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</div><h2>HL Paper 3</h2><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 \(\mathop {\lim }\limits_{x \to 0} \frac{{\tan x}}{{x + {x^2}}}\) ;</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: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find \(\mathop {\lim }\limits_{x \to 1} \frac{{1 - {x^2} + 2{x^2}\ln x}}{{1 - \sin \frac{{\pi x}}{2}}}\) .</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\mathop {\lim }\limits_{x \to 0} \frac{{\tan x}}{{x + {x^2}}} = \mathop {\lim }\limits_{x \to 0} \frac{{{{\sec }^2}x}}{{1 + 2x}}\) <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;">\(\mathop {\lim }\limits_{x \to 0} \frac{{\tan x}}{{x + {x^2}}} = \frac{1}{1} = 1\) <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>[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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\mathop {\lim }\limits_{x \to 1} \frac{{1 - {x^2} + 2{x^2}\ln x}}{{1 - \sin \frac{{\pi x}}{2}}} = \mathop {\lim }\limits_{x \to 1} \frac{{ - 2x + 2x + 4x\ln x}}{{ - \frac{\pi }{2}\cos \frac{{\pi x}}{2}}}\) <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;">\( = \mathop {\lim }\limits_{x \to 1} \frac{{4 + 4\ln x}}{{\frac{{{\pi ^2}}}{4}\sin \frac{{\pi x}}{2}}}\) <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;">\(\mathop {\lim }\limits_{x \to 1} \frac{{1 - {x^2} + 2{x^2}\ln x}}{{1 - \sin \frac{{\pi x}}{2}}} = \frac{4}{{\frac{{{\pi ^2}}}{4}}} = \frac{{16}}{{{\pi ^2}}}\) <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>[7 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: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was accessible to the vast majority of candidates, who recognised that L’Hopital’s rule was required. A few of the weaker candidates did not realise that it needed to be applied twice in part (b). Many fully correct solutions were seen.</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: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was accessible to the vast majority of candidates, who recognised that L’Hopital’s rule was required. A few of the weaker candidates did not realise that it needed to be applied twice in part (b). Many fully correct solutions were seen.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Consider 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;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 2{{\text{e}}^x} + y\tan x\) , given that <em>y</em> = 1 when <em>x</em> = 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;">The domain of the function <em>y</em> is \(\left[ {0,\frac{\pi }{2}} \right[\).</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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">By finding the values of successive derivatives when <em>x</em> = 0 , find the Maclaurin series for <em>y</em> as far as the term in \({x^3}\) .</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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Differentiate the function \({{\text{e}}^x}(\sin x + \cos x)\) and hence show that</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;">\[\int {{{\text{e}}^x}\cos x{\text{d}}x = \frac{1}{2}{{\text{e}}^x}(\sin x + \cos x) + c} .\]</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;">(ii) Find an integrating factor for the differential equation and hence find the solution in the form \(y = f(x)\) .</span></p>
<div class="marks">[9]</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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">we note that \(y(0) = 1\) and \(y'(0) = 2\) <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;">\(y'' = 2{{\text{e}}^x} + y'\tan x + y{\sec ^2}x\) <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;">\(y''(0) = 3\) <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;">\(y''' = 2{{\text{e}}^x} + y''\tan x + 2y'{\sec ^2}x + 2y{\sec ^2}x\tan x\) <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;">\(y'''(0) = 6\) <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 maclaurin series solution is therefore</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;">\(y = 1 + 2x + \frac{{3{x^2}}}{2} + {x^3} + \ldots \) <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>
<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) \(\frac{{\text{d}}}{{{\text{d}}x}}\left( {{{\text{e}}^x}(\sin x + \cos x)} \right) = {{\text{e}}^x}(\sin x + \cos x) + {{\text{e}}^x}(\cos x - \sin x)\) <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;">\( = 2{{\text{e}}^x}\cos x\) <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;">it follows that</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;">\(\int {{{\text{e}}^x}\cos x{\text{d}}x = \frac{1}{2}{{\text{e}}^x}(\sin x + \cos x) + c} \) <strong><em>AG</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) the differential equation can be written as</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;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} - y\tan x = 2{{\text{e}}^x}\) <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;">\({\text{IF}} = {{\text{e}}^{\int { - \tan x{\text{d}}x} }} = {{\text{e}}^{\ln \cos x}} = \cos x\) <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;">\(\cos x\frac{{{\text{d}}y}}{{{\text{d}}x}} - y\sin x = 2{{\text{e}}^x}\cos x\) <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;">integrating,</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;">\(y\cos x = {{\text{e}}^x}(\sin x + \cos x) + C\) <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;"><em>y</em> = 1 when <em>x</em> = 0 gives <em>C</em> = 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;">therefore</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;">\(y = {{\text{e}}^x}(1 + \tan x)\) <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>[9 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" 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 \(\int_1^\infty {\frac{1}{{x(x + p)}}{\text{d}}x,{\text{ }}p \ne 0} \) is convergent if <em>p </em>> −1 and find its value in terms of <em>p</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;">(ii) Hence show that the following series is convergent.</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;">\[\frac{1}{{1 \times 0.5}} + \frac{1}{{2 \times 1.5}} + \frac{1}{{3 \times 2.5}} + ...\]</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: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Determine, for each of the following series, whether it is convergent or divergent.</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;">(i) \(\sum\limits_{n = 1}^\infty {\sin \left( {\frac{1}{{n(n + 3)}}} \right)} \)</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) \(\sqrt {\frac{1}{2}} + \sqrt {\frac{1}{6}} + \sqrt {\frac{1}{{12}}} + \sqrt {\frac{1}{{20}}} + …\)</span></p>
<div class="marks">[11]</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) the integrand is non-singular on the domain if <em>p</em> > –1 with the latter assumed, consider</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;">\(\int_1^R {\frac{1}{{x(x + p)}}} {\text{d}}x = \frac{1}{p}\int_1^R {\frac{1}{x} - \frac{1}{{x + p}}{\text{d}}x} \) <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;">\( = \frac{1}{p}\left[ {\ln \left( {\frac{x}{{x + p}}} \right)} \right]_1^R,{\text{ }}p \ne 0\) <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;">this evaluates to</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;">\(\frac{1}{p}\left( {\ln \frac{R}{{R + p}} - \ln \frac{1}{{1 + p}}} \right),{\text{ }}p \ne 0\) <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;">\( \to \frac{1}{p}\ln (1 + p)\) <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;">because \(\frac{R}{{R + p}} \to 1{\text{ as }}R \to \infty \) <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;">hence the integral is convergent <strong><em>AG</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) the given series is \(\sum\limits_{n = 1}^\infty {f(n),{\text{ }}f(n) = \frac{1}{{n(n - 0.5)}}} \) <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;">the integral test and <em>p</em> = –0.5 in (i) establishes the convergence of the series <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>[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: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) as we have a series of positive terms we can apply the comparison test, limit form</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">comparing with \(\sum\limits_{n = 1}^\infty {\frac{1}{{{n^2}}}} \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\mathop {\lim }\limits_{n \to \infty } \frac{{\sin \left( {\frac{1}{{n(n + 3)}}} \right)}}{{\frac{1}{{{n^2}}}}} = 1\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">as \(\sin \theta \approx \theta {\text{ for small }}\theta \) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">and \(\frac{{{n^2}}}{{n(n + 3)}} \to 1\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(so as the limit (of 1) is finite and non-zero, both series exhibit the same behavior)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\sum\limits_{n = 1}^\infty {\frac{1}{{{n^2}}}} \) converges, so this series converges <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px 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: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) the general term is</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\sqrt {\frac{1}{{n(n + 1)}}} \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\sqrt {\frac{1}{{n(n + 1)}}} > \sqrt {\frac{1}{{(n + 1)(n + 1)}}} \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\sqrt {\frac{1}{{(n + 1)(n + 1)}}} = \frac{1}{{n + 1}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the harmonic series diverges <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so by the comparison test so does the given series <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[11 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: 23.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part(a)(i) caused problems for some candidates who failed to realize that the integral can only be tackled by the use of partial fractions. Even then, the improper integral only exists as a limit – too many candidates ignored or skated over this important point. Candidates must realize that in this type of question, rigour is important, and full marks will only be awarded for a full and clearly explained argument. This applies as well to part(b), where it was also noted that some candidates were confusing the convergence of the terms of a series to zero with convergence of the series itself.</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: 23.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part(a)(i) caused problems for some candidates who failed to realize that the integral can only be tackled by the use of partial fractions. Even then, the improper integral only exists as a limit – too many candidates ignored or skated over this important point. Candidates must realize that in this type of question, rigour is important, and full marks will only be awarded for a full and clearly explained argument. This applies as well to part(b), where it was also noted that some candidates were confusing the convergence of the terms of a series to zero with convergence of the series itself.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Times;"><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: 27.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\[f(x) = \ln \left( {\frac{1}{{1 - x}}} \right).\]</span></p>
</div>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Write down the value of the constant term in the Maclaurin series for \(f(x)\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Find the first three derivatives of \(f(x)\) and hence show that the Maclaurin series for \(f(x)\) up to and including the \({x^3}\) term is \(x + \frac{{{x^2}}}{2} + \frac{{{x^3}}}{3}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) Use this series to find an approximate value for ln 2 .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(d) Use the Lagrange form of the remainder to find an upper bound for the error in this approximation.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(e) How good is this upper bound as an estimate for the actual error?</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 Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Constant term = 0 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times; color: #3f3f3f;"><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: 20.0px Times; color: #3f3f3f;"><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 Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) \(f'(x) = \frac{1}{{1 - x}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f''(x) = \frac{1}{{{{(1 - x)}^2}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'''(x) = \frac{2}{{{{(1 - x)}^3}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(0) = 1;{\text{ }}f''(0) = 1;{\text{ }}f'''(0) = 2\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times; color: #3f3f3f;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note: </strong><span style="font-family: 'times new roman', times; font-size: medium;">Allow </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>FT </em></strong><span style="font-family: 'times new roman', times; font-size: medium;">on their derivatives.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(x) = 0 + \frac{{1 \times x}}{{1!}} + \frac{{1 \times {x^2}}}{{2!}} + \frac{{2 \times {x^3}}}{{3!}} + …\) </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: 20.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = x + \frac{{{x^2}}}{2} + \frac{{{x^3}}}{3}\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times; color: #3f3f3f;"><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: 20.0px Times; color: #3f3f3f;"><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 Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) \(\frac{1}{{1 - x}} = 2 \Rightarrow x = \frac{1}{2}\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\ln 2 \approx \frac{1}{2} + \frac{1}{8} + \frac{1}{{24}}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{2}{3}{\text{ (0.667)}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times; color: #3f3f3f;"><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 Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(d) Lagrange error \({\text{ = }}\frac{{{f^{(n + 1)}}(c)}}{{(n + 1)!}} \times {\left( {\frac{1}{2}} \right)^{n + 1}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{6}{{{{(1 - c)}^4}}} \times \frac{1}{{24}} \times {\left( {\frac{1}{2}} \right)^4}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\( < \frac{6}{{{{\left( {1 - \frac{1}{2}} \right)}^4}}} \times \frac{1}{{24}} \times \frac{1}{{16}}\) <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">giving an upper bound of 0.25. <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times; color: #3f3f3f;"><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 Times; color: #3f3f3f;"><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 Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(e) Actual error \( = \ln 2 - \frac{2}{3} = 0.0265\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">The upper bound calculated is much larger that the actual error therefore cannot be considered a good estimate. <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [17 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 Arial;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">In (a), some candidates appeared not to understand the term ‘constant term’. In (b), many candidates found the differentiation beyond them with only a handful realising that the best way to proceed was to rewrite the function as \(f(x) = - \ln (1 - x)\). In (d), many candidates were unable to use the Lagrange formula for the upper bound so that (e) became inaccessible.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Arial;"> </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 \(\left] { - \frac{\pi }{2},\frac{\pi }{2}} \right[{\text{ by }}f(x) = \ln (1 + \sin x)\) .</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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Show that \(f''(x) = - \frac{1}{{(1 + \sin x)}}\) .</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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Find the Maclaurin series for \(f(x)\) up to and including the term in \({x^4}\) .</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) Explain briefly why your result shows that <em>f</em> is neither an even function nor an odd function.</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p 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;">Determine the value of \(\mathop {\lim }\limits_{x \to 0} \frac{{\ln (1 + \sin x) - x}}{{{x^2}}}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(x) = \frac{{\cos x}}{{1 + \sin x}}\) <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;">\(f''(x) = \frac{{ - \sin x(1 + \sin x) - \cos x\cos x}}{{{{(1 + \sin x)}^2}}}\) <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;">\( = \frac{{ - \sin x - ({{\sin }^2}x + {{\cos }^2}x)}}{{{{(1 + \sin x)}^2}}}\) <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;">\( = - \frac{1}{{1 + \sin x}}\) <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>[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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \(f'''(x) = \frac{{\cos x}}{{{{(1 + \sin x)}^2}}}\) <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;">\({f^{(4)}}(x) = \frac{{ - \sin x{{(1 + \sin x)}^2} - 2(1 + \sin x){{\cos }^2}x}}{{{{(1 + \sin x)}^4}}}\) <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;">\(f(0) = 0,{\text{ }}f'(0) = 1,{\text{ }}f''(0) = - 1\) <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;">\(f'''(0) = 1,{\text{ }}{f^{(4)}}(0) = - 2\) <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;">\(f(x) = x - \frac{{{x^2}}}{2} + \frac{{{x^3}}}{6} - \frac{{{x^4}}}{{12}} + \ldots \) <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) the series contains even and odd powers of <em>x</em> <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>[7 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;">\(\mathop {\lim }\limits_{x \to 0} \frac{{\ln (1 + \sin x) - x}}{{{x^2}}} = \mathop {\lim }\limits_{x \to 0} \frac{{x - \frac{{{x^2}}}{2} + \frac{{{x^3}}}{6} + \ldots - x}}{{{x^2}}}\) <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;">\( = \mathop {\lim }\limits_{x \to 0} \frac{{\frac{{ - 1}}{2} + \frac{x}{6} + \ldots }}{1}\) <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;">\( = - \frac{1}{2}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Use of l’Hopital’s Rule is also acceptable.</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>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p 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 exponential series is given by \({{\text{e}}^x} = \sum\limits_{n = 0}^\infty {\frac{{{x^n}}}{{n!}}} \) .</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 the set of values of <em>x</em> for which the series is convergent.</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) Show, by comparison with an appropriate geometric series, that</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;">\[{{\text{e}}^x} - 1 < \frac{{2x}}{{2 - x}},{\text{ for }}0 < x < 2{\text{.}}\]</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) Hence show that \({\text{e}} < {\left( {\frac{{2n + 1}}{{2n - 1}}} \right)^n}\), for \(n \in {\mathbb{Z}^ + }\).</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 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) Write down the first three terms of the Maclaurin series for \(1 - {{\text{e}}^{ - x}}\) and explain why you are able to state that</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;">\[1 - {{\text{e}}^{ - x}} > x - \frac{{{x^2}}}{2},{\text{ for }}0 < x < 2.\]</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) Deduce that \({\text{e}} > {\left( {\frac{{2{n^2}}}{{2{n^2} - 2n + 1}}} \right)^n}\), for \(n \in {\mathbb{Z}^ + }\).</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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Letting <em>n</em> = 1000, use the results in parts (b) and (c) to calculate the value of e correct to as many decimal places as possible.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">using a ratio test,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\left| {\frac{{{T_{n + 1}}}}{{{T_n}}}} \right| = \left| {\frac{{{x^{n + 1}}}}{{(n + 1)!}}} \right| \times \left| {\frac{{n!}}{{{x^n}}}} \right| = \frac{{\left| x \right|}}{{n + 1}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Condone omission of modulus signs.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \to 0{\text{ as }}n \to \infty \) for all values of <em>x</em> <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">the series is therefore convergent for \(x \in \mathbb{R}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Times; color: #3f3f3f;"><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: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \({{\text{e}}^x} - 1 = x + \frac{{{x^2}}}{2} + \frac{{{x^3}}}{{2 \times 3}} + …\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( < x + \frac{{{x^2}}}{2} + \frac{{{x^3}}}{{2 \times 2}} + ...\,\,\,\,\,({\text{for }}x > 0)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{x}{{1 - \frac{x}{2}}}\,\,\,\,\,({\text{for }}x < 2)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{2x}}{{2 - x}}\,\,\,\,\,({\text{for }}0 < x < 2)\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px 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: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \({{\text{e}}^x} < 1 + \frac{{2x}}{{2 - x}} = \frac{{2 + x}}{{2 - x}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{e}} < {\left( {\frac{{2 + x}}{{2 - x}}} \right)^{\frac{1}{x}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">replacing <em>x</em> by \(\frac{1}{n}\) (and noting that the result is true for \(n > \frac{1}{2}\) and therefore \({\mathbb{Z}^ + }\) ) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{e}} < {\left( {\frac{{2n + 1}}{{2n - 1}}} \right)^n}\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px 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>
<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;">(i) \(1 - {{\text{e}}^{ - x}} = x - \frac{{{x^2}}}{2} + \frac{{{x^3}}}{6} + …\) <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;">for \(0 < x < 2\), the series is alternating with decreasing terms so that the sum is greater than the sum of an even number of terms <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;">therefore</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;">\(1 - {{\text{e}}^{ - x}} > x - \frac{{{x^2}}}{2}\) <strong><em>AG</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><em> </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;">(ii) \({{\text{e}}^{ - x}} < 1 - x + \frac{{{x^2}}}{2}\)</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;">\({{\text{e}}^x} > \frac{1}{{\left( {1 - x + \frac{{{x^2}}}{2}} \right)}}\) <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;">\({\text{e}} > {\left( {\frac{2}{{2 - 2x + {x^2}}}} \right)^{\frac{1}{x}}}\) <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;">replacing <em>x</em> by \(\frac{1}{n}\) (and noting that the result is true for \(n > \frac{1}{2}\) and therefore \({\mathbb{Z}^ + }\)</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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{e}} > {\left( {\frac{{2{n^2}}}{{2{n^2} - 2n + 1}}} \right)^n}\) <strong><em>AG</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><em> </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><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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">from (b) and (c), \({\text{e}} < 2.718282…\) and \({\text{e}} > 2.718281…\) <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;">we conclude that e = 2.71828 correct to 5 decimal places <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">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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Solutions to (a) were generally good although some candidates failed to reach the correct conclusion from correct application of the ratio test. Solutions to (b) and (c), however, were generally disappointing with many candidates unable to make use of the signposting in the question. Candidates who were unable to solve (b) and (c) often picked up marks in (d).</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;">Solutions to (a) were generally good although some candidates failed to reach the correct conclusion from correct application of the ratio test. Solutions to (b) and (c), however, were generally disappointing with many candidates unable to make use of the signposting in the question. Candidates who were unable to solve (b) and (c) often picked up marks in (d).</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;">Solutions to (a) were generally good although some candidates failed to reach the correct conclusion from correct application of the ratio test. Solutions to (b) and (c), however, were generally disappointing with many candidates unable to make use of the signposting in the question. Candidates who were unable to solve (b) and (c) often picked up marks in (d).</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;">Solutions to (a) were generally good although some candidates failed to reach the correct conclusion from correct application of the ratio test. Solutions to (b) and (c), however, were generally disappointing with many candidates unable to make use of the signposting in the question. Candidates who were unable to solve (b) and (c) often picked up marks in (d).</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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Determine whether or not the following series converge.</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;">(a) \(\sum\limits_{n = 0}^\infty {\left( {\sin \frac{{n\pi }}{2} - \sin \frac{{(n + 1)\pi }}{2}} \right)} \)</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;">(b) \(\sum\limits_{n = 1}^\infty {\frac{{{{\text{e}}^n} - 1}}{{{\pi ^n}}}} \)</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) \(\sum\limits_{n = 2}^\infty {\frac{{\sqrt {n + 1} }}{{n(n - 1)}}} \)</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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \(\sum\limits_{n = 0}^\infty {\left( {\sin \frac{{n\pi }}{2} - \sin \frac{{(n + 1)\pi }}{2}} \right)} \)</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;">\( = \left( {\sin 0 - \sin \frac{\pi }{2}} \right) + \left( {\sin \frac{\pi }{2} - \sin \pi } \right) + \left( {\sin \pi - \sin \frac{{3\pi }}{2}} \right) + \left( {\sin \frac{{3\pi }}{2} - \sin 2\pi } \right) + \ldots \) <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;">the \({n^{{\text{th}}}}\) term is ±1 for all <em>n</em>, <em>i.e.</em> the \({n^{{\text{th}}}}\) term does not tend to 0 <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;">hence the series does not converge <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>
<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;">(b) <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 ratio test <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;">\(\mathop {\lim }\limits_{n \to \infty } \frac{{{a_{n + 1}}}}{{{a_n}}} = \mathop {\lim }\limits_{n \to \infty } \left( {\frac{{{{\text{e}}^{n + 1}}}}{{{\pi ^{n + 1}}}}} \right)\left( {\frac{{{\pi ^n}}}{{{{\text{e}}^n} - 1}}} \right)\) <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;">\(\mathop {\lim }\limits_{n \to \infty } \left( {\frac{{{{\text{e}}^{n + 1}} - 1}}{{{{\text{e}}^n} - 1}}} \right)\left( {\frac{{{\pi ^n}}}{{{\pi ^{n + 1}}}}} \right) = \frac{{\text{e}}}{\pi }\,\,\,\,\,( \approx 0.865)\) <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;">\(\frac{{\text{e}}}{\pi } < 1\), hence the series converges <strong><em>R1A1</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;">\(\sum\limits_{n = 1}^\infty {\frac{{{{\text{e}}^n} - 1}}{{{\pi ^n}}} = \sum\limits_{n = 1}^\infty {{{\left( {\frac{{\text{e}}}{\pi }} \right)}^n} - {{\left( {\frac{1}{\pi }} \right)}^n} = \sum\limits_{n = 1}^\infty {{{\left( {\frac{{\text{e}}}{\pi }} \right)}^n} - \sum\limits_{n = 1}^\infty {{{\left( {\frac{{\text{1}}}{\pi }} \right)}^n}} } } } \) <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;">the series is the difference of two geometric series, with \(r = \frac{{\text{e}}}{\pi }\,\,\,\,\,( \approx 0.865)\) <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;">and \(\frac{1}{\pi }\,\,\,\,\,( \approx 0.318)\) <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;">for both \(\left| r \right| < 1\), hence the series converges <strong><em>R1A1</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;">\(\forall n,{\text{ }}0 < \frac{{{{\text{e}}^n} - 1}}{{{\pi ^n}}} < \frac{{{{\text{e}}^n}}}{{{\pi ^n}}}\) <strong><em>(M1)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;">the series \(\frac{{{{\text{e}}^n}}}{{{\pi ^n}}}\) converges since it is a geometric series such that \(\left| r \right| < 1\) <strong><em>A1R1</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;">therefore, by the comparison test, \(\frac{{{{\text{e}}^n} - 1}}{{{\pi ^n}}}\) converges <strong><em>R1A1</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>
<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;">(c) by limit comparison test with \(\frac{{\sqrt n }}{{{n^2}}}\), <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;">\(\mathop {\lim }\limits_{n \to \infty } \left( {\frac{{\frac{{\sqrt {n + 1} }}{{n(n - 1)}}}}{{\frac{{\sqrt n }}{{{n^2}}}}}} \right) = \mathop {\lim }\limits_{n \to \infty } \left( {\frac{{\sqrt {n + 1} }}{{n(n - 1)}} \times \frac{{{n^2}}}{{\sqrt n }}} \right) = \mathop {\lim }\limits_{n \to \infty } \frac{n}{{n - 1}}\sqrt {\frac{{n + 1}}{n}} = 1\) <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;">hence both series converge or both diverge <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;">by the <em>p</em>-test \(\sum\limits_{n = 1}^\infty {\frac{{\sqrt n }}{{{n^2}}} = {n^{\frac{{ - 3}}{2}}}} \) converges, hence both converge <strong><em>R1A1</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>
<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>Total [16 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 the least successfully answered question on the paper. Candidates often did not know which convergence test to use; hence very few full successful solutions were seen. The communication of the method used was often quite poor.</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;">a) Many candidates failed to see that this is a telescoping series. If this was recognized then the question was fairly straightforward. Often candidates unsuccessfully attempted to apply the standard convergence tests.</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) Many candidates used the ratio test, but some had difficulty in simplifying the expression. Others recognized that the series is the difference of two geometric series, and although the algebraic work was done correctly, some failed to communicate the conclusion that since the absolute value of the ratios are less than 1, hence the series converges. Some candidates successfully used the comparison test.</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;">c) Although the limit comparison test was attempted by most candidates, it often failed through an inappropriate selection of a series.</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find \(\mathop {\lim }\limits_{x \to 0} \left( {\frac{{1 - \cos {x^6}}}{{{x^{12}}}}} \right)\).</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;"><strong>METHOD 1</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;">\(f(0) = \frac{0}{0}\), hence using l’Hôpital’s Rule, <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;">\(g(x) = 1 - \cos ({x^6}),{\text{ }}h(x) = {x^{12}};{\text{ }}\frac{{g'(x)}}{{h'(x)}} = \frac{{6{x^5}\sin ({x^6})}}{{12{x^{11}}}} = \frac{{\sin ({x^6})}}{{2{x^6}}}\) <strong><em>A1A1</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>EITHER</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;">\(\frac{{g'(0)}}{{h'(0)}} = \frac{0}{0}\), using l’Hôpital’s Rule again, <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;">\(\frac{{g''(x)}}{{h''(x)}} = \frac{{6{x^5}\cos ({x^6})}}{{12{x^5}}} = \frac{{\cos ({x^6})}}{2}\) <strong><em>A1A1</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;">\(\frac{{g''(0)}}{{h''(0)}} = \frac{1}{2}\), hence the limit is \(\frac{1}{2}\) <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;"><strong>OR</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 \(\mathop {\lim }\limits_{x \to 0} \frac{{1 - \cos {x^6}}}{{{x^{12}}}} = \mathop {\lim }\limits_{x \to 0} \frac{{\sin {x^6}}}{{2{x^6}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0px 0px 0px 30px; font: 30px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{2}\mathop {\lim }\limits_{x \to 0} \frac{{\sin {x^6}}}{{2{x^6}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0px 0px 0px 30px; font: 30px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{2}{\text{ since }}\mathop {\lim }\limits_{x \to 0} \frac{{\sin {x^6}}}{{2{x^6}}} = 1\) <strong><em>A1 (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>METHOD 2</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;">substituting \({{x^6}}\) for <em>x</em> in the expansion \(\cos x = 1 - \frac{{{x^2}}}{2} + \frac{{{x^4}}}{{24}} \ldots \) <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;">\(\frac{{1 - \cos {x^6}}}{{{x^{12}}}} = \frac{{1 - \left( {1 - \frac{{{x^{12}}}}{2} + \frac{{{x^{24}}}}{{24}}} \right) \ldots }}{{{x^{12}}}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0px 0px 0px 30px; font: 30px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{2} - \frac{{{x^{12}}}}{{24}} + ...\) <em><strong>A1A1</strong></em><br></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;">\(\mathop {\lim }\limits_{x \to 0} \frac{{1 - \cos {x^6}}}{{{x^{12}}}} = \frac{1}{2}\) <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;"><strong>Note:</strong> Accept solutions using Maclaurin expansions.</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>[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;">Surprisingly, some weaker candidates were more successful in answering this question than stronger candidates. If candidates failed to simplify the expression after the first application of L’Hôpital’s rule, they generally were not successful in correctly differentiating the expression a \({2^{{\text{nd}}}}\) time, hence could not achieve the final three A marks.</span></p>
</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) Given that \(y = \ln \cos x\) , show that the first two non-zero terms of the Maclaurin series for <em>y </em>are \( - \frac{{{x^2}}}{2} - \frac{{{x^4}}}{{12}}\).</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) Use this series to find an approximation in terms of \(\pi {\text{ for }}\ln 2\) .</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: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \(f(x) = \ln \cos x\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(x) = \frac{{ - \sin x}}{{\cos x}} = - \tan x\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f''(x) = - {\sec ^2}x\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'''(x) = - 2\sec x\sec x\tan x\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({f^{iv}}(x) = - 2{\sec ^2}x({\sec ^2}x) - 2\tan x(2{\sec ^2}x\tan x)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = - 2{\sec ^4}x - 4{\sec ^2}x{\tan ^2}x\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(x) = f(0) + xf'(0) + \frac{{{x^2}}}{{2!}}f''(0) + \frac{{{x^3}}}{{3!}}f'''(0) + \frac{{{x^4}}}{{4!}}{f^{iv}}(0) + …\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(0) = 0,\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(0) = 0,\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f''(0) = - 1,\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'''(0) = 0,\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({f^{iv}}(0) = - 2,\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Notes: </strong>Award the <strong><em>A1 </em></strong>if all the substitutions are correct.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Allow <strong><em>FT </em></strong>from their derivatives.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px 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: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\ln (\cos x) \approx - \frac{{{x^2}}}{{2!}} - \frac{{2{x^4}}}{{4!}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = - \frac{{{x^2}}}{2} - \frac{{{x^4}}}{{12}}\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[8 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px 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: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Some consideration of the manipulation of ln 2 <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Attempt to find an angle <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px 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: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Taking \(x = \frac{\pi }{3}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\ln \frac{1}{2} \approx - \frac{{{{\left( {\frac{\pi }{3}} \right)}^2}}}{{2!}} - \frac{{2{{\left( {\frac{\pi }{3}} \right)}^4}}}{{4!}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( - \ln 2 \approx - \frac{{\frac{{{\pi ^2}}}{9}}}{{2!}} - \frac{{2\frac{{{\pi ^4}}}{{81}}}}{{4!}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\ln 2 \approx \frac{{{\pi ^2}}}{{18}} + \frac{{{\pi ^4}}}{{972}} = \frac{{{\pi ^2}}}{9}\left( {\frac{1}{2} + \frac{{{\pi ^2}}}{{108}}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px 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: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Taking \(x = \frac{\pi }{4}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\ln \frac{1}{{\sqrt 2 }} \approx - \frac{{{{\left( {\frac{\pi }{4}} \right)}^2}}}{{2!}} - \frac{{2{{\left( {\frac{\pi }{4}} \right)}^4}}}{{4!}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( - \frac{1}{2}\ln 2 \approx - \frac{{\frac{{{\pi ^2}}}{{16}}}}{{2!}} - \frac{{2\frac{{{\pi ^4}}}{{256}}}}{{4!}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\ln 2 \approx \frac{{{\pi ^2}}}{{16}} + \frac{{{\pi ^4}}}{{1536}} = \frac{{{\pi ^2}}}{8}\left( {\frac{1}{2} + \frac{{{\pi ^2}}}{{192}}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px 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: 28.5px 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: 24.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Some candidates had difficulty organizing the derivatives but most were successful in getting the series. Using the series to find the approximation for \(\ln 2\) in terms of \(\pi \) was another story and it was rare to see a good solution.</span></p>
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<br><hr><br><div class="specification">
<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;">Consider the differential equation \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = {x^2} + {y^2}\) where <em>y</em> =1 when <em>x</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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Use Euler’s method with step length 0.1 to find an approximate value of <em>y</em> when <em>x</em> = 0.4.</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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Write down, giving a reason, whether your approximate value for <em>y</em> is greater than or less than the actual value of <em>y</em> .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p 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;">use of \(y \to y + h\frac{{{\text{d}}y}}{{{\text{d}}x}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px 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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">approximate value of <em>y</em> = 1.57 <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> Accept values in the tables correct to 3 significant figures.</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 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: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the approximate value is less than the actual value because it is assumed that \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) remains constant throughout each interval whereas it is actually an increasing function <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>[1 mark]</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;">Most candidates were familiar with Euler’s method. The most common way of losing marks was either to round intermediate answers to insufficient accuracy or simply to make an arithmetic error. Many candidates were given an accuracy penalty for not rounding their answer to three significant figures. Few candidates were able to answer (b) correctly with most believing incorrectly that the step length was a relevant factor.</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;">Most candidates were familiar with Euler’s method. The most common way of losing marks was either to round intermediate answers to insufficient accuracy or simply to make an arithmetic error. Many candidates were given an accuracy penalty for not rounding their answer to three significant figures. Few candidates were able to answer (b) correctly with most believing incorrectly that the step length was a relevant factor.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function \(f(x) = \sin (p\arcsin x),{\text{ }} - 1 < x < 1\) and \(p \in \mathbb{R}\).</p>
</div>
<div class="specification">
<p>The function \(f\) and its derivatives satisfy</p>
<p style="text-align: center;">\((1 - {x^2}){f^{(n + 2)}}(x) - (2n + 1)x{f^{(n + 1)}}(x) + ({p^2} - {n^2}){f^{(n)}}(x) = 0,{\text{ }}n \in \mathbb{N}\)</p>
<p>where \({f^{(n)}}(x)\) denotes the \(n\) th derivative of \(f(x)\) and \({f^{(0)}}(x)\) is \(f(x)\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that \(f’(0) = p\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that \({f^{(n + 2)}}(0) = ({n^2} - {p^2}){f^{(n)}}(0)\).</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>For \(p \in \mathbb{R}\backslash \{ \pm 1,{\text{ }} \pm 3\} \), show that the Maclaurin series for \(f(x)\), up to and including the \({x^5}\) term, is</p>
<p style="text-align: center;">\(px + \frac{{p(1 - {p^2})}}{{3!}}{x^3} + \frac{{p(9 - {p^2})(1 - {p^2})}}{{5!}}{x^5}\).</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>Hence or otherwise, find \(\mathop {\lim }\limits_{x \to 0} \frac{{\sin (p\arcsin x)}}{x}\).</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>If \(p\) is an odd integer, prove that the Maclaurin series for \(f(x)\) is a polynomial of degree \(p\).</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>\(f’(x) = \frac{{p\cos (p\arcsin x)}}{{\sqrt {1 - {x^2}} }}\) <strong><em>(M1)A1</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>\(f’(0) = p\) <strong><em>AG</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p>\({f^{(n + 2)}}(0) + ({p^2} - {n^2}){f^{(n)}}(0) = 0\) <strong><em>A1</em></strong></p>
<p><strong>OR</strong></p>
<p>for <em>eg</em>, \((1 - {x^2}){f^{(n + 2)}}(x) = (2n + 1)x{f^{(n + 1)}}(x) - ({p^2} - {n^2}){f^{(n)}}(x)\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>A1 </em></strong>for <em>eg</em>, \((1 - {x^2}){f^{(n + 2)}}(x) - (2n + 1)x{f^{(n + 1)}}(x) = - ({p^2} - {n^2}){f^{(n)}}(x)\).</p>
<p> </p>
<p><strong>THEN</strong></p>
<p>\({f^{(n + 2)}}(0) = ({n^2} - {p^2}){f^{(n)}}(0)\) <strong><em>AG</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>considering \(f\) and its derivatives at \(x = 0\) <strong><em>(M1)</em></strong></p>
<p>\(f(0) = 0\) and \(f’(0) = p\) from (a) <strong><em>A1</em></strong></p>
<p>\(f’’(0) = 0,{\text{ }}{f^{(4)}}(0) = 0\) <strong><em>A1</em></strong></p>
<p>\({f^{(3)}}(0) = (1 - {p^2}){f^{(1)}}(0) = (1 - {p^2})p\),</p>
<p>\({f^{(5)}}(0) = (9 - {p^2}){f^{(3)}}(0) = (9 - {p^2})(1 - {p^2})p\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Only award the last <strong><em>A1</em></strong> if either \({f^{(3)}}(0) = (1 - {p^2}){f^{(1)}}(0)\) and \({f^{(5)}}(0) = (9 - {p^2}){f^{(3)}}(0)\) have been stated or the general Maclaurin series has been stated and used.</p>
<p> </p>
<p>\(px + \frac{{p(1 - {p^2})}}{{3!}}{x^3} + \frac{{p(9 - {p^2})(1 - {p^2})}}{{5!}}{x^5}\) <strong><em>AG</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><strong>METHOD 1</strong></p>
<p>\(\mathop {\lim }\limits_{x \to 0} \frac{{\sin (p\arcsin x)}}{x} = \mathop {\lim }\limits_{x \to 0} \frac{{px + \frac{{p(1 - {p^2})}}{{3!}}{x^3} + \ldots }}{3}\) <strong><em>M1</em></strong></p>
<p>\( = p\) <strong><em>A1</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>by l’Hôpital’s rule \(\mathop {\lim }\limits_{x \to 0} \frac{{\sin (p\arcsin x)}}{x} = \mathop {\lim }\limits_{x \to 0} \frac{{p\cos (p\arcsin x)}}{{\sqrt {1 - {x^2}} }}\) <strong><em>M1</em></strong></p>
<p>\( = p\) <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>the coefficients of all even powers of \(x\) are zero <strong><em>A1</em></strong></p>
<p>the coefficient of \({x^p}\) for (\(p\) odd) is non-zero (or equivalent <em>eg</em>,</p>
<p>the coefficients of all odd powers of \(x\) up to \(p\) are non-zero) <strong><em>A1</em></strong></p>
<p>\({f^{(p + 2)}}(0) = ({p^2} - {p^2}){f^{(p)}}(0) = 0\) and so the coefficient of \({x^{p + 2}}\) is zero <strong><em>A1</em></strong></p>
<p>the coefficients of all odd powers of \(x\) greater than \(p + 2\) are zero (or equivalent) <strong><em>A1</em></strong></p>
<p>so the Maclaurin series for \(f(x)\) is a polynomial of degree \(p\) <strong><em>AG</em></strong></p>
<p><strong><em>[4 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;">
[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="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that \(n > {\text{ln}}\,n\) for \(n > 0\), use the comparison test to show that the series \(\sum\limits_{n = 0}^\infty {\frac{1}{{{\text{ln}}\left( {n + 2} \right)}}} \) is divergent.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the interval of convergence for \(\sum\limits_{n = 0}^\infty {\frac{{{{\left( {3x} \right)}^n}}}{{{\text{ln}}\left( {n + 2} \right)}}} \).</p>
<div class="marks">[7]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>\({\text{ln}}\left( {n + 2} \right) < n + 2\) <em><strong>(A1)</strong></em></p>
<p>\( \Rightarrow \frac{1}{{{\text{ln}}\left( {n + 2} \right)}} > \frac{1}{{n + 2}}\) (for \(n \geqslant 0\)) <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Award A0 for statements such as \(\sum\limits_{n = 0}^\infty {\frac{1}{{{\text{ln}}\left( {n + 2} \right)}}} > \sum\limits_{n = 0}^\infty {\frac{1}{{n + 2}}} \). However condone such a statement if the above <em><strong>A1</strong> </em>has already been awarded.</p>
<p>\(\sum\limits_{n = 0}^\infty {\frac{1}{{n + 2}}} \) (is a harmonic series which) diverges <em><strong>R1</strong></em></p>
<p><strong>Note:</strong> The <em><strong>R1</strong> </em>is independent of the <em><strong>A1</strong></em>s.</p>
<p>Award <em><strong>R0</strong> </em>for statements such as "\(\frac{1}{{n + 2}}\) diverges".</p>
<p>so \(\sum\limits_{n = 0}^\infty {\frac{1}{{{\text{ln}}\left( {n + 2} \right)}}} \) diverges by the comparison test <em><strong>AG</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>\(\frac{1}{{{\text{ln}}\,n}} > \frac{1}{n}\) (for \(n \geqslant 2\)) <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>A0</strong></em> for statements such as \(\sum\limits_{n = 2}^\infty {\frac{1}{{{\text{ln}}\,n}}} > \sum\limits_{n = 2}^\infty {\frac{1}{n}} \). However condone such a statement if the above <em><strong>A1</strong> </em>has already been awarded.</p>
<p>a correct statement linking \(n\) and \(n + 2\) <em>eg</em>,</p>
<p>\(\sum\limits_{n = 0}^\infty {\frac{1}{{{\text{ln}}\left( {n + 2} \right)}}} = \sum\limits_{n = 2}^\infty {\frac{1}{{{\text{ln}}\,n}}} \) or \(\sum\limits_{n = 0}^\infty {\frac{1}{{n + 2}}} = \sum\limits_{n = 2}^\infty {\frac{1}{n}} \) <strong>A1</strong></p>
<p><strong>Note:</strong> Award <em><strong>A0</strong> </em>for \(\sum\limits_{n = 0}^\infty {\frac{1}{n}} \)</p>
<p>\(\sum\limits_{n = 2}^\infty {\frac{1}{n}} \) (is a harmonic series which) diverges</p>
<p>(which implies that \(\sum\limits_{n = 2}^\infty {\frac{1}{{{\text{ln}}\,n}}} \) diverges by the comparison test) <em><strong>R1</strong></em></p>
<p><strong>Note:</strong> The <em><strong>R1</strong> </em>is independent of the <em><strong>A1</strong></em>s.</p>
<p>Award <em><strong>R0</strong> </em>for statements such as \(\sum\limits_{n = 0}^\infty {\frac{1}{n}} \) deiverges and "\({\frac{1}{n}}\) diverges".</p>
<p>Award <em><strong>A1A0R1</strong> </em>for arguments based on \(\sum\limits_{n = 1}^\infty {\frac{1}{n}} \).</p>
<p>so \(\sum\limits_{n = 0}^\infty {\frac{1}{{{\text{ln}}\left( {n + 2} \right)}}} \) diverges by the comparison test <em><strong>AG</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>applying the ratio test \(\mathop {{\text{lim}}}\limits_{n \to \infty } \left| {\frac{{{{\left( {3x} \right)}^{n + 1}}}}{{{\text{ln}}\left( {n + 3} \right)}} \times \frac{{{\text{ln}}\left( {n + 2} \right)}}{{{{\left( {3x} \right)}^n}}}} \right|\) <em><strong>M1</strong></em></p>
