 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Despite the fact that many candidates were able to calculate the speed of the particle, many of them failed to calculate the acceleration. Implicit differentiation turned out to be challenging in this exercise showing in many cases a lack of understanding of independent/dependent variables. Very often candidates did not use the chain rule or implicit differentiation when attempting to find the acceleration. It was not uncommon to see candidates trying to differentiate implicitly with respect to <em>t </em>rather than <em>s</em>, but getting the variables muddled.</span></p>
</div>
<br><hr><br><div class="specification">
<p>Consider \(f(x) = - 1 + \ln \left( {\sqrt {{x^2} - 1} } \right)\)</p>
</div>
<div class="specification">
<p>The function \(f\) is defined by \(f(x) = - 1 + \ln \left( {\sqrt {{x^2} - 1} } \right),{\text{ }}x \in D\)</p>
</div>
<div class="specification">
<p>The function \(g\) is defined by \(g(x) = - 1 + \ln \left( {\sqrt {{x^2} - 1} } \right),{\text{ }}x \in \left] {1,{\text{ }}\infty } \right[\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the largest possible domain \(D\) for \(f\) to be a function.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of \(y = f(x)\) showing clearly the equations of asymptotes and the coordinates of any intercepts with the axes.</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>Explain why \(f\) is an even function.</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>Explain why the inverse function \({f^{ - 1}}\) does not exist.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the inverse function \({g^{ - 1}}\) and state its domain.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find \(g'(x)\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, show that there are no solutions to \(g'(x) = 0\);</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, show that there are no solutions to \(({g^{ - 1}})'(x) = 0\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\({x^2} - 1 > 0\) <strong><em>(M1)</em></strong></p>
<p>\(x < - 1\) or \(x > 1\) <strong><em>A1</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2017-08-09_om_15.40.09.png" alt="M17/5/MATHL/HP2/ENG/TZ1/12.b/M"></p>
<p>shape <strong><em>A1</em></strong></p>
<p>\(x = 1\) and \(x = - 1\) <strong><em>A1</em></strong></p>
<p>\(x\)-intercepts <strong><em>A1</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>EITHER</strong></p>
<p>\(f\) is symmetrical about the \(y\)-axis <strong><em>R1</em></strong></p>
<p><strong>OR</strong></p>
<p>\(f( - x) = f(x)\) <strong><em>R1</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p>\(f\) is not one-to-one function <strong><em>R1</em></strong></p>
<p><strong>OR</strong></p>
<p>horizontal line cuts twice <strong><em>R1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept any equivalent correct statement.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(x = - 1 + \ln \left( {\sqrt {{y^2} - 1} } \right)\) <strong><em>M1</em></strong></p>
<p>\({{\text{e}}^{2x + 2}} = {y^2} - 1\) <strong><em>M1</em></strong></p>
<p>\({g^{ - 1}}(x) = \sqrt {{{\text{e}}^{2x + 2}} + 1} ,{\text{ }}x \in \mathbb{R}\) <strong><em>A1A1</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(g'(x) = \frac{1}{{\sqrt {{x^2} - 1} }} \times \frac{{2x}}{{2\sqrt {{x^2} - 1} }}\) <strong><em>M1A1</em></strong></p>
<p>\(g'(x) = \frac{x}{{{x^2} - 1}}\) <strong><em>A1</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(g'(x) = \frac{x}{{{x^2} - 1}} = 0 \Rightarrow x = 0\) <strong><em>M1</em></strong></p>
<p>which is not in the domain of \(g\) (hence no solutions to \(g'(x) = 0\)) <strong><em>R1</em></strong></p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">g.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(({g^{ - 1}})'(x) = \frac{{{{\text{e}}^{2x + 2}}}}{{\sqrt {{{\text{e}}^{2x + 2}} + 1} }}\) <strong><em>M1</em></strong></p>
<p>as \({{\text{e}}^{2x + 2}} > 0 \Rightarrow ({g^{ - 1}})'(x) > 0\) so no solutions to \(({g^{ - 1}})'(x) = 0\) <strong><em>R1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept: equation \({{\text{e}}^{2x + 2}} = 0\) has no solutions.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">g.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.ii.</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;">Particle <em>A </em>moves such that its velocity \(v{\text{ m}}{{\text{s}}^{ - 1}}\), at time <em>t </em>seconds, is given by \(v(t) = \frac{t}{{12 + {t^4}}},{\text{ }}t \geqslant 0\).</span></p>
</div>
<div class="specification">
<p><span style="font-family: 'times new roman', times; font-size: medium;">Particle <em>B </em>moves such that its velocity \(v{\text{ m}}{{\text{s}}^{ - 1}}\) is related to its displacement \(s{\text{ m}}\), by the equation \(v(s) = \arcsin \left( {\sqrt s } \right)\).</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;">Sketch the graph of \(y = v(t)\). Indicate clearly the local maximum and write down its coordinates.</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;">Use the substitution \(u = {t^2}\) to find \(\int {\frac{t}{{12 + {t^4}}}{\text{d}}t} \).</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;"><span style="font-size: medium; line-height: normal; background-color: #f7f7f7;">Find the exact distance travelled by particle </span>\(A\) <span style="font-size: medium; line-height: normal; background-color: #f7f7f7;">between \(t = 0\) and \(t = 6\) seconds.</span></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;">Give your answer in the form \(k\arctan (b),{\text{ }}k,{\text{ }}b \in \mathbb{R}\).</span></p>
<p> </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>Find the acceleration of particle B when \(s = 0.1{\text{ m}}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a)<br><img src="images/maths_14a_markscheme.png" alt> <strong><em>A1</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>A1</strong> for</span><span style="font-family: 'times new roman', times; font-size: medium;"> correct shape and correct domain</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;">\((1.41,{\text{ }}0.0884){\text{ }}\left( {\sqrt 2 ,{\text{ }}\frac{{\sqrt 2 }}{{16}}} \right)\) <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;"><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: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(u = {t^2}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}u}}{{{\text{d}}t}} = 2t\) <strong><em>A1</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>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(t = {u^{\frac{1}{2}}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}t}}{{{\text{d}}u}} = \frac{1}{2}{u^{ - \frac{1}{2}}}\) <strong><em>A1</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>THEN</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {\frac{t}{{12 + {t^4}}}{\text{d}}t = \frac{1}{2}\int {\frac{{{\text{d}}u}}{{12 + {u^2}}}} } \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{{2\sqrt {12} }}\arctan \left( {\frac{u}{{\sqrt {12} }}} \right)( + c)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{{4\sqrt 3 }}\arctan \left( {\frac{{{t^2}}}{{2\sqrt 3 }}} \right)( + c)\) or equivalent <strong><em>A1</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>[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: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int_0^6 {\frac{t}{{12 + {t^4}}}{\text{d}}t} \) <strong><em>(M1)</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;">\( = \left[ {\frac{1}{{4\sqrt 3 }}\arctan \left( {\frac{{{t^2}}}{{2\sqrt 3 }}} \right)} \right]_0^6\) <strong><em>M1</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;">\( = \frac{1}{{4\sqrt 3 }}\left( {\arctan \left( {\frac{{36}}{{2\sqrt 3 }}} \right)} \right){\text{ }}\left( { = \frac{1}{{4\sqrt 3 }}\left( {\arctan \left( {\frac{{18}}{{\sqrt 3 }}} \right)} \right)} \right){\text{ (m)}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Accept \(\frac{{\sqrt 3 }}{{12}}\arctan \left( {6\sqrt 3 } \right)\) or equivalent.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica; min-height: 26.0px;"> </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>[3 marks]</em></strong></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;">\(\frac{{{\text{d}}v}}{{{\text{d}}s}} = \frac{1}{{2\sqrt {s(1 - s)} }}\) <strong><em>(A1)</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;">\(a = v\frac{{{\text{d}}v}}{{{\text{d}}s}}\)</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;">\(a = \arcsin \left( {\sqrt s } \right) \times \frac{1}{{2\sqrt {s(1 - s)} }}\) <strong><em>(M1)</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;">\(a = \arcsin \left( {\sqrt {0.1} } \right) \times \frac{1}{{2\sqrt {0.1 \times 0.9} }}\)</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;">\(a = 0.536{\text{ (m}}{{\text{s}}^{ - 2}})\) <strong><em>A1</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>[3 marks]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A function is defined by \(f(x) = {x^2} + 2,{\text{ }}x \ge 0\). A region \(R\) is enclosed by \(y = f(x)\),the \(y\)-axis and the line \(y = 4\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) Express the area of the region \(R\) as an integral with respect to \(y\).</p>
<p class="p1">(ii) Determine the area of \(R\), giving your answer correct to four significant figures.</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 exact volume generated when the region \(R\) is rotated through \(2\pi \) radians about the \(y\)-axis.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>\({\text{area}} = \int_2^4 {\sqrt {y - 2} {\text{d}}y} \) <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\( = 1.886{\text{ (4 sf only)}}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>M0A0A1 </em></strong>for finding \(1.886\) from \(\int_0^{\sqrt 2 } {4 - f(x){\text{d}}x} \).</p>
<p class="p1">Award <strong><em>A1FT </em></strong>for a 4sf answer obtained from an integral involving \(x\).</p>
<p class="p1"><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\({\text{volume}} = \pi \int_2^4 {(y - 2){\text{d}}y} \) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>M1 </em></strong>for the correct integral with incorrect limits.</p>
<p class="p1">\( = \pi \left[ {\frac{{{y^2}}}{2} - 2y} \right]_2^4\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1">\( = 2\pi {\text{ (exact only)}}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[3 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;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p class="p1">A function \(f\) is defined by \(f(x) = {x^3} + {{\text{e}}^x} + 1,{\text{ }}x \in \mathbb{R}\). By considering \(f'(x)\) determine whether \(f\) is a one-to-one or a many-to-one function.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p class="p1">\(f'(x) = 3{x^2} + {{\text{e}}^x}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note:</strong> <span class="Apple-converted-space"> </span>Accept labelled diagram showing the graph \(y = f'(x)\) above the <span class="s2"><em>x</em></span>-axis;</p>
<p class="p3">do not accept unlabelled graphs nor graph of \(y = f(x)\).</p>
<p class="p2"> </p>
<p class="p3"><strong>EITHER</strong></p>
<p class="p1">this is always \( > 0\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>R1</em></strong></span></p>
<p class="p3">so the function is (strictly) increasing <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p3">and thus \(1 - 1\) <span class="Apple-converted-space"> </span><span class="s3"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">this is always \( > 0\;\;\;{\text{(accept }} \ne 0{\text{)}}\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">so there are no turning points <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p3"><span class="s3">and thus </span>\(1 - 1\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"> </p>
<p class="p3"><strong>Note:</strong> <span class="Apple-converted-space"> </span><strong><em>A1</em></strong> is dependent on the first <strong><em>R1</em></strong>.</p>
<p class="p2"> </p>
<p class="p3"><strong><em>[4 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p class="p1">The differentiation was normally completed correctly, but then a large number did not realise what was required to determine the type of the original function. Most candidates scored 1/4 and wrote explanations that showed little or no understanding of the relation between first derivative and the given function. For example, it was common to see comments about horizontal and vertical line tests but applied to the incorrect function.In term of mathematical language, it was noted that candidates used many terms incorrectly showing no knowledge of the meaning of terms like ‘parabola’, ‘even’ or ‘odd’ ( or no idea about these concepts).</p>
</div>
<br><hr><br><div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">(a) Integrate \(\int {\frac{{\sin \theta }}{{1 - \cos \theta }}} {\text{d}}\theta \)</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;">(b) Given that \(\int_{\frac{\pi }{2}}^a {\frac{{\sin \theta }}{{1 - \cos \theta }}} {\text{d}}\theta = \frac{1}{2}\)</span><span style="font-family: times new roman,times; font-size: medium;"> and \(\frac{\pi }{2} < a < \pi \)</span><span style="font-family: times new roman,times; font-size: medium;">, find the value of \(a\) .</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;">(a) \(\int {\frac{{\sin \theta }}{{1 - \cos \theta }}} {\text{d}}\theta = \int {\frac{{\left( {1 - \cos \theta } \right)'}}{{1 - \cos \theta }}} {\text{d}}\theta = \ln \left( {1 - \cos \theta } \right) + C\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">(M1)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 \(\ln \left( {1 - \cos \theta } \right)\) and <em><strong>A1</strong></em> for <em>C</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;">(b) \(\int_{\frac{\pi }{2}}^a {\frac{{\sin \theta }}{{1 - \cos \theta }}} {\text{d}}\theta = \frac{1}{2} \Rightarrow \left[ {\ln \left( {1 - \cos \theta } \right)} \right]_{\frac{\pi }{2}}^a = \frac{1}{2}\) </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,times; font-size: medium;">\(1 - \cos a = {{\text{e}}^{\frac{1}{2}}} \Rightarrow a = \arccos \left( {1 - \sqrt {\text{e}} } \right)\)) or \(2.28\) <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;">[5 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;">Generally well answered, although many students did not include the constant of integration.</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Given that the graph of \(y = {x^3} - 6{x^2} + kx - 4\) has exactly one point at which the gradient is zero, find the value of <em>k </em>.</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;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 3{x^2} - 12x + k\) <strong><em>M1A1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">For use of discriminant \({b^2} - 4ac = 0\) or completing the square \(3{(x - 2)^2} + k - 12\) (<strong><em>M1)</em></strong></span></p>
<p> <span style="font-family: 'times new roman', times; font-size: medium;">\(144 - 12k = 0\) </span><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>(A1)</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium;">Note: </strong><span style="font-family: 'times new roman', times; font-size: medium;">Accept trial and error, sketches of parabolas with vertex (2,0) or use of second derivative.</span></p>
<p> </p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(k = 12\) <strong><em>A1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks] </em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Generally candidates answer this question well using a diversity of methods. Surprisingly, a small number of candidates were successful in answering this question using the discriminant of the quadratic and in many cases reverted to trial and error to obtain the correct answer.</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A ladder of length 10 m on horizontal ground rests against a vertical wall. The bottom of the ladder is moved away from the wall at a constant speed of \(0.5{\text{ m}}{{\text{s}}^{ - 1}}\). Calculate the speed of descent of the top of the ladder when the bottom of the ladder is 4 m away from the wall.</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: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">let <em>x</em>, <em>y</em> (m) denote respectively the distance of the bottom of the ladder from the wall and the distance of the top of the ladder from the ground</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">then,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x^2} + {y^2} = 100\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2x\frac{{{\text{d}}x}}{{{\text{d}}t}} + 2y\frac{{{\text{d}}y}}{{{\text{d}}t}} = 0\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">when \(x = 4,{\text{ }}y = \sqrt {84} \) and \(\frac{{{\text{d}}x}}{{{\text{d}}t}} = 0.5\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">substituting, \(2 \times 4 \times 0.5 + 2\sqrt {84} \frac{{{\text{d}}y}}{{{\text{d}}t}} = 0\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}y}}{{{\text{d}}t}} = - 0.218{\text{ m}}{{\text{s}}^{ - 1}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(speed of descent is \(0.218{\text{ m}}{{\text{s}}^{ - 1}}\))</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 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 class="p1">Let the function \(f\) be defined by \(f(x) = \frac{{2 - {{\text{e}}^x}}}{{2{{\text{e}}^x} - 1}},{\text{ }}x \in D\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Determine \(D\), the largest possible domain 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">Show that the graph of \(f\) has three asymptotes and state their equations.</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>Show that \(f'(x) = - \frac{{3{{\text{e}}^x}}}{{{{(2{{\text{e}}^x} - 1)}^2}}}\).</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 class="p1">Use your answers from parts (b) and (c) to justify that \(f\) <span class="s1">has an inverse and state its domain.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find an expression for \({f^{ - 1}}(x)\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">Consider the region \(R\) </span>enclosed by the graph of \(y = f(x)\) and the axes.</p>
<p class="p1">Find the volume of the solid obtained when \(R\) is rotated through \(2\pi \) about the \(y\)-axis.</p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">attempting to solve either \(2{{\text{e}}^x} - 1 = 0\) or \(2{{\text{e}}^x} - 1 \ne 0\) for \(x\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">\(D = \mathbb{R}\backslash \left\{ { - \ln 2} \right\}\) (or equivalent <em>eg</em> \(x \ne - \ln 2\)) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: </strong>Accept \(D = \mathbb{R}\backslash \left\{ { - 0.693} \right\}\) or equivalent <em>eg</em> \(x \ne - 0.693\).</p>
<p class="p2"> </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">considering \(\mathop {\lim }\limits_{x \to - \ln 2} f(x)\)<span class="s1"> <span class="Apple-converted-space"> </span></span><strong><em>(M1)</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\(x = - \ln 2{\text{ }}(x = - 0.693)\) </span><span class="s2"><strong><em>A1</em></strong></span></p>
<p class="p1">considering one of \(\mathop {\lim }\limits_{x \to - \infty } f(x)\)<span class="s1"> </span>or \(\mathop {\lim }\limits_{x \to + \infty } f(x)\)<span class="s1"> <span class="Apple-converted-space"> </span></span><strong><em>M1</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\(\mathop {\lim }\limits_{x \to - \infty } f(x) = - 2 \Rightarrow y = - 2\) </span><span class="s2"><strong><em>A1</em></strong></span></p>
<p class="p2"><span class="Apple-converted-space">\(\mathop {\lim }\limits_{x \to + \infty } f(x) = - \frac{1}{2} \Rightarrow y = - \frac{1}{2}\) </span><span class="s2"><strong><em>A1</em></strong></span></p>
<div> </div>
<p class="p1"><strong>Note: </strong>Award <strong><em>A0A0 </em></strong>for \(y = - 2\)<span class="s1"> </span>and \(y = - \frac{1}{2}\)<span class="s1"> </span>stated without any justification.</p>
<p class="p3"> </p>
<p class="p1"><strong><em>[5 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">\(f'(x) = \frac{{ - {{\text{e}}^x}(2{{\text{e}}^x} - 1) - 2{{\text{e}}^x}(2 - {{\text{e}}^x})}}{{{{(2{{\text{e}}^x} - 1)}^2}}}\) </span><strong><em>M1A1A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\( = - \frac{{3{{\text{e}}^x}}}{{{{(2{{\text{e}}^x} - 1)}^2}}}\) </span><strong><em>AG</em></strong></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(f'(x) < 0{\text{ (for all }}x \in D) \Rightarrow f\) is (strictly) decreasing <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: </strong>Award <strong><em>R1 </em></strong>for a statement such as \(f'(x) \ne 0\) and so the graph of \(f\) has no turning points.</p>
<p class="p2"> </p>
<p class="p1">one branch is above the upper horizontal asymptote and the other branch is below the lower horizontal asymptote <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">\(f\) has an inverse <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\( - \infty < x < - 2 \cup - \frac{1}{2} < x < \infty \) </span><strong><em>A2</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: </strong>Award <strong><em>A2 </em></strong>if the domain of the inverse is seen in either part (d) or in part (e).</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(x = \frac{{2 - {{\text{e}}^y}}}{{2{{\text{e}}^y} - 1}}\) </span><strong><em>M1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: </strong>Award <strong><em>M1 </em></strong>for interchanging \(x\) and \(y\) (can be done at a later stage).</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\(2x{{\text{e}}^y} - x = 2 - {{\text{e}}^y}\) </span><strong><em>M1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\({{\text{e}}^y}(2x + 1) = x + 2\) </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\({f^{ - 1}}(x) = \ln \left( {\frac{{x + 2}}{{2x + 1}}} \right){\text{ }}\left( {{f^{ - 1}}(x) = \ln (x + 2) - \ln (2x + 1)} \right)\) </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">use of \(V = \pi \int_a^b {{x^2}{\text{d}}y} \) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\( = \pi \int_0^1 {{{\left( {\ln \left( {\frac{{y + 2}}{{2y + 1}}} \right)} \right)}^2}{\text{d}}y} \) </span><strong><em>(A1)(A1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for the correct integrand and <strong><em>(A1) </em></strong>for the limits.</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\( = 0.331\) </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The vertical cross-section of a container is shown in the following diagram.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-10_om_11.45.14.png" alt></p>
<p class="p1">The curved sides of the cross-section are given by the equation \(y = 0.25{x^2} - 16\). The horizontal cross-sections are circular. The depth of the container is \(48\) cm.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">If the container is filled with water to a depth of \(h\,{\text{cm}}\), show that the volume, \(V\,{\text{c}}{{\text{m}}^3}\), of the water is given by \(V = 4\pi \left( {\frac{{{h^2}}}{2} + 16h} \right)\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The container, initially full of water, begins leaking from a small hole at a rate given by \(\frac{{{\text{d}}V}}{{{\text{d}}t}} =<span class="Apple-converted-space"> </span>- \frac{{250\sqrt h }}{{\pi(h + 16)}}\) where <em>\(t\) </em>is measured in seconds.</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>Show that \(\frac{{{\text{d}}h}}{{{\text{d}}t}} =<span class="Apple-converted-space"> </span>- \frac{{250\sqrt h }}{{4{\pi ^2}{{(h + 16)}^2}}}\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>State \(\frac{{{\text{d}}t}}{{{\text{d}}h}}\) and hence show that \(t = \frac{{ - 4{\pi ^2}}}{{250}}\int {\left( {{h^{\frac{3}{2}}} + 32{h^{\frac{1}{2}}} + 256{h^{ - \frac{1}{2}}}} \right){\text{d}}h} \).</p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>Find, correct to the nearest minute, the time taken for the container to become empty. (\(60\) seconds = 1 minute)</p>
<div class="marks">[10]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Once empty, water is pumped back into the container at a rate of \(8.5\;{\text{c}}{{\text{m}}^3}{{\text{s}}^{ - 1}}\). At the same time, water continues leaking from the container at a rate of \(\frac{{250\sqrt h }}{{\pi (h + 16)}}{\text{c}}{{\text{m}}^3}{{\text{s}}^{ - 1}}\).</p>
<p class="p1">Using an appropriate sketch graph, determine the depth at which the water ultimately stabilizes in the container.</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 class="p1">attempting to use \(V = \pi \int_a^b {{x^2}{\text{d}}y} \) <span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1">attempting to express \({x^2}\) in terms of <em>\(y\) ie</em> \({x^2} = 4(y + 16)\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1">for \(y = h,{\text{ }}V = 4\pi \int_0^h {y + 16{\text{d}}y} \) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">\(V = 4\pi \left( {\frac{{{h^2}}}{2} + 16h} \right)\) <span class="Apple-converted-space"> </span><strong><em>AG</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>(i) <strong>METHOD 1</strong></p>
<p>\(\frac{{{\text{d}}h}}{{{\text{d}}t}} = \frac{{{\text{d}}h}}{{{\text{d}}V}} \times \frac{{{\text{d}}V}}{{{\text{d}}t}}\) <strong><em>(M1)</em></strong></p>
<p>\(\frac{{{\text{d}}V}}{{{\text{d}}h}} = 4\pi (h + 16)\) <strong><em>(A1)</em></strong></p>
<p>\(\frac{{{\text{d}}h}}{{{\text{d}}t}} = \frac{1}{{4\pi (h + 16)}} \times \frac{{ - 250\sqrt h }}{{\pi (h + 16)}}\) <strong><em>M1A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>M1 </em></strong>for substitution into \(\frac{{{\text{d}}h}}{{{\text{d}}t}} = \frac{{{\text{d}}h}}{{{\text{d}}V}} \times \frac{{{\text{d}}V}}{{{\text{d}}t}}\).</p>
<p> </p>
<p>\(\frac{{{\text{d}}h}}{{{\text{d}}t}} = \frac{{250\sqrt h }}{{4{\pi ^2}{{(h + 16)}^2}}}\) <strong><em>AG</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>\(\frac{{{\text{d}}V}}{{{\text{d}}t}} = 4\pi (h + 16)\frac{{{\text{d}}h}}{{{\text{d}}t}}\;\;\;\)(implicit differentiation)<strong><em>(M1)</em></strong></p>
<p>\(\frac{{ - 250\sqrt h }}{{\pi (h + 16)}} = 4\pi (h + 16)\frac{{{\text{d}}h}}{{{\text{d}}t}}\;\;\;\)(or equivalent) <strong><em>A1</em></strong></p>
<p>\(\frac{{{\text{d}}h}}{{{\text{d}}t}} = \frac{1}{{4\pi (h + 16)}} \times \frac{{ - 250\sqrt h }}{{\pi (h + 16)}}\) <strong><em>M1A1</em></strong></p>
<p>\(\frac{{{\text{d}}h}}{{{\text{d}}t}} = \frac{{250\sqrt h }}{{4{\pi ^2}{{(h + 16)}^2}}}\) <strong><em>AG</em></strong></p>
<p>(ii) \(\frac{{{\text{d}}t}}{{{\text{d}}h}} = - \frac{{4{\pi ^2}{{(h + 16)}^2}}}{{250\sqrt h }}\) <strong><em>A1</em></strong></p>
<p>\(t = \int { - \frac{{4{\pi ^2}{{(h + 16)}^2}}}{{250\sqrt h }}} {\text{d}}h\) <strong><em>(M1)</em></strong></p>
<p>\(t = \int { - \frac{{4{\pi ^2}({h^2} + 32h + 256)}}{{250\sqrt h }}} {\text{d}}h\) <strong><em>A1</em></strong></p>
<p>\(t = \frac{{ - 4{\pi ^2}}}{{250}}\int {\left( {{h^{\frac{3}{2}}} + 32{h^{\frac{1}{2}}} + 256{h^{ - \frac{1}{{2}}}}} \right){\text{d}}h} \) <strong><em>AG</em></strong></p>
<p>(iii) <strong>METHOD 1</strong></p>
<p>\(t = \frac{{ - 4{\pi ^2}}}{{250}}\int_{48}^0 {\left( {{h^{\frac{3}{2}}} + 32{h^{\frac{1}{2}}} + 256{h^{ - \frac{1}{2}}}} \right)} {\text{d}}h\) <strong><em>(M1)</em></strong></p>
<p>\(t = 2688.756 \ldots {\text{ (s)}}\) <strong><em>(A1)</em></strong></p>
<p>\(45\) minutes (correct to the nearest minute) <strong><em>A1</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>\(t = \frac{{ - 4{\pi ^2}}}{{250}}\left( {\frac{2}{5}{h^{\frac{5}{2}}} + \frac{{64}}{3}{h^{\frac{3}{2}}} + 512{h^{\frac{1}{2}}}} \right) + c\)</p>
<p>when \(t = 0,{\text{ }}h = 48 \Rightarrow c = 2688.756 \ldots \left( {c = \frac{{4{\pi ^2}}}{{250}}\left( {\frac{2}{5} \times {{48}^{\frac{5}{2}}} + \frac{{64}}{3} \times {{48}^{\frac{3}{2}}} + 512 \times {{48}^{\frac{1}{2}}}} \right)} \right)\) <strong><em>(M1)</em></strong></p>
<p>when \(h = 0,{\text{ }}t = 2688.756 \ldots \left( {t = \frac{{4{\pi ^2}}}{{250}}\left( {\frac{2}{5} \times {{48}^{\frac{5}{2}}} + \frac{{64}}{3} \times {{48}^{\frac{3}{2}}} + 512 \times {{48}^{\frac{1}{2}}}} \right)} \right){\text{ (s)}}\) <strong><em>(A1)</em></strong></p>
<p>45 minutes (correct to the nearest minute) <strong><em>A1</em></strong></p>
<p><strong><em>[10 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>EITHER</strong></p>
<p class="p1">the depth stabilizes when \(\frac{{{\text{d}}V}}{{{\text{d}}t}} = 0\;\;\;ie\;\;\;8.5 - \frac{{250\sqrt h }}{{\pi (h + 16)}} = 0\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">attempting to solve \(8.5 - \frac{{250\sqrt h }}{{\pi (h + 16)}} = 0\;\;\;{\text{for }}h\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">the depth stabilizes when \(\frac{{{\text{d}}h}}{{{\text{d}}t}} = 0\;\;\;ie\;\;\;\frac{1}{{4\pi (h + 16)}}\left( {8.5 - \frac{{250\sqrt h }}{{\pi (h + 16)}}} \right) = 0\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">attempting to solve \(\frac{1}{{4\pi (h + 16)}}\left( {8.5 - \frac{{250\sqrt h }}{{\pi (h + 16)}}} \right) = 0\;\;\;{\text{for }}h\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1"><strong>THEN</strong></p>
<p class="p1">\(h = 5.06{\text{ (cm)}}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<p class="p1"><strong><em>Total [16 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 done reasonably well by a large proportion of candidates. Many candidates however were unable to show the required result in part (a). A number of candidates seemingly did not realize how the container was formed while other candidates attempted to fudge the result.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Part (b) was quite well done. In part (b) (i), most candidates were able to correctly calculate \(\frac{{{\text{d}}V}}{{{\text{d}}h}}\) and correctly apply a related rates expression to show the given result. Some candidates however made a sign error when stating \(\frac{{{\text{d}}V}}{{{\text{d}}t}}\). A large number of candidates successfully answered part (b) (ii). In part (b) (iii), successful candidates either set up and calculated an appropriate definite integral or antidifferentiated and found that \(t = C\) when \(h = 0\).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">In part (c), a pleasing number of candidates realized that the water depth stabilized when either \(\frac{{{\text{d}}V}}{{{\text{d}}t}} = 0\) or \(\frac{{{\text{d}}h}}{{{\text{d}}t}} = 0\), sketched an appropriate graph and found the correct value of \(h\). Some candidates misinterpreted the situation and attempted to find the coordinates of the local minimum of their graph.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(f(x) = \frac{{{{\text{e}}^{2x}} + 1}}{{{{\text{e}}^x} - 2}}\).</span></p>
</div>
<div class="specification">
<p><span style="font-family: 'times new roman', times; font-size: medium;">The line \({L_2}\) is parallel to \({L_1}\) and tangent to the curve \(y = f(x)\).</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 the equations of the horizontal and vertical asymptotes of the curve \(y = f(x)\).</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 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;">(i) Find \(f'(x)\).</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;">(ii) Show that the curve has exactly one point where its tangent is horizontal.</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;">(iii) Find the coordinates of this point.</span></p>
<p> </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 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;">Find the equation of \({L_1}\), the normal to the curve at the point where it crosses the <em>y</em>-axis.</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 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;">Find the equation of the line \({L_2}\).</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 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;">\(x \to - \infty \Rightarrow y \to - \frac{1}{2}\) so \(y = - \frac{1}{2}\) is an asymptote <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({{\text{e}}^x} - 2 = 0 \Rightarrow x = \ln 2\) so \(x = \ln 2{\text{ }}( = 0.693)\) is an asymptote </span><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>(M1)A1</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>[4 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: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \(f'(x) = \frac{{2\left( {{{\text{e}}^x} - 2} \right){{\text{e}}^{2x}} - \left( {{{\text{e}}^{2x}} + 1} \right){{\text{e}}^x}}}{{{{\left( {{{\text{e}}^x} - 2} \right)}^2}}}\) <strong><em>M1A1</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;"> \( = \frac{{{{\text{e}}^{3x}} - 4{{\text{e}}^{2x}} - {{\text{e}}^x}}}{{{{\left( {{{\text{e}}^x} - 2} \right)}^2}}}\)</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;">(ii) \(f'(x) = 0\) when \({{\text{e}}^{3x}} - 4{{\text{e}}^{2x}} - {{\text{e}}^x} = 0\) <strong><em>M1</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;"> \({{\text{e}}^x}\left( {{{\text{e}}^{2x}} - 4{{\text{e}}^x} - 1} \right) = 0\)</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;"> \({{\text{e}}^x} = 0,{\text{ }}{{\text{e}}^x} = - 0.236,{\text{ }}{{\text{e}}^x} = 4.24{\text{ }}({\text{or }}{{\text{e}}^x} = 2 \pm \sqrt 5 )\) <strong><em>A1A1</em></strong></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> Award <strong><em>A1 </em></strong>for zero, <strong><em>A1 </em></strong>for other two solutions.</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;"> Accept any answers which show a zero, a negative and a positive.</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;"> as \({{\text{e}}^x} > 0\) exactly one solution <strong><em>R1</em></strong></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> Do not award marks for purely graphical solution.</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 Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) (1.44, 8.47) <strong><em>A1A1</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>[8 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: 'times new roman', times; font-size: medium;">\(f'(0) = - 4\) <strong><em>(A1)</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;">so gradient of normal is \(\frac{1}{4}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(0) = - 2\) <strong><em>(A1)</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;">so equation of \({L_1}\) is \(y = \frac{1}{4}x - 2\) <strong><em>A1</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>[4 marks]</em></strong></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;">\(f'(x) = \frac{1}{4}\) <strong><em>M1</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;">so \(x = 1.46\) <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(1.46) = 8.47\) <strong><em>(A1)</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;">equation of \({L_2}\) is \(y - 8.47 = \frac{1}{4}(x - 1.46)\) <strong><em>A1</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;">(or \(y = \frac{1}{4}x + 8.11\))</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>[5 marks]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The region \(A\) is enclosed by the graph of \(y = 2\arcsin (x - 1) - \frac{\pi }{4}\), the \(y\)-axis and the line \(y = \frac{\pi }{4}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down a definite integral to represent the area of \(A\).</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>Calculate the area of \(A\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>\(2\arcsin (x - 1) - \frac{\pi }{4} = \frac{\pi }{4}\) <strong><em>(M1)</em></strong></p>