<p>\( = \left| {3x} \right|\) (as \(\mathop {{\text{lim}}}\limits_{n \to \infty } \left| {\frac{{{\text{ln}}\left( {n + 2} \right)}}{{{\text{ln}}\left( {n + 3} \right)}}} \right| = 1\) <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Condone the absence of limits and modulus signs.</p>
<p><strong>Note:</strong> Award <em><strong>M1A0</strong> </em>for \(3{x^n}\). Subsequent marks can be awarded.</p>
<p>series converges for \( - \frac{1}{3} < x < \frac{1}{3}\)</p>
<p>considering \(x = - \frac{1}{3}\) and \(x = \frac{1}{3}\) <em><strong>M1</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>M1</strong> </em>to candidates who consider one endpoint.</p>
<p>when \(x = \frac{1}{3}\), series is \(\sum\limits_{n = 0}^\infty {\frac{1}{{{\text{ln}}\left( {n + 2} \right)}}} \) which is divergent (from (a)) <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Award this <em><strong>A1</strong> </em>if \(\sum\limits_{n = 0}^\infty {\frac{1}{{{\text{ln}}\left( {n + 2} \right)}}} \) is not stated but reference to part (a) is.</p>
<p>when \(x = - \frac{1}{3}\), series is \(\sum\limits_{n = 0}^\infty {\frac{{{{\left( { - 1} \right)}^n}}}{{{\text{ln}}\left( {n + 2} \right)}}} \) <em><strong>A1</strong></em></p>
<p>\(\sum\limits_{n = 0}^\infty {\frac{{{{\left( { - 1} \right)}^n}}}{{{\text{ln}}\left( {n + 2} \right)}}} \) converges (conditionally) by the alternating series test <em><strong>R1</strong></em></p>
<p>(strictly alternating, \(\left| {{u_n}} \right| > \left| {{u_{n + 1}}} \right|\) for \(n \geqslant 0\) and \(\mathop {{\text{lim}}}\limits_{n \to \infty } \left( {{u_n}} \right) = 0\))</p>
<p>so the interval of convergence of <em>S</em> is \( - \frac{1}{3} \leqslant x < \frac{1}{3}\) <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> The final <em><strong>A1</strong> </em>is dependent on previous <em><strong>A1</strong></em>s – <em>ie</em>, considering correct series when \(x = - \frac{1}{3}\) and \(x = \frac{1}{3}\) and on the final <em><strong>R1</strong></em>.</p>
<p>Award as above to candidates who firstly consider \(x = - \frac{1}{3}\) and then state conditional convergence implies divergence at \(x = \frac{1}{3}\).</p>
<p><em><strong>[7 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>Let the Maclaurin series for \(\tan x\) be</p>
<p>\[\tan x = {a_1}x + {a_3}{x^3} + {a_5}{x^5} + \ldots \]</p>
<p>where \({a_1}\), \({a_3}\) and \({a_5}\) are constants.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find series for \({\sec ^2}x\), in terms of \({a_1}\), \({a_3}\) and \({a_5}\), up to and including the \({x^4}\) term</p>
<p>by differentiating the above series for \(\tan x\);</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find series for \({\sec ^2}x\), in terms of \({a_1}\), \({a_3}\) and \({a_5}\), up to and including the \({x^4}\) term</p>
<p>by using the relationship \({\sec ^2}x = 1 + {\tan ^2}x\).</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>Hence, by comparing your two series, determine the values of \({a_1}\), \({a_3}\) and \({a_5}\).</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>\(({\sec ^2}x = ){\text{ }}{a_1} + 3{a_3}{x^2} + 5{a_5}{x^4} + \ldots \) <strong><em>A1</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\({\sec ^2}x = 1 + {({a_1}x + {a_3}{x^3} + {a_5}{x^5} + \ldots )^2}\)</p>
<p>\( = 1 + a_1^2{x^2} + 2{a_1}{a_3}{x^4} + \ldots \) <strong><em>M1A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Condone the presence of terms with powers greater than four.</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>equating constant terms: \({a_1} = 1\) <strong><em>A1</em></strong></p>
<p>equating \({x^2}\) terms: \(3{a_3} = a_1^2 = 1 \Rightarrow {a_3} = \frac{1}{3}\) <strong><em>A1</em></strong></p>
<p>equating \({x^4}\) terms: \(5{a_5} = 2{a_1}{a_3} = \frac{2}{3} \Rightarrow {a_5} = \frac{2}{{15}}\) <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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider the differential equation \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{x}{y} - xy\) where \(y > 0\) and \(y = 2\) when \(x = 0\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">Show that putting \(z = {y^2}\) </span>transforms the differential equation into \(\frac{{{\text{d}}z}}{{{\text{d}}x}} + 2xz = 2x\).</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">By solving this differential equation in \(z\)<span class="s1">, obtain an expression for </span>\(y\) <span class="s1">in terms of </span>\(x\).</p>
<div class="marks">[9]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>METHOD 1</strong></p>
<p class="p1">\(z = {y^2} \Rightarrow y = {z^{1/2}}\)</p>
<p class="p1"><span class="Apple-converted-space">\( \Rightarrow \frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{1}{{2{z^{1/2}}}}\frac{{{\text{d}}z}}{{{\text{d}}x}}\) </span><strong><em>M1A1</em></strong></p>
<p class="p1">substituting, \(\frac{1}{{2{z^{1/2}}}}\frac{{{\text{d}}z}}{{{\text{d}}x}} = \frac{x}{{{z^{1/2}}}} - x{z^{1/2}}\) <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\(\frac{{{\text{d}}z}}{{{\text{d}}x}} + 2xz = 2x\) </span><span class="s1"><strong><em>AG</em></strong></span></p>
<p class="p1"><strong>METHOD 2</strong></p>
<p class="p1">\(z = {y^2}\)</p>
<p class="p1"><span class="Apple-converted-space">\(\frac{{{\text{d}}z}}{{{\text{d}}x}} = 2y\frac{{{\text{d}}y}}{{{\text{d}}x}}\) </span><strong><em>M1A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(\frac{{{\text{d}}z}}{{{\text{d}}x}} = 2x - 2x{y^2}\) </span><strong><em>M1A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(\frac{{{\text{d}}z}}{{{\text{d}}x}} = 2xz = 2x\) </span><strong><em>AG</em></strong></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>METHOD 1</strong></p>
<p class="p1">integrating factor \( = {{\text{e}}^{\int {2x{\text{d}}x} }} = {{\text{e}}^{{x^2}}}\) <span class="Apple-converted-space"> </span><strong><em>(M1)A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\({{\text{e}}^{{x^2}}}\frac{{{\text{d}}z}}{{{\text{d}}x}} + 2x{{\text{e}}^{{x^2}}}z = 2x{{\text{e}}^{{x^2}}}\) </span><strong><em>(M1)</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\(z{{\text{e}}^{{x^2}}} = \int {2x{{\text{e}}^{{x^2}}}{\text{d}}x} \) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p3"><span class="Apple-converted-space">\( = {{\text{e}}^{{x^2}}} + C\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1">substitute \(y = 2\) therefore \(z = 4\) when \(x = 0\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p3">\(4 = 1 + C\)</p>
<p class="p3"><span class="Apple-converted-space">\(C = 3\) </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p1">the solution is \(z = 1 + 3{{\text{e}}^{ - {x^2}}}\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p4"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>This line may be seen before determining the value of \(C\).</p>
<p class="p4"> </p>
<p class="p1">so that \(y = \sqrt {1 + 3{{\text{e}}^{ - {x^2}}}} \) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p5"><strong>METHOD 2</strong></p>
<p class="p6">\(\frac{{{\text{d}}z}}{{{\text{d}}x}} = 2x(1 - z)\)</p>
<p class="p6"><span class="Apple-converted-space">\(\int {\frac{1}{{1 - z}}{\text{d}}z = \int {2x{\text{d}}x} } \) </span><span class="s2"><strong><em>M1</em></strong></span></p>
<p class="p6"><span class="Apple-converted-space">\( - \ln (1 - z) = {x^2} + C\) </span><span class="s2"><strong><em>A1A1</em></strong></span></p>
<p class="p7">\(1 - z = {{\text{e}}^{ - {x^2} - c}}\) (or \(1 - z = B{{\text{e}}^{ - {x^2}}}\)) <strong><em>M1A1</em></strong></p>
<p class="p5">solving for \(z\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p7">\(z = 1 + A{{\text{e}}^{ - {x^2}}}\)</p>
<p class="p5"><span class="s3">\(z = 4\) </span>when \(x = 0\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p5">so \(A = 3\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p5">the solution is \(z = 1 + 3{{\text{e}}^{ - {x^2}}}\)</p>
<p class="p5">so \(y = \sqrt {1 + 3{{\text{e}}^{ - {x^2}}}} \) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p5"><strong><em>[9 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">Several misconceptions were identified that showed poor understanding of the chain rule. Although many candidates were successful in establishing the result the presentation of their work was far from what is expected in a show that question.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Part (b) was well attempted using both method 1 (integration factor) and 2 (separation of variables). The most common error was omission of the constant of integration or errors in finding its value. Candidates that used method 2 often had difficulties in integrating \(\frac{1}{{(1 - z)}}\) correctly and making \(z\) the subject often losing out on accuracy marks.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider the infinite spiral of right angle triangles as shown in the following diagram.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2017-03-01_om_17.00.25.png" alt="N16/5/MATHL/HP3/ENG/TZ0/SE/03b"></p>
<p class="p1">The \(n{\text{th}}\) triangle in the spiral has central angle \({\theta _n}\), hypotenuse of length \({a_n}\) and opposite side of length <span class="s1">1</span>, as shown in the diagram. The first right angle triangle is isosceles with the two equal sides being of length <span class="s1">1</span>.</p>
</div>
<div class="specification">
<p class="p1">Consider the series \(\sum\limits_{n = 1}^\infty {{\theta _n}} \).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Using l’Hôpital’s rule, find \(\mathop {\lim }\limits_{x \to \infty } \left( {\frac{{\arcsin \left( {\frac{1}{{\sqrt {(x + 1)} }}} \right)}}{{\frac{1}{{\sqrt x }}}}} \right)\).</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 class="p1">(i) Find \({a_1}\) and \({a_2}\) and hence write down an expression for \({a_n}\).</p>
<p class="p1">(ii) Show that \({\theta _n} = \arcsin \frac{1}{{\sqrt {(n + 1)} }}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Using a suitable test, determine whether this series converges or diverges.</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"><span class="s1">\(\mathop {\lim }\limits_{x \to \infty } \left( {\frac{{\arcsin \left( {\frac{1}{{\sqrt {(x + 1)} }}} \right)}}{{\frac{1}{{\sqrt x }}}}} \right)\) </span>is of the form \(\frac{0}{0}\)</p>
<p class="p1">and so will equal the limit of \(\frac{{\frac{{\frac{{ - 1}}{2}{{(x + 1)}^{ - \frac{3}{2}}}}}{{\sqrt {1 - \left( {\frac{1}{{x + 1}}} \right)} }}}}{{\frac{{ - 1}}{2}{x^{ - \frac{3}{2}}}}}\)<span class="s1"> <span class="Apple-converted-space"> </span></span><strong><em>M1M1A1A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <em>M1 </em></strong>for attempting differentiation of the top and bottom, <strong><em>M1A1 </em></strong>for derivative of top (only award <strong><em>M1 </em></strong>if chain rule is used), <strong><em>A1 </em></strong>for derivative of bottom.</p>
<p class="p2"> </p>
<p class="p3"><span class="Apple-converted-space">\( = \mathop {\lim }\limits_{x \to \infty } \frac{{{{\left( {\frac{x}{{(x + 1)}}} \right)}^{\frac{3}{2}}}}}{{\sqrt {\frac{x}{{x + 1}}} }} = \mathop {\lim }\limits_{x \to \infty } \left( {\frac{x}{{x + 1}}} \right)\) </span><span class="s2"><strong><em>M1</em></strong></span></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: </strong>Accept any intermediate tidying up of correct derivative for the method mark.</p>
<p class="p2"> </p>
<p class="p3"><span class="Apple-converted-space">\( = 1\) </span><span class="s2"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong><em>[6 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"> \({a_1} = \sqrt 2 ,{\text{ }}{a_2} = \sqrt 3 \)</span> <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\({a_n} = \sqrt {n + 1} \) </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="s1">(ii) <span class="Apple-converted-space"> \(\sin {\theta _n} = \frac{1}{{{a_n}}} = \frac{1}{{\sqrt {n + 1} }}\)</span></span> <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: </strong><span class="s1">Allow \({\theta _n} = \arcsin \left( {\frac{1}{{{a_n}}}} \right)\)</span> if \({a_n} = \sqrt {n + 1} \) <span class="s1">in b(i).</span></p>
<p class="p3"> </p>
<p class="p1"><span class="s1">so \({\theta _n} = \arcsin \frac{1}{{\sqrt {(n + 1)} }}\)</span> <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 class="p1">for \(\sum\limits_{n = 1}^\infty {\arcsin \frac{1}{{\sqrt {(n + 1)} }}} \) apply the limit comparison test (since both series of positive terms) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">with \(\sum\limits_{n = 1}^\infty {\frac{1}{{\sqrt n }}} \) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="s1">from (a) \(\mathop {\lim }\limits_{n \to \infty } \frac{{\arcsin \frac{1}{{\sqrt {(n + 1)} }}}}{{\frac{1}{{\sqrt n }}}} = 1\)</span>, so the two series either both converge or both diverge <span class="Apple-converted-space"> </span><strong><em>M1R1</em></strong></p>
<p class="p1">\(\sum\limits_{n = 1}^\infty {\frac{1}{{\sqrt 2 }}} \) diverges (as is a \(p\)<span class="s1">-series with \(p = \frac{1}{2}\)</span>) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">hence \(\sum\limits_{n = 1}^\infty {{\theta _n}} \) diverges <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[6 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-size: medium; font-family: 'times new roman', times;">The sequence \(\{ {u_n}\} \) is defined by \({u_n} = \frac{{3n + 2}}{{2n - 1}}\), for \(n \in {\mathbb{Z}^ + }\).</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;">Show that the sequence converges to a limit <em>L </em>, the value of which should be stated.</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: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the least value of the integer <em>N </em>such that \(\left| {{u_n} - L} \right| < \varepsilon \)<span style="font: 12.5px Helvetica;"> </span>, for all <em>n </em>> <em>N </em>where</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;">(i) \(\varepsilon = 0.1\);</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) \(\varepsilon = 0.00001\).</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 Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">For each of the sequences \(\left\{ {\frac{{{u_n}}}{n}} \right\},{\text{ }}\left\{ {\frac{1}{{2{u_n} - 2}}} \right\}\) and \(\left\{ {{{( - 1)}^n}{u_n}} \right\}\) , determine whether or not it converges.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p 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;">Prove that the series \(\sum\limits_{n = 1}^\infty {({u_n} - L)} \) diverges.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p 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;">\({u_n} = \frac{{3 + \frac{2}{n}}}{{2 - \frac{1}{n}}}\) or \(\frac{3}{2} + \frac{A}{{2n - 1}}\) <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;">using \(\mathop {\lim }\limits_{n \to \infty } \frac{1}{n} = 0\) <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;">obtain \(\mathop {\lim }\limits_{n \to \infty } {u_n} = \frac{3}{2} = L\) <strong><em>A1 N1</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;">[3 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;">\({u_n} - L = \frac{7}{{2(2n - 1)}}\) <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;">\(\left| {{u_n} - L} \right| < \varepsilon \Rightarrow n > \frac{1}{2}\left( {1 + \frac{7}{{2\varepsilon }}} \right)\) <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;"><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;">(i) \(\varepsilon = 0.1 \Rightarrow N = 18\) <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> </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) \(\varepsilon = 0.00001 \Rightarrow N = 175000\) <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;">[4 marks]</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;">\({u_n} \to L\) and \(\frac{1}{n} \to 0\) <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;">\( \Rightarrow \frac{{{u_n}}}{n} \to (L \times 0) = 0\) , hence converges <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;">\(2{u_n} - 2 \to 2L - 2 = 1 \Rightarrow \frac{1}{{2{u_n} - 2}} \to 1\) , hence converges <strong><em>M1A1</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>To award <strong><em>A1 </em></strong>the value of the limit and a statement of convergence must be clearly seen for each sequence.</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;">\({( - 1)^n}{u_n}\) does not converge <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;">The sequence alternates (or equivalent wording) between values close to \( \pm L\) <strong><em>R1</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;">[6 marks]</span><br></em></strong></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: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\({u_n} - L > \frac{7}{{4n}}\) (re: harmonic sequence) <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;">\( \Rightarrow \sum\limits_{n = 1}^\infty {({u_n} - L)} \) diverges by the comparison theorem <strong><em>R1</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>Accept alternative methods.</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;"><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">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;">The “show that” in part (a) of this problem was not adequately dealt with by a significant minority of candidates and simply stating the limit and not demonstrating its existence lost marks. Part (b), whilst being possible without significant knowledge of limits, seemed to intimidate some candidates due to its unfamiliarity and the notation. Part (c) was somewhat disappointing as many candidates attempted to apply rules on the convergence of series to solve a problem that was dealing with the limits of sequences. The same confusion was seen on part (d) where also some errors in algebra prevented candidates from achieving full marks. </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"> </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;">The “show that” in part (a) of this problem was not adequately dealt with by a significant minority of candidates and simply stating the limit and not demonstrating its existence lost marks. Part (b), whilst being possible without significant knowledge of limits, seemed to intimidate some candidates due to its unfamiliarity and the notation. Part (c) was somewhat disappointing as many candidates attempted to apply rules on the convergence of series to solve a problem that was dealing with the limits of sequences. The same confusion was seen on part (d) where also some errors in algebra prevented candidates from achieving full marks.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">The “show that” in part (a) of this problem was not adequately dealt with by a significant minority of candidates and simply stating the limit and not demonstrating its existence lost marks. Part (b), whilst being possible without significant knowledge of limits, seemed to intimidate some candidates due to its unfamiliarity and the notation. Part (c) was somewhat disappointing as many candidates attempted to apply rules on the convergence of series to solve a problem that was dealing with the limits of sequences. The same confusion was seen on part (d) where also some errors in algebra prevented candidates from achieving full marks.</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;">The “show that” in part (a) of this problem was not adequately dealt with by a significant minority of candidates and simply stating the limit and not demonstrating its existence lost marks. Part (b), whilst being possible without significant knowledge of limits, seemed to intimidate some candidates due to its unfamiliarity and the notation. Part (c) was somewhat disappointing as many candidates attempted to apply rules on the convergence of series to solve a problem that was dealing with the limits of sequences. The same confusion was seen on part (d) where also some errors in algebra prevented candidates from achieving full marks.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<p>The function \(f\) is defined by</p>
<p>\[f(x) = \left\{ {\begin{array}{*{20}{l}} {{x^2} - 2,}&{x < 1} \\ {ax + b,}&{x \geqslant 1} \end{array}} \right.\]</p>
<p>where \(a\) and \(b\) are real constants.</p>
<p>Given that both \(f\) and its derivative are continuous at \(x = 1\), find the value of \(a\) and the value of \(b\).</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>considering continuity \(\mathop {\lim }\limits_{x \to {1^ - }} ({x^2} - 2) = - 1\) <strong><em>(M1)</em></strong></p>
<p>\(a + b = - 1\) <strong><em>(A1)</em></strong></p>
<p>considering differentiability \(2x = a\) when \(x = 1\) <strong><em>(M1)</em></strong></p>
<p>\( \Rightarrow a = 2\) <strong><em>A1</em></strong></p>
<p>\(b = - 3\) <strong><em>A1</em></strong></p>
<p><strong><em>[5 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"><span class="s1">Let \(f(x)\) </span>be a function whose first and second derivatives both exist on the closed interval \([0,{\text{ }}h]\).</p>
<p class="p2">Let \(g(x) = f(h) - f(x) - (h - x)f'(x) - \frac{{{{(h - x)}^2}}}{{{h^2}}}\left( {f(h) - f(0) - hf'(0)} \right)\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">State the mean value theorem for a function that is continuous on the closed interval \([a,{\text{ }}b]\) and differentiable on the open interval \(]a,{\text{ }}b[\).</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 \(g(0)\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Find \(g(h)\).</p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>Apply the mean value theorem to the function \(g(x)\) <span class="s1">on the closed interval \([0,{\text{ }}h]\)</span> to show that there exists \(c\) <span class="s1">in the open interval \(]0,{\text{ }}h[\) </span>such that \(g'(c) = 0\).</p>
<p class="p1">(iv) <span class="Apple-converted-space"> </span>Find \(g'(x)\).</p>
<p class="p2">(v) <span class="Apple-converted-space"> </span>Hence show that \( - (h - c)f''(c) + \frac{{2(h - c)}}{{{h^2}}}\left( {f(h) - f(0) - hf'(0)} \right) = 0\).</p>
<p class="p1">(vi) <span class="Apple-converted-space"> </span>Deduce that \(f(h) = f(0) + hf'(0) + \frac{{{h^2}}}{2}{\text{ }}f''(c)\).</p>
<div class="marks">[9]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Hence show that, for \(h > 0\)</p>
<p class="p1">\(1 - \cos (h) \leqslant \frac{{{h^2}}}{2}\).</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 class="p1">there exists \(c\) in the open interval \(]a,{\text{ }}b[\) such that <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(\frac{{f(b) - f(a)}}{{b - a}} = f'(c)\) </span><strong><em>A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: </strong>Open interval is required for the <strong><em>A1</em></strong>.</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">(i) <span class="Apple-converted-space"> \(g(0) = f(h) - f(0) - hf'(0) - \frac{{{h^2}}}{{{h^2}}}\left( {{\text{ }}f(h) - f(0) - hf'(0)} \right)\)</span></p>
<p class="p1"><span class="Apple-converted-space">\( = 0\) </span><strong><em>A1</em></strong></p>
<p class="p1">(ii) <span class="Apple-converted-space"> \(g(h) = f(h) - f(h) - 0 - 0\)</span></p>
<p class="p1"><span class="Apple-converted-space">\( = 0\) </span><strong><em>A1</em></strong></p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>(\(g(x)\) is a differentiable function since it is a combination of other differentiable functions \(f\), \({f'}\) and polynomials.)</p>
<p class="p1">there exists \(c\) in the open interval \(]0,{\text{ }}h[\) such that</p>
<p class="p1"><span class="Apple-converted-space">\(\frac{{g(h) - g(0)}}{h} = g'(c)\) </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(\frac{{g(h) - g(0)}}{h} = 0\) </span><strong><em>A1</em></strong></p>
<p class="p1">hence \(g'(c) = 0\) <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p1">(iv) <span class="Apple-converted-space"> \(g'(x) = - f'(x) + f'(x) - (h - x)f''(x) + \frac{{2(h - x)}}{{{h^2}}}\left( {f(h) - f(0) - hf'(0)} \right)\)</span> <span class="Apple-converted-space"> </span><strong><em>A1A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <em>A1 </em></strong>for the second and third terms and <strong><em>A1 </em></strong>for the other terms (all terms must be seen).</p>
<p class="p2"> </p>
<p class="p1">\( = - (h - x)f''(x) + \frac{{2(h - x)}}{{{h^2}}}\left( {f(h) - f(0) - hf'(0)} \right)\)</p>
<p class="p1">(v) <span class="Apple-converted-space"> </span>putting \(x = c\) and equating to zero <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\( - (h - c)f''(c) + \frac{{2(h - c)}}{{{h^2}}}\left( {f(h) - f(0) - hf'(0)} \right) = g'(c) = 0\) </span><strong><em>AG</em></strong></p>
<p class="p1">(vi) <span class="Apple-converted-space"> \( - f''(c) + \frac{2}{{{h^2}}}\left( {f(h) - f(0) - hf'(0)} \right) = 0\)</span> <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">since \(h - c \ne 0\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">\(\frac{{{h^2}}}{2}f''(c) = f(h) - f(0) - hf'(0)\)</p>
<p class="p1"><span class="Apple-converted-space">\(f(h) = f(0) + hf'(0) + \frac{{{h^2}}}{2}f''(c)\) </span><strong><em>AG</em></strong></p>
<p class="p1"><strong><em>[9 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">letting \(f(x) = \cos (x)\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(f'(x) = - \sin (x)\) \(f''(x) = - \cos (x)\)</span> <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(\cos (h) = 1 + 0 - \frac{{{h^2}}}{2}\cos (c)\) </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(1 - \cos (h) = \frac{{{h^2}}}{2}\cos (c)\) </span><strong><em>(A1)</em></strong></p>
<p class="p1">since \(\cos (c) \leqslant 1\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(1 - \cos (h) \leqslant \frac{{{h^2}}}{2}\) </span><strong><em>AG</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: </strong>Allow \(f(x) = a \pm b\cos x\).</p>
<p class="p2"> </p>
<p class="p1"><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="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">Given that \(f(x) = \ln x\)</span>, use the mean value theorem to show that, for \(0 < a < b\), \(\frac{{b - a}}{b} < \ln \frac{b}{a} < \frac{{b - a}}{a}\).</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 class="p1">Hence show that \(\ln (1.2)\) lies between \(\frac{1}{m}\) and \(\frac{1}{n}\), where \(m\)<span class="s1">, \(n\) </span>are consecutive positive integers to be determined.</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">\(f'(x) = \frac{1}{x}\) </span><strong><em>(A1)</em></strong></p>
<p class="p1"><span class="s1">using the MVT \(f'(c) = \frac{{f(b) - f(a)}}{{b - a}}\) </span>(where \(c\) lies between \(a\) and \(b\)) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\(f'(c) = \frac{{\ln b - \ln a}}{{b - a}}\) </span><span class="s2"><strong><em>A1</em></strong></span></p>
<p class="p3"><span class="Apple-converted-space">\(\ln \frac{b}{a} = \ln b - \ln a\) </span><span class="s2"><strong><em>(M1)</em></strong></span></p>
<p class="p3">\(f'(c) = \frac{{\ln \frac{b}{a}}}{{b - a}}\)</p>
<p class="p1">since \(f'(x)\) is a decreasing function or \(a < c < b \Rightarrow \frac{1}{b} < \frac{1}{c} < \frac{1}{a}\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p3"><span class="Apple-converted-space">\(f'(b) < f'(c) < f'(a)\) </span><span class="s2"><strong><em>(M1)</em></strong></span></p>
<p class="p4"><span class="Apple-converted-space">\(\frac{1}{b} < \frac{{\ln \frac{b}{a}}}{{b - a}} < \frac{1}{a}\) </span><span class="s2"><strong><em>A1</em></strong></span></p>
<p class="p4"><span class="Apple-converted-space">\(\frac{{b - a}}{b} < \ln \frac{b}{a} < \frac{{b - a}}{a}\) </span><span class="s2"><strong><em>AG</em></strong></span></p>
<p class="p1"><strong><em>[7 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">putting \(b = 1.2,{\text{ }}a = 1\), or equivalent <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\(\frac{1}{6} < \ln 1.2 < \frac{1}{5}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2">\((m = 6,{\text{ }}n = 5)\)</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">Although many candidates achieved at least a few marks in this question, the answers revealed difficulties in setting up a proof. The Mean value theorem was poorly quoted and steps were often skipped. The conditions under which the Mean value theorem is valid were largely ignored, as were the reasoned steps towards the answer.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">There were inequalities everywhere, without a great deal of meaning or showing progress. A number of candidates attempted to work backwards and presented the work in a way that made it difficult to follow their reasoning; in part (b) many candidates ignored the instruction ‘hence’ and just used GDC to find the required values; candidates that did notice the link to part a) answered this question well in general. A number of candidates guessed the answer and did not present an analytical derivation as required.</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: 33.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the radius of convergence of the series \(\sum\limits_{n = 0}^\infty {\frac{{{{( - 1)}^n}{x^n}}}{{(n + 1){3^n}}}} \).</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: 29.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Determine whether the series \(\sum\limits_{n = 0}^\infty {\left( {\sqrt[3]{{{n^3} + 1}} - n} \right)} \) is convergent or divergent.</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The ratio test gives</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\mathop {\lim }\limits_{n \to \infty } \left| {\frac{{{u_{n + 1}}}}{{{u_n}}}} \right| = \mathop {\lim }\limits_{n \to \infty } \left| {\frac{{{{( - 1)}^{n + 1}}{x^{n + 1}}(n + 1){3^n}}}{{(n + 2){3^{n + 1}}{{( - 1)}^n}{x^n}}}} \right|\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \mathop {\lim }\limits_{n \to \infty } \left| {\frac{{(n + 1)x}}{{3(n + 2)}}} \right|\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{\left| x \right|}}{3}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">So the series converges for \( \frac{{\left| x \right|}}{3} < 1,\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;">the radius of convergence is 3 <strong><em>A1</em></strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.5px 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;">Do not penalise lack of modulus signs.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.5px 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: 29.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></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;">\({u_n} = \sqrt[3]{{{n^3} + 1}} - n\)</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;">\( = n\left( {\sqrt[3]{{1 + \frac{1}{{{n^3}}} - 1}}} \right)\) <em><strong>M1A1</strong></em><br></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;">\( = n\left( {1 + \frac{1}{{3{n^3}}} - \frac{1}{{9{n^6}}} + \frac{5}{{8{\text{l}}{n^9}}} - ... - 1} \right)\) <em><strong>A1</strong></em><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">using \({v_n} = \frac{1}{{{n^2}}}\) as the auxilliary series, <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">since \(\mathop {\lim }\limits_{n \to \infty } \frac{{{u_n}}}{{{v_n}}} = \frac{1}{3}{\text{ and }}\frac{1}{{{1^2}}} + \frac{1}{{{2^2}}} + \frac{1}{{{3^2}}} + \frac{1}{{{4^2}}} + …\) converges <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">then \(\sum {{u_n}} \) converges <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>M1A1A1M0M0A0A0 </em></strong>to candidates attempting to use the integral test.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.5px 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: 32.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 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;">Some corners were cut in applying the ratio test and some candidates tried to use the comparison test. With careful algebra finding the radius of convergence was not too difficult. Often the interval of convergence was given instead of the radius.</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 (b) was done only by the best candidates. A little algebraic manipulation together with an auxiliary series soon gave the answer.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Some corners were cut in applying the ratio test and some candidates tried to use the comparison test. With careful algebra finding the radius of convergence was not too difficult. Often the interval of convergence was given instead of the radius.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (b) was done only by the best candidates. A little algebraic manipulation together with an auxiliary series soon gave the answer.</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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Solve 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;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{y}{x} + \frac{{{y^2}}}{{{x^2}}}\) (where x > 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;">given that <em>y</em> = 2 when <em>x</em> = 1 . Give your answer in the form \(y = f(x)\) .</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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">put <em>y</em> = <em>vx</em> so that \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = v + x\frac{{{\text{d}}v}}{{{\text{d}}x}}\) <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;">the equation becomes \(v + x\frac{{{\text{d}}v}}{{{\text{d}}x}} = v + {v^2}\) <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;">leading to \(x\frac{{{\text{d}}v}}{{{\text{d}}x}} = {v^2}\) <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;">separating variables, \(\int {\frac{{{\text{d}}x}}{x} = \int {\frac{{{\text{d}}v}}{{{v^2}}}} } \) <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;">hence \(\ln x = - {v^{ - 1}} + C\) <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;">substituting for <em>v</em>, \(\ln x = \frac{{ - x}}{y} + C\) <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;"><strong>Note:</strong> Do not penalise absence of <em>C</em> at the above stages.</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;">substituting the boundary conditions,</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;">\(0 = - \frac{1}{2} + C\) <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;">\(C = \frac{1}{2}\) <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;">the solution is \(\ln x = \frac{{ - x}}{y} + \frac{1}{2}\) <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;">leading to \(y = \frac{{2x}}{{1 - 2\ln x}}\) (or equivalent form) <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> Candidates are not required to note that \(x \ne \sqrt {\text{e}} \) .</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><em>[13 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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates were able to make a reasonable attempt at this question with many perfect solutions seen.</span></p>
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<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;">Find the set of values of <em>k </em>for which the improper integral \(\int_2^\infty {\frac{{{\text{d}}x}}{{x{{(\ln x)}^k}}}} \) converges.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
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<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;">Show that the series \(\sum\limits_{r = 2}^\infty {\frac{{{{( - 1)}^r}}}{{r\ln r}}} \) is convergent but not absolutely convergent.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
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<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: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">consider the limit as \(R \to \infty \) of the (proper) integral</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;">\(\int_2^R {\frac{{{\text{d}}x}}{{x{{(\ln x)}^k}}}} \) <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;">substitute \(u = \ln x,{\text{ d}}u = \frac{1}{x}{\text{d}}x\) (<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;">obtain \(\int_{\ln 2}^{\ln R} {\frac{1}{{{u^k}}}{\text{d}}u = \left[ { - \frac{1}{{k - 1}}\frac{1}{{{u^{k - 1}}}}} \right]_{\ln 2}^{\ln R}} \) <strong><em>A1</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>Ignore incorrect limits or omission of limits at this stage.</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;">or \([\ln u]_{\ln 2}^{\ln R}\) if <em>k</em> = 1 <strong><em>A1</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>Ignore incorrect limits or omission of limits at this stage.</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;">because \(\ln R{\text{ }}({\text{and }}\ln \ln R) \to \infty {\text{ as }}R \to \infty \) <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;">converges in the limit if <em>k</em> > 1 <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;">[6 marks]</span><br></em></strong></p>
<div class="question_part_label">a.</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;">C: \({\text{terms}} \to 0{\text{ as }}r \to \infty \) <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;">\(\left| {{u_{r + 1}}} \right| < \left| {{u_r}} \right|\) for all <em>r </em><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;">convergence by alternating series test <strong><em>R1<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;">AC: \({(x\ln x)^{ - 1}}\) is positive and decreasing on \([2,\,\infty )\) <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;">not absolutely convergent by integral test using part (a) for <em>k</em> = 1 <strong><em>R1</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">b.</div>
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<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;">A good number of candidates were able to find the integral in part (a) although the vast majority did not consider separately the integral when <em>k</em> = 1. Many candidates did not explicitly set a limit for the integral to let this limit go to infinity in the anti – derivative and it seemed that some candidates were “substituting for infinity”. This did not always prevent candidates finding a correct final answer but the lack of good technique is a concern. In part (b) many candidates seemed to have some knowledge of the relevant test for convergence but this test was not always rigorously applied. In showing that the series was not absolutely convergent candidates were often not clear in showing that the function being tested had to meet a number of criteria and in so doing lost marks.</span></p>
<div class="question_part_label">a.</div>
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<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;">A good number of candidates were able to find the integral in part (a) although the vast majority did not consider separately the integral when <em>k</em> = 1. Many candidates did not explicitly set a limit for the integral to let this limit go to infinity in the anti – derivative and it seemed that some candidates were “substituting for infinity”. This did not always prevent candidates finding a correct final answer but the lack of good technique is a concern. In part (b) many candidates seemed to have some knowledge of the relevant test for convergence but this test was not always rigorously applied. In showing that the series was not absolutely convergent candidates were often not clear in showing that the function being tested had to meet a number of criteria and in so doing lost marks.</span></p>
<div class="question_part_label">b.</div>
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<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Determine whether the series \(\sum\limits_{n = 1}^\infty {\frac{{{n^{10}}}}{{{{10}^n}}}} \) is convergent or divergent.</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: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Consider</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;">\(\frac{{{u_{n + 1}}}}{{{u_n}}} = \frac{{{{(n + 1)}^{10}}}}{{{{10}^{n + 1}}}} \times \frac{{{{10}^n}}}{{{n^{10}}}}\) <em><strong>M1A1</strong></em><br></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;">\( = \frac{1}{{10}}{\left( {1 + \frac{1}{n}} \right)^{10}}\) <em><strong>A1</strong></em><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \to \frac{1}{{10}}{\text{ as }}n \to \infty \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{1}{{10}} < 1\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">So by the Ratio Test the series is convergent. <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 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: 24.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates used the Ratio Test successfully to establish convergence. Candidates who attempted to use Cauchy’s (Root) Test were often less successful although this was a valid method.</span></p>
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<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Times;"><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px 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: 25.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">The diagram shows part of the graph of \(y = \frac{1}{{{x^3}}}\) together with line segments parallel to the coordinate axes.</span></p>
</div>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Using the diagram, show that \(\frac{1}{{{4^3}}} + \frac{1}{{{5^3}}} + \frac{1}{{{6^3}}} + ... < \int_3^\infty {\frac{1}{{{x^3}}}{\text{d}}x < \frac{1}{{{3^3}}} + \frac{1}{{{4^3}}} + \frac{1}{{{5^3}}} + ...} \) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) <strong>Hence </strong>find upper and lower bounds for \(\sum\limits_{n = 1}^\infty {\frac{1}{{{n^3}}}} \).</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: 22.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) The area under the curve is sandwiched between the sum of the areas of the lower rectangles and the upper rectangles. <strong><em>M2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Therefore</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(1 \times \frac{1}{{{4^3}}} + 1 \times \frac{1}{{{5^3}}} + 1 \times \frac{1}{{{6^3}}} + ... < \int_3^\infty {\frac{{{\text{d}}x}}{{{x^3}}} < 1 \times \frac{1}{{{3^3}}} + 1 \times \frac{1}{{{4^3}}} + 1 \times \frac{1}{{{5^3}}} + ...} \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">which leads to the printed result.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times; color: #3f3f3f;"><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: 22.0px Times; color: #3f3f3f;"><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 Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) We note first that</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int_3^\infty {\frac{{{\text{d}}x}}{{{x^3}}} = \left[ { - \frac{1}{{2{x^2}}}} \right]_3^\infty = \frac{1}{{18}}} \) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Consider first</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\sum\limits_{n = 1}^\infty {\frac{1}{{{n^3}}}} = 1 + \frac{1}{{{2^3}}} + \frac{1}{{{3^3}}} + \left( {\frac{1}{{{4^3}}} + \frac{1}{{{5^3}}} + \frac{1}{{{6^3}}} + ...} \right)\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\( < 1 + \frac{1}{8} + \frac{1}{{27}} + \frac{1}{{18}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{263}}{{216}}{\text{ (1.22)}}\) (which is an upper bound) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\sum\limits_{n = 1}^\infty {\frac{1}{{{n^3}}}} = 1 + \frac{1}{{{2^3}}} + \left( {\frac{1}{{{3^3}}} + \frac{1}{{{4^3}}} + \frac{1}{{{5^3}}} + ...} \right)\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\( > 1 + \frac{1}{8} + \frac{1}{{18}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{85}}{{72}}\left( {\frac{{255}}{{216}}} \right){\text{ (1.18)}}\) (which is a lower bound) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[12 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times; color: #3f3f3f;"><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">
<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;">Many candidates failed to give a convincing argument to establish the inequality. In (b), few candidates progressed beyond simply evaluating the integral.</span></p>
</div>
<br><hr><br><div class="specification">
<p style="text-align: center;"><img src="images/Figure_1.png" alt></p>
<p style="text-align: center;">Figure 1</p>
</div>
<div class="specification">
<p style="text-align: center;"><img src="images/Figure_2.png" alt></p>
<p style="text-align: center;">Figure 2</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;">Figure 1 shows part of the graph of \(y = \frac{1}{x}\) together with line segments parallel to the coordinate axes.</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;">(i) By considering the areas of appropriate rectangles, show that</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;">\[\frac{{2a + 1}}{{a(a + 1)}} < \ln \left( {\frac{{a + 1}}{{a - 1}}} \right) < \frac{{2a - 1}}{{a(a - 1)}}.\]</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) Hence find lower and upper bounds for \(\ln (1.2)\).</span></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 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;">An improved upper bound can be found by considering Figure 2 which again shows part of the graph of \(y = \frac{1}{x}\).</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) By considering the areas of appropriate regions, show that</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;">\[\ln \left( {\frac{a}{{a - 1}}} \right) < \frac{{2a - 1}}{{2a(a - 1)}}.\]</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;">(ii) Hence find an upper bound for \(\ln (1.2)\).</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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) the area under the curve between <em>a</em> – 1 and <em>a</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;">\( = \int_{a - 1}^{a + 1} {\frac{{{\text{d}}x}}{x}} \) <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;">\( = [\ln x]_{a - 1}^{a + 1}\) <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;">\( = \ln \left( {\frac{{a + 1}}{{a - 1}}} \right)\) <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;">lower sum \( = \frac{1}{a} + \frac{1}{{a + 1}}\) <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;">\( = \frac{{2a + 1}}{{a(a + 1)}}\) <strong><em>AG</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;">upper sum \( = \frac{1}{{a - 1}} + \frac{1}{a}\) <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;">\( = \frac{{2a - 1}}{{a(a - 1)}}\) <strong><em>AG</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;">it follows that</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;">\(\frac{{2a + 1}}{{a(a + 1)}} < \ln \left( {\frac{{a + 1}}{{a - 1}}} \right) < \frac{{2a - 1}}{{a(a - 1)}}\)</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;">because the area of the region under the curve lies between the areas of the regions defined by the lower and upper sums <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;"> </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) putting</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;">\(\left( {\frac{{a + 1}}{{a - 1}} = 1.2} \right) \Rightarrow a = 11\) <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, \({\text{UB}} = \frac{{21}}{{110}}( = 0.191),{\text{ LB}} = \frac{{23}}{{132}}( = 0.174)\) <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;"><em>[9 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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) the area under the curve between <em>a</em> – 1 and <em>a</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;">\( = \int_{a - 1}^a {\frac{{{\text{d}}x}}{x}} \) <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;">\( = [\ln x]_{a - 1}^a = \ln \left( {\frac{a}{{a - 1}}} \right)\)</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;">attempt to find area of trapezium <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;">area of trapezoidal “upper sum” \( = \frac{1}{2}\left( {\frac{1}{{a - 1}} + \frac{1}{a}} \right)\) 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;">\( = \frac{{2a - 1}}{{2a(a - 1)}}\)</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;">it follows that \(\ln \left( {\frac{a}{{a - 1}}} \right) < \frac{{2a - 1}}{{2a(a - 1)}}\) <strong><em>AG</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;"> </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) putting</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;">\(\left( {\frac{a}{{a - 1}} = 1.2} \right) \Rightarrow a = 6\) <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, \({\text{UB}} = \frac{{11}}{{60}}( = 0.183)\) <strong><em>A1</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: 30.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><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><span style="font-family: times new roman,times; font-size: medium;">Many candidates made progress with this problem. This was pleasing since whilst being relatively straightforward it was not a standard problem. There were still some candidates who did not use the definite integral correctly to find the area under the curve in part (a) and part (b). Also candidates should take care to show all the required working in a “show that” question, even when demonstrating familiar results. The ability to find upper and lower bounds was often well done in parts (a) (ii) and (b) (ii).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates made progress with this problem. This was pleasing since whilst being relatively straightforward it was not a standard problem. There were still some candidates who did not use the definite integral correctly to find the area under the curve in part (a) and part (b). Also candidates should take care to show all the required working in a “show that” question, even when demonstrating familiar results. The ability to find upper and lower bounds was often well done in parts (a) (ii) and (b) (ii).</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The function <em>f </em>is defined by \(f(x) = \left\{ \begin{array}{r}{e^{ - x^3}}( - {x^3} + 2{x^2} + x),x \le 1\\ax + b,x > 1\end{array} \right.\), where \(a\) and \(b\) are constants.</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 exact values of \(a\) and \(b\) if \(f\) is continuous and differentiable at \(x = 1\).</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: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Use Rolle’s theorem, applied to \(f\), to prove that \(2{x^4} - 4{x^3} - 5{x^2} + 4x + 1 = 0\) has a root in the interval \(\left] { - 1,1} \right[\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Hence prove that \(2{x^4} - 4{x^3} - 5{x^2} + 4x + 1 = 0\) has at least two roots in the interval \(\left] { - 1,1} \right[\).</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\mathop {{\text{lim}}}\limits_{x \to {1^ - }} {{\text{e}}^{ - {x^2}}}\left( { - {x^3} + 2{x^2} + x} \right) = \mathop {{\text{lim}}}\limits_{x \to {1^ + }} (ax + b)\) \(( = a + b)\) <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;">\(2{{\text{e}}^{ - 1}} = a + b\) <em><strong>A1</strong></em></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;">differentiability: attempt to differentiate <strong>both </strong>expressions <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;">\(f'(x) = - 2x{{\text{e}}^{ - {x^2}}}\left( { - {x^3} + 2{x^2} + x} \right) + {{\text{e}}^{ - {x^2}}}\left( { - 3{x^2} + 4x + 1} \right)\) \((x < 1)\) <em><strong>A1</strong></em></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;">(or \(f'(x) = {{\text{e}}^{ - {x^2}}}\left( {2{x^4} - 4{x^3} - 5{x^2} + 4x + 1} \right)\))</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;">\(f'(x) = a\) \((x > 1)\) <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;">substitute \(x = 1\) in <strong>both </strong>expressions and equate</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;">\( - 2{{\text{e}}^{ - 1}} = a\) <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;">substitute value of \(a\) and find \(b = 4{{\text{e}}^{ - 1}}\) <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;"><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: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \(f'(x) = {{\text{e}}^{ - {x^2}}}\left( {2{x^4} - 4{x^3} - 5{x^2} + 4x + 1} \right)\) (for \(x \leqslant 1\)) <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;">\(f(1) = f( - 1)\) <em><strong>M1</strong></em></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;">Rolle’s theorem statement <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;">by Rolle’s Theorem, \(f'(x)\) has a zero in \(\left] { - 1,1} \right[\) <strong><em>R1</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 quartic equation has a root in \(\left] { - 1,1} \right[\) <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;">(ii) let \(g(x) = 2{x^4} - 4{x^3} - 5{x^2} + 4x + 1\).</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;">\(g( - 1) = g(1) < 0\) and \(g(0) > 0\) <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;">as \(g\) is a polynomial function it is continuous in \(\left[ { - 1,0} \right]\) and \(\left[ {0,{\text{ 1}}} \right]\). <strong><em>R1</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 \(g\) is a polynomial function continuous in any interval of real numbers)</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;">then the graph of \(g\) must cross the <em>x</em>-axis at least once in \(\left] { - 1,0} \right[\) <strong><em>R1</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;">and at least once in \(\left] {0,1} \right[\).</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>[7 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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Using the Maclaurin series for \({(1 + x)^n}\), write down and simplify the Maclaurin series approximation for \({(1 - {x^2})^{ - \frac{1}{2}}}\) as far as the term in \({x^4}\)</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) Use your result to show that a series approximation for arccos <em>x</em> is</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;">\[\arccos x \approx \frac{\pi }{2} - x - \frac{1}{6}{x^3} - \frac{3}{{40}}{x^5}.\]</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) Evaluate \(\mathop {\lim }\limits_{x \to 0} \frac{{\frac{\pi }{2} - \arccos ({x^2}) - {x^2}}}{{{x^6}}}\).</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) Use the series approximation for \(\arccos x\) to find an approximate value for</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;">\[\int_0^{0.2} {\arccos \left( {\sqrt x } \right){\text{d}}x} ,\]</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;">giving your answer to 5 decimal places. Does your answer give the actual value of the integral to 5 decimal places?</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;">(a) using or obtaining \({(1 + x)^n} = 1 + nx + \frac{{n(n - 1)}}{2}{x^2} + \ldots \) <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;">\({(1 - {n^2})^{ - \frac{1}{2}}} = 1 + ( - {x^2}) \times \left( { - \frac{1}{2}} \right) + \frac{{{{( - {x^2})}^2}}}{2} \times \left( { - \frac{1}{2}} \right) \times \left( { - \frac{3}{2}} \right) + \ldots \) <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;">\( = 1 + \frac{1}{2}{x^2} + \frac{3}{8}{x^4} + \ldots \) <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>
<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;">(b) integrating, and changing sign</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;">\(\arccos x = - x - \frac{1}{6}{x^3} - \frac{3}{{40}}{x^5} + C + \ldots \) <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;">put <em>x</em> = 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;">\(\frac{\pi }{2} = C\) <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;">\(\left( {\arccos x \approx \frac{\pi }{2} - x - \frac{1}{6}{x^3} - \frac{3}{{40}}{x^5}} \right)\) <strong><em>AG</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>
<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;">(c) <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;">using \(\arccos {x^2} \approx \frac{\pi }{2} - {x^2} - \frac{1}{6}{x^6} - \frac{3}{{40}}{x^{10}}\) <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;">\(\mathop {\lim }\limits_{x \to 0} \frac{{\frac{\pi }{2} - \arccos {x^2} - {x^2}}}{{{x^6}}} = \mathop {\lim }\limits_{x \to 0} \frac{{\frac{{{x^6}}}{6} + {\text{higher powers}}}}{{{x^6}}}\) <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;">\( = \frac{1}{6}\) <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;">using l’Hôpital’s Rule <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;">\({\text{limit}} = \mathop {\lim }\limits_{x \to 0} \frac{{\frac{1}{{\sqrt {1 - {x^4}} }} \times 2x - 2x}}{{6{x^5}}}\) <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;">\( = \mathop {\lim }\limits_{x \to 0} \frac{{\frac{1}{{\sqrt {1 - {x^4}} }} - 1}}{{3{x^4}}}\) <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;">\( = \mathop {\lim }\limits_{x \to 0} \frac{{ - \frac{1}{2} \times \frac{1}{{{{(1 - {x^4})}^{3/2}}}} \times - 4{x^3}}}{{12{x^3}}}\) <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;">\( = \frac{1}{6}\) <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>[5 marks]</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;">(d) \(\int_0^{0.2} {\arccos \sqrt x {\text{d}}x \approx \int_0^{0.2} {\left( {\frac{\pi }{2} - {x^{\frac{1}{2}}} - \frac{1}{6}{x^{\frac{3}{2}}} - \frac{3}{{40}}{x^{\frac{5}{2}}}} \right){\text{d}}x} } \) <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;">\( = \left[ {\frac{\pi }{2}x - \frac{2}{3}{x^{\frac{3}{2}}} - \frac{1}{{15}}{x^{\frac{5}{2}}} - \frac{3}{{140}}{x^{\frac{7}{2}}}} \right]_0^{0.2}\) <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;">\( = \frac{\pi }{2} \times 0.2 - \frac{2}{3} \times {0.2^{\frac{3}{2}}} - \frac{1}{{15}} \times {0.2^{\frac{5}{2}}} - \frac{3}{{140}} \times {0.2^{\frac{7}{2}}}\) <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;">= 0.25326 (to 5 decimal places) <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 integration of the series approximation using a GDC.</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;">using a GDC, the actual value is 0.25325 <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 the approximation is not correct to 5 decimal places <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>
<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>Total [17 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 ignored the instruction in the question to use the series for \({(1 + x)^n}\) to deduce the series for \({(1 - {x^2})^{ - 1/2}}\) and attempted instead to obtain it by successive differentiation. It was decided at the standardisation meeting to award full credit for this method although in the event the algebra proved to be too difficult for many. Many candidates used l’Hopital’s Rule in (c) – this was much more difficult algebraically than using the series and it usually ended unsuccessfully. Candidates should realise that if a question on evaluating an indeterminate limit follows the determination of a Maclaurin series then it is likely that the series will be helpful in evaluating the limit. Part (d) caused problems for many candidates with algebraic errors being common. Many candidates failed to realise that the best way to find the exact value of the integral was to use the calculator.</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Using l’Hopital’s Rule, show that \(\mathop {\lim }\limits_{x \to \infty } x{{\text{e}}^{ - x}} = 0\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Determine \(\int_0^a {x{{\text{e}}^{ - x}}{\text{d}}x} \) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) Show that the integral \(\int_0^\infty {x{{\text{e}}^{ - x}}{\text{d}}x} \) is convergent and find its value.</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 Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \(\mathop {\lim }\limits_{x \to \infty } \frac{x}{{{{\text{e}}^x}}} = \mathop {\lim }\limits_{x \to \infty } \frac{1}{{{{\text{e}}^x}}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">= 0 <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Using integration by parts </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 Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int_0^a {x{{\text{e}}^{ - x}}{\text{d}}x} = \left[ { - x{{\text{e}}^{ - x}}} \right]_0^a + \int_0^a {{{\text{e}}^{ - x}}{\text{d}}x} \) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = - a{{\text{e}}^{ - a}} - \left[ {{e^{ - x}}} \right]_0^a\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 1 - a{{\text{e}}^{ - a}} - {{\text{e}}^{ - a}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Times; color: #3f3f3f;"><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: 25.0px Times; color: #3f3f3f;"><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 Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(c)<strong><em> </em></strong>Since \({{\text{e}}^{ - a}}\) and \(a{{\text{e}}^{ - a}}\) are both convergent (to zero), the integral is convergent. <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Its value is 1. <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Times; color: #3f3f3f;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[2 marks]</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Times; color: #3f3f3f;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>Total [9 marks]</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: 23.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates made a reasonable attempt at (a). In (b), however, it was disappointing to note that some candidates were unable to use integration by parts to perform the integration. In (c), while many candidates obtained the correct value of the integral, proof of its convergence was often unconvincing.</span></p>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">By successive differentiation find the first four non-zero terms in the Maclaurin series for \(f(x) = (x + 1)\ln (1 + x) - x\).</p>
<div class="marks">[11]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Deduce that, for \(n \geqslant 2\), the coefficient of \({x^n}\) <span class="s1">in this series is \({( - 1)^n}\frac{1}{{n(n - 1)}}\).</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 class="p1">By applying the ratio test, find the radius of convergence for this Maclaurin series.</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"><span class="Apple-converted-space">\(f(x) = (x + 1)\ln (1 + x) - x\) \(f(0) = 0\) </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(f'(x) = \ln (1 + x) + \frac{{x + 1}}{{1 + x}} - 1{\text{ }}\left( { = \ln (1 + x)} \right)\) \(f'(0) = 0\) </span><strong><em>M1A1A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(f''(x) = {(1 + x)^{ - 1}}\) \(f''(0) = 1\) </span><strong><em>A1A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(f'''(x) = - {(1 + x)^{ - 2}}\) \(f'''(0) = - 1\) </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\({f^{(4)}}(x) = 2{(1 + x)^{ - 3}}\) \({f^{(4)}}(0) = 2\) </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\({f^{(5)}}(x) = - 3 \times 2{(1 + x)^{ - 4}}\) \({f^{(5)}}(0) = - 3 \times 2\) </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(f(x) = \frac{{{x^2}}}{{2!}} - \frac{{1{x^3}}}{{3!}} + \frac{{2{x^4}}}{{4!}} - \frac{{6{x^5}}}{{5!}} \ldots \) </span><strong><em>M1A1</em></strong></p>
<p class="p1">\(f(x) = \frac{{{x^2}}}{{1 \times 2}} - \frac{{{x^3}}}{{2 \times 3}} + \frac{{{x^4}}}{{3 \times 4}} - \frac{{{x^5}}}{{4 \times 5}} \ldots \)</p>
<p class="p1">\(f(x) = \frac{{{x^2}}}{2} - \frac{{{x^3}}}{6} + \frac{{{x^4}}}{{12}} - \frac{{{x^5}}}{{20}} \ldots \)</p>
<p class="p2"> </p>
<p class="p1"><strong>Note: </strong>Allow follow through from the first error in a derivative (provided future derivatives also include the chain rule), no follow through after a second error in a derivative.</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[11 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\({f^{(n)}}(0) = {( - 1)^n}(n - 2)!\) So coefficient of \({x^n} = {( - 1)^n}\frac{{(n - 2)!}}{{n!}}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="s1">coefficient of \({x^n}\)</span> is \({( - 1)^n}\frac{1}{{n(n - 1)}}\) <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p1"><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">applying the ratio test to the series of absolute terms</p>
<p class="p1"><span class="Apple-converted-space">\(\mathop {\lim }\limits_{n \to \infty } \frac{{\frac{{{{\left| x \right|}^{n + 1}}}}{{(n + 1)n}}}}{{\frac{{{{\left| x \right|}^n}}}{{n(n - 1)}}}}\) </span><strong><em>M1A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\( = \mathop {\lim }\limits_{n \to \infty } \left| x \right|\frac{{(n - 1)}}{{(n + 1)}}\) </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\( = \left| x \right|\) </span><strong><em>A1</em></strong></p>
<p class="p1">so for convergence \(\left| x \right| < 1\), giving radius of convergence as 1 <span class="Apple-converted-space"> </span><strong><em>(M1)A1</em></strong></p>
<p class="p1"><strong><em>[6 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="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;">Find \(\mathop {\lim }\limits_{x \to \frac{1}{2}} \left( {\frac{{\left( {\frac{1}{4} - {x^2}} \right)}}{{\cot \pi x}}} \right)\).</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;"><strong>using l’Hôpital’s Rule</strong> <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;">\(\mathop {\lim }\limits_{x \to \frac{1}{2}} \left( {\frac{{\left( {\frac{1}{4} - {x^2}} \right)}}{{\cot \pi x}}} \right) = \mathop {\lim }\limits_{x \to \frac{1}{2}} \left[ {\frac{{ - 2}}{{ - \pi {\text{cose}}{{\text{c}}^2}\pi x}}} \right]\)</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>A1A1</em></strong></p>
<p style="margin: 0px 0px 0px 30px; font: 29px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{ - 1}}{{ - \pi {\text{cose}}{{\text{c}}^2}\frac{\pi }{2}}} = \frac{1}{\pi }\) <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;"><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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was accessible to the vast majority of candidates, who recognised that L’Hôpital’s rule was required. However, some candidates omitted the factor \(\pi \) in the differentiation of \({\cot \pi x}\). Some candidates replaced \({\cot \pi x}\) by \(\cos \pi x{\text{/}}\sin \pi x\), which is a valid method but the extra algebra involved often led to an incorrect answer. Many fully correct solutions were seen.</span></p>
</div>
<br><hr><br><div class="specification">
<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;">Let \(f(x) = 2x + \left| x \right|\) , \(x \in \mathbb{R}\) .</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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Prove that <em>f</em> is continuous but not differentiable at the point (0, 0) .</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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Determine the value of \(\int_{ - a}^a {f(x){\text{d}}x} \) where \(a > 0\) .</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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">we note that \(f(0) = 0,{\text{ }}f(x) = 3x\) for \(x > 0\) and \(f(x) = x{\text{ for }}x < 0\)</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;">\(\mathop {\lim }\limits_{x \to {0^ - }} f(x) = \mathop {\lim }\limits_{x \to {0^ - }} x = 0\) <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;">\(\mathop {\lim }\limits_{x \to {0^ - }} f(x) = \mathop {\lim }\limits_{x \to {0^ - }} 3x = 0\) <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;">since \(f(0) = 0\) , the function is continuous when <em>x</em> = 0 <strong><em>AG</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;">\(\mathop {\lim }\limits_{x \to {0^ - }} \frac{{f(0 + h) - f(0)}}{h} = \mathop {\lim }\limits_{x \to {0^ - }} \frac{h}{h} = 1\) <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;">\(\mathop {\lim }\limits_{x \to {0^ + }} \frac{{f(0 + h) - f(0)}}{h} = \mathop {\lim }\limits_{x \to {0^ + }} \frac{{3h}}{h} = 3\) <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;">these limits are unequal <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;">so <em>f</em> is not differentiable when <em>x</em> = 0 <strong><em>AG</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 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;">\(\int_{ - a}^a {f(x){\text{d}}x = \int_{ - a}^0 {x{\text{d}}x + \int_0^a {3x{\text{d}}x} } } \) <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;">\( = \left[ {\frac{{{x^2}}}{2}} \right]_{ - a}^0 + \left[ {\frac{{3{x^2}}}{2}} \right]_0^a\) <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;">\( = {a^2}\) <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;"><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>Consider the curve \(y = \frac{1}{x},{\text{ }}x > 0\).</p>
</div>
<div class="specification">
<p>Let \({U_n} = \sum\limits_{r = 1}^n {\frac{1}{r} - \ln n} \).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>By drawing a diagram and considering the area of a suitable region under the curve, show that for \(r > 0\),</p>
<p>\[\frac{1}{{r + 1}} < \ln \left( {\frac{{r + 1}}{r}} \right) < \frac{1}{r}.\]</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>Hence, given that \(n\) is a positive integer greater than one, show that</p>
<p>\(\sum\limits_{r = 1}^n {\frac{1}{r} > \ln (1 + n)} \);</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, given that \(n\) is a positive integer greater than one, show that</p>
<p>\(\sum\limits_{r = 1}^n {\frac{1}{r} < 1 + \ln n} \).</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, given that \(n\) is a positive integer greater than one, show that</p>
<p>\({U_n} > 0\);</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, given that \(n\) is a positive integer greater than one, show that</p>
<p>\({U_{n + 1}} < {U_n}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why these two results prove that \(\{ {U_n}\} \) is a convergent sequence.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2017-08-10_om_13.46.42.png" alt="M17/5/MATHL/HP3/ENG/TZ0/SE/M/05.a"></p>
<p><strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Curve, both rectangles and correct \(x\)values required.</p>
<p> </p>
<p>area of rectangles \(\frac{1}{r}\) and \(\frac{1}{{1 + r}}\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Correct values on the \(y\)-axis are sufficient evidence for this mark if not otherwise indicated.</p>
<p> </p>
<p>in the above diagram, the area below the curve between \(x = r\) and \(x = r + 1\) is between the areas of the larger and smaller rectangle</p>
<p><strong><em>or </em></strong>\(\frac{1}{{r + 1}} < \int\limits_r^{r + 1} {\frac{{{\text{d}}x}}{x} < \frac{1}{r}} \) <strong><em>(R1)</em></strong></p>
<p>integrating, \(\int_r^{r + 1} {\frac{{{\text{d}}x}}{x} = [\ln x]_r^{r + 1}\,\,\,\left( { = \ln (r + 1) - \ln (r)} \right)} \) <strong><em>A1</em></strong></p>
<p>\(\frac{1}{{r + 1}} < \ln \left( {\frac{{r + 1}}{r}} \right) < \frac{1}{r}\) <strong><em>AG</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>summing the right-hand part of the above inequality from \(r = 1\) to \(r = n\),</p>
<p>\(\sum\limits_{r = 1}^n {\frac{1}{r}} > \sum\limits_{r = 1}^n {\ln \left( {\frac{{r + 1}}{r}} \right)} \) <strong><em>M1</em></strong></p>
<p>\( = \ln \left( {\frac{2}{1}} \right) + \ln \left( {\frac{3}{2}} \right) + \ldots + \ln \left( {\frac{n}{{n - 1}}} \right) + \ln \left( {\frac{{n + 1}}{n}} \right)\) <strong><em>(A1)</em></strong></p>
<p><strong>EITHER</strong></p>
<p>\( = \ln \left( {\frac{2}{1} \times \frac{3}{2} \times \ldots \times \frac{n}{{n - 1}} \times \frac{{n + 1}}{n}} \right)\) <strong><em>A1</em></strong></p>
<p><strong>OR</strong></p>
<p>\(\ln 2 - \ln 1 + \ln 3 - \ln 2 + \ldots + \ln (n + 1) - \ln (n)\) <strong><em>A1</em></strong></p>
<p>\( = \ln (n + 1)\) <strong><em>AG</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\sum\limits_{r = 1}^n {\frac{1}{r} = 1 + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{n} < 1 + \ln \left( {\frac{2}{1}} \right) + \ln \left( {\frac{3}{2}} \right) + \ldots + \ln \left( {\frac{n}{{n - 1}}} \right)} \) <strong><em>M1A1A1</em></strong></p>
<p>\(\left( {1 + \sum\limits_{r = 1}^{n - 1} {\frac{1}{{r + 1}} < 1 + \sum\limits_{r = 1}^{n - 1} {\ln \left( {\frac{{r + 1}}{r}} \right)} } } \right)\)</p>
<p> </p>
<p><strong>Note:</strong> <strong><em>M1 </em></strong>is for using the correct inequality from (a), <strong><em>A1 </em></strong>for both sides beginning with 1, <strong><em>A1 </em></strong>for completely correct expression.</p>
<p> </p>
<p><strong>Note:</strong> The 1 might be added after the sums have been calculated.</p>
<p> </p>
<p>\( = 1 + \ln n\) <strong><em>AG</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>from (b)(i) \({U_n} > \ln (1 + n) - \ln n > 0\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\({U_{n + 1}} - {U_n} = \sum\limits_{r = 1}^{n + 1} {\frac{1}{r} - \ln (n + 1) - \sum\limits_{r = 1}^n {\frac{1}{r} + \ln n} } \) <strong><em>M1</em></strong></p>
<p>\( = \frac{1}{{n + 1}} - \ln \left( {\frac{{n + 1}}{n}} \right)\) <strong><em>A1</em></strong></p>
<p>\( < 0\) (using the result proved in (a)) <strong><em>A1</em></strong></p>
<p>\({U_{n + 1}} < {U_n}\) <strong><em>AG</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>it follows from the two results that \(\{ {U_n}\} \) cannot be divergent either in the sense of tending to \( - \infty \) or oscillating therefore it must be convergent <strong><em>R1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept the use of the result that a bounded (monotonically) decreasing sequence is convergent (allow “positive, decreasing sequence”).</p>
<p> </p>
<p><strong><em>[1 mark]</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.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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</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: 28.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the value of \(\mathop {\lim }\limits_{x \to 1} \left( {\frac{{\ln x}}{{\sin 2\pi x}}} \right)\).</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 Times;"><span style="font-family: 'times new roman', times; font-size: medium;">By using the series expansions for \({{\text{e}}^{{x^2}}}\) and cos <em>x</em> evaluate \(\mathop {\lim }\limits_{x \to 0} \left( {\frac{{1 - {{\text{e}}^{{x^2}}}}}{{1 - \cos x}}} \right).\).</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Using l’Hopital’s rule,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\mathop {\lim }\limits_{x \to 1} \left( {\frac{{\ln x}}{{\sin 2\pi x}}} \right) = \mathop {\lim }\limits_{x \to 1} \left( {\frac{{\frac{1}{x}}}{{2\pi \cos 2\pi x}}} \right)\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{{2\pi }}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.5px 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;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\mathop {\lim }\limits_{x \to 0} \left( {\frac{{1 - {{\text{e}}^{{x^2}}}}}{{1 - \cos x}}} \right) = \mathop {\lim }\limits_{x \to 0} \left( {\frac{{1 - \left( {1 + {x^2} + \frac{{{x^4}}}{{2!}} + \frac{{{x^6}}}{{3!}} + ...} \right)}}{{1 - \left( {1 - \frac{{{x^2}}}{{2!}} + \frac{{{x^4}}}{{4!}} - ...} \right)}}} \right)\) <em><strong>M1A1A1</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>M1 </em></strong>for evidence of using the two series.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px 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;">\( = \mathop {\lim }\limits_{x \to 0} \left( {\frac{{\left( { - {x^2} - \frac{{{x^4}}}{{2!}} - \frac{{{x^6}}}{{3!}} - ...} \right)}}{{\left( {\frac{{{x^2}}}{{2!}} - \frac{{{x^4}}}{{4!}} + ...} \right)}}} \right)\) <em><strong>A1</strong></em><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px 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;">\( = \mathop {\lim }\limits_{x \to 0} \left( {\frac{{\left( { - 1 - \frac{{{x^2}}}{{2!}} - \frac{{{x^4}}}{{3!}} - ...} \right)}}{{\left( {\frac{1}{{2!}} - \frac{{{x^2}}}{{4!}} + ...} \right)}}} \right)\) <em><strong>M1A1</strong></em><br></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;">\( = \frac{{ - 1}}{{\frac{1}{2}}} = - 2\) <em><strong>A1</strong></em><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px 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;">\( = \mathop {\lim }\limits_{x \to 0} \left( {\frac{{\left( { - 2x - \frac{{4{x^3}}}{{2!}} - \frac{{6{x^5}}}{{3!}} - ...} \right)}}{{\left( {\frac{{2x}}{{2!}} - \frac{{4{x^3}}}{{4!}} + ...} \right)}}} \right)\) <em><strong>M1A1</strong></em><br></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;">\( = \mathop {\lim }\limits_{x \to 0} \left( {\frac{{\left( { - 2 - \frac{{4{x^2}}}{{2!}} - \frac{{6{x^4}}}{{3!}} - ...} \right)}}{{\left( {1 - \frac{{4{x^2}}}{{4!}} + ...} \right)}}} \right)\)</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;">\( = \frac{{ - 2}}{1} = - 2\) <em><strong>A1</strong></em><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 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 Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was well done but too often the instruction to use series in part (b) was ignored. When this hint was observed correct solutions followed. </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 Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was well done but too often the instruction to use series in part (b) was ignored. When this hint was observed correct solutions followed.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">A curve that passes through the point (1, 2) is defined by the differential equation</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\[\frac{{{\text{d}}y}}{{{\text{d}}x}} = 2x(1 + {x^2} - y){\text{ }}.\]</span></p>
</div>
<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;">(a) (i) Use Euler’s method to get an approximate value of <em>y </em>when <em>x </em>= 1.3 , taking steps of 0.1. Show intermediate steps to four decimal places in a table.</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;">(ii) How can a more accurate answer be obtained using Euler’s method?</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;">(b) Solve the differential equation giving your answer in the form </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><em style="font-family: 'times new roman', times; font-size: medium;">f</em><span style="font-family: 'times new roman', times; font-size: medium;">(</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;">) .</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: 30.5px 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: 30.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 2x(1 + {x^2} - y)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.5px 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: 30.5px 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: 30.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>A2 </em></strong>for complete table.</span></p>
<p style="margin: 0px 0px 0px 30px; font: 30.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> Award <strong><em>A1 </em></strong>for a reasonable attempt.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.5px 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: 30.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(1.3) = 2.14\,\,\,\,\,{\text{(accept 2.141)}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.5px 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: 30.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Decrease the step size <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.5px 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: 30.5px 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: 30.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) </span><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 2x(1 + {x^2} - y)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} + 2xy = 2x(1 + {x^2})\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Integrating factor is \({{\text{e}}^{\int {2x{\text{d}}x} }} = {{\text{e}}^{{x^2}}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">So, \({{\text{e}}^{{x^2}}}y = \int {(2x} {{\text{e}}^{{x^2}}} + 2x{{\text{e}}^{{x^2}}}{x^2}){\text{d}}x\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {{\text{e}}^{{x^2}}} + {x^2}{{\text{e}}^{{x^2}}} - \int {2x{{\text{e}}^{{x^2}}}{\text{d}}x} \) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {{\text{e}}^{{x^2}}} + {x^2}{{\text{e}}^{{x^2}}} - {{\text{e}}^{{x^2}}} + k\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {x^2}{{\text{e}}^{{x^2}}} + k\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(y = {x^2} + k{{\text{e}}^{ - {x^2}}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 1,{\text{ }}y = 2 \to 2 = 1 + k{{\text{e}}^{ - 1}}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(k = {\text{e}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(y = {x^2} + {{\text{e}}^{1 - {x^2}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[9 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.5px 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: 22.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Some incomplete tables spoiled what were often otherwise good solutions. Although the intermediate steps were asked to four decimal places the answer was not and the usual degree of IB accuracy was expected.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Some candidates surprisingly could not solve what was a fairly easy differential equation in part (b).</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;">The variables <em>x</em> and <em>y</em> are related by \(\frac{{{\text{d}}y}}{{{\text{d}}x}} - y\tan x = \cos x\) .</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;">(a) Find the Maclaurin series for <em>y</em> up to and including the term in \({x^2}\) given that</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;">\(y = - \frac{\pi }{2}\) 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;">(b) Solve the differential equation given that <em>y</em> = 0 when \(x = \pi \) . Give the solution in the form \(y = f(x)\) .</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: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) from \(\frac{{{\text{d}}y}}{{{\text{d}}x}} - y\tan x + \cos x\) , \(f'(0) = 1\) <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;">now \(\frac{{{{\text{d}}^2}y}}{{{\text{d}}{x^2}}} = y{\sec ^2}x + \frac{{{\text{d}}y}}{{{\text{d}}x}}\tan x - \sin x\) <strong><em>M1A1A1A1</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> Award <strong><em>A1</em></strong> for each term on RHS.</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;">\( \Rightarrow f''(0) = - \frac{\pi }{2}\) <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;">\( \Rightarrow y = - \frac{\pi }{2} + x - \frac{{\pi {x^2}}}{4}\) <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>[7 marks]</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;"> </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) recognition of integrating factor <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;">integrating factor is \({{\text{e}}^{\int { - \tan x{\text{d}}x} }}\)</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;">\( = {{\text{e}}^{\ln \cos x}}\) <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;">\( = \cos x\) <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;">\( \Rightarrow y\cos x = \int {{{\cos }^2}x{\text{d}}x} \) <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;">\( \Rightarrow y\cos x = \frac{1}{2}\int {(1 + \cos 2x){\text{d}}x} \) <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;">\( \Rightarrow y\cos x = \frac{x}{2} + \frac{{\sin 2x}}{4} + k\) <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;">when \(x = \pi ,{\text{ }}y = 0 \Rightarrow k = - \frac{\pi }{2}\) <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;">\( \Rightarrow y\cos x = \frac{x}{2} + \frac{{\sin 2x}}{4} - \frac{\pi }{2}\) <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;">\( \Rightarrow y = \sec x\left( {\frac{x}{2} + \frac{{\sin 2x}}{4} - \frac{\pi }{2}} \right)\) <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>[10 marks]</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>Total [17 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;">Part (a) of the question was set up in an unusual way, which caused a problem for a number of candidates as they tried to do part (b) first and then find the Maclaurin series by a standard method. Few were successful as they were usually weaker candidates and made errors in finding the solution \(y = f(x)\) . The majority of candidates knew how to start part (b) and recognised the need to use an integrating factor, but a number failed because they missed out the negative sign on the integrating factor, did not realise that \({{\text{e}}^{\ln \cos x}} = \cos x\) or were unable to integrate \({{{\cos }^2}x}\) . Having said this, a number of candidates succeeded in gaining full marks on this question.</span></p>
</div>
<br><hr><br><div class="specification">
<p>Consider the differential equation \(x\frac{{{\text{d}}y}}{{{\text{d}}x}} - y = {x^p} + 1\) where \(x \in \mathbb{R},\,x \ne 0\) and \(p\) is a positive integer, \(p > 1\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Solve the differential equation given that \(y = - 1\) when \(x = 1\). Give your answer in the form \(y = f\left( x \right)\).</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>Show that the \(x\)-coordinate(s) of the points on the curve \(y = f\left( x \right)\) where \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\) satisfy the equation \({x^{p - 1}} = \frac{1}{p}\).</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>Deduce the set of values for \(p\) such that there are two points on the curve \(y = f\left( x \right)\) where \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\). Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{y}{x} = {x^{p - 1}} + \frac{1}{x}\) <em><strong>(M1)</strong></em></p>
<p>integrating factor \( = {{\text{e}}^{\int { - \frac{1}{x}{\text{d}}x} }}\) <em><strong>M1</strong></em></p>
<p>\({\text{ = }}{{\text{e}}^{ - {\text{ln}}\,x}}\) <em><strong>(A1)</strong></em></p>
<p>= \(\frac{1}{x}\) <em><strong>A1</strong></em></p>
<p>\(\frac{1}{x}\frac{{{\text{d}}y}}{{{\text{d}}x}} - \frac{y}{{{x^2}}} = {x^{p - 2}} + \frac{1}{{{x^2}}}\) <em><strong>(M1)</strong></em></p>
<p>\(\frac{{\text{d}}}{{{\text{d}}x}}\left( {\frac{y}{x}} \right) = {x^{p - 2}} + \frac{1}{{{x^2}}}\)</p>
<p>\(\frac{y}{x} = \frac{1}{{p - 1}}{x^{p - 1}} - \frac{1}{x} + C\) <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Condone the absence of <em>C</em>.</p>
<p>\(y = \frac{1}{{p - 1}}{x^p} + Cx - 1\)</p>
<p>substituting \(x = 1\), \(y = - 1 \Rightarrow C = - \frac{1}{{p - 1}}\) <em><strong>M1</strong> </em></p>
<p><strong>Note:</strong> Award <em><strong>M1</strong> </em>for attempting to find their value of <em>C</em>.</p>
<p>\(y = \frac{1}{{p - 1}}\left( {{x^p} - x} \right) - 1\) <em><strong>A1</strong></em></p>
<p><em><strong>[8 marks]</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>put \(y = vx\) so that \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = v + x\frac{{{\text{d}}v}}{{{\text{d}}x}}\) <em><strong>M1(A1)</strong></em></p>
<p>substituting, <em><strong>M1 </strong></em></p>
<p>\(x\left( {v + x\frac{{{\text{d}}v}}{{{\text{d}}x}}} \right) - vx = {x^p} + 1\) <em><strong>(A1)</strong></em></p>
<p>\(x\frac{{{\text{d}}v}}{{{\text{d}}x}} = {x^{p - 1}} + \frac{1}{x}\) <em><strong>M1</strong></em></p>
<p>\(\frac{{{\text{d}}v}}{{{\text{d}}x}} = {x^{p - 2}} + \frac{1}{{{x^2}}}\)</p>
<p>\(v = \frac{1}{{p - 1}}{x^{p - 1}} - \frac{1}{x} + C\) <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Condone the absence of <em>C</em>.</p>
<p>\(y = \frac{1}{{p - 1}}{x^p} + Cx - 1\)</p>
<p>substituting \(x = 1\), \(y = - 1 \Rightarrow C = - \frac{1}{{p - 1}}\) <em><strong>M1</strong> </em></p>
<p><strong>Note:</strong> Award <em><strong>M1</strong> </em>for attempting to find their value of <em>C</em>.</p>
<p>\(y = \frac{1}{{p - 1}}\left( {{x^p} - x} \right) - 1\) <em><strong>A1</strong></em></p>
<p><em><strong>[8 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>find \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) and solve \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\) for \(x\)</p>
<p>\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{1}{{p - 1}}\left( {p{x^{p - 1}} - 1} \right)\) <em><strong>M1</strong></em></p>
<p>\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0 \Rightarrow p{x^{p - 1}} - 1 = 0\) <em><strong>A1</strong></em></p>
<p>\(p{x^{p - 1}} = 1\)</p>
<p><strong>Note:</strong> Award a maximum of <em><strong>M1A0</strong> </em>if a candidate’s answer to part (a) is incorrect.</p>
<p>\({x^{p - 1}} = \frac{1}{p}\) <em><strong>AG</strong></em></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>substitute \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0\) and their \(y\) into the differential equation and solve for \(x\)</p>
<p>\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0 \Rightarrow - \left( {\frac{{{x^p} - x}}{{p - 1}}} \right) + 1 = {x^p} + 1\) <em><strong>M1</strong></em></p>
<p>\({x^p} - x = {x^p} - p{x^p}\) <em><strong>A1</strong></em></p>
<p>\(p{x^{p - 1}} = 1\)</p>
<p><strong>Note:</strong> Award a maximum of <em><strong>M1A0</strong> </em>if a candidate’s answer to part (a) is incorrect.</p>
<p>\({x^{p - 1}} = \frac{1}{p}\) <em><strong>AG</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<p> </p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>there are two solutions for \(x\) when \(p\) is odd (and \(p > 1\) <em><strong>A1</strong></em></p>
<p>if \(p - 1\) is even there are two solutions (to \({x^{p - 1}} = \frac{1}{p}\))</p>
<p>and if \(p - 1\) is odd there is only one solution (to \({x^{p - 1}} = \frac{1}{p}\)) <em><strong>R1</strong></em></p>
<p><strong>Note:</strong> Only award the <em><strong>R1</strong> </em>if both cases are considered.</p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Use the limit comparison test to prove that \(\sum\limits_{n = 1}^\infty {\frac{1}{{n(n + 1)}}} \) converges.</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: 26.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Using the Maclaurin series for \(\ln (1 + x)\) , show that the Maclaurin series for \(\left( {1 + x} \right)\ln \left( {1 + x} \right)\) is \(x + \sum\limits_{n = 1}^\infty {\frac{{{{( - 1)}^{n + 1}}{x^{n + 1}}}}{{n(n + 1)}}} \)</span><span style="font-family: 'times new roman', times; font-size: medium;">.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">apply the limit comparison test with \(\sum\limits_{n = 1}^\infty {\frac{1}{{{n^2}}}} \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\mathop {\lim }\limits_{n \to \infty } \frac{{\frac{1}{{n(n + 1)}}}}{{\frac{1}{{{n^2}}}}} = \mathop {\lim }\limits_{n \to \infty } \frac{{{n^2}}}{{n(n + 1)}} = \mathop {\lim }\limits_{n \to \infty } \frac{1}{{1 + \frac{1}{n}}} = 1\) <em><strong>M1A1</strong></em><br></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;">(since the limit is finite and \( \ne 0\) ) both series do the same <strong><em>R1</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;">we know that \(\sum\limits_{n = 1}^\infty {\frac{1}{{{n^2}}}} \) converges and hence \(\sum\limits_{n = 1}^\infty {\frac{1}{{n(n + 1)}}} \) also converges <strong><em>R1AG</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>[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: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\((1 + x)\ln (1 + x) = (1 + x)\left( {x - \frac{{{x^2}}}{2} + \frac{{{x^3}}}{3} - \frac{{{x^4}}}{4}...} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \left( {x - \frac{{{x^2}}}{2} + \frac{{{x^3}}}{3} - \frac{{{x^4}}}{4}...} \right) + \left( {{x^2} - \frac{{x3}}{2} + \frac{{{x^4}}}{3} - \frac{{{x^5}}}{4}...} \right)\)</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>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = x + \sum\limits_{n = 1}^\infty {\frac{{{{( - 1)}^n}{x^{n + 1}}}}{{n + 1}} + \sum\limits_{n = 1}^\infty {\frac{{{{( - 1)}^{n + 1}}{x^{n + 1}}}}{n}} } \) <em><strong>A1</strong></em><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = x + \sum\limits_{n = 1}^\infty {{{( - 1)}^{n + 1}}{x^{n + 1}}\left( {\frac{{ - 1}}{{n + 1}} + \frac{1}{n}} \right)} \) <em><strong>M1</strong></em><br></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>OR</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;">\(x + \left( {1 - \frac{1}{2}} \right){x^2} - \left( {\frac{1}{2} - \frac{1}{3}} \right){x^3} + \left( {\frac{1}{3} - \frac{1}{4}} \right){x^4} - …\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = x + \sum\limits_{n = 1}^\infty {{{( - 1)}^{n + 1}}{x^{n + 1}}\left( {\frac{1}{n} - \frac{1}{{n + 1}}} \right)} \) <em><strong>M1</strong></em><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = x + \sum\limits_{n = 1}^\infty {\frac{{{{( - 1)}^{n + 1}}{x^{n + 1}}}}{{n(n + 1)}}} \) <em><strong>AG</strong></em><br></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>[3 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Candidates and teachers need to be aware that the Limit comparison test is distinct from the comparison test. Quite a number of candidates lost most of the marks for this part by doing the wrong test.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Some candidates failed to state that because the result was finite and not equal to zero then the two series converge or diverge together. Others forgot to state, with a reason, that \(\sum\limits_{n = 1}^\infty {\frac{1}{{{n^2}}}} \) converges.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Candidates and teachers need to be aware that the Limit comparison test is distinct from the comparison test. Quite a number of candidates lost most of the marks for this part by doing the wrong test.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Some candidates failed to state that because the result was finite and not equal to zero then the two series converge or diverge together. Others forgot to state, with a reason, that \(\sum\limits_{n = 1}^\infty {\frac{1}{{{n^2}}}} \) converges.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (b) finding the partial fractions was well done. The second part involving the use of telescoping series was less well done, and students were clearly not as familiar with this technique as with some others.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (c) was the least well done of all the questions. It was expected that students would use explicitly the result from the first part of 4(b) or show it once again in order to give a complete answer to this question, rather than just assuming that a pattern spotted in the first few terms would continue.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Candidates need to be informed that unless specifically told otherwise they may use without proof any of the Maclaurin expansions given in the Information Booklet. There were many candidates who lost time and gained no marks by trying to derive the expansion for \(\ln (1 + x)\).</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">In this question you may assume that \(\arctan x\) is continuous and differentiable for \(x \in \mathbb{R}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Consider the infinite geometric series</p>
<p>\[1 - {x^2} + {x^4} - {x^6} + \ldots \;\;\;\left| x \right| < 1.\]</p>
<p>Show that the sum of the series is \(\frac{1}{{1 + {x^2}}}\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence show that an expansion of \(\arctan x\) is \(\arctan x = x - \frac{{{x^3}}}{3} + \frac{{{x^5}}}{5} - \frac{{{x^7}}}{7} + \ldots \)</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">\(f\) is a continuous function defined on \([a,{\text{ }}b]\) and differentiable on \(]a,{\text{ }}b[\) with \(f'(x) > 0\) on \(]a,{\text{ }}b[\).</p>
<p class="p1">Use the mean value theorem to prove that for any \(x,{\text{ }}y \in [a,{\text{ }}b]\), if \(y > x\) then \(f(y) > f(x)\).</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 class="p1">(i) <span class="Apple-converted-space"> </span>Given \(g(x) = x - \arctan x\), prove that \(g'(x) > 0\), for \(x > 0\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Use the result from part (c) to prove that \(\arctan x < x\), for \(x > 0\).</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">Use the result from part (c) to prove that \(\arctan x > x - \frac{{{x^3}}}{3}\), for \(x > 0\).</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>Hence show that \(\frac{{16}}{{3\sqrt 3 }} < \pi < \frac{6}{{\sqrt 3 }}\).</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>\(r = - {x^2},\;\;\;S = \frac{1}{{1 + {x^2}}}\) <strong><em>A1AG</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{1}{{1 + {x^2}}} = 1 - {x^2} + {x^4} - {x^6} + \ldots \)</p>
<p><strong>EITHER</strong></p>
<p>\(\int {\frac{1}{{1 + {x^2}}}{\text{d}}x} = \int {1 - {x^2} + {x^4} - {x^6} + \ldots } {\text{d}}x\) <strong><em>M1</em></strong></p>
<p>\(\arctan x = c + x - \frac{{{x^3}}}{3} + \frac{{{x^5}}}{5} - \frac{{{x^7}}}{7} + \ldots \) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Do not penalize the absence of <em>\(c\) </em>at this stage.</p>
<p> </p>
<p>when \(x = 0\) we have \(\arctan 0 = c\) hence \(c = 0\) <strong><em>M1A1</em></strong></p>
<p><strong>OR</strong></p>
<p>\(\int_0^x {\frac{1}{{1 + {t^2}}}{\text{d}}t = } \int_0^x {1 - {t^2} + {t^4}} - {t^6} + \ldots {\text{d}}t\) <strong><em>M1A1A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Allow <em>\(x\) </em>as the variable as well as the limit.</p>
<p><strong><em>M1 </em></strong>for knowing to integrate, <strong><em>A1 </em></strong>for each of the limits.</p>
<p> </p>
<p>\([\arctan t]_0^x = \left[ {t - \frac{{{t^3}}}{3} + \frac{{{t^5}}}{5} - \frac{{{t^7}}}{7} + \ldots } \right]_0^x\) <strong><em>A1</em></strong></p>
<p>hence \(\arctan x = x - \frac{{{x^3}}}{3} + \frac{{{x^5}}}{5} - \frac{{{x^7}}}{7} + \ldots \) <strong><em>AG</em></strong></p>
<p><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">applying the \(MVT\) to the function \(f\) on the interval \([x,{\text{ }}y]\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">\(\frac{{f(y) - f(x)}}{{y - x}} = f'(c)\;\;\;({\text{for some }}c \in ]x,{\text{ }}y[)\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">\(\frac{{f(y) - f(x)}}{{y - x}} > 0\;\;\;({\text{as }}f'(c) > 0)\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">\(f(y) - f(x) > 0{\text{ as }}y > x\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">\( \Rightarrow f(y) > f(x)\) <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>If they use <em>\(x\) </em>rather than \(c\) they should be awarded <strong><em>M1A0R0</em></strong>, but could get the next <strong><em>R1</em></strong>.</p>