<p>\(x = 1 + \frac{1}{{\sqrt 2 }}\,\,\,( = 1.707 \ldots )\) <strong><em>(A1)</em></strong></p>
<p>\(\int\limits_0^{1 + \frac{1}{{\sqrt 2 }}} {\frac{\pi }{4} - \left( {2\arcsin \left( {x - 1} \right) - \frac{\pi }{4}} \right)dx} \) <strong><em>M1A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>M1 </em></strong>for an attempt to find the difference between two functions, <strong><em>A1 </em></strong>for all correct.</p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>when \(x = 0,{\text{ }}y = \frac{{ - 5\pi }}{4}\,\,\,( = - 3.93)\) <strong><em>A1</em></strong></p>
<p>\(x = 1 + \sin \left( {\frac{{4y + \pi }}{8}} \right)\) <strong><em>M1A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>M1 </em></strong>for an attempt to find the inverse function.</p>
<p> </p>
<p>\(\int_{\frac{{ - 5\pi }}{4}}^{\frac{\pi }{4}} {\left( {1 + \sin \left( {\frac{{4y + \pi }}{8}} \right)} \right){\text{d}}y} \) <strong><em>A1</em></strong></p>
<p><strong>METHOD 3</strong></p>
<p>\(\int_0^{1.38...} {\left( {2\arcsin \left( {x - 1} \right) - \frac{\pi }{4}} \right){\text{d}}x} \left| + \right.\int\limits_0^{1.71...} {\frac{\pi }{4}{\text{d}}x - \int\limits_{1.38...}^{1.71...} {\left( {2\arcsin \left( {x - 1} \right) - \frac{\pi }{4}} \right)dx} } \) <strong><em>M1A1A1A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>M1 </em></strong>for considering the area below the \(x\)-axis and above the \(x\)-axis and <strong><em>A1 </em></strong>for each correct integral.</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\({\text{area}} = 3.30{\text{ (square units)}}\) <strong><em>A2</em></strong></p>
<p><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;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The displacement, \(s\), in metres, of a particle \(t\) seconds after it passes through the origin is given by the expression \(s = \ln (2 - {e^{ - t}}),{\text{ }}t \geqslant 0\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find an expression for the velocity, \(v\), of the particle at time \(t\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find an expression for the acceleration, \(a\), of the particle at time \(t\).</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 acceleration of the particle at time \(t = 0\).</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">\(v - \frac{{{\text{d}}s}}{{{\text{d}}t}} = \frac{{{{\text{e}}^{ - t}}}}{{2 - {{\text{e}}^{ - t}}}}{\text{ }}\left( { = \frac{1}{{2{{\text{e}}^t} - 1}}{\text{ or }} - 1 + \frac{2}{{2 - {{\text{e}}^{ - t}}}}} \right)\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p2"><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">\(a = \frac{{{{\text{d}}^2}s}}{{{\text{d}}{t^2}}} = \frac{{ - {{\text{e}}^{ - t}}(2 - {{\text{e}}^{ - t}}{\text{)}} - {{\text{e}}^{ - t}} \times {{\text{e}}^{ - t}}}}{{{{(2 - {{\text{e}}^{ - t}})}^2}}}{\text{ }}\left( { = \frac{{ - 2{{\text{e}}^{ - t}}}}{{{{(2 - {{\text{e}}^{ - t}})}^2}}}} \right)\) <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>If simplified in part (a) award <strong><em>(M1)A1 </em></strong>for \(a = \frac{{{{\text{d}}^2}s}}{{{\text{d}}{t^2}}} = \frac{{ - 2{{\text{e}}^t}}}{{{{(2{{\text{e}}^t} - 1)}^2}}}\).</p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>M1A1 </em></strong>for \(a = - {{\text{e}}^{ - t}}{(2 - {{\text{e}}^{ - t}})^{ - 2}}({{\text{e}}^{ - t}}) - {{\text{e}}^{ - t}}{(2 - {{\text{e}}^{ - t}})^{ - 1}}\).</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">\(a = - 2{\text{ }}({\text{m}}{{\text{s}}^{ - 2}})\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[1 mark]</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">Mostly well done. There were a few sign errors but most candidates were correctly applying the quotient or chain rules.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Mostly well done. There were a few sign errors but most candidates were correctly applying the quotient or chain rules.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Mostly well done. There were a few sign errors but most candidates were correctly applying the quotient or chain rules.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">(a) Differentiate \(f(x) = \arcsin x + 2\sqrt {1 - {x^2}} \) , \(x \in [ - 1, 1]\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(b) Find the coordinates of the point on the graph of \(y = f (x)\) in \([ - 1, 1]\), where the </span><span style="font-family: times new roman,times; font-size: medium;">gradient of the tangent to the curve is zero.</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;">(a) \(f'(x) = \frac{1}{{\sqrt {1 - {x^2}} }} - \frac{{2x}}{{\sqrt {1 - {x^2}} }}\) \(\left( { = \frac{{1 - 2x}}{{\sqrt {1 - {x^2}} }}} \right)\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">M1A1A1</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 first term,</span><br><span style="font-family: times new roman,times; font-size: medium;"> <em><strong>M1A1</strong></em> for second term (<em><strong>M1</strong></em> for attempting chain rule).</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;">(b) \(f'(x) = 0\) <em><strong>(M1)</strong></em></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;"><span style="font-family: times new roman,times; font-size: medium;">\(x = 0.5\)</span></span> , </span><span style="font-family: times new roman,times; font-size: medium;">\(y = 2.26\)</span> <span style="font-family: times new roman,times; font-size: medium;">or </span><span style="font-family: times new roman,times; font-size: medium;">\(\frac{\pi }{6} + \sqrt 3 \) (</span><span style="font-family: times new roman,times; font-size: medium;">accept (\(0.500\), \(2.26\)) </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;"> </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>
<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 scored well on this question, showing competence at non-trivial </span><span style="font-family: times new roman,times; font-size: medium;">differentiation. The follow through rules allowed candidates to recover from minor errors in </span><span style="font-family: times new roman,times; font-size: medium;">part (a). Some candidates demonstrated their resourcefulness in using their GDC to answer </span><span style="font-family: times new roman,times; font-size: medium;">part (b) even when they had been unable to gain full marks on part (a).</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the volume of the solid formed when the region bounded by the graph of \(y = \sin (x - 1)\), and the lines <em>y</em> = 0 and <em>y</em> = 1 is rotated by \(2\pi \) about the <em>y</em>-axis.</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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">volume \( = \pi \int {{x^2}{\text{d}}y} \) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = \arcsin y + 1\) <strong><em>(M1)(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">volume \( = \pi \int_0^1 {{{(\arcsin y + 1)}^2}{\text{d}}y} \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> is for the limits, provided a correct integration of </span><em style="font-family: 'times new roman', times; font-size: medium;">y</em><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: 30.0px Helvetica;"><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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 2.608993 \ldots \pi = 8.20\) </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A2 N5</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">Although it was recognised that the imprecise nature of the wording of the question caused some difficulties, these were overwhelmingly by candidates who were attempting to rotate around the \(x\)-axis. The majority of students who understood to rotate about the \(y\)-axis had no difficulties in writing the correct integral. Marks lost were for inability to find the correct value of the integral on the GDC (some clearly had the calculator in degrees) and also for poor rounding where the GDC had been used correctly. In the few instances where students seemed confused by the lack of precision in the question, benefit of the doubt was given and full points awarded.</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">By using an appropriate substitution find</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[\int {\frac{{\tan (\ln y)}}{y}{\text{d}}y,{\text{ }}y > 0{\text{ .}}} \]</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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(u = \ln y \Rightarrow {\text{d}}u = \frac{1}{y}{\text{d}}y\) <strong><em>A1(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {\frac{{\tan (\ln y)}}{y}{\text{d}}y} = \int {\tan u{\text{d}}u} \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \int {\frac{{\sin u}}{{\cos u}}{\text{d}}u = - \ln \left| {\cos u} \right| + c} \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {\frac{{\tan (\ln y)}}{y}{\text{d}}y} = - \ln \left| {\cos (\ln y)} \right| + c\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {\frac{{\tan (\ln y)}}{y}{\text{d}}y} = \ln \left| {\sec (\ln y)} \right| + c\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates obtained the first three marks, but then attempted various methods unsuccessfully. Quite a few candidates attempted integration by parts rather than substitution. The candidates who successfully integrated the expression often failed to put the absolute value sign in the final answer.</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A stalactite has the shape of a circular cone. Its height is 200 mm and is increasing at a rate of 3 mm per century. Its base radius is 40 mm and is decreasing at a rate of 0.5 mm per century. Determine if its volume is increasing or decreasing, and the rate at which the volume is changing.</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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(V = \frac{\pi }{3}{r^2}h\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}V}}{{{\text{d}}t}} = \frac{\pi }{3}\left[ {2rh\frac{{{\text{d}}r}}{{{\text{d}}t}} + {r^2}\frac{{{\text{d}}h}}{{{\text{d}}t}}} \right]\) <strong><em>M1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">at the given instant</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}V}}{{{\text{d}}t}} = \frac{\pi }{3}\left[ {2(4)(200)\left( { - \frac{1}{2}} \right) + {{40}^2}(3)} \right]\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{ - 3200\pi }}{3} = - 3351.03 \ldots \approx 3350\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">hence, the volume is decreasing (at approximately 3350 \({\text{m}}{{\text{m}}^3}\) per century) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Few candidates applied the method of implicit differentiation and related rates correctly. Some candidates incorrectly interpreted this question as one of constant linear rates.</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider the triangle \({\text{PQR}}\) where \({\rm{Q\hat PR = 30^\circ }}\), \({\text{PQ}} = (x + 2){\text{ cm}}\) and \({\text{PR}} = {(5 - x)^2}{\text{ cm}}\), where \( - 2 < x < 5\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that the area, \(A\;{\text{c}}{{\text{m}}^2}\), of the triangle is given by \(A = \frac{1}{4}({x^3} - 8{x^2} + 5x + 50)\).</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">(i) <span class="Apple-converted-space"> </span>State \(\frac{{{\text{d}}A}}{{{\text{d}}x}}\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Verify that \(\frac{{{\text{d}}A}}{{{\text{d}}x}} = 0\) when \(x = \frac{1}{3}\).</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">(i) <span class="Apple-converted-space"> </span>Find \(\frac{{{{\text{d}}^2}A}}{{{\text{d}}{x^2}}}\) and hence justify that \(x = \frac{1}{3}\) gives the maximum area of triangle \(PQR\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>State the maximum area of triangle \(PQR\).</p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>Find \(QR\) when the area of triangle \(PQR\) is a maximum.</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 class="p1">use of \(A = \frac{1}{2}qr\sin \theta \) to obtain \(A = \frac{1}{2}(x + 2){(5 - x)^2}\sin 30^\circ \) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">\( = \frac{1}{4}(x + 2)(25 - 10x + {x^2})\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">\(A = \frac{1}{4}({x^3} - 8{x^2} + 5x + 50)\) <span class="Apple-converted-space"> </span><strong><em>AG</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">(i) <span class="Apple-converted-space"> </span>\(\frac{{{\text{d}}A}}{{{\text{d}}x}} = \frac{1}{4}(3{x^2} - 16x + 5) = \frac{1}{4}(3x - 1)(x - 5)\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span><strong>METHOD 1</strong></p>
<p class="p1"><strong>EITHER</strong></p>
<p class="p1">\(\frac{{{\text{d}}A}}{{{\text{d}}x}} = \frac{1}{4}\left( {3{{\left( {\frac{1}{3}} \right)}^2} - 16\left( {\frac{1}{3}} \right) + 5} \right) = 0\) <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">\(\frac{{{\text{d}}A}}{{{\text{d}}x}} = \frac{1}{4}\left( {3\left( {\frac{1}{3}} \right) - 1} \right)\left( {\left( {\frac{1}{3}} \right) - 5} \right) = 0\) <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p1"><strong>THEN</strong></p>
<p class="p1">so \(\frac{{{\text{d}}A}}{{{\text{d}}x}} = 0\) when \(x = \frac{1}{3}\) <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p1"><strong>METHOD 2</strong></p>
<p class="p1">solving \(\frac{{{\text{d}}A}}{{{\text{d}}x}} = 0\) for \(x\)<em> <span class="Apple-converted-space"> </span></em><strong><em>M1</em></strong></p>
<p class="p1">\( - 2 < x < 5 \Rightarrow x = \frac{1}{3}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">so \(\frac{{{\text{d}}A}}{{{\text{d}}x}} = 0\) when \(x = \frac{1}{3}\) <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p1"><strong>METHOD 3</strong></p>
<p class="p1">a correct graph of \(\frac{{{\text{d}}A}}{{{\text{d}}x}}\) versus \(x\)<em> <span class="Apple-converted-space"> </span></em><strong><em>M1</em></strong></p>
<p class="p1">the graph clearly showing that \(\frac{{{\text{d}}A}}{{{\text{d}}x}} = 0\) when \(x = \frac{1}{3}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">so \(\frac{{{\text{d}}A}}{{{\text{d}}x}} = 0\) when \(x = \frac{1}{3}\) <span class="Apple-converted-space"> </span><strong><em>AG</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>(i) \(\frac{{{{\text{d}}^2}A}}{{{\text{d}}{x^2}}} = \frac{1}{2}(3x - 8)\) <strong><em>A1</em></strong></p>
<p>for \(x = \frac{1}{3},{\text{ }}\frac{{{{\text{d}}^2}A}}{{{\text{d}}{x^2}}} = - 3.5{\text{ }}( < 0)\) <strong><em>R1</em></strong></p>
<p>so \(x = \frac{1}{3}\) gives the maximum area of triangle \(PQR\) <strong><em>AG</em></strong></p>
<p>(ii) \({A_{\max }} = \frac{{343}}{{27}}{\text{ }}( = 12.7){\text{ (c}}{{\text{m}}^2}{\text{)}}\) <strong><em>A1</em></strong></p>
<p>(iii) \({\text{PQ}} = \frac{7}{3}{\text{ (cm)}}\) and \({\text{PR}} = {\left( {\frac{{14}}{3}} \right)^2}{\text{ (cm)}}\) <strong><em>(A1)</em></strong></p>
<p>\({\text{Q}}{{\text{R}}^2} = {\left( {\frac{7}{3}} \right)^2} + {\left( {\frac{{14}}{3}} \right)^4} - 2\left( {\frac{7}{3}} \right){\left( {\frac{{14}}{3}} \right)^2}\cos 30^\circ \) <strong><em>(M1)(A1)</em></strong></p>
<p>\( = 391.702 \ldots \)</p>
<p>\({\text{QR = 19.8 (cm)}}\) <strong><em>A1</em></strong></p>
<p><strong><em>[7 marks]</em></strong></p>
<p><strong><em>Total [12 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 generally well done. Parts (a) and (b) were straightforward and well answered.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">This question was generally well done. Parts (a) and (b) were straightforward and well answered.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question was generally well done. Parts (c) (i) and (ii) were also well answered with most candidates correctly applying the second derivative test and displaying sound reasoning skills.</p>
<p>Part (c) (iii) required the use of the cosine rule and was reasonably well done. The most common error committed by candidates in attempting to find the value of \(QR\) was to use \({\text{PR}} = \frac{{14}}{3}{\text{ (cm)}}\) rather than \({\text{PR}} = {\left( {\frac{{14}}{3}} \right)^2}{\text{ (cm)}}\). The occasional candidate used \(\cos 30^\circ = \frac{1}{2}\).</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: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The particle <em>P</em> moves along the <em>x</em>-axis such that its velocity, \(v{\text{ m}}{{\text{s}}^{ - 1}}\) , at time <em>t</em> seconds is given by \(v = \cos ({t^2})\).</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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Given that <em>P</em> is at the origin O at time <em>t</em> = 0 , calculate</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) the displacement of <em>P</em> from O after 3 seconds;</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) the total distance travelled by <em>P</em> in the first 3 seconds.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the time at which the total distance travelled by <em>P</em> is 1 m.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) displacement \( = \int_0^3 {v{\text{d}}t} \) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 0.703{\text{ (m)}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) total distance \({\text{ = }}\int_0^3 {\left| v \right|{\text{d}}t} \) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 2.05{\text{ (m)}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">solving the equation \(\int_0^t {\left| {\cos ({u^2})} \right|{\text{d}}u = 1} \) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(t = 1.39{\text{ (s)}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><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>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The diagram below shows the graphs of \(y = \left| {\frac{3}{2}x - 3} \right|,{\text{ }}y = 3\) and a quadratic function, that all intersect in the same two points.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><br><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAe8AAAFYCAIAAAD1JONXAAAgAElEQVR4nO3dz2sc157+8fufVEOtnEE/LrNRuqWY2P5CJrYTd1o2Bl0Pgyw5csLY12BZQrItz7WnsWLo6LoVKwSGGNqzHFrMl9lMX9CuFxkEvZhFqN0lbbQIxcUYKpggziyOVWnrx1F1d3Wdc6reLz6LQXbutFvVjx6dqjr1OwEAsN/vdL8AvX7avPp718m5J/64+fKNEEK82rp74rOvt/+m+4UBQHcynuZCiN1XW/eHnA/ubv0shBC7L7fuX56t/6T7VQFAd0hzIXbqs87v9xL8F+/7Pz33ftH8kgCgS6S5EL9ufz2a+/vK9q9C7L6s37i/9Ur3KwKAbpHmnWn+t+0/P3m7gA4AViHNxdtzoVf/w9v+bqX+113drwYAekCai7dp/tE/Xb//ny/fzfLlpSXf9zW9KgDoAmkuhHi9XfkH96NHWzvvrLF4nuc6uY1nG7peFgBER5oLIX7eWp45eI358tKS6+RcJ0c9B2A+0vzNztZ3T7f2LbG8LeZyqOcAzJfZNN99vf304xO3n//Hk7vf/+/rA3+8vLT04cmTrpP78vp16jkA82U3zV9t3R9yPrlb//FglMtivlmvu07uRa1GPQdgvsymuYos5kEQyEzfeLZBPQdgONJ8v7CYCyHk/+H7PvUcgOFI8/0ajYYs5mIvzYUQG882lpeWdL80ADgSaa4SpjkAGI40VyHNAdiCNFchzQHYgjRXIc0B2II0VyHNAdiCNFchzQHYgjRXIc0B2II0VyHNAdiCNFchzQHYgjRXIc0B2II0VyHNAdiCNFchzQHYgjRXIc0B2II0VyHNAdiCNFchzQHYgjRXIc0B2II0VyHNAdiCNFchzQHYgjRXIc0B2II0VyHNAdiCNFchzQHYgjRXIc0B2II0VyHNAdiCNFchzQHYgjRXIc0B2II0VyHNAdiCNFchzQHYgjRXIc0B2II0VyHNAdgi5Wnu+34QBD3/56Q5AFukOc3b7bbr5BqNRs//C6Q5AFukOc2FEJcvXfri+vWe/3PSHDDfhydPvqjVdL8K/VKe5i9qNdfJ+b7f239OmgOGa7VarpNrNpu6X4h+KU/zPhdbSHPAcBvPNlwn18/psdRIeZqL/hZbSHPAcB+ePPnV6qruV2GE9Kd5P4stpDlgMpZZOqU/zftZbCHNAZOxzNIp/Wku+lhsIc0Bk7HM0ikTad7zYgtpDhiLZZZ9MpHmPS+2kOaAsVhm2ScTaS56XWwhzQFjscyyT1bSvLfFFtIcMBPLLAdlJc17W2whzQEzscxyUFbSXPS02EKaA2ZimeWgDKV5D4stpDlgIJZZDhV/mgdBcPnSpX72oR2QHhZbSHPAQMYus/S8wV8s4k9z3/e/uH7ddXLLS0t6/20HfXH9+uVLl6L/fdIcMJCByyztdrvbeIndoFZaNut118l9ePKkUSW90Wi4Tq7dbkf8+6Q5YJpms+k6uVarpfuF/MaQuBvgurn8YWVUSfd933Vy0Te2J80B03y1uvrhyZO6X8VbnueZk3IDPwsqf2qZE4td/TZkzssGIIQIgsB1chvPNnS/EBEEgbywQnslDyVxTUu73V5eWnKd3BfXr2v/8dXVYgtpDhjFkGUWz/MuX7rkOrmvVle1Z1oouSsUZYxqz8euFlu0v1oAnbQvs3RWcu0/VPZJ9Hpz3/fDkh79VGTslpeWIi62kOaAObQvs3RWcgOvj9Rw91Cj0fjw5EmNQSl/WfM879i/SZoD5tC4zGJyJQ/puRdUb0mP/hOeNAfMoWuZxfBKHtJ5Z7/Gkh7xsCDNAUPIEhb98uK4/p+aX8lDmvdp0VXSI/7KRpoDhuj21r/+tVotKyp5yIhdt5Iv6REXW0hzwBBJ3jcfVvLLly6ZX8lDRqS50FHSoyy2kOaACbq9i7sfrVZLlktbKnnIlDSXOkv6oN/HKIstpDlggmSWWYIg+Gp11bpKHjIrzUVHSb986VKUiwj7cexObKQ5YIIEllnCSr7xbMOuSh4yLs2l8J19UasN7p09dpdk0hzQTj6ZYHCfxM5KPugGOVCGprlI5C0+9gkmpDmgXW+PaI8omeKYDHPTXBr0e61+WChpDmh3+dKl5aWl2P9nU1PJQ6anuRjwm67+sU+aA3oN6BGgaarkIQvSXBrQu69+WChpDugV+yNAfd9PWSUPWZPmYmAl/fKlS0edLifNAb3ifQRos9lMXyUP2ZTmUuwXEikuZSXNAY1iXGZJ8tJnXexLcyFEEATy969YvjGK28xIc0CjuDZNDCtguj/OVqa5FGNJP+rehNR/+wFjxfJsis5KrvEJOcmwOM1FR0nvc7/Ko55fQZoDuvT/bIokdwoxgd1pLvW/l/xRLYA0B3SJ/sTHgwx5aGXC0pDmIo5N5Q9doSPNAS362TRR+7MqdUlJmkv9lHT5a92+s+cZPCAAE/S2aWI2K3koVWku+ivpB69sJc0BLRR3gRwls5U8lLY0l3or6fKEaudd/lk+MgBd1HdoH5TxSh5KZ5qLnkr6wWOINAeSd7BXKWzW6xmv5KHUprnUbUnft6UihwiQvIh38/u+/8X1666TW15aynIlD6U8zcW7Jf3YW4Q36/XOcy+kOZCwiHfzy49qVwsyqZf+NJc8zwt/jCt+g9t3XRRpDiTs2Lv52+12lM9yBmUlzcW7JV3x87zzLn/SHEjSsXfzy0qu/ghnVobSXDr2B3vn/cSkOZCko/bYEFTyCDKX5pLiJ3xnOyDNgSQdtf8dlTyKjKa5UP6o33i28eHJkzLWSXMgGYfezU8ljy67aS4d+jM/PKtOmgOJOfiQXip5V7Ke5uKIH/7yMeGkOZCYzrs9Il6Ehk6k+Vv7Ll+VNYE0B5IR/kIc8dozHESa/yYs6V9cvy6XWUhzIBnybv5Wq9XnswqyjDTfT+7EJnd+IM2BBMgrDuSHrs/niGXZoNLc9/3Net3S+Wp1VUa5XLbT/noYJt3T+Yl7Uatpfz39jMZV/kGlued54beHYRgmI3PorU/JYKVFJfwOXZudZZM2IF6e55WKRfkR22RJs2+kuYo8zs6dPT86PMIBB8QlvHBlZGj49KkzbuTdzKFAmqvIND996szqk8q5s+cp6UD/wko+WbpYWauODA3fmZ/X/aLSgDRXcffOsz8qP65+8+2Nm7co6UDPOiv50vK96jffLi3fcyPsZo4oMp7mb3Z+2Jg9kXOdnHti5uu/eK/f/WPXycnLYKenZ6rffFv95ltKOtCbfZVcfqAmSxfH83kuLY9FltN89/X2d3f/3NzZFWL35db9T1xn6rn3S+ffkDX8zvz8yNCwPPjkdJZ0DkRALQiC9ep6ZyWXU1mrusrdzNGVLKf5u3bqs84Hd7d+7vyazGt5X2jnUdhZ0meuXqWkA0dptVoThYLr5KamroSVPGxFbseDG9En0lzafbV1/+/n6i933/lq2L7H8/nJ0sXOA1HO7fkFWdJf1GqUdKBTEATlctl1cvmx/MqDhwc/Pvmx/GSppPtlpgdpLoR45f3l6ezo/a1Xu/v+IDzhKVfPV59UDh6Rq08qk6WLrpMrFYsabxwAjBJW8unpmX2VXM6j8mOXZzTHKvNp/uv216N793Gd+OPmyzedfximebvddp3cjZu3Dh6UcpaW740MDVPSgWMruZypqSuuk+PDEqPMp7kQQojdne3NysyQkxta3nrV8fXOixEnS6X8WP6oQ1Oe0qGkI+OOreThh2V0eKRcLut+valCmu/Z/fH5J++5V+s7HV/rTPNGo+E6OUXXoKQjyyJW8vCEk7v3LHXEhTQP/by1fObjyg+dl5x3prnctHNq6or6MKWkI4OazWaUSh7O6VNnip9e0P2q04Y0l97sbD36+KNHWzuHr5tL8lxolIOVko6M6KqSd57/5Ibq2GU5zf+2Xflsb5fET+5+/1/b70a5OJDmcptfxblQSjoyJeIq+aHnP9lmK3ZZTvPjHWwQpWJRfS5UUdKfP39OSUc6+L7fbSUPK87I0DDnPweBNFc5mOYRz4UeVdInCgXO/MB2jUZjPJ/vtpJXOf85YKS5ysE0j34u9OCsPHiYH8u7Tq5cLlPSYSPf9xcXFuU20XJj0W7n3NnznP8cENJc5dBzNXL/oG4rSVjS5aIhJR3WCSv53NyXPRz81W++XX1SkdcF6P6npBNprnJomnd7LpSSDtv1X8nlTE/PcP5zcEhzlaOuoyoVi6dPnen5mJYlXR7ZlHQYrv9KHs7I0PDiwqLuf1BqkeYqR6W5PBfaT0mhpMN8cVVyOfL8J48ZGhzSXOWoNPd9v+dzoZR0WCHGSi7n3NnzE4WC7n9WmpHmKoo71srl8ujwSG/nQhUlfXFhkZIOvdrt9p35+bgquRzOfyaANFdRpHmr1XKd3O35hViOdUo6DCFXEUeHR+Kq5HI4/5kA0lxFvZvEsXvk9lnSOfSRpHa7fW12Nt5KHjaV0eERzn8OGmmuok7z3u4LjXLoz8196Tq58XyeJ7MgGZv1uqzk/Vx6e9Rw/2cySHMVdZoHQVAYe//Q54X2P4/Kj0+fOkNJx6CFlfzc2fOHPiux/8mP5bn/MwGkucqx+3Yqnhcay1DSMVADreRyVh485PmfySDNVY5Nc/m80HjPF1HSkYAEKrkcnv+ZGNJcJcqe+tdmZ2M/F7pvWElHvBKo5OGh6zq59eq67n9xJpDmKlHSvNlsuk5uafneQD8VlHTEIrFKLufGzVuuk+NRLckgzVWipHkQBOP5/Lmz5wf9wZBDSUdvgiBIrJKHkx/LT5ZKuv/pWUGaq0R8euGLWm2g50L3TVjS78zPU9IRRbvdniyVEqvkcjj/mTDSXCVimsttW6anZ5L5kMiRJb0w9j5Py4VCEASybYwMDSewHtg5k6WL4/k85z8TQ5qrRH+y+OLC4sjQcFzbtkQcSjrUPM8rFYsJV3I5cmOWjWcbut+DDCHNVaKneezbtkQfWdKjv1RkQWcl13JYsjFL8khzla4islQsDvpSRUUPOnf2vOvkrs3Ottvtgb4nMF9YySdLFxP+fVFOZa3KgymSR5qrdJXmA9q2JfrcuHlrdHiEkp5lGlfJO4eNWbQgzVW6SsaBbtsScSjpWaa9kofDxixakOYq3fbcQW/bEnEo6VljSCWXw4WJupDmKt0GopZLFQ8dSnp2mFPJ5UyWLhbG3ufCxOSR5io91Ns78/MjQ8PaP1FyKOnpFgTB8+fPDankcrgwUSPSXKWHHJTbtmi5JuyoT5cs6ZOlEttlpEmr1ZooFMyp5HLk9bL8OqgFaa7SW6stFYunT53R/rnqHEp6mgRBUC6XXSeXH8sbUsnD4cJEjUhzld7iT+5tpPFSxUOnslaVJb1ULFLS7RVW8qmpK+ZUcjnywsRms6n7Tcoo0lyltzQ34VJFxedtZGjYdXIvajXOU9mls5Kb1hXk5MfypWJR9/uUXaS5Ss9LE4ZcqnjoVNaqk6WLlHS7hJV8enrGtEouhwsTtSPNVXpOc3mp4tTUFe2fsaNmafkeJd0K5ldyOefOnufCRL1Ic5V+ThsuLiyODo+YWaPkUNLNZ34ll8OFiSYgzVX6SXPP8wb9AOhYhpJuJlsquRz5KGd2TNSLNFfp85K+yVJJ166KXQ0l3TS2VPLw+HGdXLlc1v22ZR1prtJnmpt2J5F6KOkm8H3fokouR94xRA/QjjRX6f92m4lCIbEHQPc/YUmfKBT4cCav0WhYVMnDyY/lr83O6n7zQJor9Z/mZt5JpJ6VBw9lSV+vrlPSk+H7/uLCouvkTp8686j8WPsxEH24Y8gcpLlK/2keBIHcSUP7p66roaQnqdlsjufz1lVyOWxlbg7SXCWWjU1MvpNIPWFJL5fLlPRBsLeSh0cIm/+YgzRXieVINf9OIsVU1qry4rOJQoEHg8Wr0WjISj4396V1lVzOubPnx/N5ftIbgjRXiat3lMtlw+8kUs/Kg4f5sTwlPS62V3I58o6hF7Wa7rcTb5HmKnGluS13Eimmsladnp6hpPevs5Jr/7b2M9wxZBrSXCXGNUH5TCJ767kcSno/0lHJ5XArv4FIc5UY09yuO4kUQ0nvTWoquRx5DFDMjUKaq8R7vr5ULFpxo3+UoaRHl6ZKLqeyVh0dHuEZQ6YhzVXiTfPU1PPwIx2WdHa1Poq8fSw1lVwOt/KbiTRXif1a2olCwbRHhvY5Kw8enj51xnVyiwuLlPRO7Xb72uys6+TOnT1v490GR01lrToyNHxnfl73G4z9SHOV2NPcxhv9o4wsa+P5PCVdkt/o0eGRGzdvaf/uxDvcym8s0lwl9jQPgmA8n7doH67o01nSs3xyLK2VPJz8WH6yVNL9NuMQpLnKIO5alq0tHWfDDk7GS3qKK7kcirnJSHOVQaS51Tf6R5lH5ccZLOmpr+RyTp86M1Eo6H6zcTjSXGVAOwrZuw9X9MlUSU99JZfDHluGI81VBnTspr6ey8lCSfc8LwuVXM65s+cnCgWuXDIWaa4yuCaShXouJ8UlXVbykaHhdFdyORRz85HmKoM7fDNSz+V0lvR2uz2I9zNhnudNlkqyktu+907EOXf2fGHsfYq5yUhzlYGWkfXqekbquZy5uS9Hh0ds73dBELyo1WQlT81tvccOxdwKpLnKQI9guU3u9PSM9s9qYrP6pHLu7HnXyV2bnbWxpHueVyoW5aMBM1LJ5cjvGsXccKS5yqD7yOLCotVPsehtbty8ZV1J76zkS8v3tL+HSc6j8mM2v7UCaa4y6MRJwVMsehu7SnpmK7kcnkphC9JcJYH+mM16Lsf8kp7lSi6Hp1JYhDRXSSBoMlvPw7AwtqRnvJLLoZhbhDRXSaY2Li4spuAhc/2MaSWdSi6HYm4X0lwlmXzJeD0Pg8OQku553gfj4xmv5HIo5nYhzVUSa4vUczl6SzqVvHMo5tYhzVUSixXqeWeIaCnpnudNFApU8nAo5tYhzVWSLIl35ucze3HLwblx89bI0LDr5F7UaoO+aSUIgnK5LCt5+h4L1dvIYr5eXR/oO494keYqSaY59fxgoEyWLrpObrJUGtwDhVutlqzk09Mz/CgNh2JuI9JcJeEFXOr5wVlavjegkh5W8vxYnkreOayYW4o0V0k4zannh05lrSpLeqlYjKukU8kVQzG3FGmukvzFFVm+NVQ9cZV0Krl65HaJFHMbkeYqyad5BjdWjD79l3Qq+bEjLyiimNuINFfRcuHz4sJipvY973Z6K+lU8igji/mLWm2gRzgGhDRX0ZLmsp5n5LFEvU23Jb3ZbFLJowwPGLIaaa6i66ZE2SKp5+oJS/p6df2oAAqCQP6uQyU/dnjAkFE26/Vu17tIcxVdB3emnhraz4QlvfjphVarte9tbDQaspJzmVCUOX3qzEShQDE3Qbvddp2cPB0dPdNJcxWNVWXj2Ybr5KiTUWZp+V5+LN9Z0n3fl5X89KkzvIdR5vb8AsXcKL7vyxCInumkuYrG49v3/cLY++fOntf+ObdiKmtVeZX0RKHwolajknc7+bF88dMLWg51KHSV6b+Tf49hGIYxfxT98nfaXxzDMAwTZTbrdcWJDVZaVFzdK4mb9brr5NhrmxnczM196Tq5ZrOp8TjHoTzPW15acp3chydPqnNcIs1VtKd5EATFTy/kx/LaP/NMKqeyVh0ZGr4zP6/xIMdBvu93leMSaa6iPc2FEM1m03Vyt+cXtH/ymfSNLOaD23AYvQmC4PKlS4fn+E591sm5ztj1+l93xZudHzZmT+Tc0cr2r6S5kglpLoSYLJV4zhwT+8idbxcXFnUf4OjW37Yrn7mf/Nv2D9/d/f5/X+99lTRXMSTN2SmXGcSw863FduqzTm5orv5y97evkeYqhqS52Nspl3v9mbiGnW/ttvvj80/GZus/dX6NNFcxJ83lnb7c68/ENWywZbfdH59/8t7Q8tarjq+R5irmpLkQYr267nKvPxPHcB+/5d68rD++u/xPQyfub736bamFNFcx6ojnXn8mrpH38VPM7bT7+sd/v/vnH16/2rp7Yuq59+pl/WnN+0WQ5mpGpbngZiImjuF2IXvtet9fcN77eLnuvd4V4uet5Q/cEzNPf9iR/Zw0VzEtzbmZiOlzKmvV0eERbhdKJdJcxbQ0F3s3E3G1ItPbyKsSuV0olUhzFQPTXAgx9/nc6PAINxMx3c6j8mPXyZXLZd2HMAaCNFcxM815cCjT28irErldKK1IcxUz01zwZCKm++GqxNQjzVWMPfqDIBjP50+fOqM9IxgrRu6VWCoWdR+5GCDSXMXYNBd7VyuytyITZeRViQcfhI00Ic1VTE5zwd6KTLRhr8SMIM1VDE9zeTp0enpGe14wJs+5s+fZKzELSHMVw9NcCFEul10n96j8WHtkMGbO0vI98w9jxII0VzH/Y+D7PqdDmaOmslbNj+VLxSJbsmQBaa5ifpqLvdOhN27e0p4djGkzPT3Dyc/sIM1VrEhzIcS12VmeZcHsG+78zBrSXMWWNJfPspgsXdSeIIw5c/rUGe78zBTSXMWWNBdCvKjVuDuUCefGzVuuk2s0GroPTCSHNFexKM2DIJgoFPJjeS4/Z1afVEaHR67Nzuo+KpEo0lzFojQXQrRaLTbLZarffDtZuug6uXa7rfuQRKJIcxW70lwIsbiwyOXnGR95gfmLWk33wYikkeYq1qU5l59nfMLdtbjAPINIcxXr0lwI0Wg0WG/J7PBooSwjzVVsTHPBektWR66xrFfXdR+A0IM0V7E0zVlvyeDIm/gnCgXWWDKLNFexNM0F6y3ZG27iB2muYm+aCyHuzM+z3pKRWXnwkJv4QZqrWJ3mrLdkZFhjgUSaq1id5oL1lmwMayyQSHMV29NccH1L2kdex/LV6qruAw36keYqKUjzcL2F/VvSN9wrhE6kuUoK0lwI0Ww2eXxoKkc+8JN7hSCR5irpSHOx9/jQpeV72gOIiWvknrfpOD4RC9JcJTWfliAIip9eGBkaZr0lHfOo/Jg9b7EPaa6SmjQXQniex/OJUjOnT50Zz+fZ8xadSHOVNKW52Hs+Ec+Dtn3kJYk8Vwj7kOYqKUtzsfc8aC5YtHfkJYnc9omDSHOV9KV5u90ez+d54Jyls/qkwiWJOApprpK+NBd7D5ybmrqiPZuYbuf0qTM8Ig5HIc1VUpnmQoiNZxuuk7s9v6A9npjow3I51EhzlbSmeRAELKDbNSyX41ikuUpa01ywgG7VsFyOKEhzlRSnudhbQOcKdMOnslZluRxRkOYq6U5zsXcFOlvmmjzywc3NZlP3wQLTkeYqqU9zsbdlLlu4mDlyM5aNZxu6DxNYgDRXyUKaB0FQKhY5I2rgyOfDzX0+p/sYgR1Ic5UspLkQot1uF8be54yoUfOo/HhkaPiD8XHOfCIi0lwlI2ku9s6Injt7XnuKMdW9M5+Fsfc584noSHOV7KS5EGKzXuceUUNmsnSRM5/oFmmukqk0F0KsV9e5R1T7yHs+X9Rqug8HWIY0V8lamgdBMPf5HJe4aJzb8wvc84nekOYqWUtzwSUuBkT53OdznPlED0hzlQymuRCi3W5PFAojQ8MEepIjHw43c/UqUY7ekOYq2UxzIUS73Xad3OlTZ7hmMbEol9cjchELekaaq2Q2zYUQzWaTQE9mKmvV/Fie6xHRJ9JcJctpLvYCnYvQBx3lclOtVqul+xsOu5HmKhlPc8FF6ElFOZeWo3+kuQppLvYeVESgE+UwHGmuQppLBDpRDvOR5iqkeUjeJkqgxxvlHF2IEWmuwuetE4Eeb5SzazniRZqrkOb7EOhxRTnbsCB2pLkKaX4Qgd5/lLNWjkEgzVVI80PJk6KTpYvcWESUwxykuQppfhT5eGjuFCXKYQ7SXIU0Vwhv/V99UtEelyaP3IOFKMegkeYqpLmaDHR2W1TM0vK90eGR8Xze8zzd3y6kHGmuQpofq91uj+fzo8MjPODi4Mj9ykvFIttpIQGkuQppHkW73S4Vi66Tu3HzlvYANWempq64Tu7a7Cz7lSMZpLkKaR5R+Ai6qakrnBetrFXPnT3vOrn16jpRjsSQ5iqkeVfklYsZPy/6qPw4P5bnyEHySHMVPpPdkudFM7uMfuPmLdfJTRQKbFaO5JHmKqR5D8Jl9OnpGe3xmthU1qqTpYtyodz3fd3fBGQRaa5CmvcmCIJyuSxXXbJw8eLKg4dydYXdV6ARaa5Cmvej0WiM5/Opv9ZlenqG1RWYgDRXIc375Pv+tdlZ+XDR9JX0sJKXy2WuXYF2pLkKaR6LzXq9MPb+6PDI3NyX2iM4lqmsVcNK3mg0dL/BgBCkuRppHpd2u724sOg6ufxYfuXBQ+1x3M/cnl+Q+65QyWEU0lyFNI9Xs9mcKBTkwouN16SvPHgobwsqFYvsuwLTkOYqpHnsgiCQu+nKG0dtyfTVJxV5AeJ4Ps8hATOR5iqk+YD4vi+fYWR+pq8+qcgdV+STPFlagbFIcxXSfKDa7bbJmb7y4KHs4zLHuScIhst6mu/uNJ9eHXOdnOuMzVb+23u92/mnpHkCOnv6ubPntW8JUFmr3p5fkOvj5Dgsku00f/3D0+Xv/mfnjRBvdrYefey8d+H7HzvjnDRPjO/7L2o1ebfRyNDw9PRM8tenrzx4ODV1RV6vUvz0wma9zroKLJLtNH/HT5tXfz+0vPWq40ukefKazaa8llFezjg9PTPoKxqXlu9NTV2R9wHJ6w65qxM2Is33vNq6O/rHzZdvOr9Gmuvi+36j0ZD3kcq2Plm6eOPmrbgK+8qDhzdu3gqXxV0n9+jhw0ajQRmHvUhzIcTua++/v776yd2tn/f9AWmune/7zWZzvbouF2HC5fWpqStzc1+uPHi48uCh+vkYlbXqyoOHS8v35ua+nCxdDBfE5XLKxrONZrNJiCMFSPPX25V/2Pt4j12v/3Xfuvkf/vCP//Knf5XT+Z+FX9w3/J3B/Z3b84vXPr9evPDZmdP/b+i9vwtDOfpMFKds3RkAAAHNSURBVAp35udf1GrNZpNzm0iZ1Kd5Z1jvm9/P1n96+7d2d7brldkTOffE/a1Xv+U5aW7s3/mXP/1rEASe57Varc16/Q9/+MfO2azXO8fzPM/zKOBIt9SneXS/eN9Puc4/b+78Gn6JlRYAtiDNQ7uvtu4PffR0+/U73Zw0B2AF0vyt3Z2/rHz02crWS643B2CjLKf57uvtpx+/XUN/7+Plf/v/2zu77/4N0hyALbKc5scjzQHYgjRXIc0B2II0VyHNAdiCNFchzQHYgjRXIc0B2II0VyHNAdiCNFchzQHYgjRXIc0B2II0VyHNAdiCNFchzQHYgjRXIc0B2II0VyHNAdiCNFchzQHYgjRXIc0B2II0VyHNAdiCNFchzQHYgjRXIc0B2II0VyHNAdiCNFchzQHYgjRXIc0B2II0VyHNAdiCNFchzQHYgjRXIc0B2II0VyHNAdiCNFchzQHYgjRXIc0B2II0VyHNAdiCNFchzQHYgjRXIc0B2II0VyHNAdiCNFchzQHYgjRXIc0B2II0VyHNAdiCNFchzQHYgjRXIc0B2II0VyHNAdiCNFchzQHYgjRXIc0B2II0VyHNAdiCNFfxPM/3fd2vAgCO93+RcBBNvt3NTQAAAABJRU5ErkJggg==" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Given that the minimum value of the quadratic function is −3, find an expression for the area of the shaded region in the form \(\int_0^t {(a{x^2} + bx + c){\text{d}}x} \), where the constants <em>a</em>, <em>b</em>, <em>c</em> and <em>t</em> are to be determined. (Note: The integral does not need to be evaluated.)</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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\left| {\frac{3}{2}x - 3} \right| = 0\) when <em>x</em> = 2 <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the equation of the parabola is \(y = p{(x - 2)^2} - 3\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">through \((0,{\text{ }}3) \Rightarrow 3 = 4p - 3 \Rightarrow p = \frac{3}{2}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the equation of the parabola is \(y = \frac{3}{2}{(x - 2)^2} - 3{\text{ }}\left( { = \frac{3}{2}{x^2} - 6x + 3} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">area \( = 2\int_0^2 {\left( {3 - \frac{3}{2}x} \right) - \left( {\frac{3}{2}{x^2} - 6x + 3} \right){\text{d}}x} \) <strong><em>M1M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>M1</em></strong> for recognizing symmetry to obtain \(2\int_0^2 , \)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>M1</em></strong> for the difference,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>A1</em></strong> for getting all parts correct.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \int_0^2 {( - 3{x^2} + 9x){\text{d}}x} \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><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">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This was a difficult question and, although many students obtained partial marks, there were few completely correct solutions.</span></p>
</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 shaded region <em>S </em>is enclosed between the curve \(y = x + 2\cos x\), for \(0 \leqslant x \leqslant 2\pi \), and the line \(y = x\), as shown in the diagram below.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><br><img src="images/Schermafbeelding_2014-09-12_om_06.15.17.png" alt></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 the coordinates of the points where the line meets the curve.</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 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 region \(S\) is rotated by \(2\pi \) about the \(x\)-axis to generate a solid.</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;">(i) Write down an integral that represents the volume \(V\) of the solid.</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;">(ii) Find the volume \(V\).</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 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \(\frac{\pi }{2}(1.57),{\text{ }}\frac{{3\pi }}{2}(4.71)\) <strong><em>A1A1</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;">hence the coordinates are \(\left( {\frac{\pi }{2},{\text{ }}\frac{\pi }{2}} \right),{\text{ }}\left( {\frac{{3\pi }}{2},{\text{ }}\frac{{3\pi }}{2}} \right)\) <strong><em>A1</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>[3 marks]<br></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: 21.0px Helvetica;"><span style="font-size: medium; font-family: 'times new roman', times;">(i) \(\pi \int_{\frac{\pi }{2}}^{\frac{{3\pi }}{2}} {\left( {{x^2} - {{(x + 2\cos x)}^2}} \right){\text{d}}x} \) <strong style="font-weight: bold;"><em style="font-style: italic;">A1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; min-height: 25.0px;"><span style="font-size: medium; font-family: 'times new roman', times;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-size: medium; font-family: 'times new roman', times;"><strong style="font-weight: bold;">Note:</strong> Award <strong style="font-weight: bold;"><em style="font-style: italic;">A1 </em></strong>for \({x^2} - {(x + 2\cos x)^2}\), <strong style="font-weight: bold;"><em style="font-style: italic;">A1 </em></strong>for correct limits and <strong style="font-weight: bold;"><em style="font-style: italic;">A1 </em></strong>for \(\pi \).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"><span style="font-size: medium; font-family: 'times new roman', times;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-size: medium; font-family: 'times new roman', times;">(ii) \(6{\pi ^2}{\text{ }}( = 59.2)\) <strong style="font-weight: bold;"><em style="font-style: italic;">A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; min-height: 25.0px;"><span style="font-size: medium; font-family: 'times new roman', times;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-size: medium; font-family: 'times new roman', times;"><strong style="font-weight: bold;">Notes:</strong> Do not award <strong style="font-weight: bold;">ft </strong>from (b)(i).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"><span style="font-size: medium; font-family: 'times new roman', times;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-size: medium; font-family: 'times new roman', times;"><strong style="font-weight: bold;"><em style="font-style: italic;">[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;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider the curve, \(C\) defined by the equation \({y^2} - 2xy = 5 - {{\text{e}}^x}\)<span class="s1">. The point A </span>lies on \(C\) <span class="s1">and has coordinates \((0,{\text{ }}a),{\text{ }}a > 0\)</span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of \(a\).</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">Show that \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{2y - {{\text{e}}^x}}}{{2(y - x)}}\).</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">Find the equation of the normal to \(C\) <span class="s1">at the point A</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 class="p1">Find the coordinates of the second point at which the normal found in part (c) intersects \(C\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Given that \(v = {y^3},{\text{ }}y > 0\)<span class="s1">, find \(\frac{{{\text{d}}v}}{{{\text{d}}x}}\) </span>at \(x = 0\).</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 class="p1">\({a^2} = 5 - 1\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">\(a = 2\) <span class="Apple-converted-space"> </span><strong><em>A1</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">\(2y\frac{{{\text{d}}y}}{{{\text{d}}x}} - \left( {2x\frac{{{\text{d}}y}}{{{\text{d}}x}} + 2y} \right) = - {{\text{e}}^x}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1A1A1A1</em></strong></span></p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>M1 </em></strong>for an attempt at implicit differentiation, <strong><em>A1 </em></strong><span class="s2">for each part.</span></p>
<p class="p1">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{2y - {{\text{e}}^x}}}{{2(y - x)}}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>AG</em></strong></span></p>
<p class="p3"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">at \(x = 0,{\text{ }}\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{3}{4}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1">finding the negative reciprocal of a number <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2">gradient of normal is \( - \frac{4}{3}\)</p>
<p class="p2">\(y = - \frac{4}{3}x + 2\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">substituting linear expression <span class="Apple-converted-space"> </span>(<strong><em>M1)</em></strong></p>
<p class="p2">\({\left( { - \frac{4}{3}x + 2} \right)^2} - 2x\left( { - \frac{4}{3}x + 2} \right) + {{\text{e}}^x} - 5 = 0\) <span class="s1">or equivalent</span></p>
<p class="p1">\(x = 1.56\) <span class="Apple-converted-space"> </span><span class="s2"><strong><em>(M1)A1</em></strong></span></p>
<p class="p3">\(y = - 0.0779\) <span class="Apple-converted-space"> </span><span class="s2"><strong><em>A1</em></strong></span></p>
<p class="p3">\((1.56,{\text{ }} - 0.0779)\)</p>
<p class="p4"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(\frac{{{\text{d}}v}}{{{\text{d}}x}} = 3{y^2}\frac{{{\text{d}}y}}{{{\text{d}}x}}\) </span><strong><em>M1A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(\frac{{{\text{d}}v}}{{{\text{d}}x}} = 3 \times 4 \times \frac{3}{4} = 9\) </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Parts (a) to (c) were generally well done.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Parts (a) to (c) were generally well done.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Parts (a) to (c) were generally well done although a significant number of students found the equation of the tangent rather than the normal in part (c).</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Whilst many were able to make a start on part (d), fewer students had the necessary calculator skills to work it though correctly.</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">There were many overly complicated solutions to part (e), some of which were successful.</p>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">If \(y = \ln \left( {\frac{1}{3}(1 + {{\text{e}}^{ - 2x}})} \right)\), show that \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{2}{3}({{\text{e}}^{ - y}} - 3)\) .</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: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(y = \ln \left( {\frac{1}{3}(1 + {{\text{e}}^{ - 2x}})} \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{ - \frac{2}{3}{{\text{e}}^{ - 2x}}}}{{\frac{1}{3}(1 + {{\text{e}}^{ - 2x}})}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{ - 2{{\text{e}}^{ - 2x}}}}{{1 + {{\text{e}}^{ - 2x}}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({{\text{e}}^y} = \frac{1}{3}(1 + {{\text{e}}^{ - 2x}})\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Now \({{\text{e}}^{ - 2x}} = 3{{\text{e}}^y} - 1\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow \frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{ - 2(3{{\text{e}}^y} - 1)}}{{1 + 3{{\text{e}}^y} - 1}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = - \frac{2}{{3{{\text{e}}^y}}}(3{{\text{e}}^y} - 1)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = - \frac{2}{3}(3 - {{\text{e}}^{ - y}})\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{2}{3}({{\text{e}}^{ - y}} - 3)\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({{\text{e}}^y} = \frac{1}{3}(1 + {{\text{e}}^{ - 2x}})\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({{\text{e}}^y}\frac{{{\text{d}}y}}{{{\text{d}}x}} = - \frac{2}{3}{{\text{e}}^{ - 2x}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Now \({{\text{e}}^{ - 2x}} = 3{{\text{e}}^y} - 1\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow {{\text{e}}^y}\frac{{{\text{d}}y}}{{{\text{d}}x}} = - \frac{2}{3}(3{{\text{e}}^y} - 1)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow \frac{{{\text{d}}y}}{{{\text{d}}x}} = - \frac{2}{3}{{\text{e}}^{ - y}}(3{{\text{e}}^y} - 1)\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{2}{3}( - 3 + {{\text{e}}^{ - y}})\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{2}{3}({{\text{e}}^{ - y}} - 3)\) <strong>AG</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Only two of the three <strong><em>(A1)</em></strong> marks may be implied.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><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: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Solutions were generally disappointing with many candidates being awarded the first 2 or 3 marks, but then going no further.</span></p>
</div>
<br><hr><br><div class="specification">
<p>A point P moves in a straight line with velocity \(v\) ms<sup>−1</sup> given by \(v\left( t \right) = {{\text{e}}^{ - t}} - 8{t^2}{{\text{e}}^{ - 2t}}\) at time <em>t</em> seconds, where <em>t</em> ≥ 0.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the first time <em>t</em><sub>1</sub> at which P has zero velocity.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for the acceleration of P at time <em>t</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of the acceleration of P at time <em>t</em><sub>1</sub>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>attempt to solve \(v\left( t \right) = 0\) for <em>t</em> or equivalent <em><strong>(M1)</strong></em></p>
<p><em>t</em><sub>1</sub> = 0.441(s) <em><strong> A1</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>\(a\left( t \right) = \frac{{{\text{d}}v}}{{{\text{d}}t}} = - {{\text{e}}^{ - t}} - 16t{{\text{e}}^{ - 2t}} + 16{t^2}{{\text{e}}^{ - 2t}}\) <em><strong>M1A1</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>M1</strong> </em>for attempting to differentiate using the product rule.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(a\left( {{t_1}} \right) = - 2.28\) (ms<sup>−2</sup>) <em><strong>A1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p 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 \(f(x) = x{(x + 2)^6}\).</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;">Solve the inequality \(f(x) > x\).</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 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 \(\int {f(x){\text{d}}x} \).</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 0.0px 0.0px; font: 21.0px Helvetica;"><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 Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">sketch showing where the lines cross or zeros of \(y = x{(x + 2)^6} - x\) <strong><em>(M1)</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;">\(x = 0\) <strong><em>(A1)</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;">\(x = - 1\) and \(x = - 3\) <strong><em>(A1)</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;">the solution is \( - 3 < x < - 1\) or \(x > 0\) <strong><em>A1A1</em></strong></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> Do not award either final <strong><em>A1 </em></strong>mark if strict inequalities are not given.</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>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;">separating into two cases \(x > 0\) and \(x < 0\) <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;">if \(x > 0\) then \({(x + 2)^6} > 1 \Rightarrow \) always true <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;">if \(x < 0\) then \({(x + 2)^6} < 1 \Rightarrow - 3 < x < - 1\) <em><strong>(M1)</strong></em></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;">so the solution is \( - 3 < x < - 1\) or \(x > 0\) <strong><em>A1A1</em></strong></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> Do not award either final <strong><em>A1 </em></strong>mark if strict inequalities are not given.</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>METHOD 3</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(x) = {x^7} + 12{x^6} + 60{x^5} + 160{x^4} + 240{x^3} + 192{x^2} + 64x\) <strong><em>(A1)</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;">solutions to \({x^7} + 12{x^6} + 60{x^5} + 160{x^4} + 240{x^3} + 192{x^2} + 63x = 0\) are <strong><em>(M1)</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;">\(x = 0,{\text{ }}x = - 1\) and \(x = - 3\) <strong><em>(A1)</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;">so the solution is \( - 3 < x < - 1\) or \(x > 0\) <strong><em>A1A1</em></strong></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> Do not award either final <strong><em>A1 </em></strong>mark if strict inequalities are not given.</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>METHOD 4</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;">\(f(x) = x\) when \(x{(x + 2)^6} = x\)</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;">either \(x = 0\) or \({(x + 2)^6} = 1\) <strong><em>(A1)</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;">if \({(x + 2)^6} = 1\) then \(x + 2 = \pm 1\) so \(x = - 1\) or \(x = - 3\) <strong><em>(M1)(A1)</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;">the solution is \( - 3 < x < - 1\) or \(x > 0\) <strong><em>A1A1</em></strong></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> Do not award either final <strong><em>A1 </em></strong>mark if strict inequalities are not given.</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 Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 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: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 1 </strong>(by substitution)</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;">substituting \(u = x + 2\) <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;">\({\text{d}}u = {\text{d}}x\)</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;">\(\int {(u - 2){u^6}{\text{d}}u} \) <strong><em>M1A1</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;">\( = \frac{1}{8}{u^8} - \frac{2}{7}{u^7}( + c)\) <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;">\( = \frac{1}{8}{(x + 2)^8} - \frac{2}{7}{(x + 2)^7}( + c)\) <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;"><strong>METHOD 2 </strong>(by parts)</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;">\(u = x \Rightarrow \frac{{{\text{d}}u}}{{{\text{d}}x}} = 1,{\text{ }}\frac{{{\text{d}}v}}{{{\text{d}}x}} = {(x + 2)^6} \Rightarrow v = \frac{1}{7}{(x + 2)^7}\) <strong><em>(M1)(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;">\(\int {x{{(x + 2)}^6}{\text{d}}x = \frac{1}{7}x{{(x + 2)}^7} - \frac{1}{7}\int {{{(x + 2)}^7}{\text{d}}x} } \) <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;">\( = \frac{1}{7}x{(x + 2)^7} - \frac{1}{{56}}{(x + 2)^8}( + c)\) <strong><em>A1A1</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>METHOD 3 </strong>(by expansion)</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;">\(\int {f(x){\text{d}}x = \int {\left( {{x^7} + 12{x^6} + 60{x^5} + 160{x^4} + 240{x^3} + 192{x^2} + 64x} \right){\text{d}}x} } \) <strong><em>M1A1</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;">\( = \frac{1}{8}{x^8} + \frac{{12}}{7}{x^7} + 10{x^6} + 32{x^5} + 60{x^4} + 64{x^3} + 32{x^2}( + c)\) <strong><em>M1A2</em></strong></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> Award <strong><em>M1A1 </em></strong>if at least four terms are correct.</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 Helvetica;"><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;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the function \(f\) , defined by \(f(x) = x - a\sqrt x \) , where \(x \geqslant 0\), \(a \in {\mathbb{R}^ + }\) .</span></p>
</div>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">(a) Find in terms of \(a\)</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> (i) the zeros of \(f\) ;</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> (ii) the values of \(x\) for which \(f\) is decreasing;</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> (iii) the values of \(x\) for which \(f\) is increasing;</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> (iv) the range of \(f\) . </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(b) State the concavity of the graph of \(f\) .</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;">(a)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(i) \(x - a\sqrt x \) <em><strong>M1</strong></em></span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"><em><strong> </strong></em></span><span style="font-family: times new roman,times; font-size: medium;">\(\sqrt x \sqrt x - a = 0\) <em><strong>(A1)</strong></em></span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"><em><strong> </strong></em></span><span style="font-family: times new roman,times; font-size: medium;">2 \(x = 0\), \(x = {a^2}\) <em><strong>A1 N2</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) \(f'(x) = 1 - \frac{a}{{2\sqrt x }}\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1</span></strong></em></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> </span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\(f\)</span></span><span style="font-family: times new roman,times; font-size: medium;"> is decreasing when \(f' < 0\) <em><strong>(M1)</strong></em></span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> \(1 - \frac{a}{{2\sqrt x }} < 0 \Rightarrow \frac{{2\sqrt x - a}}{{2\sqrt x }} < 0 \Rightarrow x > \frac{{{a^2}}}{4}\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(iii) </span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\(f\)</span> is increasing when \(f' > 0\)</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> \(1 - \frac{a}{{2\sqrt x }} > 0 \Rightarrow \frac{{2\sqrt x - a}}{{2\sqrt x }} > 0 \Rightarrow x > \frac{{{a^2}}}{4}\) <em><strong>A1</strong></em></span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"><strong> Note:</strong> Award the <em><strong>M1</strong> </em>mark for either (ii) or (iii).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(iv) minimum occurs at \(x = \frac{{{a^2}}}{4}\)</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> minimum value is </span><span style="font-family: times new roman,times; font-size: medium;">\(y = - \frac{{{a^2}}}{4}\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;"> (M1)A1</span></strong></em></p>
<p style="margin-left: 30px;"><em><strong><span style="font-family: times new roman,times; font-size: medium;"> </span></strong></em><span style="font-family: times new roman,times; font-size: medium;">hence \(y \geqslant - \frac{{{a^2}}}{4}\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;"> A1</span></strong></em></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[10 marks]</span></strong></em></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) concave up for all values of \(x\) <em><strong>R1</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[1 mark]</span></strong></em></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;">Total [11 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;">This was generally a well answered question.</span></p>
</div>
<br><hr><br><div class="question">
<p>By using the substitution \({x^2} = 2\sec \theta \), show that \(\int {\frac{{{\text{d}}x}}{{x\sqrt {{x^4} - 4} }} = \frac{1}{4}\arccos \left( {\frac{2}{{{x^2}}}} \right) + c} \).</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><strong>EITHER</strong></p>
<p>\({x^2} = 2\sec \theta \)</p>
<p>\(2x\frac{{{\text{d}}x}}{{{\text{d}}\theta }} = 2\sec \theta \tan \theta \) <strong><em>M1A1</em></strong></p>
<p>\(\int {\frac{{{\text{d}}x}}{{x\sqrt {{x^4} - 4} }}} \)</p>
<p>\( = \int {\frac{{\sec \theta \tan \theta {\text{d}}\theta }}{{2\sec \theta \sqrt {4{{\sec }^2}\theta - 4} }}} \) <strong><em>M1A1</em></strong></p>
<p><strong>OR</strong></p>
<p>\(x = \sqrt 2 {(\sec \theta )^{\frac{1}{2}}}{\text{ }}\left( { = \sqrt 2 {{(\cos \theta )}^{ - \frac{1}{2}}}} \right)\)</p>
<p>\(\frac{{{\text{d}}x}}{{{\text{d}}\theta }} = \frac{{\sqrt 2 }}{2}{(\sec \theta )^{\frac{1}{2}}}\tan \theta {\text{ }}\left( { = \frac{{\sqrt 2 }}{2}{{(\cos \theta )}^{ - \frac{3}{2}}}\sin \theta } \right)\) <strong><em>M1A1</em></strong></p>
<p>\(\int {\frac{{{\text{d}}x}}{{x\sqrt {{x^4} - 4} }}} \)</p>
<p>\( = \int {\frac{{\sqrt 2 {{(\sec \theta )}^{\frac{1}{2}}}\tan \theta {\text{d}}\theta }}{{2\sqrt 2 {{(\sec \theta )}^{\frac{1}{2}}}\sqrt {4{{\sec }^2}\theta - 4} }}{\text{ }}\left( { = \int {\frac{{\sqrt 2 {{(\cos \theta )}^{ - \frac{3}{2}}}\sin \theta {\text{d}}\theta }}{{2\sqrt 2 {{(\cos \theta )}^{ - \frac{1}{2}}}\sqrt {4{{\sec }^2}\theta - 4} }}} } \right)} \) <strong><em>M1A1</em></strong></p>
<p><strong>THEN</strong></p>
<p>\( = \frac{1}{2}\int {\frac{{\tan \theta {\text{d}}\theta }}{{2\tan \theta }}} \) <strong><em>(M1)</em></strong></p>
<p>\( = \frac{1}{4}\int {{\text{d}}\theta } \)</p>
<p>\( = \frac{\theta }{4} + c\) <strong><em>A1</em></strong></p>
<p>\({x^2} = 2\sec \theta \Rightarrow \cos \theta = \frac{2}{{{x^2}}}\) <strong><em>M1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>This <strong><em>M1 </em></strong>may be seen anywhere, including a sketch of an appropriate triangle.</p>
<p> </p>
<p>so \(\frac{\theta }{4} + c = \frac{1}{4}\arccos \left( {\frac{2}{{{x^2}}}} \right) + c\) <strong><em>AG</em></strong></p>
<p><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 class="p1">The graph of \(y = \ln (5x + 10)\) is obtained from the graph of \(y = \ln x\) by a translation of \(a\) units in the direction of the \(x\)-axis followed by a translation of \(b\) units in the direction of the \(y\)-axis.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of \(a\) and the value of \(b\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The region bounded by the graph of \(y = \ln (5x + 10)\), the \(x\)-axis and the lines \(x = {\text{e}}\) and \(x = 2{\text{e}}\), is rotated through \(2\pi \) radians about the \(x\)-axis. Find the volume generated.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p>\(y = \ln (x - a) + b = \ln (5x + 10)\) <strong><em>(M1)</em></strong></p>
<p>\(y = \ln (x - a) + \ln c = \ln (5x + 10)\)</p>
<p>\(y = \ln \left( {c(x - a)} \right) = \ln (5x + 10)\) <strong><em>(M1)</em></strong></p>
<p><strong>OR</strong></p>
<p>\(y = \ln (5x + 10) = \ln \left( {5(x + 2)} \right)\) <strong><em>(M1)</em></strong></p>
<p>\(y = \ln (5) + \ln (x + 2)\) <strong><em>(M1)</em></strong></p>
<p><strong>THEN</strong></p>
<p>\(a = - 2,{\text{ }}b = \ln 5\) <strong><em>A1A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept graphical approaches.</p>
<p> </p>
<p><strong>Note:</strong> Accept \(a = 2,{\text{ }}b = 1.61\)</p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(V = \pi {\int_e^{2e} {\left[ {\ln (5x + 10)} \right]} ^2}{\text{d}}x\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1">\( = 99.2\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><span class="s1"><strong><em>[2 marks]</em></strong></span></p>
<p class="p1"><span class="s1"><strong><em>Total [6 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="question">
<p class="p1">Two cyclists are at the same road intersection. One cyclist travels north at \(20\,{\text{km}}\,{{\text{h}}^{ - 1}}\). The other cyclist travels west at \(15\,{\text{km}}\,{{\text{h}}^{ - 1}}\).</p>
<p class="p1">Use calculus to show that the rate at which the distance between the two cyclists changes is independent of time.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><strong>METHOD 1</strong></p>
<p>attempt to set up (diagram, vectors) <em>(</em><strong><em>M1)</em></strong></p>
<p>correct distances \(x = 15t,{\text{ }}y = 20t\) <strong><em>(A1) (A1)</em></strong></p>
<p>the distance between the two cyclists at time \(t\) is \(s = \sqrt {{{(15t)}^2} + {{(20t)}^2}} = 25t{\text{ (km)}}\) <strong><em>A1</em></strong></p>
<p>\(\frac{{{\text{d}}s}}{{{\text{d}}t}} = 25{\text{ (km}}\,{{\text{h}}^{ - 1}})\) <strong><em>A1</em></strong></p>
<p>hence the rate is independent of time <strong><em>AG</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>attempting to differentiate \({x^2} + {y^2} = {s^2}\) implicitly <em>(</em><strong><em>M1)</em></strong></p>
<p>\(2x\frac{{{\text{d}}x}}{{{\text{d}}t}} + 2y\frac{{{\text{d}}y}}{{{\text{d}}t}} = 2s\frac{{{\text{d}}s}}{{{\text{d}}t}}\) <em>(</em><strong><em>A1)</em></strong></p>
<p>the distance between the two cyclists at time \(t\) is \(\sqrt {{{(15t)}^2} + {{(20t)}^2}} = 25t{\text{ (km)}}\) <strong><em>(A1)</em></strong></p>
<p>\(2(15t)(15 + 2(20t)(20) = 2(25t)\frac{{{\text{d}}s}}{{{\text{d}}t}}\) <strong><em>M1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>M1</em></strong> for substitution of correct values into their equation involving \(\frac{{{\text{d}}s}}{{{\text{d}}t}}\).</p>
<p> </p>
<p>\(\frac{{{\text{d}}s}}{{{\text{d}}t}} = 25{\text{ (km}}\,{{\text{h}}^{ - 1}})\) <strong><em>A1</em></strong></p>
<p>hence the rate is independent of time <strong><em>AG</em></strong></p>
<p><strong>METHOD 3</strong></p>
<p>\(s = \sqrt {{x^2} + {y^2}} \) <strong><em>(A1)</em></strong></p>
<p>\(\frac{{{\text{d}}s}}{{{\text{d}}t}} = \frac{{x\frac{{{\text{d}}x}}{{{\text{d}}t}} + y\frac{{{\text{d}}y}}{{{\text{d}}t}}}}{{\sqrt {{x^2} + {y^2}} }}\) <strong>(<em>M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>M1</em></strong> for attempting to differentiate the expression for \(s\).</p>
<p> </p>
<p>\(\frac{{{\text{d}}s}}{{{\text{d}}t}} = \frac{{(15t)(15) + (20t)(20)}}{{\sqrt {{{(15t)}^2} + {{(20t)}^2}} }}\) <strong><em>M1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>M1</em></strong> for substitution of correct values into their \(\frac{{{\text{d}}s}}{{{\text{d}}t}}\).</p>
<p> </p>
<p>\(\frac{{{\text{d}}s}}{{{\text{d}}t}} = 25{\text{ (km}}\,{{\text{h}}^{ - 1}})\) <strong><em>A1</em></strong></p>
<p>hence the rate is independent of time <strong><em>AG</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p class="p1">Reasonably well done. Most successful candidates determined that \(s = 25t \Rightarrow \frac{{{\text{d}}s}}{{{\text{d}}t}} = 25\) from \(x = 15t\) and \(y = 20t\). A number of candidates did not use calculus while a few candidates correctly used implicit differentiation.</p>
</div>
<br><hr><br><div class="question">
<p class="p1">A bicycle inner tube can be considered as a joined up cylinder of fixed length <span class="s1">\(200\) cm </span>and radius \(r\) cm. The radius \(r\) increases as the inner tube is pumped up. Air is being pumped into the inner tube so that the volume of air in the tube increases at a constant rate of \(30{\text{ c}}{{\text{m}}^3}{{\text{s}}^{ - 1}}\). Find the rate at which the radius of the inner tube is increasing when \(r = 2{\text{ cm}}\).</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p class="p1">\(V = 200\pi {r^2}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note:</strong> <span class="Apple-converted-space"> </span>Allow \(V = \pi h{r^2}\) if value of \(h\) is substituted later in the question.</p>
<p class="p2"> </p>
<p class="p3"><strong>EITHER</strong></p>
<p class="p1">\(\frac{{{\text{d}}V}}{{{\text{d}}t}} = 200\pi 2r\frac{{{\text{d}}r}}{{{\text{d}}t}}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p4"> </p>
<p class="p1"><strong>Note:</strong> <span class="Apple-converted-space"> </span>Award <strong><em>M1</em></strong> for an attempt at implicit differentiation.</p>
<p class="p4"> </p>
<p class="p1">at \(r = 2\) we have \(30 = 200\pi 4\frac{{{\text{d}}r}}{{{\text{d}}t}}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p3"><strong>OR</strong></p>
<p class="p1">\(\frac{{{\text{d}}r}}{{{\text{d}}t}} = \frac{{\frac{{{\text{d}}V}}{{{\text{d}}t}}}}{{\frac{{{\text{d}}V}}{{{\text{d}}r}}}}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p1">\(\frac{{{\text{d}}V}}{{{\text{d}}r}} = 400\pi r\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p1">\(r = 2\) we have \(\frac{{{\text{d}}V}}{{{\text{d}}r}} = 800\pi \) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p3"><strong>THEN</strong></p>
<p class="p1">\(\frac{{{\text{d}}r}}{{{\text{d}}t}} = \frac{{30}}{{800\pi }}\;\;\;\left( { = \frac{3}{{80\pi }} = 0.0119} \right){\text{ }}({\text{cm}}\,{{\text{s}}^{ - 1}}{\text{)}}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p3"><strong><em>[5 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p class="p1">This question was well understood and a large percentage appreciated the need for implicit differentiation although some candidates did not recognise the need to treat h as a constant till late in the question. A number of candidates found the answer \(\frac{{3\pi }}{{80}}\) instead of \(\frac{3}{{80\pi }}\) due to a basic incorrect use of the GDC.</p>
</div>
<br><hr><br><div class="question">
<p>The region \(R\) is enclosed by the graph of \(y = {e^{ - {x^2}}}\), the \(x\)-axis and the lines \(x = - 1\) and \(x = 1\).</p>
<p>Find the volume of the solid of revolution that is formed when \(R\) is rotated through \(2\pi \) about the \(x\)-axis.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>\(\int_{ - 1}^1 {\pi {{\left( {{{\text{e}}^{ - {x^2}}}} \right)}^2}{\text{d}}x} \;\;\;\left( {\int_{ - 1}^1 {\pi {{\text{e}}^{ - 2{x^2}}}{\text{d}}x} \;\;\;{\text{or}}\;\;\;\int_0^1 {2\pi {{\text{e}}^{ - 2{x^2}}}{\text{d}}x} } \right)\) <strong><em>(M1)(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>M1</em></strong> for integral involving the function given; <strong><em>A1</em></strong> for correct limits; <strong><em>A1</em></strong> for \(\pi \) and \({{{\left( {{{\text{e}}^{ - {x^2}}}} \right)}^2}}\)</p>
<p> </p>
<p>\( = 3.758249 \ldots = 3.76\) <strong><em>A1</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p class="p1">Most candidates answered this question correctly. Those candidates who attempted to manipulate the function or attempt an integration wasted time and obtained 3/4 marks. The most common errors were an extra factor ‘2’ and a fourth power when attempting to square the function. Many candidates wrote down the correct expression but not all were able to use their calculator correctly.</p>
</div>
<br><hr><br><div class="specification">
<p>Consider the curve defined by the equation \(4{x^2} + {y^2} = 7\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of the normal to the curve at the point \(\left( {1,{\text{ }}\sqrt 3 } \right)\).</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>Find the volume of the solid formed when the region bounded by the curve, the \(x\)-axis for \(x \geqslant 0\) and the \(y\)-axis for \(y \geqslant 0\) is rotated through \(2\pi \) about the \(x\)-axis.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>\(4{x^2} + {y^2} = 7\)</p>
<p>\(8x + 2y\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\) <strong><em>(M1)(A1)</em></strong></p>
<p>\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = - \frac{{4x}}{y}\)</p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>M1A1 </em></strong>for finding \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = - 2.309 \ldots \) using any alternative method.</p>
<p> </p>
<p>hence gradient of normal \( = \frac{y}{{4x}}\) <strong><em>(M1)</em></strong></p>
<p>hence gradient of normal at \(\left( {1,{\text{ }}\sqrt 3 } \right)\) is \(\frac{{\sqrt 3 }}{4}\,\,\,( = 0.433)\) <strong><em>(A1)</em></strong></p>
<p>hence equation of normal is \(y - \sqrt 3 = \frac{{\sqrt 3 }}{4}(x - 1)\) <strong><em>(M1)A1</em></strong></p>
<p>\(\left( {y = \frac{{\sqrt 3 }}{4}x + \frac{{3\sqrt 3 }}{4}} \right)\,\,\,(y = 0.433x + 1.30)\)</p>
<p><strong>METHOD 2</strong></p>
<p>\(4{x^2} + {y^2} = 7\)</p>
<p>\(y = \sqrt {7 - 4{x^2}} \) <strong><em>(M1)</em></strong></p>
<p>\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = - \frac{{4x}}{{\sqrt {7 - 4{x^2}} }}\) <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>M1A1 </em></strong>for finding \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = - 2.309 \ldots \) using any alternative method.</p>
<p> </p>
<p>hence gradient of normal \( = \frac{{\sqrt {7 - 4{x^2}} }}{{4x}}\) <strong><em>(M1)</em></strong></p>
<p>hence gradient of normal at \(\left( {1,{\text{ }}\sqrt 3 } \right)\) is \(\frac{{\sqrt 3 }}{4}\,\,\,( = 0.433)\) <strong><em>(A1)</em></strong></p>
<p>hence equation of normal is \(y - \sqrt 3 = \frac{{\sqrt 3 }}{4}(x - 1)\) <strong><em>(M1)A1</em></strong></p>
<p>\(\left( {y = \frac{{\sqrt 3 }}{4}x + \frac{{3\sqrt 3 }}{4}} \right)\,\,\,(y = 0.433x + 1.30)\)</p>
<p><strong><em>[6 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Use of \(V = \pi \int\limits_0^{\frac{{\sqrt 7 }}{2}} {{y^2}{\text{d}}x} \)</p>
<p>\(V = \pi \int\limits_0^{\frac{{\sqrt 7 }}{2}} {\left( {7 - 4{x^2}} \right){\text{d}}x} \) <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Condone absence of limits or incorrect limits for <strong><em>M </em></strong>mark.</p>
<p>Do not condone absence of or multiples of \(\pi \).</p>
<p> </p>
<p>\( = 19.4\,\,\,\left( { = \frac{{7\sqrt 7 \pi }}{3}} \right)\) <strong><em>A1</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Prove by mathematical induction that, for \(n \in {\mathbb{Z}^ + }\),</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[1 + 2\left( {\frac{1}{2}} \right) + 3{\left( {\frac{1}{2}} \right)^2} + 4{\left( {\frac{1}{2}} \right)^3} + ... + n{\left( {\frac{1}{2}} \right)^{n - 1}} = 4 - \frac{{n + 2}}{{{2^{n - 1}}}}.\]</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Using integration by parts, show that \(\int {{{\text{e}}^{2x}}\sin x{\text{d}}x = \frac{1}{5}{{\text{e}}^{2x}}} (2\sin x - \cos x) + C\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Solve the differential equation \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \sqrt {1 - {y^2}} {{\text{e}}^{2x}}\sin x\), given that <em>y</em> = 0 when <em>x</em> = 0,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">writing your answer in the form \(y = f(x)\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) (i) Sketch the graph of \(y = f(x)\) , found in part (b), for \(0 \leqslant x \leqslant 1.5\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Determine the coordinates of the point P, the first positive intercept on the <em>x</em>-axis, and mark it on your sketch.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) The region bounded by the graph of \(y = f(x)\) and the <em>x</em>-axis, between the origin and P, is rotated 360° about the <em>x</em>-axis to form a solid of revolution.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Calculate the volume of this solid.</span></p>