<p class="p1"><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>\(g(x) = x - \arctan x \Rightarrow g'(x) = 1 - \frac{1}{{1 + {x^2}}}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">this is greater than zero because \(\frac{1}{{1 + {x^2}}} < 1\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">so \(g'(x) > 0\) <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>(\(g\) is a continuous function defined on \([0,{\text{ }}b]\) and differentiable on \(]0,{\text{ }}b[\) with \(g'(x) > 0\) on \(]0,{\text{ }}b[\) for all \(b \in \mathbb{R}\))</p>
<p class="p1"><span class="s1">(If </span>\(x \in [0,{\text{ }}b]\) then) from part (c) \(g(x) > g(0)\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">\(x - \arctan x > 0 \Rightarrow \arctan x < x\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p2">(as <em>\(b\) </em>can take any positive value it is true for all <span class="s2">\(x > 0\)) <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></span></p>
<p class="p2"><span class="s2"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">let \(h(x) = \arctan x - \left( {x - \frac{{{x^3}}}{3}} \right)\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p2">(\(h\) is a continuous function defined on \([0,{\text{ }}b]\) and differentiable on <span class="s1">\(]0,{\text{ }}b[\) with \(h'(x) > 0\) on \(]0,{\text{ }}b[\))</span></p>
<p class="p1">\(h'(x) = \frac{1}{{1 + {x^2}}} - (1 - {x^2})\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">\( = \frac{{1 - (1 - {x^2})(1 + {x^2})}}{{1 + {x^2}}} = \frac{{{x^4}}}{{1 + {x^2}}}\) <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p1">\(h'(x) > 0\) hence \(({\text{for }}x \in [0,{\text{ }}b]){\text{ }}h(x) > h(0)( = 0)\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">\( \Rightarrow \arctan x > x - \frac{{{x^3}}}{3}\) <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p3"> </p>
<p class="p1"><strong>Note: </strong>Allow correct working with \(h(x) = x - \frac{{{x^3}}}{3} - \arctan x\).</p>
<p class="p1"><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of \(x - \frac{{{x^3}}}{3} < \arctan x < x\) <strong><em>M1</em></strong></p>
<p>choice of \(x = \frac{1}{{\sqrt 3 }}\) <strong><em>A1</em></strong></p>
<p>\(\frac{1}{{\sqrt 3 }} - \frac{1}{{9\sqrt 3 }} < \frac{\pi }{6} < \frac{1}{{\sqrt 3 }}\) <strong><em>M1</em></strong></p>
<p>\(\frac{8}{{9\sqrt 3 }} < \frac{\pi }{6} < \frac{1}{{\sqrt 3 }}\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award final <strong><em>A1 </em></strong>for a correct inequality with a single fraction on each side that leads to the final answer.</p>
<p> </p>
<p>\(\frac{{16}}{{3\sqrt 3 }} < \pi < \frac{6}{{\sqrt 3 }}\) <strong><em>AG</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<p><strong><em>Total [22 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">Most candidates picked up this mark for realizing the common ratio was \( - {x^2}\).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Quite a few candidates did not recognize the importance of ‘hence’ in this question, losing a lot of time by trying to work out the terms from first principles.</p>
<p class="p1">Of those who integrated the formula from part (a) only a handful remembered to include the ‘\( + c\)’ term, and to verify that this must be equal to zero.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Most candidates were able to achieve some marks on this question. The most commonly lost mark was through not stating that the inequality was unchanged when multiplying by \(y - x{\text{ as }}y > x\).</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">The first part of this question proved to be very straightforward for the majority of candidates.</p>
<p class="p1">In (ii) very few realized that they had to replace the lower variable in the formula from part (c) by zero.</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Candidates found this part difficult, failing to spot which function was required.</p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Many candidates, even those who did not successfully complete (d) (ii) or (e), realized that these parts gave them the necessary inequality.</p>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider the differential equation \(\frac{{{\text{d}}y}}{{{\text{d}}x}} + \left( {\frac{{2x}}{{1 + {x^2}}}} \right)y = {x^2}\), <span class="s1">given that \(y = 2\) when \(x = 0\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that \(1 + {x^2}\)<span class="s2"> </span>is an integrating factor for this differential equation.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Hence solve this differential equation. Give the answer in the form \(y = f(x)\).</p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>METHOD 1</strong></p>
<p class="p1">attempting to find an integrating factor <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(\int {\frac{{2x}}{{1 + {x^2}}}{\text{d}}x = \ln (1 + {x^2})} \) </span><strong><em>(M1)A1</em></strong></p>
<p class="p1">IF is \({{\text{e}}^{\ln (1 + {x^2})}}\) <span class="Apple-converted-space"> </span><strong><em>(M1)A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\( = 1 + {x^2}\) </span><strong><em>AG</em></strong></p>
<p class="p1"><strong>METHOD 2</strong></p>
<p class="p1">multiply by the integrating factor</p>
<p class="p1"><span class="Apple-converted-space">\((1 + {x^2})\frac{{{\text{d}}y}}{{{\text{d}}x}} + 2xy = {x^2}(1 + {x^2})\) </span><strong><em>M1A1</em></strong></p>
<p class="p1">left hand side is equal to the derivative of \((1 + {x^2})y\)</p>
<p class="p1"><strong><em>A3</em></strong></p>
<p class="p1"><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\((1 + {x^2})\frac{{{\text{d}}y}}{{{\text{d}}x}} + 2xy = (1 + {x^2}){x^2}\) </span><strong><em>(M1)</em></strong></p>
<p class="p1">\(\frac{{\text{d}}}{{{\text{d}}x}}\left[ {(1 + {x^2})y} \right] = {x^2} + {x^4}\)</p>
<p class="p1"><span class="Apple-converted-space">\((1 + {x^2})y = \left( {\int {{x^2} + {x^4}{\text{d}}x = } } \right){\text{ }}\frac{{{x^3}}}{3} + \frac{{{x^5}}}{5}( + c)\) </span><strong><em>A1A1</em></strong></p>
<p class="p1">\(y = \frac{1}{{1 + {x^2}}}\left( {\frac{{{x^3}}}{3} + \frac{{{x^5}}}{5} + c} \right)\)</p>
<p class="p1"><span class="Apple-converted-space">\(x = 0,{\text{ }}y = 2 \Rightarrow c = 2\) </span><strong><em>M1A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(y = \frac{1}{{1 + {x^2}}}\left( {\frac{{{x^3}}}{3} + \frac{{{x^5}}}{5} + 2} \right)\) </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[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="specification">
<p class="p1">Consider the function \(f(x) = \frac{1}{{1 + {x^2}}},{\text{ }}x \in \mathbb{R}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Illustrate graphically the inequality, \(\frac{1}{5}\sum\limits_{r = 1}^5 {f\left( {\frac{r}{5}} \right) < \int_0^1 {f(x){\text{d}}x < \frac{1}{5}\sum\limits_{r = 0}^4 {f\left( {\frac{r}{5}} \right)} } } \).</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">Use the inequality in part (a) to find a lower and upper bound for \(\pi \).</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">Show that \(\sum\limits_{r = 0}^{n - 1} {{{( - 1)}^r}{x^{2r}} = \frac{{1 + {{( - 1)}^{n - 1}}{x^{2n}}}}{{1 + {x^2}}}} \).</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>Hence show that \(\pi = 4\left( {\sum\limits_{r = 0}^{n - 1} {\frac{{{{( - 1)}^r}}}{{2r + 1}} - {{( - 1)}^{n - 1}}\int_0^1 {\frac{{{x^{2n}}}}{{1 + {x^2}}}{\text{d}}x} } } \right)\).</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><em><img src="images/Schermafbeelding_2016-01-21_om_10.34.21.png" alt> A1A1A1</em></strong></p>
<p class="p1"><strong><em>A1 </em></strong>for upper rectangles, <strong><em>A1 </em></strong>for lower rectangles, <strong><em>A1 </em></strong>for curve in between with \(0 \le x \le 1\)</p>
<p class="p1">hence \(\frac{1}{5}\sum\limits_{r = 1}^5 {f\left( {\frac{r}{5}} \right) < \int_0^1 {f(x){\text{d}}x < \frac{1}{5}\sum\limits_{r = 0}^4 {f\left( {\frac{r}{5}} \right)} } } \) <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>attempting to integrate from \(0\) to \(1\) <strong><em>(M1)</em></strong></p>
<p>\(\int_0^1 {f(x){\text{d}}x = [\arctan x]_0^1} \)</p>
<p>\( = \frac{\pi }{4}\) <strong><em>A1</em></strong></p>
<p>attempt to evaluate either summation <strong><em>(M1)</em></strong></p>
<p>\(\frac{1}{5}\sum\limits_{r = 1}^5 {f\left( {\frac{r}{5}} \right) < \frac{\pi }{4} < \frac{1}{5}\sum\limits_{r = 0}^4 {f\left( {\frac{r}{5}} \right)} } \)</p>
<p>hence \(\frac{4}{5}\sum\limits_{r = 1}^5 {f\left( {\frac{r}{5}} \right) < \pi < \frac{4}{5}\sum\limits_{r = 0}^4 {f\left( {\frac{r}{5}} \right)} } \)</p>
<p>so \(2.93 < \pi < 3.33\) <strong><em>A1A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Accept any answers that round to \(2.9\) and \(3.3\).</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><strong>EITHER</strong></p>
<p>recognise \(\sum\limits_{r = 0}^{n - 1} {{{( - 1)}^r}{x^{2r}}} \) as a geometric series with \(r = - {x^2}\) <strong><em>M1</em></strong></p>
<p>sum of \(n\) terms is \(\frac{{1 - {{( - {x^2})}^n}}}{{1 - - {x^2}}} = \frac{{1 + {{( - 1)}^{n - 1}}{x^{2n}}}}{{1 + {x^2}}}\) <strong><em>M1AG</em></strong></p>
<p><strong>OR</strong></p>
<p>\(\sum\limits_{r = 0}^{n - 1} {{{( - 1)}^r}(1 + {x^2}){x^{2r}} = (1 + {x^2}){x^0} - (1 + {x^2}){x^2} + (1 + {x^2}){x^4} + \ldots } \)</p>
<p>\( + {( - 1)^{n - 1}}(1 + {x^2}){x^{2n - 2}}\) <strong><em>M1</em></strong></p>
<p>cancelling out middle terms <strong><em>M1</em></strong></p>
<p>\( = 1 + {( - 1)^{n - 1}}{x^{2n}}\) <strong><em>AG</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\sum\limits_{r = 0}^{n - 1} {{{( - 1)}^r}{x^{2r}} = \frac{1}{{1 + {x^2}}} + {{( - 1)}^{n - 1}}\frac{{{x^{2n}}}}{{1 + {x^2}}}} \)</p>
<p>integrating from \(0\) to \(1\) <strong><em>M1</em></strong></p>
<p>\(\left[ {\sum\limits_{r = 0}^{n - 1} {{{( - 1)}^r}\frac{{{x^{2r + 1}}}}{{2r + 1}}} } \right]_0^1 = \int_0^1 {f(x){\text{d}}x + {{( - 1)}^{n - 1}}\int_0^1 {\frac{{{x^{2n}}}}{{1 + {x^2}}}{\text{d}}x} } \) <strong><em>A1A1</em></strong></p>
<p>\(\int_0^1 {f(x){\text{d}}x = \frac{\pi }{4}} \) <strong><em>A1</em></strong></p>
<p>so \(\pi = 4\left( {\sum\limits_{r = 0}^{n - 1} {\frac{{{{( - 1)}^r}}}{{2r + 1}} - {{( - 1)}^{n - 1}}\int_0^1 {\frac{{{x^{2n}}}}{{1 + {x^2}}}{\text{d}}x} } } \right)\) <strong><em>AG</em></strong></p>
<p><em><strong>[4 marks] </strong></em></p>
<p><em><strong>Total [14 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">
<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;">Use L’Hôpital’s Rule to find \(\mathop {\lim }\limits_{x \to 0} \frac{{{{\text{e}}^x} - 1 - x\cos x}}{{{{\sin }^2}x}}\) .</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: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">apply l’Hôpital’s Rule to a \(0/0\) type limit</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;">\(\mathop {\lim }\limits_{x \to 0} \frac{{{{\text{e}}^x} - 1 - x\cos x}}{{{{\sin }^2}x}} = \mathop {\lim }\limits_{x \to 0} \frac{{{{\text{e}}^x} - \cos x + x\sin x}}{{2\sin x\cos x}}\) <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;">noting this is also a \(0/0\) type limit, apply l’Hôpital’s Rule again <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;">obtain \(\mathop {\lim }\limits_{x \to 0} \frac{{{{\text{e}}^x} + \sin x + x\cos x + \sin x}}{{2\cos 2x}}\) <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;">substitution of <em>x</em> = 0 <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;">= 0.5 <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;">[6 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-size: medium; font-family: 'times new roman', times;">The vast majority of candidates were familiar with L’Hôpitals rule and were also able to apply the technique twice as required by the problem. The errors that occurred were mostly due to difficulty in applying the differentiation rules correctly or errors in algebra. A small minority of candidates tried to use the quotient rule but it seemed that most candidates had a good understanding of L’Hôpital’s rule and its application to finding a limit.</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">A function \(f\) is given by \(f(x) = \int_0^x {\ln (2 + \sin t){\text{d}}t} \).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down \(f'(x)\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">By differentiating \(f({x^2})\)</span>, obtain an expression for the derivative of \(\int_0^{{x^2}} {\ln (2 + \sin t){\text{d}}t} \) with respect to \(x\).</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">Hence obtain an expression for the derivative of \(\int_x^{{x^2}} {\ln (2 + \sin t){\text{d}}t} \) <span class="s1">with respect to \(x\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(\ln (2 + \sin x)\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><span class="s1"><strong>Note: <span class="Apple-converted-space"> </span></strong></span>Do not accept \(\ln (2 + \sin t)\)<span class="s1">.</span></p>
<p class="p3"><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">attempt to use chain rule <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\(\frac{{\text{d}}}{{{\text{d}}x}}\left( {f({x^2})} \right) = 2xf'({x^2})\) </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p2"><span class="Apple-converted-space">\( = 2x\ln \left( {2 + \sin ({x^2})} \right)\) </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">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(\int_x^{{x^2}} {\ln (2 + \sin t){\text{d}}t = \int_0^{{x^2}} {\ln (2 + \sin t){\text{d}}t - \int_0^x {\ln (2 + \sin t){\text{d}}t} } } \) </span><strong><em>(M1)(A1)</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(\frac{{\text{d}}}{{{\text{d}}x}}\left( {\int_x^{{x^2}} {\ln (2 + \sin t){\text{d}}t} } \right) = 2x\ln \left( {2 + \sin ({x^2})} \right) - \ln (2 + \sin x)\) </span><strong><em>A1</em></strong></p>
<p class="p1"><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;">
<p class="p1">Many candidates answered this question well. Many others showed no knowledge of this part of the option; candidates that recognized the Fundamental Theorem of Calculus answered this question well. In general the scores were either very low or full marks.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Many candidates answered this question well. Many others showed no knowledge of this part of the option; candidates that recognized the Fundamental Theorem of Calculus answered this question well. In general the scores were either very low or full marks.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Many candidates answered this question well. Many others showed no knowledge of this part of the option; candidates that recognized the Fundamental Theorem of Calculus answered this question well. In general the scores were either very low or full marks.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The function \(f\) is defined by \(f(x) = {{\text{e}}^x}\sin x,{\text{ }}x \in \mathbb{R}\).</p>
</div>
<div class="specification">
<p class="p1">The Maclaurin series is to be used to find an approximate value for \(f(0.5)\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">By finding a suitable number of derivatives of \(f\), </span>determine the Maclaurin series for \(f(x)\) as far as the term in \({x^3}\).</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 class="p1">Hence, or otherwise, determine the exact value of \(\mathop {\lim }\limits_{x \to 0} \frac{{{{\text{e}}^x}\sin x - x - {x^2}}}{{{x^3}}}\).</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>Use the Lagrange form of the error term to find an upper bound for the absolute value of the error in this approximation.</p>
<p class="p2">(ii) <span class="Apple-converted-space"> </span>Deduce from the Lagrange error term whether the approximation will be greater than or less than the actual value of \(f(0.5)\).</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">attempt to use product rule <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\(f'(x) = {{\text{e}}^x}\sin x + {{\text{e}}^x}\cos x\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2"><span class="Apple-converted-space">\(f''(x) = 2{{\text{e}}^x}\cos x\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2"><span class="Apple-converted-space">\(f''(x) = 2{{\text{e}}^x}\cos x - 2{{\text{e}}^x}\sin x\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2">\(f(0) = 0,{\text{ }}f'(0) = 1\)</p>
<p class="p2"><span class="Apple-converted-space">\(f''(0) = 2,{\text{ }}f'''(0) = 2\) </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p2"><span class="Apple-converted-space">\({{\text{e}}^x}\sin x = x + {x^2} + \frac{{{x^3}}}{3} + \ldots \) </span><span class="s1"><strong><em>(M1)A1</em></strong></span></p>
<p class="p1"><strong><em>[7 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>METHOD 1</strong></p>
<p class="p2"><span class="Apple-converted-space">\(\frac{{{{\text{e}}^x}\sin x - x - {x^2}}}{{{x^3}}} = \frac{{x + {x^2} + \frac{{{x^3}}}{3} + \ldots - x - {x^2}}}{{{x^3}}}\) </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p2"><span class="s1">\( \to \frac{1}{3}\) as \(x \to 0\)</span> <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"><span class="Apple-converted-space">\(\mathop {\lim }\limits_{x \to 0} \frac{{{{\text{e}}^x}\sin x - x - {x^2}}}{{{x^3}}} = \mathop {\lim }\limits_{x \to 0} \frac{{{{\text{e}}^x}\sin x + {{\text{e}}^x}\cos x - 1 - 2x}}{{3{x^2}}}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2"><span class="Apple-converted-space">\( = \mathop {\lim }\limits_{x \to 0} \frac{{2{{\text{e}}^x}\cos x - 2}}{{6x}}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2"><span class="Apple-converted-space">\( = \mathop {\lim }\limits_{x \to 0} \frac{{2{{\text{e}}^x}\cos x - 2{{\text{e}}^x}\sin x}}{6} = \frac{1}{3}\) </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">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>attempt to find \({{\text{4}}^{{\text{th}}}}\) derivative from the \({{\text{3}}^{{\text{rd}}}}\) derivative obtained in (a) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\(f''''(x) = - 4{{\text{e}}^x}\sin x\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2">Lagrange error term \( = \frac{{{f^{(n + 1)}}(c){x^{n + 1}}}}{{(n + 1)!}}\) <span class="s1">(where </span><em>c </em>lies between 0 <span class="s1">and \(x\)</span>)</p>
<p class="p2"><span class="Apple-converted-space">\( = - \frac{{4{{\text{e}}^c}\sin c \times {{0.5}^4}}}{{4!}}\) </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1">the maximum absolute value of this expression occurs when \(c = 0.5\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>This <strong><em>A1 </em></strong>is independent of previous <strong><em>M </em></strong><span class="s2">marks.</span></p>
<p class="p2">therefore</p>
<p class="p2">upper bound \( = \frac{{4{{\text{e}}^{0.5}}\sin 0.5 \times {{0.5}^4}}}{{4!}}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p2"><span class="Apple-converted-space">\( = 0.00823\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>the approximation is greater than the actual value because the Lagrange error term is negative <strong><em>R1</em></strong></p>
<p class="p1"><strong><em>[7 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 part of the question was well answered by most candidates. In a few cases candidates failed to follow instructions and attempted to use known series; in a few cases mistakes in the determination of the derivatives prevented other candidates from achieving full marks; part (b) was also well answered using both the Maclaurin expansion or L’Hôpital rule; again in most cases that candidates failed to achieve full marks were due to mistakes in the determination of derivatives.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Part (a) of the question was well answered by most candidates. In a few cases candidates failed to follow instructions and attempted to use known series; in a few cases mistakes in the determination of the derivatives prevented other candidates from achieving full marks; part (b) was also well answered using both the Maclaurin expansion or L’Hôpital rule; again in most cases that candidates failed to achieve full marks were due to mistakes in the determination of derivatives.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Part (c) was poorly answered with few candidates showing familiarity with this part of the option. Most candidates quoted the formula and managed to find the \({4^{{\text{th}}}}\) derivative of \(f\) but then could not use it to obtain the required answer; in other cases candidates did obtain an answer but showed little understanding of its meaning when answering (c)(ii).</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider the infinite series \(S = \sum\limits_{n = 0}^\infty {{u_n}} \) where \({u_n} = \int_{nx}^{(n + 1)\pi } {\frac{{\sin t}}{t}{\text{d}}t} \).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Explain why the series is alternating.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Use the substitution \(T = t - \pi \) in the expression for \({u_{n + 1}}\) to show that \(\left| {{u_{n + 1}}} \right| < \left| {{u_n}} \right|\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Show that the series is convergent.</p>
<div class="marks">[9]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that \(S < 1.65\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="s1">as \(t\) </span>moves through the intervals \([0,{\text{ }}\pi ],{\text{ }}[\pi ,{\text{ }}2\pi ],{\text{ }}[2\pi ,{\text{ }}3\pi ],{\text{ }}[3\pi ,{\text{ }}4\pi ]\), <span class="s1"><em>etc</em></span>, the sign of \(\sin t\), (and therefore the sign of the integral) alternates \( + ,{\text{ }} - ,{\text{ }} + ,{\text{ }} - \), <span class="s1"><em>etc</em>, so that the series is alternating <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></span></p>
<p class="p1"><span class="s1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>R1 </em></strong></span>only if it includes a clear reason that justifies that the sign of the integrand alternates between − and + <span class="s1">and this pattern is valid for all the terms.</span></p>
<p class="p3">The change of signs can be justified by a labelled graph of \(y = \sin (x)\) or \(y = \frac{{\sin x}}{x}\) <span class="s2">that shows the intervals \([0,{\text{ }}\pi ],{\text{ }}[\pi ,{\text{ }}2\pi ],{\text{ }}[2\pi ,{\text{ }}3\pi ],{\text{ }} \ldots \)</span></p>
<p class="p3"><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> \({u_{n + 1}} = \int_{(n + 1)\pi }^{(n + 2)\pi } {\frac{{\sin t}}{t}{\text{d}}t} \)</span></p>
<p class="p1"><strong><em>(M1)</em></strong></p>
<p class="p1">put \(T = t--\pi \) <span class="s1">and \({\text{d}}T = {\text{d}}t\) <span class="Apple-converted-space"> </span></span><strong><em>(M1)</em></strong></p>
<p class="p1">the limits change to \(n\pi ,{\text{ }}(n + 1)\pi \)</p>
<p class="p1">\(\left| {{u_{n + 1}}} \right| = \int_{n\pi }^{(n + 1)\pi } {\frac{{\left| {\sin (T + \pi )} \right|}}{{T + \pi }}{\text{d}}T} \) (or equivalent) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2">\(\left| {\sin (T + \pi )} \right| = \left| {\sin (T)} \right|\) or \(\sin (T + \pi ) = - \sin (T)\) <span class="Apple-converted-space"> </span><span class="s2"><strong><em>(M1)</em></strong></span></p>
<p class="p2">\( = \int_{n\pi }^{(n + 1)\pi } {\frac{{\left| {\sin T} \right|}}{{T + \pi }}{\text{d}}T} \)</p>
<p class="p2"><span class="Apple-converted-space">\( < \int_{n\pi }^{(n + 1)\pi } {\frac{{\left| {\sin T} \right|}}{T}{\text{d}}T = \left| {{u_n}} \right|} \) </span><span class="s2"><strong><em>A1AG</em></strong></span></p>
<p class="p1">(ii) <span class="Apple-converted-space"> \(\left| {{u_n}} \right| = \int_{n\pi }^{(n + 1)\pi } {\frac{{\sin t}}{t}{\text{d}}t} \)</span></p>
<p class="p1"><span class="Apple-converted-space">\( < \int_{n\pi }^{(n + 1)\pi } {\frac{1}{t}{\text{d}}t} \) </span><strong><em>M1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\( = [\ln t]_{n\pi }^{(n + 1)\pi }\) </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\( = \ln \left( {\frac{{n + 1}}{n}} \right)\) </span><strong><em>A1</em></strong></p>
<p class="p1">\( \to \ln 1 = 0\) as \(n \to \infty \)</p>
<p class="p2"><span class="s2">from part (i) \(\left| {{u_n}} \right|\) </span>is a decreasing sequence and since \(\mathop {\lim }\limits_{n \to \infty } \left| {{u_n}} \right| = 0\), <span class="Apple-converted-space"> </span><span class="s2"><strong><em>R1</em></strong></span></p>
<p class="p1">the series is convergent <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p1"><strong><em>[9 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">attempt to calculate the partial sums \(\sum\limits_{i = 0}^{n - 1} {{u_i} = \int_0^{n\pi } {\frac{{\sin t}}{t}{\text{d}}t} } \) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">the first partial sums are</p>
<p class="p1"><img src="images/Schermafbeelding_2017-02-06_om_16.13.20.png" alt="M16/5/MATHL/HP3/ENG/TZ0/SE/M/05.c"></p>
<p class="p1">two consecutive partial sums for \(n \geqslant 4\) <span class="Apple-converted-space"> </span><strong><em>A1A1</em></strong></p>
<p class="p1">(<span class="s1"><em>eg</em> \({S_4} = 1.49\) </span>and \({S_5} = 1.63\) or \({S_{100}} = 1.567 \ldots \) and \({S_{101}} = 1.573 \ldots \))</p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>These answers must be given to a minimum of 3 significant figures.</p>
<p class="p1">the sum to infinity lies between any two consecutive partial sums,</p>
<p class="p3"><span class="s2"><em>eg </em></span>between 1.49 and 1.63 <span class="Apple-converted-space"> </span><span class="s2"><strong><em>R1</em></strong></span></p>
<p class="p1">so that \(S < 1.65\) <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>A1A1R1 </em></strong>to candidates who calculate at least two partial sums for only odd values of \(n\) and state that the upper bound is less than these values.</p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Very few candidates presented a valid reason to justify the alternating nature of the series. In most cases candidates just reformulated the wording of the question by saying that it changed signs and completely ignored the interval over which the expression had to be integrated to obtain each term.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) Most candidates achieved 1 or 2 marks for attempting the given substitution; in most cases candidates failed to find the correct limits of integration for the new variable and then relate the expressions of the consecutive terms of the series. In part (ii) very few correct attempts were seen; in some cases candidates did recognize the conditions for the alternating series to be convergent but very few got close to establish that the limit of the general term was zero.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">A few good attempts to use partial sums were seen although once again candidates showed difficulties in identifying what was needed to show the given answer. In most cases candidates just verified with GDC that in fact for high values of <span class="s1"><em>n </em></span>the series was indeed less than the upper bound given but could not provide a valid argument that justified the given statement.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1"><span class="s1">The curves \(y = f(x)\) and \(y = g(x)\) </span>both pass through the point \((1,{\text{ }}0)\) and are defined by the differential equations \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = x - {y^2}\) and \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = y - {x^2}\) <span class="s1">respectively.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that the tangent to the curve \(y = f(x)\) <span class="s1">at the point \((1,{\text{ }}0)\) </span>is normal to the curve \(y = g(x)\) <span class="s1">at the point \((1,{\text{ }}0)\)</span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find \(g(x)\).</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 class="p1">Use Euler’s method with steps of \(0.2\) <span class="s1">to estimate \(f(2)\) </span>to \(5\) <span class="s1">decimal places.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Explain why \(y = f(x)\) cannot cross the isocline \(x - {y^2} = 0\), for \(x > 1\).</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>(i) Sketch the isoclines \(x - {y^2} = - 2,{\text{ }}0,{\text{ }}1\).</p>
<p>(ii) On the same set of axes, sketch the graph of \(f\).</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>gradient of \(f\) at \((1,{\text{ }}0)\) is \(1 - {0^2} = 1\) and the gradient of \(g\) at \((1,{\text{ }}0)\) is \(0 - {1^2} = - 1\) <strong><em>A1</em></strong></p>
<p>so gradient of normal is \(1\) <strong><em>A1</em></strong></p>
<p>= Gradient of the tangent of \(f\) at \((1,{\text{ }}0)\) <strong><em>AG</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>\(\frac{{{\text{d}}y}}{{{\text{d}}x}} - y = - {x^2}\)</p>
<p>integrating factor is \({{\text{e}}^{\int { - 1{\text{d}}x} }} = {{\text{e}}^{ - x}}\) <strong><em>M1</em></strong></p>
<p>\(y{{\text{e}}^{ - x}} = \int { - {x^2}{{\text{e}}^{ - x}}{\text{d}}x} \) <strong><em>A1</em></strong></p>
<p>\( = {x^2}{{\text{e}}^{ - x}} - \int {2x{{\text{e}}^{ - x}}{\text{d}}x} \) <strong><em>M1</em></strong></p>
<p>\( = {x^2}{{\text{e}}^{ - x}} + 2x{{\text{e}}^{ - x}} - \int {2{{\text{e}}^{ - x}}{\text{d}}x} \)</p>
<p>\( = {x^2}{{\text{e}}^{ - x}} + 2x{{\text{e}}^{ - x}} + 2{{\text{e}}^{ - x}} + c\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Condone missing \( + c\) at this stage.</p>
<p> </p>
<p>\( \Rightarrow g(x) = {x^2} + 2x + 2 + c{{\text{e}}^x}\)</p>
<p>\(g(1) = 0 \Rightarrow c = - \frac{5}{{\text{e}}}\) <strong><em>M1</em></strong></p>
<p>\( \Rightarrow g(x) = {x^2} + 2x + 2 - 5{{\text{e}}^{x - 1}}\) <strong><em>A1</em></strong></p>
<p><strong><em>[6 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">use of \({y_{n + 1}} = {y_n} + hf'({x_n},{\text{ }}{y_n})\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">\({x_0} = 1,{\text{ }}{y_0} = 0\)</p>
<p class="p1">\({x_1} = 1.2,{\text{ }}{y_1} = 0.2\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">\({x_2} = 1.4,{\text{ }}{y_2} = 0.432\) <span class="Apple-converted-space"> </span><strong><em>(M1)(A1)</em></strong></p>
<p class="p1">\({x_3} = 1.6,{\text{ }}{y_3} = 0.67467 \ldots \)</p>
<p class="p1">\({x_4} = 1.8,{\text{ }}{y_4} = 0.90363 \ldots \)</p>
<p class="p1">\({x_5} = 2,{\text{ }}{y_5} = 1.1003255 \ldots \)</p>
<p class="p1">answer \( = 1.10033\) <span class="Apple-converted-space"> </span><strong><em>A1 <span class="Apple-converted-space"> </span>N3</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>A0 </em></strong>or <strong><em>N1 </em></strong><span class="s1">if \(1.10\) </span>given as answer.</p>
<p class="p1"><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">at the point \((1,{\text{ }}0)\), the gradient of \(f\) is positive so the graph of <span class="s1">\(f\) </span>passes into the first quadrant for \(x > 1\)</p>
<p class="p1">in the first quadrant below the curve \(x - {y^2} = 0\) the gradient of \(f\) is positive <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">the curve \(x - {y^2} = 0\) has positive gradient in the first quadrant <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">if \(f\) were to reach \(x - {y^2} = 0\) it would have gradient of zero, and therefore would not cross <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) and (ii)</p>
<p class="p1"><strong><em><img src="images/Schermafbeelding_2016-01-21_om_12.34.00.png" alt> A4</em></strong></p>
<p class="p2"> </p>
<p><strong>Note: </strong>Award <strong><em>A1 </em></strong>for 3 correct isoclines.</p>
<p>Award <strong><em>A1 </em></strong>for \(f\) not reaching \(x - {y^2} = 0\).</p>
<p>Award <strong><em>A1 </em></strong>for turning point of \(f\) on \(x - {y^2} = 0\).</p>
<p>Award <strong><em>A1 </em></strong>for negative gradient to the left of the turning point.</p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>A1 </em></strong>for correct shape and position if curve drawn without any isoclines.</p>
<p><em><strong>[4 marks]</strong></em></p>
<p><em><strong>Total [20 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[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="question">
<p>Use the integral test to determine whether the infinite series \(\sum\limits_{n = 2}^\infty {\frac{1}{{n\sqrt {\ln n} }}} \) is convergent or divergent.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>consider \(I = \int\limits_2^N {\frac{{{\text{d}}x}}{{x\sqrt {\ln x} }}} \) <strong><em>M1A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Do not award <strong><em>A1 </em></strong>if \(n\) is used as the variable or if lower limit equal to 1, but some subsequent <strong><em>A </em></strong>marks can still be awarded. Allow \(\infty \) as upper limit.</p>
<p> </p>
<p>let \(y = \ln x\) <strong><em>(M1)</em></strong></p>
<p>\({\text{d}}y = \frac{{{\text{d}}x}}{x},\) <strong><em>(A1)</em></strong></p>
<p>\(\left[ {2,{\text{ }}N} \right] \Rightarrow \left[ {\ln 2,{\text{ }}\ln N} \right]\)</p>
<p>\(I = \int\limits_{\ln \,2}^{\ln \,N} {\frac{{{\text{d}}y}}{{\sqrt y }}} \) <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Condone absence of limits, or wrong limits.</p>
<p> </p>
<p>\( = \left[ {2\sqrt y } \right]_{\ln 2}^{\ln N}\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> <strong><em>A1 </em></strong>is for the correct integral, irrespective of the limits used. Accept correct use of integration by parts.</p>
<p> </p>
<p>\( = 2\sqrt {\ln N} - 2\sqrt {\ln 2} \) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> <strong><em>M1 </em></strong>is for substituting their limits into their integral and subtracting.</p>
<p> </p>
<p>\( \to \infty {\text{ as }}N \to \infty \) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Allow “\( = \infty \)”, “limit does not exist”, “diverges” or equivalent.</p>
<p>Do not award if wrong limits substituted into the integral but allow \(N\) or \(\infty \) as an upper limit in place of \(\ln N\).</p>
<p> </p>
<p>(by the integral test) the series is divergent (because the integral is divergent) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Do not award this mark if \(\infty \) used as upper limit throughout.</p>
<p> </p>
<p><strong><em>[9 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>Let \(S = \sum\limits_{n = 1}^\infty {\frac{{{{(x - 3)}^n}}}{{{n^2} + 2}}} \).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the limit comparison test to show that the series \(\sum\limits_{n = 1}^\infty {\frac{1}{{{n^2} + 2}}} \) is convergent.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the interval of convergence for \(S\).</p>
<div class="marks">[9]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(\mathop {\lim }\limits_{n \to \infty } \frac{{\frac{1}{{{n^2} + 2}}}}{{\frac{1}{{{n^2}}}}} = \mathop {\lim }\limits_{n \to \infty } \frac{{{n^2}}}{{{n^2} + 2}} = \left( {\mathop {\lim }\limits_{n \to \infty } \left( {1 - \frac{2}{{{n^2} + 2}}} \right)} \right)\) <strong><em>M1</em></strong></p>
<p>\( = 1\) <strong><em>A1</em></strong></p>
<p>since \(\sum\limits_{n = 1}^\infty {\frac{1}{{{n^2}}}} \) converges (a \(p\)-series with \(p = 2\)) <strong><em>R1</em></strong></p>
<p>by limit comparison test, \(\sum\limits_{n = 1}^\infty {\frac{1}{{{n^2} + 2}}} \) also converges <strong><em>AG</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>The <strong><em>R1 </em></strong>is independent of the <strong><em>A1</em></strong>.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>applying the ratio test \(\mathop {\lim }\limits_{n \to \infty } \left| {\frac{{{{(x - 3)}^{n + 1}}}}{{{{(n + 1)}^2} + 2}} \times \frac{{{n^2} + 2}}{{{{(x - 3)}^n}}}} \right|\) <strong><em>M1A1</em></strong></p>
<p>\( = \left| {x - 3} \right|{\text{ }}\left( {{\text{as }}\mathop {\lim }\limits_{n \to \infty } \frac{{({n^2} + 2)}}{{{{(n + 1)}^2} + 2}} = 1} \right)\) <strong><em>A1</em></strong></p>
<p>converges if \(\left| {x - 3} \right| < 1\) (converges for \(2 < x < 4\)) <strong><em>M1</em></strong></p>
<p>considering endpoints \(x = 2\) and \(x = 4\) <strong><em>M1</em></strong></p>
<p>when \(x = 4\), series is \(\sum\limits_{n = 1}^\infty {\frac{1}{{{n^2} + 2}}} \), convergent from (a) <strong><em>A1</em></strong></p>
<p>when \(x = 2\), series is \(\sum\limits_{n = 1}^\infty {\frac{{{{( - 1)}^n}}}{{{n^2} + 2}}} \) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>EITHER</strong></p>
<p>\(\sum\limits_{n = 1}^\infty {\frac{1}{{{n^2} + 2}}} \) is convergent therefore \(\sum\limits_{n = 1}^\infty {\frac{{{{( - 1)}^n}}}{{{n^2} + 2}}} \) is (absolutely) convergent <strong><em>R1</em></strong></p>
<p><strong>OR</strong></p>
<p>\(\frac{1}{{{n^2} + 2}}\) is a decreasing sequence and \(\mathop {\lim }\limits_{n \to \infty } \frac{1}{{{n^2} + 2}} = 0\) so series converges by the alternating series test <strong><em>R1</em></strong></p>
<p> </p>
<p><strong>THEN</strong></p>
<p>interval of convergence is \(2 \leqslant x \leqslant 4\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>The final <strong><em>A1 </em></strong>is dependent on previous <strong><em>A1</em></strong>s – <em>ie</em>, considering correct series when \(x = 2\) and \(x = 4\) and on the final <strong><em>R1</em></strong>.</p>
<p> </p>
<p><strong><em>[9 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The mean value theorem states that if \(f\) is a continuous function on \([a,{\text{ }}b]\) and differentiable on \(]a,{\text{ }}b[\) then \(f’(c) = \frac{{f(b) - f(a)}}{{b - a}}\) for some \(c \in ]a,{\text{ }}b[\).</p>
<p>The function \(g\), defined by \(g(x) = x\cos \left( {\sqrt x } \right)\), satisfies the conditions of the mean value theorem on the interval \([0,{\text{ }}5\pi ]\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For \(a = 0\) and \(b = 5\pi \), use the mean value theorem to find all possible values of \(c\) for the function \(g\).</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>Sketch the graph of \(y = g(x)\) on the interval \([0,{\text{ }}5\pi ]\) and hence illustrate the mean value theorem for the function \(g\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{g(5\pi ) - g(0)}}{{5\pi - 0}} = - 0.6809 \ldots {\text{ }}\left( { = \cos \sqrt {5\pi } } \right)\) (gradient of chord) <strong><em>(A1)</em></strong></p>
<p>\(g’(x) = \cos \left( {\sqrt x } \right) - \frac{{\sqrt x \sin \left( {\sqrt x } \right)}}{2}\) (or equivalent) <strong><em>(M1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>M1 </em></strong>to candidates who attempt to use the product and chain rules.</p>
<p> </p>
<p>attempting to solve \(\cos \left( {\sqrt c } \right) - \frac{{\sqrt c \sin \left( {\sqrt c } \right)}}{2} = - 0.6809 \ldots \) for \(c\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>M1 </em></strong>to candidates who attempt to solve their \(g’(c) = \) gradient of chord.</p>
<p>Do not award <strong><em>M1 </em></strong>to candidates who just attempt to rearrange their equation.</p>
<p> </p>
<p>\(c = 2.26,{\text{ }}11.1\) <strong><em>A1A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Condone candidates working in terms of \(x\).</p>
<p> </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><img src="images/Schermafbeelding_2018-02-09_om_11.32.05.png" alt="N17/5/MATHL/HP3/ENG/TZ0/SE/M/04.b"></p>
<p>correct graph: 2 turning points close to the endpoints, endpoints indicated and correct endpoint behaviour <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Endpoint coordinates are not required. Candidates do not need to indicate axes scales.</p>
<p> </p>
<p>correct chord <strong><em>A1</em></strong></p>
<p>tangents drawn at their values of \(c\) which are approximately parallel to the chord <strong><em>A1A1</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Award <strong><em>A1A0A1A0 </em></strong>to candidates who draw a correct graph, do not draw a chord but draw 2 tangents at their values of \(c\). Condone the absence of their \(c - \) values stated on their sketch. However do not award marks for tangents if no \(c - \) values were found in (a).</p>
<p> </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 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;">Consider the infinite series \(\sum\limits_{n = 1}^\infty {\frac{{(n - 1){x^n}}}{{{n^2} \times {2^n}}}} \) .</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;">Find the radius of convergence.</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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the interval of convergence.</span></p>
<div class="marks">[9]</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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">using the ratio test, \(\frac{{{u_{n + 1}}}}{{{u_n}}} = \frac{{n{x^{n + 1}}}}{{{{(n + 1)}^2}{2^{n + 1}}}} \times \frac{{{n^2}{2^n}}}{{(n - 1){x^n}}}\) <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;">\( = \frac{{{n^3}}}{{{{(n + 1)}^2}(n - 1)}} \times \frac{x}{2}\) <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;">\(\mathop {\lim }\limits_{n \to \infty } \frac{{{u_{n + 1}}}}{{{u_n}}} = \frac{x}{2}\) <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 radius of convergence <em>R</em> satisfies</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;">\(\frac{R}{2} = 1\) so <em>R</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;"><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;">considering <em>x</em> = 2 for which the series is</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;">\(\sum\limits_{n = 1}^\infty {\frac{{(n - 1)}}{{{n^2}}}} \)</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;">using the limit comparison test with the harmonic series <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;">\(\sum\limits_{n = 1}^\infty {\frac{1}{n}} \), which diverges</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;">consider</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;">\(\mathop {\lim }\limits_{n \to \infty } \frac{{{u_n}}}{{\frac{1}{n}}} = \mathop {\lim }\limits_{n \to \infty } \frac{{n - 1}}{n} = 1\) <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;">the series is therefore divergent for <em>x</em> = 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;">when <em>x</em> = –2 , the series is</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;">\(\sum\limits_{n = 1}^\infty {\frac{{(n - 1)}}{{{n^2}}} \times {{( - 1)}^n}} \)</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;">this is an alternating series in which the \({n^{{\text{th}}}}\) term tends to 0 as \(n \to \infty \) <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;">consider \(f(x) = \frac{{x - 1}}{{{x^2}}}\) <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;">\(f'(x) = \frac{{2 - x}}{{{x^3}}}\) <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;">this is negative for \(x > 2\) so the sequence \(\{ |{u_n}|\} \) is eventually decreasing <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;">the series therefore converges when <em>x</em> = –2 by the alternating series test <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;">the interval of convergence is therefore [–2, 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>[9 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 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;">Consider the differential equation \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{{y^2}}}{{1 + x}}\), where <em>x </em>> −1 and <em>y </em>= 1 when <em>x </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;">Use Euler’s method, with a step length of 0.1, to find an approximate value of <em>y </em>when <em>x </em>= 0.5.</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;">(i) Show that \(\frac{{{{\text{d}}^2}y}}{{{\text{d}}{x^2}}} = \frac{{2{y^3} - {y^2}}}{{{{(1 + x)}^2}}}\).</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;">(ii) Hence find the Maclaurin series for <em>y</em>, up to and including the term in \({x^2}\)<span style="font: 7.0px Helvetica;"> </span>.</span></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: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Solve the differential equation.</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 value of <em>a </em>for which \(y \to \infty \) as \(x \to a\).</span></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 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 the first step of</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;">\({y_{n + 1}} = {y_n} + (0.1)f({x_n},\,{y_n})\) with \({y_0} = 1,{\text{ }}{x_0} = 0\) <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;">\({y_1} = 1.1\) <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;">\({y_2} = 1.1 + (0.1)\frac{{{{1.1}^2}}}{{1.1}} = 1.21\) <strong> <em>(M1)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;">\({y_3} = 1.332(0)\) <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;">\({y_4} = 1.4685\) <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;">\({y_5} = 1.62\) <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;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) recognition of both quotient rule and implicit differentiation <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;">\(\frac{{{{\text{d}}^2}y}}{{{\text{d}}{x^2}}} = \frac{{(1 + x)2y\frac{{{\text{d}}y}}{{{\text{d}}x}} - {y^2} \times 1}}{{{{(1 + x)}^2}}}\) <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>Award <strong><em>A1 </em></strong>for first term in numerator, <strong><em>A1 </em></strong>for everything else correct.</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;">\( = \frac{{(1 + x)2y\frac{{{y^2}}}{{1 + x}} - {y^2} \times 1}}{{{{(1 + x)}^2}}}\) <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;">\( = \frac{{2{y^3} - {y^2}}}{{{{(1 + x)}^2}}}\) <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><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;">(ii) attempt to use \(y = y(0) + x\frac{{{\text{d}}y}}{{{\text{d}}x}}(0) + \frac{{{x^2}}}{{2!}}\frac{{{{\text{d}}^2}y}}{{{\text{d}}{x^2}}}(0) + ...\) <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;">\( = 1 + x + \frac{{{x^2}}}{2}\) <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>Award <strong><em>A1 </em></strong>for correct evaluation of \(y(0),{\text{ }}\frac{{dy}}{{dx}}(0),{\text{ }}\frac{{{d^2}y}}{{d{x^2}}}(0)\), <strong><em>A1 </em></strong>for correct series.</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;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[8 marks]</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;">(i) separating the variables \(\int {\frac{1}{{{y^2}}}{\text{d}}y = \int {\frac{1}{{1 + x}}{\text{d}}x} } \) <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;">obtain \( - \frac{1}{y} = \ln (1 + x) + (c)\) <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;">impose initial condition \( - 1 = \ln 1 + c\) <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;">obtain \(y = \frac{1}{{1 - \ln (1 + x)}}\) <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> </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) \(y \to \infty \) if \(\ln (1 + x) \to 1\) , so <em>a</em> = e – 1 <strong><em>(M1)A1</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>: To award <strong><em>A1 </em></strong>must see either \(x \to e - 1\) or <em>a</em> = <em>e</em> – 1 . Do not accept <em>x</em> = <em>e</em> – 1.</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;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[6 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 had a good knowledge of Euler’s method and were confident in applying it to the differential equation in part (a). A few candidates who knew the Euler’s method completed one iteration too many to arrive at an incorrect answer but this was rare. Nearly all candidates who applied the correct technique in part (a) correctly calculated the answer. Most candidates were able to attempt part (b) but some lost marks due to a lack of rigour by not clearly showing the implicit differentiation in the first line of working. Part (c) was reasonably well attempted by many candidates and many could solve the integrals although some did not find the arbitrary constant meaning that it was not possible to solve (ii) of the 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 had a good knowledge of Euler’s method and were confident in applying it to the differential equation in part (a). A few candidates who knew the Euler’s method completed one iteration too many to arrive at an incorrect answer but this was rare. Nearly all candidates who applied the correct technique in part (a) correctly calculated the answer. Most candidates were able to attempt part (b) but some lost marks due to a lack of rigour by not clearly showing the implicit differentiation in the first line of working. Part (c) was reasonably well attempted by many candidates and many could solve the integrals although some did not find the arbitrary constant meaning that it was not possible to solve (ii) of the 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-size: medium; font-family: 'times new roman', times;">Most candidates had a good knowledge of Euler’s method and were confident in applying it to the differential equation in part (a). A few candidates who knew the Euler’s method completed one iteration too many to arrive at an incorrect answer but this was rare. Nearly all candidates who applied the correct technique in part (a) correctly calculated the answer. Most candidates were able to attempt part (b) but some lost marks due to a lack of rigour by not clearly showing the implicit differentiation in the first line of working. Part (c) was reasonably well attempted by many candidates and many could solve the integrals although some did not find the arbitrary constant meaning that it was not possible to solve (ii) of the part (c).</span></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: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Show that the solution of the differential equation</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;">\[\frac{{{\text{d}}y}}{{{\text{d}}x}} = \cos x{\cos ^2}y{\text{,}}\]</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;">given that \(y = \frac{\pi }{4}{\text{ when }}x = \pi {\text{, is }}y = \arctan (1 + \sin x){\text{.}}\)</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) Determine the value of the constant <em>a </em>for which the following limit exists</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;">\[\mathop {\lim }\limits_{x \to \frac{\pi }{2}} \frac{{\arctan (1 + \sin x) - a}}{{{{\left( {x - \frac{\pi }{2}} \right)}^2}}}\]</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;">and evaluate that limit<em>.</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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) this separable equation has general solution</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;">\(\int {{{\sec }^2}y{\text{d}}y = \int {\cos x{\text{d}}x} } \) </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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\tan y = \sin x + c\) </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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the condition gives</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;">\(\tan \frac{\pi }{4} = \sin \pi + c \Rightarrow c = 1\) <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;">the solution is \(\tan y = 1 + \sin x\) <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;">\(y = \arctan (1 + \sin x)\) <strong><em>AG</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><em>[5 marks]</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><em> </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;">(b) the limit cannot exist unless \(a = \arctan \left( {1 + \sin \frac{\pi }{2}} \right) = \arctan 2\) <strong><em>R1A1</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;">in that case the limit can be evaluated using l’Hopital’s rule (twice) limit is</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;">\(\mathop {\lim }\limits_{x \to \frac{\pi }{2}} \frac{{{{\left( {\arctan (1 + \sin x)} \right)}^\prime }}}{{2\left( {x - \frac{\pi }{2}} \right)}} = \mathop {\lim }\limits_{x \to \frac{\pi }{2}} \frac{{y'}}{{2\left( {x - \frac{\pi }{2}} \right)}}\) <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;">where <em>y</em> is the solution of the differential equation</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;">the numerator has zero limit (from the factor \(\cos x\) in the differential equation) <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;">so required limit is</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;">\(\mathop {\lim }\limits_{x \to \frac{\pi }{2}} \frac{{y''}}{2}\) <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;">finally,</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;">\(y'' = - \sin x{\cos ^2}y - 2\cos x\cos y\sin y \times y'(x)\) <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;">since \(\cos y\left( {\frac{\pi }{2}} \right) = \frac{1}{{\sqrt 5 }}\) <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;">\(y'' = - \frac{1}{5}{\text{ at }}x = \frac{\pi }{2}\) <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;">the required limit is \( - \frac{1}{{10}}\) <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;"><strong><em>[12 marks]</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><em>Total [17 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 Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates successfully obtained the displayed solution of the differential equation in part(a). Few complete solutions to part(b) were seen which used the result in part(a). The problem can, however, be solved by direct differentiation although this is algebraically more complicated. Some successful solutions using this method were seen.</span></p>
</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: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the radius of convergence of the infinite series</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;">\[\frac{1}{2}x + \frac{{1 \times 3}}{{2 \times 5}}{x^2} + \frac{{1 \times 3 \times 5}}{{2 \times 5 \times 8}}{x^3} + \frac{{1 \times 3 \times 5 \times 7}}{{2 \times 5 \times 8 \times 11}}{x^4} + \ldots {\text{ .}}\]</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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Determine whether the series \(\sum\limits_{n = 1}^\infty {\sin \left( {\frac{1}{n} + n\pi } \right)} \) is convergent or divergent.</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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the <em>n</em>th term is</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;">\({u_n} = \frac{{1 \times 3 \times 5 \ldots (2n - 1)}}{{2 \times 5 \times 8 \ldots (3n - 1)}}{x^n}\) <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;">(using the ratio test to test for absolute convergence)</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;">\(\frac{{\left| {{u_{n + 1}}} \right|}}{{\left| {{u_n}} \right|}} = \frac{{(2n + 1)}}{{(3n + 2)}}\left| x \right|\) <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;">\(\mathop {\lim }\limits_{n \to \infty } \frac{{\left| {{u_{n + 1}}} \right|}}{{\left| {{u_n}} \right|}} = \frac{{2\left| x \right|}}{3}\) <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;">let <em>R</em> denote the radius of convergence</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;">then \(\frac{{2R}}{3} = 1\) so \(r = \frac{3}{2}\) <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;"><strong>Note:</strong> Do not penalise the absence of absolute value signs.</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>[7 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;"><span style="font-family: 'times new roman', times; font-size: medium;">using the compound angle formula or a graphical method the series can be written in the form <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;">\(\sum\limits_{n = 1}^\infty {{u_n}} \) where \({u_n} = {( - 1)^n}\sin \left( {\frac{1}{n}} \right)\) <strong><em>A2</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;">since \(\frac{1}{n} < \frac{\pi }{2}\) <em>i.e.</em> an angle in the first quadrant, <strong><em>R1</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;">it is an alternating series <strong><em>R1</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;">\({u_n} \to 0{\text{ as }}n \to \infty \) <strong><em>R1</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;">and \(\left| {{u_{n + 1}}} \right| < \left| {{u_n}} \right|\) <strong><em>R1</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;">it follows that the series is convergent <strong><em>R1</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>[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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Solutions to this question were generally disappointing. In (a), many candidates were unable even to find an expression for the <em>n</em>th term so that they could not apply the ratio test.</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;">Solutions to this question were generally disappointing. In (b), few candidates were able to rewrite the <em>n</em>th term in the form \(\sum {{{( - 1)}^n}\sin \left( {\frac{1}{n}} \right)} \) so that most candidates failed to realise that the series was alternating.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the functions \(f\) and \(g\) given by \(f(x) = \frac{{{{\text{e}}^x} + {{\text{e}}^{ - x}}}}{2}{\text{ and }}g(x) = \frac{{{{\text{e}}^x} - {{\text{e}}^{ - x}}}}{2}\).</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: 18.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Show that \(f'(x) = g(x)\) and \(g'(x) = f(x)\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the first three non-zero terms in the Maclaurin expansion of \(f(x)\).</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Hence find the value of \(\mathop {{\text{lim}}}\limits_{x \to 0} \frac{{1 - f(x)}}{{{x^2}}}\).</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: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find the value of the improper integral \(\int_0^\infty {\frac{{g(x)}}{{{{\left[ {f(x)} \right]}^2}}}{\text{d}}x} \).</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: 18.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">any correct step before the given answer <strong><em>A1AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em>, \(f'(x) = \frac{{{{\left( {{{\text{e}}^x}} \right)}^\prime } + {{\left( {{{\text{e}}^{ - x}}} \right)}^\prime }}}{2} = \frac{{{{\text{e}}^x} - {{\text{e}}^{ - x}}}}{2} = g(x)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">any correct step before the given answer <strong><em>A1AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em>, \(g'(x) = \frac{{{{\left( {{{\text{e}}^x}} \right)}^\prime } - {{\left( {{{\text{e}}^{ - x}}} \right)}^\prime }}}{2} = \frac{{{{\text{e}}^x} + {{\text{e}}^{ - x}}}}{2} = f(x)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><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: 18.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">statement and attempted use of the general Maclaurin expansion formula <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(0) = 1;{\text{ }}g(0) = 0\) (or equivalent in terms of derivative values) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(x) = 1 + \frac{{{x^2}}}{2} + \frac{{{x^4}}}{{24}}\) or \(f(x) = 1 + \frac{{{x^2}}}{{2!}} + \frac{{{x^4}}}{{4!}}\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px 'Times New Roman'; color: #3f3f3f;"><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: 18.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\({{\text{e}}^x} = 1 + x + \frac{{{x^2}}}{{2!}} + \frac{{{x^3}}}{{3!}} + \frac{{{x^4}}}{{4!}} + \ldots \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\({{\text{e}}^{ - x}} = 1 - x + \frac{{{x^2}}}{{2!}} - \frac{{{x^3}}}{{3!}} + \frac{{{x^4}}}{{4!}} + \ldots \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">adding and dividing by 2 <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(x) = 1 + \frac{{{x^2}}}{2} + \frac{{{x^4}}}{{24}}\) or \(f(x) = 1 + \frac{{{x^2}}}{{2!}} + \frac{{{x^4}}}{{4!}}\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Notes: </strong>Accept 1, \(\frac{{{x^2}}}{2}\) and \(\frac{{{x^4}}}{{24}}\) or 1, \(\frac{{{x^2}}}{{2!}}\) and \(\frac{{{x^4}}}{{4!}}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font: 23.0px 'Times New Roman';"> </span>Award <strong><em>A1 </em></strong>if two correct terms are seen.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px 'Times New Roman'; color: #3f3f3f;"><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>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">attempted use of the Maclaurin expansion from (b) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\mathop {{\text{lim}}}\limits_{x \to 0} \frac{{1 - f(x)}}{{{x^2}}} = \mathop {{\text{lim}}}\limits_{x \to 0} \frac{{1 - \left( {1 + \frac{{{x^2}}}{2} + \frac{{{x^4}}}{{24}} + \ldots } \right)}}{{{x^2}}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\mathop {{\text{lim}}}\limits_{x \to 0} \left( { - \frac{1}{2} - \frac{{{x^2}}}{{24}} - \ldots } \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = - \frac{1}{2}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">attempted use of L’Hôpital and result from (a) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\mathop {{\text{lim}}}\limits_{x \to 0} \frac{{1 - f(x)}}{{{x^2}}} = \mathop {{\text{lim}}}\limits_{x \to 0} \frac{{ - g(x)}}{{2x}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\mathop {{\text{lim}}}\limits_{x \to 0} \frac{{ - f(x)}}{2}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = - \frac{1}{2}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><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: 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;">use of the substitution \(u = f(x)\) and \(\left( {{\text{d}}u = g(x){\text{d}}x} \right)\) <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;">attempt to integrate \(\int_1^\infty {\frac{{{\text{d}}u}}{{{u^2}}}} \) <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;">obtain \(\left[ { - \frac{1}{u}} \right]_1^\infty \) or \(\left[ { - \frac{1}{{f(x)}}} \right]_0^\infty \) <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;">recognition of an improper integral by use of a limit or statement saying the integral converges <strong><em>R1</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;">obtain 1 <strong><em>A1 N0</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;">\(\int_0^\infty {\frac{{\frac{{{{\text{e}}^x} - {{\text{e}}^{ - x}}}}{2}}}{{{{\left( {\frac{{{{\text{e}}^x} + {{\text{e}}^{ - x}}}}{2}} \right)}^2}}}{\text{d}}x = \int_0^\infty {\frac{{2\left( {{{\text{e}}^x} - {{\text{e}}^{ - x}}} \right)}}{{{{\left( {{{\text{e}}^x} + {{\text{e}}^{ - x}}} \right)}^2}}}{\text{d}}x} } \) <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;">use of the substitution \(u = {{\text{e}}^x} + {{\text{e}}^{ - x}}\) and \(\left( {{\text{d}}u = {{\text{e}}^x} - {{\text{e}}^{ - x}}{\text{d}}x} \right)\) <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;">attempt to integrate \(\int_2^\infty {\frac{{2{\text{d}}u}}{{{u^2}}}} \) <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;">obtain \(\left[ { - \frac{2}{u}} \right]_2^\infty \) <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;">recognition of an improper integral by use of a limit or statement saying the integral converges <strong><em>R1</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;">obtain 1 <strong><em>A1 N0</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>[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;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">A differential equation is given by \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{y}{x}\) , where <em>x </em>> 0 and <em>y </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 Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Solve this differential equation by separating the variables, giving your answer in the form <em>y </em>= <em>f </em>(<em>x</em>) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p 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;">Solve the same differential equation by using the standard homogeneous substitution <em>y </em>= <em>vx </em>.</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;">Solve the same differential equation by the use of an integrating factor.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p 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 <em>y </em>= 20 when <em>x </em>= 2 , find <em>y </em>when <em>x </em>= 5 .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p 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;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{y}{x} \Rightarrow \int {\frac{1}{y}{\text{d}}y = \int {\frac{1}{x}{\text{d}}x} } \) <strong><em>M1</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;">\( \Rightarrow \ln y = \ln x + c\) <strong><em>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;">\( \Rightarrow \ln y = \ln x + \ln k = \ln kx\)</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;">\( \Rightarrow y = kx\) <em><strong>A1</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;"><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: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(y = vx \Rightarrow \frac{{{\text{d}}y}}{{{\text{d}}x}} = v + x\frac{{{\text{d}}v}}{{{\text{d}}x}}\) <strong><em>(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;">so \(v + x\frac{{{\text{d}}v}}{{{\text{d}}x}} = v\) <strong><em>M1</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;">\( \Rightarrow x\frac{{{\text{d}}v}}{{{\text{d}}x}} = 0 \Rightarrow \frac{{{\text{d}}v}}{{{\text{d}}x}} = 0\,\,\,\,\,({\text{as }}x \ne 0)\) <strong><em>R1</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;">\( \Rightarrow v = k\)</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;">\( \Rightarrow \frac{y}{x} = k\,\,\,\,\,( \Rightarrow y = kx)\) <strong><em>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><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: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} + \left( {\frac{{ - 1}}{x}} \right)y = 0\) <strong><em>(M1)</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;">\({\text{IF}} = {{\text{e}}^{\int {\frac{{ - 1}}{x}{\text{d}}x} }} = {{\text{e}}^{ - \ln x}} = \frac{1}{x}\) <strong><em>M1A1</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;">\({x^{ - 1}}\frac{{{\text{d}}y}}{{{\text{d}}x}} - {x^{ - 2}}y = 0\)</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;">\( \Rightarrow \frac{{{\text{d}}[{x^{ - 1}}y]}}{{{\text{d}}x}} = 0\) <strong> <em>(M1)</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;">\( \Rightarrow {x^{ - 1}}y = k\,\,\,\,\,( \Rightarrow y = kx)\) <strong><em>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><em>[5 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;">\(20 = 2k \Rightarrow k = 10{\text{ so }}y(5) = 10 \times 5 = 50\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">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;">This question allowed candidates to demonstrate a range of skills in solving differential equations. Generally this was well done with candidates making mistakes in algebra rather than the techniques themselves. For example a common error in part (a) was to go from \(\ln y = \ln x + c\) to \(y = x + c\)</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: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">This question allowed candidates to demonstrate a range of skills in solving differential equations. Generally this was well done with candidates making mistakes in algebra rather than the techniques themselves. For example a common error in part (a) was to go from \(\ln y = \ln x + c\) to \(y = x + c\)</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: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">This question allowed candidates to demonstrate a range of skills in solving differential equations. Generally this was well done with candidates making mistakes in algebra rather than the techniques themselves. For example a common error in part (a) was to go from \(\ln y = \ln x + c\) to \(y = x + c\)</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;">This question allowed candidates to demonstrate a range of skills in solving differential equations. Generally this was well done with candidates making mistakes in algebra rather than the techniques themselves. For example a common error in part (a) was to go from \(\ln y = \ln x + c\) to \(y = x + c\)</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<p>The function \(f\) is defined by</p>
<p>\[f\left( x \right) = \left\{ {\begin{array}{*{20}{c}}<br> {\left| {x - 2} \right| + 1}&{x < 2} \\ <br> {a{x^2} + bx}&{x \geqslant 2} <br>\end{array}} \right.\]</p>
<p>where \(a\) and \(b\) are real constants</p>
<p>Given that both \(f\) and its derivative are continuous at \(x = 2\), find the value of \(a\) and the value of \(b\).</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>considering continuity at \(x = 2\)</p>
<p>\(\mathop {{\text{lim}}}\limits_{x \to {2^ - }} f\left( x \right) = 1\) and \(\mathop {{\text{lim}}}\limits_{x \to {2^ + }} f\left( x \right) = 4a + 2b\) <em><strong>(M1)</strong></em></p>
<p>\(4a + 2b = 1\) <em><strong>A1</strong></em></p>
<p>considering differentiability at \(x = 2\)</p>
<p>\(f'\left( x \right) = \left\{ {\begin{array}{*{20}{c}}<br> { - 1}&{x < 2} \\ <br> {2ax + b}&{x \geqslant 2} <br>\end{array}} \right.\) <em><strong>(M1)</strong></em></p>
<p>\(\mathop {{\text{lim}}}\limits_{x \to {2^ - }} f'\left( x \right) = - 1\) and \(\mathop {{\text{lim}}}\limits_{x \to {2^ + }} f'\left( x \right) = 4a + b\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> The above <em><strong>M1</strong> </em>is for attempting to find the left and right limit of their derived piecewise function at \(x = 2\).</p>
<p>\(4a + b = - 1\) <em><strong>A1</strong></em></p>
<p>\(a = - \frac{3}{4}\) and \(b = 2\) <em><strong>A1</strong></em></p>
<p><em><strong>[6 marks]</strong></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The mean value theorem states that if \(f\) is a continuous function on \([a,{\text{ }}b]\) and differentiable on \(]a,{\text{ }}b[\) <span class="s1">then \(f'(c) = \frac{{f(b) - f(a)}}{{b - a}}\) </span>for some \(c \in ]a,{\text{ }}b[\).</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>Find the two possible values of \(c\) for the function defined by \(f(x) = {x^3} + 3{x^2} - 2\) on the interval \([ - 3,{\text{ }}1]\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Illustrate this result graphically.</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 class="p1">(i) <span class="Apple-converted-space"> </span>The function \(f\) is continuous on \([a,{\text{ }}b]\), differentiable on \(]a,{\text{ }}b[\) and \(f'(x) = 0\) for all \(x \in ]a,{\text{ }}b[\). Show that \(f(x)\) is constant on \([a,{\text{ }}b]\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Hence, prove that for \(x \in [0,{\text{ }}1],{\text{ }}2\arccos x + \arccos (1 - 2{x^2}) = \pi \).</p>
<div class="marks">[9]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>(i) \(f'(x) = 3{x^2} + 6x\) <strong><em>A1</em></strong></p>
<p>gradient of chord \( = 1\) <strong><em>A1</em></strong></p>
<p>\(3{c^2} + 6c = 1\)</p>
<p>\(c = \frac{{ - 3 \pm 2\sqrt 3 }}{3}{\text{ }}( = - 2.15,{\text{ }}0.155)\) <strong><em>A1A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept any answers that round to the correct 2sf answers \(( - 2.2,{\text{ }}0.15)\).</p>
<p class="p2"> </p>
<p class="p3">(ii) <span class="Apple-converted-space"> <img src="images/Schermafbeelding_2016-01-07_om_11.50.57.png" alt></span></p>
<p>award <strong><em>A1</em></strong> for correct shape and clear indication of correct domain, <strong><em>A1</em></strong> for chord (from \(x = - 3\) to \(x = 1\)) and <strong><em>A1</em></strong> for two tangents drawn at their values of \(c\) <strong><em>A1A1A1</em></strong></p>
<p><strong><em>[7 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>(if a theorem is true for the interval \([a,{\text{ }}b]\), it is also true for any interval \([{x_1},{\text{ }}{x_2}]\) which belongs to \([a,{\text{ }}b]\))</p>
<p>suppose \({x_1},{\text{ }}{x_2} \in [a,{\text{ }}b]\) <strong><em>M1</em></strong></p>
<p>by the \(MVT\), there exists \(c\) such that \(f'(c) = \frac{{f({x_2}) - f({x_1})}}{{{x_2} - {x_1}}} = 0\) <strong><em>M1A1</em></strong></p>
<p>hence \(f({x_1}) = f({x_2})\) <strong><em>R1</em></strong></p>
<p>as \({x_1},{\text{ }}{x_2}\) are arbitrarily chosen, \(f(x)\) is constant on \([a,{\text{ }}b]\)</p>
<p> </p>
<p><strong>Note:</strong> If the above is expressed in terms of \(a\) and \(b\) award <strong><em>M0M1A0R0</em></strong>.</p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>(if a theorem is true for the interval \([a,{\text{ }}b]\), it is also true for any interval \([{x_1},{\text{ }}{x_2}]\) which belongs to \([a,{\text{ }}b]\))</p>
<p>suppose \(x \in [a,{\text{ }}b]\) <strong><em>M1</em></strong></p>
<p>by the \(MVT\), there exists \(c\) such that \(f'(c) = \frac{{f(x) - f(a)}}{{x - a}} = 0\) <strong><em>M1A1</em></strong></p>
<p>hence \(f(x) = f(a) = \) constant <strong><em>R1</em></strong></p>
<p>(ii) attempt to differentiate \((x) = 2\arccos x + \arccos (1 - 2{x^2})\) <strong><em>M1</em></strong></p>
<p>\( - 2\frac{1}{{\sqrt {1 - {x^2}} }} - \frac{{ - 4x}}{{\sqrt {1 - {{(1 - 2{x^2})}^2}} }}\) <strong><em>A1A1</em></strong></p>
<p>\( = - 2\frac{1}{{\sqrt {1 - {x^2}} }} + \frac{{4x}}{{\sqrt {4{x^2} - 4{x^4}} }} = 0\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Only award <strong><em>A1</em></strong> for \(0\) if a correct attempt to simplify the denominator is also seen.</p>
<p> </p>
<p>\(f(x) = f(0) = 2 \times \frac{\pi }{2} + 0 = \pi \) <strong><em>A1AG</em></strong></p>
<p> </p>
<p><strong>Note:</strong> This <strong><em>A1</em></strong> is not dependent on previous marks.</p>
<p> </p>
<p><strong>Note:</strong> Allow any value of \(x \in [0,{\text{ }}1]\).</p>
<p><em><strong>[9 marks]</strong></em></p>
<p><em><strong>Total [16 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) This was well done by most candidates.</p>
<p class="p1">(ii) This was generally poorly done, with many candidates failing to draw the curve correctly as they did not appreciate the importance of the given domain. Another common error was to draw the graph of the derivative rather than the function.</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>This was very poorly done. A lot of the arguments seemed to be stating what was being required to be proved, eg ‘because the derivative is equal to 0 the line is flat’. Most candidates did not realise the importance of testing a point inside the interval, so the most common solutions seen involved the Mean Value Theorem applied to the end points. In addition there was some confusion between the Mean Value Theorem and Rolle’s Theorem.</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>It was pleasing that so many candidates spotted the link with the previous part of the question. The most common error after this point was to differentiate incorrectly. Candidates should be aware this is a ‘prove’ question, and so it was not sufficient simply to state, for example, \(f(0) = \pi \).</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>Use l’Hôpital’s rule to determine the value of</p>
<p>\[\mathop {\lim }\limits_{x \to 0} \frac{{{{\sin }^2}x}}{{x\ln (1 + x)}}.\]</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>attempt to use l’Hôpital’s rule, <strong><em>M1</em></strong></p>
<p>\({\text{limit}} = \mathop {\lim }\limits_{x \to 0} \frac{{2\sin x\cos x}}{{\ln (1 + x) + \frac{x}{{1 + x}}}}\)\(\,\,\,\)or\(\,\,\,\)\(\frac{{\sin 2x}}{{\ln (1 + x) + \frac{x}{{1 + x}}}}\) <strong><em>A1A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>A1 </em></strong>for numerator <strong><em>A1 </em></strong>for denominator.</p>
<p> </p>
<p>this gives 0/0 so use the rule again <strong><em>(M1)</em></strong></p>
<p>\( = \mathop {\lim }\limits_{x \to 0} \frac{{2{{\cos }^2}x - 2{{\sin }^2}x}}{{\frac{1}{{1 + x}} + \frac{{1 + x - x}}{{{{(1 + x)}^2}}}}}\)\(\,\,\,\)or\(\,\,\,\)\(\frac{{2\cos 2x}}{{\frac{{2 + x}}{{{{(1 + x)}^2}}}}}\) <strong><em>A1A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>A1 </em></strong>for numerator <strong><em>A1 </em></strong>for denominator.</p>
<p> </p>
<p>\( = 1\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> This <strong><em>A1 </em></strong>is dependent on all previous marks being awarded, except when the first application of L’Hopital’s does not lead to 0/0, when it should be awarded for the correct limit of their derived function.</p>
<p> </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="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;">Solve the differential equation</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;">\[(x - 1)\frac{{{\text{d}}y}}{{{\text{d}}x}} + xy = (x - 1){{\text{e}}^{ - x}}\]</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;">given that <em>y</em> = 1 when <em>x</em> = 0. Give your answer in the form \(y = f(x)\).</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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">writing the differential equation in standard form gives</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;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} + \frac{x}{{x - 1}}y = {{\text{e}}^{ - x}}\) <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;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int {\frac{x}{{x - 1}}{\text{d}}x = \int {\left( {1 + \frac{1}{{x - 1}}} \right){\text{d}}x = x + \ln (x - 1)} } \) <strong><em>M1A1</em></strong></span></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;">hence integrating factor is \({{\text{e}}^{x + \ln (x - 1)}} = (x - 1){{\text{e}}^x}\) <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;">hence, \((x - 1){{\text{e}}^x}\frac{{{\text{d}}y}}{{{\text{d}}x}} + x{{\text{e}}^x}y = x - 1\) <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;">\( \Rightarrow \frac{{{\text{d}}\left[ {(x - 1){{\text{e}}^x}y} \right]}}{{{\text{d}}x}} = x - 1\) <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;">\( \Rightarrow (x - 1){{\text{e}}^x}y = \int {(x - 1){\text{d}}x} \) <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;">\( \Rightarrow (x - 1){{\text{e}}^x}y = \frac{{{x^2}}}{2} - x + c\) <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;">substituting (0, 1), <em>c</em> = –1 <strong><em>(M1)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;">\( \Rightarrow (x - 1){{\text{e}}^x}y = \frac{{{x^2} - 2x - 2}}{2}\) <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;">hence, \(y = \frac{{{x^2} - 2x - 2}}{{2(x - 1){{\text{e}}^x}}}\) (or equivalent) <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>[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;">Apart from some candidates who thought the differential equation was homogenous, the others were usually able to make a good start, and found it quite straightforward. Some made errors after identifying the correct integrating factor, and so lost accuracy marks.</span></p>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Prove by induction that \(n! > {3^n}\), for \(n \ge 7,{\text{ }}n \in \mathbb{Z}\).</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence use the comparison test to prove that the series \(\sum\limits_{r = 1}^\infty {\frac{{{2^r}}}{{r!}}} \) converges.</p>
<div class="marks">[6]</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">if \(n = 7\) <span class="s1">then </span>\(7! > {3^7}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">so true for \(n = 7\)</p>
<p class="p1">assume true for \(n = k\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1"><span class="s1">so </span>\(k! > {3^k}\)</p>
<p class="p1">consider \(n = k + 1\)</p>
<p class="p1">\((k + 1)! = (k + 1)k!\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">\( > (k + 1){3^k}\)</p>
<p class="p1">\( > 3.3k\;\;\;({\text{as }}k > 6)\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">\( = {3^{k + 1}}\)</p>
<p class="p1">hence if true for \(n = k\) then also true for \(n = k + 1\). As true for \(n = 7\), so true for all \(n \ge 7\). <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Do not award the <strong><em>R1 </em></strong>if the two <strong><em>M </em></strong>marks have not been awarded.</p>
<p class="p3"><em><strong>[5 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>consider the series \(\sum\limits_{r = 7}^\infty {{a_r}} \), where \({a_r} = \frac{{{2^r}}}{{r!}}\) <strong><em>R1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award the <strong><em>R1 </em></strong>for starting at \(r = 7\)</p>
<p> </p>
<p>compare to the series \(\sum\limits_{r=7}^\infty {{b_r}} \) where \({b_r} = \frac{{{2^r}}}{{{3^r}}}\) <strong><em>M1</em></strong></p>
<p>\(\sum\limits_{r = 7}^\infty {{b_r}} \) is an infinite Geometric Series with \(r = \frac{2}{3}\) and hence converges <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award the <strong><em>A1 </em></strong>even if series starts at \(r = 1\).</p>
<p> </p>
<p>as \(r! > {3^r}\) so \((0 < ){a_r} < {b_r}\) for all \(r \ge 7\) <strong><em>M1R1</em></strong></p>
<p>as \(\sum\limits_{r = 7}^\infty {{b_r}} \) converges and \({a_r} < {b_r}\) so \(\sum\limits_{r = 7}^\infty {{a_r}} \) must converge</p>
<p> </p>
<p><strong>Note: </strong>Award the <strong><em>A1 </em></strong>even if series starts at \(r = 1\).</p>
<p> </p>
<p>as \(\sum\limits_{r = 1}^6 {{a_r}} \) is finite, so \(\sum\limits_{r = 1}^\infty {{a_r}} \) must converge <strong><em>R1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>If the limit comparison test is used award marks to a maximum of <strong><em>R1M1A1M0A0R1</em></strong>.</p>
<p><em><strong>[6 marks]</strong></em></p>
<p><em><strong>Total [11 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>Consider the differential equation \(\frac{{{\text{d}}y}}{{{\text{d}}x}} + \frac{x}{{{x^2} + 1}}y = x\) where \(y = 1\) when \(x = 0\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that \(\sqrt {{x^2} + 1} \) is an integrating factor for this differential equation.</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>Solve the differential equation giving your answer in the form \(y = f(x)\).</p>
<div class="marks">[6]</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>integrating factor \( = {{\text{e}}^{\int {\frac{x}{{{x^2} + 1}}{\text{d}}x} }}\) <strong><em>(M1)</em></strong></p>
<p>\(\int {\frac{x}{{{x^2} + 1}}{\text{d}}x = \frac{1}{2}\ln ({x^2} + 1)} \) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>M1 </em></strong>for use of \(u = {x^2} + 1\) for example or \(\int {\frac{{f'(x)}}{{f(x)}}{\text{d}}x = \ln f(x)} \).</p>
<p> </p>
<p>integrating factor \( = {{\text{e}}^{\frac{1}{2}\ln ({x^2} + 1)}}\) <strong><em>A1</em></strong></p>
<p>\( = {{\text{e}}^{\ln \left( {\sqrt {{x^2} + 1} } \right)}}\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>A1 </em></strong>for \({{\text{e}}^{\ln \sqrt u }}\) where \(u = {x^2} + 1\).</p>
<p> </p>
<p>\( = \sqrt {{x^2} + 1} \) <strong><em>AG</em></strong></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>\(\frac{{\text{d}}}{{{\text{d}}x}}\left( {y\sqrt {{x^2} + 1} } \right) = \frac{{{\text{d}}y}}{{{\text{d}}x}}\sqrt {{x^2} + 1} + \frac{x}{{\sqrt {{x^2} + 1} }}y\) <strong><em>M1A1</em></strong></p>
<p>\(\sqrt {{x^2} + 1} \left( {\frac{{{\text{d}}y}}{{{\text{d}}x}} + \frac{x}{{{x^2} + 1}}y} \right)\) <strong><em>M1A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>M1 </em></strong>for attempting to express in the form \(\sqrt {{x^2} + 1} \times {\text{(LHS of de)}}\).</p>
<p> </p>
<p>so \(\sqrt {{x^2} + 1} \) is an integrating factor for this differential equation <strong><em>AG</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\sqrt {{x^2} + 1} \frac{{{\text{d}}y}}{{{\text{d}}x}} + \frac{x}{{\sqrt {{x^2} + 1} }}y = x\sqrt {{x^2} + 1} \) (or equivalent) <strong><em>(M1)</em></strong></p>
<p>\(\frac{{\text{d}}}{{{\text{d}}x}}\left( {y\sqrt {{x^2} + 1} } \right) = x\sqrt {{x^2} + 1} \)</p>
<p>\(y\sqrt {{x^2} + 1} = \int {x\sqrt {{x^2} + 1} {\text{d}}x{\text{ }}\left( {y = \frac{1}{{\sqrt {{x^2} + 1} }}\int {x\sqrt {{x^2} + 1} {\text{d}}x} } \right)} \) <strong><em>A1</em></strong></p>
<p>\( = \frac{1}{3}{({x^2} + 1)^{\frac{3}{2}}} + C\) <strong><em>(M1)A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>M1 </em></strong>for using an appropriate substitution.</p>
<p> </p>
<p><strong>Note: </strong>Condone the absence of \(C\).</p>
<p> </p>
<p>substituting \(x = 0,{\text{ }}y = 1 \Rightarrow C = \frac{2}{3}\) <strong><em>M1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>M1 </em></strong>for attempting to find their value of \(C\).</p>
<p> </p>
<p>\(y = \frac{1}{3}({x^2} + 1) + \frac{2}{{3\sqrt {{x^2} + 1} }}{\text{ }}\left( {y = \frac{{{{({x^2} + 1)}^{\frac{3}{2}}} + 2}}{{3\sqrt {{x^2} + 1} }}} \right)\) <strong><em>A1</em></strong></p>
<p><strong><em>[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" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Show that \(n! \geqslant {2^{n - 1}}\), for \(n \geqslant 1\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p 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;">Hence use the comparison test to determine whether the series \(\sum\limits_{n = 1}^\infty {\frac{1}{{n!}}} \) converges or diverges.</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: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">for \(n \geqslant 1,{\text{ }}n! = n(n - 1)(n - 2) \ldots 3 \times 2 \times 1 \geqslant 2 \times 2 \times 2 \ldots 2 \times 2 \times 1 = {2^{n - 1}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow n! \geqslant {2^{n - 1}}{\text{ for }}n \geqslant 1\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px 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: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(n! \geqslant {2^{n - 1}} \Rightarrow \frac{1}{{n!}} \leqslant \frac{1}{{{2^{n - 1}}}}{\text{ for }}n \geqslant 1\) <strong><em>A1</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;">\(\sum\limits_{n = 1}^\infty {\frac{1}{{{2^{n - 1}}}}} \) is a positive converging geometric series <strong><em>R1</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;">hence \(\sum\limits_{n = 1}^\infty {\frac{1}{{n!}}} \) converges by the comparison test <strong><em>R1</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>[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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) of this question was found challenging by the majority of candidates, a fairly common ‘solution’ being that the result is true for <em>n</em> = 1, 2, 3 and therefore true for all <em>n</em>. Some candidates attempted to use induction which is a valid method but no completely correct solution using this method was seen. Candidates found part (b) more accessible and many correct solutions were seen. The most common problem was candidates using an incorrect comparison test, failing to realise that what was required was a comparison between \(\sum {\frac{1}{{n!}}} \) and \(\sum {\frac{1}{{{2^{n - 1}}}}} \).</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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) of this question was found challenging by the majority of candidates, a fairly common ‘solution’ being that the result is true for <em>n</em> = 1, 2, 3 and therefore true for all <em>n</em>. Some candidates attempted to use induction which is a valid method but no completely correct solution using this method was seen. Candidates found part (b) more accessible and many correct solutions were seen. The most common problem was candidates using an incorrect comparison test, failing to realise that what was required was a comparison between \(\sum {\frac{1}{{n!}}} \) and \(\sum {\frac{1}{{{2^{n - 1}}}}} \).</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the series \(\sum\limits_{n = 2}^\infty {\frac{1}{{{n^2}\ln n}}} \) converges.</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>(i) Show that \(\ln (n) + \ln \left( {1 + \frac{1}{n}} \right) = \ln (n + 1)\).</p>
<p>(ii) Using this result, show that an application of the ratio test fails to determine whether or not \(\sum\limits_{n = 2}^\infty {\frac{1}{{n\ln n}}} \) converges.</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>(i) State why the integral test can be used to determine the convergence or divergence of \(\sum\limits_{n = 2}^\infty {\frac{1}{{n\ln n}}} \).</p>
<p>(ii) Hence determine the convergence or divergence of \(\sum\limits_{n = 2}^\infty {\frac{1}{{n\ln n}}} \).</p>
<div class="marks">[8]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>\((0 < )\frac{1}{{{n^2}\ln (n)}} < \frac{1}{{{n^2}}},{\text{ }}({\text{for }}n \ge 3)\) <strong><em>A1</em></strong></p>
<p>\(\sum\limits_{n = 2}^\infty {\frac{1}{{{n^2}}}} \) converges <strong><em>A1</em></strong></p>
<p>by the comparison test ( \(\sum\limits_{n = 2}^\infty {\frac{1}{{{n^2}}}} \) converges implies) \(\sum\limits_{n = 2}^\infty {\frac{1}{{{n^2}\ln (n)}}} \) converges <strong><em>R1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Mention of using the comparison test may have come earlier.</p>
<p>Only award <strong><em>R1</em></strong> if previous 2 <strong><em>A1</em></strong>s have been awarded.</p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>\(\mathop {\lim }\limits_{n \to \infty } \left( {\frac{{\frac{1}{{{n^2}\ln n}}}}{{\frac{1}{{{n^2}}}}}} \right) = \mathop {\lim }\limits_{n \to \infty } \frac{1}{{\ln n}} = 0\) <strong><em>A1</em></strong></p>
<p>\(\sum\limits_{n = 2}^\infty {\frac{1}{{{n^2}}}} \) converges <strong><em>A1</em></strong></p>
<p>by the limit comparison test (if the limit is \(0\) and the series represented by the denominator converges, then so does the series represented by the numerator, hence) \(\sum\limits_{n = 2}^\infty {\frac{1}{{{n^2}\ln (n)}}} \) converges <strong><em>R1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Mention of using the limit comparison test may come earlier.</p>
<p>Do not award the <strong><em>R1</em></strong> if incorrect justifications are given, for example the series “converge or diverge together”.</p>
<p>Only award <strong><em>R1</em></strong> if previous 2 <strong><em>A1</em></strong>s have been awarded.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span><strong>EITHER</strong></p>
<p class="p2">\(\ln (n) + \ln \left( {1 + \frac{1}{n}} \right) = \ln \left( {n\left( {1 + \frac{1}{n}} \right)} \right)\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong>OR</strong></p>
<p class="p2">\(\ln (n) + \ln \left( {1 + \frac{1}{n}} \right) = \ln (n) + \ln \left( {\frac{{n + 1}}{n}} \right)\)</p>
<p class="p2">\( = \ln (n) + \ln (n + 1) - \ln (n)\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong>THEN</strong></p>
<p class="p2">\( = \ln (n + 1)\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>AG</em></strong></span></p>
<p class="p2">(ii) <span class="Apple-converted-space"> </span>attempt to use the ratio test \(\frac{n}{{(n + 1)}}\frac{{\ln (n)}}{{\ln (n + 1)}}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p2">\(\frac{n}{{n + 1}} \to 1{\text{ as }}n \to \infty \) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p2">\(\frac{{\ln (n)}}{{\ln (n + 1)}} = \frac{{\ln (n)}}{{\ln (n) + \ln \left( {1 + \frac{1}{n}} \right)}}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p2">\( \to 1\;\;\;({\text{as }}n \to \infty )\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p2">\(\frac{n}{{(n + 1)}}\frac{{\ln (n)}}{{\ln (n + 1)}} \to 1\;\;\;({\text{as }}n \to \infty )\;\;\;\)<span class="s1">hence ratio test is inconclusive <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></span></p>
<p class="p3"> </p>
<p class="p1"><strong>Note:</strong> <span class="Apple-converted-space"> </span>A link with the limit equalling \(1\) and the result being inconclusive needs to be given for <strong><em>R1</em></strong>.</p>
<p class="p1"><em><strong>[6 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="s1">(i) <span class="Apple-converted-space"> </span></span>consider \(f(x) = \frac{1}{{x\ln x}}\;\;\;({\text{for }}x > 1)\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="s1">\(f(x)\) </span>is continuous and positive <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">and is (monotonically) decreasing <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note:</strong> <span class="Apple-converted-space"> </span>If a candidate uses \(n\) rather than \(x\)<span class="s1">, award as follows</span></p>
<p class="p1"><span class="s1">\(\frac{1}{{n\ln n}}\) </span>is positive and decreasing <span class="Apple-converted-space"> </span><strong><em>A1A1</em></strong></p>
<p class="p3">\(\frac{1}{{n\ln n}}\) is continuous for \(n \in \mathbb{R},{\text{ }}n > 1\) <strong><em>A1</em></strong> (only award this mark if the domain has been explicitly changed).</p>
<p class="p4"> </p>
<p class="p3">(ii) <span class="Apple-converted-space"> </span>consider \(\int_2^R {\frac{1}{{x\ln x}}{\text{d}}x} \) <span class="Apple-converted-space"> </span><span class="s2"><strong><em>M1</em></strong></span></p>
<p class="p3">\( = \left[ {\ln (\ln x)} \right]_2^R\) <span class="Apple-converted-space"> </span><span class="s2"><strong><em>(M1)A1</em></strong></span></p>
<p class="p3">\( \to \infty {\text{ as }}R \to \infty \) <span class="Apple-converted-space"> </span><span class="s2"><strong><em>R1</em></strong></span></p>
<p class="p1">hence series diverges <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p4"> </p>
<p class="p3"><strong>Note:</strong> <span class="Apple-converted-space"> </span>Condone the use of \(\infty \) in place of \(R\).</p>
<p class="p2"> </p>
<p class="p1"><strong>Note:</strong> <span class="Apple-converted-space"> </span>If the lower limit is not equal to \(2\), but the expression is integrated correctly award <strong><em>M0M1A1R0A0</em></strong>.</p>
<p class="p1"><em><strong>[8 marks]</strong></em></p>
<p class="p1"><em><strong>Total [17 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">In this part the required test was not given in the question. This led to some students attempting inappropriate methods. When using the comparison or limit comparision test many candidates wrote the incorrect statement \(\frac{1}{{{n^2}}}\) converges, (<em>p</em>-series) rather than the correct one with \(\sum {} \). This perhaps indicates a lack of understanding of the concepts involved.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">There were many good, well argued answers to this part. Most candidates recognised the importance of the result in part (i) to find the limit in part (ii). Generally a standard result such as \(\mathop {\lim }\limits_{n \to \infty } \left( {\frac{n}{{n + 1}}} \right) = 1\) can simply be quoted, but other limits such as \(\mathop {\lim }\limits_{n \to \infty } \left( {\frac{{\ln n}}{{\ln (n + 1)}}} \right) = 1\) need to be carefully justified.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Candidates need to be aware of the necessary conditions for all the series tests.</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>The integration was well done by the candidates. Most also made the correct link between the integral being undefined and the series diverging. In this question it was not necessary to initially take a finite upper limit and the use of \(\infty \) was acceptable. This was due to the command term being ‘determine’. In q4b a finite upper limit was required, as the command term was ‘show’. To ensure full marks are always awarded candidates should err on the side of caution and always use limit notation when working out indefinite integrals.</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;">The Taylor series of \(\sqrt x \) about <em>x</em> = 1 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;">\[{a_0} + {a_1}(x - 1) + {a_2}{(x - 1)^2} + {a_3}{(x - 1)^3} + \ldots \]</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: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the values of \({a_0},{\text{ }}{a_1},{\text{ }}{a_2}\) and \({a_3}\).</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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Hence, or otherwise, find the value of \(\mathop {\lim }\limits_{x \to 1} \frac{{\sqrt x - 1}}{{x - 1}}\).</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: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">let \(f(x) = \sqrt x ,{\text{ }}f(1) = 1\) <strong><em>(A1)</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;">\(f'(x) = \frac{1}{2}{x^{ - \frac{1}{2}}},{\text{ }}f'(1) = \frac{1}{2}\) <strong><em>(A1)</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;">\(f''(x) = - \frac{1}{4}{x^{ - \frac{3}{2}}},{\text{ }}f''(1) = - \frac{1}{4}\) <strong><em>(A1)</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;">\(f'''(x) = \frac{3}{8}{x^{ - \frac{5}{2}}},{\text{ }}f'''(1) = \frac{3}{8}\) <strong><em>(A1)</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;">\({a_1} = \frac{1}{2} \cdot \frac{1}{{1!}},{\text{ }}{a_2} = - \frac{1}{4} \cdot \frac{1}{{2!}},{\text{ }}{a_3} = \frac{3}{8} \cdot \frac{1}{{3!}}\) <strong><em>(M1)</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;">\({a_0} = 1,{\text{ }}{a_1} = \frac{1}{2},{\text{ }}{a_2} = - \frac{1}{8},{\text{ }}{a_3} = \frac{1}{{16}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px 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 \(y = 1 + \frac{1}{2}(x - 1) - \frac{1}{8}{(x - 1)^2} + \frac{1}{{16}}{(x - 1)^3} + \ldots \)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px 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: 32.0px 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: 31.0px 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: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\mathop {\lim }\limits_{x \to 1} \frac{{\sqrt x - 1}}{{x - 1}} = \mathop {\lim }\limits_{x \to 1} \frac{{\frac{1}{2}(x - 1) - \frac{1}{8}{{(x - 1)}^2} + \ldots }}{{x - 1}}\) <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;">\( = \mathop {\lim }\limits_{x \to 1} \left( {\frac{1}{2} - \frac{1}{8}(x - 1) + \ldots } \right)\) <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;">\( = \frac{1}{2}\) <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;"><strong> </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;">using l’Hôpital’s rule, <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;">\(\mathop {\lim }\limits_{x \to 1} \frac{{\sqrt x - 1}}{{x - 1}} = \mathop {\lim }\limits_{x \to 1} \frac{{\frac{1}{2}{x^{ - \frac{1}{2}}}}}{1}\) <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;">\( = \frac{1}{2}\) <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;"><strong> </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 3</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;">\(\frac{{\sqrt x - 1}}{{x + 1}} = \frac{1}{{\sqrt x + 1}}\) <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;">\(\mathop {\lim }\limits_{x \to 1} \frac{1}{{\sqrt x + 1}} = \frac{1}{2}\) <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;"><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;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates achieved full marks on this question but there were still a large minority of candidates who did not seem familiar with the application of Taylor series. Whilst all candidates who responded to this question were aware of the need to use derivatives many did not correctly use factorials to find the required coefficients. It should be noted that the formula for Taylor series appears in the Information Booklet.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Many candidates achieved full marks on this question but there were still a large minority of candidates who did not seem familiar with the application of Taylor series. Whilst all candidates who responded to this question were aware of the need to use derivatives many did not correctly use factorials to find the required coefficients. It should be noted that the formula for Taylor series appears in the Information Booklet.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Use an integrating factor to show that the general solution for \(\frac{{{\text{d}}x}}{{{\text{d}}t}} - \frac{x}{t} = - \frac{2}{t},{\text{ }}t > 0\) is \(x = 2 + ct\), where <em>\(c\) </em>is a constant.</p>