<div class="marks">[17]</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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">prove that \(1 + 2\left( {\frac{1}{2}} \right) + 3{\left( {\frac{1}{2}} \right)^2} + 4{\left( {\frac{1}{2}} \right)^3} + ... + n{\left( {\frac{1}{2}} \right)^{n - 1}} = 4 - \frac{{n + 2}}{{{2^{n - 1}}}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">for <em>n</em> = 1</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{LHS}} = 1,{\text{ RHS}} = 4 - \frac{{1 + 2}}{{{2^0}}} = 4 - 3 = 1\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so true for <em>n</em> = 1 <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">assume true for <em>n</em> = <em>k</em> <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so \(1 + 2\left( {\frac{1}{2}} \right) + 3{\left( {\frac{1}{2}} \right)^2} + 4{\left( {\frac{1}{2}} \right)^3} + ... + k{\left( {\frac{1}{2}} \right)^{k - 1}} = 4 - \frac{{k + 2}}{{{2^{k - 1}}}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">now for <em>n</em> = <em>k</em> +1</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">LHS: \(1 + 2\left( {\frac{1}{2}} \right) + 3{\left( {\frac{1}{2}} \right)^2} + 4{\left( {\frac{1}{2}} \right)^3} + ... + k{\left( {\frac{1}{2}} \right)^{k - 1}} + (k + 1){\left( {\frac{1}{2}} \right)^k}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 4 - \frac{{k + 2}}{{{2^{k - 1}}}} + (k + 1){\left( {\frac{1}{2}} \right)^k}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 4 - \frac{{2(k + 2)}}{{{2^k}}} + \frac{{k + 1}}{{{2^k}}}\,\,\,\,\,\)(or equivalent) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 4 - \frac{{(k + 1) + 2}}{{{2^{(k + 1) - 1}}}}\,\,\,\,\,\)(accept \(4 - \frac{{k + 3}}{{{2^k}}}\)) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Therefore if it is true for <em>n</em> = <em>k</em> it is true for <em>n</em> = <em>k</em> + 1. It has been shown to be true for <em>n</em> = 1 so it is true for all \(n{\text{ }}( \in {\mathbb{Z}^ + })\). <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> To obtain the final <strong><em>R</em></strong> mark, a reasonable attempt at induction must have been made.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[8 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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {{{\text{e}}^{2x}}\sin x{\text{d}}x = - \cos x{{\text{e}}^{2x}} + \int {2{{\text{e}}^{2x}}\cos x{\text{d}}x} } \) <strong><em>M1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = - \cos x{{\text{e}}^{2x}} + 2{{\text{e}}^{2x}}\sin x - \int {4{{\text{e}}^{2x}}\sin x{\text{d}}x} \) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(5\int {{{\text{e}}^{2x}}\sin x{\text{d}}x = - \cos x{{\text{e}}^{2x}} + 2{{\text{e}}^{2x}}\sin x} \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {{{\text{e}}^{2x}}\sin x{\text{d}}x = \frac{1}{5}{{\text{e}}^{2x}}(2\sin x - \cos x) + C} \) <strong><em>AG</em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {\sin x{{\text{e}}^{2x}}{\text{d}}x = \frac{{\sin x{{\text{e}}^{2x}}}}{2} - \int {\cos x\frac{{{{\text{e}}^{2x}}}}{2}{\text{d}}x} } \) <strong><em>M1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{\sin x{{\text{e}}^{2x}}}}{2} - \cos x\frac{{{{\text{e}}^{2x}}}}{4} - \int {\sin x\frac{{{{\text{e}}^{2x}}}}{4}{\text{d}}x} \) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{5}{4}\int {{{\text{e}}^{2x}}\sin x{\text{d}}x = \frac{{{{\text{e}}^{2x}}\sin x}}{2} - \frac{{\cos x{{\text{e}}^{2x}}}}{4}} \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {{{\text{e}}^{2x}}\sin x{\text{d}}x = \frac{1}{5}{{\text{e}}^{2x}}(2\sin x - \cos x) + C} \) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {\frac{{{\text{d}}y}}{{\sqrt {1 - {y^2}} }} = \int {{{\text{e}}^{2x}}\sin x{\text{d}}x} } \) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\arcsin y = \frac{1}{5}{{\text{e}}^{2x}}(2\sin x - \cos x)( + C)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">when \(x = 0,{\text{ }}y = 0 \Rightarrow C = \frac{1}{5}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(y = \sin \left( {\frac{1}{5}{{\text{e}}^{2x}}(2\sin x - \cos x) + \frac{1}{5}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) </span><img 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" alt><span class="Apple-style-span" style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 14px; line-height: 20px; display: inline; float: none;"><span class="Apple-style-span" style="font-family: 'times new roman', times; font-size: medium; display: inline; float: none; line-height: normal;"> <strong><em>A1</em></strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">P is (1.16, 0) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1</em></strong> for 1.16 seen anywhere, <strong><em>A1</em></strong> for complete sketch.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Allow FT on their answer from (b)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \(V = \int_0^{1.162...} {\pi {y^2}{\text{d}}x} \) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 1.05\) <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Allow FT on their answers from (b) and (c)(i).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<div class="question_part_label">B.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part A: Given that this question is at the easier end of the ‘proof by induction’ spectrum, it was disappointing that so many candidates failed to score full marks. The <em>n</em> = 1 case was generally well done. The whole point of the method is that it involves logic, so ‘let n = k’ or ‘put n = k’, instead of ‘assume ... to be true for n = k’, gains no marks. The algebraic steps need to be more convincing than some candidates were able to show. It is astonishing that the R1 mark for the final statement was so often not awarded.</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: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part B: Part (a) was often well done, although some faltered after the first integration. Part (b) was also generally well done, although there were some errors with the constant of integration. In (c) the graph was often attempted, but errors in (b) usually led to manifestly incorrect plots. Many attempted the volume of integration and some obtained the correct value.</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: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A rocket is rising vertically at a speed of \(300{\text{ m}}{{\text{s}}^{ - 1}}\) when it is 800 m directly above the launch site. Calculate the rate of change of the distance between the rocket and an observer, who is 600 m from the launch site and on the same horizontal level as the launch site.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
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" alt></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">let <em>x</em> = distance from observer to rocket</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">let <em>h</em> = the height of the rocket above the ground</span><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: 29.0px Helvetica;"><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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}h}}{{{\text{d}}t}} = 300{\text{ when }}h = 800\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = \sqrt {{h^2} + 360\,000} = {({h^2} + 360\,000)^{\frac{1}{2}}}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}x}}{{{\text{d}}h}} = \frac{h}{{\sqrt {{h^2} + 360\,000} }}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">when h = 800</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}x}}{{{\text{d}}t}} = \frac{{{\text{d}}x}}{{{\text{d}}h}} \times \frac{{{\text{d}}h}}{{{\text{d}}t}}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{300h}}{{\sqrt {{h^2} + 360\,000} }}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 240{\text{ (m}}{{\text{s}}^{ - 1}})\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">METHOD 2</strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({h^2} + {600^2} = {x^2}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2h = 2x\frac{{{\text{d}}x}}{{{\text{d}}h}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}x}}{{{\text{d}}h}} = \frac{h}{x}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{800}}{{1000}}\left( { = \frac{4}{5}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}h}}{{{\text{d}}t}} = 300\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}x}}{{{\text{d}}t}} = \frac{{{\text{d}}x}}{{{\text{d}}h}} \times \frac{{{\text{d}}h}}{{{\text{d}}t}}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{4}{5} \times 300\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 240{\text{ (m}}{{\text{s}}^{ - 1}})\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">METHOD 3</strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x^2} = {600^2} + {h^2}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2x\frac{{{\text{d}}x}}{{{\text{d}}t}} = 2h\frac{{{\text{d}}h}}{{{\text{d}}t}}\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">when <em>h</em> = 800, <em>x</em> =1000</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}x}}{{{\text{d}}t}} = \frac{{800}}{{1000}} \times \frac{{{\text{d}}h}}{{{\text{d}}t}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 240{\text{ (m}}{{\text{s}}^{ - 1}})\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">METHOD 4</strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Distance between the observer and the rocket \( = {({600^2} + {800^2})^{\frac{1}{2}}} = 1000\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Component of the velocity in the line of sight \( = \sin \theta \times 300\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(where \(\theta = \) angle of elevation) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\sin \theta = \frac{{800}}{{1000}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">component \( = 240{\text{ (m}}{{\text{s}}^{ - 1}})\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Questions of this type are often open to various approaches, but most full solutions require the application of ‘related rates of change’. Although most candidates realised this, their success rate was low. This was particularly apparent in approaches involving trigonometric functions. Some candidates assumed constant speed – this gained some small credit. Candidates should be encouraged to state what their symbols stand for.</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">A particle moves such that its velocity \(v\,{\text{m}}{{\text{s}}^{ - 1}}\) is related to its displacement \(s\,{\text{m}}\), by the equation \(v(s) = \arctan (\sin s),{\text{ }}0 \leqslant s \leqslant 1\). The particle’s acceleration is \(a\,{\text{m}}{{\text{s}}^{ - 2}}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the particle’s acceleration in terms of \(s\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Using an appropriate sketch graph, find the particle’s displacement when its acceleration is \(0.25{\text{ m}}{{\text{s}}^{ - 2}}\).</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"><span class="Apple-converted-space">\(\frac{{{\text{d}}v}}{{{\text{d}}s}} = \frac{{\cos s}}{{{{\sin }^2}s + 1}}\) </span><strong><em>M1A1</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\(a = v\frac{{{\text{d}}v}}{{{\text{d}}s}}\) </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p3"><span class="Apple-converted-space">\(a = \frac{{\arctan (\sin s)\cos s}}{{{{\sin }^2}s + 1}}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>EITHER</strong></p>
<p class="p1"><img src="images/Schermafbeelding_2017-02-03_om_15.30.17.png" alt="M16/5/MATHL/HP2/ENG/TZ2/08.b_01/M"> <strong><em>(M1)</em></strong></p>
<p class="p1"><strong>OR</strong></p>
<p class="p1"><img src="images/Schermafbeelding_2017-02-03_om_15.31.30.png" alt="M16/5/MATHL/HP2/ENG/TZ2/08.b_02/M"> <strong><em>(M1)</em></strong></p>
<p class="p1"><strong>THEN</strong></p>
<p class="p1">\(s = 0.296,{\text{ }}0.918{\text{ (m)}}\) <strong><em>A1</em></strong></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), a large number of candidates thought that \(\frac{{{\text{d}}v}}{{{\text{d}}t}} = \frac{{{\text{d}}v}}{{{\text{d}}s}}\) rather than \(\frac{{{\text{d}}v}}{{{\text{d}}t}} = \frac{{{\text{d}}s}}{{{\text{d}}t}} \times \frac{{{\text{d}}v}}{{{\text{d}}s}} = v\frac{{{\text{d}}v}}{{{\text{d}}s}}\).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">In part (b), quite a few of these candidates then went on to find a value of \(s\) that was outside the domain \(0 \leqslant s \leqslant 1\).</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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The function <em>f</em> has inverse \({f^{ - 1}}\) and derivative \(f'(x)\) for all \(x \in \mathbb{R}\). For all functions with these properties you are given the result that for \(a \in \mathbb{R}\) with \(b = f(a)\) and \(f'(a) \ne 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[({f^{ - 1}})'(b) = \frac{1}{{f'(a)}}.\]</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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Verify that this is true for \(f(x) = {x^3} + 1\) at <em>x</em> = 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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Given that \(g(x) = x{{\text{e}}^{{x^2}}}\), show that \(g'(x) > 0\) for all values of <em>x</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Using the result given at the start of the question, find the value of the gradient function of \(y = {g^{ - 1}}(x)\) at <em>x</em> = 2.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) With <em>f</em> and <em>g</em> as defined in parts (a) and (b), solve \(g \circ f(x) = 2\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Let \(h(x) = {(g \circ f)^{ - 1}}(x)\). Find \(h'(2)\).</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(2) = 9\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({f^{ - 1}}(x) = {(x - 1)^{\frac{1}{3}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(({f^{ - 1}})'(x) = \frac{1}{3}{(x - 1)^{ - \frac{2}{3}}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(({f^{ - 1}})'(9) = \frac{1}{{12}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(x) = 3{x^2}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{1}{{f'(2)}} = \frac{1}{{3 \times 4}} = \frac{1}{{12}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> The last </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>M1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> and </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> are independent of previous marks.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[6 marks]</em></strong></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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(g'(x) = {{\text{e}}^{{x^2}}} + 2{x^2}{{\text{e}}^{{x^2}}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(g'(x) > 0\) as each part is positive <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><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: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">to find the <em>x</em>-coordinate on \(y = g(x)\) solve</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2 = x{{\text{e}}^{{x^2}}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 0.89605022078 \ldots \) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">gradient \( = ({g^{ - 1}})'(2) = \frac{1}{{g'(0.896 \ldots )}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{{{{\text{e}}^{{{(0.896 \ldots )}^2}}}\left( {1 + 2 \times {{(0.896 \ldots )}^2}} \right)}} = 0.172\) to 3sf <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(using the \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) function on gdc \(g'(0.896 \ldots ) = 5.7716028 \ldots \)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{1}{{g'(0.896 \ldots )}} = 0.173\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \(({x^3} + 1){{\text{e}}^{{{({x^3} + 1)}^2}}} = 2\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = - 0.470191 \ldots \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) <strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\((g \circ f)'(x) = 3{x^2}{{\text{e}}^{{{({x^3} + 1)}^2}}}\left( {2{{({x^3} + 1)}^2} + 1} \right)\) <strong><em>(M1)(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\((g \circ f)'( - 0.470191 \ldots ) = 3.85755 \ldots \) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(h'(2) = \frac{1}{{3.85755 \ldots }} = 0.259{\text{ }}(232 \ldots )\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> The solution can be found without the student obtaining the explicit form of the composite function.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"> </strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">METHOD 2</strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(h(x) = ({f^{ - 1}} \circ {g^{ - 1}})(x)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(h'(x) = ({f^{ - 1}})'\left( {{g^{ - 1}}(x)} \right) \times ({g^{ - 1}})'(x)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{3}{\left( {{g^{ - 1}}(x) - 1} \right)^{ - \frac{2}{3}}} \times ({g^{ - 1}})'(x)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(h'(2) = \frac{1}{3}{\left( {{g^{ - 1}}(2) - 1} \right)^{ - \frac{2}{3}}} \times ({g^{ - 1}})'(2)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{3}{(0.89605 \ldots - 1)^{ - \frac{2}{3}}} \times 0.171933 \ldots \)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 0.259{\text{ }}(232 \ldots )\) <strong><em>A1 N4</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">There were many good attempts at parts (a) and (b), although in (b) many were unable to give a thorough justification.</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 many good attempts at parts (a) and (b), although in (b) many were unable to give a thorough justification.</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 good solutions to parts (c) and (d)(ii) were seen although many were able to answer (d)(i) 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;">Few good solutions to parts (c) and (d)(ii) were seen although many were able to answer (d)(i) correctly.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A family of cubic functions is defined as \({f_k}(x) = {k^2}{x^3} - k{x^2} + x,{\text{ }}k \in {\mathbb{Z}^ + }\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Express in terms of <em>k</em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \({{f'}_k}(x){\text{ and }}{{f''}_k}(x)\) ;</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) the coordinates of the points of inflexion \({P_k}\) on the graphs of \({f_k}\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Show that all \({P_k}\) lie on a straight line and state its equation.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) Show that for all values of <em>k</em>, the tangents to the graphs of \({f_k}\) at \({P_k}\) are parallel, and find the equation of the tangent lines.</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: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) (i) \({{f'}_k}(x) = 3{k^2}{x^2} - 2kx + 1\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({{f''}_k}(x) = 6{k^2}x - 2k\)<span style="font: 19.0px Helvetica;"> </span><strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii)<span style="font: 19.0px Helvetica;"> </span>Setting \(f''(x) = 0\)<span style="font: 19.0px Helvetica;"> </span><strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow 6{k^2}x - 2k = 0 \Rightarrow x = \frac{1}{{3k}}\)<span style="font: 19.0px Helvetica;"> </span><strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f\left( {\frac{1}{{3k}}} \right) = {k^2}{\left( {\frac{1}{{3k}}} \right)^3} - k{\left( {\frac{1}{{3k}}} \right)^2} + \left( {\frac{1}{{3k}}} \right)\)<span style="font: 19.0px Helvetica;"> </span><strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{7}{{27k}}\)<span style="font: 19.0px Helvetica;"> </span><strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Hence, \({P_k}{\text{ is }}\left( {\frac{1}{{3k}},\frac{7}{{27k}}} \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b)<span style="font: 19.0px Helvetica;"> </span>Equation of the straight line is \(y = \frac{7}{9}x\)<span style="font: 19.0px Helvetica;"> </span><strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">As this equation is independent of <em>k</em>, all \({P_k}\) lie on this straight line<span style="font: 19.0px Helvetica;"> </span><strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><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: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c)<span style="font: 19.0px Helvetica;"> </span>Gradient of tangent at \({P_k}\) :</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'({P_k}) = f'\left( {\frac{1}{{3k}}} \right) = 3{k^2}{\left( {\frac{1}{{3k}}} \right)^2} - 2k\left( {\frac{1}{{3k}}} \right) + 1 = \frac{2}{3}\)<span style="font: 19.0px Helvetica;"> </span><strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">As the gradient is independent of <em>k</em>, the tangents are parallel.<span style="font: 19.0px Helvetica;"> </span><strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{7}{{27k}} = \frac{2}{3} \times \frac{1}{{3k}} + c \Rightarrow c = \frac{1}{{27k}}\)<span style="font: 19.0px Helvetica;"> </span><strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The equation is \(y = \frac{2}{3}x + \frac{1}{{27k}}\)<span style="font: 19.0px Helvetica;"> </span><strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [13 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates scored the full 6 marks for part (a). The main mistake evidenced was to treat <em>k</em> as a variable, and hence use the product rule to differentiate. Of the many candidates who attempted parts (b) and (c), few scored the R1 marks in either part, but did manage to get the equations of the straight lines. </span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A triangle is formed by the three lines \(y = 10 - 2x,{\text{ }}y = mx\) and \(y = -\frac{1}{m}x\), where \(m > \frac{1}{2}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the value of <em>m </em>for which the area of the triangle is a minimum.</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: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">attempt to find intersections <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">intersections are \(\left( {\frac{{10}}{{m + 2}},\frac{{10m}}{{m + 2}}} \right){\text{ and }}\left( {\frac{{10m}}{{2m - 1}}, - \frac{{10}}{{2m - 1}}} \right)\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">area of triangle \( = \frac{1}{2} \times \frac{{\sqrt {100 + 100{m^2}} }}{{(m + 2)}} \times \frac{{\sqrt {100 + 100{m^2}} }}{{(2m - 1)}}\) <strong><em>M1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{50(1 + {m^2})}}{{(m + 2)(2m - 1)}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">minimum when \(m = 3\) <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[8 marks]</span><br></em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates had difficulties with this question and did not go beyond the determination of the intersection points of the lines; in a few cases candidates set up the expression of the area, in some cases using unsimplified expressions of the coordinates.</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">A particle moves in a straight line such that its velocity, \(v\,{\text{m}}\,{{\text{s}}^{ - 1}}\) , at time <em>t </em>seconds, is given by</p>
<p class="p1">\(v(t) = \left\{ {\begin{array}{*{20}{c}} {5 - {{(t - 2)}^2},}&{0 \le t \le 4} \\ {3 - \frac{t}{2},}&{t > 4} \end{array}.} \right.\)</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of <em>\(t\) </em>when the particle is instantaneously at rest.</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">The particle returns to its initial position at \(t = T\).</p>
<p class="p1">Find the value of <em>T</em>.</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>\(3 - \frac{t}{2} = 0 \Rightarrow t = 6{\text{ (s)}}\) <strong><em>(M1)A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>A0</em></strong> if either \(t = - 0.236\) or \(t = 4.24\) or both are stated with \(t = 6\).</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 class="p1">let <em>\(d\) </em>be the distance travelled before coming to rest</p>
<p class="p1">\(d = \int_0^4 {5 - {{(t - 2)}^2}{\text{d}}t + \int_4^6 {3 - \frac{t}{2}{\text{d}}t} } \) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)(A1)</em></strong></span></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>M1 </em></strong>for two correct integrals even if the integration limits are incorrect. The second integral can be specified as the area of a triangle.</p>
<p class="p3"> </p>
<p class="p1">\(d = \frac{{47}}{3}\;\;\;( = 15.7){\text{ (m)}}\) <span class="Apple-converted-space"> </span><span class="s1"><em>(</em><strong><em>A1)</em></strong></span></p>
<p class="p1">attempting to solve \(\int_6^T {\left( {\frac{t}{2} - 3} \right){\text{d}}t = \frac{{47}}{3}} \) (or equivalent) for <em>\(T\) <span class="Apple-converted-space"> </span></em><strong><em>M1</em></strong></p>
<p class="p1">\(T = 13.9{\text{ (s)}}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[5 marks]</em></strong></p>
<p class="p1"><strong><em>Total [7 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Part (a) was not done as well as expected. A large number of candidates attempted to solve \(5 - {(t - 2)^2} = 0\) for \(t\). Some candidates attempted to find when the particle’s acceleration was zero.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Most candidates had difficulty with part (b) with a variety of errors committed. A significant proportion of candidates did not understand what was required. Many candidates worked with indefinite integrals rather than with definite integrals. Only a small percentage of candidates started by correctly finding the distance travelled by the particle before coming to rest. The occasional candidate made adroit use of a GDC and found the correct value of \(t\) by finding where the graph of \(\int_0^4 {5 - {{(t - 2)}^2}{\text{d}}t + \int_4^x {3 - \frac{t}{2}{\text{d}}t} } \) crossed the horizontal axis.</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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(f(x) = \frac{{a + b{{\text{e}}^x}}}{{a{{\text{e}}^x} + b}}\), where \(0 < b < a\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Show that \(f'(x) = \frac{{({b^2} - {a^2}){{\text{e}}^x}}}{{{{(a{{\text{e}}^x} + b)}^2}}}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) <strong>Hence</strong> justify that the graph of <em>f</em> has no local maxima or minima.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) Given that the graph of <em>f</em> has a point of inflexion, find its coordinates.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(d) Show that the graph of <em>f</em> has exactly two asymptotes.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(e) Let <em>a</em> = 4 and <em>b</em> =1. Consider the region <em>R</em> enclosed by the graph of \(y = f(x)\), the <em>y</em>-axis and the line with equation \(y = \frac{1}{2}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the volume <em>V</em> of the solid obtained when <em>R</em> is rotated through \(2\pi \) about the <em>x</em>-axis.</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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \(f'(x) = \frac{{b{{\text{e}}^x}(a{{\text{e}}^x} + b) - a{{\text{e}}^x}(a + b{{\text{e}}^x})}}{{{{(a{{\text{e}}^x} + b)}^2}}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{ab{{\text{e}}^{2x}} + {b^2}{{\text{e}}^x} - {a^2}{{\text{e}}^x} - ab{{\text{e}}^{2x}}}}{{{{(a{{\text{e}}^x} + b)}^2}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{({b^2} - {a^2}){{\text{e}}^x}}}{{{{(a{{\text{e}}^x} + b)}^2}}}\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) <strong><em>EITHER</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(x) = 0 \Rightarrow ({b^2} - {a^2}){{\text{e}}^x} = 0 \Rightarrow b = \pm a{\text{ or }}{{\text{e}}^x} = 0\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">which is impossible as \(0 < b < a\) and \({{\text{e}}^x} > 0\) for all \(x \in \mathbb{R}\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(x) < 0\) for all \(x \in \mathbb{R}\) since \(0 < b < a\) and \({{\text{e}}^x} > 0\) for all \(x \in \mathbb{R}\) <strong><em>A1R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(x)\) cannot be equal to zero because \({{\text{e}}^x}\) is never equal to zero <strong><em>A1R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) <strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f''(x) = \frac{{({b^2} - {a^2}){{\text{e}}^x}{{(a{{\text{e}}^x} + b)}^2} - 2a{{\text{e}}^x}(a{{\text{e}}^x} + b)({b^2} - {a^2}){{\text{e}}^x}}}{{{{(a{{\text{e}}^x} + b)}^4}}}\) <strong><em>M1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1</em></strong> for each term in the numerator.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{({b^2} - {a^2}){{\text{e}}^x}(a{{\text{e}}^x} + b - 2a{{\text{e}}^x})}}{{{{(a{{\text{e}}^x} + b)}^3}}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{({b^2} - {a^2})(b - a{{\text{e}}^x}){{\text{e}}^x}}}{{{{(a{{\text{e}}^x} + b)}^3}}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(x) = ({b^2} - {a^2}){{\text{e}}^x}{(a{{\text{e}}^x} + b)^{ - 2}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f''(x) = ({b^2} - {a^2}){{\text{e}}^x}{(a{{\text{e}}^x} + b)^{ - 2}} + ({b^2} - {a^2}){{\text{e}}^x}( - 2a{{\text{e}}^x}){(a{{\text{e}}^x} + b)^{ - 3}}\) <strong><em>M1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Award </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for each term.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = ({b^2} - {a^2}){{\text{e}}^x}{(a{{\text{e}}^x} + b)^{ - 3}}\left( {(a{{\text{e}}^x} + b) - 2a{{\text{e}}^x}} \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = ({b^2} - {a^2}){{\text{e}}^x}{(a{{\text{e}}^x} + b)^{ - 3}}(b - a{{\text{e}}^x})\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>THEN</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f''(x) = 0 \Rightarrow b - a{{\text{e}}^x} = 0 \Rightarrow x = \ln \frac{b}{a}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f\left( {\ln \frac{b}{a}} \right) = \frac{{{a^2} + {b^2}}}{{2ab}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">coordinates are \(\left( {\ln \frac{b}{a},\frac{{{a^2} + {b^2}}}{{2ab}}} \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(d) \(\mathop {\lim }\limits_{x - \infty } f(x) = \frac{a}{b} \Rightarrow y = \frac{a}{b}\) horizontal asymptote <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\mathop {\lim }\limits_{x \to + \infty } f(x) = \frac{b}{a} \Rightarrow y = \frac{b}{a}\) horizontal asymptote <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(0 < b < a \Rightarrow a{{\text{e}}^x} + b > 0\) for all \(x \in \mathbb{R}\) (accept \(a{{\text{e}}^x} + b \ne 0\))</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so no vertical asymptotes <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Statement on vertical asymptote must be seen for <strong><em>R1</em></strong>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><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: 29.0px Helvetica;"><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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(e) \(y = \frac{{4 + {{\text{e}}^x}}}{{4{{\text{e}}^x} + 1}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(y = \frac{1}{2} \Leftrightarrow x = \ln \frac{7}{2}\) (or 1.25 to 3 sf) <strong><em>(M1)(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(V = \pi \int_0^{\ln \frac{7}{2}} {\left( {{{\left( {\frac{{4 + {{\text{e}}^x}}}{{4{{\text{e}}^x} + 1}}} \right)}^2} - \frac{1}{4}} \right){\text{d}}x} \) <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 1.09\) (3 sf) <strong><em>A1 N4</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [19 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was well attempted by many candidates. In some cases, candidates who skipped other questions still answered, with some success, parts of this question. Part (a) was in general well done but in (b) candidates found difficulty in justifying that f’(x) was non-zero. Performance in part (c) was mixed: it was pleasing to see good levels of algebraic ability of good candidates who successfully answered this question; weaker candidates found the simplification required difficult. There were very few good answers to part (d) which showed the weaknesses of most candidates in dealing with the concept of asymptotes. In part (e) there were a large number of good attempts, with many candidates evaluating correctly the limits of the integral and a smaller number scoring full marks in this part.</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">Points A , B and T lie on a line on an indoor soccer field. The goal, [AB] , is 2 metres wide. A player situated at point P kicks a ball at the goal. [PT] is perpendicular to (AB) and is 6 metres from a parallel line through the centre of [AB] . Let PT <span class="s1">be \(x\) metros and let \(\alpha = {\rm{A\hat PB}}\) measured in degrees. Assume that the ball travels along the floor.</span></p>
<p class="p1" style="text-align: center;"><span class="s1"><img src="images/Schermafbeelding_2017-02-03_om_11.38.31.png" alt="M16/5/MATHL/HP2/ENG/TZ2/11"></span></p>
</div>
<div class="specification">
<p class="p1"><span class="s1">The maximum for \(\tan \alpha \) </span>gives the maximum for \(\alpha \).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of \(\alpha \) when \(x = 10\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that \(\tan \alpha = \frac{{2x}}{{{x^2} + 35}}\).</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">(i) <span class="Apple-converted-space"> </span>Find \(\frac{{\text{d}}}{{{\text{d}}x}}(\tan \alpha )\).</p>
<p class="p2">(ii) <span class="Apple-converted-space"> </span>Hence or otherwise find the value of \(\alpha \) <span class="s1">such that \(\frac{{\text{d}}}{{{\text{d}}x}}(\tan \alpha ) = 0\).</span></p>
<p class="p2"><span class="s1">(iii) <span class="Apple-converted-space"> </span>Find \(\frac{{{{\text{d}}^2}}}{{{\text{d}}{x^2}}}(\tan \alpha )\) </span>and hence show that the value of \(\alpha \) <span class="s1">never exceeds 10°.</span></p>
<div class="marks">[11]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the set of values of \(x\) for which \(\alpha \geqslant 7^\circ \).</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 class="p1"><strong>EITHER</strong></p>
<p class="p1"><span class="s1">\(\alpha = \arctan \frac{7}{{10}} - \arctan \frac{5}{{10}}{\text{ }}( = 34.992 \ldots ^\circ - 26.5651 \ldots ^\circ )\) <span class="Apple-converted-space"> </span></span><strong><em>(M1)(A1)(A1)</em></strong></p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for \(\alpha = {\rm{A\hat PT}} - {\rm{B\hat PT}}\), <strong><em>(A1) </em></strong><span class="s1">for a correct \({\rm{A\hat PT}}\) </span>and <strong><em>(A1) </em></strong><span class="s1">for a correct \({\rm{B\hat PT}}\)</span>.</p>
<p class="p1"><strong>OR</strong></p>
<p class="p1"><span class="s1">\(\alpha = \arctan {\text{ }}2 - \arctan \frac{{10}}{7}{\text{ }}( = 63.434 \ldots ^\circ - 55.008 \ldots ^\circ )\) <span class="Apple-converted-space"> </span></span><strong><em>(M1)(A1)(A1)</em></strong></p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for \(\alpha = {\rm{P\hat BT}} - {\rm{P\hat AT}}\), <strong><em>(A1) </em></strong><span class="s1">for a correct \({\rm{P\hat BT}}\) </span>and <strong><em>(A1) </em></strong><span class="s1">for a correct \({\rm{P\hat AT}}\).</span></p>
<p class="p1"><strong>OR</strong></p>
<p class="p1"><span class="s1">\(\alpha = \arccos \left( {\frac{{125 + 149 - 4}}{{2 \times \sqrt {125} \times \sqrt {149} }}} \right)\) <span class="Apple-converted-space"> </span></span><strong><em>(M1)(A1)(A1)</em></strong></p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for use of cosine rule, <strong><em>(A1) </em></strong>for a correct numerator and <strong><em>(A1) </em></strong>for a correct denominator.</p>
<p class="p1"><strong>THEN</strong></p>
<p class="p3"><span class="Apple-converted-space">\( = 8.43^\circ \) </span><span class="s2"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>EITHER</strong></p>
<p class="p2"><span class="Apple-converted-space">\(\tan \alpha = \frac{{\frac{7}{x} - \frac{5}{x}}}{{1 + \left( {\frac{7}{x}} \right)\left( {\frac{5}{x}} \right)}}\) </span><span class="s1"><strong><em>M1A1A1</em></strong></span></p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>M1 </em></strong><span class="s2">for use of \(\tan (A - B)\)</span>, <strong><em>A1 </em></strong>for a correct numerator and <strong><em>A1 </em></strong>for a correct denominator.</p>
<p class="p1"><span class="Apple-converted-space">\( = \frac{{\frac{2}{x}}}{{1 + \frac{{35}}{{{x^2}}}}}\) </span><strong><em>M1</em></strong></p>
<p class="p1"><strong>OR</strong></p>
<p class="p2"><span class="Apple-converted-space">\(\tan \alpha = \frac{{\frac{x}{5} - \frac{x}{7}}}{{1 + \left( {\frac{x}{5}} \right)\left( {\frac{x}{7}} \right)}}\) </span><span class="s1"><strong><em>M1A1A1</em></strong></span></p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>M1 </em></strong><span class="s2">for use of xxx</span>, <strong><em>A1 </em></strong>for a correct numerator and <strong><em>A1 </em></strong>for a correct denominator.</p>
<p class="p1">\( = \frac{{\frac{{2x}}{{35}}}}{{1 + \frac{{{x^2}}}{{35}}}}\) <strong><em>M1</em></strong></p>
<p class="p1"><strong>OR</strong></p>
<p class="p2"><span class="Apple-converted-space">\(\cos \alpha = \frac{{{x^2} + 35}}{{\sqrt {({x^2} + 25)({x^2} + 49)} }}\) </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p2"><span class="s1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>M1 </em></strong></span>for either use of the cosine rule or use of \(\cos (A - B)\)<span class="s1">.</span></p>
<p class="p1"><span class="Apple-converted-space">\(\sin \alpha \frac{{2x}}{{\sqrt {({x^2} + 25)({x^2} + 49)} }}\) </span><strong><em>A1</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\(\tan \alpha = \frac{{\frac{{2x}}{{\sqrt {({x^2} + 25)({x^2} + 49)} }}}}{{\frac{{{x^2} + 35}}{{\sqrt {({x^2} + 25)({x^2} + 49)} }}}}\) </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p1"><strong>THEN</strong></p>
<p class="p2"><span class="Apple-converted-space">\(\tan \alpha = \frac{{2x}}{{{x^2} + 35}}\) </span><span class="s1"><strong><em>AG</em></strong></span></p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> \(\frac{{\text{d}}}{{{\text{d}}x}}(\tan \alpha ) = \frac{{2({x^2} + 35) - (2x)(2x)}}{{{{({x^2} + 35)}^2}}}{\text{ }}\left( { = \frac{{70 - 2{x^2}}}{{{{({x^2} + 35)}^2}}}} \right)\)</span> <strong><em>M1A1A1</em></strong></p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>M1 </em></strong>for attempting product or quotient rule differentiation, <strong><em>A1 </em></strong>for a correct numerator and <strong><em>A1 </em></strong>for a correct denominator.</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span><strong>METHOD 1</strong></p>
<p class="p1"><strong>EITHER</strong></p>
<p class="p3"><span class="Apple-converted-space">\(\frac{{\text{d}}}{{{\text{d}}x}}(\tan \alpha ) = 0 \Rightarrow 70 - 2{x^2} = 0\) </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p3"><span class="Apple-converted-space">\(x = \sqrt {35} {\text{ (m) }}\left( { = 5.9161 \ldots {\text{ (m)}}} \right)\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p3"><span class="Apple-converted-space">\(\tan \alpha = \frac{1}{{\sqrt {35} }}{\text{ }}( = 0.16903 \ldots )\) </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">attempting to locate the stationary point on the graph of</p>
<p class="p1"><span class="Apple-converted-space">\(\tan \alpha = \frac{{2x}}{{{x^2} + 35}}\) </span><strong><em>(M1)</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(x = 5.9161 \ldots {\text{ (m) }}\left( { = \sqrt {35} {\text{ (m)}}} \right)\) </span><strong><em>A1</em></strong></p>
<p class="p4"><span class="Apple-converted-space">\(\tan \alpha = 0.16903 \ldots {\text{ }}\left( { = \frac{1}{{\sqrt {35} }}} \right)\) </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p1"><strong>THEN</strong></p>
<p class="p4"><span class="Apple-converted-space">\(\alpha = 9.59^\circ \) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p5"><strong>METHOD 2</strong></p>
<p class="p5"><strong>EITHER</strong></p>
<p class="p6"><span class="Apple-converted-space">\(\alpha = \arctan \left( {\frac{{2x}}{{{x^2} + 35}}} \right) \Rightarrow \frac{{{\text{d}}\alpha }}{{{\text{d}}x}} = \frac{{70 - 2{x^2}}}{{{{({x^2} + 35)}^2} + 4{x^2}}}\) </span><span class="s2"><strong><em>M1</em></strong></span></p>
<p class="p6"><span class="Apple-converted-space">\(\frac{{{\text{d}}\alpha }}{{{\text{d}}x}} = 0 \Rightarrow x = \sqrt {35} {\text{ (m) }}\left( { = 5.9161{\text{ (m)}}} \right)\) </span><span class="s2"><strong><em>A1</em></strong></span></p>
<p class="p5"><strong>OR</strong></p>
<p class="p5">attempting to locate the stationary point on the graph of</p>
<p class="p5"><span class="Apple-converted-space">\(\alpha = \arctan \left( {\frac{{2x}}{{{x^2} + 35}}} \right)\) </span><strong><em>(M1)</em></strong></p>
<p class="p5"><span class="Apple-converted-space">\(x = 5.9161 \ldots {\text{ (m) }}\left( { = \sqrt {35} {\text{ (m)}}} \right)\) </span><strong><em>A1</em></strong></p>
<p class="p5"><strong>THEN</strong></p>
<p class="p7"><span class="Apple-converted-space">\(\alpha = 0.1674 \ldots {\text{ }}\left( { = \arctan \frac{1}{{\sqrt {35} }}} \right)\) </span><span class="s2"><strong><em>(A1)</em></strong></span></p>
<p class="p6"><span class="Apple-converted-space">\( = 9.59^\circ \) </span><span class="s2"><strong><em>A1</em></strong></span></p>
<p class="p5">(iii) <span class="Apple-converted-space"> \(\frac{{{{\text{d}}^2}}}{{{\text{d}}{x^2}}}(\tan \alpha ) = \frac{{{{({x^2} + 25)}^2}( - 4x) - (2)(2x)({x^2} + 35)(70 - 2{x^2})}}{{{{({x^2} + 35)}^4}}}{\text{ }}\left( { = \frac{{4x({x^2} - 105)}}{{{{({x^2} + 35)}^3}}}} \right)\)</span> <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p5">substituting \(x = \sqrt {35} {\text{ }}( = 5.9161 \ldots )\) into \(\frac{{{{\text{d}}^2}}}{{{\text{d}}{x^2}}}(\tan \alpha )\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p5"><span class="s3">\(\frac{{{{\text{d}}^2}}}{{{\text{d}}{x^2}}}(\tan \alpha ) < 0{\text{ }}( =- 0.004829 \ldots )\) </span>and so \(\alpha = 9.59^\circ \) is the maximum value of \(\alpha \) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p6">\(\alpha \) never exceeds 10° <span class="Apple-converted-space"> </span><span class="s2"><strong><em>AG</em></strong></span></p>
<p class="p5"><strong><em>[11 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">attempting to solve \(\frac{{2x}}{{{x^2} + 35}} \geqslant \tan 7^\circ \) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for attempting to solve \(\frac{{2x}}{{{x^2} + 35}} = \tan 7^\circ \).</p>
<p class="p1">\(x = 2.55\) and \(x = 13.7\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p3"><span class="Apple-converted-space">\(2.55 \leqslant x \leqslant 13.7{\text{ (m)}}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">This question was generally accessible to a large majority of candidates. It was pleasing to see a number of different (and quite clever) trigonometric methods successfully employed to answer part (a) and part (b).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">This question was generally accessible to a large majority of candidates. It was pleasing to see a number of different (and quite clever) trigonometric methods successfully employed to answer part (a) and part (b).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">The early parts of part (c) were generally well done. In part (c) (i), a few candidates correctly found \(\frac{{\text{d}}}{{{\text{d}}x}}(\tan \alpha )\) in unsimplified form but then committed an algebraic error when endeavouring to simplify further. A few candidates merely stated that \(\frac{{\text{d}}}{{{\text{d}}x}}(\tan \alpha ) = {\sec ^2}\alpha \).</p>
<p class="p1">Part (c) (ii) was reasonably well done with a large number of candidates understanding what was required to find the correct value of \(\alpha \) in degrees. In part (c)(iii), a reasonable number of candidates were able to successfully find \(\frac{{{{\text{d}}^2}}}{{{\text{d}}{x^2}}}(\tan \alpha )\) in unsimplified form. Some however attempted to solve \(\frac{{{{\text{d}}^2}}}{{{\text{d}}{x^2}}}(\tan \alpha ) = 0\) for \(\chi \) rather than examine the value of \(\frac{{{{\text{d}}^2}}}{{{\text{d}}{x^2}}}(\tan \alpha )\) at \(x = \sqrt {35} \).</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Part (d), which required use of a GCD to determine an inequality, was surprisingly often omitted by candidates. Of the candidates who attempted this part, a number stated that \(x \geqslant 2.55\). Quite a sizeable proportion of candidates who obtained the correct inequality did not express their answer to 3 significant figures.</p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A lighthouse L is located offshore, 500 metres from the nearest point P on a long straight shoreline. The narrow beam of light from the lighthouse rotates at a constant rate of \(8\pi \) radians per minute, producing an illuminated spot S that moves along the shoreline. You may assume that the height of the lighthouse can be ignored and that the beam of light lies in the horizontal plane defined by sea level.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="font: normal normal normal 27px/normal Helvetica; text-align: center; margin: 0px;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAVoAAADKCAIAAABrIh/WAAAMAUlEQVR4nO3cT2gc5x3G8TnFlzRxVZ/6J7tkTxIIEopAJ5lAmio6SMYEE1BJC5JACgR80cUrBC31wSmsidRYUFJWrlJIAu4sNb3YCYNB7EFmkQ6mSAM9mJUQRSxmWTrGh+HtYXZnZ2VZu1rNzPvOO98Pe4icoBlLO8++M783jyEAQAghhBHXgdy6tTycyebar+l1+3lcRwfQXWxx4HlWKVzNDV4vHbyI97gAuos5Dp7bxenc4LJVd+M9LoDuiAMATcQBgCbiAEATcQCgiTgA0KRIHDy3//nAJiIAqdSIg8bWSuFRPd5TAXCMlG1IHXHgHm5t5H+3ZB3FeyYAjpO4SZkNy4BaYl4ddFer1VZXVxcXFxcXFzc3N2WfDpAiasVBtVodGRkxDGNxcXFqasowjNXVVdknBaSFWnFw8+bNkZGRarXqfbm6umoYxt7entyzAlJCrTgwDOPu3bv+l47jGIZx7949iacEpAdxAKBJrTg48Wbhr1995TiO3BMD0kCtOAg+SvT+4dcffJDLZD++ds22bdlnB2hOrTgQQtRqtbt37158482Biz/2Bo07OzvvXb6cy2TX7qyxTACio1wceLztSf6XjuOs3VnLZbLvXb68s7Mj8cQAjSUjDjy2bX987Vouk83fuFGr1aScGKCxJMWBEMJxnK83NrxlwsOHD+M/MUBjCYsDz/7+/qcLC94yYX9/P84TAzSWyDjwlEzTe8RYMs14zgrQW4LjQAhRq9XyN24wiQRCoWgcnEm5XPaWCV9vbDCJBPqmQxwIIRzH+fzWLW+ZwCQS6I8mceDZ2dnxJpGf37rFMgE4K63iQDCJBM5Btzjw2LbtTyLZsAT0SM848JRM05tQMIkEeqFzHIjAJPLThQU2LAGnUzQOetx30KOHDx8yiQS6SkUcCCFqtZo/iWTDEnCitMSBx69OYBIJvCxdcSA6J5HlcjmKQwAJlbo48FCdALwspXHg8SaRbFgCPKmOAxGoTmASCaQ9Djz+JLJkmjxiRGoRB01UJwDEQQdK3JFmisaBRH51AiXuSBvi4GT+JPLzW7eYRCIliINXojoBaUMcdEGJO9KDOOgJJe5IA+KgV0wioT3i4GyoToDGFI0DWfsOekGJO3RFHPSJEnfohzjoH5NIaIY4OC9K3KEN4iAclLhDA8RBaPb39ylxR6IRByFjEonkIg7CR4k7Eoo4iAol7kgc4iBClLgjWYiDyFHijqRQNA404zgOJe5QH3EQH0rcoTjiIG6UuENZxIEEVCdATcSBNP4kkg1LUARxIBMl7lAKcSAfJe5QhKJxoNO+g15QnQAVEAcKocQdchEHyqHEHbIQByryJ5GfLiwwiURsiAN1UZ2AmBEHSqPEHXEiDhKAEnfEgzhIBiaRiAFxkCSUuCNSxEHy+NUJTCIRLkXjAKejxB1RIA4SjEkkwkUcJBsl7ggRcaADStwRCuJAE47jrN1ZozoB50EcaIUSd5wHcaAbStzRN0XjgH0H50SJO/pAHOiMEnecCXGgOUrc0TviIBXK5TIbltAVcZAWlLijK+IgXShxxymIg9ShOgGvQhykFCXueBlxkGrehiVK3OEhDtKOEnf4FI0DxIzqBAjiAD5K3EEcoAMl7mlGHOA4JpGpRRzgZFQnpBBxgNNQ4p4qxAG6oMQ9PRSNA/YdqIZJZBoQB+gVJe7aIw5wNn6J+9qdNZYJmiEOcGaUuOuKOECfmETqhzhA/yhx1wxxgPOixF0bxAHCESxxl30u6BNxgNBQ4p50xAFCRol7chEHCB8l7gmlaBxAA5S4Jw5xgAhRnZAsxAEiFyxxZ5mgMuIAMaHEXX3EAeJDibviiAPEjeoEZREHkIASdzUpGgfsO0gDvzqBEndFEAeQKTiJLJfLsk8n7YgDyEd1giKIA6iCEnfpiAMohBJ3uYgDKIdJpCzEAVREdYIUxAHURYl7zIgDKI0S9zgRB0gAJpHxUDQOgGMocY8BcYAkocQ9UsQBkqdkmpS4R4E4QCIxiYwCcYAEo8Q9XMQBko0S9xARB9ABJe6hUDQO2HeAs6LE/fyIA2jFtm1K3PtGHEBDlLj3hziAnihx7wNxAJ1RnXAmxAE0FyxxZ5lwOuIAqUCJey+IA6QFJe5dEQdIF6oTTkEcII0ocT8RcYCUosT9ZYrGARAPfxJZMk0eMRIHSDuqE3zEASAEJe5CCOIA8FHiThwAHdI8iSQOgONSW+JOHAAn80vc8zdupGQSqWgcsO8AikhViTtxAHSRnkkkcQD0JA0l7sQB0CvtS9yJA+BsdnZ2/BJ3zZYJxAFwZrqWuBMHQJ/0K3EnDoBz0anEnTgAzkubEnfiAAiHBiXuisYBkES1Wi3RJe7EARCy5Ja4EwdA+BJa4k4cAFFJXHUCcQBEK0El7sQBEDm/OkHxEnfiAIiJ+iXuisYB+w6gJcWrE4gDIG7KlrgTB4AEapa4EweANKpNIokDQCalqhOIA0A+RUrciQNAFdJL3IkDQCFyJ5EqxsH29vbFN968NDBQrVZlnwsggVfi/vZbmd9+8slnn3128+bNeK4F5eJge3vbaBkZGVFqKgvExnGcK1NThmH86PXXDcOYmpqK4aCGEMJbnCjyuvjGm4ZhZH7+i0sDA4ZhvPXTn0k/JV68pLwuvHbhwmsX3n4r410UUV8Ltm0bQohyuVwyTUVev5meNgzj0sDApZ9cMgzjzpdfSj8lXrykvH71/vuGYXhZYBjGd99+G+nharWacjcL1Wp1ZGTE+/vPzs7KPh1AmuC1sLm5GcMRlYsDIYTjOHt7e3t7e7JPBJDMuxZi27CoYhwAkII4SCi3YT/6R2H+o+KuG+0hZn+Zt+rNP3hamh+bKGw1ojoiJIs/Dp7bxenjTzUHZ2/fe2Q3Intj66duLQ1mc5mhK9HFQfMQ2WHiQCnuYeVv+YlMNpcZmsgXLftZfXv7PyG9CSStDtzd9cl3W2/lum0uT2SywzMbuyRC7zp+htEdYqgdB5DvWaVw1b9S3MOtjfxkbrJoaxQHorVkGFuyjuScTxIRB+nj2sUrxy4T92np999oFgdu3VoejnTpqx/iIH1cu3glM9R5v+ZqdrMgWB10499PFUpb5cfbNSH8n+G/67a5ND6Uy4zOFZ+03yUN2yp6d5jZ4ZmVH+x6+8/vFebeWf5hd3NlZrS17Kzb36/MDb70H3fEwbEni3Xb+u72zPy6/V/v3HKD8+u7gdxo2D8UZocz2VxmdK7wgAdD4XCfluZHW08Nwk9piXEw1HovvjjcWpsbzObGVyq8aU7i2sWP5s0DVwgh3IMHG4+OhGjGwcT8nza2Dl3x4sC8PpyZXrefC+G9aT5spkNjt5SfbF2rR1Z+zHt2u7J1UK+sTIyvVBq1yhd/WNk69J7j7BbnhweXrbrbOkQrDjqeLHqruWwu8+FC4ZvHhy+a39m/iW1sreT/8vjwhRBCNJ6sz4yyxAiN9wttPkr8e8X7IYdEZhwEhgujcwUz3L+YRp7bxenhmUKpctgRlp0rrMBdpVu3ltuXtBCisXV73P+QP7LyY7ngv21d54FXa5l27Gahc7FQt5bbAeSt75rf1g+L4PAocEScV922ikvj3hU0uWTuhjXrUeRmAadxD8yFQS80v7M6VvInxkHnB7UQnRFwLA7curU8/KpH033GwZGVf59fbvT8W7yrtyvPQvmOxEEyuIeV+81nAaML5lNXdIuDjk/jbnHQvqqPHbXvOBgLcfoFn2s/uN/5m3IPzIXB0J7BEweJ4h4+/mK2eSNw+s1CxyfGkZUf63KzMJ7f8G9GGk+siv+0su+bheCdrdvY3qxws3Burr2xcGwbWKiXkqQ4aGzdHn+X/W29ceuP/vWoeS29ODCvN9f2dWsp8LHQMZFuPFmfGc2NL5fsuhBuY3dj7p3rpQPvynx57fCsUrjacZ/vP9PtMw6aTysC33OI33UoXLt4JfigzduhOP5HK6TnbtI3Kb9imYo2t75t3f/eXM9P+g+TXbt4pfUzHM5/X20/umsFRHvOFxhKtZ/gjk2Mz7Z/8u19r4FBY/AR42TRfhb88s+lr6YDzx3/3RxYBH6hzQ1zDBpD5doP7tv/a9jWejTDBf4XJgBN/weg+Dselu2uLgAAAABJRU5ErkJggg==" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">When S is 2000 metres from P,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) show that the speed of S, correct to three significant figures, is \({\text{214}}\,{\text{000}}\) metres per minute;</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) find the acceleration of S.</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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) the distance of the spot from P is \(x = 500\tan \theta \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the speed of the spot is</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}x}}{{{\text{d}}t}} = 500{\sec ^2}\theta \frac{{{\text{d}}\theta }}{{{\text{d}}t}}{\text{ }}( = 4000\pi {\sec ^2}\theta )\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">when \(x = 2000,{\text{ }}{\sec ^2}\theta = 17{\text{ }}(\theta = 1.32581 \ldots )\left( {\frac{{{\text{d}}\theta }}{{{\text{d}}t}} = 8\pi } \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow \frac{{{\text{d}}x}}{{{\text{d}}t}} = 500 \times 17 \times 8\pi \) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">speed is \({\text{214 000}}\) (metres per minute) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> If their displayed answer does not round to \({\text{214 000}}\), they lose the final <strong><em>A1</em></strong>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) \(\frac{{{{\text{d}}^2}x}}{{{\text{d}}{t^2}}} = 8000\pi {\sec ^2}\theta \tan \theta \frac{{{\text{d}}\theta }}{{{\text{d}}t}}\) <strong>or</strong> \(500 \times 2{\sec ^2}\theta \tan \theta {\left( {\frac{{{\text{d}}\theta }}{{{\text{d}}t}}} \right)^2}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[\left( {{\text{since }}\frac{{{{\text{d}}^2}\theta }}{{{\text{d}}{t^2}}} = 0} \right)\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {\text{43}}\,{\text{000}}\,{\text{000 (}} = 4.30 \times {10^7}){\text{ (metres per minut}}{{\text{e}}^2})\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><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">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This was a wordy question with a clear diagram, requiring candidates to state variables and do some calculus. Very few responded appropriately.</span></p>
</div>
<br><hr><br><div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">Using the substitution \(x = 2\sin \theta \) , show that\[\int {\sqrt {4 - {x^2}} } {\text{d}}x = Ax\sqrt {4 - {x^2}} + B\arcsin \frac{x}{2} + {\text{constant ,}}\]where \(A\) and \(B\) are constants whose values you are required to find.</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;">\(\int {\sqrt {4 - {x^2}} } {\text{d}}x\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(x = 2\sin \theta \)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({\text{d}}x = 2\cos \theta {\text{d}}\theta \) <em><strong>A1</strong></em></span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\( = \int {\sqrt {4 - 4{{\sin }^2}\theta } } \times 2\cos \theta {\text{d}}\theta \) <em><strong>M1A1</strong></em></span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\( = \int {2\cos \theta \times } 2\cos \theta {\text{d}}\theta \)</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\( = 4\int {{{\cos }^2}\theta {\text{d}}\theta } \)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">now \(\int {{{\cos }^2}\theta {\text{d}}\theta } \)</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\( = \int {\left( {\frac{1}{2}\cos 2\theta + \frac{1}{2}} \right)} {\text{d}}\theta \) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;"> M1A1</span></strong></em></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\( = \left( {\frac{{\sin 2\theta }}{4} + \frac{1}{2}\theta } \right)\) </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;">so original integral</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\( = 2\sin 2\theta + 2\theta \)</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\( = 2\sin \theta \cos \theta + 2\theta \)</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\( = \left( {2 \times \frac{x}{2} \times \frac{{\sqrt {4 - {x^2}} }}{2}} \right) + 2\arcsin \left( {\frac{x}{2}} \right)\)</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\( = \frac{{x\sqrt {4 - {x^2}} }}{2} + 2\arcsin \left( {\frac{x}{2}} \right) + C\) </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> Do not penalise omission of \(C\).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\left( {A = \frac{1}{2},{\text{ }}B = 2} \right)\)</span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[8 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;">For many candidates this was an all or nothing question. Examiners were surprised at the number of candidates who were unable to change the variable in the integral using the given substitution. Another stumbling block, for some candidates, was a lack of care with the application of the trigonometric version of Pythagoras' Theorem to reduce the integrand to a multiple of \({\cos ^2}\theta \) . However, candidates who obtained the latter were generally successful in completing the question.</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A particle moves in a straight line in a positive direction from a fixed point O.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The velocity <em>v</em> m \({{\text{s}}^{ - 1}}\) , at time <em>t</em> seconds, where \(t \geqslant 0\) , satisfies the differential equation</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[\frac{{{\text{d}}v}}{{{\text{d}}t}} = \frac{{ - v(1 + {v^2})}}{{50}}.\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The particle starts from O with an initial velocity of 10 m \({{\text{s}}^{ - 1}}\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) (i) Express as a definite integral, the time taken for the particle’s velocity to decrease from 10 m \({{\text{s}}^{ - 1}}\) to 5 m \({{\text{s}}^{ - 1}}\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) <strong>Hence</strong> calculate the time taken for the particle’s velocity to decrease from 10 m \({{\text{s}}^{ - 1}}\) to 5 m \({{\text{s}}^{ - 1}}\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) (i) Show that, when \(v > 0\) , the motion of this particle can also be described by the differential equation \(\frac{{{\text{d}}v}}{{{\text{d}}x}} = \frac{{ - (1 + {v^2})}}{{50}}\) where <em>x</em> metres is the displacement from O.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Given that <em>v</em> =10 when <em>x</em> = 0 , solve the differential equation expressing <em>x</em> in terms of <em>v</em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) <strong>Hence</strong> show that \(v = \frac{{10 - \tan \frac{x}{{50}}}}{{1 + 10\tan \frac{x}{{50}}}}\).</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: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) (i) <strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Attempting to separate the variables <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}v}}{{ - v(1 + {v^2})}} = \frac{{{\text{d}}t}}{{50}}\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Inverting to obtain \(\frac{{{\text{d}}t}}{{{\text{d}}v}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}t}}{{{\text{d}}v}} = \frac{{ - 50}}{{v(1 + {v^2})}}\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>THEN</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(t = - 50\int_{10}^5 {\frac{1}{{v(1 + {v^2})}}} {\text{d}}v\,\,\,\,\,\left( { = 50\int_5^{10} {\frac{1}{{v(1 + {v^2})}}{\text{d}}v} } \right)\) <strong><em>A1</em></strong> <strong><em>N3</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \(t = 0.732{\text{ (sec)}}\,\,\,\,\,\left( { = 25\ln \frac{{104}}{{101}}(\sec )} \right)\) <strong><em>A2</em></strong> <strong><em>N2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) (i) \(\frac{{{\text{d}}v}}{{{\text{d}}t}} = v\frac{{{\text{d}}v}}{{{\text{d}}x}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Must see division by <em>v</em> \((v > 0)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}v}}{{{\text{d}}x}} = \frac{{ - (1 + {v^2})}}{{50}}\) <strong><em>AG</em></strong> <strong><em>N0</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Either attempting to separate variables or inverting to obtain \(\frac{{{\text{d}}x}}{{{\text{d}}v}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\frac{{{\text{d}}v}}{{1 + {v^2}}} = - \frac{1}{{50}}\int {{\text{d}}x} }\) (or equivalent) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Attempting to integrate both sides <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\arctan v = - \frac{x}{{50}} + C\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1</em></strong> for a correct LHS and <strong><em>A1</em></strong> for a correct RHS that must include <em>C</em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><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: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">When \(x = 0{\text{ , }}v = 10{\text{ and so }}C = \arctan 10\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 50(\arctan 10 - \arctan v)\) <strong><em>A1 N1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) Attempting to make \(\arctan v\) the subject. <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\arctan v = \arctan 10 - \frac{x}{{50}}\) <strong>A1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(v = \tan \left( {\arctan 10 - \frac{x}{{50}}} \right)\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Using tan(<em>A</em> − <em>B</em>) formula to obtain the desired form. <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(v = \frac{{10 - \tan \frac{x}{{50}}}}{{1 + 10\tan \frac{x}{{50}}}}\) <strong><em>AG N0</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[14 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [19 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">No comment.</span></p>
</div>
<br><hr><br><div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the gradient of the curve \({{\text{e}}^{xy}} + \ln \left( {{y^2}} \right) + {{\text{e}}^y} = 1 + {\text{e}}\) at the point (0, 1) .</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;">\({{\text{e}}^{xy}} + \ln \left( {{y^2}} \right) + {{\text{e}}^y} = 1 + {\text{e}}\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({{\text{e}}^{xy}}\left( {y + x\frac{{{\text{d}}y}}{{{\text{d}}x}}} \right) + \frac{2}{y}\frac{{{\text{d}}y}}{{{\text{d}}x}} + {{\text{e}}^y}\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\) , at (0, 1) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1A1A1A1A1</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(1\left( {1 + 0} \right) + 2\frac{{{\text{d}}y}}{{{\text{d}}x}} + {\text{e}}\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(1 + 2\frac{{{\text{d}}y}}{{{\text{d}}x}} + {\text{e}}\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = - \frac{1}{{2 + {\text{e}}}}\) (\( = -0.212\)) <em><strong>M1A1 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;">Implicit differentiation is usually found to be difficult, but on this occasion there were many </span><span style="font-family: times new roman,times; font-size: medium;">correct solutions. There were also a number of errors in the differentiation of \({e^{xy}}\) , and </span><span style="font-family: times new roman,times; font-size: medium;">although these often led to the correct final answer, marks could not be awarded.</span></p>
</div>
<br><hr><br><div class="specification">
<p>A water trough which is 10 metres long has a uniform cross-section in the shape of a semicircle with radius 0.5 metres. It is partly filled with water as shown in the following diagram of the cross-section. The centre of the circle is O and the angle KOL is \(\theta \) radians.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-09_om_11.09.30.png" alt="M17/5/MATHL/HP2/ENG/TZ1/08"></p>
</div>
<div class="specification">
<p>The volume of water is increasing at a constant rate of \(0.0008{\text{ }}{{\text{m}}^3}{{\text{s}}^{ - 1}}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for the volume of water \(V{\text{ }}({{\text{m}}^3})\) in the trough in terms of \(\theta \).</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate \(\frac{{{\text{d}}\theta }}{{{\text{d}}t}}\) when \(\theta = \frac{\pi }{3}\).</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>area of segment \( = \frac{1}{2} \times {0.5^2} \times (\theta - \sin \theta )\) <strong><em>M1A1</em></strong></p>
<p>\(V = {\text{area of segment}} \times 10\)</p>
<p>\(V = \frac{5}{4}(\theta - \sin \theta )\) <strong><em>A1</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><strong>METHOD 1</strong></p>
<p>\(\frac{{{\text{d}}V}}{{{\text{d}}t}} = \frac{5}{4}(1 - \cos \theta )\frac{{{\text{d}}\theta }}{{{\text{d}}t}}\) <strong><em>M1A1</em></strong></p>
<p>\(0.0008 = \frac{5}{4}\left( {1 - \cos \frac{\pi }{3}} \right)\frac{{{\text{d}}\theta }}{{{\text{d}}t}}\) <strong><em>(M1)</em></strong></p>
<p>\(\frac{{{\text{d}}\theta }}{{{\text{d}}t}} = 0.00128{\text{ }}({\text{rad}}\,{s^{ - 1}})\) <strong><em>A1</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>\(\frac{{{\text{d}}\theta }}{{{\text{d}}t}} = \frac{{{\text{d}}\theta }}{{{\text{d}}V}} \times \frac{{{\text{d}}V}}{{{\text{d}}t}}\) <strong><em>(M1)</em></strong></p>
<p>\(\frac{{{\text{d}}V}}{{{\text{d}}\theta }} = \frac{5}{4}(1 - \cos \theta )\) <strong><em>A1</em></strong></p>
<p>\(\frac{{{\text{d}}\theta }}{{{\text{d}}t}} = \frac{{4 \times 0.0008}}{{5\left( {1 - \cos \frac{\pi }{3}} \right)}}\) <strong><em>(M1)</em></strong></p>
<p>\(\frac{{{\text{d}}\theta }}{{{\text{d}}t}} = 0.00128\left( {\frac{4}{{3125}}} \right)({\text{rad }}{s^{ - 1}})\) <strong><em>A1</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;">The diagram below shows two concentric circles with centre O and radii 2 cm and 4 cm.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The points P and Q lie on the larger circle and \({\rm{P}}\hat {\text{O}}{\text{Q}} = x\) , where \(0 < x < \frac{\pi }{2}\)</span><span style="font-family: times new roman,times; font-size: medium;"> .</span></p>
<p><br><img style="display: block; margin-left: auto; margin-right: auto;" 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" alt></p>
</div>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">(a) Show that the area of the shaded region is \(8\sin x - 2x\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(b) Find the maximum area of the shaded region.</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;">(a) shaded area area of triangle area of sector, <em>i.e.</em> <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\left( {\frac{1}{2} \times {4^2}\sin x} \right) - \left( {\frac{1}{2}{2^2}x} \right) = 8\sin x - 2x\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1A1AG</span></strong></em></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>EITHER</strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">any method from GDC gaining \(x \approx 1.32\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">maximum value for given domain is \(5.11\) <em><strong>A2</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;">\(\frac{{{\text{d}}A}}{{{\text{d}}x}} = 8\cos x - 2\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">set \(\frac{{{\text{d}}A}}{{{\text{d}}x}} = 0\)</span><span style="font-family: times new roman,times; font-size: medium;">, hence \(8\cos x - 2 = 0\) <em><strong>M1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\cos x = \frac{1}{4} \Rightarrow x \approx 1.32\) </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;">hence \({A_{\max }} = 5.11\) <em><strong>A1</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;">[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;">Generally a well answered question.</span></p>
</div>
<br><hr><br><div class="question">
<p class="p1">An earth satellite moves in a path that can be described by the curve \(72.5{x^2} + 71.5{y^2} = 1\) where \(x = x(t)\) and \(y = y(t)\) are in thousands of kilometres and \(t\) is time in seconds.</p>
<p class="p1">Given that \(\frac{{{\text{d}}x}}{{{\text{d}}t}} = 7.75 \times {10^{ - 5}}\) when \(x = 3.2 \times {10^{ - 3}}\), find the possible values of \(\frac{{{\text{d}}y}}{{{\text{d}}t}}\).</p>
<p class="p1">Give your answers in standard form.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p class="p1"><strong>METHOD 1</strong></p>
<p class="p1">substituting for \(x\) and attempting to solve for \(y\) (or vice versa) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(y = ( \pm )0.11821 \ldots \) </span><strong><em>(A1)</em></strong></p>
<p class="p1"><strong>EITHER</strong></p>
<p class="p1"><span class="Apple-converted-space">\(145x + 143y\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0{\text{ }}\left( {\frac{{{\text{d}}y}}{{{\text{d}}x}} = - \frac{{145x}}{{143y}}} \right)\) </span><strong><em>M1A1</em></strong></p>
<p class="p1"><strong>OR</strong></p>
<p class="p1"><span class="Apple-converted-space">\(145x\frac{{{\text{d}}x}}{{{\text{d}}t}} + 143y\frac{{{\text{d}}y}}{{{\text{d}}t}} = 0\) </span><strong><em>M1A1</em></strong></p>
<p class="p1"><strong>THEN</strong></p>
<p class="p1">attempting to find \(\frac{{{\text{d}}x}}{{{\text{d}}t}}{\text{ }}\left( {\frac{{{\text{d}}y}}{{{\text{d}}t}} = - \frac{{145(3.2 \times {{10}^{ - 3}})}}{{143\left( {( \pm )0.11821 \ldots } \right)}} \times (7.75 \times {{10}^{ - 5}})} \right)\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(\frac{{{\text{d}}y}}{{{\text{d}}t}} = \pm 2.13 \times {10^{ - 6}}\) </span><strong><em>A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: </strong>Award all marks except the final <strong><em>A1 </em></strong>to candidates who do not consider ±.</p>
<p class="p2"> </p>
<p class="p1"><strong>METHOD 2</strong></p>