<p class="p1">The weight in kilograms of a dog, <em>\(t\) </em>weeks after being bought from a pet shop, can be modelled by the following function:</p>
<p class="p1">\[w(t) = \left\{ {\begin{array}{*{20}{c}} {2 + ct}&{0 \le t \le 5} \\ {16 - \frac{{35}}{t}}&{t > 5} \end{array}.} \right.\]</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">Given that \(w(t)\) is continuous, find the value of \(c\).</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">Write down</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>the weight of the dog when bought from the pet shop;</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>an upper bound for the weight of the dog.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Prove from first principles that \(w(t)\) is differentiable at \(t = 5\).</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>integrating factor \({e^{\int { - \frac{1}{2}{\text{d}}t} }} = {e^{ - \ln t}}\left( { = \frac{1}{t}} \right)\) <strong><em>M1A1</em></strong></p>
<p>\(\frac{x}{t} = \int { - \frac{2}{{{t^2}}}{\text{d}}t = \frac{2}{t} + c} \) <strong><em>A1A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>A1 </em></strong>for \(\frac{x}{t}\) and <strong><em>A1 </em></strong>for \({\frac{2}{t} + c}\).</p>
<p> </p>
<p>\(x = 2 + ct\) <strong><em>AG</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">given continuity at \(x = 5\)</p>
<p class="p1">\(5c + 2 = 16 - \frac{{35}}{5} \Rightarrow c = \frac{7}{5}\) <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>\(2\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>any value \( \ge 16\) <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>Accept values less than \(16\) if fully justified by reference to the maximum age for a dog.</p>
<p class="p1"><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\mathop {\lim }\limits_{h \to 0 - } \left( {\frac{{\frac{7}{5}(5 + h) + 2 - \frac{7}{5}(5) - 2}}{h}} \right) = \frac{7}{5}\) <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p1">\(\mathop {\lim }\limits_{h \to 0 + } \left( {\frac{{16 - \frac{{35}}{{5 + h}} - 16 + \frac{{35}}{5}}}{h}} \right)\;\;\;\left( { = \mathop {\lim }\limits_{h \to 0 + } \left( {\frac{{\frac{{ - 35}}{{5 + h}} + 7}}{h}} \right)} \right)\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">\( = \)\(\mathop {\lim }\limits_{h \to 0 + } \left( {\frac{{\frac{{ - 35 + 35 + 7h}}{{(5 + h)}}}}{h}} \right) = \mathop {\lim }\limits_{h \to 0 + } \left( {\frac{7}{{5 + h}}} \right) = \frac{7}{5}\) <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p1">both limits equal so differentiable at \(t = 5\) <span class="Apple-converted-space"> </span><strong><em>R1AG</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>The limits \(t \to 5\) could also be used.</p>
<p class="p1">For each value of \(\frac{7}{5}\) obtained by standard differentiation award <strong><em>A1</em></strong>.</p>
<p class="p1">To gain the other 4 marks a rigorous explanation must be given on how you can get from the left and right hand derivatives to the derivative.</p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>If the candidate works with \(t\) and then substitutes \(t = 5\) at the end award as follows</p>
<p class="p1">First <strong><em>M1 </em></strong>for using formula with <em>\(t\) </em>in the linear case, <strong><em>A1 </em></strong>for \(\frac{7}{5}\)</p>
<p class="p1">Award next 2 method marks even if \(t = 5\) not substituted, <strong><em>A1 </em></strong>for \(\frac{7}{5}\)</p>
<p class="p1"><em><strong>[6 marks]</strong></em></p>
<p class="p1"><em><strong>Total [14 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;">
<p class="p1">This was generally well done. Some candidates did not realize \({e^{ - \ln t}}\) could be simplified to \(\frac{1}{t}\).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">This part was well done by the majority of candidates.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">This part was well done by the majority of candidates.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Some candidates ignored the instruction to prove from first principles and instead used standard differentiation. Some candidates also only found a derivative from one side.</p>
<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: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the power series \(\sum\limits_{k = 1}^\infty {k{{\left( {\frac{x}{2}} \right)}^k}} \).</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;">(i) Find the radius of convergence.</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) Find the interval of convergence.</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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the infinite series \(\sum\limits_{k = 1}^\infty {{{( - 1)}^{k + 1}} \times \frac{k}{{2{k^2} + 1}}} \).</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;">(i) Show that the series is convergent.</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) Show that the sum to infinity of the series is less than 0.25.</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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) consider \(\frac{{{T_{n + 1}}}}{{{T_n}}} = \frac{{\left| {\frac{{(n - 1){x^{n + 1}}}}{{{2^{n + 1}}}}} \right|}}{{\left| {\frac{{n{x^n}}}{{{2^n}}}} \right|}}\) <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;">\( = \frac{{(n + 1)\left| x \right|}}{{2n}}\) <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;">\( \to \frac{{\left| x \right|}}{2}{\text{ as }}n \to \infty \) <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 radius of convergence satisfies</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;">\(\frac{R}{2} = 1\), <em>i.e. R</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;"><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;">(ii) the series converges for \( - 2 < x < 2\), we need to consider \(x = \pm 2\) <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;">when <em>x</em> = 2, the series is \(1 + 2 + 3 + \ldots \) <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;">this is divergent for any one of several reasons <em>e.g.</em> finding an expression for or a comparison test with the harmonic series or noting that \(\mathop {\lim }\limits_{n \to \infty } {u_n} \ne 0\) etc. <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;">when <em>x</em> = – 2, the series is \( - 1 + 2 - 3 + 4 \ldots \) <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;">this is divergent for any one of several reasons</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;"><em>e.g.</em> partial sums are</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;">\( - 1,{\text{ }}1,{\text{ }} - 2,{\text{ }}2,{\text{ }} - 3,{\text{ }}3 \ldots \) or noting that \(\mathop {\lim }\limits_{n \to \infty } {u_n} \ne 0\) <em>etc.</em> <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;">the interval of convergence is \( - 2 < x < 2\) <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;"><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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) this alternating series is convergent because the moduli of successive terms are monotonic decreasing <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;">and the \({n^{{\text{th}}}}\) term tends to zero as \(n \to \infty \) <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> </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) consider the partial sums</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;">0.333, 0.111, 0.269, 0.148, 0.246 <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;">since the sum to infinity lies between any pair of successive partial sums, it follows that the sum to infinity lies between 0.148 and 0.246 so that it is less than 0.25 <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>Note:</strong> Accept a solution which looks only at 0.333, 0.269, 0.246 and states that these are successive upper bounds.</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><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;">
<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;">Most candidates found the radius of convergence correctly but examining the situation when \(x = \pm 2\) often ended in loss of marks through inadequate explanations. In (b)(i) many candidates were able to justify the convergence of the given series. In (b)(ii), however, many candidates seemed unaware of the fact the sum to infinity lies between any pair of successive partial sums.</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;">Most candidates found the radius of convergence correctly but examining the situation when \(x = \pm 2\) often ended in loss of marks through inadequate explanations. In (b)(i) many candidates were able to justify the convergence of the given series. In (b)(ii), however, many candidates seemed unaware of the fact the sum to infinity lies between any pair of successive partial sums.</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 Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Show that the solution of the homogeneous differential equation</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;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{y}{x} + 1,{\text{ }}x > 0,\)</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;">given that \(y = 0{\text{ when }}x = {\text{e, is }}y = x(\ln x - 1)\).</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) Determine the first three derivatives of the function \(f(x) = x(\ln x - 1)\).</span></p>
<p style="margin: 0px 0px 0px 30px; font: 21px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> (ii) Hence find the first three non-zero terms of the Taylor series for <em>f</em>(<em>x</em>) about <em>x </em>= 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: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) <strong>EITHER</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;">use the substitution <em>y</em> = <em>vx</em></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;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}}x + v = v + 1\) <strong><em>M1A1</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;">\(\int {{\text{d}}v = \int {\frac{{{\text{d}}x}}{x}} } \)</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;">by integration</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;">\(v = \frac{y}{x} = \ln x + c\) <strong><em>A1</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>OR</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;">the equation can be rearranged as first order linear</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;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} - \frac{1}{x}y = 1\) <strong><em>M1</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;">the integrating factor <em>I</em> is</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;">\({{\text{e}}^{\int { - \frac{1}{x}{\text{d}}x} }} = {{\text{e}}^{ - \ln x}} = \frac{1}{x}\) <strong><em>A1</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;">multiplying by <em>I</em> gives</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;">\(\frac{{{\text{d}}}}{{{\text{d}}x}}\left( {\frac{1}{x}y} \right) = \frac{1}{x}\)</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;">\(\frac{1}{x}y = \ln x + c\) <strong><em>A1</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>THEN</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;">the condition gives <em>c</em> = –1</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;">so the solution is \(y = x(\ln x - 1)\) <strong><em>AG</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>[5 marks]</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> </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;">(b) (i) \(f'(x) = \ln x - 1 + 1 = \ln x\) <strong><em>A1</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;">\(f''(x) = \frac{1}{x}\) <strong><em>A1</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;">\(f'''(x) = - \frac{1}{{{x^2}}}\) <strong><em>A1</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> </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;">(ii) the Taylor series about <em>x</em> = 1 starts</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;">\(f(x) \approx f(1) + f'(1)(x - 1) + f''(1)\frac{{{{(x - 1)}^2}}}{{2!}} + f'''(1)\frac{{{{(x - 1)}^3}}}{{3!}}\) <strong><em>(M1)</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;">\( = - 1 + \frac{{{{(x - 1)}^2}}}{{2!}} - \frac{{{{(x - 1)}^3}}}{{3!}}\) <strong><em>A1A1A1</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>[7 marks]</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> </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>Total: [12 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 Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part(a) was well done by many candidates. In part(b)(i), however, it was disappointing to see so many candidates unable to differentiate \(x(\ln x - 1)\) correctly. Again, too many candidates were able to quote the general form of a Taylor series expansion, but not how to apply it to the given function.</span></p>
</div>
<br><hr><br><div class="specification">
<p style="text-align: left;">The function \(f\) is defined by \(f(x){\text{ }}={\text{ }}{(\arcsin{\text{ }}x)^2},{\text{ }} - 1 \leqslant x \leqslant 1\).</p>
<p> </p>
</div>
<div class="specification">
<p>The function \(f\) satisfies the equation \(\left( {1 - {x^2}} \right)f''\left( x \right) - xf'\left( x \right) - 2 = 0\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that \(f'\left( 0 \right) = 0\).</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>By differentiating the above equation twice, show that</p>
<p>\[\left( {1 - {x^2}} \right){f^{\left( 4 \right)}}\left( x \right) - 5x{f^{\left( 3 \right)}}\left( x \right) - 4f''\left( x \right) = 0\]</p>
<p>where \({f^{\left( 3 \right)}}\left( x \right)\) and \({f^{\left( 4 \right)}}\left( x \right)\) denote the 3rd and 4th derivative of \(f\left( x \right)\) respectively.</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>Hence show that the Maclaurin series for \(f\left( x \right)\) up to and including the term in \({x^4}\) is \({x^2} + \frac{1}{3}{x^4}\).</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>Use this series approximation for \(f\left( x \right)\) with \(x = \frac{1}{2}\) to find an approximate value for \({\pi ^2}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(f'\left( x \right) = \frac{{2\,{\text{arcsin}}\,\left( x \right)}}{{\sqrt {1 - {x^2}} }}\) <strong><em>M1A1</em></strong></p>
<p><strong>Note:</strong> Award <em><strong>M1</strong> </em>for an attempt at chain rule differentiation.<br>Award <em><strong>M0A0</strong> </em>for \(f'\left( x \right) = 2\,{\text{arcsin}}\,\left( x \right)\).</p>
<p>\(f'\left( 0 \right) = 0\) <em><strong>AG</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>differentiating gives \(\left( {1 - {x^2}} \right){f^{\left( 3 \right)}}\left( x \right) - 2xf''\left( x \right) - f'\left( x \right) - xf''\left( x \right)\left( { = 0} \right)\) <em><strong>M1A1</strong></em></p>
<p>differentiating again gives \(\left( {1 - {x^2}} \right){f^{\left( 4 \right)}}\left( x \right) - 2x{f^{\left( 3 \right)}}\left( x \right) - 3f''\left( x \right) - 3x{f^{\left( 3 \right)}}\left( x \right) - f''\left( x \right)\left( { = 0} \right)\) <em><strong>M1A1</strong></em></p>
<p><strong>Note</strong>: Award <em><strong>M1</strong> </em>for an attempt at product rule differentiation of at least one product in each of the above two lines.<br>Do not penalise candidates who use poor notation.</p>
<p>\(\left( {1 - {x^2}} \right){f^{\left( 4 \right)}}\left( x \right) - 5x{f^{\left( 3 \right)}}\left( x \right) - 4f''\left( x \right) = 0\) <em><strong>AG</strong></em></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>attempting to find <strong>one of</strong> \(f''\left( 0 \right)\), \({f^{\left( 3 \right)}}\left( 0 \right)\) or \({f^{\left( 4 \right)}}\left( 0 \right)\) by substituting \(x = 0\) into relevant differential equation(s) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Condone \(f''\left( 0 \right)\) found by calculating \(\frac{{\text{d}}}{{{\text{d}}x}}\left( {\frac{{2\,{\text{arcsin}}\,\left( x \right)}}{{\sqrt {1 - {x^2}} }}} \right)\) at \(x = 0\).</p>
<p>\(\left( {f\left( 0 \right) = 0,\,f'\left( 0 \right) = 0} \right)\)</p>
<p>\(f''\left( 0 \right) = 2\) and \({f^{\left( 4 \right)}}\left( 0 \right) - 4f''\left( 0 \right) = 0 \Rightarrow {f^{\left( 4 \right)}}\left( 0 \right) = 8\) <em><strong>A1</strong></em></p>
<p>\({f^{\left( 3 \right)}}\left( 0 \right) = 0\) and so \(\frac{2}{{2{\text{!}}}}{x^2} + \frac{8}{{4{\text{!}}}}{x^4}\) <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Only award the above <em><strong>A1</strong></em>, for correct first differentiation in part (b) leading to \({f^{\left( 3 \right)}}\left( 0 \right) = 0\) stated or \({f^{\left( 3 \right)}}\left( 0 \right) = 0\) seen from use of the general Maclaurin series.<br><strong>Special Case:</strong> Award <em><strong>(M1)A0A1</strong></em> if \({f^{\left( 4 \right)}}\left( 0 \right) = 8\) is stated without justification or found by working backwards from the general Maclaurin series.</p>
<p>so the Maclaurin series for \(f\left( x \right)\) up to and including the term in \({x^4}\) is \({x^2} + \frac{1}{3}{x^4}\) <em><strong>AG</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>substituting \(x = \frac{1}{2}\) into \({x^2} + \frac{1}{3}{x^4}\) <em><strong>M1</strong></em></p>
<p>the series approximation gives a value of \(\frac{{13}}{{48}}\)</p>
<p>so \({\pi ^2} \simeq \frac{{13}}{{48}} \times 36\)</p>
<p>\( \simeq 9.75\,\,\left( { \simeq \frac{{39}}{4}} \right)\) <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Accept 9.76.</p>
<p><em><strong>[2 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">
<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 in the interval \(\left] { - k,{\text{ }}k} \right[\), where \(k > 0\). The gradient function \({f'}\) exists at each point of the domain of \(f\).</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 following diagram shows the graph of \(y = f(x)\), its asymptotes and its vertical symmetry axis.</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_2014-09-17_om_14.31.15.png" alt></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"> </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) Sketch the graph of \(y = f'(x)\).</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;">Let \(p(x) = a + bx + c{x^2} + d{x^3} + \ldots \) be the Maclaurin expansion of \(f(x)\).</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;">(b) (i) Justify that \(a > 0\).</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;">(ii) Write down a condition for the largest set of possible values for each of the parameters \(b\), \(c\) and \(d\).</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) State, with a reason, an upper bound for the radius of convergence.</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)<br><img src="images/maths_5_markscheme.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;"><strong><em>A1</em></strong> for shape, <strong><em>A1 </em></strong>for passing through origin <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>Asymptotes not required.</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>[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;">(b) \(p(x) = \underbrace {f(0)}_a + \underbrace {f'(0)}_bx + \underbrace {\frac{{f''(0)}}{{2!}}}_c{x^2} + \underbrace {\frac{{{f^{(3)}}(0)}}{{3!}}}_d{x^3} + \ldots \)</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;">(i) because the <em>y</em>-intercept of \(f\) is positive <strong><em>R1</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) \(b = 0\) <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;">\(c \geqslant 0\) <strong><em>A1A1</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: <em>A1</em> </strong>for \( > \) and <strong style="font-weight: normal;"><em>A1 </em></strong>for \( = \).</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;">\(d = 0\) <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>
<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) as the graph has vertical asymptotes \(x = \pm k,{\text{ }}k > 0\), <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">the radius of convergence has an upper bound of \(k\) <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>Accept \(r < k\).</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>
<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;">Overall candidates made good attempts to parts (a) and most candidates realized that the graph contained the origin; however many candidates had difficulty rendering the correct shape of the graph of \(f'\). Part b(i) was also well answered although some candidates where not very clear and digressed a lot. Part (ii) was less successful with most candidates scoring just part of the marks. A small number of candidates answered part (c) correctly with a valid reason.</span></p>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the differential equation</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\[x\frac{{{\text{d}}y}}{{{\text{d}}x}} - 2y = \frac{{{x^3}}}{{{x^2} + 1}}.\]</span></p>
</div>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Find an integrating factor for this differential equation.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Solve the differential equation given that \(y = 1\) when \(x = 1\) , giving your answer in the forms \(y = f(x)\) .</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: 21.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Rewrite the equation in the form</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} - \frac{2}{x}y = \frac{{{x^2}}}{{{x^2} + 1}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Integrating factor \( = {{\text{e}}^{\int { - \frac{2}{x}{\text{d}}x} }}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {{\text{e}}^{ - 2\ln x}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{{{x^2}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Times; color: #3f3f3f;"><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 \(\frac{1}{{{x^3}}}\) as applied to the original equation.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Times; color: #3f3f3f;"><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: 21.0px Times; color: #3f3f3f;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[5 marks]</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Times; color: #3f3f3f;"><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: 21.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Multiplying the equation,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{1}{{{x^2}}}\frac{{{\text{d}}y}}{{{\text{d}}x}} - \frac{2}{{{x^3}}}y = \frac{1}{{{x^2} + 1}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{\text{d}}}{{{\text{d}}x}}\left( {\frac{y}{{{x^2}}}} \right) = \frac{1}{{{x^2} + 1}}\) <strong><em>(M1)(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{y}{{{x^2}}} = \int {\frac{{{\text{d}}x}}{{{x^2} + 1}}} \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \arctan x + C\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Substitute \(x = 1,{\text{ }}y = 1\) . <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(1 = \frac{\pi }{4} + C \Rightarrow C = 1 - \frac{\pi }{4}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(y = {x^2}\left( {\arctan x + 1 - \frac{\pi }{4}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[8 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Times; color: #3f3f3f;"><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: 25.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">The response to this question was often disappointing. Many candidates were unable to find the integrating factor successfully. </span></p>
</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 real and imaginary parts of a complex number \(x + {\text{i}}y\) are related by the differential equation \((x + y)\frac{{{\text{d}}y}}{{{\text{d}}x}} + (x - y) = 0\).</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;">By solving the differential equation, given that \(y = \sqrt 3 \) when <em>x</em> =1, show that the relationship between the modulus <em>r</em> and the argument \(\theta \) of the complex number is \(r = 2{{\text{e}}^{\frac{\pi }{3} - \theta }}\).</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;">\((x + y)\frac{{{\text{d}}y}}{{{\text{d}}x}} + (x - y) = 0\)</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;">\( \Rightarrow \frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{y - x}}{{x + y}}\)</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;">let \(y = vx\) <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;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = v + x\frac{{{\text{d}}v}}{{{\text{d}}x}}\) <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;">\(v + x\frac{{{\text{d}}v}}{{{\text{d}}x}} = \frac{{vx - x}}{{x + vx}}\) <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;">\(x\frac{{{\text{d}}v}}{{{\text{d}}x}} = \frac{{v - 1}}{{v + 1}} - v = \frac{{v - 1 - {v^2} - v}}{{v + 1}} = \frac{{ - 1 - {v^2}}}{{1 + v}}\) <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;">\(\int {\frac{{v + 1}}{{1 + {v^2}}}{\text{d}}v = - \int {\frac{1}{x}{\text{d}}x} } \) <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;">\(\int {\frac{v}{{1 + {v^2}}}{\text{d}}v + \int {\frac{1}{{1 + {v^2}}}{\text{d}}v = - \int {\frac{1}{x}{\text{d}}x} } } \) <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;">\( \Rightarrow \frac{1}{2}\ln \left| {1 + {v^2}} \right| + \arctan v = - \ln \left| x \right| + k\) <strong><em>A1A1</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;">Notes:</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 \(\frac{1}{2}\ln \left| {1 + {v^2}} \right|\), </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 other two terms.</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;">Do not penalize missing <em>k</em> or missing modulus signs at this stage.</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;">\( \Rightarrow \frac{1}{2}\ln \left| {1 + \frac{{{y^2}}}{{{x^2}}}} \right| + \arctan \frac{y}{x} = - \ln \left| x \right| + k\) </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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow \frac{1}{2}\ln 4 + \arctan \sqrt 3 = - \ln 1 + k\) <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;">\( \Rightarrow k = \ln 2 + \frac{\pi }{3}\) <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;">\( \Rightarrow \frac{1}{2}\ln \left| {1 + \frac{{{y^2}}}{{{x^2}}}} \right| + \arctan \frac{y}{x} = - \ln \left| x \right| + \ln 2 + \frac{\pi }{3}\)</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;">attempt to combine logarithms <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;">\( \Rightarrow \frac{1}{2}\ln \left| {\frac{{{y^2} + {x^2}}}{{{x^2}}}} \right| + \frac{1}{2}\ln \left| {{x^2}} \right| = \ln 2 + \frac{\pi }{3} - \arctan \frac{y}{x}\)</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;">\( \Rightarrow \frac{1}{2}\ln \left| {{y^2} + {x^2}} \right| = \ln 2 + \frac{\pi }{3} - \arctan \frac{y}{x}\) <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;">\( \Rightarrow \sqrt {{y^2} + {x^2}} = {{\text{e}}^{\ln 2 + \frac{\pi }{3}\arctan \frac{y}{x}}}\) <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;">\( \Rightarrow \sqrt {{y^2} + {x^2}} = {{\text{e}}^{\ln 2}} \times {{\text{e}}^{\frac{\pi }{3} - \arctan \frac{y}{x}}}\) <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;">\( \Rightarrow r = 2{{\text{e}}^{\frac{\pi }{3} - \theta }}\) <strong><em>AG</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><em>[15 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;">Most candidates realised that this was a homogeneous differential equation and that the substitution \(y = vx\) was the way forward. Many of these candidates reached as far as separating the variables correctly but integrating \(\frac{{v + 1}}{{{v^2} + 1}}\) proved to be too difficult for many candidates – most failed to realise that the expression had to be split into two separate integrals. Some candidates successfully evaluated the arbitrary constant but the combination of logs and the subsequent algebra necessary to obtain the final result proved to be beyond the majority of candidates.</span></p>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Consider the differential equation</p>
<p>\[\frac{{{\text{d}}y}}{{{\text{d}}x}} = f\left( {\frac{y}{x}} \right),{\text{ }}x > 0.\]</p>
<p>Use the substitution \(y = vx\) to show that the general solution of this differential equation is</p>
<p>\[\int {\frac{{{\text{d}}v}}{{f(v) - v}} = \ln x + } {\text{ Constant.}}\]</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, or otherwise, solve the differential equation</p>
<p>\[\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{{x^2} + 3xy + {y^2}}}{{{x^2}}},{\text{ }}x > 0,\]</p>
<p>given that \(y = 1\) when \(x = 1\). Give your answer in the form \(y = g(x)\).</p>
<div class="marks">[10]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(y = vx \Rightarrow \frac{{{\text{d}}y}}{{{\text{d}}x}} = v + x\frac{{{\text{d}}v}}{{{\text{d}}x}}\) <strong><em>M1</em></strong></p>
<p>the differential equation becomes</p>
<p>\(v + x\frac{{{\text{d}}v}}{{{\text{d}}x}} = f(v)\) <strong><em>A1</em></strong></p>
<p>\(\int {\frac{{{\text{d}}v}}{{f(v) - v}} = \int {\frac{{{\text{d}}v}}{x}} } \) <strong><em>A1</em></strong></p>
<p>integrating, Constant \(\int {\frac{{{\text{d}}v}}{{f(v) - v}} = \ln x + } {\text{ Constant}}\) <strong><em>AG</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>EITHER</strong></p>
<p>\(f(v) = 1 + 3v + {v^2}\) <strong><em>(A1)</em></strong></p>
<p>\(\left( {\int {\frac{{{\text{d}}v}}{{f(v) - v}} = } } \right)\,\,\,\int {\frac{{{\text{d}}v}}{{1 + 3v + {v^2} - v}} = \ln x + C} \) <strong><em>M1A1</em></strong></p>
<p>\(\int {\frac{{{\text{d}}v}}{{{{(1 + v)}^2}}} = (\ln x + C)} \) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> <strong><em>A1 </em></strong>is for correct factorization.</p>
<p> </p>
<p>\( - \frac{1}{{1 + v}}\,\,\,( = \ln x + C)\) <strong><em>A1</em></strong></p>
<p><strong>OR</strong></p>
<p>\(v + x\frac{{{\text{d}}v}}{{{\text{d}}x}} = 1 + 3v + {v^2}\) <strong><em>A1</em></strong></p>
<p>\(\int {\frac{{{\text{d}}v}}{{1 + 2v + {v^2}}} = \int {\frac{1}{x}{\text{d}}x} } \) <strong><em>M1</em></strong></p>
<p>\(\int {\frac{{{\text{d}}v}}{{{{(1 + v)}^2}}}\,\,\,\left( { = \int {\frac{1}{x}{\text{d}}x} } \right)} \) <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> <strong><em>A1 </em></strong>is for correct factorization.</p>
<p> </p>
<p>\( - \frac{1}{{1 + v}} = \ln x( + C)\) <strong><em>A1A1</em></strong></p>
<p><strong>THEN</strong></p>
<p>substitute \(y = 1\) or \(v = 1\) when \(x = 1\) (<strong><em>M1)</em></strong></p>
<p>therefore \(C = - \frac{1}{2}\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> This <strong><em>A1 </em></strong>can be awarded anywhere in their solution.</p>
<p> </p>
<p>substituting for \(v\),</p>
<p>\( - \frac{1}{{\left( {1 + \frac{y}{x}} \right)}} = \ln x - \frac{1}{2}\) <strong><em>M1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award for correct substitution of \(\frac{y}{x}\) into their expression.</p>
<p> </p>
<p>\(1 + \frac{y}{x} = \frac{1}{{\frac{1}{2} - \ln x}}\) <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award for any rearrangement of a correct expression that has \(y\) in the numerator.</p>
<p> </p>
<p>\(y = x\left( {\frac{1}{{\left( {\frac{1}{2} - \ln x} \right)}} - 1} \right)\,\,\,{\text{(or equivalent)}}\) <strong><em>A1</em></strong></p>
<p>\(\left( { = x\left( {\frac{{1 + 2\ln x}}{{1 - 2\ln x}}} \right)} \right)\)</p>
<p><strong><em>[10 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 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;">Solve the differential equation</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;">\({x^2}\frac{{{\text{d}}y}}{{{\text{d}}x}} = {y^2} + 3xy + 2{x^2}\)</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;">given that <em>y</em> = −1 when <em>x</em> =1. Give your answer in the form \(y = f(x)\) .</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: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">put <em>y</em> = <em>vx</em> so that \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = v + x\frac{{{\text{d}}v}}{{{\text{d}}x}}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">substituting, <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;">\(v + x\frac{{{\text{d}}v}}{{{\text{d}}x}} = \frac{{{v^2}{x^2} + 3v{x^2} + 2{x^2}}}{{{x^2}}}{\text{ }}( = {v^2} + 3v + 2)\) <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;">\(x\frac{{{\text{d}}v}}{{{\text{d}}x}} = {v^2} + 2v + 2\) <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;">\(\int {\frac{{{\text{d}}v}}{{{v^2} + 2v + 2}} = \int {\frac{{{\text{d}}x}}{x}} } \) <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;">\(\int {\frac{{{\text{d}}v}}{{{{(v + 1)}^2} + 1}} = \int {\frac{{{\text{d}}x}}{x}} } \) <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;">\(\arctan (v + 1) = \ln x + c\) <strong><em>A1</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;"> Condone absence of c at </span><strong style="font-family: 'times new roman', times; font-size: medium;">this</strong><span style="font-family: 'times new roman', times; font-size: medium;"> stage.</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;">\(\arctan (\frac{y}{x} + 1) = \ln x + c\) </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: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">When <em>x</em> = 1, <em>y</em> = −1 <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>c</em> = 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;">\(\frac{y}{x} + 1 = \tan \ln x\)</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;">\(y = x(\tan \ln x - 1)\) <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>[11 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;">Most candidates recognised this differential equation as one in which the substitution <em>y</em> = <em>vx</em> would be helpful and many reached the stage of separating the variables. However, the integration of \(\frac{1}{{{v^2} + 2v + 2}}\) proved beyond many candidates who failed to realise that completing the square would lead to an arctan integral. This highlights the importance of students having a full understanding of the core calculus if they are studying this option.</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">Let \(f(x) = {{\text{e}}^x}\sin x\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that \(f''(x) = 2\left( {f'(x) - f(x)} \right)\).</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">By further differentiation of the result in part (a) , find the Maclaurin expansion of \(f(x)\), as far as the term in \({x^5}\).</p>
<div class="marks">[6]</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">\(f'(x) = {{\text{e}}^x}\sin x + {{\text{e}}^x}\cos x\) <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p1">\(f''(x) = {{\text{e}}^x}\sin x + {{\text{e}}^x}\cos x - {{\text{e}}^x}\sin x + {{\text{e}}^x}\cos x = 2{{\text{e}}^x}\cos x\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">\( = 2\left( {{{\text{e}}^x}\sin x + {{\text{e}}^x}\cos x - {{\text{e}}^x}\sin x} \right)\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">\( = 2\left( {f'(x) - f(x)} \right)\) <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></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>\(f(0) = 0,{\text{ }}f'(0) = 1,{\text{ }}f''(0) = 2(1 - 0) = 2\) <strong><em>(M1)A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>M1 </em></strong>for attempt to find \(f(0)\), \(f'(0)\) and \(f''(0)\).</p>
<p> </p>
<p>\(f'''(x) = 2\left( {f''(x) - f'(x)} \right)\) <strong><em>(M1)</em></strong></p>
<p>\(f'''(0) = 2(2 - 1) = 2,{\text{ }}{f^{IV}}(0) = 2(2 - 2) = 0,{\text{ }}{f^V}(0) = 2(0 - 2) = - 4\) <strong><em>A1</em></strong></p>
<p>so \(f(x) = x + \frac{2}{{2!}}{x^2} + \frac{2}{{3!}}{x^3} - \frac{4}{{5!}} + \ldots \) <strong><em>(M1)A1</em></strong></p>
<p>\( = x + {x^2} + \frac{1}{3}{x^3} - \frac{1}{{30}}{x^5} + \ldots \)</p>
<p><em><strong>[6 marks]</strong></em></p>
<p><em><strong>Total [10 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the exact value of \(\int_0^\infty {\frac{{{\text{d}}x}}{{(x + 2)(2x + 1)}}} \).</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: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(\frac{1}{{(x + 2)(2x + 1)}} = \frac{A}{{x + 2}} + \frac{B}{{2x + 1}} = \frac{{A(2x + 1) + B(x + 2)}}{{(x + 2)(2x + 1)}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = - 2 \to A = - \frac{1}{3}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = - \frac{1}{2} \to B = \frac{2}{3}\) <strong><em>A1 N3</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(I = \frac{1}{3}\int_0^h {\left[ {\frac{2}{{(2x + 1)}} - \frac{1}{{(x + 2)}}} \right]{\text{d}}x} \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{3}\left[ {\ln (2x + 1) - \ln (x + 2)} \right]_0^h\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{3}\left[ {\mathop {\lim }\limits_{h \to \infty } \left( {\ln \left( {\frac{{2h + 1}}{{h + 2}}} \right)} \right) - \ln \frac{1}{2}} \right]\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{3}\left( {\ln 2 - \ln \frac{1}{2}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{2}{3}\ln 2\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>If the logarithms are not combined in the third from last line the last three <strong><em>A1 </em></strong>marks cannot be awarded.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px 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: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [9 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 Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Not a difficult question but combination of the logarithms obtained by integration was often replaced by a spurious argument with infinities to get an answer. \(\log (\infty + 1)\) was often seen.</span></p>
</div>
<br><hr><br><div class="specification">
<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;">Consider the differential equation \(\frac{{{\text{d}}y}}{{{\text{d}}x}} + y\tan x = {\cos ^2}x\), given that <em>y</em> = 2 when <em>x</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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Use Euler’s method with a step length of 0.1 to find an approximation to the value of <em>y</em> when <em>x</em> = 0.3.</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: 35.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Show that the integrating factor for solving the differential equation is \(\sec x\).</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;">(ii) Hence solve the differential equation, giving your answer in the form \(y = f(x)\).</span></p>
<div class="marks">[10]</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;">use of \(y \to y + \frac{{h{\text{d}}y}}{{{\text{d}}x}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 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;"><img src="data:image/png;base64,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" alt></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 \(y(0.1)\) and <strong><em>A1</em></strong> for \(y(0.2)\)</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;"> </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;">\(y(0.3) = 2.23\) <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><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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \({\text{IF}} = {{\text{e}}^{\left( {\int {\tan x{\text{d}}x} } \right)}}\) <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;">\({\text{IF}} = {{\text{e}}^{\left( {\int {\frac{{\sin x}}{{\cos x}}{\text{d}}x} } \right)}}\) <strong><em>(M1)</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;"> Only one of the two </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;"> above may be implied.</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;">\( = {{\text{e}}^{( - \ln \cos x)}}{\text{ (or }}{{\text{e}}^{(\ln \sec x)}})\) </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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \sec x\) <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> </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;">(ii) multiplying by the IF <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;">\(\sec x\frac{{{\text{d}}y}}{{{\text{d}}x}} + y\sec x\tan x = \cos x\) <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;">\(\frac{{\text{d}}}{{{\text{d}}x}}(y\sec x) = \cos x\) <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;">\(y\sec x = \sin x + c\) <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;">putting \(x = 0,{\text{ }}y = 2 \Rightarrow c = 2\)</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;">\(y = \cos x(\sin x + 2)\) <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;"><strong><em>[10 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;">Most candidates knew Euler’s method and were able to apply it to the differential equation to answer part (a). Some candidates who knew Euler’s method completed one iteration too many to arrive at an incorrect answer. Surprisingly few candidates were able to efficiently use their GDCs to answer this question and this led to many final answers that were incorrect due to rounding errors.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates were able to correctly derive the Integration Factor in part (b) but some lost marks due to not showing all the steps that would be expected in a “show that” question. The differential equation was solved correctly by a significant number of candidates but there were errors when candidates multiplied by \(\sec x\) before the inclusion of the arbitrary constant.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(g(x) = \sin {x^2}\), where \(x \in \mathbb{R}\).</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 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Using the result \(\mathop {{\text{lim}}}\limits_{t \to 0} \frac{{\sin t}}{t} = 1\), or otherwise, calculate \(\mathop {{\text{lim}}}\limits_{x \to 0} \frac{{g(2x) - g(3x)}}{{4{x^2}}}\).</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;">Use the Maclaurin series of \(\sin x\) to show that \(g(x) = \sum\limits_{n = 0}^\infty {{{( - 1)}^n}\frac{{{x^{4n + 2}}}}{{(2n + 1)!}}} \)</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence determine the minimum number of terms of the expansion of \(g(x)\) required to approximate the value of \(\int_0^1 {g(x){\text{d}}x} \) to four decimal places.</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 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;">\(\mathop {{\text{lim}}}\limits_{x \to 0} \frac{{\sin 4{x^2} - \sin 9{x^2}}}{{4{x^2}}}\) <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;">\( = \mathop {{\text{lim}}}\limits_{x \to 0} \frac{{\sin 4{x^2}}}{{4{x^2}}} - \frac{9}{4}\mathop {{\text{lim}}}\limits_{x \to 0} \frac{{\sin 9{x^2}}}{{9{x^2}}}\) <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;">\( = 1 - \frac{9}{4} \times 1 = - \frac{5}{4}\) <strong>A1</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;">\(\mathop {{\text{lim}}}\limits_{x \to 0} \frac{{\sin 4{x^2} - \sin 9{x^2}}}{{4{x^2}}}\) <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;">\( = \mathop {{\text{lim}}}\limits_{x \to 0} \frac{{8x\cos 4{x^2} - 18x\cos 9{x^2}}}{{8x}}\) <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;">\( = \frac{{8 - 18}}{8} = - \frac{{10}}{8} = - \frac{5}{4}\) <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;"><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;">since \(\sin x = \sum\limits_{n = 0}^\infty {{{( - 1)}^n}\frac{{{x^{(2n + 1)}}}}{{(2n + 1)!}}} \) \(\left( {{\text{or }}\sin x = \frac{x}{{1!}} - \frac{{{x^3}}}{{3!}} + \frac{{{x^5}}}{{5!}} - \ldots } \right)\) <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;">\(\sin {x^2} = \sum\limits_{n = 0}^\infty {{{( - 1)}^n}\frac{{{x^{2(2n + 1)}}}}{{(2n + 1)!}}} \) \(\left( {{\text{or }}\sin x = \frac{{{x^2}}}{{1!}} - \frac{{{x^6}}}{{3!}} + \frac{{{x^{10}}}}{{5!}} - \ldots } \right)\) <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;">\(g(x) = \sin {x^2} = \sum\limits_{n = 0}^\infty {{{( - 1)}^n}\frac{{{x^{4n + 2}}}}{{(2n + 1)!}}} \) <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>
<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;">let \(I = \int_0^1 {\sin {x^2}{\text{d}}x} \)</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;">\( = \sum\limits_{n = 0}^\infty {{{( - 1)}^n}\frac{1}{{(2n + 1)!}}} \int_0^1 {{x^{4n + 2}}{\text{d}}x{\text{ }}\left( {\int_0^1 {\frac{{{x^2}}}{{1!}}{\text{d}}x - } \int_0^1 {\frac{{{x^6}}}{{3!}}{\text{d}}x + } \int_0^1 {\frac{{{x^{10}}}}{{5!}}{\text{d}}x - \ldots } } \right)} \) <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;">\( = \sum\limits_{n = 0}^\infty {{{( - 1)}^n}\frac{1}{{(2n + 1)!}}} \frac{{[{x^{4n + 3}}]_0^1}}{{(4n + 3)}}{\text{ }}\left( {\left[ {\frac{{{x^3}}}{{3 \times 1!}}} \right]_0^1 - \left[ {\frac{{{x^7}}}{{7 \times 3!}}} \right]_0^1 + \left[ {\frac{{{x^{11}}}}{{11 \times 5!}}} \right]_0^1 - \ldots } \right)\) <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;">\( = \sum\limits_{n = 0}^\infty {{{( - 1)}^n}\frac{1}{{(2n + 1)!(4n + 3)}}} {\text{ }}\left( {\frac{1}{{3 \times 1!}} - \frac{1}{{7 \times 3!}} + \frac{1}{{11 \times 5!}} - \ldots } \right)\) <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;">\( = \sum\limits_{n = 0}^\infty {{{( - 1)}^n}{a_n}} \) where \({a_n} = \frac{1}{{(4n + 3)(2n + 1)!}} > 0\) for all \(n \in \mathbb{N}\)</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;">as \(\{ {a_n}\} \) is decreasing the sum of the alternating series \(\sum\limits_{n = 0}^\infty {{{( - 1)}^n}{a_n}} \)</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;">lies between \(\sum\limits_{n = 0}^N {{{( - 1)}^n}{a_n}} \) and \(\sum\limits_{n = 0}^N {{{( - 1)}^n}{a_n}} \pm {a_{N + 1}}\) <strong><em>R1</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 for four decimal place accuracy, we need \(\left| {{a_{N + 1}}} \right| < 0.00005\) <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;"><br><img src="images/Schermafbeelding_2014-09-17_om_14.28.18.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;">since \({a_{2 + 1}} < 0.00005\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">so \(N = 2\) (or 3 terms) <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>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) of this question was accessible to the vast majority of candidates, who recognised that L’Hôpital’s rule could be used. Most candidates were successful in finding the limit, with some making calculation errors. Candidates that attempted to use \(\mathop {{\text{lim}}}\limits_{x \to 0} \frac{{\sin x}}{x} = 1\) or a combination of this result and L’Hôpital’s rule were less successful.</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) most candidates showed to be familiar with the substitution given and were successful in showing the result.<br></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;">Very few candidates were able to do part (c) successfully. Most used trial and error to arrive at the answer.</span></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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Using the Maclaurin series for the function \({{\text{e}}^x}\), write down the first four terms of the Maclaurin series for \({{\text{e}}^{ - \frac{{{x^2}}}{2}}}\).</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) Hence find the first four terms of the series for \(\int_0^x {{{\text{e}}^{ - \frac{{{u^2}}}{2}}}} {\text{d}}u\).</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) Use the result from part (b) to find an approximate value for \(\frac{1}{{\sqrt {2\pi } }}\int_0^1 {{{\text{e}}^{ - \frac{{{x^2}}}{2}}}{\text{d}}x} \).</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) \({{\text{e}}^x} = 1 + x + \frac{{{x^2}}}{{2!}} + \frac{{{x^3}}}{{3!}} + \frac{{{x^4}}}{{4!}} + \ldots \)</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;">putting \(x = \frac{{ - {x^2}}}{2}\) <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;">\({{\text{e}}^{ - \frac{{{x^2}}}{2}}} \approx 1 - \frac{{{x^2}}}{2} + \frac{{{x^4}}}{{{2^2} \times 2!}} - \frac{{{x^6}}}{{{2^3} \times 3!}} \approx \left( {1 - \frac{{{x^2}}}{2} + \frac{{{x^4}}}{8} - \frac{{{x^6}}}{{48}}} \right)\) <strong><em>A2</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>
<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) \(\int_0^x {{{\text{e}}^{ - \frac{{{u^2}}}{2}}}{\text{d}}u \approx \left[ {u - \frac{{{u^3}}}{{3 \times 2}} + \frac{{{u^5}}}{{5 \times {2^2} \times 2!}} - \frac{{{u^7}}}{{7 \times {2^3} \times 3!}}} \right]_0^x} \) <strong><em>M1(A1)</em></strong></span></p>
<p style="margin: 0px 0px 0px 30px; font: 27px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = x - \frac{{{x^3}}}{{3 \times 2}} + \frac{{{x^5}}}{{5 \times {2^2} \times 2!}} - \frac{{{x^7}}}{{7 \times {2^3} \times 3!}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0px 0px 0px 30px; font: 27px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\left( { = x - \frac{{{x^3}}}{6} + \frac{{{x^5}}}{{40}} - \frac{{{x^7}}}{{336}}} \right)\)</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;">(c) putting <em>x</em> = 1 in part (b) gives \(\int_0^1 {{{\text{e}}^{ - \frac{{{x^2}}}{2}}}{\text{d}}x \approx } 0.85535 \ldots \) <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;">\(\frac{1}{{\sqrt {2\pi } }}\int_0^1 {{{\text{e}}^{ - \frac{{{x^2}}}{2}}}{\text{d}}x \approx } 0.341\) <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>
<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;"><strong><em>Total [9 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 one of the most successfully answered questions. Some candidates however failed to use the data booklet for the expansion of the series, thereby wasting valuable time.</span></p>
</div>
<br><hr><br><div class="specification">
<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;">Consider the infinite series \(\sum\limits_{n = 1}^\infty {\frac{{{n^2}}}{{{2^n}}}{x^n}} \).</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;">Find the radius of convergence.</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;">Find the interval of convergence.</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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Given that <em>x</em> = – 0.1, find the sum of the series correct to three significant figures.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p 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;">\(\mathop {\lim }\limits_{n \to \infty } \frac{{{u_{n + 1}}}}{{{u_n}}} = \mathop {\lim }\limits_{n \to \infty } \frac{{\frac{{{{(n + 1)}^2}{x^{n + 1}}}}{{{2^{n + 1}}}}}}{{\frac{{{n^2}{x^n}}}{{{2^n}}}}}\) <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;">\( = \mathop {\lim }\limits_{n \to \infty } \frac{{{{(n + 1)}^2}}}{{{n^2}}} \times \frac{x}{2}\) <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;">\( = \frac{x}{2}\) (since \(\lim \to \frac{x}{2}{\text{ as }}n \to \infty \)) <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;">the radius of convergence <em>R</em> is found by equating this limit to 1, giving <em>R</em> = 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>[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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">when <em>x</em> = 2, the series is \(\sum {{n^2}} \) which is divergent because the terms do not converge to 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;">when <em>x</em> = –2, the series is \(\sum {{{( - 1)}^n}{n^2}} \) which is divergent because the terms do not converge to 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;">the interval of convergence is \(] - 2,{\text{ }}2[\) <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;"><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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">putting <em>x</em> = – 0.1, <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;">for any correct partial sum <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;">– 0.05</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;">– 0.04</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;">– 0.041125</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;">– 0.041025</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;">– 0.0410328 <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;">the sum is – 0.0410 correct to 3 significant figures <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">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;">It was pleasing that most candidates were aware of the Radius of Convergence and Interval of Convergence required by parts (a) and (b) of this problem. Many candidates correctly handled the use of the Ratio Test for convergence and there was also the use of Cauchy’s n<sup>th</sup> root test by a small number of candidates to solve part (a). Candidates need to take care to justify correctly the divergence or convergence of series when finding the Interval of Convergence.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">It was pleasing that most candidates were aware of the Radius of Convergence and Interval of Convergence required by parts (a) and (b) of this problem. Many candidates correctly handled the use of the Ratio Test for convergence and there was also the use of Cauchy’s n<sup>th</sup> root test by a small number of candidates to solve part (a). Candidates need to take care to justify correctly the divergence or convergence of series when finding the Interval of Convergence.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The summation of the series in part (c) was poorly handled by a significant number of candidates, which was surprising on what was expected to be quite a straightforward problem. Again efficient use of the GDC seemed to be a problem. A number of candidates found the correct sum but not to the required accuracy.</span></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: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the differential equation \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{y}{{x + \sqrt {xy} }}\), for \(x,{\text{ }}y > 0\).</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;">(a) Use Euler’s method starting at the point \((x,{\text{ }}y) = (1,{\text{ }}2)\), with interval \(h = 0.2\), to find an approximate value of <em>y </em>when \(x = 1.6\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Use the substitution \(y = vx\) to show that \(x\frac{{{\text{d}}v}}{{{\text{d}}x}} = \frac{v}{{1 + \sqrt v }} - v\).</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) (i) Hence find the solution of the differential equation in the form \(f(x,{\text{ }}y) = 0\), given that \(y = 2\) when \(x = 1\).</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;">(ii) Find the value of \(y\) when \(x = 1.6\).</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) let \(f(x,{\text{ }}y) = \frac{y}{{x + \sqrt {xy} }}\)</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;">\(y(1.2) = y(1) + 0.2f(1,{\text{ }}2){\text{ }}( = 2 + 0.1656 \ldots )\) <strong><em>(M2)(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;">\( = 2.1656 \ldots \) <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;">\(y(1.4) = 2.1656 \ldots + 0.2f(1.2,{\text{ }}2.1256 \ldots ){\text{ }}( = 2.1656 \ldots + 0.1540 \ldots )\) <strong><em>(M1)</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: <em>M1</em></strong> is for attempt to apply formula using point \(\left( {1.2,{\text{ }}y(1.2)} \right)\).</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;">\( = 2.3197 \ldots \) <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;">\(y(1.6) = 2.3197 \ldots + 0.2f(1.4,{\text{ }}2.3197 \ldots ){\text{ }}( = 2.3297 \ldots + 0.1448 \ldots )\)</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;">\( = 2.46\) (3sf) <strong><em>A1 N3</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[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;">(b) \(y = vx \Rightarrow \frac{{{\text{d}}y}}{{{\text{d}}x}} = v + x\frac{{{\text{d}}v}}{{{\text{d}}x}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{y}{{x + \sqrt {xy} }} \Rightarrow v + x\frac{{{\text{d}}v}}{{{\text{d}}x}} = \frac{{vx}}{{x + \sqrt {v{x^2}} }}\) <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;">\( \Rightarrow v + x\frac{{{\text{d}}v}}{{{\text{d}}x}} = \frac{{vx}}{{x + x\sqrt v }}{\text{ (as }}x > 0)\) <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;">\( \Rightarrow x\frac{{{\text{d}}v}}{{{\text{d}}x}} = \frac{v}{{1 + \sqrt v }} - v\) <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><em>[3 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;">(c) (i) \(x\frac{{{\text{d}}v}}{{{\text{d}}x}} = \frac{v}{{1 + \sqrt v }} - v\)</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;">\(x\frac{{{\text{d}}v}}{{{\text{d}}x}} = \frac{{ - v\sqrt v }}{{1 + \sqrt v }} \Rightarrow \frac{{1 + \sqrt v }}{{ - v\sqrt v }}{\text{d}}v = \frac{1}{x}{\text{d}}x\) <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;">\(\int {\frac{{1 + \sqrt v }}{{ - v\sqrt v }}{\text{d}}v = \int {\frac{1}{x}{\text{d}}x} } \) <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;">\(\frac{2}{{\sqrt v }} - \ln v = \ln x + C\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; 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 penalize absence of \( + C\) at this stage; ignore use of absolute values on</span><span style="font-size: medium;"><span style="font-family: 'times new roman', times;"><span style="font-family: 'times new roman', times;"> \(</span></span><span style="font-family: 'times new roman', times;"><span style="background-color: #f7f7f7;">v\)</span><span style="background-color: #f7f7f7;">and \(</span>x\)</span></span> <span style="font-family: 'times new roman', times; font-size: medium; background-color: #f7f7f7;">(which are positive anyway).</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;">\(2\sqrt {\frac{x}{y}} - \ln \frac{y}{x} = \ln x + C\) as \(y = vx \Rightarrow v = \frac{y}{x}\) <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;">\(y = 2\) when \(x = 1 \Rightarrow \sqrt 2 - \ln 2 = 0 + C\) <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;">\(2\sqrt {\frac{x}{y}} - \ln \frac{y}{x} = \ln x + \sqrt 2 - \ln 2\)</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;">\(2\sqrt {\frac{x}{y}} - \ln \frac{y}{x} - \ln x - \sqrt 2 + \ln 2 = 0\) \(\left( {2\sqrt {\frac{x}{y}} - \ln y - \sqrt 2 + \ln 2 = 0} \right)\) <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;">(ii) \(2\sqrt {\frac{{1.6}}{y}} - \ln \frac{y}{{1.6}} - \ln 1.6 - \sqrt 2 + \ln 2 = 0\) <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;">\(y = 2.45\) <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>[9 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;">Part (a) was well answered by most candidates. In a few cases calculation errors and early rounding errors prevented candidates from achieving full marks, but most candidates scored at least a few marks here. In part (b) some candidates failed to convincingly show the given result. Part (c) proved to be a hard question for many candidates and a significant number of candidates had difficulty manipulating the algebraic expression, and either had the incorrect expression to integrate, or incorrectly integrated the correct expression. Many candidates reached as far as separating the variables correctly but integrating proved to be too difficult for many of them although most realised that the expression on v had to be split into two separate integrals. Most candidates made good attempts to evaluate the arbitrary constant and arrived at a correct or almost correct expression (sign errors were a common error) which allowed follow through for part b (ii). In some cases however the expression obtained was too simple or was omitted and it was not possible to grant follow through marks.</span></p>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that \(y = \frac{1}{x}\int {f(x){\text{d}}x} \) is a solution of the differential equation</p>
<p class="p1">\(x\frac{{{\text{d}}y}}{{{\text{d}}x}} + y = f(x),{\text{ }}x > 0\).</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 class="p1">Hence solve \(x\frac{{{\text{d}}y}}{{{\text{d}}x}} + y = {x^{ - \frac{1}{2}}},{\text{ }}x > 0\), given that \(y = 2\) when \(x = 4\).</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><strong>METHOD 1</strong></p>
<p>\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = - \frac{1}{{{x^2}}}\int {f(x){\text{d}}x + \frac{1}{x}f(x)} \) <strong><em>M1M1A1</em></strong></p>
<p>\(x\frac{{{\text{d}}y}}{{{\text{d}}x}} + y = f(x),{\text{ }}x > 0\) <strong><em>AG</em></strong></p>
<p> </p>
<p><strong>Note:</strong> <strong><em>M1</em></strong> for use of product rule, <strong><em>M1</em></strong> for use of the fundamental theorem of calculus, <strong><em>A1</em></strong> for all correct.</p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>\(x\frac{{{\text{d}}y}}{{{\text{d}}x}} + y = f(x)\)</p>
<p>\(\frac{{{\text{d}}(xy)}}{{{\text{d}}x}} = f(x)\) <strong><em>(M1)</em></strong></p>
<p>\(xy = \int {f(x){\text{d}}x} \) <strong><em>M1A1</em></strong></p>
<p>\(y = \frac{1}{x}\int {f(x){\text{d}}x} \) <strong><em>AG</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 class="p1">\(y = \frac{1}{x}\left( {2{x^{\frac{1}{2}}} + c} \right)\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1A1</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note:</strong> <span class="Apple-converted-space"> </span><strong><em>A1</em></strong> for correct expression apart from the constant, <strong><em>A1</em></strong> for including the constant in the correct position.</p>
<p class="p2"> </p>
<p class="p3">attempt to use the boundary condition <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">\(c = 4\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1">\(y = \frac{1}{x}\left( {2{x^{\frac{1}{2}}} + 4} \right)\) <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>Condone use of integrating factor.</p>
<p class="p3"><em><strong>[5 marks]</strong></em></p>
<p class="p3"><em><strong>Total [8 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">This question allowed for several different approaches. The most common of these was the use of the integrating factor (even though that just took you in a circle). Other candidates substituted the solution into the differential equation and others multiplied the solution by \(x\) and then used the product rule to obtain the differential equation. All these were acceptable.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">This was a straightforward question. Some candidates failed to use the hint of ‘hence’, and worked from the beginning using the integrating factor. A surprising number made basic algebra errors such as putting the \( + c\) term in the wrong place and so not dividing it by \(\chi \).</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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the differential equation</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;">\[x\frac{{{\text{d}}y}}{{{\text{d}}x}} = y + \sqrt {{x^2} - {y^2}} ,{\text{ }}x > 0,{\text{ }}{x^2} > {y^2}.\]</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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Show that this is a homogeneous differential equation.</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 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 general solution, giving your answer in the form \(y = f(x)\) .</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="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 equation can be rewritten as</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;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{y + \sqrt {{x^2} - {y^2}} }}{x} = \frac{y}{x} + \sqrt {1 - {{\left( {\frac{y}{x}} \right)}^2}} \) <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;">so the differential equation is homogeneous <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>[1 mark]</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;">put <em>y</em> = <em>vx</em> so that \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = v + x\frac{{{\text{d}}v}}{{{\text{d}}x}}\) <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;">substituting,</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;">\(v + x\frac{{{\text{d}}v}}{{{\text{d}}x}} = v + \sqrt {1 - {v^2}} \) <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;">\(\int {\frac{{{\text{d}}v}}{{\sqrt {1 - {v^2}} }} = \int {\frac{{{\text{d}}x}}{x}} } \) <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;">\(\arcsin v = \ln x + C\) <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;">\(\frac{y}{x} = \sin (\ln x + C)\) <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;">\(y = x\sin (\ln x + C)\) <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>
<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 function \(f(x) = \frac{{1 + ax}}{{1 + bx}}\) can be expanded as a power series in <em style="font-family: 'times new roman', times; font-size: medium;">x</em>, within its radius of convergence R, in the form \(f(x) \equiv 1 + \sum\limits_{n = 1}^\infty {{c_n}{x^n}} \) .</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) (i) Show that \({c_n} = {( - b)^{n - 1}}(a - b)\).</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) State the value of R.</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;">(b) Determine the values of <em>a</em> and <em>b</em> for which the expansion of <em>f</em>(<em>x</em>) agrees with that of \({{\text{e}}^x}\) up to and including the term in \({x^2}\) .</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;">(c) Hence find a rational approximation to \({{\text{e}}^{\frac{1}{3}}}\) .</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 Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) (i) \(f(x) = (1 + ax){(1 + bx)^{ - 1}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = (1 + ax)(1 - bx + ...{( - 1)^n}{b^n}{x^n} + …\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">it follows that</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\({c_n} = {( - 1)^n}{b^n} + {( - 1)^{n - 1}}a{b^{n - 1}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {( - b)^{n - 1}}(a - b)\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Times; color: #3f3f3f;"><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: 24.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \({\text{R}} = \frac{1}{{\left| b \right|}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Times; color: #3f3f3f;"><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: 24.0px Times; color: #3f3f3f;"><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: 24.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) to agree up to quadratic terms requires</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(1 = - b + a,{\text{ }}\frac{1}{2} = {b^2} - ab\) <strong><em>M1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">from which \(a = - b = \frac{1}{2}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Times; color: #3f3f3f;"><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: 24.0px Times; color: #3f3f3f;"><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: 24.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) \({{\text{e}}^x} \approx \frac{{1 + 0.5x}}{{1 - 0.5x}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">putting \(x = \frac{1}{3}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\({{\text{e}}^{\frac{1}{3}}} \approx \frac{{\left( {1 + \frac{1}{6}} \right)}}{{\left( {1 - \frac{1}{6}} \right)}} = \frac{7}{5}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Times; color: #3f3f3f;"><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: 24.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [12 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 Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates failed to realize that the first step was to write <em>f</em>(<em>x</em>) as \((1 + ax){(1 + bx)^{ - 1}}\) . Given the displayed answer to part(a), many candidates successfully tackled part(b). Few understood the meaning of the ‘hence’ in part(c).</span></p>
</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 the first three terms of the Maclaurin series for \(\ln (1 + {{\text{e}}^x})\) .</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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Hence, or otherwise, determine the value of \(\mathop {\lim }\limits_{x \to 0} \frac{{2\ln (1 + {{\text{e}}^x}) - x - \ln 4}}{{{x^2}}}\) .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p 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>METHOD 1</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;">\(f(x) = \ln (1 + {{\text{e}}^x});{\text{ }}f(0) = \ln 2\) <strong><em>A1</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;">\(f'(x) = \frac{{{{\text{e}}^x}}}{{1 + {{\text{e}}^x}}};{\text{ }}f'(0) = \frac{1}{2}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px 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>A0</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for \(f'(x) = \frac{1}{{1 + {{\text{e}}^x}}};{\text{ }}f'(0) = \frac{1}{2}\)</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;"> </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;">\(f''(x) = \frac{{{{\text{e}}^x}(1 + {{\text{e}}^x}) - {{\text{e}}^{2x}}}}{{{{(1 + {{\text{e}}^x})}^2}}};{\text{ }}f''(0) = \frac{1}{4}\) </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: 32.0px 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>M0A0</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for \(f''(x){\text{ if }}f'(x) = \frac{1}{{1 + {{\text{e}}^x}}}\) is used</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;"> </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;">\(\ln (1 + {{\text{e}}^x}) = \ln 2 + \frac{1}{2}x + \frac{1}{8}{x^2} + …\) </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: 32.0px 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: 32.0px 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: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\ln (1 + {{\text{e}}^x}) = \ln (1 + 1 + x + \frac{1}{2}{x^2} + …)\) <strong>M1A1</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;">\( = \ln 2 + \ln (1 + \frac{1}{2}x + \frac{1}{4}{x^2} + …)\) <strong>A1</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;">\( = \ln 2 + \left( {\frac{1}{2}x + \frac{1}{4}{x^2} + ...} \right) - \frac{1}{2}{\left( {\frac{1}{2}x + \frac{1}{4}{x^2} + ...} \right)^2} + …\) <strong><em>A1</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;">\( = \ln 2 + \frac{1}{2}x + \frac{1}{4}{x^2} - \frac{1}{8}{x^2} + …\) <strong><em>A1</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;">\( = \ln 2 + \frac{1}{2}x + \frac{1}{8}{x^2} + …\) <strong><em>A1</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>[6 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;"><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;">\(\mathop {\lim }\limits_{x \to 0} \frac{{2\ln (1 + {{\text{e}}^x}) - x - \ln 4}}{{{x^2}}} = \mathop {\lim }\limits_{x \to 0} \frac{{2\ln 2 + x + \frac{{{x^2}}}{4} + {x^3}{\text{ terms & above}} - x - \ln 4}}{{{x^2}}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0px 0px 0px 30px; font: 28px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \mathop {\lim }\limits_{x \to 0} \left( {\frac{1}{4} + {\text{powers of }}x} \right) = \frac{1}{4}\) <strong><em>M1A1</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 + … as evidence of recognition of cubic and higher powers.</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>M1AOM1A0</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for a solution which omits the cubic and higher powers.</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>[4 marks]</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;"> </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;">METHOD 2</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;">using l’Hôpital’s Rule</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;">\(\mathop {\lim }\limits_{x \to 0} \frac{{2\ln (1 + {{\text{e}}^x}) - x - \ln 4}}{{{x^2}}} = \mathop {\lim }\limits_{x \to 0} \frac{{2{{\text{e}}^x} \div (1 + {{\text{e}}^x}) - 1}}{{2x}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0px 0px 0px 30px; font: 28px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \mathop {\lim }\limits_{x \to 0} \frac{{2{{\text{e}}^x} \div {{(1 + {{\text{e}}^x})}^2}}}{2} = \frac{1}{4}\) <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>[4 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<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;">In (a), candidates who found the series by successive differentiation were generally successful, the most common error being to state that the derivative of \(\ln (1 + {{\text{e}}^x})\) is \({(1 + {{\text{e}}^x})^{ - 1}}\). Some candidates assumed the series for \(\ln (1 + x)\) and \({{\text{e}}^x}\) attempted to combine them. This was accepted as an alternative solution but candidates using this method were often unable to obtain the required series.</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;">In (b), candidates were equally split between using the series or using l’Hopital’s rule to find the limit. Both methods were fairly successful, but a number of candidates forgot that if a series was used, there had to be a recognition that it was not a finite series. </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 function <em>f</em> is defined by \(f(x) = {{\text{e}}^{({{\text{e}}^x} - 1)}}\) .</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;">(a) Assuming the Maclaurin series for \({{\text{e}}^x}\) , show that the Maclaurin series for \(f(x)\)</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;">is \(1 + x + {x^2} + \frac{5}{6}{x^3} + \ldots {\text{ .}}\)</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) Hence or otherwise find the value of \(\mathop {\lim }\limits_{x \to 0} \frac{{f(x) - 1}}{{f'(x) - 1}}\) .</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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \({{\text{e}}^x} - 1 = x + \frac{{{x^2}}}{2} + \frac{{{x^2}}}{6} + \ldots \) <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;">\({{\text{e}}^{{{\text{e}}^x} - 1}} = 1 + \left( {x + \frac{{{x^2}}}{2} + \frac{{{x^3}}}{6}} \right) + \frac{{{{\left( {x + \frac{{{x^2}}}{2} + \frac{{{x^3}}}{6}} \right)}^2}}}{2} + \frac{{{{\left( {x + \frac{{{x^2}}}{2} + \frac{{{x^3}}}{6}} \right)}^3}}}{6} + \ldots \) <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;">\( = 1 + x + \frac{{{x^2}}}{2} + \frac{{{x^3}}}{6} + \frac{{{x^2}}}{2} + \frac{{{x^3}}}{2} + \frac{{{x^3}}}{6} + \ldots \) <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;">\( = 1 + x + {x^2} + \frac{5}{6}{x^3} + \ldots \) <strong><em>AG</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><em>[5 marks]</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><em> </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;">(b) <strong>EITHER</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;">\(f'(x) = 1 + 2x + \frac{{5{x^2}}}{2} + \ldots \) <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;">\(\frac{{f(x) - 1}}{{f'(x) - 1}} = \frac{{x + {x^2} + 5{x^3}/6 + \ldots }}{{2x + 5{x^2}/2 + \ldots }}\) <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;">\( = \frac{{1 + x + \ldots }}{{2 + 5x/2 + \ldots }}\) <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;">\( \to \frac{1}{2}{\text{ as }}x \to 0\) <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;"><strong><em>[5 marks]</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>OR</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;">using l’Hopital’s rule, <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;">\(\mathop {\lim }\limits_{x \to 0} \frac{{{{\text{e}}^{({{\text{e}}^x} - 1)}} - 1}}{{{{\text{e}}^{({{\text{e}}^x} - 1)}} - 1' - 1}} = \mathop {\lim }\limits_{x \to 0} \frac{{{{\text{e}}^{({{\text{e}}^x} - 1)}} - 1}}{{{{\text{e}}^{({{\text{e}}^x} + x - 1)}} - 1}}\) <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;">\( = \mathop {\lim }\limits_{x \to 0} \frac{{{{\text{e}}^{({{\text{e}}^x} + x - 1)}}}}{{{{\text{e}}^{({{\text{e}}^x} + x - 1)}} \times ({{\text{e}}^x} + 1)}}\) <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;">\( = \frac{1}{2}\) <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;"><strong><em>[5 marks]</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><em>Total [10 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;">Many candidates obtained the required series by finding the values of successive derivatives at <em>x</em> = 0 , failing to realise that the intention was to start with the exponential series and replace <em>x</em> by the series for \({{\text{e}}^x} - 1\). Candidates who did this were given partial credit for using this method. Part (b) was reasonably well answered using a variety of methods.</span></p>
</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;">Determine whether the series \(\sum\limits_{n = 1}^\infty {\sin \frac{1}{n}} \) is convergent or divergent.</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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Show that the series \(\sum\limits_{n = 2}^\infty {\frac{1}{{n{{(\ln n)}^2}}}} \) is convergent.</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">comparing with the series \(\sum\limits_{n = 1}^\infty {\frac{1}{n}} \) <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;">using the limit comparison test <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;">\(\mathop {\lim }\limits_{n \to \infty } \frac{{\sin \frac{1}{n}}}{{\frac{1}{n}}}\left( { = \mathop {\lim }\limits_{x \to 0} \frac{{\sin x}}{x}} \right) = 1\) <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;">since \(\sum\limits_{n = 1}^\infty {\frac{1}{n}} \) diverges, \(\sum\limits_{n = 1}^\infty {\sin \frac{1}{n}} \) diverges <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>
<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;">using integral test <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;">let \(u = \ln x\) <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;">\( \Rightarrow \frac{{{\text{d}}u}}{{{\text{d}}x}} = \frac{1}{x}\)</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;">\(\int {\frac{1}{{x{{(\ln x)}^2}}}{\text{d}}x = \int {\frac{1}{{{u^2}}}{\text{d}}u = - \frac{1}{u}\left( { = - \frac{1}{{\ln x}}} \right)} } \) <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;">\( \Rightarrow \int_2^\infty {\frac{1}{{x{{(\ln x)}^2}}}{\text{d}}x = \mathop {\lim }\limits_{a \to \infty } } \left[ { - \frac{1}{{\ln x}}} \right]_2^a\)</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;">\( = \mathop {\lim }\limits_{a \to \infty } \left( { - \frac{1}{{\ln a}} + \frac{1}{{\ln 2}}} \right)\) <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;">as \(a \to \infty ,{\text{ }} - \frac{1}{{\ln a}} \to 0\) <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;">\( \Rightarrow \int_2^\infty {\frac{1}{{x{{\left( {\ln x} \right)}^2}}}} {\text{d}}x = \frac{1}{{\ln 2}}\)<br></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;">hence the series is convergent <strong><em>AG</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>[7 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;">This question was found to be the hardest on the paper, with only the best candidates gaining full marks on it. Part (a) was very poorly done with a significant number of candidates unable to start the question. More students recognised part (b) as an integral test, but often could not progress beyond this. In many cases, students appeared to be guessing at what might constitute a valid test.</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;">This question was found to be the hardest on the paper, with only the best candidates gaining full marks on it. Part (a) was very poorly done with a significant number of candidates unable to start the question. More students recognised part (b) as an integral test, but often could not progress beyond this. In many cases, students appeared to be guessing at what might constitute a valid test.</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: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the general solution of the differential equation \(t\frac{{{\text{d}}y}}{{{\text{d}}t}} = \cos t - 2y\) , for <em>t </em>> 0 .</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;">recognise equation as first order linear and attempt to find the IF <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;">\({\text{IF}} = {{\text{e}}^{\int {\frac{2}{t}{\text{d}}t} }} = {t^2}\) <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;">solution \(y{t^2} = \int {t\cos t{\text{d}}t} \) <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;">using integration by parts with the correct choice of <em>u </em>and <em>v</em> <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;">\(\int {t\cos t{\text{d}}t = t\sin t + \cos t( + C)} \) <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;">obtain \(y = \frac{{\sin t}}{t} + \frac{{\cos t + C}}{{{t^2}}}\) <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>
<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;">Perhaps a small number of candidates were put off by the unusual choice of variables but in most instances it seemed that candidates who recognised the need for an integration factor could make a good attempt at this problem. Candidates who were not able to simplify the integrating factor from \({e^{2\ln t}}\) to \({t^2}\) rarely gained full marks. A significant number of candidates did not gain the final mark due to a lack of an arbitrary constant or not dividing the constant by the integration factor.</span></p>
</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;">Consider the infinite series</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;">\[\frac{1}{{2\ln 2}} - \frac{1}{{3\ln 3}} + \frac{1}{{4\ln 4}} - \frac{1}{{5\ln 5}} + \ldots {\text{ .}}\]</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;">(a) Show that the series converges.</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) Determine if the series converges absolutely or conditionally.</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;">(a) applying the alternating series test as \(\forall n \geqslant 2,\frac{1}{{n\ln n}} \in {\mathbb{R}^ + }\) <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;">\(\forall n,\frac{1}{{(n + 1)\ln (n + 1)}} \leqslant \frac{1}{{n\ln n}}\) <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;">\(\mathop {\lim }\limits_{n \to \infty } \frac{1}{{n\ln n}} = 0\) <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;">hence, by the alternating series test, the series converges <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>[4 marks]</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;">(b) as \(\frac{1}{{x\ln x}}\) is a continuous decreasing function, apply the integral test to determine if it converges absolutely <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;">\(\int_2^\infty {\frac{1}{{x\ln x}}{\text{d}}x = \mathop {\lim }\limits_{b \to \infty } \int_2^b {\frac{1}{{x\ln x}}{\text{d}}x} } \) <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;">let \(u = \ln x\) then \({\text{d}}u = \frac{1}{x}{\text{d}}x\) <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;">\(\int {\frac{1}{u}{\text{d}}u = \ln u} \) <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;">hence, \(\mathop {\lim }\limits_{b \to \infty } \int_2^b {\frac{1}{{x\ln x}}{\text{d}}x = \mathop {\lim }\limits_{b \to \infty } \left[ {\ln (\ln x)} \right]_2^b} \) which does not exist <strong><em>M1A1A1</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;">hence, the series does not converge absolutely <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;">the series converges conditionally <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>[11 marks]</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>Total [15 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;">Part (a) was answered well by many candidates who attempted this question. In part (b), those who applied the integral test were mainly successful, but too many failed to supply the justification for its use, and proper conclusions.</span></p>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(\int\limits_4^\infty {\frac{1}{{{x^3}}}{\text{d}}x} \).</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Illustrate graphically the inequality \(\sum\limits_{n = 5}^\infty {\frac{1}{{{n^3}}}} < \int\limits_4^\infty {\frac{1}{{{x^3}}}{\text{d}}x} < \sum\limits_{n = 4}^\infty {\frac{1}{{{n^3}}}} \).</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>Hence write down a lower bound for \(\sum\limits_{n = 4}^\infty {\frac{1}{{{n^3}}}} \).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an upper bound for \(\sum\limits_{n = 4}^\infty {\frac{1}{{{n^3}}}} \).</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>\(\int\limits_4^\infty {\frac{1}{{{x^3}}}{\text{d}}x} = \mathop {{\text{lim}}}\limits_{R \to \infty } \int\limits_4^R {\frac{1}{{{x^3}}}{\text{d}}x} \) <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> The above <em><strong>A1</strong> </em>for using a limit can be awarded at any stage.<br>Condone the use of \(\mathop {{\text{lim}}}\limits_{x \to \infty } \).</p>
<p>Do not award this mark to candidates who use \(\infty \) as the upper limit throughout.</p>
<p>= \(\mathop {{\text{lim}}}\limits_{R \to \infty } \left[ { - \frac{1}{2}{x^{ - 2}}} \right]_4^R\left( { = \left[ { - \frac{1}{2}{x^{ - 2}}} \right]_4^\infty } \right)\) <em><strong>M1</strong></em></p>
<p>\( = \mathop {{\text{lim}}}\limits_{R \to \infty } \left( { - \frac{1}{2}\left( {{R^{ - 2}} - {4^{ - 2}}} \right)} \right)\)</p>
<p>\( = \frac{1}{{32}}\) <em><strong>A1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p> <img src="data:image/png;base64,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"> <em><strong>A1A1A1A1</strong></em></p>
<p><em><strong>A1</strong> </em>for the curve<br><em><strong>A1</strong> </em>for rectangles starting at \(x = 4\)<br><em><strong>A1</strong> </em>for at least three upper rectangles<br><em><strong>A1</strong> </em>for at least three lower rectangles</p>
<p><strong>Note:</strong> Award<em><strong> A0A1</strong></em> for two upper rectangles and two lower rectangles.</p>
<p>sum of areas of the lower rectangles < the area under the curve < the sum of the areas of the upper rectangles so</p>
<p>\(\sum\limits_{n = 5}^\infty {\frac{1}{{{n^3}}}} < \int\limits_4^\infty {\frac{1}{{{x^3}}}{\text{d}}x} < \sum\limits_{n = 4}^\infty {\frac{1}{{{n^3}}}} \) <em><strong>AG</strong></em></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>a lower bound is \(\frac{1}{{32}}\) <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Allow <strong>FT</strong> from part (a).</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>\(\sum\limits_{n = 5}^\infty {\frac{1}{{{n^3}}}} < \frac{1}{{32}}\) <em><strong>(M1)</strong></em></p>
<p>\(\frac{1}{{64}} + \sum\limits_{n = 5}^\infty {\frac{1}{{{n^3}}}} = \frac{1}{{32}} + \frac{1}{{64}}\) <em><strong>(M1)</strong></em></p>
<p>\(\sum\limits_{n = 4}^\infty {\frac{1}{{{n^3}}}} < \frac{3}{{64}}\), an upper bound <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Allow <em><strong>FT</strong> </em>from part (a).</p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>changing the lower limit in the inequality in part (b) gives</p>
<p>\(\sum\limits_{n = 4}^\infty {\frac{1}{{{n^3}}}} < \int\limits_3^\infty {\frac{1}{{{x^3}}}{\text{d}}x} \left( { < \sum\limits_{n = 3}^\infty {\frac{1}{{{n^3}}}} } \right)\) <em><strong>(A1)</strong></em></p>
<p>\(\sum\limits_{n = 4}^\infty {\frac{1}{{{n^3}}}} < \mathop {{\text{lim}}}\limits_{R \to \infty } \left[ { - \frac{1}{2}{x^{ - 2}}} \right]_3^R\) <em><strong>(M1)</strong></em></p>
<p>\(\sum\limits_{n = 4}^\infty {\frac{1}{{{n^3}}}} < \frac{1}{{18}}\), an upper bound <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Condone candidates who do not use a limit.</p>
<p><em><strong>[3 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">
<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 infinite series \(\sum\limits_{n = 1}^\infty {\frac{2}{{{n^2} + 3n}}} \).</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;">Use a comparison test to show that the series converges.</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;"><strong>EITHER</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;">\(\sum\limits_{n = 1}^\infty {\frac{2}{{{n^2} + 3n}}} < \sum\limits_{n = 1}^\infty {\frac{2}{{{n^2}}}} \) <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;">which is convergent <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 given series is therefore convergent using the comparison test <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>OR</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;">\(\mathop {{\text{lim}}}\limits_{n \to \infty } \frac{{\frac{2}{{{n^2} + 3n}}}}{{\frac{1}{{{n^2}}}}} = 2\) <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;">the given series is therefore convergent using the limit comparison test <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>
</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 were able to answer part (a) and many gained a fully correct answer. A number of candidates ignored the factor 2 in the numerator and this led to candidates being penalised. In some cases candidates were not able to identify an appropriate series to compare with. Most candidates used the Comparison test rather than the Limit comparison test.</span></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;">The general term of a sequence \(\{ {a_n}\} \) is given by the formula \({a_n} = \frac{{{{\text{e}}^n} + {2^n}}}{{2{{\text{e}}^n}}},{\text{ }}n \in {\mathbb{Z}^ + }\).</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) Determine whether the sequence \(\{ {a_n}\} \) is decreasing or increasing.</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) Show that the sequence \(\{ {a_n}\} \) is convergent and find the limit <em>L</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;">(c) Find the smallest value of \(N \in {\mathbb{Z}^ + }\) such that \(\left| {{a_n} - L} \right| < 0.001\), for all \(n \geqslant N\).</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) \({a_n} = \frac{{{{\text{e}}^n} + {2^n}}}{{2{{\text{e}}^n}}} = \frac{1}{2} + \frac{1}{2}{\left( {\frac{2}{{\text{e}}}} \right)^2} > \frac{1}{2} + \frac{1}{2}{\left( {\frac{2}{{\text{e}}}} \right)^{n + 1}} = {a_{n + 1}}\) <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;">the sequence is decreasing (as terms are positive) <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 reference to the sum of a constant and a decreasing geometric sequence.</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>Accept use of derivative of \(f(x) = \frac{{{{\text{e}}^x} + 2x}}{{2{{\text{e}}^x}}}\) (and condone use of n) and graphical methods (graph of the sequence or graph of corresponding function \(f\) or graph of its derivative \({f'}\)).</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 a list of consecutive terms of the sequence clearly decreasing (<em>eg</em> \(0.8678 \ldots ,{\text{ }}0.77067 \ldots ,{\text{ }} \ldots \)).</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>
<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) \(L = \mathop {\lim }\limits_{n \to \infty } {a_n} = \mathop {\lim }\limits_{n \to \infty } \frac{1}{2} + \frac{1}{2}{\left( {\frac{2}{{\text{e}}}} \right)^n} = \frac{1}{2} + \frac{1}{2} \times 0 = \frac{1}{2}\) <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;"><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;">(c) \(\left| {{a_n} - \frac{1}{2}} \right| = \left| {\frac{1}{2} + \frac{1}{2}{{\left( {\frac{2}{{\text{e}}}} \right)}^n} - \frac{1}{2}} \right| = \left| {\frac{1}{2}{{\left( {\frac{2}{{\text{e}}}} \right)}^n}} \right| < \frac{1}{{1000}}\) <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;"><strong>EITHER</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;">\( \Rightarrow {\left( {\frac{{\text{e}}}{2}} \right)^n} > 500\) <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;">\( \Rightarrow n > 20.25 \ldots \) <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: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow {\left( {\frac{2}{{\text{e}}}} \right)^n} < 500\)</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;">\( \Rightarrow n > 20.25 \ldots \) <strong><em>(A1)(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 style="font-weight: normal;">Note:</strong> <strong style="font-weight: normal;"><em>A1</em></strong> for correct inequality; <strong style="font-weight: normal;"><em>A1 </em></strong>for 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>THEN</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;">therefore \(N = 21\) <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>[4 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 were successful in answering part (a) using a variety of methods. The majority of candidates scored some marks, if not full marks. Surprisingly, some candidates did not have the correct graph for the function the sequence represents. They obviously did not enter it correctly into their GDCs. Others used one of the two definitions for showing that a sequence is increasing/decreasing, but made mistakes with the algebraic manipulation of the expression, thereby arriving at an incorrect answer. Part (b) was less well answered with many candidates ignoring the command terms ‘show that’ and ‘find’ and just writing down the value of the limit. Some candidates attempted to use convergence tests for series with this sequence. Part (c) of this question was found challenging by the majority of candidates due to difficulties in solving inequalities involving absolute value.</span></p>
</div>
<br><hr><br><div class="specification">
<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;">Consider the series \(\sum\limits_{n = 1}^\infty {{{( - 1)}^n}\frac{{{x^n}}}{{n \times {2^n}}}} \).</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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the radius of convergence of the series.</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: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Hence deduce the interval of convergence.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p 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;">using the ratio test (and absolute convergence implies convergence) <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;">\(\mathop {\lim }\limits_{n \to \infty } \left| {\frac{{{u_{n + 1}}}}{{{u_n}}}} \right| = \mathop {\lim }\limits_{n \to \infty } \left| {\frac{{\frac{{{{( - 1)}^{n + 1}}{x^{n + 1}}}}{{(n + 1){2^{n + 1}}}}}}{{\frac{{{{( - 1)}^n}{x^n}}}{{(n){2^n}}}}}} \right|\) <strong><em>A1A1</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>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for numerator, </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 denominator.</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;">\( = \mathop {\lim }\limits_{n \to \infty } \left| {\frac{{{{( - 1)}^{n + 1}} \times {x^{n + 1}} \times n \times {2^n}}}{{{{( - 1)}^n} \times (n + 1) \times {2^{n + 1}} \times {x^n}}}} \right|\)</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;">\( = \mathop {\lim }\limits_{n \to \infty } \frac{n}{{2(n + 1)}}\left| x \right|\) <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;">\( = \frac{{\left| x \right|}}{2}\) <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;">for convergence we require \(\frac{{\left| x \right|}}{2} < 1\) <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;">\( \Rightarrow \left| x \right| < 2\)</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;">hence radius of convergence is 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>[7 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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">we now need to consider what happens when \(x = \pm 2\) <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;">when <em>x</em> = 2 we have \(\sum\limits_{n = 1}^\infty {\frac{{{{( - 1)}^n}}}{n}} \) which is convergent (by the alternating series test) <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;">when <em>x</em> = −2 we have \(\sum\limits_{n = 1}^\infty {\frac{1}{n}} \) which is divergent <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;">hence interval of convergence is \(] - 2,{\text{ }}2]\) <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;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<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;">Most candidates were able to start (a) and a majority gained a fully correct answer. A number of candidates were careless with using the absolute value sign and with dealing with the negative signs and in the more extreme cases this led to candidates being penalised. Part (b) caused more difficulties, with many candidates appearing to know what to do, but then not succeeding in doing it or in not understanding the significance of the answer gained.</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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates were able to start (a) and a majority gained a fully correct answer. A number of candidates were careless with using the absolute value sign and with dealing with the negative signs and in the more extreme cases this led to candidates being penalised. Part (b) caused more difficulties, with many candidates appearing to know what to do, but then not succeeding in doing it or in not understanding the significance of the answer gained.</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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Solve the differential equation</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;">\[{x^2}\frac{{{\text{d}}y}}{{{\text{d}}x}} = {y^2} + xy + 4{x^2},\]</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;">given that <em>y</em> = 2 when <em>x</em> =1. Give your answer in the form \(y = f(x)\).</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: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">put \(y = vx\) so that \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = v + x\frac{{{\text{d}}v}}{{{\text{d}}x}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the equation becomes \(v + x\frac{{{\text{d}}v}}{{{\text{d}}x}} = {v^2} + v + 4\) <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;">\(\int {\frac{{{\text{d}}v}}{{{v^2} + 4}} = \int {\frac{{{\text{d}}x}}{x}} } \) <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;">\(\frac{1}{2}\arctan \left( {\frac{v}{2}} \right) = \ln x + C\) <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;">substituting\((x,{\text{ }}v) = (1,{\text{ }}2)\)</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;">\(C = \frac{\pi }{8}\) <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;">the solution is</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;">\(\arctan \left( {\frac{y}{{2x}}} \right) = 2\ln x + \frac{\pi }{4}\) <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;">\(y = 2x\tan \left( {2\ln x + \frac{\pi }{4}} \right)\) <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>[9 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;">Most candidates recognised this differential equation as one in which the substitution \(y = vx\) would be helpful and many carried the method through to a successful conclusion. The most common error seen was an incorrect integration of \(\frac{1}{{4 + {v^2}}}\) with partial fractions and/or a logarithmic evaluation seen. Some candidates failed to include an arbitrary constant which led to a loss of marks later on.</span></p>