<p class="p1"><span class="Apple-converted-space">\(y = ( \pm )\sqrt {\frac{{1 - 72.5{x^2}}}{{71.5}}} \) </span><strong><em>M1A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = ( \pm )0.0274 \ldots \) </span><strong><em>(M1)(A1)</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(\frac{{{\text{d}}y}}{{{\text{d}}t}} = ( \pm )0.0274 \ldots \times 7.75 \times {10^{ - 5}}\) </span><strong><em>(M1)</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(\frac{{{\text{d}}y}}{{{\text{d}}t}} = \pm 2.13 \times {10^{ - 6}}\) </span><strong><em>A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: </strong>Award all marks except the final <strong><em>A1 </em></strong>to candidates who do not consider ±.</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[6 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p class="p1">Find the equation of the normal to the curve \(y = \frac{{{{\text{e}}^x}\cos x\ln (x + {\text{e}})}}{{{{({x^{17}} + 1)}^5}}}\) at the point where \(x = 0\).</p>
<p class="p1">In your answer give the value of the gradient, of the normal, to three decimal places.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>\(x = 0 \Rightarrow y = 1\) <strong><em>(A1)</em></strong></p>
<p>\(y'(0) = 1.367879 \ldots \) <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> The exact answer is \(y'(0) = \frac{{{\text{e}} + 1}}{{\text{e}}} = 1 + \frac{1}{{\text{e}}}\).</p>
<p> </p>
<p>so gradient of normal is \(\frac{{ - 1}}{{1.367879 \ldots }}\;\;\;( = - 0.731058 \ldots )\) <strong><em>(M1)(A1)</em></strong></p>
<p>equation of normal is \(y = - 0.731058 \ldots x + c\) <strong><em>(M1)</em></strong></p>
<p>gives \(y = - 0.731x + 1\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> The exact answer is \(y = - \frac{{\text{e}}}{{{\text{e}} + 1}}x + 1\).</p>
<p>Accept \(y - 1 = - 0.731058 \ldots (x - 0)\)</p>
<p> </p>
<p><strong><em>[7 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p class="p1">Surprisingly many candidates ignored that fact that paper 2 is a calculator paper, attempted an algebraic approach and wasted lots of time. Candidates that used the GDC were in general successful and achieved 7/7. A number of candidates either found the equation of the tangent or used the positive reciprocal for the normal and many did not find the value of \(y\) corresponding to \(f(0)\).</p>
</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;">Sand is being poured to form a cone of height \(h\) cm and base radius \(r\) cm. The height remains equal to the base radius at all times. The height of the cone is increasing at a rate of \(0.5{\text{ cm}}\,{\text{mi}}{{\text{n}}^{ - 1}}\).</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;">Find the rate at which sand is being poured, in \({\text{c}}{{\text{m}}^3}\,{\text{mi}}{{\text{n}}^{ - 1}}\), when the height is 4 cm.</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: 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;">volume of a cone is \(V = \frac{1}{3}\pi {r^2}h\)</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;">given \(h = r,{\text{ }}V = \frac{1}{3}\pi {h^3}\) <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;">\(\frac{{{\text{d}}V}}{{{\text{d}}h}} = \pi {h^2}\) <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;">when \(h = 4,{\text{ }}\frac{{{\text{d}}V}}{{{\text{d}}t}} = \pi \times {4^2} \times 0.5{\text{ (using }}\frac{{{\text{d}}V}}{{{\text{d}}t}} = \frac{{{\text{d}}V}}{{{\text{d}}h}} \times \frac{{{\text{d}}h}}{{{\text{d}}t}})\) <strong><em>M1A1</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;">\(\frac{{{\text{d}}V}}{{{\text{d}}t}} = 8\pi {\text{ }}( = 25.1){\text{ (c}}{{\text{m}}^3}\,{\text{mi}}{{\text{n}}^{ - 1}})\) <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;"><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;">volume of a cone is \(V = \frac{1}{3}\pi {r^2}h\)</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;">given \(h = r,{\text{ }}V = \frac{1}{3}\pi {h^3}\) <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;">\(\frac{{{\text{d}}V}}{{{\text{d}}t}} = \frac{1}{3}\pi \times 3{h^2} \times \frac{{{\text{d}}h}}{{{\text{d}}t}}\) <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;">when \(h = 4,{\text{ }}\frac{{{\text{d}}V}}{{{\text{d}}t}} = \pi \times {4^2} \times 0.5\) <strong><em>M1A1</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;">\(\frac{{{\text{d}}V}}{{{\text{d}}t}} = 8\pi {\text{ }}( = 25.1){\text{ (c}}{{\text{m}}^3}\,{\text{mi}}{{\text{n}}^{ - 1}})\) <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;"><strong>METHOD 3</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;">\(V = \frac{1}{3}\pi {r^2}h\)</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;">\(\frac{{{\text{d}}V}}{{{\text{d}}t}} = \frac{1}{3}\pi \left( {2rh\frac{{{\text{d}}r}}{{{\text{d}}t}} + {r^2}\frac{{{\text{d}}h}}{{{\text{d}}t}}} \right)\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px '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> Award <strong><em>M1 </em></strong>for attempted implicit differentiation and <strong><em>A1 </em></strong>for each correct term on the RHS.</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;">when \(h = 4,{\text{ }}r = 4,{\text{ }}\frac{{{\text{d}}V}}{{{\text{d}}t}} = \frac{1}{3}\pi \left( {2 \times 4 \times 4 \times 0.5 + {4^2} \times 0.5} \right)\) <strong><em>M1A1</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;">\(\frac{{{\text{d}}V}}{{{\text{d}}t}} = 8\pi {\text{ }}( = 25.1){\text{ (c}}{{\text{m}}^3}\,{\text{mi}}{{\text{n}}^{ - 1}})\) <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;"><strong><em>[5 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="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">By using the substitution \(x = \sin t\) , find \(\int {\frac{{{x^3}}}{{\sqrt {1 - {x^2}} }}{\text{d}}x} \) .<br></span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 12px/normal Helvetica; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = \sin t,{\text{ d}}x = \cos t\,{\text{d}}t\)</span></p>
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 12px/normal Helvetica; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {\frac{{{x^3}}}{{\sqrt {1 - {x^2}} }}{\text{d}}x} = \int {\frac{{{{\sin }^3}t}}{{\sqrt {1 - {{\sin }^2}t} }}\cos t\,{\text{d}}t} \)</span><span style="font-family: 'times new roman', times; font-size: medium;"> </span><em style="font-style: italic;"><strong>M1</strong></em></p>
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 12px/normal Helvetica; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \int {{{\sin }^3}t\,{\text{d}}t} \) <strong> <em>(A1)</em></strong></span></p>
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 12px/normal Helvetica; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \int {{{\sin }^2}t\sin t\,{\text{d}}t} \)</span></p>
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 12px/normal Helvetica; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \int {(1 - {{\cos }^2}t)\sin t\,{\text{d}}t} \)</span><span style="font-family: 'times new roman', times; font-size: medium;"> <strong><em>M1A1</em></strong></span></p>
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 12px/normal Helvetica; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \int {\sin t\,{\text{d}}t - \int {{{\cos }^2}t\sin t\,{\text{d}}t} } \)</span></p>
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 12px/normal Helvetica; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = - \cos t + \frac{{{{\cos }^3}t}}{3} + C\) <strong><em>A1A1</em></strong></span></p>
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 12px/normal Helvetica; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = - \sqrt {1 - {x^2}} + \frac{1}{3}{\left( {\sqrt {1 - {x^2}} } \right)^3} + C\) <strong><em>A1</em></strong></span></p>
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 12px/normal Helvetica; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\left( { = - \sqrt {1 - {x^2}} \left( {1 - \frac{1}{3}(1 - {x^2})} \right) + C} \right)\)</span></p>
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 12px/normal Helvetica; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\left( { = - \frac{1}{3}\sqrt {1 - {x^2}} (2 + {x^2}) + C} \right)\)</span></p>
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 12px/normal Helvetica; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-family: 'times new roman', times; font-size: medium;">Just a few candidates got full marks in this question. Substitution was usually incorrectly done and lead to wrong results. A cosine term in the denominator was a popular error. Candidates often chose unhelpful trigonometric identities and attempted integration by parts. Results such as \(\int {{{\sin }^3}t\,{\text{d}}t = \frac{{{{\sin }^4}t}}{4} + C} \) were often seen along with other misconceptions concerning the manipulation/simplification of integrals were also noticed. Some candidates unsatisfactorily attempted to use \(\arcsin x\) . However, there were some good solutions involving an expression for the cube of \(\sin t\) in terms of \(\sin t\) and \(\sin 3t\) . Very few candidates re-expressed their final result in terms of <em>x</em>.</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">A cone has height <em>h </em>and base radius <em>r </em>. Deduce the formula for the volume of this cone by rotating the triangular region, enclosed by the line \(y = h - \frac{h}{r}x\) and the coordinate axes, through \(2\pi \) about the <em>y</em>-axis.</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;">\(x = r - \frac{r}{h}y{\text{ or }}x = \frac{r}{h}(h - y){\text{ (or equivalent)}}\) <span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>(A1)</em></strong></span></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {\pi {x^2}{\text{d}}y} \)</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\( = \pi \int_0^h {{{\left( {r - \frac{r}{h}y} \right)}^2}{\text{d}}y} \) <strong><em>M1A1</em></strong></span> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>M1 </em></strong>for \(\int {{x^2}{\text{d}}y} \) and <strong><em>A1 </em></strong>for correct expression.</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">Accept \(\pi \int_0^h {{{\left( {\frac{r}{h}y - r} \right)}^2}{\text{d}}y{\text{ and }}\pi \int_0^h {{{\left( { \pm \left( {r - \frac{r}{h}x} \right)} \right)}^2}{\text{d}}x} } \)</span></p>
<p> </p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\( = \pi \int_0^h {\left( {{r^2} - \frac{{2{r^2}}}{h}y + \frac{{{r^2}}}{{{h^2}}}{y^2}} \right){\text{d}}y} \) <strong><em>A1</em></strong></span></p>
<p><strong style="font-family: 'times new roman', times; font-size: medium;">Note: </strong><span style="font-family: 'times new roman', times; font-size: medium;">Accept substitution method and apply markscheme to corresponding steps.</span></p>
<p> </p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\( = \pi \left[ {{r^2}y - \frac{{{r^2}{y^2}}}{h} + \frac{{{r^2}{y^3}}}{{3{h^2}}}} \right]_0^h\) <strong><em>M1A1</em></strong></span> </p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>M1 </em></strong>for attempted integration of any quadratic trinomial.</span></p>
<p> </p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\( = \pi \left( {{r^2}h - {r^2}h + \frac{1}{3}{r^2}h} \right)\) <strong><em>M1A1</em></strong></span> </p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>M1 </em></strong>for attempted substitution of limits in a trinomial.</span></p>
<p> </p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{3}\pi {r^2}h\) <strong><em>A1</em></strong></span> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Throughout the question do not penalize missing d<em>x</em>/d<em>y </em>as long as the integrations are done with respect to correct variable.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 14px; line-height: 20px;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[9 marks]</span><br></em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates attempted this question using either the formula given in the information booklet or the disk method. However, many were not successful, either because they started off with the incorrect expression or incorrect integration limits or even attempted to integrate the correct expression with respect to the incorrect variable.</span></p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Two non-intersecting circles C<sub>1</sub> , containing points M and S , and C<sub>2</sub> , containing points N and R, have centres P and Q where PQ \( = 50\) . The line segments [MN] and [SR] are common tangents to the circles. The size of the reflex angle MPS is \( \alpha\), the size of the obtuse angle NQR is \( \beta\) , and the size of the angle MPQ is \( \theta\) . The arc length MS is \({l_1}\) and the arc length NR is \({l_2}\) . This information is represented in the diagram 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="data:image/png;base64,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" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The radius of C<sub>1</sub> is \(x\) , where \(x \geqslant 10\) and the radius of C<sub>2</sub> is \(10\).</span></p>
</div>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">(a) Explain why \(x < 40\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(b) Show that cosθ = x −10 </span><span style="font-family: times new roman,times; font-size: medium;">50</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;">(c) (i) Find an expression for MN in terms of \(x\) .</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> (ii) Find the value of \(x\) that maximises MN.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(d) Find an expression in terms of \(x\) for</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> (i) \( \alpha\) ;</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> (ii) \( \beta\) .<br></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(e) The length of the perimeter is given by \({l_1} + {l_2} + {\text{MN}} + {\text{SR}}\).</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> (i) Find an expression, \(b (x)\) , for the length of the perimeter in terms of \(x\) .</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> (ii) Find the maximum value of the length of the perimeter.</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> (iii) Find the value of \(x\) that gives a perimeter of length \(200\).</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;">(a) PQ \( = 50\) and non-intersecting <em><strong>R1</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[1 mark]</span></strong></em></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) a construction QT (where T is on the radius MP), parallel to MN, so that </span><span style="font-family: times new roman,times; font-size: medium;">\({\text{Q}}\hat {\text{T}}{\text{M}} = 90^\circ \) (angle between tangent and radius \( = 90^\circ \) ) <em><strong>M1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">lengths \(50\), \(x - 10\) and angle \( \theta\) marked on a diagram, or equivalent <em><strong>R1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Other construction lines are possible.</span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[2 marks]</span></strong></em></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;">(c) (i) MN \( = \sqrt {{{50}^2} - {{\left( {x - 10} \right)}^2}} \) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) maximum for MN occurs when \(x = 10\) <em><strong>A1</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[2 marks]</span></strong></em></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;">(d) (i) \(\alpha = 2\pi - 2\theta \) <em><strong>M1</strong></em></span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\( = 2\pi - 2\arccos \left( {\frac{{x - 10}}{{50}}} \right)\) </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;">(ii) \(\beta = 2\pi - \alpha \) ( \( = 2\theta \) ) <em><strong>A1</strong></em></span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\( = 2\left( {{{\cos }^{ - 1}}\left( {\frac{{x - 10}}{{50}}} \right)} \right)\)</span><span style="font-family: times new roman,times; font-size: medium;"> </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1</span></strong></em></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[4 marks]</span></strong></em></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;">(e) (i) </span><span style="font-family: times new roman,times; font-size: medium;">\(b(x) = x\alpha + 10\beta + 2\sqrt {{{50}^2} - {{\left( {x - 10} \right)}^2}} \) <em><strong>A1A1A1</strong></em></span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\( = x\left( {2\pi - 2\left( {{{\cos }^{ - 1}}\left( {\frac{{x - 10}}{{50}}} \right)} \right)} \right) + 20\left( {\left( {{{\cos }^{ - 1}}\left( {\frac{{x - 10}}{{50}}} \right)} \right)} \right) + 2\sqrt {{{50}^2} - {{\left( {x - 10} \right)}^2}} \)</span><span style="font-family: times new roman,times; font-size: medium;"> </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">M1A1</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) maximum value of perimeter \( = 276\) <em><strong>A2</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(iii) perimeter of \(200\) cm \(b(x) = 200\) <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">when \(x = 21.2\) <em><strong>A1</strong></em></span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[9 marks]</span></strong></em></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;">Total [18 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;">This is not an inherently difficult question, but candidates either made heavy weather of it or avoided it almost entirely. The key to answering the question is in obtaining the displayed answer to part (b), for which a construction line parallel to MN through Q is required. Diagrams seen by examiners on some scripts tend to suggest that the perpendicularity property of a tangent to a circle and the associated radius is not as firmly known as they had expected. Some candidates mixed radians and degrees in their expressions.</span></p>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A straight street of width 20 metres is bounded on its parallel sides by two vertical walls, one of height 13 metres, the other of height 8 metres. The intensity of light at point P at ground level on the street is proportional to the angle \(\theta \) where \(\theta = {\rm{A\hat PB}}\), as shown in the diagram.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><br><img style="display: block; margin-left: auto; margin-right: auto;" 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" 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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find an expression for \(\theta \) in terms of <em>x</em>, where <em>x</em> is the distance of P from the base of the wall of height 8 m.</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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Calculate the value of \(\theta \) when <em>x</em> = 0.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Calculate the value of \(\theta \) when <em>x</em> = 20.</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: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Sketch the graph of \(\theta \), for \(0 \leqslant x \leqslant 20\).</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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Show that \(\frac{{{\text{d}}\theta }}{{{\text{d}}x}} = \frac{{5(744 - 64x - {x^2})}}{{({x^2} + 64)({x^2} - 40x + 569)}}\).</span></p>
<div class="marks">[6]</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: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Using the result in part (d), or otherwise, determine the value of <em>x</em> corresponding to the maximum light intensity at P. Give your answer to four significant figures.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The point P moves across the street with speed \(0.5{\text{ m}}{{\text{s}}^{ - 1}}\). Determine the rate of change of \(\theta \) with respect to time when P is at the midpoint of the street.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\theta = \pi - \arctan \left( {\frac{8}{x}} \right) - \arctan \left( {\frac{{13}}{{20 - x}}} \right)\) (or equivalent) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Accept \(\theta = 180^\circ - \arctan \left( {\frac{8}{x}} \right) - \arctan \left( {\frac{{13}}{{20 - x}}} \right)\) (or equivalent).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"> </strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">OR</strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\theta = \arctan \left( {\frac{x}{8}} \right) + \arctan \left( {\frac{{20 - x}}{{13}}} \right)\) (or equivalent) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \(\theta = 0.994{\text{ }}\left( { = \arctan \frac{{20}}{{13}}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \(\theta = 1.19{\text{ }}\left( { = \arctan \frac{5}{2}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">correct shape. <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">correct domain indicated. <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><img src="data:image/png;base64,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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">attempting to differentiate one \(\arctan \left( {f(x)} \right)\) term <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\theta = \pi - \arctan \left( {\frac{8}{x}} \right) - \arctan \left( {\frac{{13}}{{20 - x}}} \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}\theta }}{{{\text{d}}x}} = \frac{8}{{{x^2}}} \times \frac{1}{{1 + {{\left( {\frac{8}{x}} \right)}^2}}} - \frac{{13}}{{{{(20 - x)}^2}}} \times \frac{1}{{1 + {{\left( {\frac{{13}}{{20 - x}}} \right)}^2}}}\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\theta = \arctan \left( {\frac{x}{8}} \right) + \arctan \left( {\frac{{20 - x}}{{13}}} \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}\theta }}{{{\text{d}}x}} = \frac{{\frac{1}{8}}}{{1 + {{\left( {\frac{x}{8}} \right)}^2}}} + \frac{{ - \frac{1}{{13}}}}{{1 + {{\left( {\frac{{20 - x}}{{13}}} \right)}^2}}}\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>THEN</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{8}{{{x^2} + 64}} - \frac{{13}}{{569 - 40x + {x^2}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{8(569 - 40x + {x^2}) - 13({x^{2}} + 64)}}{{({x^2} + 64)({x^2} - 40x + 569)}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{5(744 - 64x - {x^2})}}{{({x^2} + 64)({x^2} - 40x + 569)}}\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Maximum light intensity at P occurs when \(\frac{{{\text{d}}\theta }}{{{\text{d}}x}} = 0\). <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">either attempting to solve \(\frac{{{\text{d}}\theta }}{{{\text{d}}x}} = 0\) for <em>x</em> or using the graph of either \(\theta \) or \(\frac{{{\text{d}}\theta }}{{{\text{d}}x}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>x</em> = 10.05 (m) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><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>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}x}}{{{\text{d}}t}} = 0.5\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">At <em>x</em> = 10, \(\frac{{{\text{d}}\theta }}{{{\text{d}}x}} = 0.000453{\text{ }}\left( { = \frac{5}{{11029}}} \right)\). <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">use of \(\frac{{{\text{d}}\theta }}{{{\text{d}}t}} = \frac{{{\text{d}}\theta }}{{{\text{d}}x}} \times \frac{{{\text{d}}x}}{{{\text{d}}t}}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}\theta }}{{{\text{d}}t}} = 0.000227{\text{ }}\left( { = \frac{5}{{22058}}} \right){\text{ (rad }}{{\text{s}}^{ - 1}})\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Award </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>(A1)</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for \(\frac{{{\text{d}}x}}{{{\text{d}}t}} = - 0.5\) and </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for \(\frac{{{\text{d}}\theta }}{{{\text{d}}t}} = - 0.000227{\text{ }}\left( { = - \frac{5}{{22058}}} \right){\text{ }}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"> </strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Implicit differentiation can be used to find \(\frac{{{\text{d}}\theta }}{{{\text{d}}t}}\). Award as above.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[4 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was reasonably well done. While many candidates exhibited sound trigonometric knowledge to correctly express <em>θ </em>in terms of <em>x</em>, many other candidates were not able to use elementary trigonometry to formulate the required expression for <em>θ</em>.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (b), a large number of candidates did not realize that <em>θ </em>could only be acute and gave obtuse angle values for <em>θ</em>. Many candidates also demonstrated a lack of insight when substituting endpoint <em>x</em>-values into <em>θ</em>.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (c), many candidates sketched either inaccurate or implausible graphs.</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: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (d), a large number of candidates started their differentiation incorrectly by failing to use the chain rule correctly.</span></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: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">For a question part situated at the end of the paper, part (e) was reasonably well done. A large number of candidates demonstrated a sound knowledge of finding where the maximum value of <em>θ </em>occurred and rejected solutions that were not physically feasible.</span></p>
<div class="question_part_label">e.</div>
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<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (f), many candidates were able to link the required rates, however only a few candidates were able to successfully apply the chain rule in a related rates context.</span></p>
<div class="question_part_label">f.</div>
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<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">An electricity station is on the edge of a straight coastline. A lighthouse is located in the sea 200 m from the electricity station. The angle between the coastline and the line joining the lighthouse with the electricity station is 60°. A cable needs to be laid connecting the lighthouse to the electricity station. It is decided to lay the cable in a straight line to the coast and then along the coast to the electricity station. The length of cable laid along the coastline is <em>x</em> metres. This information is illustrated in the diagram below.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><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: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The cost of laying the cable along the sea bed is US$80 per metre, and the cost of laying it on land is US$20 per metre.</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: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find, in terms of <em>x</em>, an expression for the cost of laying the cable.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the value of <em>x</em>, to the nearest metre, such that this cost is minimized.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">let the distance the cable is laid along the seabed be <em>y</em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({y^2} = {x^2} + {200^2} - 2 \times x \times 200\cos 60^\circ \) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(or equivalent method)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({y^2} = {x^2} - 200x + 40000\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">cost</span><span style="font-family: 'times new roman', times; font-size: medium;"> = <em>C</em> = 80<em>y</em> + 20<em>x</em> </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>(M1)</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(C = 80{({x^2} - 200x + 40000)^{\frac{1}{2}}} + 20x\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 55.2786 \ldots = 55\) (m to the nearest metre) <strong><em>(A1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\left( {x = 100 - \sqrt {2000} } \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><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>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Some surprising misconceptions were evident here, using right angled trigonometry in non right angled triangles etc. Those that used the cosine rule, usually managed to obtain the correct answer to 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;">Some surprising misconceptions were evident here, using right angled trigonometry in non right angled triangles etc. Many students attempted to find the value of the minimum algebraically instead of the simple calculator solution.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Sketch the curve \(y = \frac{{\cos x}}{{\sqrt {{x^2} + 1} }},{\text{ }} - 4 \leqslant x \leqslant 4\) showing clearly the coordinates of the <em>x-</em>intercepts, any maximum points and any minimum points.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Write down the gradient of the curve at <em>x </em>= 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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the equation of the normal to the curve at <em>x </em>= 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><span><strong><em><img 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" alt> A1A1A1A1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>A1 </em></strong>for correct shape. Do not penalise if too large a domain is used,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>A1 </em></strong>for correct <em>x</em>-intercepts,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>A1 </em></strong>for correct coordinates of two minimum points,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>A1 </em></strong>for correct coordinates of maximum point.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Accept answers which correctly indicate the position of the intercepts, maximum point and minimum points. </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><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: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[4 marks]</span><br></em></strong></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: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">gradient at <em>x</em> = 1 is –0.786 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[1 mark]</span><br></em></strong></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: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">gradient of normal is \(\frac{{ - 1}}{{ - 0.786}}( = 1.272...)\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">when <em>x</em> = 1, <em>y</em> = 0.3820... <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Equation of normal is <em>y</em> – 0.382 = 1.27(<em>x</em> – 1) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(( \Rightarrow y = 1.27x - 0.890)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><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">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates were able to make a meaningful start to this question, but many made errors along the way and hence only a relatively small number of candidates gained full marks for the question. Common errors included trying to use degrees, rather than radians, trying to use algebraic methods to find the gradient in part (b) and trying to find the equation of the tangent rather than the equation of the normal in part (c).</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: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates were able to make a meaningful start to this question, but many made errors along the way and hence only a relatively small number of candidates gained full marks for the question. Common errors included trying to use degrees, rather than radians, trying to use algebraic methods to find the gradient in part (b) and trying to find the equation of the tangent rather than the equation of the normal in part (c).</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: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates were able to make a meaningful start to this question, but many made errors along the way and hence only a relatively small number of candidates gained full marks for the question. Common errors included trying to use degrees, rather than radians, trying to use algebraic methods to find the gradient in part (b) and trying to find the equation of the tangent rather than the equation of the normal in part (c).</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A jet plane travels horizontally along a straight path for one minute, starting at time \(t = 0\) , where \(t\) is measured in seconds. The acceleration, \(a\) , measured in ms<sup>−2</sup>, of the jet plane is given by the straight line graph below.</span></p>
<p><br><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" alt></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 an expression for the acceleration of the jet plane during this time, in terms of \(t\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Given that when \(t = 0\) the jet plane is travelling at \(125\) ms<sup>−1</sup>, find its maximum velocity in ms<sup>−1</sup> during the minute that follows.</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;">Given that the jet plane breaks the sound barrier at \(295\) ms<sup>−1</sup>, find out for how long the jet plane is travelling greater than this speed.</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;">equation of line in graph \(a = - \frac{{25}}{{60}}t + 15\) </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;">\(\left( {a = - \frac{5}{{12}}t + 15} \right)\)</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;">\(\frac{{{\text{d}}v}}{{{\text{d}}t}} = - \frac{5}{{12}}t + 15\) </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,times; font-size: medium;">\(v = - \frac{5}{{24}}{t^2} + 15t + c\) <em><strong>(A1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">when \(t = 0\) , \(v = 125\) ms<sup>−1</sup></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(v = - \frac{5}{{24}}{t^2} + 15t + 125\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">from graph or by finding time when \(a = 0\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">maximum \(= 395\) ms<sup>−1</sup> <em><strong>A1</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><strong><span style="font-family: times new roman,times; font-size: medium;">EITHER</span></strong></p>