</div>
<br><hr><br><div class="question">
<p class="p1">The function \(f\) is defined by \(f(x) = {{\text{e}}^{ - x}}\cos x + x - 1\).</p>
<p class="p1">By finding a suitable number of derivatives of \(f\), determine the first non-zero term in its Maclaurin series.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>\(f(0) = 0\) <strong><em>A1</em></strong></p>
<p>\(f'(x) = - {{\text{e}}^{ - x}}\cos x - {{\text{e}}^{ - x}}\sin x + 1\) <strong><em>M1A1</em></strong></p>
<p>\(f'(0) = 0\) <strong><em>(M1)</em></strong></p>
<p>\(f''(x) = 2{{\text{e}}^{ - x}}\sin x\) <strong><em>A1</em></strong></p>
<p>\(f''(0) = 0\)</p>
<p>\({f^{(3)}}(x) = - 2{{\text{e}}^{ - x}}\sin x + 2{{\text{e}}^{ - x}}\cos x\) <strong><em>A1</em></strong></p>
<p>\({f^{(3)}}(0) = 2\)</p>
<p>the first non-zero term is \(\frac{{2{x^3}}}{{3!}}\;\;\;\left( { = \frac{{{x^3}}}{3}} \right)\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award no marks for using known series.</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">Most students had a good understanding of the techniques involved with this question. A surprising number forgot to show \(f(0) = 0\). Some candidates did not simplify the second derivative which created extra work and increased the chance of errors being made.</p>
</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;">Consider the differential equation \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{{y^2} + {x^2}}}{{2{x^2}}}\) for which <em>y</em> = −1 when <em>x</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;">(a) Use Euler’s method with a step length of 0.25 to find an estimate for the value of <em>y</em> when <em>x</em> = 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;">(b) (i) Solve the differential equation giving your answer in the form \(y = f(x)\) .</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 value of <em>y</em> when <em>x</em> = 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: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Using an increment of 0.25 in the <em>x</em>-values <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><img 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" alt></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> The <strong><em>A1</em></strong> marks are awarded for final column.</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;">\( \Rightarrow y(2) \approx - 0.304\) <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;">(b) (i) let <em>y</em> = <em>vx</em> <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;">\( \Rightarrow \frac{{{\text{d}}y}}{{{\text{d}}x}} = v + x\frac{{{\text{d}}v}}{{{\text{d}}x}}\) <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;">\( \Rightarrow v + x\frac{{{\text{d}}v}}{{{\text{d}}x}} = \frac{{{v^2}{x^2} + {x^2}}}{{2{x^2}}}\) <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;">\( \Rightarrow x\frac{{{\text{d}}v}}{{{\text{d}}x}} = \frac{{1 - 2v + {v^2}}}{2}\) <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;">\( \Rightarrow x\frac{{{\text{d}}v}}{{{\text{d}}x}} = \frac{{{{(1 - v)}^2}}}{2}\) <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;">\( \Rightarrow \int {\frac{2}{{{{(1 - v)}^2}}}{\text{d}}v = \int {\frac{1}{x}{\text{d}}x} } \) <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;">\( \Rightarrow 2{(1 - v)^{ - 1}} = \ln x + c\) <strong><em>A1A1</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;">\( \Rightarrow \frac{2}{{1 - \frac{y}{x}}} = \ln x + c\)</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 \(x = 1,{\text{ }}y = - 1 \Rightarrow c = 1\) <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;">\( \Rightarrow \frac{{2x}}{{x - y}} = \ln x + 1\)</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;">\( \Rightarrow y = x - \frac{{2x}}{{1 + \ln x}}{\text{ }}\left( { = \frac{{x\ln x - x}}{{1 + \ln x}}} \right)\) <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> </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) when \(x = 2,{\text{ }}y = - 0.362\,\,\,\,\,\left( {{\text{accept 2}} - \frac{4}{{1 + \ln 2}}} \right)\) <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>[13 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>Total [20 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;">Part (a) was well done by many candidates, but a number were penalised for not using a sufficient number of significant figures. Part (b) was started by the majority of candidates, but only the better candidates were able to reach the end. Many were unable to complete the question correctly because they did not know what to do with the substitution <em>y</em> = <em>vx</em> and because of arithmetic errors and algebraic errors.</span></p>
</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: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Given that \(y = \ln \left( {\frac{{1 + {{\text{e}}^{ - x}}}}{2}} \right)\), show that \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{{{\text{e}}^{ - y}}}}{2} - 1\).</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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Hence, by repeated differentiation of the above differential equation, find the Maclaurin series for <em>y</em> as far as the term in \({x^3}\), showing that two of the terms are zero.</span></p>
<div class="marks">[11]</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: 33.0px 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: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(y = \ln \left( {\frac{{1 + {{\text{e}}^{ - x}}}}{2}} \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{ - 2{{\text{e}}^{ - x}}}}{{2(1 + {{\text{e}}^{ - x}})}} = \frac{{ - {{\text{e}}^{ - x}}}}{{1 + {{\text{e}}^{ - x}}}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">now \(\frac{{1 + {{\text{e}}^{ - x}}}}{2} = {{\text{e}}^y}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow 1 + {{\text{e}}^{ - x}} = 2{{\text{e}}^y}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow {{\text{e}}^{ - x}} = 2{{\text{e}}^y} - 1\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow \frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{ - 2{{\text{e}}^y} + 1}}{{2{{\text{e}}^y}}}\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px 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;"> Only one of the two above </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;"> marks may be implied.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px 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: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow \frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{{{\text{e}}^{ - y}}}}{2} = - 1\) </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>AG</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px 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;"> Candidates may find \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) as a function of x and then work backwards from the given answer. Award full marks if done correctly.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px 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: 33.0px 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: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(y = \ln \left( {\frac{{1 + {{\text{e}}^{ - x}}}}{2}} \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow {{\text{e}}^y} = \frac{{1 + {{\text{e}}^{ - x}}}}{2}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow {{\text{e}}^{ - x}} = 2{{\text{e}}^y} - 1\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow x = - \ln (2{{\text{e}}^y} - 1)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow \frac{{{\text{d}}x}}{{{\text{d}}y}} = - \frac{1}{{2{{\text{e}}^y} - 1}} \times 2{{\text{e}}^y}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow \frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{2{{\text{e}}^y} - 1}}{{ - 2{{\text{e}}^y}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow \frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{{{\text{e}}^{ - y}}}}{2} - 1\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px 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: 35.0px 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: 35.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">when \(x = 0,{\text{ }}y = \ln 1 = 0\) <strong><em>A1</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;">when \(x = 0,{\text{ }}\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{1}{2} - 1 = - \frac{1}{2}\) <strong><em>A1</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;">\(\frac{{{{\text{d}}^2}y}}{{{\text{d}}{x^2}}} = - \frac{{{{\text{e}}^{ - y}}}}{2}\frac{{{\text{d}}y}}{{{\text{d}}x}}\) <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;">when \(x = 0,{\text{ }}\frac{{{{\text{d}}^2}y}}{{{\text{d}}{x^2}}} = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}\) <strong><em>A1</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;">\(\frac{{{{\text{d}}^3}y}}{{{\text{d}}{x^3}}} = \frac{{{{\text{e}}^{ - y}}}}{2}{\left( {\frac{{{\text{d}}y}}{{{\text{d}}x}}} \right)^2} - \frac{{{{\text{e}}^{ - y}}}}{2}\frac{{{{\text{d}}^2}y}}{{{\text{d}}{x^2}}}\) <strong><em>M1A1A1</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;">when \(x = 0,{\text{ }}\frac{{{{\text{d}}^3}y}}{{{\text{d}}{x^3}}} = \frac{1}{2} \times \frac{1}{4} - \frac{1}{2} \times \frac{1}{4} = 0\) <strong><em>A1</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;">\(y = f(0) + f'(0)x + \frac{{f''(0)}}{{2!}}{x^2} + \frac{{f'''(0)}}{{3!}}{x^3}\)</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;">\( \Rightarrow y = 0 - \frac{1}{2}x + \frac{1}{8}{x^2} + 0{x^3} + \ldots \) <strong><em>(M1)A1</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;">two of the above terms are zero <strong><em>AG</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>METHOD 2</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;">when \(x = 0,{\text{ }}y = \ln 1 = 0\) <strong><em>A1</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;">when \(x = 0,{\text{ }}\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{1}{2} - 1 = - \frac{1}{2}\) <strong><em>A1</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;">\(\frac{{{{\text{d}}^2}y}}{{{\text{d}}{x^2}}} = \frac{{ - {{\text{e}}^{ - y}}}}{2}\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{ - {{\text{e}}^{ - y}}}}{2}\left( {\frac{{{{\text{e}}^{ - y}}}}{2} - 1} \right) = \frac{{ - {{\text{e}}^{2y}}}}{4} + \frac{{{{\text{e}}^{ - y}}}}{2}\) <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;">when \(x = 0,{\text{ }}\frac{{{{\text{d}}^2}y}}{{{\text{d}}{x^2}}} = - \frac{1}{4} + \frac{1}{2} = \frac{1}{4}\) <strong><em>A1</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;">\(\frac{{{{\text{d}}^3}y}}{{{\text{d}}{x^3}}} = \left( {\frac{{{{\text{e}}^{ - 2y}}}}{2} - \frac{{{{\text{e}}^{ - y}}}}{2}} \right)\frac{{{\text{d}}y}}{{{\text{d}}x}}\) <strong><em>M1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 35.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">when \(x = 0,{\text{ }}\frac{{{{\text{d}}^3}y}}{{{\text{d}}{x^3}}} = - \frac{1}{2} \times \left( {\frac{1}{2} - \frac{1}{2}} \right) = 0\) <strong><em>A1</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;">\(y = f(0) + f'(0)x + \frac{{f''(0)}}{{2!}}{x^2} + \frac{{f'''(0)}}{{3!}}{x^3}\)</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;">\( \Rightarrow y = 0 - \frac{1}{2}x + \frac{1}{8}{x^2} + 0{x^3} + \ldots \) <strong><em>(M1)A1</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;">two of the above terms are zero <strong><em>AG</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>[11 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: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates were successful in (a) with a variety of methods seen. In (b) the use of the chain rule was often omitted when differentiating \({{{\text{e}}^{ - y}}}\) with respect to <em>x</em>. A number of candidates tried to repeatedly differentiate the original expression, which was not what was asked for, although partial credit was given for this. In this case, they often found problems in simplifying the algebra.</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;">Many candidates were successful in (a) with a variety of methods seen. In (b) the use of the chain rule was often omitted when differentiating \({{{\text{e}}^{ - y}}}\) with respect to <em>x</em>. A number of candidates tried to repeatedly differentiate the original expression, which was not what was asked for, although partial credit was given for this. In this case, they often found problems in simplifying the algebra.</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;">Each term of the power series \(\frac{1}{{1 \times 2}} + \frac{1}{{4 \times 5}}x + \frac{1}{{7 \times 8}}{x^2} + \frac{1}{{10 \times 11}}{x^3} + \ldots \) has the form \(\frac{1}{{b(n) \times c(n)}}{x^n}\), where \(b(n)\) and \(c(n)\) are linear functions of \(n\).</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) Find the functions \(b(n)\) and \(c(n)\).</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) Find the radius of convergence.</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 interval of convergence.</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) \(b(n) = 3n + 1\) <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;">\(c(n) = 3n + 2\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; 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>\(b(n)\) and \(c(n)\) may be reversed.</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>[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;">(b) consider the ratio of the \({(n + 1)^{{\text{th}}}}\) and \({n^{{\text{th}}}}\) terms: <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;">\(\frac{{3n + 1}}{{3n + 4}} \times \frac{{3n + 2}}{{3n + 5}} \times \frac{{{x^{n + 1}}}}{{{x^n}}}\) <em><strong>A1</strong></em></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;">\(\mathop {{\text{lim}}}\limits_{n \to 0} \frac{{3n + 1}}{{3n + 4}} \times \frac{{3n + 2}}{{3n + 5}} \times \frac{{{x^{n + 1}}}}{{{x^n}}}x\) <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;">radius of convergence: \(R = 1\) <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>[4 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;">(c) any attempt to study the series for \(x = -1\) or \(x = 1\) <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;">converges for \(x = 1\) by comparing with <em>p</em>-series \(\sum {\frac{1}{{{n^2}}}} \) <strong><em>R1</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;">attempt to use the alternating series test for \(x = -1\) <strong><em>(M1)</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>At least one of the conditions below needs to be attempted for <strong><em>M1</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: 21.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(\left| {{\text{terms}}} \right| \approx \frac{1}{{9{n^2}}} \to 0\) and terms decrease monotonically in absolute value <em><strong>A1</strong></em></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;">series converges for \(x = -1\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">interval of convergence: \(\left[ { - 1,{\text{ 1}}} \right]\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; 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 the <strong><em>R1</em></strong>s only if an attempt to corresponding correct test is made;</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 the final <strong><em>A1 </em></strong>only if at least one of the <strong><em>R1</em></strong>s is awarded;</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 study of absolute convergence at end points.</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>[6 marks]</em></strong></span></p>
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<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
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<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;">Given that \(\frac{{{\text{d}}y}}{{{\text{d}}x}} - 2{y^2} = {{\text{e}}^x}\) and <em>y</em> = 1 when <em>x</em> = 0, use Euler’s method with a step length of 0.1 to find an approximation for the value of <em>y</em> when <em>x</em> = 0.4. Give all intermediate values with maximum possible accuracy.</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: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = {{\text{e}}^x} + 2{y^2}\) <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><em> </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></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;">required approximation = 3.85 <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>[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: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates seemed familiar with Euler’s method. The most common way of losing marks was either to round intermediate answers to insufficient accuracy despite the advice in the question or simply to make an arithmetic error. Many candidates were given an accuracy penalty for not rounding their answer to three significant figures.</span></p>
</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: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the functions \(f(x) = {(\ln x)^2},{\text{ }}x > 1\) and \(g(x) = \ln \left( {f(x)} \right),{\text{ }}x > 1\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Find \(f'(x)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Find \(g'(x)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) Hence, show that \(g(x)\) is increasing on \(\left] {1,{\text{ }}\infty } \right[\).</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;">Consider the differential equation</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;">\[(\ln x)\frac{{{\text{d}}y}}{{{\text{d}}x}} + \frac{2}{x}y = \frac{{2x - 1}}{{(\ln x)}},{\text{ }}x > 1.\]</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;">(i) Find the general solution of the differential equation in the form \(y = h(x)\).</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) Show that the particular solution passing through the point with coordinates \(\left( {{\text{e, }}{{\text{e}}^2}} \right)\) is given by \(y = \frac{{{x^2} - x + {\text{e}}}}{{{{(\ln x)}^2}}}\).</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;">(iii) Sketch the graph of your solution for \(x > 1\), clearly indicating any asymptotes and any maximum or minimum points.</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: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) attempt at chain rule <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;">\(f'(x) = \frac{{2\ln x}}{x}\) <em><strong>A1</strong></em></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;">(ii) attempt at chain rule <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;">\(g'(x) = \frac{2}{{x\ln x}}\) <em><strong>A1</strong></em></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;">(iii) \(g'(x)\) is positive on \(\left] {1,{\text{ }}\infty } \right[\) <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;">so \(g(x)\) is increasing on \(\left] {1,{\text{ }}\infty } \right[\) <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>[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;">(i) rearrange in standard form:</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;">\(\frac{{{\text{d}}y}}{{{\text{d}}x}} + \frac{2}{{x\ln x}}y = \frac{{2x - 1}}{{{{(\ln x)}^2}}},{\text{ }}x > 1\) <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;">integrating factor:</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;">\({{\text{e}}^{\int {\frac{2}{{x\ln x}}{\text{d}}x} }}\) <strong><em>(M1)</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;">\( = {{\text{e}}^{\ln \left( {{{(\ln x)}^2}} \right)}}\)</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;">\( = {(\ln x)^2}\) <em><strong>(A1)</strong></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;">multiply by integrating factor <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;">\({(\ln x)^2}\frac{{{\text{d}}y}}{{{\text{d}}x}} + \frac{{2\ln x}}{x}y = 2x - 1\)</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;">\(\frac{{\text{d}}}{{{\text{d}}x}}\left( {y{{(\ln x)}^2}} \right) = 2x - 1{\text{ }}\left( {{\text{or }}y{{(\ln x)}^2} = \int {2x - 1{\text{d}}x} } \right)\) <em><strong>M1</strong></em></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;">attempt to integrate: <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;">\({(\ln x)^2}y = {x^2} - x + c\)</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;">\(y = \frac{{{x^2} - x + c}}{{{{(\ln x)}^2}}}\) <em><strong>A1</strong></em></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;">(ii) attempt to use the point \(\left( {{\text{e, }}{{\text{e}}^2}} \right)\) to determine c: <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;"><em>eg</em>, \({(\ln {\text{e}})^2}{{\text{e}}^2} = {{\text{e}}^2} - {\text{e}} + {\text{c}}\) or \({{\text{e}}^2} = \frac{{{{\text{e}}^2} - {\text{e}} + {\text{c}}}}{{{{(\ln {\text{e}})}^2}}}\) or \({{\text{e}}^2} = {{\text{e}}^2} - {\text{e}} + {\text{c}}\)</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;">\({\text{c}} = {\text{e}}\) <strong><em>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;">\(y = \frac{{{x^2} - x + {\text{e}}}}{{{{(\ln x)}^2}}}\) <em><strong>AG</strong></em></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;">(iii) <br><img src="images/Schermafbeelding_2014-09-10_om_10.21.28.png" alt></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;">graph with correct shape <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;">minimum at \(x = 3.1\) (accept answers to a minimum of 2 s.f) <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;">asymptote shown at \(x = 1\) <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> </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>Note: </strong><em>y</em>-coor<span style="font-family: 'times new roman', times; font-size: medium;">dinate of minimum not required for <strong><em>A1</em></strong>;</span></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;"> Equation of asymptote not required for <strong><em>A1 </em></strong>if VA appears on the sketch.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> Award <strong><em>A0 </em></strong>for asymptotes if more than one asymptote are shown</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica; min-height: 36.0px;"> </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>[12 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" style="padding-left: 20px; padding-right: 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;">Using the integral test, show that \(\sum\limits_{n = 1}^\infty {\frac{1}{{4{n^2} + 1}}} \) is convergent.</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: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Show, by means of a diagram, that \(\sum\limits_{n = 1}^\infty {\frac{1}{{4{n^2} + 1}}} < \frac{1}{{4 \times {1^2} + 1}} + \int_1^\infty {\frac{1}{{4{x^2} + 1}}{\text{d}}x} \).</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) Hence find an upper bound for \(\sum\limits_{n = 1}^\infty {\frac{1}{{4{n^2} + 1}}} \)</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p 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;">\(\int {\frac{1}{{4{x^2} + 1}}{\text{d}}x = \frac{1}{2}\arctan 2x + k} \) <strong><em>(M1)(A1)</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;"> Do not penalize the absence of “+</span><em style="font-family: 'times new roman', times; font-size: medium;">k</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: 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;">\(\int_1^\infty {\frac{1}{{4{x^2} + 1}}{\text{d}}x = \frac{1}{2}\mathop {\lim }\limits_{a \to \infty } } [\arctan 2x]_1^a\) </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: 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;"> Accept \(\frac{1}{2}[\arctan 2x]_1^\infty \).</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;">\( = \frac{1}{2}\left( {\frac{\pi }{2} - \arctan 2} \right)\,\,\,\,\,( = 0.232)\) </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;"><span style="font-family: 'times new roman', times; font-size: medium;">hence the series converges <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>[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;">(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 class="Apple-style-span" style="line-height: 20px; display: inline; float: none;"><img 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" alt><span class="Apple-style-span" style="display: inline; float: none; line-height: normal;"><strong><em> A2</em></strong></span></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;">The shaded rectangles lie within the area below the graph so that \(\sum\limits_{n = 2}^\infty {\frac{1}{{4{n^2} + 1}}} < \int_1^\infty {\frac{1}{{4{x^2} + 1}}{\text{d}}x} \). Adding the first term in the series, \(\frac{1}{{4 \times {1^2} + 1}}\), gives \(\sum\limits_{n = 1}^\infty {\frac{1}{{4{n^2} + 1}}} < \frac{1}{{4 \times {1^2} + 1}} + \int_1^\infty {\frac{1}{{4{x^2} + 1}}{\text{d}}x} \) <strong><em>R1AG</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;">(ii) upper bound \( = \frac{1}{5} + \frac{1}{2}\left( {\frac{\pi }{2} - \arctan 2} \right)\,\,\,\,\,( = 0.432)\) <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">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;">This proved to be a hard question for most candidates. A number of fully correct answers to (a) were seen, but a significant number were unable to integrate \({\frac{1}{{4{x^2} + 1}}}\) successfully. Part (b) was found the hardest by candidates with most candidates unable to draw a relevant diagram, without which the proof of the inequality was virtually impossible.</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;">This proved to be a hard question for most candidates. A number of fully correct answers to (a) were seen, but a significant number were unable to integrate \({\frac{1}{{4{x^2} + 1}}}\) successfully. Part (b) was found the hardest by candidates with most candidates unable to draw a relevant diagram, without which the proof of the inequality was virtually impossible.</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: 24.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Prove that \(\mathop {\lim }\limits_{H \to \infty } \int_a^H {\frac{1}{{{x^2}}}{\text{d}}x} \) exists and find its value in terms of \(a{\text{ (where }}a \in {\mathbb{R}^ + })\).</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: 27.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Use the integral test to prove that \(\sum\limits_{n = 1}^\infty {\frac{1}{{{n^2}}}} \) converges.</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: 24.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(\sum\limits_{n = 1}^\infty {\frac{1}{{{n^2}}}} = L\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">The diagram below shows the graph of \(y = \frac{1}{{{x^2}}}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px 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: 24.0px Times;"><img 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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Times;"> </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;">(i) Shade suitable regions on a copy of the diagram above and show that</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;">\(\sum\limits_{n = 1}^k {\frac{1}{{{n^2}}}} + \int_{k + 1}^\infty {\frac{1}{{{x^2}}}} {\text{d}}x < L\) .</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) Similarly shade suitable regions on another copy of the diagram above and</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;">show that \(L < \sum\limits_{n = 1}^k {\frac{1}{{{n^2}}}} + \int_k^\infty {\frac{1}{{{x^2}}}} {\text{d}}x\) .</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Hence show that \(\sum\limits_{n = 1}^k {\frac{1}{{{n^2}}}} + \frac{1}{{k + 1}} < L < \sum\limits_{n = 1}^k {\frac{1}{{{n^2}}}} + \frac{1}{k}\)</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p 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;">You are given that \(L = \frac{{{\pi ^2}}}{6}\).</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;">By taking <em>k </em>= 4 , use the upper bound and lower bound for <em>L </em>to find an upper bound and lower bound for \(\pi \) . Give your bounds to three significant figures.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\mathop {\lim }\limits_{H \to \infty } \int_a^H {\frac{1}{{{x^2}}}{\text{d}}x} = \mathop {\lim }\limits_{H \to \infty } \left[ {\frac{{ - 1}}{x}} \right]_a^H\) <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;">\(\mathop {\lim }\limits_{H \to \infty } \left( {\frac{{ - 1}}{H} + \frac{1}{a}} \right)\) <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;">\( = \frac{1}{a}\) <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>
<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;">as \(\left\{ {\frac{1}{{{n^2}}}} \right\}\) is a positive decreasing sequence we consider the function \(\frac{1}{{{x^2}}}\)</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;">we look at \(\int_1^\infty {\frac{1}{{{x^2}}}} {\text{d}}x\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int_1^\infty {\frac{1}{{{x^2}}}} {\text{d}}x = 1\) <em><strong>A1</strong><strong><br></strong></em></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;">since this is finite (allow “limit exists” or equivalent statement) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.5px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\sum\limits_{n = 1}^\infty {\frac{1}{{{n^2}}}} \) converges <em><strong>AG</strong></em></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>
<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)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><img 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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;">attempt to shade rectangles <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;">correct start and finish points for rectangles <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;">since the area shaded is less that the area of the required staircase we have <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;"><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\sum\limits_{n = 1}^k {\frac{1}{{{n^2}}}} + \int_{k + 1}^\infty {\frac{1}{{{x^2}}}} {\text{d}}x < L\)</span> </span><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>AG</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;">(ii)</span></p>
<p><img 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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;">attempt to shade rectangles <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;">correct start and finish points for rectangles <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;">since the area shaded is greater that the area of the required staircase we have <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;"><span style="font-family: 'times new roman', times; font-size: medium;">\(L < \sum\limits_{n = 1}^k {\frac{1}{{{n^2}}}} + \int_k^\infty {\frac{1}{{{x^2}}}} {\text{d}}x\)</span> <em><strong>AG</strong></em></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;">Alternative shading and rearranging of the inequality is acceptable.</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><em>[6 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: 27.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int_{k + 1}^\infty {\frac{1}{{{x^2}}}} {\text{d}}x = \frac{1}{{k + 1}},{\text{ }}\int_k^\infty {\frac{1}{{{x^2}}}} {\text{d}}x = \frac{1}{k}\) <em><strong>A1A1</strong></em><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 17.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\sum\limits_{n = 1}^k {\frac{1}{{{n^2}}}} + \frac{1}{{k + 1}} < L < \sum\limits_{n = 1}^k {\frac{1}{{{n^2}}}} + \frac{1}{k}\) <em><strong>AG</strong></em><br></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;"><strong><em>[2 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: 17.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{205}}{{144}} + \frac{1}{5} < \frac{{{\pi ^2}}}{6} < \frac{{205}}{{144}} + \frac{1}{4}{\text{ }}\left( {1.6236... < \frac{{{\pi ^2}}}{6} < 1.6736...} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 17.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\sqrt {6\left( {\frac{{205}}{{144}} + \frac{1}{5}} \right)} < \pi < \sqrt {6\left( {\frac{{205}}{{144}} + \frac{1}{4}} \right)} \) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 17.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(3.12 < \pi < 3.17\) <strong><em>A1 N2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 17.0px 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>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates correctly obtained the result in part (a). Many then failed to realise that having obtained this result once it could then simply be stated when doing parts (b) and (d)</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates correctly obtained the result in part (a). Many then failed to realise that having obtained this result once it could then simply be stated when doing parts (b) and (d)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In part (b) the calculation of the integral as equal to 1 only scored 2 of the 3 marks. The final mark was for stating that ‘because the value of the integral is finite (or ‘the limit exists’ or an equivalent statement) then the series converges. Quite a few candidates left out this phrase.</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 Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates correctly obtained the result in part (a). Many then failed to realise that having obtained this result once it could then simply be stated when doing parts (b) and (d)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Candidates found part (c) difficult. Very few drew the correct series of rectangles and some clearly had no idea of what was expected of them.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates correctly obtained the result in part (a). Many then failed to realise that having obtained this result once it could then simply be stated when doing parts (b) and (d)</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: 21.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Though part (e) could be done without doing any of the previous parts of the question many students were probably put off by the notation because only a minority attempted it.</span></p>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider the differential equation \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = f(x,{\text{ }}y)\) where \(f(x,{\text{ }}y) = y - 2x\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch, on one diagram, the four isoclines corresponding to \(f(x,{\text{ }}y) = k\) where <em>\(k\) </em>takes the values \(-1\), \(-0.5\), \(0\) and \(1\). Indicate clearly where each isocline crosses the <em>\(y\) </em>axis.</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>A curve, \(C\), passes through the point \((0,1)\) and satisfies the differential equation above.</p>
<p>Sketch \(C\) on your diagram.</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>A curve, \(C\), passes through the point \((0,1)\) and satisfies the differential equation above.</p>
<p>State a particular relationship between the isocline \(f(x,{\text{ }}y) = - 0.5\) and the curve \(C\), at their point of intersection.</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 class="p1">A curve, \(C\), passes through the point \((0,1)\) and satisfies the differential equation above.</p>
<p class="p1">Use Euler’s method with a step interval of \(0.1\) to find an approximate value for <em>\(y\) </em>on \(C\), when \(x = 0{\text{.}}5\).</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" style="text-align: center;"><img 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" alt></p>
<p class="p1"><strong><em>A1 </em></strong>for 4 parallel straight lines with a positive gradient <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>A1 </em></strong>for correct <em>\(y\) </em>intercepts <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 style="text-align: center;"><img 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" alt></p>
<p><strong><em>A1 </em></strong>for passing through \((0,1)\) with positive gradient less than \(2\)</p>
<p><strong><em>A1 </em></strong>for stationary point on \(y = 2x\)</p>
<p><strong><em>A1 </em></strong>for negative gradient on both of the other \(2\) isoclines <strong><em>A1A1A1</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 class="p1">The isocline is perpendicular to \(C\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1"><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\({y_{n + 1}} = {y_n} + 0.1({y_n} - 2{x_n})\;\;\;( = 1.1{y_n} - 0.2{x_n})\) <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>Also award <strong><em>M1A1 </em></strong>if no formula seen but \({y_2}\) is correct.</p>
<p class="p3"> </p>
<p class="p1">\({y_0} = 1,{\text{ }}{y_1} = 1.1,{\text{ }}{y_2} = 1.19,{\text{ }}{y_3} = 1.269,{\text{ }}{y_4} = 1.3359\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1">\({y_5} = 1.39{\text{ to 3sf}}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p3"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span><em>M1 </em></strong>is for repeated use of their formula, with steps of \(0.1\).</p>
<p class="p3"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Accept \(1.39\) or \(1.4\) only.</p>
<p class="p1"><em><strong>[4 marks]</strong></em></p>
<p class="p1"><em><strong>Total [10 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;">
<p class="p1">Some candidates ignored the instruction to prove from first principles and instead used standard differentiation. Some candidates also only found a derivative from one side.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Parts (b) and (c) were attempted by very few candidates. Few recognized that the gradient of the curve had to equal the value of \(k\) on the isocline.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Parts (b) and (c) were attempted by very few candidates. Few recognized that the gradient of the curve had to equal the value of \(k\) on the isocline.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Those candidates who knew the method managed to score well on this part. On most calculators a short program can be written in the exam to make Euler’s method very quick. Quite a few candidates were losing time by calculating and writing out many intermediate values, rather than just the \(x\) and\(y\) values.</p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Let the differential equation \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \sqrt {x + y} ,{\text{ }}(x + y \geqslant 0)\) satisfying the initial conditions <em>y </em>= 1 when <em>x </em>= 1. Also let <em>y </em>= <em>c </em>when <em>x </em>= 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: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Use Euler’s method to find an approximation for the value of <em>c </em>, using a step length of <em>h </em>= 0.1 . Give your answer to four decimal places.</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: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">You are told that if Euler’s method is used with <em>h </em>= 0.05 then \(c \simeq 2.7921\) , if it is used with <em>h </em>= 0.01 then \(c \simeq 2.8099\) and if it is used with <em>h </em>= 0.005 then \(c \simeq 2.8121\).</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;">Plot on graph paper, with <em>h </em>on the horizontal axis and the approximation for <em>c</em> on the vertical axis, the four points (one of which you have calculated and three of which have been given). Use a scale of 1 cm = 0.01 on both axes. Take the horizontal axis from 0 to 0.12 and the vertical axis from 2.76 to 2.82.</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;">Draw, by eye, the straight line that best fits these four points, using a ruler.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Use your graph to give the best possible estimate for <em>c </em>, giving your answer to three decimal places.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">using \({x_0} = 1,{\text{ }}{y_0} = 1\)</span></p>
<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;">\({x_n} = 1 + 0.1n,{\text{ }}{y_{n + 1}} = {y_n} + 0.1\sqrt {{x_n} + {y_n}} \) (<strong><em>M1)(M1)(A1)</em></strong></span><span style="font-size: medium; 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: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>If they have not written down formulae but have \({x_1} = 1.1\) and \({y_1} = 1.14142…\) award <strong><em>M1M1A1</em></strong>.</span></p>
<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;"> </span></p>
<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;">gives by GDC \({x_{10}} = 2,{\text{ }}{y_{10}} = 2.770114792…\) </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: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so \(a \simeq 2.7701{\text{ (4dp)}}\) <strong><em>A1 N6</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px 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;">Do not penalize over-accuracy.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px 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: 19.0px 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: 23.0px Helvetica;"><br><img 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" alt></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;">points drawn on graph above <strong><em>A1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px 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: 23.0px 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 scales, </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 2 points correctly plotted, </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 other 2 points correctly plotted (second and third </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;">dependent on the first being correct).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px 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: 23.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[3 marks]</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: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">suitable line of best fit placed on graph <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>[1 mark]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">letting \({\text{h}} \to {\text{0}}\) we approach the <em>y </em>intercept on the graph so <strong><em>(R1)</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;">\(c \simeq 2.814{\text{ (3dp)}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px 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 2.815.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px 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: 22.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was done well. We would recommend that candidates write down the equation they are using, in this case, \({y_{n + 1}} = {y_n} + 0.1\sqrt {{x_n} + {y_n}} \) , to ensure they get all the method marks. Beyond this the answer is all that is needed (or if a student wishes to show working, simply each of the values of \({{x_n}}\) and \({{y_n}}\)) . Many candidates wasted a lot of time by writing out values of each part of the function, perhaps indicating they did not how to do it more quickly using their calculators.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (b) Surprisingly when drawing the graph a lot of candidates had (0.01, 2.8099) closer to 2.80 than 2.81</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most realised that the best possible estimate was given by the <em>y</em>-intercept of the line they had drawn.</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: 22.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was done well. We would recommend that candidates write down the equation they are using, in this case, \({y_{n + 1}} = {y_n} + 0.1\sqrt {{x_n} + {y_n}} \) , to ensure they get all the method marks. Beyond this the answer is all that is needed (or if a student wishes to show working, simply each of the values of \({{x_n}}\) and \({{y_n}}\)) . Many candidates wasted a lot of time by writing out values of each part of the function, perhaps indicating they did not how to do it more quickly using their calculators.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (b) Surprisingly when drawing the graph a lot of candidates had (0.01, 2.8099) closer to 2.80 than 2.81</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most realised that the best possible estimate was given by the <em>y</em>-intercept of the line they had drawn.</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: 22.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was done well. We would recommend that candidates write down the equation they are using, in this case, \({y_{n + 1}} = {y_n} + 0.1\sqrt {{x_n} + {y_n}} \) , to ensure they get all the method marks. Beyond this the answer is all that is needed (or if a student wishes to show working, simply each of the values of \({{x_n}}\) and \({{y_n}}\)) . Many candidates wasted a lot of time by writing out values of each part of the function, perhaps indicating they did not how to do it more quickly using their calculators.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (b) Surprisingly when drawing the graph a lot of candidates had (0.01, 2.8099) closer to 2.80 than 2.81</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most realised that the best possible estimate was given by the <em>y</em>-intercept of the line they had drawn.</span></p>
<div class="question_part_label">c.</div>
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<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was done well. We would recommend that candidates write down the equation they are using, in this case, \({y_{n + 1}} = {y_n} + 0.1\sqrt {{x_n} + {y_n}} \) , to ensure they get all the method marks. Beyond this the answer is all that is needed (or if a student wishes to show working, simply each of the values of \({{x_n}}\) and \({{y_n}}\)) . Many candidates wasted a lot of time by writing out values of each part of the function, perhaps indicating they did not how to do it more quickly using their calculators.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (b) Surprisingly when drawing the graph a lot of candidates had (0.01, 2.8099) closer to 2.80 than 2.81</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most realised that the best possible estimate was given by the <em>y</em>-intercept of the line they had drawn.</span></p>
<div class="question_part_label">d.</div>
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