<p><br><img 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" alt></p>
<p><span style="font-family: times new roman,times; font-size: medium;">graph drawn and intersection with \(v = 295\) ms<sup>−1</sup> <em><strong>(M1)(A1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em><strong>\(</strong></em></span><span style="font-family: times new roman,times; font-size: medium;">t = 57.91 - 14.09 = 43.8\) <em><strong>A1</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;">\(295 = - \frac{5}{{24}}{t^2} + 15t + 125 \Rightarrow t = 57.91...\)</span><span style="font-family: times new roman,times; font-size: medium;">; \(14.09...\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(t = 57.91... - 14.09... = 43.8\left( {8\sqrt {30} } \right)\) <em><strong>A1</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;">This question was well answered by a large number of candidates and indicated a good understanding of calculus, kinematics and use of the graphing calculator. Some candidates worked in \(x\) and \(y\) rather than \(a\), \(v\) and \(t\) but mostly obtained correct solutions. Although the majority of candidate used integration throughout the question some correct solutions were obtained by considering the areas in the diagram.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well answered by a large number of candidates and indicated a good understanding of calculus, kinematics and use of the graphing calculator. Some candidates worked in \(x\) and \(y\) rather than \(a\), \(v\) and \(t\) but mostly obtained correct solutions. Although the majority of candidate used integration throughout the question some correct solutions were obtained by considering the areas in the diagram.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well answered by a large number of candidates and indicated a good understanding of calculus, kinematics and use of the graphing calculator. Some candidates worked in \(x\) and \(y\) rather than \(a\), \(v\) and \(t\) but mostly obtained correct solutions. Although the majority of candidate used integration throughout the question some correct solutions were obtained by considering the areas in the diagram.</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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A particle, A, is moving along a straight line. The velocity, \({v_A}{\text{ m}}{{\text{s}}^{ - 1}}\), of A <em>t</em> seconds after its motion begins is given by</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[{v_A} = {t^3} - 5{t^2} + 6t.\]</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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Sketch the graph of \({v_A} = {t^3} - 5{t^2} + 6t\) for \(t \geqslant 0\), with \({v_A}\) on the vertical axis and <em>t</em> on the horizontal. Show on your sketch the local maximum and minimum points, and the intercepts with the <em>t</em>-axis.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Write down the times for which the velocity of the particle is increasing.</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: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Write down the times for which the magnitude of the velocity of the particle is increasing.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">At <em>t</em> = 0 the particle is at point O on the line.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find an expression for the particle’s displacement, \({x_A}{\text{m}}\), from O at time <em>t</em>.</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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A second particle, B, moving along the same line, has position \({x_B}{\text{ m}}\), velocity \({v_B}{\text{ m}}{{\text{s}}^{ - 1}}\) and acceleration, \({a_B}{\text{ m}}{{\text{s}}^{ - 2}}\), where \({a_B} = - 2{v_B}\) for \(t \geqslant 0\). At \(t = 0,{\text{ }}{x_B} = 20\) and \({v_B} = - 20\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find an expression for \({v_B}\) in terms of <em>t</em>.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the value of <em>t</em> when the two particles meet.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><img src="data:image/png;base64,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" alt><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;"> <strong><em>A1A1A1</em></strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1</em></strong> for general shape, <strong><em>A1</em></strong> for correct maximum and minimum, <strong><em>A1</em></strong> for intercepts.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Follow through applies to (b) and (c).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(0 \leqslant t < 0.785,{\text{ }}\left( {{\text{or }}0 \leqslant t < \frac{{5 - \sqrt 7 }}{3}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(allow \(t < 0.785\))</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">and \(t > 2.55{\text{ }}\left( {{\text{or }}t > \frac{{5 + \sqrt 7 }}{3}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(0 \leqslant t < 0.785,{\text{ }}\left( {{\text{or }}0 \leqslant t < \frac{{5 - \sqrt 7 }}{3}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(allow \(t < 0.785\))</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2 < t < 2.55,{\text{ }}\left( {{\text{or }}2 < t < \frac{{5 + \sqrt 7 }}{3}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(t > 3\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><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.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">position of A: \({x_A} = \int {{t^3} - 5{t^2} + 6t{\text{ d}}t} \) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x_A} = \frac{1}{4}{t^4} - \frac{5}{3}{t^3} + 3{t^2}\,\,\,\,\,( + c)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">when \(t = 0,{\text{ }}{x_A} = 0\), so \(c = 0\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}{v_B}}}{{{\text{d}}t}} = - 2{v_B} \Rightarrow \int {\frac{1}{{{v_B}}}{\text{d}}{v_B} = \int { - 2{\text{d}}t} } \) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\ln \left| {{v_B}} \right| = - 2t + c\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({v_B} = A{e^{ - 2t}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({v_B} = - 20\) when <em>t</em> = 0 so \({v_B} = - 20{e^{ - 2t}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x_B} = 10{e^{ - 2t}}( + c)\) <strong><em>(M1)(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x_B} = 20{\text{ when }}t = 0{\text{ so }}{x_B} = 10{e^{ - 2t}} + 10\) <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">meet when \(\frac{1}{4}{t^4} - \frac{5}{3}{t^3} + 3{t^2} = 10{e^{ - 2t}} + 10\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(t = 4.41(290 \ldots )\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Part (a) was generally well done, although correct accuracy was often a problem.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Parts (b) and (c) were also generally quite well done.</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 (b) and (c) were also generally quite well done.</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;">A variety of approaches were seen in part (d) and many candidates were able to obtain at least 2 out of 3. A number missed to consider the \(+c\) , thereby losing the last mark.</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;">Surprisingly few candidates were able to solve part (e) correctly. Very few could recognise the easy variable separable differential equation. As a consequence part (f) was frequently left.</span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Surprisingly few candidates were able to solve part (e) correctly. Very few could recognise the easy variable separable differential equation. As a consequence part (f) was frequently left.</span></p>
<div class="question_part_label">f.</div>
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<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The function <em>f</em> is defined by</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[f(x) = {({x^3} + 6{x^2} + 3x - 10)^{\frac{1}{2}}},{\text{ for }}x \in D,\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">where \(D \subseteq \mathbb{R}\) is the greatest possible domain of <em>f</em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Find the roots of \(f(x) = 0\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Hence specify the set <em>D</em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) Find the coordinates of the local maximum on the graph \(y = f(x)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(d) Solve the equation \(f(x) = 3\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(e) Sketch the graph of \(\left| y \right| = f(x),{\text{ for }}x \in D\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(f) Find the area of the region completely enclosed by the graph of \(\left| y \right| = f(x)\)</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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) solving to obtain one root: 1, – 2 or – 5 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">obtain other roots <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) \(D = x \in [ - 5,{\text{ }} - 2] \cup [1,{\text{ }}\infty {\text{)}}\) (or equivalent) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> <strong><em>M1</em></strong> is for 1 finite and 1 infinite interval.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><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: 27.0px Helvetica;"><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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) coordinates of local maximum \( - 3.73 - 2 - \sqrt 3 ,{\text{ }}3.22\sqrt {6\sqrt 3 } \) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(d) use GDC to obtain one root: 1.41, – 3.18 or – 4.23 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">obtain other roots <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(e)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><img src="data:image/png;base64,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" alt><span class="Apple-style-span" style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 14px; line-height: 20px; display: inline; float: none;"><span class="Apple-style-span" style="font-family: 'times new roman', times; font-size: medium; display: inline; float: none; line-height: normal;"> <strong><em>A1A1A1</em></strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1</em></strong> for shape, <strong><em>A1</em></strong> for max and for min clearly in correct places, <strong><em>A1</em></strong> for all intercepts.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Award <strong><em>A1A0A0</em></strong> if only the complete top half is shown.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><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: 27.0px Helvetica;"><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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(f) required area is twice that of \(y = f(x)\) between – 5 and – 2 <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">answer 14.9 <strong><em>A1 N3</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>M1A0A0</em></strong> for \(\int_{ - 5}^{ - 2} {f(x){\text{d}}x = 7.47 \ldots } \) or <strong><em>N1</em></strong> for 7.47.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><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: 27.0px Helvetica;"><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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [14 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This was a multi-part question that was well answered by many candidates. The main difficulty was sketching the graph and this meant that the last part was not well answered.</span></p>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The function <em>f</em> is defined on the domain [0, 2] by \(f(x) = \ln (x + 1)\sin (\pi x)\) .</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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Obtain an expression for \(f'(x)\) .</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Sketch the graphs of <em>f</em> and \(f'\) on the same axes, showing clearly all <em>x</em>-intercepts.</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: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the <em>x</em>-coordinates of the two points of inflexion on 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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the equation of the normal to the graph of <em>f</em> where <em>x</em> = 0.75 , giving your answer in the form <em>y</em> = <em>mx</em> + <em>c</em> .</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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the points \({\text{A}}\left( {a{\text{ }},{\text{ }}f(a)} \right)\) , \({\text{B}}\left( {b{\text{ }},{\text{ }}f(b)} \right)\) and \({\text{C}}\left( {c{\text{ }},{\text{ }}f(c)} \right)\) where <em>a</em> , <em>b</em> and <em>c</em> \((a < b < c)\) are the solutions of the equation \(f(x) = f'(x)\) . Find the area of the triangle ABC.</span></p>
<div class="marks">[6]</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: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(x) = \frac{1}{{x + 1}}\sin (\pi x) + \pi \ln (x + 1)\cos (\pi x)\) <strong><em>M1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 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: 24.0px Helvetica;"><img 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" alt><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;"> <em><strong>A4</strong></em></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1A1</em></strong> for graphs, <strong><em>A1A1</em></strong> for intercepts.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><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: 24.0px Helvetica;"><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: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">0.310, 1.12 <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(0.75) = - 0.839092\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so equation of normal is \(y - 0.39570812 = \frac{1}{{0.839092}}(x - 0.75)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(y = 1.19x - 0.498\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{A}}(0,{\text{ }}0)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{B(}}\overbrace {0.548 \ldots }^c,\overbrace {0.432 \ldots }^d)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{C(}}\overbrace {1.44 \ldots }^e,\overbrace { - 0.881 \ldots }^f)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Accept coordinates for B and C rounded to 3 significant figures.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">area \(\Delta {\text{ABC}} = \frac{1}{2}|\)(</span><em style="font-family: 'times new roman', times; font-size: medium;">c</em><strong style="font-family: 'times new roman', times; font-size: medium;"><em>i</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> + </span><em style="font-family: 'times new roman', times; font-size: medium;">d</em><strong style="font-family: 'times new roman', times; font-size: medium;"><em>j</em></strong><span style="font-family: 'times new roman', times; font-size: medium;">) \( \times \) (</span><em style="font-family: 'times new roman', times; font-size: medium;">e</em><strong style="font-family: 'times new roman', times; font-size: medium;"><em>i</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> + </span><em style="font-family: 'times new roman', times; font-size: medium;">f</em><strong style="font-family: 'times new roman', times; font-size: medium;"><em>j</em></strong><span style="font-family: 'times new roman', times; font-size: medium;">)\(|\) </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>M1A1</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{2}(de - cf)\) <em><strong>A1</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 0.554\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the graph of \(y = x + \sin (x - 3),{\text{ }} - \pi \leqslant x \leqslant \pi \).</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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Sketch the graph, clearly labelling the <em>x</em> and <em>y</em> intercepts with their values.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the area of the region bounded by the graph and the <em>x</em> and <em>y</em> axes.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><img 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" alt><span style="font-family: 'times new roman', times; font-size: medium;"> <strong><em>A1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1</em></strong> for shape,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for </span><em style="font-family: 'times new roman', times; font-size: medium;">x</em><span style="font-family: 'times new roman', times; font-size: medium;">-intercept is 0.820, accept \(\sin ( - 3){\text{ or }} - \sin (3)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for </span><em style="font-family: 'times new roman', times; font-size: medium;">y</em><span style="font-family: 'times new roman', times; font-size: medium;">-intercept is −0.141.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 37.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[3 marks]</em></strong></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: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(A = \int_0^{0.8202} {\left| {x + \sin (x - 3)} \right|{\text{d}}x \approx 0.0816{\text{ sq units}}} \) <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><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>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates attempted this question successfully. In (a), however, a large number of candidates did not use the zoom feature of the GDC to draw an accurate sketch of the given function. In (b), some candidates used the domain as the limits of the integral. Other candidates did not take the absolute value of the integral.</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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates attempted this question successfully. In (a), however, a large number of candidates did not use the zoom feature of the GDC to draw an accurate sketch of the given function. In (b), some candidates used the domain as the limits of the integral. Other candidates did not take the absolute value of the integral.</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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the curve with equation \(f(x) = {{\text{e}}^{ - 2{x^2}}}{\text{ for }}x < 0\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the coordinates of the point of inflexion and justify that it is a point of inflexion.</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: 26.0px Helvetica;"><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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Using the graph of \(y = f'(x)\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;"><img 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" alt> <strong><em>A1</em></strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The maximum of \(f'(x)\) occurs at <em>x</em> = −0.5 . <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Using the graph of \(y = f''(x)\). <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><img 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" alt><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;"> <strong><em>A1</em></strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The zero of \(f''(x)\) occurs at <em>x</em> = −0.5 . <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>THEN</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Do not award this <strong><em>A1</em></strong> for stating <em>x</em> = ±0.5 as the final answer for <em>x</em> .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f( - 0.5) = 0.607( = {{\text{e}}^{ - 0.5}})\) <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Do not award this <strong><em>A1</em></strong> for also stating (0.5, 0.607) as a coordinate.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Correctly labelled graph of \(f'(x)\) for \(x < 0\) denoting the maximum \(f'(x)\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(<em>e.g.</em> \(f'( - 0.6) = 1.17\) and \(f'( - 0.4) = 1.16\) stated) <strong><em>A1</em></strong> <strong><em>N2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Correctly labelled graph of \(f''(x)\) for \(x < 0\) denoting the maximum \(f'(x)\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(<em>e.g.</em> \(f''( - 0.6) = 0.857\) and \(f''( - 0.4) = - 1.05\) stated) <strong><em>A1</em></strong> <strong><em>N2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(0.5) \approx 1.21\). \(f'(x) < 1.21\) just to the left of \(x = - \frac{1}{2}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">and \(f'(x) < 1.21\) just to the right of \(x = - \frac{1}{2}\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(<em>e.g.</em> \(f'( - 0.6) = 1.17\) and \(f'( - 0.4) = 1.16\) stated) <strong><em>A1</em></strong> <strong><em>N2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f''(x) > 0\) just to the left of \(x = - \frac{1}{2}\) and \(f''(x) < 0\) just to the right of \(x = - \frac{1}{2}\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(<em>e.g.</em> \(f''( - 0.6) = 0.857\) and \(f''( - 0.4) = - 1.05\) stated) <strong><em>A1</em></strong> <strong><em>N2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(x) = - 4x{{\text{e}}^{ - 2{x^2}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f''(x) = - 4{{\text{e}}^{ - 2{x^2}}} + 16{x^2}{{\text{e}}^{ - 2{x^2}}}\,\,\,\,\,\left( { = (16{x^2} - 4){{\text{e}}^{ - 2{x^2}}}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Attempting to solve \(f''(x) = 0\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = - \frac{1}{2}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Do not award this <strong><em>A1</em></strong> for stating \(x = \pm \frac{1}{2}\) as the final answer for <em>x</em> .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f\left( { - \frac{1}{2}} \right) = \frac{1}{{\sqrt {\text{e}} }}{\text{ }}( = 0.607)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Do not award this <strong><em>A1</em></strong> for also stating \(\left( {\frac{1}{2},\frac{1}{{\sqrt {\text{e}} }}} \right)\) as a coordinate.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Correctly labelled graph of \(f'(x)\) for \(x < 0\) denoting the maximum \(f'(x)\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(<em>e.g.</em> \(f'( - 0.6) = 1.17\) and \(f'( - 0.4) = 1.16\) stated) <strong><em>A1</em></strong> <strong><em>N2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Correctly labelled graph of \(f''(x)\) for \(x < 0\) denoting the maximum \(f'(x)\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(<em>e.g.</em> \(f''( - 0.6) = 0.857\) and \(f''( - 0.4) = - 1.05\) stated) <strong><em>A1</em></strong> <strong><em>N2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(0.5) \approx 1.21\). \(f'(x) < 1.21\) just to the left of \(x = - \frac{1}{2}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">and \(f'(x) < 1.21\) just to the right of \(x = - \frac{1}{2}\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(<em>e.g.</em> \(f'( - 0.6) = 1.17\) and \(f'( - 0.4) = 1.16\) stated) <em><strong>A1</strong> <strong>N2</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f''(x) > 0\) just to the left of \(x = - \frac{1}{2}\) and \(f''(x) < 0\) just to the right of \(x = - \frac{1}{2}\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(<em>e.g.</em> \(f''( - 0.6) = 0.857\) and \(f''( - 0.4) = - 1.05\) stated) <strong><em>A1 N2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates adopted an algebraic approach rather than a graphical approach. Most candidates found \(f'(x)\) correctly, however when attempting to find \(f''(x)\), a surprisingly large number either made algebraic errors using the product rule or seemingly used an incorrect form of the product rule. A large number ignored the domain restriction and either expressed \(x = \pm \frac{1}{2}\) as the <em>x</em>-coordinates of the point of inflection or identified \(x = \frac{1}{2}\) rather than \(x = - \frac{1}{2}\). Most candidates were unsuccessful in their attempts to justify the existence of the point of inflection.</span></p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Below is a sketch of a Ferris wheel, an amusement park device carrying passengers </span><span style="font-family: times new roman,times; font-size: medium;">around the rim of the wheel.</span></p>
<p><br><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" alt></p>
</div>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">(a) The circular Ferris wheel has a radius of 10 metres and is revolving at a rate of 3 radians per minute. Determine how fast a passenger on the wheel is going vertically upwards when the passenger is at point A, 6 metres higher than the centre of the wheel, and is rising.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(b) The operator of the Ferris wheel stands directly below the centre such that the bottom of the Ferris wheel is level with his eyeline. As he watches the passenger his line of sight makes an angle \(\alpha \) with the horizontal. Find the rate of change of \(\alpha \) at point A.</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;">(a)</span></p>
<p><img 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" alt></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\frac{{{\text{d}}\theta }}{{{\text{d}}t}} = 3\) </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;">\(y = 10\sin \theta \) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\frac{{{\text{d}}y}}{{{\text{d}}\theta }} = 10\cos \theta \) </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,times; font-size: medium;">\(\frac{{{\text{d}}y}}{{{\text{d}}t}} = \frac{{{\text{d}}y}}{{{\text{d}}\theta }}\frac{{{\text{d}}\theta }}{{{\text{d}}t}} = 30\cos \theta \) </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,times; font-size: medium;">at \(y = 6\) , </span><span style="font-family: times new roman,times; font-size: medium;">\(\cos \theta = \frac{8}{{10}}\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">(M1)(A1)</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\( \Rightarrow \frac{{{\text{d}}y}}{{{\text{d}}t}} = 24\) (metres per minute) (accept \(24.0\)) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1</span></strong></em></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[7 marks]</span></strong></em></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) </span><span style="font-family: times new roman,times; font-size: medium;">\(\alpha = \frac{\theta }{2} + \frac{\pi }{4}\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">M1A1</span></strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = \frac{1}{2}\frac{{{\text{d}}\theta }}{{{\text{d}}t}} = 1.5\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1</span></strong></em></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[3 marks]</span></strong></em></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;">Total [10 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;">Many students were unable to get started with this question, and those that did were generally very poor at defining their variables at the start.</span></p>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A particle moves in a straight line with velocity <em>v </em>metres per second. At any time <em>t </em>seconds, \(0 \leqslant t < \frac{{3\pi }}{4}\), the velocity is given by the differential equation \(\frac{{{\text{d}}v}}{{{\text{d}}t}} + {v^2} + 1 = 0\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">It is also given that <em>v </em>= 1 when <em>t </em>= 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: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find an expression for <em>v </em>in terms of <em>t </em>.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Sketch the graph of <em>v </em>against <em>t </em>, clearly showing the coordinates of any intercepts, and the equations of any asymptotes.</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: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Write down the time <em>T </em>at which the velocity is zero.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Find the distance travelled in the interval [0, <em>T</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find an expression for <em>s </em>, the displacement, in terms of <em>t </em>, given that <em>s </em>= 0 when <em>t </em>= 0 .</span></p>
<div class="marks">[5]</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: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Hence, or otherwise, show that \(s = \frac{1}{2}\ln \frac{2}{{1 + {v^2}}}\).</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: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}v}}{{{\text{d}}t}} = - {v^2} - 1\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">attempt to separate the variables <strong><em>M1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {\frac{1}{{1 + {v^2}}}{\text{d}}v = \int { - 1{\text{d}}t} } \) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\arctan v = - t + k\) <strong> <em>A1A1</em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium;"> </strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Do not penalize the lack of constant at this stage.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><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: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">when <em>t</em> = 0, <em>v</em> = 1 <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow k = \arctan 1 = \left( {\frac{\pi }{4}} \right) = (45^\circ )\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow v = \tan \left( {\frac{\pi }{4} - t} \right)\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[7 marks]</span><br></em></strong></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: 11.0px Times;"><img 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" alt><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> A1A1A1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong> </strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>A1 </em></strong>for general shape,</span></p>
<p style="margin: 0px 0px 0px 30px; font: 11px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> A1 </em></strong>for asymptote,</span></p>
<p style="margin: 0px 0px 0px 30px; font: 11px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"> <strong><em>A1 </em></strong>for correct <em>t </em>and <em>v </em>intercept.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Do not penalise if a larger domain is used.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><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: 11.0px Times;"><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>
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<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \(T = \frac{\pi }{4}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) area under curve \( = \int_0^{\frac{\pi }{4}} {\tan \left( {\frac{\pi }{4} - t} \right){\text{d}}t} \) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 0.347\left( { = \frac{1}{2}\ln 2} \right)\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><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.</div>
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<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(v = \tan \left( {\frac{\pi }{4} - t} \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(s = \int {\tan \left( {\frac{\pi }{4} - t} \right){\text{d}}t} \) <strong> <em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {\frac{{\sin \left( {\frac{\pi }{4} - t} \right)}}{{\cos \left( {\frac{\pi }{4} - t} \right)}}} {\text{ d}}t\)</span><span style="font-family: 'times new roman', times; font-size: medium;"> </span><strong style="font-family: 'times new roman', times; font-size: medium;"> <em>(M1)</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \ln \cos \left( {\frac{\pi }{4} - t} \right) + k\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">when \(t = 0,{\text{ }}s = 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(k = - \ln \cos \frac{\pi }{4}\) <em><strong>A1</strong></em><strong><em><br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(s = \ln \cos \left( {\frac{\pi }{4} - t} \right) - \ln \cos \frac{\pi }{4}\left( { = \ln \left[ {\sqrt 2 \cos \left( {\frac{\pi }{4} - t} \right)} \right]} \right)\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[5 marks]</span><br></em></strong></p>
<div class="question_part_label">d.</div>
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<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 1<br></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{\pi }{4} - t = \arctan v\) <strong> <em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(t = \frac{\pi }{4} - \arctan v\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(s = \ln \left[ {\sqrt 2 \cos \left( {\frac{\pi }{4} - \frac{\pi }{4} + \arctan v} \right)} \right]\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(s = \ln \left[ {\sqrt 2 \cos (\arctan v)} \right]\) <strong> <em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><img 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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><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: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(s = \ln \left[ {\sqrt 2 \cos \left( {\arccos \frac{1}{{\sqrt {1 + {v^2}} }}} \right)} \right]\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \ln \frac{{\sqrt 2 }}{{\sqrt {1 + {v^2}} }}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{2}\ln \frac{2}{{1 + {v^2}}}\) <strong> <em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong> </strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><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: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(s = \ln \cos \left( {\frac{\pi }{4} - t} \right) - \ln \cos \frac{\pi }{4}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = - \ln \sec \left( {\frac{\pi }{4} - t} \right) - \ln \cos \frac{\pi }{4}\) <strong> <em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = - \ln \sqrt {1 + {{\tan }^2}\left( {\frac{\pi }{4} - t} \right)} - \ln \cos \frac{\pi }{4}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = - \ln \sqrt {1 + {v^2}} - \ln \cos \frac{\pi }{4}\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \ln \frac{1}{{\sqrt {1 + {v^2}} }} + \ln \sqrt 2 \) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{2}\ln \frac{2}{{1 + {v^2}}}\) <strong> <em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong> </strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 3<br></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(v\frac{{dv}}{{ds}} = - {v^2} - 1\) <strong> <em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {\frac{v}{{{v^2} + 1}}dv = - \int {1ds} } \) <strong> <em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{1}{2}\ln ({v^2} + 1) = - s + k\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">when \(s = 0\,,{\text{ }}t = 0 \Rightarrow v = 1\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow k = \frac{1}{2}\ln 2\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow s = \frac{1}{2}\ln \frac{2}{{1 + {v^2}}}\) <strong> <em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;"> </span></em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[4 marks]</span><br></em></strong></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This proved to be the most challenging question in section B with only a very small number of candidates producing fully correct answers. Many candidates did not realise that part (a) was a differential equation that needed to be solved using a method of separating the variables. Without this, further progress with the question was difficult. For those who did succeed in part (a), parts (b) and (c) were relatively well done. For the minority of candidates who attempted parts (d) and (e) only the best recognised the correct methods.</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: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This proved to be the most challenging question in section B with only a very small number of candidates producing fully correct answers. Many candidates did not realise that part (a) was a differential equation that needed to be solved using a method of separating the variables. Without this, further progress with the question was difficult. For those who did succeed in part (a), parts (b) and (c) were relatively well done. For the minority of candidates who attempted parts (d) and (e) only the best recognised the correct methods.</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: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This proved to be the most challenging question in section B with only a very small number of candidates producing fully correct answers. Many candidates did not realise that part (a) was a differential equation that needed to be solved using a method of separating the variables. Without this, further progress with the question was difficult. For those who did succeed in part (a), parts (b) and (c) were relatively well done. For the minority of candidates who attempted parts (d) and (e) only the best recognised the correct methods.</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: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This proved to be the most challenging question in section B with only a very small number of candidates producing fully correct answers. Many candidates did not realise that part (a) was a differential equation that needed to be solved using a method of separating the variables. Without this, further progress with the question was difficult. For those who did succeed in part (a), parts (b) and (c) were relatively well done. For the minority of candidates who attempted parts (d) and (e) only the best recognised the correct methods.</span></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: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This proved to be the most challenging question in section B with only a very small number of candidates producing fully correct answers. Many candidates did not realise that part (a) was a differential equation that needed to be solved using a method of separating the variables. Without this, further progress with the question was difficult. For those who did succeed in part (a), parts (b) and (c) were relatively well done. For the minority of candidates who attempted parts (d) and (e) only the best recognised the correct methods.</span></p>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">The diagram shows the plan of an art gallery <em>a </em>metres wide. [AB] represents a doorway, leading to an exit corridor <em>b </em>metres wide. In order to remove a painting from the art gallery, CD (denoted by <em>L </em>) is measured for various values of \(\alpha \) , as represented in the diagram.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><br><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" 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: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">If </span><span style="font: 12.5px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\alpha \)</span> </span><span style="font-family: 'times new roman', times; font-size: medium;">is the angle between [CD] and the wall, show that \(L = \frac{a }{{\sin \alpha }} + \frac{b}{{\cos \alpha }}{\text{, }}0 < \alpha < \frac{\pi }{2}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"> </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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: arial, helvetica, sans-serif;"><span style="font-family: 'times new roman', times; font-size: medium;">If <em>a </em>= 5 and <em>b </em>= 1, find the maximum length of a painting that can be removed through this doorway.</span><br></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: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Let <em>a </em>= 3<em>k </em>and <em>b </em>= <em>k </em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Find \(\frac{{{\text{d}}L}}{{{\text{d}}\alpha }}\).</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Let <em>a </em>= 3<em>k </em>and <em>b </em>= <em>k </em>.</span><span style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Find, in terms of <em>k </em>, the maximum length of a painting that can be removed from the gallery through this doorway.</span></p>
<div class="marks">[6]</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: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Let <em>a </em>= 3<em>k </em>and <em>b </em>= <em>k </em>.</span><span style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the minimum value of <em>k </em>if a painting 8 metres long is to be removed through this doorway.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(L = {\text{CA}} + {\text{AD}}\) <em style="font-style: italic;"><strong style="font-weight: bold;">M1</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{sin}}\alpha {\text{ = }}\frac{a}{{{\text{CA}}}} \Rightarrow {\text{CA}} = \frac{a}{{\sin \alpha }}\) <em style="font-style: italic;"><strong style="font-weight: bold;">A1</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\cos \alpha = \frac{b}{{{\text{AD}}}} \Rightarrow {\text{AD}} = \frac{b}{{\cos \alpha }}\) <em style="font-style: italic;"><strong style="font-weight: bold;">A1</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(L = \frac{a}{{\sin \alpha }} + \frac{b}{{\cos \alpha }}\) <em style="font-style: italic;"><strong style="font-weight: bold;">AG</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><em style="font-style: italic;"><strong style="font-weight: bold;">[2 marks]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 12px/normal Times; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">\(a = 5{\text{ and }}b = 1 \Rightarrow L = \frac{5}{{\sin \alpha }} + \frac{1}{{\cos \alpha }}\)</span></p>
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 12px/normal Times; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 12px/normal Times; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong style="font-weight: bold;">METHOD 1</strong></span></p>
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 12px/normal Times; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><em style="font-style: italic;"><strong style="font-weight: bold;"><img 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" alt> (M1)</strong></em></span></p>
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 12px/normal Times; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">minimum from graph \( \Rightarrow L = 7.77\) <strong><em>(M1)A1</em></strong></span></p>
<p style="font-family: arial, helvetica, sans-serif; font: normal normal normal 11px/normal Helvetica; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">minimum of <em>L </em>gives the max length of the painting <strong><em>R1</em></strong></span></p>
<p style="font-family: arial, helvetica, sans-serif; font: normal normal normal 11px/normal Helvetica; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<p style="font-family: arial, helvetica, sans-serif; font: normal normal normal 11px/normal Helvetica; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="font-family: arial, helvetica, sans-serif; font: normal normal normal 11px/normal Helvetica; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}L}}{{{\text{d}}\alpha }} = \frac{{ - 5\cos \alpha }}{{{{\sin }^2}\alpha }} + \frac{{\sin \alpha }}{{{{\cos }^2}\alpha }}\) <em style="font-style: italic;"><strong> (M1)</strong></em></span></p>
<p style="font-family: arial, helvetica, sans-serif; font: normal normal normal 11px/normal Helvetica; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}L}}{{{\text{d}}\alpha }} = 0 \Rightarrow \frac{{{{\sin }^3}\alpha }}{{{{\cos }^3}\alpha }} = 5 \Rightarrow \tan \alpha = \sqrt[{3{\text{ }}}]{5}{\text{ }}(\alpha = 1.0416...)\) <strong> <em>(M1)</em></strong></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;">minimum of <em>L </em>gives the max length of the paintin</span></span><span style="font-family: 'times new roman', times; font-size: medium;">g <strong><em>R1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">maximum length = 7.77 </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 12px/normal Times; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}L}}{{{\text{d}}\alpha }} = \frac{{ - 3k\cos \alpha }}{{{{\sin }^2}\alpha }} + \frac{{k\sin \alpha }}{{{{\cos }^2}\alpha }}\,\,\,\,\,{\text{(or equivalent)}}\) <em style="font-style: italic;"><strong style="font-weight: bold;">M1A1A1</strong></em></span></p>
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 12px/normal Times; margin: 0px;"><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;">\(\frac{{{\text{d}}L}}{{{\text{d}}\alpha }} = \frac{{ - 3k{{\cos }^3}\alpha + k{{\sin }^3}\alpha }}{{{{\sin }^2}\alpha {{\cos }^2}\alpha }}\) <strong><em>(A1)</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}L}}{{{\text{d}}\alpha }} = 0 \Rightarrow \frac{{{{\sin }^3}\alpha }}{{{{\cos }^3}\alpha }} = \frac{{3k}}{k} \Rightarrow \tan \alpha = \sqrt[3]{3}\,\,\,\,\,(\alpha = 0.96454...)\) <strong><em>M1A1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(\tan \alpha = \sqrt[3]{3} \Rightarrow \frac{1}{{\cos \alpha }} = \sqrt {1 + \sqrt[3]{9}} \,\,\,\,\,(1.755...)\) <strong><em>(A1)</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{and }}\frac{1}{{\sin \alpha }} = \frac{{\sqrt {1 + \sqrt[3]{9}} }}{{\sqrt[3]{3}}}\,\,\,\,\,(1.216...)\) <strong> <em>(A1)</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(L = 3k\left( {\frac{{\sqrt {1 + \sqrt[3]{9}} }}{{\sqrt[3]{3}}}} \right) + k\sqrt {1 + \sqrt[3]{9}} \,\,\,\,\,(L = 5.405598...k)\) <strong><em>A1 N4</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<p> </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: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(L \leqslant 8 \Rightarrow k \geqslant 1.48\) <em><strong>M1A1</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the minimum value is 1.48</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 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;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was very well done by most candidates. Parts (b), (c) and (d) required a subtle balance between abstraction, differentiation skills and use of GDC. </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (b), although candidates were asked to justify their reasoning, very few candidates offered an explanation for the maximum. Therefore most candidates did not earn the R1 mark in part (b). Also not as many candidates as anticipated used a graphical approach, preferring to use the calculus with varying degrees of success. In part (c), some candidates calculated the derivatives of inverse trigonometric functions. Some candidates had difficulty with parts (d) and (e). In part (d), some candidates erroneously used their alpha value from part (b). In part (d) many candidates used GDC to calculate decimal values for \(\alpha \) and <em>L</em>. The premature rounding of decimals led sometimes to inaccurate results. Nevertheless many candidates got excellent results in this question.</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; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was very well done by most candidates. Parts (b), (c) and (d) required a subtle balance between abstraction, differentiation skills and use of GDC. </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (b), although candidates were asked to justify their reasoning, very few candidates offered an explanation for the maximum. Therefore most candidates did not earn the R1 mark in part (b). Also not as many candidates as anticipated used a graphical approach, preferring to use the calculus with varying degrees of success. In part (c), some candidates calculated the derivatives of inverse trigonometric functions. Some candidates had difficulty with parts (d) and (e). In part (d), some candidates erroneously used their alpha value from part (b). In part (d) many candidates used GDC to calculate decimal values for \(\alpha \) and <em>L</em>. The premature rounding of decimals led sometimes to inaccurate results. Nevertheless many candidates got excellent results in this question.</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: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was very well done by most candidates. Parts (b), (c) and (d) required a subtle balance between abstraction, differentiation skills and use of GDC. </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (b), although candidates were asked to justify their reasoning, very few candidates offered an explanation for the maximum. Therefore most candidates did not earn the R1 mark in part (b). Also not as many candidates as anticipated used a graphical approach, preferring to use the calculus with varying degrees of success. In part (c), some candidates calculated the derivatives of inverse trigonometric functions. Some candidates had difficulty with parts (d) and (e). In part (d), some candidates erroneously used their alpha value from part (b). In part (d) many candidates used GDC to calculate decimal values for \(\alpha \) and <em>L</em>. The premature rounding of decimals led sometimes to inaccurate results. Nevertheless many candidates got excellent results in this question.</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: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was very well done by most candidates. Parts (b), (c) and (d) required a subtle balance between abstraction, differentiation skills and use of GDC. </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (b), although candidates were asked to justify their reasoning, very few candidates offered an explanation for the maximum. Therefore most candidates did not earn the R1 mark in part (b). Also not as many candidates as anticipated used a graphical approach, preferring to use the calculus with varying degrees of success. In part (c), some candidates calculated the derivatives of inverse trigonometric functions. Some candidates had difficulty with parts (d) and (e). In part (d), some candidates erroneously used their alpha value from part (b). In part (d) many candidates used GDC to calculate decimal values for \(\alpha \) and <em>L</em>. The premature rounding of decimals led sometimes to inaccurate results. Nevertheless many candidates got excellent results in this question.</span></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: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was very well done by most candidates. Parts (b), (c) and (d) required a subtle balance between abstraction, differentiation skills and use of GDC. </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (b), although candidates were asked to justify their reasoning, very few candidates offered an explanation for the maximum. Therefore most candidates did not earn the R1 mark in part (b). Also not as many candidates as anticipated used a graphical approach, preferring to use the calculus with varying degrees of success. In part (c), some candidates calculated the derivatives of inverse trigonometric functions. Some candidates had difficulty with parts (d) and (e). In part (d), some candidates erroneously used their alpha value from part (b). In part (d) many candidates used GDC to calculate decimal values for \(\alpha \) and <em>L</em>. The premature rounding of decimals led sometimes to inaccurate results. Nevertheless many candidates got excellent results in this question.</span></p>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the area of the region enclosed by the curves \(y = {x^3}\) and \(x = {y^2} - 3\) .<br></span></p>
<p> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"> </p>
<p> </p>
<p> </p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><img src="data:image/png;base64,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" alt></p>
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 11px/normal Helvetica; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">intersection points <strong><em>A1A1</em></strong></span></p>
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 11px/normal Helvetica; margin: 0px;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note: </strong><span style="font-family: 'times new roman', times; font-size: medium;">Only either the </span><em style="font-family: 'times new roman', times; font-size: medium;">x</em><span style="font-family: 'times new roman', times; font-size: medium;">-coordinate or the </span><em style="font-family: 'times new roman', times; font-size: medium;">y</em><span style="font-family: 'times new roman', times; font-size: medium;">-coordinate is needed.</span></p>
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 11px/normal Helvetica; margin: 0px;"> </p>
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 11px/normal Helvetica; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></p>
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 11px/normal Helvetica; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = {y^2} - 3 \Rightarrow y = \pm \sqrt {x + 3} \,\,\,\,\,\left( {{\text{accept }}y = \sqrt {x + 3} } \right)\) <strong> <em>(M1)</em></strong></span></p>
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 11px/normal Helvetica; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">\(A = \int_{ - 3}^{ - 1.111...} {2\sqrt {x + 3} \,{\text{d}}x + \int_{ - 1.111...}^{1.2739...} {\sqrt {x + 3} - {x^3}{\text{d}}x} } \) <strong><em>(M1)A1A1</em></strong></span></p>
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 11px/normal Helvetica; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">= 3.4595... + 3.8841...</span></p>
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 11px/normal Helvetica; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">= 7.34 (3sf) <strong><em>A1</em></strong></span></p>
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 11px/normal Helvetica; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 11px/normal Helvetica; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">\(y = {x^3} \Rightarrow x = \sqrt[3]{y}\) <strong><em>(M1)</em></strong></span></p>
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 11px/normal Helvetica; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">\(A = \int_{ - 1.374...}^{2.067...} {\sqrt[3]{y}} - ({y^2} - 3){\text{d}}y\) <strong> <em>(M1)A1</em></strong></span></p>
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 11px/normal Helvetica; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">= 7.34 (3sf) <strong><em>A2</em></strong></span></p>
<p style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font: normal normal normal 11px/normal Helvetica; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This question proved challenging to most candidates. Just a few candidates were able to calculate the exact area between curves. Those candidates who tried to express the functions in terms <em>x</em> of instead of <em>y</em> showed better performances. Determining only \(\sqrt {x + 3} \) was a common error and forming appropriate definite integrals above and below the <em>x</em>-axis proved difficult. Although many candidates attempted to sketch the graphs, many found only one branch of the parabola and only one point of intersection; as the graph of the parabola was not complete, many candidates did not know which area they were trying to find. Not many split the integral correctly to find areas that would add up to the result. Premature rounding was usually seen and consequently final answers proved inaccurate.</span></p>
<p> </p>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Consider the graphs \(y = {{\text{e}}^{ - x}}\) and \(y = {{\text{e}}^{ - x}}\sin 4x\) , for \(0 \leqslant x \leqslant \frac{{5\pi }}{4}\)</span><span style="font-family: times new roman,times; font-size: medium;"> .</span></p>
</div>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">(a) On the same set of axes draw, on graph paper, the graphs, for \(0 \leqslant x \leqslant \frac{{5\pi }}{4}\). </span><span style="font-family: times new roman,times; font-size: medium;">Use a scale of \(1\) cm to \(\frac{\pi }{8}\) </span><span style="font-family: times new roman,times; font-size: medium;">on your \(x\)-axis and \(5\) cm to \(1\) unit on your \(y\)-axis.</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;">(b) Show that the \(x\)-intercepts of the graph \(y = {{\text{e}}^{ - x}}\) sin 4x are \(\frac{{n\pi }}{4}\)</span> <span style="font-family: times new roman,times; font-size: medium;">, \(n = 0\), \(1\), \(2\), \(3\), \(4\), \(5\).</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;">(c) Find the \(x\)-coordinates of the points at which the graph of \(y = {{\text{e}}^{ - x}}\sin 4x\) meets </span><span style="font-family: times new roman,times; font-size: medium;">the graph of \(y = {{\text{e}}^{ - x}}\) . Give your answers in terms of \( \pi\).</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;">(d) (i) Show that when the graph of \(y = {{\text{e}}^{ - x}}\sin 4x\) meets the graph of \(y = {{\text{e}}^{ - x}}\) , </span><span style="font-family: times new roman,times; font-size: medium;">their gradients are equal.</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> (ii) Hence explain why these three meeting points are not local maxima of the </span><span style="font-family: times new roman,times; font-size: medium;">graph \(y = {{\text{e}}^{ - x}}\sin 4x\) .</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;">(e) (i) Determine the \(y\)-coordinates, \({y_1}\) , \({y_2}\) and \({y_3}\), where \({y_1} > {y_2} > {y_3}\) , of the </span><span style="font-family: times new roman,times; font-size: medium;">local maxima of \(y = {{\text{e}}^{ - x}}\sin 4x\) for \(0 \leqslant x \leqslant \frac{{5\pi }}{4}\)</span><span style="font-family: times new roman,times; font-size: medium;"> . You do not need to show </span><span style="font-family: times new roman,times; font-size: medium;">that they are maximum values, but the values should be simplified.</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> (ii) Show that </span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\({y_1}\) , \({y_2}\) and \({y_3}\)</span> form a geometric sequence and determine the common ratio \(r\) .</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;">(a)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img 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" alt> <em><strong> A3</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 correct shape,</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"><em><strong> A1</strong></em> for correct relative position.</span></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[3 marks]</span></strong></em></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) \({{\text{e}}^{ - x}}\sin \left( {4x} \right) = 0\) <em><strong>(M1)</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\sin \left( {4x} \right) = 0\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(4x = 0\), </span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\(\pi \), </span></span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\(2\pi \), </span></span></span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\(3\pi \), </span></span></span></span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\(4\pi \), </span></span></span></span>\(5\pi \) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(x = 0\), \(\frac{\pi }{4}\), </span><span style="font-family: times new roman,times; font-size: medium;">\(\frac{2\pi }{4}\), </span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\(\frac{3\pi }{4}\), </span></span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\(\frac{4\pi }{4}\), </span></span></span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\(\frac{5\pi }{4}\</span></span></span>)</span> <em><strong><span style="font-family: times new roman,times; font-size: medium;">AG</span></strong></em></p>
<p><em><strong><span style="font-family: times new roman,times; font-size: medium;">[3 marks]</span></strong></em></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;">(c) \({{\text{e}}^{ - x}} = {{\text{e}}^{ - x}}\sin \left( {4x} \right) = 0\) </span><span style="font-family: times new roman,times; font-size: medium;">or reference to graph</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\sin 4x = 1\), <em><strong>M1</strong></em></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(\sin 4x = 1\), \(frac{\pi }{2}\), </span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\(frac{5\pi }{2}\), </span></span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\(frac{9\pi }{2}\)</span></span> <em><strong>A1</strong></em></span></p>
<address><span style="font-family: times new roman,times; font-size: medium;">\(x = \frac{\pi }{8}\), </span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\(\frac{5\pi }{8}\), </span></span><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;"><span style="font-family: times new roman,times; font-size: medium;">\(\frac{9\pi }{8}\)</span></span> <em><strong> A1 N3</strong></em></span></address><address><em><strong><span style="font-family: times new roman,times; font-size: medium;">[3 marks]</span></strong></em></address><address><span style="font-family: times new roman,times; font-size: medium;"> </span></address><address><span style="font-family: times new roman,times; font-size: medium;">(d) (i) \(y = {{\text{e}}^{ - x}}\sin 4x\)</span></address><address><span style="font-family: times new roman,times; font-size: medium;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = - {{\text{e}}^{ - x}}\sin 4x + 4{{\text{e}}^{ - x}}\cos 4x\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">M1A1</span></strong></em></address><address><span style="font-family: times new roman,times; font-size: medium;">\(y = {{\text{e}}^{ - x}}\)</span></address><address><span style="font-family: times new roman,times; font-size: medium;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = - {{\text{e}}^{ - x}}\) </span><em><strong><span style="font-family: times new roman,times; font-size: medium;">A1</span></strong></em></address><address><span style="font-family: times new roman,times; font-size: medium;">verifying equality of gradients at one point <em><strong>R1</strong></em></span></address><address><span style="font-family: times new roman,times; font-size: medium;">verifying at the other two <em><strong>R1</strong></em></span></address><address><span style="font-family: times new roman,times; font-size: medium;">(ii) since \(\frac{{{\text{d}}y}}{{{\text{d}}x}} \ne 0\) </span><span style="font-family: times new roman,times; font-size: medium;">at these points they cannot be local maxima <em><strong>R1</strong></em></span></address><address><em><strong><span style="font-family: times new roman,times; font-size: medium;">[6 marks]</span></strong></em></address><address><em><strong><span style="font-family: times new roman,times; font-size: medium;"> </span></strong></em></address><address><span style="font-family: times new roman,times; font-size: medium;">(e) (i) maximum when \(y' = 4{{\text{e}}^{ - x}}\cos 4x - {{\text{e}}^{ - x}}\sin 4x = 0\) <em><strong>M1</strong></em></span></address><address><span style="font-family: times new roman,times; font-size: medium;">\(x = \frac{{\arctan \left( 4 \right)}}{4}\), \(\frac{{\arctan \left( 4 \right) + \pi }}{4}\), \(\frac{{\arctan \left( 4 \right) + 2\pi }}{4}\), ...</span></address><address><span style="font-family: times new roman,times; font-size: medium;">maxima occur at</span></address><address><span style="font-family: times new roman,times; font-size: medium;">\(x = \frac{{\arctan \left( 4 \right)}}{4}\), \(\frac{{\arctan \left( 4 \right) + 2\pi }}{4}\), \(\frac{{\arctan \left( 4 \right) + 4\pi }}{4}\) <em><strong>A1</strong></em></span></address><address><span style="font-family: times new roman,times; font-size: medium;">so \({y_1} = {{\text{e}}^{ - \frac{1}{4}\left( {\arctan \left( 4 \right)} \right)}}\sin \left( {\arctan \left( 4 \right)} \right)\) (\( = 0.696\)) <em><strong>A1</strong></em></span></address><address><span style="font-family: times new roman,times; font-size: medium;">\({y_2} = {{\text{e}}^{ - \frac{1}{4}\left( {\arctan \left( 4 \right) + 2\pi } \right)}}\sin \left( {\arctan \left( 4 \right) + 2\pi } \right)\) <em><strong>A1</strong></em></span></address><address style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\(\left( { = {{\text{e}}^{ - \frac{1}{4}\left( {\arctan \left( 4 \right) + 2\pi } \right)}}\sin \left( {\arctan \left( 4 \right)} \right) = 0.145} \right)\)</span></address><address><span style="font-family: times new roman,times; font-size: medium;">\({y_3} = {{\text{e}}^{ - \frac{1}{4}\left( {\arctan \left( 4 \right) + 4\pi } \right)}}\sin \left( {\arctan \left( 4 \right) + 4\pi } \right)\) <em><strong>A1</strong></em></span></address><address style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">\(\left( { = {{\text{e}}^{ - \frac{1}{4}\left( {\arctan \left( 4 \right) + 4\pi } \right)}}\sin \left( {\arctan \left( 4 \right)} \right) = 0.0301} \right)\) <em><strong> N3</strong></em></span></address><address><span style="font-family: times new roman,times; font-size: medium;">(ii) for finding and comparing \(\frac{{{y_3}}}{{{y_2}}}\) and \(\frac{{{y_2}}}{{{y_1}}}\) <em><strong>M1</strong></em></span></address><address><span style="font-family: times new roman,times; font-size: medium;">\(r = {{\text{e}}^{ - \frac{\pi }{2}}}\) <em><strong>A1</strong></em></span></address><address><span style="font-family: times new roman,times; font-size: medium;"><strong>Note:</strong> Exact values must be used to gain the <em><strong>M1</strong></em> and the <em><strong>A1</strong></em>.</span></address><address><em><strong><span style="font-family: times new roman,times; font-size: medium;">[7 marks]</span></strong></em></address><address><em><strong><span style="font-family: times new roman,times; font-size: medium;"> </span></strong></em></address><address><em><strong><span style="font-family: times new roman,times; font-size: medium;">Total [22 marks]</span></strong></em></address>
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<h2 style="margin-top: 1em">Examiners report</h2>
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<p><span style="font-family: times new roman,times; font-size: medium;">Although the final question on the paper it had parts accessible even to the weakest candidates. The vast majority of candidates earned marks on part (a), although some graphs were rather scruffy. Many candidates also tackled parts (b), (c) and (d). In part (b), however, as the answer was given, it should have been clear that some working was required rather than reference to a graph, which often had no scale indicated. In part d(i), although the functions were usually differentiated correctly, it was often the case that only one point was checked for the equality of the gradients. In part e(i) many candidates who got this far were able to determine the \(y\)-coordinates of the local maxima numerically using a GDC, and that was given credit. Only the exact values, however, could be used in part e(ii).</span></p>
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